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WORKS OF PROF. I. 0. BAKER
PUBLISHED BY
JOHN WILEY & SONS.
A Treatise on Hasonry Construction.
Containing Materials and Methods of Testing Strengtli.etc; Combinations of Materials — Composi- tion, etc.; Foundations — Testing the Bearing Power of Soils, etc ; Masonry Structure— Stabi.itv Against Sliding, Overturning, Crushing, etc., etc., etc. Ninth Edition, E.xtensively Revised. 8vo, about 600 pages, ito figures and 6 folding plates, cloth, ^5.00.
Engineers' Surveying Instruments.
Their Construction, Adjustment, and Use. Second Edition. Revi'ied and Hreat y Enlarged. i2mo, ix + 391 pages, Sd figures, clotli, 53.00.
Ready December i, iqoz : A Treatise on Roads and Pavements.
8vo, 600 pages, 150 figures, cloth, ^5 00.
A TREATISE
OK
MASONRY CONSTRUCTION.
IRA C, BAKEE, C. E,,
PROFESSOR OF CIVIL EN-GIXEERING, UNIVERSITY OF ILLINOIS,
^IXTH EDITION, REVISED AND PARTIALLY REWRITTEN,
FIFTH THOUSAifD
NEW YORK :
JOHN WILEY & SONS.
London; CHAPMAN & HALL, Limited.
1902.
Copyright, !389, 189'
BY
IRA O. BAKER.
ROBERT DRUMMOND, PRINTER, NEW YORK.
Urban PianiUni
l^no
PREFACE. i>nt
The present volume is an outgrowth of the needs of the author's own class-room. The matter is essentially that presented to his classes for a number of years past, a considerable part having been used in the form of a blue-print manuscript text-book. It is now published for the greater convenience of his own students, and with the hope that it may be useful to others. The author knows of no work which treats of any considerable part of the field covered by this volume. Nearly all of the matter is believed to be entirely new.
The object has been to develop principles and methods and to give such examples as illustrate them, rather than to accumulate details or to describe individual structures. The underlying prin- ciples of ordinary practice are explained ; and, where needed, ways are pointed out whereby it may be improved. The common theo- ries are compared with the results of actual practice ; and only those are recommended which have been verified by experiments or experience, since true theory and good practice are always in accord. The author has had the benefit of suggestions and advice from practical masons and engineers, and believes that the information here presented is reliable, and that the examples cited represent good practice. The general prices are the average of a large number actually paid ; and the special prices are representa- tive. The structures illustrated are actual ones. The accredited illustrations are from well-autlienticated copies of working drawings, and are presented without any modification whatever ; while those not accredited are representative of practice so common that a single name could not properly be attached.
In the preparation of the book the endeavor has been to observe a logical order and a due proportion between different parts. Great care has been taken in classifying and arranging the matter. It will be helpful to the reader to notice that tlie volume is divided successively into parts, chapters, articles, sections having small-cap- ital black-face side-heads, sections having lower-case black-face side- heads, sections having lower-case italic side-heads, and sections hav- ing simply the serial number. In some cases the major subdivis*
IV PREFACE.
ions of the sections are indicated by small numerals. The constant aim has been to present tiie subject clearly and concisely.
Every precaution has been taken to present the work in a form for convenient practical use and ready reference. Numerous cross references are given by section number ; and whenever a figure or a table is mentioned, the citation is accompanied by the number of the page on which it may be found. The table of contents shows the general scope of the book ; the running title assists in finding the different parts ; and a very full index makes everything in the book easy of access. There are also a number of helps for the student, which the experienced teacher will not fail to recognize and appreciate.
Although the book has been specially arranged for engineering and architectural students, it is hoped that the information con- cerning the strengths of the materials, the data for facilitating the making of estimates, the plans, the tables of dimensions, and the costs of actual structures, will prove useful to the man of experience. Considering the large amount of practical details presented and the great difference in the methods employed by various construc- tors, it is probable that practical men will find much to criticise The views here expressed are, however, the results of observation throughout the entire country, and of consultation and corresj^ond- ence with many prominent and practical men, and represent average good practice. The experienced engineer may possibly also feel that some subjects should have been treated more fully ; but it is neither wise nor possible to give in a single volume minute details. These belong to technical journals, proceedings of societies, and special reports of particular work.
No pains have been spared in verifying data and checking re- sults. The tables of cubic contents have been computed by differ- ent processes by at least two persons, and to at least one more place than is recorded. Should any error, either of printer or author, be discovered — as is very possible in a work of so much detail, despite the great care used, — the writer will be greatly obliged by prompt notification of the same.
The author gi-atefully acknowledges his indebtedness to many engineers for advice and data, and to his former pupil and present co-laborer. Prof. A. N. Talbot, for many valuable suggestions.
Champaign, III., July 9, 1889.
PREFACE FOR NINTH EDITION.
The order of the subdivisions of Art. 2, Chap. I, has been changed, and pages 7-11 have been rewritten. Chapter III — Cemenfc and Lime — and Chapter lY — Mortar and Concrete — have been entirely rewritten. Chapter IIIa — Sand, Gravel, and- Broken Stone — has been added. The Definitions of Kinds of Masonry — pages 136 and 137 — have been rewritten and new illustrations have been prepared. The specifications for the different classes of stone masonr}^ — pages 142, 144, and 147 — have been rewritten. Many minor changes have been made in various parts of the book.
Champaign, III., June 27, 1899.
TABLE OF CONTENTS.
PART I. THE MATERIALS.
PAGE
CHAPTER I. NATURAL STONE.
Introduction 1
Aet. 1. Requisites for Good Building Stone. ........ 3
Art. 2. Testing Building Stone 5
Weight , . 6
Hardness and Toughness 7
Strength. Crushing Strength. Transverse Strength. Elasticity. . 8 Durability. Destructive Agents : mechanical, chemical. Resisting Agents : chemical composition, physical structure, seasoning. Meth- ods of Testing Durability : absorptive power, methods and results ; effect of frost, methods and results ; effect of atmosphere, methods
and results. Methods of Preserving 14
Art. 3. Classification and Description of Building Stones. . . 23 Classification : geological, chemical, physical. Description of Trap, Granite, Marble, Limestone, and Sandstone. Location of Quarries. Weight of Stone.
CHAPTER II. BRICK.
Process of manufacture. Classification. Requisites for good Brick. Methods of Testing : absorbing power, transverse strength, crushing strength ; results. Size. Cost 33
CHAPTER III. LIME AND CEMENT.
Classification , . . 48
Art. 1. Common Lime 4^
Methods of manufacturing, testing, and preserving. Cost.
Art. 2. Hydraulic Lime , . 51
Art. 3. Hydraulic Cement , , 51
Description : Portland, Natural, Pozzuolana. Weight. Cost.
Art. 4. Methods of Testing Hydraulic Cement 56
Color, Thoroughness of Burning, Activity, Soundness, Fineness, Strength.
vii
vni TABLE OF CONTENTS.
PAG»;
Art. 5. Specifications for Cement (57
Quality : Germau, English, FrcDch, American, Philadelphia. De- livery aud Storage.
CHAPTER IIIa. SAND, GRAVEL. AND BROKEN STONE.
Art. 1. Sand 79a
Requisites for Good Sand : Durability, Sharpness, Cleanness, Fine- ness, Voids. Stone Screenings. Cost. Weight.
Art. 2. Gravel and Broken Stone 79A
Gravel. Broken Stone. Voids. Weight. Cost.
PAET II. PREPARING AND USING THE MATERIALS.
CHAPTER IV. MORTAR, CONCRETE, AND ARTIFICIAL STONE.
Art. 1 Mortar 81
Lime Mortar. Cement Mortar : proportions and preparation. Data for Estimates. Strength : tensile, compressive, adhesive. Cost. Effect of Re-tempering. Lime vrith Cement. Mortar Impervious to Water. Effect of Freezing.
Art. 3. Concrete 106
Mortar. Aggregate. Proportions : theory, determination, data for estimates Mixing. Laying. Strength. Cost.
Art. 3. Aiitificial Stone 1136
Portland. McMurtrie. Frear. Ransome. Sorel.
CHAPTER V. QUARRYING.
Methods of Quarrying : by hand tools ; by explosives, — the drills, the explosives ; by channeling and wedging 116
CHAPTER VI. STONE CUTTING.
Art. 1. Tools 125
Eighteen hand tools illustrated and described. Machine tools de- scribed.
Art. 2. Methods op Forming the Surfaces 129
Four methods illu.strated and described.
Art. 3. Methods of Finishing the Surfaces 131
Eight methods illustrated and described.
CHAPTER VII. STONE MASONRY. Definitions : parts of the wall, kinds of masonry. Ashlar Masonry : dressing, bond, backing, pointing, mortar required, when employed, specifications. Squared-stone Masonry : description, mortar required, specifications. Rubble Masonry : description, mortar required, when employed, specifications. Slope-wall Masonry. Stone Paving. Rip-
TABLE OF CONTEXTS.
PAGE
rap. Strength of Stone Masonry : examples, safe pressure. Meas- urement of masonry. Cost : quarrying, dressing, price of stone ; examples — U. S. public buildings, railroads, tunnels, bridge piers, arch culverts ; summary 135
CHAPTER VIII. BRICK MASONRY. Mortar. Bond. Compressive Strength : results of experiments, safe pressure. Transverse Strength : strain on lintel. Measurement of Brick-work. Data for Estimates : brick, labor, mortar required. Cost. Specifications : for buildings, sewers, arches. Brick vs. Stone Masonry. Brick Masonry Impervious to Water. Efflorescence. . . 161
PART III. FOUNDATIONS. CHAPTER IX. INTRODUCTORY.
Definitions, and Plan of Proposed Discussion 183
CHAPTER X. ORDINARY FOUNDATIONS.
Outline of Contents 186
Art. 1. The Soil 186
Examination of the Site. Bearing power of Soils : rock, clay, sand, semi-liquid soils ; summary. Methods of Improving Bearing Power : increasing depth, drainage, springs, consolidating the soil, sand piles, layers of sand.
Art. 2. Designing the Footings 199
Load to be Supported. Area Required. Center of Pressure and Center of Base. Independent Piers. Effect of AVind. Offsets for ' Masonry Footings. Timber Footings. Steel-rail Footings. Inverted Arches.
Art. 3. Preparing the Bed 213
On Rock. On Firm Earth, In "Wet Ground : coffer-dam, con- crete, grillage.
CHAPTER XI. PILE FOUNDATIONS.
Definitions ... 216
Art. 1. Descriptions, and Methods of Driving Piles 216
Description : iron piles ; screw piles ; disk piles ; sheet piles ; bear ing piles, — specifications, caps and shoes, splicing. Pile Driving Ma- chines : drop-hammer, — friction clutch, nipper ; steam-hammer, drop- hammer vs. steam-hammer ; gunpowder pile-drivers ; driving with dynamite ; driving with water jet ; jet vs. hammer. Cost of Piles. Cost of Pile Driving : railroad construction, bridge construction, [ bridge repairs, foundations, harbor and river work.
TABLE OF CONTENTS.
PAGW
Art. 2. Bearing Power of Piles 233
Methods of Determining Supporting Power. Rational Formula. Comparison of Empirical Formulas: Beaufoy's, Nystrom's, Mason's, Sander's, Mc Alpine's, Trautwine's, the Author's. Supporting Power Determined by Experiment : examples, factor of safety ; supporting power of screw and disk piles.
Art. 3. Arrangement of the Foundation 250
Position of Piles. Sawing-ofE. Finishing Foundation : piles and grillage, piles and concrete, lateral yielding. Cushing's Pile Founda- tion.
CHAPTER XII. FOUNDATIONS UNDER WATER. Difficulties to be 0\t;rcome. Outline of Contents. . . 257
Art. 1. The Coffer-Dam Process 258
Construction of the Dam. Leakage, pumps. Preparing the Foundation
Art. 2. The Crib and Open Caisson Process 266
Definitions. Principle. Construction of the Caisson. Construc- tion of the Crib. Excavating tne Site.
Art. '6. Dredging through Wells 271
Principle. Excavator. Noted Examples : Poughkeepsie, Atcha- falaya, aud Hawkesbury bridges; brick cylinders. Frictional Resist- ance. Cost.
Art. 4. Pneumatic Process 278
Vacuum Process. Plenum Process. History. Pneumatic Piles, bearing power. Pneumatic Caissons : the caisson, the crib, the coffer- dam, machinery, air-lock. Excavators: sand lift, mud-pump, water column, blasting. Rate of Sinking. Guiding the Caisson. Noted Examples : Havre de Grace, Blair, St. Louis, Brooklyn, Forth Bridges. Physiological Effects of Compressed Air. Examples of Cost : at Havre de Grace, Blair, and Brooklyn, and in Europe.
Art. 5. The Freezing Process 307
Principle. History. Details of Process. Examples. Advantages. Cost. Art. 6. C(jmparison of Methods 309
PAET IV. MASONRY STRUCTURES.
CHAPTER XIII. MASONRY DAMS.
Classification op Dams 311
Art. 1. Stability of Gravity Dams 312
Principles. ■ Stability against Sliding : destroying forces, resisting forces, co-efficient of friction, condition of equilibrium, factor of safety. Stability against Overturning : by moments, — overturning mo-
TABLE OF CONTEXTS.
PAGE
ment, resisting moment, condition for equilibrium, factor of safety ; by resolution of forces.. Stability against Crushing : method of find- ing maximum pressure, tension on masonry, limiting pressure.
Art. 2. Outlines op the Design 336
"Width on Top. The Profile : theory, examples. The Plan : straight crest vs. straight toe ; gravity vs. arch dams ; curved gravity dams. Qualitj" of Masonry. Bibliography.
Art. 3. Rock-Fill Dams 334
Wood. Earth. Rock-fill and masonry dams compared.
CHAPTER XIV. RETAINING WALLS.
Definitions. Methods of Failure. Difficulties. ....... 338
Art. 1. Theoretical Formulas 340
The Thre-j Assumptions. Theories : Coulomb's, Weyrauch's, Rankine's.
Abt. 3. Empirical Rules 349
English Rules. American Rules. Details of Construction : quality of masonry, drainage, land ties, relieving arches.
CHAPTER XV. BRIDGE ABUTMENTS.
Discussion of General Forms. Quality of Masonr}-. Foundation. Wing Abutment, — design, and table of contents of various sizes. U- Abutment, — design and table of contents of various sizes. T- Abut- ment,— design and table of contents of various sizes 353
CHAPTER XVI. BRIDGE PIERS.
Selection of Site and Arrangement of Spans. . . . 366
Art. 1. Theory of Stability , . 367
Methods of Failure. Stability against Sliding : effect of wind, cur- rent, ice ; resisting forces. Stability against Overturning: by mo- ments; by resolution of forces. Stability against Crushing. Example of method of computing stability.
Art. 2. Det.uls of Construction 377
Dimensions : on top, at bottom. Batter. Cross Section. Specifica- tions. Examples; Cairo, Grand Forks, Blair, Henderson, St. Croix River ; iron tubular ; -wooden barrel. Tables of Contents of different styles aud sizes of bridge piers. Specifications.
CHAPTER XVII. CULVERTS.
Art. 1. Water Way Required 391
The Factors. The Formulas : Meyer's, Talbot's. Practical method of finding area of water way. Art. 2. Box and Pipe Culverts 396
Stone ^ox CulveH : foundation, end walls, cover, specifications.
Xii TABLE OF CONTENTS.
PAQg
Examples : Standard, "West Shore. Canadian. Table of Contents and cost of the various styles and sizes 396
Vitrijkd Pipe Culverts : Construction. Example. Table of Con- tents 407
Iron Pipe Culverts : Construction. Size and Weight of Pipe. Ex- amples : A., T. & S. F., and C, B. & Q. standards. Table of Quan- tity of Materials Required 412
Timber Culvert : C, M. & St. P. standard box culverts. C, B. &
Q. standard barrel culvert 417
Art. 3. Akch Ctjlvekt 419
General Form : splay of wing walls, joining wings and body, seg- mental vs. semi-circular. Examples : diagrams illustrating details, and also tables giving dimensions, and contents, and cost, of all sizes of each of the standard forms of the Illinois Central. C, K. & N., A., T. & S.-F. (both semi-circular and segmental), and a standard form. Specifications.
CHAPTER XVIII. MASONRY ARCHES.
Definitions : parts and kinds of arches ; line of resistance 440
Art. 1. Theory of the Masonry Arch 444
External Forces. Methods of Failure. Criteria of Safety : sliding, rotation, crushing, — unit pressure, open joints. Location of Line of Resistance : hypothesis of least pressure ; hypothesis of least crown thrust, joint of rupture ; Winkler's hypothesis ; Navier's principle. Rational Theory of the Arch : symmetrical load, — two methods ; unsymmetrical load ; criterion for line of resistance. Scheflier's Theory : two examples ; erroneous application ; reliability of. Ran- kiue's Theory : curvature of linear arch, method of testing stability, reliability. Other Theories. Theory of the Elastic Arch. Stability of Abutments and Piers.
Art. 2. Rules Derived from Practice 194
Empirical Formulas : thickness of the arch at the crown, — Ameri- can, French, English practice ; thicknessat the springing, — American, French, English practice ; dimensions of abutments. Dimensions of Actual Arches and Abutments. Illustrations of Arches. Minor De- tails: backing, spandrel filling, drainage. Brick Arches ; bond ; ex- amples,— tunnel, Philadelphia sewers, Washington sewers. Specifica- tions : stone arches, brick arches.
Art. 3. Arch Centers 515
Load to be supported, method of computing. Outline forms of Centers : solid rib, built rib, braced wooden rib, trussed frame. Ex- amples: centers for Vosburg tunnel, stone bridges, and Cabin John Arch. Striking Centers : method, time.
TABLE OF CONTENTS. xiii
APPENDIX I. SPECIFICATIONS FOR MASONRY.
PAGE
General Railroad Masonry 529
Masonry of Railroad Buildings 534
Architectural Masonry 539
APPENDIX 11. SUPPLEMENTARY NOTES.
Labor Required in Quarrying 544
Cost of Cutting Granite , . 545
Cost of Laying Cut Stone . 545
Cost of Breaking Stone for Concrete ^ . 54^
Cost of Imbedding Large Stones in Concrete 547
Crushing Strength of Sewer Pipe 547
Holding Power of Drift-bolta 547
MASONRY CONSTRUCTIOK
INTRODUCTION.
Under this general head will be discussed the subjects relating to the use of stone and brick as employed by the engineer or archi- tect in the construction of buildings, retaining walls, bridge piers, culverts, arches, etc., including the foundations for the same. For convenience, the subject will be divided as follows :
Part I. Description and Characteristics of the Materials-
Part II. Methods of Preparing and Using the Materials.
Part III. Foundations.
Part I\^. Masonry Structures.
" The first cost of masonry should be its only cost. Though supersti ucturefr decay and drift away, though embankments should crumble aud wash out, masonry should stand as one great mass of solid rock, firm and enduring.'^
— Anonyiau»L8.
F>ARX I.
THE MATERIALS,
CHAPTER I. NATURAL STONE.
Art. 1. Requisites for Good Building Stone.
1. The qualities which are most important in stone used for construction are cheapness^, durability, strength, and beauty.
2. Cheapness. The primary factor which determines the value of a stone for structural purposes is its cheapness. The items which contribute to the cheapness of a stone are abundance, proximity of quarries to place of use, facility of transportation, and the ease with which it is quarried and worked.
The wide distribution and the great variety of good building stone in this country are such that suitable stone should everywhere be cheap. That such is not the case is probably due either to a lack of the developmcT^t of home resources or to a lack of confidence in home products. Tlie several State and Government geological surveys have done much to increase our knowledge of the building stones of this country.
The lack of confidence in home resources has very frequently caused stones of demonstrated good quality to be carried far and wide, and frequently to be laid down upon the outcropping ledges of material in every way their equal. The first stone house erected in San Francisco, for example, was built of stone brought from China ; and at the present day the granites mostly employed there are brought from New England or from Scotland. Yet there are no stones in our country more to be recommended than the Califor- nia granites. Some of tlie prominent public and private buildings in Cuicinnati are constructed of stone that was carried by water and
3
NATURAL STONE. [CHAP. I.
railway a distance of about 1500 miles. Within 150 miles of Cin- cinnati, in the sub-carboniferous limestone district of Kentucky, there are very extensive deposits of dolomitic limestone that afford a beautiful building stone, which can be quarried at no more ex- pense than that of the granite of Maine. Moreover, this dolomite is easily carved, and requires not more than one third the labor to give it a surface that is needed by granite. Experience has shown that the endurance of this stone under the influence of weather is very great ; yet because it has lacked authoritative indorsement there has been little market for it, and lack of confidence in it has led to the transportation half-way across the continent of a stone little, if any, superior to it.
Development of local resources follows in the wake of good in- formation concerning them, for the lack of confidence in home prod- ucts can not be attributed to prejudice.
The facility with which a stone may be quarried and worked is an element affecting cheapness. To be cheaply worked, a stone must not only be as soft as durability will allow, but it should have no flaws, knots, or hard crystals.
3. Dtjeability. Next in importance after cheapness is dura- bility. Rock is supposed to be the type of all that is unchangeable and lasting ; but the truth is that, unless a stone is suited to the conditions in which it is placed, there are few substances more liable to decay and utter failure. The durability of stone is a subject upon which there is very little reliable knowledge. The question of endurance under the action of weather and other forces can not be readily determined. The external aspect of the stone may fail to give any clue to it ; nor can all the tests we yet know determine to a certainty, in the laboratory, just how a given rock will with- etand the effect of our variable climate and the gases of our cities. If our land were what is known as a rainless country, and if the temperature were uniform throughout the year, the selection of a durable building stone would be much simplified. The cities o'' northern Europe are full of failures in the stones of importanl structures. The most costly building erected in modern times, per* haps the most costly edifice reared since the Great Pyramid, — the Parliament House in London, — was built of a stone taken on thfc recommendation of a committee representing the best scientific and technical skill of Great Britain. The stone selected was submitted
ART. 2. J TESTS OF BvJILDilfG STONES. 5
to various tests, but the corroding influence of a London atmc^phere was overlooked. The great structure was built, and now it seems questionable whether it can be made to endure as long as a timber building would stand, so great is the efEect of the gases of the atmosphere upon the stone. This is only one of the numerous in- stances that might be cited in which a neglect to consider the climatic conditions of a particular locality in selecting a building material has proved disastrous.
" The great difference which may exist in the durability of stones of the same kind, presenting little difference in appearance, is strikingly exemplified at Oxford, England, where Christ Church Cathedral, built in the twelfth or thirteenth century of oolite from a quarry about fifteen miles away, is in good preservation, while many colleges only two or three centuries old, built also of oolite from a quarry in the neighborhood of Oxford, are rapidly crumbling to pieces. " *
4. Strength. The strength of stone is in some instances a cardinal quality, as when it is to form piers or columns to support great weights, or capstones that span considerable intervals. It is also an indispensable attribute of stone that is ';o be exposed to mechanical violence or unusual wear, as in steps, Imtels, door- jambs, e^e.
5. Beauty. This element is of more importance to the archi- tect than to the engineer ; and yet the latter can not afford to neglect entirely the element of beauty in the design of his most utilitarian structures. The stone should have a durable and pleas- ing color.
Art. 2. Tests of the Quality of Building Stones.
6. As a general rule, the densest, hardest, and most uniform stone will most nearly meet the preceding requisites for a good building stone. The fitness of stone for structural purposes can ba determined approximately by examining a fresh fracture. It should be bright, clean, and sharp, without loose grains, and free from any dull, earthy appearance. The stone should contain no "drys,"«.e., seams containing material not thoroughly cemented together, nor "crow-foots,'* i.e., veins containing dark-colored, uncemented material.
* Rankine's Civil Engineering, p. 362.
NATURAL STONE. [CHAP. I.
The more formal tests employed to determine the qualities of a building stone are: (1) weight or density, (2) hardness and tough- ness, (3) strength, (4) durability.
1. Weight of Stone.
7. Weight or density is an important property, since upon it depends to a large extent the strength and durability of the stone.
If it is desired to find the exact weight per cubic foot of a given stone, it is generally easier to find its specific gravity first, and then multiply by 62.4, — weight, in pounds, of a cubic foot of water. This method obviates, on the one hand, the expense of dressing a sample to regular dimensions, or, on the other, hand, the in- accuracy of measuring a rough, irregular piece. Notice, however, that this method determine^ the weight of a cubic foot of the solid stone, which will be more than the weight of a cubic foot of the material as used for structural purposes. In finding the specific gravity there is some difficulty in getting the correct disj^lacement of porous stones, — and all stones are more or less porous. There are various methods of overcoming this difficulty, which give slightly different results. The following method, recommended by General Gillmore, is most frequently used:
All loose grains and sharp corners having been removed from the sample and its weight taken, it is immersed in water and weighed there after all bubbling has ceased. It is then taken out of the water, and, after being compressed lightly in bibulous paper to absorb the water on its surface, is weighed again. The specific gravity is found by dividing the weight of the dry stone by the difference between the weight of the saturated stone in air and in water. Or expressing this in a formula,
W„ Specific gravity =
w;- w/
in which IF„ represents the weight of dry stone in air, W^ the weight of saturated stone in air, IF,- the weight of stone immersed in water.
The following table contains the weight of the stones most fre- quently met with.
ART. 2.]
TESTS OF BUILDING STONES.
TABLE 1. Weight of Building Stones.
Kind of Stonb.
Pounds per Cubic Foot.
Min.
Max.
Mean.
Granites . . Limestones Marbles. . . Sandstones Slates
161 146 157 127 160
178 174 180 151 175
167 158 170 139
174
2. Hardness and Toughness.
8. The apparent hardness of a stone depends upon (1) the hardness of its component minerals and (2) their state of aggrega- tion. The hardness of the component minerals is determined by the resistance they offer to being scratched; and varies from that of talc which can easily be scratched with the thnmb-nail, to that of quartz which scratches glass. But however hard the mineral constituents of a stone are, the apparent hardness of the stone itself depends upon the state of aggregation of the particles. Many rocks composed of hard materials work readily, because their grains are loosely coherent ; while others composed of softer materials are quite tough and difficult to work, owing to the tenacity with which the particles adhere to each other. Obviously a stone in which the grains adhere closely and strongly one to another will be stronger and more durable than one which is loose textured and friable.
The toughness of a stone depends upon the force with which the particles of the component minerals are held together.
Both hardness and toughness should exist in a stone used for stoops, pavements, road-metal, the facing of piers, etc. No experi- ments have been made in this country to test the resisting power of stone when exposed to the different kinds of service. A table of the resistance of stones to abrasion is often quoted,* but as it contains only foreign stones, which are described by local names, it is not of much value.
* For example, Mahan's Civil Engineering, p. 13.
NATURAL STONE. [CHAP. I.
3. Strength.
Under this head will be included (1) crnshing or compressive strength, (2) transverse strength, (3) elasticity. Usually, when simply the strength is referred to, the crushing strength is intended.
9. Crushing Strength. The crushing strength of a stone is tested by applying measured force to cubes until they are crushed. The results for the crushing strength vary greatly with the details of the experiments. Several points, which should not be neglected either in planning a series of experiments or in using the results obtained by experiment, will be taken up separately, although they are not entirely independent.
10. Form of Test Specimen. Experiments show that all brittle materials when subjected to a compressive load fail by shearing on certain definite angles. For brick or stone, the plane of rupture makes an angle of about 60° with the direction of the compressing force. For this reason, the theoretically best form of test specimen would be a prism having a height of about one and a half times the least lateral dimension. The result is not materially different if the height is three or four times the least lateral dimension. But if the test specimen is broader than high, the material is not free to fail along the above plane of rupture, and consequently the strength per unit of bed-area is greater than, when the height is greater than the breadth.
However, notwithstanding the fact that theoretically the test specimen should be higher than broad, it is quite the universal custom to determine the crushing strength of stone by testing cubes.
11. Size of the Cube. Although the cube is the form of test specimen generally adopted, there is not equal unanimity as to the size of the cube; but it is conclusively proven that the strength per square inch of bed-area is independent of the size of the cube, and therefore the size of the test specimen is immaterial.
General Gillmore, in 1875, made two sets of experiments which seems to prove that the relation between the crushing strength and the size of the cube can be expressed by the formula
?/ = a Vx,
in which y is the total crnshing pressure in pounds per square inch
AET. 2.] STRENGTH OF BUILDING STOKES. 9
of bed-area, a is the crushing pressure of a 1-inch cube of the same material, and x is the length in inches of an edge of the cube under trial. For two samples of Berea (Ohio) sandstone, a was 7000 and 9500 lbs., respectively.*
Eesults by other observers with better machines, particularly by General Gillmore f with the large and accurate testing-machine at Watertown (Mass.) Arsenal, I uniformly show this supposed law to be without any foundation. Unfortunately the above relation between strength and bed-area is frequently quoted, and has found a wide acceptance among engineers and architects.
Two inches is the most common size of the cube for compression tests.
12. Cushions. Homogeneous stones in small cubes appear in all cases to break as shown in Fig. 1. The forms of the fragments a and b are, approxi- mately, either conical or pyramidal. The more or less disk-shaped pieces c and d are detached from the sides of the cube with a kind of explosion. In the angles e and /, the stone is generally found crushed and ground into powder. This general form of breakage occurs also in non-homogeneous stones when ^iq. i.
crushed on their beds, but in this case the modification which the grain of the stone produces must be taken into account.
The nature of the material in contact with the stone while nnder pressure is a matter of great moment. If the materials which press upon the top and bottom of the specimen are soft and yielding and press out sidewise, they introduce horizontal forces which materially diminish the apparent crushing strength of the stone. If the pressing surfaces are hard and unyielding, the resistance of these surfaces adds considerable to the apparent strength.
* Report on Strength of Building Stone, Appendix, Report of Chief of Engineers of U. S. A. for 1875.
t Notes on the Compressive Resistance of Freestone, Brick Piers, Hydraulic Cements, Mortars, and Concrete, Q. A. GiUmore. John Wiley & Sons, New York, 1888.
X Report on the " Tests of Metals," etc., for the year ending June 30, 1884, pp. 126, 166, 167, 197, 212, 213, 215 ; the same being Sen. Ex. Doc. No. 35, 49th Cong., 1st Session. For a discussion of these data by the author, see Engineering News, vol. lix. pp. 511-512.
10 NATURAL STONE. [CHAP. I.
Formerly steel, wood, lead, and leather were much used as pressing surfaces. Under certain limitations, the relative crushing strengths of stones with these different pressing surfaces are 100, 89, 65, and 62 respectively.*
Tests of the strength of blocks of stone are useful only in com- paring different stones, and give no idea of the strength of struct- ures built of such stone (see § 246) or of the crushing strength of stone in large masses in its native bed (see § 273).
Then, since it is not possible to have the stone under the same conditions while being tested, that it is in the actual structure, it is best to test the stone under conditions that can be accurately described and readily duplicated. Therefore it is rapidly coming to be the custom to test^ the stone between metal pressing surfaces. Under these conditions the strength of the specimen will vary greatly with the degree of smoothness of its bed-surfaces. Hence, to obtain definite and precise results, these surfaces should be rubbed or ground perfectly smooth ; but as this is tedious and expensive, it is quite common to reduce the bed-surfaces to planes by plastering them with a thin coat of plaster of Paris. With the stronger stones, specimens with jjlastered bed will show less strength than those having rubbed beds, and this difference will vary also with the length of time the plaster is allowed to harden. With a stone having a strength of 5,000 to 6,000 pounds per square inch, allowing the plaster to attain its maximum strength, this differ- ence varied from 5 to 20 per cent., the mean for ten trials being almost 10 per cent, of the strength of the specimen with rubbed beds.
13. Dressing the Cube. It is well known that even large stones can be broken by striking a number of comparatively light blows along any particular line ; in which case the force of the blows gradually weakens the cohesion of the particles. This principle finds application in the preparation of test specimens of stone. If the specimen is dressed by hand, the concussion of the tool greatly affects its internal conditions, particularly with test specimens of small dimensions. With 2-inch cubes, the tool-dressed specimen usually shows only about 60 per cent, of the strength of the sawed
* Report on Building Stones, in Report of Chief of Engineers, U. S. A., 1875, App. II. ; also bound separately, page 29.
ART. 2.]
STRENGTH OF BUILDING STONES.
11
sample. The sawed sample most nearly represents the conditions of actual practice.
Unfortunately, experimenters seldom state whether the specimens were tool-dressed or sawed. The disintegrating effect of the tool in dressing is greater with small than with large specimens. This may account for the difference in strength of different sizes of test specimen as seems to be shown by some experiments.
All stones are strongest when laid on their natural bed, i.e., when the pressure is perpendicular to the stratification ; and with sedimentary rocks there is a very great difference in the two positions. Hence, in preparing the test specimen the natural bed should be marked, and the cube should be tested upon its native bed.
14. Data on Crushing Strength. The strength of the principal classes of building stone in use in the United States is about as follows :
TABLE 2. CBUsmNG Strength of Cubes of Stone.
|
Ultimate Crushing Strength. |
||||
|
Kinds of Stone. |
Pounds per Square Inch. |
Tons per Square Foot. |
||
|
Min. |
Max. |
Min. |
Max. |
|
|
Trap Rocks of N. J Granite |
20,000 12,000 8,000 7,000 5,000 |
24,000 21,000 20,000 20,000 15,000 |
1,440 860 580 500 360 |
1.730 1,510 1,440 1,440 1,080 |
|
Marble |
||||
|
Limestorie |
||||
|
Sandstbne |
||||
15. Crushing Strength of Slabs. Oniy a few experiments have been made to determine the crushing strength of slabs of stone. The strength per square inch of bed-surface was considerably greater than that for cubes ; but a study of the results of all of the reliable experiments * fails to discover any simple relation between
*See Report on "Tests of Metals, etc.," for 1884.— Sen. Ex. Doo. No. 35, 49th Cong., 1st Sesoion,— pp. 126 and 212.
12 NATURAL STONE. [CHAP. I.
the crushing strength of cubes and slabs. It is probable that the effect of the pressing surface is so great as to completely mask the variation due to height of specimen. More experiments on this subject are very much needed.
16. Transverse Strength. When stones are used for lintels, etc., their transverse strength becomes important. The ability of a stone to resist as a beam depends upon its tensile strength, since that is always much less than its compressive strength. A knowl- edge of the relative tensile and compressive strength of stones is valuable in interpreting the effect of different pressing surfaces in compressive tests, and also in determining the thickness required for lintels, sidewalks, cover-stones for box culverts, thickness of footing courses, etc.
Owing to the small cross section of the specimen employed in determining the transverse strength of stones, — usually a bar 1 inch square, — the manner of dressing the sample affects the apparent transverse strength to a greater degree than the compressive strength (see § 13) ; and it is even more unfortunate, since the strength of the stone as used in actual practice is nearly proportional to the strength of sawed samples.
The following formulas are useful in computing the breaking load of a slab of stone. Let W represent the concentrated center load phis half of the weight of the beam itself, in pounds ; and let b, d, and I represent the breadth, depth, and length, in inches, respectively. Let R = the modulus of rupture, in lbs. per sq. in. ; let C = the weight, in pounds, required to break a bar 1 inch square and 1 foot long between bearings ; and let L = the length of the beam in feet. Then
The equivalent uniformly distributed weight is equal to twice the concentrated center load. '
Table 3 on the following page gives the values of R, the mod- ulus of rupture, and of C, the co-efficient of transverse strength, required in the above formulas.
Example, — To illustrate the method of using the above formulas, assume that it is desired to know the breaking load for a limestone slab 3 inches thick, 4 feet wide, and 6 feet long. Then Z* = 48 ;
ART. 2.]
STRENGTH OF BUILDING STONES.
13
TABLE 3. Tbansverse Strength of Stone, Brick, and Mortar.
MaTEKIAIj.
,, „ -D liCo EFFICIENT OF TRANS-
Modulus of Rupture. |, ^^^^^^ Strength.
Max. I Min. ' Aver, i Max.
Min.
Blue-stone flagging
Granite
Limestone
" oolitic, from Ind., sawed
Marble
Sandstone
Slate
Brick (§59)
Concrete — see § 157/
Mortar, neat Portland, 1 year old. . Mortar, 1 part Portland cement, 1
part sand, 1 j^ear old
Mortar, 1 part Portland cement, 2
parts sand, 1 year old
Mortar, neat Rosendale, 1 year old. Mortar, 1 part Rosendale cement,
1 part sand, 1 year old
Mortar, 1 part Rosendale cement,
2 parts sand, 1 year old
4,511 2,700 3,500 2,590 2,880 2,340 9,000 1,796
715 690 479
|
360 |
2,700 |
251 |
20 |
|
900 1,800 1 |
150 |
50 |
|
|
140 1 1,500 |
140 |
8 |
|
|
2,190 , 2,338 |
144 |
122 |
|
|
144 1 2,160 |
160 |
8 |
|
|
576 1,260 |
130 |
32 |
|
|
1,800 |
5,400 |
500 |
100 |
|
269 |
800 1,158* 945* 682* |
100 |
15 |
|
415 |
600 |
39 |
23 |
|
348 |
526 |
38 |
19 |
|
338 |
405 |
26 |
18 |
Aver.
150 100
83 130 120
70 300
45
64*
52*
38* 33
29
22
d = ^; I = 72; R = 1500 lbs.,— the "average" value from the table; — and C = 83. Substituting these values, we have
2 h ff 2 V 48 V Q
GOOD pounds;
or, using the other form,
W =
Id
48 v 0 (7 = :^ 83 = 5976 pounds.
L ^ 6
which agrees with the preceding except for omitted decimals. Hence the breaking load for average quality of limestone is 6000 pounds concenti'ated along a Ime half-way between the ends ; the uniformly distributed load is twice this, or 12,000 pounds. The * Only one experiment.
14
Natural stone.
[chap. I.
question of wliat margin should be allowed for safety is one that can not be determined in the abstract ; it depends upon the accuracy with which the maximum load is estimated, upon the manner the load is applied — whether with shock or not, — upon the care with which the stone was selected, etc. This subject will be discussed further in connection with the use of the data of the above table in subsequent parts of this volume.
17. Elasticity. But very few experiments have been made to determine the co-efficient of elasticity, the elastic limit, and the •'set'' of stone. Data on these points would be valuable in deter- mining the effect of combining masonry and metal, of joining different kinds of masoni-y, or of joining new masonry to old ; in calculating the effect of loading a masonry arch ; in proportioning abutments and piers of railroad bridges subject to shock, etc. The following is all the data that can be found:
TABLE 4. Co-efficient of Elasticity op Stone, Brick, and Mortak.
Material.
Haverstraw Freestone *
Portland Stone (oolite limestone)f
Marblef
Portland Granite:}:
Siatef
Grafton Limestone^
Richmond Granite:}:
Brick, medium — mean of 16 experiments*
Louisville Cement Mortar, 4 months old : X
Neat cement
1 part cement, 1 part sand
1 part cement, 2 parts sand
Ulster Co. (N. Y.) Cement Mortar, 23 months
old:*
2 parts cement, 3 parts sand
1 part cement, 3 parts sand
l*K>rtland Cement Mortar, 22 months old *
Pounds per Square Inch.
950,000 1,530,000 2,500,000 5,500,000 7,000,000 8,000,000 13,000,000 3,500,000
800,000
600,000
1,300,000
640,000
535.000
1,525,000
* U. S. testing-machine, Watertown, Mass. + Tredgold, as quoted by Stoney. X History of St. Louis Bridge, pp. 334-28.
ART. 2.] STRENGTH OF BUILDING STONES. 15
18. Bibliographical. A large number of tests have been ajiplied lo the building stones of the United States. For the results and details of some of the more important of these tests see: Keporfc on Strength of Building Stone, Gen. Q. A. Gillmore, Ajjpeu. II, Eeport of Chief of Engineers, U. S. A., for 1875; Teuth Census of the U. S., Vol. X, Eeport on the Quarry Industry, pp. 330-35; the several annual reports of tests made with the U. S. Government testing machine at the Watertown (Mass.) Arsenal, published by the U. S. War Department under the title Eeport on Tests of Metals and Other Materials; Transactions of the American Society of Civil Engineers, Vol. II, pp. 145-51 and pp. 187-92; Journal of the Association of Ea- gineering Societies, Vol. Y, pp. 176-79, Yol. IX, pp. 33-43; Engineering Keivs, Vol. XXXI, p. 135 (Feb. 15, 1884); and the reports of the various State Geological Surveys, and the com- missioners of the various State capitols and of other public buildings.
By way of comparison the following reports of tests of building stones of Great Britain may be interesting: Proceedings of the Institute of Civil Engineers, Vol. CVII (1891-92), pp. 341-69; abstract of the above. Engineering JVeios, Vol. XXVIII, pp. 279-82 (Sept. 22, 1892).
In consulting the above references or in using the results, the details of the manner of making of the experiments should be kept clearly in mind, particularly the method of prej^aring and bedding the specimen.
4. DUEABILITY.
19. '* Although the art of building has been practiced from the earliest times, and constant demands have been made in every age for the means of determining the best materials, yet the process of ascertaining the durability of stone appears to have received but little definite scientific attention, and the processes usually employed for solving this question are still in a very unsatisfactory state. Hardly any department of technical science is so much neglected as that which embraces the study of the nature of stone, and all the varied resources of lithology in chemical, microscopical, and physical methods of investigation, wonderfully developed within the last
16 NATURAL STONE. [CHAP. l.
quarter century, have never yet been properly applied to the selec- tion and protection of stone used for building purposes/'*
Examples of the rapid decay of building stones have already been referred to, and numerous others could be cited, in which a stone which it was supposed would last forever has already begun to decay. In every way, the question of durability is of more interest to the architect than to the engineer ; although it is of enough importance to the latter to v/arrant a brief discussion here.
20. Destructive Agents. The destructive agents may be clas- sified as mechanical, chemical, and organic. The last are unim- portant, and will not be considered here.
21. Mechanical Agents. For our climate the mechanical agents are the most efficient. These are frost, wind, rain, fire, pressure, and friction.
The action of frost is usually one of the main causes of rapid decay. Two elements are involved, — the friability of the material and its power of absorbing moisture. In addition to the alter- nate freezing and thawing, the constant variations of temperature from day to day, and even from hour to hour, give rise to molecular motions which affect the durability of stone as a building material. This effect is greatest in isolated columns, — as monuments, bridge piers, etc.
The effect of rain depends upon the solvent action of the gases which it contains, and upon its meclianical effect in the wear of pattering drops and streams trickling down the face of the wall.
A gentle breeze dries out the moisture of a building stone and tends to j)reserve it; but a violent wind wears it away by dashing sand grains, street dust, ice particles, etc., against its face. The extreme of such action is illustrated by the vast erosion of the sand- .stone in the jilateaus of Colorado, Arizona, etc., into tabular mesasi, isolated joillars, and grotesquely-shaped hills, by the erosive force of sand grains borne by the winds. The effect is similar to that of the . sand blast as used in various processes of manufacture.. A violent wind also forces the rain-water, with all the corrosive acids it con- . tains, into the pores of stones, and carries off the loosened grains, *thus keeping a fresh surface of the stone exposed. Again, the gwaying of tall edifices by the wind must cause a continual motion,
* Tenth Census of the U. S., Vol. X., Report on the Quarry Industry, p. 864.
ART. 2.] DURABILITY OF BUILDING STONES. 17
not only in the joints between the blocks, but among the grains of the stones themselves. Many of these have a certain degree of flexibility, it is true; and yet the play of the grains must gradually increase, and a tendency to disintegration result.
Experience in great fires in the cities shows that there is no stone which can withstand the fierce heat of a mass of burning buildings. Sandstones seem to be the least affected by great heat, and granite most.
Friction affects sidewalks, pavements, etc., and has already been referred to (§ 8). It may also affect bridge piers, sea-walls, docks, etc.
The effect of pressure in destroying stone is one of the least impoitance, provided the load to be borne does not too nearly equal the crushing strength. The pressure to which stone is subjected does not generally exceed one tenth of the ultimate strength as determined by methods already described.
22. Chemical Agents. The principal ones are acids. Every constituent of stone, except quartz, is subject to attack by acids; and the carbonates, which enter as chief constituents or as cement- ing materials, yield very readily to such action. Oxygen and am- monia by their chemical action tend to destroy stones. In cities or manufacturing districts sulphur acids and carbonic acid have a very marked effect. These all result from the combustion of gas, coal, etc., and some are also the residuary gases of many kinds of manufactories. The nitric acid in the rain and the atmosphere exerts a perceptible influence in destroying building stone.
23. Resisting Agents. The durability of a building stone de- pends upon three conditions; viz., the chemical and mineralogical nature of its constituents, its physical structure, and the character and position of its exposed surfaces.
24. Chemical Composition. The chemical composition of the principal constituent mineral and of the cementing material has an important effect upon the durability of a stone.
A siliceous stone, other things being equal, is more durable than a limestone; but the durability of the former plainly depends upon the state of aggregation of the individual grains and their cement- ing bond, as well as on the chemical relation of the silica to the other chemical ingredients. A dolomitic limestone is more durable than a pure limestone.
18 NATL'EAL STOXE, ^ [CHAP. I..
A stone that absorbs moisture abundantly and rapidly is apt to- be injured by alternate freezing and thawing; hence clayey constit- uents are injurious. An argillaceous stone is generally compact, and often has no pores visible to the eye; yet such will disintegrate rapidly either by freezing and thawing, or by corrosive vapors.
The presence of calcium carbonate, as in some forms of marble and in earthy limestones, renders a building material liable to rapid attack by acid vapors. In some sandstones the cementing material is the hydrated form of ferric oxide, which is soluble and easily removed. Sandstones in Avhich the cementing material is siliceous are likely to be the most durable, although they are not so easily w^orked as the former. A stone that has a high per cent, of alumina (if it be also non-crystalline), or of organic matter, or of protoxide of iron, will usually disintegrate rapidly. Such stones are gen- erally of a bluish color.
25. Seasoning. The thorough drying of a stone before, and the preservation of this dryness after, its insertion in masonry are com- monly recognized as important factors of its durability; but the exact nature of the process of seasoning, and of the composition of the quarry-sap removed by thorough drying, have never been determined. The quarry water may contain little else than ordinary Well-water, or may be a solution more or less nearly saturated, at the ordinary temperature, with carbonate of calcium, silica, double salts of calcium and magnesium, etc. In the latter case, hardening re- sults from the drying, and an exact knowledge of its nature might throw important light on the best means for the artificial jJreserva- tion of stone. Again, water may exist in large quantity, in chemical combination, in the silicates (e.g., chlorite, kaolin, etc.), or in the hydrated iron oxides which constitute the cement of a building stone.
26. Physical Structure. The physical properties v/hich con- tribute to durability are hardness, toughness, homogeneity, con- tiguity of the grains, and the structure — whether crystalline or amorphous.
Although hardness (resistance to crushing) is often regarded as the most important element, yet resistance to weathering does not necessarily depend upon hardness alone, but upon hardness and the non-absorbent properties of the stone. A hard material of close and firm texture is, however, in those qualities at least, especially
ART. 2.] DURABILITY OF BUILDING STONES. V.*
fitted to resist friction, as in stoops, pavements, and road metal, and the wear of rain-drops, dripping rain-water, the blows of the waves, etc.
Porosity is an objectionable element. An excessive porosity in- creases the layer of decomposition which is caused by the acids of the atmosphere and of the rain, and also deepens the penetration of frost and promotes its work of disintegration.
If the constituents of a rock differ greatly in hardness, texture^ solubility, porosity, etc., the weathering is unequal, the surface is roughened, and the sensibility of the stone to the action of frost is increased.
The principle which obtains in applying an artificial cement, such as glue, in the thinnest film in order to secure the greatest binding force finds its analogy in the building stones. The thinner the films of the natural cement and the closer the grains of the pre- dominant minerals, the stronger and more durable the stone. One source of weakness in the famous brown-stone of New York City lies in the separation of the rounded grains of quartz and feldspar by a superabundance of ocherous cement. Of course the further sejxiration produced by' fissure, looseness of lamination, empty <3avities and geodes, and excess of mica tends to deteriorate still further a weak building stone.
Experience has generally shown that a crystalline structure re- sists atmospheric attack better than an amorphous one. This prin- ciple has been abundantly illustrated in the buildings of New York City. The same fact is generally true with the sedimentary rocks also, a crystalline limestone or good marble resisting erosion better than earthy limestone. A stone that is compactly and finely granular will exfoliate more easily by freezing and thawing than one that is •coarse-grained. A stone that is laminar in structure absorbs mois- ture unequally and will be seriously affected by unequal expansion and conti-action, — especially by freezing and thawing. Such a stone will gradually separate into sheets. A stone that has a gninular texture, as contrasted with one that is crystalline or fibrous, will crumble sooner by frost and by chemical agents, because of the easy dislodgment of the individual grains.
The condition of the surface, whether rough or polished, in- fluences the durability, — the smoother surface being the better.
20 NATURAL STONE. [CHAP.
The stone is more durable if the exposed surface is vertical than if inclined. The lamination of the stone should be horizontal.
27. Methods of Testing Durability. It has long been recog- nized that there are two ways in which we can form a judgment of the durability of a building stone, and these may be distinguished as natural and artificial.
28. Natural Methods, These must always take the precedence whenever they can be used, because they involve (1) the exact agencies concerned in the atmospheric attack upon stone, and (2) long periods of time far beyond the reach of artificial experiment.
One method is to visit the quarry and observe whether the ledges that have been exposed to the weather are deeply corroded, or whether these old surfaces are still fresh. In apj^lying this test, consideration must be given to the modifying effect of geological phenomena. It has been pointed out that ^'tlie length of time the ledges have been exposed, and the changes of actions to which they may have been subjected during long geological periods, are unknown; and since different quarries may not have been exposed to the same action, they do not always afford definite data for re- liable comparative estimates of durability, except where different specimens occur in the same quarry."
North of the glacial limit, all the products of decomposition have been planed away and deposited as drift-formation over the length and breadth of the land. The rocks are therefore, in gen- eral, quite fresh in appearance, and possess only a slight dej)th of cap or worthless rock. The same classes of rock, however, in the South are covered with rotten products fi-om long ages of atmos- pheric action.
A study of the surfaces of old buildings, bridge piers, monu- ments, tombstones, etc., which have been exposed to atmospheric influences for years, is one of the best sources of reliable information concerning the durability of stone. A durable stone will retain tlie tool-marks made in working it, and preserve its edges and corners sharp and true.
29. Artificial Methods of Testing Durability. The older but less satisfactory methods are: determining (1) the resistance to crushing, (2) the absorjitive power, (3) the resistance to the expan- sion of frost, by saturating the stone with some solution which will crystallize in the pores of the stone and produce an effect similar to frost, (4) the solubility ia acids, and (5) microscopical examination.
A i;t.
2.]
DURABILITY OF BUILDING STONES.
21
30. Absorptive Power. The ratio of absorption depends largely on the density, — a dense stone absorbing less water than a lighter, more porous one. Com^Dactness is therefore a matter of impor- tance, especially in cold climates; for if the water in a stone is once allowed to freeze, it destroys the surface, and the stone very speedily crumbles away. Other things being equal, the less the absorption the better the stone.
To determine the absorptive power, dry the specimen and weigh, it carefully; then soak it in water for 24 hours, and weigh again. The increase in weight will be the amount of absor2:)tion. Table 4 shows the weight of Avater absorbed by the stone as compared with the weight of the dry stone — that is, if 300 units of dry stone weigh 301 units after immersion, the absorption is 1 in 300, and is recorded fis 1-300.
Dr. Hiram A. Cutting, State Geologist of Vermont, determined the absorptive power * by placing the specimens in water under the receiver of an air-pump, and found the ratio of absorption a little larger than is given in the following table. It is believed that the results given below more nearly represent the conditions of actual practice. The values in the ''Max." column are the means of two or three of the largest results, and those in the "Min.'' column of two or three of the smallest. The value in the last column is the mean for 20 or more specimens.
TABLE 5. Absorptive Power of Stoxe, Brick, and Mortar.
Ratio of Absorption.
|
Kind of Material. |
Max. |
Miu. |
Average. |
|
Granites |
1-150 1-150 1-20 1-15 1-4 1-2 |
0 0 1-500 1-240 1-50 1-10 |
1-750 - 300 |
|
Marbles |
|||
|
Limestones |
1-38 |
||
|
Sandstones |
|||
|
Bricks |
1-10 |
||
|
Mortars |
|||
31. Effect of Frost. To determine the probable effect of frost upon a stone, carefully wash, dry, and weigh samples, and then wet * Yan Nostrand's Engin'g Mag., vol. xxiv. pp. 491-95.
22 NATURAL STONE. [CHAP. I.
them and expose to alternate freezing and thawing, after which wash, dry, and weigh again. The loss in weight measures the rela- tive durability.
A quicker way of accomplishing essentially the same result is to heat the specimens to 500'^ or 600° F., and plunge them, Avhile hot, into cold water. The following comparative results were obtained by the latter method : *
Relative Ratio of Loss.
White brick 1
Red brick 2
Brown-stone (sandstone from Conn.). . , 5
Nova Scotia sandstone 14
32. Brard's Test. Brard's method of determining the effect of frost is much used, although it does not exactly conform to the con- ditions met with in nature. It consists in weighing carefully some small pieces of the stone, which are then boiled in a concentrated sohition of sulphate of soda and afterwards hung up for a few days in the open air. The salt crystallizes in the pores of the stone, expands, and produces an effect somewhat similar to frost, as it causes small pieces to separate in the form of dust. The specimens are again weighed, and those which suffer the smallest loss of weight are the best. The test is often repeated several times. It will be seen that this method depends upon the assumption that the action of the salt in crystallizing is similar to that of water in freezing. This is not entirely correct, since it substitutes chemical and mechanical action for merely mechanical, to disintegrate the stone, thus giving the specimen a worse character than it really deserves. The following results were obtained by this method: f
Relative Ratio of Loss.
Hard brick 1
Light dove-colored sandstone from Seneca, Ohio 2
Coarse-grained sandstone from Nova Scotia 2
Coarse-grained sandstone from Little Falls, N. J 5
Coarse dolomite marble from Pleasautville, N. Y 7
Coarse-grained sandstone from Conn 13
Soft brick 16
Fine-grained sandstone from Conn 19
* Tenth Census of the U. S., vol. x., Report on the Quarry Industry, p. 384. For & table showing essentially the same results, see Van Nostrand's Engin'g Mag., vol. Xiv. p. 537.
t Tenth Census, vol. x., Report of the Quarry Industry, p. 385.
AI;T. 2. J DURABILITY OF BUILDIKG STONES. 23
33. Effect of the Atmosphere. To determine the effect of the atmosphere of a large city, where coal is used for fuel, soak clean small pieces of the stone for several days in water which contains one per cent, of sulphuric^and hydrochloric acids, agitating frequently. If the stone contains any earthy matter likely to be dissolved by the gases of the atmosphere, the water will be more or less cloudy or muddy. The following results were obtained by this method: *
Relative Ratio of Loss.
White brick 1
Red brick 5
Nova Scotia stone , 9
Brown-stone 30
34. Microscopical Examination. It is now held that the best method of determining the probable durability of a building stone is to study its surface, or thin, transjDarent slices, under a micro- scope. This method of study in recent years has been most fruit- ful in developing interesting and valuable knowledge of a scientific and truly practical character. An examination of a section by means of the microscope will show, not merely the various substances which compose it, but also the method according to which they are arranged and by which they are attached to one another. For example, "^pyrites is considered to be the enemy of the quarryman and constructor, since it decomposes with ease, and stains and dis- colors the rock. Pyrites in sharp, well-defined crystals sometimes decomposes with great difficulty. If a crystal or grain of pyrites is embedded in soft, porous, light-colored sandstones, like those which come from Ohio, its presence will with certainty soon demonstrate itself by the black spot which will form about it in the porous stone, and which will permanently disfigure and mar its beauty. If the same gi-ain of pyrites is situated in a very hard, compact, non- absorbent stone, the constituent minerals of which are not rifted or cracked, this grain of pyrites may decompose and the products bo washed away, leaving the stone untarnished."
35. Methods of Preserving. Vitruvius, the Eoman architect, two thousand years ago recommended that stone should be quarried in summer when driest, and that it should be seasoned by being allowed to lie two years before being used, so as to allow the natural
* Tenth Census, vol. x., Report on the Quarry Industry, p. 385.
24 NATURAL STONE. [CHAP. I.
sap to evaporate. It is a notable fact, that in the erection of St. Paul's Cathedral in London, England, Sir Christopher Wren re« quired that the stone, after being quarried, should be exposed for three years on the sea-beach, before its introduction into the building.
The surfaces of buildings are often covered vpith a coating of paint, coal-tar, oil, paraflBne, soap and alum, rosin, etc., to preserve them.
Another method of treatment consists in bathing the stone ia successive solutions, the chemical actions bringing about the forma- tion of insoluble silicates in the pores of the stone. For example, if a stone front is first washed with an alkaline fluid to remove dirt, and this followed by a succession of baths of silicate of soda or potash, and the surface is then bathed in a solution of chloride of lime, an insoluble lime silicate is formed. The soluble salt is then washed away, and the insoluble silicate forms a durable cement and checks disintegration. If lime-water is substituted for chloride oi lime, there is no soluble chloride to wash away.
There are a gi-eat many applications that have been used for the prevention of the decay of building stones, as paint, oil, coal-tar, bees- wax, rosin, paraffine, etc. , and numerous chemical preparations similar to that mentioned in the paragraph just above ; but all are expensive, and none have proved fairly satisfactory.*
It has already been stated that, in order to resist the effects of both pressure and weathering, a stone should be placed on its nat- ural bed. This simple precaution adds considerably to the dura- bility of any stone.
Aet. 3. Classification and Description of Building Stones.
36. Classification. Building stones are variously classified according to geological position, physical structure, ai~-d chemical composition.
37. Geological Classification. The geological position of rocks iias but little connection with their properties as building materials. As a general rule, the more ancient rocks are the stronger and the
* For an elaborate and valuable article by Prof. Eggleston on the causes of decay and the methods of preserving building stones, see Trans. Am. Soc. of C. E., voL XV. pp- 647-704 ; and for a discussion on the same, see same volume, pp. 705-16.
ART 3.] DESCRIPTION OF BUILDING STONES. 25
more durable ; but to this there are many exceptions. According to the usual geological classification, rocks are divided into igneous, metamorphic, and sedimentary. Greenstone, basalt, and lava ara examples of igneous rocks ; granite, marble, and slate, of meta- morj^hic ; and sandstone, limestone, and clay, of sedimentary. Al- though clay can hardly be classed with building stones, it is not entirely out of place in this connection, since it is employed in making bricks and cement, which are important elements ol masonry.
38. Physical Classification. With respect to the structural character of large masses, rocks are divided into stratified and un» stratified.
In their more minute structure the unstratified rocks present, for the most part, an aggregate of crystalline grains, firmly adhering together. Granite, trap, basalt, and lava are examples of this class.
In the more minute structure of stratified rocks, the follo«-ing varieties are distinguished : 1. Compact crystalline structure : ac- companied by great strength and durability, as in quartz-rock and marble. 2. Slaty structure, easily split into thin layers ; accom- panied by both extremes of strength and durability, clay-slate and hornblende-slate being the strongest and most durable. 3. The granular crystalline sti-ucture, in which crystalline grains either adhere firmly together, as in gneiss, or are cemented into one masj by some other material, as in sandstone ; accompanied by all degree? of compactness, porosity, strength, and durability, the' lowest ex- treme being sand. 4. The compact granular structure, in which the grains are too small to be visible to the unaided eye, as in blue limestone ; accompanied by considerable strength and durability. 5- Porous, granular structure, in which the grains are not crystal- line, and are often, if not always, minute shells cemented together; accompanied by a low degree of strength and durability. 6. The conglomerate structure, where fragments of one material are embed- ded in a mass of another, as graywacke; accompanied by all degrees of strength and durability.
A study of the fractured surface of a stone is one means of determining its structural character. The even fracture, when the surfaces of division are planes in definite positions, is characteristic of a crystalline structure. The uneven fracture, when the broken Burface presents sharp projections, is characteristic of a gi-anular
26 NATURAL STONE. [CHAP. I.
structure. The slaty fracture gives an even surface for planes of division parallel to the lamination, and uneven for other directions of division. The conchoidal fracture presents smooth concave and ')onvey surfaces, and is characteristic of a hard and compact struct- ure. The earthy fracture leaves a rough, dull surface, and indi- cates softness and brittleness.
39. Chemical Classification. Stones are divided into three classes with respect to their chemical composition, each distin- guished by the earth which forms its chief constituent , viz., sili- ceoui;' stones, argillaceous stones, and calcareous stones.
Siliceous Stones are those in which silica is the characteristic earthy constituent. With a few exceptions their structure is crystalline- gi-anular, and the crystalline grains contained in them are hard and durable ; hence weakness and decay in them generally arise from the decomposition or disintegration of some softer and more perish- able material, by which the grains are cemented together, or, when they are porous, by the freezing of water in their pores. The prin- cipal siliceous stones are granite, syenite, gneiss, mica-slate, green- stone, basalt, trap, porphyry, quartz-rock, hornblende-slate, and sand stone.
Argillaceous or Clayey Stones are those in which alumina, although it may not always be the most abundant constituent, exists in suf- ficient quantity to give the stone its characteristic properties. The principal kinds are slate and graywacke-slate.
Calcareous Stones are those in which carbonate of lime pre- dominates. They effervesce with the dilute mineral acids, which combine with the lime and set free carbonic acid gas. Sulphuric acid forms an insoluble compound with the lime. Nitric and mu- riatic acids form compounds with it, which are soluble in water. By the action of intense heat the carbonic acid is expelled in gas- ecus form, and the lime is left in its caustic or alkaline state, when it is called quicklime. Some calcareous stones consist of pure car- bonate of lime; in others it is mixed with sand, clay, and oxide of iron, or combined with carbonate of magnesia. The durability of calcareous stones depends upon their compactness, those which are porous being disintegrated by the freezing of water, and by the chemical action of an acid atmosphere. They are, for the most part, easily wrought. The principal calcareous stones are marble,
ART. 3.] DESCRIPTION OF BUILDING STONEC. 27
compact limestone, granular limestone (the calcareous stone of the geological classification), and magnesian limestone or dolomite.
40. Description of Building Stones. A few of the more prominent classes of building stones will now be briefly described.
41. Trap. Although trap is the strongest oi building materials, and CACcodingly durable, it is little used, owing to the great diffi- culty with which it is quarried and wrought. It is an exceedingly tough rock, and, being generally without cleavage or bedding, is especially intractable under the hammer or cliisel. It is, however, sometimes used with excellent effect in.cyclopean architecture, the blocks of various shapes and sizes being fitted together with no effort to form regular courses. The '•' Palisades" (the bluff' skirting the western shore of the Hudson Eiver, opposite and above Xew York) are composed of trap-rock, — much used for road-metal, street pavements, and railroad ballast.
42. Granite. Granite is the strongest and most durable of all the stones in common use. It generally breaks with regularity, and may be quarried in simple shapes with facility ; but it is ex- tremely hard and tough, and therefore can only be wrought into elaborate forms with a great expenditure of labor. For this reason the use of granite is somewhat limited. Its strength and durability commend it, however, for foundations, docks, piers, etc., and for massive buildings ; and for these purposes it is in use the world over.
The larger portion of our granites are some shade of gi'ay in color, though -pink and red varieties are not uncommon, and black varieties occasionally occur. They vary in texture from very fine and homogeneous to coarsely porphyritic rocks, in which the indi- vidual grains are an inch or more in length. Excellent granites are found in New England, throughout the Alleghany belt, in the Eocky Mountains, and in the Sierra Nevada. Very large granite quarries exist at Vinalhaven, Maine ; Gloucester and Quincy, Mas- sachusetts; and at Concord, New Hampshire. These quarries fur- nish nearly all the granite used in this country. An excellent granite, which is largely used at Chicago and in the Northwest, is found at St. Cloud, Minnesota.
At the Vinalhaven quarry a single block 300 feet long, 20 feet wide, and 6 to 10 feet thick was blasted out, being afterwards broken up. Until recently the largest single block ever quarried and
28 NATURAL STONE. [CIIAP. I
dressed in this country was that used for the General Wool Mcnu- ment, now in Troy, New York, which measured, when completed, 60 feet in height by 5^ feet square at the base, being only 9 feet shorter than the Egyptian Obelisk now in Central Park, New York. In 1887 the Bodwell Granite Company took out from its quarries in Maine a granite shaft 115 feet long, 10 feet square at the base, and weighing 850 tons. It is claimed that this is the largest single quarried stone on record.
43. Marbles. In common language, any limestone which will take a good polish is called a marble ; but the name is properly applied only to limestones which have been exposed to metamoi'phic action, and have thereby been rendered more crystalline in texture, and have had their color more or less modified or totally removed. Marbles exhibit great diversity of color and texture. They are pure white, mottled white, gray, blue, black, red, yellow, or mot- tled with various mixtures of these colors. Marble is confessedly the most beautiful of all building materials, but is chiefly employed for interior decorations.
44. Limestones. Limestones are comj^osed chiefly or Ui-gely of carbonate of lime. There are many varieties of limestone, which differ in color, composition, and value for engineering and building purposes, owing to the differences in the character of the deposits and chemical combinations entering into them. ''If the rock is compact, fine-grained, and has been deposited by chemical agencies, we have a variety of limestone known as travertine. If it contains much sand, and has a more or less conchoidal fracture, we have a siliceous limestone. If the silica is very fine-grained, it is horn- stone. If the silica is distributed in nodules or flakes, either in seams or throughout the mass, it is cherty limestone; if it contains silica and clay in about equal proportions, hydraulic limestone ; if clay alone is the principal impurity, argillaceous limestone ; if iron is the principal impurity, ferruginous limestone ; if iron and clay exceed the lime, ironstone. If the ironstone is decomposed, and the iron hydrated, it is rottenstone; if carbonate of magnesia forms one third or less, magnesian limestone ; if carbonate of magnesia forms more than one third, dolomitic limestone."
The lighter-colored and fine-grained limestones, when sawed and nsed as ashlars, are deservedly esteemed as among our best building materials. They are, however, less easily and accurately worked
ART. 3.] DESCRIPTION OF BUILDING STONES. 21'
under the chisel than sandstones, and for this reason and their greater rarity are far less generally used. The gray limestones, like that of Lockport, New York, when hammer-dressed, have the ap- pearance of light granite, and, since they are easily wrought, they are advantageously used for trimmings in buildings of brick.
Some of the softer limestones possess qualities which specially commend them for building materials. For example, the cream- colored limestone of the Paris basin {calcau'e grassier) is so soft that it may be dressed with great facility, and yet hardens on exposure, and is a duralDle stone. "Walls laid up of this material are frequently planed cown to a common surface, and elaborately ornamented at small expense. The Topeka stone, found and now largely used in Kansas, has the same qualities. It may be sawed out in blocks almost as easily as wood, and yet is handsome and durable when placed in j)osition. The Bermuda stone and coquina are treated in the same way.
Large quantities of limestones and dolomites are quarried in nearly all of the "Western States. These are mostly of a dull grayish color, and their uses are chiefly local. The light-colored oolitic limestone of Bedford, Indiana, is, however, an exception to this rule. Not only are the lasting qualities fair and the color pleasing, but its fine even grain and softness render it admirably adapted for carved work. It lias been very widely used within the last few years. This stone is often found in layers 20 and 30 feet thick, and is much used for bridge piers and other massive work. There are noted I'rnestone quarries at Dayton and Sandusky, Ohio; at Bedford, Ellettsville, and Salem, Indiana; at Joliet, Lemont, Grafton, and Chester, Illinois; and at Cottonwood, Kansas.
45. Sandstones. "Sandstones vary much in color and fitness for architectural purposes, but they include some of the most beautiful, durable. . nd highly valued materials used in construction. What- ever their differences, they have this in common, that they are chiefly composed of sand — that is, grains of quartz — to a greater or less degree cemented and consolidated. They also frequently con- tain other ingredients, as lime, iron, ialumina, manganese, etc., by which the color and texture are modified. "Where a sandstone is composed exclusively of grains of quartz, without foreign matter, it may be snow-white in color. Examples of this variety are known in many localities. They are rarely used for building, though capa-
30 NATURAL STONE. [CHAP. I.
"ble of being employed for that purpose with excellent effect. They have been more generally valued as furnishing material for the man- ufacture of glass. The color of sandstones is frequently bright and handsome, and constitutes one of the many qualities -which have rendered them so popular. It is usually caused by iron; when gray, blue, or green, by the protoxide, as carbonate or silicate ; when brown, by the hydrated oxide ; when red, by the anhydrous oxide. The purple sandstones usually derive this shade of color from a small quantity of manganese.
" The texture of sandstones varies with the coarseness of the sand of which they are composed, a7id the degree to which it is con- solidated. Usually the material which unites the grains of sand is silica; and this is the best of all cements. This silica has been deposited from solution, and sometimes fills all the interstices be- tween the grains. If the process of consolidation has been carried far enough, or the quartz grains have been cemented by fusion, the sandstone is converted into quartzite, — one of the strongest and most durable of rocks, but, in the ratio of its compactness, difficult to work. Lime and iron often act as cements in sandstones, but both are more soluble and less strong than silica. Hence the finest and most indestructible sandstones are such as consist exclusively of grains of quartz united by siliceous cement. In some sandstones part of the grains are fragments of feldspar, and these, being liable to decomposition, are elements of weakness in the stone. The very fine-grained sandstones often contain a large amount of clay, and thus, though very handsome, are generally less strong than those which are more purely siliceous.
" The durability of sandstones varies with both their physical and chemical composition. "When nearly pure silica and well ce- mented, sandstones are as resistant to weather as granite, and very much less affected by the action of fire. Taken as a whole, they may be regarded as among the most durable of building materials. When first taken from the quarry, and saturated witli quarry water (a weak solution of silica), they are frequently very soft, but on ex- posure become much harder by the precipitation of the soluble silica contained in them.
46. *' Since they form an important part of all the groups of sedimentary rocks, sandstones are abundant in nearly all countries; and as they are quarried with great ease, and are wrought with th»
ART. 3.] DESCRIPTION OF BUILDING STONES. 31
hammer and chisel with much greater facility than limestones, granites, and most other kinds of rocks, these qualities, joined to their various and pleasant colors and their durability, have made them the most popular and useful of building stones. In the United States we have a very large number of sandstones which are extensively used for building purposes.
" x\mong these may be mentioned the Dorchester stone of New Brunswick, and Broivn-sione of Connecticut and New Jersey. These have been much used in the buildings of the Atlantic cities. The latter has been very popular, but experience has shown it to be seriously lacking in durability.
"^ Among the sandstones most frequently employed in the build- ing of the interior are : —
1. " The Ohio stone, derived from the Berea grit, a member of the Lower Carboniferous series in Northern Ohio. The principal quarries are located at Amherst and Berea. The stone from Am- herst is generally light drab in color, very homogeneous in texture, and composed of nearly pure silica. It is very resistant to fire and weathering, and is, on the whole, one of the best and handsomest building stones known. The Berea stone is lighter in color than the Amherst, but sometimes contains sulphide of iron, and is then liable to stain and decomjjose.
2. '' Tlie Waverly sandstone, also derived from the Lower Car- boniferous series, comes from Southern Ohio. This is a fi le- grained homogeneous stone of a light-drab or dove color, works with facility, and is very handsome and durable. It forms the material of which many of the finest buildings of Cincinnati are constructed, and is, justly, highly esteemed there and elsewhere.
3. " The Lake Siqnrior sandstone is a dark, purplish-brown stone of the Potsdam age, quarried at Bass Island, Marquette, etc. This is rather a coarse stone, of medium strength, but homogeneous and durable, and one much used in the Lake cities.
4. " TJie St. Genevieve stone is a fine-grained sandstone of a del- icate drab or straw color, very homogeneous in tone and texture. It is quarried at St. Genevieve, Missouri, and is one of the hand- somest of all our sandstones.
5. " The Medina sandstone, which forms the base of the Upper Silurian series in Western New York, furnishes a remarkably strong
32 KATURAL STONE. [CHAP. L
and durable stone, much used for pavement and curbing in the Lake cities.
6. " The coal-measures of Pennsylvania, Ohio, and other Western States supply excellent sandstones for building purposes at a large number of localities. These vary in color from white to dark red or purple, though generally gray or drab. While strong and durable, they are mostly coarser and less handsome than the sand- ■stones which have been enumerated above. This is the source from ■which are derived the sandstones used in purely engineering struct- ures." *
47. Other Names. There is a great variety of names of more or less local application, derived from the appearance of the stone, the use to which it is put, etc., which it would be impossible to classify. The same stone often passes under entirely different names in different localities; and stones entirely different in their essential characteristics often pass under the same name.
48. Location of Quarries. For information concerning the location of quarries, character of product, etc., see: Tenth Census of the U. S., Vol. X, Keport on Quarry Industry, pp. 107-363; Keport of Smithsonian Institution, 1885-86, Part II, pp. 357-488; Merrill's Stones for Building and Decoration, pp. 45-312 — substan- tially the same as the preceding — and the reports of the various State geological surveys.
49. Cost. See §§ 226-38.
* Prof. J. S. Newberry.
CHAPTER II. BRICK.
51. Brick is made by submitting clay, which has been prepared properly and moulded into shape, to a temperature which converts it into a semi-vitrified mass.
Common brick is a most valuable substitute for stone. Its comparative cheapness, the ease with which it is transported and handled, and the facility with which it is worked into structures of any desired form, are its valuable characteristics. It is, when prop- erly made, nearly as strong as the best building stone. It is but slightly affected by change of temperature or of humidity; and is also lighter than stone.
Notwithstanding the good qualities which recommend brick as a substitute for stone, it is very little used in engineering structures. It is employed in the construction of sewers and bridge piers, and for the lining of tunnels. Brick could many times be profitably substituted for iron, stone, or timber in engineering structures. This is especially true since recent improvements in the process of manufacture have decreased the cost while they have increased the quality and the uniformity of the product. The advantages of employing brick-work instead of stone masonry will be discussed in connection with brick masonry in Chapter VIII. Probably one thing which has prevented the more general use of brick in engi- neering is the variable quality of the product and the trouble of proper inspection.
52. Peocess of Manufacture. The Clay. The quality of the brick depends primarily upon the kind of clay. Common clays, of which the common brick is made, consist principally of silicate of alumina; but they also usually contain lime, magnesia, and oxide of iron. The latter ingredient is useful, improving the product by giving it hardness and strength; hence the red brick of the Eastern States is often of better quality than the white and yellow brick made in the West. Silicate of lime renders the clay too fusible,
33
34 BRICK. [chap. II..
and causes the bricks to soften and to become distorted in the pro- cess of burning. Carbonate of lime is certain to decompose in burning, and the caustic lime left behind absorbs moisture, prevents the adherence of the mortar, and promotes disintegration.
Uncombined silica, if not in excess, is beneficial, as it preserves the form of the brick at high temperatures. In excess it destroys the cohesion, and renders the bricks brittle and weak. Twenty-five per cent, of silica is a good proportion.
53. Moulding. In the old process the clay is tempered with water and mixed to a plastic state in a pit with a tempering wheel, or in a primitive pug-mill; and then the soft, plastic clay is pressed into the moulds by hand. This method is so slow and laborious that it has beeu almost entirely displaced by more economical and expeditious ones in which the work is done wholly by machinery. There is a great variety of machines for preparing and moulding the clay, which, however, may be grouped into three classes, accord- ing to the condition of the clay when moulded: (1) soft-mud machines, for which the clay is reduced to a soft mud by adding about one quarter of its volume of water; (2) stiff-mud machines, for which the clay ^s reduced to a stiff mud; and (3) dry-clay machines, with which the dry, or nearly dry, clay is forced into the moulds by a heavy pressure without having been reduced to a plastic mass. These machines may also be divided into two classes, accord- ing to the method of filling the moulds: (1) Those in which a con- tinuous stream of clay is forced from the pug-mill through a die and is afterwards cut up into bricks; and (2) those in which the clay is forced into moulds moving under the nozzle of the pug-mill.
54. Burning. The time of burning varies with the character of the clay, the form and size of kiln, and the kind of fuel. With the older processes of burning, the brick, when dry enough, is built up in sections — by brick-makers called "arches," — which are usually about 5 bricks (3|^ feet) wide, 30 to 40 bricks (20 to 30 feet) deep, and from 35 to 50 courses high. Each section or ''arch" has an opening — called an "eye" — at the bottom in the center of its width, which runs entirely through the kiln, and in which the fuel used in burning is placed. After the bricks are thus stacked up, the entire pile is enclosed with a wall of green brick, and the joints between the casing bricks are carefully stopped with mud. Burning, includ- ing drying, occupies from 6 to 15 days. The brick is first subjected
CLASSIFICATIOX OF COMMON" BEICK. 35
to a moderate heat, and when all moisture has been expelled, the heat is increased slowly until the "arch-brick/' i. e., those next to the "eye," attain a white heat. This temperature is kept up until the burning is complete. Finally, all oj)enings are closed, and the mass slowly cools.
With the more modern processes of burning, the principal yards have permanent kilns. These are usually either a rectangular space surrounded, except for very wide doors at the ends, by permanent brick walls having fire-boxes on the outside; or the kiln may be entirely enclosed — above as well as on the sides — with brick masonry. The latter are usually circular, and are sometimes made in com- partments, each of which has a separate entrance and independent connection with the chimney. The latter may be built within the kiln or entirely outside, but a downward draught is invariably -secured. The fuel, usually fine coal, is placed near the top of the kiln, and the down draught causes a free circulation of the flame and heated gases about the material being burned. While some compartments are being fired others are being filled, and still others are being emptied.
55. Fire Brick. Fire bricks are used whenever very high temjDeratures are to be resisted. They are made either of a very nearly pure clay, or of a mixture of pure clay and clean sand, or, in rare cases, of nearly jjure silica cemented with a small propoition of clay. The presence of oxide of iron is very injurious, and, as a rule, the presence of 6 per cent, justifies the rejection of the brick. In specifications it should generally be stijiulated that fire brick should contain less than 6 j^er cent, of oxide of iron, and less tiian an aggregate of 3 per cent, of combined lime, soda, potash, and magnesia. The sulphide of iron — pyrites — is even worse in its effect on fire brick than the substances first named.
When intended to resist only extremely high heat, silica should be in excess; and if to be exposed to the action of metallic oxides, which would tend to unite with silica, alumina should be in excess.
Good fire brick should be uniform in size, regular in shape, homogeneous in texture and composition, easily cut, strong, and infusible.
56. Classification of Common Brick. Bricks are classified accordiug to (1) the way in which they are moulded; (2) their position in the kiln while being burned; and (3) their form or use.
36 BRICK. [chap. II.
1' The method of moulding gives rise to the following terms :
Soft-mud Brich. One moulded from clay which has been reduced to a soft mud by adding water. It may be either hand-moulded or machine-moulded.
Stiff -7)111(1 Brick. One moulded from clay in the condition of stiff mud. It is always machine-moulded.
Pressed Brick. One moulded from dry or semi-dry clay.
Ee-jjressed Brick. A soft-mud brick which, after being par- tially dried, has been subjected to an enormous pressure. It is also called, but less appropriately, pressed brick. The object of the re-pressing is to render the form more regular and to increase the strength and density.
Slop Brick. In moulding brick by hand, the moulds are some- times dipped into water just before being filled with clay, to pre- vent the mud from sticking to them, Brick moulded by this process is known as slop brick. It is deficient in color, and has a comparatively smooth surface, with rounded edges and corners. This kind of brick is now seldom made.
Sanded Brick. Ordinarily, in making soft-mud brick, sand is sprinkled into the moulds to prevent the clay from sticking ; the brick is then called sanded brick. The sand on the surface is of no serious advantage or disadvantage. In hand-moulding, when sand is used for this purpose, it is certain to become mixed with the clay and occur in streaks in the finished brick, which is very undesira- ble ; and owing to details of the process, which it is here unneces- sary to explain, every third brick is especially bad.
MacJi ine-made Brick. Brick is frequently described as "ma- chine-made;" but this is very indefinite, since all grades and kinds are made by machinery.
2. When brick was generally burned in the old-style up-draught kiln, the classification according to position was important ; but with the new styles of kilns and improved methods of burning, the quality is so nearly uniform throughout the kiln, that the classifica- tion is less important. Three grades of brick are taken from the old-style kiln:
Arch or Clinker Bricks. Those which form the tops and sides of the arches in which the fire is built. Being over-burned and par- tially vitrified, they are hard, brittle, and weak.
REQUISITES FOR GOOD BRICK. 3?
Body, Cherry, or Hard Bricks. Those taken from the interior of the pile. The best bricks in the kiln.
Salmon, Pale, or Soft Bricks. Those which form the exterior of the mass. Being underburned, they are too soft for ordinary work, unless it be for filling. The terms salmon and pale refer to the color of the brick, and hence are not applicable to a brick made of a clay that does not burn red. Although nearly all brick clays burn red, yet the localities where the contrary is true are sufficiently numerous to make it desirable to use a different term in designating the quality. There is, necessarily, no relation between color, and strength and density. Brick-makers naturally have a prejudice against the term soft brick, which doubtless explains the nearly universal prevalence of the less appropriate term — salmon.
3. The form or use of bricks gives rise to the following classifi- cation:—
Compass Brick, l^hose having one edge shorter than the other. Used in lining shafts, etc.
Feather-edge Brick. Those of which one edge is thinner than the other. Used in arches ; and more properly, but less frequently, called voussoir brick.
Face Brick. Those which, owing to uniformity of size and color, are suitable for the face of the wall of buildings. Sometimes face bricks are simply the best ordinary brick ; but generally the term is applied only to re-pressed or pressed brick made specially for this purpose. They are a little larger than ordinary bricks (§ 62).
Sewer Brick. Ordinary hard brick, smooth, and regular in form.
Paving Brick. Very hard, ordinary brick. A vitrified cla} block, very much larger than ordinary brick, is sometimes use<3 for paving, and is called a paving brick, but more often, and more properly, a brick imving-block.
57. Requisites for Good Beick. 1. A good brick should have plane faces, parallel sides, and diarp edges and angles. 2. It should be of fine, compact, uniform texture ; should be quite hard; and should give a clear ringing sound when struck a sharp blow. 3. It should not absorb more than one tenth of its weight of water. 4. Its specific gravity should be 2 or more. 5. The crushing strength of half brick, when ground flat and pressed between thick metaJ
B8 BRICK. [chap. II.
plates, should be at least 7,000 pounds per square inch. 6. fts mod- ulus of rupture should be at least 1,000 pounds per square mch.
1. In regularity of form re-pressed brick ranks first, dry-clay brick next, then stiff-mud brick, and soft-mud brick last. Regu- larity of form depends largely upon the method of burning.
2. The compactness and uniformity of texture, which greatly influence the durability of brick, depend mainly upon the method of moulding. As a general rule, hand-moulded bricks are best in this respect, since the clay in them is more uniformly tempered be- fore being moulded ; but this advantage is partially neutralized by the presence of sand seams (§ 56). Machine-moulded soft-mud bricks rank next in compactness and uniformity of texture. Then come machine-moulded stiff-mud bricks, which vary greatly in durability with the kind of machine used in their manufacture. By some of the machines, the brick is moulded in layers (parallel to any face, according to the kind of machine), which are not thor- oughly cemented, and which separate under the action of the frost. In compactness, the dry-clay brick comes last. However, the rela- tive value of the products made by the different processes varies with the nature or the clay used.
3. The absorptive power is one of the most important elements, since it greatly affects the durability of the brick, particularly its resistance to the effect of frost (see §§ 31 and 32). Very soft, un- der-burned brick will absorb from So to 33 per cent, of their weight of water. Weak, light-red ones, such as are frequently used in fill- ing in the interior of walls, will absorb about 20 to 25 per cent. ; while the best brick will absorb only 4 or 5 per cent. A brick may be called good which will absorb not more than 10 per cent. See Table 9 (page 45).
4. The specific gravity of a brick does not indicate its quality^ and depends mainly upon the amount of burning and the kind of fuel employed. Over-burned arch bricks, being both smaller and heavier than the better body bricks, have a considerably greater specific gravity, although inferior in quality.
5. The crushing strength is not a certain index of the value of a brick, although it is always one of the 3tems determined in testing brick — if a testing-machine is at hand. For any kind of service, thfc durability of a brick is of greater importance than its ability to resist crushing, — the latter is only remotely connected with dura-
ABSORBIIfG POWER. 3ft
bility. Tests of the crushing strength of individual bricks are use- ful only in comparing different kinds of brick, and give no idea of the strength of walls built of such bricks (see § 246). Furthermore, the crushing strength can not be determined accurately, since it varies greatlv with the size of the specimen and with the details of the experiments (see § 60).
6. Owing to both the nature of the quality tested and the facility with which such a test can be made, the determination of the transverse strength is one of the best means of judging of the quality of a brick. The transverse strength depends mainly upon the toughness of the brick, — a quality of prime importance in bricks used for paving, and also a quality greatly affecting the resistance to frost.
58. Absorbing Power. The less the amount of water absorbed by a brick the greater, in all probability, will be its durability. The amount of water absorbed is, then, an important consideration 'n determining the quality of a brick. There are different methods in use for determining the amount of water taken up by a brick, and these lead to slightly different results. Some experimenters dry the bricks in a hot-air chamber, while some dry them simj^ly by ex- posing them in a dry room; some experimenters immerse the bricks in water in the open air, while others immerse them under the re- ceiver of an air-pump; some immerse whole brick, and some use small pieces; and, again, some dry the surface with bibulous paper, while others allow the surface to dry by evaporation. Air-dryiug most nearly represents the conditions of actual exposure in ma- sonry structures, since water not expelled in that way is in such a condition as not to do any harm by freezing. Immersion in the open air more nearly represents actual practice than immersion in a vacuum. The conditions of actual practice are best represented by testing whole brick, since some kinds have a more or less im- pervious skin. Drying the surface by evaporation is more accurate than drying it with paper; however, neither process is suscei^tible ot mathematical accuracy.
The absorbing power given in Table 9, page 45, was determined by (1) drying whole brick in a steam-heated room for three weeks, (2) weighing and (3) immersing them in water for forty-four hours; and then (4) drying for four hours — until all the water on the surface was evaporated, — and, finally, (5) again weighing them.
40
BRICK.
[chap. II.
The results in the table represent the mean of several observations. If the brick had been kiln-dried, or weighed before the surface water was entirely removed, the apparent absorption would have been greater.
Comparing the absorbing power of brick as given in the table on page 45 with that of stone on page 20, we see the absorbing power of the best brick is about equal to that of average lime- stone and sandstone, and much greater than marble and granite. For a method of rendering brick non-absorbent, see §§ 263-64.
59. Transverse Strength. The experiments necessary to determine the transverse strength of brick are easily made (§ IG), give definite results, and furnish valuable information concerning the practical value of the brick; hence this test is one of the best in use.
Table 6 gives the results of experiments made by the author on Illinois brick. The averages represent the results of from six to fifteen
TABLE 6.
Transverse Strength of Illinois Brick.
(Summarized from Table 9, page 45.)
|
Kef. No. |
Kind of Brick. |
Modulus op Rupture in Lbs. perSq. In.* |
Co-EFPiciENT OP Trans- verse Strength.* |
||||
|
Max. |
Mill. |
Average. |
Max. |
Min. |
Aver. |
||
|
1 2 3 4 |
Soft - clay, hand - moulded, — best 50;? in kiln Soft-clay, machine-mould- ed,—best 50% in kiln Stiff-clay, machine-mould- ed,—best 50;? in kiln Dry- clay (pressed) |
2,233 2,354 1,475 495 4,348 |
846 1.135 764 150 2,235 |
1,409 1,712 1,114 336 3,217 |
124 142 82 27 241 |
47 63 42 8 124 |
78 95 62 19 |
|
5 |
Secret Process |
178 |
|||||
experiments on brick from three localities. The ''Max." and *' Min." columns contain the average of the two highest and the two lowest results respectively.
The results in Table 7 were obtained under the direction of the Chief Engineer of the Lehigh Valley E. B. Each result represents
* For deflnition, see § 16.
CEUSHING STEENGTH.
41
the mean of seven to nine experiments on bricks from different localities. The results in Table 6 are considerably greater than
TABLE 7. Teansverse Strength of Eastern Brick.
|
Designation of Brick. |
Modulus of Rupture in Lbs. per S(J. In. |
CO-EFFICIKNT OF TRANS- VERSE Strength. |
||||
|
Max. |
Min. |
Average. |
Max. |
Min. |
Average. |
|
|
Very hard |
1 1 1,796 944 645 : 444 |
1,045 710 504 269 |
1,352 805 597 373 |
100 52 36 25 |
58 39 28 15 |
75 |
|
Hard |
45 |
|||||
|
Medium Soft |
32 21 |
|||||
those in Table T, the difference being due probably more to recent improvements in the manufacture of brick and to the method of selection than to locality. The brick from which the results in Table 6 were derived were obtained from manufacturers well known for the high quality of their products.
60. Crushing Strength. It has already been explained (§§ 7 to 14) that the results for the crushing strength of stone vary greatly with the details of the experiments; but this difference is even greater in the case of brick than in that of stone. In testing stone the uniform practice is to test cubes (§ 10) whose faces are carefully dressed to parallel planes. In testing brick there is no settled custom. (1) Some experimenters test half brick while others test whole ones; (2) some grind the pressed surfaces accurately to planes, and some level up the surfaces by putting on a thin coat of plaster of Paris, while others leave them in the rough; and (3) some test the brick set on end, some on the side, and others laid flat- wise.
1. From a series of experiments * on soft brick, the author con- cludes that the crushing strength per square inch of a quarter of a brick is about half that of a whole one; and that a half brick is about tiuo thirds, and three quarters of a brick about ^re sixths, as strong per square inch as a whole one ; or, in other words, the strength of a quarter, a half, and three quarters of a brick, and a
* Engineering News, vol. xxi. p.
42 BRICK. [chap. II.
whole one, are to each other as 3, 4, 5, and 6 respectively. The reason for this difference is apparent if a whole brick be conceived as being made up of a number of cubes placed side by side, in which case it is clear that the interior cubes will be stronger than the exterior ones because of the side support derived from the latter. For experiments showing the marked effect of this lateral support, see § 273. The quarter brick and the half brick have less of this lateral support than the whole one, and hence have correspondingly less crushing strength.
2. The strength of the specimen will vary greatly with the degree of smoothness of its bed-surfaces. To determine the difference between reducing the pressed surfaces to a plane and leaving them in the rough, the author selected six bricks of regular form and apparently of the same strength, and tested three in the rough and the other three after having reduced the pressed surfaces to j)lanes by laying on a coating of plaster of Paris, which, after drying, was ground off to a plane. The amount of plaster remaining on the surfaces was just sufficient to fill up the depressions. Both sets were tested in a hydraulic press between cast-iron, parallel (self- adjusting), pressing surfaces. The average strength of those that were plastered was 2.06 times the strength of those that were not plastered. This difference will vary Avith the relative strength of the brick and the plaster. The average strength of the bricks whose surfaces were plastered was 9,170 pounds per square inch, which is more than that of the plaster used; and therefore it is highly probable that if the surfaces had been reduced to planes by grind- ing, the difference in strength would have been still greater. See also the last paragraph of § 12.
3. As before stated, some experimenters test brick flatwise, some edgewise, and some endwise. Since bricks are generally employed in such a position that the pressure is on the broadest face, it seems a little more satisfactory to lay the brick flatwise while testing it; but since the only object in determining the crushing strength of brick is to ascertain the relative strength of different bricks, — the crushing strength of the brick is only remotely connected with the crushing strength of the brick-masonry (§ 246), — the position of the brick while being tested is not a matter of vital importance. Doubt- less the principal reason for testing them on end or edgewise is to bring them within the capacity of the testing-machine. However,
CRUSHING STRENGTH. 43
there is one good reason against testing brick flatwise; viz., all homogeneous granular bodies fail under compression by shearing along planes at about 45^ with the pressed surfaces, and hence if the height is not sufficient to allow the shearmg stresses to act freely, an abnormal strength is developed. See also § 10.
The relative strength of brick tested m the three positions — flat- wise, edgewise, and endwise — varies somewhat with the details of the experiments; but it is reasonably well settled that the strength of homogeneous brick flatwise between steel or cast-iron pressing surfaces is one and a half to two times as much as when the brick is tested on end. A few experiments by the author * seem to indicate that the strength edgewise is a little more than a mean between the strength flatwise and endwise. If the brick is laminated (see para- graph 2, § 57), the relative strength for the three positions — flat- wise, edgewise, and endwise — will vary greatly with the direction of the grain.
61. Comparatively few experiments have been made to deter- mine the strength of brick, and they are far from satisfactory, since the manner of making the experiment is seldom recorded. The differences in the details of the experiments, together with the differences in the quality of the bricks themselves, are sufficient to cause a wide variation in the results obtained by different observers. The following data are given for reference and comparisons.
The results in Table 8 (page 44) were made with the U. S. testing-machine at the Watertown (Mass.) Arsenal. f In each experiment the pressed surfaces were " carefully ground flat and set in a thin facing of plaster of Paris, and then tested between steel pressing surfaces. "
The experiments given in Table 9 (page 45) were made by the author, on Illinois brick. The bricks were crushed between self- adjusting cast-iron pressing surfaces. Although No. 11 shows an average absorption, a moderate transverse strength, and a high crush- ing strength, this particular brand of brick disintegrated rapidly by the frost. This is characteristic of this class of brick, and is caused by the clay's being forced into the moulds or through the die in such a way as to leave the brick in lamince, not well cemented together. A critical examination of the brick with the unaided eye gave no indi-
* Engineering News, vol. xxi. p. 88.
+ Compiled from the annual reports for 1883-85.
44
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46 BRICK. [chap. II.
cation of a laminated structure, and yet compressing the brick in two positions — sidewise and edgewise — never failed to reveal such structure. The crushing strength in the table was obtained when the pressure was applied to the edges of the laminae. In experi- ments Nos. 12, 13, and 1-4 the pressed surfaces were so nearly mathe- matical planes that possibly these bricks stood more than they would have done if their beds had been plastered. The strength of No. 15 was beyond the capacity of the machine; a whole brick, on end, stood 11,083 lbs. per sq. in. without any cracks or snapping sounds — which usually occur at about half of the ultimate strength.
Kankine says that "■ strong red brick, when set on end, should require at least 1,100 lbs. per sq. in. to crush them; weak red ones, 550 to 800 lbs. per sq. in.; and fire bricks, 1,700 lbs. per. sq. in."*
Experiments on the brick in general use in Berlin gave for *' ordinary" brick, on edge, a strength of 2,930 lbs. per sq. in.; and for " selected" brick, 3,670 lbs. per sq. in.f
The brick used in the New York reservoir, when laid flat and packed with sand, showed an average strength, for four specimens, of 2,770 lbs. per sq. in.; and two samples tested between wood averaged 2,660 lbs. per sq. in. J Prof. Pike§ tested half brick flat- wise between sheets of pasteboard with the following results: St. Louis brick, 6,417 lbs. per sq. in. (the average of six trials); and pressed brick, 2,519 lbs. per sq. in. (the average of thirteen sam- ples from ten localities).
62. Size and Weight. In England the legal standard size for brick is 8f X 4f X 2f inches. In Scotland the average size is about 94^ X 4J X 3^ inches; in Germany, 9|^ X 4| X 2f inches; in Austria, 11^ X 5|- X 2f inches; in Cuba, 11 X 5| X 2f inches; and in South America, 12f X 6^ X 2|^ inches.
In the United States there is no legal standard, and the dimen- sions vary with the maker. In the Eastern States 8^ X 4 X 2^ inches is a common size for brick, of which 23 make a cubic footj btit in the West the dimensions are usually a little smaller. The National Brick-makers' Association in 1887 and the National
* Civil Engineering, pp. 366 and 769.
t Van Nostrand's Engineering Magazine, vol. xxxiv. p. 340. From abstracts of the Inst, of C. E.
X Jour. Frank. Inst., vol. Ixv. p. 333; also Trans. Am. Soc. of C. E., vol. ii. pp. 185-86.
§ Jour. Assoc. Engineering Soc, vol. iv. pp. 366-67.
SIZE, WEIGHT, AND COST. 47
Traders and Builders' Association in 1889 adopted 85 x 4 X 2y inches as the standard size for common brick, and 8| X 4^ X ^ for face brick. The price should vary with the size. If, reckoned according to cubic contents, brick 8x4x3 inches is worth 810 per thousand, brick 8y x 4:^ X 2j is worth $12.33 per thousand, and 8|^ X 4| X 2^ is worth $15 per thousand. Further, where brick is laid by the thousand, small bricks are doubly expensive. Since bricks shrink in burning, in proportion to the temperature to which they are exposed, the amount differing with the different kinds of clays, it is impossible to have the size exactly uniform. Re-pressed and machine-moulded bricks are more nearly uniform in size than hand-moulded.
The size of brick and the thickness of the mortar joint should be such that brick may be laid flat, edgewise, or set vertically, and still fit exactly These proportions are seldom realized.
Re-pressed brick weighs about 150 lbs. per cu. ft. ; common hard brick, 125 ; inferior, soft brick, 100. Common bricks will average about 4^ lbs. each.
63. Cost. Brick is sold by the thousand. At Chicago, in 1887, the " best sewer" brick cost $9 ; common brick, from $6 to $7.
CHAPTER III. LIME AND CEMENT.
64. Classification. Considered as materials for nse in the builder's art, the prodncts of calcination of limestone are classified as common lime, hydraulic lime, and hydraulic cement. If the limestone is nearly pure carbonate of lime, the product is common lime, which will slake upon the addition of water, and mortar made of it will harden by absorbing carbonic acid from the air, but will not harden under water. If the limestone contains more impuri- ties, the product is hydraulic lime, which will slake upon the addi- tion of water, and mortar made of it will harden either in air or under water by the chemical action between the hydraulic lime and the water used in making the mortar. If the limestone contains still more impurities, the product is hydraulic cement, which will not slake upon the addition of water but must be reduced to a paste by grinding, and which will set either in air or under water by the chemical action between the cement and the water used in making the mortar. Common lime is sometimes called air-lime, because a paste or mortar made from it requires exposure to the air to enable it to " set," or harden. The hydraulic limes and cements are also called water-limes and water-cements, from their property of hardening under water.
Common lime is used in making the mortar for most architect- ural masonry, and until recently it was generally employed in engineering masonry; but the opinion is rapidly gaining ground that only cement mortar should be employed in engineering struct- ures requiring great strength or being subject to shock. On most first-class railroads hydraulic cement mortar is used in all masonry structures. This change in practice is largely due to the better appreciation of the superiority of hydraulic cement as a building material. Although it has been manufactured for about fifty years, the amount used was comparatively limited until within recent years. At present large quantities are imported from
48
ART. 1.] COMMON" LIME. 49
Europe, and very much more is made in this country. Hydraulic lime is neither manufactured nor used in this country.
The following discussion concerning common and hydraulic limes is given as preliminary to the study of hydraulic cements rather than because of the importance of these materials in engineer- ing construction
Art. 1. Common Lime.
65. Desceiition. The limestones which furnish the common lime are seldom, if ever, pure; but usually contain, besides the car- bonate of lime, from 3 to 10 per cent, of impurities, — such as silica, alumina, magnesia, oxide of manganese, and traces of the alkalies. Lime — variously designated as common lime, quicklime, or caustic lame — is a protoxide of calcium, and is produced when marble, or any other variety of pure or nearly pure carbonate of lime, is calcined with a heat of sufficient intensity and duration to expel the carbonic acid. It has a specific gravity of 2.3, is amorphous, highly caustic, has a great avidity for water, and when brought into contact with it will rapidly absorb nearly a quarter of its weight of that substance. This absorption is accompanied and followed by a great elevation of temperature, by the evolution of hot and slightly caustic vapor, by the bursting of the lime into pieces; and finally the lime is reduced to a powder, the volume of which is from two and a half to three and a half times the volume of the original lime — the increase of bulk being proportional to the purity of the lime- stone. In this condition the lime is said to be slaked, and is ready for use in making mortar.
The paste of common lime is unctuous and impalpable to sight and touch ; hence these limes are sometimes called fat or rich limes, as distinguished from others known as poor or meager limes. These latter usually contain more or less silica and a greater proportion of other impurities than the fat limes. In slaking they exhibit a more moderate elevation of temperature; evolve less vapor; are seldom reduced to an impalpable homogeneous powder; yield thin paste; and expand less. They are less valuable for mortar than the fat limes, but are extensively employed as fertilizers. When used for building purposes they should, if practicable, be reduced to powder by grinding, in order to remove all danger of subsequent slaking.
50 LIME AND CEMENT. [CHAP. III..
66. Testing. Grood lime may be known by the following characteristics: 1. Freedom from cinders and clinkers, with not more than 10 per cent, of other impurities, — as silica, alumina, etc. 2. Chiefly in hard lumps, with but little dust. 3. Slakes readily in water, forming a very fine smooth paste, without any residue. 4. Dissolves in soft water, when this is added in sufficient quanti- ties. These simple tests can be readily applied to any sample of lime.
67. Preserving. As lime abstracts water from the atmosphere and is thereby slaked, it soon crumbles into a fine powder, losing all those qualities which render it of value for mortar. On this account great care must be taken that the lime to be used is freshly burned, as may be known by its being in hard lumps rather than in powder. Lime is shipped either in bulk or in casks. If in bulk, it is impossible to preserve it for any considerable time; if in casks, it may be preserved for some time by storing in a dry place.
Common lime, when mixed to a paste with water, may be kept for an indefinite time in that condition without deterioration, if protected from contact with the air so that it will not dry up. It is customary to keep the lime paste in casks, or in the wide, shallow boxes in which it was slaked, or heaped up on the ground, covered over with the sand to be subsequently incorporated with it in mak- ing mortar. It is convenient for some purposes to keep the slaked lime on hand in a state of powder, which may be done in casks under cover, or in bulk in a room set apart for that purpose. The common limes contain impurities which prevent a thorough, uniform, and prompt slaking of the entire mass, and hence the necessity of slaking some days before the lime is to be used, to avoid all danger to the masonry by subsequent enlargement of volume and change of condition.
A paste or mortar of common lime will not harden under water, nor in continuously damp places excluded from contact with the air. It will slowly harden in the air, from the surface toward the interior, by desiccation and the gradual absorption of carbonic-acid gas, by which process is formed a subcarbonate with an excess of hydrated base.
68. Cost. Lime is sold by the barrel (about 230 pounds net), or by the bushel (75 pounds). At Chicago the average price, in 1898, was from 55 to 60 cents per barrel.
art. 2.] hydraulic lime. 51
Art. 2. Hydraulic Lime.
69. Desceiption. Hydraulic lime is like common lime in that it will slake, and differs from it in that it will harden nnder water. Hydraulic lime may be either argillaceous or siliceous. The former is derived from limestones containing from 10 to '^0 per cent, of clay, homogeneously mixed with carbonate of lime as the principal ingredient; the latter from siliceous limestones containing from 12 to 18 per cent, of silica. Small percentages of oxides of iron, car- bonates of magnesia, etc., are generally present.
During the burning, the carbonic acid is expelled, and the silica and alumina entering into combination with a portion of the lime form both the silicate and the aluminate of lime, leaving in the burnt product an excess of quick or caustic lime, which induces slaking, and becomes hydrate of lime when brought into contact "with water. The product owes its hydraulicity to the crystallizing energy of the aluminate and the silicate of lime.
Hydraulic lime is slaked by sprinkling with just sufficient water to slake the free lime. The free lime has a greater avidity for the water than the hydraulic elements, and consequently the former absorbs the water, expands, and disintegrates the whole mass while the hydraulic ingredients are not affected. Hydraulic lime is usually slaked, screened, and packed in sacks or barrels before being sent to market. It may be kept without injury in this form as long as it is protected from moisture and air.
No hydraulic lime is manufactured in the United States. It is manufactured in several localities in Europe, notably at Teil and Scilly, in France, from which places large quantities were formerly brought to this country.
Art. 3. Hydraulic Cement.
70. Classification. Hydraulic cement may be divided accord- ing to the method of manufacture into three classes, viz. : Portland cement, natural cement, and pozzuolana. The first two differ from the third in that the ingredients of which the first two are composed must be roasted before they acqnire the property of hardening under water, while the ingredients of the third need only to be pulverized .and mixed with water to a paste.
S^ LIME AND CEMENT. [CHAP. Ill,
71. Portland. Portland cement is produced by calcining a mixture containing from 75 to 80 per cent, of carbonate of lime and 20 to 23 per cent, of clay, at such a high temperature that the silica and alumina of the clay combines with the lime of the limestone. As the quantity of uncombined lime is not sufficient to cause the mass to slake to a powder upon the addition of water, the cement must be reduced to powder by grinding.
To secure a complete chemical combination of the clay and the lime, it is necessary that the raw materials shall be reduced to a powder and be thoroughly mixed before burning, and also necessary that the calcination shall take place at a high temperature. These are the distinguishing characteristics of the manufacture of Portland cement.
In a general way Portland cement differs from natural cement by being heavier, slower setting, and stronger.
72. Portland cement derives its name from the resemblance which hardened mortar made of it bears to a stone found in the isle of Portland, off the south coast of England. Portland cement was made first in England about 1843, and in America about 1874.
Until recent years nearly all the Portland cement used in this country was imported, but at present (1898) about one fifth of the consumption is of domestic manufacture. The best American Portland is better than the best imported, and is sold equally cheap. In 1896 Portland cement was made at twenty-six places in the United States. Raw material suitable for the manufacture of Port- land cement exists in great abundance in nature, and with proper care a high-class Portland cement may be produced in almost any part of the country.
In recent years the amount of cement used in this country has greatly increased, but the proportion of Portland used has increased at a much more rapid rate. In 1887 only about one fifth was Portland, while in 1897 one third was Portland.
73. Natural Cement. N"atural cement is produced by calcining at a comparatively low temperature either a natural argillaceous limestone or a natural magnesian limestone without pulverization or the admixture of other materials. The stone is quarried, broken into pieces, and burned in a kiln. The burnt cement is then crushed into small fragments, ground, packed, and sent to market.
In the process of manufacture natural cement is distinguished
ART. 3.] HYDRAULIC CEMENT. 53
from Portland, in nsing a natural instead of an artificial mixture and in calcining at a lower temperature. As a product, natural cement is distinguished from Portland in weighing less, being less strong, and as a rule setting more quickly.
In Europe in making this class of cement argillaceous limestone is generally nsed, and the product is called Roman cement. In the United States magnesian limestone is usually employed in making this cement; and formerly there was great diversity in the term nsed to designate the product, domestic, American, and natural being employed. In the early editions of this volume, the author called this class of cement Eosendale, from the place where it was first made in this country — Rosendale, Ulster Co., N. Y. The term natural is now quite generally used, and on the whole it seems the best.
74. In 1896 natural cement was made in sixty-eight places in seventeen states in this country, and it may safely be assumed that there is no very large area in which a stone can not be found from which some grade of natural cement can be made.
Nearly one half of the natural cement made in this country comes from Ulster Co., N. Y., and nearly half of the remainder comes from near Louisville, Kentucky.
75. PozzuoLANA. Pozzuolana is a term applied to a combina- tion of silica and alumina which, when mixed with common lime and made into mortar, has the property of hardening under water. There are several classes of materials possessing this property.
Pozzuolana proper is a material of volcanic origin, and is the first substance known to possess the peculiar property of hydrau- licity. The discovery was made at Pozzuoli, near the base of Mount Vesuvius, — hence the name. Vitruvius and Pliny both mention that pozzuolana was extensively used by the Romans before their day; and Vitruvius gives a formula for its use in monolithic masonry, which with slight variations has been followed in Italy ever since. It is as follows: " 12 parts pozzuolana, well pulverized; 6 parts quartzose sand, well washed; and 9 parts rich lime, well slaked."
Trass is a volcanic earth closely resembling pozzuolana, and is employed substantially in the same way. It is found on the Rhine between Mayence and Cologne, and in various localities in Holland.
Arenes is a species of ocherous sand containing so large a pro-
54 LIME AXD CEMEN"T. [CHAP. III.
portion of clay that it can be mixed into a paste with water without the addition of lime, and used in that state for common mortar. Mixed with rich lime it yields hydraulic mortar of considerable energy.
Brick dust mixed with common lime produces a feebly hydraulic mortar.
76. Slag Cement. Slag cement is by far the most important of the pozzuolana cements. It is the product obtained by mixing powdered slaked lime and finely pulverized blast-furnace slag. The amount of slag cement manufactured is very small as compared with Portland or natural cement, and apparently much more is manufactured in Europe than in America. Probably most of the so-called pozzuolana cements are slag cements. It is claimed that slag cement mortar will not stain the stone laid with it.
77. Weight. Cement is generally sold by the barrel, although not necessarily in a barrel. Imported cement is always sold in barrels, but American cement is sold in barrels, or in bags, or less frequently in bulk.
Portland cement usually weighs 400 pounds per barrel gross, and 370 to 380 pounds net. A bag of Portland usually weighs 95 pounds, of which four are counted a barrel.
Natural cement made in or near Eosendale, N. Y., weighs 318 pounds per barrel gross, and 300 net. Cement made in Akron, !N". Y., Milwaukee, Wis., Utica, 111., Louisville, Ky., weighs 285 pounds per barrel gross, and 2G5 net. Cloth bags usually contain one third, and joaper bags one fourth of a barrel.
Slag oenient weighs from 325 to 350 pounds net per barrel.
78. Cost. The price of hydraulic cement has decreased greatly in recent years, owing chiefly to the development of the cement industry in this country. At present the competition among domestic manufacturers governs the price. In 1898 the jDrices in car-load lots were about as follows :
Imjiorted Portland cement at Atlantic ports $1.50 to $2 per barrel in wood, and at Chicago $2 to $2.o0. American Portland at eastern mills is $1.50 to $1.75 in wood, and in the Mississippi valley $1.75 to $2. The price in paper bags is about 10 cents per barrel less than in wood, and about 15 cents per barrel cheaper in cloth bags than in wood — provided the cloth bags are returned to the mill, freight prepaid.
ART. 4.] TESTS OF CEMEK-T. 55
Xaiural cement in the Rosendale (X. Y.) district costs f. o. b. mills 50 cents per barrel (300 pounds net) in bulk, 60 cents in paper, and 70 cents in wood. The price at the western mills in recent years was 50 cents per barrel (2G5 pounds net) in cloth (the sacks to be returned, freight prepaid), 55 Cents in paper, and 60 cents in wood.
Slag cement is made in this country only at Chicago, where it sells at prices but little below those of similar grades of Portland cements. The imported pozzuolana sells substantially the same as similar grades of Portland.
Art. 4. Tests of Cement.
79. The value of a cement varies greatly with the chemical composition, the temperature of calcination, the fineness of grind- ing, etc. ; and a slight variation in any one of these items may greatly affect the physical properties of the product. Unless the process of manufacture is conducted with the utmost care, two lots of cement of the same brand are liable to differ considerably in physical properties. Therefore the testing of cement to determine its fitness for the use proposed is a matter of very great imj^ortance. The properties of a cement which are examined to determine its €onstructive value are: (1) color, (2) thoroughness of burning, (3) activity, (4) soundness, (5) fineness, (6) strength.
80. Color. The color of the cement powder indicates but little, since it is chiefly due to oxides of iron and manganese, which in no way affect the cementitious value; but for any given brand, variations in shade may indicate differences in the character of the rock or in the degree of burning.
With Portland cement, gray or greenish gray is generally con- sidered best; bluish gray indicates a probable excess of lime, and brown an excess of clay. An undue proportion of under-burned material is generally indicated by a yellowish shade, with a marked difference between the color of the hard-burned, nnground particles retained by a fine sieve and the finer cement which passes through the sieve.
Natural cements are usually brown, but vary from very light to very dark.
Slag cement has a mauve tint — a delicate lilac.
56 IIME AND CEMEXT. [CHAP. III.
81. Thoroughness of Burning. The higher the temperature of burning the greater the weight of the clinker (the unground cement). Two methods have been employed in utilizing this prin- ciple as a test of the thoroughness of burning, viz. : (1) determine the weight of a unit of volume of the ground cement, and (2) determine the specific gravity of the cement.
82. "Weight. For any particular cement the weight varies with the temperature of burning, the degree of fineness in grinding, and the density of packing. Other things being the same, the harder- burned varieties are the heavier. The finer a cement is ground the more bulky it becomes, and consequently the less it weighs. Hence light weight may be caused by laudable fine grinding or by objec- tionable under-burning.
The weight per unit of volume is usually determined by sifting the cement into a measure, and striking the top level with a straight- edge. In careful work the height of fall and the size of the meas- uring vessel are specified. The weight per cubic foot is neither exactly constant, nor can it be determined precisely; and is of very little service in determining the value of a cement. However, it is often specified as one of the requirements to be fulfilled. The fol- lowing values, determined by sifting the cement with a fall of three feet into a box having a capacity of one tenth of a cubic foot, may be taken as fair averages for ordinary cements. The difference in weight for any particular kind is mainly due to a difference in fine- ness:
Portland 75 to 90 lbs. per cubic foot, or 94 to 112 lbs. per bushel. Natural 50 to 56 lbs. per cubic foot, or 62 to 70 lbs. per bushel.
Specifications for the reception of cement frequently specify the net weight per barrel ; but this is a specification for quantity and not quality.
83. Specific Gravity. The determination of the specific gravity of a cement is the only real test of the thoroughness of burning. The specific gravity is determined by immersing a known weight of the cement in a liquid which will not act upon it (usually turpen- tine or benzine), and obtaining the volume of the liquid displaced. The specific gravity is equal to the weight of the cement (in grammes) divided by the displaced volume (in cubic centimetres).
A variety of forms of apparatus for use in making this test are
ART. 4.] TESTS OF CEMENT. 57
upon the market, but as several of the volumeters in ordinary use in chemical and physical laboratories are suitable for this purpose, it is unnecessary to describe any of them here. As a slight differ- ence in specific gravity is frequently accompanied by a considerable difference in the quality of the cement, great care is necessary in making the test. It is necessary that all the air-bubbles contained in the cement powder be eliminated, so that the volume obtained be that of the cement particles only. The cement should be passed through a sieve, say Xo. 80, to eliminate the lumps. The tempera- ture of the liquid should not be above 60° Fahr., and should not change during the test. A change of 1° C. in the turpentine between the readings of the volumeter will make a difference of 0.08 in the resalting specific gravity.
The specific gravity of Portland cement varies from 3.00 to 3.25, usually between 3.05 and 3.17. Natural cement varies from 2.75 to 3.05, and is usually between 2.80 and 3.00. Slag cement has a specific gravity of 2.72 to 2.76. The specific gravity of cement decreases with age owing to the absorption of water and carbonic acid from the air.
German authorities state that the specific gravity of fresh Port- land cement is between 3.12 and 3.25. English specifications re- quire 3.10 for fresh Portland and 3.07 for cement 3 months old. By the specifications of the Canadian Society of Civil Engineers the minimum for fresh Portland is 3.09. Many specifications fix 3.00 or 3.05 for the lower limit.
84. Activity. When cement powder is mixed with water to a plastic condition and allowed to stand, the cement chemically com- bines with the water and the entire mass gradually becomes firm and hard. This process of solidifying is called setting. Cements differ very widely in their rate and manner of setting. Some occupy but a few minutes in the operation, while others require several hours. Some begin to set comparatively early and take considerable time to complete the process, while others stand con- siderable time without apparent change and then set very quickly.
A knowledge of the activity of a cement is of importance both in testing and in using a cement, since its strength is seriously impaired if the mortar is disturbed after it has begun to set. Ordinarily the moderately slow-setting cements are preferable, since they need not be handled so rapidly and may be mixed in larger
58 LIME AND CEMEN"T. [CHAP. III.
quantities; but in some cases it is necessary to use a rapid-setting cement, as for example when an inflow of water is to be prevented.
To determine the rate of setting, points have been arbitrarily fixed where the set is said to begin and to end. It is very difficult to determine these points with exactness, particularly the latter; but an exact determination is not necessary to judge of the fitness of a cement for a particular use. For this purpose it is ordinarily sufficient to say that a mortar has begun to set when it has lost its plasticity, i.e., when its form cannot be altered without producing a fracture; and that it has set hard when it will resist a slight pressure of the thumb-nail. Cements will increase in hardness long after they can not be indented with the thumb-nail.
For an accurate determination of rate of set two standards are in use, viz. : Clillmore's and the German.
85. Gillmore's Test. Mix the cement with water to a stiff plastic mortar (see §§ 103—4), and make a cake or pat 2 or 3 inches in diameter and about I iuch thick. The mortar is said to have begun to set when it will just support a wire yV-inch in diameter weighing ^ pound, and to have " set hard " when it will bear a -/j- inch wire weighing 1 poand. A loaded wire used for this purpose is frequently called a Vicat needle, after Vicat, its inventor. The interval between the time of adding the water and the time when the light wire is just supported is the time of beginning to set, and the interval between the time the light wire is supported and the time when the heavy one is just supported is the time of setting.
86. German Test.* " A slow-setting cement (one setting in not less than two hours) shall be mixed three minutes, and a quick- setting cement (one setting in less than two hours) one minute, with water to a stiff paste. The consistency of the cement paste for this cake shall be such that, when wrought with a trowel on the plate, the paste will only begin to run towards the edge of the same after the paste has been repeatedly jarred. As a rule, 27 to 30 per cent, of water will suffice to give the necessary consistency to a Portland cement paste, f
" For the exact determination of the time of beginning to set, and for determining the time of setting, a standard needle 300
♦Specifications of the Prussian Minister of Public Worlts, July 28, 1887. t Apparently this mortar is more moist than the " plastic mortar " ordinarily •employed in this country (see §§ 103-4).
ART. 4.] TESTS OF CEMENT. 59
grammes (11 oz.) in weight and 1 sqnare millimetre (0.0006 square inch) in cross-section is used. A metal ring 4 centimetres (1.575 inches) in height and 8 centimetres (3.15 inches) clear diameter (inside) is placed on a glass plate, filled with cement paste of the above consistency, and brought under the needle,* The moment at which the needle is no longer capable of completely penetrating the cement cake is considered the beginning of the time of setting. The time elapsing between this and the moment when the standard needle no longer leaves an appreciable imj^ression on the hardened cake is considered the time of setting."
To facilitate the making of this test, an apparatus is provided which consists of a light rod freely sliding through an arm; and carrying in its lower end the penetrating needle. The amount of penetration is read by an index moving over a graduated scale.
87. Elements Affecting Rate of Set. The amount of water emjiloyed is important. For data as to the amount of water to be used, see §§ 103—4. The less the water, the more rapid the set.
It is usually specified that the temperature of the water and air shall be from 60° to 65° F. The higher the temperature, the more rapid the set. To prevent the surface of the test specimen from hardening by drying, it is specified that the pat shall be immersed in water at 60° to 65° F. The setting under water is much slower than in air even though the air be saturated with moisture and be at the same temperature as the water, due to the mechanical action of the water.
Other things being the same, the finer the cement is ground the quicker it sets.
Cements usually become slower setting with age, particularly if exposed to the air — Portlands usually but slightly.
The standard tests for activity are usually made on neat cement on account of the interference of the sand grains with the descent of the needle. The rate of setting of neat mortar gives but little indication of what the action may be with sand. Sand increases the time of setting — but very differently for different cements. With some cements a mortar composed of one part cement to three parts sand will require twice as long to set as a neat mortar, while with other cements the time will be eight or ten times as long.
* For an illustration of the apparatus see Trans. Amer. Soc. of C. E., vol. zzx. p. 11.
60 LIME AND CEMENT. [CHAP. III.
Sulphate of lime (plaster of Paris) greatly influences the rate of setting of Portland cements. The addition of 1 or 2 per cent, is sufficient to change the time of setting from a few minutes to several hours. Cement which has been made slow-setting by the addition of sulphate of lime, usually becomes quick-setting again after exposure to the air; cement which has not had its time of setting changed by the addition of sulphate of lime, usually becomes slower setting with age and may finally lose the power of setting. Cement which has become slow-setting by the addition of sulphate of lime will become quick-setting if mixed with a solution of carbonate of soda.
A weak solution of chloride of lime usually causes the cement to set more slowly; while a strong solution usually accelerates the rate of setting.
88. Time of Set. A few of the quickest natural cements when tested neat with the minimum of water will begin to set in 5 to 10 minutes, and set hard in 15 to 20 minutes; while the majority will begin to set in 20 to 30 minutes and will set hard in 40 to 60 minutes; and a few of the slowest will not begin to set under 60 minutes.
The quickest of the Portlands will begin to set in 20 to 40 min- utes; but the majority will not begin to set under 2 or 3 hours, and will not set hard under 6 or 8 hours. The 1887 standard German specifications reject a Portland cement which begins to set in less than 30 minutes or which sets hard in less than 3 hours.
89. Soundness. Soundness refers to cue ability of a cement to retain its strength and form unimpaired for an indefinite period. Soundness is a most important element; since if a cement ultimately loses its strength it is worthless, and if it finally expands it becomes a destructive agent. A cement may be unsound because of the presence in it of some active elements which cause the mortar to expand or contract in setting, or the unsoundness may be due to exterior agencies which act upon the ingredients of the cement. Most unsound cements fail by swelling and cracking under the action of expansives; but sometimes the mortar fails by a gradual softening of the mass without material change of form. The ex- pansive action is usually due to free lime or free magnesia in the cement, but may be caused by sulphur compounds. The principal
ART. 4.] TESTS OF CEMENT. 61
exterior agencies acting npon a cemeut are air, sea-water, and •extremes of heat and cold.
The presence of small quantities of free lime in the cement is a frequent cause of unsoundness. The lime slakes, and causes the jnortar to swell and crack — and perhaps finally disintegrate. The degree of heat employed in the burning, and the fineness, modify the eSect of the free lime. Lime burned at a high heat slakes more slowly than when burned at a low temperature, and is there- fore more likely to be injurious. Finely ground lime slakes more quickly than coarsely ground, and hence with fine cement the lime may slake before the cement has set, and therefore do no harm. The lime in finely ground cements will air-slake sooner than that in coarsely ground.
Free magnesia in cement acts very much like free lime. The action of the magnesia is much slower than that of lime, and hence its presence is a more serious defect, since it is less likely to be detected before the cement is used. The effect of magnesia in cement is not thoroughly understood, but seems to vary with the composition of the cement, the degree of burning, and the amount of water used in mixing. It was formerly held that 1^ or 2 per cent, of magnesia in Portland cement was dangerous; but it is now known that 5 per cent, is not injurious, while 8 per cent, may pro- duce expansion. Since many of the natural cements are made of magnesium limestone, they contain much more magnesia than Portland cements; but chemists are not agreed as to the manner in which the different constituents are combined, and consequently are not agreed either as to the amount or effect of free magnesia in such a cement. Fortunately, it is not necessary to resort to a chemical analysis to determine the amount of lime or magnesia present, for a cement which successfully stands the ordinary test for soundness (§ 92) for 7, or at most 28 days, may be used with reasonable con- fidence.
The effect of lime and magnesia seems to be more serious in water than in air, and greater in sea-water than in fresh water.
90. The action of sulphur in a cemeut is extremely variable, depending upon the state in which it may exist and upon the nature of the cement. Sulphur may occur naturally in the cement or may be added in the form of sulphate of lime (plaster of Paris)
62 LIME AND CEMENT. [CHAP. III.
to retard the time of set (§ 87). Under certain conditions the sulphur may form sulphides, which on exposure to the air oxidize and form sulphates and cause the mortar to decrease in strength. Many, if not all, of the slag cements contain an excess of sulphides, and are therefore unfit for use in the air, particularly a very dry atmosphere, although under water they may give satisfactory results and compare favorably with Portland cement.
91. Tests of Soundness. Several methods of testing soundness have been recommended. Of those mentioned below, the first two are called cold tests, since the mortar is tested at ordinary tempera- tures; and the others accelerated or hot tests.
92. The Pat Test. The ordinary method of testing soundness is to make small cakes or pats of neat mortar 3 or 4 inches in diameter, about half an inch thick and having thin edges, upon a sheet of glass, and examine from day to day, for 28 days (if possible), to see if they show any cracks or signs of distortion. The amount of water used in mixing (see § 104) within reason- able limits seems to have no material effect on the result. The German standard specifications require the cake to be kept 24 hours in a closed box or under a damp cloth, and then stored in water. The French, to make sure that the pats do not get dry before immersion, recommend that the cakes be immersed immedi- ately after mixing without waiting for the mortar to set. Some really sound natural cements will disintegrate if immersed before setting has begun.
The first evidence of bad quality is the loosening of the pat from the glass, which generally takes place, if at all, within one or two days. Good cement will remain firmly attached to the glass for two weeks at least. The cracks due to expansion occur usually at the edges of the pat, and radiate from the center. These cracks should not be confused with irregular hair-like shrinkage cracks, which appear over the entire surface when the pats are made too wet and dry out too much while setting.
93. A cement high in sulphides, as for example one made of blast-furnace slag, will successfully pass the above, the usual, test for soundness; and still the mortar when exposed in the air will show a marked decrease in strength and perhaps finally dis- integrate. The presence of an excess of sulphides may be sus- pected in any cement made from blast-furnace slag. A slag
AKT. 4.] TESTS OF CEMENT. 63
cement is indicated by a manve or delicate lilac tint of the dry- powder.
Therefore, in making the pat test, it is wise to expose a pat in the air as well as one under water. Any sulphides in the cement will be revealed by brown or yellowish blotches on the pat exposed in air, and also by a greenish color of the interior of the pat exposed under water. The pat in air is not as good a test of expansives as the pat under water, owing to a possible deficiency of water and to greater shrinkage cracks.
If there are any considerable indications of sulphides, before accepting the cement a chemical analysis should be made to deter- mine the sulphur and the probable ultimate action of the cement. Any cement containing sulphides in appreciable quantities is at least doubtful and should probably be rejected. Slag cements usually contain 1 to 1.5 per cent, of sulphides.
Another excellent method of examining for the presence of sul- phides is, in making the test for tensile strength (§g 99-111^), to store part of the briquettes in air and part in water. Any material difference in strength between the two lots is sufficient ground for rejecting the cement for use in a dry place. Of course due con- sideration should be given to the possible effect of evajaoration of water from the briquettes stored in air.
94. Expansion Test. Various experimenters test the soundness of cement by measuring the expansion of a bar of cement mortar. The French Commission recommend the measurement of the expan- sion of a bar 32 inches long by \ inch square, or the measurement of the increase of circumference of a cylinder. The German standard tests require the measurement of the increase in length of a prism 4 inches long by 2 inches square. The apparatus for making these tests can be had in the market. The tests require very delicate manipulation to secure reliable results.
95. Accelerated Tests. The ordinary tests extending over a reasonable period, sometimes fail to detect unsoundness; and many efforts have been made to utilize heat to accelerate the action, with a view of determining from the effect of heat during a short time what would be the action in a longer period under normal condi- tions. Some of these tests have been fairly successful, but none have been extensively employed. It is difficult to interpret the tests, as the results vary with the per cent, of lime, magnesia, sul-
64 LIME AND CEMENT. [CHAP. III.
phates, etc., present, and with their proportions relative to each other and to the whole. There is a great diversity as to the value of accelerated tests. Many natural cements which go all to pieces in the accelerated tests, particularly the boiling test, still stand well in actual service. This is a strong argument against drawing adverse conclusions from accelerated tests when applied to Portland ■-cement.
The warm-water test, proposed by Mr. Faija,* a British authority, is made with a covered vessel partly full of water maintained at a temperature of 100° to 115° F., in the upper part of which the pat is placed until set. When the pat is set, it is placed in the water for 24 hours. If the cement remains firmly attached to the glass and shows no cracks, it is very probably sound.
The liot-water test, proposed by Mr. Maclay,f an American authority, is substantially like Faija's test above, except that Maclay recommends 195° to 200° F.
The hoiliiig test, suggested by Professor Tetmajer, the Swiss authority, consists in placing the mortar in cold water immediately after mixing, then gradually raising the temperature to boiling after about an hour, and boiling for three hours. The test specimen consists of a small ball of such a consistency that when flattened to half its diameter it neither cracks nor runs at the -edges.
The kiln tests consist of exposing a small cake of cement mortar, after it has set, to a temperature of 110° to 120° C. (166° to 248° F.) in a drying oven until all the water is driven off. If no edge cracks appear, the cement is considered of constant volume.
The Jiarne test is made by placing a ball of the cement paste, about 2 inches in diameter, on a wire gauge and applying the flame of a Bunsen burner gradually until at the end of an hour the temperature is about 90° C. (194° F.). The heat is then in- creased until the lower part of the ball becomes red-hot. The appearance of cracks probably indicates the presence of an expansive element.
♦Trans. Am. Soe. of C. E., vol. xvii. p. 223; vol. xxx. p. 57. f Trans. Am. Soc. of C. E., vol. xxvii. p. 412.
ART. 4. J TESTS OF CEMENT. 65
The cliloride-of-Ume test is to mix the paste for the cakes with a solution of 40 grammes of calcium chloride per liter of water, allow to set, immerse in the same solution for 24 hours, and then examine for checking and softening. The chloride of lime accel- erates the hydration of the free lime. The chloride in the solution used in mixing causes the slaking before setting of only so much of the free lime as is not objectionable in the cement. The chloride of calcium has no effect upon free magnesia.
96. Fineness. The question of fineness is wholly a matter of economy. Cement until ground is a mass of partially vitrified clinker, which is not affected by water, and which has no setting power. It is only after it is ground that the addition of water induces crystallization. Consequently the coarse particles in a cement have no setting power whatever, and may for practical purposes be considered as so much sand and essentially an adul- terant.
There is another reason why cement should be well ground. A mortar or concrete being composed of a certain quantity of inert material bound together by cement, it is evident that to secure a strong mortar or concrete it is essential that each piece of aggregate shall be entirely surrounded by the cementing material, so that no two pieces are in actual contact. Obviously, then, the finer a cement the greater surface will a given weight cover, and the more economy will there be in its use.
Fine cement can be produced by the manufacturers in three ways: 1, by supplying the mill with comparatively soft, under-burnt rock, which is easily reduced to powder; 2, by more thorough grinding; or 3, by bolting through a sieve and returning the ungronnd particles to the mill. The first process produces an in- ferior quality of cement, while the second and third add to the cost of manufacture.
It is possible to reduce a cement to an impalpable powder, but the proper degree of fineness is reached when it becomes cheaper to use more cement in proportion to the aggregate than to pay the extra cost of additional grinding.
97. Measuring Fineness. The degree of fineness is determined by weighing the per cent, which will not pass through sieves of a specified number of meshes per square inch. In the past, three sieves have been used for this purpose, viz., sieves having 50, 75,
66 LIME AND CEMENT. [CHAP. III..
and 100 meshes per linear inch, or 2,500, 5,625, and 10,000 meshes per square inch respectively. These sieves are usually referred to by the number of meshes per linear inch, the first being known as No. 50, the second as No. 75, and the third as No. 100. In each case the diameter of the mesh is about equal to that of the wire. The per cent, left on the coarser sieves has no special significance, and hence the use of more than one sieve has been almost aban- doned. More recently in this country a No. 120 sieve (14,400 meshes per square inch) has been employed, and sometimes a No. 200. On the continent of Europe the sieve generally nsed has 70 meshes per linear centimetre, corresponding to 175 meshes per linear inch (30,625 per square inch).
98. Data on Fineness. Nearly all Portland cements are so ground as not to leave more than 20 per cent, on a No. 100 sieve, and many of them will not leave more than 10 per cent, on a No. 100 sieve or more than 20 per cent, on a No. 200 sieve; and some manufacturers claim less than 10 per cent, on a No. 200 sieve. As a rule, American Portlands are finer ground than German, and German finer than English.
Most of the natural cements are usually ground so as to give not more than 20 per cent, on the No. 100 sieve, and many of them will not leave more than 10 per cent, on the No. 100 sieve, and a few will leave only 10 per cent, on the No. 200 sieve.
A common sj^ecification is that not more than 10 per cent, shall be left on a No. 50 sieve. Such a test simply prevents the adultera- tion of the cement with very coarse particles, but does not insure any considerable proportion of impalpable powder (approximately that which will pass a No. 200 sieve), which alone gives value to the cement.*
Since the natural cement is not so hard burned as the Portland, there is more impalpable powder in proportion to the per cent, left on the test sieve than with the Portland; and consequently a severe test for fineness is not as important for natural cement as for
♦There has recently been introduced an article called sand-cement, which is made by mixing cement and silica sand and grinding the mixture. The grind ■ ing of the mixture greatly increases the fineness of the cement. A mixture of 1 part cement and 3 parts silica sand when reground will carry nearly as much sand as the original pure cement, which shows the striking effect of the very flue grinding of the cement.
.ART. 4.] TESTS OF CEMENT. 67
Portland. Farther, since natural cement is much cheaper than Portland, it is more economical to use more cement than to require extra fineness. Again, since natural cement is weaker, it is not ordinarily used with as large a proportion of sand as Portland, and hence fineness is not as important with natural as with Portland.
Por various specifications for fineness, see Art. 5, pages 7Sd- 78h, particularly Tables 10c and lOd, jjages 78/", 7Sg.
99. Tensile Strength. The strength of cement mortar is usually determined by submitting a specimen having a cross section •of 1 square inch to a tensile stress. The reason for adopting tensile tests instead of compressive is the greater ease of making the former and the less variation in the results. Mortar is eight to ten times as strong in compression as in tension.
The accurate determination of the tensile strength of cement is a much less simple process than at first appears. Many things, apparently of minor importance, exert such a marked influence upon the results that it is only by the greatest care that trustworthy tests can be made. The variations in the results of different experienced operators working by the same method and upon the same material are frequently very large. In one particular test case,* the lowest of nine results was but 30 per cent, of the highest, the remainder being evenly distributed between the two extremes. Similar varia- tions are not at all unusual. The variation is chiefly due to differ- ences in making the test specimen. Unfortunately, there is at present no detailed standard method of procedure in making the tests, and consequently all that can be done is to observe with the most conscientious care the rules that have been formulated, and draw the specifications in accordance with the personal equation of the one to make the tests.
100. Neat vs. Sand Tests, It is very common to test neat-cement mortar, but there are two serious objections to this practice. First, most neat cements decrease in tensile strength after a time. This decrease seems to be due to a change in the molecular structure of the cement, the crystals growing larger with increase of age, thus producing a crowding which results in a decrease of the tensile strength. This decrease is most marked with high-grade Portlands
* Engineen'ing Xeics, vol. xxxv. pp. 150-51.
68 LIME AND CEMENT. [CHAP. III.
which attain their strength rapidly, and usually occurs between three months and a year. A second objection to neat tests is that coarsely-ground cements show greater strength than finely-ground cements, although the latter mixed with the usual proportion of sand will give the greater strength.
On the other hand, more skill is required to secure uniform results with sand than with neat cement.
101. The Sand. The quality of the sand employed is of great importance, for sands looking alike and sifted through the same sieve give results varying 30 to 40 per cent.
The standard sand employed in the official German tests is a natural quartz sand obtained at Freienwalde on the Oder, passing a sieve of GO meshes per square centimetre (20 per linear inch) and caught upon a sieve of 120 meshes per square centimetre (2S per linear inch). The standard "sand" recommended by the Com- mittee of the American Society of Civil Engineers is crushed quartz, used in the manufacture of sand-paper, which passes a No. 20 sieve (wire No. 28 Stubs's gauge) and is caught on a No. 30 sieve (wire No. 30 Stubs's gauge), the grains being from 0.03 to 0.02 inch in. diameter.
The crushed quartz consists of sharp, glossy splinters, while the standard German sand is composed of nearly spherical grains having a rough surface like ground glass. The quartz contains about 50 per cent, of voids, while the German standard sand contains only about 40 (see Table 10^, page 79r.) The crushed quartz will give less strength than standard sand. Ordinarily common building sand will give a higher strength than standard sand, since usually the former consists of grains having a greater variety of sizes, and con- sequently there are fewer voids to be filled by the cement (see Table lOg, page 79i.)
102. The Amount of Water. The amount of water necessary to make the strongest mortar varies with each cement. It is com- monly expressed in per cents, by weight, although in part at least it depends upon volume. The variation in the amount of water required depends upon the degree of fineness, the specific gravity, the weight per unit of volume, and the chemical composition. If the cement is coarsely ground, the voids are less, and consequently the volume of water required is less. If the specific gravity of one cement is greater than that of another, equal volumes of cement
ART. 4.] TESTS OF CEMENT, 69
will require different volumes of water. The chemical compositioa has the greatest inflneuce upon the amount of water necessary. Part of the water is required to combine chemically with the cement, and part acts physically in reducing the cement to a plastic mass; and the portion required for each of these effects differs with differ- ent cements. The dryness and porosity of the sand may also appreciably affect the quantity of water required. The finer the sand, the greater the amount of water required. Again, the same consistency may be arrived at in two ways — by using a small quan- tity of water and working thoroughly, or by using a larger quantity and working less. (For instructions concerning mixing, see § 106).
Attempts have been made to establish a standard consistency, but there is no constant relation between the consistency and the maximum strength. With one cement a particular consistency may give maximum strength, while with another cement a different con- sistency may be required to develop the greatest strength. The relationship between consistency and strength will vary also with the details of the experiment. In reporting the results of tests the quantity of water employed should be stated.
There are two distinct standards of consistency for the mortar employed in testing cements, — the plastic and the dry.
103. Plastic Mortar. This grade of mortar is that com- monly employed in the United States and England, and is fre- quently used in France.* There are two methods of identifying this degree of consistency, viz. : the Tetmajer method and the Boulogne method. The Tetmajer method requires more water than the Boulogne method — for Portland this excess is about 3 per cent, of the weight of the cement, and for natural about 5 per cent.
The Tetmajer method is much used on the continent of Europe. It is as follows: The plasticity shall be such that a rod 0.4 of an inch in diameter and weighing 0.G6 pounds will penetrate 1.25 inches into a box 3 inches in diameter and 1.57 inches deep, filled with the mortar, f
The Boulogne method is frequently used in France. It is as
* See foot note, page 71.
t For an illustration of the apparatus, see Trans, Amer. Soc, of C. E., vol. xxx. p,ll.
70 LIME AND CEME]srT. [CHAP. III.
follows: * " The quantity of water is ascertained by a preliminary experiment. It is recommended to commence with a rather smaller quantity of water than may be ultimately required, and then to make fresh mixings with a slight additional quantity of water. The mortar is to be vigorously worked for five minutes with a trowel on a marble slab to bring it to the required consistency, after which the four following tests are to be applied to determine whether the proportion of water is correct: 1. The consistency of the mortar should not change if it be ganged for an additional period of three miuutes after the initial five minutes. 2. A small quantity of the mortar dropped from the trowel upon the marble slab from a height of about 0.50 metres (20 inches) should leave the trowel clean, and retain its form approximately without cracking. 3. A small quan- tity of the mortar worked gently in the hands should be easily moulded into a ball, on the surface of which water should appear. When this ball is dropped from a height of 0.50 metres (20 inches), it should retain a rounded shaj^e without cracking. 4. If a slightly smaller quantity of water be used, the mortar should be crumbly, and crack when dropped upon the slab. On the other hand, the addition of a further quantity of water — 1 to 2 per cent, of the weight of the cement — would soften the mortar, rendering it more sticky, and preventing it from retaining its form when allowed to fall upon the slab."
104. With any particular cement the exact amount of water to produce the above degree of plasticity can be determined only by trial, but as a rule the quantity required by the Boulogne method will be about as follows:
For neat cement: Portland, 23 to 25 per cent.; natural, from 30 to 40, usually from 32 to 36 per cent.
For 1 part cement to 1 part sand: Portland cement, 13 to 15 per cent, of the total weight of cement and sand; natural, 17 to 20, usually 18 to 19 per cent.
For 1 part cement to 2 parts sand: Portland, 12 to 13 per cent, of the total weight of the sand and cement; natural, 12 to 16, usually 13 to 15 per cent.
For 1 part cement to 3 parts sand: Portland, 11 to 12 per cent.
* rrom abstracts of lust, of C. E.
ART. 4.] TESTS OF CEMENT. 71
of the total weight of the sand and cement; natural, 12 to 13 per cent.
105. Dry Mortar. This grade of mortar is employed in the German and French * governmental tests of tensile strength. The rules for the identification of this degree of consistency are not very specific. " Dry mortars " are usually described as being " as damp as moist earth."
The German government does not recognize tensile tests of neat cement mortar; but for 1 to 3 sand mortars specifies that the weight of water irsed for Portland cement shall be equal to 10 per cent, of the total weight of the sand and cement.
The French Commission gives a rule f for 1 to 2, 1 to 3, and 1 to 5 mortars, with either Portland or natural cement, which is equivalent to the following formula:
w = ^WR + 45,
in which w = the weight, in grammes, of water required for 1,000 grammes of the sand and cement;
W = the weight, in grammes, of water required to re- duce 1,000 grammes of neat cement to plastic mortar (see § 104);
H = the ratio of the weight of the cement to the weight of the sand and cement.
For a 1 to 3 mortar the preceding formula gives 8.5 per cent., which seems to show that the French standard requires less water than the German.
The cement laboratory of the city of Philadelphia employs the above formula, but uses GO for the constant instead of 45. For a 1 to 3 mortar, the Philadelphia formula gives 10 per cent., which agrees with the German standard.
106. Mixing the Mortar. The sand and cement should be thoroughly mixed dry, and the water required to reduce the mass to the proper consistency should be added all at once. The mixing
* The French Commission recommends dry mortar for tensile tests only ; and also recommends that, after an international agreement to that effect, plastlo mortars be employed for all tests to the exclusion of dry mortars.
t Carter and Gieseler's Conclusions adopted by the French Commission iu reference to Tests of Cements, p. 21.
72
LIME AND CEMENT.
[chap. III.
should be prompt and tliorougli. The mass should not be simply turned, but the mortar should be rubbed against the top of the slate or glass mixing-table with a trowel, or in a mortar with a pestle. Insufficient working greatly decreases the strength of the mortar — frequently one half. The inexperienced operator is very liable to use too much water and too little labor. With a slow- setting cement a kilogramme of the dry materials should be strongly and rapidly rubbed for not less than 5 minutes, when the consist- ency should be such that it will not be changed by an additional mixing for 3 minutes.
Usually the mortar is mixed with a trowel on a stone slab; but when many batches are required, there is a decided advantage in mixing the mortar with a hoe in a short Y-shaped trough on the floor. Various machines have been devised with which to mix the mortar. The jig mixer* is an apparatus in which the materials are placed in a covered cup, and shaken rapidly up and down. The Faija mixer f consists of a cylindrical pan in which a mixer
formed of four blades revolves. The
rr^-j^ZSlTT *' latter seems to give the better result,
bnt neither are used to any considerable extent.
107. The Form of Briquette. The )riqnette recommended by the Committee of the American Society of Civil En- gineers, Fig. 2, is the form ordinarily used in this country and in England. The form generally emjiloyed in con- tinental Europe is somewhat similar to the above, except that the section is 5 square centimetres (0.8 square inch) and the reduction to produce the minimum ^^ section is by very much more abrupt
curves. J The latter form gives only 70 to 80 per cent, as much strength as the former.
* For illustrated description, see Trans. Anaer. Soc. of C. E., vol. xxv. p. 300-1.
t For British form, see Trans. Am. Soc. of C. E., vol. xvii. p. 223 ; and for the American form, see catalogue of Eiehle Bros. Testing Machine Co., Philadelphia.
J For an elaborate discussion of the best form of briquette, see Johnson's Materials of Construction, p. 432-38.
ART. 4.] TESTS OF CEMENT. 73
The moulds are made of brass and are single or multiple, the latter being preferred where a great number of briquettes is required. The moulds are in two parts, to facilitate removal from the briquette without breaking it.
108. Moulding the Briquette. In moulding the briquette there are two general methods employed, corresponding to the two stand- ard consistencies of the mortar.
109. Plastic Mortar. The rules of this section (109) apply to liand-moulding .
The Committee of the American Society of Civil Engineers' recommendations are as follows: " The moulds while being charged should be laid directly on glass, slate, or some non-absorbing material. The mortar should be firmly pressed into the moulds with a trowel, without ramming, and struck off level. The mould- ing must be completed before incipient setting begins. As soon as the briquettes are hard enough to bear it, they should be taken from the moulds and kept covered with a damp cloth until they are immersed."
The French Commission recommends the following method : * " The moulds are placed upon a plate of marble or polished metal which has been well cleaned and rubbed with an oiled cloth. Six moulds are filled from each ganging if the cement be slow-setting, and four if it be quick-setting. Sufficient material is at once placed in each mould to more than fill it. The mortar is pressed into the mould with the fingers so as to leave no voids, and the side of the mould tapped several times with the trowel to assist in disengaging the bubbles of air. The excess of mortar is then removed by slid- ing a knife-blade over the top of the mould so as to produce no compression upon the mortar. The briquettes are removed from the mould when sufficiently firm, and are allowed to remain for 24 hours npon the plate in a moist atmosphere, protected from currents of air or the direct rays of the sun, and at a nearly constant tem- perature of 15° to 18° C. (59° to 64.4° F.)."
110. Various machines have been devised for moulding bri- quettes of plastic mortar, but none are used to any considerable extent, t
* Carter and Gieseler's Conclusions adopted by the French Commission in reference to Tests of Cements, p. 23.
+ For an illustrated description of Russell's lever machine, see Trans. Amer. Soc.
74 LIME AND CEMENT. [CHAP. III.
In Canada, and to some extent in England, the briquettes are moulded by applying a pressure of 20 pounds per square inch on the snrface of the briquette.* Some advocate a pressure of 1,000 to 1,500 pounds upon the upper face of the briquette, f
111. Dry Mortar. The rules of this section (111) are for liand- moulding.
The German standard rules are: \ "On a metal or thick glass plate five sheets of blotting-paper soaked in water are laid, and on these are placed five moulds wetted with water. 250 grammes (8.75 oz.) of cement and 750 grammes (2G.25 oz.) of standard sand are weighed, and thoroughly mixed dry in a vessel. Then 100 cubic centimetres (100 grammes or 3.5 oz.) of fresh water are added, and the whole mass thoroughly mixed for five minutes. With the mortar so obtained, the moulds are at once filled, with one filling, so high as to be rounded on top, the mortar being well pressed in. By means of an iron trowel 5 to 8 centimetres (1.96 inches to 3.14 inches) wide, 35 centimetres (13.79 inches) long, and weighing about 250 grammes (8.75 oz.), the projecting mortar is pounded, first gently and from the side, then harder into the moulds, until the mortar grows elastic and water flushes to the surface. A pounding of at least one minute is absolutely essential. An addi- tional filling and pounding in of the mortar is not admissible, since the test pieces of the same cement should have the same densities at the different testing stations. The mass projecting over the mould is now cut off with a knife, and the surface smoothed. The mould is carefully taken off and the test piece placed in a box lined with zinc, which is to be provided with a cover, to prevent a non- uniform drying of tlie test j^ieces at different temperatures. Twenty-four hours after being made, tlie test pieces are placed under water, and care must be taken that they remain under water during the whole period of hardening."
The French Commission recommend the following for sand
of C. E., vol. xxvii. p. 441 ; ditto of Jamieson's lever machine, see The Transit (Iowa State University), December, 1889, or Enginee7'ing News, vol. xxv. p. 138, or Trans. Amer. Soc. of C. E., vol. xxv. p. 302.
* Trans. Canadian Soc. of C. E., vol. ix. p. 56, " Final Report of the Committee on a Standard Method of Testing Cements."
f Spalding's Hydraulic Cement, p. 135.
J Engineering News, vol. xvi. p. 316.
ART. 4.] TESTS OF CEMENT. 75
mortars: " Sufficient mortar is gauged at once to make six briquettes, requiring 250 grammes of cement and 750 grammes of normal sand. The mould is placed upon a metal plate, and upon top of it is fitted a guide having the same section as the mould and a height of 125 millimetres (5 inches), 180 grammes of the mortar are introduced and rouglily distributed in the mould and guide with a rod. By means of a metallic pestle weighing 1 kilogramme, and having a base of the form of the briquette but of slightly less dimensions, the mortar is pounded softly at first, then stronger and stronger until a little water escapes under the bottom of the mould. The pestle and guide are then removed and the mortar cut off level with the top of the mould."
Ilia. The Bohme hammer apparatus is much used, particularly in Germany. It consists of an arrangement by which the mortar is compacted in the mould by a succession of blows of a hammer weighing 2 kilogrammes (4.4 pounds) upon a plunger sliding in a guide placed upon top of the mould. The machine is arranged to lock after striking 150 blows. A high degree of density is thus produced, and more regular results are obtained than by hand. The apparatus is slow.*
The Tetmajer apparatus f is similar in character to the Bobme hammer. " It consists of an iron rod carrying a weight upon its lower end, which is raised through a given height and dropped upon the mortar in the mould. The ram weighs 3 kilogrammes. This machine is used in the Zurich laboratory, and Prof. Tetrtiajer regu- lates the number of blows by requiring a certain amount of work to be done upon a unit volume of mortar, — 0.3 kilogrammetre of work per gramme of dry material of which the mortar is composed. This apparatus is subject to the same limitations in practice as the Bohme hammer, in being very slow in use and somewhat expensive in first cost."
lllh. Storing the Briquettes. It is usual to store the briquettes under a damp cloth or in a moist chamber for 24 hours, and then immerse in water at a temperature of 60° to 65° F. For one-day tests, the briquettes are removed from the moulds and immersed as
* For an illustrated description, see Engineering News, vol. xvii. p. 200 ; Trans. Amer. Soc. of C. E., vol. xxx. p. 24.
f French Commission's Report, vol. i. p. 287.
76 LIME AND CEMENT. [CHAP. III.
soon as they have began to set. The volume of the water should be at least four times the volnme of the immersed briquettes, and the water should be renewed every seven days.
The briquettes should be labeled or numbered to preserve their identity. Neat-cement briquettes may be stamped with steel dies, as may also sand briquettes, provided a thin layer of neat cement is spread over one end in which to stamp the number.
111c. Age when Tested. Since in many cases it is impracticable to extend the tests over a longer time, it has become customary to break the briquettes at one and seven days. This practice, together with a demand for high tensile strength, has led manufacturers to increase the proportion of lime in their cements to the highest possible limit, which brings them near the danger-line of unsound- ness. A high strength at 1 or 7 days is usually followed by a decrease in strength at 28 days. Steadily increasing strength at long periods is better proof of good quality than high results during the first few days. The German standard test recognizes only breaks at 28 days. The French standard permits, for slow-setting cements, tests at 7 and 28 days, and 3 and 6 months, and 1, 2, etc., years; and for rapid-setting cements, from 3 to 24 hours for neat mortar and 24 hours for sand mortars. In all cases the time is counted from the instant of adding the water when mixing the briquette. The briquettes should be tested as soon as taken from the water.
111(7. The Testing Machine. There are two types in common use. In one the weight is applied by a stream of shot, which runs from a reservoir into a pail suspended at the end of the steelyard arm; when the briquette breaks the arm falls, automatically cutting off the flow of shot. In the other type, a heavy weight is slowly drawn along a graduated beam by a cord wound on a wheel turned by the operator. The first is made by Fairbanks Scale Co. , and the second by Riehle Bros., and also by Tinius Olsen, both of Phila- delphia.
Fig. 3 represents a cement-testing machine which can be made by an ordinary mechanic at an expense of only a few dollars. Athough it does not have the conveniences and is not as accurate as the more elaborate machines, it is valuable where the quantity of work will not warrant a more expensive one, and in many cases is amply sufficient. It was devised by F. W. Bruce
ART. 4.]
TESTS OF CEMENT.
for use at Fort Marion, St. Aagastine, Fla., and reported to the Engineering News (vol. v. pp. 104:-96) by Lientenant "W. M. Black, U. S. A.
The machine consists essentially of a counterpoised wooden lever 10 feet long, working on a horizontal pin between two broad uprights 20 inches from one end. Along the top of the long arm runs a grooved wheel carrying a weight. The distances from the fulcrum in feet and inches are marked on the surface of the lever. The clamp for holding the briquette for tensile tests is suspended from the short arm, 18 inches from the fulcrum. Pressure for shearing and compressive stresses is communicated through a loose upright, set under the long arm at any desired distance (generally 6 or 12 inches) from the fulcrum. The lower clip for tensile strains is fastened to the bed-plate. On this plate the cube to be crushed
TF, fixed weight, block for crushing.
W, rolling weight. TI' C, tensile strain clips.
, counterpoise. B\ block for shearing. B,
rests between blocks of wood, and to it is fastened an upright with a square mortise at the proper height for blocks to be sheared. The rail on which the wheel runs is a piece of light T-iron fastened on top of the lever. The pin is iron and the pin-holes are reinforced by iron washers. The clamps are wood, and are fastened by clevis joints to the lever arm and bed-plate respectively. When great stresses are desired, extra Aveights are hung on the end of the long arm. Pressures of 3,000 pounds have been developed with this machine. ,
For detailed drawings of a more elaborate home-made cement- testing machine, see Proceedings Engineers' Club of Philadelphia, vol. V. p. 194, or Engineering Neius, vol. xv. p. 310.
llle. The Clips. The most important part of the testing machine are the clips, by means of which the stress is applied to the briquette. 1. The form must be such as to grasp the
78
LIME AND CEMENT.
[chap. III.
briquette on four symmetrical surfaces. 2. The surface of con- tact must be large enough to prevent the briquette from being crushed between the points of contact. 3. The clip must turn without appreciable friction when under stress. 4. The clip must not spread ap- preciably while subjected to the maximum load.
The form of clip recommended by the Committee of the American Society of Civil Engineers is shown in Fig. 4. This ■^ form does not offer sufficient bearing sur- face, and the briquette is frequently crushed at the point of contact. The difficulty is remedied somewhat by the use of rubber- tipi^ed clips.
Whatever the form of the machine or clips, great care should be taken to center the briquette in the machine.
111/. The Speed. The rate at which the stress is applied makes a material difference in the strength. The following data are given by H. Faija,* an English
authority, as showing the effect of a variation in the speed of
applying the stress :
Rate. Tensile Strength.
100 pounds in 120 seconds 400 pounds.
100 " " 60 " 415
100 " " 30 " 430
100 " " 15 " 450
100 " ■■ 1 <■ 493
The French and German standard specifications require 660 pounds per minute. The American Society of Civil Engineers recommends 400 pounds per minute for strong mixtures, and half this speed for weak mixtures. The Canadian Society of Civil Engineers recommends 200 pounds per minute.
111^. Data on Tensile Strength. Owing to the great variation
Fig. 4.
* Trans. Amer. Soc. of C. E., vol. xvii. p. 227.
AKT. 4.]
TESTS OF CEMENT.
78a
in the manner of making the tests, it is not possible to give any very valuable data on the strength that good cement should show. In 1885 a Committee of the American Society of Civil Engineers recommended the values given in Table 10 below. At least the minimum values there given are required in ordinary specifications, and the maximum values are sometimes employed. Many of the
TABLE 10. Tensile Strength op Cement Mortaks.
|
Age of Mortar when Tested. |
Average Tensile Strength IN Pounds per Square Inch. |
|||
|
Portland. |
Natural. |
|||
|
Clear Cement. |
Min. |
Max. |
Min. |
Max. |
|
1 day— 1 hour, or until set, in air, the remainder of the time in water |
100 |
140 |
40 |
80 |
|
1 week— 1 day in air, the remainder of the time in water |
250 |
550 |
60 |
100 |
|
4 weeks— 1 day in air, the remainder of the time in water |
350 |
700 |
100 |
150 |
|
1 year — 1 day in air, the remainder of the time in water |
450 |
800 |
300 |
400 |
|
1 Part Cement to 1 Part Sand. |
||||
|
1 week— 1 day in air, the remainder of the time in water |
30 50 200 |
50 |
||
|
4 weeks— 1 day in air, the remainder of the time in water |
80 |
|||
|
1 year — 1 day in air, the remainder of the time in water |
300 |
|||
|
1 Part Cement to 3 Parts Sand. |
||||
|
( week — 1 day in air, the remainder of the time in water |
80 100 200 |
125 200 350 |
||
|
i weeks — 1 day in air, the remainder of the time in water |
||||
|
t year — 1 day in air, the remainder of the time in water |
||||
Tfeetter cements commonly give results above the maximum values in the table. Natural cement, neat plastic mortar, will generally show 50 to 75 pounds per square inch in 7 days, and 100 to 200 in
LIME AND CEMENT.
[chap. III.
:28 days. Good Portland cement, neat plastic mortar, will show 100 to 200 pounds per sqaare inch in one day, 400 to 600 in 7 days, and 600 to 800 in 28 days. With 3 parts sand, Portland cement, plastic mortar, will give at least 100 pounds per square inch in 7 days, and 200 in 28 days. Of course the strength varies greatly with the method of testing. In consulting authorities on this subject, it should be borne in mind that the strength of cement, particularly Portland, has greatly increased in the past 10 years. The specifications should be drawn to correspond with the personal equation of the one who is to test the cement.
For various specifications for tensile strength, see Art. 5, pages 78c-7Sh, particularly Tables 10c and lOd, pages 78/, 78^.
For additional data on the strength of mortars composed of different proportions of cement and sand, see Fig. 5, page 91.
lllh. Equating the Results. It not infrequently occurs that several samples of cement are submitted, and it is required to determine which is the most economical. One may be high-priced and have great strength; another may show great strength neat
TABLE 10a. Relative Economy op Cements Tested Neat at 7 Days.
A B C D E
|
Fin |
ENESS. |
Tensile Strength. |
Cheapness. |
||
|
.a |
|||||
|
c8 |
m ® |
> |
$ |
o |
|
|
o . |
d |
S 3 |
Is |
4^ |
|
|
2h |
(2«= |
^ |
a $2.30 |
100.0 |
|
|
90.0 |
98.1 |
628 |
81.5 |
||
|
88.0 |
95.9 |
771 |
100.0 |
2.34 |
98.3 |
|
88.7 |
96.6 |
477 |
61.9 |
2.40 |
95.8 |
|
91.8 |
100.0 |
391 |
50.7 |
2.45 |
93.8 |
|
81.5 |
88.8 |
660 |
85.6 |
2.47 |
93.1 |
Relative Economy.
OJ « u jj
79.95 94.26
57.28 47.55 70.79
and be coarsely ground. If the cement is tested neat, then strength, fineness, and cost should be considered ; but if the cement
ART. 5.]
SPECIFICATIONS FOR CEMENT.
78c
is tested with the proportion of sand usually employed in practice, then only strength and cost need to be considered.
Table 10a (page 78b) shows the method of deducing the relative economy when the cement is tested neat; and Table 10b shows the
TABLE 106. Relative Economy of Cements Tested with Sand at 7 Days.
|
Tensile Strength 1 C. TO 3 s. |
Cheapness. |
Relative Economy. |
||||
|
Cements. |
Pounds per Square Inch. |
Relative. |
Cost per Barrel. |
Relative. |
Product of Relative Strength and Relative Cost. |
Rank. |
|
A B C D E |
168 176 166 135 135 |
95.4 100.0 94.3 76.7 76.7 |
$2.30 2.34 2.40 2.45 2.47 |
100.0 98.3 95.8 93.8 93.1 |
95.40 98.30 90.33 71.94 71.40 |
2 1 3 4 5 |
method when the cement is tested with sand. The data are from actual practice, and the cements are the same in both tables. Results similar to the above could be deduced for any other age; the circumstances under which the cement is to be used should determine the age for which the comparison should be made.
The above method of equating the results gives the advantage to a cement which gains its strength rapidly and which is liable to be unsound. Therefore this method should be used with discretion, particularly with short-time tests.
Art. 5. Specifications for Cement.
llli. Cement is so variable in quality and intrinsic value that no considerable quantity should be accepted without testing it to see that it conforms to a specified standard. A careful study of Art. 4, preceding, will enable any one to prepare such specifications as will suit the special requirements, and also give the instructions
78(? LIME AND CEMENT. [CHAP. III.
necessary for applying the tests. A few specifications will be given to serve as guides in preparing others.
SPECIFICATIONS FOR QUALITY.
my. (jERMAN Portland. The following are the most im- portant paragraphs from the standard specifications of the German government as given in the oflicial circular issued by the Minister of Public Works of Prussia under date of July 28, 1887:*
" Time of Setting. According to the purpose for which it is intended, quick or slow-setting Portland cement may be demanded. Slow-setting cements are those that set in about two hours." The test is made as described in §86.
" Constancy of Volume. The volume of Portland cement should remain constant. The decisive test of this should be that a cake of cement, made on a glass plate, protected from sudden drying and placed under water after 24 hours, should show, even after long submersion, no signs of crumbling or of cracking at the edges." For method of making the test, see § 92.
" Fineness of Grinding. Portland cement must be ground so fine that no more than 10 per cent, of a sample shall be left on a sieve of 900 meshes per square centimetre (5,800 per square inch). The thickness of the wires of the sieve to be one-half the width of the meshes." Notice that a sieve having 900' meshes per square centimetre (5,800 per sq. in.) is the standard, although sieves of 5,000 meshes per square centimetre (32,000 per sq. in.) are frequently used.
" Tests of Strength. The binding strength of Portland cement is to be determined by testing a mi.\ture of cement and sand. The test is to be con- ducted for tensile and compressive strength according to a uniform method, and is to be performed upon test specimens of like form, like cross section, and with like apparatus. It is recommended, besides, to determine the strength of neat cement. The tests for tension are to be made upon briquettes of 5 sq. cm. (0.78 sq. in.) cross section at the place of rupture, the tests for compression upon cubes of 50 sq. cm. (7.8 sq. in.) area."
" Tensile and Compressive Strength. Slow-setting Portland cement, when mixed with standard sand in the proportion of 1 part of cement to 3 of sand, by weight, 28 days after being mixed — one day in air and 27 in water — must , possess a tensile strength of not less than 16 kilog. per square centimetre (225 lbs. per square inch), and a maximum compressive strength of 160 kilog. per square centimetre (2,250 lbs. persq. in.). Qtiick-setting cements generally show a lower strength after 28 days than that given above. The time of setting must, therefore, be given when stating figures relative to strength." The test is made as described in the second paragraph of § 111 or the first paragraph of § lllo.
* Translation from Trans. Amer. Soc. of C. E., vol. yxx. pp. 10-21.
J\.RT. 5.J SPECIFICATIONS FOR CEMENT. 78«
11 11-. English Portland. In Great Britain there are no •official specifications, but the following proposed * by Mr. Henry Faija are much used :
" Fineness to be such that the cement will all puss through a sieve having 625 holes (25') to the square inch, and leave only 10 per cent, residue when sifted through a sieve having 2,500 holes (50') to the square inch.
" Expansion or Contraction, A pat made and submitted to moist heat and warm water at a temperature of 100° to 115° F., shall show no sign of expan- sion or contraction (blowing) in twenty-four hours.
" Tensile Strength. Briquettes of slow-setting Portland, which have been gauged, treated, and tested in the prescribed manner, to carry an average ten- sile strain, witliout fracture, of at least 176 lbs. per sq. in. at the expiration of ■3 days from gauging; and those tested at the expiration of 7 days, to show an increase of at least 50 per cent, over the strength of those at 3 days, but to carry a minimum of 350 lbs. per sq. in.
"For quick-setting Portland, afleast 176 lbs. pcf sq. in. at 3 days, and an increase at 7 days of 30 to 25 per cent., but a minimum of 400 lbs. per sq. In. Very high tensile strengths at early dates generally indicate a cement verging on an unsound one."
111^. French Portland. The following are the requirements of the Services Maritimes des Fonts et Chaussees,f and are fre- quently employed in France:
" Density. A liter measure is loosely filled with cement, previously screened through a sieve of 180 meshes to the linear inch, and weighed. This test is used for comparison of diflfereut lots of the same cement, the weight of 1 liter of which must exceed a certain figure determined for the cement in question. No general requirement as to density is made."
" Chemical Composition. Cement containing more than 1 per cent, of sul- phuric anhydride (=1.7 per cent, sulphate of lime) is rejected, while that con- taining more than 4 per cent, of oxide of iron is declared suspicious. Cement containing less than 44 parts of silica and alumina to 100 of lime is also con- sidered suspicious."
Tim,e of Setting. The test for time of setting is made as described in § 86 {page 58). " Cement which begins to set in less than 30 minutes or sets com- pletely in less than 3 hours is refused."
" Constancy of Volume. Pats on glass are immersed in sea-water kept at a temperature of 59° to 65° F., and examined for cracking or change of form."
" Tensile Strength. The amount of water to be employed is determined as
* Trans. Amer. Soc, of C. E., vol. xvii. p. 225 ; vol. xxx. (1893) p. 60. f Candlot's "Ciments and Chaux HydrauUcs," Paris, 1891, pp. 150-61.
78/
LIME AND CEMENT.
[chap. III.
in third paragraph of § 103 (page 69). The briquettes are moulded as de- scribed in in the third paragraph of § 109, page 73.
" For neat cement, the tensile strength at 7 days must be at least 20 kilog. per sq. cm. (284 lbs. per sq. in.); at 28 days, 35 kilog. per sq. cm. (497 lbs. per sq. in.); at 12 weeks, 45 kilog. per sq. cm. (639 lbs. per sq. in.). The tensile strength at 28 days must exceed that at 7 days by at least 5 kilog. per sq. cm. (71 lbs. per sq. in.). The tensile strength at 12 weeks must be greater than that at 28 days unless the latter shall be at least 55 kilog. per sq. cm. (781 lbs. per .sq. in.).
"For 3 parts crushed quartz to 1 part cement, with 12 per cent, water [moulded as described in the third paragraph of §111], the tensile strength must be at 7 days at least 8 kilog. per sq. cm. (114 lbs. per sq. in.); at 28 days at least 15 kilog. per sq. era. (213 lbs. per sq. in.); and at 12 weeks, 18 kilog. per sq. cm. (256 lbs. per sq. in.). The strength at 12 weeks must in all cases be greater than that at 28 days."
lllwi. American Practice. Tables 10c and 10c? give the average requirements for fineness and tensile strength of Portland and natural cements, for various classes of work in the United States. These values may be regarded as representative of the average American practice:
TABLE 10c.
American Requirements for Fineness and Strength of Portland
Cement.
AvKBAGE American Pkactick AS Represented by
38 U. S. A. Engineers. 10 Cities
6 Railways
6 Bridges
3 Aqueducts
81 Specifications
Per cent. Passing
Sieve. No.
50 100
95 97 95 97
96
84 89 80 88 80 85
Tensilk Strength, Lbs. per S<j. In.
Neat Cement.
1
131 161 115 119 110 134
Mortar.
lto2.
1 to 3.
Age when Tested, Days.
402 388 319 347 333 384
28
547 534 483 487 400 528
150 145 123 142 125 146
28
200 200 175 250 200 216
119 132 108 132 132 118
189 197 150 200 225 189
Airf. 5.]
SPECIFICATIONS FOR CEMENT.
:8g
TABLE Wd.
Amekican Requikements for Fineness and Strength of Natural
Cement.
Average American Practice as Represented by
24 U. S. A. Engineers
10 Cities
4 Railways
2 Bridges
3 Aqueducts
51 Specifications
Per cent.
Passing
Sieve.
No.
|
50 |
100 |
|
91 |
72 |
|
93 |
81 |
|
95 |
|
|
95 |
92
79
Tensile Strength. Lbs. per Sq. In.
Neat Cement.
1 to 2 Mortar.
Age when Tested. Days.
38 70 65 55 60 63
102 134 105
87 117 109
164 237 162
185 200
178
34 40 47 35 50 40
28 77
80 70 75
77
llln. Philadelphia: Natural and Portland, The follow- ing is an abstract of the specifications used in 1897 by the Depart- ment of Public Works of the City of Philadelphia. These specifications are inserted as showing the extreme of American practice in the high degree of fineness and great strength required. Compare these results with those in Tables 10c and lOd. The Philadelphia specifications are not included in these tables.
NATURAL CEMENT.
" Specific Gravity. The specific gravity shall not be less than 2.7.
" Fineness. The residue shall not leave more than 2 per cent on a No. 50 sieve, nor 15 on a Xo. 100 sieve, nor 35 ou a No. 200 sieve, the sieves having 2,400, 10,200, and 35,700 meshes per square inch and the diameter of the wire being 0.0090, 0.0045, and 0.0020 of an inch respectivel}-.
" Constancy of Volume. Pats of neat cement one half inch thick with thin edges, immersed in water after hard set, shall show no signs of checking or disintegration.
" Time of Setting. It shall begin to set in not less than 10 minutes, and set hard in less than 30 minutes.
" Tensile Strength. The tensile strength of dry mortar [see last paragraph of g 105] shall not be less than in the accompanying table :
ISh
LIME AND CEMENT.
[chap. III.
|
Tensile Strength. Pounds per Square Inch. |
||
|
Neat. |
1 Cement to ~' Quartz. |
|
|
24 hours (in water after set hard) |
100 200 300 |
|
|
7 days (1 day in air, 6 days in water) |
125 |
|
|
28 days (1 day in air, 27 days in water) |
200 |
PORTLAND CEMENT.
" Specific Oravity. The specific gravity shall not be less than 3.0.
" Fineness. The residue shall not be less than 1 per cent, on a No. 50 sieve, 10 on a No. 100 sieve, aud 30 on a No. 200 sieve.
" Constancy of Volume. Same as for natural cement above.
" Time of Setting. The cement shall not develop initial set in less than 30 minutes.
" Ti-nsile Strength. The tensile strength of dry mortar [see last paragragh of ^ 105] shall not be less than in the accompanying table :
|
Tensile Strength. Pounds per Square Inch. |
||
|
Neat. |
1 Cement to 2 Quartz. |
|
|
24 hours (in water after hard set) |
175 500 600 |
|
|
7 days (1 day in air, 6 days in water) |
170 |
|
|
28 days (1 day in air, 27 days in water) |
240 |
SPECIFICATIONS FOR DELIVERY AND STORAGE.
lllo. The preceding specifications prescribe the quality of the cement; and the following refer to the quantity, the sampling, and the storage. The tests under the former are made in the laboratory, those under the latter on the work.
Package. The cement shall be delivered in strong barrels* lined with
* It is customary to specify that the cement, particularly Portland, shall be delivered iu barrels. The only reason for shipping in barrels is that the cement is better protected from the weather in barrels than in bags. The arguments in
^RT. 5.] SPECIFICATIONS FOR CEMENT. 78 i
paper so as to be reasonably protected from the air and dampness. Each package shall be labeled with the brand, the manufacturer's name, and the gross weight.
WeigJU. The net weight of a barrel of cement shall be understood to be 375 pounds of Portland, and 300 pounds of Eastern natural or 265 pounds of Western natural [see § 77, page 54]; and bags shall contain an aliquot part of a barrel. A variation of 2 per cent, is allowable in the weight of individual packages. Any broken barrel or torn bag may be rejected or accepted at half its original weight, — at the option of the Inspector.
Time of Delivery. The inspection and tests will occupy at least ten * days, and the Contractor shall submit the cement for sampling at least ten * days before desiring to use it. The Inspector shall be promptly notified upon the receipt of each shipment.
Sampling. The cement from which to test the quality shall be selected by taking, from the interior of each of six \ well-distributed barrels or bags in each car-load, suflicient cement to make from five to ten briquettes. These sixf portions, after/being thrown together and thoroughly .mixed, will be assumad to represent the average of the whole car-load.
Storage. All cement when delivered shall be fully protected from the weather ; and shall not be placed upon the ground without proper blocking under it. Accepted cement may be re-inspected at any time ; and if found to be damaged, it shall be rejected. Any cement damaged by water to such an extent as to show upon the outside of the barrel will be rejected.
Iiispectiori Marks. Cement which has been accepted may be so labeled by the Inspector ; and the Contractor shall preserve these labels from deface- ment and shall prevent their imitation. Rejected cement shall be so marked ; and the Contractor shall promptly remove such cement.
Basis for Rejecting. Each shipment of cement shall be tested for quantity and quality. If the average weight of the barrels or bags tested is less than the weight specified, a corresponding deduction shall be made in the price ; and if ten per cent, fails to conform to the requirements for quality, the entire
favor of shipping in bags are : 1. The cost is less, since the cost of the barrel is eliminated. 2. The cement is more easily handled, since the weight of a unit is less. 3. In cloth bags the cement improves by seasoning, i.e., the contact with the air hydrates any free lime due to improper chemical combination or imperfect calcination. 4. The practice of shipping in barrels is only a survival from the time when the best cement was of European manufacture, which of necessity was shipped in barrels because of the excessive moisture in the holds of vessels. 5. In Europe Portland cement is usually shipped in cotton-ducli bags.
* For important work this time is usually made thirty days.
f This is the number specified by the Pennsylvania Railroad, a road noted for careful and thorough work. It is frequently specified that ten samples shall be taken ; and in important workjwhero a single barrel of poor cement may materially affect the strength of the work, it is sometimes specified that each and every barrel shall be tested.
TSy LIME AXD CEMENT. [CHAP. III.
shipment may be rejected. The failure of a shipment to meet the specifica- tions for quality may prohibit further use of that brand on the work.
Barrels containing a large proportion of lumps shall be rejected.
Refusal to Test. The Engineer reserves the right to refuse to test any brand which in his judgment is unsuitable for the work.* A barrel or bag which is not plainly labeled with the brand and maker's name shall not be tested, and shall be immediately removed.
* This provision is sometimes inserted to avoid the trouble and delay of testing any brand which the Engineer is reasonably certain is unfit for the work owing to its general reputation for poor quality or lack of uniformity.
CHAPTER nil SAND, GRAVEL, AND BROKEN STONE.
112. Sand is used in making mortar; and gravel, or sand and broken stone, in making concrete. The qualities of the sand and broken stone have an important effect upon the strength and cost of the mortar and the concrete. The effect of the variation in these materials is generally overlooked, even though the cement is subject to rigid specifications.
Art. 1. Sand.
113. Sand is mixed with lime or cement to reduce the cost of the mortar; and is added to lime also to prevent the cracking which would occur if lime were used alone. Any material may be used to dilute the mortar, provided it has no effect upon the durability of the cementing material and is not itself liable to decay. Pulverized stone, powdered brick, slag, or coal cinders may be used ; but natural sand is by far the most common, although fine crushed stone, or "stone screenings," are sometimes employed and are in some respects better than natural sand.
In testing cement a standard natural sand or crushed quartz is employed; but in the execution of actual work usually local natural sand must be employed for economic reasons. Before commencing any considerable work, all available natural sands and possible sub- stitutes should be examined to determine their values for use in mortar.
114. Requisites for Good Sand. To be suitable for use in mortar, the sand should be sharp, clean, and coarse; and the grains should be composed of durable minerals, and the size of the grains should be such as to give a minimum of voids, i.e., interstices between the grains.
The usual specifications are simply: " The sand shall be sharp, clean, and coarse. ""
114a. Durability. As a rule ocean and lake sands are more
79a
79J SAND. [chap. Ilia.
durable than glacial sands. The latter are rock meal ground in the geological mill, and usually consist of silica with a considerable ad- mixture of mica, hornblende, feldspar, carbonate of lime, etc. The silica is hard and durable ; but the mica, hornblende, feldspar, and carbonate of lime are soft and friable, and are easily decomposed by the gases of the atmosphere and the acids of rain-water. The lake and ocean sands are older geologically ; and therefore are usually nearly pure quartz, since the action of the elements has eliminated the softer and more easily decomposed constituents. Some ocean sands are nearly pure carbonate of lime, which is soft and friable, and are therefore entirely unfit for use in mortar. These are known as calcareous sands.
The glacial sands frequently contain so large a proportion of soft and easily decomposed constituents as to render them unfit for use in exposed work, as for example in cement sidewalks. Instead of constructing exposed work with poor drift sand, it is better either to ship natural silica sand a considerable distance or to secure crushed quartz. Crushed granite is frequently used instead of sand in cement sidewalk construction; but granite frequently contains mica, hornblende, and feldspar which render it unsuitable for this kind of work.
However, as a rule the physical condition of the sand is of more importance than its chemical composition.
114Z). Sharpness. Sharp sand, i.e., sand with angular grains, is preferred to that with rounded grains because (1) the angular grains are rougher and therefore the cement will adhere better; and (2) the angular grains offer greater resistance to moving one on the other under compression. On the other hand, the sharper the sand the greater the proportion of the interstices between the grains (compare line 4 of Table 10^, page 79i, with the preceding lines of the table) ; and consequently the greater the amount of cement required to produce a given strength or density. But a high degree of sharpness is more important than a small per cent, of voids.
The sharpness of sand can be determined approximately by rubbing a few grains in the hand, or by crushing it near the ear and noting if a grating sound is produced; but an examination through a small lens is better. Sharp sand is often difficult to obtain, and the requirement that " the sand shall be sharp" is practically a dead letter in most specifications.
ART. 1.] CLEANKESS. 79C
114c. Cleanness. Clean sand is necessary for the strongest mortar, since an envelop of loam or organic matter aboat the sand grains will prevent the adherence of the cement. The cleanness of sand may be judged by pressing it together in the hand while it is damp; if the sand sticks together when the pressure is removed, it is entirely unfit for mortar purposes. The cleanness may also be tested by rubbing a little of the dry sand in the palm of the hand; if the hand is nearly or quite clean after throwing the sand out, it is probably clean enough for mortar. The cleanness of the sand may be tested quantitatively by agitating a quantity of sand with water in a graduated glass flask; after allowing the mixture to settle, the amount of precipitate and of sand may be read from the graduation. Care should be taken that the precipitate has fully settled, since it will condense considerably after its upper surface is clearly marked.
Sand is sometimes washed. This may be done by placing it on a wire screen and playing upon it with a hose; or by placing it in an inclined revolving screen and drenching with water. When only comparatively small quantities of clean sand are required, it can be washed by shoveling into the upper end of an inclined V-shaped trough and playing upon it with a hose, the clay and lighter organic matter floating away and leaving the clean sand in the lower portion of the trough, from which it can be drawn off by removing for a short time plugs in the sides of the trough. Sand can be washed fairly clean by this method at an expense of about 10 cents per cubic yard exclusive of the cost of the water. For a sketch and description of an elaborate machine for washing sand by paddles revolving in a box, see Engineering Xe^vs^ vol. xli. page 111 (Feb. 16, 1899). By this method the cost of thoroughly washing dirty sand is about 15 cents per cubic yard.
Although it is customary to require that only clean sand shall be used in making mortar, a small quantity of very finely powdered clay will not materially decrease the strength of the mortar. In some instances clay to the amount of 10 per cent, of the sand seems not to decrease the strength of the mortar.* Mortar containmg ■tonsiderable clay is much more dense, plastic, and water-tight; and IS occasionally convenient for plastering surfaces and stopping leaky joints. Such mortar is not affected by the presence of water.
* Report of Chief of Engineers, U. S. A., 1894, pp. 3001-10; and Trans. Amer. Sor*. of C. E., vol. xiv. p. 164.
79d SAND. [chap. ma.
Ill eugiaeering literature but few definite specifications for the cleanness of sand can be found, a diligent search revealing only the following: For bridge work on the New York Central and Hudson Eiver E. E., the specifications required that the sand shall be so clean as not to soil white paper when rubbed on it. For the retain- ing walls on the Chicago Sanitary Canal, the suspended matter when shaken with water was limited to 0.5 per cent. For the dam on the Monongahela Eiver, built under the direction of the U. S. A. engineers, the suspended matter was limited to 1 per cent. For the dam at Portage, N. Y., built by the State Engineer, the " aggregate of the impurities " was limited to 5 to 8 per cent. The contamination permissible in any particular case depends upon the cleanness of the sand available and upon the difficulty of obtaining perfectly clean sand. Sand employed in masonry con- struction frequently contains 5, and sometimes 10, per cent, of suspended matter.
114fZ. Fineness. Coarse sand is preferable to fine, since (1) the former has less surface to be covered and hence requires less cement; and (2) coarse sand requires less labor to fill the interstices with the cement. The sand should be screened to remove the pebbles, the fineness of the screen depending upon the kind of work in which the mortar is to be used. The coarser the sand the better, even if it may properly be designated fine gravel, provided the diameter of the largest pebble is not too nearly equal to the thickness of the mortar joint.
Table lOe gives the results of a series of experiments to deter- mine the effect of the size of grains of sand upon the tensile strength of cement mortar. The briquettes were all made at the same time by the same person from the same cement and sand, the only difference being in the fineness of the sand. The table clearly shows that coarse sand is better than fine. Notice that the results in line 4 of the table are larger than those in line 3. This is probably due to the fact that the sand for line 4 has a greater range of sizes and consequently fewer voids. If this explanation is true, then since the sand in each line of the lower half of the table has greater variety of sizes than those in the upper half, the coarse sand is relatively better than appears from Table lOe.
Table 10/ shows the fineness of natural sands employed in actual construction; and as the sands were to all appearances of the same character, this table also shows at least approximately the
ART. 1.]
FINENESS.
79e
TABLE lOe.
Effect of Fineness of Sand upon the Tensile Stkength of 1 : 2 Cement Mortak.
|
Ref. No. |
Sand caught between the two sieves stated BELOW. |
Tensile Strength |
, IN POUNDS PER SQUARE INCH, AFTER |
|||
|
7 Days. |
IMo. |
3 Mos. |
6 Mos. |
12 Mos. |
||
|
1 |
No. 4 and No. 8 |
243 |
442 |
539 |
470 |
665 |
|
2 |
" 8 " " 16 |
269 |
345 |
473 |
512 |
572 |
|
3 |
" 16 " " 20 |
186 |
250 |
313 |
397 |
396 |
|
4 |
" 20 " " 30 |
211 |
281 |
322 |
402 |
440 |
|
5 |
" 30 " " 50 |
149 |
205 |
238 |
275 |
318 |
|
6 |
" 50 " " 75 |
122 |
214 |
260 |
275 |
308 |
|
7 |
" 75 " " 100 |
98 |
153 |
211 |
208 |
253 |
|
8 |
Passing No. 100 |
98 |
155 |
161 |
229 |
271 |
TABLE 10/.
Tensile Strength of a 1 : 3 Cement Mortar with Natural Sands differing chiefly in Fineness.
|
Fineness. |
||||||||||
|
Ref. No. |
Per Cent., by |
weight, caught |
on Sieve |
No. |
Per Cent PASSING No. 100. |
|||||
|
4 |
8 |
16 |
20 |
30 |
50 |
75 |
100 |
5 2 z o |
||
|
1 |
0 |
26 |
21 |
16 |
11 |
9 |
8 |
7 |
2 |
700 |
|
2 |
0 |
29 |
29 |
13 |
10 |
12 |
5 |
1 |
447 |
|
|
3 |
0 |
22 |
21 |
11 |
17 |
20 |
8 |
1 |
370 |
|
|
4 |
0 |
13 |
15 |
10 |
19 |
33 |
6 |
1 |
341 |
|
|
5 |
0 |
9 |
10 |
6 |
11 |
45 |
15 |
2 |
332 |
|
|
6 |
0 |
13 |
15 |
7 |
8 |
38 |
15 |
4 |
^ |
309 |
|
7 |
0 |
0 |
0 |
0 |
1 |
6 |
69 |
23 |
2 |
246 |
|
8 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
6 |
94 |
200 |
|
9 |
0 |
0 |
0 |
2 |
3 |
15 |
45 |
30 |
5 |
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79/ SAND. [chap. uia.
effect of fineness upon tensile strength. This table agrees with the preceding in showing that the coarser sand makes the stronger mortar. This conclusion is perfectly general.
If the voids are filled with cement, uniform coarse grains give greater strength than coarse and fine mixed ; or, in other words, for rich mortar coarse grains are more important than small voids. But if the voids are not filled, then coarse and fine sand mixed give greater strength than uniform coarse grains; or, in other words, for lean mortar a small proportion of voids is more important than coarse grains.*
As a rale, the sand ordinarily employed in making cement mortar is mucli too fine to give maximum strength or to permit the use of a minimum amount of cement. For example, the sands in lines 13 and 14 of Table 10^ (page 79i) are much used in actual work, and have approximately the same degree of fineness as the sands in the last three lines of Table 10/, which give a much weaker mortar than the preceding sands of Table 10/
114e. Specifications seldom contain any numerical requirement for the fineness of the sand. The two following are all that can be found. For the retaining- wall masonry on the Chicago Sanitary Canal the requirements were that not more than 50 per cen^ shall pass a No. 50 sieve, and not more than 12 per cent, shall pass a No. 80 sieve. For the Portage Dam on the Genesee Kiver, built by the New York State Engineer, the specifications were that at least 75 per cent, should pass a No. 20 sieve and be caught on a No. 40.
The fineness of the sand employed in several noted works is as follows, the larger figures being the number of the sieve, and the smaller figures preceding the number of a sieve being the per cent, retained by that sieve, and the small number after the last sieve number being the per cent, passing that sieve: Poe Lock, St. Mary's Fall Canal, ^ 20 '' 30 ^ 40 *'; concrete for pavement foundations in the City of Washington, D. C, » 3 ' G « 8 '^ 10 ^ 30 '^ 40^60^80^; Genesee (N. Y.) Storage Dam, "20*30^50^ 100 *; Rough River (Ky.) Improvement, " 20 " 30 ^^ 50 '^; St. Regis sand, Soulanges Canal, Canada, ^^ 20 -^^ 30 " 50 " ; Grand Coteau
* Report of Chief of Engineers, U. S. A., 1896, p. 2862, or Jour. West. Soe. of Engrs., vol. ii. p. 519 ; and Report of Operations of the Engineering Department of the District of Columbia, 1896, p. 195.
ART. 1.] VOIDS. 79^
sand,* Soulanges Canal, Canada, " 20 '" 30 ^ 50 ^. Tables 10/ and 10^ show the fineness of a number of natural sands employed in actual work,
114/. Voids. The smaller the proportion of voids, i.e., the interstices between the grains of the sand, the less the amount of cement required, and consequently the more economical the saud.
The proportion of voids may be determined by filling a vessel with sand and then determining the amount of water that can be put into the vessel with the sand. This quantity of water divided by the amount of water alone which the vessel will contain is the proportion of voids in the sand. The quantities of water as above may be determined by volumes or by weight. The proportion of voids may be determined for the sand loose or rammed, the latter being the more appropriate, since the mortar is either compressed or rammed when used. In either case it is more accurate to drop the sand through the water than to pour the water upon the sand, since with the latter method it is difficult to eliminate the air- bubbles, — particularly if the sand be first rammed. If the sand is dirty and the water is poured upon it, there is liability of the clay's being washed down and puddling a stratum Avhich will prevent the water penetrating to the bottom. If the bubbles are not excluded, or if the water does not penetrate to the bottom, the result obtained is less than the true proportion of voids. Again, if the sand is dropped through a considerable depth of water, there is liability that the sand may become separated into strata having a single size of grains in each, in which case the voids will be greater than if the several sizes were thoroughly mixed.
The per cent, of voids varies with the moisture of the sand. A small per cent, of moisture has a surprising effect upon the volume and consequently upon the per cent, of voids. For example, fine sand containing 2 per cent, of moisture uniformly distributed has nearly 20 per cent, greater volume than the same sand when perfectly dry. This effect of moisture increases with the fineness of the sand and decreases with the amount of water present.
114^. Table 10^7, page 79^, shows the voids of a number of both artificial and natural sands. An examination of the table shows
* A 1 to 2 mortar ■with this sand was only 79 per cent, as strong as the pre- ceding; and with a 1 to 3 mortar only 71 per cent. — Trans. Can. Soc. of C. E., vol. ix. p. 297.
79A SAND. [chap. Ilia.
that the voids of natural sand when rammed vary from 30 to 37 per cent. Sands Nos. 10, 11, and 12 are very good; but Xos. 13 and 14 are very poor. All five are frequently employed in actual work. Compare the fineness of these sands with those in Table 10/, page 79e.
114/i. The following observations may be useful in investigating the relative merits of different sands:
The proportion of voids is independent of the size of the grains, but depends upon the gradation of the sizes; and varies with the form of the grains and the roughness of the surface. A mass of perfectly smooth spheres of uniform size would have the same proportion of voids, whether the spheres be large or small. A mass of perfectly smooth spheres packed as closely as possible would have 26 per cent, of voids; but if the sj^heres are packed as loosely as possible the voids would be 48 per cent. A promiscuous mass of bird-shot has about 36 per cent, of voids. The difference between this and the theoretical minimum per cent, for perfectly smooth spheres is due to the variation in size, to roughness of the surface, and to not securing in all parts of the mass the arrangement of the shot necessary for minimum voids. German standard sand has grains nearly spherical and nearly uniform in size, having slightly rough surface, and has 41 per cent, voids loose (see line 2, Table 10^). The difference in the per cent, of voids between this sand and a mass of spheres uniform in size and perfectly spherical is due to irregularities in form and to roughness of surface of the sand grains, and to not securing the arrangement of the grains necessary for minimum voids. Crushed stone retained between the same sieves as German standard sand has 55 per cent, of voids (see lines 1 to 3 of Table 10^), the excess of this over German standard sand being due to the rough surfaces and sharp corners preventing the grains from fitting closely together.
If the mass consists of a mixture of two sizes such that the smaller grains can occupy the voids between the larger, then the proportion of voids may be very much smaller than with a single size of grains. For this reason a mixture of two grades of sand of widely different sizes has a smaller per cent, of voids than any one size alone, — compare lines 1 to 9 with the remainder of Table 10^^'.
The best sand is that which has grains of several sizes such tliat the smaller grains fit into the voids of the larger, the j)roportion of any particular size being only sufficient to fill the voids between
ART. 1.1
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the grains of the next larger size. If the grains are spherical and the diameter of the smaller is about one fifth of the diameter of the larger, the smaller grains will just fit into the interstice between the larger ones. The smaller the voids the greater the economy, and the denser and stronger the mortar.
The finer the sand the more nearly uniform the size of the grains, and consequently the greater the proportion of voids. Also the finer the sand the less sharp it is, and consequently the greater the surface to be covered. Therefore a coarse sand is to be preferred to a very fine one — see Tables lOe and 10/, page ?9e. Further, the advantage of coarse sand over fine increases as the proportion of cement decreases, since with the smaller proportions of cement the Toids are not filled.
114?'. Conclusion. An examination of the preceding data shows that very fine sand makes a much weaker mortar than coarse sand, and also that natural sands vary considerably in the proportion of voids and consequently differ in the amount of cement required to produce any particular strength. Therefore before adopting a sand for a work of any considerable magnitude, all available sands should be carefully examined with reference to (1) their effects upon the strength of the mortar, (2) their per cent, of voids or the amount of cement required with each, and (3) their cost. If mortar of any particular strength is desired, the proportion of cement should be adjusted according to the fineness and voids of the best available sand.
114/. Stone Sceeenings. The finer particles screened out of crushed stone are sometimes used instead of sand. For the physical characteristics of stone screenings see Nos. 16 and 17, page 7 9 1.
Experiments show that sandstone screenings give a slightly stronger mortar than natural sand, probably because of the greater sharpness of the grains. Crushed limestone usually makes a con- siderably stronger mortar, in both tension and compression, than natural sand, and this difference seems to increase with the age of the mortar.* Part of the greater strength is unquestionably due to the greater sharpness of the limestone screenings, and the part
* Annual Report of Chief of Engineers, U. S. A., 1893, Part 3, p. 3015 ; do. 1894, Part 4, p. 2321; do. 1895, Part 4, p. 2953; Jour. West. Soc. of Engrs., vol. ii, pp. 394 and 400.
ART. 2.] GRAVEL. 79^
that increases with the age of the mortar seems to be due to some ■chemical action between the limestone and the cement.
114^-. Cost and Weight of Sand. The price of reasonably good sand varies from 40 cents to 81. GO per yard, according to locality.
Sand is sometimes sold by the ton. It weighs, when dry, from 80 to 115 pounds per cubic foot (see Table 10^^, page 79t), or about 1 to 1^ tons per cubic yard.
Art. 2. Gravel and Broken Stone.
115. The term gravel is sometimes used as meaning a mixture of coarse pebbles and sand, and sometimes as meaning pebbles with- out sand. In this volume, gravel will be understood as a mixture of coarse pebbles and sand.
115r/. Gravel and broken stone are mixed with cement mortar to make an artificial stone called concrete (Art. 2, Chap. IV). The quality of the concrete varies greatly with the condition of the gravel or broken stone, but unfortunately too little attention is given to the character of this component.
1155. Gkavel. To be suitable for use in making concrete, gravel should be clean, and it should be composed of durable minerals, and the size of the pebbles and grains should be such as to give minimum voids.
The investigation of the suitability of gravel for use in concrete is essentially the same as that of sand, which has been fully con- sidered in the preceding article.
The physical characteristics of pebbles and gravel are given near the foot of Table lOh, page 80. Judging from the little data that •can be found in engineering literature and from all the information gathered by an extensive correspondence, gravels No. 16 and No. 17 of the table are representative of the gravels employed in actual work.
Concerning No. 18 notice that 65 per cent, passed a No. 5 screen ; and therefore this mixture could more properly be called gravelly sand. If one fifth of the material passing the No. 5 sieve be omitted, the voids of the remainder will be only 15 per cent, when rammed ; in other words, if one-tenth of this gravel were sifted on a No. 5 sieve and tliat portion I'etained on the sieve were mixed with the remainder of the original, the voids would be reduced to 15 per cent., which would improve the quality of the
791 BROKEN STONE. [CHAP. lUa.
gravel for making concrete. This is a valuable hint as to the pos- sible advantage of sifting even a portion of the gravel.
115c. Broken Stone. Any hard and durable stone is suitable for use in making concrete. It is usual to specify that the stone for concrete shall be broken to pass, every way, through a 2-inch ring, although it is sometimes broken to pass a 1-inch ring. The stone should be broken small enough to be conveniently handled and easily incorporated with the mortar. The finer the stone is broken the greater its cost, and the greater the surface to be coated ; and consequently the greater the amount of cement required. Approximately cubical pieces are preferable to long, thin, splintery fragments, since the latter are liable to break under pressure or while being rammed into place, and thus leave two uncemented surfaces.
115d. Voids. The proportion of voids, i.e., interstices between the fragments, may be determined in either of two ways as follows :
1. The voids may be found by filling a vessel with the aggregate, and then pouring in water until the vessel is full. The amount of water required to fill the voids divided by the amount of water alone the vessel will contain is the proportion of voids in the aggregate. The amount of water in each case may be determined by weight or by volume.
For some precautions applicable in this case, particularly in determining the voids of broken stone containing considerable fine material, see § 114/. If the material is porous, it is best to wet it, so as to determine the voids exterior to the fragments. The water absorbed by the material should not be included in the voids, since when the concrete is mixed the aggregate is usually dampened, particularly if it is porous. Of course in wetting the aggregate before determining the voids no loose water should remain in the pile. The voids may be determined for the material either loose or compacted. The proportion of the voids is found to determine the amount of mortar required to fill the voids of the concrete in place ; and therefore it is better to determine the voids in the com- pacted mass, since the concrete is usually rammed when laid. The compacting may be done by shaking or by ramming, the latter being the better since it more nearly agrees with the conditions under which the concrete is used, and further since in compacting by shaking the smaller pieces work to the bottom and the larger to the top, which separation increases the voids.
ART. 2.] VOIDS. 79w>
This method usually gives results slightly too small, owing to the difficulty of excluding all the air-bubbles. However, a high degree of accuracy can not be expected, since the material is neither uniform in composition nor uniformly mixed.
2. To find the voids determine the specific gravity of a frag- ment of the material (§ 7) , and from that the weight of a unit of volume of the solid; and also weigh a unit of volume of the aggre- gate. The difference between these weights divided by the first gives the proportion of voids.
115e. Table lOA, page 80, shows the per cent, of voids in various grades of broken stones used in making concrete.
The per cent, of voids in broken stone varies with the hardness of the stone, the form of the fragments, and the relative propor- tions of the several sizes present. The last is the most important. If broken stone jDassing a 3^-inch ring and not a ^-inch screen be separated into three sizes, any one size will give from 52 to 54 per cent, of voids loose, while equal parts of any two of the three sizes will give 48 to 50 j)er cent., and a mixture in which the volume of the smallest size is equal to the sum of the other two gives a trifle less than 48 per cent. Notice, however, that un- screened crushed stone has only 32 to 35 per cent, voids — see lines 7 and 11 of Table lOh. This is a very excellent reason for not screening the broken stone to be used in making concrete.
A mass of pebbles has only about three fourths as many voids as a mass of broken etone having pieces retained between the same screens. Notice, however, that gravel, i.e. pebbles and sand, has a less proportion of voids than pebbles alone.
115/. Cost and Weight. The cost of breaking stone for con- crete varies from 50 to 75 cents per cubic yard according to kind of stone and size of plant.* The original cost of the stone and transportation expenses are too variable to attempt to generalize. Ordinarily the cost of broken stone is not more than 11.50 to $2.00 per cubic yard f. o. b. cars at destination.
The weight of broken stone varies from 85 to 120 lbs. per cubic foot (see Table lOh, page 80) ; or about 2200 to 3200 pounds per cubic yard.
* For additional datii, see Supplemental Notes, No. 5, p. 546.
80
BROKEN STONE.
[chap. Ilia.
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PART II.
METHODS OF PREPAKING AND USING THE MATERIALS.
CHAPTEE IV. MORTAR, CONCRETE, AND ARTIFICIAL STONE.
Art. 1. Mortar.
116. Mortar is a mixture of the paste of cement or lime with Band. In common mortar, the cementing snbstance is ordinary lime; in hydraulic mortar, it is hydraulic cement.
117. Common Lime Mortar. Mortar made of the paste of common or fat lime is extensively used on account of (1) its intrin- sic cheapness, (2) its great economic advantage owing to its great increase of volume in slaking, and (3) the simplicity attending the mixing of the mortar. On account of the augmentation of volume, the paste of fat lime shrinks in hardening, to such an extent that it can not be employed as mortar without a large dose of sand.
As a paste of common lime sets or hardens very slowly, even in the open air, unless it be subdivided into small particles or thin films, it is important that the volume of lime paste in common mortar should be but slightly in excess of what is sufficient to coat all the grains of sand and to fill the voids between them. If this limit be exceeded, the strength of the mortar will be impaired. With most sands the proper proportions will be from 2.5 to 3 volumes of sand to 1 volume of lime paste. Generally, if either less or more sand than this be used, the mortar will be injured, — in the former case from excess of lime paste, and in the latter from
81
82 MORTAR. [chap. IV.
porosity. Notice that the volume of the resulting mortar is about equal to the volume of the sand alone.
118. The ordinary method of slaking lime consists in placing the lumps in a layer 6 or 8 inches deep in either a water-tight box, or a basin formed in the sand to be used in mixing the mortar, and pouring upon the lumps a quantity of water 2^ to 3 times the volume of the lime.
This process is liable to great abuse at the hands of the work- men. They are apt either to use too much water, which reduces the slaked lime to a semi-fluid condition and thereby injures its binding qualities; or, not having used enough water in the first place, to seek to remedy the error by adding more after the slaking has well progressed and a portion of the lime is already reduced to powder, thus suddenly depressing the temperature and chilling the lime, which renders it granular and lumpy. It is also very im- portant that the lime should not be stirred while slaking. The essential point is to secure the reduction of all the lumps. Cover- ing the bed of lime with a tarpaulin or with a layer of sand retains the heat and accelerates the slaking. All the lime necessary for any required quantity of mortar should be slaked at least one day before it is incorporated with the sand.
After the lime is slaked the sand is spread evenly over the paste/ and the ingredients are thoroughly mixed with a shovel or hoe, a little water being added occasionally if the mortar is too stiff.
119. Mortar composed of common lime and sand is not fit for thick walls, because it depends upon the slow action of the atmos- phere for hardening it; and, being excluded from the air by the surrounding masonry, the mortar in the interior of the mass hardens only after the lapse of years, or perhaps never.* The mortar of cement, if of good quality, sets immediately ; and, as far as is known, continues forever to harden without contact with the air. Cement mortar is the only material whose strength increases with age. Owing to its not setting when excluded from the air, common lime mortar should never be used for masonry construction under water, or in soil that is constantly wet; and, owing to its weakness, it is unsuitable for structures requiring great strength, or
*Lime mortar taken from the walls of ancient buildings has been found to be only 50 to 80 per cent, saturated with carbonic acid after nearly 2,000 years of ex- posure. Lime mortar 2,000 years old has been found in subterranean vaults, in exactly the condition, except for a thin crust on top, of freshly mixed mortar.
AET. l.J METHODS OF PROPOKTIONING. 83
subject to shock. Its use iu engineering masonry has been aban- doned on all first-class railroads. Cement is so cheap that it could profitably be substituted for lime in the mortar for ordinary masonry.
120. Hydraulic Lime Mortar. With mortars of hydraulic lime the volume of sand sliould not be less than 1.8 times that of the lime paste, in order to secure the best results regardless of cost. The usual proportions are, however, for ordinary work, the same as in common mortars, care being taken to incorporate sufficient paste to coat all the grains of sand and to fill up the voids between them.
121. Hydraulic Cement Mortar. Hydraulic cement mortar hardens simultaneously and uniformly throughout the mass, and if the cement is good continues to gain in hardness with age, — the slow-setting cements for a longer time than the quick-setting. For the best results the cement paste should be just sufficient to coat the grains and fill the voids of the sand. More cement than this adds to the cost and weakens the mortar (see § 100). If the amount of cement is not sufficient to coat all the grains and fill the voids, the mortar will be weak and porous, and hence will not be durable. A dense, impervious mortar is particularly desirable for masonry exposed to sea-water, to exclude the water from the interior of the mass and prevent its chemical as well as physical action upon the cement.
122. Methods of Proportioning. In laboratory work the propor- tions of the cement and sand are uniformly determined by weigh- ing; but there is no uniform practice of measuring the proportions on the work. One of the three following methods is generally employed.
1. By Weight. The most accurate but least common method is to weigh the ingredients for each batch. This method is incon- venient in practice, and adds somewhat to the cost of the work; and therefore occasionally the weight of a unit of volume of the sand and of the cement is determined, and the relative volumes of the ingredients are fixed accordingly, the actual proportioning being done by volumes. Cement is bought and sold by weight, and hence it is very appropriate to proportion the mortar by weight.
2. Packed Cement and Loose Sa^id. A commercial barrel of cement is mixed with one or more barrels of loose sand, i.e., the proportioning is done by mixing one volume of packed cement with
84 MORTAR. [chap. IV.
one or more Yolames of loose sand. This method is frequently used. As far as the cement is concerned, it is as accurate as the first, since the weight and volume of a barrel of cement may readily be known when only whole barrels are used, — as is usually the case. Even though the cement is received in bags, the barrel of packed cement is still a convenient unit, for an integral number of bags, usually three or four, are equal in weight to a barrel. As far as the sand is concerned this method is not as accurate as the first. The weight of the sand is affected by the amount of moisture present; but a small amount of moisture affects the volume in a greater proportion than the weight. For example, the addition of 2 per cent, of water (by weight) thoroughly mixed with dry sand increases the volume of the sand nearly 20 per cent.* Therefore if the mortar is proportioned by volumes, damp sand will give a richer mortar than dry sand. The effect of moisture on the volume is greater the finer the sand, and decreases as the amount of moisture increases. Measuring the sand by volumes is inaccurate also owing to the packing of the saud.
Except for the inaccuracies in measuring the sand, this method gives practically the same results for Portland as the first method, since ordinarily a unit of volume of packed cement and of sand weighs substantially the same; viz., 100 pounds per cubic foot. Since natural cement when packed in barrels usually weighs about 75 pounds per cubic foot, a mortar of 1 part natural cement to 1 part sand by weight is equivalent to 1^ parts cement to 1 part sand by volumes of j^acked cement and loose sand.
3. Loose Cement and Loose Sajid. A volume of loose cement is mixed with one or more volumes of loose sand. The actual propor- tioning is usually done by emptying a bag or fractional part of a barrel of cement into a wheelbarrow, and filling one or more wheel- barrows equally full of sand. As far as the sand is concerned, this metiiod is as inaccurate as the second; and it is also subject to great variations owing to differences in specific gravity, fineness and packing of the cement. Even though inaccurate, it is very fre- quently employed. It is the most convenient method when the cement is shipped in bulk, — which is only rarely.
Occasionally the actual proportioning is done by throwing into
* Feret, Chief of Laboratory Fonts et Chauss^es, Id Engineering News, vol. xxvii. p. 310. For similar data see Eeport of Chief of Engineers, U. 8. A., 1895, p. 2935.
ART. 1.] MIXING THE MORTAR. 85
the mortar-box one shovelful of cement to one or more shovelfuls of sand. This is very crude, and should never be permitted.
Since a commercial barrel of Portland will make 1.1 to 1.4 barrels if measured loose, a mortar composed of 1 part Portland cement to 1 part sand, by weight, is equivalent to 0.7 to 0.8 parts cement to 1 part sand by volumes of loose cement and loose sand ; and a mortar composed of 1 part natural cement to 1 part sand, by weight, is equivalent to 0.50 to 0.T5 parts cement to 1 part of sand by volumes of loose cement and loose sand.
122^. For a tabular statement incidentally showing the relative amounts of cement required by the three methods of proportioning, see Table 11, page 88.
123. Proportions in Practice. The proportions commonly used in practice are : for Portland cement, 1 volume of cement to 2 or 3 volumes of sand; and for natural cement, 1 volume of cement to 1 or 2 volumes of sand. The specifications are usually defective in not defining which method is to be employed in proportioning. This is a matter of great importance. Compared with the second method of proportioning in § 129, the third requires for Portland only 0.7 to 0.8 as much cement, and for natural cement only 0.4 to 0.5 as much.
124. Mixing the Mortar. When the mortar is required in small quantities, as for use in ordinary masonry, it is mixed as follows : About half the sand to be used in a batch of mortar is spread evenly over the bed of the mortar-box, then the dry cement is spread evenly over the sand, and finally the remainder of the sand is spread on top. The sand and cement are then mixed with a hoe or by turning and re-turning with a shovel. The mixing can be done more economically with a shovel than with a hoe; but the effectiveness of the shovel varies greatly with the manner of using it. It is not sufficient to simply turn the mass; but the sand and cement should be allowed to run off from the shovel in such a manner as to thoroughly mix them. Owing to the difficulty of getting laborers to do this, the hoe is sometimes prescribed. If skillfully done, twice turning with a shovel will thoroughly mix the dry ingredients; although fonr turnings are sometimes specified, and occasionally as high as six (see § 2G0). It is very important that the sand and cement be thoroughly mixed. When thoroughly mixed it will have a uniform color.
The dampness of the sand is a matter of some importance. If
86 MOKTAR. [chap. IY.
the sand is very damp when it is mixed with the cement, suflBcient moisture may be given off to cause the cement to set partially, which may materially decrease its strength. This is particularly noticeable with quick-setting cements.
The dry mixture is then shoveled to one end of the box, and water is poured into the other. The sand and cement are then drawn down with a hoe, small quantities at a time, and mixed with water until enough has been added to make a stiif paste. The mortar should be vigorously worked to insure a uniform product. When the mortar is of the proper plasticity the hoe should be clean when drawn out of it, or at most but very little mortar should stick to the hoe.
Cements vary greatly in their capacity for water (see § 104), the naturals requiring more than the Portlands, and the fresh-ground more than the stale. An excess of water is better than a deficiency, particularly with a quick-setting cement, as its capacity for com- bining with water is very great; and farther an excess is better than a deficiency, owing to the possibility of the water evaporating before it has combined with the cement. On the other hand, an excess of water makes a porous and weak mortar. If the mortar is stiff, the brick or stone should be dampened before laying; else the brick will absorb the water from the mortar before it can set, and thus destroy the adherence of the mortar. In hot dry weather, the mortar in the box and also in the wall should be shielded from the direct rays of the sun.
When mortar is required in considerable quantities, as in making concrete, it is usually mixed by machinery (see § 156w).
125. Gkout. This is merely a thin or liquid mortar of lime or cement. The interior of a wall is sometimes laid up dry, and the grout, which is poured on top of the wall, is expected to find its way downwards and fill all voids, thus making a solid mass of the wall. G-rout should never be used when it can be avoided. If made thin, it is porous and weak; and if made thick, it fills only the upper portions of the wall. To get the greatest strength, the mortar should have only enough water to make a stiff paste — the less water the better.
126. Data for Estimates. The following will be found use- fiil ill estimating the amounts of the different ingredients necessary to i^roduce any required quantity of mortar:
Lime weighs about 230 pounds per barrel. One barrel of lime
ART. 1.] DATA FOR ESTIMATES. 87
will make about 2^ barrels (0.3 ca. yd.) of stiff lime paste. One barrel of lime paste and three barrels of sand will make about three barrels (0.4 cu. yd.) of good lime mortar. One barrel of unslaked lime will make about 6.75 barrels (0.95 cu. yd.) of 1 to 3 mortar.
Portland cement weighs 370 to 380 pounds per barrel net (see § 77, page 54). The capacity of a Portland cement barrel varies from 3.20 to 3.75 cu. ft., the average being 3.49* or practically 3.50 cu. ft. A barrel of Portland will make from 1.1 to 1.4 bar- rels if measured loose. A cubic foot of packed Portland cement (105 pounds) and about 0.33 cu. ft. of water will make 1 cu. ft. of stiff paste; and a cubic foot of loose cement (gently shaken down but not compressed) will make about 0.8 cu. ft. of stiff paste.
Natural cement weighs from 2G5 to 300 pounds per barrel net (see § 77, page 54). The capacity of a natural cement barrel varies from 3.37 to 3.80 cu. ft., the average being 3.52,* or practically 3.50 cu. ft. A barrel of natural cement will make from 1.33 to 1.50 barrels if measured loose. Volume for volume, natural cement will make about the same amount of paste as Portland; or a cubic foot of packed natural cement (75 pounds) and about 0.45 cu. ft. of water will make 1 cu. ft. of stiff paste, and a cubic foot of loose cement (gently shaken down, but not compressed) will maKe about 0.8 ou. ft. of stiff j^aste.
128. Quantities for a Yard of Mortar. Table 11, page 88, shows the approximate quantities of cement and sand required for a cubic yard of mortar by the three methods of proportioning described in § 122. The table is based upon actual tests made by mixing "d^ cubic feet of the several mortars; f but at best such data can be only approximate, since so much depends upon the specific gravity, fineness, compactness, etc., of the cement; upon the fine- ness, humidity, sharpness, compactness, etc., of the sand; and npon the amount of water used in mixing. The sand employed in deducing Table 11 contained 37 per cent, of voids when measured loose; and the plasticity of the mortar was such that moisture flushed to the surface when the mortar was struck with the back of the shovel used in mixing.
The volume of the resulting mortar is always les& than the sum
* The Technogeaph, University of Illinois, No, 11, p. 104. + By L. C. Sabin, Assistant U, S. Engineer — see Report of Chief of Engineers, U, S. A., 1894, p. 2326.
MORTAR.
[chap. IV.
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AKT. i.J
DATA FOE ESTIMATES.
«9
TABLE 12. Amount of Mortar required for a Cubic Yard of Masonry.
|
Ref. No |
Dbsckiption op Masonry. |
MORTAB, cu. yd. |
|
|
Min. |
Max. |
||
|
1 |
Ashlar, — 18" courses and ^" joints |
0.03 0.06 0.10 0.25 0.35 0.33 0.20 0.12 0.20 |
0 04 |
|
3 |
12" " " " " |
0.08 |
|
|
3 4 5 6 7 |
Brickwork,— standard size (§ 256) and \" joints " f" toi" " .... " " " r tor " •.-. Concrete— see Tables \Zd and 13e, pages 112^', 112/i. Rubble, — small, rough stones |
0.15 0.35 0.40 0.40 |
|
|
8 9 10 1 |
large stones, rough hammer- dressed Squared-stone masonry, — 18" courses and f" joints 12" " " " " .... |
0.30 0.15 0.25 |
of the volumes of the cement and sand, or of the paste and sand, because part of the paste enters the Toids of the sand; but the volume of the mortar is always greater than the sum of the volumes of the paste and the solids in the sand, because of imperfect mixing and also because the paste coats the grains of sand and thereby increases their size and consequently the volume of the interstices between them. This increase in volume varies with the dampness and compactness of the mortar. For example, the volume of a rather dry mortar with cement paste equal to the voids, when compacted enough to exclude great voids, was 126 per cent, of the sum of the volumes of the paste and solids of the sand; and the same mortar when rammed had a volume of 102 to 104 per cent. If the paste is more than equal to the voids, the per cent, of in- crease is less ; and if the paste is not equal to the voids, the per cent, of increase is more. The excess of the volume of the mortar over that of the sand increases with the fineness of the sand and with the amount of mortar used in mixing.
129. Mortar for a Yard of Masonry. Table 12, page 89, gives
90 MORTAR. [CHAP, IV.
data concerning the amount of mortar required per cubic yard for the different classes of masonry, extracted from succeeding pages of this volume; and are collected here for greater convenience in making estimates.
130. Strength of Mortae. The strength of mortar is dependent upon the strength of the cementing material, upon the strength of the sand, and upon the adhesion of the former to the latter. The kind and amount of strength required of mortar depends upon the kind and purpose of the masonry. If the blocks are large and well dressed, and if the masonry is subject to com- pression only, the mortar needs only hardness or the property of resisting compression; hard sharp grains of sand with comparatively little cementing material would satisfy this requirement fairly well. If the blocks are small and irregular, the mortar should have the capacity of adhering to the surfaces of the stones or bricks, so as to prevent their displacement; in this case a mortar rich in a good cementing material should be used. If the masonry is liable to be subject to lateral or oblique forces, the mortar should possess both adhesion and cohesion.
131. Tensile Strength. E'ig. 5 shows the effect of time upon the strength of various mortars. The diagram represents the average results of a great number of experiments made in connec- tion with actual practice. Eesults which were uniformly extremely high or low as compared with other experiments were excluded on the assumption that the difference was due to the method of mould- ing and testing. Since the individual values jilotted were them- selves means, there were no very erratic results, and consequently the lines are quite reliable. There were fewer experiments for the larger proportions of sand to cement, and hence the curves are less accurate the larger the proportion of sand.
The line for the strength of lime mortar probably represents the maximum value that can be obtained by exposing the mortar freely to the air in small briquettes. This line is not well determined.
Unusually hard-burned Portland cements when tested neat will show a greater strength than that given in the diagrams. Very fine cement when mixed with sand will show greater strength ■than that given by Fig. 5. Again, the diagram shows neat cement, both Portland and natural, stronger than any proportion of sand, while frequently neat cement mortar is not as strong as a mortar composed of one part sand and one part cement — particularly at
ART. 1.]
TENSILE STRENGTH.
91
the greater ages. However, notwithstanding these exceptions, it is believed that the results represent fair average practice. The proportions of sand to cement were determined by weight.
132. The results in Fig. 5 are tabulated in another form in Fig. 6, to show the effect of varying the proportions of the sand
100
Fig. 5. — Diagram showing Effect of Time ox Strength of Mortars.
and cement, and also to show the relative strength of natural and Portland cement mortars at difiereut ages. The curves of Fig. 6 are especially useful in discussing the question of the relative economy of Portland and natural cement (§ 13G). For example, assume that we desire to know the strength of a 1 to 2 natural cement mortar a year old, and also the proportions of a Portland cement mortar of equal strength. iVt the bottom of the lower
92
MORTAR.
[chap. IV.
right-hand diagram of Fig. 6 find the proportion of sand in the mortar, which in this case is 2; follow the corresponding line np nntil it intersects the " natural " line. The elevation of this in- tersection above the base, as read from the figure at the side of the diagram, is the strength of the specified mixture, which in this
60a 1 1 r- — r— 1 1 1 1 I : 1 . 1 1 1 1 ,600
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700 600 500 400 300 200 100
0 12 3 4 5 6 7
Parts ^and to I Part Cement by Weight
Fig. 6. — Diagram showing Relative Strength of Cement Mortars.
case is about 250 pounds per square inch. The second part of the problem then is to determine the proportions of a Portland cement mortar which will have a strength of 250 pounds per square inch. Find the 250 point on the scale at the side of the diagram, and imagine a horizontal line passing through this point and intersect-
AtCT. 1.] COMPRESSIVE STRENGTH. 93
ing the " Portland " line; from this point of intersection draw a ■vertical line to the base of the diagram, and this point of intersec- tion gives the required number of volumes of sand to one volume of cement, which in this case is 5.5. Therefore a 1 to 2 natural mortar a year old has a strength of 250 pounds per square inch, and is then equivalent to a 1 to 5.5 Portland mortar.
133. Compressive Strength. But few experiments have been made upon the compressive strength of mortar. An examination of the results of about sixty experiments made with the Watertown testing-machine seems to show that the compressive strength of mortar, as determined by testing cubes, is from 8 to 10 times the tensile strength of the same mortar at the same age. This ratio increases with the age of the mortar and with the proportion of sand. The standard German specifications require that the com- pressive strength of cement mortar shall be at least 10 times the tensile strength.
Data determined by submitting cu^es of mortar to a compressive stress are of little or no value as showing the strength of mortar when employed in thin layers, as in the joints of masonry. The strength per unit of bed area increases rapidly as the thickness of the test specimen decreases, but no experiments have ever been made to determine the law of this increase for mortar.
134. Adhesive Strength. Unfortunately very few experiments have been made on the adhesive strength of mortars, i.e., the power with which mortars stick to brick, stone, etc. It is com- monly assumed that, after the lapse of a moderate time, the adhesive and cohesive strengths of cement mortars are about equal, and tbat in old work the former exceeds the latter. Modern experiments, however, fail to establish the truth of this assumption, and indicate rather that the adhesion of mortar to brick or stone is much less, during the first few months, than its tensile strength ; and also that the relation between the adhesive strength and cohesive strength (the resistance of the mortar to pulling asunder) is very obscure. The adhesion of mortars to brick or stone varies greatly with the different varieties of these materials, and particu- larly with their porosity. The adhesion also varies with the quality of the cement, the character, grain, and quantity of the sand, the amount of water used in tempering, the amount of moisture in the stone or brick, and the age of the mortar. Some cements which exhibit high tensile strength give low values for adhesion; and con-
94
MORTAR.
[chap. IV.
TABLE 13. — Adhesive Stkength of Mortals.
|
o |
a a < |
Kind of Cement used. |
Materials Cemented to- gether. |
Average adhesive strength In pounds per square inch. |
, |
||||
|
i |
15 0 |
h 0" |
S 3 0) to 0 |
zi. ii |
Authority. |
||||
|
1 2 3 4 5 6 |
- |
Hard brick |
*23 *15 |
Robertson 1858 |
|||||
|
16 28 30 |
Sawed limest'ne Cut granite Folislied marble Bridgewater brick |
57 41 38 19 24.1 168 |
I.J.Mann 1883 |
||||||
|
|
II 11 II |
||||||||
|
Hydraulic lime Portland |
11 11 11 |
||||||||
|
7 8 9 10 11 12 13 14 15 16 17 |
+Brick |
21.0 102 117 |
18.7 38 53 9-15 5 25.5 45 73 *59 *30 12.3 12.0 |
15.3 20 26 |
13.2 9 16 |
||||
|
Prof. Warren.. '87 |
|||||||||
|
§ " |
|||||||||
|
Quicklime Lime and cement Hydraulic lime |
|||||||||
|
tBrick |
■■35J 213 |
' ' 30.4 105 146 |
|||||||
|
20.9 24 48 |
17.5 14 45 |
Dr. Bohme. . . .1883 |
|||||||
|
t " |
Prof. Warren.. '87 |
||||||||
|
§ " |
|||||||||
|
Quick-setting cement Slow-setting cement. |
Robertson 1858 |
||||||||
|
" |
Croton brick Fine-cut granite |
30.S 27.5 78 1197 IITl 1166 49 |
15.7 20.8 |
6.8 9.2 |
■5.2 7.9 |
Gen. GIllmore.'63 |
|||
|
18 |
42 48 56 9U 95 110 180 |
||||||||
|
19 20 21 22 |
I.J. Mann 1882 |
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|
Cut granite Polished marble Bridgewater brick |
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|
11 |
II II II |
||||||||
|
II |
|||||||||
|
,, |
[1 II 11 |
||||||||
|
23 |
Sandstone Staffordshire brick |
11 II 11 |
|||||||
|
24 |
*40 *36 *18 *5 46.9 |
||||||||
|
Building News,'8(y |
|||||||||
|
25 |
Gray stock brick Common soft '• Hard brick |
||||||||
|
26 |
11 11 it |
11 11 11 |
|||||||
|
27 |
Lime and pozzuolaua |
J. White 1832 |
|||||||
|
28 |
TTBrick |
68.8 |
Bauschinger..l873 |
||||||
|
29 |
T " |
24.2 '28.1 14.2 12.8 |
|||||||
|
30 |
11 |
t " |
54.0 41.9 |
56.9 38.9 |
.1 11 |
||||
|
31 |
Hydraulic lime |
+ " |
39.3 |
22.6 Dr. Bohme.... 1883 |
|||||
|
32 |
IT " |
Bauschinger..l873 |
|||||||
|
33 |
Hydraulic lime |
IT " |
|||||||
|
34 |
Brick |
♦83 *15 *40 •18 |
Rondelet 1831 |
||||||
|
35 |
|||||||||
|
36 |
11 |
Hard brick |
Robertson 1858 |
||||||
|
37 |
27U |
II |
Soft brick |
||||||
|
38 39 |
Portland Sawed slate |
1162 1155 1175 |
I.J. Mann....l88S |
||||||
|
40 |
Polished marble |
f( 11 11 |
|||||||
|
41 |
*8 24 |
J. White 1832 |
|||||||
|
42 |
320 Rnsfindalft |
Croton brick |
68 |
40 |
Gen.Gillmore 1863 |
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|
4S |
lyr |
Quicklime Good quicklime Ordinary hydraulic lime Good hydraulic lime |
♦21 ♦51 |
Vicat 1818 |
|||||
|
44 |
|||||||||
|
45 |
11 11 |
*85 *140 |
<i 11 |
||||||
|
46 |
11 II |
11 11 |
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|
47 |
Materiala in air |
45 78 96 48 40 126 |
70 99 44 63 70 47 29 • 83 62 |
Mallet 182» |
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48 |
|||||||||
|
49 |
Portland |
Gault-clay brick |
J. Grant .1871 |
||||||
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50 |
Stock brick in |
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51 |
Stock brick in |
11 ii |
|||||||
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52 |
Staf . blue brick |
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„ |
II II |
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|
S3 |
Staf. blue brick in wntpr |
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|
II II |
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S4 |
" Fareham red hriok in air_ |
1. « |
|||||||
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55 |
Fareham red |
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11 II |
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•Proportions of sand not given, but presumably about those indicated in headings of table.
+ Standard sand used in mixture. t Clean river-sand used in mixture.
i Crushed sandstone used in mixture.
I Coarse particles in cement sifted out before testing. T Fine river-sand used in mixture.
ART. 1.] COST OF MORTAR. 95
versely, cements which are apparently poor when tested for cohesion, show excellent adhesive qualities.
The table* on the preceding page gives all the reliable data known. A comparison of the table with the diagram on page 92 shows that the adhesion of a mortar is far less than its tensile strength at the same age, but fails to show any definite relation between the two. In the experiments by Dr. Bohme at the Eoyal Testing Laboratory at Berlin the mortar was made with standard quartz sand, and the tensile strength of the mortar and its adhesion to common brick were determined separately. By comparing the tensile and adhesive strengths at the same ages, it was found that the former was always about ten times greater than the latter when the mortar consisted of one part of cement to three or four parts of sand, and from six to eight times greater when the cement was used neat or with one or two parts of sand. In the experiments made by Prof. "Warren, of Sydney University, New South Wales, the tensile strength of neat Portland cement mortar was three and a half times its adhesion to brick. The result of twelve thousand special tests by Mr. Mann was that pure Portland cement of -425 pounds tensile and 5,640 pounds compressive strength per square inch has but 60 to 80 pounds adhesion to limestone, and that the ratio of tensile to adhesive strength varies from 5 to 1 to 9 to 1.
135. Cost of Mortar. Knowing the ]}Tice of the materials it is very easy, by the use of Table 11, page 88, to compute the cost of the ingredients required for a cubic yard of mortar. The expense for labor is quite variable, depending upon the distance the materials must be moved, the quantity mixed at a time, etc. As a rough approximation it may be assumed that a common laborer can mix 3 yards per day, at a cost of, say, 50 cents per cubic yard„ If the mixing is done by machinery, the cost may be as low as 25 cents per cubic yard. The cost of a cubic yard of mortar composed of 1 part Portland cement and 2 parts sand, both by weight is then about as follows :
Cement 2.80 bbls. (see page 88) @ $3.00 = $8.40
Sand 0. 78 cu. yd. (seepage 88) @ .50= .39
Labor, handling materials and mixing , . J day @ $1.50 = .50
Total cost of\ cubic yard of mortar = $9.39
♦Compiled by Emil Kuichling, for the report for 1888 of the Executive Board of the City of Rochester, N. Y.
96
MORTAR.
[chap. IV.
136. Natural vs. Portland Cement Mortar. It is sometimes a question whether Portland or natural cement should be used. If a quick-setting cement is required, then natural cement is to be preferred, since as a rule the natural cements are quicker setting, although there are many and marked exceptions to this rule. Other things being the same, a slow-setting cement is preferable, since
13
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P'^rts Sand toj Part Cement by We/ght
Fig. 7a.— Cost of Cement Mortar.
it is not so liable to set before reacliing its place in the wall. This is an important item, since with a quick-setting cement any slight delay may necessitate the throwing away of a boxful of mortar or the removal of a stone to scrape out the partially-set mortar.
Generally, however, this question should be decided upon economical grounds, which makes it a question of relative strength and relative prices. Tlie tensile strength of natural and Portland cement mortars is shown in Fig. G, jmge 92. The cost of mortar of various proportions of sand may be computed as in the preceding section; but as the cost of labor is uncertain and is substantially the same for both kinds of mortar, it is sufficient to deal with the cost of the materials only. Assuming Portland cement to cost $3 per barrel, natural 81 per barrel, and sand 50 cents per cubic yard, and using Table 11, j^age 88, the cost of the materials, in a cnbie yard of mortar is as in Fig. 7a.
ART. 1.] NATURAL TS. PORTLAND CEMENT MORTAR.
97
500
to c
Ssoo
«0 100
I
2 3 4 5 6 7 d 9 10 II 12 15 Cost of Forfar in Dollars per Cubic Yard
Fig. 7b. — Relative Economy of Natural and Portland Cements.
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Age of Mortar 6 Honths |
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5 60
50
40
30
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OIZ545670 fhrti Sanct to I fhrt Cement by V\^iqht
Fig. 7c. — Economic Proportion of Sand.
98 MORTAR. [chap. IV.
By plotting the strength of Portland and natural cement mortar 6 months old and the cost of a yard of mortar as given in Fig. 7a, Fig. It is obtained, which shows the relation between the strength at 6 months and the cost of the mortar made of the two kinds of cement. Notice that for any tensile strength under about 370 pounds per square inch, either natural or Portland cement may be used, but that the former is the cheaper. In other words, Fig. 1h shows that if a strength of about 370 pounds per square inch at 6 months is sufficient, natural cement is the cheaper. Nearly all carefully conducted tests of the strength of cement mortar 6 months old or over give a similar result, except that the above limit is usually between 300 and 350 pounds. A considerable change in prices does not materially alter the result, and hence the conclusion may be drawn that if a strength of 300 to 350 pounds per square inch at 6 months is sufficient, natural cement is more economical than Portland. Incidentally Fig. 7c, page 97, shows the same relation. However, in this connection it should not be forgotten that other considerations than strength and cost may govern the choice of a cement ; for example, uniformity of product, rapidity of set, and soundness are of equal or greater importance than strength and cost.
Mortar made of two brands of Portland or natural cement will differ considerably in economic values, and hence to be of the highest value the above comparison should be made between the most economical Portland and the most economical natural cement as determined by the method described in § lllh.
Short-time tests do not warrant any general conclusion as to the relative economy of natural and Portland cements, since the strength at short times varies greatly with the activity of the cement. For example, the two upper diagrams of Fig. 6, page 92, when plotted as in Fig. 1h show Portland to be the more economical, while other similar experiments show natural cement to be the more economical.
137. Economic Proportion of Sand. Fig. 7f, page 97, shows the ratio of strength to cost for different proportions of sand, for both Portland and natural cement ; in other words, Fig. 7c shows the tensile strength in pounds per square inch for each dollar of the cost of a cubic yard of mortar. For example, if a natural cement mortar at 6 months has a tensile strength of 280 pounds per square inch, and costs 82.95 per yard, the strength per dollar is: 280 -j-
ART. 1.] EFFECT OF RE-TEMPERING. 99
2.95 = 94.9 pounds per square inch. In this way Fig. 7c was constructed, using the cost of mortar as given in Fig. 7a and the strength as determined by L. C. Sabin in connection with the con- struction of the Poe lock on the St. Mary's Falls Canal.* Accord- ing to this diagram the most economic mortar, either natural or Portland, consists of 3 parts sand to 1 part cement, by weight.
A study of the results of other experiments shows that the above conclusions are not general. The maximum ratio as above is different for different ages for the same cement, and at the same age is different for different cements. The above ratio varies (1) with the activity of the cement, which determines the strength neat at different ages; (2) with the fineness, which determines the sand-carrying power of the cement; (3) with the fineness of the sand, which determines the surface to be covered by the cement; and (-4) with the cost of the cement and the sand. If the strength of any particular cement with the various proportions of sand is known for a particular age, and the price of the cement and sand also is known, the most economic proportion of sand can be com- puted as above. To determine the most economic mortar, the most economic cement should be selected as described in § 111^, and then be mixed with the most economical proportion of sand as above.
Strictly, the maximum ratio of strength to cost determined as above is not necessarily the most economical mortar. The work in hand may not require a mortar as strong as that giving the maxi- mum ratio of strength to cost, in which case a mortar having a smaller proiDortion of cement may be used; and similarly, if the work requires a mortar stronger than that giving the maximum ratio of strength and cost, then a mortar must be used which con- tains a greater proportion of cement.
138. Effect of Re-tempeking. Frequently, in practice, cement mortar which has taken an initial set, is re-mixed and used. Masons generally claim that re-tempering, i.e., adding water and re-mixing, is beneficial; while engineers and architects usually specify that mortar which has taken an initial set shall not be used.
Ee-tempering makes the mortar slightly less "short" or *' brash," that is, a little more plastic and easy to handle. Ke- tempering also increases the time of set, the increase being very
« Report of Chief of Engineers, U. S. A., 1893, page 3019, Table 4.
100 MORTAR. [chap. IV.
different for different cements. Bat on the other hand, re-temper- ing nsually weakens a cement mortar. A quick-setting natural cement sometimes loses 30 or 40 per cent, of its strength by being re-tempered after standing 20 minutes, and 70 or 80 per cent, by being re-tempered after standing 1 hour. With slow-setting cements, particularly Portlands, tbe loss by re-tempering immedi- ately after initial set (§ 84) is not material. A mortar which has been insufficiently worked is sometimes made appreciably stronger by re-tempering, the additional labor in re-mixing more than com- pensating for the loss caused by breaking the set.
The loss of strength by re-tempering is greater for quick-setting tban for slow-setting cement, and greater for neat than for sand mortar, and greater with fine sand than with coarse. The loss increases with the amount of set. If mortar is to stand a consider- able time, the injury will be less if it is re-tempered several times during the interval than if it is allowed to stand undisturbed to the end of the time and is then re-mixed. Ee- tempered mortar shrinks mo'o in setting than ordinary mortar. This fact sometimes accounts for the cracks which frequently appear upon a troweled surface.
The only safe rule for practical work is to require the mortar to be thoroughly mixed, and then not permit any to be used which has taken an initial set (§ 84). This rule should be more strenuously insisted upon with natural than with Portland cements, and more with quick-setting than with slow-setting varieties.
139. Lime with Cement. Cement mortar before it begins to set has no cohesive or adhesive properties, and is what the mason calls " poor," " short," " brash "; and consequently is difficult to use. It will not stick to the edge of the brick or stone already laid sufficiently to give mortar with which to strike the joint. The addition of a small per cent, of lime paste makes the mortar " fat " or " rich," and more pleasant to work. The substitution of 10 to 20 per cent, of lime paste for an equal volume of the cement paste does not materially decrease the strength of the mortar, and frequently the addition of this amount of lime slightly increases its strength. In all cases the substitution of 10 to 20 per cent, of lime decreases the cost more rapidly than the strength, and hence is economical; but the substitution of more than about 20 per cent, decreases the strength more rapidly than the cost, and hence is not economical. The economy of using lime with cement is, of course,
ART. 1.] MORTAR IMPERVIOUS TO WATER. 101
greater with Portland than with natural cement owing to the greater cost of the former.
If the mortar is porous, i.e., if the voids of the sand are not filled with cement, the addition of lime will make the mortar more dense and plastic, and will also increase its strength and cost. The increase in strength is not proportional to the increase in cost, but the increased plasticity and density justify the increased cost — the former adds to the ease of using the mortar, and the latter to its durability.
The addition of lime does not materially affect the time of set, and usually slightly increases it.
It has lonor been an American practice to reinforce lime mortar by the addition of hydraulic cement. The mortar for the *' ordinary brickwork" of the United States public buildings is composed of "one fourth cement, one half sand, and one fourth lime." The cement adds somewhat to the strength of the mortar, but not proportionally to the increase in the cost of the mortar.
140. MoETAR Impervious to Water. IS^early every failure of masonry is due to the disintegration of the mortar in the outside of the joints. Ordinary mortar — either lime or cement — absorbs water freely, common lime mortar absorbing from 50 to 60 per cent, of its own weight, and the best Portland cement mortar from 10 to 20 per cent. ; and consequently they disintegrate under the action of frost. Mortar may be made practically non-absorbent by the addition of alum and potash soap. One per cent., by weight, of powdered alum is added to the dry cement and sand, and thoroughly mixed; and about one per cent, of any potash soap (ordinary soft-soap made from wood ashes is very good) is dissolved in the water used in making the mortar. The alum and soap com- bine, and form compounds of alumina and the fatty acids, wliich are insoluble in water. These compounds are not acted upon by the carbonic acid of the air, and add considerably to the early strength of the mortar, and somewhat to its ultimate strength.
With lime mortar, the alum and soaj) has a slight disadvantage in that the compounds which render the mortar impervious to water also prevent the air from coming in contact with the lime, and consequently prevent the setting of the mortar. On the other hand, the alum and soap compounds add considerably to both the early and the ultimate strength of the mortar.
This method of rendering mortar impervious is an application
102 MORTAE. [chap. IV.
of the principle of Sylvester's method of repelling moistnre from external walls by applying alam and soap washes alternately on the outside of the wall (see § 2G3), The same principle is applied in McMurtrie's artificial stone (see § 162). The alum and soap are easily used, and do not add greatly to the cost of the mortar. The mixture could be advantageously used in plastering, and in both cement and lime mortars of outside walls or masonry in damp places. It has been very successfully used in the plastering of cellar and basement walls. It should be employed in all mortar used for pointing (§ 204).
The addition of a small amount of very finely powdered clay (§ 114c) decreases the permeability of mortar; but since clay absorbs and parts with water with the changing seasons, the use of clay is not efficient in preventing disintegration by freezing and thawing.
141. Feeezing of Mortar. The freezing of mortar before it has set has two effects: (1) the low temperature retards the setting and hardening action; and (2) the expansive force of the freezing water tends to destroy the cohesive strength of the mortar.
142. Effect on Lime Mortar. The freezing of lime mortar retards the evaporation of the water, and consequently delays the combination of the lime with the carbonic gas of the atmosphere. The expansive action of the freezing water is not very serious upon lime mortar, since it hardens so slowly. Consequently lime mortar is not seriously injured by freezing, provided it remains frozen until fully set. Alternate freezing and thawing somewhat damages its adhesive and cohesive strength. However, even if the strength of the mortar were not materially affected by freezing and tliawing, it is not permissible to lay masonry during freezing weather; for example, if the mortar in a thin wall freezes before setting and afterwards thaws on one side only, the wall may settle injuriously.
When masonry is to be laid in lime mortar during freezing weather, frequently the mortar is mixed with a minimum of water and then thinned to the proper consistency by adding hot water just before using. This is undesirable practice (see § 118). When the very best results are sought, the brick or stone should be warmed — enough to thaw off any ice upon the surface is sufficient — before being laid. They may be warmed either by laying tliem on a furnace, or by suspending them over a slow fire, or by wetting with hot water, or by blowing steam through a hose against them.
143. Effect on Cement Mortar. Owing to the retardation of the
AET. 1.] EFFECT OF FREEZING, 103
low temperature, the setting and hardening may be so delayed that the water may be dried out of the mortar and not leave enough for the chemical action of hardening; and consequently the mortar will be Aveak and crumbly. This would be substantially the same as using mortar with a dry porous brick. Whether the water evapo- rates to an injurious extent or not depends upon the humidity of the air, the temperature of the mortar, the activity of the cement, and the extent of the exposed surface of the mortar. The mortar in the interior of the Avail is not likely to be injured by the loss of water while frozen; but the edges of the joints are often thus seri- ously injured. In the latter case the damage may be fully repaired by pointing the masonry (§ 204) after the mortar has fully set.
On the other hand when the cement has partially set, if the expansive force of the freezing water is greater than the cohesive strength of the mortar, then the bond of the mortar is broken, and on thawing out the mortar will crumble. Whether this action will take place or not will depend chiefly upon the strength and activity of the cement, upon the amount of free water present, and ui:)on the hardness at the time of freezing. The relative effects of these several elements is not known certainly; but it has been proven conclusively that for the best results the following precautions should be observed: 1. Use a quick-setting cement. 2. Make the mortar richer than for ordinary temperatures. 3. Use the mini- mum quantity of water in mixing the mortar. 4. Prevent freezing as long as possible.
There are various ways of preventing freezing: 1. Cover the masonry with tarpaulin, straw, manure, etc. 2. Warm the stone and the ingredients of the mortar. Heating the ingredients is not of much advantage, particularly with Portland cement. 3. Instead of trying to maintain a temperature above the freezing point of fresh water, add salt to the water to prevent its freezing. The usual rule for addmg salt is: "Dissolve 1 pound of salt in 18 gallons of water when the temperature is at 32° Fahr., and add 3 ounces of salt for every 3° of lower temperature." The above rule gives a slight excess of salt. The following rule is scientifically correct and easier remembered: " Add one per cent, of salt for each Fahrenheit degree below freezing." Apparently salt slightly decreases the strength of cement mortar setting in air, and slightly increases the strength when setting in water.*
* Report of Chief of Engineers, U. S. A., 1895, pp. 2963-74, 3015.
104 MORTAR, [chap. IV,
Alternate freezing and thawing is more damaging than contin- uous freezing, since with the former the bond may be repeatedly broken; and the damage due to successive disturbance increases with the number.
144. Practice has shown that Portland cement mortar of the usual proj^ortions laid in the ordinary way is not materially injured by alternate freezing or thawing, or by a temperature of 10° to 15° F. below freezing, except perhaps at the exposed edges of the joints. Under the same conditions natural cement mortar is liable to be materially damaged.
By the use of salt, even in less proportions than specified above, or by warming the materials, masonry may be safely laid with Portland at a temperature of 0° F. ; and the same may usually be done with natural cement, although it will ordinarily be necessary to re-point the masonry in the spring. Warming the materials is not as effective as using salt.
145. Change of Volume in Setting. The Committee of the American Society of Civil Engineers draw the following conclu- sions:* 1. Cement mortars hardening in air diminish in linear dimensions, at least to the end of twelve weeks, and in most cases progressively. 2. Cement mortars hardening in water increase in like manner, but to a less degree. 3. The contractions and expan- sions are greatest in neat cement mortars. 4. The quick-setting cements show greater expansions and contractions than the slow- setting cements. 5. The changes are less in mortars containing sand. 6. The changes are less in water than in air. 7. The con- traction at the end of twelve weeks is as follows: for neat cement mortar, 0.14 to 0.32 per cent.; for a mortar composed of 1 part cement and 1 part sand, 0.08 to 0.17 per cent. 8. The expansion at the end of twelve weeks is as follows: for neat cement, 0.04 to 0.25 per cent. ; for 1 part cement and 1 part sand, 0.0 to 0.08 per cent. 9. The contraction or expansion is essentially the same in all directions.
146. Elasticity, Compression, and Set of Mortar. For data on elasticity see page 14. The evidence is so conflicting that it is impossible to determine the coefficient of compression and of
* See the " Report of Progress of the Committee on the Compressive Strength of Cements and the Compression of Mortars and Settlement of Masonry," in the Transactions of that Society, vol. xvii. pp. 213-37 ; also a similar report in vol. xvi. pp. 717-32.
ARl-. L.j ELASTICITY, COMPRESSION, AND SET OF MOETAR. 105
set of mortar, even approximately. For much valuable data on this and related subjects, see the " Report of Progress of the Com- mittee on the Compressive Strength of Cements and the Compres- sion of Mortars and Settlement of Masonry," in the Transactions of the American Society of Civil Engineers, vol. xvi. pp. 717-32, vol. xvii. pp. 213-17, and also vol. xviii. pp. 2G-4-80. The several annual reports of tests made with the United States Government testing-machine at Watertown contain valuable data — particularly the report for 188-4, pp. 09-247 — bearing indirectly upon this and related subjects; but since some of the details of the experiments are wanting, and since the fundamental principles are not well enough understood to carry out intelligently a series of experiments. it is impossible to draw any valuable conclusions from the data.
106 CONCRETE. [chap. IV.
Art. 2. Concrete.
147. Concrete consists of mortar in which is embedded small pieces of some hard material. The mortar is often referred to as the matrix; and the embedded fragments, as the aggregate. Con- crete is a species of artificial stone. It is sometimes called beton, the French equivalent of concrete.
" Concrete is admirably adapted to a variety of most important uses. For foundations in damp and yielding soils and for subter- ranean and submarine masonry, under almost every combination of circumstances likely to be met with in practice, it is superior to brick masonry in strength, hardness, and durability; is more economical; and in some cases is a safe substitute for the best natural stone, while it is almost always preferable to the poorer varieties. For submarine masonry, concrete possesses the advan- tage that it can be laid, under certain precautions, without exhaust- ing the water and without the use of a diving-bell or submarine armor. On account of its continuity and its impermeability to water, it is an excellent material to form a substratum in soils infested with springs; for sewers and conduits; for basement and sustaining walls; for columns, piers, and abutments; for the hearting and backing of walls faced with bricks, rubble, or ashlar work; for pavements in areas, basements, sidewalks, and cellars; for the walls and floors of cisterns, vaults, etc. Groined and vaulted arches, and even entire bridges, dwelling-houses, and fac- tories, in single monolithic masses, with suitable ornamentation, have been constructed of this material alone."
The great value of concrete in all kinds of foundations is slowly coming to be appreciated. It enables the engineer to build his superstructure on a monolith as long, as wide, and as deep as he may think best, which cannot fail in parts, but, if rightly propor- .tioned, must go all together — if it fails at all.
148. The Mortar. The matrix may be either lime or cement -mortar, but is usually the latter. The term concrete is almost
universally understood to be cement 'mortar with pebbles or broken stone embedded in it. Lime mortar is wholly unfit for use in large masses of concrete since it does not set when excluded from the air (see § 119).
ART. 3.] THE AGGREGATE. 107
The cement mortar may be made as already described in Art. 1 preceding.
149. The Aggkegate. The aggregate may consist of small pieces of any hard material, as. pebbles, broken stone, broken brick, shells, slag, coke, etc. It is added to the mortar to reduce the cost, and within limits also adds to the strength of the concrete. Ordinarily either broken stone or gravel is used. Coke or blast- furnace slag is used when a light and not strong concrete is desired, as for the foundation of a pavement on a bridge or for the floors of a tall building. Of course a soft porous aggregate makes a weak concrete.
Whatever the aggregate it should be free from dust, loam, or any weal^ material. The pieces should be of graduated sizes, so that the smaller shall fit into the Toids between the larger. "When this condition is satisfied less cement will be required and conse- quently the cost of the concrete will be less, and at the same time its strength will be greater. Other things being equal, the rougher the surfaces of the fragments the better the cement adheres, and consequently the stronger the concrete.
150. It is sometimes specified that the broken stone to be used in making concrete shall be screened to practically an uniform size; bat this is unwise for three reasons; viz. : 1. With graded sizes the smaller pieces fit into the spaces between the larger, and conse- quently less mortar is required to fill the spaces between the fragments of the stone. Therefore the unscreened broken stone is more economical than screened broken stone. 2. A concrete con- taining the smaller fragments of broken stone is stronger than though they were replaced with cement and sand. Experiments show that sandstone screenings give a considerably stronger mortar than natural sand of equal fineness, and that limestone screenings make stronger mortar than sandstone screenings, the latter giving from 10 to 50 per cent, stronger mortar than natural sand.* Hence, reasoning by analogy, we may conclude that including the finer particles of broken stone will make a stronger concrete than replacing them with mortar made* of natural sand. Farther, experiments show that a concrete containing a considerable propor-
* Annual Report of Chief of Engineers, U. S. A., 1893, Part 3, p. 3015 ; do. 1894, Part 4, p. 2321 ; do. 1895, Part 4, p. 2953 ; Jour. West. Soc. of Eng'rs, vol. ii. pp. 394 and 400.
108 coxcRExr. [chap. iv.
tioa of broken stone is stronger tlian the mortar alone (see the second and third paragraphs of § 153). Since the mortar alone is -weaker than the concrete, the less the proportion of mortar the stronger the concrete, provided the voids of the aggregate are filled; and there- fore concrete made of broken stone of graded sizes is stronger than that made of practically one size of broken stone. 3. A single size of broken stone has a greater tendency to form arches while being rammed into place, than stone of graded sizes.
Therefore concrete made with screened stone is more expensive and more liable to arch in being tamped into place, and is less dense and weaker than concrete made with unscreened stone.
In short, screening the stone to nearly one size is not only a needless expense, bnt is also a positive detriment.
The dust should be removed, since it has no strength of itself and adds greatly to the surface to be coated, and also prevents the contact of the cement and the body of the broken stone. Particles of the size of sand grains may be allowed to remain if not too fine nor in excess. The small particles of broken stone should be removed if to do so reduces the proportion of voids (§§ 115^/, lloe).
151. Gravel vs. Broken Stone. Often there is debate as to the relative merits of gravel and broken stone as the aggregate for con- crete ; but when compared upon the same basis there is no room for doubt.
In the preceding section it was shown that finely crushed stone gave greater tensile and compressive strengths than equal propor- tions of sand; and hence reasoning by analogy, the conclusion is that concrete composed of broken stone is stronger than that con- taining an equal proportion of gravel. This element of strength is due to the fact that the cement adheres more closely to the rough surfaces of the angular fragments of broken stone than to the smooth surface of the rounded pebbles.
Again, part of the resistance of concrete to crushing is due to the frictional resistance of one piece of aggregate to moving on another; and consequently for this reason broken stone is better than gravel. It is well known that broken stone makes better macadam than gravel, since the rounded pebbles are more easily displaced than the angular fragments of broken stone. Concrete differs from macadam only in the use of a better binding material; and the greater the frictional resistance between the particles the stronger the mass or the less the cement required.
ART. 2.] THEORY OF THE PROPORTIONS. 109
A series of experiments* made by the Citj' of Washington, D, C, to determine the relative value of broken stone and gravel for concrete, which are summarized in § loTJ, page li2y, i;i\cs the following resalts:
Strength of Gravbl Concrete in terms of Broken Stone Concrete.
Concrete made with Natural Cement. Portland Cement.
38 per cent. 76 per cent.
91 " ••
119 " "
73 " "
108 " "
93 " "
|
Age of |
Concrete |
|
WHEN tested. |
|
|
10 |
days. |
|
45 |
" |
|
3 months. |
|
|
6 |
" |
|
1 |
year. |
96 43 83
Mean 68
Each result is the mean for two 1-foot cubes, excejot that the values for a year are the means for five cubes. Xotice that the gravel concrete is relatively weaker for the earlier ages, owing probably to the greater internal friction of the broken-stone concrete.
In a series of forty-eight French experiments,! the crushing strength of gravel concrete with Portland cement is only 79 per ■cent, as great as that of broken-stone concrete. The gravel had 40 per cent, of voids, while the broken stone had 47 per cent., which favored the gravel concrete (see § 154). The results of these tests are shown graphically in Fig. 8, page ll'2a.
152. Since frequently gravel is cheajDer than broken stone, a mixture of broken stone and gravel may make a more efficient con- crete than either alone, i. e., may give greater strength for the same cost, or give less cost for the same strength.
153. Theory of the Propoetions. The voids in the aggre- gate should always be filled witli mortar. If there is not enough mortar to fill the voids, the concrete will be weak and porous. On the other hand, more mortar than enough to fill the voids of the aggregate increases the cost of the concrete and also decreases its strength. The decrease in strength due to an excess of mortar is usually greater than would be produced by substituting the same amount of aggregate, since ordinarily the sand and the aggregate have approximately the same per cent, of voids, while the sand has the greater, -and also the smoother, surface.
* Report of Engineer Commissioner of the District of Columbia for 1897, p. 165. t Cements at Chaux Hydrauliques, E. Candlot, Paris, 1891, pp. 215, and 340-41.
]10
CONCRETE.
[chap. IV.
A correctly proportioned concrete is always stronger than the mortar alone. For example, Table 13a* shows that a concrete containing a considerable proportion of pebbles is stronger than the mortar alone — compare lines 2, 5, and 8 with the preceding line of each gronp, respectively. The results are for gravel concrete, and they would be more striking for broken-stone concrete, since the cement adheres better to broken stone than to either sand or gravel.
TABLE 13a. Relative Strength op Mortar and Gravel Conckete.
|
Portland Cement. |
Tested when CS Days old. |
||||
|
Rep. No. |
Proportions. |
Crusliing Ptienp;th. lUs. per sq. in. |
Strength of the |
||
|
Cement. |
Sand. |
Pebbles. |
Concrete in terms of that, of the Mortar. |
||
|
I |
1 |
2 |
0 |
2 158 |
100 per ceut. |
|
0 |
o |
2 783 |
129 " " |
||
|
3 |
5 |
2 414 |
12G " " |
||
|
4 |
1 |
3 |
0 |
1 40G |
100 per cent. |
|
5 |
5 |
1 661 |
114 " " |
||
|
6 |
6.5 |
1 534 |
109 " '• |
||
|
7 |
1 |
4 |
0 |
1068 |
100 per cent. |
|
8 |
5 |
1 291 |
121 " " |
||
|
9 |
8.5 |
1 221 |
114 " " |
The average strength of twenty-four cubes ranging from 3 to IG inches on a side, made under the direction of Gen. Q. A. Gill- more,! and composed of 1 volume of cement, 3 volumes of sand, and G volumes of broken stone, was 15 per cent, more than that of corresponding cubes made of the mortar alone. In another series of the same experiments, J the average strength of eight cubes of
*Dr. II. Dycberhoff, a Germau authority, as quoted iu " Der Portland Cement und seine Anwendungen im Bauwesen," p. 90.
f Notes on the Compressive Resistance of Freestones, Brick Piers, Hydraulic Cement, Mortar, and Concretes, Q. A. Gillmore. John Wiley & Sons, New York, 1888, pp. 137-40 and 143-^6.
J Ihid., pp. 141^2.
ART. 2.]
THEORY OF THE TROPORTIONS.
Ill
concrete composed of 1 part cement, 1^ parts sand, and 6 parts broken stone was 95 per cent, of that of corresponding cubes of the mortar alone, which is interesting as showing that a lean concrete is nearly as strong as a very rich mortar,
A correctly proportioned concrete is also stronger than either a richer or a leaner mixture — see Table 13/, page 112^.
154. For the strongest and densest concrete, the voids of the aggregate should be filled with a rich strong mortar; but if a cheaper concrete is desired, fill the voids of the aggregate with sand and add as much cement as the cost will justify. In other words, to make a cheap concrete, use as lean a mortar as the circumstances warrant, bat use enough of it to fill the voids of the aggregate. Sand is so cheap that there is no appreciable saving by omitting it; and the use of it makes the concrete more dense.
The strength of a concrete varies nearly with the amount and strength of the cement used, provided the mortar is not more than enough to fill the voids. Table 13b shows the strength of con- crete in terms of the cement employed. The data from which
TABLE 135. Relation between the Crushing Strength of Concrete and the Proportion of Cement. Mortar Equal to the Voids io the Aggregate.
|
Ref. No. |
Composition of Mortar. Volumes Loose. |
Proportion of Cement. |
Crushing Strength, Pounds per Square Inch. |
||||
|
Cement. |
Sand. |
Actual. |
Relative. 1.00 |
Actual. |
Theoretical. |
Relative. |
|
|
1 |
1 |
0.50 |
4,467 |
5,000 |
1.00 |
||
|
2 |
2 |
0.33 |
0.67 |
3,781 |
3,300 |
0.66 |
|
|
3 |
3 |
0.25 |
0.50 |
2,553 |
2,500 |
0.50 |
|
|
4 |
4 |
0.20 |
0.40 |
2,015 |
2,000 |
0.40 |
|
|
5 |
5 |
0.17 |
0.3S |
1.796 |
1.600 |
0.32 |
|
|
6 |
G |
0.14 |
0.28 ' |
1,:;;65 i 1.400 |
0.28 |
this table was made are the same as those suuimarized in Table 13/, page 1125-, The actual crushing strengths v^ere plotted, and it was found that they could be reasonably well represented by a right line passing through the origin of co-ordinates. The values for this average line are shown in next to the last column of Table 13h.
112a
CONCRETE.
[chap. IV.
These experiments seem to jirove that the strength of concrete varies as the quantity of cement, provided the voids are filled with mortar. The same conclusion is jiroved by the data summarized
Portland Cemeni -Barrels per Cubic Yard
Fig. 8. — Relation between the Strength of the Concrete and the Amount of Cement.
in Fig. 8. The diagram presents the results of forty-eiglit experi- ments on 4-inch cubes.* Each point represents two experiments, the age of the mortar in one being 7 days and in the other 28 days. The points with one circle around them represent the strength of broken-stone concrete, and the points with two circles gravel con- crete. Both the sand and the gravel employed in these experiments were very coarse, and consequently the amount of cement per cubic yard is unusually great.
155. When mortar is mixed with broken stone, the film of mortar surrounding each fragment increases the volume of the resulting concrete. Table 13c, page 112J, gives the result of fifteen experiments to determine this increase in volume. The mortar was
* Candlot's Cements et Chaux Hydrauliques, jjp. 3i0-il.
ART. 2.]
THEORY OF THE PROPORTIONS.
1126
moderately dry, and the concrete was fjiiite dry, moisture flushino- to the surface only after vigorous tamping. Tiie broken stone was Ko. 10 of Table lOh, page 80, and contained 28 per cent, of voids when rammed.
Line 4 of Table 13c shows that if the mortar is equal to the voids, the volume of the rammed concrete is 7^ P^r cent, more than the volume of the rammed broken stone alone. Possibly part of
TABLE 13c. Increase of Volume by Mixing Moktar with Broken Stone.
|
Ref. No. |
Volume of Mortar in terms of the Voids in the Broken Stone.* |
Volume of Rammed Concrete in terms of the Volume of Rammed Stone. |
Voids in the Rammed Concrete (while wet). |
|
1 |
70 per cent. |
105.0 per cent. |
15.3 per cent. |
|
2 |
80 " " |
105.5 •' " |
12.2 " " |
|
3 |
90 " " |
106.5 " " |
9.5 " " |
|
4 |
100 " " |
107.5 " " |
7.0 " " |
|
5 |
110 " " |
109.0 " " |
4.9 " " |
|
6 |
120 " " |
110.5 " " |
2.8 " " |
|
7 |
130 " " |
112.5 " " |
1.2 " " |
|
8 |
140 " " |
114.0 " " |
0.0 " " |
the increase of volume was due to imperfect mixing, although it was believed that the mass was perfectly mixed. The table also shows that the voids in this concrete are equal to 7 per cent, of its volume; in other words, even though the volume of the mortar is equal to the volume of the voids, the voids are not filled. Appar- ently the voids can be entirely filled with this grade of mortar only when the mortar is about 40 per cent, in excess of the voids.
The increase in volume in Table 13c may be regarded as the maximum, since the mortar was quite dry and the stone unscreened. With moderately wet mortar and the same stone, the increase in volume Avas only about half that in the table; and with moist mortar and stone ranging between 2 inches and 1 inch, there was no appreciable increase of volume. With pebbles the increase is onlv about two thirds that with broken stone of tlie same size. With fine gravel (Xo. 18, page 80) the per cent, of increase was considerably greater than in Table 13c; with mortar equal to 150 per cent, of the voids, it was possible to fill only about 5 to 7 per
112c CONCRETE. [CHAP. IV.
cent, of the yoids. The mortar used in Table 13c was 1 volume of cement to 3 volumes of sand, both measured loose; but with richer mortars the increase in volume was a little less, and with leaner mortars a little more. These differences are so small that they may be disregraded.
Notice that the voids in Table 13c are for the wet concrete. When the concrete has dried out the voids will be more; since ordinarily all the water employed in making the concrete does not enter into chemical combination with the cement, and consequently when the concrete dries out the space occupied by the free water is empty.
156. Methods of Determining the Proportions. There are two methods of fixing the proportions for a concrete; viz.: 1. adjust the proportions so that the voids of the aggregate shall be filled with mortar, and the voids of the sand with cement paste; or, 2, fix the proportions without reference to the voids in the materials. These two methods will be considered in order.
156a. With Reference to the Voids. To find the correct pro- portions for a concrete, first determine the per cent, of voids in the rammed aggregate (§ 115fZ). Next determine the voids in the sand. Then use that proportion of cement which will fill the voids of the sand with cement paste (see § 120). The amount of mortar to be used depends upon the per cent, of voids in the aggregate and the density desired in the concrete (see Table 13c, page 112J).
The details of the method of determining the amount of mortar and of cement will be illustrated by the following example. Assume the aggregate to be broken stone, unscreened except to remove the dust, containing 28 per cent, of voids when rammed (see No. 10, Table lOA, page 80). Also assume that a concrete of maximum density is desired; and that therefore the mortar should be equal to about 140 per cent, of the voids (see Table 13c, page 112Z*). The aggregate compacts 5 per cent, in ramming (No. 10, Table IQh), and therefore a yard of loose material will equal 0.95 of a yard rammed. Adding mortar equal to 140 per cent, of the voids increases the volume to about 114 percent. (Table 13c); and tliere- fore adding the mortar will increase the volume of the rammed aggregate to 0.95 X 1.14 = 1.08 cu. yd., which is the volume of concrete produced by a yard of loose aggregate. To produce a yard of concrete will therefore require 1 -4- 1.08 = 0.93 en. yd. of loose broken stone. Since the mortar is to be equal to 140 per cent, of
ART. 2.] METHODS OF DETERMINING THE PROPORTIONS. 112d
the voids, a yard of concrete will require 1.40 X 0.28 = 0.39 cu. yd. of mortar. Assume the rammed sand to contain 37 per cent, of voids (see Table 10^, page 79 i). Therefore to fill the voids of the sand with cement paste will require 37 per cent, as much packed cement as loose sand ; or in other words, the proportions of the mortar should be about 1 volume packed cement to 2^ vohnnes loose sand. Interpolating from Table 11, page 88, we see that to produce a yard of this mortar will require about 2.40 bbl. of Port- land cement and 0.79 cu. yd. of sand. Consequently a yard of the concrete will require 0.39 X 2.40 = 0.94 bbl. of Portland cement, and 0.39 X 0.79 = 0.31 cu. yd. of sand. The quantities for a cubic yard of the rammed concrete are: 0.94 bbl. of packed Port- land cement, 0.31 cu. yd. of loose sand, and 0.93 cu. yd. of loose broken stone; and since 1 bbl. = 0.13 cu. yd., the proportions are: 1 volume of packed Portland cement, 2^ volumes of loose sand, and 7^ volumes of loose broken stone.
156b. }yitliout Reference to ihe Voids. Usually the proportions of a concrete are fixed without any reference to the method to be employed in measuring the cement, and also without reference to the voids in the sand and in the aggregate. The proportions are usually stated in volumes, that of the cement being the unit. For example, a concrete is described as being 1 part cement, 2 parts sand, and 4 parts broken stone.
This method is inexact, in the first place, since it does not state the degree of compactness of the cement. If the unit of cement is a commercial barrel of packed cement, the resulting concrete will be much richer than if the cement were measured loose (see § 126). In the second place, this method, in name and usually in fact, takes no account of the proportion of voids in either tht sand or the aggregate. If the stone is screened to practically one size, it may have 45 to 50 per cent, of voids when rammed; but if it is unscreened except to remove the dust, it may have only 30 per cent, of voids (see Table lOA, page 80).
156c. To exj^lain the method of testing whether or not the voids are filled in a concrete described in the above form, take the com- mon proportions: 1 volume cement, 2 volumes sand, and 4 volumes broken stone. If the cement is measured by volumes loose, as is usually the case, 1 volume of dry cement will make about 0.8 of a volume of paste. If tlie sand is the best, it will probably have about 30 percent, of voids when rammed (see Table 10^, page 79t);
Il2e coiircRETE. [chap. IV.
and hence the 2 vohimes of sand will contain about 0.6 of a Yolume of voids. The cement is then 25 per cent, more than enough to fill the voids of the sand. The cement and sand when rammed will make 2 + (0.8 — 0.6) = 2.2 + volumes of mortar.* If the broken stone is unscreened, it will probably have about 30 per cent, voids when rammed (see Table lOh, page 80) ; and hence the 4 volames of stone will contain 1.2 volumes of voids. The excess of mortar is then 2.2 — 1.2 = 1.0 units, or 83 per cent, more than enough to fill the voids of the broken stone. The mortar and the broken stone will make 4 + (2.2 — 1.2) = 5.0 + volumes of rammed concrete. f
For the materials assumed, the preceding proportions are very uneconomical, since there is 25 per cent, more cement than the voids in the sand and 83 per cent, more mortar than the voids in the broken stone. The possible saving in cement may be computed as follows: 25 per cent, of the cement could be omitted iu making the mortar. The mortar would then be 2 volumes, of which 0.8 of a volume, or 40 per cent., is in excess of the voids in the aggre- gate. The omission of this surplus mortar is equivalent to omitting 0.40 X 0.75 = 30 per cent, of the original cement. The total surplus of cement is then 25 + 30 == 55 j^er cent. If the above proportions were intended to give a concrete of maximum density, then the mortar employed should be about 40 per cent, in excess of the void (§ 155). In this case, the surplus mortar would be (2.0 — 1.40 X 1.2) = 0.32 volumes, or 16 per cent, of the total mortar; and the surplus cement in this mortar would be (0.75x0.16) = 12 per cent. Therefore the total surplus cement is 25 + 12 = 37 per cent. Even in this case the proportions are uneconomical.
15Qd. The above example shows how extravagant the above proportions are with the best grades of sand and broken stone. If the sand lias 37| per cent, of voids and the broken stone 40 per cent., then with the preceding proportions there will be practically no surplus cement, and there will be an excess of mortar of about 25 per cent. In other words, with coarse sand and screened stone, the voids of the sand will be filled with cement paste, and the voids
* The mortar when rammed will make from 2 to 4 per cent, more volume than the sum of the sand and the excess of the paste (see the last piaragraph of § 128, page 87).
f The volume of the concrete will he slightly more than 5.0 units, since some sand will remain between the fragments of stone, and thereby increase the volume (see Table 13c, page 1126.)
ART. 2.] DATA FOU ESTIMATES. 113/
of the broken stone will be filled with mortar. However, it ia exceedingly nneconomical to use a very porous aggregate and attempt to make a very dense concrete.
The above comparisons show how unscientific it is to proportion concrete regardless of the condition of the materials to be used.
156e. Occasionally specifications state the quality of the mortar to be used, and require the mortar and the aggregate to be so pro- portioned that the mortar shall at least be equal to the voids in the aggregate. Under this method of procedure, to guard against lack of uniformity in the aggregate, imperfect mixing, and insufficient tamping, it is customary to require more than enough mortar to fill the voids, this excess varying from 0 to 50 per cent., but usually being from 15 to 25. Apparently 15 per cent, is frequently used in Germany.*
Xotice that this method is an approximation to that discussed in § 15G« preceding.
156/'. Data for Estimates. Table 13cl and Table 13e, pages 112^ and 112/i, give the quantities of cement, sand, and broken stone required to make a cubic yard of concrete, for the two methods of proportioning described in § 156a and § 1563, respectively. Each table gives the quantities for unscreened and also for screened broken stone; and Table 13f7 gives also the quantities of cement and gravel required for a cubic yard of concrete.
The barrel of cement in both tables is the commercial barrel of packed cement.
156^. Taile 13d is recommended for general use. The first line gives a concrete 'of the maximum density and maximum strength, i.e., tlie quantity of mortar is sufficient to fill the voids (see § 155); and the successive lines give concretes of decreasing density and strength. The third and subsequent lines give concretes containing mortar equal to the voids, the mortar in the third line being 1 to 3, in the fourth 1 to 4, etc.
The quantities were computed as described in § 156a, and were afterwards checked by making 8-inch cubes of concrete. While the results are only approximate for any particular case, it is believed that they represent average conditions with reasonable accuracy.
The quantities in the table are for stone uniform in quality, and
* Der Portland Cement und seine Anwendungen im Bauwesen, pp. 124 and 128.
n2g
CONCEETE.
[chap. IV.
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ART. 2.] INGREDIENTS FOR A YARD OF CONCRETE.
113/i
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il'Zl CONCRETE. [CHAP. IV,
for concrete thoroughly and vigoronsly rammed; and if it is desired certainly to secure the densest concrete, it might be wise to increase somewhat the cement and sand given in the first line of Table 13d. The per cent, of increase should vary with the circumstances of the case in hand (see § lo6e).
The proportions of the concretes can be determined by remem- bering that a barrel of cement is equal to 0.13 cu. yd. For example, for unscreened broken stone and Portland cement, the 0.0-4 bbl. of cement is equal to 0.12 cu. yd. ; and the 2:>roportions are: 1 volume of packed cement, 2.5 volumes of loose sand, and 7.5 volumes of loose unscreened broken stone. If it be assumed that a barrel of packed cement will make 1.25 barrels when measured loose (see § 126), the above proportions become: 1 volume loose cement, 2.0 volumes loose sand, and 6.0 volumes loose unscreened broken stone.
1567i. Table 13e is given for use in determining the ingredients required for a concrete designed in the ordinary way — see § loQb. The quantities were computed substantially as illustrated in 156c. This table is not as accurate as Table 13f/, and besides many of the proportions are uneconomical (see the second paragraph of § 156c).
156/. Proportions from Practice. While a statement of the proportions used in practice may be of interest, it can not be of any great value since it is impracticable, if not impossible, to describe fully the circumstances and limitations under which the work was done. Farther the specifications and records from which such data must be drawn are frequently very indefinite. It is believed that the following examples are as accurate as it is possible or practicable to make them, and also that they are representative of the best American practice.
For foundations for pavements: 1 volume oi natural cement, 2 volumes of sand, and 4 or 5, and occasionally 6, volumes of broken stone; or 1 volume of Portland cement, 3 volumes of sand, and 6 or 7 volumes of broken stone. Occasionally gravel is specified, and more rarely gravel and broken stone mixed.
For foundations and minor railroad work: 1 volume of natural cement, 2 volumes of sand, and 2 to 6, usually 4 or 5, parts of broken stone. See also pages 532 and 535.
For important bridge and tunnel Avork : 1 part of Portland cement, 3 parts of sand, and 4 or 5 parts of broken stone.
ART. 2.] PROPORTIONS FROM PRACTICE. 112/
For steel-grillage foundations : 1 part Portland cement, 1 part sand, and 2 parts broken stone.
For the ]\Ielan steel and concrete construction the usual pro- portions are: 1 volume of Portland cement, 2^ volumes of sand, 5 volumes of broken stone.
For the retaining walls on the Chicago Sanitary Canal : 1 part natural cement, 14^ parts sand, and 4 parts unscreened limestone.
For the dams, locks, etc., on the Illinois and Mississippi Canal: 1 volume of loose Portland cement, 8 volumes of gravel and broken stone; or 1 volume loose natural cement and 5 volumes gravel and broken stone.
For the Poe Lock of the St. Mary's Fall Canal: 1 part natural cement, \\ parts of sand, and -4 parts of sandstone broken to pass a 2^-inch ring and not a f-inch screen. The broken stone had 46 jier cent, voids loose and 38 when rammed.
In harbor improvements the proj^ortions of concrete range from the richest (used to resist the violent action of waves and ice) to the very lowest (used for filling in cribwork). At Buffalo, N. Y., an extensive breakwater built in 1800 by the U. S. A. engineers, consisted of concrete blocks on the faces and a backing of concrete deposited in place. Portland was used for the blocks and natural for the backing, the proportions being: 1 volume cement, 3 sand, and 8^ of broken stone and pebbles mixed in equal parts.
For the concrete blocks used in constructing the Mississippi Jetties the proportions were: 1 part Portland cement, 1 part sand, 1 part gravel, and 5 parts broken stone.
For incidental information concerning proportions used in prac- tice, see Cost of Concrete, § 158rt, page Wlv.
156/. Water Required. There is a considerable diversity of oijinion among engineers as to the amount of water to be used in making concrete. According to one extreme, the amount of water should be snch that the concrete will quake when tamped; or in other words, it should have the consistency of liver or jelly. According to the other extreme, the concrete should be mixed so dry that when thoroughly tamped moisture just flushes to the sur- face. The advocates of wet mixture claim that it makes the stronger and more dense concrete; while the advocates of dry mix- ture claim the opposite. The difference in practice is not as great as in theory; the apparent difference is chiefly due to differences in condition.
112/t CONCRETE. [chap. IV.
It is unquestionably true that dry mixtures of neat cement, and also of cement and sand, are stronger than wet mixtures, provided the amount of water is sufficient for the crystallization of the cement. It is also certainly true then in even a dry mortar or con- crete, the water is considerably in excess of that necessary for the crystallization of the cement, this excess increasing with the amount of sand and aggregate. Of course the excess water is an element of weakness. Bnt the amount of water to be used in making con- crete is usiially a question of expediency and cost, and not a ques- tion of the greatest attainable strength regardless of expense.
1. Dry mixtures set more quickly and gain strength more rapidly than wet ones; and therefore if quickset and early strength are desired, dry concrete should be preferred. 2. Wet concrete contains a great number of invisible pores, while dry concrete is liable to contain a considerable number of visible voids; and for this reason there is liability that wet concrete will be pronounced the more dense, even though both have the same density. 3. Wet concrete is more easily mixed; and therefore if the concrete is mixed by hand and the supervision is insufficient or the labor is careless, or if the machine by which it is mixed is inefficient, wet mixtures are to be preferred. 4. Wet mixtures can be compacted into place with less effort than dry; but on the other hand the excess of water makes the mass more porous than though the concrete had been mixed dry and thoroughly compacted by ramming. Dry con- crete must be compacted by ramming, or it will be weak and porous; therefore if the concrete can not be rammed into place, it should be mixed wet and then the weight of the stones will bury themselves in the mortar, and the mortar will flow into the voids. 5. A rich concrete can be compacted much easier than a lean one, owing to the lubricating effect of the mortar; and hence rich con- cretes can be mixed dryer than lean ones. The quaking of concrete frequently is due more to an excess of mortar than to an excess of water. G. Lean concretes sliould be mixed dry, since if wet the cement will find its way to the bottom of the layer and destroy the uniformity of the mixture. 7. Machine-made concrete may be mixed dryer than hand-made, owing to the more thorough incor- ;poration of the ingredients. 8. Gravel concrete can be more easily ■ compacted than broken stone, and hence may be mixed dryer. >Cement and sand alone is more easily compacted than when mixed rwith coarser material, particularly broken stone; and therefore
ART, 2.] ■ WATER REQUIRED. 1121
mortar to be deposited in mass should be mixed dryer than concrete. 9. In mixing dry by hand there is a tendency for the cement to ball up, or form nodules of neat cement, while in mixing wet this does not occur. 10. If wet concrete is deposited in a wood form, there is liability of the water exuding between the planking and carrying away part of the cement and thus weakening the face — which should be the strongest part of the mass.
The conclusion is that sometimes wet concrete must be used regardless of any question of strength and cost; while with thorough mixing and vigorous ramming, dry concrete is strongest but also most expensive to mix and lay.
156Z,-. The following experiments are the only ones of any im- portance made to determine the relative strength of wet and dry concretes. The mean crushing strength of four hundred and ninety-six 1-foot cubes * made with mortar as " dry as damp eartli " was 11 per cent, stronger than cubes made Avith mortar of the "ordinary consistency used by the average mason," and 13 j)er cent, stronger than cubes that " quaked like liver under moderate ramming." The cubes were made of five brands of Portland cement, with broken stone and five proportions of sand varying from 1 to 1 to 1 to 5 ; half the cubes had a little more mortar than enough to fill the voids, while the other half had only about 80 per cent, as much mortar as voids. One quarter of the cubes were stored in water, one quarter in a cellar, one quarter under a wet cloth, and one quarter in the open air; and all were broken when approximately 2 years old. The difference in the amount of mortar made no appreciable difference in the strength.
The mean of twelve cubes of dry concrete was 51 per cent. stronger than corresponding cubes of quaking concrete, f
A few minor experiments have been found confirming the above, and none have been found that contradict them.
156/. The amount of water required to produce any particular plasticity varies so greatly with the proportions of the ingredients, the kind and fineness of the cem_ent, the dampness of the sand, the kind of aggregate, etc., that it is scarcely possible to give any valu- able general data. The water varies from 10 to 40 pounds per cubic foot of concrete. The only general rule that can be given is that for
* Geo. W. Rafter, in Report of the New York State Engineer for 1897, pp. 375-460, particularly Table i, page 398.
t Feret, Engineering Neics, vol. xxvii, p. 311.
112m CONCEETE. [chap. IV^
dry concrete the aggregate should be wet but have no free water ia the lieap; and that the mortar should be damp enough to show water only when it is thoroughly rammed, or so that water will flush to the surface when it is tightly squeezed for a considerable time in the hand.
In the experiments referred to in the first paragraph of the ■ preceding section, the average quantity of water for the different ' grades of dry mortar was 19.8 lbs. per cu. ft., and for the plastic ' 21.4, and for the wet 22.5, the sand being reasonably dr}-.
158/;?. Mixing. — The value of the concrete dejjends greatly upon the thoroughness of the mixing. Every grain of sand and every fragment of agg.'egate should have cement adhering to every point of its surface. Thorough mixing should cause the cement not only to adhere to all the surfaces, but should force it into intimate contact at every point. It is possible to increase the strength of really good concrete 100 per cent, by prolonged tritura- tion and rubbing together of its constituents. The longer and more thorough the mixing the better, provided the time does not trench upon the time of set or the working does not break and pulverize the angles of the stone. Uniformity of the mixture is as important as intimacy of contact between the ingredients. Of course thorough- ness of mixing adds to the cost, and it may be wiser to use more cement, or more concrete, and less labor.
Concrete may be mixed by hand or by machinery. The latter is the better; since the work is more quickly and more thoroughly done, and since ordinarily the ingredients are brought into more intimate contact. jMachine mi.-cing is frequently specified. If any considerable quantity is required, machine mixing is the cheaper, ordinarily costing only about half as much as hand mixing.
156w. Hand Mixing. The sand and aggregate are usually measured in wheelbarrows, the quantit}'' being adjusted for a Ijag or barrel of cement. The dry cement and sand are mixed as described in the first paragraph of § 124 (page 85), which see. The proper quantity of water is then added, preferably with a spray to secure greater uniformity, and prevent the washing away of the cement. The mass should be again turned until it is of nniform consistency. The broken stone, having previously been sprinkled but having no free water in the heap, is then added. The whole is then turned until every fragment is covered with cement. Specifications usually require concrete to be turned at least four
ART. 2.] MIXING. 112 n
times, and frequently six. The concrete appears wetter each time it is turned, and should appear too dry until the very last.
If gravel is used instead of broken stone, the mixing is done as ■described for cement and sand.
156o. Machine Mixing. A variety of concrete-mixing machines are in use. Some forms are intermittent and some continuous in their action. Some of the latter automatically measure the in- gredients. A simple variety of the former consists of a cubical box revolved slowly about a diagonal axis. The dry materials are inserted through a door, and the water is admitted through the axis daring the process of mixing. Eight or ten revolutions are sometimes specified; but eighteen or twenty are more frequently specified and give a much better concrete. Sometimes an inclined cylinder or long box revolving about the long axis is employed. Another form consists of a vertical box having a series of inclined shelves projecting alternately from opposite sides, the materials being thrown in at the top and becoming mixed by falling sncces- sively from the inclined shelves. A modification of this form sub- stitutes rods for the shelves, the mixing being accomplished by the ingredients in their descent striking the rods. Still another type form consists of a spiral conveyor or a bladed screw-sliaft revolving in a trough in which the materials are thrown. All of these forms, and also modifications of them, are to be had on the market.
1567). Laying. After mixing, the concrete is conveyed in wheel- barrows or in buckets swung from a crane, deposited in layers G to 8 inches tliick, and compacted by ramming. In dumping, the mass should not be allowed to fall from any considerable height, as doing so separates the ingredients. If in handling, the larger fragments become separated, they should be returned and be worked into the muss with the edge of a shovel.
The rammer usually employed consists of a block of iron having a face G to 8 inches square and weighing anything up to 30 or 40 pounds. The face of the rammer is sometimes corrugated, to keep the surface of the layer rough and thus afford a better bond with the next, and also to transfer the compacting effect of the blow to the bottom of the layer. The tamping should be vigorous enougli to thoroughly compact the mass; but too severe or too long-con- tinued pounding injures the strength of the concrete by forcing the broken stone to the bottom of the layer, or by disturbing the incipient set of the cement.
112o CONCRETE. [CHAP. IV.
When one layer is laid on another already partially set, the entire surface of the latter should be thoroughly wet; but water should not stand in puddles. In case the first layer is fully set, it is wise to sweep the surface with neat cement paste to make sure that the two layers adhere firmly. If the sand or gravel contains any appreciable clay and the concrete is mixed wet, clay is liable to be flushed to the surface and prevent the adherence of the next layer; therefore under these conditions particular care should be given to secure a good union between the layers. After the con- crete is in 2)lace it should be protected from the sun, and not be disturbed by walking ujion it until fully set: this limit should be at least 12 hours and is frequently specified as 4 or 5 days.
l5Qq. Depositing Concrete under Water. In laying concrete under water, an essential requisite is tiiat tlie materials shall not fall from any height, but be deposited in the allotted jilace in a compact mass; otherwise the cement will be separated from the other ingredients and the strength of the work be seriously im- paired. If the concrete is allowed to fall through the water, its ingredients will be deposited in a series, the heaviest — the stone- — ■ at the bottom and the lightest — the cement — at the to]:), a fall of even a few feet causing an appreciable separation. Of course con- crete should not be used in running water, as the cement would be washed out.
A common method of depositing concrete under water is to place it in a A^-shaped box of wood or plate-iron, which is lowered to the bgttom by a crane. The box is so constructed that, on reaching the bottom, a pin may be drawn out by a string reaciiing to the surface, thus j^ermitting one of the sloping sides to swing open and allowing the concrete to fall out. The box is then raised to be refilled. It usually has a lid. Concrete under water should not be rammed; but, if necessary, may be leveled by a rake or other suitable tool immediately after being deposited.
A long box or tube, called a freinie, is also sometimes used. It consists of a tube open at top and bottom, built in detachable sec- tions so that the length may be adjusted to the depth of water. The tube is susjjended from a crane, or movable frame running on a track, by which it is moved about as the work progresses. The upper end is hopper-shaped, and is kept above the water; the lower end rests against the bottom. The tremie is filled in the beginning by placing the lower end in a box with a movable bottom, filling
ART. 2 ] STRENGTH. Il2p
the tube, lowering all to the bottom, and then detaching tlie bottom of the box. The tnbe is kept full of concrete, as the mass issues from the bottom more is thrown in at the top.
Concrete has also b^en successfully deposited under water by enclosing it in paper bags, and lowering or sliding them down a chute into place. The bags get wet and the pressure of the con- crete soon bursts them, thus allowing the concrete to unite into a. solid mass. Concrete is also sometimes dejiosited under Avater by enclosing it in open-cloth bags, the cement oozing through the meshes sufficiently to unite the whole into a single mass.
When concrete is deposited in water, a pulpy gelatinous fluid is washed from the cement and rises to the surface. This causes the water to assume a milky hue; hence the term laitance, which French engineers apply to this substance. It is more abundant in salt water than in fresh water. It sets very slowly, and sometimes scarcely at all, and its interposition between the layers of concrete forms strata of separation. The proportion of laitance is greatly diminished by using large immersing boxes, or a tremie, or paper or cloth bags.
157. Strength. The strength of concrete depends upon the kind and amount of cement, and upon the kind, size, and strength of the ballast. Mortar adheres to broken stone better than to pebbles, and therefore concrete containing the former is stronger than that containing the latter (see § 151). If the sizes of the indi- vidual pieces of the ballast are so adjusted that the smaller fit into the interstices of the larger, successively, then the cementing material will act to the best advantage and consequently the con- crete will be stronger. Hamming the concrete after it is in place brings the pieces of aggregate into closer contact, and consequently makes it stronger. The strength of concrete also depends somewhat u.pon the strength of the ballast, but chiefly upon the adhesion of the cement to the ballast.
There are comparatively few experiments ujion the strength of concrete in which the data was complete enough to make the results of any considerable value.
157a. Compressive Strength. In a series of experiments made by Geo. W, Eafter* to determine the crushing strength of concrete, three varieties of Portland cement were used, all of which were
* Report of the New York State Engineer, 1897, pp. 375-460.
112^
CONCRETE.
[chap. IV,
equal to the maximum both neat and with sand in Table 10, page 78a. The sand was pure, clean, sharp silica, containing o'l per cent, of voids. The aggregate was sandstone broken to pass a 2-inch ring, having 37 per cent, voids when tamped. In half the blocks the mortar was a little more than enough to fill the voids; and in the other half the mortar was equal to about 80 per cent, of the voids. The mortar was mixed as " dry as damp earth."
The test specimens were 1-foot cubes, and were stored under water for four months and then buried in sand. The age when tested ranged from 550 to G50 days, the average being about 600. The cubes were crushed on the U. S. Watertown Arsenal testing- machine. The means are shown in Table 13/. The individual results agreed well among themselves.
TABLE 13/. Crushing Strength op Portland Concrete. Voids of broken stone practically filled with mortar — see the text. Age when tested 600 daj-s.
|
Ref. No. |
Composition |
op Mortar. |
No. OF Cubes Tested. |
Crushing |
Strength. |
|
Cement. |
Sand. |
lbs. per sq. iu. |
tons per sq. ft. |
||
|
1 |
1 |
3 |
4,467 |
322 |
|
|
2 |
2 |
6 |
3,731 |
268 |
|
|
3 |
3 |
6 |
2,553 |
184 |
|
|
4 |
4 |
6 |
2,015 |
145 |
|
|
5 |
5 |
2 |
1,796 |
129 |
|
|
6 |
6 |
1 |
1,365 |
98 |
The cubes summarized in Table 13/" were stored under water. Companion blocks stored in a cool cellar gave 82 per cent, as much strength; those fully exposed to the Aveather, 81 per cent.; and those covered with burlap and wetted several times a day for about three months and afterwards exposed to the weather, 80 per cent.
The cubes of Table 13/ were mixed as " dry as damp earth." Companion blocks of which the mortar was mixed to the " ordinary consistency nsed by the average mason," gave 90 per cent, as much strength; and those mixed to "quake like liver nnder moderate ramming," 88 per cent.
ART. 2.]
COMPRESSIVE STRENGTH.
1127
157^. Table log shows the results of a series of experiments made by A. W. Dow, Inspector of Asphalt and Cement, "Washing- ton, D.'C*
TABLE 13g. Crushing Strength op Concrete in Pounds per Square Inch.
|
Composition of Concrete BY Volumes Loose. |
Voids IN Aggregate. |
Age of Cubes when Broken. |
|||||||||
|
Ref. Ho. |
Mortar. |
Apgregafe in Sizes from 214" to jV'- |
Per Cents. of volume |
Per Cent. of Voids filled with Mortar |
10 Days. |
45 Days. |
3 Mos. |
6 Mos. |
1 Year. |
||
|
Cement |
Sand. |
Broken Stone. |
Gravel. |
||||||||
|
1 9, |
2 2 2 2, 2 2 2 2 2 2 2 2 |
6 6* 6t 3 4 6 6* 6t 3 4 |
Nan 6 3 2 Portl 6 3 2 |
iral Ce 45.3 45.7 39.5 29.3 35.5 37.8 and Ce 45.3 45.7 39.5 29.3 35.5 37.8 |
ment. 83.9 83.9 96.2 129.1 107.0 100.6 ment. 83.9 83.9 96.2 129.1 107.0 100.6 |
228 |
539 |
375 596 |
795 |
915 829 |
|
|
R |
800 |
||||||||||
|
4 5 6 |
87 108 |
421 364 |
361 593 |
344 632 |
763 841 915 |
||||||
|
7 8 |
908 |
1,790 |
2,260 1,630 |
2,510 1,530 |
3,060 1.850 |
||||||
|
9 |
2 700 |
||||||||||
|
10 11 19, |
694 950 |
1,630 1,850 |
2,680 |
1.840 2,070 |
2,820 2,750 2,840 |
||||||
* Coarse. t Three fourths ordinary stone, one fourth granolithic.
The strength of the cement is shown in Table 13h. Notice that the Portland cement did not gain strength proportionally as fast as the natural cement; for example, the Portland mortar in line 7 is two and two-thirds times as strong as the preceding natural-cement mortar, wliile that in line 10 is not quite as strong as the natural- cement mortar immediately preceding.
* Report of the Operations of the Engineering Department of the District ol Columbia for the year ending June 30, 1897, pp. 160-66.
112s
CONCRETE.
[chap. IV.,
TABLE 137*. Tensile Stkength of Cement used in Table l'6g.
|
Rep No. |
AOE WHEN Tested. |
Parts Standard Quartz to 1 hart Cement. |
Tensile Steength |
IN. LBS. PER SQ. IN. |
|
Natural. |
Portland. |
|||
|
1 0 3 |
1 day. 7 days. 7 •' 7 " 1 nio. 1 " 3 " 3 " 6 '• 6 " 1 vear. |
0 0 o 3 3 3 2 3 2 3 2 3 |
9(5 180 91 188 |
441 889 |
|
4 5 |
248 |
|||
|
6 |
429 |
|||
|
7 |
327 |
|||
|
8 |
398 |
|||
|
9 |
414 |
|||
|
10 |
428 |
|||
|
11 |
485 |
|||
|
12 |
474 |
|||
The fineness of the sand was as follows:* "3" 6 '-^ 8" 10'" 20 '^ 40^ 60- 80"-^ 100 "-5 and contained 44.1 per cent, of voids. With the natural cement the water used was 0.317 cu. ft. (20 lbs.) per ca, ft. of rammed concrete, and with Portland cement 0.24 cu. ft. (12 lbs.) — in both cases including the moisture in the sand.f
The broken stone was gneiss broken to pass a 2^-inch ring, none passing a No. 10 sieve, the voids for each particular concrete being as stated in Table 13_^. The gravel was clean quartz passing a l|-inch ring and only 3 per cent, passing a No. 10 ring, and had 29 j)er cent, of voids. The per cent, of voids in the aggregate filled with mortar is stated in Table 13^. Each result in the table is the mean of two cubes, except those for one year, which are the mean of five. Owing to the friction of the press with which the tests were made, the results are 3 to 8 per cent, too high.
157c. Table 13i shows the relative strength of rich and lean
*For explanation of the nomenclature, see the second paragraph of § 114e. f The sand contained 4.4 per cent, of water, which increased the volume of the aand and made the mortar slightly richer than as stated.
ART. 2.]
COMPRESSIVE STRENGTH.
112^
TABLE 13t. Relative Strength of Rich and Lean Concretes.
|
I |
'ropohtions. |
Crushing Strength. |
|||||
|
Rbf. No. |
One Week. |
Four Weeks. |
|||||
|
Cement. |
Sand. |
Bi-oken Stone. |
|||||
|
i |
|||||||
|
Lbs. per f-q. in. |
Relative. |
Lbs. per sq. in. |
Relative. |
||||
|
Portia |
id sand-cement |
||||||
|
1 |
1 |
n |
3 |
412 |
0.77 |
490 |
0.66 |
|
2 |
4 |
446 |
0.83 |
679 |
0.92 |
||
|
3 |
^ |
5:;6 |
1.00 |
741 |
1.00 |
||
|
4 |
1 |
2 |
4 |
316 |
0.61 |
441 |
0.60 |
|
5 |
5 |
275 |
0.53 |
477 |
0.64 |
||
|
6 |
6 |
521 |
1.00 |
639 |
1.00' |
||
|
7 |
1 |
3 |
5 |
, 144 |
0.69 |
374 |
0.85. |
|
8 |
6 |
110 |
0.52 |
182 |
0.57 |
||
|
9 |
7 |
210 |
1.00 |
332 |
i.oa |
||
|
English Porthind cement |
|||||||
|
10 |
1 |
2 |
2 |
494 |
0.60 |
565 |
0.81 |
|
11 |
3 |
611 |
0.75 |
555 |
0.8a |
||
|
12 |
4 |
819 |
1.00 |
613 |
0.8& |
||
|
13 |
5 |
581 |
0.71 |
680 |
0.97 |
||
|
14 |
6 |
500 |
0.61 |
698 |
1.00 |
||
|
15 |
1 |
3 |
3 |
333 |
205 |
0.53 |
|
|
16 |
4 |
366 |
0.95 |
||||
|
17 |
5 6 |
386 357 |
1 00 |
||||
|
18 |
|
0.92 |
|||||
|
German Portland cement |
|||||||
|
19 |
1 |
2 |
4 5 6 |
626 703 728 |
0.86 |
||
|
20 |
0.97 |
||||||
|
31 |
1.00 |
11'2h COSrCRETE. [CIIAP. IV.
concretes.* The water was equal to 20 per cent, of the weight of the cement and the sand. The test specimens for the Portland sand-cement were 9 inches square and 12 inches high, and for the remainder 12-inch cubes. All were crashed between sheets of rubber (see § 12, page 0). Each value in the table is the result for a single cube. Table 13i is valuable chiefly as showing the relative strength of rich and lean concretes. The table shows that a moderately lean concrete is stronger than a very rich one, which is in accordance with the conclusion from Table 13a, page 110, that a concrete is stronger than the mortar alone. Table 13i also shows tliat the strength of the concrete increases with the richness of the mortar, which agrees with Table loZ*, page 111, and Fig. 8, page 112a.
157d. For data on the crushing strength of gravrl concrete, see Table 13a, page 110.
For data on the crushing strength of gravel and broken-stone corncretes approximately 17 days old, see Fig. 8, page 112rr.
157e. Tlie strength of concrete made of coke does not increase with age owing to the soft and friable nature of the aggregate. Apparently the maximum strength of 1 volume loose cement, 3 volumes sand, and 5 volumes crushed coke is about 600 to 700 lbs. per sq. in. with Portland, and about 300 to 350 with natural cement.
157/. Transverse Strength. Table 13/, page 112y, is a summary of 191 tests on concrete bars 30 inches long and 4 inches square. f The cement stood 497 lbs. per sq. in. neat at 7 days, and 209 lbs. with 3 parts sand at 4 weeks. In most of the bars the mortar was made of pulverized sandstone^ although in some cases river and pit sands were used. The aggregate was generally broken sandstone, but gravel and broken whinstone were also used. " In each case the voids in the ' sand ' were filled with cement, and those in the aggregate with mortar."
The results are tabulated in the order of the ratio of the cement to the total sand and aggregate. Xotice that the results in the last line are proportionally higher than those in the remainder of the table. This difference is probably due to tlie fact that the speci- mens for tlie first four lines were mado with natural sand and stone, while in those for the last line only crushed sandstone was used for both the sand and the aggregate.
* W. B. Anderson, Student Can. Soc. C. E., in Trans. Can. Soc. C. E., vol. xiii., Part 1.
t A. F. Bruce, in Proc. of lust, of C. E. (London), vol. cxiii, pp. 217-28.
ART. 3. J
TRANSVERSE STRENGTH.
112y
TABLE 13 j.
]\IoDULus OF Rupture op Portland Co>crete Bahs, Pounds per
Square Inch.
|
Composition. |
Age in AVeeks when Tested. |
|||||||||
|
Ref. No. |
Cement |
Sand. |
Aggre- gate. |
1 |
4 |
8 |
13 |
19 |
S6 |
39 |
|
1 2 3 4 5 |
2 2i 3 2i 3 |
3 5 5 6 7 |
95 37 37 |
145 144 88 81 113 |
215 165 129 130 154 |
266 194 176 156 187 |
301 268 191 193 216 |
303 236 214 199 243 |
320 259 214 212 263 |
157^. In connection with the construction of the Poe Lock of the St. Mary's Falls Canal* a series of one hundred and forty-seven concrete beams 10 inches square were tested. The experiments were very carefully conducted, but there were so many variables that it is impossible to draw any general conclusions therefrom. The beams made with Portland cement were tested when about 19 months old and those with natural cement when about 12 months.
157//. Weight of Concrete. The weight of concrete varies with the materials and the proportions, and with the amount of ramming. The weight varies from 130 to 160 lbs. per cu. ft., but is usually from 140 to 150. The difference in weight of the con- crete due to the aggregate and to the ramming is greater than that due to the difference in weight between Portland and natural cement. The maximum difference between Portland and natural concrete, due to the greater weight of Portland cement, is 4 or 5 lbs. per cubic foot. Concrete made of blast-furnace slag weighs from 110 to 120 lbs, per cubic foot; and that made of coke from 80 to 90 lbs. per cu. ft.
l5Sa. Cost of Conckete. The cost of concrete varies greatly with the materials, the proportions, the cost of material and labor, etc.
The following is the analysis of the composition and cost of the concrete employed for the foundations of the sea-wall at Lovell's Island, Boston Harbor: f
* Report of Chief of Engineers, U. S. A., 1895. Part 4, pp. 2922-31.
t Compiled from Qillmore's Limes, Hydraulic Cements and Mortars, p. 247.
112w • CONCRETE. [CHAP. IV.
Cement, 0.83 bbl 0.12 cu. yd. @ $1 54 = $1 26
Sand 0.25 cu. yd. @ 70 17
Gravel 0.90 cu. yd. @ 27 24
Total materials 1 .27 cu. yd. $1 67
Labor, making mortar 0.06 days @ 1 20 = 08
Labor, making concrete 0.11 days @ 1 20 13
Labor, t aiisportiug concrete 0.06 days @ 1 20 08
Labor, packing concrete 0.03 days @ 1 20 04
Total labor 0. 26 days 33
Tools, implements, etc 11
Total cost 1 cu. yd. of concrete, in j)lace $2 11
The proportions for this concrete were 1 cement, 3 sand, and 4 gravel. It was tinnsually cheap, owing partly to the use of pebbles instead of broken stone. If the latter had been used, it would have cost j^robably 4 to 6 times as much as the gravel. The amount of labor required was also unusually small, this item alone being frequently 6 to 8 times as much as in this case.
The following is the analysis * of the cost of nearly 10,000 yards of concrete as laid for the foundations of a blast-furnace plant near Troy, N. Y., in 1886. The conditions were unusually favorable for cheap work. The concrete consisted of 1 volame of packed cement to 7 of sand, gravel, and broken stone.
Cement, 1.23 bbl 0.18 cu. yd. @ 61 00 = $1 23
Sand 0.10 " @ 0 30= 03
Gravel 0.36 " @ 0 30 = 11
Broken stone 0.74 " @ 1 41 = 1 04
Total materials 1.38 " =$12 41
Labor, handling cement 0.02 day @ 1 00 = 02
unloading stone 0.14 " @ 1 00 = 14
mixing ....0.85 " @ 100= 85
" superintendence 0.01 " @ 9 61 = 10
Total labor 1.02." = 109
Total cost of a cubic yard of concrete, in place = |3 52
* Trans. Am. Soc. of C. E., voL xv. p. 875.
ART. 2.] COST OF CONCRETE. 112z
The following is the cost of the concrete used in the construc- tion of Hiland Avenue reservoir, Pittsburg, Penn.* The stone was broken so as to pass through a 2^-inch ring. The mortar was 1 part liosendale natural cement to 2 jiarts sand. The concrete was 1 part mortar to 2^ of stone. The concrete was mixed by hand. Common laborers received $1.25 per day, and foremen ^2.50. The contract price was $G.OO per yard.
Quarrying stoue $0 45
Transpor, iug stone 50
Breaking sloue 35
Cement @ $1.35 per bbl 180
Sand, cost of digging 10
Water 05
Labor, mixing and laying 75
Incidentals 05
Total cost per cubic yard, in place $4 05
The following is the cost of concrete in the foundations of an electric power-house at Pittsburg, Pa., in 1890. f The proportions were 1 volume of packed cement, 3 volumes of sand, and 5 volumes of broken stone. The cost of labor was abnormally high. The day was ten working hours.
Portland cement 1.28 bbl 0.17 cu. yd. @|2.60 $3.33
Sand 0.50 " @ 1.30 0.65
Broken stone 0.90 " @ 1.35 1.13
Labor 0.91 day @ 1.75 1.59
Superintendence 0.07 " @ 3.00 0.21
7^otal cost per cu. yd., in p/ac(! $6 90
The following is the cost of constructing the concrete retain- ing wall on the Chicago Sanitary Canal. J The average height of the wall was 10 ft. in Sec. 1-4, and 22 ft. in Sec. 15. The thickness on top was 6 ft., and at the bottom it was equal to half the height. The stone was -taken from the adjacent canal excavation. The body of the wall was made with natural cement, but the coping and facing, each 3 inches thick, were made with Portland cement,
* Einilo Low in Engineering TWfo.s, vol. xiii. p. 51, 52.
t E. T. Chibas in The Polytechnic, Rensselaer Polytechnic Institute, vol., vii. p. 145.
X Jour. West. Soc. of Eng'rs, vol. iii. pp. 1310-32.
lV2y CONCRETE. [chap. iv»
The proportions were 1 volume of cement, 1^ volumes of sand, and 4 volumes of unscreened limestone. The cost of plant employed in Sec. 14 was 80,600, and in Sec. 15 was $25,4-20. The contract price for the concrete in Sec. 14 was 12.74, and in Sec. 15 13.40 per on. yd.
Items of Expense.
Labor, general f 0.078
on the wall ....
mixing concrete
placing and removing forms. ...
transporting materials
quarrying stone
crushing stone
Total for labor $0,975 $1,074
|
Cost per 1 Sec. 14 |
Cubic yard. Sec. 15 |
|
$0,078 |
$0,082 |
|
.108 |
AH: |
|
.121 |
.250 |
|
.150 |
.142 |
|
.143 |
.081 |
|
.303 |
.275 |
|
.073 |
.128 |
Material, cement, natural @ $0.65 per bbl. 0.863 .930
" Portland® $2.25 " " .805 .180
sand @|1.35percu. yd. .465 .476
Total for materials $ 1 . 633 $1 . 586
Machinery, cost of operating 407 .567
Total cost per cu. yd $3,015 $3 . 227
For additional data concerning the cost of concrete, see §§ 233-34, page 157.
1586. The following items relate only to the labor of making concrete.
Table 13^' gives the details of the cost per cubic yard of the labor required in mixing and laying concrete for the Buffalo, ]^. Y., breakwater, constructed in 1887-89. The data were communicated by Capt. F. A. ]\Iahan, Corps of Engineers, U. S. A., who had charge of the work. The total amount of concrete laid was 14,587 cu, yds. The conditions under which the work was done varied considerably from year to year.*
Table 13m gives the details of the labor required in mixing and laying concrete in the construction of the Boyd's Corner dam.f
* The work is fuUj' described in Report of Chief of Eugiueors, U. S. A., for 1890, pp. 2808-35.
t Fi-nm an account of the construction of the Boyd's Corner dam on the Croton Kiver near New York. City, by J. James R. Croes, in Trans. Am. Soc. of C. E., vol. ill. p. 360.
ART. 2.]
COST OF CONCRETE.
U2z
TABLE 13k. Cost of Mixing and Laying Concrete.
Ref.
No.
10
Items.
Transporting cement from store-house.
Measuring cement
Mixing cement paste
Measuring sand and pebbles
Measuring broken stone
Mixing concrete
Transporting concrete
Spreading and ramming concrete
Placing forms
Building temporary railway
Total labor per cu. yd ,
Concrete mixed by
hand.
.078
.212
.172
.070 .557 .185 .270 .240
$1,790
iiiachiiiery.
1887 1889
$0.
128
26
186
285
198
152
445
502
176
$0,098 .024 .084 .116 .101 .103 .160 .892 .263 .181
$2. 098: $1,528
TABLE 13to. Labor Required i:: .Mixing and Laying Concrete.
Kind op Labor.
Mixers— hand work, days . . Derrick and car men, days.
Engine, hours.
Handling sand, days
Handling stone, days
Carts, days
Ramming, days
Labor per Cubic Yard.
New York Storage Reservoir. St. Louis Reservoir
Mixed on level and wheeled in
2s=
i-0.161
' 0.065 0.125
2.2.'%^
!• 0.227
■0.114
0.076 0.078
Hoisted by
steam and run
on cars.
00 t)
o* >
C « = O « 3
0.145 0.088 0.152 0.065 0.127 0.046 0.071
»n 0*
fe
0.121 0.070 0.108 0.071 0.098 0.035 0.073
All work on level — wheeled in.
j- 0.183
o.nss
0.125
-0 1:34
0 0.17 0.107
0 250
0.068 0.128
113a CONCRETE. [chap. IV.
158c. The cost of mixing and laying 6 inches of concrete for a pavement foundation is about 7 cents jier sq. yd., for 1 part cement, 2 parts sand, and 4 parts broken stone, turned six times — exclusive of casting into place. With gravel instead of broken stone, the cost is about 6 cents per sq. yd. ; and with four turnings instead of six, the cost is about half a cent less than the prices above.
158^. Economic Concrete. The relative economy of natural and Portland cement mortars can be investigated as explained in §§ 136, 137.
The relative strengths of gravel and of broken-stone concretes <are stated in the last two paragraphs of § 151. The relative economy of concrete made with broken stone and gravel will vary with the cost of each; but as a rule, when gravel costs less than 30 per cent, of that of broken stone, gravel is more economical.
The strengths of both broken-stone and gravel concretes are given in Table 13^5^, page 112r, for both natural and Portland cements at different ages. A study of these results shows that the relative strength of natural and Portland concrete is different at different ages. For example, taking averages for 10 days, the Portland concrete was 6 times as strong as the natural concrete; while at a year the Portland concrete was only 3 times as strong as the natural concrete. At 45 days and also at 6 months, tlie Port- land concrete was 4 times stronger than the natural concrete; and at 3 months 5 times as strong. Taking averages for like dates and compositions, the Portland cement concrete was 3.7 times as strong as natural cement concrete. "With the data in Table 13d or 13^, page 112i7 or 112//, it is easy to compute the cost of 'each kiud of concrete, if the cost of a cubic yard of Portland cement 'Concrete is more than 3.7 times that of a cubic yard of natural cement concrete, then the latter is on the average the more econom- ical; but if the Portland cement concrete costs less than 3.7 times that of the natural cement concrete, then the former is on the average the more economical. Of course the relative cost will vary with the condition of the cement market and with the locality.
IbSe. The following example, from actual practice, illustrates the possibilities in the way of combinations between Portland and natural cements, and gravel and broken stone. The specifications called for a concrete composed of 1 volume of natural cement, 2 volumes of sand, and 4 volumes of screened broken stone. The contractor found that at current prices a concrete composed of 1 volume of Portland cement and 9 volumes of gravel would cost
ART. 3.] ARTIFICIAL STONE. Il3b
about the same as the concrete specified. A test of the strength of the two concretes showed that at a week the Portland-gravel con- crete was 1.52 times as strong as the natural cement and broken- stone concrete; and at a month 1.59 times as strong. Therefore the Portland-gravel concrete was the more economical, and was used.
Art. 3. Artificial Stone.
159. Several kinds of artificial stone have come into use within the hist twenty-five years for architectural and artistic purposes, and for the pavements of cellars, for footpaths, areas, and other locali- ties not subjected to the tread of heavy animals. They are all a combination of hydraulic cement and sand, pebbles, etc. Some of them possess very considerable merit, and are of value in districts where durable and cheap building-stone is not supplied by nature.
The strength and hardness of all varieties of artificial stone vary directly with the ultimate strength and hardness attainable by the hydraulic ingredients employed. An obvious means of improving the quality of the stone, therefore, is the employment of the highest grades of cement.
160. Beton-Coignet. As made by its inventor, Coignet, of Paris, its usual ingredients are: Portland cement, siliceous hydraulic lime (like that obtained at Teil, France), and clean sand, mixed together with a little fresh water. The proportions are varied con- siderably for different kinds of work. The dry ingredients are first thoroughly mixed by hand, and again in a mill after moistening them very slightly with clean water. Moulds are then filled with the mixture, which is compacted by ramming. The peculiarities of this stone result from (1) the small quantity of water used in its manufacture, (2) a judicious choice of the qualities and proportions of the ingredients, and (3) the thoroughness with which the mixing is done. It is nothing more than hydraulic concrete, from which the coarse fragments have been omitted, and upon which have been conferred all the advantages to be derived from their thorough manipulation. It is used in France to a considerable extent in constructing the walls of houses, and in repairing masonry, — as bridge piers, culverts, etc.
In this country a mixture of either natural or Portland cement and sand is frequently, but improperly, called Beton-Coignet.
161. Portland Stone. This is a mixture of Portland cement and sand, or sand and gravel, compacted into form by tamping.
11-i ARTIFICIAL STONE. [cHAP. lY^
When properly made it possesses the essential requisites of strength and hardness in a degree proportionate to the value of the cement employed. The proportions of 1 measure of dry cement to 2 or "21- measures of sand will answer for most purposes. The manipulation should be prolonged and thorough to insure the production of a homogeneous stone. It is much used for flagging, for which pur- pose the surface layer, to the thickness of about half an inch, may advantageously be composed of 1 measure of cement to 1^ or li of sand.
162. McMuRTRlE Stone. This stone consists essentially of the Portland stone described above, in the pores of which are formed compounds of alumina with the fatty acids by the double decom- position of alum and a potash soap (see § 140, page 101). These compounds are insoluble in water, are not acted upon by the car- bonic acid of the air, and add considerably to the early strength of the stone and somewhat to its ultimate strength.
The peculiar merit of this stone is that its power of absorbing^ water is decreased by the use of the alum and the soap. All mor- tars and most of the artificial stones absorb water freely,- — porous mortar from 50 to GO per cent, of its own weight and the best Port- land from 10 to 20 per cent., — and consequently they disintegrate rapidly under the action of frost. The absorbed water also dissolves the salts of magnesia, lime, soda, and potash (of all of which there is always more or less in cement), and on evaporating leaves a white efflorescence on the surface, which injures the appearance of the wall. For these reasons the ordinary artificial stones are in dis- repute for architectural purposes. The absorptive power of the Mc- Murtrie stone is about twice that of granite, about equal to that of the best limestones, and about one tenth or less of that of the best sandstones. It has been used in Washington, D. C, to a limited extent, the window trimmings of the National Museum and also the fronts of a few stores and dwellings being of this stone. It a^^pears to have given entire satisfaction.
163. Frear Stone. This is composed of siliceous sand and good Portland cement, to which gum shellac is added. The composition used by the inventor was 1 measure of cement and 2^ measures of sand moistened with an alkaline solution of shellac of sufficient strength to furnish an ounce of the shellac to a cubic foot of stone. The shellac adds to the early strength of the stone ; but it is not certain that it adds to the ultimate strength, nor is it certain that
AKI. 3] SOKEL STOXE. 115
the shellac may not decay and ultimately prove an element of weakness.
\> lieu mixed, it is rammed into wooden moulds, and after setting is laid away to season, — which requires several months for best results. It was much used in architectural work in the West a few years ago, but did not give satisfaction.
164. Ransome Stone. This is made by forming in the in- terstices of sand, gravel, or any pulverized stone a hard and insoluble cementing substance, by the natural decomposition of two chemical compounds in solution. Sand and the silicate of soda are mixed in the proportion of a gallon of the latter to a bushel of the former and rammed into moulds, or it may be rolled into slabs for footpaths, etc. At this stage of the process the blocks or slabs may be easily cut into any desired form. They are then immersed, under pressure, in a hot solution of chloride of €alcium, after which they are thoroughly drenched with cold water — for a longer or shorter period, according to their size — to wash ■out the chloride of sodium formed dui-ing the operation. In England grindstones are frequently made by this process.
165. SOREL Stone. Some years ago, M. Sorel, a French chemist, discovered that the oxychloride of magnesium possessed hydraulic energy in a remarkable degree. This cement is the basis of the Sorel stone. It is formed by adding a solution of chloride of mag- nesium, of the proper strength and in the proper proportions, to the oxide of magnesium. The strength of this stone, as well as its hardness, exceeds that of any other artificial stone yet produced, and may, when desirable, be made equal to that of the natural stone which furnishes the powder or sand used in its fabrication- The process is patented, and is used mainly in making emery-wheels. By incorporating large pebbles and cobble-stones in the mixture the stone can be made quite cheaply, and is therefore suitable for ioundations and plain massive walls.
CHAPTER V. QUARRYING.
166. This is so large a subject that it cannot be more than en- tered upon here ; for greater detail, see treatises on Quarrying, Rock- blasting, and Tunneling.
167. Sources of Building Stones. The bowlders, Avhich are scattered promiscuously over the surface of the ground and also frequently buried in it, furnish an excellent building stone for massive structures where strength is essential. They are usually of tough
, granite or of a slaty structure, and are difficult to work. Sometimes they have a cleavage plane or rift, along which they may be split. They can be broken into irregular pieces by building a fire about them, and drenching them while hot with water, or they may be broken by explosives.
Of course by far the greater quantity of stone is taken directly from quarries. All building-stone deposits have usually a certain amount of covering, consisting either of a portion of the same de- posit, which has been disintegrated by atmospheric influences, or of a later deposit. This covering is called the ''cap-rock" or "strip- ping." In opening the quarry, the solid portions of cap-rock are broken up by blasting, and the whole is carted out of the way. After a sufficient space is stripped, the next step necessary, when the quarry rock does not stand out in cliffs, is to excavate a narrow space on one side for a quarry face, either by blasting or by some of the methods to be described presently.
168. Methods of Quarrying. After a considerable area has tlius been laid bare, the stone is quarried in one of three ways.
169. J. By Hand Tools. When the stone is thin-bedded, it may be quarried by hand-tools alone. The principal tools are pick, crow- bar, drill, hammer, wedge, and plug and feathers. The layers are forced apart by the crow-bar or wedges. The flat pieces are broken up with the hammer or by drilling holes for the plug and feathers.
116
QUARRYIXG BY EXPLOSIVES. 117
The plug is a Barrow wedge with plane faces; the feathers are wedges flat on one side and ronnded on the other (Fig. 25, page 128). When a plug is placed between two feathers, the three will slip into a cylindrical hole ; if the plug is then driven, it exerts a great force. If these plugs and feathers are placed a few inches apart in a row, and all driven at the same time, the stone will be cracked along the line of the holes, even though it be comparatively thick.
The drill used to cut the holes for the plug and feathers is a bar of steel furnished with a wide edge sharpened to a blunt angle and hardened. It is operated by one man, who holds the drill witli one hand and drives it with a hammer in the other, rotating the drill between blows. The holes are usually from f to f of an inch in diameter.
Sandstones and limestones occurring in layers thin enough to be quarried as above are usually of inferior qiiality, suitable only for slope walls, paving, riprap, concrete, etc.
170. JJ.' By Explosives. Generally, the cheapest method of quarrying small blocks is by the use of explosives. However, ex- plosives are used mainly for detaching large blocks, which are after- wards worked up by means of wedges. In this method of quarry- ing, drill-holes are put down to the depth to which the rock is to be split, and the requisite amount of powder or other explosive put in, covered with sand, and fired by a fuse. Sometimes numerous charges in a line of drill-holes are fired simultaneously by means of electricity.
Quick-acting explosives, like dynamite, have a tendency to shatter the stone and break it in many directions, the texture being affected by the sudden explosion in the same manner as by the blow of a hammer. Coarse gunpowder is generally preferred for quarrying stone. Light charges of powder lightly covered with sand are better than heavy charges tightly tamped ; * and experience goes to show that better work is done by repeated light blasts in the same hole, than by a single heavy blast. By means of light charges often re- peated, a mass of rock may be detached without being broken up, which would be badly shattered by a single charge strong enough to detach it.
In each locality the structure of the rock mi;st be carefully
* For an article showing that an air-space should be left between th«» exploaive and the tampins, see Eiujineering Xews, vol. xviii. p. 332.
118 QUARKYIN-G. [chap. Y,
studied with a view to take advantage of the cleavage planes and natural Joints. For quarrying each -class of rocks there is a charac- teristic method employed, which is, however, varied in detail in different quarries. The minor details of quarry methods are as various as the differences existing in the textures, structures, and modes of occurrence of the rocks quarried. Much depends upon how the blast is made. The direction in which the rock is most liable to break depends upon the structure of the rock and the shape of the drill-hole. Even such an apparently unimportant matter as the form of the bottom of the drill-hole into which the explosive is put has a very marked effect. If bored with a hand- drill, the hole is generally triangular at the bottom, and a blast in such a hole will break the rock in three directions. In some quar- ries the lines of fracture are made to follow predetermined directions by putting the charge of powder into canisters of special forms.*
171. Drills. The holes are bored by jumpers, churn-drills, or machine-drills. The first is a drill similar to the one used for drill- ing holes for plugs and feathers (§ 169), except that it is larger and longer. It is usually held by one man, who rotates it between the alternating blows from hammers in the hands of two other men. Churn-drills are long, heavy drills, usually 6 to 8 feet in length. They are raised by the workmen, let fall, caught on the rebound, raised and rotated a little, and then dropped again, thus cutting a hole without being driven by the hammer. They are more eco- nomical than jumpers, especially for deep holes, as they cut faster and make larger holes than hand-drills.
172. Machine rock-drills bore much more rapidly than hand- drills, and also more economically, provided the work is of sufficient magnitude to justify the preliminary outlay. They drill in any direction, and can often be used in boring holes so located that they could not be bored by hand. They are worked either by steam directly, or by air compressed by steam or water-power and stored in a tank called a receiver and thence led to the drills through iron pipes.
A variety of rock-drilling machines has been invented,! but they can be grouped in two classes, viz., percussion-drills and rotat- ing drills. The method of action of the percussion-drill is the same
* See Report on Quarry Industry in Vol. X. of the 10th Census, pp. 33, 34. + For a full account of the more important ones, see Drinker's " Tunneling.''
QUAKRYIXG BY EXPLOSIVES. 119
as that of the churn-drill already described. The usual form is that of a cylinder, in which a piston is moved by steam or com- pressed air, and the drill is attached to this piston so as to make a stroke with every complete movement of the piston. An automatic device causes it to rotate slightly at each stroke.
173. In the rotating drills, the drill-rod is a long tube, revolving about its axis. The end of the tube — hardened so as to form an annular cutting edge — is kept in contact with the rock, and by its rotation cuts in it a cylindrical hole, generally with a solid core in the center. The drill-rod is fed forward, or into the hole, as the drilling proceeds. The debris is removed from the hole by a con- stant stream of water which is forced to the bottom of the hole through the hollow drill-rod, and which carries the debris up througli the narrow space between the outside of the drill-rod and the sides of the hole.
The diamond drill is the only form of rotary rock-drill exten- sively used in this country. The tube has a head at its lower end, in which are set a number of carbons or black diamonds. The diamonds usually project slightly beyond the circumference of the head, which is perforated to permit the ingress and egress of the water used in removing the debris from the hole and at the same time prevent the head from binding in the hole. When it is desir- able to know the precise nature and stratification of the rock pene- trated, the cutting points are so arranged as to cut an annular groove in the rock, leaving a solid core, which is broken off and lifted out whenever the head is brought up. Where it is not desired to pre- serve the core intact, a solid boring-bit is used instead of the core- bit. They are made of any size up to 15 inches in diameter.
174. Bxplosives.* The principal explosives are gunpowder, nitro-glycerine, and dynamite. Only a coarse-grained and cheap variety of the first is used in quarrying, the others being too sudden and too strong in their action.
The pressure exerted by gunpowder when fired in a confined space depends upon the relative weight and quality of powder used, and upon the space occupied by the gases evolved. The absolute force of gunpowder, the force which it exerts when it exactly fills the space in which it is confined, has never been satisfactorily ascer-
* For a full account of all the various explosives, see Drinker's " Tunneliug,*' and Drinker's " Modern Explosives."
120 QUARRYING. [CHAP. V.
tuined. It has been variously estimated at from 15,000 to 1,500,000 pounds per square inch. Experiments by Gen. Rodman sliow that for the powder used in gunnery the absolute force of explosion is at least 200,000 pounds per square inch. " In ordinary quarrying, a cubic yard of solid rock in place (or about 1.9 cubic yards piled up after being quarried) requires from ^ to f pound of powder. In very refractory rock, lying badly for quarrying, a solid yard may require from 1 to 2 pounds. In some of the most successful great blasts for the Holyhead Breakwater, Wales, (where several thou- sands of pounds of powder were exploded, usually by galvanism, at a single shot,) from 2 to 4 cubic yards (solid) were loose ited per pound of powder ; but in many instances not more than 1 to 1^ yards. Tunnels and shafts require 2 to 6 pounds per solid yard, usually 3 to 5 pounds. Soft, partially decomposed rock frequently requires more than harder ones." *
The explosion of the powder splits and loosens a mass of rock whose volume is approximately proportional to the cube of the line of least resistajice, — that is, of the shortest distance from the charge to the surface of the rock, — and may be roughly estimated at iivice that cube ; but this proportion varies. much in different cases. The oiwiinary rule for the weight of powder in' small blasts is
Powder, in poitnds, = (Line of Resistance, infect,)' -^ 32.
Powder is sold in kegs of 25 lbs., costing about §2.00 to 82.25 per keg, exclusive of freight, — which is very high, owing to the risk.
175. Most of the explosives which of late years have been tak- ing the place of gunpowder consist of a powdered substance, partly saturated Avith uitro-glycerine — a fluid produced by mixing glycerine with nitric and sulphuric acids. Xitro-glycerine, and the powders containing it, are always exploded by means of sharp j^ercussion, which is applied by means of a cap and fuse. The cap is a hollow copper cylinder, about ^ inch in diameter and an incli or two in length, containing a cement composed of fulminate of mercury and some inert substance. The cap is called single-force, double-force, etc., according to the amount of explosive it contains.
The principal advantages of nitro-glycerine as an explosive con- sist (1) in its instantaneous development of force, due to the fact that, pound for pound, it produces at least three and a half times * Traut'ft'iiie's Engineer's Pocket-book.
QUARRYING BY EXPLOSIVES. 121
as much gas, and twice as much heat, as gunpowder ; and (2) in its high specific gravity,^which permits the use of small drill-holes.
Nitro-glycerine is rarely used in the liquid state in ordinary quarrying or blasting, owing to the liability of explosion through accidental percussion, and owing to its liability to leakage. It ex- plodes so suddenly that very little tamping is required, the mere weight of moist sand, earth, or water being sufficient. This fact, and the additional one that nitro-glycerine is unaffected by immer- sion in water and is heavier than water, render it particularly suit- able for sub-aqueous work, or for holes containing water. If the rock is seamy, the nitro-glycerine must be confined in water-tight casings. Such casings, however, necessarily leave some spaces be- tween the rock and the explosive, which diminishes the effect of the latter. The liquid condition of nitro-glycerine is useful in causing it to fill the drill-hole completely, so that there are no empty spaces in it to waste the foi'ce of the explosion. On the other hand, the liquid form is a disadvantage, because when thus used in seamy rock without a containing vessel portions of the nitro-glycerine leak away and remain unexploded and unsuspected, and may cause acci- dental explosion at a future time.
The price of nitro-glycerine is from 50 to 60 cents per quart.
176. Dynamite is the name given to any explosive which con- tains nitro-glycerine mixed with a granular absorbent. If the absorbent is inert, the mixture is called true dynamite; if the absorbent itself contains explosive substances, the mixture is called false dynamite. The absorbent, by its gi-anular and compressible condition, acts as a cushion to the nitro-glycerine, and protects it from percussion and from the consequent danger of explosion, but does not diminish its power when exploded. Nitro-glycerine undergoes no change in composition by being absorbed ; and it then freezes, burns, explodes, etc., under the same conditions as to pressure, temperature, etc., as when in the liquid form. The cushioning effect of the absorbent merely renders it more difficult to bring about sufficient percussive pressure to cause explosion. The absorption of the nitro-glycerine in dynamite renders the lat- ter available in horizontal holes or in holes drilled upward. True dynamite loses only a very small percentage of its explosive power when saturated with water, but is then much more difficult to ex- plode.
123 QUAREYIXG. [CHAP. V.
True dynamites must contain at least 50 per cent, of nitro- glycerine, otherwise the latter will be too^ompletely cushioned by the absorbent, and the powder will be too difficult to explode. False dynamites, on the contrary, may contain as small a percentage of nitro-glycerine as may be desired, some containing as little as 15 per cent. The added explosive substances in the false dynamites generally contain large quantities of oxygen, which are liberated upon explosion, and aid in effecting the complete combustion of any noxious gases arising from the nitro-glycerine. The false are generally inferior to the true dynamites, since the bulk of the former is increased in a higher ratio than the power; and as the cost of the work is largely dependent upon the size of the drill- holes, there is no economic gain.
Dynamites which contain large percentages of nitro-glycerine explode with great suddenness, tending to break the rock into small fragments. They are most useful in blasting very hard rock. In such rock dynamite containing 75 per cent, of nitro-glycerine is roughly estimated to have about 6 times the force of an equal weight of gunpowder ; but in soft rock or clay its power, at equal cost, is inferior to that of common gunpowder, because its action is akin to a sudden blow, rather than to a continued push. For soft or decomposed rocks, sand, and earth, the lower grades <f dynamite, or those containing a smaller percentage of nitro-glycei- ine, are more suitable. They explode with less suddenness, and their tendency is rather to upheave large masses of rock than to splinter small masses.
*' Judgment must be exercised as to the grade and quantity of explosive to be used in any given case. Where it is not objection- able to break the rock into small pieces, or where it is desired to do so for convenience of removal, the higher shattering grades are use- ful. Where it is desired to get the rock out in large masses, as in quarrying, the lower grades are preferable. For very difficult work in hard rock, and for submarine blasting, the highest grades, con- taining 70 to 75 per cent, of nitro-glycerine, are used. A small charge does the same execution as a larger charge of lower grade, and of course does not require the drilling of so large a hole. In submarine work their sharp explosion is not deadened by the water. For general railroad work, ordinary tunneling, mining of ores, etc., the average grade, containing 40 per cent, of nitro-glycer-
NITRO-GLTCERINE EXPLOSIVES. 12S
ine, is used ; for quarrying, 35 per cent. ; for blasting stumps, trees, piles, etc., 30 per cent.; for sand and earth, 15 per cent."
177. A great variety of dynamites is made. Each manufacturer usually makes a number of grades, containing different percentages of nitro-glycerine, and gives to his powder some fanciful name. Dynamite is sold in cylindrical, paper-co'^ered cartridges, from ^ of an inch to 2 inches in diameter^ and 6 to 8 inches long, or longer, which are packed in boxes containing 25 or 50 pounds each. They are furnished, to order, of any required size. The price per pound ranges from 15 cents for 15 per cent. nitro-gl3'cerine to 50 cents for 75 per cent, nitro-glycerine.
Table 14 (page 124) gives the names of all the explosives con- taining nitro-glycerine, with the per cent, in each case.*
178. Ill' By Channeling and Wedging. By channeling is meant the process of cutting long narrow channels in rock to free the sides of large blocks of stone. Quite a large number of machines have been invented for doing this work, all of which make the channels by one form or the other of the machine drills already described (see the second paragraph of § 172). The machines are mounted upon a track on the bed of the quarry, and can be moved forward as the work progresses. If the rock is in layers, it is only necessary to cut the channels part way through the layer, when the block can be detached with wedges, the groove guiding the fracture. If the rock is not in layers, after the necessary channels have been cut around the block, it is necessary to under-cut the block in order ta release it. This is accomplished by drilling a series of holes along the bottom, which process is called "gadding" by quarry-men. The block is then split from its bed by means of Avedges. The method of channeling and wedging is much employed in quarrying marble, the massive limestones, and the thick-bedded sandstones. The method is very economical and expeditious, except in granite and the hardest sandstones. For illustrations of the two principal clian- neling machines and also quarries being worked by this method, see Eeport on the Quarry Industry, pp. 44-52, in Vol. X. ci the Tenth Census of the United States.
*W. C. Foster, in Etigineering Xewa^ vol. xix. p. 25-t. For a list of all the explo- sives employed as blasting agents, together with a description of their composition and references to the literature of each, see Engineering Xews, vol. xix. pp. 533-34, and vol. xx. pp. 8-10.
124
QUARRYING.
[chap. Y.
TABLE 14. List of lixPLosivEs containing Nitro-glycerine.
Name of Explosive.
Per cent, of Nitro- glycerine.
^tna powder, No. 1
" 3XX...
" 3
'' 3X.... " 4X...
" 5
Auiinouia powder
Asbestos powder
Atlas powder, A
" B-f
" B
" C+ ,
" c
'• D+
" D
" E+
" E
" F+
Brady's dynamite
Brain's powder
Colon iii powder
Dualiu (Dittmar's)
Dynamite (Nobel's, Kiesel- gulir dynamite),
Old No. 1 Old No. 2 Old No. 3
Electric powder
Explosive gelatine
Forcite, 2 grades
Fulgurite (solid)
" (liquid)
Gelatine dynamite, A. . .
No. 1
"< << <( 2
Gelatine explosive de
guerre.
Gelignite
Giant powder, No. 1
" New '• 1
" " 2 extra
" 2
" 2c
" XXX..
" M
Giant powder (Nobel's), No. 2
65 50 40 35 25 15 16 to
20
varies 75 60 50 45 40 35 30 25 20 15 33 40 40 50
75
40
25
33
93
70
60
90
97.5
58
38.8
70,
89.3
56.5
75
50
45
40
33
27
20
20
Name op Explosive.
Glyxoline
Hecla powder, No. IXX
Gun Sawdust
" No. IX....
" 1
" 2X....
" 2
" 3X....
"3
Hercules powder, No. IXX " 1.... " 2SSS " 2SS.. " 2S...
3S... 3....
4S... 4.... (some
Horsley's powder
varieties)
Judson Giant Powder, No. 2 Judsou powder, FFF
FF
F
RRP
Lithof racteur
Metalline Nitroleum
Mica powder, No. 1
Per cent.
of
Nitro-
gljcerine.
3.
Miners' Powder Co.'s Dy- namite
Neptune powder
Nitro Tolnol
Norrbin & Ohlsson's pow- der
Pontopolite
Porifera Nitroleum
Rendrock
Sebastin, No. 1
" 2
Selenitic powder
Seranim
Vigorite (U. S.) ..
Vitrite, No. 1
" 3
Vulcan powder
75 16 to 20 50 40 35 30 35 30 75 65 55 50 45 40 35 30 35 20
20
40
20
15
10 5 to 6
53 varies
40
52
33 32.7
70
25 to 50
varies 33.4
78
68
varies
43.8
32.6
CHAPTER VI.
BTONE CUTTING.
Art. 1. Tools.
179. In order to describe intelligibly the various methods of preparing stones for use in masonry, it will be necessary to begin with a description of the tools used in stone-cutting, as the names of many kinds of dressed stones are directly derived from those of the tools used in dressing them.
"With a view to securing uniformity in the nomenclature of building stones and of stone masonry, a committee of the American Society of Civil Engineers prepared a classification and recommended that all specifications should be made in accordance therewith. The old nomenclature Avas very unsystematic and objectionable on many grounds. The new system is good in itself, is recommended by the most eminent authority, has been quite generally adopted by en- gineers, and should therefore be strictly adhered to. The following description of the liand tools used in stone cutting is from the report of the American Society's committee.^"
180. Hand Tools. "The Double Face Hammer, Fig. 9, is a heavy tool weighing from 20 to 30 pounds, used for rough- ly shaping stones as they come from the quarry and for knocking off projections. This is used only for the rougliest work.
" The Face Hammer, Fig. 10, has one blunt and one cutting end, and is used for the same purpose as the double face hammer where less weight is C required. The cutting end is used for roughly squaring
stones, preparatory to the use Fig. lo.— Face hammer.
of finer tools.
D
Fig. 9.— Double Face Hammer.
* Trans. Am. Soc. of C. E., voL vi. pp. 297-304.
125
126
STONE CUTTING.
[chap. V"I.
"The Cavil, Fig. 11, has one blunt and one pyramidal, or pointed, end, and weighs from 15 to 20 pounds. It is used in quarries for roughly shaping stone for transportation.
The Pick, Fig. 12, somewhat resembles the Fig. 11.— Cavil, pick used in digging, and is used for rough dress- ing, mostly on limestone and sandstone. Its length varies from 15 to 24 inches, the thickness at the eye being about 2 inches.
" The Ax, or Peaoi Ham- mer, Fig. 13, has two opposite [Up cutting edges. It is used for making drafts around the arris, or edge, of stones, and in re- ducing faces, and sometimes ^'^- ^s.-pick. joints, to a level. Its length is about 10 inches, and the cutting
D
edge about 4 inches. It is used after the point and before the patent ham- mer.
''The Tooth Ax, Fig. 14, is like Fig. 13.— Ax. the ax, except that its cutting edges
are divided into teeth, the number of which varies with the kind of work required. This tool is not used in granite and gneiss cutting.
" The Bush Ha m in e r , Fig. 15, is a square prism of steel whose ends are cut into a number of pyramidal points. The length of the hammer is from 4 to 8 inches, and the cutting
face from 2 to 4 inches square.
J
Fig. 14.— Tooth Ax.
The points vary in number and in size with the work to be done. One end is sometimes made with a cutting edge like that of Fig. 15.— Bush Hammer. ^]^g j^x.
The Crandall, Fig. 16, is a malleable-iron bar about two feet
ART. 1.]
TOOLS.
127
In this end is a slot 3 inches
long, slightly flattened at one end.
long and f inch wide. Through this
slot are passed ten double-headed
points of 5-inch square steel, 9
inches long, which are held in
place by a key.
''The Patent Hammer, Fig.
17, is a double-headed tool so Fig. ig.-Crandali,.
formed as to hold at each end a set of wide thin chisels. The tool
is in two parts, which are held to- gether by the bolts .which hold the chisels. Lateral motion is prevented by four guards on one of the pieces.
Fig. 17.— Patent Hammer. The tool without the teeth is
5-|- X 2f X li inches. The teeth are 2f inches wide. Their thickness
varies from -jig to ^ of an inch. This tool is
used for giving a finish to the surface of stones. " The Hand Hammer, Fig. 18, weighing
from 2 to 5 pounds, is used in drilling holes, fig. i8.-Hand hammer.
and in pointing and chiseling the harder rocks.
''The Mallet, Fig. 19, is used where the softer limestones and
sandstones are to be cut.
"The Pitching Chisel, Fig. 20, is usually of l|-inch octagonal steel, spread on the cutting edge to a rectangle of | X 2^ inches. It is used to make a well-defined edge to
the face of a stone, a line being marked on the joint surface to
which the chisel is applied and the portion of the stone outside of
the line broken off by a blow with the hand-hammer on the head
of the chisel.
"The Point, Fig. 21, is made of round or octagonal rods of
steel, from \ inch to 1 inch in diameter. It is made about 12
inches long, with one end brought to a point.
It is used until its length is reduced to about CC
5 inches. It is employed for dressing off the (T
irregular surface of stones, either for a perma- nent finish or preparatory to the use of the ax. ^^°- 21.— Point.
According to the hardness of the stone, either the hand-hammer
or the mallet is used with it.
Fig. 19.— Mallkt.
:>
128
STOJfE CUTTING.
[chap. VI.
"The Chisel, Fig. 22, of round steel of ^ to | inch iu diameter
and about 10 inches long, with one end brought
I to a cutting edge from ^ inch to 2 iuclies
wide, is used for cutting drafts or margins on
the face of stones.
'^The Tooth Chisel, Fig. 23, is the same
d
d
Fig. 22. — Chisel.
as the chisel, except that the cutting edge is divided into teeth. It is used only on mar bles and sandstones.
''The Splitting c^ Chisel, Fig. 24, is used chiefly on the softer, stratified stones, and sometimes on fine architectural carvings in granite.
''The Plug, a truncated wedge of steel, and the Feathers of half-round malleable iron, Fig. 25, are used for splitting uustrati- fied stone. A row of holes is made with the Drill, Fig. 26, on the
Fig. 23. Tooth Chisel.
Fig. 24. Splitting Chisel.
Fitt. -25. Plug and Ieathees.
Fig. 26.— Drills.
line on which the fracture is to be made ; in each of these holes two feathers are inserted, and the plugs lightly driven in between them. The plugs are then gradually driven home by light blows of the hand hammer on each in succession until the stone splits."
181. Machine Tools. In all large stone-yards machines are used to prepare the stone. There is great variety in their form, but since the surface never takes its name from the tool which forms it, it will be neither necessary nor profitable to attempt a de- scription of individual machines. They include stone-saws, stone- cutters, stone-planers, stone-grinders, and stone-polishers.
The saws may be either drag, circular, or band saws ; the cut- ting may be done by sand and water fed into the kerf, or by carbons or black diamonds. Several saws are often mounted side by side and operated by the same power.
The term " stone-cutter" is usually applied to the machine which
AET. 2. J METHOD OF EORMIXG SURFACES. 129
attacks the rough stone and reduces the inequalities somewhat. After this treatment the stone goes in succession to the stone- planer, stone-grinder, and stone-polisher.
Those stones which are homogeneous, strong and tough, and comparatively free from grit or hard spots, can be worked by ma- chines which resemble those used for iron ; but the harder, more brittle stones require a mode of attack more nearly resembling that employed in dressing stone by hand. Stone-cutters and stone- planers employing both forms of attack are made.
Stone-grinders and stone-polishers differ only in the degree of fineness of the surface produced. They are sometimes called "rub- bing-machines." Essentially they consist of a large iron plate re- volving in a horizontal plane, the stone being laid upon it and braced to prevent its sliding. The abradent is sand, which is abundantly supplied to the surface of the revolving disk. A small stream of water works the sand under the stone and also carries away the debris.
Art. 2. Method of forming the Surfaces.
182. It is important that the engineer should understand the methods employed by the stone-cutter in bringing stones to any re- quired form. The surfaces most frequently required in stone cutting are plane, cylindrical, warped, helicoidal, conical, spherical, and sometimes irregular surfaces.
183. Plane Surfaces. In squaring up a rough stone, the first thing the stone-cutter does is to draw a line, with iron ore or black lead, on the edges of the stone, to indicate as nearly as possible the required plane surface. Then with the hammer and the pitching- tool he pitches off all debris or waste material above the lines, thereby reducing the surface approximately to a plane. With a chisel he then cuts a draft around the edges of this surface, i. c, he forms nar- row plane surfaces along the edges of the stone. To tell when the drafts are in the same plane, he uses two straight- edges having parallel sides and equal widths. See Fig. 27. The projections fig.27.
on the surface are then removed by the pitching chisel or the point, until the straight-edge will just touch the drafts and the inter- mediate surface when applied across the stone in any direction.
130
STONE CUTTING.
[chap. VI..
The surface is usually left a little " slack," i. e., concave, \<^ allow room for the mortar ; however, the surface should be but a very little concave.
The surface is then finished with the ax, patent hammer, bu»a hammer, etc., according to the degree of smoothness required.
184. To form a second plane surface at right angles to the first one, the workman draws a line on the cut face to form the inter» section of the two planes ; he also draws a line on the ends of the stone approximately in the required plane. With the ax or the chisel he then cuts a draft at each end of the stone until a steel square fits the angle. He then joins these drafts by two others at right angles to them, and brings the whole surface to the same plane. The other faces may be formed in the same way.
If the surfaces are not at right angles to each other, a bevel is used instead of a sqnare, the same general method being pursued.
185. Cylindrical Surfaces. These may be either concave or convex. The former are frequently required, as in arches; and the latter sometimes, as in the outer end of the face-stones of an arch. The stone is first reduced to a paralellopipedon, after which the curved surface is produced in either of two ways : (1) by cutting a circular draft on the two ends and applying a straight-edge along the rectilinear elements (Fig. 28); or (2) by cutting a draft along the line of intersection of the plane and cylindrical surface, and. applying a curved templet to the required surface (Fig. 29).
Fig.
Fig. 29.
186. Conical Surfaces may be formed by a process very similai to the first one given above for cylindrical surfaces. Such surfaces are seldom used.
187. Spherical Surfaces are sometimes employed, as in domes. They are formed by essentially the same general method as cylin- drical surfaces.
188. Warped Surfaces. Under this head are included what
-ART. 3.] METHODS OF FINISHING SURFACES. 131
the stone-cutters call " twisted surfaces, " helicoidal surfaces, and the general warped surface. None of these are common in ordinary stone-work.
The method of forming a surface equally twisted right and left will be de- scribed ; by obvious modifications the same method can be applied to secure other forms. Two twist rules are required, the angle between the upper and lower edges ^^*^- ^*'-
being half of the required twist. Drafts are then cut in the ends of the stone until the tops of the twist rules, when applied as in Fig. 30, are in a plane. The remainder of the projecting face is removed until a straight-edge, when applied parallel to the edge of the stone, will just touch the end drafts and the intermediate surface.
If the surface is to be twisted at only one end, a parallel rule and a twist rule are used.
189. Making the Drawings. The method of making work- ing drawings for constructions in stone will appear in subsequent chapters, in connection with the study of the structures them- selves; but for detailed instructions, see the text-books on Stere- otomy or Stone Cutting.
Art. 3. Methods of Finishing the Surfaces.*
190. "All stones used in building are divided into three classes, according to the finish of the surface; viz. :
I. Rough stones that are used as they come from the quarry.
II. Stones roughly squared and dressed.
III. Stones accurately squared and finely dressed.
" In practice, the line of separation between them is not very distinctly marked, but one class gradually merges into the next.
191. I. " Unsquared Stones. This class covers all stones which are used as they come from the quarry, without other preparation than the removal of very acute angles and excessive pro- jections from the general figure. The term ^ backing,^ which is frequently applied to this class of stone, is inappropriate, as it prop- erly designates material used in a certain relative position in a wall, whereas stones of this kind may be used in any position.
192. II. " Squared Stones. This class covers all stones that
* This article is taken from the report of the committee of the American Socieljr of Civil Engineers previously referred to.
13a STONE CUTTIXG. [CHAP. VI.
are roughly squared and roughly dressed on beds and joints. The dressing is usually done with the face hammer or ax, or in soft stones with the tooth hammer. In gneiss it may sometimes be necessary to use the point. The distinction between this class and the third lies in the degree of closeness of, the joints. Where the dressing on the joints is such that the distance between the general planes of the surfaces of adjoining stones is one half inch or more, the stones properly belong to this class.
*' Three subdivisions of this class may be made., depending on the character of the face of the stones:
" (a) Q,uarry-faced stones are those whose faces are left un- touched as they come from the quarry.
'^ (b) Pitch-faced stones are those on wliich the arris is clearly defined by a line beyond which the rock is cut away by the pitching chisel, so as to give edges that are approximately true.
" (c) Drafted Stones are those on which the face is surrounded by a chisel draft, the space inside the draft being left rough. Ordi- narily, however, this is done only on stones in which the cutting of the joints is such as to exclude them from this class.
" In ordering stones of this ciass the specifications should always state the width of the bed and end joints which are expected, and also how far the surface of the face may project beyond the plane of the edge. In practice, the projection varies between 1 inch and 6 inches. It should also be specified whether or not the faces are to be drafted.
193. III. " Cut Stones. This class covers all squared stones with smoothly-dressed beds and joints. As a rule, all the edges of cut stones are drafted, and batween the drafts the stone is smoothly dressed. The face, however, is often left rough where construction is massive.
"In architecture there are a great many ways in which the faces
of cut stone may be dressed.
. ^ - -- \ \ ;■
but the following are those that will usually be met in engineering work:
" Rough-pointed. When it is necessary to remove an inch Fig. 31.-ROUGH-POINTED. or jnore from the face of a
stone, it is done bv th? pick or heavy point until the projections.
ART. 3.]
METHODS OF FI^'"ISHI^"G SURFACES.
183
vary from ^ inch to 1 inch. The stone is then said to be rough- pointed (Fig. 31). In dressing
Fig. 32. — Fine-pointed.
limestone and granite, this operation precedes all others.
"Fine-pointed. (Fig. 32). If a smoother finish is desired, rough pointing is followed by fine pointing, which is done with a fine point. Fine point- ing is used only where the finish made by it is to be final, and never as a preparation for a final finish by another tool.
" Crandalled. This is only a speedy method of pointing, the effect being the same as fine pointing, except that the dots on the stone are more regular. The variations of level are about ^ inch, and the rows are made parallel. When other rows at right angles to the first are introduced, the stone is said to be cross-crandalled. Fig. 33.
Fig. 33.— Crandalled.
Fig. 34. — Axed.
" Axed, or Pean-hammered, and Patent-hammered. These two
vary only in the degree of smoothness of the surface which is pro- duced. The number of blades in a patent hammer varies from 6 to 12 to the inch; and in precise specifications the number of cuts to the inch must be stated, such as 6-cut, 8-cut, 10-cut, 12-cut. The effect of axing is to cover the surface with chisel marks, which are made parallel as far as practicable. Fig. 34. Axing is a final finish.
" Tooth-axed. The tooth-ax is practically a number of points, and it leaves the surface of a stone in the same condition as fine pointing. It is usually, however, only a preparation for bush-ham- mering, and the work is then done without regard to effect so long as the surface of the stone is sufficiently leveled.
" Bush-hammered. The roughnesses of a stone are pounded off by
134
STONE CUTTING.
[chap. VI.
the bush hammer, and the stone is then said to be 'bushed/
This kind of 'finish is dangerous
Fig. 35.— Bush-hammered.
Fig. 36.— Rubbed.
on sandstone, as experience has shown that sandstone thus treated is very apt to scale. In dressing limestone which is to have a bush- hammered finish, the usual se- quence of operation is (1) rough- pointing, (2) tooth-axing, and (3) bush-hammering. Fig. 35.
" Rubbed. In dressmg sandstone and marble, it is very common to give the stone a plane surface at once by the use of tlife stone-saw [§ 181]. Any roughnesses left by the saw are removed by rubbing with grit or sandstone [§ 181]. Such stones, therefore, have no margins. They are frequently used in architecture for string-courses, lintels, door-jambs, etc. ; and they are also well adapted for use in facing the walls of lock- chambers and in other localities where a stone surface is liable to be rubbed by vessels or other moving bodies. Fig. 36.
" Diamond Panels. Sometimes the space between the margins is sunk immediately adjoining them and then rises gradually until the four planes form an apex at the middle of tlie panel. In general, such panels are called diamond panels, and the one just described. Fig. 37, is called a sunk diamond panel. When the surface of the stone rises grad- ually from the inner lines of the margins to the middle of the panel, it is called a raised diamond panel. Both kinds of finish are common on bridge quoins and similar work. The details of this method should be given in the specifications."
FiQ. 37.— Diamond Panel.
CHAPTER VII. STONE MASONRY.
In preparing specifications, it is not safe to depend alone upon the terms in common use to designate the various classes of masonry; but every specification should contain an accurate description of the character and quality of the work desired. Whenever practicable, samples of each kind of cutting and masonry should be prepared beforehand, and be exhibited to the persons who propose to under- take the work.
194. Definitions of Parts of the Wall.* Face, the front surface of a wall; hack, the inside surface.
Facing, the stone which forms the face or outside of the wall. Backing, the stone which forms the back of the wall. Filling, the interior of the wall.
Batter. The slope of the surface of the wall.
Course. A horizontal layer of stone in the wall.
Joints. The mortar-layer between the stones. The horizontal joints are called bed-Joints or Bim^p]y beds; the vertical joints are sometimes called the builds. Usually the horizontal joints are called beds, and the vertical ones Joints.
Coping. A course of stone on the top of the wall to protect it.
Fainting. A better quality of mortar put in the face of the joints to help them to resist weathering.
Bond. The arrangement of stones m adjacent courses (§ 202).
Stretcher. A stone whose greatest dimension lies parallel to the face of the wall.
Header. A stone whose greatest dimension lies perpendicular to the face of the wall.
Quoin. A corner-stone. A quoin is a header for one face and a stretcher for the other.
DoivelSo Straight bars of iron which enter a hole in the upper side of one stone and also a hole in the lower side of the stone next •above.
Cramps. Bars of iron having the ends turned at right angles to
* The definitions in this chapter are in accordance with the recommendations of the Committee of the American Society of Civil Engineers previously referred to, and conform to the best practice. Unfortunately they are not universally adopted.
135
136
STONE MASONKY.
[chap. VII.
to the body of the bar, which enter holes in the upper side of ad- jacent stones.
195. Definitions of Kinds of Masonry. Stone masonry is classified (1) according to the degree of finish of the face of the stones, as quarry-faced, pitch-faced, pointed, bush-hammered, etc. ; (2) according to whether the horizontal joints are more or less con- tinuous, as range, broken range, and random; and (3) according to the care employed in dressing the beds and joints, as ashlar, sqnared-stone, and rubble.
196. Quarry-faced Masonry. That in which the face of the stone is left as it comes from the quarry. Fig. 38.
Pitch-faced Masonry. That in which the face edges of the beds are pitched to a right line. Fig. 39.
Cut-stone Masonry. That in which the face of the stone is finished by one of the methods described in §§ 190-193.
197. Range. Masonry in which a course is of the same thick- ness throughout. Fig. 40.
BroTcen Range. Masonry in which a course is not continuous thronghout. Fig. 41.
Random. Masonry which is not laid in courses at all.
Fig. 38.
Fig. 39.
Fig. 42.
~~T~—
Fig. 40.— Range.
Fig. 41.— Broken Range.
Fig. 42.— Random.
Any one of these three terms may be employed to designate the coursing of either ashlar (§ 196) or sqnare-stone masonry (§ 197), but can not be applied to rubble (§ 198).
198. Ashlar. Cut-stone masonry, or masonry composed of any of the various kinds of cut-stone mentioned in § 193. According to the Report of the Committee of the American Society of Civil Engineers, " when the dressing of the joints is such that the dis- tance between the general planes of the surfaces of adjoining stones is one half inch or less, the masonry belongs to this class. ' ' From
DEFINITIONS OF KINDS OF MASONRY.
137
its derivation ashlar apparently means large, square blocks; but practice seems to have made it synonymous with " cut-stone," and this secondary meaning has been retained for convenience. The coursing of ashlar is described by prefixing range, broken range, or random; and the finish of the face is described by prefixing the name of the cut-stone (see §§ 190-93) of which the masonry is composed.
Small Ashlar. Cut-stone masonry in which the stones are less than one foot thick. The term is not often used.
Rough Ashlar. A term sometimes given to squared-stone masonry (§ 197), either quarry-faced or pitch-faced, when laid as range-work ; but it is more logical and more expressive to call such work range squared-stone masonry.
Dimension Sfo?ies. Cut-stones, all of whose dimensions have been fixed in advance. " If the specifications for ashlar masonry are so written as to prescribe the dimensions to be used, it will not be necessary to make a new class for masonry composed of suck stones. ' '
Squared-stone Masonry. Work in which the stones are roughly squared and roughly dressed on beds and joints (§ 192). The distinction between squared-stone masonry and ashlar (§ 196) lies in the degree of closeness of the joints. According to the Eeport of the Committee of the American Society of Civil Engineers, " when the dressing on the joints is such that the distance between the general planes of the surface of adjoining stones is one half inch or more, the stones properly belong to this class ; ' ' nevertheless, such masonry is often classed as ashlar or cut-stone masonry.
Bubble Masonry.
(§ 191).
Uncoursed Bubble. laid without any at- tempt at regular courses. Fig. 43.
Coursed Bubble. Unsquared-stone ma- sonry which is leveled off at specified heights to an approximately horizontal surface. It may be specified that the stone shall be rough
Masonry composed of unsquared stone Masonry composed of unsquared stones
^^^
Fig. 43.
Fig. 44.
]y shaped with the hammer, so as to fit approximately. Fig. 44.
138 STOISTE MASON"RT. [CHAP. VII.
199. Genesal Rules. Eankine gives the following rules to be observed in the building of all classes of stone masonry:
" I. Build the masonry, as far as possible, in a series of courses, perpendicular, or as nearly so as possible, to the direction of the pressure which they have to bear; and by breaking joints avoid all long continuous joints parallel to that pressure.
" II. Use the largest stones for the foundation course.
" III. Lay all stones which consist of layers in such a manner that tl>e principal pressure which they have to bear shall act in a direction perpendicular, or as nearly so as possible, to the direction of the layers. This is called laying the stone on its natural led, and is of primary importance for strength and durability.
''IV. Moisten the surface of dry and porous stones before bed- ding them, in order that the mortar may not be dried too fast and reduced to powder by the stone absorbing its moisture.
"V. Fill every part of every joint, and all spaces between the stones, with mortar, taking care at the same time that such spaces shall be as small as possible."
Another and very important rule is: the rougher the stones, the better the mortar should be. The principal object of the mortar is to equalize tiie pressure; and the more nearly the stones are reduced to closely fitting surfaces, the less important is the mortar. Not infrequently this rule is exactly reversed ; i. e., the finer the dressing, the better the quality of the mortar used.
200. Ashlar Masonry. For definitions of this class of masonry and its subdivision, see § 196.
The strength of a mass of ashlar masonry depends upon the size of the blocks in each course, upon the accuracy of the dressing, and upon the bond.
In order that the stones may not be liable to be broken across, no soft stone, such as the weaker kinds of sandstone and granular limestone, should have a length greater than 3 times its depth; but in harder materials, the length may be 4 or 5 times the depth. The breadth in soft materials may range from 1^ to 2 times the depth ; in hard materials, it may be 3 times the depth.
201. Dressing. The closeness with which stones fit is depend- ent solely upon the accuracy with which the surfaces in contact are wrought, or dressed, and is of special importance in the case of bed-joints. If any part of the surface projects beyond the plane
ASHLAR MASONRY. 139
of the chisel-draft, that projecting part will have to bear an undue share of the pressure, the joint will gape at the edges, — constituting what is called an open joint, — and the whole will be wanting in stability. On the other hand, if the surface of the bed is concave, having been dressed down below the plane of the chisel-draft, the pressure is concentrated on the edges of the stone, to the risk of splitting them off. Such joints are said to he flushed. They are more diflBcult of detection, after the masonry has been built, than open joints ; and are often executed by design, in order to give a neat appearance to the face of the building. Their occurrence must therefore be guarded against by careful inspection during the progress of the stone cutting.
Great smoothness is not desirable in the joints of ashlar masonry intended for strength and stability ; for a moderate degree of rough- ness adds at once to the resistance to displacement by sliding, and to the adhesion of the mortar. When the stone has been dressed so that all the small ridges and projecting points on its surface are reduced nearly to a plane, the pressure is distributed nearly uni- formly, for the mortar serves to transmit the pressure to the small depressions. ' Each stone should first be fitted into its place dry, in order that any inaccuracy of figure may be discovered and cor- rected by the stone-cutter before it is finally laid in mortar and settled in its bed.
The thickness of mortar in the joints of the very best ashlar masonry — for example, the United States post-office and custom- house buildings in the principal cities — is about ^ of an inch ; in first-class railroad masonry — for example, important bridge piers and abutments, and large arches — the joints are from i to |- of an inch. No cutting should be allowed after the stone has been set in mortar, for fear of breaking the adhesion of the mortar.
A chisel-draft 1^ or 2 inches wide is usually cut at each exterior corner.
202. Bond. No side-joint of any course should be directly above a side- joint in the course below ; but the stones should overlap, or break joint, to an extent of from 1 to 1^ times the depth of the course. This is called the ho7id of the masonry. The effect is that each stone is supported by at least two stones of the course below, and assists in supporting at least two stones of the course above. The
140 STOXE MASOXRY. [CHAP. YIL
object is twofold : first, to distribute the pressure, so that inequali- ties of load on the upper part of the structure (or of resistance at the foundation) may be transmitted to and spread over an increas- ing area of bed in proceeding downwards (or upwards) ; and second, to tie the building together, i. e., to give it a sort of tenacity, both lengthwise and from face to back, by means of the friction of the stones where they overlap.
The strongest bond is that in which each course at the face of the strvicture contains a header and a stretcher alternately, the outer end of each header resting on the middle of a stretcher of the course below, so that rather more than one third of the area of the face consists of ends of headers. This proportion may be deviated from when circumstances require it, but in every case it is advisable that the ends of headers should not form less than owe fourth of the whole area of the face of the structure. A header should extend entirely through the wall, and should be over the middle of the stretcher in the course below.
A trick of masons is to use "blind-headers," or short stones that look like headers on the outside but do not go deeper into the wall than the adjacent stretchers. When a course has been put on toy) of these, they are completely covered up ; and, if not suspected, the fraud will never be discovered unless the weakness of the wall reveals it.
Where very great resistance to displacement of the masonry is required (as in the upper courses of bridge piers, or over openings, or where new masonry is joined to old, or where there is danger of unequal settlement), the bond is strengthened by dowels or by cramp-irons (§ 195) of, say, l^-inch round iron set with cement mortar.
203. Backing. Ashlar is usually backed with rubble masonry (§ 213), which in such cases is specified as coursed rubble. Special care should be taken to secure a good bond between the rubble backing and the ashlar facing. Two stretchers of the ashlar fac- ing having the same width should not be placed one immediately above the other. The proportion and length of the headers in the rubble backing should be the same as in the ashlar facing. The " tails '' of the headers, or the parts which extend into the rubble backing, may be left rough at the back and sides; but their upper and lower beds should be dressed to the general plane of the bed of
ASHLAR MASONRY. 141
the course. These ''tails" may taper slightly in breadth, but should not taper in depth.
The backing should be carried up at the same time with the face-work, and in courses of the same depth; and the bed of each course should be carefully built to the same plane with that of the ashlar facing. The rear face of the backing should be lined to a fair surface.
204. Pointing. In laying masonry of any character, whether with common or hydraulic mortar, the exposed edges of the joints will naturally be deficient in density and hardness. The mortar in the joints near the surface is especially subject to dislodgmeut, since the contraction and expansion of the masonry is liable either to separate the stone from the masonry or to crack the mortar in the joint, thus permitting the entrance of rain-water, which, freezing, forces the mortar from the joints. Therefore it is usual, after the masonry is laid, to refill the joints as compactly as possible, to the depth of at least half an inch, with mortar prepared especially for this purpose. This operation is called pointing.
The very best cement mortar should be used for pointing, as the best becomes dislodged all too soon. Clear Portland cement mor- tar is the best, although 1 volume of cement to 1 of sand is fre- quently used in first-class work. The moi-tar, when ready for use, should be rather incoherent and quite deficient in plasticity. Before applying the pointing, the joint should be well cleansed by scrap- ing and brushing out the loose matter, and then be well moistened. Of course, the cleansing out of the joints can be most easily done v/hile the mortar is new and soft. The depth to which the mortar shall be dug out is not often specified ; it is usually cleaned out about half an inch deep, but should be at least an inch. In the Brooklyn bridge piers the joints were cleared 1^ inches' deep.
The mortar is applied with a mason's trowel, and the joint well calked with a calking iron and hammer. In the very best Avork, the joint is also rubbed smooth with a steel polishing tool. Walls should not be allowed to dry too rapidly after pointing ; therefore, pointing m hot weather should be avoided.
205. Amount of Mortar. The amount of mortar required for ashlar masonry varies with the size of the blocks, and also with the closeness of the dressing. With f- to i-inch joints and 12- to 20-inch courses, there will be about 2 cubic feet of mortar jmt
142 STONE MASONRY. [CHAP. VII-
cubic yard; with larger blocks and closer joints, i. e., in the best masonry, there will be abont 1 cubic foot of mortar per yard of masonry. Laid in 1 to 2 mortar, ordinary ashlar will require ^ to ^ of a barrel of cement per cubic yard of masonry.
For the quantities of cement and sand required for a cubic yard of mortar of different compositions, see page 88.
206. When Employed. Ashlar masonry is used for piers, abut- ments,, arches, and parapets of bridges; for hydraulic works; for facing-qnoins, and string courses; for the coping of inferior kinds of masonry and of brick work ; and, in general, for works in which great strength and stability are required.
207. Specifications for Ashlar. The specifications for ashlar, or " first-class masonry " as employed on the railroads, are about as follows : *
Ashlar shall consist of range pitch-faced masonry. The stone shall be of durable quality; and shall be free from seams, powder cracks, drys, flaws, or other imperfections.
All foundation courses sball be laid with selected, large, flat stones not less
than f inches in thickness, nor of less superficial surface than fifteen (15)
square feet.
The courses shall be not less than inches thick nor more tban
inches.^: The courses shall be continuous around and through the wall ; and DO course shall be thicker than the one below it, except that the footing course may be thinner than the one next above. Stretchers shall be at least twice as wide as thick, and at least four times as long as thick. Headers shall be, for at least three fourths of their length, not less than twice as wide as thick; and shall extend entirely through the wall, or have a length not less than five times the thickness of the course. The masonry shall consist of headers and stretchers alieruatiug; at least one third § of the face of the wall shall consist of headers. Stretchers of the same width shall not be placed immediately one above the other ; but this shall not apply to the ends of stretchers where headers come centrally between stretchers. Every header shall be immediately over a stretcher of the course next below. Joints on the face of the wall shall be broken at least three quarters of the thickness of the course.
The beds and the vertical joints for 12 inches back from the face of the wall shall be dressed, before being brought to the wall, so as to form mortar
* For complete specifications for railroad and also other kinds of masonry, see Appendix I, page 529.
f Frequently 12 ; sometimes 18.
J The courses of the classes of masonry referred to above usually range from 14 to 30 inches ; but, of course, may vary according to the circumstances, and for some purposes may be as low as 10 inches.
§ Often specified as one fourth.
SQUARE-STOKED MASONRY. 143-
joints not less than one quarter inch nor more than one half inch in thickness. All stones shall be laid on the natural bed. No part of a stone shall extend beyond the back edge of the under bed. All corners and batter lines shall have a neat chisel-draft one and one half inches -wide on each face. The pro- jections of the rock- face must not exceed four inches beyond the draft-lines ; and in tunnel side-walls, the projection must not exceed two inches. The face-edge of the joiut shall be pitched to a straight line.
The backing shall consist of stone of the same thickness as the correspond- ing face stone. When walls exceed four feet in thickness, there shall be as many headers of the same size in the back of the wall as in the face, so ar- ranged that a header in the rear of the wall shall be between two headers in the front. The backing shall be so laid as to leave no spaces between the stones over six inches wide, which spaces shall be filled with spalls set in cement mortar. No spalls shall be allowed in the bed joints.
The coping shall be formed of large flat stones, which shall extend entirely across the wall when the same is not more than six feet wide. The steps of wing walls shall be capped with stone covering the entire step and extending under the step next above at least twelve inches. Coping and step stones shall be at least twelve inches thick, and have such projections as the engineer may direct [usually 3 to 6 inches]. The tops and faces of copings and step stones shall be bush-hammered, and their joints and beds cut to one quarter inch throughout.
208. Sqtjared-stone Masonry. For definitions of this class of masonry and its subdivisions, see § 197. The distinction between squared-stone masonry and ashlar lies in the degree of closeness of the joints. According to the Report of the Committee of the American Society of Civil Engineers, " when the dressing on the joints is such that the distance between the general planes of the surfaces of adjoining stones is one half inch or more, the stones properly belong to this class; " however, such masonry is freqi;ently classed as ashlar or cut-stone masonry.
Squared-stone masonry is usually quarry-faced, random-work, although pitch-faced range-work is not uncommon. The quoins and the sides of openings are usually reduced to a rough-smooth surface with the face-hammer, the ordinary ax, or the tooth-ax. This work is a necessity where door or window frames are inserted; and it greatly improves the general effect of the wall, if used wherever a corner is turned.
209. Squared-stone masonry is distinguished, on the one hand, from ashlar in having less accurately dressed beds and joints, and, on the other hand, from rubble in being more carefully constructed. In ordinary practice, the field covered by this class is not very definite. The specifications for " second-class masonry" as used
144 STONE MASONRY. [CHAP. VII.
on railroads nsually conform to the above description of qnarry-faced, range sqnared-stone masonry; but sometimes this grade of masonry is designated " superior rubble."
210. Amount of Mortar Required. The amount of mortar required for squared-stone masonry varies with the size of the stones and with the quality of the masonry ; as a rough average, ■one sixth to one quarter of the mass is mortar. When laid in 1 to 2 mortar, squared-stone masonry will require ^ to f of a barrel of cement per cubic yard of masonry.
For quantities of cement and sand required for mortars of various compositions, see the table on page 88.
211. Backing and Pointing. The statements concerning the backing and pointing of ashlar (§§ 203 and 204) apply substantially to squared-stone masonry. As the joints of squared-stone masonry are thicker than those of ashlar, the pointing should be done pro- portionally more carefully; while as a rale it is done much more carelessly. The mortar is often thrown into the joint with a trowel, and then trimmed top and bottom to give the appearance of a thinner joint. Such work is called ribbon pointing. Trimming the pointing adds to the appearance but not to the durability. When not trimmed it is called dashed pointing.
212. Specifications for Squared-stone Masonry. Squared-stone masonry is employed for the piers and abutments of lighter bridges, for small arches, for box-culverts, for basement walls, etc. The specifications are about as follows : *
The stones shall be of durable quality; and shall be free from seams, powder cracks, drys, or other imperfections.
The courses shall be not less than 10 inches thick.
Stretchers shall be at least twice as wide as thick, and at least four times as long as thick. Headers shall be at least five times as long as thick, and at least as wide as thick. There shall be at least one header to three stretchers. Joints on the face shall be broken at least 8 inches.
The beds and vertical joints for 8 inches back from the face of the wall shall be dressed to make joints one half to one inch thick. The front edge of the joint shall be pitched to a straight line. All corners and batter-lines shall be hammer-dressed.
The backing shall consist of stones not less in thickness than the facing. At least one half of the backing shall be stones containing 3 cubic feet. The backing shall be laid in full mortar beds; and the vertical joints shall
* For complete specifications for masonry for various purposes, see Appendix I, page 529.
BUBBLE MASONRY. 145
also be filled with mortar. The spaces between the large stones shall be filled with spalls set in mortar.
The coping shall be formed of large flat stones of such thickness as the engineer may direct, but in no case to be less than eight inches (8). The upper surface of the coping shall be bush-hammered, and the joints and beds shall be dressed to one half an inch (^") throughout. Each stone must extend sniirely across the wall when the wall is not more than four feet (4) thick.
213. Rubble Masonry. For definitions connected with this class of masonry, see § 198.
The stones used for rubble masonry should be prepared by simply knocking off all the weak angles of the block. It should be cleansed from dust, etc., and moistened, before being placed on its bed. This bed is prepared by spreading over the top of the lower course an ample quantity of good, ordinary-tempered mortar in which the stone is firmly embedded. The vertical joints should be carefully filled with mortar. The interstices between the larger masses of stone are filled by thrusting small fragments or chippings of stone into the mortar. In heavy walls of rubble masonry, the precaution should be observed to give the stones the same position in the masonry that they had in the quarry, i. e., to lay them on their "natural bed," since stone offers more resistance to pressure in a direction perpendicular to the quarry-bed than in any other. The directions of the laminas in stratified stones show the position of the quarry-bed.
To connect the parts well together and to strengthen the weak points, tliroughs or binders should be used in all the courses, and the angles should be constructed of cut or hammered stone.
When carefully executed with good mortar, rubble possesses all the strength and durability required in structures of an ordinary char- acter, and is much less expensive than ashlar. The difficulty is m getting it well executed. The most common defects are (1) not bring- ing the stones to an even bearing; (3) leaving large vertical openings between the several stones; (3) laying up a considerable height of the wall dry, with only a little mortar on the face and back, and then pouring mortar on the top of the wall; (4) using insufficient cement, or that of a poor quality. The last defect is usually obviated by furnishing the cement to the contractor ; and the second and third defects may be detected by probing the vertical Joints with a small steel rod. In order to secure good rubble, great skill and
146 STONE MASONET. [CHAP. VII.
care are required on the part of the mason, and constant watchful- ness on the part of the inspector.
A very stable wall can be built of rubble masonry without any dressing, except a draft on the quoins by which to plumb the cor- ners and carry them up neatly, and a few strokes of the hammer to spall off any projections or surplus stone. This style of work is not generally advisable, as very few mechanics can be relied upon to take the proper amount of care in leveling up the beds and filling the joints; and as a consequence, one small stone may jar loose and fall out, resulting probably in the downfall of a considerable part of the wall. Some of the naturally bedded stones are so smooth and uniform as to need no dressing or spalliug up; a wall of such stones is very economical, since there is no expense of cutting and no time is lost in hunting for the right stone, and yet strong, massive work is assured. However, many of the naturally bedded stones have inequalities on their surfaces, and in order to keep them level in the course it becomes necessary to raise one corner by placing spalls or chips of stone under the bed, and to fill the vacant spaces well and full with mortar. It is just here that the disadvantage of this style of work becomes apparent. Unless the mason places these spalls so that tlie stone rests firmly, /. e., does not rock, it will work loose, particularly if the structure is subject to shock, as the walls of cattle- guards, etc. Unless these spalls are also distributed so as to support all parts of the stone,' it is liable to be broken by the weight above it. A few such instances in the same work may occasion con- siderable disaster.
One of the tricks of masons is to put "nigger-heads" (stones from which the natural rounded surface has not been taken off) into the interior of the wall.
214. Rubble masonry h sometimes laid without any mortar, as in slope walls (§ 218), paving (§ 219), etc., in which case it is called dry rubble; but as such work is much more frequently designated as slope- wall masonry and stone-paving, it is better to reserve the term rubble for undressed stone laid in mortar. Occasionally box culverts are -built of the so-called dry rubble; but as such construc- tion is not to be commended, there is no need of a term to desig- nate that kind of masonry.
215. Amount of Mortar Required. If rubble masonry is com- posed of small and irregular stones, about one third of the mass
BUBBLE MASONRY. 14*!
^ill consist of mortar; if the stones are larger and more regular, one fifth to one quarter will be mortar. Laid in 1 to 2 mortar, ordinary rubble requires from one half to one barrel of cement per cubic yard of masonry.
For the amount of cement and sand required for mortar of va- rious compositions, see the table on page 88.
216. "When Employed. Rubble masonry of the quality described above is frequently employed for the smallest sizes of bridge abut- ments, small arch culverts, box and open culverts, foundations of buildings, etc., and for backing for ashlar masonry (§ 200).
217. Specifications for Rubble Masonry.* The following re- quirements, if properly complied with, will secure what is generally known among railroad engineers as superior rubble.
Rubble masonry shall consist of coursed rubble of good quality laid in cement mortar. No stone shall be less than six inches (6") in thickness, unless otherwise directed by the engineer. No stone shall measure less than twelve inches (13") in its least horizontal dimension, or less than its thickness. At least one fourth of the stone in the face shall be headers, evenly distributed throughout the wall. The stones shall be roughly squared on joints, beds, and faces, laid so as to break joints and in full mortar beds. All vertical spaces shall be flushed with good cement mortar and then be packed full with spalls. No spalls will be allowed in the beds. Selected stones shall be used at all angles, and shall be neatly pitched to true lines and laid on hammer-dressed beds; draft lines may be required at the more prominent angles.
The top of parapet walls, piers, and abutments shall be capped with stones extending entirely across the wall, and having a front and end projection of not less than four inches (4"). Coping stones shall be neatly squared, and laid with joints of less than one half inch (i"). The steps of wing-walls shall be capped with stone covering the entire step, and extending at least six inches (9') into the wall. Coping and step stones shall be roughly hammer- dressed on top, their outer faces pitched to true lines, and be of such thickness (not less than six inches) and have such projections as the engineer may direct.
' ' The specifications for rubble masonry will apply to rabble masonry laid Iry, except as to the use of the mortar (see § 214)."
218. Slope-wall Masonry. A slope-wall is a thin layer of masonry used to preserve tlie slopes of embankments, excavations, canals, river banks, etc., from rain, waves, weather, etc. The usual specifications are as follows: —
The stones must reach entirely through the wall, and be not less than four inches (4") thick and twelve inches (12") long They must be laid with broken joints; and the joints must be as close and free from spalls as possible.
* For complete specifications for masonry for various purposes, see Appendix I.
148 STONE MASOXRT. [CHAP. VII.
219. Stone Paving. Stone paving is used for the inverts of arch cuiverts, for protecting the lower end of arches from undermining, and for foundations of box culverts and small arches. It is usually classed as dry rubble masonry, although it is occasionally laid with cement mortar. The usual specifications are about as follows :
Stone paving shall be made of flat stones from eight inches (8") to fifteen inches (15 ) in depth, set on edge, closely laid and well bedded in the soil, and shall present an even top surface.
220. Riprap. Eiprap is stone laid, without mortar, about the base of piers, abutments, etc., to prevent scour, and on banks to prevent wash. Wlien used for the protection of piers, the stones are dumped in promiscuoiTsly, their size depending upon the material at hand and the velocity of the current; stones of 15 to 25 cubic feet each are frequently employed. When used for the protection of banks, the riprap is laid by hand to a uniform thick- ness.
221. Strength of Stone Masonry. The results obtained by testing small specimens of stone (see § 14) are useful in determin- ing the relative strength of different kinds of stone, but are of no value in determining the ultimate strength of the same stone when built into a masonry structure. The strength of a mass of masonry depends upon the strengtli of the stone, the size of the blocks, the accuracy of the dressing, the proportion of headers to stretchers, and the strength of the mortar. A variation in any one of these items may greatly change the strength of the masonry.
The importance of the mortar as affecting the strength of masonry to resist direct compression is generally overlooked. The mortar acts as a cushion (§ 13) between the blocks of stone, and if it has insufficient strength it will be squeezed out laterally, pro- ducing a tensile strain in the stone; weak mortar thus causes the stone to fail by tension instead of by compression. No experiments have ever been made upon the strength of stone masonry under the conditions actually occurring in masonry structures, owing to the lack of a testing-machine of sufficient strength. Experiments made upon brick piers (§ 246) 12 inches square and from 2 to 10 feet high, laid in mortar composed of 1 volume Portland cement and 2 sand, show that the strength per square inch of the masonry is only about one sixth of the strength of the brick. An increase of 50 per cent, in the strength of the brick produced no appreciable
STEEXGTH OF STOXE MASOXEY. 149
effect on the strength of the masonry; but the substitution of cement mortar (1 Portland and 2 sand) for lime mortar (1 lime and 3 sand) increased the strength of the masonry 70 per cent. The method of failure of these piers indicates that the mortar squeezed out of the joints and caused the brick to fail by tension. Since the mortar is the weakest element, the less mortar nsed the stronger the wall; therefore the thinner the joints and the larger the blocks, the stronger the masonry, provided the surfaces of the stones do not come in contact.
It is generally stated that the working strain op stone masonry should not exceed one twentieth to one tenth of the strength of the stone; but it is clear, from the experiments on the brick piers re- ferred to above, that the strength of the masonry depends upon the strength of the stone only in a remote degree. In a general way it may be said that the results obtained by testing small cubes may vary 50 per cent, from each other (or say 25 per cent, from the mean) owing to undetected differences in the material, cutting, and manner of applying the pressure. Experiments also show that stones crack at about half of their ultimate crushing strength. Hence, when the greatest care possible is exercised in selecting and bedding the stone, the safe working strength of the stone alone should not be regarded as more than three eighths of the ultimate strength. A further allowance, depending upon the kind of struc- ture, the quality of mortar, the closeness of the joints, etc., should be made to insure safety. Experiments npon even comparatively large monoliths give but little indication of the strength of masonry. The only practicable way of determining the actual strength of masonry is to note the loads carried by existing structures. How- ever, this method of investigation will give only the load which does not crush the masonry, since probably no structure ever failed owing to the crushing of the masonry. After an extensive correspondence and a thorough search through engineering literature, the following list is given as showing the maximum pressure to which the several classes of masonry have been subjected.
222. Pressure Allowed. Early builders used much more mas- sive masonry, proportional to the load to be carried, than is cus- tomary at present. Experience and experiments have shown that such great strength is unnecessary. The load on the monolithic piers '•upporting the large chiirches in Europe does not exceed 3(?
150 STONE MASOXRY. [CHAP. VII.
tons per sq. ft. (420 lbs. per sq. in.),* or about one thirtieth of the ultimate strength of the stone alone. The stone-arch bridge of 140 ft. span at Pont-y-Prydd, over the Taff, in Wales, erected in 1750, is supposed to have a pressure of 72 tons per sq. ft. (1,000 lbs. per sq. in.) on hard limestone rubble masonry laid in lime mortar.f Rennie subjected good hard limestone rubble in columns 4 feet square to 22 tons per sq. ft. (300 lbs. per sq. in.).| The granite piers of the Saltash Bridge sustain a pressure of 9 tons per sq. ft. (125 lbs. per sq. in.).
The maximum pressure on the granite masonry of the towers of the Brooklyn Bridge is about 28 1^ tons per sq. ft. (about 400 lbs. per sq. in.). The maximum pressure on the limestone masonry of this bridge is about 10 tons per sq. ft. (125 lbs. per sq. in.). The face stones ranged in cubical contents from 1^ to 5 cubic yards; the stones of the granite backing averaged about 1^ cu. yds., and of the limestone about 1|- cu. yds. per piece. The mortar was 1 volume of Rosendale cement and 2 of sand. The stones were rough-axed, or pointed to |^-inch bed-joints and |-inch vertical face-joints.§ These towers are very fine examples of the mason's art.
In the Rookery Building, Chicago, granite columns about 3 feet square sustain 30 tons per sq. ft. without any signs of weakness.
In the Washington Monument, Washington, D. C, the normal pressure on the lower joint of the walls of the shaft is 20.2 tons per sq. ft. (280 lbs. per sq. in.), and the maximum pressure brought upon any joint under the action of the wind is 25.4 tons per sq. ft. (350 lbs. per sq. in.).]]
The pressure on the limestone piers of the St. Louis Bridge was, before completion, 38 tons per sq. ft. (527 lbs. per sq. in.); and after completion the pressure was 19 tons per sq. ft. (273 lbs. per sq. in.) on the piers and 15 tons per sq. ft. (108 lbs. per sq. in.) on the abut- ments.^
The limestone masonry in the towers of the Niagara Suspension
* In this connection it is convenient to remember that 1 ton per square foot is equivalent nearly to 14 (exactly 13.88) pounds per square inch, f The Technograph, University of Illinois, No. 7, p. 27. X Proc. Inst, of C. E., vol. x. p. 241.
§ F. CoUingwood, asst. engineer, in Trans. Am. Soc. of C. E. II Report of Col. T. L. Casey, U. S. A. , engineer in charge. \ History of St. Louis Bridge, pp. 370-74.
MEASUREMENT OF MASONRY. 151
Bridge failed under 36 tons per sq. ft., and were taken down, — how- ever, the masonry was not well executed. *
At the South Street Bridge, Philadelphia, the pressure on the limestone rubble masonry in the pneumatic piles is 15.7 tons per sq. ft. (220 lbs. per sq. in. ) at the bottom and 12 tons per sq. ft. at the top. '' This is unusually heavy, but there are no signs of weak- ness."! The maximum pressure on the rubble masonry (laid in cement mortar) of some of the large masonry dams is from 11 to 14 tons per sq. ft. (154 to 195 lbs. per sq. in.). The Quaker Bridge Dam is designed for a maximum pressure of 16f tons per sq. ft. (230 lbs. per sq. in.) on massive rubble masonry in best hydraulic cement mortar. J
223. Safe Pressure. In the light of the preceding examples it may be assumed that the safe load for the different classes of masonry is about as follows, provided each is the best of its class :
Concrete 5 to 15 tons per square foot.
Rubble, 10 to 15 " "
Squared stone, 15 to 20 " " " "
Limestone ashlar, . . . . 20 to 25 " " " "
Granite ashlar, 30 " " " "
224. Measurement of Masonry. The method of determining the quantity of masonry in a strttcttire is frequently governed l)y trade rules or local custom, and these vary greatly with locality. Masons have voluminotts and arbitrary rules for the measurement of masonry; for example, the masons and stone-ctttters of Boston at one time adopted a code of thirty-six complicated rules for the measurement of hammer-dressed granite. As an example of the indefiuiteness and arbitrariness of all such rules, we quote the follow- ing, which are said to be customary in Pennsylvania : " All open- ings less than 3 feet wide are counted solid. All openings more than 3 feet wide are taken out, but 18 inches is added to the running measurement for every jamb built. Arches are counted solid from the spring of the arch, and nothing allowed for arching. The corners of buildings are measured twice. Pillars less than 3 feet square are counted on three sides as lineal measurement, multiplied by the fourth side and depth; if more than 3 feet, the two opposite
* Trans. Am. Soc. of C. E., vol. xvii. pp. 204^13. t Und., vol. vli. pp. 305-6.
X Engineering Xeivs, vol. xix. p. 75.
STONE MASONRY. [CHAP. VII.
sides are taken; to each side 18 inches for each jamb is added to lineal measurement tliereof ; the whole multiplied by the smaller side and multiplied by the depth."
A well-established custom has all the force of law, unless due notice is given to the contrary. The more definite, and therefore better, method is to measure the exact solid contents of the masonry, and pay accordingly. In "net measurement" all openings are de- ducted; in "gross measurement" no openings are deducted.
The quantity of masonry is usually expressed in cubic yards. The perch is occasionally employed for this purpose; but since the supposed contents of a perch vary from 16 to 25 cubic feet, the term is very properly falling into disuse. The contents of a masonry structure are obtained by measuring to the neat lines of the design. If a wall is built thicker than specified, no allowance is made for the masonry outside of the limiting lines of the design; but if the masonry does not extend to the neat lines, a deduction is made for the amount it falls short. Of course a reasonable working allow- ance must be made when determining whether the dimensions of the masonry meet the specifications or not.
In engineering construction it is a nearly uniform custom to measure all masonry in cubic yards; but in architectural construc- tion it is customary to measure water tables, string-courses, etc., by the lineal foot, and window-sills, lintels, etc., by the square foot. In engineering, all dressed or cut-stone work, such as copings, bridge seats, cornices, water-tables, etc., is paid for in cubic yards, with an additional price per square foot for the surfaces that are dressed, cut, or bush-hammered.
225. Classification of Railroad Masonry. The stone masonry required in the construction of a railroad is usually classified about as follows: first-class masonry, second-class masonry, rubble masonry (sometimes called third-class masonry, §209), rubble masonry laid dry (§ 214), stone paving, slope-walls, and riprap. First-class ma- sonry is equivalent to ashlar (§§ 200-7) ; this head generally includes bridge abutments and piers of the larger class, and arch culverts of greater span than 10 feet. Sometimes second-class masonry is speci- fied as squared-stone masonry (§§ 208-12), and sometimes as superior rubble (§§ 213-17); it is used in less important structures than first- class masonry.
Frequently specifications recognize also the following classifica-
ESTIMATES OF COST. 153
tion : first-class arcli masonry, second-class arch masonry, first-class bridge-pier masonry, second-class bridge-pier masonry, and pedestal masonry. The quality of work thus specified is the same as for first- class and second-class masonry respectively, the only difference being peculiar to the form of the masonry structure, as will be dis- cussed 171 succeeding chapters. The specifications for each structure should give the quantities of each kind of masonry.
For complete specifications for railroad masonry, see Appendix I.
226. Estimates of Cost of Masonry. The following estimates of the cost of masonry, from Trautwine's Engineer's Pocket-hook,* are pronounced by experts to be as accurate as such averages can be stated, since every item is liable to great variation. The estimates are based on the assumption that a mason receives $3.50 and a laborer $2.00 per day of 8 hours.
227. " Quarrying. f After the preliminary expenses of purchas- ing the site of a good quarry, cleaning off the surface earth and disintegrated top rock, and providing the necessary tools, trucks, cranes, etc., the total net expenses fox getting out the rough stone for masonry ready for delivery may be roughly estimated thus : Stones of such size as two men can readily lift, measured in piles, will cost per cubic yard from i to ^ the daily wages of a quarry laborer. Large stones, ranging from ^ to 1 cubic yard each, got out by blasting, from 1 to 2 daily wages per cubic yard. Larger stones, ranging from 1 to 1^ cubic yards each, in which most of the work must be done by wedges in order that the individual stones shall come out in tolerably regular shape and conform to stipulated dimen- sions, from 2 to 4 daily wages per cubic yard. The lower prices are low for sandstone, while the higher ones are high for granite. Under ordinary circumstances, about 1^ cubic yards of good sandstone can be quarried at the same cost as 1 of granite — or, in other words, calling the cost of granite 1, that of sandstone will be f ; hence the means of the foregoing limits may be regarded as rather full prices for sandstone, rather scant for granite, and about fair for limestone or marble.
228. " Dressing.^ In the first place, a liberal allowance should be made for waste. Even when the stone wedges out handsomely on all sides in large blocks of nearly the required shape and size,
* Published by permission. + See Note 1, Appendix II. X See Notes 2 and 3, Appendix II.
154 STONE MASONRY. [CHAP. VII.
from ^ to :|^ of the rough block will generally not more than cover waste of dressing. In moderate-sized blocks (say averaging about ^ a cubic yard each) got out by blasting, from i to ^ will not be too much for stone of medium character as to straight splitting. The last allowance is about right for well-scabbled dressing. The smaller the stones the greater must be the allowance for waste. In large operations it becomes expedient to have the stones dressed, as far as possible, at the quarry, in order to diminish the cost of trans- portation, which, when the distance is great, constitutes an impor- tant item — especially when by land and on common roads.
229. " Ashlar. Average size of the stones, say 5 feet long, 2 feet wide, and 1.4 feet thick — or two such stones to a cubic yard. Then, supposing the stone to be of granite or gneiss, the cost per cubic yard of ashlar facing will be :
"Getting out the stone from the quarry by blasting, allow- ing i for waste in dressing, 1^ cubic yards at f 3.00
per yard $4 00
Dressing 14 sq. ft. of face at 35 cents, 4 90
Dressing 52 sq. ft. of beds and joints at 18 cents, ... 9 36
Net cost of the dressed stone at the quarry, . . . $18 26 Hauling (say 1 mile), loading, and unloading, .... 1 20
Mortar, say, 40
Laying, including scaffold, hoisting machinery, etc., . 2 00
Net cost |21 86
Profit to contractor, say 15 per cent., 3 28
Total cost per cubic yard, $25 14
" Dressing will cost more if the faces are to be rounded or moulded. If the stones are smaller than we have assumed, there will be more square feet per cubic yard to be dressed. If, in the foregoing case, the stones be perfectly well dressed on all sides, in- cluding the back, the cost per cubic yard would be increased about $10; and if some of the sides be curved, as in arch stones, say $12 or $14; and if the blocks be carefully wedged out to given dimen- sions, $16 or $18. Under these conditions the net cost of the dressed stone at the quarry will be $28, $31, and $35 per cubic yard, respectively.
"If the stone be sandstone with good natural beds, the getting out may be put at $3.00 per cubic yard. Face dressing at 26 cents
MARKET PRICE OF STONE. 155
pel sq, IL, say 13.64 per cu. yd. Beds and joints at 13 cents per sq. It., say ^6'.?6 per cu. yd. The total cost, then, is $19.55 instead of $25.14 for granite, and the net cost $17.00 instead of the $21.86 per cu. yd. for granite. The total cost of large, well-scabbled, ranged sandstone masonry in mortar may be taken at about $10 per cu. yd. 230. " Rubble. With stones averaging about |- cubic yard each, and common labor at $1 per day, the cost of granite ruhhle, such as is generally used as backing for the foregoing ashlar, will be about as follows :
Getting out the stone from the quarry by blasting, allow- ing I for vaste in scabbling, 1| cu. yds. @ $3.00, . $3 43
Hauling 1 mile, loading and unloading, 1 20
Mortar (2 cu. ft., or 1.6 struck bushels of quicklime, and 10 cu. ft. or 8 struck bushels of sand or graveJ, and mixing), 1 50
Scabbling, laying, scaffolding, hoisting machinery, etc., 2 50
Net cost, $8 63
Profit to contractor, say 15 per cent., 1 30
Total cost per cubic yard, $9 93
'* Common ruihle of small stones, the average size being such as two men can handle, costs to get it out of the quarry about 80 cts. per yard of pile, or, to allow for waste, say $1.00. Hauling ] mile, $1.00. It can be roughly scabbled and laid for $1. 20 more. Mortar, as above, $1.50. Total net cost, $4.70; or with 15 per cent, profit, $5.40, at the above wages for labor."
231. Market Price of Stone. The average market quotations to builders and contractors for the year 1888 were about as follows, f.o.h. (free on board) at the quarry :
Granite— rough $0 40 to $0 50 per cubic foot.
Limestone — common rubble, ... 1 00 " 1 50 per cubic yard.
" good range rubble, . . 1 50 " 2 00 " " "
" bridge stone 08 " 10 per cubic foot,
" dimension stone, ... 25 " 35 " " "
" copings, 20 " 35 " " "
Sandstone, 35 " 1 00 per cubic yard.
232. Cost of Masonry.* TJ. S. Public Buildings. The following table gives the average contract price during the past few years for cutting the stone for the United States government buildings : f
* For additional data, see Notes 1-6, Appendix II, pages 511-16. t American Architect, vol. xxii. pp. 6, 7.
156
STONE MASOIfEY.
[chap. VII.
TABLE 15. Cost op Cutting Stone for U. S. Public Bueldings.
|
Kind op Surface. |
Granite. |
Marble. |
Limestone and Sandstone. |
|||
|
Min. |
Max. |
Min. |
Max. |
Min. |
Max. |
|
|
Beds and joints, per sq. f t. . . . Pean-hammered, " " " ... Plain face, 6-cut, " " " . . . |
$0 30 45 |
$0 35 50 65 75 88 1 10 |
$0 20 30 |
10 25 35 |
$0 12 15 |
$0 15 20 |
|
" 8-cut, " " " ... |
||||||
|
" 10-cut, " " " ... |
||||||
|
" 12-cut, " " " ... |
||||||
|
Rubbed, " " " ... |
40 50 |
20 25 |
25 |
|||
|
Tooled, " " " ... |
30 |
|||||
The following table shows the contract price for the masonry of the United States public buildings :
TABLE 16. Cost of Masonry in U. S. Public Buildings.
Kind of Work.
Random rubble, limestone
" " sandstone
Squared masonry, sandstone
Coursed masonry, sandstone
Squared masonry, limestone
" " granite
Rock-face ashlar, "
" " " and cut-stone granite, avg.
Cut granite, basement and area walls
Rock-face ashlar, and cut and moulded trim- mings, Stony Point. Mich., sandstone. .
Trimmings. Bedford limestone, bid
Rock-face ashlar, granite, retaining wall . . . Dressed coping, " " " ...
White sandstone,— furnished only
Armijo " " "
Cut and moulded sandstone of superstructure " average bid. . . . " " " limestone, lowest bid .... .
average bid
Rock-face ashlar, cut and moulded trim- mings, Middlesex brownstoue
Cut and moulded, Bedford limestone
" " .sandstone
" " " limestone
" " sandstone
" granite, superstructure
Harrisburg, Va Cincinnati. O.. Denver, Col. . . . Pittsburgh, Pa.
Columbus, O. . . Memphis, Tenn Pittsburgh, Pa.
Fort Wayne, Ind. .
Memphis, Tenn. . .
Dallas, Tex
Denver, Col
Council Bluffs, la.
Cost Date. I per Cu. Ft.
Rochester, N. Y. Loiiisville, Ky. . .
Dallas, Tex
Hannibal, Mo.. . . Des Moines, la. . Pittsburgh, Pa...
1885 1884 1883 1886 1885 1885 1884 1886 1886 1886 1886
1885 1885 1886 1886 1885 1885 1885 1885 1885 1885
1884 1885 1885 1885 1887 1886
$0 20 20 20 35 60 70 68 30 1 38
1 60
2 00
1 52 1 65
1 00
2 50 35 73
1 91
2 VI
1 87
2 33
2 41 2 00 2 46
1 83
2 27
3 00
ACTUAL COST. 157
233. Railroad Masonry. Tlie following are tlie average prices actually paid in the construction of the Cincinnati Southern Rail- road, in 1873-77 : *
First-class bridge masonry, per cu. yd., . . . . • . $10 39
Second-class bridge masonry, in cement, per cu. yd., . 7 40
Second-class bridge masonry, dry, per cu. yd., . . . 7 02
First-class arch masonry, per cu. yd., 11 24
Second-class arch masonry, in cement, per cu. yd., ... 8 61
Second-class arch masonry, (fr^/, per cu. yd., 7 75
Brick-work in tunnels, per cu. yd 8 50
Brick-work in buildings, per cu. yd., 7 00
Box-culvert masonry, in cement, per cu. yd., 4 89
Box-culvert masonry, dry, per cu. yd., 4 32
Concrete, percu. yd., 5 52
Slope walls, per cu. yd., 4 41
Stone paving, per cu. yd. , 2 41
234. Tunnel Masonry. The following are the average pricesf paid in 1883-87 on the new Croton Aqueduct tunnel which su^jplies New York City with water. The mortar was 2 sand to 1 Eosendale cement.
Dimension-stone masonry (granite), $42 50
Brick-work lining, per cu. yd., 10 14
Brick-work backing, per cu. yd. 8 49
Rubble masonry, lining, per cu. yd 5 05
Concrete lining, 3 stone to 1 Roscudale cement, per cu. yd., 5 67
Concrete lining, 5 stone to 1 Roseudale, per cu. yd., . . 5 16
Concrete backing, 3 stone to 1 Roseudale, per cu. yd., . 4 73
Concrete backing, 5 stone to 1 Roseudale, per cu. yd., . 4 22
Fine-hammered face (6-cut) for cut stone, per sq. ft., , . 84
Rough-poiuted face for cut stone, per sq. ft., .... 50 Additional for all kinds of masonry laid in Portland
cement mortar, 2 to 1, per cu. yd., 1 78
Additional for all kinds of masonry laid in Rosendale
cement mortar, 1 to 1, per cu. yd., 1 20
235. Bridge-pier Masonry. The following are the details of the cost, to the contractor, of heavy first-class limestone masonry for bridge-piers erected in 1887 by a prominent contracting firm :
* Report of the Chief Engineer, December 1, 1877, Exhibit 3. t Report of the Commissioners, Table 4.
158 STONE MASONET. [CHAP. VIL.
Cost of stone (purchased), $4 50
Sand and cement, 52
Freight, 1 79
Laying, 1 40
Handling materials 65
Derricks, tools, etc., 40
Superintendence, office expense, etc., 68
Total cost per cubic yard $9 94
The following data coucerning the cost in 1887 of granite piera — two fifths cut-stone facing and three fifths rubble backing — ^are furnislied by the same firm. The rock was very hard and tough.
Facing : —
Quarrying, including opening quarry, $3 75
Cutting to dimensions, 6 75
Laying, 1 76
Transportation 2 miles, superintendence, and general ex- penses, . 2 05
Total cost per cubic yard, .... ... $14 31
Backing : —
Quarrying, $3 10
Dressing 3 60
Laying, 1 75
Sundries, 2 05
Total cost per cubic yard, $10 50
The first-class limestone masonry in the piers of the bridges across the Missouri at Plattsmouth (1879-80) cost the company $18.60 per cubic yard, exclusive of freight, engineering expenses, and tools.* The cost of first-class masonry in smallei piers usually ranges from $12 to $14 per cubic yard.
At Chicago in 1887 the contract price for the masonry in bridge piers and abutments was about as follows : Concrete, 1 Portland cement, 3 sand, 6 broken stone, $9.00 per en. yd.; concrete, 1 natural cement, 3 sand, 5 broken stone, $6.00 per cu. jd.; stone facing and coping, $30.00 per cu. yd.
236. Arch-culvert Masonry. The following are the details of tiie cost of the sandstone arch culvert (613 cu. yds.) at Nichols Hollow, on the Indianapolis, Decatur and Springfield Railroad,
* Report of the Chief Engineer, Geo. S. Morison.
ACTUAL COST.
J53
built iu 1887. Scale of wages per day of 10 hours — foreman, $3.50 ; cutters, $3.00 ; mortar mixer, 11.50 ; laborer, $1.25 ; water- boy, 50 cents ; carpenters, $2.50. f
TABLE 17.
Actual Cost op Akch Masonky on Indianapolis, Decatur and Spring
FIELD Railroad.
Cost.
Items.
Materials : —
Stone — 613 cu. yds. of sandstone @ $1 50
Cement— 130 bbls. German Portland® $3 17 = $412 50 40 " English " @ 3 25 = 130 00 80 " Louisville " @ 96 = 28 75
Sand— 7 car-loads® $5 50
Total for materials
Cutting : —
Cutters and helpers
Templates, bevels, straight-edges, etc
Repairs of cutters' tools
Water-boy
Total for cutting
Laying : —
Masons, 110 days @ $3.50
Masons' helpers
Mortar mixer
Water-boy
Arch centers, building and erecting
Derrick, stone chute, etc
Laying track
Total for laying
Pointing
Grand Total :
Total for labor
Total for materials
Total cost of masonry
$1,370 48 12 24 11 00 01
52 39 11 75
$1,445 62
$384 87
453 66
121 72
11 75
37 65
14 63
7 70
$1,032 08
$30 00
$2,507 60 1,529 25
09 02
$2 36
$0 63 74 20 02 06 02 01
$1 68
$0 05
$4 09 2 50
$4,036 85 $6 59
238. Snmmary of Cost. The following table, compiled from a large amount of data, will be convenient for hasty reference. Of course any such table must be used with caution, since such items are subject to great variation.
+ Data furnished by Edwin A. Hill, chief engineer.
160
STONE MASONRY.
[chap. VII.
TABLE 18. Summary of Cost of Masonry.
Description of 3Iasonry.
Arch masonry, first-class
Arch masoniy, second-class (iu cement).
Box-culvert masonry, iu cement
Brick masonry (see g 258)
Bridge masonry, first-class
Bridge masonry, second-class (in cement)
Concrete
Coping
Dimension-stone masonry, granite
Paving
Slope-wall masonry
Squared-stone masonry
Riprap
Rubble, first-class
Rubble, second-class (in cement)
Cost per Cubic Yard.
Min.
Max. Average.
$12 00 10 00
5 00 10 00 20 00 12 00
6 00 14 00 60 00
4 00
5 00 10 00
2 50
6 00 5 00
110 00 8 00
3 50 8 00
14 00 10 00
4 00 12 00 50 00
2 00
3 00 7 00 1 50
5 00 3 00
CHAPTER Vlli. BRICK MASONRY.
239. MORTAE. Lime mortar is generally employed lor brick masonry, particularly in architectural constructions. Many of the leading railroads lay all brick masonry in cement mortar, and the practice should be followed more generally. The weakest part of a brick structure is the mortar. The primary purpose of the mortar is to form an adhesive substance between the bricks ; the second is to form a cushion to distribute the pressure uniformly over the surface. If the mortar is weaker than the brick, the ability of the masonry to resist direct compression is thereby con- siderably reduced. For the reason, see § 13; for the amount, see the Table 19, page 164.
If the strains upon a wall were only those arising from a direct pressure, the strength of the mortar would in most cases be of comparatively little importance, for the crushing strength of aver- age quality mortar is far higher than the dead load which under ordinary circumstances is put upon a wall ; but, as a matter of fact, in buildings the load is rarely that of a direct crushing weight, other and more important strains being developed by the system of construction. Thus the roof tends to throw the walls out, the rafters being generally so arranged as to produce a considerable outward thrust against the wall. The action of the wind also produces aside strain which is practically of more importance than either of the others. In many cases the contents of a building exert an outward thrust upon the walls ; for example, barrels piled against the sides of a warehouse produce an outward pressure against the walls.
In many brick constructions the use of cement mortar is abso- lutely necessary — as, for example, in tall chimneys, where the bear- ing is so small that great strength of the cementing material is required.
240. The thickness of the mortar-joints should be about i to f of an inch. Thicker joints are very common, but should be avoided. If the bricks are even fairly good, the mortar is the weaker part of
161
162 BRICK MASONRY. [CHAP. VIII.
the wall ; hence the less mortar the better. Besides, a thin layer of mortar is stronger under compression than a thick one (see § 15). The joints should be as thin as is consistent with their insuring a uni- form bearing and allowing rapid work in spreading the mortar. The joints of outside walls should be thin in order to decrease the dis- integration by weathering. The joints of inside walls are usually made from | to ^ inch thick.
Brick should not be merely laid, but every one should be rubbed and pressed down in such a manner as to force the mortar into the pores of the bricks and produce the maximum adhesion ; with quick- setting cement this is still more important than with lime mortar. For the best work it is specified that the brick shall be laid with a ^' shove joint ;" that is, that the brick shall first be laid so as to project over the one below, and be pressed into the mortar, and then be shoved into its final position.
Lime mortar is liable to work out of the joints, owing to the action of the elements and to changes of temperature. Hence it is customary either (1) to lay the face in mortar containing more lime than that used for the interior, or (2) to lay the face in a mortar containing more or less cement, or "^ (3), in rare cases, to point the joints with neat cement mortar. Whatever the kind of mortar used, the finish of the face of the joint is important. The most
Fia. 47. - durable joint is finished as shown in Fig. 47, although, unfortunately for durability, it" is customary to make the slope in the opposite direction.
241. Since brick have great avidity for water, it is best to dampen them before laying. If the m.ortar is stiff and the brick dry, the latter absorb the water so rapidly that the mortar does not set properly, and will crumble in the fingers when dry. Neglect in this particular is the cause of most of the failures of brick-work. Since an excess of water in the brick can do no harm, it is best to thoroughly drench them with water before laying. Lime mortar is sometimes made very thin, so that the brick will not absorb all the water. This process interferes Avith the setting of the mortar, and particularly with the adhesion of the mortar to the brick. Watery mortar also contracts excessively in drying (if it ever does dry), which causes undue settlement and, possibly, cracks or distortion, Wetting the brick before laying will also remove the dust from the surface, which otherwise would prevent perfect adhesion.
BOND.
163
|
1 ' 1 1 ' 1 1 ' 1 1 ' 1 1 1 1 |
|
1 ' 1 1 ' 1 1 1 1 1 1 II |
|
1 ' 1 1 ' 1 1 1 1 1 1 II |
|
1 1 1 1 1 1 1 1 1 II |
|
1 ' 1 1 ' 1 1 ' 1 1 ' 1 1 1 1 |
Fig. 48. — English Bond.
242. SONO. The bricks used in a given wall being of uniform size are laid according to a uniform system, which is called the bond of the brick-work. As in ashlar masonry, so in brick-work, a lieader is a brick whose length lies perpendicular to the face of the wall; and a stretcher is one whose length lies parallel with the face. Brick should be made of such a size that two headers and a mortar- joint will occupy the same length as a stretcher.
243. English Bond. This consists in laying entire courses of
headers and stretchers, which some- times alternate, as in Fig. 48; but generally only one course of headers is laid for every two, three, four, etc., courses of stretchers. In ordinary practice the custom is to lay four to six courses of stretchers to one of head- ers. The stretchers bind the walls together lengthwise ; the headers, crosswise. The proportionate numbers of the courses of headers and stretchers should depend on the relative importance of transverse and longitudinal strength. The proportion of one course of headers to two of stretchers is that which gives equal tenacity to the wall lengthwise and crosswise.
In building brick-work in English bond, it is to be borne in mind that there are twice as many vertical or side Joints in a course of headers as there are in a course of stretchers ; and that unless in laying the headers great care be taken to make these joints very thin, two headers will occupy a little more space than one stretcher, and the correct breaking of the joints — exactly a quarter of a brick — ■ will be lost. This is often the case in carelessly built brick-work, in which at intervals vertical joints are seen nearly or exactly above each other in successive courses.
244. Flemish Bond. This consists of a header and a stretcher alternately in each course, so placed
that the outer end of each header lies on the middle of a stretcher in the course below (Fig. 49). The number of vertical joints in each course is the same, so that there is no risk of the correct breaking of the joints by a quarter of a brick being lost; and the wall presents a neater appearance than one built in
Fig. 49.— Flemish Bond.
164
BEICK MASONRY.
[chap. Till.
English bond. The latter, however, when correctly built, is stronger and more stable than Flemish bond.
245. Hoop-iron Bond. Pieces of hoop-iron are frequently laid flat in the bed-joints of brick-work to increase its longitudinal tenacity, about 2 inches of the ends of each piece being bent down and inserted into the vertical joints. Although thin strips of iron are generally employed, it would be better to use thicker pieces ; the value of the iron for this purpose depends wholly upon the rigidity of the ends which are turned down, and this will vary about as the square of the thickness. The strip of iron should be nearly as thick as the mortar-joint. This means of strengthening masonry is frequently employed over openings and to connect interior brick walls Avith stone fronts.
246. Compressive Strength of Brick Masonry. Experi- ments at AVatertown, Mass., with the United States testing-machine, upon piers 12 inches square and from 1 ft. 4 in. to 10 ft. high, gave results as follows :*
TABLE 19.
Strength of Brick Masonrt compared with that op the Brick and
THE Mortar.
|
« |
B-2-fe |
b |
||||||
|
g S o |
O . |
|||||||
|
z; B |
w a |
|||||||
|
Pu, |
T P! Z |
|||||||
|
H |
U n |
|||||||
|
n |
«ss |
HO |
||||||
|
?> |
Strength of the |
z^ |
||||||
|
b |
«^ . |
Pier in terms |
"Z ^ |
|||||
|
a |
°u |
O H Z; |
OF THE Strength |
5f: |
||||
|
s |
W o |
^"^ |
OF THE Brick. |
Hh b |
||||
|
Composition op the Mortab. |
u |
0" |
Sa« |
a ^ |
||||
|
6 |
B. |
5^ |
"ksS |
B a |
||||
|
1<5 |
w |
f as |
fc m a -< |
5^ |
||||
|
u |
° 5 « |
o s |
||||||
|
H |
o |
«»< |
n o ^iri |
a a |
||||
|
Bi |
5 m |
& CD B « g a J H g n K |
||||||
|
ft. |
a |
52 |
S == K K |
Min, |
Max. |
Mean. |
||
|
« |
^ |
P |
02 |
m |
||||
|
1 |
1 lime, 3 sand |
15 |
1,508 |
124 |
.06 |
.18 |
.10 |
}9, |
|
2 |
2 mortar (1 lime, 3 sand), 1 Rosen- |
|||||||
|
dale cement |
1 |
1,646 |
183 |
.11 |
9 |
|||
|
3 |
2 mortar (1 lime, 3 sand), 1 Port- |
|||||||
|
land cement |
1 1 8 |
1,411 1,972 2,544 |
192 162 545 |
.09 .13 .17 |
7 |
|||
|
4 |
1 Rosendale cement, 2 sand 1 Portland cement, 2 sand |
^9, |
||||||
|
5 |
.10 |
.27 |
4.7 |
|||||
|
fi |
Clear Rosendale |
521 3,483 |
||||||
|
7 |
Clear Portland cement |
1 |
2,375 |
.16 |
0 7 |
|||
* Report on " Tests of Metals, etc.," for the year ending June 30, 1884, pp. 69-122.
COMPRESSIVE STRENGTH. 165
The brick had an average strength of nearly 15,000 lbs. per sq. in., tested flatwise between steel. The mortar was 14^ months old when it was tested. The piers were built by a common mason, with only ordinary care; and they were from a year and a half to two years old when tested. Their strength varied with their height; and in a general way the experiments show that the strength of a prism 10 ft. high, laid in either lime or cement mortar, is about two thirds that of a 1-foot cube. A deduction derived from so few experiments (22 in all) is not, however, conclusive. The different lengths of the piers tested occurred in about equal numbers. The piers began to show cracks at one half to two thirds of their ultimate strength.
In attempting to draw conclusions' from any experiments, it must be borne in mind continually that the result of a single trial may possibly be greatly in error. In this case this precaution is very important, since the difference between experiments apparently exactly alike was in some cases as much as 50 per cent. A great variation in the results is characteristic of all experiments on stone, brick, mortar, etc. Except on the ground of a variation in ex- periments, it is difficult to explain why mortar No. 4 is weaker than No. 2, while the masonry is stronger ; or why the masonry of No. 5 is stronger than that of No. 7.
Of course the apparent efficiency of the masonry, as given in the table, depends upon the manner in which the strengths of the brick and mortar were determined, as well as upon the method of testing the masonry. For example, if the brick had been tested on end the apparent efficiency of the masonry would have been con- siderably more ; or if the mortar had been tested in thin sheets the strength of the masonry relative to that of the mortar would not have been so great.*
247. Some German experimentsf gave results as in the table
* It should be mentioned that the mortar with which these piers were built appears to be much weaker than similar mortar under like conditions. (Compare page 72, and pages 126, 166, 188, 197 of the Report of Tests of Metals, etc., made at Watertown in 1884.) Ordinarily, mortar is eight to ten times as strong in compression as in tension, whereas the first six mortars in the preceding table were but little stronger in compression than such mortar should have been in tension. The officer in charge is " unable to offer any explanation. The cement was bought on the market; the maker's name is not known. The cement was not tested." However, the experi- ments are consistent with themselves, and therefore show relative strengths correctly. + Van Nostrand's Engin'g Mag., vol. xxxiv. p. 240, from the Abstracts of the Inst, of C. E. (London), vol. 79, p. 376.
166
BRICK MASOISTRY.
[chap. VIII.
below. It is not stated how the strength of the brick or of the masonry was determined.* The term cement refers to Portland cement. According to the building regulations of Berlin, the safe load for brick masonry is one tenth of the results in the table.
TABLE 20. Relative Strength op Brick and Brick Masonry.
|
;Avkrage Crush- ing Strength OF Brick, in lbs. PER SQ. IN. |
Ultimate Strength, in lbs. per sq. in., of Brick-work with Mortar composed op— |
||||
|
Kind op Brick. |
1 Lime, 2 Sand. |
7 Lime, 1 Cement, 16 Sand. |
1 Cement, 6 Sand. |
1 Cement, 3 Sand. |
|
|
Clinker stock |
5,390 3,669 2,930 2,759 2,617 1,195 |
2,370 1,620 1,290 1,210 1,150 580 |
2,590 1,760 1.390 1,320 1,250 570 |
2,960 2,020 1,610 1,520 1,440 650 |
3 410 |
|
Selected " |
2,820 1 850 |
||||
|
Ordinary " |
|||||
|
Perforated |
1 710 |
||||
|
Porous |
1,650 750 |
||||
|
Porous perforated |
Table 19 shows conclusively that the strength of brick masonry is mainly dependent upon the strength of the mortar. An in- crease of 50 per cent, in the strength of the brick shows no appreciable effect on the strength of the masonry. Notice, however, that the masonry in the fifth line of Table 19 is 70 per cent, stronger than that in the first, due to the difference between a good Portland cement mortar and the ordinary lime mortar. In Table 20 notice that brick laid in a 1 to 3 Portland cement mortar is nearly 50 per cent, stronger than in a 1 to 2 lime mortar. Similar experiments f show that masonry laid in mortar composed of 1 part Rosendale cement and 2 parts sand is 56 per cent, stronger than when laid in mortar composed of 1 part lime and 4 parts sand. A member of the Institute of Civil Engi- neers (London) says| that brick-work laid in lime is only one fourth as strong as when laid in clear Portland cement. Probably the dif- ference in durability between cement mortar and lime mortar is considerably greater than their difference in strength.
* If the strength of the brick (in any line of the table) be represented by 100, that of the masonry is 44, 48, 55, and 63, respectively, which shows that the values in the table were not derived directly from experiments.
t Report of Experiments on Building Materials for the City of Philadelphia with the U. S. testing-machine at Watertown, Mass., pp. 32, 38.
X Proc. Inst, of C. E., vol. xvii. p. 441.
TRANSVERSE STRENGTH. 167
248. Pressure allowed in Practice. The pressure at the base of a brick shot-tower in Baltimore, 246 feet high, is estimated at 6-^ tons per sq. ft. (about 90 lbs. per sq. in.). The pressure at the base of a brick chimney at Glasgow, Scotland, 468 ft. high, is estimated at 9 tons per sq. ft. (about 125 lbs. per sq. in.); and in heavy gales this is increased to 15 tons per sq. ft. (210 lbs. per sq. in.) on the leeward side. The leading Chicago architects allow 10 tons per sq. ft. (140 lbs. per sq. in.) on the best brick- work laid in 1 to 2 Port- land cement mortar ; 8 tons for good brick-work in 1 to 2 Rosendale cement mortar ; and 5 tons for ordinary brick- work in lime mortar. Ordinary brick piers have been known to bear 40 tons per sq. ft. (560 lbs. per sq. in.) for several days without any sign of failure.
Tables 19 and 20 appear to show that present practice is very conservative with regard to the pressure allowed on brick masonry. According to Table 19 (page 164), the ultimate strength of the best brick laid in ordinary lime mortar is 110 tons per sq. ft.; if laid in 1 to 2 Portland cement mortar, 180 tons ; and by Table 20 (page 166) the strength of ordinary brick in 1 to 2 lime mortar is 100 tons per sq. ft., and in 1 to 3 Portland cement mortar 140 to'^s. From the above, it would seem, that reasonably good brick laid in good lime mortar should be safe under a pressure of 20 tons per sq. ft., and that the best brick in good Portland cement mortar should be safe under 30 tons per sq. ft. The nominal pressure allowed upon brick masonry depends upon the kind of materials employed ; the degree of care with which it is executed ; whether it is for a temporary or per- manent, an important or unimportant structure ; and, it may be added, the care with which the nominal maximum load is estimated.
249. Transverse Strength of Brick Masonry. Masonry is seldom employed where any strain except direct compression will come upon it, but sometimes it is subject to transverse strain. The transverse strength of brick-work depends theoretically upon the tensile strength of the brick and upon the adhesion and cohesion of the mortar, but practically the strength of the mortar deter- mines the strength of the masonry. For example, in the case of a high wall whose upper portion is overthrown by a lateral force or pressure of any kind, the failure is due either (1) to the breaking of the adhesion in the bed- joints and of the cohesion of the side-jofnts, or (2) to the ru^jture of the mortar in the bed-joints alone. The latter method of failure, however, is improbable, since the cohesion
J 68 BRICK MASONRY. [CHAP. VUL
of cement mortars is always much greater than their adhesion (com- pare §§ 134 and 137); and hence, in estimating the resistance of the wall to overturning, it becomes necessary to fix values for both the cohesive and adhesive strength of the mortar at the time when the structure is first exposed to the action of the lateral force or pres- sure, and also to ascertain the relative areas of beds and side-joints in the assumed section of rupture. In good brick-work the aggre- gate area of the side-joints, in any section parallel to tlie beds, will amount to about one seventh of the total area of such section. Hence, when the masonry is liable to be subjected to transverse strains the adhesive strength of the mortar is more important than its cohesive strength.
The adhesion of mortar to brick or stone has already been dis- cussed (§ 137). While the experiments uniformly show a relatively low adhesive power, it is well known that when old walls are de- molished the adhesion of even common lime mortar is found to be very considerable. Although the adhesive power of mortar may be small as compared with its tensile strength, good brick masonry has a considerable transverse strength.
Experiments made under the author's direction * indicate that brick beams bonded as regular masonry have a modulus of rupture equal to about twice the tensile strength of the mortar when built with ordinary care, and about three times when built with great care. When the beams are constructed as piers, i. e., with no interlocking action, the modulus of rupture is about equal to the tensile strength of the mortar.
250. Application. To illustrate the practical application of the fact that brick-work has a transverse strength, let it be required to compute the strain which may come upon a lintel, or girder used to support a brick wall over an opening, f
Let H = the height, in feet, of the wall above the opening ; H„ = the height, in feet, of the wall that produces a maxi- mum strain on the lintel ; Hs = the height, in feet, of the masonry when it will just support itself over the opening ; 8 = the span, in feet ; t = the thickness, in feet, of the wall ;
* The Technogkaph, University of Illinois, No. 7 (1892-93), pp. 29-37. t The principle of the following computations is from an editorial in Engineering (London), vol. xiv. pp. 44 and 72.
TRAXSYERSE STRENGTH. 169
R =■ the modulus of rupture, in pounds per square inch, of the brick-work ;
pr= the weight, in pounds, of a cubic foot of the wall. W varies from 100 to 140 pounds, and for conven- ience is here assumed to be 144 ; the error is always on the safe side ;
Ml = the bending moment on the lintel, in pounds per square inch.
Consider the masonry as a beam fixed at both ends and loaded uniformly. Then, by the principles of the resistance of materials, when the masonry is just self-supporting, one twelfth of the weight of the wall above the opening muUvplied by the span is equal to one sixth of the tensile strength multiplied by the thickness and also the square of the depth of the wall. The weight of the wall above the opening is W 8 H^ t. Hence
^{WSHJ)S=\{lUR)tH:, (1)
or
"'-is (^)
Notice that the weight of the wall over any given opening increases as the height, while the resistance increases as the, square of the height. The height for which the masonry isl self-supporting is given by equation (2) , for a height greater' than Hg the masonry would be more than self-supporting ; and for a height less than H^ the masonry would need extraneous support.
To find the height of the wall producing a maximum stress in the lintel, notice that the bending moment on the lintel is equal to the moment of the load minus the moment of the resistance of the brick-work over the opening ; or, in algebraic language,
Ml = -^{WSHt) S - U^UE)iH\
170 BRICK MASONRY. [CHAP. VIII.
Differentiating the above equation, regarding Jf, and H as the variables, and finding the maximum value of H in the usual way, we get
The fact that the value of H^ in equation (3) is one half of that of Hg in equation (2), shows that the maximum stress on the lintel occurs when the height of the wall is half of its self- supporting height, at which time one half of the wall will be self-supporting and one half will require extraneous support. Or, in other words, the greatest stress on a lintel due to a wall of any height Avill not be greater than that due to a distributed load of
i WH„,St = i W^. St = nearly 18 '^ pounds. . (4)
251. Examplex. To apply the above formula, assume that it is proposed to cut a 10-foot opening through an old brick wall, and that it is desirable to know whether the brick-work will be self-sup- porting, the wall rising 40 feet above the top of the opening. Sub- stituting the above data in equation (2) gives
(10)' 40 = \-w^ ', or i? = 1.25 lbs. per sq. in.
Hence, to be self-supporting across the opening, the wall must be capable of supjsorting a tensile strain of 1.25 pounds per square inch. It would be poor lime mortar that would not bear eight or ten times this. Notice that if the wall were only 4 feet high over the opening, instead of 40 feet, as above, the strength required would be 12.5 pounds ]Der square inch.
For another illustration, assume that a brick wall 1 foot thick is to be built over a 10-foot opening, and that we wish to know whether a timber 10 inches deep and 12 inches wide will sustain the load. Assuming the beam as being fixed at the ends, the timber will sustain a uniformly distributed load of 10 tons with a deflection of one twelfth of an inch. This is equivalent to the entire weight of the wall when 14 feet high. If the wall is to be carried higher
TRAXSTERSE STREiJinTH. 171
than this, the girder must be supported temporarily, or time must be given for the mortar to set.
However, before the wall is 14 feet above the opening, the brick- work at the bottom will have attained some strength, and therefore the load on the girder will not be as great as above. The average strength of the brick-work will always be at least the average between the strength at the top and the bottom ; that is, the average strength will always be more than half of that at the bottom. Since 10 tons is the maximum load allowed on the girder, and since the maximum load which comes upon it is half of the entire weight of the masonry above the opening,* the timber will receive its maximum load when the wall is twice 14 feet, or 28 feet, above the opening. The masonry may be run up 28 feet without necessitating any extraneous support for the lintel, provided time enough is allowed for the mortar to develop the average tensile strength found by substituting in (4) the maximum load allowed on the girder, and solving for R. Mak- ing this substitution gives
18 riOV 1 20000 = — ^-~ — , from which R = 0.90 lb. per sq. in. ft
With an average strength of 0.90 lb. per sq. in., the wall will become self-supporting when 55 feet above the opening.
252. Custom differs as to the manner of estimating the pressure on a girder due to a superincumbent mass of masonry. One extreme consists in assuming the masonry to be a fluid, and taking the load on the lintel as the weight of all the masonry above the opening. The opposite extreme consists in assuming the pressure to be the weight of the masonry included in a triangle of which the open- ing is the base and whose sides make 45° with this line. Both of these methods differ materially from the one discussed above ; and neither is defensible. As the wall is several days in building, the masonry first laid attains considerable streugth before the wall is completed; and hence, owing to the cohesion of the mortar, the final weight on the girder can not be equal to or compared with any fluid Folume.
The principle involved in the second method would be applicable
* See discussion of equation (3), above.
172 BRICK MASONRY. [CHAP. VIII.
to a wall composed wholly of perfectly smootli bricks. In a dry wall, the angle which the side lines make with the base would depend upon the bond and upon the relative length and breadth of the bricks. Assuming the boundary lines to make an angle of 45°
with the base, the method gives a load -^ times that (§ 250)
which takes account of the transverse strength of the masonry, i. e., the frictional and tensile resistance of the wall. If E is relatively large and S is small, this fraction will be more than unity, under which conditions the second method is safe. But if E is small and ;iS^ is large, then this fraction is less than one, Avhich shows that under these conditions the second method is unsafe.
The method of § 250 is quite simple and perfectly general. The substantial correctness of this method, illustrated in § 251, is proven by the fact that large openings are frequently cut through walls without providing any extraneous support ; and also by the fact that walls are frequently supported over openings on timbers entirely inadequate to carry the load if the masonry did not have considerable strength as a beam. The discussion in § 251 also makes clear why frequently a temporary support is sufficient. After the masonry has been laid a short time, the strength of the mortar causes it to act as a beam. The discussion also shows the advantage of using cement mortar (or better, quick-setting cement mortar) when it is desired that the masonry shall early become self-sup- porting.
253. Measukement of Beick-WORK. The method of determin- ing the quantity of brick masonry is governed by voluminous trade rules or by local customs, which are even more arbitrary than those for stone masonry (§ 224, which see).
The quantity is often computed in perches, but there is no uni- formity of understanding as to the contents of a perch. ■ It ranges from 16| to 25 cubic feet.
Brick-work is also often measured by the square rod of exterior surface. No wall is reckoned as being less than a brick and a half in thickness (13 or 13^ inches), and if thicker the measurement is still expressed in square rods of this standard thickness. Unfor- tunately the dimensions adopted for a square rod are variable, the following values being more or less customai-y : 16^ feet square or
DATA FOR ESTIMATES, 173
272i square feet, 18 feet square or 324 square feet, and 16-j square feet.
The volume of a brick is sometimes used as a unit in stating: the contents of a wall. The contents of the Avail are found by multi- plying the number of cubic feet in the wall by the number of brick which it is assumed make a cubic foot ; but as the dimensions of brick vary greatly (see § 62), this method is objectionable. A cubic foot is often assumed to contain 20 brick, and a cubic yard 600. The last two quantities are frequently used interchangeably, although the assumed volume of the cubic yard is thirty times that of the cubic foot.
Brick-work is also sometimes measured by allowing a certain number of brick to each superficial foot, the number varying with the thickness of the wall. A 4-inch wall (thickness = width of one brick) is frequently assumed to contain 7 bricks per sq. ft. ; a 9-inch wall (thickness = width of two bricks), 14 bricks per sq. ft.; a 13- inch wall (thickness = width of three bricks), 21 bricks per sq. ft., €tc. ; the number of brick j^er square foot of the face of the wall being seven times the thickness of the wall in terms of the width of a brick.
254. The only relief from such arbitrary, uncertain, and indefi- nite customs is to specify that the masonry will be paid for by the cubic yard, — gross or net measurement, according to the structure or the preference of the engineer or architect.
In engineering the uniform custom is to measure the exact solid contents of the wall.
255. Data for Estimates. Number of Brick Required. Since the size of brick varies greatly (§ 62), it is impossible to state a rule which shall be equally accurate in all localities. If the brick be of standard size (8jX4x25- inches), and laid with ^- to f-inch joints, a cubic yard of masonry will require about 410 brick; or a thousand brick will lay about 2j cubic yards. If the joints are \- to f-inch, a cubic yard of masonry will require about 495 brick; or a thousand brick will lay about 2 cubic yards. "With face brick (8f X 4^ x 2i inches) and ^-inch joints, a cubic yard of masonry will require about 496 brick; or a thousand face brick will lay about 2 cubic yards.
In making estimates for the number of bricks required, an al- lowance must be made for breakage, and for waste in cutting brick to fit angles, etc. With good brick, in massive work this allowance
17-i BRICK MASONRY. [CHAP. VIII.
need not exceed 1 or 2 per cent.; but in buildings 3 to 5 per cent, is none too much.
256. Amount of Mortar Required. The proportion of mortar to brick will vary with the size of the brick and with the thickness of the joints. With the standard size of brick (8^x4x2^ inches), a cubic yard of masonry, laid with |- to f-inch joints, will require from 0.35 to 0.40 of a cubic yard of mortar; or a thousand brick will require 0.80 to 0.90 of a cubic yard. If the joints are i to f inch, a cubic yard of masonry will require from 0.25 to 0.30 of a cubic yard of mortar; or a thousand brick will require from 0.45 to 0.55 of a cubic yard. If the joints are ^ of an inch, a cubic yard of masonry will require from 0.10 to 0.15 of a cubic yard of mortar; or a thousand brick will require from 0.15 to 0.20 of a cubic yard.
With the above data, and the table on page 86, the amount of cement and sand required for a specified number of brick, or for a given number of yards of masonry, can readily be determined.
257. Labor Required. " A bricklayer, with a laborer to keep him supplied with materials, will lay on an average, in common house- walls, about 1,500 bricks per day of 10 working hours; in the neater outer faces of brick buildings, from 1,000 to 1,200; in good ordinary street fronts, from 800 to 1,000 ; and in the very finest lower-story faces used in street fronts, from 150 to 300 according to the number of angles, etc. In plain massive engineering work, he should aver- age about 2,000 bricks per day, or 4 cu. yds. of masonry ; and in large arches, about 1,500, or 3 cu. yds.''*
In the United States Government buildings the labor per thou- sand, including tools, etc., is estimated at seven eighths of the wages for ten hours of mason and helper.
Table 21, opposite, f gives the actual labor, per cubic yard, re- quired on some large and important jobs.
258. Cost. In the construction of the Cincinnati Southern R. E., during 1873-77, the brick lining of tunnels cost S8.50 per cu. yd.; brick- work in buildings, $7.00.1 The average price paid for the brick-work in the new Croton Aqueduct tunnel, which supplies New York City with water, was, including everything, $10.14 per cu. yd.
* Trautwine's Engineer's Pocket-Book, p. 671.
+ Trans. Am. Soc. of C. E.
X Report of the Chief Engineer, Dec. 1, 1877, Exhibit 3.
BPECIFICATIONS. 175
TABLE 21. Labor required for Brick Masonry.
Location and Description op the Masonry.
Work required, ih Days per Cubic Tasd
High Bridge Enlargement, N. Y. City —
Lining wall and flat arches laid with very close joints.
Washington (D. C.) Aqueduct —
Circular conduit, 9 feet in diameter with walls 12 inches thick
St. Louis Water Works —
Semi-circular conduit, 6 feet in diameter.
Kew York City Storage Reservoir —
Lining of gate-house walls and arches — rough work . .
0.714
0.439 0.364
0.304
for lining, and 18.49 for backing. The mortar was composed of 1 part Eosendale natural cement and 2 parts of sand.*
In Chicago in 188?. the price of brick laid in lime in interior walls was about ^11 per thousand, equivalent to about 87 per cu. yd. The wages of masons were from 45 to 50 cents per hour, and of common labor from 20 to 25 cents per hour.
259. Specifications for Brick Masonry. For Buildings. There is not even a remote approach to uniformity in the specifica- tions for the brick-work of buildings. Ordinarily the specifications for the brick masonry are very brief and incomplete. The following conform closely to ordinary construction. Of course, a higher grade of workmanship can be obtained by more stringent specifications.!
The brick in the exterior walls must be of good quality, hard-burned; fine, compact, and uniform in texture ; regular in shape, and uniform in size.| One fourth of the brick in the interior walls may be what is known as soft or salmon brick (see 2, § 56). The brick must be thoroughly wet before being laid. The joints of the exterior walls shall be from i to | inch thick.§ The joints of interior division-walls may be from | to i inch thick. The mortar shall be composed of 1 part of fresh, well-slaked lime and 2| to 3 parta
* Report of the Aqueduct Commission, 1883-87, Table 4.
t For specifications for masonry for various purposes, see Appendix I.
J See § 57, page 37.
§ For the best work, omit this item and insert the following : T?ie outside woBm thdU, be faced with the best pressed brick of uniform color, laid in colored mortar, wUk joints not exceeding one eighth of an inch in thickness. Face brick are made a llttl» larger (§ 62) than ordinary brick to compensate for the thinner joints.
176 BRICK MASOISTRY. [CHAP. VIII.
of clean, sharp sand.* The lime-paste and the sand shall be thoroughly mixed before being used. The joints shall be well filled with the above mortar ; no grout shall be used in the work. The bond must consist of live courses of stretchers to one of headers, and shall be so arranged as to thor- oughly bind the exterior and interior portions of the wall to each other.
The contractor must furnish, set up, and take away his own scaffolding ; he must build in such strips, plugs, blocks, scantling, etc., as are required for securing the wood-work ; and must also assist in placing all iron-work, as beams, stairways, anchors, bed-plates, etc., connected with the brick-work.
260. For Sewers. The following are the specifications employed, in 1885, in tlie construction of brick sewers in Washington, D. C. :
" The best quality of whole new brick, burned hard entirely through, free from injurious cracks, with true even faces, and with a crushing strength of not less than 5,000 pounds per square inch, shall be used, and must be thor- oughly wet by immersion immediately before laying. Every brick is required to be laid in full mortar joints, on bottom, sides, and ends, which for each brick is to be performed by one operation. In no case is the joint to be made by working in mortar after the brick has been laid. Every second course shall be laid with a line, and joints shall not exceed three eighths of an inch. The brick-work of the arches shall be properly bonded, and keyed as directed by the engineer. No portion of the brick-work shall be laid drj' and afterwards grouted.
" The mortar shall be composed of cement and dry sand, in the proportion of 300 pounds of cement and 2 barrels of loose sand, thoroughly mixed dry, and a sufficient quantity of water afterwards added to form a rather stiff paste It shall be used within an hour after mixing, and not at all if once set.
"The cement shall be of the best quality, freshlj^ burned, and equal in every respect to the Round Top or Shepardstown cement, manufactured upon the formula of the engineer-commissioner of the District of Columbia, capable of being worked for twenty minutes in mortar without loss of strength, and shall be tested in such manner as the engineer may direct. After being mixed with water, allowed to set in air for twenty-four hours, and then immersed in water for six days, the tensile strength must be as follows :
Neat cement 95 lbs. per sq. in
One part cement and one part sand. ....... .56 " " " "
" " " " two parts " 22 " " " "
" three " " 12 " " " "
'The sand used shall be clean, sharp, free from loam, vegetable matter, or Bther dirt, and capable of giving the above results with the cement.
" The water shall be fresh and clean, free from earth, dirt, or sewerage.
* For masonry that is to be subjected to a heavy pressure, omit this item and insert the following ; The mortar must be composed of 1 part lime-paste, 1 part cement, and 2 parts of clean, sharp sand. Or, if a heavier pressure is to he resisted, specify that some particular £rrade of cement mortar is to be used. '.See §§ 246 and 247.»
SPECIFICATIOXS. 177
" Tight mortar-boxes shall be provided by the contractor, and no mortar shall be made except in such boxes.
"The proportions given are intended to form a mortar in which every particle of sand shall be enveloped by the cement ; and this result must be attained to the satisfaction of the engineer and under his direction. The thorough mixing and incorporation of all materials (preferably by machine labor) will be insisted upon. If by hand labor, the dry cement and sand shall be turned over with shovels by skilled workmen not less than six times before the water is added. After adding the water, the paste shall again be turned over and mixed with shovels by skilled workmen not less than three times be- fore it is used."
261. For Arches. The specifications for the brick arch masonry on the Atchison, Topeka and Santa Fe Railroad are as follows :
"The bricks must be of the best quality of smooth, hard-burnt, paving bricks, well tempered and moulded, of the usual size, compact, well shaped, free from lime, cracks, and other imperfections, and must stand a pressure of 4,000 pounds per square inch without crushing. No bats will be allowed in the work except for making necessary closures. All bricks will be culled on the ground after delivery, and selected in strict accordance with these specifications.
"The mortar must be made of 1 measure of good natural hydraulic cement and 2 measures of clean, sharp sand — or such other proportion as may be prescribed by the engineer — well mixed together with clean water, in clean mortar-beds constructed of boards, and must be used immediately after being mixed.
" The brick must be laid flush in cement mortar, and must be thoroughly wet when laid. All joints and beds must be thoroughly filled with mortar so as to leave no empty spaces whatever in the masonry of the walls and arches, which must be solid throughout. The thickness of mortar- joints must be as follows : In the walls and in the arch between bricks of the same ring, not less than three eighths of an inch (f ") nor more than one half inch (|"). In the arch between rings, not less than one half inch (|") nor more than five eighths of an inch (f"). Each brick is to be driven into place by blows of a mallet. The bricks must be laid in the walls with the ordinary English bond, five stretcher courses to one header course. They must be laid in the arch in concentric rings, each longitudinal line of bricks breaking joints with the adjoining lines in the same ring and in the ring under it. No headers to be used in the arch."
262. Bbice vs. Stone Masonry. Brick masonry is not much used, except in the walls of buildings, in lining tunnels, and in con- structing sewers, the general opinion being that brick-work is in every way inferior to stone masonry. This belief may have been well founded when brick was made wholly by hand, by inexpert operatives, and imperfectly burned in the old-time kilns, the prod-
178 BRICK MASONRY. [CHAP. VIII,
uct being then generally poor ; but things have changed, and since the manufacture of brick has become a business conducted on a large scale by enterprising men, with the aid of a variety of machines and improved kilns, the product is more regular in size and quality and stronger than formerly. Brick is rapidly displacing stone for the largest and best buildings in the cities, particularly in Chicago • and St. Petersburg, where the vicissitudes of the climate try masonry very severely. There are many engineering structures in which brick could be profitably employed instead of stone ; as, for example, the walls of box-culverts, cattle-guards, etc., and the less important bridge piers and abutments, particularly of highway bridges.
Brick-work is superior to stone masonry in several respects, as follows : 1. In many localities brick is cheaper than stone, since the former can be made near by while the latter must be shipped. 2. As brick can be laid by less skillful masons than stone, it costs less to lay it. 3. Brick is more easily handled than stone, and can be laid without any hoisting apparatus. 4. Brick requires less fit- ting at corners and openings. 5. Brick masonry is less liable to great weakness through inaccurate dressing or bedding. 6. Brick- work resists fire better than limestone, granite, or marble, sand- stone being the only variety of stone that can compare with brick in this respect. 7. Good brick stands the efEect of weathering and of the acids in the atmosphere better than sandstones, and in dura- bility even approaches some of the harder stones (see §§ 31-33). 8. All masonry fails when the mortar in its joints disintegrates or becomes dislodged; therefore brick masonry will endure the vicissi- tudes of the weather as Avell as stone masonry, or even better, since the former usually has thinner joints.
Brick-work is not as strong as ashlar masonry, but costs less ;. while it is stronger and costs more than ordinary rubble.
263. Beick Masonry Impervious to Water. It sometimes be- comes necessary to prevent the percolation of water through brick walls. A cheap and effective process has not yet been discovered, and many expensive trials have proved failures. The following account* gives the details of two experiments that were entirely suc- cessful.
" The face walls of the back bays of the gate-houses of the new
* Abstract of a paper by Wm. L. Dearborn, in Trans. Am. Soc. of C. E. , toI. L pp. 303-8'
MASONRY IMPEEVIOUS TO WATER. 179
Croton reservoir, located north of Eighty-sixth Street, in Centi'al Park, Xew York City, were built of the best quality of hard-burnt brick, laid in mortar composed of hydraulic cement of New York [Ulster Co. Rosendale] and sand mixed in the proportion of one measure of cement to two of sand. The space between the walls was 4 feet, and was filled with concrete. The face walls were laid up with great care, and every precaution was taken to have the joints well filled and to insure good work. The Avails are 12 inches thick and 40 feet high; and the bays, when full, generally have 36 feet of water in them.
" When the reservoir was first filled and the water let into the gate-houses, it was found to filter through these walls to a consider- able amount. As soon as this was discovered the water was drawn out of the bays, with the intention of attempting to remedy or pre- vent this infiltration. After carefully considering several modes of accomplishing the object desired, I [Dearborn] came to the conclu- sion to try ' Sylvester's Process for Repelling Moisture fi-om Exter nal Walls.'
" The process consists in using two washes or solutions for cov- ering the surface of the walls — one composed of Castile soap and water, and one of alum and water. The proportions are three quarters of a pound of soap to one gallon of water, and half a pound of alum to four gallons of water, both substances to be perfectly dissolved in water before being used. The walls should be perfectly clean and dry, and the temperature of the air not below 50° Fahr. when the comjjositions are applied,
" The first, or soap-wash, should be laid on, when boiling hot, with a flat brush, taking care not to form a froth on the brick-work. This wash should remain 24 hours, so as to become dry and hard before the second, or alum, wash is applied, which should be done in the same manner as the first. The temperature of this wash, when applied, maybe 60° or 70° Fahr.; and this also should remain 24 hours before a second coat of the soap-wash is put on. These coats are to be applied alternately until the walls are made impervious to water. The alum and soap thus combined form an insoluble compound, filling the pores of the masonry and entirely "oreventing the water from entering the walls.
"Before applying these compositions to the walls of the bays some experiments were made to test the absorption of water by
ISO BKICK MASONEY. [CHAP. YUt
bricks under pressure after being covered with these washes, in order to determine how many coats the walls would require to render them impervious to waiter. To do this, a strong wooden box large enough to hold two bricks was made, put together with screws, and in the top was inserted a 1-inch pipe 40 feet long. In this box were placed two bricks, after being made j)erfectly dry, which were then covered with a coat of each of the washes, as before directed, and weighed. They were then subjected to a column of water 40 feet high ; and after remaining a sufficient length of time they were taken out and weighed again, to ascertain the amount of water they had absorbed. The bricks were then dried, and again coated with the washes and weighed, and subjected to pressure as before, this operation being repeated until the bricks were found not to absorb any water. Four coatings rendered the bricks impenetrable under the pressure of a 40-foot head. The mean weight of the bricks (dry) before being coated was 3^ lbs. ; the mean absorption was one half- pound of water. A hydrometer was used in testing the solutions.
''As this experiment was made in the fall and winter (1863), after the temporary roofs were put on to the gate-house, artificial heat had to be resorted to to dry the walls and keep the air at a proper temperature. The cost was 10 cents per sq. ft. As soon as the last coat had become hard, the water was let into the bays, and the walls were found to be perfectly impervious to water, and they remain so in 1870, after about 6^ years.
264. "The brick arch of the footway of High Bridge is the arc of a circle, 29^ feet radius, and is 12 inches thick; the width on top is 17 feet, and the length covered is 1,381 feet. The first two courses of the brick of the arch are composed of the best hard-burnt brick, laid edgewise in mortar composed of 1 part, by measure, of hydraulic cement of New York [Eosendale natural] and 2 parts of sand. The top of these bricks, and the inside of the granite coping against which the two top courses of brick rest, was covered, when perfectly dry, with a coat of asphalt one half an inch thick, laid on when the asphalt was heated to a temperature of from 360° to 518° Fahr. On top of this was laid a course of brick flatwise, dipped in asphalt, and laid when the asphalt was hot; and the joints were run full of hot asphalt. On top of this, a course of pressed brick was laid flatwise in hydraulic cement mortar, forming the paving and floor of the bridge.
EFFLORESCENCE. 181
" The area of the bridge covered with asphalted brick was 23,065 sq. ft. There were used 94,200 lbs. of asphalt, 33 barrels of coal tar, 10 cu. yds. of sand, and 93,800 bricks. The asphalt was the Trini- dad variety ; and was mixed with 10 per cent., by measure, of coal tar, and 25 per cent, of sand. The time occupied was 109 days of masons, and 148 days of laborers. Two masons and two laborers will melt and spread, of the first coat, 1,650 sq. ft. per day. The total cost of this coat was 5^ cents per sq. ft., exclusive of duty on asphalt.
''There were three grooves, 2 inches wide by 4 inches deep, made entirely across the brick arch immediately under the first coat of asphalt, thus dividing the arch into four equal parts. The grooves were filled with elastic paint cement. This arrangement was intended to guard against the evil effects of the contraction of the arch in winter ; for, since it was expected to yield slightly at these points and at no other, the elastic cement would prevent any leakage there. The entire experiment has proved a very successful one, and the bridge has remained perfectly tight.
*'In proposing the above plan for working the asphalt with the brick-work, the object was to avoid depending on a large continuous surface of asphalt, as is usual in covering arches, which very fre- quently cracks from the greater contraction of the asphalt than that of the masonry with which it is in contact, the extent of the asphalt on this work being only about one quarter of an inch to each brick. This is deemed to be an essential element in the success of the im- pervious covering."
265. Effloeescence. Masonry, particularly in moist climate or in damp places — as cellar walls, — is frequently disfigured by the formation of a white efflorescence on the surface. This deposit generally originates with the mortar, but frequently spreads over the entire face of the wall. The water which is absorbed by the mortar dissolves the salts of soda, potash, magnesia, etc., contained in the lime or cement, and on evaporating deposits these salts as a white efflorescence on the surface. With lime mortar the deposit is frequently very heavy, particularly on plastering ; and, usually, it is heavier with natural than with Portland cement. The efflo- rescence sometimes originates in the brick, particularly if the brick was burned with sulphurous coal, or was made from clay contain- ing iron pyrites; and when the brick gets wet, the water dissolves
182 BRICK MASONRY. [CHAP. VIII.
the sulphates of lime and magnesia, and on evaporating leaves the crystals of these salts on the surface. Frequently the efflorescence on the brick is due to the absorption by the brick of the impreg- nater -^-ater from the mortar.
This efflorescence is objectionable because of the unsightly ap- pearance which it often produces, and also because the crystalliza- tion of these salts within the pores of the mortar and of the brick or stone causes disintegration which is in many respects like frost.
As a preventive, Gillmore recommends* the addition of 100 lbs. of quicklime and 8 to 12 lbs, of any cheap animal fat to each barrel of cement. The lime is simply a vehicle for the fat, which should be thoroughly incorporated with the lime before slaking. The ob- ject of the fat IS to saponify the alkaline salts. The method is not entirely satisfactory, since the deposit is only made less prominent and less effective, and not entirely removed or prevented.
The efflorescence may be entirely prevented, whatever its origin, by applying Sylvester's washes (see § 263) to the entire external sur- faces of the wall ; and, since usually the efflorescence is due to the water absorbed by the mortar, it can generally be prevented, and can always be much diminished, by using mortar which is itself im- pervious to water (see § 141). The latter is the cheaper method, particula.rly if the impervious mortar be used only for the face of the joints. If the wall stands in damp ground, one or more of the horizontal joints just above the surface should be laid in impervious mortar, or better, the brick for several courses should be rendered impervious and be laid in impervious mortar to j)revent the wall's absorbmg moisture from below.
* "Limes, Hydraulic Cements, and Mortars," p, 296.
F»ART III.
FOUNDATIONS.
CHAPTER IX. INTRODUCTORY.
265. Definitions. The term foundation is ordinarily used in- differeii Jy for either the lower courses of a structure of masonry or the artjficial arrangement, whatever its character, on which these courses rest. For greater clearness, the term foundation will here be restricted to the artificial arrangement, whether timber or mason- ry, Avhich supports the main structure ; and the prepared surface upon which this artificial structure rests will be called the heel of the foundation. There are many cases in which this distinction can not be adhered to strictly.
267. Importance of the Subject. The foundation, whether for the more important buildings or for bridges and culverts, is the most critical part of a masonry structure. The failures of works of masonry due to faulty workmanship or to an insufficient thickness of the walls are rare in comparison with those due to defective foundations. "When it is necessar}^ as so frequently it is at the present day, to erect gigantic edifices — as high buildings or long- span bridges — on Aveak and treacherous soils, the highest construc- tive skill is required to supplement the weakness of the natural foundation by such artificial preparations as will enable it to sustain such massive and costly burdens with safety.
Probably no branch of the engineer's art requires more ability and skill than the construction of foundations. The conditions governing safety are generally capable of being calculated with as much practical accuracy m this as in any other part of a con-
183
184 FOUNDATION'S: I]S"TRODUCTOET. [CHAP. IX.
struction ; but, unfortunately, practice is frequently based upon empirical rules rather than upon a scientific application of funda- mental principles. It is unpardonable that any liability to danger or loss should exist from the imperfect comprehension of a subject of such vital importance. Ability is required in determining the conditions of stability ; and gi-eater skill is required m fulfilling these conditions, that the cost of the foundation may not be pro- portionally too great. The safety of a structure may be imperiled, or its cost unduly increased, according as its foundations are laid with insufficient stability, or with provision for security greatly in excess of the requirements. The decision as to what general method of procedure will probably be best in any particular case is a ques- tion that can be decided with reasonable certainty only after long experience in this branch of engineering ; and after having decided upon the general method to be followed, there is room for the exercise of great skill in the means employed to secure the desired end. The experienced engineer, even with all the information which he can derive from the works of others, finds occasion for the use of all his knowledge and best common sense.
The determination of the conditions necessary for stability can be reduced to the application of a few fundamental principles Avhich may be studied from a text-book ; but the knowledge required to determine beforehand the method of construction best suited to the case in hand, together with its probable cost, comes only by personal experience and a careful study of the experiences of others. The object of Part III. is to classify the principles employed in con- structing foundations, and to give such brief accounts of actual practice as will illustrate the applications of these principles.
268. Plan of Proposed Discussion. In a general way, soils may be divided into three classes : (1) ordinary soils, or those which are capable, either in their normal condition or after that condition has been modified by artificial means, of sustaining the load that is to be brought upon them ; (2) compressible soils, or those that are incapable of directly supporting the given pressure with any reason- able area of foundation ; and (3) semi-liquid soils, or those in which the fluidity is so great that they are incapable of supporting any considerable load. Each of the above classes gives rise to a special method of constructing a foundation.
1. With a soil of the first class, the bearing power may be in-
PLAN OF PEOPOSED DISCUSSION"., 185
creased by compacting the surface or by drainage ; or the area of the foundation may be increased by the use of masonry footing courses, inverted masonry arches, or one or more layers of timbers, railroad rails, iron beams, etc. Some one of these methods is or- dinarily employed in constructing foundations on land ; as, for example, for buildings, bridge abutments, sewers, etc. Usually all of these methods are inapplicable to bridge piers, i. e., for founda- tions under water, owing to the scouring action of the current and also to the obstruction of the channel by the greatly extended base of the foundation.
2. With compressible soils, the area of contact may be increased by suppoi'ting the structure upon piles of wood or iron, which are sustained by the friction of the soil on their sides and by the direct pressure on the soil beneath their bases. This method is frequently employed for both buildings and bridges.
3. A semi-fluid soil must generally be removed entirely and the structure founded upon a lower and more stable stratum. This method is specially applicable to foundations for bridge piers.
There are many cases to which the above classification is not strictly applicable.
For convenience in study, the construction of foundations will be discussed, in the three succeeding chapters, under the heads Ordinary Foundations, Pile Foundations, and Foundations under Water. However, the methods employed in each class ar« not entirely distinct from those used in the others.
CHAPTER X. ORDINARY FOUNDATIONS.
269. In this chapter will be discussed the method of construct- ing the foundations for buildings, bridge abutments, culverts, or, in general, for any structure founded upon dry, or nearly dry, ground. This class of foundations could appropriately be called Foundations for Buildings, since these are the most numerous of the class.
This chapter is divided into three articles. The first treats of the soil, and includes (a) the methods of examining the site to de- termine the nature of the soil, (b) a discussion of the bearing power of different soils, and (c) the methods of increasing the bearing power of the soil. The second article treats of the method of de- signing the footing courses, and includes (a) the method of deter- mining the load to be supported, and (b) the method of increasing the area of the foundation. The third contains a few remarks con- cerning the practical work of laying the foundation.
Art. 1. The Soil.
270. Examination of the Site. The nature of the soil to be built upon is evidently the first subject for consideration, and if it has not already been revealed to a considerable depth, by excava- tions for buildings, wells, etc., it will be necessary to make an ex- amination of the subsoil preparatory to deciding upon the details of the foundation. It will usually be suJBficient, after having dug the foundation pits or trenches, to examine the soil with an iron rod or a post-auger from 3 to 5 feet further, the depth depending upon the nature of the soil, and the weight and importance of the intended structure.
In soft soil, soundings 40 or 50 feet deep can be made by driving a small (say f-inch) gas-pipe with a hammer or maul from a tem- porary scaffold, the height of which will of course depend upon the length of the sections of the pipe. If samples of the soil are desired,
186
ART. 1.] THE SOIL. 187
use a 2-inch pipe open at the lower end. If much of this kind of work is to be done, it is advisable to fit up a hand pile-driving machine (see § 335), using a block of wood for the dropping weight. Borings 50 to 100 feet deep can be made very expeditiously in common soil or clay with a common wood-auger turned by men, with levers 2 or 3 feet long. The auger will bring up samples suf- ficient to determine the nature of the soil, but not its compactness, since it will probably be comj^ressed somewhat in being cut off.
When the testing must be made through sand or loose soil, it may be necessary to drive down an iron tube to prevent the soil from falling into the hole. The sand may be removed from the inside of the tube with an auger, or with the " sand-pump" used in digging artesian wells. When the subsoil is composed of various strata and the structure demands extraordinary precaution, borings must be made with the tools employed for boring artesian wells.*
271. If the builder desires to avoid, on the one hand, the unnec- essarily costly foundations which are frequently constructed, or, on the other hand, those insufficient foundations evidences of which are often seen, it may be necessary, after opening the trenches, to determine the supporting power of the soil by applying a test load.
In the case of the capitol at Albany, 'N. Y., the soil was tested by applying a measured load to a square foot and also to a square yard. The machine used was a mast of timber 12 inches square, held vertical by guys, with a cross-frame to hold the weights. For the smaller area, a hole 3 feet deep was dug in the blue clay at the bottom of the foundation, the hole being 18 inches square at the top and 14 inches at the bottom. Small stakes were driven into the ground in lines radiating from the center of the hole, the tops being brought exactly to the same level ; then any change in the surface of the ground adjacent to the hole could readily be detected and measured by means of a straight-edge. The foot of the mast was placed in the hole, and weights applied. No change in the surface of the adjacent ground was observed until the load reached 5.9 tons per sq. ft., when an uplift of the surrounding earth was noted in the form of a ring with an irregularly rounded surface, the contents of which, above the previous surface, measured 0.09 cubic feet. Similar experiments were made by applying the load to
* For illustrations of tools for this purpose, see Engineering News, vol. 21, p.3S4.
188 ORDINAEY FOUNDATIONS. [CHAP. X.
a square yard with essentially the same results. The several loads were allowed to remain for some time, and the .settlements observed.* Similar experiments were made in connection with the construc- tion of the Congressional Library Building, Washington, D. C, with a frame which rested upon 4 foot-plates each a foot square. The frame could be moved from place to place on wheels, and the test was applied at a number of places.
272. Bearing Power of Soils. It is scarcely necessary to say that soils vary greatly in their bearing power, ranging as they do from the condition of hardest rock, through all intermediate stages, to a soft or semi-liquid condition, as mud, silt, or marsh. The best method of determining the load which a specific soil will bear is by direct experiment (§ 271); but good judgment and ex- perience, aided by a careful study of the nature of the soil — its com- pactness and the amount of water contained in it — will enable one to determine, with reasonable accuracy, its probable supporting power. The following data are given to assist in forming an estimate of the load which may safely be imposed upon different soils.
273. Rock. The ultimate crushing strength of stone, as deter- mined by crushing small cubes, ranges from 180 tons per square foot for the softest stone — such as are easily worn by running water or exposure to the weather — to 1,800 tons per square foot for the hardest stones (see page 11). The crushing strength of slabs, i. e., of prisms of a less height than width, increases as the height de- creases. A prism one half as high as wide is about twice as strong as a cube of the same material. If a slab be conceived as being made up of a number of cubes placed side by side, it is easy to see wliy the slab is stronger than a cube. The exterior cubes prevent the detachment of the disk-like pieces (Fig. 1, page G) from the sides of the interior cubes ; and hence the latter are greatly strengthened, which materially increases the strength of the slab. In testing cubes and slabs the pressure is applied uniformly over the entire upper surface of the test specimen ; and, reasoning from analogy, it seems probable that when the pressure is applied to only a small part of the surface, as in the case of foundations on rock, the strength will be much greater than that of cubes of the same material.
The table on page 190 contains the results of experiments made
* W. J. McAlpine, the engineer in charge, in Trans. Am. Soc. C. E., vol. ii. p. 287.
AET. 1,] THE SOIL. 189
by the author, and shows conclusively that a unit of material has a much greater power of resistance Avhen it forms a portion of a larger mass than when isolated in the manner customary in making ex- periments on crushing strength.
The ordinary '^ crushing strength" given in next to the last column of Table 22 was obtained by crushing cubes of the identical materials employed in the other experiments. The concentrated pressure was applied by means of a hardened steel die thirty-eight sixty-fourths of an inch in diameter (area = 0,277 sq. in.). All the tests were made between self-adjusting parallel plates of a hydro- static testing-machine. No packing was used in either series of experiments ; that is to say, the pressed surfaces were the same in both series. However, the block of limestone 7 inches thick (Ex- periments Nos. 8 and 13) is an exception in this respect. This block had been sawed out and was slightly hollow, and it was thought not to be worth while to dress it down to a plane. As pre- dicted before making the test, the block split each time in the di- rection of the hollow. If the bed had been flat, the block would doubtless have shown a gi-eater strength. The concentrated pres- sure was generally applied near the corner of a large block, and hence the distance from the center of the die to the edge of the block is to the nearest edge. Frequently the block had a ragged edge, and therefore these distances are only approximate. The quantity in the last column — ''Ratio" — is the crushing load per square inch for concentrated pressures divided bv the crushing load per square inch for uniform pressure.
The experiments are tabulated in an order intended to show that the strength under concentrated pressure varies (1) with the thick- ness of the block and (2) with the distance between the die and the edge of the material being tested. It is clear that the strength increases very rapidly with both the thickness and the distance from the edge to the point where the pressure is applied. Therefore we conclude that the compressive strength of cubes of a stone gives little or no idea of the ultimate resistance of the same material when in thick and extensive layers in its native bed.
274. The safe bearing power of rock is certainly not less than one tenth of the ultimate crushing strength of cubes; that is to say, the safe bearing power of solid rock is not less than 18 tons per sq. ft. for the softest rock and 180 for the strongest. It is safe to say
190
OEDINART FOUNDATIONS.
[chap. X.
TABLE 22.
Compressive Strength when the Pressure is applied on only a Part OF the Upper Surface.
6
9
10
7 11 12
8 13
14
Material.
Lime Mortar Marble
Brick
Limestone. . . Sandstone. . . Limestone. . .
Sandstone. . . Limestone. . .
|
o o |
s § |
|
|
P3 |
H |
|
|
o |
Q |
•«) |
|
m |
b |
|
|
te |
||
|
Ed |
Eh |
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Clay, which for years has safely carried, without appreciable settlement, buildings concentrating 1| to 2 tons per square foot (20 to 28 pounds per square inch), when tested in the form of cubes was crushed with 4 to 8 pounds per square inch. In this case the average " ratio" is 4.3.
that almost any rock, from the hardness of granite to that of a soft crumbling stone easily worn by exposure to the weather or to run- ning water, when well bedded will bear the heaviest load that can be brought upon it by any masonry construction.
It scarcely ever occurs in practice that rock is loaded with the full amount of weight which it is capable of sustaining, as the extent of base necessary for the stability of the structure is generally suffi- cient to prevent any undue pressure coming on the rock beneath.
275. Clay. The clay soils vary from slate or shale, which will support any load that can come upon it, to a soft, damp clay which will squeeze out in every direction when a moderately heavy pros-
AET. 1.] THE SOIL. 191
sure is brought upon it. Foundations on clay should be laid at such depths as to be unaffected by the weather ; since clay, at even considerable depths, will gain and lose considerable water as the seasons change. The bearing power of clayey soils can be very much improved by drainage (§ 285), or by preventing the penetra- tion of water. If the foundation is laid upon undrained clay, care must be taken that excavations made in the immediate vicinity do not allow the clay under pressure to escape by oozing away from under the building. When the clay occurs in strata not horizontal, great care is necessary to prevent this flow of the soil. When coarse sand or gravel is mixed with the clay, its supporting power is greatly increased, being greater in proportion as the quantity of these materials is greater. When they are present to such an extent that the clay is just sufficient to bind them together, the combination will bear as heavy loads as the softer rocks.
276. The following data on the bearing power of clay will be of assistance in deciding upon the load that may safely be imposed upon any particular clayey soil. From the experiments made in connection with the construction of the capitol at Albany, N. Y., as described in § 271, the conclusion was drawn that the extreme supporting power of that soil was less than 6 tons per sq. ft., and that the load which might be safely imposed upon it was 2 tons per sq, ft. " The soil was blue clay containing from 60 to 90 per cent, of alumina, the remainder being fine siliceous sand. The soil con- tains from 27 to 43, usually about 40, per cent, of water ; and vari- ous samples of it weighed from 81 to 101 lbs. per cu. ft." In the case of the Congressional Library (§ 271), the ultimate supporting- power of ''yellow clay mixed with sand" was 134- tons per sq. ft.;. and the safe load was assumed to be 2^ tons per sq. ft. Experi- ments made on the clay under the piers of the bridge across the Missouri at Bismarck, with surfaces 1^ inches square, gave an aver- age ultimate bearing power of 15 tons per sq. ft.*
The stiffer varieties of what is ordinarily called clay, when kept dry, will safely bear from 4 to 6 tons per sq. ft.; but the same clay, if allowed to become saturated with water, can not be trusted to bear more than 2 tons per sq. ft. At Chicago, the load ordinarily put on a thin layer of clay (hard above and soft below, resting on a
* Report of the engineer, Geo. S. Morison.
192 ORDINARY FOUXDATIONS. [CHAP. X.
thick stratum of quicksand) is 14^ to 2 tons per sq. ft. ; and the set- tlement, which usually reaches a maximum in a year, is about 1 inch per ton of load. Experience in central Illinois shows that, if the foundation is carried down below the action of frost, the clay «ubsoil will bear 1|- to 2 tons per sq. ft. without appreciable settling. Jiankine gives the safe load for comjiressible soils as 1^ to If tons per sq. ft.
277. Sand. The sandy soils vary from coarse gravel to fine sand. The former when of sufficient thickness forms one of the firmest and best foundations ; and the latter when saturated with water is practically a liquid. Sand when dry, or wet sand when prevented from spreading laterally, forms one of the best beds for a founda- tion. Porous, sandy soils are, as a rule, unaffected by stagnant water, but are easily removed by running water ; in the former case they present no difficulty, but in the latter they require extreme care at the hands of the constructor, as will be considered later.
278. Compact gravel or clean sand, in beds of considerable thickness, protected from being carried away by water, may be loaded with 8 to 10 tons per sq. ft. with safety. In an experiment in France, clean river-sand compacted in a trench supported 100 tons per sq. ft. Sand well cemented with clay and compacted, if protected from water, will safely carry 4 to 6 tons per sq. ft.
The piers of the Cincinnati Suspension Bridge are founded on a bed of coarse gravel 12 feet below low-water, although solid lime- stone was only 12 feet deeper ; if the friction on the sides of the pier* be disregarded, the maximum pressure on the gravel is 4 tons per sq. ft. The piers of the Brooklyn Suspension Bridge are founded 44 feet below the bed of the river, upon a layer of sand 2 feet thick resting upon bed-rock ; the maximum pressure is about 5^ tons per sq. ft.
At Chicago sand and gravel about 15 feet below the surface are successfully loaded with 2 to 2^ tons per sq. ft. At Berlin the safe load for sandy soil is generally taken at 2 to 2^ tons per sq. ft. The Washington Monument, Washington, D. C, rests upon a bed of very fine sand two feet thick underlying a bed of gravel and bowl- ders; the ordinary pressure on certain parts of the foundation is not far from 11 tons per sq, ft., Avhich the wind may increase to nearly 14 tons per sq. ft.
* For the amount of such friction, see §§ 418-19 and § 455.
AfeT. 1.] THE SOIL. 193
279. Semi-Liquid Soils. With a soil of this class, as mud, silt, or quicksand, it is customary (1) to remove it entirely, or (2) to sink piles, tubes, or caissons through it to a solid substratum, or \'d) to consolidate the soil by adding sand, earth, stone, etc. The method of performing these operations will be described later. Soils of a soft or semi-liquid character should never be relied upon for a foundation when anything better can be obtained ; but a heavy superstructure may be supported by the upward pressure of a semi- iiquid soil, in the same way that water bears up a floating body.
According to Rankine,* a building will be supported Avhen the
(1 I SI 11 ty \^ : 1 per unit of area, in which ex- pression 7V is the weight of a unit volume of the soil, h is the depth of immersion, and a is the angle of repose of the soil li a = 5°, then according to the preceding relation the supporting power of the soil is 1.4 w h per unit of area ; it a = 10°, it is 2.0 to h ; and if « = 15°, it IS 2.9 w h. The weight of soils of this class, i. e., mud, silt, and quicksand, varies from 100 to 130 lbs. per cu. ft. Eankine gives this formula as being applicable to any soil ; but since it takes no account of cohesion, for most soils it is only roughly ap- proximate, and gives results too small. The following experiment seems to show that the error is considerable. '*' A 10-foot square base of concrete resting on mud, whose angle of repose was 5 to 1 [a =11^°], bore 700 lbs. per sq. ft."f This is 2^ times the result by the above formula, using the maximum value of w.
Large buildings have been securely founded on quicksand by making the base of the immersed part as large and at the same time as light as possible. Timber in successive layers (§ 309) or grillage on piles (§ 320) is generally used in such cases. This class of foun- dations is frequently required in constructing sewers in water-bear- ing sands, and though apparently presenting no difficulties, such foundations often demand great' skill and ability.
280. It is difficult to give results of the safe bearing power of soils of this class. A considerable part of the supporting power is derived from the friction on the vertical sides of the foundation ; hence the bearing power depends in part upon the area of the side surface in contact with the soil. Furthermore, it is difficult to de-
* See Rankine's Civil Engineering, p. 379. + Proc. Inst, of C. E., vol. xviii. p. 493.
194
ORDINARY FOUNDATIONS.
TCHAP. X.
termine the exact suijporting power of a plastic soil, since a consid- erable settlement is certain to take place with the lanse of time. The experience at New Orleans with alluvial soil an*^ » f'*™' experi- ments* that have been made on quicksand seem to indicate mat with a load of ^ to 1 ton per square foot the settlement will not be excessive.
281. Bearing Power: Summary. Gathering together the results of the preceding discussion, Ave have the following table •
TABLE 23. Safe Bearing Power of Soils.
|
Kind of Material. |
Safe Bearing Power IN Tons pee Sq. Ft. |
|
|
Min. |
Max. |
|
|
Rock — the hardest — in thick layers, in native bed (§ 274) *' equal to best ashlar masonry (^ 274) |
200 25 15 5 4 2 1 8 4 2 0.5 |
30 |
|
" " " ' ' brick " " |
20 |
|
|
" " " poor " " " |
10 |
|
|
Clay in thick beds always dry (§ 276) |
6 |
|
|
" " " " moderately dry (§ 276) |
4 |
|
|
" soft (§ 276) |
2 |
|
|
Gravel and coarse sand, well cemented (§ 278) |
10 |
|
|
Sand, compact and well cemented, " " clean, dry " |
6 4 |
|
|
Quicksand, alluvial soils, etc. (§ 280) |
1 |
|
• 282. Conclusion. It is well to notice that there are some prac- tical considerations that modify the pressure which may safely be put upon a soil. For example, the pressure on the foundation of a tall chimney should be considerably less than that of the low mas- sive foundation of a fire-proof vault. In the former case a slight inequality of bearing power, and consequent unequal settling, might endanger the stability of the structure ; while in the latter no seri- ous harm would result. The pressure per unit of area should be less for a light structure subject to the passage of heavy loads — as,
* Trans. Am. Soc. of C. E., vol. xiv. p. 182 ; Engineering, vol. xx. p. 103 ; Proc, Inst, of C. E., vol. xvii. p. 443 ; Cleeman's Railroeid Practice, pp. 103-4.
AET. 1.] THE SOIL. • 195
for example, a railroad viaduct — than for a heavy structure subject only to a quiescent load, since the shock and jar of the moving load are far more serious than the heavier quiescent load.
The determination of the safe bearing power of soils, particular- ly when dealing with those of a semi-liquid character, is not the only question that must receive careful attention. In the founda- tions for buildings, it may be necessary to provide a safeguard against the soil's escaping by being pressed out laterally into excava- tions in the vicinity. In the foundations for bridge abutments, it maybe necessary to consider what the effect will be if the soil around the abutment becomes thoroughly saturated with water, as it may during a flood; or what the effect will be if the soil is deprived of its lateral support by the washing away of the soil adjacent to the abutment. The provision to prevent the wash and undermining action of the stream is often a very considerable part of the cost of the structure. The prevention of either of these liabilities is a prob- lem by itself, to the solution of which any general discussion will contribute but little.
283. IMPEOVING THE BEAEING POWEE OF THE SOIL. When the soil directly under a proposed structure is incapable, in its nor mal state, of sustaining the load that will be brought upon it, the bearing power may be increased (1) by increasing the depth of the foundation, (2) by draining the site, (3) by compacting the soil, or (4) by adding a layer of sand.
284. Increasing the Depth. The simplest method of increas- mg the bearing power is to dig deeper. Ordinary soils will bear more weight the greater the depth reached, owing to their becom- ing more condensed from the superincumbent weight. Depth is especially important with clay, since it is then less liable to be dis- placed laterally owing to other excavations in the immediate vicin- ity, and also because at greater depths the amount of moisture in it will not vary so much.
In any soil, the bed of the foundation should be below the reach of frost. Even a foundation on bed-rock should be below the frost line, else water may get under the foundation through fissures, and, freezing, do damage.
285. Drainage. Another simple method of increasing the bear- ing power of a soil is to drain it. The water may find its wa}' to the bed of the foundation down the side of the wall, or by percola-
196 ORDI]*ARY FOUXDATIONS. [CHAP. X.
tion througli the soil, or througli a seam of sand. In most cases the bed ean be sufficiently drained by covering it with a layer of gravel — the thickness depending upon the plasticity of the soil, — and then surrounding the building with a tile-drain laid a little below the foundation. In extreme cases, it is necessary to enclose the entire site with a puddle-wall to cut off drainage water from a higher area.
286. Springs. In laying foundations, springs are often met with, and sometimes prove very troublesome. The water may be excluded from the foundation pit by driving sheet piles, or by plug- ging the spring with concrete. If the flow is so strong as to wash the cement out before it has set, a heavy canvas covered with pitch, etc., upon which the concrete is deposited, is sometimes used ; or the water may be carried away in temporary channels, until the concrete in the artificial bed shall have set, when the water-ways may be filled with semi-fluid cement mortar. Below is an account of the ' method of stopping a very troublesome spring encountered in laying the foundation of the dry-dock at the Brooklyn Navy Yard.
"The dock is a basin composed of stone masonry resting on piles. The foundation is 42 feet below the surface of the ground and 37 feet below mean tide. In digging the pit for the founda- tion, springs of fresh water were discovered near the bottom, which, proved to be very troublesome. The upward pressure of the water was so great as to raise the foundation, however heavily it was loaded. The first indication of undermining by these springs was the settling of the piles of the dock near by. In a day it made a cavity in which a pole was run down 20 feet below the foundation timbers. Into this hole were thrown 150 cubic feet of stone, which settled 10 feet during the night ; and 50 cubic feet more, thrown in the following day, drove the spring to another place, where it burst through a bed of concrete 2 feet thick. This new cavity was filled with concrete, but the precaution was taken of putting in a tube so as to permit the water to escape ; still it burst through, and the opera- tion was repeated several times, until it finally broke out through a heavy body of cement 14 feet distant. In this place it undermined the foundation piles. These were then driven deeper by means of followers ; and a space of 1,000 square feet around the spring was then planked, forming a floor on which was laid a layer of brick in
ART. 1.] THE SOIL. 197
dry cemeut, and on that a layer of brick set in mortar, and the foundation was completed over all. Several vent-holes were left through the floor and the foundation for the escape of the water. The work was completed in 1851, and has stood well ever since." *
287. Consolidating the Soil. A soft, clayey soil can be greatly improved by spreading a thin layer of sand, dry earth, or broken stone over the bed of the foundation and pounding it into the soil. If the soil is very soft, compacting the surface will be insufficient ; in this case the soil may be consolidated to a considerable depth by driving short piles into it. For this purpose small piles — say 6 feet long and 6 inches in diameter — serve better than large ones ; and they can be driven with a hand-maul or by dropping a heavy block of wood with a tackle attached to any simple frame, or by a hand pile-driver (§ 335). They may be driven as close together as necessai'y, although 2 to 4 feet in the clear is usually sufficient. The latter method of compacting the soil is far more efficient than pounding the surface. In the case of impact upon earth, the im- mediate layers are compressed at once, and by their inertia and adhesion to the surrounding soil they intercept the effect of the blow, and thus prevent the consolidation of the lower strata. Even though the effect of a blow is not communicated to any considerable depth, the heavy masses of masonry make themselves felt at great depth, and hence for heavy buildings it is necessary to consolidate the lower strata. This can be done most easily and most efficiently by driving piles (see Art. 2).
In this connection it is necessary to remember that clay is com- pressible, while sand is not. Hence this method of consolidating soils is not applicable to sand, and is not very efficient in soils largely composed of it.
288. Sand Piles. Experiments show that in compacting the yoil by driving piles, it is better to withdraw them and immediately fill the holes with sand, than to allow the wooden piles to remain. This advantage is independent of the question of the durability of the wood. When the wooden pile is driven, it compresses the soil an amount nearly or quite equal to the volume of the pile, and when the latter is withdrawn this consolidation remains, at least temporarily. If the hole is immediately filled with sand this com-
* DelafieWs Foundations in Compressible Soils, p. 14 — a pamphlet published br the Engineer's Department of the U. S. Army.
198 ORDINARY FOUXDATIONS. [CHAP. X.
pression is retained permanently, and the consolidation may be still farther increased by ramming the sand in in thin layers, owing to the ability of the latter to transmit pressure laterally. And further, the sand pile will support a greater load than the wooden pile; for, since the sand acts like innumerable small arches reaching from one side of the hole to the other, more of the load is transmitted to the soil on the sides of the hole. To secure the best results, the sand should be fine, sharp, clean, and of uniform size.
289. When the piles are driven primarily to compact the soil, it is customary to load them and also the soil between them, either by cutting the piles off near the surface and laying a tight platform of timber on top of them (see § 320), or by depositing a bed of con- crete between and over the heads of the piles (see § 319).
If the soil is very soft or composed largely of sand, this method is ineffective; in which case long piles are driven as close together as is necessary, the supporting power being derived either from the resting of the piles upon a harder substratum or from the buoyaiicy due to immersion in the semi-liquid soil. This method of securing a foundation by driving long piles is very expensive, and is seldom resorted to for buildings, since it is generally more economical to increase the area of the foundation.
290. Layers of Sand. If the soil is very soft, it may be ex- cavated and replaced by sand. The method of using sand for j^iles has been described in § 288, which see. The opportunities for the use of sand in foundations are numerous, and the employment of it would, in many constructions, promote economy and stability. The simplest method of using sand for this purpose is to excavate a trench or pit to the proper depth, and fill it by depositing succes- sive layers of sand, each of which should be thoroughly settled by a heavy beetle before laying the next. To cause the sand to pack firmly, it should be slightly moistened before being placed in the trench.
Sand, when used in this wa}', possesses the valuable proj^erty of assuming a new position of equilibrium and stability should the soil on which it is laid yield at any of its points ; not only does this take place along the base of the sand bed, but also along its edges or sides. The bed of sand must be thick enough to distribute the pressure on its upper surface over the entire base. The4-e is no way of telling what this thickness should be, except by trial.
ART. 2.] DESIGNING THE FOOTING. 199
291. The followiug examples, cited by Trautwine,* are interest- ing as showing the surprising effect of even a thin layer of sand or gravel :
" Some portions of the circular brick aqueduct for supplying Boston with water gave a great deal of trouble when its trenches passed through running quicksands and other treacherous soils. Concrete was tried, but the wet quicksand mixed itself with it and hilled it. Wooden cradles, etc., also failed ; and the difficulty was overcome by simply depositing in the trenches about two feet in depth of strong gravel.
"Smeaton mentions a stone bridge built upon a natural bed of gravel only about 2 feet thick, overlying deep mud so soft that an iron bar 40 feet long sank to the head by its own weight. Although a wretched precedent for bridge building, this example illustrates the bearing power of a thick layer of well-compacted gravel."
Art. 2. Designing the Footing.
292. Load to be Supported. The first step is to ascertain the
load to be supported by the foundation. This load consists of three parts : (1) the building itself, (2) the movable loads on the floors and the snoAV on the roof, and (3) the part of the load that may be transferred from one part of the foundation to the other by the force of the wind.
293. The weight of the building is easily ascertained by calcu- lating the cubical contents of all the various materials in the struct- ure. If the weight is not equally distributed, care must be taken to ascertain the proportion to be carried by each part of the foun- dation. For example, if one vertical section of the wall is to con- tain a number of large windows while another will consist entirely of solid masonry, it is evident that the pressure on the foundation under the first section will be less than that under the second.
In this connection it must be borne in mind that concentrated pressures are not transmitted, undiminished, through a solid mass in the line of application, but spread out in successively radiating lines ; hence, if any considerable distance intervenes between the foundation and the point of application of this concentrated load,
* Engineer's Pocket-book (ed. 1885), p. 634.
200
OKDINARY POUND ATIOifS.
[chap. X,
the pressure will be nearly or quite uniformly distributed over the entire area of the base. The exact distribution of the pressure can not be computed.
The following data will be useful in determining the weight of the structure ■
TABLE 24. Weight of Masonry.
Kind of Masonry.
Weight
LBS. PER CU. FT
Brick-work, pressed brick, thin joints , ,
" ordinary quality
" soft brick, thick joints
Concrete, 1 cement, 3 sand, and 6 broken stone
Granite — 6 per cent, more than the corresponding limestone. . Limestone, ashlar, largest blocks and thinnest joints
" " 12" to 20" courses and |- to |-inch joints.. .
" squared-stone (see § 208)
" rubble, best
" " rough
Mortar, 1 Rosendale cement and 2 sand
' ' common lime, dried
Sandstone — 14 per cent, less than the corresponding limestone
145 125 100 140
160 155 148 142 136 116 100
Ordinary lathing and plastering weighs about 10 lbs. per sq. ft. The weight of floors is approximately 10 lbs. per sq. ft. for dwell- ings ; 25 lbs. per sq. ft. for public buildings ; and 40 or 50 lbs. per sq. ft. for warehouses. The weight of the roof varies with the kind of covering, the span, etc. A shingle roof may be taken at 10 lbs. per sq. ft., and a roof covered with slate or corrugated iron at 25 lbs. per sq. ft.
294. The movable load on the floor depends upon the nature of the building. For dwellings, it does not exceed 10 lbs. per sq. ft. ; for large office buildings, it is usually taken at 30 lbs. per sq. ft. ; for churches, theatres, etc., the maximum load — a crowd of people — may reach 100 lbs. per sq. ft. ; for stores, warehouses, factories.
ART. 2.] DESIGNIXG THE FOOTIXG. 201
etc., the load -svill be from 100 to 400 lbs. per sq. ft., according to the purposes for which they are used.
The preceding loads are the ones to be used in determining the strength of the floor, and not in designing the footings; for there is no probability that each and every square foot of floor will have its maximum load at the same time. The amount of moving load to be assigned in any particular case is a matter of judgment. At Chicago in designing tall steel-skeleton office buildings, it is the practice to assume that nearly all of the maximum live load reaches the girders, that a smaller per cent, reaches the columns, and that no live load reaches the footings. -In many cities the building law specifies the live load to be assumed as reaching the footing.
Attention must be given to the manner in which the weight of the roof and floors is transferred to the walls. For example, if the floor joists of a warehouse run from back to front, it is evident that the back and front walls alone will carry the weight of the floors and of the goods placed upon them, and this will make the pressure upon the foundation under them considerably greater than under the other walls. Again, if a stone-front is to be carried on an arch or on a girder having its bearings on piers at each side of the build- ing, it is manifest that the weight of the whole superincumbent structure, instead of being distributed equally on the foundation under the front, will be concentrated on that part of the founda- tion immediately under the piers.
295. The pressure of the wind against towers, tall chimneys, etc., will cause a concentration of the weight of the structure upon one side of the foundation. The maximum liorizontal pressure of the wind is usually taken as 50 lbs. per sq. ft. on a flat surface per- pendicular to the wind, and on a cylinder at about 30 lbs. per sq. ft. of the projection of the surface. The pressure upon an inclined surface, as a roof, is about 1 lb. per sq. ft. per degree of inclination to the horizontal. For example, if the roof has an inclination of 30° with the horizontal, the pressure of the wind will be about 30 lbs. per sq. ft.
The effect of the wind will be considered in §§ 301-4.
296. Akea Required. Having determined the pressure which may safely be brought upon the soil, and having ascertained the weight of each part of the structure, the area required for the foun- dation is easily determined by dividing the latter by the former.
202 ORDINARY FOUNDATIONS [CHAP. X.
Then, having found the area of foundation, the base of the struct- ure must be extended by footings of masonry, concrete, timber, etc., so as to (1) cover that area and (2) distribute the pressure uni- formly over it. The two items will be considered in inverse order. 297. Center of Pressure and Center of Base. In construct- ing a foundation the object is not so much to secure an absolutely unyielding base as to secure one that will settle as little as possible, and uniformly. All soils will yield somewhat under the pressure of any building, and even masonry itself is compressed by the weight of the load above it. The pressure per square foot should, there- fore, be the same for all parts of the building, and particularly of the foundation, so that the settlement may be uniform. This can be secured only when the axis of the load (a vertical line through the center of gravity of the weight) passes through the center of the area of the foundation. If the axis of pressure does not coincide exactly with the axis of the base, the ground will yield most on the side which is pressed most ; and as the ground yields, the base as- sumes an inclined position, and carries the lower part of the struct- ure with it, thus producing unsightly cracks, if nothing more.
The coincidence of the axis of pressure with the axis of resist- ance is of first importance. This principle is self-evident, and yet the neglect to observe it is the most frequent cause of failure in the foundations of buildings.
Fig. 50 is an example of the way in which this principle is
violated. The shaded portion represents a heavily loaded exte- rior wall, and the light portion a lightly loaded interior wall. The foundations of the two walls are rigidly connected together at their intersection. The center • of the load is under the shaded Fig. 50. scction, and the center of the
area is at some point farther to the left ; consequently the exterior wall is caused to incline outward, producing cracks at or near the corners of the building. Doubtless the two foundations are con- nected in the belief that an increase of the bearing surface is of first importance ; but the true principle is that the coincidence of the axis of pressure with the axis of resistance is the most important.
AKT. 2.]
DESIGNIKG THE FOOTIJSTG.
203
Fig. 51 is another illustration of the same principle. The foun- dation is continuous under the opening, and hence the center of the foundation is to the left of the center of pressure ; conse- quently the wall inclines to the right, pro- ducing cracks, usually over the opening.*
298. The center of the load can be made to fall inside of the center of foundation by extending the footings outwards, or by cur- tailing the foundations on the inside. The latter finds exemplification in the properly constructed foundation of a wall containing a number of openings. For example, in Fig. 52, if the foundation is uniform under the entire front, the center of pressure must be outside of the center of the base ; and conse- quently the two side walls will incline outward, and show cracks over the openings. If the width of the foundation under the openings be decreased, or if this part of the foundation be omitted entirely, the center of pressure will fall inside of the center of base and the walls will tend to incline inwards, and hence be stable.
299. Conclusions. One conclusion to be drawn from the above examples is that the foundation of a wall should never be connected with that of another wall either much heavier or much lighter than itself. Both are equally objectionable.
A second conclusion is that the axis of the load should strike a little inside of the center of the area of the base, to make sure that it will not be outside. Any inward inclination of the wall is ren- dered impossible by the interior walls of the building, the fioor- beams, etc. ; while an outward inclination can be counteracted only by anchors and the bond of the masonry. A slight deviation of the axis of the load outward from the center of the base has a marked effect, and is not easily counteracted by anchors.
* For an account showing the violation of this principle in the construction of the Cooper Institute Building, New York City, and the method used to remedy it, see Hanitary U/igineer, vol. xiL pp. 465-68.
Fig. 52.
204
ORDIN"ARY FOUNDATIONS.
[chap. X.
The above conclusions may be summarized in the following principle : All foundalions should be so constructed as to cornpress tlie ground slightly concave npivards, rather than convex iip- zoards. On even slightly compressible soils, a small difEerence in the pressure on the foundation will be sufficient to cause the bed to become convex upwards. At Chicago, an omission of 1 to 2 per cent, of the weight (by leaving openings) usually causes sufficient convexity to prod-uce unsightly cracks. With very slight differences of pressure on the foundation, it is sufficient to tie the building together by careful bonding, by hoop-iron built in over openings, and by heavy bars built in where one wall joins another.
300. Independent Piers. The art of constructing founda- tions on compressible soil has been brought to a high degree of development by the architects of Chicago. The special feature of the practice in that city is what is called "the method of independ- ent piers ;" that is, each tier of columns, each pier, each wall, etc. , has its own independent foundation, the area of which is propor- tioned to the load on that part.* The interior walls are fastened to the exterior ones by anchors which slide in slots. For a detailed account of the methods employed in one of the best and largest buildings erected there, see Sanitary Engineer, Dec. 10, 1885.
301. Effect of the Wind. Overturning. The preceding dis- cussion refers to the total weight that is to come upon the foun-
jj jp dation. The pressure of the wind against towers,
tall chimneys, etc. , transfers the point of applica- tion of the load to one side of the foundation. The method of computing the position of the center of the pressure on the foundation under the action of the wind is illustrated in Fig. 53, in which ABED represents a vertical section of the
tower; rt is a point horizontally opposite the center of the surface exposed to the pressure of the wind and vertically above the center of grav- FiG. 53. ity of the tower;
* This method was first made known to the public by Frederick Bauman, of Chi- cago, in a pamphlet entitled " The Method of Constructing Foundations on Isolated Piers," published by him in 187'2. The above examples and principles are from that pamphlet.
AKT. 2.] DESIGNING THE FOOTING. 20(
C is the position of the center of pressure when there is no wind ;
IN is the center when the wind is acting. For convenience, let
P = the maximum pressure on the foundation, per unit of area;
2) = the pressure of the wind per unit of area (see § 295);
H = the total pressure of the wind against the exposed surface ;
W = the weight of that part of the structure above the section considered, — in this case, A B ;
S = the area of the horizontal cross section ;
/ = the moment of inertia of this section ;
I = the distance A B ;
h = the distance a C ;
d = the distance iV^ C; M = the moment of the wind.
"When there is no horizontal force acting, the load on ^ ^ is uniform ; but when there is a horizontal force acting — as, for ex- ample, the wind blowing from the right, — the pressure is greatest near A and decreases towards B. To find the law of the variation of this pressure, consider the tower as a cantilever beam. The maximum pressure at A will be that due to the weight of the tower plus the compression due to flexure ; and the pressure at B will be the compression due to the weight minus the tension due to flexure.
W
The uniform pressure due to the weight is —^. The strain at A due
to flexure is, by the principles of the resistance of materials, Then the maximum pressure per unit of area at A is
Ml
and the minimum pressure at B is
S 21 ^'^f
Equations (1) and (2) are perfectly general ; they are applicable to any cross section, and also to any system of horizontal and ver- tical forces. In succeeding chapters they will be emploved in finding the unit pressure in masonry dams, bridge piers, arches, etc.
306
OEDIK^ARY FOUXDATIONS.
[chap. X.
The value of / in the above formulas is given in Fig. 54 for the sections occurring most frequently in practice. Xotice that / is th© dimension parallel to the direction of the wind, and J. the dimen- sion perpendicular to the direction of the wind.
I-^\,bP
Fig. 54.
I = ^n{l*- h^)
302. If the area of the section A B, Fig. 53, is a rectangle, S = I b, and I = -^^b P. Substituting these values in equation (1) gives
p=K+n- (3)
The moment of the wind, M, is equal to the product of its total pressure, H, and the distance, //, of the center of pressure above the horizontal section considered; or M= H.h. H is equal to the pressure per unit of area, jh miilfiplied by the area of the sur- face exposed to the pressure of the wind. Substituting the above value of M in equation (3) gives
W . GH.h
^4)
P =
lb
bV
To still further simplify the above formula, notice that Fig. 53 gives the proportion
H: W::NC:aC, from which
H.aC= W.NC;
or, changing the nomenclature,
Hh= Wd.
Notice that the last relation can also be obtained directly by the principle of moments. Substituting the value of H. h, as above, in equation (4) gives
^ ~ Ib^ bV ' ^^'
which is a convenient form for practical application.
ART. 2.] DESIGNING THE FOOTING. 207
An examination of equation (5) shows that when d ==. N C = \l, the maximum pressure at A is twice the average. Notice also that under these conditions the pressure at B is zero. This is equiva- lent to what is known, in the theory of arches, as the principle of the middle third. It shows that as long as the center of pressure lies in the middle third, the maximum pressure is not more than twice the average pressure, and that there is no tension at B.
The above discussion of the distribution of the pressure on the foundation is amply sufficient for the case in hand ; however, the subject is discussed more fully in the chapter on Stability of Masonry Dams (see Chapter XIII).
303. The average pressure per unit on A B has already been adjusted to the safe bearing power of the soil, and if the maximum pressure at A does not exceed the iiltimate bearing power, the occa- sional maximum pressure due to the wind will do no harm ; but if this maximum exceeds or is dangerously near the ultimate strength of the soil, the base must be widened.
304. Sliding. The pressure of the wind is a force tending to slide the foundation horizontally. This is resisted by the friction caused by the weight of the entire structure, and also by the earth around the base of the foundation, and hence there is no need, in this connection, of considering this manner of failure.
305. Designing the Footing. The term footing is usually un- derstood as meaning the bottom course or courses of masonry which extend beyond the faces of the Avail. It will be used here as apply- ing to the material — whether masonry, timber, or iron — employed to increase the area of the base of the foundation. "Whatever the character of the soil, footings should extend beyond the face of the wall (1) to add to the stability of the structure and lessen the dan- ger of the work's being thrown out of plumb, and (2) to distribute the weight of the structure over a larger area and thus decrease the settlement due to the compression of the gi'ound. To serve the first purpose, footings must be securely bonded to the body of the wall; and to produce the second effect, they must have sufficient strength to resist the transverse strain to which they are exposed. In ordinary buildings the distribution of the weight is more impor- tant than adding to the resistance to overturning, and hence only the former will be considered here.
The area of the foundation may be increased until the inherent
208 OKDINAET FOUXDATIOXS. [CHAP. X.
bearing power of the area covered is suflBcient to support the load (1) by extending the bottom courses of masonry, or (2) by the use of one or more layers of timbers, railroad rails, or steel I-beams, or (3) by resting the structure upon inverted masonry arches.
306. Off-sets of Masonry Footings. The area of the foundation having been determined and its center having been located -with reference to the axis of the load (§ 29T), the next step is to deter- mine how m.uch narrower each footing course may be than the one nrxt below it. The projecting part of the footing resists as a beam fixed at one end and loaded uniformly. The load is the pressure on the earth or on the course next below. The off-set of such a course depends upon the amount of the pressure, the transverse strength of the material, and the thickness of the course.
To deduce a formula for the relation between these quantities, let
P = the pressure, in tons per square foot, at the bottom of the footing course under consideration ;
a = the modulus of rupture of the material, in pounds jDer square inch ;
p = the greatest possible projection of the footing course, in
inches ; t = the thickness of the footing course, in inches.
The part of the footing course that projects beyond the one above it, is a cantilever beam uniformly loaded. From the principles of the resistance of materials, we know that the upward pressure of the earth against the part that projects multiplied by one half of the length of the projection is equal to the continued product of one sixth of the modulus of rupture of the material, the breadth of the footing course, and the square of the thickness. Expressing this relation in the above nomenclature and reducing, we get the for- mula
-or, with sufficient accuracy,
P = lt\^ (7)
Hence the projection available with any given thickness, or the thickness required for any given projection, may easily be computed
ART. 2.]
DE3IGXIXG THE FOOTIXG.
209
by equation (7). Notice that with the off-set given by the above iormula the stone would be on the point of breaking.
307. The margin to be allowed for safety will depend upon the care used in computing the loads, in selecting the materials for the footing courses, and in bedding and placing them. If all the loads have been allowed for at their probable maximum value, and if the material is to be reasonably uniform in quality and laid with care, then a comparatively small margin for safety is sufficient ; but if all the loads have not been carefully computed, and if the job is to be done by an unknown contractor, and neither the material nor the work is to be carefully inspected, then a large margin is neces- sary. As a general rule, it is better to assume, for each particular case, a factor of safety in accordance with the attendant conditions of the problem than blindly to use the results deduced by the application of some arbitrarily assumed factor. The following table is given for the convenience of those who may wish to use 10 as a factor of safety.
TABLE 25.
Safe Off-set for Masonry Footing Courses, in Terms of the Thick- ness OP THE Course, using 10 as a Factor of Safety. For limitations, see § 308.
Kind of Stone.
Blue-stone Uaggiug (see page 13).
Granite (see page 13)
Limestone (see page 13)
Sandstone (see page 13)
Slate (see page 13)
Be«t Hard Brick (see pages 40, 41)
Hard Brick (see pages 40, 41)
( 1 Portland )
Concrete (see page 112c) -<2 sand [ (3 pebbles ) (iPortiand , ,
Concrete (see page 112t)) ^ 3 sand <- * - ^'^^ ( 5 pebbles
4 weeks old
old
R, IN LBS. PERSQ. IN.
2,700 1,800 1,500 1,200 5,400
1,500 800
150
80
Off-set for a Pres- sure, IN TONS pbr sq. FT., ON THE Bottom op THE Course, op
0.5
3.6 2.9
2.7 2.6 5.0
2.7 1.9
0.8 0.6
1.0
2.6
2.1 1.9 1.8 3.6
1.9 1.4
0.6 0.4
2.0
1.8 1.5 1.3 1.3 2.5
1.3
0.8
0.4 0.3
To illustrate the method of using the preceding table, assume that it is desired to determine the off-set for a limestone footing course when the pressure on the bed of the foundation is 1 ton per square foot, using 10 as a factor of safety. In the table, opposite
210 ORDIXAEY FOUNDATIOXS. [CHAP. X»
limestone, in next to the last column, we find the quantity 1.9. This shows that, under the conditions stated, the off-set may be 1.9 times the thickness of the course.
The values in the table agree very well with the practice of the principal architects and engineers for hammer-dressed stones laid in good cement mortar.
If it is desired to use any other factor of safety, it is only neces- sary to substitute for R, in the preceding formula, the desired frac- tional part of that quantity as given in the second column of the- above table. For examj^le, assume that it is necessary to use lime- stone in the foundation, and that it is required to draw in the foot- ing courses as rapidly as possible. Assume also that the pressure, P, on the base of the foundation is 2 tons per square foot. If the limestone is of the best, and if it is laid with great care, it will be sufficient to use 4 as a factor of safety. Under these conditions, equation (7) as above gives
That is, the projection may be 2.3 times the thickness of the course.
308. Strictly, the above computations are correct only for the lower off-set, and then only when the footing is composed of stones whose thickness is equal to the thickness of the course and which project less than half their length, and which are also well bedded. The resistance of two or more courses to bending varies as the square of their depth, and the bending due to the uniform pressure on the base will also increase as the square of the sum of the projections, and therefore the successive off-sets should be proportional to the thickness of the course; or, in other words, the values as above are applicable to any course, provided no stone projects more than half its length beyond the top course.
The preceding results will be apjilicable to built footing courses only when the pressure above the course is less than the safe strength of the mortar (see § 133 and § 161a). The proper projection for rubble masonry lies somewhere between the values given for stone and those given for concrete. If the rubble consists of large stones well bedded in good strong mortar, then the values for this class of masonry will be but little less than those given in the table. If the rubble consists of small irregular stones laid with Portland or nat-
ART. 2.] DESIGNING THE FOOTING. 211
■nral cement mortar, the projection should not much exceed that given for concrete. If the rabble is laid in lime mortar, the pro- jection of the footing course should not be more than half that allowed when cement mortar is used.
309. Timber Footing. In very soft earth it would be inexpe- dient to use masonry footings, since the foundation would be very deep or occupy the space usually devoted to the cellar. One method of overcoming this difficulty consists in constructing a timber grat- ing, sometimes called a grillage, by setting a series of heavy timbers firmly into the soil, and laying another series transversely on top of these. The timbers may be fastened at their intersections by spikes or drift-bolts (§ 381) if there is any possibility of sliding, which is unlikely in the class of foundations here considered. The earth should be packed in between and around the several beams. A flooring of thick planks, often termed a ijlatform, is laid on top of the grillage to receive the lowest course of masonry. In extreme cases, the timbers in one or more of the courses are laid close to- gether. Timber should never be used except where it will be always wet.
The amount that a course of timber may project beyond the one next above it can be determined by equation (7), page 208. Making R in that equation equal to 1,000 — the value ordinarily used, — and solving, we obtain the following results for the safe jirojection: If the pressure on the foundation is 0.5 ton per square foot, the safe projection is 7. 5 times the thickness of the course ; if the pressure is 1 ton per square foot, the safe projection is 5.3 times the thick- ness of the course ; and if the pressure is 2 tons per square foot, the safe projection is 3.7 times the thickness of the course. The above values give a factor of safety of about 10. To use any other factor, insert in equation (7), above, the corresponding fractional part of the ultimate transverse strength of the particular timber to be used, and solve.
The above method of computation is not applicable to two or more courses of timber, if one is transverse to the other.
310. This method of increasing the area of the footing is much used at Xew Orleans. The Custom-house at that place is founded upon a 3-inch plank flooring laid 7 feet below the street pavement. A grillage, consisting of timbers 12 inches square laid side by side, is laid upon the floor, over which similar timbers are placed trans- versely, 2 feet apart in the clear.
212 ORDINARY FOUNDATIONS. [CHAP. X.
Most of the buildings of the World's Colnmbiau Exposition, Chicago, 1893, were founded upon timber footings.
311. Steel Footing. Very recently, steel, usually in the form of railroad rails or I-beams, has been used instead of timber in foundations. The rails or I-beams are placed side by side, and concrete is rammed in between them.
Steel is superior to timber for this purpose, in that the latter can be used only Avhere it is always wet, while the former is not affected by variations of wetness and dryness. Twenty years' ex- perience in this use of steel at Chicago shows that after a short time the surface of the metal becomes encased in a coating which 2:)re- vents further oxidation. The most important advantage, however, in this use of steel is that the off-set can be much greater with steel than with wood or stone; and hence the foundations may be shal- low, and still not occupy the cellar space.
The proper projections for the steel beams can be computed by a formula somewhat similar to that of § 306; but the steel footing is appropriately a part of the steel-skeleton construction, and hence will not be considered here. For a presentation of the method of computations formerly employed in Chicago, see Engmeering News, vol. xxvi. page 122; and for adverse criticisms thereon, see ibid., pages 265, 312, -415, and vol. xxxii. page 387. Concerning the effect of the strength of the base of the column, see Johnson's " Modem Framed Structure "5," pages 444-46. For a discussion which consider.5 the deflection of l!ie several beams, see Btigineering^ Record, vol. xxxix. pages 333-34, 354-56, 383, 407-8. The last is the most exact method of analj^sis, and also secures the greatest economy of material.
312. Inverted Arch. Inverted arches are frequently built under and between the bases of piers, as shown in Fig. 55. Employed in
this Avay, the arch simply distributes the pressure over a greater area; but it is not well adapted to this use, for (1) it is nearly impossible to prevent the end piers of a series from being pushed outward by the thrust of the ^''^■^^" arch, and (2) it is generally impos-
sible, with inverted arches, to make the areas of the different parts of the foundiition proportional to the load to be supported (see §
ART. 3.] PREPAEING THE BED. 21?
297). The only advantage the inverted arch has over masonry footings is in the shallower foundation obtained.
313. In a few cases masonry piers have been sunk to a solid sub- stratum by excavating the material from the inside, and then resting arches on these piers. This is an exj^ensive method, and has essen- tially the same objections as the inverted arch.
Art. 3. Prepaeixg the Bed.
314. On Rock To prepare a rock bed to receive a foundation it is generally only necessary to cut away the loose and decayed por- tions of the rock, and to dress it to a plane surface as nearly perpen- dicular to the direction of the pressure as is practicable. If there are any fissures, they should be filled with concrete. A rock that is very much broken can be made amply secure for a foundation by the liberal use of good cement concrete. The piers of the Xiagara Cantilever Bridge are founded upon the top of a bank of bowlders, which were first cemented together with concrete.
Sometimes it is necessary that certain parts of a structure start from a lower level than the others. In this case care should be taken (1) to keep the mortar-joints as thin as possible, (2) to lay the lower j)ortions in cement, and (3) to proceed slowly with the work ; otherwise the greater quantity of mortar in the wall on the lower portions of the slope will cause greater settling there and a consequent breaking of the joints at the stepping-places. The bonding over the off-sets should receive particular attention.
315. On Firm Earth. For foundations in such earths as hard clay, clean dry gravel, or clean sharp sand, it is only necessary to dig a trench from 3 to G feet deep, so that the foundation may be below the disintegrating effect of frost. Provision should also be made for the drainage of the bed of the foundation.
With this class of foundations it often happens that one part of the structure starts from a lower level than another. When this is the case great care is required. All the precautions mentioned in the second paragraph of § 314 should be observed, and great care should also be taken so to proportion the load per unit of area that the settlement of the foundation may be uniform. This is difficult to do, since a variation of a few feet in depth often makes a great difference in the supporting power of the soil.
214 ORDIXARY FOUXDATIOXS. [CHAP. X.
316. In Wet Ground. The difficulty in soils of this class is in disposing of the water, or in preventing the semi-liquid soil from running into the excavation. The difficulties are similar to those met with in constructing foundations underwater — see Chapter XII. Tln-ee general methods of laying a foundation in this kind of soil will be briefly described.
317. Coffer-Dam. If the soil is only moderately wet — not satu- rated,— it is sufficient to inclose the area to be excavated with sheet piles (boards driven vertically into the ground in contact with each other). This curbing is a simple form of a coffer-dam (Art. 1, Chap. XII). The boards should be sharpened wholly from one side ; this point being placed next to the last pile driven causes them to crowd together and make tighter joints. The sheeting may be driven by hand, by a heavy weight raised by a tackle and then dropped, or by an ordinary pile-driver (§§ 335-3G). Unless the amount of water is quite small, it will be necessary to drive a double row of sheeting, breaking joints. It will not be possible to entirely prevent leaking. The water that leaks in may be bailed out, or pumped — either by hand, or by steam (see § 395).
To prevent the sheeting from being forced inward, it may be braced by shores placed horizontally from side to side and abutting against wales (horizontal timbers which rest against the sheet piles). The bracing is put in successively from the top as the excavation proceeds ; and as the masonry is built up, short braces between the sheeting and the masonry are substituted for the long braces which previously extended from side to side. Iron screws, somewhat similar to jack-screws, are used, instead of timber shores, in exca- vating trenches for the foundations of buildings, for sewers, etc.
If one length of sheeting will not reach deep enough, an addi- tional section can be placed inside of the one already in position, when the excavation has reached a sufficient depth to require it. Ordinary planks 8 to 12 inches wide and 1^ or 2 inches thick are used.
For a more extended account of the use of coffer-dams, see Chapter XII — Foundations Under Water, Art. 1 — Coffer-Dams.
318. In some cases the soil is more easily excavated if it is first drained. To do this, dig a hole — a sump — into which the water will drain and from which it may be pumped. If necessary, several sumps may be sunk, and deepened as the excavation proceeds.
ART. 3.] PREPARING THE BED. 215
Quicksand or soft alluvium may sometimes be pumped out along with the water by a centrifugal or a mud pump (§ 395 and § 448). On large jobs, such material is sometimes taken out with a clam- shell or Milroy dredge (§ 412).
319. Concrete. Concrete can frequently be used advantage- ously in foundations in wet soils. If the water can be removed, the concrete should be deposited in continuous layers, about 6 inches thick, and gently rammed until the water begins to ooze out on the upper surface (see § 153). If the water can not be removed, the concrete may be deposited under the water (see § 154), although it is more difficult to insure good results by this method than when the concrete is deposited in the open air.*
320. Grillage. If the semi-liquid soil extends to a considerable depth, or if the soft soil which overlies a solid substratum can not be removed readily, it is customary to drive piles at uniform distances over the area, and construct a grillage (see § 380) on top of them. This construction is very common for bridge abutments (Chapter XV). The piles should be sawed off (§ 3TS) below low-water, which usually necessitates a coffer-dam (§ 317, and Art. 1 of Chapter XII), and the excavation of the soil a little below the low- water line.
For a more extended account of this method of laying a founda- tion, see §§ 380-82.
321. In excavating shallow pits in sand containing a small amount of water, dynamite cartridges have been successfully used to drive the water out. A hole is bored with an ordinary auger and the cartridge inserted and exploded. The explosion drives the water back into the soil so far that, by working rapidly, the hole can be excavated and a layer of concrete placed before the water returns.
322. Conclusion. It is hardly worth while here to discuss this subject further. It is one on which general instruction can not be given. Each case must be dealt with according to the attendant circumstances, and a knowledge of the method best adapted to any given conditions comes only by experience.
* For tlie composition, cost, etc. , of concrete, see Art. 2 of Chap, iv, pp. 106-13t.
CHAPTER XL PILE FOUNDATIONS.
323. Definitions. Pile. Although a pile is generally unde^ stood to be a round timber driven into the soil to support a loadj the term has a variety of applications which it will be well to explain.
Bearing Pile. One used to sustain a vertical load. This is the ordinary pile, and usually is the one referred to when the word pile is employed without qualification.
Slteet Piles. Thick boards or timbers driven in close contact to inclose a space, to prevent leakage, etc. Generally they are con- siderably wider than thick; but are sometimes square, in which case- they are often called dose }) Has.
False Pile. A timber added to a pile after driving, to supple' ment its length.
Foundation Pile. One driven to increase the supporting power of the soil under a foundation.
Screiu Pile. An iron shaft to the bottom of which is attached a broad-bladed screw having only one or two turns.
Disk Pile. A bearing pile near the foot of which a disk is keyed or bolted to give additional bearing power.
Pneuniatie Pile. A metal cylinder which is sunk by atmos- pheric pressure. Tliis form of pile will be discussed in the next chapter (see § 431).
Art. 1. Descriptions, and Methods of Driving.
3^4. Iron Piles. Both cast and wrought iron are employed for ordinary bearing piles, sheet piles, and for cylinders. Iron cylin- ders are generally sunk either by dredging the soil from the inside (§ 415), or by the pneumatic process (see the next chapter, particu- larly §§ 431-35). For another method of employing iron cylinders, see §§ 384-85.
216
AET. 1.] DESCKIPTIONS, AND METHODS OF DRIVING. 217
Cast-iron piles are beginning to be used as substitutes for com- mon wooden ones. Lugs or flanges are usually cast on the sides of the piles, to which bracing may be attached for securing them in position. A wood block is laid upon the top of the pile to receive the hammer used in driving it; and, after being driven, a cap with a socket in its lower side is placed ujion the pile to receive the load. The supporting power is sometimes increased by keying on an iron disk. The advantages claimed for cast-iron piles are: (1) thev are not subject to decay; (2) they are more readily driven than wooden ones, especially in stony ground or stiff clay; and (3) they possess greater crushing strength, which, however, is an advantage only when the pile acts as a column (see § 355). The principal disadvan- tage is that they are deficient in transverse resistance to a suddenly applied force. This objection applies only to the handling of the piles before being driven, and to such as are liable, after being driven, to sudden lateral blows, as from floating ice, logs, etc.
Recently, rolled sections of wrought-iron have been employed to a, limited degree for bearing-piles, but present prices prohibit an ex- tended use of wrought-iron piles. It is possible that iron may take the place of wood for piles where they are alternately wet and dr}?-, or where they are difficult to drive; but where the piles are always, wet — as is usually the case in foundation work, — wood is as durable as iron; and hence, on account of cheapness, is likely to have the preference.
325. Screw Piles. These are generally wholly of iron, although the stem is sometimes wood. The screw pile usually consists of a rolled-iron shaft, 3 to 8 inches in diameter, having at its foot one or two turns of a cast-iron screw, the blades of which may vary from 1 ^ to 5 feet in diameter. The piles ordinarily employed for light- houses exposed to moderate seas or to heavy fields of ice have a shaft 3 to 5 inches in diameter and blades 3 to 4 feet in diameter, the screw weighing from 600 to 700 pounds. For bridge piei-s, the shafts are from 6 to 8 inches and the blades from 4 to 6 feet in diameter, the screw w^eighing from 1,500 to 4,000 pounds.
Screw piles were invented by Mitchell of Belfast, and are largely used in Europe, but not to any great extent in this countr}'. They liave been used in founding small light-houses on the sea-shore, for signal stations in marine surveying, for anchorage for buoys, and for various purposes inland.
318 PILE FOUNDATIONS. [CHAP. XI.
For founding beacons, etc., the screw pile has the special advan- tage of not being drawn out by the upward force of the waves against the superstructure. Even when all cohesion of the ground is de- stroyed in screwing down a pile, a conical mass, with its apex at the bottom of the pile and its base at the surface, would have to be lifted to draw the pile out. The supporting power also is consider- abl ' owing to the increased bearing surface of the screw blade. Screw piles have, therefore, an advantage in soft soil. They could also be used advantageously in situations where the jar of driving ordinary piles might disturb the equilibrium of adjacent structures.
326. These piles are usually screwed into the soil by men work- ing with capstan bars. Sometimes a rope is wound around the shaft and the two ends pulled in opposite directions by two capstans, and sometimes the screw is turned by attaching a large cog-wheel to the shaft by a friction-clutch, which is rotated by a worm-screw operated by a hand crank. Of course steam or horse-power could be used for this purpose.
The screw will penetrate most soil . It will pass through loose pebbles and stones without much difficulty, and push aside bowlders of moderate size. Ordinary clay does not present much obsti'uction; clean, dry sand gives the most difficulty. The danger of twisting off the shaft limits the depth to which they may be sunk. Screw piles with blades 4 feet in diameter have been screwed 40 feet into a mixture of clay and sand. The resistance to sinking increases very rapidly with the diameter of the screw; but under favorable circumstances an ordinary screw pile can be sunk very quickly. Screws 4 feet in diameter have, in less than two hours, been sunk by hand-labor 20 feet in sand and clay, the surface of which was 20 feet below the water. For depths of 15 to 30 feet, an average of 4 to 8 feet per day is good work for wholly hand-labor.
For an illustrated and detailed account of the founding of a rail- road bridge pier on screw piles, see Engineering News, Vol. XIII. pp. 210-12.
327. Disk Files. These differ but little from screw piles, a flat disk, instead of a screw, being keyed on at the foot of the iron stem. Disk piles are sunk by the water-jet (§ 343). One of the few cases in which they have been used in this country was in founding an ocean pier on Coney Island, near New York City. The shafts were wrought-iron, lap-welded tubes, 8f inches outside diameter, in
AKT. 1.] DESCKIPTIOJSrS, AND METHODS OF DRIVING. 219
sections 12 to 20 feet long ; the disks were 2 feet in diameter and 9 inches thick, and were fastened to the shaft by set-screws. Many of the piles were 57 feet long, of which 17 feet was in the sand.*
328. Sand Piles. For an accoiint of the method of using sand as piles, see § 2SS.
329. Sheet Piles. These are flat piles, which, being driven successively edge to edge, form a vertical or nearly vertical sheet for the purpose of preventing the materials of a foundation from spreading, or of guarding them against the undermining action of water. They may be made either of timber or iron. Ordinarily sheet piles are simply thick planks, sharpened and driven edge to edge. Sometimes they have a tongue on one edge and a correspond- ing groove on the other, to aid in guiding them into place while driving. When heavy timbers are employed as sheet piling, wooden blocks or iron lugs are fastened on the edges to assist in guiding them into position. Sheet piles should be sharpened wholly, or at least mainly, from one side, and the long edge placed next to the pile already driven. This causes them to crowd together and make comparatively close joints.
When a space is to be inclosed with sheet piling, two roAvs of guide piles are first driven at regular intervals of from 6 to 10 feet, and to opposite sides of these, near the toj), are notched or bolted a pair of parallel string-pieces, or wales, from 5 to 10 inches square, so fastened to the guide piles as to leave a space between the wales equal to the thickness of the sheet jDiles. If the sheeting is to stand more than 8 or 10 feet above the ground, a second pair of wales is required near the level of the ground. The sheet piles are driven (§§ 334-45) between the wales, working from both ends towards the middle of the space between a pair of guide piles, so that the last or central pile acts as a wedge to tighten the whole.
330. Wooden Bearing Piles. Spruce and hemlock answer very well, in soft or medium soils, for foundation piles or for piles always under water ; the hard pines, elm, and beech, for firmer soils ; and the hard oaks, for still more compact soils. Where the pile is alternately wet and dry, white or post oak and yellow or southern pine are generally used.
* For a detailed and illustrated description of this work, see an article by Charles Macdonald, C.E., in Trans. Am. See. of C. E., Vol. VIII. pp. 227-37.
220 PILE FOUNDATIONS. [CHAP. XI
Piles should never be less than 8 inches in diameter at the small end and never more than 18 inches at the large end. Specifications usually require that these dimensions shall not be less than 10 nor more than 14 inches respectively. Piles should be straight-gi'ained, should be trimmed close, and should have the bark removed.
331. Specifications for Piles. The ordinary specifications are about as follows :*
Piles, whether used in foundations, trestle-work, or pile bridges, shall be of good qualitj% sound, white oak^or such other timber as the engineer maj' direct, not less than ten inches (10") in diameter at the smaller end and 14 inches (14") at the larger, and of such lengths as the engineer may require. They must be straight-grained, must be trimmed close, and must have all the bark taken off before being driven. They must be cut off square at the butt, and be properlj^ sharpened. If required by the engineer, the point shall be shod with iron shoes [see § 332], and the head hooped with iron bands of ap- proved size and form [see § 332], which will be paid for by the pound.
332. Pile Caps and Shoes. To prevent bruising and splitting in driving, 2 or 3 inches of the head is usually chamfered off. As an additional means of preventing splitting, the head is often hooped with a strong iron band, 2 to 3 inches wide and -I to 1 inch thick. The expense of removing these bands and of replacing the broken ones, and the consequent delays, led to the introduction, recently, of a cap for the protection of the head of the pile. The cap consists of a cast-iron block with a tapered recess above and below, the chamfered head of the pile fitting into the lower recess and a cushion piece of hard wood, upon which the hammer falls, fitting into the upper one. The cap preserves the head of the pile, adds to the effectiveness of the blows (§ 361), and keeps the pile head in place to receive the blows of the hammer.
A further advantage of the pile cap is that it saves piles. In hard driving, without the cap the head is crushed or broomed to such an extent that the pile is adzed or sawed off several times before it is completely driven, and often after it is driven a portion of the head must be sawed off to secure sound wood upon which to rest the grillage or platform (§ 380). In ordering piles for any special work where the driving is hard, allowance must be made for this loss.
Piles are generally sharpened before being driven, and some-
* See also " Piling" in the general specifications for railway masonry, as given in Appendix I.
ART. 1.] DESCRIPTIONS, AND METHODS OF DRIVING. 221
times, particularly in stony ground, the point is protected by an iron shoe. The shoe may be only two V -shaped loops of bar iron placed over the point, in planes at right angles to each other, and spiked to the piles ; or it may be a wrought or cast iron socket, of which there are a number of forms on the market.
333. Splicing Piles. It frequently happens, in driving piles in swampy places, for false-works, etc., that a single pile is not long enough, in which case two are spliced together. A common method of doing this is as follows :* after the first j)ile is driven its head is cut off square, a hole 2 inches in diameter and 12 inches deep is bored in its head, and an oak treenail, or dowel-pin, 23 inches long, is driven into the hole ; another pile, similarly squared and bored, is placed upon the lower pile, and the driving continued. Spliced in this way the pile is deficient in lateral stiffness, and the upper section is liable to bounce off while driving. It is better to reinforce the splice by flatting the sides of the piles and nailing on, wnth say 8-inch spikes, four or more pieces 2 or 3 inches thick, 4 or 5 inches wide, and 4 to 6 feet long. In the erection of the bridge over the Hudson at Poughkeepsie, K. Y., two piles were thus spliced together to form a single one 130 feet long.
Piles may be made of any required length or cross-section by bolting and fishing together, sidewise and lengthwise, a number of squared timbers. Such piles are frequently used as guide piles in sinking pneumatic caissons (§ 436). Hollow-built piles, 40 inches in diameter and 80 feet long, were used for this purpose in con- structing the St. Louis Bridge (§ 457). They were sunk by pump- ing the sand and water from the inside of them with a sand pump (§ 448).
334. PILE-DKIVING Machines. Pile-driving machines may be classified according to the character of the driving power, which may be (1) a falling weight, (2) the force of an explosive, or (3) the erosive action of a jet of water. Piles are sometimes set in holes bored with a well-auger, and the earth rammed around them. This is quite common in the construction of small highway bridges in the prairie States, a 10- or a 12-inch auger being generally used. The various pile-driving machines will now be briefly described and compared.
* See " Piling" in the General Specifications for Railroad Masonry, as given in Appendix I.
222 PILE FOUXDATIOXS. [CHAP. XI.
335. Drop-hammer Pile-driver. The usual method of driving piles is by a succession of blows given with a heavy block of wood or iron — called a ram, monkey, or hammer — which is carried by a rope or chain passing over a pulley fixed at the top of an upright frame, and allowed to fall freely on the head of the pile. The machine for doing this is called a drop-hammer pile-driver, or a monkey pile-driver — usually the former. The machine is generally placed upon a car or scow.
The frame consists of two uprights, called leaders, from 10 to 60 feet long, placed about 2 feet apart, which guide the falling weight in its descent. The leaders are either wooden beams or iron chan- nel-beams, usually the former. The hammer is generally a mass of iron weighing from 500 to 4,000 jiounds (usually about 2,000) with grooves in its sides to fit the guides and a staple in the top by which it is raised. The rope employed in raising the hammer is usually wound up by a steam-engine placed on the end of the scow or car, opposite the leaders.
A car pile-driver is made especially for railroad work, the leaders resting upon an auxiliary frame, by wliich piles may be driven 14 to 16 feet in advance of the end of the track ; and the frame is pivoted so that piles may be driven on either side of the track. This method of pivoting the frame carrying the leaders is also sometimes applied to a machine used in driving piles for foun- dations.
In railroad construction, it is not possible to use the pile-driving car with its steam-engine in advance of the track ; hence, in this kind of work, the leaders are often set on blocking and the ham- mer is raised by horses hitched directly to the end of the rope. Portable engines also are sometimes used for this purpose. Occa- sionally the weight is raised by men with a windlass, or by pulling directly on the rope.
A machine used for driving sheet piles differs from that de- scribed above in one particular, viz. : it has but one leader, in front of which the hammer moves up and down. With this construction, the machine can be brought close up to the wall of a coffer-dam (§ 317 and § 390), and the pile already driven does not interfere with the driving of the next one.
336. There are two methods of detaching the weight, i. e., of letting the hammer fall: (1) by a nipper, and (2) by a friction-clutch.
ART, 1.] DESCRIPTIOXS, AXD METHODS OF DRIVIXG. 223
1. The nipper consists of a block wliicli slides freely between the leaders and which carries a pair of hooks, or tongs, projecting from its lower side. The tongs are so arranged that when lowered on to the top of the hammer they automatically catch in the staple in the top of the hammer, and hold it while it is being lifted, until they are disengaged by the upper ends of the arms striking a pair of inclined surfaces in another block, the trip, Avhich may be placed between the leaders at any elevation, according to the height of fall desired.
AVith this form of machine, the method of operation is as fol- lows : The pile being in place, with the hammer resting on the head of it and the tongs being hooked into tlie staple in tlie top of the hammer, the rope is wound up until the upper ends of the tongs strike the trip, which disengages the tongs and lets the hammer fall. As the hoisting rope is unwound the nipper block follows the hammer, and, on reaching it, the tongs automatically catch in the staple, and the j^receding operations may be repeated. This method is objectionable owing to the length of time required {ci) for the nipper to descend after the hammer has been dropped, and (^) to move the trip when the height of fall is changed. Some manufac- turers of pile-driving machinery remove the last objection by making an adjustable trip which is raised and lowered by a light line pass- ing over the top of the leaders. This is a valuable improvement.
When the rope is wound up by steam, the maximum speed is from 6 to 14 blows per minute, dependmg upon the distance the hammer falls. The speed can not be increased by the skill of the operator, although it could be by making the ni^^per block heavier.
2. The method by using vl friction-clutch, or friction-drum, as it is often called, consists in attaching the rope permanently to the staple in the top of the hammer, and droppmg the hammer by set- ting free the winding drum by the use of a fnction-clutch. The advantages of this method are {a) that the hammer can be dropped from any height, thus securing a light or heavy blow at pleasure; and {h) that no time is lost in waiting for the nipper to descend and in adjusting the trip.
When the rope is wound up by steam, the speed is from 20 to 30 blows per minute, but is largely dependent upon the skill of the man Avho controls the friction-clutch. The hammer is caught on the rebound, is elevated with the speed of a falling body, and hence
924
PILE FOUNDATICXS.
[chap. XI.
the absolute maximum speed is attained. The rope, by which the hammer is elevated, retards the falling weight ; and hence, for an equal effect, this form requires a heavier hammer than when the nipper is used. Although the friction-drum pile-driver is much more efficient, it is not as generally used as the nipper driver. The former is a little more ex})eiisive in first cost.
337. Steam-hammer Pile-driver. As regards frequency of use, the next machine is probably the steam-hammer pile-driver, invented by Nasmyth* in 1839. It consists essentially of a steam cylinder (stroke about 3 feet), the piston-rod of which carries a weight of about 3,500 pounds. The steam-cylinder is fastened to and between the tops of two I-beams about 8 to 10 feet long, the beams being united at the bottom by a piece of iron in the shape of a frustum of a cone, which has a hole through it. The under side '^f this connecting piece is cut out so as to fit the top of the pile. The striking weight,wliich works up and down between the two I-beams as guides, has a cylindrical projection on the bottom which passes through the hole in the piece connecting the feet of the guides and strikes the pile. The steam to operate the ham- mer is conveyed from the boiler through a flex- ible tube. Fig. 56 shows the striking weight of the latest form of steam-hammer. It differs from that described above in having four rods for guides, instead of the two I-beams.
The whole mechanism can be raised and lowered by a rope passing over a pulley in the top of the leaders. After a pile has been placed in position for driving, the machine is lowered upon the top of it and entirely let go, the pile being its only support. When steam is admitted below the piston, it rises, carrying the striking weight with it, until it strikes a trip, which cuts off' the steam, and the hammer falls by its At the end of the down stroke the valves are again
own weight.
* It is ordinarily called Nasmyth's hammer, but Bourdon should at least share the credit (see Engineering News, vol. xiii. pp. 59. 60).
ART. 1.] DESCRIPTIOXS, AND METHODS OF DRIVING. 225
automatically reversed, and the stroke repeated. By altering the adjustment of this trip-piece, the length of stroke (and thus the force of the blows) can be increased or diminished. The admission and escape of steam to and from the cylinder can also be controlled directly by the attendant, and the number of blows per minute is increased or diminished by regulating the supply of steam. The machine can give 60 to 80 blows per minute.
338. Drop-hammer vs. Steam-hammer. The drop-hammer is capable of driving the pile against the greater resistance. The maximum fall of the drop-hammer is 40 or 50 feet, while that of the steam-hammer is about 3 feet. The drop-hammer ordinarily weighs about 1 ton, while the striking weight of the steam-hammer usually weighs about 1^ tons. The energy of the maximum blow of the drop-hammer is 45 foot-tons (= 45 ft. X 1 ton), and the energy of the maximum blow of the steam-hammer is 4.5 foot-tons (=3 ft. X 1|- tons). The energy of the maximum blow of the drop-hammer is, therefore, about 10 times that of the steam- hammer.
However, the effectiveness of a blow does not dej)end alone upon its energy. A considerable part of the energy is invariably lost by the compression of the materials of the striking surfaces, and the gi'eater the velocity the greater this loss. An extreme illustration of this would be trying to drive piles by shooting rifle-bullets at them. A 1-ton hammer falling 45 ft. has 10 times the energy of a li-ton hammer falling 3 ft., but in striking, a far larger part of the former than of the latter is lost by the compression of the pile head. In constructing the foundation of the Brooklyn dry dock, it wa& practically demonstrated that "there was little, if any, gain in having the fall more than 45 feet." The loss due to the compres- sion depends upon the material of the pile, and whether the head of it is bruised or not. The drop-hammer, using the pile-cap and the friction-drum, can drive a pile against a considerably harder resist- ance than the steam-hammer.
It is frequently claimed that the steam-hammer can drive a pile agamst a greater resistance than the drop-hammer. As compared with the old style drop-hammer, i. e., without the friction-drum and the pile-cap, this is probably true. The striking of the weight upon the head of the pile splits and brooms it very much, which materially diminishes the effectiveness of the blow. In hard driving
226 PILE FOUNDATIONS. [CHAP. XI,
with the drop-hammer, without the pile-cap, the heads of the piles, even when hooped, will crush, bulge out, and frequently split for many feet below the hoop. For this reason, it is sometimes speci- fied that piles shall not be driven with a drop-hammei-.
The rapidity of the blows is an important item as affecting the efficiency of a pile-driver. If the blows are delivered rapidly, the soil does not have sufficient time to recompact itself about the pile. With the steam-driver the blows are delivered in such quick succession that it is probable that a second blow is de- livered before the pile has recovered from the distortion produced by the first, which materially increases the effectiveness of the second blow. In this respect the steam-hammer is superior to the drop-hammer, and the friction-clutch driver is superior to the nipper driver.
In soft soils, the steam-hammer drives piles faster than either form of the drop-hammer, since after being placed in position on the head of the pile it pounds away without the loss of any time.
339. In a rough way the first cost of the two drivers — exclusive of scow or car, hoisting engine, and boiler, which are the same in each — is about |>80 for the drop-hammer driver, and about 1800 for the steam-driver. Of course these prices will vary greatly. The per cent, for wear and tear is greater for the drop-hammer than for the steam-hammer. For work at a distance from a machine-shop the steam-driver is more liable to cause delays, owing to breakage of some part whicli can not be readily repaired.
340. Gunpowder Pile-driver. This machine was invented by Shaw, of Philadelphia, in 1870. The expansive force of gunpowder is utilized both in driving the pile and in raising the ram. The essential parts of the machine are the ram and gun. The former consists of a mass of iron weighing generally about 1,500 pounds, which terminates below in a sort of piston ; this piston fits tightly into a chamber in another mass of iron, the gun. The ram travels between vei-tical guides much as in the other machines ; and the gun and ram are hoisted as is the steam-hammer. The ram having been raised to the top of the guides, and the gun placed upon the top of the pile, a cartridge of from 1 to 3 ounces of gunpowder is placed in the cylinder, or gun, and the ram is allowed to descend. The piston enters the cylinder, compresses the air, and generates heat enough to ignite the cartridge, when the expansive force of
ART. 1.] DESCRIPTIOXS, AXD METHODS OF DRIVING. 227
the powder forces the pile down and the ram up. A cartridge is thrown into tlie gun each time as the ram ascends. The rapidity •of the blows is limited by the skill of the operator and by the heat- ing of the gun. Thirty to forty blows, of from 5 to 10 feet each, can be made per minute.
341. The only advantage of this machine is that the hammer does not come in contact with the head of the pile, and hence does not injure it. The disadvantages are (1) that it is of no assistance in handling the pile ; (2) that it is not economical ; (3) that the gases soon destroy the gun ; (4) that a leakage of gas occurs as the gun gets hot, which renders it less efficient as the rapidity of firing is increased ; and (5) that the gun gets so hot as to explode the cartridge before the descent of the ram, which, of course, is an entire loss of the explosive. Its first cost is great. It is not now used.
342. Driving Piles with Dynamite. It has been proposed to drive piles by exploding dynamite placed directly upon the top of the pile. It is not known that this method has been used except in a few instances. It would be a slow method, but might prove valuable where only a few piles were to be driven by saving the transportation of a machine ; or it might be employed in locations Avhere a machine could not be operated. The higher grades of dynamite are most suitable for this purpose.*
343. Driving Piles with Water Jet. Although the water jet is not strictly a pile-driving machine, the method of sinking piles by its use deserves careful attention, because it is often the cheapest and sometimes the only means by which piles can be sunk in mud, silt, or sand.
The method is very simple. A jet of water is forced into the soil just below the point of the pile, thus loosening the soil and allowing the pile to sink, either by its own weight or with very light blows. The water may be conveyed to the point of the pile through a flexible hose held in place by staples driven into the pile ; and after the pile is sunk, the hose may be withdrawn for use again. An iron pipe may be substituted for the hose. It seems to make very little difference, either in the rapidity of the sinking or in the accuracy with which the pile preserves its position, whether the nozzle is exactly under the middle of the pile or not.
* For a brief description of explosives, see pp. 119-24.
228 PILE POUNDATIONS. [CHAP. XI.
The water jet seems to have been first used in engineering in 1852, at the suggestion of General Geo. B. McClellan. It has been extensively employed on the sandy shores of the Gulf and South Atlantic States, where the compactness of the sand makes it diffi- cult to obtain suitable foundations for light-houses, wharves, etc. Another reason for its use in that section is, that the jialmetto piles — the only ones that will resist the ravages of the teredo — are too soft to withstand the blows of the drop-hammer pile-driver. By employing the water jet the necessity for the use of the j)ile-hammer is removed, and consequently palmetto piles become available. The jet has also been employed in a great variety of ways to facili- tate the passage of common piles, screw and disk piles, cylinders, caissons, etc., etc., through earthy material.*
344. The efficiency of the jet depends upon the increased fluidity given to the material into which the piles are sunk, the actual dis- placement of material being small. Hence the efficiency of the jet is greatest in clear sand, mud, or soft clay ; in gravel, or in sand con- taining a large percentage of gravel, or in hard clay, the jet is almost useless. For these reasons the engine, pump, hose, and nozzle should be arranged to deliver large quantities of water with a mod- erate force, rather than smaller quantities with high initial velocity. In gravel, or in sand containing considerable gravel, some benefit might result from a velocity sufficient to displace the pebbles and drive them from the vicinity of the pile ; but it is evident that any practicable velocity would be powerless in gravel, except for a very limited depth, or where circumstances favored the prompt removal of the pebbles.
The error most frequently made in the application of the water jet is in using pumps with insufficient capacity. Both direct-acting and centrifugal pumps are frequently employed. The former affords the greater power ; but the latter has the advantage of a less first cost, and of not being damaged as greatly by sand in the water used.
The pumping plant used in sinking the disk-piles for the Coney Island pier (see § 327), " consisted of a Worthington pump with a 12-inch steam cylinder, 8^-inch stroke, and a water cylinder 7^ inches in diameter. The suction hose was 4 inches in diameter,
* See a pamphlet — "The Water Jet as an Aid to Engineering Construction" — published (1881) by the Engineer Department of the U. S. Army.
ART. 1.] DESCKIPTIOXS, AXD METHODS OF DRIVIXG. 229
and the discharge hose, which was of four-ply gum, was 3 inches. The boiler was upright, 42 inches in diameter, 8 feet high, and contained 62 tubes 2 inches in diameter. An abundance of steam was supplied by the boiler, after the exhaust had been turned into the smoke-stack and soft coal used as fuel. An average of about 160 pounds of coal was consumed in sinking each j)ile. With the power above described, it was found that piles could be driven in clear sand at the rate of 3 feet per minute to a depth of 12 feet ; after which the rate of progress graduall}' diminished, until at 18 feet a limit was reached beyond Avhich it was not practicable to go without considerable loss of time. It frequently happened tliat the pile would " bring up ' on some tenacious material which was assumed to be clay, and through which the water jet, unaided, could not be made to force a passage. In such cases it was found that by raising the pile about 6 inches and allowing it to drop sud- denly, with the jet still in operation, and repeating as rapidly as possible, the obstruction was finally overcome ; although in some in- stances five or six hours were consumed iu sinking as many feet." *
In the shore-protection work on the Great Lakes, under the direction of the United States Army engineers, the pumping plant '■'consisted of a vertical tubular boiler, with an attached engine having an 8 X 12-inch cylinder, and giving about 130 revolutions per minute to a 42-inch driving-wheel. A No. 4 Holly rotary pump, with 18-inch pulley, Avas attached by a belt to the driving-wheel of the engine, giving about 300 revolutions per minute to the pump. The pump was supplied with a 4-inch suction pipe, and discharged through a 3-inch hose about 50 feet iu length. The hose was pro- vided Avith a nozzle 3 feet in length and 2 inches in diameter. The boiler, engine, pump, and pile-driver were mounted on a i^latform 12 feet in width and 24 feet in length." f
345. Jet vs. Hammer. It is hardly possible to make a compari- son between a water-jet and a hammer pile-driver, as the conditions most favorable for each are directly opposite. For example, sand yields easily to the jet, but offers great resistance to driving with the hammer ; on the other hand, in stiff clay the hammer is much
* Chas. McDonald, in Trans. Am. Soc. of C. E., vol. vlii. pp. 227-37. + "The Water-Jet as an Aid to Engineering Construction," p. 11 ; — a pamphlet published (1881) by the Engineer Department of the U. S. Army.
230 PILE FOUND \TIOXS. [CHAP. XI.
more expeditious. For inland work the hammer is better, owing to the difficulty of obtaining the large quantities of water required for ihe jet ; but for river and harbor work the jet is the most advan- tageous. Under equally favorable conditions there is little or no difference in cost or speed of the two methods.*
The Jet and the hammer are often advantageously used together, especially in stiff clay. The efficiency of the water-jet can be greatly increased by bringing the weight of the pontoon upon which the machinery is placed, to bear upon the pile by means of a block and tackle.
346. Cost of Piles. At Chicago and at points on the Missis- sippi above St. Louis, pine 2Ji^e- cost from 10 to 15 cents per lineal foot, according to length and location. Soft-ioood piles, including rock elm, can be had in almost any locality for 8 to 10 cents per foot. Oak piles 20 to 30 feet long cost from 10 to 12 cents per foot ; 30 to 40 feet long, from 12 to 14 cents per foot ; 40 to 60 feet long, from 20 to 30 cents per foot.
347. Cost of Pile Driving. There are many items that affect the cost of work, which can not be included in a brief summary, but which must not be forgotten in using such data in making estimates. Below are the details for the several classes of work.
348. Railroad Construction. The following table is a summary of the cost, to the contractor, of labor in driving piles (exclusive of hauling) in the construction of the Chicago branch of the Atchison, Topeka and Santa Fe K. K. The piles were driven, ahead of the track, with a horse-power drop-hammer weighing 2,200 i:)Ounds. The average depth driven was 13 feet. The table includes the cost of driving piles for abutments for Howe truss bridges and for the false work for the erection of the same. These two items add considerably to the average cost. The contractor received the same price for all classes of work. The work was as varied as such jobs usually are, piles being driven in all kinds of soil. Owing to the large amount of railroad work in progress in 1887, the cost of material and labor was about 10 per cent, higher than the aver- age of the year before and after. Cost of labor on pile-driver : 1 foreman at $4 per day, 6 laborers at |2, 2 teams at $3.50; total cost of labor = $23 per day.
* Report of Chief of Engineers U. S. A., 1883, pp. 1264-72.
ABl. 1.] DESCRIPTIONS, AND METHODS OF DRIVING. 231
Cost of Pile Driving in Railroad Construction.
Number of piles included in this report 4,409
'• " lineal feet included in this report 109,568
Average length of the piles, in feet 24.8
Number of days employed in driving 494
" " lineal feet driven per day 221.8
Cost of driving, per pile $2.53
" " " " foot 10.4 cents.
349. Railroad Eepairs. The following are the data of pile driving for repairs to bridges on the Indianapolis, Decatur and Springfield R. R. The work was done from December 21, 1885, to January 5, 1886. The piles varied from 12 to 32 feet in length, the average being a little over 21 feet. The average distance driven was about 10 feet. The hammer weighed 1,650 pounds; the last fall was 37 feet, and the corresponding penetration did not exceed 2 inches. The hammer was raised by a rope attached to the draw- bar of a locomotive — comjDaratively a very expensive way.
TABLE 26. Cost of Piles for Bridge Repairs.
Items of Expense.
Total.
Per Pile.
I^aftor ; Loading and unloading piles, 71^ days $16.00
Bridge gang, driving, 12 days
Engine crew, transportation and driving, 13 days. Train crew. " "' " "
Supplies : Engine supplies
6 pile rings and 2 plates
Repairs
Total expense for driving .
Material : 4,192 feet oak piles at 1Z]4 cts $565.92
153.75 45.90 71.50 23.49 13.29 11.04
$334.97
Total COST $900.89
$0.08 0.78 0.23 0.37 0.13 0.06 0.05
1.70
Per Foot.
0.4 cts.
3.7
1.1
1.6
0.5
0.3
0.3
.9 cts.
$2.86 1 13.5 cts.
56 21.4 cts.
On the same road, 9 piles, each 20 feet long, were driven 9 feet, for bumping-posts, with a 1,650-pound hammer dropping 17 feet. The hammer was raised with an ordinary crab-Avinch and single line, with double crank worked by four men. The cost for labor was 8.3 cents per foot of ])ile, and the total expense was 21.8 cents per foot.
350. Bridge Construction. The following table gives the cost of labor in driving the piles for the Northern Pacific R. R. bridge over the Red River, at Grand Forks, Dakota, constructed in 1887. The soil was sand and clay. The penetration under a 2,250-pound hammer falling 30 feet was from 2 to 4 inches. The foreman re- ceived $5 per day, the stationary engineer 83.50, and laborers $2.
232
PILE FOUNPATIONS.
[chap. XI.
TABLE 27 Cost of Labor in Driving Piles in Bridge Construction.
|
Kind of Labor. |
o Ed u a |
gs Hffl |
0 H « g |
a > P-( |
si > |
|
$68.95 432.70 78.75 |
$63.65 252.92 |
$53.50 430.50 47.50 |
$37.00 215.45 179.80* |
$61.60 |
|
|
Driving.. . — |
565.80 131. 90t |
||||
|
$580.40 |
$316.57 |
$531.50 |
$432.25 |
$759.30 |
|
|
224 7,238 32.3 1.1 |
102 3,710 |
104 7,023 38.2 4.1 |
121 4,6.39 38.4 6.6 |
167 |
|
|
Total number of feet remaining in the structure.. Average length of piles " " " " Average length of piles cut oflf |
7,316 43.8 3.7 |
||||
|
Cost per foot of pile remaining in the structure. . . |
8.0 cts. |
8. 5 cts. |
7.6 cts. |
9.3 cts. |
10.4 cts. |
Average cost for driving, per foot remaining in the structure = 8.8 cents.
* Sawed off under 8 feet of water.
+ Including $70.25 for excavating and bailing in order to get at the sawing.
351. Foundation Piles. The contract price for the foundation piles — white oak — for the raih-oad bridge over the Missouri Eiver, at Sibley, Mo. , was 22 cents per foot for the piles and 28 cents per foot for driving and sawing off below water. They were 50 feet Icng^ and were driven in sand and gravel, in a coffer-dam 16 feet deep, by a drop-hammer weighing 3,203 pounds, falling 36 feet. The ham' mer was raised by steam power.
352. In the construction of a railroad in southern Wisconsin during 1885-87, the contract price — the lowest competitive bid — for the piles, in place, under the piers of several large bridges averaged as in the following table. The piles were driven in a strong current and sawed off under water, hence the comparatively great expense.
TABLE 28. Contract Price op Foundation Piles.
|
Kind of Driving. |
Contract Price per Lineal Foot. |
||
|
For Part remaining in Structure. |
For Pile Heads Sawed oflf. |
||
|
Rock Elm Pine Oak Oak |
Ordinary Hard |
40 cents 40 " 48 " 50 " |
15 cents 20 " 25 " 30 " |
AET. 2.] BEAKIXG POWER OF PILES. 233
353. In 1887 the contract price for piles in the foundations of bridge piers in the river at Chicago was 35 cents per foot of pile left in the foundation. This pricp corered cost of timber (10 to 15 cents), driving, and cutting off 12 to 14 feet below the surface of the water, — about 17 feet being left in the foundation.
The cost of driving and sawing off may be estimated about as follows : (17 + 13) feet of pile at 13 cents per foot = $3.90 ; 17 feet of pile, left in the structure, at 35 cents per foot = $5.95. $5.95 — $3.90 = $2.05 = the cost per pile of driving and sawing off, which is equivalent to nearly 7 cents j)er foot of total length of pile. In this case the waste or loss in the pile heads cut off adds consider- ably to the cost of the piles remaining in the structure. In mak- ing estimates this allowance should never be overlooked.
354. Harbor and River "Work. In the shore-protection work at Chicago, done in 1882 by the Illinois Central R. K., a crew of 9 men, at a daily expense, for labor, of $17.25, averaged 6o piles per 10 hours in water 7 feet deep, the piles being 24 feet long and being driven 14 feet into the sand. The cost for labor of handling, sharp- ening, and driving, was a little over 26 cents per pile, or 1.9 cents per foot of distance driven, or 1.1 cents per foot of pile.* Both steam-hammers and water- jets were used, but not together. N'otice that this is very cheap, owing (1) to the use of the jet, (2) to little loss of time in moving the driver and getting the pile exactly in the predetermined place, (3) to the piles not being sawed off, and (4) to the skill gained by the workmen in a long job.
On the Mississippi Eiver, under the direction of the U. S. Army engineers, the cost in 1882 for labor for handling, sharpen- ing, and driving, was $3.11 per pile, or 20 cents per foot driven The piles were 35 feet long, the depth of water 15.5 feet, and the depth driven 13.6 feet. The water- jet and drop-hammer were used together. Tlie large cost was due, in part at least, to the current, which was from 3 to 6 miles per hour.f
Art. 2. Bearing Power of Piles.
355. Two cases must be distinguished ; that of columnar piles or those whose lower end rests upon a hard stratum, and that of ordi- nary bearing piles or those whose supporting power is due to the
* Report of the Chief of Engineers, U. S. A., for 1883, pp. 136&-70. + Ibid., p. 1260.
234 PILE FOUNDATIONS. [CHAP. XI.
friction of the earth on the sides of the pile. In the first case, the bearing power is limited by the strength of the pile considered as a column ; and, since the earth prevents lateral deflection, at least to a considerable degree, the strength of such a pile will approximate closely to the crushing strength of the material. This class of piles needs no further consideration here,
356. Methods of Determining Supporting Power. There are two general methods of determining the supporting power of ordinary bearing piles: first, by considering the relation between the supporting power and the length and size of the pile, the weight of the hammer, height of fall, and the distance the pile was moved by the last blow ; or, second, by applying a load or direct pressure to each of a number of piles, observing the amount each will support, and expressing the result in terms of the depth driven, size of pile, and kind of soil. The first method is applicable only to piles driven by the impact of a hamm.er ; the second is applicable to any pile, no matter how driven.
1. If the relation between the supporting power and the length and size of pile, the weight of the hammer, the height of fall, and the distance the pile was moved by the last blow can be stated in a formula, the supporting power of a pile can be found by insert- ing these quantities in the formula and solving it. The relation between these quantities must be determined from a consideration of the theoretical conditions involved, and hence such a formula is a rational formula.
2. By applying the second method to piles under all the con- ditions likely to occur in practice, and noting the load supported, the kind of soil, amount of surface of pile in contact with the soil, otc, etc., data could be collected by which to determine the sup- porting power of any pile. A formula expressing the su^^porting power in terms of these quantities is an empirical foj-nmla.
357. Rational Formulas. The deduction of a rational for- mula for the supporting power of a pile is not, strictly, an appro- priate subject for mathematical investigation, as the conditions can not be expressed with mathematical precision. However, as there is already a great diversity of formulas in common use, which give widely divergent results, a careful investigation of the subject is necessary.
The present practice in determining the bearing power of piles is
ART. 2.] BEAEIXG POWER OF PILES. 235
neither scientific nor creditable. Many engineers, instead of in- quiring into the relative merits of the different formulas, take an average of all the formulas they can find, and feel that they have a result based on the combined wisdom of the profession. This prac- tice is exactly like that of the ship's surgeon who poured all his medicines into a black jug, and whenever a sailor was ailing gave him a spoonful of the mixture. Other engineers, knowing the great diversity and general unreliability of the formulas, reject them all and trust to their own experience and judgment. The self- reliant engineer usually chooses the latter course, while the timid one trusts to the former.
To correctly discriminate between the several formulas, it is necessary to have a clear understanding of all the conditions in- volved. The object of the following discussion is to discover the general principles which govern the problem.
358. When the ram strikes the head of the pile, the first effect is to compress both the head of the pile and the ram. The more the ram and pile are compressed the greater the force required, until finally the force of compression is sufficient to drive the pile through the soil. The amount of the pressure on the head of the pile when it begins to move, is what we wish to determine.
To produce a formula for the pressure exerted upon the pile by the impact of a descending weight, let
W = the weight of the ram, in tons ;
w — " " " pile "
S = the section of the ram, in sq. ft.;
s = " " " pile " "
L = the length of the ram, in feet ;
I = " " " pile "
E = the co-efficient of elasticity of the ram, in tons per sq. ft. ;
h = the height of fall, in feet ;
d = the penetration of the pile, i. e., the distance the pile is moved by the last blow, in feet. The distance d is the amount the pile as a whole moves, and not the amount the top of the head moves. This can be found accu- rately enough by measuring the movement of a point, say, 2 or 3 feet below the head.
P — the pressure, in tons, which will just move the pile the very
236 PILE FOUNDATIONS. [CHaP. XI.
small distance d, — that is to say, the pressure produced by the last blow; or, briefly, P may be called the sup- porting power. Then Wh is the accumulated energy of the ram at the instant it strikes the head of the pile. This energy is spent (1) in compress- ing the ram, (2) in compressing the head of the pile, (3) in moving the pile as a whole against the resistance of the soil, (4) in overcom- ing the inertia of the pile, (5) in overcoming the inertia of the soil at the lower end of the j^ile, and (6) by the friction of the ram against guides and air. These will be considered in order.
1. The energy consumed in compressing the hammer is repre- sented by the product of the mean pressure and the compression, or shortening, of the ram. The pressure at any point in a striking weight varies as the amount of material above that point ; that is to say, the pressure at any point of the hammer varies inversely as its distance from the lower surface. The pressure at the lower surface is P, and that at the upper one is zero ; hence the mean pressure is I P. From the principles of the resistance of materials, the com-
p L
pression, or the shortening, is ^^-^, in which p is the uniform pres-
sure. From the above, p = ^ P. Consequently the shortening is
IPL
2 SB'
If the fibers of the face of the ram are not seriously crushed, the mean pressure will be one half of the maximum pressure due to im- pact ; or the mean pressure during the time the ram and pile are
1 P^ L being compressed is ^P. Then the energy consumed is— -^7-=^.
The yielding of the material of the ram is j^robably small, and might be omitted, but as it adds no complication, as will presently appear, it is included.
3. The mean pressure on the head of the pile is ^P, as above. For simplicity assume that the pile is of uniform section through- out. To determine the shortening, notice that for the part of the pile above the ground the maximum pressure is uniform through- out, but that for the part under the surface the maximum pressure varies as some function of the length. If the soil were homogeneous, the pressure would vary about as the length in the ground ; and
ART. 2.] BEARIK& POWER OF PILES. 237
1 PI
hence the shortening would be - • — . But, remembering that the
resistance is generally greater at the lower end than at the upper, and that any swaying or vibration of the upper end will still further diminish the resistance near the top, it is probable that the mean pressure is below the center. It will here be assumed that the mean pressure on the fibers of the pile is two thirds of that on the head,
2 PI which is equivalent to assuming that the shortening is when
3 se
the pile is wholly immersed. If only a part of the pile is in contact
PI' 2 PI Pi 2\
with the soil, the shortening will be ■ — ■ + - — i — — [/' -|- _ /j^
in which /' is the exposed portion and l^ the part immersed. For simplicity in the following discussion the shortening of the pile
2i P I
will be taken at - — . If a formula is desired for the case when 6 se
the top projects above the ground, it will only be necessary to sub- stitute (I' +f Z,) for I in equations (1) and (2) below.
1 P^ I
Then the energy lost in the compression of the pile is .
3 se
3. The energy represented by the penetration of the pile is P d.
4. In the early stage of the contact between the ram and the pile, part of the energy of the ram is being used up in overcoming the inertia of the pile ; but in the last stage of the compression, this energy is given out by the stoppage of the pile. At most, the effect of the inertia of the pile is small ; and hence it will be neglected.
5. The energy lost in overcoming the inertia of the soil at the lower end of the pile will vary with the stiffness of the soil and with the velocity of penetration. It is impossible to determine the amount of this resistance, and hence it can not be included in a formula. Omitting this element causes the formula to give too great a support- ing power. The error involved can not be very great, and is to be covered by the factor of safety adopted.
6. The friction of the ram against the guides and against the air diminishes the effect of the blow, but the amount of this can not be computed. Omitting this element will cause the formula for the supporting power to give too great a result. The friction against the air increases very rapidly with the height of fall, and hence the
238 PILE FOUNDATIONS. [CHAP. XI*
smaller the fall the more nearly will the formula give the true sup- porting power.
359. Equating the energy of the falling weight with that con- sumed in compressing the pile and ram, and in the penetration of the pile, as discussed in paragraphs 1, 2, and 3 above, we have
'^" = 1^ + 1^ + ^" w
Solving equation (1) gives
_ V _ , 12 S Bse 36 cP S' E' s' e
3 Ls e-{-4:l S B ' {3 L s e -\- 4 I S B)'
6 d S Bse
3 Lse + Al S B
. . (2)
An examination of equation (3) shows that the pressure upon the pile varies with the height of fall, the weight, section, length, and co-efficient of elasticity of both ram and pile, and with the penetra- tion. It is easy to see that the weight of the ram and the height of the fall should be included. The penetration is the only element which varies with the nature of the soil, and so of course it also should be included. It is not so easy to see that the length, section, and co-efficient of elasticity of the material of the pile and ram should be included. If any one will try to drive a large nail into hard wood with a piece of leather or rubber intervening between the hammer and the head of the nail, he will be impressed with the fact that the yielding of the leather or rubber appreciably diminishes the effectiveness of the blow. Essentially the same thing occurs in trying to drive a large nail with a small hammer, except that in this case it is the yielding of the material of the hammer which dimin- ishes the effect of the blow. In driving piles, the materials of the pile and ram act as the rubber in the first illustration; and, reason- ing by analogy, those elements which determine the yielding of the materials of the pile and ram should be included in the formula. Obviously, then, the pressure due to impact Avill be greater the harder the material of the pile. Notice also that if the head of the pile is bruised, or ''broomed," the yielding will be increased; and, consequently, the pressure due to the blow will be decreased.
ART. 2.] BEARING POWER OF PILES. 339
360. The Author's Formula for Practice. To simplify equation (2), put
6 S E se _ d Lse +4:1 S E ~ ^'
and then equation (2) becomes
P = V-Zq Wh + q' cV - q d. .... (3)
Equation (3) can be simplified still further by computing q for the conditions as they ordinarily occur in practice. Of course, in this case it will only be possible to assume some average value for the various quantities. Assume the section of the pile to be 0.8 sq. ft.; the section of the ram, 2 sq. ft.; the length of the ram, 2.5 ft.; the length of the pile,* 25 ft. ; the co-eflBcient of elasticity of the ram, 1,080,000 tons per sq. ft.; and the co-efficient of elasticity of the pile, 108,000 tons per sq. ft. (an average value for oak, elm, pine, etc., but not for palmetto and other soft woods). Computing the corresponding value of q, Ave find it to be 5,160; but to secure round numbers, we may take it at 5,000, which also gives a little additional security.
Equation (3) then becomes
P = 100 ( VWh + {bO(iy - 50 d), ... (4)
wliich is the form to he used in jiractice.
Equation (4) is approximate because of the assumptions made in deducing equation (1), and also because of the average value taken for q\ but probably the error occasioned by these aj)proximations is not material.
361. Notice that, since the co-efficient of elasticity of sound material was used in deducing the value of q, equation (4) is to be applied only on condition that the last blow is struck upon sound Avood; and therefore the head of the test pile should be sawed off so as to present a solid surface for the last, or test, blow of the hammer. {This limitatio7i is exceedingly important.) Since the penetration per blow can be obtained more accurately by taking the mean dis- tance for two or three blows than by measuring the distance for a single one, it is permissible to take the mean penetration of two or
* The quantity to be used here is the length out of the ground pliLS about two thirds of the part in the ground (see paragraph 2 of § 353).
240
PILE F0UXDATI02s"S.
[chap. XI.
tliree blows; but their number and force should be such as not to crush the head of the pile.
In this connection the following table, given by Don. J. Whitte- naore, in the Transactions of the American Society of Civil Engi- neers, vol. xii. p. 442, to show the gain in efficiency of the driving power by cutting off the bruised or broomed head of the pile, is very instructive. The pile was of green Norway pine; the ram was of the Nasmyth type, and weighed 2,800 pounds.
Table showing the Gain in Efficiency of the Driving Power bi Cutting off the Broomed Head of the Pile.
3d ft. of penetration required 5 blows.
4th " " " 15
5th " " " 20
6th " " " 29
7th " " " 35
8th " " " ...... 46
9th " " 61
10th " " '•• 73
11th " " " 109
12th " " " 153
13th " " " 257
14th " " " ....... 684
Head of the pile adzed off.
15th ft. of penetration required 275
16th " " " 572
17th " " " 833
18th " " " . 825
Head of the pile adzed off.
19th ft. of penetration required . 213
20th " " " 275
21st " " " 371
22d " " " 378
Total number of blows, 5,228
Notice that the average penetration per blow was 2^ times greater during the 15th foot than during the 14th; and nearly 4 times greater in the 19th than in the 18th. It does not seem unreason- able to believe that the first blows after adzing the head off were (Correspondingly more effective than the later ones; consequently, it is probable that the first blows for the 15th foot of penetration were more than 5 times as efficient as the last ones for the 14th foot, and also that the first blows for the 19th foot were 8 or 10 times more efficient than the last ones for the 18th foot. Notice also that since the head was only "^ adzed off," it is highly probable that the spongy wood was not entirely removed.
ART. 2. J BEARIXG POWER OF PILES. 341
If the penetration for the last blow before the head Avas adzed off were used in the formula, the apparent supporting power would be yery much greater than if the penetration for the first blow after adzing off is employed. This shows how unscientific it is to pre- scribe a limit for the penetration without specifying the accompany- ing condition of the head of the pile, as is ordinarily done.
362. Weisbach's Formula. Equation (2), page 238, is essentially equivalent to Weisbach's formula foi- the supporting power of a pile. Weisbach assumes that the pressure is uniform throughout, and obtains the formula*
in which H = —j—, and H^ = -j.
363. Rankine's Formula. Equation (2), page 238, is also essen- tially equivalent to Kankine's formula ; and differs from it, only because he assumes the pressure to vary directly as the length of the pile, and neglects the compression of the ram. Rankine's formula is f
Equation (2) differs from "Weisbach's and Rankine's on the safe side.
364. Empirical Formitlas. General Principles. (1) An empiri- cal formula should be of correct form; (2) the constants in it should be correctly deduced ; and (3) the limits Avithin which it is applica- ble should be stated.
For example, suppose that it were desired to determine the equation of the straight line A B, Fig. 57. Since the given line is straight, we will as- sume that the empirical formula is of the form y = m x. We might find m by measur- ing the ordinates 1, 2, 3, and place m equal to their mean. If 1, 2, 3, be the numerical values of the respective ordinates, the for- mula becomes y = 2 x, which gives the line 0 C. The mean ordinate to 0 C is equal to fio. 57.
the mean ordinate to A B, but the two are not by any means the
* Mechanics of Engineering, 6th ed. (Coxa's Trauslation), p. 701- + Civil Engineering, p. 602.
24:2 PILE FOUNDATIONS. [CHAP. XI.
same line. It is evident that this empirical formula is of the wrong
form.
For another illustration, assume that some law is correctly repre- sented by the curve A B, Fig. 58. The form of the empirical formula may be such as to give the curve CD. These curves coincide a c exactly at tAvo points, and the mean ordinate
to the two is the same. To use a com- mon expression, we may say that, "on the average, the empirical formula agrees exactly
Fig. 58. with the facts ;" but it is, nevertheless, not
even approximately true. The constants were not correctly de- duced.
Even if of the correct form and correctly deduced, an empirical formula can be safely applied only within the limits of those values from which it was deter- mined. For example, a law may be repre- sented by the curve A B, Fig. 59. From observations made in the region C E, the em- Fig. 59.
pirical formula has been determined, which gives the curve C E D, which between the limits C and E is all that can be desired, but which is grossly in error between the limits E and D. To use an empirical formula intelligently, it is absolutely necessary that the limits within which it is applicable should be known.
Of course, the observations from which the empirical formula was deduced can not be used to test the correctness of the formula; such a procedure can check only the mathematical work of deriving the constants.
Elementary as the preceding principles are, many empirical formulas are worthless owing to a disregard of these conditions in deducing them.
365. Comparison of Empirical Formulas. We will now briefly consider the empirical formulas that are most frequently employed to determine the supporting power of piles.*
HasweWs formula for the dynamic effect of a falling body is f P = 4.426 W V, "as deduced from experiments."
The experiments consisted in letting a weight of a few ounces
* For explanation of the nomenclature, see p. 23.5.
t Haswell's Engineers' and Mechanics' Pocket-Book, p. 419.
AKT. 2.] BEARING POWER OF PILES. 243
fall a few inches upon a coiled spring ; and hence the formula is entirely inapplicable to pile driving.
Beaufoy's formula is P=: 0.5003 WV^, '^as determined by experiment." This formula was deduced under the same conditions as Haswell's^ and hence is useless for pile driving. The difference between the formulas is due to the fact that Haswell used only one "weight and one spring, and varied the height of the fall, while Beau- foy employed one weight and springs of such relative stiffness as would stop the weight in nearly the same distance for different heights of fall.* Notice that Haswell's; and also Beaufoy's foi-mula, would give the same bearing power for all soils, other things being the same.
Ny Strom's formula] is P = , ,„ , — -r^—-,. In a later book,t Nvs- •^ -^ ' {y['-\-w) d ^ -
^ Wli trom gives the formula P = — — —-, assuming that "about 25 per
cent, of the energy of the ram is lost by the crushing of the head of the pile." Both of these formulas are roughly approximate, theo- retical formulas, although frequently cited as "practical formulas."
W h
Mason's formula § is P = , „, , r— ,. As in the preceding
( P^ + iv) a
cases, this is frequently referred to as a "practical formula ;" but an examination of the original memoir shows that it is wholly a theo- retical formula with no pretensions of being anything else. It is also sometimes referred to as having been " tested by a series of experiments ;" but apparently the only basis for this is that the piles upon which Fort Montgomery (Eouse's Point, N. Y.) stood from 1846 to 1850 without any sign of failure, when tested by this formula, showed a co-efficient of safety of 3^^. The evidence is not conclusive: (1) the factor is large enough to cover a considerable error in the formula; (2) since the formula assumes that all of the energy in the descending ram is expended in overcoming the resist- ance to penetration, the computed bearing power is too small, and consequently the co-efficient of safety is even greater than as stated;
* Van Nostrand's Engin'g Mag., vol. xvii. p. 325. + Nystrom's Pocket-Book, p. 158. X New Mechanics, p. 134.
§ Resistance of Piles, J. L. Mason, p. 8; No. 5 of Papers on Practical Engineering, published by the Engineering Department of the U. S. Army.
244 PILE FOUNDATIONS. [CHAP. XL
and (3) it is probably safe to say that after a pile has stood a short
time its bearing power is greater than at the moment the driving
ceased, owing to the settlement of the earth about it.
Wh Sander's formula* is P' = -T-r, in which P' is the safe bear-
o a
ing power. This formula was deduced on the assumptions that the
energy of the falling weight was wholly employed in forcing the
pile into the ground, — i. e., on the assumption that P d ^= Wit, or
W h P = — ;— , — and that the safe load was one eighth of the ultimate d •'
supporting power. It is therefore a roughly approximate, theoreti- cal formula.
Notice that, since some of the energy is always lost, P d, the energy represented by the movement of the pile, must always be less than W li, the energy of the hammer ; hence, P is always less
than — -j-; or, in mathematical language, P< — —. This relation is
It tt
very useful for determining the greatest possible value of the sup-
porting power. P will always be considerably less than — ^ ; and
this difference is greater the lighter the weight, the greater the fall, the softer the material of the pile, or the more the head Ib bruised. When d is very small, say \ inch or less, the difference is so great as to make this relation useless.
Trautioine'' s formula,^ in the nomenclature of page 235, is
P = — ^. It was deduced from the observed sapporting
power of piles driven in soft soil. Strictly speaking, it is applicable only under conditions similar to those from which it was dednced ; and hence it is inapplicable for hard driving and to piles whose heads are not bruised about the same amount as were the experi- mental ones. No formula can be accurate which does not, in some way, take cognizance of the condition of the head of the pile. For example, experiments Nos. 3 and 4 of the table on page 246 are the same except in the condition of the heads of the piles, and yet
* Jour. Frank. Inst., 3d series, vol. xxii. p. — . t Engineer's Pocket-Book, Ed. 1885, p. 643.
AKT. 2.] BEAEIXG POAVEK OF PILES. 245
the load supported by the former was 2^ times that supported by the
latter. This formula is not applicable to piles driven with a steam
hammer, since according to it the energy represented by the sinking.
of the pile is greater than the total energy in the descending weight.
For example, if W — 1| tons, h = 2 feet, and d = 1 inch = ^j of a
Wh foot, the formula P < — 7— becomes P < 36 tons. Trautwine's
a
formula gives P = 49 tons; that is to say, Trautwine's formala
makes the supporting power one third more than it would be if 710
energy were lost.
Engineering News formula* the most recent and the most
popnlar, is P ' = -^ , in which P' is the safe load in tons; and
« -)- 1
d' is the penetration, in inches, under the last blow, which is
assumed to be appreciable and at an approximately uniform rate.
366. The Authors Enqjirical Formula. Certain assumptions
and approximations were made in deducing equation (3), page 239.
If it is thought not desirable to trust entirely to theory, then the
formula
P = V2q Wh -{-(fd' - qd . . . . (7)
may be considered as giving only the form which the empirical formula should have. Under this condition q becomes a numerical co-efficient to be determined by experiment, which must be mad«» by driving a pile and measuring d, after which the sustaining power must be determined by applying a direct pressure. The last, or test, blow should be struck on sound wood.
367. Table 29 gives all the experiments on the supporting- power of piles for which the record is complete. Unfortunately these experiments do not fulfill the conditions necessary for a proper determination of q in equation (7). It is known that in some of the cases the head of the pile was coni^iderably broomed, and there is internal evidence that this was so in the others.
The data of the following table substituted in equation (7) give values of q from 1.5 to 337, with an average of 130. The range of these results shows the inconsistency of the experiments, and the smallness of the average shows that the last blow was not struc> ^o sound wood. This value of q is of no practical use
* Engineering News. vol. xx. pp. 511, 512 (Dee. 29, 1888;.
246
PILE FOLXDATIOXS.
[chap. XI.
TABLE 29. Data of Experiments on the Supporting Power of Piles.
|
P !d |
at a |
s o S |
|||
|
Id |
o S |
? H |
Q OEh |
||
|
m b |
W a 5 |
5 a |
> r « Big" |
AUTHORITT, |
|
|
a u |
2 ■< o |
M J |
sc 2; |
H o as |
|
|
l« |
n a, H O |
||||
|
1 |
0.455 |
5 |
0.031 |
30.2 |
Circular of the Office of Chief of Engineers U. S. A., Nov. 12, '81, pp. 2, 3. |
|
2 |
0.8 |
86 |
15 |
7.3 |
Trautwine's Pocket-Book, ed. 1885, p. 643. |
|
3 |
1.12 |
80 |
0.042 |
112.0 |
Jour. Frank. Inst., vol. 55, p. 101. |
|
4 |
1.1 |
30 |
0.042 |
45.9 |
Delafield's "Foundations in Compicssible Soils," pp. 17, 18; — a pamphlet published by En- gineers' Department of U. S. A. |
|
5 |
0.95 |
29 |
0.125 |
50.0 |
Trautwine in Railroad Gazette, July 8, 1887, p. 453. |
368. As confirming the reliability of \X\q form of equations (3), (4), and (7), it is interesting to notice that A. C. Hertiz* found, from the records of the driving and afterwards pulling up of nearly 400 piles, the following relation :
d =
Wh
P
500'
which may be put in the form
P = i/500 Wh + (250 (7)' - 250 cl
(8)
Equation (8) has exactly the form of equation (3), page 239, although deduced in an entirely different way. The value (250) of the constant q in equation (8) is less than that in equation (4), page 239, which shows that the heads of the piles were broomed. The value of q in equation (8) is greater than that deduced from the data of Table 29, which shows that the piles from which equation (8) was determined were not bruised as much as those in the above table.
369. Supporting Power Determined by Experiment. It is not certain that the bearing power of a pile when loaded with a con- tinued quiescent load will be the same as that during the very short
* Proc. Inst, of C. E., vol. Ixiv. pp. 311-15 ; republished in Van Nostrand's Maga- zine, vol. XXV. pp. 373-76.
ART. 2.] BEARING POWER OF PILES. 247
period of the blow. The friction on the sides of the pile will have a greater effect in the former case, while the resistance to penetra- tion of the point will be greater in the latter. This, and the fact that the supporting power of piles sunk by the Avater-jet can be determined in no other way, shows the necessity of experiments to determine the bearing power under a steady load.
Unfortunately no extended experiments have been made in this direction. We can give only a collection of as many details as pos- sible concerning the piles under actual structures and the loads which they sustain. In this way, we may derive some idea of the sustaining power of piles under various conditions of actual practice.
370. Ultimate Load. In constructing a light-house at Proctors- ville. La., in 1856-57, a test pile, 12 inches square, driven 29.5 feet, bore 29.9 tons without settlement, but with 31.2 tons it "settled slowly." The soil, as determined by borings, had the following character : " For a depth of 9 feet there was mud mixed with sand ; then followed a layer of sand about 5 feet thick, next a layer of sand mixed with clay from 4 to G feet thick, and then followed fine clay. By draining the site the surface was lowered about 6 inches. The pile, by its own weight, sank 5 feet 4 inches." The above load is equivalent to a frictional resistance of 600 lbs. per sq. ft. of surface of pile in contact with the soil. This pile is No. 1 of the table on page 246.
At Philadelphia in 1873, a pile was driven 15 ft. into "soft river mud, and 5 hours after 7.3 tons caused a sinking of a very small fraction of an inch ; under 9 tons it sank f of an inch, and under 15 tons it sank 5 ft." The above load is equivalent to 320 lbs. per sq. ft. of surface of contact. This pile is No. 2 of the table on page 246.
In the construction of the dock at the Pensacola navy yard, a pile driven 16 feet into clean white sand sustained a direct pressure of 43 tons without settlement, while 45 tons caused it to rise slowly; and it required 46 tons to draw a pile that had been driven 16 feet into the sand. This is equivalent to a frictional resistance of 1,900 lbs. per sq. ft. This pile is No. 4 of the table on page 246.
" In the construction of a foundation for an elevator at Buffalo, N. Y., a pile 15 inches in diameter at the large end, driven 18 ft., bore 25 tons for 27 hours without any ascertainable effect. The weight was then gradually increased until the total load on the
248 PILE FOUJv^DATIOXS. [CHAP. XI.
pile was 37^ tons. Up to this weight there had been no depression of the pile, but with 37^ tons there was a gradual depression which aggregated | of an inch, beyond whicli there was no depression until tlie weight was increased to 50 tons. With 50 tons there was a further depression of ^ of an inch, making the total depression 1^ inches. Then the load was increased to 75 tons, under which the total depression reached 3| inches. The experiment was not carried beyond this point. The soil, in order from the top, was as follows : 2 ft. of blue clay, 3 ft. of gravel, 5 ft. of stiff red clay,
2 ft. of quicksand, 3 ft. of red clay, 2 ft. of gravel and sand, and
3 ft. of very stiff blue clay. All the time during this experiment there were three pile-drivers at work on the foundation, thus keep- ing up a tremor in the ground. The water from Lake Erie had free access to the pile through the gravel."* This is equivalent to a frictional resistance of 1,850 lbs. per sq. ft. This is pile No. 5 of the table on page 246.
371. In making some repairs at the Hull docks, England, several hundred sheet-piles were drawn out. They were 12 X 10 inches, driven an average depth of 18 feet in stiff blue clay, and the average force required to pull them was not less than 35.8 tons each. The frictional resistance was at least 1,875 lbs. per sq. ft. of surface in contact with the soil, f
372. Safe Load. The piles under the bridge over the Missouri at Bismarck, Dakota, were driven 32 ft. into the sand, and sustain 20 tons each — equivalent to a frictional resistance of GOO lbs. per sq. ft. The piles at the Plattsmouth bridge, driven 28 ft. into the sand, sustain less than 13^ tons, of which about one fifth is live load, — equivalent to a frictional resis'tance of 300 lbs. per sq. ft.
At the Hull docks, England, piles driven 16 ft. into " alluvial mud " sustain at least 20 tons, and according to some 25 tons ; for the former, the friction is about 800 lbs. per sq. ft. The piles under the Eoyal Border bridge "were driven 30 to 40 ft. into sand and gravel, and sustain 70 tons each," — the friction being about 1,400 lbs. per sq. ft.
373. "The South Street bridge approach, Philadelphia, fell by the sinking of the foundation piles under a load of 24 tons each.
* By courtesy of John C. Trautwine, Jr. , from private correspondence of John E. Payne and W. A. Haven, engineers in charge. + Proc. Inst, of C. E., vol. Ixiv. pp. 311-15.
AeT. 2.] BEARING POWER OF PILES. 249
They were driven to an absolute stoppage by a 1-ton hammer fall- ing 32 feet. Their length was from 24 to 41 feet. The piles were driven through mud, then tough clay, and into hard gravel."* According to Trau twine's formula their ultimate supporting power was 164 tons, and according to the Engineering News formula the safe load was 64 tons. It is probable that the last blow was struck on a broomed head, which would greatly reduce the penetration, and that consequently their supporting power was greatly over- estimated.. If the penetration when the last blow was struck on sound wood were 2 inches, then according to Trau twine's formula the tdtimate supporting power was 54.7 tons, and according to the Engineering Neivs formula the safe load was 21.3 tons.
374. Supporting Power of Screw and Disk Piles. The sup- porting power depends upon the nature of the soil and the dejothto which the pile is sunk. A screw pile " in soft mud above clay and sand " supported 1.8 tons per sq. ft. of blade, f A disk pile in " quicksand " stood 5 tons per sq. ft. under vibrations. % Charles McDonald, in constructing the iron ocean-pier at Coney Island, as- sumed that the safe load upon the flanges of the iron disks sunk into the sand, was 5 tons per sq. ft. ; but " many of them really support as much as 6.3 tons per sq. ft. continually and are subject to occa- sional loads of 8 tons per sq. ft., without causing any settlement that can be detected by the eye."§
375. Factor of Safety. On account of the many uncertainties in connection with piles, a wide margin of safety is recommended by all authorities. The factor of safety ranges from 2 to 12 according to the importance of the structure and according to the faith in the formula employed or the experiment taken as a guide. At best, the formulas can give only the siipporting power at the time when the driving ceases. If the resistance is derived mainly from fric- tion, it is probable that the supporting power increases for a time after the driving ceases, since the co-efficient of friction is usually greater after a period of rest. If the supporting power is derived mainly from the resistance to penetration of a stiff substratum, the bearing power for a steady load will probably be smaller than the
* Trans. Am. Soc. of C. E., vol. vii. p. 264. tProc. Inst, of C. E., vol. xvii. p. 451. Xlbid., p. 443. § Trans. Am. Soc. C. E., vol. \iii. p. 236.
250 PILE FOUNDATIONS. [OHAP. XL
force required to drive it, as most materials require a less force to change their form slowly than rapidly. If the soil adjoining the piles becomes wet, the supporting power will be decreased; and vibrations of the structure will have a like effect.
The formulas in use for determining the supporting power of piles are so unreliable, that it is quite impossible to determine the factor of safety for any existing structure with anything like accu- racy.
The factor to be employed should vary with the nature of the etructure. For example, the abutments of a stone arch should bo constructed so that they will not settle at all ; but if a railroad pile trestle settles no serious damage is done, since the track can be shimmed up occasionally. In a few cases, a small settlement has taken place in a rail-road trestle when the factor of safety was 3 or 4, as computed by equation (4), page 239.
Art. 3. Areangement of the Foundation.
376. Disposition of the Piles. The length of the piles to be used is determined by the nature of the soil, or the conveniences for driving, or the lengths most easily obtained. The safe bearing power may be determined from the data presented in §§ 370-73, or, better, by driving a test pile and applying equation (4), page 239. Then, knowing the weight to be supported, and having decided upon the length of piles to be used, and having ascertained their safe bearing power, it is an easy matter to determine how many piles are required. Of course, the number of piles under the different parts of a structure should be proportional to the weights of those parts.
If the attempt is made to drive piles too close together, they are liable to force each other up. To avoid this, the centers of the piles should be, at least, 2^ or 3 feet apart. Of course, they may be farther apart, if a less number will give sufficient supporting power, or if a greater area of foundation is necessary to prevent overturning.
When a grillage (§ 380) is to be placed on the head of the piles, great care must be taken to get the latter in line so that the lowest course of grillage timber, in this case called capping, may rest squarely upon all the piles of a row. In driving under water, a
Ar.T. 3.] AKEAXGEMEXT OF THE FOUNDATION. 251
convenient way of marking the positions of the piles is to construct a light frame of narrow boards, called a spider, in which the posi- tion of the piles is indicated by a small square opening. This frame may be held in place by fastening it to the sides of the coffer-dam, or to the piles already driven, or to temporary supports. Under ordinary circumstances, it is reasonably good work if the center of the pile is under the cap. Piles frequently get considerably out of place in driving, in which case they may sometimes be forced back with a block and tackle or a jack-screw. When the heads of the piles are to be covered with concrete, the exact position of the piles is comparatively an unimportant matter.
In close driving, it is necessary to commence at the center of the area and work towards the sides ; for if the central ones are left until the last, the soil may become so consolidated that they can scarcely be driven at all.
377. Butt vs. Top Down. According to Eankine* all piles should be driven large end down, having first been sharpened to a point 1|- to 2 times as long as the diameter of the pile. This is at least of doubtful utility. If the pile is supported wholly by fric- tion, then the supporting power will be greater when the small end is down. If the soil is semi-liquid, the buoyancy would be slightly greater when the large end is down ; but the buoyancy constitutes but a very small jmrt of the supporting power, and the difference in buoyancy between top and bottom down is still less. If the pile derives its support mainly from a solid substratum, then its bearing power would be greater with the large end down ; but, in this case, it should not be sharpened. For close driving, it is frequently recommended that, to prevent the piles from forcing each other up, they should be driven butt end down. Notice, however, that if the soil is non-compressible, as pure sand, or if the piles are driven so close as to compress the soil considerably, it will rise and carry the piles with it, whether they were driven with the big or the little end down. Piles are generally driven small end down, but never- theless practical experience shows that there are conditions in which it is apparently impossible to drive them in this way, even in comparatively isolated positions. These conditions appear to occur most frequently in swamps, and in connection with quicksand.
* " Civil Engineering," p. 602.
352 PILE FOUXDATIONS. [CHAP. XI.
378. Sawing-OFF the Piles. When piles are driven, it is generally necessary to saw them off either to bring them to the same height, or to get the tops lower than they can be driven, or to secure sound wood upon Avhich to rest the timber platform that carries the masonry. When above water, piles are usually sawed off by hand ; and when below, by machinery — usually a circular saw on a vertical shaft held between the leaders of the pile driver or mounted upon a special frame, and driven by the engine used in driving the piles. The saw-shaft is sometimes attached to a vertical shaft held between the leaders by parallel bars, by which arrangement the saw can be swung in the arc of a circle and several piles be cut off with- out moving the machine. The piles are sometimes sawed off with what is called a pendulum saw, i.e., a saw-blade fastened between two arms of a rigid frame which extends into the water and is free to swing about an axis above. The saw is swung by men pushing on the frame. The first method is the better, particularly when the piles are to be sawed off under mud or silt.
Considerable care is required to get the tops cut off in a hori- zontal plane-. It is not necessary that this shall be done with mathe- matical accuracy, since if one pile does stand up too far the excess load upon it will either force it down or crush the cap until the other piles take part of the weight. Under ordinary conditions, it is a reasonably good job if piles on land are sawed within half an inch of the same height ; and under water, within one inch. When a machine is used on land, it is usually mounted upon a track and drawn along from pile to pile, by which device, after having leveled up the track, a whole row can be sawed off Avith no further atten- tion. When sawing under water, the depth below the surface is indicated by a mark on the saAV-shaft, or a target on the saw- shaft is observed upon with a leveling instrument, or a leveling rod is read upon some part of the saw-frame, etc. In sawing piles off under water, from a boat, a great deal of time is consumed (par- ticularly if there is a current) in getting the boat into position ready to begin work.
Piles are frequently sawed off under 10 to 15 feet of water, and occasionally under 20 to 25 feet.
379. Finishing the Foundation. There are two cases : (^) when the heads of the piles are not under water ; and (2) when they are under water.
ART. 3.] ARRANGEMENT OF THE FOUND ATIOJST. 253
1. When the piles are not under water there are again two case:' •. (a) when a timber grillage is used ; and (b) when concrete alone ":o used.
2. "When the piles are sawed off under water, the timber struct- ure (in this case called a crib) which intervenes between the piles and the masonry is put together first, and then sunk into place. The construction is essentially the same as when the jjiles are not under water, but differs from that case in the manner of getting the tim- ber into iU final resting place. The methods of constructing foun- dations under water, including that by the use of timber cribs, will be discussed in Art. 2 of the next chapter.
380. Piles and Grillage. This is a stout frame of one or more courses of timber drift-bolted or pinned to the tops of the piles and to each other, upon which a floor of thick boards is placed to receive the bottom courses of masonry. For illustrated examples, see Fig. 84, page 3G3, Fig. 86, page 380, and Fig. 90, page 386.
The timbers which rest upon the heads of the piles, called cajjs, are usually about 1 foot square, and are fastened by boring a hole through each and into the head of the pile and driving into the hole a plain rod or bar of iron having about 25 per cent, larger cross section than the hole.
381. These rods are called .drift-bolts, and are usually either a rod 1 inch in diameter (driven into a f-inch auger hole), or a bar 1 inch square (driven into a |-iuch hole). Formerly jag-bolts, or rag-bolts, /. e., bolts whose sides were jagged, or barbed, were used for this and similar purposes ; but universal experience shows that smooth rods hold much the better. In some experiments made at the Poughkeepsie bridge (§ 414), it was found that a 1-inch rod driven into a |f-inch hole in hemlock required on the average a force of 2^ tons per linear foot of rod to withdraw it; and a 1-incli rod driven into a f-inch hole in white or Norway pine required 5 tons per linear foot of rod to withdraw it.* The old-style jag- bolt was square because it was more easily barbed ; and probably this is the reason why square drift-bolts are now more common. Another advantage of the round drift-bolt, over the square one, is that the latter does not cut or tear the wood as much as the former. The ends of the rods should be slightly rounded with a hammer.
Transverse timbers are put on top of the caps and drift-bolteu to them. Old bridge-timbers, timbers from false works, etc., are
* For additinnal data, see Note 8, page 547.
254 PILE FOUNDATIONS. [CHAP. XI.
frequently used, and are ordinarily as good for tliis purpose as new. As many courses may be added as is necessary, each perpendicular to the one beVow it. The timbers of the top course are laid close together, or, as before stated, a floor of thick boards is added on top to receive the masonry. ,
This form of construction is very common in the foundations of bridge abutments. Of course no timber should be used in a foun- dation, except where it will always be wet.
382. Piles and Concrete. A thick layer of concrete, resting partly on the heads of the piles and partly on the soil between them, is frequently employed instead of the timber grillage as above. Objection is sometimes made to the j^latform (§ 380) as a bed for a foundation that, owing to the want of adhesion between wood and mortar, the masonry might slide off from the platform if any un- equal settling should take place. To obviate this, the concrete is frequently substituted for the grillage and platform.
However, there is but slight probability that a foundation will ever fail on account of the masonry's sliding on timber, since, ordi- narily, this could take place only when the horizontal force is nearly half of the downward pressure.* This could occur only with dams, retaining walls, or bridge abutments, and rarely, if ever, with these. One of the fundamental principles of all masonry construction is to build the courses perpendicular to the line of pressure, which condition alone would prevent slipping. Any pos- sibility of slipping can be prevented also by omitting one or more of the timbers in the top course — the omitted timbers being per- pendicular to the direction of the forces tending to produce sliding, — or by building the top of the grillage in the form of steps, or by driving drift-bolts into the platform and leaving their upper ends projecting.
Although the use of concrete, as above, may not be necessary to prevent sliding, it adds materially to the supporting power of the foundation ; it utilizes the bearing power of the soil between the piles as well as the supporting power of the piles themselves, which is a very important consideration in soft soils. Another ad- vantage of this form of construction is that the concrete can be laid without exhausting the water or sawing off the piles. Frequently
* See Table 36, page 315.
ART. 3.] AREANGEMENT OF THE FOUIf CATIONS'. 255
concrete can also be used advantageously in connection with timbei* grillage to pack in around the timbers.
383. Lateral Yielding. Notice that, although the masonry may not slide off from tlie timber platform (§ 382), the foundation may yield laterally by the piles themselves being pushed over. If the piles reach a firm subsoil, it will help matters a little to remove the upper and more yielding soil from around the tops of the piles and fill in with broken stone ; or a wall of piles may be driven around the foundation — at some distance from it, — and timber braces be placed between the wall of piles and the foundation. When the foundation can not be buttressed in front, the structure may be prevented from moving forward by rods which bear on the face of the wall and are connected with plates of iron or blocks of stone imbedded in the earth at a distance behind the wall (see § 551), or the thrust of the earth against the back of the wall may be decreased by supporting the earth immediately behind the foundation proper upon a grillage and platform resting on piles, or the same result may be attained by constructing relieving arches against the back of the Avail (see § 552).
384. CusHiNG's Pile Foundation. The desire to utilize the cheapness and efficiency of ordinary piles as a foundation for bridge piers and at the same time secure greater durability than is pos- sible with piles alone, led to the introduction of what is known as Cushing^s pile foundation, first used in 1868, at India Point, Rhode Island, It consists of square timber piles in intimate contact with each other, forming a solid mass of bearing timber. Surrounding the pile cluster is an envelope of cast or wrought iron, sunk in the mud or silt only enough to protect the piles, all voids between piles and cylinders being filled with hydraulic concrete.
Several such foundations have been used, and have proved satisfactory in every respect. The only objection that has ever been urged against them is that the piles may rot above the water line. If they do rot at all, it will be very slowly ; and time alone can tell whether this is an important objection.
In making a foundation according to the Gushing system, the piles may be driven first and the cylinder sunk over them, or the piles can be driven inside the cylinder after a few sections are in place. In the latter case, however, the cylinders may be sub- jected to undue strains and to subsequent damage from shock and.
256 PILE FOrNDATIONS. [CHAP. XI.
Tibration; and besides, the sawing off of the piles would be very difficult and inconvenient, and they would have to be left at irreg- ular heights and with battered tops. On the other hand, if the ■piles are driven first, there is danger of their spreading and there- \>y interfering with the sinking of the cylinder.
The special advantages of the Gushing piers are : (1) cheajjness, (2) ability to resist scour, (3) small contraction of the water way, and (4) rapidity of construction.
385. Example. The railroad bridge over the Tenas River, near Mobile, rests on Gushing piers. There are thirteen, one being a pivot pier. Each, excepting the pivot pier, is made of two cast- n-on cylinders, 6 feet in exterior diameter, located 16 feet between centers. The cylinders were cast in sections 10 feet long, of metal 1| inches thick, and united by interior flanges 2 inches thick and 3 inches wide. The sections are held together by 40 bolts, each 1^ inches in diameter. The lower section in each pier was pro- vided with a cutting-edge, and the top section was cast of a length Bufficient to bring the pier to its proper elevation.
The pivot pier is composed of one central cylinder 6 feet in diameter, and six cylinders 4 feet in diameter arranged hexagonally. The radius of the pivot circle, measuring from the centers of cylin- ders, is 12^ feet. Each cylinder is capped with a cast-iron plate 2i inches thick, secured to the cylinder with twenty 1-inch bolts.
The piles are sawed pine, not less than 10 inches square at the •small end. They were driven first, and the cylinder sunk over them. In each of the large cylinders, 12 piles, and in each of the smaller cylinders, 5 piles, were driven to a depth not less than 20 feet below the bed of the river. The piles had to be in almost per- fect contact for their whole length, which was secured by driving their points in contact as near as possible, and then pulling their tops together and holding them by 8 bolts 1|- inches in diameter. In this particular bridge the iron cylinders were sunk to a depth not less than 10 feet below the river bed ; but usually they are not sunk more than 3 to 7 feet. The piles were cut off at low water, the water pumped out of the cylinder, and the latter then filled to the top with concrete.
CHAPTER XII, FOUNDATIONS UNDER WATER.
386. The class of foundations to be discussed in this chapter could appropriately be called Foundations for Bridge Piers, since the latter are about the only ones that are laid under water. In this class of work the chief difficulty is in excluding the water prelim- inary to the preparation of the bed of the foundation and the con- struction of the artificial structure. This usually requires great resources and care on the part of the engineer. Sometimes the preservation of the foundation from the scouring action of the cur- rent is an important matter.
Preventing the undermining of the foundation is generally not a matter of much difficulty. In quiet water or in a sluggish stream but little protection is required ; in which case it is sufficient to de- posit a mass of loose stone^ or riprap, around the base of the pier. If there is danger of the riprap's being undermined, the layer must be extended farther from the base, or be made so thick that, if undermined, the stone Avill fall into the cavity and prevent further damage. A willow mattress sunk by placing stones npon it is an economical and efficient means of protecting a structure against scour. A pier may be protected also by inclosing it with a row of piles and depositing loose rock between the pier and the piles. In minor structures the foundation may be protected by driving sheet piles around it.
If a large quantity of stone be deposited around the base of the pier, the velocity of the current, and consequently its scouring action, will be increased. Such a deposit is also an obstruction to navigation, and therefore is seldom permitted. In many cases the only absolute security is in sinking the foundation below the scour- ing action of the water. The depth necessary to secure this adds to the difficulty of preparing the bed of the foundation.
387. The principal difficulty in laying a foundation under water consists in excluding the water. If necessary, masonry can be laid under water by divers ; but this is very expensive and is rarely re- sorted to.
257
358 FOUKDATIOIfS UNDER WATER. [CHAP. XII.
Tliere are five methods in use for laying foundations under water: (1) the method of excluding the water from the bed of the founda- tion by the use of a coffer-dam; (2) the method of founding the pier, without excluding the water, by means of a timber crib sur- mounted by a water-tight box in which the masonry is laid; (3) the method of sinking iron tubes or masonry wells to a solid substratum by excavating inside of them; (4) the method in which the water is excluded by the presence of atmospheric air; and (5) the method of freezing a wall of earth around the site, inside of which the excava- tion can be made and the masonry laid. These several methods will be discussed separately in the order named.
Art. 1. The Coffer-Dam Process.
388. A coffer-dam is an inclosure from which the water is pumped and in which the masonry is laid in the open air. This method con- sists in constructing a coffer-dam around the site of the proposed foundation, pumping out the water, preparing the bed of the foun- dation by driving piles or otherwise, and laying the masonry on the inside of the coffer-dam. After the masonry is above the water the coffer-dam can be removed.
389. Construction of the Dam.* The construction of coffer- dams varies greatly. In still, shallow water, a well-built bank of clay and gravel is sufficient. If there is a slow current, a wall of bags partly filled with clay and gravel does fairly well; a row of cement barrels filled with gravel and banked up on the outside has also been used. If the water is too deep for- any of the above methods, a single or double row of sheet piles may be driven and banked up on the outside with a deposit of impervious soil sufficient to prevent leaking. If there is much of a current, the puddle on the outside will be washed away; or, if the water is deep, a large quantity of material will be required to form the puddle-waH; and hence the preceding methods are of limited application.
390. The ordinary method of constructing a coffer-dam in deep water or in a strong current is shown in Fig. 60. The area to be inclosed is first surrounded by two rows of ordinary piles, m, m. On the outside of the main piles, a little below the top, are bolted two
* See also § 317, page 214.
AET. 1.]
THE COFFER-DAM PROCESS.
259
longitudinal pieces, w, w, called wales; and on the inside are fastened two similar pieces, g, g, which serve as guides for the sheet piles, s, s, ■while being driven. A rod, r, connects the top of the opposite main piles to prevent spreading when the puddle is put in. The timber, t, is put on primarily to carry the footway, /, and is some- times notched over, or otherwise fastened to, the pieces iv, lo to pre- vent the puddle space from spreading, h and b are braces extend- ing from one side of the coffer-dam to the other. These braces are put in position successively from the top as the water is pumped
Fig. 60.
out; and as the masonry is built up, they are removed and the sides of the dam braced by short struts resting against the pier.
The resistance to overturning is derived principally from the main piles, m, m. The distance apart and also the depth to which they should be driven depends upon the kind of bottom, the depth of water, and the danger from floating ice, logs, etc. Rules and formulas are here of but little use, judgment and experience being the only guides. The distance between the piles in a row is usually from 4 to 6 feet.
The dimensions of the sheet piles (§ 329) employed will depend upon the depth and the number of longitudinal waling pieces used. Two thicknesses of ordinary 2-incli plank are generally employed. Sometimes for the deeper dams, the sheet piles are timbers 10 or 12 inches square.
The thickness of the dam will depend upon (1) the width of gang- way required for the workmen and machinery, (2) the thickness re^
260 rOUXDATIOXS under water. [chap. XII.
quired to prevent ovc^rturning, and (3) tlie thickness of puddle necessary to prevent leakage througli the wall. The thickness of shallow dams will usually be determined by the first consideration ; but for deep dams the thickness Avill be governed by the second or third requirement. If thb braces, b, I, are omitted, as is sometimes done for greater convenience in working in the coffer-dam, then the main ^^iles, m, m, must be stronger and the dam wider in order to resist the lateral pressure of the water. A rule of thumb frequently used for this case is: "For depths of less than 10 feet make the width 10 feet, and for depths over 10 feet give an additional thick- ness of 1 foot for each additional 3 feet of wall." Trautwine's rule is to make the thickness of the puddle-wall three fourths of its height; but in no case is the wall to be less than 4 feet thick. If the coffer-dam is well braced across the inclosed area, the puddle- wall may vary from 3 feet for shallow depths to 10 feet for great depths; the former width has been successfully employed for depths of 18 to 20 feet, although it is considerably less than is customary.
The puddle-wall should be constructed of impervious soil, of which gravelly clay is best. It is a common idea that clay alone, or clay and fine sand, is best. With pure claj', if a thread of water ever so small finds a passage under or through the puddle, it will steadily wear a larger opening. On the other hand, with gravelly clay, if the water should wash out the clay or fine sand, the larger particles will fall into the space and intercept fii'st the coarser sand, and next the particles of loam which are drifting in the current of water; and thus the whole mass puddles itself better than the engineer could do it with his own hands. An embankment of gravel is com- paratively safe, and becomes tighter every day. While a clay em- bankment may be tighter at first than a gravelly one, it is always liable to breakage. Before putting in the puddling, all soft mud and loose soil should be removed from between the rows of sheet piles. The puddling should be deposited in layers, and compacted as much as is possible without causing the sheet piles to bulge so much as to open the joints.
391. Coffer-dams are sometimes constructed by building a strong crib, and sinking it. The crib may be composed either of uprights framed into caps and sills and covered on the outside with tongued and grooved planks, or of squared timbers laid one on top of the other, log-house fashion, and well calked. The outer uprights are
AET. 1.] THE COFFER-DAM PEOCESS. 'Z6\.
braced against the inside uprights and sills to prevent crushing inwards. This crib may be built on land, launched, towed to its final place, and sunk by piling stones on top or by throwing them into cells of the crib-work which are boarded up for that purpose. The bottom of the stream may be leveled off to receive the crib by dredging, or the dam may be made tight at the bottom by driving sheet piles around it. The crib must be securely bolted together (see § 381) vertically, or the buoyancy of the water will lift off the upper courses.
A movable coffer-dam is sometimes constructed in the same general way, except that it is made in halves to allow of removal from around the finished pier. The two halves are joined together by fitting timbers between the projecting courses of the crib, and then passing long bolts vertically through the several courses. Some of the compartments are made water-tight to facilitate the move- ment of the crib from place to place.*
Coffer-dams are also built by sinking an open crib, similar to the above, and then sheeting it on the outside by driving piles around it after it is sunk. For shallow depths, this method is very efficient.
392. Sometimes two coffer-dams are employed, one inside of the other, the outer one being used to keep out the water, and the inner one to keep the soft material from flowing into the excavation. The outer one may be constructed in any of the ways described above. The inner one is usually a frame- work sheeted with boards, or a crib of squared timbers built log-house fashion with tight joints. The inner crib is sunk (by weighting it with stone) as the excavation proceeds. The advantages of the use of the inner crib are (1) that the coffer-dam is smaller than if the saturated soil were allowed to take its natural slope from the inside of the dam to the bottom of the excavation ; (2) the space between the crib and the dam can be kept full of impervious material in case of any trouble with the out- side dam ; (3) the feet of the sheet piling are always covered, which lessens the danger of undermining or of an inflow of water and mud under the dam ; and (4) it also reduces to a minimum the material to be excavated.
393. Iron has been used in a few instances as a sheeting for cof- fer-dams. Plates are riveted together to form the walls, and stayed
* For an illustrated example, see Proc. Engineer's Club of Philadelphia, vol. iv. No. 4.
262 FOUNDATIONS UNDEK WATER, [CHAP. XII.
on the inside by horizontal rings made of angle iron. Wood is cheaper and more easily wrought, and therefore generally preferred.
394. Leakage. A serious objection to the use of coffer-dams is the difficulty of preventing leakage under the dam. One of the simplest devices to prevent this is to deposit a bank of gravel around the outside of the dam ; then if a vein of water escapes below the sheet piling, the weight of the gravel will crush down and fill the hole before it can enlarge itself enough to do serious damage. If the coffer-dam is made of crib-work, short sheet piles may be driven around the bottom of it ; or hay, willows, etc., may be laid around the bottom edge, upon which puddle and stones are deposited ; or a broad flap of tarpaulin may be nailed to the lower edge of the crib and spread out loosely on the bottom, upon which stones and puddle are placed. A tarpaulin is frequently used when the bottom is very irregular, — in which case it would cost too much to level off the site of the dam ; and it is particularly useful where the bottom is rocky and the sheet piles can not be driven.
When the bed of the river is rock, or rock covered with but a few feet of mud or loose soil, a coffer-dam only sufficiently tight to keep out the mud is constructed. The mud at the bottom of the inclosed area is then dredged out, and a bed of concrete deposited under the water (§ 154), Before the concrete has set, another coffer- dam is constructed, inside of the first one, the latter being made water- tight at the bottom by settling it into the concrete or by driving sheet piles into it. However, the better and moi-e usual method is to sink the masonry upon the bed of concrete by the method de- scribed in Art, 2 (pages 2G'J-7l).
It is nearly impossible to prevent considerable leakage, unless the bottom of the crib rests upon an impervious stratum or the sheet piles are driven into it. Water will find its way through nearly any depth or distance of gravelly or sandy bottom. Trying to [)ump a river dry through the sand at the bottom of a coffer-dam is expen- sive. However, the object is not to prevent all infiltration, but only to so reduce it that a moderate amount of bailing or pumping will keep the water oat of the way. Probably a coffer-dam was never built that did not require considerable pumping ; and not infre- quently the amount is very great, — so great, in fact, as to make it clear that some other method of constructing the foundation should have been chosen.
AET. 1.] THE COFFER-DAM PROCESS. 263
Seams of sand are very troublesome. Logs or stones under the edge of the dam are also a cause of considerable annoyance. It is sometimes best to dredge away the mud and loose soil from the site of the proposed coffer-dam ; but, when this is necessary, it is usu- ually better to construct the foundation without the use of a coffer- dam,— see Art. 3 of this chapter (page 266). Coffer-dams should be used only in very shallow water, or Avhen the bottom is clay or some material impervious to water.
395. Pumps. In constructing foundations, it is frequently neces- sary to do considerable bailing or pumping. The method to be em- ployed in any jDarticular case will vary greatly with the amount of water present, the depth of the excavation, the appliances at hand, etc. The pumps generally used for this kind of work are (1) the ordi- nary wooden hand-pump, (2) the steam siphon, (3) the pulsometer, and (4) the centrifugal pump. Rotary and direct-acting steam pumps are not suitable for use in foundation work, owing to the deleterious effect of sand, etc., in the water to be pumped.
1. Hand Poioer. When the lift is small, water can be bailed •out faster than it can be pumped by hand ; but the labor is propor- tionally more fatiguing. The ordinary hand foundation-pump con- sists of a straight tube at the bottom of which is fixed a common flap valve, and in which works a piston carrying another valve. The tube is either a square wooden box or a sheet-iron cylinder, — usually the latter, since it is lighter and more durable. The pump is oper- ated by applying the power directly to the upper end of the piston- rod, the pump being held n position by stays or ropes. There are more elaborate foundation-pumps on the market.
2. The steam siplion is the simplest of all pumps, since it has no movable parts whatever. It consists essentially of a discharge pipe — open at both ends — through the side of which enters a smaller pipe having its end bent up. The lower end of the discharge pipe dips into the water ; and the small pipe connects with a steam boiler. The steam, in rushing out of the small pipe, carries with it the air in the upper end of the discharge pipe, thus tending to form a vacuum in the lower end of that pipe ; the water then rises in the discharge pipe and is carried out with the steam. Although it is possible by the use of large quantities of steam to raise small quan- tities of water to a great height, the steam siphon is limited prac- tically to lifting water only a few feet. Its cheapness and simplicity
264 FOIJNDATIOXS UNDEK WATER. [CHAP. XII.
are recommendations in its favor, and its eflBciency is not much less than that of other forms of pumps. A common form of the steam siphon resembles, in external appearance, the Eads sand-pumjj represented in Fig. 66 (page 293).
3. The pulsometer is an improved form of the steam siphon. It may properly be called a steam pump which dispenses with all mov- able parts except the valves. The height to which it may lift water is practically unlimited.
4. The centrifugal ])umif' consists of a set of blades revolving in a short cylindrical case which connects at its center with a suction (or inlet) pipe, and at its circumference with a discharge pipe. The blades being made to revolve rapidly, the air in the case is carried outward by the centrifugal force, tending to produce a vacuum in the suction pipe ; the water then enters the case and is discharged likewise. The distance from the water to the pump is limited by the height to which the ordinary pressure of the air will raise the water ; f but the height to which a centrifugal pump can lift the water is limited only by the velocity of the outer ends of the revolv- ing blades. When a quick application with a discharge of large quantities of water is the most imjDortant consideration, the cen- trifugal pump is of great value. Since there are no valves in action while the pump is at work, the centrifugal pump will allow sand and large gravel — in fact almost anything that can enter between the arms — to pass. Pumps having a G-inch to 10-inch discharge pipe are the sizes most frequently used in foundation work.
396. Preparing the Foundation. After the water is pumped out, the bed of the foundation may be prepared to receive the masonry by any of the processes described in §§ 283-91, which see. Ordinarily the only preparation is to throw out, usually with hand shovels, the soft material. The masonry may be started directly upon the hard substratum, or upon a timber grillage i-esting on the soil (§§ 309-10) or on piles (§ 380).
397. Cost. It is universally admitted that estimates for the cost of foundations under water are very unreliable, and none are more so than those contemplating the use of a coffer-dam. The estimates of the most experienced engineers frequently differ greatly
* Frequently, but improperly, called a rotary pump.
t Some forms of centrifugal pumps must be immersed in the liquid to be raised.
ART. 1.] THE COFFER-DAil PROCESS. 265
from the actual cost. The difficulties of the case have already been discussed (§ 394).
For the cost of piles and driving, see §§ 346-54. The timber will cost, according to locality, anywhere from 815 to 825 per thousand feet, board measure. The cost of labor in placing the timber can not be given, since it varies greatly with the design, size, depth, etc. The iron in drift-bolts> screw-bolts, and spikes, is usually estimated at 3 1 to 5 cents per pound in place. Excavation in coffer-dams frequently costs as high as 81 to $1.50 per cubic yard, including the necessary pumping.
398. Example. The following example is interesting as show- ing the cost under the most favorable conditions. The data are for a railroad bridge across the Ohio River at Point Pleasant, W. Va.* There were three 250-foot spans, one 400-foot, and one 200-foot. There were two piers on land and four in the water ; and all ex- tended about 90 feet above low water. The shore piers were founded on piles — driven in the bottom of a pit — and a grillage, con- crete being rammed in around the timber. The foundations under water were laid by the use of a double coffer-dam '(§ 392). The water was 10 feet deep ; and the soil was 3 to 6 feet of sand and gravel resting on dry, compact clay. The foundations consisted of a layer of concrete 1 foot thick on the clay, and two courses of timbers. The quantities of materials in the six foundations, and the total cost, are as follows :
Pine timber in cribs inside of coffer-dams, and in foundations, 273,210 ft. B.M.
Oak timber in coffer dams, main and sheet piling 344,412 " "
Poplar timber in coffer-dams 3,597 " "
Round piles in foundation and coffer-dams 13,571 lin. ft.
Excavation in foundations 4,342 cu. yds.
Concrete " " 649 " "
Riprap 997 "
The total cost of foundations, including labor of all kinds, derricks, barges, engines, pumps, iron, tools, ropes, and everything necessary for the rapid com- pletion of the work, was f 64,652.62.
In the construction of the bridge over the Missouri River, near Plattsmouth, Neb., a concrete foundation 49 feet long, 21 feet wide, and 32 feet deep, laid on shore, the excavation being through clay, bowlders, shale, and soapstone, to bed-rock (32 feet below
* Engineering News, vol. xiii. p. 338.
266 FOUNDATIONS UNDER WATER. [CHAP. XII.
surface of the water), cost $39,607.2 3, or $42.81 per yard for the concrete laid.*
399. For the relative cost of foundations, see Art. G, page 309.
400. Conclusion. Uncertainty as to what trouble and expense a coffer-dam will develop usually causes engineers to choose some other method of laying the foundations for bridge piers. Coffer-dams are applicable in shallow depths only ; hence one objection to found- ing bridge piers by this process, particularly in rivers subject to scour or liable to ice gorges, is the danger of their being either un- dermined or pushed off the foundation. When founded in mud or sand, the first mode of failure is most to be feared. This danger is diminished by the use of piles or large quantities of riprap ; but such a foundation needs constant attention. When founded on rock, there is a possibility of the piers being pushed off the founda- tion ; for, since it is not probable that the coffer-dam can be pumped perfectly dry and the bottom cleaned before laying the masonry or depositing the concrete,' there is no certainty that there is good union between the base of the pier and the bed-rock.
Coffer-dams are frequently and advantageously employed in laying foundations in soft soils not under water, as described in §§ 316-21 (pages 214-15).
Art. 2. The Crib and Open-Caisson Process.
401. Definitions. Unfortunately there is an ambiguity in the use of the word caisson. Formerly it always meant a strong, water- tight box having vertical sides and a bottom of heavy timbers, in which the pier is built and which sinks, as the masonry is added, until its bottom rests upon the bed prepared for it. With the in- troduction of the compressed-air process, the term caisson was ap- plied to a strong, water-tight box — open at the bottom and closed at the top — upon Avhich the pier is built, and which sinks to the bottom as the masonry is added. At present, the word caisson gen- erally has the latter meaning. In the pneumatic process, a water- tight box— open at the top — is usually constructed on the roof of the working chamber ('^*' pneumatic chamber''), inside of which the masonry is built ; this box also is called a caisson. The caisson
* Exclusive of cost of building.s, tools, and engineering expenses. These items amounted to 6 per cent, of the total cost of the entire bridge.
ART. 2.] THE CRIB AND OPEN-CAISSOK PROCESS. 267
open at the bottom is sometimes called an inverted caisson, and the one open at the top an erect caisson. The latter when built over an inverted, or pneumatic, caisson, is sometimes called a coffer-dam. For greater clearness the term caisson will be used for the inverted, or pneumatic, caisson ; and the erect caisson, which is built over a pneumatic caisson, will be called a coffer-clam. A caisson employed in otlier than pneumatic work will be called an oi^en caisson.
402. Principle. This method of constructing the foundation consists in building the pier in the interior of an open caisson, which sinks as the masonry is added and finally rests upon the bed prepared for it. The masonry usually extends only a foot or two below extreme low Avater, the lower part of the structure being com- posed of timber crib-work, called simply a crih. The open caisson is built on the top of the crib, which is practically only a thick bottom for the box. The timber is employed because of the greater facil- ity with which it may be put into place, as will appear presently. Timber, when always wet, is as durable as masonry ; and ordinarily there is not much difference in cost between timb^- and stone.
If the soil at the bottom is soft and unreliable, or if there is danger of scour in case the crib Avere to rest directly upon the bot- tom, the bed is prepared by dredging away the mud (§ 407) to a sufficient depth or by driving piles which are afterwards sawed off (§ 3TS) to a horizontal plane.
403. Construction of the Caisson. The construction of the caisson differs materially with its depth. The simplest form is made by erecting studding by toe- nailing or tenoning them mto the top course of the crib and spiking planks on the outside. For a caisson 6 or 8 feet deep, Avhich is about as deep as it is wise to try with this simple construction, it is sufficient to use studding 6 inches wide, 3 inches thick, and 6 to 8 feet long, spaced 3 feet ajDart, mortised and tenoned into the deck course of the crib. The sides and floor (the upper course of the crib) should be thoroughly calked with oakum. The sides may be braced from the masonry as the sinking proceeds. When the crib is grounded and the masonry is above the water, the sides of the box or caisson are knocked off.
When the depth of water is more than 8 to 10 feet, the caisson is constructed somewhat after the general method shown in Fig. 61. The sides are formed of timbers framed together and a covering of thick planks on the outside. The joints are carefully calked to
268
FOUNDATIONS UNDER WATER.
[chap. XII.
make the caisson water-tight. In deep caissons, the sides can be built up as the masonry progresses, and thus not be in the way of the masons. The sides and bottom are held together only by the heavy vertical rods ; and after the caisson has come to a bearing upon the soil and after the masonry is above the water, the rods are detached and the sides removed, the bottom only remaining as a part of the permanent structure.
For an illustration of the form of caisson employed in sinking a foundation by the compressed-air process, see Plate I.
404. The caisson should be so contrived that it can be
Fig. 61.
grounded, and afterwards raised in case the bed is found not to be accurately leveled. To effect this, a small sliding gate is some- times placed in the side of the caisson for the purpose of filling it with water at pleasure. By means of this gate, the caisson can be filled and grounded; and by closing the gate and pumping out the water, it can be set afloat. The same result can be accomplished by putting on and taking off stone.
Since the caisson is a heavy, unwieldy mass, it is not possible to control the exact position in which it is sunk ; and hence it should be larger than the base of the proposed pier, to allow for a little ad- justment to bring the pier to the desired location. The margin to
4RT. 2.] THE CRIB AXD OPEN-CAISSON PROCESS. 269
be allowed will depend uiion the depth of water, size of caisson, facilities, etc. A foot all round is probably none too much under favorable conditions, and generally a greater margin should be allowed.
405. Construction of the Crib. The crib is a timber struct- ure below the caisson, which transmits the pressure to the bed of the foundation. A crib is essentially a grillage (see § 309 and § 380) which, instead of being built in place, is first constructed and then sunk to its final resting place in a single mass. A crib is usually thicker, /. e., deeper, than the grillage. If the pressure is great, the crib is built of successive courses of squared timbers in contact; but if the pressure is small, it is built more or less open. In either case, if the crib is to rest upon a soft bottom, a few of the lower ■courses are built open so that the higher portions of the bed may be squeezed into these cells, and thus allow the crib to come to an even bearing. If the crib is to rest upon an uneven rock bottom, the site is first leveled up by throwing in broken stone. If the bot- tom is rough or sloping, the lower courses of the crib are sometimes made to conform to the bottom as nearly as possible, as determined from soundings. This method requires care and judgment to pre- vent the crib from sliding off from the inclined bed, and should be used with great caution, if at all.
The crib is usually built afloat. Owing to the buoyancy of the water, about one third of a crib made wholly of timber would pro- ject above the water, and would require an inconveniently large weight to sink it ; therefore, it is best to incorporate considerable stone in the crib-work. If the crib is more or less open, this is done by putting a floor into some of the open spaces or pockets, which are then filled with stone. If the crib is to be solid, about every third timber is omitted and the space filled with broken stone.
The timbers of each course should be securely drift-bolted (§ 381) to those of the course below to prevent the buoyancy of the upper portion from pulling the crib a})art, and also to prevent any possi- bility of the upper part's sliding on the lower.
406. Timber in Foundations. The free use of timber in foundations is the chief difl'erence between American and European methods of founding masonry in deep water. The consideration that led to its introduction in foundations was its cheapness. Many of the more important bridges built some years ago rest upon crib-
270 FOUND ATIOKS UNDER WATER. [CHAP. XII.
work of round logs notched at tlieir intersection and secured hj drift-bolts. At present, cribs are always built of squared timber. As a rule, there is now but very little difference between the cost of timber and masonry in foundations. The principal advantage in the use of the timber in foundations under water is the facility with which it is put into position. Soft wood or timber which in the air has comparatively little durability, is equally as good for this purpose as the hard woods. It has been conclusively proved that any kind of timber will last practically forever, if completely immersed in water.
407. Excavating the Site. When a pier is to be founded in a sluggish stream, it is only necessary to excavate a hole m the bed of the stream, in which the crib (or the bottom of the caisson) may rest. The excavation is usually made with a dredge, any form of which can be employed. The -dipper dredge is the best, but the clam-shell or the endless chain and bucket dredge are sometimes used. If the bottom is sand, mud, or silt, the soil maybe removed (1) by pumping it with the water through an ordinary centrifugal pump (§ 395), — the suction hose of which is kept in contact with, or even a little below, the bottom, — or (2) by the Eads sand-pump (§ -±48). With either of these methods of excavating, a simple frame or light coflfer-dam may be sunk to keep part of the loose soil from running into the excavation.
408. If the stream is shallow, the current swift, and the bottom. soft, the site may be excavated or scoured out by the river itself. To make the current scour, construct two temporary wing-dams, which diverge up stream from the site of the proposed pier. The wings can be made by driving stout stakes or small piles into the bed of the stream, and placing solid panels — made by nailing ordi- nary boards to light uprights — against the piles with their lower edge on the bottom. The wings concentrate the current at the location of the pier, increase its velocity, and cause it to scour out the bed of the stream. This process requires a little time, usually one to three days, but the cost of construction and operation is comparatively slight.
When the water is too deep for the last method, it is sometimes possible to suspend the caisson a little above the bed of the stream, in which case the current will remove the sand and silt from under it. At the bridge over the Mississippi at Quincy, 111., a hole 10 feet
ART. 3.] DREDGING THROUGH WELLS. 271
deep was thus scoured out. If the water is already heavily charged with sedimeut. it may drop the sediment on striking the crib and thus fill up instead of scour out. Notwithstanding the hole is liable to be filled up by the gradual action of the current or by a sudden flood, before the crib has been placed in its final position, this method is frequently more expeditious and less expensive than using a coffer-dam.
409. If the crib should not rest squarely upon the bottom, it can sometimes be brought down with a water-jet (§ 34 ^^ in the hands of a diver. However, the engineer should not employ r. diver unless absolutely necessary, as it is very expensive.
410. If the soft soil extends to a considerable depth, or if the necessary spread of foundation can not be obtained without an un- desirable obstruction of the channel, or if the bottom is liable to scour, then piles may be driven, upon which the crib or caisson may finally rest. Before the introduction of the compressed-air process, this was a very common method of founding bridge piers in our western rivers ; and it is still frequently employed for small piers. The method of driving and sawing off the piles has already been described — see Chapter XI.
The mud over and around the heads of the piles may be sucked off with a pump, or it may be scoured out by the current (§ 408). The attempt is sometimes made to increase the bearing power of the foundation by filling in between the heads of the piles with broken stone or concrete ; but this is not good practice, as the stone does but little good, is difficult to place, and is liable to get on top of the piles and prevent the crib from coming to a proper bearing.
Art. 3. Dredging Through Wells.
411. A timber crib is frequently sunk by excavating the material through apartments left for that purpose, thus undermining the crib and causing it to sink. Hollow iron cylinders, or wells of masonry with a strong curb, or ring, of timber or iron beneath them, are sunk in the same way.
This method is applicable to foundations both on dry land and under water. It is also sometimes employed in sinking shafts in tunneling and mining.
412. Excavators. The soil is removed from under the crib
272 FOUNDATIOJS^S UNDER WATER. [CHAP. XII.
with a clam-shell dredge, or with an endless chain and bucket dredge, or with the Eads sand-pump, or, for small jobs, with the sand-pump employed in driving artesian wells.
The clam-shell dredge consists of the two halves of a hemi- spherical shell, Avhich rotate about a horizontal diameter ; the edges of the shell are forced into the soil by the weiglit of the machine itself, and the pull upon the chain to raise the excavator draws the two halves together, thus forming a hemispherical bucket which incloses the material to be excavated. The Morris and Cumming dredge consists of two quadrants of a short cylinder, hinged and operated similarly to the above. The orange-peel dredge (shown at A in Fig. 62, page 274) appears to have the jireference for this kind of work. It consists of a frame from which are suspended a num- ber of spherical triangular spades which are forced vertically into the ground by their own weight ; the pull upon the excavator to lift it out of the mud draws these triangles together and encloses the earth to be excavated. There are several forms of dredges similar to the above, but differing from them in details.
For a description of the Eads sand -pump, see § 448.
413. In one case in France, the soil was excavated by the aid of compressed air. An 8-inch iron tube rested on the bottom, with its top projecting horizontally above the water ; and compressed air was discharged through a small pipe into the lower end of the 8-inch tube. The weight of the air and water in the tube was less than an equal height of the water outside ; and hence the water in the tube was projected from the top, and carried with it a portion of the mud, sand, etc. Pebbles and stones of considerable size were thus thrown out. See § 447.
414. Noted Examples.— Poughkeepsie Bridge. The Pough- keepsie bridge, which crosses the Hudson at a point about 75 miles above New York City, is founded upon cribs, and is the boldest ex- ample of timber foundation on record. It is remarkable both for ihe size of the cribs and for the depth of the foundation.
There are four river piers. The crib for the largest is 100 feet long, 60 feet wide at the bottom and 40 feet at the top, and 104 ■feet high. It is divided, by one longitudinal and six transverse walls, into fourteen compartments through which the dredge worked. The side and division walls terminate at the bottom with a 12" X 12" oak stick, which served as a cutting edge. The exterior walls
ART. 3. J DREDGIXG THROUGH WELLS. ^1^
and the longitudinal division wall were built solid, of triangular cross section, for 20 feet above the cutting edge, and above that they were hollow. The gravel used to sink the crib was deposited in these hollow walls. The longitudinal walls were securely tied to each other by the end and cross division walls, and each course of timber was fastened to the one below by 450 1-inch drift-bolts 30 inches long. The timber was hemlock, 12 inches square. The fourteen compartments in which the clam-shell dredges worked were 10 X 13 feet in the clear. The cribs were kept level while sinking by excavating from first one and then the other of the com- partments. Gravel was added to the pockets as the crib sunk. \Yhe7i hard bottom was reached, the dredging pockets were filled with concrete deposited under water from boxes holding one cubic yard each and opened at the bottom by a latch and trip-line.
After the crib was in position, the masonry was started in a floating caisson which finally rested upon the top of the crib. Sinking the crib and caisson separately is a departure from the ordinary method. Instead of using a floating caisson, it is generally considered better to construct a coffer-dam on top of the crib, in .which to start the masonry. If the crib is sunk first, the stones which are thrown into the pockets to sink it are liable to be left projecting above the top of the crib and thus prevent the caisson from coming to a full and fair bearing.
The largest crib was sunk through about 53 feet of water, 20 feet of mud, 45 feet of clay and sand, and 17 feet of sand and gravel. It rests, at 134 feet below high water, upon a bed of gravel 16 feet thick overlying bed-rock. The timber work is 110 feet high, including the floor of the caisson, and extends to 14 feet below high water (T feet below low water), at which point the masonry com- mences and rises 39 feet. On top of the masonry a steel tower 100 feet high is erected. The masonry in plan is 25 X 87 feet, and has nearly vertical faces. The lower chord of the channel span is 130 feet and the rail is 212 feet above high water.
The other piers are nearly as large as the one here described. Tiie cribs each contain an average of 2,500,000 feet, board measure, of timber and 350 tons of wrought iron.
415. Atchafalaya Bridge. This bridge is over the Atchafalaya bayou or river, at Morgan City, La., about 80 miles west of New Orleans. " The soil is alluvial to an unknown depth, and is subject
274
FOUNDATIONS UNDER -WATER.
[chap. XII.
to rapid and extensive scour ; and no stone suitable for piers could be found within reasonable distance. Hence iron cylinders were idopted. They are foundation and pier combined. The cylinders were sunk 120 feet below high water— from 70 to 115 feet below the mud line— by dredging the material from the inside with-a Milroy excavator. Fig. 62 shows the excavator and the appliances for handling the cylinders.
Fig. 62.— Sinking Iron Pile by Dredging.
The cylinders are 8 feet in outside diameter. Below the level of the river bed, they are made of cast iron 1^ inches thick, in lengths of 10|- feet ; the sections were bolted together through in- side flanges with 1-inch bolts spaced 5 inches apart. Above the river bottom, the cylinders are made of wrought-iron plates | inches thick, riveted together to form short cylindrical sections with angle- iron flanges. The bolts and spacing to unite the sections are the same as in the cast-iron portions.
The cylinders were filled with concrete and capped with a heavy
AET. 3.] DREDGIXG THROUGH WELLS. 275
cast-irou plate. Two such cylinders, braced together, form the pier between two 250-feet spans of a railroad bridge.
The only objection to such piers relates to their stability. These have stood satisfactorily since 1SS3,
416. Hawkesbury Bridge. The bridge over the Hawkesbury Eiver in south-eastern Australia is remarkable for the depth of the foundation. It is founded upon elliptical iron caissons 48 X 20 feet at tlie cutting edge, which rest upon a bed of hard gravel 126 feet below the river bed, 185 feet below high water, and 227 feet below the track on the bridge. The soil penetrated was mud and sand. The caissons were sunk by dredging through three tubes, 8 feet in diameter, terminating in bell-mouthed extensions, which met the cutting edge. The spaces between the dredging tubes and the outer shell were filled with gravel as the sinking progressed. The caissons were filled to low water with concrete, and above, with cut- stone masonry.
417. Brick Cylinders. In Germany a brick cylinder was sunk 256 feet for a coal shaft. A cylinder 25|- feet in diameter was sunk 76 feet through sand and gravel, when the frictional resistance became so great that it could be sunk no further. An interior cylinder, 15 feet in diameter, was then started in the bottom of the larger one, and sunk 180 feet further through running quicksand. The soil was removed without exhausting the water.
A brick cylinder — outer diameter 46 feet, thickness of wall 3 feet — was sunk 40 feet in dry sand and gravel without any difiiculty. It was built 18 feet high (on a wooden curb 21 inches thick), and weighed 300 tons before the sinking was begun. The interior earth was excavated slowly, so that the sinking was about 1 foot per day, — the walls being built up as it sank.
In Europe and India masonry bridge piers are sometimes sunk by this process, a sufficient number of vertical openings being left through which the material is brought up. It is generally a tedious and slow operation. To lessen the friction a ring of masonry is some- times built inside of a thin iron shell. The last was the method em- ployed in putting down the foundations for the new Tay bridge.*
418. Frictional Resistance. The friction between cylinders and the soil depends upon the nature of the soil, the depth sunk, and the method used in sinking. If the cylinder is sunk by either
* For an illustrated account, see Engineering News, vol. xiv. pp. 66-68.
276
FOUNDATIONS UNDER WATEE.
[chap. XII.
of the pneumatic processes (§§ 425 and 426), the flow of the water or the air along the sides of the tube greatly diminishes the fric- tion. It is impossible to give any very definite data.
The following table* gives the values of the co-efficient of fric- tion f for materials and surfaces which occur in sinking foundations for bridge piers. Each result is the average of at least ten experi- ments. "All materials were rounded off at their face to sledge shape and drawn lengthwise and horizontally over the gravel or sand, the latter being leveled and bedded as solid as it is likely to be in its natural position. The riveted sheet iron contained twenty-five rivets on a surface of 2.53 X 1.67 = 4.22 square feet; the rivet-heads were half-round and |f inch in diameter." Notice that for dry materials and also for wet gravel and sand, the frictional resistance at starting is smaller than during motion, which is con- trary to the ordinary statement of the laws of friction.
TABLE 30. Co-efficient op Friction of Materials and Surfaces used in Foun- dations.
Kind op Materials.
Sheet iron witbout rivets on gravel and sand.
" " with " " " " " .
Cast iron (unplaned) on gravel and sand. . . . . Granite (rouglil}- worked) on gravel and sand
Pine (sawed) on gravel and sand
Sheet iron without rivets on sand
" " with " " "
Cast iron (unplaned) on sand
Granite (roughly worked) on sand
Pine (sawed) on sand
For Dry BIatkrials.
.3: !>t-5 ffi =S
0.40 0.40 0.37 0.43 0.41 0.54 0.73 O.oO 0.65 0.66
OS
0.46 0.49 0.47 0.54 0.51 0.63 0.84 0.61 0.70 0.73
For Wet Materials.
cS
0.33 0.47 0.36 0.41 0.41 0.37 0.52 0.47 0.47 0.58
e|
0.44 0.55 0.50 0.48 0.50 0.32 0.50 0.38 0.53 0.48
419. Values from Actual Practice. Cast Iron. During the construction of the bridge over the Seine at Orival, a cast-iron
* Bj' A. Schmoll in " Zeitschrift des Vereines Deutscher Ingenieure," as repub- lished in Selected Abstracts of Inst, of C. E., vol. lii. pp. 298-302.
t The co-efficient of friction is equal to the total friction divided by the total normal pressure; that is to say, it is the friction per unit of pressure perpendicular to the surfaces in contact.
AET. 3.] DEEDGIXG THROUGH WELLS. 27?
cylinder, standing in an extensive and rather uniform bed of gravel, and having ceased to move for thirty-two hours, gave a frictional re- sistance of nearly 200 lbs, per sq, ft. * At a bridge over the Danube near Stadlau, a cylinder sunk 18,75 feet into the soil (the lower 3,75 feet being "solid clay") gave a frictional resistance of 100 lbs. per sq. ft.* According to some European experiments, the friction of cast-iron cylinders in sand and river mud was from 400 to 600 lbs. per sq. ft. for small depths, and 800 to 1,000 for depths from 20 to 30 feet.f At the first Harlem River bridge, Xew York City, the frictional resistance of a cast-iron pile, while the soil around it was still loose, was 528 lbs. per. sq. ft. of surface ; and later 716 lbs. per sq. ft. did not move it. From these two experiments, McAlpine, the en- gmeer in charge, concluded that 'H.OOO lbs. per sq. ft. is a safe value for moderately fine material." X At the Omaha bridge, a cast-iron pile sunk 27 feet in sand, with 15 feet of sand on the inside, could not be withdrawn with a pressure equivalent to 25-4 lbs. per sq. ft. of surface in contact with the soil ; and after removal of the sand from the inside, it moved with 200 lbs. per sq. ft.§
Wrought Iron. A wrought-iron pile, penetrating 19 feet into coarse sand at the bottom of a river, gave 280 lbs. per sq. ft. : an- other, in gravel, gave 300 to 335 lbs. per sq. ft.||
Masonry. In the silt on the Clyde, the friction on brick and concrete cylinders was about 3^ tons per sq. ft.°[ The friction on the brick piers of the DufPerin (India) Bridge, through clay, was 900 lbs, per sq, ft.**
Fneumatic Caissons. For data on the frictional resistance of pneumatic caissons, see § 455.
Piles. For data on the frictional resistance of ordinary piles, see §§ 370-71.
420. Cost. It is difl&cult to obtain data under this head, since but comparatively few foundations have been put down by this process. Furthermore, since the cost varies so much with
* Van Nostrand's Engin'g Mag., voL xx. pp. 121-23. t Proc. Inst, of C. E., vol. 1. p. 131.
X McAlpine in Jour. Frank. Inst., vol. Iv. p. 105 ; also Proc. Inst, of C. E., vol xxvii. p. 286.
§ Vdn Nostrand's Engin'g Mag., vol. viii. p. 471. 1 Proc. Inst, of C. E., vol. xv. p. 290. H Ibid., vol. xxxiv. p. 35. ** JLngineerhiy Xews, vol. xix. p. 160.
278 FOUNDATIONS UNDEX WATER. [CHAP. XII.
the depth of water, strength of current, kind of bottom, danger of floods, requirements of navigation, etc., etc., no such data are valu- able unless accompanied by endless details.
Cribs. The materials in the cribs will cost, in place, about as follows : timber from $30 to $40 per thousand feet, boi^rd measure ; drift and screw bolts from 3|- to 5 ceyts per pound ; concrete from 'H to $6 per cubic yard. Under ordinarily favorable conditions, the sinking by dredging will cost about $1 per cubic yard.
Iron Tubes. Wrought-iron plate work will cost, exclusive of freight, from 3 to 4^ cents per pound ; cast-iron tubes, exclusive of freight, 1| to 2 cents per pound.
421. For the relative cost of different methods, see Art. 6 of this chapter.
422. Conclusion. A serious objection to this method of sink- ing foundations is the possibility oi meeting wrecks, logs, or other obstructions, in the underlying materials ; but unless the freezing process (see Art. 5 of this chapter) shall pi'ove all that is claimed for it, the method by dredging through tubes or wells is the only one that can be applied to depths which much exceed 100 feet — the limit of the pneumatic process.
Art. 4. Pneumatic Process.
424. The principle involved is the utilization of the difference between the pressure of the air inside and outside of an air-tight chamber. The air-tight chamber may be either an iron cylinder, which becomes at once foundation and pier, or a box — open below and a'r-tight elsewhere — upon the top of which the masonry pier rests. The former is called a pnetnnaficpilej the latter a jjneu- ■matic caisson. The pneumatic pile is seldom used now. There are two processes of utilizing this difference of pressure, — the vac2tum and the 2)Ie)mm.
425. Vacuum Process. The vacuum process consists in ex- hausting the air from a cylinder, and using the pressure of the at- mosphere upon the top of the cylinder to force it down. Exhausting the air allows the water to flow past the lower edge into the air- chamber, thus loosening the soil and causing the cjdinder to sink. By letting the air in, the water subsides, after which the exhaustion may be repeated and the pile sunk still farther. The vacuum
AKT. 4.] PXEUMATIC PROCESS. 279
should be obtained suddenly, so that the pressure of the atmosphere shall have the effect of a blow ; hence, the pile is connected by a large flexible tube with a large air-chamber — usually mounted upon a boat, — from which the air is exhausted. When communication is 0})ened between the pile and the receiver, the air rushes from the former into the latter to establish equilibrium, and the external pressure causes the pile to sink.
To increase the rapidity of sinking, the cylinders may be forced down by a lever or by an extra load applied for that purpose. In c;ise the resistance to sinking is very great, the material may be re- moved from the inside by a sand-pump (§ 448), or a Milroy or clam- shell dredge (§ 412) ; but ordinarily no earth is removed from the inside. Cylinders have been sunk by this method 5 or 6 feet by a single exhaustion, and 34 feet in 6 hours.
The vacuum process has been superseded by the plenum process.
426. Plenum, or Compressed-air, Process. The plenum, or compressed-air, process consists in pumping air into the air-chamber, so as to exclude the water, and forcing the pile or caisson down by a load placed upon it. An air-lock (§ 4.31) is so arranged that the workmen can pass into the caisson to remove the soil, logs, and bowlders, and to watch tlie j^rogress of the sinking, without re- leasing the pressure. The vacuum process is applicable only in mud or sand; but the compressed-air process can be applied in all kinds of soil.
427. History of Pneumatic Processes. It is said that Papin, the eminent physicist — born at Blois in 1647, — conceived the idea of employing a continued supply of compressed air to enable work- men to build under a large diving-bell. In 1779, Coulomb pre- sented to the Paris Academy of Science a paper detailing a plan for executing all sorts of operations under water by the use of com- pressed air. His proposed apparatus was somewhat like that now in general use.
In England in 1831, Earl Dundonald, then Lord Cochrane, took out a patent for a device for sinking tubular shafts through earth and water, by means of compressed air. His air-lock was much like modern ones, and was to be placed at the top of the main shaft. His invention was made with a view to its use in tunneling under the Thames, and in similar enterprises. In 1841, Bush also took out a patent in England for a plan of sinking foundations by the
280 FOUXDATIOXS UNDER WATER [CHAP. XII.
aid of compressed air. A German, by name G. Pfaun Muller, made a somewhat similar design for a bridge at Mayence, in 1850 ; but as his plan was not executed, it was, like the patents of Cochrane and Bush, little known till legal controversies in regard to patent-rights dragged them from obscurity.
428. The first practical application of the plenum process was made in France in 1841 by M. Triger. In order to reach a vein of coal on a sandy island in the Loire, opposite to Chalons, he sunk an iron tube about 40 inches in diameter, some 60 feet, by the blows of heavy weights. The fine sand was removed from the in- terior by means of a scoop bucket. On reaching a layer of coarse gravel, he could not force the tube through. He therefore capped his tube with an air-lock, and by compressed air forced out the water which had all the while filled the tube, and sent workmen to the bottom. The pressure he used was never greater than two at- mospheres. The water was discharged through a small tube, into which, several feet from the bottom, a jet of air was allowed to enter, thus diminishing the specific gravity of the column till it was rapidly blown out. In 1845, Triger read a paper on the sinking of a tube about 6 feet in diameter to a depth of 82 feet by the same method, and suggested the use of it for the construction of deep foundations for bridges.
Dr. Potts, of England, generally has the credit of inventing the vacuum process, for which he took out a patent in 1848. Many times in sinking foundations by the vacuum process, the com- pressed-air process was resorted to so that men could enter the pile to remove obstructions ; and finally the many advantages of the compressed-air process caused it to entirely supersede the vacuum process. At present the term " pneumatic process " is practically synonymous with compressed-air process.
429. The first foundations sunk entirely by the compressed-air process were the pneumatic piles for the bridge at Eochester, Eng- land, put down in 1851. The depth reached was 61 feet.
The first pneumatic caisson W' as employed at Kehl, on the east- ern border of France, for the foundations of a railroad bridge across the Rhine.
430. The first three pneumatic pile foundations in America were constructed in South Carolina between 1856 and 1860. Im- mediately after the civil war, a number of pneumatic piles were
ART. 4.] PNEUMATIC PROCESS. 281
sunk in western rivers for bridge piers. The first pneumatic cais- sons in America were those for the St. Louis bridge (§ 457), put down in 1870. At that time these were the largest caissons ever constructed, and the depth reached — 109 feet 8^ inches — has not yet been exceeded.
Of late years, the pneumatic caisson has almost entirely super- seded the pneumatic pile ; in fact the plenum-pneumatic caisson has almost entirely superseded, except in very shallow water or in water over about 80 or 100 ft. deep, all other methods of founding bridge piers.
431. Pneumatic Piles. Although pneumatic cylinders are now rarely employed, they will be briefly described because of their historic interest.
The cylinders are made of either wrought or cast iron. The wrought-iron cylinders are composed of plates, about half an inch thick, riveted together and strengthened by angle iroos on the m- side, and re-inforced at the cuttting edge by j)lates on the outsida both to increase the stiffness and to make the hole a little larger so as to diminish friction. The cast-iron cylinders are composed of sections, from 6 to 10 feet long and 3 to 8 feet in diameter, bolted together by inside flanges, the lower section being cast with a sharp edge to facilitate penetration. Two of these tubes, braced together, are employed for ordinary bridge piers ; and six small ones around a large one for a pivot pier. They are filled with concrete, with a few courses of masonry or a heavy iron cap at the toja.
Fig. 63 shows the arrangement of the essential parts of a pneu- matic pile. The apparatus as shown is arranged for sinking by the plenum process ; for the vacuum process the arrangement differs only in a few obvious particulars. The upper section constitutes the air-lock. The doors a and h both open downwards. To enter the cylinder, the workmen pass into the air-lock, and close the door a. Opening the cock d allows the comjiressed air to enter the lock ; and when the pressure is equal on both sides, the door h is opened and the workmen pass down the cylinder by means of a ladder. To save loss of air, the air-lock should be opened very seldom, or made very small if required to be opened often.
The air-supply pipe connects with a reservoir of compressed air on a barge. If the air were pumped directly into the pile without, the intervention of a storage reservoir, as was done in the early ap-
382
FOUNDATION'S UNDER WATEE.
[chap. XII.
plications of the plenum process, even a momentary stoppage of the <!ngine would endanger the lives of the workmen.
432. The soil may be excavated by ordinary hand tools, elevated to the air-lock by a windlass and bucket, and passed out through the main air-lock. Sometimes a double air-lock with one large and one small compartment is used, the former being opened only to let gangs of workmen pass and the latter to allow the passage of the
Fig. 63.— Pneumatic Pile.
skip, or bucket, containing the excavated material. Sometimes an auxiliary lock, g f, is employed. The doors / and g are so con- nected by parallel bars (not shown) that only one can be. opened at a time. The excavated material is thrown into the chute, the door/ is closed, which opens g, and the material discharges itself on the outside.
Mud and sand are blown out with the sand-lift (§ 447) or sand- pump (§ 448) without the use of any air-lock.
433. The cylinders are guided in their descent by a frame-work resting upon piles or upon two barges. One of the chief difficulties in
ART. 4.] PXEUMATIC PKOCESS. 2SS
sinking pneumatic piles is to keep them vei^ical. If the cylinder becomes inclined, it can generalh^ be righted ( L) by placing wooden wedges under the lower side of the cutting edge, or (2) by excavat- ing under the upper side so that the air may escape and loosen the material on that side, or (3) by drilling holes through the upper- most side of the cylinder through which air may escape and loosen the soil, or (4) by straining the top over with props or tackle. If several pneumatic piles are to form a pier, they should bo sunk one at a time, for when sunk at the same time they are liable to run together.
434. Bearing Power. The frictional resistance of iron cylinders has been discussed in §§ 418-19, page 275-77, which see.
Mc Alpine, in sinking the piers of the Harlem bridge, New York City, devised a very valuable but simple p— -
and cheap method of increasing the bear- ing power of a pneumatic cylinder (see Fig. 64). He attached to the lower end of the cylindrical column a hollow conical iron section, the large end of which is much larger than the main cylinder. The base of the pier was still further in- V:--':'[':::^'^^:^y / '•'^■••^:. creased by driving short sheet piles ■A'---'-:-.; ' ""' .■.■•'■
obliquely under the lower edge of the •.•••••••■••.•■ v ••.... •
conical base and removing the soil from Fm. 64.
under them, after which the whole was filled in with concrete.*
In cold climates the contraction of the iron cylinder upon the masonry filling might rupture the former; hence, it is sometimes recommended to fill the pile below the frost line with asphaltic con- crete. It has also been proposed to line the cylinders with thick, soft wood staves, which will compress under the contraction of the iron cylinder. However, the danger from this cause is not very serious; for, after the concrete has set, it is strong enough to support the load if the iron case were removed.
435. After the cylinder has reached the required depth, concrete enough to seal it is laid in compressed air; and when this has set, the remainder can be laid in the open air. A short distance at the top is usually filled with good masonry, and a heavy iron cap put over all.
* Jour. Frank. Inst., vol. Iv. pp. 98 and 177.
284 FOUXDATIOXS UXDER WATEK. [CHAP. XII.
436. Pneumatic Caissons. A imcumatic caisson is an immense box — open below, bnt air-tight and water-tight elsewhere, — upon the top of wliich the masonry pier is built. The essential difference between the pneumatic pile and the pneumatic caisson is one of de- gree rather than one of quality. Sometimes the caisson envelops the entire masonry of the pier ; but in the usual form the masonry envelo^DS the iron cj'linder and rests upon an enlargement of the lower end of it. The pneumatic pile is sunk to the final depth be- fore being filled with concrete or masonry; but with the caisson the masonry is built upward while the whole pier is being sunk downward, the masonry thus forming the load which forces the caisson into the soil. A pneumatic caisson is, practically, a gigantic diving bell upon the top of which the masonry of the pier rests.
Fig. 65 is a section of a pier of the bridge across the Missouri Kiver near Blair, Neb.,* and shows the general arrangement of the pier and pneumatic caisson. The tube extending through the mid- dle of the caisson and pier, known as the air-shaft, is for the ascent and descent of the men. The air-lock — situated at the Junction of the two cylinders which form the air-shaft — consists of a short sec- tion of a large cylinder which enveloi^s the ends of the two sections. of the air-shaft, both of wliich communicate with the air-lock by doors as shown in Fig. 65. The apartment in which the men are at work is known as the working diamhcr or air-cliamher. The small cylinders shown on each side of the air-shaft are employed in supplying concrete for filling the working chamber when the sinking is completed. The pipes seen in the air-chamber and projecting above the masonry are employed in discharging the mud and sand, as will be described presently. The timbers which appear in the lower central portion of the working chamber are parts of the trusses which support the central portions of the roof of the caisson.
The masonry is usually begun about 2 feet below low water, the space intermediate between the masonry and the roof of the working chamber being occupied by timber crib-work, either built solid or filled with concrete. In Fig. 65 the masonry rests directly upon the roof of the air-chamber, which construction was adopted for the channel piers of this bridge to reduce to a minimum the obstruction to the flow of the water.
Frequently a coffer-dam is built upon the top of the crib (see
* From the report of Geo. S. Morison, chief engineer of the bridge.
AKT. 4. J
PXEUMATIC PROCESS.
•ZSo
Plate I); but in this particular case the masonry was kept above the surface of the water, hence no coffer-dam was employed. When
Fia. 65.— Pneumatic Caisson.— Blair Bridge.
the coffer-dam is not used, it Is necessary to regulate the rate of sinking by the speed with whic'.: the masonry can be built, which is liable to cause inconvenience and delay. When the coffer-dam is
'^86 FOUNDATIONS UNDER WATER. [CHAP. XII.
dispensed witli, it is necessary to go on with the constrnctiou of the masonry whether or not the additional weight is needed in sinking tne caisson.
437. The details of the construction of pneumatic caissons can be explained best by the description of a particular case.
438. Foundation of the Havre de Grace Bridge. Foldin£ Plate I * shows the details of the construction of the caisson, crib, and cofier-dam employed in 1884 in sinking pier Xo. 8 of the Baltimore and Ohio R. R. bridge across the Susquehanna River at Havre de Grace, Md. The timber work of Fig. 06 (page 293) also shows some of the details of the construction of the walls of the working chamber.
439. The Caisson. The details of the construction of the caisson areas follows: Six courses of timber, 12 X 12 inch, one lying on top of the other, formed the skeleton of the walls of the working cham- ber. These timbers were first put up with a batter of f of an inch horizontal to 1 foot vertical; they were not halved at the corners, but every alternate piece was carried through with a full section, '' log-house" fashion. These timbers were fastened at the corners, intersections, and several intermediate points, with drift-bolts (§ 381) 1 inch square and 22 inches long. Inside of this timber shell, threa courses of 3-inch plank, placed diagonally, were spiked to the hori- zontal timbers and to each other by G-inch and 7-inch boat-spikes. Inside of the diagonal planking was another course of 3-inch plank placed vertically and Avell spiked, the head of each spike being wrapped with oakum to prevent leakage. The vertical seams were thoroughly calked.
A strong and thoroughly braced truss (see also Fig. 66, page 293) was nest erected longitudinally through the center of the working chamber. The first course in the deck of the working chamber was then placed in position on the central truss and side walls. The work- ing chamber was 9 feet 3 inches high from bottom of shoe to the underside of deck, which was higher than required for working, but was adopted so as to permit greater depth of the central truss. Out- side of the horizontal timbers, after they had been adzed to a true surface, were then placed the 12- by 14-inch sticks (shown at the ex-
* Compiled from the original working drawings. The accompanying description is from personal inspection aided by an article in Engineering JVews by Col. Wm. M Patton, engineer in charge.
AKT. -i.] PNEUMATIC PKOCESS. 28^
treme left of Fig. 66) 15 feet long, extending 2 feet below the bottom horizontal timber and having their lower ends beveled as shown. These timbers extended 6 feet above the horizontal members, and were shouldered at the upper end so that three of the deck courses rested upon them. "Four screw-bolts were passed through each outside post and through the entire wall; and, in addition tc these, two drift-bolts, 1 inch square and 30 inches long, in each ver- tical served to more thoroughly bind the wall together. This com- pound of timber and planking formed the walls of the working chamber. After the first deck course was in place, a few jiieces of the second course were laid diagonally to give it stiffness; the under- side of this deck or roof was then lined with planks and thoroughly calked, and a false bottom put into the w^orking chamber prepara- tory to launching it.
After the caisson was launched the deck courses, eight in all, were put on. The first course was made of single-length timbers, reaching from inside to inside of the vertical wall posts, and resting on top of the horizontal timbers and inside planking and also on the top chord of the central truss, and being fastened to these members by 22-inch drift-bolts. The second course was laid diagonally and was made of varying lengths of timbers. The third course was laid from side to side across the caisson, and the fourth course longi- tudinally and resting on the shoulders of the 12 X 14 inch verticals. The fifth course was laid across, the sixth diagonally — crossing the second course, — and the seventh and eighth courses extended to the extreme ovitside limits of the caisson and rested on the heads of the vertical posts. This general arrangement of the top courses, resting as they did on the heads and shoulders of the outside verticals, gave a direct bearing on the posts and relieved the wall bolts of the great shearing strain to which they would otherwise have been subjected.
The outside posts were bolted to the deck courses by one 3-foot screw-bolt and two 30-inch drift-bolts, fastening them to the longi- tudinal and diagonal courses respectively. The several deck courses were bolted to each other by 22-inch drift-bolts (not shown in the illustrations), spaced 5 feet apart along each stick. All the timbers in the deck were bedded in cement mortar and the vertical Joints were grouted, so as to give a full and uniform bearing for each stick and also decrease the leakage and danger from fire.
The center truss (see also Fig. 66) was constructed to bear a uni-
§88 FOUNDATIONS UNDER -WATER. [CHAP. XII.
formly distributed load, or to act as a cantilever. It was composed of a top and bottom chord, each made of two 12 X 12 inch sticks, with posts and diagonals of wood, and vertical and diagonal tie-rods 1.J inch m diameter; the iron vertical rods extended through the first deck courses, and the top chord was also bolted to the deck with drift-bolts. The object of this was to enable the truss to act as a stiffening rib to the deck, independently of its action as a girder. The bottom chord was also extended to the ends, and by means of straps and bolts acted both as a strut and tie-brace for the ends of the caisson, and constituted the only end bracing.
The sides of the caissons were braced against outside pressures by IG X 10 inch timbers abutting against the walls and bottom chord of the center truss, and against pressure from the inside by 2-inch iron tie-rods extending from out to out of the caisson, none of which are shown. All the timber used, except the planking and outside posts and the bracing in the working chamber, was 12 X 12 inch. Iron straps, extending 6 feet on the sides and ends, were placed at the corners and bolted to the caisson timbers. These straps were made of bar-iron 3x1 inch and prevented spreading of the walls of the caisson under excessive pressure within. Planks were spiked to the lower part of the posts ; and also a narrow plank, called a shoe, was spiked under the bottom of the posts (see Fig. 66).
440. "The construction was simple and strong ; in no case was there any bending or springing of the w^alls. The arrangement of the cutting edge with square shoulders was a departure from the ordinary V-shape (compare Figs. 65 and 66, pages 285 and 293), and was found to possess many advantages. It enabled the men to better regulate the sinking of the caisson by giving an increased bear- ing surface. With this support, the material could be cleaned out from under one side or end ; the caisson could be leveled ; and, if the material was softer in one spot than another, the caisson could be prevented from tipping. It further afforded a good surface for blocking up when it was found desirable to support the caisson during the removal of the material ; and it gave also greater security in case of a ' blow-out ' or the failure of air-pressure. " *
When it is anticipated that gravel or bowlders will be met with in sinking, the cutting edge is usually shod with iron. The iron cutting edge was omitted in all the caissons for this bridge, and it is * Col. Wm. M. Patton, engineer in charge for the railroad company.
ART. -i.] PNEUMATIC PROCESS. 289
claimed that the experience here shows that ''in no case is an iron shoe either advantageous or necessary."
441. The Crib. The construction of the crib is shown very fully in Plate I. The timbers were all 12 X 12 inches square, bolted to each other by 22-inch drift-bolts — spaced 5 or 6 feet apart, — and were dovetailed at the corners aud connections. The parts of all the walls of the crib were firmly bolted to the deck of the caisson.
Ordinarily the division walls of the crib are built vertically from top to bottom ; but in this case, they were off-set, as shown, to secure a better bond in the mass of concrete. If the walls are built solid from top to bottom, the concrete filling is thereby divided into a number of separate monolithic columns ; but in the construction as above, the concrete forms practically a single solid mass. The walls are built solid, owing to the difficulty of getting the concrete thoroughly packed in around so many timbers. Large stones, such as could be handled by one man, were bedded in mortar as the suc- cessive layers of concrete were formed, and over and around these another layer of concrete was rammed. In most localities there is but little difference in cost between a solid timber crib and one with timber pockets filled with concrete.
442. The Coffer-dam. Uprights were first placed at intervals of about D^ feet, and connected by mortise and tenon to caps and sills. This frame-work was held down to the crib by rods 2 inches in diameter, having hooks at the lower end which passed into eye- bolts in the sides of the crib. On the sides of the dam, the upper end of these rods passed through 12 X 12 inch timbers resting on the sides of the dam and projecting about 2 feet outside ; and at the ends of the dam, they passed through short pieces bolted to one of the cross timbers and projecting beyond the end of the dam.
Owing to the great depth required, the coffer-dam was built in sections, the connecting rods being made in sections with swivel connections. The second section was not added until the depth sunk required it. When the top section of the dam was put on, the projecting ends of the timbers through which the connecting rods passed were sawed off. The bottom section was sheeted with three courses of 3-inch plank, and the top section with two thick- nesses. The joint between the coffer-dam and the crib, and also 'he sheeting, were well calked.
The sides of the coffer-dam were braced against the pressure of
290
FOUNDATIONS UNDER WATER.
[chap. XII.
the water, by 13 X 12 inch timbers resting on the top of each sec- tion, and by a system of bracing in the middle of each section. "When the masonry was completed, the coffer-dam was removed by disconnecting the vertical rods.
443. Machinery Barge. The machinery barge was an ordinary flat-boat fitted up for the purpose. At one end of the barge there were three boilers each of fifty horse-power. In the middle were two large air-compressors, designed by the contracting engineer. Gen. Wm. Sooy Smith. One furnished all the compressed air re- quired, the other being ready for use in case of any accident or break-down. At the other end of the boat were two Worth iugton steam pumps to furnish water for the excavating plant used in the caisson. There were also a small engine and a dynamo which fur- nished the current for the electric lamps used in the caisson and, at night, on the outside.
444. Material Required. Table 31 gives the dimensions and quantities of materials in the pneumatic foundations of this bridge, and Table 32 (page 302) gives the cost.
TABLE 31.
Dimensions and Quantities of Materials in Foundations of
Havre de Grace Bridge.*
|
Number of the Pier. |
|||||
|
Description. |
n. |
m. |
IV. |
vm. |
IX. |
|
Dimensions: Caissons:— length at bottom, in feet widtii " " " " height from cutting edge, in feet. . height of working chamber, in feet Crib: — length, in feet |
63.3 25.9 17.2 9.2 61.5 24.2 40.0 203.473 179,939 2,068 330 1,649 000 11,313 34,181 4,638 2,472 |
67.3 25.9 17.2 9.2 61.5 24.2 42.0 215,565 197.910 31,517 401 1,893 623 15,651 36,832 700 2,572 |
79.4 32.8 17.2 9.2 77.3 31.1 22.2 316,689 143.993 108,518 631 1,635 126 32,881 40.909 11.730 3,392 |
70.9 32.6 17.2 9.2 69.1 30.8 41.0 281,540 219,680 85,759 559 2,581 526 31.026 44,861 10.0:M 3,235 |
78.2 42.3 19.3 9.2 76.4 40.5 |
|
32.8 |
|||||
|
Quantities- Timber in the caisson, feet, board measure. " " " crib, " " " coffer-dam." " Concrete in working chamber, cubic yards. . . " " crib, shafts, etc., " '" ... " below cutting edge, " " ... |
465.125 203,824 126,532 839 3,172 624 33,435 |
||||
|
59,245 |
|||||
|
11,237 |
|||||
|
3,535 |
|||||
• The data by courtesy of Sooysmith & Co., contractors for the pneumatic foundations.
445. Position of the Air-lock. Before the construction of the St. Louis bridge, the air-lock had always been placed at the top
ART. 4.] PNEUMATIC PROCESS. 291
of the air-shaft, and was of such construction that to lengthen the shaft, as the caisson sunk, it was necessary to detacli the lock, add a section to the shaft, and then replace the lock on top. This was not only inconvenient and an interruption to the other work, but required the men to climb the entire distance under compressed air, which is exceedingly fatiguing (see § 460). To overcome these objections, Eads placed the air-lock at the bottom of the shaft. This position is objectionable, since in case of a " blow-out," i. e., a rapid leakage of air, — not an unfrequent occurrence, — the men may not be able to get into the lock in time to escape drowning. If the lock is at the top, they can get out of the way of the water by climbing up in the shaft.
At the Havre de Grace bridge, the air-shaft was constructed of wrought iron, in sections 15 feet long. The air-lock was made by placing diaphragms on the inside flanges of the opposite ends of the top section. A new section and a third diaphragm could be added without disturbing the air-lock ; and when the third diajihragm was in place, the lower one was removed preparatory to using it again. Some engineers compromise between these two positions, and leave the air-lock permanently at some intermediate point in the pier (see Fig. 65, page 285).
446. Excavators. In the early application of the pneumatic method, the material was excavated with shovel and pick, elevated in buckets or bags by a windlass, and stored in the air-lock. When the air-lock was full, the lower door was closed, and the air in the lock was allowed to escape until the upper door could be opened, and then the material was thrown out. This method was expensive and slow.
In the first application of the pneumatic process in America (§ 430), Gen. Wm. Sooy Smith invented the auxiliar}' air-lock, ^ /, Fig. 63 (page 282), through which to let out the excavated mate- rial. The doors, /' and g, are so connected together that only one of them can be opened at a time. The excavated material being thrown into the chute, the closing of the door / opens g, and the material slides out. This simple device is said to have increased threefold the amount of work that could be done.
447. Sand-lift. This is a device, first used by Gen. Wm. Sooy Smith, for forcing the sand and mud out of the caisson by means of the pressure in the working chamber. It consists of a pipe.
292 FOUNDATIONS UNDER WATER. [CHAP. XII.
reaching from the working chamber to the surface (see Fig. 63 and Plate I), controlled by a valve in the working chamber. The sand is heaped up around the lower end of the pipe, the valve opened, and the pressure forces a continuous stream of air, sand, and water up and out. For another application of this principle, see § 413.
In sand, this method of excavating is very efficient, being eight to ten times as expeditious as the auxiliary air-lock. Of course, the efficiency varies with the depth, i. e., with the pressure. When the soil is so impervious that the water in the working chamber can not be forced out under the edge of the caisson, it is made to pass through the sand-lift pipe.
The "goose-neck,^' or elbow at the top of the discharge pipe, is worn away very rapidly by the impact of the ascending sand and pebbles. At the Havre de Grace bridge, it was of chilled iron 4 inches thick on the convex side of the curve, and even then lasted only two days. At the Brooklyn bridge, the discharge pipe ter- minated with a straight top, and the sand was discharged against a block of granite placed in an inclined position over the upper end.
Although the sand-lift is efficient, there are some objections to it : (1) forcing the sand out by the pressure in the cylinder de- creases the pressure, which causes, particularly in pneumatic piles or small caissons, the formation of vapors so thick as to prevent the workmen from seeing ; (2) the diminished pressure allows the water to flow in under the cutting edge ; and (3) if there is much leakage, the air-compressors are unable to supply the air fast enough.
448. Mud-pump. During the construction of the St. Louis bridge, Capt. Eads invented a mud-pump, which is free from the above objections to the sand-lift, and which in mud or silt is more efficient than it. This device is generally called a sand-pump, but is more jiroperly a mud-pump.
The principle involved in the Eads pump is the same as that employed in the atomizer, the inspirator, and the injector; viz., the principle of the induced current. This principle is utilized by dis- charging a stream of water with a high velocity on the outside of a small pipe, which produces a partial vacuum in the latter ; when the pressure of the air on the outside forces the mud through the small pipe and into the current of water by which the mud is carried away. The current of water is the motive power.
ART. 4.]
PNEUMATIC PROCESS.
293
Fig. 6G is an interior view of the caisson of the Baltimore and Ohio R. E. bridge at Havre de Grace, Md., and shows the general aoTangement of the pipes and mud-pump. The pump itself is a
294 FOUNDATIONS UXDER WATER. [CHAP. XII.
hollow pear-shaped casting, about 15 inches in diameter and 15 inches long, a section of which is shown in the corner of Fig. 66. The water is forced into the pump at a, impinges against the coni- cal casing, d, flows around this lining and escapes upwards through a narrow annular space, /. The interior casing gives the water an even distribution around the end of the suction pipe. The flow of the water through the pump can be regulated by screwing the suc- tion pipe in or out, thus closing or opening the annular space, /. To prevent the too rapid feeding or the entrance of lumps, which might choke the pipe, a strainer — simply a short piece of pipe, plugged at the end, having a series of ^-inch to |-inch holes bored in it — was put on the bottom of the suction pipe. The discharge pipe of the mud-pump terminates in a " goose-neck ^' through which the material is discharged horizontally.
The darkly shaded portions of the section of the pump wear away rapidly ; and hence they are made of the hardest steel and conscructed so as to be readily removed. Difllerent engineers have different methods of providing for the renewal of these parts, the outline form of the pump varying with the method employed. The pump used at the St. Louis bridge was cylindrical in outline, but otherwise essentially the same as the above.
449. In order to use the mud-pump, the material to be exca- vated is first mixed into a thin paste by playing upon it with a jet of water. This pump is used only for removing mud, silt, and soil containing small quantities of sand ; pure sand or soil containing large quantities of sand is " blown out •" with the sand-lift.
The water is delivered to the mud-pump under a pressure, ordi- narily, of 80 or 90 pounds to the square inch. At the St. Louis bridge, it was found that a mud-pump of 3^-incli bore was capable of raising 20 cubic yards of material 120 feet per hour, the water pressure being 150 pounds per square inch.*
450. Water-column. A combination of the pneumatic process and that of dredging in the open air through tubes has been em- ployed extensively in Europe. It seems to have been used first at the bridge across the Ehine at Kehl. The same method was used at the Brooklyn bridge. The principle is rudely illustrated in
* History of the St. Louis Bridge, p. 213.
ART. 4.]
PNEUMATIC PROCESS.
295
|
J^tr |
Jiir |
|||||
|
Loci |
Lock |
|||||
|
k |
||||||
|
^ |
k -^ |
|||||
|
/ tTor^in^ |
|
Cfiamher \ |
||||
|
r- |
Fig. 67.
Pig. 67. The central shaft, which is open top and bottom, projects a little below the cutting edge, and is kept full of water, the greater height of water in the column balancing the pressure of the air in the chamber. The workmen simply push the mate- rial under the edge of a water- shaft, from whence it is exca- vated by a dredge (§ 412).
451. Blasting. Bowlders or points of rock may be blasted in compressed air without any ap- preciable danger of a "blow- out " or of injuring the ear- drums of the workmen. This point was settled in sinking the foundations of the Brooklyn bridge ; and since then blasting has been resorted to in many cases. Bowl- ders are sometimes "carried down," i. e., allowed to remain on the surface of the soil in the working chamber as the excavation pro- ceeds, and subsequently imbedded in the concrete with which the air-chamber is filled.
452. Rate of Sinking. The work in the caisson usually con- tinues day and night, winter and summer. The rate of progress varies, of course, with the kind of soil, and particularly with the number of bowlders encountered. At the Havre de Grace bridge, the average rate of progress was 1.37 ft. per day; at Plattsmouth, 2.22 ft. ; and at Blair, 1.75 ft. per day.
453. Guiding the Caisson. Formerly it was the custom to control the descent of the caisson by suspension screws connected with a frame-work resting upon piles or pontoons. In a strong current or in deep water, it may be necessary to support the caisson partially in order to govern its descent ; but ordinarily the suspension is needed only until the caisson is well imbedded in the soil. The caisson may be protected from the current by constructing a break- water above and producing dead water at the pier site.
After the soil has been reached, the caisson can be kept in its course by removing the soil from the cutting edge on one side or the other of the caisson. In case the caisson does not settle down
296 FOUNDATIONS UNDER WATER. [CHAP. XII.
after the soil has been removed from under the cutting edge, a re- duction of a few pounds in the air pressure in the working chamber is usually sufficient to produce the desired result. At the Havre de Grace bridge, it was found that by allowing the discharged mate- rial to pile up against the outside of the caisson, the latter could bemoved laterally almost at will. The top of the caisson was made 3 feet larger, all round, than the lower course of masonry, to allow for deviation in sinking. The deviation of the caisson, which was founded 90 feet below the water, was less than 18 inches, even thougli neither suspension screws nor guide piles were employed.
In sinking the foundations for the bridge over the Missouri Kiver near Sibley, Mo., it was necessary to move the caisson con- siderably horizontally without sinking it much farther. This was accomplished by placing a number of posts — 12 inches square — in an inclined position between the roof of the working chamber and a temporary timber platform resting on the ground below. When these posts had been wedged up to a firm bearing, the air pressure was released. The water flowing into the caisson loosened the soil on the outside, and the weight of the caisson com- ing on the inclined posts caused them to rotate about their lower ends, which forced the caisson in the desired direction. In this way, a lateral movement of 3 or 4 feet was secured while sinking about the same distance.
A caisson is also sometimes moved laterally, while sinking, by attaching a cable which is anchored off to one side and kept taut.
454. A new method of controlling the descent of the caisson has been recently introduced, which is specially valuable in swift cur- rents or in rivers subject to sudden rises. It was used first in the construction of the piers for a bridge across the Yazoo River near Vicksburg, Miss. A group of 72 piles, each 40 feet long, was driven into the river bed, and sawed off under the water ; the caisson was then floated into place, and lowered until the heads of the piles rested against the roof of the working chamber. As the work proceeded, the piles were sawed off to allow the caisson to sink. One of the reasons for employing piles in this case, was that, if the caisson did not finally rest upon bed-rock, they would assist in sup- porting the pier.
That such ponderous masses can be so certainly guided in their
ART. 4. J PNEUMATIC PROCESS. 297
descent to bed-rock, is not the least valuable nor least interesting fact connected with this method of sinking foundations.
455. Fkictional Resistance. At the Havre de Grace bridge, the normal frictional resistance on the timber sides of the pneumatic caisson was 280 to 350 lbs. per sq. ft. for depths of 40 to 80 feet, the soil being silt, sand, and mud ; when bowlders were encoun- tered, the resistance was greater, and when the air escaped in large quantities the resistance was less. At the bridge over the Missouri Eiver near Blair, Neb., the frictional resistance usually ranged be- tween 350 and 450 lbs. per sq. ft., the soil being mostly fine sand with some coarse sand and gravel and a little clay. At the Brook- lyn bridge the frictional resistance at times was 600 lbs. per sq. ft. At Cairo, in sand and gravel, the normal friction was about 600 lbs. per sq. ft.
For data on the friction of iron cylinders and masonry shafts, see §§ 418-19, pages 275-77; and for data on the friction of ordi- nary piles, see §§ 370-72, pages 247-48.
456. Filling the Air-chamber. When the caisson has reached the required depth, the bottom is leveled off — by blasting, if necessary, — and the working chamber and shafts are filled with concrete. Sometimes only enough concrete is placed in the bottom to seal the chamber water-tight, and the remaining space is filled with sand. This was done at the east abutment of the St. Louis bridge, the sand being pumped in from the river with the sand- pump previously used for excavating the material from under the caisson.
457. Noted Examples. The St. Louis Bridge. The founda- tions of the steel-arch bridge over the Mississippi at St. Louis are the deepest ever sunk by the pneumatic process, and at the time of construction (1870) they were also very much the largest. The caisson of the east abutment was an irregular hexagon in plan, 83 X 70 feet at the base, and 64 X 48 feet at the top— 14 feet above the cutting edge. The working chamber was 9 feet high. The cutting edge finally rested on the solid rock 94 feet below low water. The maximum emersion was 109 feet 8-|^ inches, the greatest depth at which pneumatic work has yet been done. The other caissons were almost as large as the one mentioned above, but were not sunk as deep.
The caissons were constructed mainly of wood ; but the side
298 FOUNDATIONS UNDEK "WATER. [CHAP. XII.
walls and the roof were covered with plate iron to prevent leakage, and strengthened by iron girders on the inside. This was the first pneumatic caisson constructed in America ; and the use of large quantities of timber was an important innovation, and has become one of the distinguishing characteristics of American practice. In all subsequent experience in this country (except as mentioned in § 458), the iron lining for the working chamber has been dispensed with. The masonry rested directly upon the roof of the caisson, i. e., no crib-work was employed. In sinking the first pneumatic foundation an iron coffer-dam was built upon the top of the caisson ; but the last — the largest and deepest — was sunk without a coffer- dam,— a departure from ordinary European practice, which is occa- sionally followed in this country (see § 436).
458. The Brooklyn Bridge. The foundations of the towers of the suspension bridge over the East Eiver, between New York City and Brooklyn, are the largest ever sunk by the pneumatic process. The foundation of the New York tower, which was a little larger and deeper than the other, was rectangular, 172 X 102 feet at the bottom of the foundation, and 157 X 77 feet at the bottom of the masonry. The caisson proper was 31|^ feet high, the roof being a solid mass of timber 22 feet thick. The working chamber was 9| feet high. The bottom of the foundation is 78 feet below mean high tide, and the bottom of the masonry is 46J feet below the same. From the bottom of the foundation to the top of the balustrade on the tower is 354 feet, the top of the tower being 276 feet above mean high tide.
To make the working chamber air-tight, the timbers were laid in pitch and all seams calked ; and in addition, the sides and the roof were covered with plate iron. As a still further precaution, the inside of the air-chamber was coated with varnish made of rosin, menhaden oil, and Spanish brown.
For additional details see the several annual reports of the en- gineers in charge, and also numerous articles in the engineering newspapers and magazines from 1869 to 1872.
459. Forth Bridge. For an illustrated account of the pneumatic foundation work of the bridge across the Frith of Forth, Eng- land, see Engineering Neivs, vol. xiii. pages 242-43. The caissons employed there differed fro-m those described above (1) in being made almost wholly of iron, (2) in an elaborate system of cages for
ART. 4.] PNEUMATIC PROCESS. 299
hoisting the material from the inside, and (3) in the use of inter- locked hydraulic apparatus to open and close the air-locks. Each of the two deep-water piers consists of four cylindrical caissons 70 feet in diameter the deepest of which rests 96 feet below high tide.
460. Physiological Effect of Compressed Air. In the ap- plication of the compressed-air process, the question of the ability of the human system to bear the increased pressure of the air be- comes very important.
After entering the air-lock, as the pressure increases, the first sensation experienced is one of great heat. As the pressure is still further increased a pain is felt in the ear, arising from the abnormal pressure upon the ear-drum. The tubes extending from the back of the mouth to the bony cavities over which this membrane is stretched, are so very minute that compressed air can not pass through them with a rapidity sufficient to keep up the equilibrium of pressure on both sides of the drum (for which purpose the tubes were designed by nature), and the excess of pressure on the outside causes the pain. These tubes can be distended, thus relieving the pain, by the act of swallowing, or by closing the nostrils with the thumb and finger, shutting the lips tightly, and inflating the cheeks. Either action facilitates the passage of the air through these tubes, and establishes the equilibrium desired. The relief is only momentary, and the act must be repeated from time to time, as the pressure in the air-lock increases. This pain is felt only while the air in the lock is being "equalized," i. e., while the air is being admitted, and is most severe the first time compressed air is encountered, a little experience generally removing all unpleasant sensations. The passage through the lock, both going in and com- ing out, should be slow ; that is to say, the compressed air should be let in and out gradually, to give the pressure time to equalize itself throughout the various parts of the body.
When the lungs and whole system are filled thoroughly with the denser air, the general effect is rather bracing and exhilarating. The increased amount of oxygen breathed in compressed air very much accelerates the organic functions of the body, and hence labor in the caisson is more exhaustive than in the open air ; and on get- ting outside again, a reaction with a general feeling of prostration sets in. At moderate depths, however, the laborers in the caisson.
300 FOUNDATIONS UNDER WATER. [CHAP. XII.
after a little experience, feel no bad effects from the compressed air, either while at work or afterwards.
Eemaining too long in the working chamber causes a form of paralysis, recently named caisson disease, which is sometimes fatal. The injarious effect of compressed air is much greater on men ad- dicted to the use of intoxicating liquors than on others. Only sound, able-bodied men should be permitted to work in the caisson.
In passing through the air-lock on leaving the air-chamber, the workman experiences a great loss of heat owing (1) to the expan- sion of the atmosphere in the lock, (3) to the expansion of the free gases in the cavities of the body, and (3) to the liberation of the gases held in solution by the liquids of the body. Hence, on com- ing out the men should be protected from currents of air, should drink a cup of strong hot coffee, dress warmly, and lie down for a short time.
461. No physiological difficulty is encountered at small depths ; but this method is limited to depths not much exceeding 100 feet, owing to the deleterious effect of the compressed air upon the work- men. At the east abutment of the St. Louis bridge (§ 457), the caisson was sunk 110 feet below the surface of the water. Except in this instance, the compressed-air process has never been apjjlied at a greater depth than about 90 feet. Theoretically, the depth, in feet, of the lower edge of the caisson below the surface divided by 33 is equal to the number of atmospheres of pressure. The press- ure is never more than this, and sometimes, owing to the fric- tional resistance to the flow of the water through the soil, it is a little less. Therefore the depth does not exactly indicate the pressure ; but the rule is sufficiently exact for this purpose. At St. Louis, at a depth of 110 feet, the men were able to work in the compressed air only four hours per day in shifts of two hours each, and even then worked only part of the time they were in the air- chamber.
With reasonable care, the pneumatic process can be applied at depths less than 80 or 90 feet without serious consequences. At great depths the danger can be greatly decreased by observing the following precautions, in addition to those referred to above : (1) In hot weather cool the air before it enters the caisson ; * (2) in cold
* This was done in 1888 at the bridge over the Ohio River at Cairo, 111. — prob- ably the first example. The temperature of the air was reduced 20° F.
AKT. 4.] PNEUMATIC PKOCESS. 301
weather warm the air in the lock when the men come out ; and (3) raise and lower them by machinery.
For an exhaustive account of the various aspects of this subject, see Dr. Smithes article on the " Physiological Effect of Compressed Air," in the Report of the Engineer of the Brooklyn Bridge.*
462. Cost. The contract for pneumatic foundation is usually let at specified prices per unit for the materials left permanently in the structure and for the material excavated, including the neces- sary labor and tools. The prices for material in place are about as follows : Timber in caisson proper, from $40 to $50 per thousand feet, board measure, according to the locality in which the work is done ; and the timber in the crib- work and coffer-dam about $5 to $7 per thousand less. The concrete, which is usually composed of broken stone and suflBcient 1 to 2 or 1 to 3 Portland cement mortar to completely fill the voids, costs, exclusive of the cement, from $5 to $7 per cubic yard for that in the crib, and about twice this sum for that in the air-chamber and under the cutting edge. The wrought- iron spikes, drift-bolts, screw-bolts, and cast-iron washers cost from 3^ to 6 cents per pound, f The caisson and filling costs from $14 to $20 per cubic yard ; and the crib and filling from $8 to $10.
The price for sinking, including labor, tools, machinery, etc., ranges, according to the kind of soil, from 18 to 40, or even 50, cents per cubic foot of the volume found by multiplying the area of the caisson at the cutting edge by the final depth of the latter below low water. In sand or silt the cost is 18 to 20 cents, and in stiff clay and bowlders 40 to 50 cents.
463. Examples. The table on page 302 gives the details of the cost of the pneumatic foundation of the Havre de Grace bridge, as fully described in §§ 438-44.
The table on page 303 gives the details of the cost of the pneu- matic caissons of the bridge across the Missouri River near Blair, Neb. The caissons (Fig. 65, page 285) were 54 feet long, 24 feet wide, and 17 feet high. In the two shore piers, Nos. I and IV of the table, the caissons were surmounted by cribs 20 feet high ; but in the channel piers, the masonry rested directly upon the roof of the
* Priae Essay of the Alumni Association of the College of Physicians and Sur- geons of New York City, 1S73.
t There are usually from 140 to 150 pounds of iron per thousand feet (board meas- ure) of timber.
302
FOUNDATIONS UNDER WATER.
[chap. XII.
TABLE 32. Cost, to the R. R. Co., op Foundations op Havre de Grace Bridge.
|
N0MBKR OP THE Pier. |
|||||
|
Items. |
II. |
III. |
IV. |
VIII. |
IX. |
|
Depth of cutting edge below low water, feet Depth of cutting edge below mud line, feet Displacement below low water, cu. ft. " mud line, cu. ft . . Caisson : timber, @ $46.80 per M |
68.3 55.5 112,124 94,504 $9,522.54 1,456.12 5,775.00 16.82 8,421.14 1.291.14 14,016..50 10.76 96.78 14.45 22,424.80 000 |
70.7 58.7 123,402 106,269 $10,088.44 1,587.15 7,017.50 18.37 9,262.19 1,4.54.85 16,090.50 11.10 1.375.00 236.15 24.680.40 10,902.50 |
59.9 .32.3 159.588 84.014 $14,820.94 2.596.23 13,247.50 19.19 6,738.87 1,179.36 13,897.50 10.91 5,078.64 892.29 31.917.60 2,205.00 |
76.0 55 2 189,578 127,586 $13,176.07 2.242.40 18,987.50 24.34 8,936.58 1,749.35 21,943.50 9.91 4,013.52 684.20 37,915.60 9,205.00 |
65.0 32.6 231.691 107,836 $21,767.85 |
|
iron, ® 534 cts. per lb concrete. @ $17.50 per cu. yd. total eo.st, per net cu. yd Crib • timber, @, $46.80 per M |
3.295.38 25,602.50 22.10 9 538.96 |
||||
|
1,445.93 |
|||||
|
concrete, ® $8.50 per net cu. yd . . total cost, per cu. yd |
26,962.00 10.09 |
||||
|
CoCEer-dam: timber, © $40 80 per M iron, @ 514 cts. per lb Cost of sinlting. @ 20 cts. per cu. ft. of displacement below low water Concrete below cutting edge, @ $17.50 . . |
5.921.70 899.22 46,.3.38.20 10,920.00 |
||||
|
63,018.47 19.93 |
71,792.18 21.58 |
90,368.93 25.20 |
109,648.72 23.30 |
141,772.44 |
|
|
Total cost per cu. yd. of foundation be- low masonry, including coffer-dams. |
23.44 |
Average total cost of the foundation, to R. B. Co., per net cubic yard $22.69.
caisson. The work was done, in 1882-83, by the bridge company^s men under the direction of the engineer.
464. In 1869-72, thirteen cylinders were sunk by the plenum- pneumatic process for the piers of a bridge over the Schuylkill Eiver at South Sti-eet, Philadelphia. There were three piers, one of which was a pivot pier. There were two cylinders, 8 feet in diameter and 82 feet long, sunk through 22 feet of water and 30 feet of " sand and tough compact mud intermingled with bowlders ;" two cylinders, 8 feet in diameter and 57 feet long, sunk through 23 feet of water and 5 feet of soil as above ; one cylinder, G feet in diameter and 64 feet long, sunk through 22 feet of water and 18 feet of soil as above ; and 8 columns, 4 feet in diameter and aggre- gating 507 feet, sunk through 22 feet of water and 18 feet of soil as above. A 10-foot section of the 8-foot cylinder weighed 14,600 pounds, of the 6-foot, 10,800 pounds, and of the 4-foot, 6,800 pounds. The cylinders rested upon bed-rock, and were bolted to
* Data by courtesy of Sooysmith & Co., contracting engineers for the pneumatic foundations.
AKT. 4.]
PNEUMATIC PKOCESS.
303
it. The actual cost to the contractor, exclusive of tools and ma- chinery, was as in Table 34 (page 304).
TABLE 33. Cost of Pneumatic Foundations of Blair Bridge*
Items.
Number of the Pier.
III.
IV.
Total distance caisson was lowered after comple
tion
Final depth of cutting edge below surface of water " " '■ '■ ■' mud line
55.6 ft. 51.9 '•
47.7 "
54.5 ft. 52.3 " 51.0 "
Caisson and filling, cost of
" '• " " per cubic yard
Crib and filling, cost of
" " •' '• ■■ per cubic yard
Air-lock, shafts, etc., cost of
Sinking caisson, cost of, including erection and re- moval of machiiierj-
Sinking caisson, cost of, per cubic foot of displace- ment below position of cutting edge when caisson was completed
Sinking caisson, cost of. i)er cubic foot of displace- ment below surface of water
Sinking caisson, cost of, per cubic foot of displace- ment below mud line
Total cost t of foundation
" " " " per cubic yard
1,753.51 '$12,386.56
14.31
7,368.16
8.85
1,481.60
5,772.52
8.0 cts. 8.6 "
15.12
1,567.42 5,629.37
8.0 cts. 8.3 "
9.3 " 8.5
(26,375 79 $19,583.35
15.98, 23.87
56.2 ft. 53.4 " 49.4 •'
$13,819.34 16 74
1,536.80 6,888.16
9.5 cts.
9.9 "
10.8 " !
$22.244..30,
27.081
68.5 ft. 57.0 •' 54.7 "
$11,252.45
13.77
6.303.46
7.59
1,. 02 1. 08
7.084.26
7.1 cts.
9.6 '•
10.0 " $26,161.25 15.85
Average costt of the foundations, per cubic yard $20.70.
465. ''Excavation in the Brooklyn caisson J cost for labor only, including the men on top, about §5.25 per cubic yard [19 cents per cubic foot]. Kunniug the six air-compressors added to this $3.60 j^er hour, or about 47 cents per yard; lights added $0.56 more: and these with other contingencies nearly equaled the cost of labor. The great cost was due to the excessive hardness of the material over much of the surface, the caisson finally resting, for nearly its whole extent, on a mass of bowlders or hard- pan. The concrete in the caisson cost, for every expense, about
* Compiled from the report of Geo. S. Morison, chief engineer of the bridge.
t Exclusive of engineering expenses and cost of tools, machinery, and buildings. In a note to the author, Mr. Morison, the engineer of the bridge says : " It is impos- sible to divide the buildings, tools, and engineering expenses between the substruct- ure and other portions of the work. The bulk of the items of tools and machinery [$12,369.88], however, relates to the foundations." The engineering expenses and buildings were nearly 3 per cent, of the total cost of the entire bridge. The cost of tools and machinery was equal to a little over 13 per cent, of the cost of the founda- tions as above. Including these items would add nearly one sixth to the amounts in the last three lines.
X For a brief description, see § 458.
S04
FOUNDATIONS UNDER WATER.
[chap. XII.
TABLE 34. Cost of Pneumatic Piles at Philadelphia in 1869-73.*
|
Diameter of Cylinders. |
|||
|
Items of Expense. |
4-ft. |
6-ft. |
8- ft. |
|
Cost of cast iron, @ $59. .50 per ton '• •' bolts, @ 9% cents per lb " " grouted rubble masonry (exclusive of labor), @ $5.40 |
$11.239 36 S2,0.53.75 -189.84 93.31 1,266 79! 3.58.40 6,693.50} 911.88 $19,689.49 $3,417.34 $23.10 $33. .54 2.50 5.60 13.20 14.25 |
$13,577.90 670.02 2,779.97 |
|
|
9.036.51 |
|||
|
$26,064.40 |
|||
|
$51.35 |
|||
|
■' '• materials for mason/y per lineal foot of cylinder — " " sinking and laying masonry per lineal foot of cylinder |
10.00 32.51 |
||
|
Total cost,t per lineal foot, of cylinder in place |
$38.80 $53.39 |
$93.76 |
$15.50 per cubic yard. The caisson and filling together aggregated 16,898 cubic yards ; and the approximate cost per yard for every expense was $20.71." J The foundation therefore cost about $30 per cubic yard.
The pneumatic foundations for the channel piers of the bridge over the Missouri at Plattsmouth, Neb., cost as follows: One foundation, consisting of a caisson 50 ft. long, 20 ft. wide, and 15.5 ft. high, surmounted by a crib 14.15 ft. high, sunk through 13 ft. of water and 20 ft. of soil, cost $19.29 per cubic yard of net volume. Another, consisting of a caisson 50 ft. long, 20 ft. wide, and 15.5 ft. high, surmounted by a crib 3G.25 ft. high, sunk through 10 ft. of water and 44 ft. of soil, cost $14.45 per cubic yard of net volume. §
466. European Examples. The following •([ is interesting as showing the cost of pneumatic work in Europe :
" At Moulins, cast-iron cylinders, 8 feet 2^ inches in diameter, with a filling of concrete and sunk 83 feet below water into marl, cost $62.94 per lineal foot, or $29.71 for the iron work, and $33.23
* Compiled from an article by D. McN. Stauffer, engineer in charge, in Trans. Am. Soc. of C. E., vol. Y\\. pp. 287-309.
t Exclusive of tools and machinery.
X F. Collingwood, assistant engineer Broolvlyn bridge, in Trans. Am. Soc. of C. E.
§ Compiled from the report of Geo. S. Morison, chief engineer of the bridge.
T[ By Jules Gaudard, as translated from the French by L. F. Vernon-Haj'court for the Proceedings of the Institute of Civil Engineers (London).
ART. 4.] PXEUMATIC PEOCESS. 305
for sinking and concrete. At Argenteuil, with cylinders 11 feet 10 inches in diametei', the sinking alone cost $42.12 per lineal foot [nearly $10 per cubic yard], where a cylinder was sunk 53|^ feet in three hundred and ninety hours. [The total cost of this founda- tion was $3-4.09 per cubic yard, see table on page 310.] At Orival, where a cylinder was sunk 49 feet in twenty days, the cost of sinking was $36.83 per lineal foot. At Bordeaux, with the same-sized cylinders, a gang of eight men conducted the sinking of one cylin- der, and usually 34 cubic yards were excavated every twenty-four houi's. The greatest depth reached was 55f feet below the ground, and 7 1 feet below high Avater. In the regular course of working, a cylinder was sunk in from nine to fifteen days, and the whole opera- tion, including preparations and filling with concrete, occupied on the average 25 days. One cylinder, or a half pier, cost on the aver- age $11,298.40, of which $1,461 was for sinking. M. Morandiere estimates the total cost of a cylinder sunk like those at Argenteuil, to a depth of 50 feet, at $7,012.80.
467. '' Considering next the cost of piers of masonry on wrought- iron caissons of excavation, the foundations of the Lorient viaduct over the ScorfE cost the large sum of $24.11 per cubic yard, owing to difficulties caused by the tides, the labor of removing the bowlders from underneath the caisson, and the large cost of plant for only tAvo piers. The foundation of the Kehl bridge cost still more, about $28.23 * per cubic yard ; but this can not be regarded as a fair in- stance, being the first attempt [see § 429] of the kind.
"The foundations of the Xantes bridges, sunk 56 feet below low-water level, cost about $14.84 per cubic yard. The average cost per pier was as follows :
Caisson (41 feet 4 inches by 14 feet 5 inclies), 50 tons of wrought
iron @ $116.88 $5,844
Coffer-dam, 3 tons of wrought iron @ $58.44 175
Excavation, 916 cubic yards® $4.47 4,091
Concrete 4, 188
Masonry, plant, etc 1,870
Average cost per pier $16,168
"One pier of the bridge over the Meuse at Rotterdam, with a
* Notice the slight inconsistency between this qiiantity and the one in the third line from the last of the table on page 310, both being from the same article.
306 FOUNDATIONS UNDER WATER. [CHAP. XII.
caisson of 222 tons and a coffer-dam casing of 94 tons, and sunk 75 feet below high water, cost $70,858, or $13.97 per cubic yard.
" The Vichy bridge has five piers built on caissons 34 feet by 13 feet, and two abutments on caissons 26 feet by 24 feet. The foun- dations were sunk 23 feet in the ground, the upper portion con- sisting of shingle and conglomerated gravel, and the last 10 feet of marl. The cost of the bridge was as follows :
Interest for eight months, and depreciation of plant worth $19,480. . $3,896
Cost of preparations, approach bridge, and staging 4, 904
Caissons (seven), 150i tons @ $113.38 17,108
Sinking 9,823
Concrete and masonry 5, 303
Contractor's bonus and general expenses 6,107
Total cost of five foundations $47,141
The cost per cubic yard of the foundation below low water was $16.69, of which the sinking alone cost $3.50 in gravel, and $4.37 in marl.
"At St. Maurice, the cost per cubic yard of foundation was $15.94, exclusive of staging."
468. Conclusion. Except in very shallow or very deep water, the compressed-air process has almost entirely superseded all others. The following are some of the advantages of this method. 1. It is reliable, since there is no danger of the caisson's being stopped, before reaching the desired depth, by sunken logs, bowlders, etc., or by excessive friction, as in dredging through tubes or shafts in cribs. 2. It can be used regardless of the kind of soil overlying the rock or ultimate foundation. 3. It is comparatively rapid, since the sinking of the caisson and the building up of the pier go on at the same time. 4. It is comparatively economical, since the weight added in sinking is a part of the foundation and is permanent, and the removal of the material by blowing out or by pumping is as uniform and rapid at one depth as at another, — the cost only being increased somewhat by the greater depth. 5. This method allows ample opportunity to examine the ultimate foundation, to level the bottom, and to remove any disintegrated rock. 6. Since the rock can be laid bare and be thoroughly washed, the concrete can be com- menced upon a perfectly clean surface ; and hence there need be no question as to the stability of the foundation.
ART. 5.] THE FREEZING PROCESS. 307
Art. 5. The Freezing Process.
469. Principle. The presence of water has always been the great obstacle in foundation work and in shaft sinking, and it is only very recently that any one thought of transforming the liquid soil into a solid wall of ice about the space to be excavated. The method of doing this consists in inclosing the site to be ex- cavated, by driving into the ground a number of tubes through which a freezing mixture is made to circulate. These consist of a large tube, closed at the lower end, inclosing a smaller one, open at the lower end. The freezing mixture is forced down the inner tube, and rises through the outer one. At the top, these tubes connect with a reservoir, a refrigerating machine, and a pump. The freezing liquid is cooled by an ice-making machine, and then forced through the tubes until a wall of earth is frozen around them of suflBcient thickness to stand the external pressure, when the excavation can proceed as in dry ground.
470. History. This method was invented by F. H. Poetsch, M.D., of Aschersleben, Prussia, in 1883. It has been applied in but three cases. The first was at the Archibald colliery, near Schweidlingen, Prussia, where a vein of quicksand, 20 feet thick, was encountered at a depth of about 150 feet below the surface. Here twenty-three pipes were used, and 35 days consumed in the freezing process, under local difficulties. The second was at the Centrum mine, near Berlin, where about 107 feet of quicksand, etc., was penetrated. Engineers had been baffled for years in their attempts to sink a shaft here ; but in 33 days Mr. Poetsch had, with only 16 freezing tubes, secured a 6-foot wall of ice around the shaft area, and the shaft was excavated and curbed without difficulty. The third piece of work was at the Eimilia mine, Fensterwalde, Austria, in 1885, where an 8^-foot shaft was sunk through 115 feet of quick- sand.*
471. Details of the Process. In the last case mentioned above, " 12 circulatory tubes were used, sunk in a circle about 14 feet in diameter, from 12 to 15 days being required to sink them t depth of about 100 feet. The outside tubes were 8^ inches in
* As this volume is going through the press, this method is being applied in two places in tliis country^Iron Mountain, Mich., and Wyoming, Penn. — in sinking mine-shafts.
308 FOUNDATION'S UNDER WATER. [CHAP. XII.
diameter, and made of plate iron 0.15 inch thick. The tubes were snnk by aid of the water-jet. They were given a very slight incli- nation outward at the bottom to avoid any deviation in sinking that might interfere with the line of the shaft. The fi-eezing liquid employed was a solution of chloride of calcium, which con- geals at a temperature of —35° C. ( —31° F.). The circulation of the liquid through the tubes was secured by a small pump with a piston 6 inches in diameter and a 12-inch stroke. At the begin- ning of the operation, this pump made 30 double strokes per min- ute, which was equivalent to the passage of 0.6 gallon of the liquid through each tube per minute ; at the end of the oi3eration, when it was only necessary to maintain the low temperature, the pump strokes were reduced to 15 per minute. The refrigerating machine employed was one of a model guaranteed by the maker to produce 1,100 pounds of ice per hour. The motive-power was supplied by a small engine of about 5 horse-power. The ammoniac pump had a piston 2.8 inches in diameter and a 9.2-inch stroke, and made 30 strokes per minute. The pressure maintained was about 10 atmos- pheres. The quantity of ammoniacal liquid necessary to charge the apparatus was 281 gallons ; and under normal conditions the daily consumption of this liquid was 0.78 gallon,
"The actual shaft excavation was commenced 63 days after the freezing apparatus had been set in motion. The freezing machine was in operation 240 days. The work was done without difficulty, and a progress of 1.64 feet per day was made. The timbering was very light, but no internal pressure of any kind was observed. The brick masonry used for finally lining the shaft was about 11 inches thick. When the shaft was finished, the tubes were withdrawn without difficulty, by circulating through them a hot, instead of a cold, solution of the chloride of calcium, thus thawing them loose from the surrounding ice. The tubes were entirely uninjured, and Gould be used again in another similar operation.
472. " The material in the above plant is estimated to have cost $15,000, and $4,800 more for mounting and installation. The daily expense of conducting the freezing process is estimated at $11. The total expense for putting down the shaft is estimated at $128.66 per linear foot."* The last is equivalent to about $2.25 per cubic foot.
* Engineering News, vol. xiv. pp. 24, 25, translated from Le O&nie Civil of June 13,
1885.
AKT. 6.] COMPAKISON" OF METHODS. 30&
473. Modification for Foundations under Water. For sinking foundations under water, two methods of applying this process have been proposed. One of these consists in combining the pneumatic and freezing processes. A pneumatic caisson is to be sunk a short distance into the river-bed, and then the congealing tubes are applied, and the entire mass between the caisson and the rock is frozen solid. When the freezing is completed, the caisson will be practically sealed against the entrance of water, and the air-lock can be removed and the masonry built up as in the open air.
The other method consists in sinking an open caisson to the river-bed, and putting the freezing tubes down through the water. When the congelation is completed, the water can be pumped out and the work conducted in the open air.
474. Advantages Claimed. It is claimed for this process that it is expeditious and economical, and also that it is particularly valuable in that it makes possible an accurate estimate of the total cost before the work is commenced, — a condition of affairs unat- tainable by any other known method in equally difficult ground. It has an advantage over the pneumatic process in that it is not limited by depth. It can be applied horizontally as well as vertically, and hence is specially useful in sub-aqueous tunneling, particularly in soils which, with compressed air, are treacherous.
475. Difficulties Anticipated. So far it has been used only in sinking shafts for mines. Two difficulties are anticipated in ap- plying it to sink foundations for bridge piers in river beds ; viz., (1) the difficulty in sinking the pipes, owing to striking sunken logs, bowlders, etc.; and (3) the possibility of encountering running water, which will thaw the ice-wall. These difficulties are not in- surmountable, but experience only can demonstrate how serious they are.
476. Cost. See § 472, and compare with table on page 310.
Art. 6. Comparison of Methods.
477. The following comparison of the different methods is fron: an article by Jules Gaudard on Foundations, as translated by L. F. Vernon-Harcourt for the proceedings of the Institute of Civil En- gineers (London). Except as showing approximate relative costs in Europe, it is not of much value, owing to improvement made since the article was written, to the differences between European and
310
FOUNDATIONS UNDER WATER.
[chap. XII.
American practice, and to differences in cost of materials in the two countries.
478. " M. Croizette Desnoyers has framed a classification of the methods of foundations most suitable for different depths, and also an estimate of the cost of each. These estimates, however, must be considered merely approximate, as unforeseen circumstances pro- duce considerable variations in works of this nature.
TABLE 35. Cost of Vabious Kinds op Foundations in Europe.
Kind of Foundation.
Depth
IN Feet.
Min. Max
Cost per Cubic Yard.
Min. Max
On piles after compression of the ground, siiallow depth. " " " " greater depth .
By sinking wells
By pumping
.33
under favorable circumstances
" " unfavorable circumstances
On concrete under water, small amount of silt
*' " " " large '• " "
By means of compressed air* under favorable circumstances. . . ^ " " " " " unfavorable circumstances:
Lorient viaduct
Kehl bridge t
Argenteuil bridge
Bordeaux bridge
^2.92 4.39
2.92 4.39 14.85
4.37 9.00
13.39
[50 ft.] [70 " ] [50 " ]
$24, 29 34, 40
$4.39 7.30
9.00
4.39 13.39
17.77
9.00 11.93
16.17
11
71 09 17
* See also §§ 466-67. t See foot-note on page 305.
"When the foundations consist of disconnected pillars or piles, the above prices must be applied to the whole cubic content, includ- ing the intervals between the parts ; but of course at an equal cost Bolid piers are the best.
479. " For pile-work foundations the square yard of base is prob- ably a better unit than the cubic yard. Thus the foundations of the Vernon bridge, with piles from 24 to 31 feet long, and with cross-timbering, concrete, and caisson, cost $70 per square yard of base. According to estimates made by M. Picquenot, if the foun- dations had been put in by means of compressed air, the cost would have been $159.64 ; with a caisson, not water-tight, sunk down, $66.27 ; with concrete poured into a space inclosed with sheeting, $62.23 ; and by pumping, $83.56 per square yard of base."
PART IV.
MASONRY STRUCTURES.
CHAPTER XIII. MASONRY DAMS.
480. It is not the intention here to discuss every feature of masonry dams ; that has been done in the special reports and arti- cles referred to in § 520, page 334. The fundamental principles will be considered, particularly with reference to their applica- tion in the subsequent study of retaining walls, bridge abutments, bridge piers, and arches. The discussions of this chapter are applicable to masonry dams, reservoir walls, or to any wall which counteracts the pressure of water mainly by its weight.
There are two ways in which a masonry dam may resist the thrust of the water ; viz., (1) by the inertia of its masonry, and (2) as an arch. 1. The horizontal thrust of the water may be held in equilibrium by the resistance of the masonry to sliding forward or to overturning. A dam which acts in this way is called a gravity dam. 2. The thrust of the water may be resisted by being trans- mitted laterally to the side-hills (abutments) by the arch-like action of the masonry. A dam which acts in this way is called an arched dam.
Only two dams of the pure arch type have ever been built. The almost exclusive use of the gravity type is due to the uncertainty of our knowledge concerning the laws governing the stability of masonry arches. This chapter will be devoted mainly to gravity dams, those of the arch type being considered only incidentally. Arches will be discussed fully in Chapter XVIII.
811
313 MASOXRY DAMS. [CHAP. XIII,
Art. 1. Stability of Gravity Dams.
481. Principles. By the principles of liydrostatics we know (1) that the pressure of a liquid upon any surface is equal to the weight of a volume of the liquid whose base is the area of the im- mersed surface and whose height is the vertical distance of the center of gravity of that surface below the upper surface of the water ; (2) that this pressure is always perpendicular to the pressed surface ; and (3) that, for rectangular surfaces, this pressure may be con- sidered as a single force applied at a distance below the upper surface of the liquid equal to f of the depth.
482. A gravity dam may fail (1) by sliding along a horizontal joint, or (2) by overturning about the front of a horizontal joint, or (3) by crushing the masonr}^, particularly at the front of any horizontal joint. However, it is admitted that by far the greater number of failures of dams is due to defects in the founda- tion. The method of securing a firm foundation has already been discussed in Part III ; and, hence, this subject will be considered here only incidentally. There is not much probability that a dam will fail by sliding forward, but it may fail by overturning or by the crushing of the masonry. These three methods of failure will be considered separately and in the above order.
483. In the discussions of this article it will be necessary to consider only a section of the wall included between two vertical planes — a unit distance apart — perpendicular to the face of the wall, and then so arrange this section that it will resist the loads and pressure put upon it ; that is, it is sufficient, and more convenient, to consider the dam as only a unit, say 1 foot, long.
484. NOMENCLATIJEE. The following nomenclature will be used throughout this chapter :
H = the horizontal pressure, in pounds, of the water against a section of the back of the wall 1 foot long and of a height equal to the height of the wall. Fr= the weight, in pounds, of a section of the wall 1 foot long. w = the weight, in pounds, of a cubic foot of the masonry. h = the height, in feet, of the wall ; i. e. , h = E F, Fig. 68. I = the length of the base of the cross section ; i. e., I = A B,
Fig. 68. t = the width of the wall on tojj ; i. e., t = D E, Fig. 68.
AKT. 1.]
STABILITY OF GEATITT DAMS.
313
h = the batter of the wall, i. e., the inclination of the surface per foot of rise — h' being used for the batter of the up- stream face and h^ for that of the down-stream face. x-= A C = the distance from the down-stream face of any joint to the point in which a vertical through the center of gravity of the wall pierces the plane of the base. d = the distance the center of pressure deviates from the center of the base. 62.5 = the weight, in pounds, of a cubic foot of water,
485. Stability against Sliding. The horizontal pressure of the water tends to slide the dam forward, and is resisted by the friction due to the weight of the wall.
486. Sliding Force. The horizontal pressure of the water against an elementary section of the wall, by principle (1) of § 481, is equal to the area of the section multiplied by half the height of the wall, and that product by the weight of a cubic unit of water; or
H=h XlXih X 62.5 = 31.25 h\
(1)
Notice that II is the same whether the pressed area is inclined or vertical ; that is to say, H is the horizontal component of the total pressure on the surface.
487. Resisting Forces. The weight of an elementary section of the wall is equal to the area of the vertical n E
cross section multiplied by the weight of a cubic unit of the masonry. The area of the cross section, ABED, Fig. 68, equals
EFxDE+^EFxFB+^D GxAG
= ht+^h'h'+^h'h^ ... (2)
Then the weight of the elementary sec- tion of the wall is
W=w{ht + \h'h' + yi'b;) . (3)
The vertical pressure of the water on the inclined face increases the pressure on the foundation, and, consequently, adds to the resistance against sliding. The vertical pressure on E B is equal to the horizontal projection of that area multiplied by the distance of the center of gravity of the surface below the top of the water and by the weight of a cubic unit of
ac F
Fig. 68.
314 MASONRY DAMS. [CHAP. XIII.
water, or, the vertical pressure = FB X 1 X ^ h X Q2.5 = h b' X ^h X 62.5 = 31.25 h'b'.
488. If the earth rests against the heel of the dam (the bot- tom of the inside face), it will increase the pressure on the foun- dation, since earth weighs more than water ; on the other hand, the horizontal pressure of the earth will be a little greater than that of an equal height of water. However, since the net resistance with the earth upon the heel of the wall is greater than with an equal depth of water, it will be assumed that the water extends to the bottom of the wall.
If the water finds its way under and around the foundation of the wall, even in very thin sheets, it will decrease the pressure of the wall on the foundation, and, consequently, decrease the stability of the wall. The effective weight of the submerged por- tion of the wall will be decreased 62 1- lbs. per cu. ft. However, the assumption that water in hydrostatic condition finds its way under or into a dam is hardly admissible ; hence the effect of buoyancy will not be considered. *
489. Co-efficient of Friction. The values of the co-efficient of friction most frequently required in masonry computations are given in the table on page 315. There wiU be frequent reference to this table in subsequent chapters ; and therefore it is made more full than is required in this connection. The values have been collected from the best authorities, and are believed to be fair averages. See also the table on page 276.
490. Condition for Equilibrium. In order that the wall may not slide, it is necessary that the product found by multiplying the co-efficient of friction by the sum of the weight of the wall and the vertical pressure of the water shall be greater than the horizontal pressure of the water. That is to say, in order that the dam may not slide it is necessary that /x {W -\- 31.25 h^ h') shall be greater than H; or, in mathematical language,
H 31.25 h'
W H- 31.25 h' b'^ w{ht + ih'y -\-^ ?i' b,) H- 31.25 A' b' '
* Since the above was written, Jas. B. Francis presented a paper (May 16, 1888) before the American Society of Civil Engineers, which seems to show that water pressure is communicated, almost undiminished, through a layer of Portland cement mortar (1 part cement and 2 parts sand) 1 foot thick.
A«T. L]
STABILITY OF GRAVITY DAMS.
315
TABLE 36. Co-efficients of Friction fob Dbt Masonry.
Description of the Masonry.
Soft limestone on soft limestone, both well dressed
Brick-work ou brick-work, with slightly damp mortar
Hard brick-work on hard brick-work, with slightly damp mortar
Point-dressed granite on like granite
" " " " well-dressed granite
Common brick on common brick
" " " hard limestone ^
Hard limestone on hard limestone, with moist mortar
Beton blocks (pressed) on like beton blocks
Fine-cut granite on pressed " "
Well-dressed granite ou well dressed granite
Polished limestone on polished limestone
Well-dressed granite on like grMnite. with fresh mortar
Common brick on common brick, with wet mortar
Polished marble ou common brick
Point-dressed granite on gravel
" " " dry clay
" " " "sand ,
'• " " " moist clay
Wrought iron on well-dressed limestone
" " " hard, well dressed limestone, wet
Oak, flatwise, on limestone
" endwise, on limestone
CO-KFFICIENT.
0.75 0.75 0.70 0.70 0.65 0.65 0.65 0.65 0.65 0.60 0.60 0.60 0.50 0.50 0.45
0.60 0.50 0.40 0.33 0.50 0.25 0.65 0.40
which reduced becomes
62.5 A
^ ^ w (2 ^ + h {b' + bj) + 62.5 h b''
. . (4)
The weight of a cubic foot of masonry, w, varies between 125 lbs. for concrete or poor brick-work, and 160 lbs. for granite ashlar. Dams are usually built of rubble, which weighs about 150 lbs. per cu. ft. To simplify the formula, we will assume that the masonry weighs 125 lbs. per cu. ft.; i. e., that the weight of a cubic foot of masonry is twice that of water. This assumption is on the safe side, whatever the kind of masonry.* Making this substitution in (4)
* Increased safety generally requires increased cost of construction, and hence it is not permissible to use approximate data simply because the error is on the side toward safety. It will be shown that there is no probability of any dam's failing by sliding, and that the size, and consequently the volume and cost, are determined by
316 MASOKRY DAMS. [CHAP. XIII.
gives
other things being the same, the thinner the wall at the top, the easier it will slide. If the section of the wall is a triangle, i. e., if / = 0, then by equation (5) we see that the dam is safe against sliding when
''^"•^wk) (^^
An examination of the table on page 315 shows that there is no probability that the co-eflBcient of friction will be less than 0.5; and inserting this vdue of jj. in (6) shows that sliding can not take place if (f b' + b^ > or = 1. To prevent overturning, {b' + ^i) is usually = or > 1 (see Fig. 72, page 328); and, besides, a con- siderable thickness at the top (see § 509) is needed to resist the shock of waves, etc. Hence there is no probability of the dam's failing by sliding forward. Further, the co-efficient of friction in the table on page 315 takes no account of the cohesion of the mor- tar, which ma}^ have a possible maximum value, for best Portland mortar, of 36 tons per sq. ft. (500 lbs. per sq. in.); and this gives still greater security. Again, the earth on, and also in front of, the toe of the wall adds greatly to the resistance against sliding. Fi- nally, it is customary to build masonry dams of uncoursed rubble (§§ 213-17), to prevent the bed- joints from becoming channels for the leakage of water; and hence the stones are thoroughly inter- locked,— which adds still further resistance. Therefore it is certain that there is no danger of any masonry dam's failing by sliding for- ward under the pressure of still water.
491. It has occasionally happened that dams and retaining walls have been moved bodily forward, sliding on their base; but such an occurrence is certainly unusual, and is probably the result of the wall's having been founded on an unstable material, perhaps on an inclined bed of moist and uncertain soil. In most that was said in Part III concerning foundations, it was assumed that the founda*
the dimensions required to prevent crushing and overturning; hence this approxima- tion involves no increase in the cost.
AET. 1.] STABILITY OF GKAYITY DAMS. 31?
tion was required to support only a vertical load. AVlien the struct- ure is subjected also to a lateral pressure, as in dams, additional means of security are demanded to prevent lateral yielding.
When the foundation rests upon piles a simple expedient is to drive piles in front of and against the edge of the bed of the founda- tion; but obviously this is not of much value except when the piles reach a firmer soil than that on which the foundation directly rests. If the piles reach a firm subsoil, it will help matters a little if the upper and more yielding soil is removed from around the top of the pile, and the place filled with broken stone, etc. Or a wall of piles may be driven around the foundation at some distance from it, and timber braces or horizontal buttresses of masonry may be jjlaced at intervals from the foundation ' to the piles. A low masonry wall is sometimes used, instead of the wall of piles, and connected with the foot of the main wall by horizontal buttresses, whose feet, on the counter-wall, are connected by arches in a horizontal plane in order to distribute the pressure more evenly.
In founding a dam upon bed-rock, the resistance to sliding on the foundation may be greatly increased by leaving the bed rough ; and, in case the rock quarries out with smooth surfaces, one or more longitudinal trenches may be excavated in the bed of the foundation, and afterwards be filled with the masonry.
In the proposed Quaker Bridge dam the maximum horizontal thrust of the water is equal to 0.597 of the weight of the masonry.
492. Stability against Overturning. The horizontal pres- sure of the water tends to tijD the wall forward about the front of any joint, and is resisted by the moment of the weight of the wall. Eor the present, it will be assumed that the wall rests upon a rigid base, and therefore can fail only by overturniug as a whole.
The conditions necessary for stability against overturning can be completely determined either by considering the moments of the several forces, or by the principle of resolution of forces. In the following discussion, the conditions will be first determined by mo- ments, and afterward by resolution of forces.
493. A. By Moments. The Overturning Moment. The pressure of the water is perpendicular to the pressed surface. If the water presses against an inclined face, then the pressure makes the same angle with the horizontal that the surface does with the vertical. Since there is a little difficulty in finding the arm of this force, it is
318
MASONEY DAMS.
[chap. XIIL
more convenient to deal with the horizontal and vertical components of the pressure.
The horizontal pressure of the water can be found by equation (1), page 313. The arm of this force is equal to -^ 1i (principle 3, § 481). Hence the moment tending to overturn the wall is equal to
\Hh = ^ 31.25 ¥ = 10.42 h\
(7)
which, for convenience, represent by J/j .
494. The Resisting Moments. The forces resisting the over- turning are (1) the weight of the wall and (2) the vertical pressure of the water on the inclined face.
The weight of the wall can be computed by equation (3), page 313. It acts vertically through the center of gravity of the cross section.
The center of gravity can be found algebraically or graphically. There are several ways in each case, but the following graphical solution is the sim- plest. In Fig. 69, draw the diagonals D B and A E, and lay off J[ / = ^ / ; then draw D J, and mark the middle of it Q. The center of gravity, 0, of the area ABED is at a distance from Q towards B equal to ^ ^ ^. This method is appli- cable to any four-sided figure.
The position of the center of gravity can also be found algebraically by the principle that the moment of the entire mass about any point, as ^, is equal to the moment of the part A D G, plus che moment of the portion D E F G, plus the moment of the part E B F, — all about the same point, A. Stating this principle alge- braically gives
= i^h'y-\-ht-^ih'b,)x, . ... (8)
m which x = the distance A C. Solving (8) gives
z = —
^h{b' + bj + i
(9)
ART. I. J STABILITY OF GRAVITY DAMS. 310
The arm of the weight is ^ C (:= x), and therefore the mo- ment is
Wx AC=w[ht-\-^h'{y + b^)]x, . . . (10)
which, for convenience, represent by M, .
495. The vertical pressure of the water on the inclined face, E B, has been computed in § 487, which see. This force acts ver- tically between i^^and B, at a distance from B equal to \ F B; the arm of this force \s A B - \ F B = I - I hh' = h h^ + t ^ ^Jih'. Therefore, the moment of the vertical pressure on the inclined face is
31.25 h' h' (li b^ + t + ^k V), .... (11)
which, for convenience, represent by J/3 . Of course, if the pressed face is vertical, J/3 will be equal to zero.
496. The moment to resist overturning is equal to the sum of (10) and (11) above, or J/, + J/3 .
The moment represented by the sum of J/^ and J/3 can be deter- mined directly by considering the pressure of the water as acting perpendicular to E B at ^ F B from B ; the arm of this force is a line from A perpendicular to the line of action of the pressure. If the cross section were known, it would be an easy matter to measure this arm on a diagram; but, in designing a dam, it is necessary to know the conditions requisite for stability before the cross section can be determined, and hence the above method of solution is the better.
497. Condition for Equilibrium. In order that the wall may not turn about the front edge of a joint, it is necessary that the overturning moment, J/, , as found by equation (7), shall be less than the sum of the resisting moments, J/^ and J/3 , as found by equations (10) and (11); or, in other words, the factor against over-.
turning = -^-^^ — '- (12)
498. Factor of Safety against Overturning. In computing the stability against overturning, the vertical pressure of the water against the inside face is frequently neglected; i.e., it is assumed that J/3 , as above, is zero. This assumption is always on the safe side. Computed in this way, the factor of safety against overturn- ing for the proposed Quaker Bridge dam, which when completed
320 MASOXRY DAMS [CHAP. XIII.
will be considerably the largest dam in the world, varies between 2.07 and 3.68. Krantz,* who included the vertical component in his computations, considers a factor of 2.5 to 5.55 as safe, the larger value being for the largest dam, owing to the more serious conse- quences of failure. The greater the factor of safety provided for, the greater is the first cost; and the less the factor of safety, the greater the expense of maintenance, including a possible reconstruc- tion of the structure.
499. B. By Resolution of Forces. In Fig. 70, K is the center of pressure of the water on the back of the wall. K B =\ E B. o is the center of gravity of the wall, — found as already described. Through K draw a line, K a, perpendicular to E B; through o draw a vertical line o a. To any convenient scale lay off ab equal to the total pressure of the water against E B, and to the same scale make af equal to the weight of an elementary section of the wall. Complete the parallelogram a h ef. The diagonal ae intersects the base of the
wall at N.
500. On the assumption that the masonry and foundation
are absolutely incompressible (the compressibility will be considered
presently), it is clear that the wall will not overturn as long as the
resultant ae intersects the base AB between A and B. The factor
A C against overturning is -^^--„ which is the equivalent of equation (12).
The wall can not slide horizontally on the base, when the angle JVaCis less than the angle of repose, i. e., when tan NaC is, less than the co-eflacient of friction. The factor against sliding is equal to the co-efficient of friction divided by fan NaC, which is only another way of stating the conclusion drawn from equation (4), page 315.
501. Stability against Crushing. The preceding discussion of the stability against overturning is on the assumption that the masonry does not crush. This method of failure will now be con-
* " Study of Reservoir Walls," Mahan's translation, p. 53.
ART. 1.]
STABILITY OF GRAVITY DAMS.
321
sidered. When the reservoir is empty, the pressure tending to produce crushing is tlie weight of the dam alone, which pressure is distributed uniformly over the horizontal area of the wall. When the reservoir is full, the thrust of the water modifies the distribution of the pressure, increasing the pressure at the front of the wall and decreasing it at the back. We will now determine the law of the variation of the pressure.
Let A B, Fig. 71, represent the base of a vertical section of the dam ; or A B may represent the rect- angular base (whose width is a unit) of any two bodies which are pressed against each other by any forces whatever.
FiQ. 71.
Jlf=the resulting moment (about ^) of
all the external forces. In the
case of a dam, M = M^ — M^, — see
equations (7) and (11). W = the total normal pressure on A B.
In the case of a dam, W = the weight of the masonry. P = the maximum pressure, per unit of area, at A. p = the change in unit pressure, per unit of distance, from A
towards B. X = any distance from A towards B. P — J} X = the pressure per unit at a distance x from A. Y = a, general expression for a vertical force.
The remainder of the nomenclature is as in § 484, page 313. Taking moments about A gives
M- Wx+ r (P -px)dx.x = 0; . . . (13)
M-Wx^^Pf-\pV = ^ (14)
For equilibrium, the sum of the forces normal to -4 ^ must also be equal to zero ; or
:^^F=-r+ r {P -px)dx = 0, , . . (15)
from which
pT = 'iPl-2W. . , . . , , (16)
323 MASONRY DAMS. [CHAP. XIIL
502. Maximnm Pressure. Combining (16) with (14) and re ducing, _
4r_6J^ 6^
I r '^ r ^ ^
tf the stability against overturning be determined algebraically,' ■?'. e., by equation (12), then JIfand x are known, and P can be computed by equation (17).
If the wall is symmetrical x = ^l, and (17) becomes
W 6 M
Equation (18) is a more general form of equation (1), page 205, since in the latter there is but one external force acting, and that is horizontal.
W
In equation (18), notice that — is the uniform pressure ouAB
due to the weight of the wall ; also that -^ is the increase of pres-
sure at A due to the tendency to overturn, and that consequently the uniform pressure at B is decreased a like amount.
503. The maximum pressure may be found also in another way. Assume that N, Fig. 71, is the center of pressure. Let j9j {— B L) represent the pressure at B, and^^ (= ^-S')that at A ; and any intermediate ordinate of the trapezoid A B L K will represent the pressure at the corresponding point. Then, since the forces acting on A B must be in equilibrium for translation, the area of the trapezoid will represent the entire pressure on the base A B. Stated algebraically, this is
Pi^^ l=W. (19)
ifJi&o, since the forces acting on A B must be in equilibrium for rotation, the moment of the pressure to the right of N must be equal to that to the left ; that is to say, the center of gravity of the trapezoid A B L ^must lie in the line N J. By the principles of analytical mechanics, the ordinate ^ ^ to the center of gravity AB LEis,
-^IP_P^\ ...... (20)
ART. 1.] STABILITY OF GRAVITY DAMS. 323
Solvmg (19) and (20) gives
If the wall is a right-angled triangle with the right angle at A,
X = -^I, which, substituted in the above expression, shows that the
2 W pressure at A is — - — , and also that the pressure at B is zero, — all
of which is as it should be. Equation (21) is a jjef'fectly general expression for the pressure between any tioo plane surfaces pressed t ofj ether hy normal forces. Notice that equation (21) is identical with the first two terms of the right-hand side of equation (17).
The form of (21) can be changed by substituting for x its value \l — d\ then
^'^ - / + r ^ ^
Equation (22) gives the pressure at A due to the weight of the wall ; but it will also give the maximum pressure on the base due to both the vertical and the horizontal forces, provided d be taken as the distance from the middle of the base to the point in which the resultant of all the forces cuts the base. Therefore we may write
P-^^'^. (23)
504. Equation (23) is the equivalent of equation (17), page 322. It is well to notice that equation (23) is limited to rectangular hori- zontal cross-sections, since it was assumed that the pressure on the section varies as the distance back from the toe. If the stability against overturning is determined algebraically, as by equation (12), then equation (17) is the more convenient ; but if the stability is determined graphically, as in Fig. 70, then equation (23) is the
2 W simpler. Notice that \i d = \l, P — —r-, which is in accordance
with what is known in the theory of arches as the principle of the middle third ; that is, as long as the center of pressure lies within the middle third of the joint, the maximum pressure is not more than twice the mean, and there is no tension in any part of the joint.
324: MASONET DAMS. [CHAP. XIII.
IF
Notice, in equation (23), that -y- is the uniform load on the base;
6 Wd and also that — y. — is the increase of pressure due to the eccentric- ity of the load. It is immaterial whether the deviation d is caused by the form of the wall or by forces tending to produce overturn- ing.
505. Tension on the Masonry. By an analysis similar to that above, it can be shown that the decrease in pressure at B, due to the overturning moment, is equal to the increase at ^4. If d — ^I, then by equation (23) the increase at A and decrease at i? is W, that is to say, the pressure at ^ is 2 W and that at B is zero. Therefore, if the center of pressure departs more than ^ I from the center of the base, there will be a minus pressure, i. e. tension, at B. Under this condition, the triangle A V K' , in Fig. 71, page 321, represents the total pressure, and the triangle J5 FX'the total tension on the masonry, — A K' being the maximum pressure at A, and B L' the maximum tension at B.
If a good quality of cement mortar is used, it is not unreason- able to count upon a little ■ resistance from tension. As a general rule, it is more economical to increase the quantity of stone than the quality of the mortar ; but in dams it is necessary to use a good mortar to prevent (1) leakage, (2) disintegration on the water side, and (3) crushing. If the resistance due to tension is not included in the computation, it is an increment to the computed margin of safety.
506. If the masonry be considered as incapable of resisting by tension, then when d in equation (23) exceeds^? the total pres- sure will be borne on A V, Fig. 71. In this case A N' (the distance from A to the point where the resultant pierces the base) will be less than ^ L It A K" represents the maximum pressure P, then the area of the triangle A V K" will represent the total weight W. The area of A V K" ^ \ A K" Y. AV = \P Y Z A N'\ Hence \Py'^AN'^ W,ox
2 W 2 W ^^TAW'^^'^iilr-d) ^^^^
To illustrate the difference between equations (23) and (24)^
ART. 1.] STABILITY OF GRAVITY DAMS. 525
assume that the distance from the resultant to the center of the base is one quarter of tlie length of the base, /. e., assume that d =■ \l. Then, by equation (23), the maximum pressure at A is
^ - I ^ r-4. ~^^ r ^'^^^
and by equation (2-4) it is
2 W W ^-3(^/_x/)--3 ; ^-^)
That is to say, if the masonry is capable of resisting tension, equa- tion (25) shows that the maximum pressure is 2^ times the pressure due to the weight alone ; and if the masonry is incapable of resist- ing tension, equation (20) shows that the maximum pressure is 2f times the pressure due to the weight alone.
Notice that equation (24) is not applicable when d is less than ^I ; in that case, equation (23) must be nsed.
507. Limiting Pressure. As a preliminary to the actual design- ing of the section, it is necessary to fix upon the maximum pressure per square foot to which it is proposed to subject the masonry. Of course, the alloAvalile pressure depends upon the quality of the masonry, and also upon the conditions assumed in making the com- putations. It appears to be the custom, in practical computations, to neglect the vertical pressure on the inside face of the dam, i. e., to assume that J/j , equation (11), page 319, is zero ; this assumption is always on the safe side, and makes the maximum pressure on the outside toe appear greater than it really is. Computed in this way, the maximum pressure on rubble masonry in cement mortar in some of the great dams of the world is from 11 to 14 tons per sq. ft. The proposed Quaker Bridge dam is designed for a maximum pressure of 16.6 tons per sq. ft. on massive rubble in Portland cement mortar.
For data on the strength of stone and brick masonry, see §§ 221-23 and §§ 246-48, respectively.
508. The actual pressure at the toe will probably be less than that computed as above. It was assumed that the weight of the wall was uniformly distributed over the base ; but if the batter is considerable, it is probable that the pressure due to the weight of the wall will not vary uniformly from one side of the base to the
326 MASOXRY DAMS. [CHAP. XIII.
other, but will be greater on the central portions. The actual maximum will, therefore, probably occur at some distance back from the toe. Neither the actual maximum nor the point at which it occurs can be determined.
Professor Kankine claims that the limiting pressure for the out- side toe should be less than for the inside toe. Xotice that the preceding method determines the maximum vertical pressure. When the maximum pressure on the inside toe occurs, the only force acting is the vertical pressure ; but when the maximum on the outside occurs, the thrust of the water also is acting, and there- fore the actual pressure is the resultant of the two. With the pres- ent state of our knowledge, we can not determine the effect of a horizontal component upon the vertical resistance of a block of stone, but it must weaken it somewhat.
AkT. 2. OUTLIXES OF THE DeSIGX.
509. Width on Top. As far as the forces already considered are concerned, the width of the wall at the top might be nothing, since at this point there is neither a pressure of water nor any weight of masonry. But in practice we must consider the shock of waves and ice, Avhich in certain cases may acquire great force and prove very destructive to the upper portion of the dam. This force can not be computed, and hence the width on top must be assumed. This width depends to a certain extent upon the height and length of the dam. The top of large dams may be used as a roadway. Krantz * says that it is " scarcely possible to reduce the top vridth below 2 metres (6.5 ft.) for small ponds, nor necessary to make it more than 5 metres (16.4 ft.) for the largest."
Fig. 72, page .328, gives the width on top of Krantz's profile type, and also of the profile recommended by the engineers of the Aqueduct Commission for the proposed Quaker Bridge dam.
510. The Profile. In designing the vertical cross section of a gravity dam to resist still water, it is necessary to fulfill three con- ditions : (] ) To prevent sliding forward, equation (4), page 315, must be satisfied; (2) to resist overturning, equation (12), page 319, must be satisfied ; and (3) to resist crushing, equation (23), page 323, or (24), page 324, must be satisfied. As these equations really
* " Study of Reservoir Walls," Mahan's translation, p. 35.
AET. 2.] OUTLINES OF THE DESIGN". 327
involve only three variables, viz. : h, bx, and h', — the height of the dam and the batter of the two faces, — they can be satisfied exactly. It has been shown that there is no danger of the dam's sliding for- ward even if the width on top is zero ; and hence there are practi- cally but two conditions to be fulfilled and two variables to be determined. To prevent overturning when the reservoir is full, equation (12) must be satisfied ; and to prevent crushing, equation (23) — or (2i) — must be satisfied for the points (Figs. 09, 70, etc.) when the reservoir is full, and for B when the reservoir is empty.
Although it is possible to satisfy these conditions exactly, the theoretical profile can be obtained only by successive approxima- tions. This is done by dividing the profile into elementary hori- zontal layers, beginning at the top, and determining the dimension of the base of each layer separately. The theoretical width at the top being zero and the actual width being considerable, a portion of the section at the top of the dam will be rectangular. A layer being given, and the profile of the portion above it being known, certaiii dimensions are assumed for the lower base of the layer ; and the stability against overturning is then determined by appl^'iug equa- tion (12), or by the method of Fig. 70 (page 320). The maximum pressure at A is then found by applying equation (17) or (^3), after which the maximum pressure at B when the reservoir is empty must be determined by applying equation (23). If the first dimen- sions do not give results in accordance with the limiting conditions, others must be assumed and the computations repeated. A third approximation will probably rarely be needed.
It is not necessary to attempt to satisfy these equations precisely, since there are a number of unknown and unknowable factors, as the weight of the stone, the quality of the mortar, the character of the foundation, the quality of the masonry, the hydrostatic pressure under the mass, the amount of elastic yielding, the force of the waves and of the ice, etc., which have more to do with the ultimate stability of a dam than the mathematically exact profile. It is therefore sufficient to assume a trial profile, being guided in this by the matters referred to in § 511 and § 512, and test it at a few points by applying the preceding equations ; a few modifications to more nearly satisfy the mathematical conditions cr to simplify the profile is as far as it is wise to carry the theoretical determination of the profile.
328
MASOXRY DAMS.
[chap. XIII.
511. Krautz's Study of Reservoir Walls, translated from the French by Capt. F. A, Mahan, U. S. A., gives the theoretical pro- files for dams from 16.40 ft. (5 metres) to 164 ft. (50 metres) high. The faces are arcs of circles. The mathematical Avork of determin- ing the profiles is not given ; luit it is evident that the polygonal profile was deduced as above described, and that an arc of a circle was then drawn to average the irregularities. The largest of these profiles is shown in Fig. 72 by the broken line. The others are simply the upper portion of the largest, with the thickness and the height of the portion above the water decreased somewhat and the radius of the faces modified correspondingly.
..53.'i2.....
Ji?±t3.iC
^ibi^^a.17
-^---r
The larger profile of Fig. 72 is that recommended by the engi- neers of the Aqueduct Commission for the proposed Quaker Bridge dam. The profiles of most of the high masonry dams of the world
AET. 2.] OUTLINES OF THE DESIGN. 329
are exceedingly extravagant, and hence it is not worth while to give examples.
512. Prof. Wm. Cain has shown * that the equations of condi- tion are nearly satisfied by a cross section composed of two tra- pezoids, the lower and larger of which is the lower part of a triangle having its base on the foundation of the dam and its apex at the surface of the water, and the upper trapezoid having for its top the predetermined width of the dam on top (§ 509), and for its sides nearly vertical lines which intei'sect the sides of the lower trapezoid. The width of the dam at the bottom is obtained by applying the equations of condition as above. The relative batter of the up- stream and down-stream faces depends upon the relative factors of safety for crushing and overturning. This section gives a factor of safety which increases from bottom to top, — an important feature.
513. The Plan. If the wall is to be one side of a rectangular reservoir, all the vertical sections will be alike ; and therefore the heel, the toe, and the crest will all be straight. If the wall is to be a dam across a narrow valley, the height of the masonry, and conse- quently its thickness at the bottom, will be greater at the center than at the sides. In this case the several vertical cross sections may be placed so that (1) the crest Avill be straight, or (2) so that the heel will be straight in plan, or (3) so that the toe will be straight in plan. Since the up-stream face of the theoretical pro- file is nearly vertical (see Fig. 72), there will be very little difference in the form of the dam whether the several cross sections are placed in the first or the secoud position as above. If the crest is straight, the heel, in plan, will be nearly so ; if the crest is straight, the toe, in plan, will be the arc of a circle such that the middle ordinate to a chord equal to the span (length of the crest) will be equal to the maximum thickness of the dam ; and if the toe is made straight, the crest will become a circle of the same radius. This shows that strictly speaking it is impossible to have a straight gravity dam across a valley, since either the crest or toe must be curved. The question then arises as to the relative merits of these two forms.
514. Straight Crest vs. Straight Toe. The amount of masonry
* Engineering News, voL xix. pp. 51^13.
330 MASONEY DAMS. [CHAP. XIII.
in the two forms is the same, since the vertical sections at all points are alike in both.*
The stability of the two forms, considered only as gravity dams, is the same, since the cross sections at like distances from the center are the same.
The form with a curved crest and straight toe will have a slight advantage due to its possible action as an arch. However, it is not necessary to discuss further the relative advantages of these two types, since it will presently be shown that both the toe and the crest of a gravity dam should be curved.
515. Gravity vs. Arch Dams. A dam of the pure gravity type is one in which the sole reliance for stability is the weight of the masonry. A dam of the pure arch type is one relying solely upon the arched form for stability. With the arched dam, the pressure of the water is transmitted laterally through the horizontal sections to the abutments (side hills). The thickness of the masonry is so small that the resultant of the horizontal pressure of the Avater and the weight of the masonry passes outside of the toe ; and hence, considered only as a gravity dam, is in a state of unstable equilib- rium. If such a dam fails, it will probably be by the crushing of the masonry at the ends of the horizontal arches. In the present state of our knowledge concerning the elastic yielding of masonry, we can not determine, with any considerable degree of accuracy, the distribution of the pressure over the cross section of the arch (see Art. 1, Chap. XVIII).
If it were not for the incompleteness of our knowledge of the laws governing the stability of masonry arches, the arch dam would doubtless be the best type form, since it requires less masonry for any particular case than the pure gravity form. The best infor- mation we have in regard to the stability of masonry arches is de- rived from expe}-ience. The largest vertical masonry arch in the world has a span of only 220 feet. There are but two dams of the pure arch type in the world, viz. : the Zola f in France and the
* If the valley across which the dam is built has any considerable longitudinal slope, as it usually will have, there will be a slight difference according to the relative posi- tion of the two forms. If two ends remain at the same place, the straight toe throws the dam farther up the valley, makes the base higher, and consequently slightly de- creases the amount of raasonrj^.
+ For description, see Report on Quaker Bridge Dam, Engineering Neios, vol. xix. p. 6 et seq.
ART. 2.] OUTLINES OF THE DESIGN. 331
Bear Valley* in Southern California. The length of the former is 205 feet on top, height 122 feet, and radius 158 feet; the length of the latter is 230 feet on top, height 64 feet, radius of top 335 feet and of the bottom 226 feet. The experience with large arches is so limited (see Table 63, page 502), as to render it un- wise to make the stability of a dam depend wholly upon its action as an arch, except under the most favorable conditions as to rigid side-hills and also under the most unfavorable conditions as to cost of masonry. Notice that with a dam of the pure arch type, the failure of one joart is liable to cause the failure of the whole ; while with a gravity section, there is much less danger of this. Further, since the average pressure on the end arch stones increases with the span, the arch form is most suitable for short dams.
516. Curved Gravity Dams. Although it is not generally wise to make the stability of a dam depend entirely upon its action as an arch, a gravity dam should be built in the form of an arch, /. e., with both crest and toe curved, and thus secure some of the advan- tages of the arch type. The vertical cross section should be so jjro- portioned as to resist the water pressure by the weight of the masonry alone, and then any arch-like action will give an addi- tional margin for safety. If the section is proportioned to resist by its weight alone, arch action can take place only by the elastic 5nelding of the masonry under the water pressure ; but it is known that masonry will yield somewhat, and that therefore there will be some arch action in a curved gravity dam. Since but little is known about the elasticity of stone, brick, and mortar (see § 16), and noth- ing at all about the elasticity of actual masonry, it is impossible to determine the amount of arch action, i. e., the amount of pres- sure that is transmitted laterally to the abutments (side-hills).
That it is possible for a dam to act as an arch and a gravity dam at the same time is shown as follows : " Conceive a dam of the pure arch type, of thin rectangular cross section so as to have no appreciable gravity stability. Conceive the dam to be made up of successive horizontal arches with key-stones vertically over each other. The thrust in each arch will increase with the depth, but the spans will, under the ordinary practical conditions, decrease with the depth, so that the tendency to 'settle at the crown ' (move horizontally) will be approximately equal in each. If now we adopt
* For description, see Engineering News, vol. six. pp. 513-15.
332 MASOXRY DAMS. [CHAP. XIII.
a triangular in place of a rectangular cross section, we increase the areas and decrease the unit pressures from arch-thrust as we go down, and hence decrease compression and consequent horizontal ' settlement ' of the arches ; in other words, we introduce a tendency in the water face of the dam to rotate about its lower edge. But this is precisely the tendency which results from the elastic action of the mass in respect to gravity stability, which latter we have at the same time introduced by adojDting the gravity section. Hence the two act in perfect harmony, and there will be a certain size of triangular section (theoretically, — practically it could not be exact) at which precisely half the stability will be due to arch action and half to gravity action, each acting without any appreciable conflict or interference with the other.'" *
517. In addition to the increased stability of a curved gravity dam due to arch action, the curved form has another advantage. The pressure of the water on the back of the arch is everywhere perpendicular to the up-stream face, and can be decomposed into two components — one perpendicular to the chord (the span) of the arch, and the other parallel to the chord of the arc. The first component is resisted by the gravity and arch stability of the dam, and the second throws the entire up-stream face into compression. The aggregate of this lateral pressure is equal to the water pressure on the projection of the up-stream face on a vertical plane perpen- dicular to the span of the dam. This pressure has a tendency to close all vertical cracks and to consolidate the masonry transversely, — which effect is very desirable, as the vertical joints are always less perfectly filled than the horizontal ones. This pressure also pre- pares the dam to act as an arch eai'lior than it would otlierwise do, and hence makes available a larger amount of stability due to arch action.
The compression due to these lateral components is entirely in- dependent of the arch action of the dam, since the arch action would take place if the pressure on the dam were everywhere per- pendicular to the chord of the arch. Further, it in no way weakens the dam, since considered as a gravity dam the effect of the thrust of the water is to relieve the pressure on the back face, aiid con- sidered as an arch the maximum pressure occurs at the sides of the down-stream face.
* Editorial in Engineering News, vol. six. p. 272.
4.KT. 2.] OUTLINES OF THE DESIGN. 333
The curved dam is a little longer than a straight one, and hence would cost a little more. The difference in length between a chord and its arc is given, to a close degree of approximation, by the formula
in which a = the length of the arc, c = the length of the chord, and r = the radius. This shows that the increase in length due to the arched form is comparatively slight. For example, if the chord is equal to the radius, the arch is only ^\, or 4 per cent., longer than the chord. Furthermore, the additional cost is less, proportionally, than the additional quantity of masonry ; for example, 10 per cent, additional masonry will add less than 10 per cent, to the cost.
518. Of the twent^^-five most important masonry dams in the world, two are of the pure arch type, fifteen are of the curved gravity type, and eight are of the straight gravity type. The eight highest dams are of the curved gravity type.*
519. dUALITY OF THE Masoney. It is a well settled principle that any masonry structure which sustains a vertical load should have no continuous vertical joints. Dams support both a horizontal and a vertical pressure, and hence neither the vertical nor the hori- zontal joints should be continuous. This requires that the masonry shall be broken ashlar (Fig. 39, jiage 136) or random squared-stone masonry (Fig. 44, page 137), or uncoursed rubble (Fig. 45, page 13 7). The last is generally employed, particularly for large dams. The joints on the faces should be as thin as possible, to diminish the effect of the weather on the mortar and also the cost of repointing. In ordinary walls much more care is given to filling comjsletely the horizontal than the vertical ones ; but in dams and reservoir walls it is important that the vertical joints also shall be completely filled.
To prevent leakage, it is very important that all spaces between the stones should be filled completely with good mortar, or better, witii mortar impervious to water (see § 141). If the stone itself is not impervious, the wall may be made water tight by the ap- plication of Sylvester's washes (§ 263) to the inside face of the dam.
* For source of information concerning these dam?, see § 520 — Bibliography of Masonrj- UdLis.
334 MASOJSTEY DAMS. [CHAP. XIII.
520. BiBLlOGKAPHY OF MASONRY Dams. Design and Construc- tion of Masonry Dams, Rankiiie, (Miscellaneous Scientific Papers, pp. 550-61.) Study of Reservoir Walls, Krantz, (translated from the French by Capt. F. A. Mahan, U. S. A.) Profiles of High Masonry Dams, McMaster, (published in Van Nostraud's Engineer- ing Magazine and also as No. 6 of Van Nostrand's Science Series. ) Strains in High Masonry Dams, E. Sherman Gould, (Van Nostrand's Engineering Magazine, vol. 30, p. 265 et seq.). Histori- cal and Descriptive Revieio of Earth and Masonry Dams, with Plans, David Gravel, (Scientific American Supplement, No. 595 (May 28, 1887), pp. 9496-9500.) Wegmann's Design and Con- struction of Masonry Da?)is gives an account of methods em- ployed in determining the profile of the proposed Quaker Bridge dam, and also contains illustrations of the high masonry dams of the world. For a general discussion of high masonry dams, including a consideration of the best form for the horizontal cross section, a full description of the proposed Quaker Bridge dam and a comparison of it with other great dams, and many valuable points concerning practical details, see numerous re- ports, correspondence, and editorials in Engineering Neivs, Jan- uary to June, 1888 (vol. 19). The above articles contain many references to the literature, mostly French, of high masonry dams.
Aet. 3. Rock Fill Dams.
521. There are three well-known types of dams, which have been in use from time immemorial : earth bank, timber crib-work, and masonry. Eecent engineering practice on the Pacific coast has introduced another type, viz.: the Rock Fill Dam, which is of too much importance to pass by without a mention here, although strictly it can not be classed as masonry construction.
A rock fill dam consists of an embankment of irregular stones thrown in loosely, except that sometimes the faces are laid by hand. If the overflow is to discharge over the crest, the largest stones should be placed on the down-stream slope. The dam may be made practically water tight (1) by filling the voids with smaller stones, gravel, sand, and earth, or (2) by placing any desired thickness of earth and puddle on the up-stream face, or (3) by covering the water slope with one or more thicknesses of planking, which is calked and sometimes also pointed. Either the first or second method
ART. 2.] OUTLINES OF THE DESIGX. 335
would make a dam practically water tight from the beginning, and it would grow tighter with age ; the third method, if carefully exe- cuted, would make the dam absolutely water tight at the beginning, but would decay, since the upper part of the sheeting would ordi- narily be alternately wet and dry.
A great number of rock fill dams have been built on the Pacific slope in the past few years, for mining and irrigating purposes. A dam of this character has recently been completed on the Hassa- \-ampa Eiver in Arizona, of the following dimensions : " Height, 110 ft.; base, 135 ft.; top width, 10 ft.; length on top, 400 ft.;, water slope, 20 ft. horizontal to 47 ft. vertical (^ to 1); back slopes, 70 ft. horizontal to 180 ft. vertical (f to 1); contents, 4G,000 cu. yds. ;. cost, by contract, S2.40 per cu. yd." * It is proposed to build a dam of this character in California 250 feet high, which is about 80 feet higher than any existing masonry dam, and practically is nearly the same amount higher than the proposed Quaker Bridge dam (Fig. 72, page 328).
522. '' Earth dams are good and useful when only still water not running over the crest is to be dealt with. Counting reservoir walls as dams, which they are, earth dams are vastly more used than any other. They must be made with the greatest care, and, if of any considerable height, an inner wall of puddle is necessary to their integrity. They must be carried down to firm and impervious sub- soil of some kind, or they are worthless. Any considerable leak is at once fatal to them ; and they are also subject to serious injury from muskrats, crabs, etc. Nevertheless, many earth dams of great age and great height exist, and bid fair to exist for ages, showing that it is entirely possible to make them secure."
Stone-filled timber cribs have been very much used for dams ; but such structures are sure to rot in time, since the timber can not always be kept wet. It seems probable that in most instances where cribs have been used a rock-fill dam would have been better, cheaper, and more durable.
Masonry dams of all sizes, proportions, and ages exist in great abundance, and the entire suitability of masonry for the construction of dams is well established. This class of dams is to be preferred where large quantities of stone are not near at hand, or where leak- age is undesirable because of loss of water or of injury to land be-
* Engineering News, vol. xx. p. 232.
336 MASOXRY DAMS, [CHAP. XIII.
low, or where space is valuable, or where the surroundings require a dam of good appearance.
523. " These three types afford an adequate choice for nearly all i'equirenieuts, but it is obvious that they are open to certain com- mon objections from which the fourth type — a rock-fill dam — is ffee. They are all comparatively costly ; they require a good deal of labor, and much of it skilled and faithful labor, for their con- struction ; they can only with great inconvenience be constructed with water around them, wliich for the most part must be kept away by costly coifer-dams or diversions of channels ; above all, a leak is always a source of danger, and is apt to be destructive. They are all of them, as it were, during all their existence, in unstable equilibrium — all right so long as the balance of forces remains un- disturbed, and seriously endangered by a variety of causes which may disturb it. On the other hand a rock-fill dam is by the very process of its construction, if conducted with reasonable judgment, a structure which tends to improve with time, and which can not be injured but may be benefited by causes which threaten the other and more artificial types ; in other words, it is a structure which may not be very tight, but which is in stable equilibrium as respects all disturbing causes, being improved and never injured by them.
"A rock-fill dam is appropriate where the bed on which it rests is either rock, hard-pan, stiff clay, or some other imjDervious and almost unwashable material. The bed may be more or less over- laid with gravel or loose material without harm, if it be possible to remove the loose material in advance, and if there be current enough to remove it from under the foot of the dam, as the work of construction progresses, it will not even involve extra expense or delay, and the dam may be begun on top of the stratum without apparent regard to it ; but whenever there is any considerable stratum of loose material, a rock-fill dam can only be built by back- ing it with earth or puddle as a timber dam would be, and the necessity of providing a proper apron to receive the overflow may make a timber or crib dam the more economical. It is obvious that the place of all places for the proper use of such a rock-fill dam is where leakage is of no importance, either from the loss of "water or from injury to land below ; where skilled labor is scarce and costly, and simplicity of work rather than aggregate quantities
ART. 2.] OUTLINES OF THE DESIGN. 337
the important consideration ; where good materials for masonry are scarce or absent ; and where the surroundings do not demand at- tention to the question of appearance." *
The greatest economy in this form of dam occurs when the fill is made in water ; and it is particularly advantageous in the canali- zation of rivers, i. e., in forming pools in rivers for the benefit of navigation. It has been proposed to use rock-fill dams exclusively in the construction of the Nicaragua canal.
524. In California the cost of this class of dams varies from $2 to $3 per cubic yard, including all accessories, which is said to be about 50 per cent, cheaper than for earth dams of equal area of transverse cross section.
* Editorial in Engimerirm News, vol. xx. p. 70.
CHAPTER XIV. RETAINING WALLS.
625. Definitions. Retaining loall is a wall of masonry for sustaining the pressure of earth deposited behind it after it is built. A retaining wall is sometimes called a sustaining wall.
Face toall, or dujje wall, is a s]3ecies of retaining wall built against the face of earth in its undisturbed and natural position. Obviously it is much less important and involves less difficulties than a true retaining wall.
Buttresses are projections in the front of the wall to strengthen it. They are not often used, on account of their unsightliness, ex- cept as a remedy when a wall is seen to be failing.
Counterforts are projections at the rear of the wall to increase its strength. They are of doubtful economy, and were much more frequently used formerly than now.
Land-ties are long iron rods which connect the face of the wall with a mass of masonr}^, a large iron plate, or a large wooden post bedded in the earth behind the wall, to give additional resistance to overturning.
Surcharge. If the material to be supported slopes up and back from the top of the wall, the earth above the top is called the sur- charge.
Eetaining walls are frequently employed in railroad work, on canals, about harbors, etc.; and the principles involved in their construction have more or less direct application in arches, in tun- neling and mining, in timbering of shafts, and in the excavation of deep trenches for sewers, etc., and in military engineering.
526. Method of Failtjee. A retaining wall may fail (1) by revolving about the front of any horizontal joint, or (2) by sliding on the plane of any horizontal joint, or (3) by the bulging of the body of the masonry. The first is much the most frequent mode of
338
DIFFICULTIES. 339
failure, and the second is the least frequent. The wall can not fail by the center's bulging out, unless some force acts to keep the top from moving forward, — as in a cellar wall, the abutments of arches, etc.
527. Difficulties. In the discussion of the stability of dams, it was shown that in order to completely determine the effect of the thrust of the water against the wall, it is necessary to know (1) the amount of the pressure, (2) its point of application, and (3) the direction of its line of action. Similarly, to determine the effect of the thrust of a bank of earth against a wall, it is necessary to know (1) the amount of the pressure, (2) its point of application, and (3) its line of action. The determination of these three quan- tities requires three equations. The resistance of the wall both to sliding and to overturning can be found with sufficient accuracy, as has already been explained in Chapter XIII — Dams;— ^but the other elements of the problem are, in the present state of our knowledge, indeterminate.
The origin of the difficulties may be explained briefly as follows. A B represents a retaining wall ; A D \s, the sur- face of the ground. The earth has a tendency to break away and come down some line as CD. The force tending to bring the earth down is its weight ; the forces tending to keep it from coming down are the friction and cohesion along the line CD. The pressure against the wall depends upon the form of B C the line CD. If the constants of weight, friction, Fig. 73.
and cohesion of any particular ground were known, the form of CD and also the amount of the thrust on the wall could be determined. Notwithstanding the fact that since the earliest ages constructors have known by practical experience that a mass of earthwork will exert a severe lateral pressure upon a wall or other retaining structure, there is probably no other subject connected with the constructor's art in which there exists the same lack of exact ex- perimental data. This lack is doubtless due, in part at least, to a reliance upon theoretical investigations. Of course, mathematical investigations unsupported by experiments or experience are a very uncertain guide.
This subject will be discussed further under the heads (1) Theoretical Formulas, and (2) Empirical Rules.
yf
340 RETAINING WALLS. [CHAP. XIV.
Art. 1. Theoretical Formulas.
528. A great variety of theories have been presented, but all rest upon an uncertain foundation of assumption, and all are more or less defective and self-contradictory. All theories of the stability of retaining walls involve the three following assumptions :
529. First Assumption. All theories assume that the surface of rupture, C D, Fig. 73, is a plane. This is equivalent to assum- inof that the soil is devoid of cohesion, and is inelastic and homo- geneous, and also that if a mass of such material be sustained by a wall, there is a certain plane, called the plane of rupture, along which the particles are m equilibrium, i. e., are just on the point of moving. This assumption would be nearly correct in the case of clean, sharp sand, but would be considerably in error with a tough, tenacious soil.
This assumption gives the data by which the amount of the thrust of the earth can be computed; that is to say, this assumption furnishes the conditions from which one of the equations may be established.
530. Second Assumption. A second assumption which is always made is that the point of application of the lateral pressure of the earth is one third of the height of the wall from the bottom. The total pressure on the wall varies as some function of the height ; and it is assumed to vary as the square of the height, and that therefore the center of pressure is at a point two thirds of the depth below the top. This is equivalent to assuming that the varia- tion of the pressure in a mass of earth is the same as in a liquid, I. e., that the material is devoid of internal friction.
This assumption furnishes the second of the equations required to determine the effect of the thrust of earth against a retaining wall.
531. Third Assumption. The third equation is obtained by assuming the direction of the pressure. There are different theories based on different assumptions as to this direction.
The theories of the stability of retaining walls in most frequent use will now be stated, and the underlying assumptions and the defects of each will be pointed out.
ART. 1.] THEORETICAL FORMULAS. 341
532. Coulomb's Theory. The theory advanced by Coulomb in 1784 was the first to even approximate the actual conditions, and his method is the basis of nearly all formulas used by engineers at the present time. It has been taken up and followed out to its consequences by Prony (1802), Mayniel (1808), Fran^aise (1820), Navier (1826), Audoy and Poncelet (1840), Hagen (1853), Scheffler (1857), and Moseley, as well as a host of others, in recent times.
Coulomb assumed (1) that the line D C, Fig. 73 (page 339), is a straight line, down which the prism A C D tends to slide; (3) that the resultant pressure is applied at a point two thirds of the depth below the top; and (3) that the pressure exerted by this mass on the wall is normal to its back face, which is equivalent to neglecting the friction of the earth against the back of the wall. He decomposed the weight, W, of the prism A C D, Fig. 74, and the reaction, R, of the wall into two components respectively, parallel and perpendicular to the surface of rupture, D C. The difference of these parallel components, P^— P„, he placed equal to the prism's resistance to sliding; and ^ c assumed the latter to be equal to /j. iVj, in which Fig. 74.
/x is the co-efficient of friction. There is some prism, A CD, the pressure of which against the wall is just sufficient to cause sliding. The amount of this pressure will depend ujDon the weight, w, of a unit of volume of the backing; upon the height, h, of the wall; upon the co-efficient of friction, fx, of earth on earth; and upon the distance A D, which call x.
Under the conditions assumed, it is possible to state a value o\ R in terms of h, iv, //, and x. Coulomb assumed R to vary as x, and differentiated the value of R to find the position of the surface of rupture, D C, for a maximum pressure on the wall. This leads to the simple conclusion that the lateral pressure exerted by a bank of earth with a horizontal top is simply that due to the wedge-shaped mass included between the vertical back of the wall and a line bi- secting the angle between the vertical and the slope of repose of the material;* that is, the pressure of the earth against the wall A B,
* For an algebraic demonstration, see Moseley's Mechanics of Engineering (2(J Amer. Ed.), pp. 413-16; for a graphical demonstration, see Van Nostrand's Engineer- ing Magazine, vol. ix. p. 202, and vol. xxii. p. 267.
342 EETAINING WALLS. [CHAP. XIV.
Fig. 74, is equal to the pressure of the prism ACE sliding along a
perfectly smooth plane C E, which bisects the angle of repose, A CD. No satisfactory proof lias been given of the correctness of this
procedure by either Coulomb or any one else; and no defense has ever been made against a number of serious objections to it which have been raised. Experiments show that the lateral pressure of the prism A B C, Fig. 75, between two boards A B and A C, against A B, " is quite as much when the board A C is at the slope of repose, It} to 1, as when it is at half the angle; and there was hardly any difference
(vhether the board was horizontal, or at a slope of -| to 1, or at
any intermediate slope,"*
533. By this theory the pressure of the wedge A C D (Fig.
74) is
P = iiv h' tan= iA CD, (1)
in which w is the weight of a unit of the material to be supported, and U is the height of the wall. This thrust is assumed to act two thirds of A C, Fig. 74, below A. Or, in other words, the thrust of the prism is equivalent to the pressure of a liquid Avhose weight per unit of volume is w tan'' \ A CD.
Equating the moment of the overturning force and the moments of resistance in terms of the unknown thickness, and solving the equation, gives the thickness which the wall must have to be on the point of overturning. For example, assume that it is desired to determine the thickness, t, of a vertical rectangular wall. Eepre- sent the weight of a cubic foot of the masonry by W. Then placing the moment of the wall equal to the amount of the thrust of the earth, gives
Wilt .\t = P.\li. (2)
Solving equations (1) and (2) gives
t = h tan \A CD \/ -^ (3)
* Benj. Baker, an eminent English engineer, in a very interesting and instructive article on " The Actual Lateral Pressure of Earthwork," reprinted in Van Nostrand's Engineering Magazine, vol. xxv. pp. 333-42, 353-71, and 492-505, from Proc. of the Inst, of C. E., vol. Ixv. pp. 140-241.
ART. 1.] THEORETICAL FORMULAS. 343
Numerous tables have been computed which give, to a great number of decimal places, tlie thickness of a rectangular wall in terms of its height, the arguments being the ratio of the weights of a unit of volume of the wall and backing, and the angle of repose. Such tables are of but little practical value, as will appear presently.
534. Surcharged Walls. The rule that the plane of rupture bisects the angle between the natural slope of the earth and the back of the wall, holds good only when the top surface of the bank is horizontal and the back of the wall vertical. The formula for a surcharged wall, or for the case in which the back is not vertical, or for both combined, may be deduced * in the same general way as above; but the results for each case are too complicated for ordinary use, and each is subject to the same errors as the formula for a ver- tical wall and level top surface. There are a number of exceedingly ingenious gi'aphical solutions of the resulting equations, f
535. Reliability of Coulomb's Theory. It is generally conceded that the results obtained by this method have but little practical value. "■ Experiments and practical experience show that walls, which according to this theory are on the point of overturning, possess on the average a factor of safety of about tu'o." % One of the author's students experimented with fine shot, which appear to fulfill the fundamental assumptions of this theory, and found that the observed resistance was 1.97 times that computed by Coulomb's formula.§ The uncertainties of the fundamental assumptions and the questionableness of some of the mathematical processes are sufficient explanation of the difference between the theory and practice.
536. Weyrauch's Theory. This is the latest one, having been proposed in 18T8. It was first brought to the attention of American engineers by Professor J. A. Du Bois's translations of Winkler's " Neue Theorie des Erddruckes," and Weyrauch's paper on retain- ing walls published in "Zeitschrift fiir Baukunde," 1878, Band i. Heft 2, which translation was published in the Journal of the Frank-
* See Moseley's Mechanics of Engineering, pp. 424-26.
+ See Van Nostrand's Engineering Magazine, vol. ix. p. 304 ; and do., voL xxv. p. 35.5. For references to elaborate graphical treatises on retaining walls, see Du Bois's Graphical Statics, pp. Iv-lvi of Introduction.
X Benj. Baker in " The Actual Lateral Pressure of Earthwork." See foot-note on page 342.
§ See M. Fargusson"s Bachelor's Thesis, University of Illinois.
344
RETAIKIXG AVALLS.
[chap. XIV.
lin Institute, vol. cviii. pp. 361-87. The following presentation of this theory is drawn mainly from that article.
This theory assumes (1) that the surface of rupture is a plane, (2) that the point of application of the resultant of the lateral pressure of the earth is at a point one third of the height of the wall from the bottom, and (3) that there is no friction between the earth and the back of the wall. It is claimed that these three are the only assumptions involved in this theory, and that the direction of the resultant pressure is deduced from the fundamental rela- tions necessary for equilibrium under the conditions assumed.
The analysis to establish the equations for the amount and direc- tion of the thrust of the earth is too long and too complicated to be attempted here ; consequently, only the final equations will be given.
Ta Let E = the thrust of earth against the wall. 10 = the weight of a unit of the
earth. h = the height of the wall. a = the angle the back of wall
makes with the vertical. d = the angle which E makes with the normal to the back of the wall. 6 = the angle of the upper surface with the horizontal. /3 = the angle of the plane of rupture with the vertical. 0 = the angle of repose with the horizontal. 537. General Formulas. For a plane earth-surface, horizontal or sloping up at any angle, and the back of the wall vertical or leaning forward at any angle, the general relations are *
E =
¥ w
cos (0 — a) _{n + 1) cos a_\ 2 cos {a + 6)'
. . (*)
in which
_ i /sin (0 + ^) sin (0 — e) ~ cos {a -\- 6) cos {a — e)'
(5)
* See Howe's Retaining Walls for Earth, pp. 46, 47; and also Van Nostrand's Engineering Magazine, vol. xxii. pp. 26.5-77.
T. l.J THEORETICAL FORMULAS. 345
The value of d required in (5) can be deduced from
tan 6 - siQ(3^-6)-A^sin2(n^-e)
^ _ cos (2 or - e) + A' cos 2 {a - e)' ' ' ^^^
in which
„ cos e — V cos" e — cos* d> , ,
K= , -, ^ (7)
cos 0 • V'/
538. Horizontal Earth-surface. If the upper surface of the earth is horizontal, then 6=0, and
_ tan a ¥ w
~ sin {a +T) • ~Y'' (^)
and 6 can be found from
sin 0 sin 2 a tan d = r^ ^r- (9)
1 — sm 0 cos 2 a ^ '
If the back of the wall is vertical, a = 0 ; and equation (9) gives 6 = 0. Therefore
^=tan=(45°-|)^4^.* (10)
539. Surcharge at the Natural Slope. If the upper surface of earth has the natural slope, e = cp ; and therefore
L cos a J 2 cos [a -\- o) ^ '
and 6 is determined from
tan<? = /'°^7.<'^-^">, ^U)
1 — sm 0 sm (0 — 2 «') ^ '
If the back of the wall is vertical, a = 0, and S = <p, which shows that B acts parallel to the top surface of the earth. In this case
U=icos(p hUv (13)
* Compare with equation (1), page 343.
346 EETAINING WALLS. [CHAP. XIV.
540. The general equations for Weyrauch's theory, viz., equa- tions (4), (5), (6), and (7), have not been solved for any special case, except for e = 0, and e = <p. The reduction is very long and tedious.
541. The formulas for each of the above cases may be solved graphically,* but the explanations are too long to be given here.
542. Reliability of Weyrauch's Theory, On behalf of this theory it is claimed f that the only errors in it are those due to the neglect of the cohesion of the backing, and to assuming that the surface of rupture is a plane ; and also that '' it is free from all the objections which may be urged against all others, and can be used with confidence," These claims are not supported by the facts.
Weyrauch's theory is unquestionably subject to any errors which may be involved in the assumptions that the surface of rupture is a plane (see § 529), and that the point of application of the resultant pressure of the earth is at two thirds of the height of the wall from the top (see § 530), Second, the analysis purports to be perfectly general ; I but it is evidently inapplicable to a wall inclined toward the earth to be supported, since the formulas make the thrust of the earth increase with the backward inclination of the wall, Ic fact the theory makes no difference between a wall leaning forward and one leaning backward. For a wall inclining at the angle of repose, it gives a very great lateral pressure — see eqs. (8) and (9). Third, the mathematical process of determining the position of the Burface of rupture is at least questionable. Fourth, the theory errs on the safe side, because it neglects a vertical component of the earth pressure which is independent of friction. §
Weyrauch's theory differs from Coulomb's only in the form of the results and in the manner of deducing them ; || and hence is of no practical value.
543. Weyrauch's method of deducing the direction of the earth
* See Jour. Frank. Inst., vol. cviii. pp. 380-85; Van Nostrand's Engineering Magazine, vol. xxii. pp. 266-73 ; Howe's Retaining Walls for Earth, pp. 7-13.
+ By its authior. Prof. Wej-rauch, and also by the translator, Prof. Du Bois,— see Jour. Frank. Inst., vol. cviii. pp. -486-87.
X See Jour. Frank. Inst., vol. cviii. p. 377 ; and also Howe's Retaining Walls for Earth, p. 2.
§ In proof that such a component exists, see experiments by Siegler in Annales de* fbnts et C/iausses, reprinted in Scientific American Supplement, vol. xxiv. pp. 9724-25,
[ Van Nostrand's Engineering Magazine, vol. xxii. pp. 265-77.
^RT. 1.] THEORETICAL FORMULAS. 34?
pressure assumes that there is no friction between the eai-th and the back of the wall, or, in other words, that the angle, d, which the thrust of the earth makes with the back of the wall, does not de- pend upon the structure of the wall for its value. The formula in this form fails to agree with ordinary experience ; and hence it has been proposed * to modify the general formula by considering that the angle between the resultant pressure of the earth and the back of the wall is never less than the angle of friction between the earth and the wall. The method of doing this is as follows :
If 0' represents the co-efficient of friction between the earth and the wall, then the direction of E must make an angle with the normal to the back face of the wall equal at least to 0'. To intro- duce 0' into Professor Weyrauch's theory, it is necessary to find the value of 6 as given by his formula, and see if it is greater or less than 0'. If it is less, use the value of 0' to determine the direction of E; if greater, use the value of 6 and omit 0' altogether. The value of 0' can not be determined accurately ; but unless tlie back of the wall is exceedingly smooth, 0' will be greater than 0. If the back of the wall is rough rubble (§ 213) or is stepped, 0' will be considerably larger than 0. If the friction between the earth and the wall be neglected, i. e., if it is assumed that 0' = 0, then when rough rubble retaining walls are proportioned according to Wey- rauch's theory, they will have a factor of safety considerably larger than appears from the computations.
This modification is inconsistent with the general theory, since the fundamental equations were established for that value of d which would produce equilibrium, and the corresponding value of the thrust was deduced accordingly. It is certainly incorrect to use one direction in determining the value of the thrust and another in applying it. Further, it is not reasonable to believe that the thrust ever makes an angle with the normal to the back of the wall greater than the angle of friction, since one of the fundamental conditions of statics is that if the resultant pressure makes an angle with the normal greater than the angle of repose, motion takes place. This modification of Weyrauch's theory purports to give the relations for a state of equilibrium, and yet violates the fundamental condition necessary for equilibrium. Xeither the original theory nor the above modification of it are of any practical value.
* By Prof. Cain in Van Nostrand's Engineering Magazine, voL xxv. p. 93.
348 DETAINING WALLS. [CHAP. XIV.
544. Rankine'S Theory. There is another class of theories, which, in addition to the assumptions of § 530 and § 531, assume that the thrust of the earth makes an angle with the back of the wall equal to the angle of repose of the earth. Different writers arrive at their results in different ways, but most of them proceed trom a consideration of the conditions of equilibrium of the earth particles, and arrive at their results by integration. Of the formulas deduced in the latter way, Rankine's * are the best known. All the theories of this class have essentially the same limitations and de- fects as Coulomb's and Weyrauch's.
545. Applicability of Theoeetical Formulas. It is generally conceded that the ordinary theories — Coulomb's, Weyrauch's, and Eankine's, — types of the only ones for which there is any consider- able show of reasonableness, — are safe ; but " to assume upon theo- retical grounds a lateral thrust which practice shows to be excessive, and then compensate for it by giving no factor of safety to the wall, although the common way, is not a scientific mode of procedure." This is only another reason for the statement, already made, that theoretical investigations are of but little value in designing re- taining walls. The problem of the retaining wall is not one that admits of an exact mathematical solution; the conditions can not be expressed in algebraic formulas. Something must be assumed in any event, and it is far more simple and direct to assume the thick- ness of the wall at once than to derive the latter from equations based upon a number of uncertain assumptions.
Bear in mind that none of the above formulas apply if the back of the wall inclines towards the earth to be supported, or if the wall has a curved profile, or if the upper surface is irregular. It seems to be conceded that in these cases the surface of rupture is not a plane, and hence no theory yet proposed will apply.
In this connection it seems necessary to warn the student that not all theories for retaining walls are as nearly correct as those referred to above. Some of them, although having all the prestige of antiquity and offering the advantages of extended tables for their application, are totally valueless, being based upon unwarranted assumptions, and violating the fundamental principles of mechanics.
546. Theoretical investigations of many engineering problems which in every-day practice need not be solved with extreme accu-
* Civil Engineering, pp. 401-07.
ART. 2.] EMPIRICAL RULES. 349
racy, are useful in determining the relations of the various elements involved, and thus serve as a skeleton about which to group the results of experience ; but the preceding discussion shows that the present theories of the stability of retaining walls are not sufficiently exact to serve even as a guide for future investigations. Further- more, the stability of a retaining wall is not a purely mathematical problem. Often the wall is designed and built before the nature of the backing is known; and the variation of the backing, due to rain, frost, shock, extraneous loads, etc., can not be included in any formula.
Art. 2. Empirical Eules.
547. English Rules. The eminent English engineer Benjamin Baker, who has had large experience in this line in the construc- tion of the underground railroads of London, says, "Experience has shown that a wall [to sustain earth having a level top surface], whose thickness is one fourth of its height, and which batters 1 or 2 inches per foot on the face, possesses sufficient stability when the backing and foundation are both favorable. This allows a factor of safety of about two to cover contingencies. It has also been proved by experience that under no ordinary conditions of surcharge or heavy backing is it necessary to make a retaining wall on a solid foundation more than double the above, or one half of the height in thickness. Within these limits the engineer must vary the strength according to the conditions affecting the particular case. Outside of these limits, the structure ceases to be a retaining wall in the ordinary acceptation of the term. As a result of his own experi- ence, the author [Benj. Baker] makes the thickness of retaining walls in ground of an average character equal to one third of the height from the top of the footings.
"'Hundreds of revetments have been built by royal engineer officers in accordance with Gen. Fansliawe's rule of some fifty years ago, which was to make the thickness of a rectangular brick wall, retaining ordinary material, 24 per cent, of the height for a batter of \, 25 per cent, for ^, 26 per cent, for ^, 27 per cent, for r^, 28 per cent, for yV. 30 per cent, for ^\, and 32 per cent, for a vertical wall.' " *
548. Trautwine's Rule. Trautwinef recommends that " the
* Van Nostrand's Engineering Magazine, vol. xxv. p. 370, from Proc. Inst, of C. E.
t Engineer's Pocket-Book (Ed. 1885), p. 683.
350 RETAINING WALLS. [CHAP. XIV.
tliickness of tlie top of the footing course of a vertical or nearly vertical wall which is to sustain a backing of sand, gravel, or earth, level top surface, when the backing is deposited loosely (as when dumped from cars, carts, etc.), for railroad practice, should not be less than the following :
Wall of cut-stone, or of first-class large-ranged rubble in mortar, 35 per cent.
" " good common scabbled mortar-rubble, or brick 40 per cent.
" " well scabbled dry rubble 50 per cent.
When the backing is somewhat consolidated in horizontal layers, each of these thicknesses may be reduced; but no rule can be given for this. Since sand or gravel has no cohesion, the full dimensions as above should be used, even though the backing be deposited in layers. A mixture of sand, or earth with pebbles, paving stones, bowlders, etc., will exert a greater pressure against the wall than the materials ordinarily used for backing ; and hence when such backing has to be used, the above thicknesses should be increased, say, about ^ to | part."
549. Details of Construction. The arrangement of the foun- dation of a retaining wall is an important matter, but has already been sufficiently discussed (see Part III, and also §§ 491 and 551). It is universally admitted that a large majority — by some put at nine out of ten, and by others at ninety-nine out of a hundred — of failures of retaining walls are due to defects in the foundation.
Retaining walls are constructed of ashlar or brick, or of either ashlar or brick backed with rubble, or of rubble either with mortar or dry. As the pressure at each bed-joint is concentrated towards the face of the wall, the larger and most regular stones should be placed on the front. Occasional stones or even courses should project beyond the back of the wall, so that the backing can rest upon them, thus increasing the resistance of the wall to overturn- ing. This object is also promoted by building the back in steps. The coping should consist of large flat stones extending clear across the wall.
As a rule, the greatest thrust comes against retaining walls when the mortar is green and least able to resist it, which is a reason for preferring cement to lime mortar. If the backing is to be filled in before the mortar hardens, it should be deposited in thin, horizon- tal layers, or the wall should be supported temporarily by shores.
550. Drainage. Next to a faulty foundation, water behind the
AKT. 2.] EMPIRICAL RULES. 351
wall is the most frequent cause of the failure of retaining walls. The water not only adds to the weight of the backing material, but also softens the material and changes the angle of repose so as to greatly increase its lateral thrust. With clayey soil, or any material resting upon a stratum of clay, this action becomes of the greatest importance. To guard against the possibility of the backing's be- coming saturated with water, holes, called weepers, are left through the wall. One weep-hole, three or four inches wide and the depth of a course of masonr}^, is generally sufficient for every three or four square yards of front of the wall. When the backing is clean sand, the weep-holes will allow all the water to escape ; but if the backing is retentive of water, a vertical layer of stones or coarse gravel should be placed next to the wall to act as a drain. An ordinary drain at the back of the wall is often useful.
Waen the backing is liable to be reduced to quicksand or mud by saturation with water, and when this liability can not be removed by efficient drainage, one way of making provision to resist the additional pressure which may arise from such saturation is to cal- culate the requisite thickness of wall as if the earth were a fluid. A puddle-wall is sometimes built against the back of dock-walls to keeji out the water.
The resistance of the wall to sliding is materially increased by laying the lower courses of masonry with an inclination inward. An objection to inclining the joints, particularly in dry masonry, is that the water will enter them and be carried to the backing. This objection is sometimes met by building the face with horizon- tal courses, and inclining the courses in the back of the wall. The back of the wall for 2 or 3 feet from the top should have a batter of at least 1 inch in 1 foot, in order that the frost may lift the earth and not break the joints of the masonry.
Walls are sometimes built with both faces inclined toward the material to be supported, and sometimes with a curved profile ; but it is generally considered unwise to do either, owing to the extra expense and trouble in construction.
551. Land Ties. Retaining walls may have their stability in- creased by being tied or anchored by iron rods to vertical plates of iron or blocks of stones imbedded in a firm stratum of earth at a distance behind the wall. " The holding power, per foot of breadth, of a rectangular vertical anchoring plate, the depth of whose upper
352 RETAINING WALLS. [CHAP. XIY.
and lower edges below the surface are respectively a:, and x^, may be approximately calculated from the following formula :
„ a;„' — a-,' 4 sin 0 .^^.
H=tv-^— — '- -^, (14)
2 cos 2 0 ^ '
in which H is the holding-power of the plate in pounds per foot of breadth, w is the weight in pounds of a cubic foot of the earth, and 0 its angle of repose. The center of pressure of the plate is about two thirds of its height below its upper edge, — at which point the tie-rod should be attached.
''If the retaining wall depends on the tie-rods alone for its security against sliding forward, they should be fastened to plates on the face of the wall in the line of the resultant pressure of the earth behind the wall, that is, at one third [see § 530] of the height of the wall above its base. But if the resistance to sliding forward is to be distributed between the foundation and the tie-rods, the latter should be placed at a higher level. For example, if half the horizontal thrust is to be borne by the foundation and half by the tie-rods, the latter should be fixed to the wall at two thirds of its height above the base." *
652. Relieving Arches. In extreme cases, the pressure of the
earth may be sustained by relieving-arches. These consist of a row
Ejjroa-v.-.' ■— -• of arches having their axes and the faces of their
piers at right angles to the face of a bank of earth. There may be either a single row of them or several ^%JM^MM^\ tiers; and their front ends may be closed by a ver- ^^~^:V:! tical wall, — which then presents the appearance of a retaining wall, although the length of the arch- ways is such as to prevent the earth from abutting
Fig. 77. against it. Fig. 77 represents a vertical transverse
section of such a wall, with two tiers of relieving arches be- Jiind it.
To determine the conditions of stability of such a structure as a whole, the horizontal pressure against the vertical plane OD may be determined, and compounded with the weight of the combined mass of masonry and earth OAED, to find the resultant pressure on the foundation.
*Raakine's Civil Ens^ineering, p. 411.
CHAPTER XV.
BRIDGE ABUTMENTS.
653. General Forms. There are four forms of abutments in more or less general use. 1. A plain wall parallel to the current, shown in elevation at Fig. 78, with or without the wings ^ 1) F and BEG. The slopes may be finished with an inclined coping, as A D, or offset at each course, as B E — usually the latter. This form may appropriately be called the straight abutment. 2. The wings may be swung around into the bank at any angle, as shown (in plan) in Fig. 79. The angle 0 is usually about 30°. This form is known
A
B
B
4^^^^:~a:
D E
Fig. 79.
D E
Fig. 80.
Fig. 81.
as the loing abutment. 3. When 0 of Fig. 79 becomes 90°, we have Fig. 80, which is called the U ahutment. 4. If the wings of Fig. 80 are moved to the center of the head-wall, we get Fig. 81, which is known as the T abutment.
The abutment of an ordinary bridge has two offices to perform, viz., (1) to support one end of the bridge, and (2) to keep the earth embankment from sliding into the water. In Fig. 78, the portion D E G F serves both these purposes, while the wings A D F and BEG act only as retaining walls. In Figs. 79 and 80, the portion D E performs both offices, while the wings A D and B E are merely retaining walls. In Fig. 81 the " head " D E supports the bridge, and the ''tail," or ''stem," A B carries the train; hence the whole structure acts as a retaining wall and also supports the load. The abutment proper may fail (1) by sliding forward, (2) by bulging, or (3) by crushing; however, it is improbable that it will fail by sliding forward. Its dimensions are to be determined as for a retaining wall (Chap. XIV); but the mathematical theory of the lateral
353
354 BRIDGE ABUTMENTS. [CHAP. XV.
pressure of earth is a much less perfect guide for designing bridge abutments than it is for simple retaining Avails. The weight of the bridge helps the abutment to resist the thrust of the earth; but, on the other hand, the weight of the train on the embankment in- creases the lateral pressure against the abutment.
554. The form of the abutment to be adopted for any particular case will depend upon the locality, — whether the banks are low and flat, or steep and rocky; whether the current is swift or slow; and also upon the relative cost of earthwork and masonry. If the shore is flat, and not liable to be cut away by the current, an abutment like Fig. 78 will be sufficient and most economical. However, this form is seldom used, owing to the danger of the water's flowing along immediately behind the wall.
The form of Fig. 79 may be adopted when there is a contraction of the waterway at the bridge site, since deflecting the wing walls, above and below, slightly increases the amount of Avater that can pass. This advantage can be obtained, to some degree, with the straight abutment (Fig. 78) by thinning the wings on the front and leaving the back of the wings and abutments in one straight line. There is not only no hydraulic advantage, but there is a positive disadvantage, in increasing the deflection of the wings beyond, say, 10° or 15°. The more the wing departs from the face line as it SAvings round into the embankment, the greater its length and also the greater is the thrust upon it. The wings are not usually ex- tended to the toe, B, of the embankment slope, but stop at a height, depending upon the angle of deflection and the slope, such that the earth flowing around the end of the wall will not get into the chan- nel of the stream. It can be shoAvn mathematically that, if the toe of the earth Avhich flows around the end of the Aving is to be kept three or four feet back from the straight line through the face of the abutment, an angle of 25° to 35° is best for economy of the material in the wing walls. This angle varies slightly with the pro- portions adopted for the Aving wall and with the details of the masonry. This form of construction is objectionable, since the foot of the slope in front of the wing is liable to be washed away j but this could be remedied somewhat by rii^rapping the slope, or, better, by making the wings longer.
Fig. 78 is one extreme of Fig. 79, and Fig. 80 is the other. As the wing swings back into the embankment the thrust upon it in-
WING ABUTMENT. 355
creases, reaching its maximum at an angle of about 45°; when the wing is thrown farther back the outward thrust decreases, owing to the filling up of the slope in front of the wing. Bringing the wings perpendicular to the face of the abutment, as in Fig. 80, also de- creases the lateral pressure of the earth, owing to the intersection of the surfaces of rupture for the two sides, which is equivalent to re- moving part of the ''prism of maximum thrust." If the banks of the stream are steep, the base of the wing walls of Fig. 80 may be stepped to fit the ground, thereby saving masonry. Under these conditions, also the wing abutment. Fig. 79, can be treated in the same way; but the saving ig considerably less. When the masonry is stepped off in this way, the angle thus formed becomes the weak- est part of the masonry; but, as the masonry has a large excess of strength, there is not much probability of danger from this cause, provided the work is executed with reasonable care.
655. Fig. 81 is the most common form of abutment. For equal amounts of masonry, Aving abutments give better protection to the embankments than T abutments. The latter are more stable, be- cause the center of gravity of the masonry is farther back from the line of the face of the abutment, about which line the abutment must turn or along which it will first crush. The amount of ma- sonry in tall T abutments can be decreased by building the tail wall hollow, or by introducing arches under it. The more massive the masonry, the cheaper it can be constructed; and, for this reason, it is probable that the simple T abutment is cheaper than the U abut- ment, although the latter may have less masonry in it. On the other hand, the opportunities for inspecting the masonry during construc- tion are better with the U than with the T abutment, and hence the former is usually better built than the latter. This is an important item, since it is somewhat common for railroad masonry to fail by being shaken to pieces by the passage of trains.
556. Wing Abutment. Fig. 82 shows a common form of the wing abutment. This one is finished with stone pedestal blocks — marked B in plan, A in elevation, and C in section, — which is not always done. The thickness of pedestal blocks and the thickness of the coping under the pedestal blocks vary slightly with the span (see § 558). The height of the parapet wall, or dirt wall (the wall which keeps back the top of the embankment, marked F W in section), will vary with the style of the bridge, but should not have
356
BRIDGE ABUTMENTS.
[chap. XV.
a thickness less than four tenths of its height (see §§ 547 and 548). The bridge often rests directly upon the coping. The top dimen- sions of the abutment will depend somewhat upon the size and form of bridge : but for railroad bridges it will usually not be less than 5 ft. wide by 20 ft. long, nor more than 6 ft. by 23 ft.
u
Z
U3
<
/u "■'
t~-^<-<* , ft" 3jqjrj ijsxNSO
The usual batter is 1 in 12; sometimes 1 in 24. For heights under about 20 ft., the top dimensions and the batter determine the thickness at the bottom. For greater heights, the quite uniform
WING ABUTMENT.
357
TABLE 37.
Quantity of ]\Iasonry in Wing Abutments of the General Form
SHOWN IN Fig. 82. See g 557.
|
1 g |
Dimensions of the |
Area of Lowest i |
Masonry in one Abutment, |
|||||||
|
Is gg |
Bottom of abutment. |
Course |
EXCLUSIVE of Footing, Copings, and Pedestals.* |
|||||||
|
"3 |
is |
|||||||||
|
^2 |
o |
& |
m |
^ |
^ |
|||||
|
°5 |
■^ |
•" !X |
■6 |
tao |
be |
|||||
|
SO a 2; |
_M CO |
o a |
1/ |
^ |
a |
a |
t |
|||
|
EP |
U |
O |
3 o |
c |
p |
3 o |
||||
|
H |
J |
o |
H |
H |
O |
H |
(2 |
H |
||
|
feet. |
/ee^ |
feet. |
feet. |
sqft. |
sq.ft. |
sq.ft. |
cu. ft. |
cu. ft. |
cu.ft. |
CM. yds. |
|
5 |
22.2 |
6.8 |
18.9 |
1.51 |
165 |
316 |
709 |
640 |
230 |
57.7 |
|
6 |
22.2 |
7.0 |
20.6 |
155 |
184 |
339 |
863 |
821 |
230 |
70 8 |
|
22.3 |
7 2 |
22.3 |
ICl |
203 |
364 |
1.021 |
1.020 |
230 |
84.1 |
|
|
8 |
22.3 |
7^3 |
24.0 |
j 163 |
223 |
386 |
l.lS.'i |
1,238 |
230 |
98.1 |
|
9 |
22.4 |
7.5 |
25 7 |
168 |
243 |
411 |
1.348 |
1.475 |
S30 |
113 0 |
|
10 |
22.4 |
7.7 |
27.4 |
172 |
264 |
436 |
1,518 |
1.732 |
230 |
128.8 |
|
11 |
22.5 |
7.8 |
29.1 |
176 |
285 |
461 |
i.«92 |
2.011 |
230 |
145.6 |
|
12 |
22.5 |
8.0 |
30.8 |
180 |
306 |
486 |
1.869 |
2.310 |
2.30 |
162.6 |
|
13 |
22.5 |
8.2 |
32.5 |
185 |
328 |
513 |
2 052 |
2,632 |
230 |
182.0 |
|
14 |
22.6 |
8.3 |
34.2 |
188 |
351 |
539 |
2.23S |
2.975 |
230 |
201.6 |
|
15 |
22.6 |
8.5 |
35.9 |
192 |
374 |
566 |
2.429 |
3.341 |
230 |
222.2 |
|
16 |
22.7 |
8.7 |
37.6 |
197 |
398 |
595 |
2.623 |
3,731 |
230 |
243.8 |
|
ir |
22.7 |
8.8 |
39.4 |
200 |
422 |
622 |
2.822 |
4.144 |
230 |
266.5 |
|
18 |
22.7 |
9.0 |
41.0 |
204 |
447 |
651 |
3.024 |
4,580 |
230 |
290.1 |
|
19 |
22.8 |
9.1 |
42.8 |
207 |
472 |
679 |
3.232 |
5.041 |
230 |
314.9 |
|
20 |
22.8 |
9.3 |
44.5 |
' 212 |
497 |
709 |
3.442 |
5.526 |
230 |
340.6 |
|
21 |
22.9 |
9.5 |
46.2 |
, 217 |
523 |
740 1 |
3.657 |
6.038 |
230 |
367.5 |
|
22 |
22.9 |
9.7 |
47.9 |
222 |
550 |
772 ; |
3.876 |
6.577 |
2.30 |
395.6 |
|
23 |
23.0 |
9.8 |
49.6 |
225 |
577 |
802 |
4,100 |
7.143 |
230 |
424.9 |
|
24 |
23.0 |
10.0 |
51.3 |
230 |
604 |
834 |
4..327 |
7.735 |
230 |
455.3 |
|
25 |
23.0 |
10.2 |
53.0 |
2a5 |
633 |
868 |
4.559 |
8,354 |
230 |
486.7 |
|
26 |
23.1 |
10.3 |
.54.7 |
238 |
661 |
899 |
4.T96 |
9.002 |
230 |
519.5 |
|
27 |
23.1 |
10.5 |
56.4 |
243 |
690 |
933 |
5.036 |
9.678 |
230 |
553.4 |
|
28 |
23.2 |
10.7 |
58.1 |
248 |
720 |
968 |
5.281 |
10.384 |
230 |
588.7 |
|
29 |
23.2 |
10.8 |
59.8 |
251 |
750 |
1,001 |
5.530 |
11.120 |
230 |
625.1 |
|
30 |
23 3 |
11.0 |
61.5 |
i 256 |
780 |
1,036 |
5.784 |
11.880 |
230 |
662.9 |
|
31 |
23.3 |
11.2 |
63.2 |
261 |
811 |
1,072 |
6.041 |
12.682 |
230 |
701.9 |
|
32 |
Zi.S |
11.3 |
64.9 |
263 |
843 |
1,106 |
6,303 |
13.509 |
230 |
742.9 |
|
33 |
23.4 |
11.5 |
66.6 |
269 |
8T5 |
1,144 |
6,569 |
14,309 |
230 |
784.0 |
|
34 |
23.4 |
11.7 |
68.4 |
273 |
907 |
1,180 |
6.841 |
15.259 |
230 |
827.0 |
|
35 |
23.5 |
11.8 |
70.1 |
277 |
940 |
1,217 |
7.116 |
16.182 |
230 |
871.4 |
|
36 |
23.5 |
12.0 |
71.8 |
282 |
973 |
1,255 |
7,395 |
17.139 |
230 |
917.2 |
|
37 |
23.6 |
12 2 |
73.5 |
t 288 |
1,007 |
1.295 |
7,679 |
18,127 |
230 |
964.2 |
|
38 |
23.6 |
12.3 |
75.2 |
290 |
1.042 |
1,332 |
7,967 |
19,150 |
230 |
1,012.8 |
* Dimension stone in two pedestal blocks = 64 cu. feet.
" " '• coping of one abutment =234 " "
Total dimension stone in " " =298 "
rule is to make the thickness four tenths of the height. The amount of masonry in the abutment is computed in accordance witli this rule, although the actual quantity is usually more than that required by it. Since there is no objection to the wall's being rough, no
358 BRIDGE ABUTMEXTS. [CHAP. XV.
stones' are cut out to secure the specified thickness, and hence the actual quantity of masonry usually exceeds the amount required. The spread of the footing courses and foundation will depend, of course, upon the location.
The wings should be proportioned according to the rules for retaining walls (see §§ 547 and 548). The wings are not always pro- longed u^ntil their outer ends intersect the foot of the embankment slope; but are frequently stopped with an end height of 3 to 5 feet above the footing. The thickness of the wing wall decreases from the body of the abutment toward the tail in proportion to the height. For appearance, the top of the wing is usually made unifo^'m from head to tail, being usually from 2| to 3^ feet, according to the size of the structure. The steps should be capped with stones, not less than 1 foot thick, covering the entire step and extending under the step above not less than 1 foot.
557. Contents of Wing Abutments. The table on page 357 gives the quantities of masonry in wing abutments of the form shown in Fig. 82. Since the outlines of such structures are not simple geometrical figures, it is necessary to make more or less ap- proximations in computing the cubical contents. For exariple, in Fig. 82 the wings are stepped off to fit the slope of the emba ikment as shown; and hence the corner of each course projects beyond the earthwork. The amount of masonry in these projecting corners varies as the thickness of the courses, and for any particular abut- ment it could be found accurately; but, in computing a table of general results, it is necessary to assume some thickness for the courses. In this case the courses were assumed to be 1 foot thick. The back of the " head " was assumed to conform strictly to the batter line, although in construction it would be stepped. The dimensions of the parapet wall will vary with the thickness of the pedestal blocks used, and also with the style of the bridge. The contents of the parapet as given in the table are for the dimensions shown in Fig. 82.
Footing courses were not included in the table, since they vary with the nature of the foundation. The area of the lowest course of masonry is given, from which the areas of the footing courses and of the foundation pit may be determined. The thickness at the top and the batter, as in Fig. 82, give, for any height found in the table, a thickness of wall at the bottom of at least four tenths of its
U ABUTMENT. 359
height (see §548); for heights greater than in the table, the back of tlie wall must be stepped to keep the thickness four tenths of the height. *
558. U Abutment. Fig. S3 shows the standard plans of the Atchison, Topeka and Santa Fe R. R.f for U abutments. This is the only form of bridge abutment used on this road, except in special cases. The T abutment was once the standard, but was abandoned about fifteen years ago. J
The specifications under which these abutments are built, require as follows : '"l. Bed-plate pedestal blocks to be 2 feet thick, and placed symmetrically with regard to the plates. 2. Coping under pedestal blocks to be 18 inches thick for all spans exceeding 100 feet, 16 inches for 90 feet, and 14 inches for spans under 90 feet, — said coping to be through stones, and spaced alike from both sides of abutment. 3. Distances from front of dirt wall to front of bridge seat, and from grade line to top of bridge seat, and thickness of dirt wall, to vary for different styles and lengths of bridges. 4. Front walls to be 22 feet wide under bridge seat for all spans of 100 to 160 feet inclusive. 5. Total width of bridge seat to be 5^ feet, for all spans. 6. Steps on back of walls to be used only when necessary to keep thickness ^-^ of the height. 7. In case piling is not used, footing courses may be added to give secure foundation. 8. Length of wing walls to be determined by a slope of 1|^ to 1 at the back end of the walls — as shown by dotted line in front elevation, — thence by a slope of 1 to 1 down the. outside — as shown on side elevation — to the intersection of the ground line with face of abutment. This rule may be modified in special cases. 9. Dimensions not given on the drawing are determined by the style and length of bridge, and are to be found on special sheet."
559. Although this road is noted for the excellency of its masonry, this design could be improved by leaving a weep hole in the side walls, 2 or 3 inches wide and the depth of a course of
* In computing the contents of masonry structures, it is necessary to remember that the volume of any mass which is made up of prisms, wedges, and pyramids — or cones — must be determined by the prismoidal formula ; but if the mass is composed wholly of prisms and wedges, the contents can be correctly found by using the aver- age of the end areas.
t Published by permission of A. A. Robinson, Chief Engineer.
X Compare with § 555.
360
BEIDGE ABUTMENTS.
[chap. XV.
ddOdDO
FRONT ELEIVXTlOI*.
Fig. 83.— U Abotment.-A. T. & S. F. R. R
U ABUTilEXT.
361
TABLE 38.
Quantity of Masonky in U Abutments of the General Form SHOWN IN Fig. 83. See 8 560.
|
So |
Dimensions |
OP THE |
a |
Quantity op Masonky, ex- |
|||||||||||||
|
Bottom of the |
z. |
clusive OF |
|||||||||||||||
|
I? « oo |
Abutment. |
^ |
Coping.* |
||||||||||||||
|
Ed . 'J |
|5 |
EXABfPLES OF |
THE Method or |
||||||||||||||
|
©a |
O O |
Cm |
USING THE Table. |
||||||||||||||
|
Hg |
n |
«M |
al |
||||||||||||||
|
^ |
s a |
1! |
|||||||||||||||
|
2o |
."2 |
o |
eS |
2S |
"§■ |
o§ |
|||||||||||
|
a H |
r^ |
u |
B <! |
<o |
^iu |
||||||||||||
|
CE |
'^ |
H |
< |
H |
a |
H |
|||||||||||
|
1 feet. |
feet. |
feet. |
feet. |
feet. |
CM. ft. |
cu. ft. |
1 |
||||||||||
|
1 |
22.2 |
5.1 |
113 |
3.1 |
Ill |
6.0 |
1 |
di — — |
''''''' s |
||||||||
|
2 |
22.3 |
5.2 |
115 |
3.2 |
225 |
12.3 |
e |
S' ' - ^ ' |
' ^ z :: i ^ i i |
||||||||
|
3 |
22.5 |
5.2 |
119 |
3.2 |
342 |
18.8 |
5 |
OWt-m'^l- |
OO00Or-.X00 1 1-. |
||||||||
|
4 |
22.7 |
5.3 |
120 |
3.3 |
462 |
25.2 |
1 |
o OS c; CO «o t'. |
|||||||||
|
5 |
22.8 |
5.4 |
124 |
3.4 |
584 |
32.0 |
^ |
»»' |
CO o? |
||||||||
|
6 |
23.0 |
5.5 |
126 |
3.5 |
709 |
39.0 |
8 |
II II II II II 1 |
II II II II II II II II |
||||||||
|
7 |
23.2 |
5.6 |
129 |
3.6 |
837 |
46.0 |
S |
||||||||||
|
8 |
23.3 |
5.7 |
132 |
3.7 |
968 |
53.3 |
8 |
||||||||||
|
9 10 |
23.5 23 7 |
5.8 5.8 |
135 138 |
3.8 4.0 |
1,101 1,238 |
60.8 68.4 |
1 |
^-XX |
|||||||||
|
11 |
23.8 |
5.9 |
141 |
4.4 |
1,377 |
76.8 |
s |
00 |
|||||||||
|
12 13 |
24.0 24.2 |
6.0 6.1 |
144 147 |
4.8 5.2 |
1,520 1,665 |
86.0 96.0 |
iT |
If |
II II II II |
OB •a |
|||||||
|
14 |
24.3 |
6.2 |
150 |
5.6 |
1,814 |
106.8 |
Os |
x> |
d- - d |
>no ^ |
|||||||
|
15 |
24.5 |
^■l |
153 |
6.0 |
1,966 |
118.4 |
Oc |
"^S{? |
|||||||||
|
16 |
24.7 |
6.3 |
156 |
6.4 |
2,120 |
130.8 |
g |
o |
OJtt |
Jl"i'So-- - |
|||||||
|
17 18 |
24.8 25.0 |
6.8 7.2 |
169 180 |
6.8 7.2 |
2,288 2,478 |
144.0 158.0 |
1 |
"^ |
-X |
+4 |
'5 S Xoo ^ |
||||||
|
19 20 |
25.2 25.3 |
7.6 8.0 |
191 203 |
7.6 8.0 |
2;688 2,920 |
172.8 188.4 |
S5x |
X> o o |
|||||||||
|
21 |
25.5 |
8.4 |
214 |
8.4 |
3,174 |
204.8 |
i? |
•^o |
CJTT |
- ■, a, o •'^ c r -g |
|||||||
|
22 |
25.7 |
8.8 |
226 |
8.8 |
3,449 |
222.0 |
s |
X|j |
+4 |
||||||||
|
23 |
25.8 |
9.2 |
238 |
9.2 |
3,746 |
240.0 |
ts |
||||||||||
|
24 |
26.0 |
9.6 |
250 |
9.6 |
4,066 |
258.8 |
Ci |
||||||||||
|
25 |
26.2 |
10.0 |
262 |
10.0 |
4,408 |
278.4 |
s |
Xll^«"' |
Br eT^ ^ |
||||||||
|
26 |
26.3 |
10.4 |
274 |
10.4 |
4,772 |
298.8 |
|||||||||||
|
27 |
26.5 |
10.8 |
286 |
10.8 |
5,160 |
320.0 |
i ^ |
— ,-• C* OCO - 1 S' ' ^-H g |
|||||||||
|
28 |
26.7 |
11.2 |
299 |
11.2 |
5,570 |
342.0 |
';^ |
II — "ScSio |
01 35 a be |
||||||||
|
29 |
26.8 |
11.6 |
311 |
11.6 |
6,003 |
364.8 |
o |
= 5§-S.S |
— 2 "3 c □ ■« o- - c °-S |
||||||||
|
30 31 |
27.0 27.2 |
12.0 12.4 |
324 337 |
12.0 12.4 |
6,460 6,941 |
388.4 412.8 |
.« |
fjs' ' C taoo- .a »•« |
|||||||||
|
32 |
27.3 |
12.8 |
350 |
12.8 |
7,445 |
438.0 |
5 . |
^ §^S |
|||||||||
|
33 |
27.5 |
13.2 |
363 1 |
13.2 |
7,973 |
464.0 |
» g |
CM,. .. .. « « o- - - - - |
: s r : |
||||||||
|
34 |
27.7 |
13.6 |
376 |
13.6 |
8,526 |
490.8 |
^1 |
B |
|||||||||
|
35 |
27.8 |
14.0 |
390 |
14.0 |
9,103 |
518.4 |
Q Szmz a o |
s — - |
|||||||||
|
*F( |
jr dimen |
sions |
of copin |
J and |
pedestal |
blocks. |
|||||||||||
|
see 86 |
cond pa |
ragrai |
3h of § 55 |
«. |
« |
362
BRIDGE ABUTMENTS.
LCHAP. XV.
masonry, for each 4 or 5 square yards of wing wall. Cinders, or sand and gravel are sometimes used to fill in between the wing walls to give a better drainage, and also to decrease the lateral thrust of the earth.
560. Contents of U Abutments. The table on page 361 gives the contents of U abutments of the form shown in Fig. 83. The
|
u |
u |
u |
L 1 |
i-J |
u |
U |
l.J |
|
n |
n |
p |
r-i |
m |
r-j |
r-> |
n |
|
V |
Kj |
1 1 |
\j |
'J |
l_ J |
0 |
'J |
|
V^!9 Sietjdiii |
on^ |
J U U iJ i-J i-Jl
n n n n r. ,,,. Ij 'J u 'J 'J ^-^l'' •
T ABUTMENT
quantities were computed on the basis that the thickness of the walls was four tenths the height, except that no wall was taken of a less thickness than that given by the thickness at the top and the batter as in the drawing.
561. T Abutment. Fig. 84 shows the ordinary form of T abut-
T ABUTMENT.
363
TABLE 39.
Quantity op Masonry ix T Abutments of the General Form
SHOWN IN Fig. 84. See §562.
|
1 C a. ' *= o go |
Dimensions op the |
Quantity of Masonry, |
||||||||||
|
BOTTOii Ui THE HeAD. |
Exclusive of |
Coping. |
||||||||||
|
h ^ o |
o |
Example of the Method of |
||||||||||
|
' |
o |
using the Table. |
||||||||||
|
§5 si' |
•53 |
a o |
i |
i |
=1 |
|||||||
|
feet. |
feet. |
feet. |
feet. |
cu. ft. |
cu.ft. |
CU. ft. |
1 |
|||||
|
5 |
22.8 |
5.8 |
133 |
607 |
12.5 |
60 |
5 W m ai^ |
oT |
||||
|
6 |
23.0 |
6.0 |
138 |
743 |
18.0 |
73 |
Os II II II II II II II II II II II II II II |
|||||
|
7 |
23.2 |
6.2 |
143 |
883 |
24.5 |
84 |
C C< CO 00 0 |
■■ "2 |
||||
|
8 |
23 3 |
6.3 |
148 |
1,029 |
33.0 |
96 |
^> XaOGOO |
•^j" |
||||
|
9 1 |
23.5 |
6.5 |
153 |
1,179 |
40.5 |
108 |
•" y-XXX |
QO OC ■^ |
0 ; 1 |
|||
|
10 11 ! |
23.7 23.8 |
6.7 6.8 |
158 163 |
1,334 1,495 |
50.0 60.5 |
130 133 |
XXX |
|||||
|
13 i |
24.0 |
7.0 |
168 |
1,660 |
72.0 |
144 |
§ jxxx |
II II II |
||||
|
13 j 14 1 |
24.3 24.3 |
7.2 7.3 |
173 178 |
1,831 2,006 |
84.5 98.0 |
156 168 |
^ «_ooo ■-r ^ 0 |
IT |
CO : II • b |
|||
|
15 |
24.5 |
7.5 |
184 |
2,188 |
113.5 |
180 |
00 ^ 0 II II |
X |
OClOO |
a |
||
|
16 17 |
34.7 24.8 |
7.7 7.8 |
189 195 |
2,374 2,566 |
138.0 144.5 |
193 304 |
1^ S^ |
QCad-*' II II II .a |
\ i : S |
|||
|
18 |
25.0 |
8.0 |
200 1 |
2,763 |
163.0 |
316 |
||||||
|
19 20 i 21 |
25.2 25.3 25.5 |
8.3 8.3 8.5 |
206 311 1 317 |
2,966 3,174 3,388 |
180.5 300.0 330.5 |
338 340 252 |
"S-s oi- - X"2 II lldiiif ^>^ |
|||||
|
22 |
35.7 |
8.7 |
323 |
3,608 |
343.0 |
264 |
ilH ^ifrF"S |
|||||
|
23 |
25.8 |
8.8 |
328 |
3,833 |
264.5 |
276 |
||||||
|
24 |
26.0 |
9.0 |
234 |
4,064 |
388.0 |
288 |
||||||
|
25 |
26.2 |
9.2 |
240 |
4,301 |
313.5 |
300 |
||||||
|
26 |
26.3 |
9.3 |
246 |
4,544 |
338.0 |
312 |
||||||
|
27 |
26.5 |
9.5 |
252 |
4,793 |
364.5 |
324 |
1-3 1^0 ^i,^ =, ^ g:= |
|||||
|
28 |
26.7 |
9.7 |
258 |
5,047 |
393.0 |
336 ' |
||||||
|
29 |
26.8 |
9.8 |
264 |
5,308 |
430.5 |
348 |
||||||
|
30 |
27.0 |
10.0 |
270 |
5,575 |
450.0 |
360 |
||||||
|
31 32 33 |
27.2 27.3 27.5 |
10.2 10.3 10.5 |
276 282 289 |
5,848 6,127 6,413 |
480.5 513.0 544.5 |
372 384 396 |
S-: 81^^ Is 2 lists |
|||||
|
34 |
27.7 |
10.7 |
295 |
6,705 |
578 . 0 |
408 |
"-^ ^ ... |
|||||
|
35 |
27.8 |
10.8 |
301 |
7,003 |
613.5 |
420 |
•S3 » .fc— a |
|||||
|
Area |
5f coping |
J on 2 wi |
ngs, per f |
t. of len{ |
rth= 5 |
sq. ft. |
||||||
|
Area |
of copinj |
J on brid |
geseat |
= 138 |
e |
364 BRIDGE ABUTMENTS. [CHAP. XT-
ment. For railroad bridges the head is usually not less than 5 ft- X 20 ft., nor more than 6 ft. X 22 ft., under the coping, according to the size of the bridge. The tail wall is usually 10 or 12 ft. wide, and of such length that the foot of the slope of the embankment will just reach to the back of the head wall. The batter on the head wall is 1 to 12 or 1 to 24 all around. The tail wall is generally built vertical on the sides and the end. Notice the batter at the top of the free end of the tail wall. This is known as the "frost batter," and is to prevent the frost from dislocating the corner of the masonry. The drainage of the ballast pocket should be pro- vided for by leaving a space between the ends of two stones. Formerly the tail wall was sometimes only 7 or 8 feet wide, in which case the ties were laid directly upon the masonry without the inter- vention of ballast ; but this practice has been abandoned, as being very destructive of both rolling stock and masonry.
According to the common theories for retaining walls, T abut- ments with dimensions as above have very large factors of stability against sliding, and overturning, and crushing.
562. Contents of T Abutments. The table on page 363 gives the contents of the abutments of the form shown in Fig. 84. The height of the tail above the under side of the bridge-seat coping will vary with the thickness of the pedestal blocks, and with the style of the bridge ; and hence the table gives the quantities in the abutment below the bridge-seat coping and above the footing. The quantity of masonry above this line will vary also with the amount of ballast used. The term "wedge" in the table is used to designate that part of the tail included between the head and a vertical plane through the lower edge of the back face of the head.
563. Foundation. Usually but little difficulty is encountered in securing a foundation for bridge abutments. Frequently the foundation is shallow, and can be put down without a coffer-dam, or at most with only a light curb (see §§ 316-20). Where the ground is soft or liable to scour, a pile foundation and grillage is generally employed. For the method of doing this, see Art. 3, Chapter XI ; and for examples of this kind of foundation, see Fig. 84 (page 362), Fig. 86 (page 380), and Fig. 90 (page 386).
Where there is no danger of underwashing, and where the foun- dation will at all times be under water, the masonry may be started upon a timber platform consisting of timbers from, say, 8 to 13
QUALITY OF MASONKT. 365
mches thick, laid side by side upon sills, and covered by one or more layers of timbers or thick planks, according to the depth of the foundation and the magnitude of the structure. For an exam- ple of a foundation of this class, see Plate II. For a discussion of the method of failure by sliding on the foundation, see § 491.
564. Quality of Masonry.— Bridge abutments are built of first-class masonry (§ 307) or of second-class (§§ 209 and 312), ac- cording to the importance of the structure. See also the specifica- tions for bridge pier masonry (§§ 591-600). The coping should be composed of as large stones as practicable — not less than 13 inches thick, and 15 or 18 inches thick is better and more frequently used.
Sometimes, the bed plates of the bridge rest directly upon the coping, but usually upon a stone pedestal block (see Figs. 83 and 83), in which case small pedestals, upon which the rail stringers rest (see Fig. 90, page 386), are also generally used.
565. Cost. For data on the cost of masonry, see §§ 232-38.
CHAPTER XVI. BRIDGE PIERS.
566. The selection of the site of the bridge and the ai-rangement of the spans, altliough important in themselves, do not properly be- long to the part of the ^^I'oblem here considered ; therefore they will be discussed only briefly. The location of the bridge is usually a compromise between the interests of the railroad or highway, and of the river. On navigable streams, the location of a bridge, its height, position of piers, etc., are subject to the approval of engi- neers appointed for the purpose by the United States Government. The law requires that the bridge shall cross the main channel nearly at right angles, and that the abutments shall not contract nor the piers obstruct the water way. For the regulations governing the various streams, and also reports made on special cases, see the various annual reports of the Chief of Engineers, U. S. A., particu- larly Appendix X3 , of the Report for 1878.
The arrangement of the spans is determined mainly by the rela- tive expense for foundations, and the increased expense per linear foot of long spans. Where the piers are low and foundations easily secured, with a correspondingly light cost, short spans and an in- creased number of piers are generally economical, provided the piers do not dangerously obstruct the current or the stream is not navi- gable. On the other hand, where the cost of securing proper foun- dations is great and much difficulty is likely to be encountered, long spans and the minimum number of piers is best. Sound judgment and large experience are required in comparing and deciding upon the plan best adapted to the varying local conditions.
Within a few years it has become necessary to build bridge piers of very great height, and for economical considerations iron has been substituted for stone. The determination of the stability of such piers is wholly a question of finding the stress in frame struc- tures,— the consideration of which is foreign to our subject.
366
ART. 1.] THEORY OF STABILITY. 367
Art. 1. Theory of Stability.
567. Method of Failure. A bridge pier may fail in any one of three ways : (1) by sliding on any section on account of the ac- tion of the wind against the train, bridge, and exposed part of the pier, and of the current of the stream against the immersed part of the pier ; or (2) by overturning at any section when the moment of the' horizontal forces above the section exceeds the moment of the weight on the section ; or (3) by crushing at any section under the combined weight of the pier, the bridge, and the train. The dimensions of piers are seldom determined by the preceding condi- tions ; the dimensions required at the top (§ 58-1) for the bridge seat, together with a slight batter for appearance, generally give sufficient stability agamst sliding, overturning, and crushing. How- ever, the method of determining the stability will be briefly out- lined and illustrated by an example.
568. Stability against Sliding. Effect of the "Wind. The pressure of the wind against the truss alone is usually taken at 50 lbs. per sq. ft. against twice the vertical projection of one truss, which for well-proportioned iron trusses will average about 10 sq. ft. per linear foot of span. The pressure of the wind against the truss and train together is usually taken at 30 lbs. per sq. ft. of truss and train. The train exposes abgut 10 sq. ft. of surface per linear foot. The pressure of the wind against any other than a flat surface is not known with any certainty ; for a cylinder, it is usually assumed that the pressure is two thirds of that against its vertical projection.
569. Effect of Current. For the pressure of the current of water against an obstruction, Weisbach's Mechanics of Engineering (page 1,030 of Coxe's edition) gives the formula,
P = swhf^, ....... (1)
in which P is the pressure in pounds, s the exposed surface in sq. ft., k a co-efficient depending upon the ratio of width to length of the pier, iv the weight of a cubic foot of water, v the velocity in ft. per sec, and g the acceleration of gravity. For piers with rectangular cross section, Tc varies between 1.47 and 1.33, the first being for square piers and the latter for those 3 times as long a&
368 BRIDGE PIERS. [CHAP. XVI.
Wide ; for cylinders, h — about 0.T3. Tlie law of the variation of the velocity with depth is not certainly known; but it is probable that the velocity varies as the ordinates of an ellipse, the greatest velocity being a little below the surface. Of course, the water has its maxinnim effect when at its highest stage.
570. Effect of Ice. The pier is also liable to a horizontal press- ure due to floating ice. The formulas for impact are not applica- ble to this case. The assumption is sometimes made that the field of ice which may rest against the pier, will simply increase the sur- face exposed to the pressure of the current. The greatest pressure possible will occur when a field of ice, so large that it is not stopped by the impact, strikes the pier and plows past, crushing a channel through it equal to the greatest width of the pier. The resulting horizontal pressure is equal to the area crushed multiplied by the crushing strength of the ice. The latter varies with the tempera- ture; but since ice will move down stream in fields only when melting, we desire its minimum strength. The crushing strength of floating ice is sometimes put at 20 tons per sq. ft. (300 lbs. per sq. inch); but in computing the stability of the piers of the St. Louis steel-arch bridge, it was taken at 600 lbs. per sq. inch (43 tons per sq. ft.). According to experiments made under the author's direction,* the crushing strength of ice at 23° F., varies between 370 and 760 lbs. per sq. in.
Occasionally a gorge of ice may form between the piers, and dam the water back. The resulting horizontal pressure on a pier will then be equal to the hydrostatic pressure on the width of the pier and half the span on either side, due to the difference between the level of the water immediately above and below the bridge opening. A pier is also liable to blows from rafts, boats, etc. ; but as these can not occur simultaneously with a field of ice, and will probably be smaller than that, it will not generally be necessary to consider them.
A lateral pressure on the pier is possible, due to the earth's be- ing washed away from one side and not from the opposite. It will be on the safe side, and near enough for this purpose, to assume that this effect is equal to the pressure of a liquid whose density is the difference between that of the water and the saturated soil dis- placed. Under these conditions, the actual tendency to slide is
<= TuE Technogkapp, University of Illinois, No. 9 (1894-95), pp. 38-48.
AET. 1.] THEOKY OF STABILITY. 369
equal to the square root of the sum of the down stream forces and the lateral thrust. However, this refinement is unnecessary, par- ticularly since a pier which is reasonably safe against overturning and crushing will be amply safe against sliding.
571. Resisting Forces. The resisting force is the friction due to the combined ^Yeigllt of the train, bridge, and the part of the pier above the section considered. For the greatest refinement, it would be necessary to compute the forces tending to slide the pier for two conditions : viz., (1) with a wdnd of 50 lbs. per sq. ft. on truss and pier, in which case the weight of the train should be omitted from the resisting forces ; and (2) with a wind of 30 lbs. per sq. ft. on truss, train, and pier, in which case the weight of a train of empty box cars should be included in the resisting forces. For a table of weights of masonry, see page 200. If the water can find its way under the foundation in thin sheets, the weight of the part of the pier that is immersed in the water will be diminished by 62^ lbs. per cu. ft. by buoyancy ; but if it finds its way under any section by absorption only, then no allowance need be made for buoyancy.
The resisting force is equal to the product of the total weight and the co-efiicient of friction. For values of the co-efficient of friction, see the table on page 315. The tenacity of the mortar is usually neglected, although it is a very considerable element of strength (see § 137).
572. Stability against Overturning. The forces which tend to produce sliding also tend to produce overturning, and the forces which resist sliding also resist overturning ; hence, there remains to determine only their points of application. The stability can be determined either by moments or by resolution, as was explained for dams ; but in this case, it is easier by moments, since there are sev- eral horizontal forces, and it requires considerable work to find their resultant as demanded by the method by resolution of forces.
573. A. By Moments. By this method, it is necessary to find the arm of the forces, i. e., the perpendicular distance from the line of action of the forces to a point about which the pier tends to turn. This is the same method as that used in §§ 493-98, which see.
The center of pressure of the wind on the truss is practically at the middle of its height ; that of the wind on the train is 7 to 9 feet above the top of the rail ; and that of the wind on the pier is at the middle of the exposed part. The arm for the pressure of the
370 BRIDGE PIERS. [CHAP. XVI.
ice should be measured from high water. The center of pressure of the current is not easily determined, since the law of the varia- tion of the velocity with the depth is not known ; but it will j)roba- bly be safe to take it at one third the depth. Finally, the downward forces will usually act vertically through the center of the pier.
From these data the overturning and resisting moments can easily be computed. For equilibrium, the summation of the former must be less than the latter. The above principles will be furtlier elucidated in §§ 579-80 by an example.
574. B. By Resolution of Forces, This is the method explained in § 499 (page 320). In that case the problem was very sim- ple, since there were but two forces ; but in the present case there are several horizontal forces and also several vertical ones. Tlie first step is to find a single force which is equivalent in every respect to the combined effect of all the horizontal forces ; the second is to fiud an equivalent for all of the vertical forces ; and the third is to find the resultant of these two forces.
The horizontal distance, :c, of the point of application of the re- sultant of all the vertical forces, back from the toe of the pier, is found by the equation,
sum of the moments of the vertical forces .„.
2; ^z - '■ - , , , [liiY
sum of the vertical forces
The weight of the train and bridge act vertically through the center of the pier ; and if the pier is symmetrical, as it usually is, the weight of the pier will also act through its center. Therefore, x in equation (2) will usually be half the length of the pier.
The vertical distance, y, of the point of application of the re- sultant of all the horizontal forces above any horizontal joint is found by the equation,
sum of the moments of the horizontal forces , ,
sum of the horizontal forces
Having found x and y, as above, draw a vertical line at a distance X back from the down stream end of the pier ; on this line lay off a distance y above the horizontal joint under consideration. The point thus determined corresponds to a of Fig. 70 (page 320). Con- struct the parallelogram of forces by laying off, to any convenient
ART. 1.1 THEORY OF STABILITY. 371
scale, (1) a horizontal line equal to the sum of all the horizontal forces acting on the pier, and (2) a vertical line equal to the sum of all the vertical forces ; and complete the diagram by drawing the resultant. The stability of the pier is determined by the ratio of ^ C to N C, Fig. 70.
575. Stability against Crushing. Represent the maximum pressure by P, the total weight on the section by W, the area of the section by S, the moment of inertia of the section by /, the length of the section by /, and the overturning moment by M ; then from equation (1), page 205, we have
--| + # <^)
Tor the particular case in which the pier has a rectangular horizon- tal cross section, the above formula becomes the same as equation (18), (page 3,22,) as deduced for an element of a masonry dam.
The method of applying the above equation will be explained in § 581 by an example.
576. Example of Method of Computing Stability. Fig. 85 shows the dimensions of the channel pier of the Illinois Central E. R. bridge over the Ohio River at Cairo, 111. This pier stands be-
' tween two 523-foot spans. Its stability will now be tested by the preceding principles.
577. Stability against Sliding. We will examine the stabil- ity against sliding on the top footing course. The wind surface of the truss = 10 sq. ft. X 523 = 5,230 sq. ft. The wind pressure against the truss at 30 lbs. per sq. ft. = 30 lbs. X 5,230 =156,900 lbs. — 78 tons ; and the Avind pressure on the truss at 50 lbs. = 50 lbs. X 5,230 = 261,500 lbs. = 131 tons.
The wind pressure on train at 30 lbs. per sq. ft. = 30 lbs. X 523 X 10 = 156,900 lbs = 78 tons.
The pressure of the wind against a section of the pier 52 ft. long, is 20 lbs. X 52 X 11 = 14,560 lbs. = 7 tons.
The pressure due to the ice is found as follows: Assume the thickness to be 1 foot , and also assume the crushing strength of ice to be 200 lbs. per sq. m. =, sa}-, 15 tons per sq. ft. The pier is 16 ft. wide at the high-water line. Hence the resistance required in the pier to crush its way through a field of ice is 15 tons X 16 X 1 = 240 tons.
372
BRIDGE PIERS.
[chap. XVI.
e
TT^^ if
k.^
At' ->l
SCALE
Fig. 85.— Channel Pier, Cairo Bridok.
ART. 1.] THEORY OF STABILITY. 373
The pressure due to the current is found as follows: From
§ 569, F = swk ^— . s represents the exposed surface = 70 ft. X
19 ft. = 1,330 sq. ft., which value is equivalent to assuming that the river may scour to the top of the footing courses, k represents a co-efficient, which, if the pier were rectangular, would be about 1.4, and if the pier were cylindrical would equal about 0.73. We will assume it to be 1.1, — a trifle more than the mean of these two values, w = 62.5 lbs. per cu. ft. The surface velocity at the bridge site was measured* " when the Mississippi and the Ohio were at about the same stage," and found to be 4 miles per hour (=6 ft. per second); but as high water may occur in the Ohio at the time of moderately low water in the Mississippi, the possible maximum velocity is greater than the above, and hence we will as- sume that it is 10 ft. per second. The velocity of the water at various depths below the surface of a stream varies as the ordinate of an ellipse; but the effect of the mean velocity is approximated with sufficient accuracy for this purpose by assuming that the mean pressure is half of that due to the surface velocity. Substituting these numbers, the above equation becomes P — 1,330 X 1-1 X 62. 5 X VV — *^0- 5 ^0^^ — '^^ ^ons with sufficient accuracy. Divid- ing this by 2 to get the pressure corresponding to the mean velocity, we have the pressure of the current equal to 35 tons. Collecting the preceding results, we have:
Wind on truss, 78 tons.
" train, 78 "
" " pier, 7 "
Pressure of ice, ... 240 "
" " water, 35 "
Total force tending to slide the pier on the foot- ing = 438 tons.
578. The weight of the bridge will be assumed at 2 tons per lineal foot; and hence the total weight is 2 tons X 523 = 1,046 tons.
The weight of a train of empty cars is about 0. 5 ton per lineal
* Third Annual Report of the Illinois Society of Engineers, p. 78.
374 BRIDGE PIEES. . [CHAP. XVI.
foot; and hence the total weight of the train is 0.5 tons X 523 = 261 tons.
The amount of masonry below the higli- water line = 67,946 cu. ft.; the amount above the high water line = 24,534 cu. ft.; and hence the total masonry = 92,480 cu. ft. We will assume the weight of the masonry to be 150 lbs. per cubic foot. Then the weight of the masonry is 150 lbs. x 92,480 = 6,936 tons.
Collecting these results, we have:
Weight of the bridge, 1,046 tons.
" " " train of empty cars, 361 "
" " " masonry, 6,936 "
Total weight to resist sliding = 8,343 tons.
Sliding cannot take place, if the co-efficient of friction is equal to or greater than 438 ~ 8,243 = 0.053. For values of the co-ef- ficients of friction, see the table on page 315. In the above ex- ample, the factor of safety against sliding is at least 12 to 15.
579. Stability against Overturning. We will consider the stability against overturning about the top of tlie upper footing course. The wind on the truss = 78 tons; the arm of this force = heiy/ht of the pier (123 ft.) + ludf the depth of the tniss (30 ft.) = 153 ft.; and therefore the moment of this force = 78 tons X 153 ft. = 11,934 foot-tons.
The pressure of the wind on the train = 78 tons; and the arm of this pressure = distance from footing to top of pier (123 ft.) + distance from top of pier to top of rail (8 ft.) + distance from top df rail to center of train (8 ft.) = 139 ft. Therefore the moment oi this pressure is 78 tons X 139 ft. = 10,842 foot-tons.
The pressure of the wind against the pier is 7 tons (§ 577); the arm of this force = ^ (202 + 150) — 79 = 97 ft. ; and the moment of this force = 679 foot-tons.
The pressure of the ice is 240 tons, the arm is 70 ft., and the moment is 16,800 foot-tons.
The pressure of the water is 35 tons. The center of pressure lies somewhere between one third and one half of the depth from the top; and as the increased area at the base of the pier compen- sates in part for the decrease of velocity with the depth, we will as- sume that it is at half the depth. The arm then is 36 ft., and the moment is 35 tons x 36 ft. = 1,260 foot-tons.
AKT. 1.] THEORY OF STABILITY. 375
|
Collecting these results, we haver |
|
|
Moment of the wind on the truss, . |
U.984 foot-tons. |
|
" " " " " " train, . . |
. 10,842 |
|
" " " " " " pier, . . . |
679 |
|
" " " pressure of the ice, . . |
. 16,800 |
|
" " " " " << current. |
. 1,260 |
|
Total overturning moment |
= 41,515 foot-tons. |
580. The total weight above the joint considered is (§ 578) 8,243 tons. This force acts vertically down through the center of the pier; hence the arm is 31.5 ft., and the total moment resisting overturning is 8,243 X 31.5 = 259,654 foot-tons. The factor of safety against overturning about the top of the upper footing course is 259,654 -f- 41,515 = 6.3.
Assuming the train to be off the bridge, and that the wind pressure on the truss is 50 lbs. per sq. ft., and following the method pursued above, it is found tliat the factor of safety against over- turning these conditions is 0.4.
581. Stability against Crushing. The maximum pressure on the section will occur when the loaded train is on the bridge and all the horizontal forces are acting with their full intensity. The load when an emi)ty train is on the bridge is (§ 578) 8,243 tons. Assuming that a loaded train will weigh \\ tons per lineal foot, we must add (0.75 tons X 523 =) 392 tons to the above for the difference between a loaded and an unloaded train. Then the total direct pressure is 8,243 + 392 — 8,635 tons. The area of the sec- tion at the top of the footing course is 1,160 sq. ft. Hence, the maximum direct pressure is 8,635 -h 1,160 = 7.4 tons per sq. ft.
The moment to overturn, M, = 41,515 foot-tons. The greatest length of the section = 63 ft. The moment of inertia of the sec- tion about an axis through its center and perpendicular to its length = 287,917 (ft.). From § 575. the maximum pressure
P_JL , 1^
Substituting the above quantities in this equation gives
^ = ^-^+ fx287^917 = ^'^ + ^-^ " ^^-^ *^''' P^"" '^- ^*- Since it is highly improbable that all the forces will act at the same time with the intensity assumed in the preceding computa-
376 BKIDGE PIERS. [CHAP. XVI.
tions, we may conclude that the pressure will never exceed 11.9 tons per sq. ft. A comparison of this with the values of the com- pressive strength of masonry as given in § ^22 (page 149) shows that this pressure is entirely safe.
Since this is an unusually high pier under an unusually long span, and since the overturning and resisting moments and also the top dimensions of the pier vary with the span, we may draw the conclusion that any pier which has sufficient room on top for the bridge seat (§ 584) and ivhich has a batter of 1 in 12, or 1 in 24, is safe against any mode of failure.
582. Pressure on the Bed of the Foundation. The caisson is 70 feet long, 30 feet wide, and 50 feet high. The load on the base is equal to the weight on the top of the footing j^lus the weight of the footings plus the weight of the caisson. The weight above the footing = 8,635 tons (§ 581). Tiie weight of the footings = 1,300 sq. ft. x 4 ft. X 150 lbs. - 390 tons. The weight of the caisson = 70 ft. X 30 ft. X 50 ft. X 100 lbs. = 5,250 tons. The total weight on the bed = 8,635 + 390 + 5,250 = 14,- 275 tons. The area = 70 ft. X 30 ft. = 2,100 sq. ft. The direct pressure per unit of area — 14,275 -h 2,100 = 6.8 tons per sq. ft.
The overturning moment, M, is equal to the moment about the top of the footing (§ 581) plus the product of the sum of the hori- zontal forces and tlie distance from the footing to the base of the caisson; or, the moment about the base = 41,515 foot-tons -|- 438 tons X 54 ft. == 65,167 foot-tons. The moment of inertia, /, = ^ 30 (70)' = 857,500 (ft.). I = 70 ft. The concentrated pressure caused by the tendency to overturn is i^/_65A67^xTO_ 2 / 2 X 857,500
The caisson was sunk all the way through, and rests, on sand ; consequently the water will find its way freely under the entire foundation, thus causing buoyancy to act with its full force. This upward force of the water will be equal to the volume of the im- mersed masonry multiplied by the weight of a cubic foot of water; or the buoyancy = (67,946 + 5,200 + 105,000) X 62.4 = 5,558 tons. The lifting efEect of buoyancy is (5,558 h- 2,100 =) 2.62 tons per sq. ft.
Therefore, the total pressure is not greater than 6.8 + 2.7 — 2.6 = 6.9 tons per sq. ft.
ART. 2.] DETAILS OF COXSTKUCTIO^'. 377
The pressure would never be so much, for the following reasons : 1. There is no probability that both spans will be covered by a train of maximum weight at the same time that the maximum effects of the wind, of the current, and of the ice occur. 2. The friction on the sides of the caisson will sustain part of the load. A friction of 600 lbs. per sq. ft., which was about the amount experienced in sinking these piei's (see § 455), would decrease this pressure about 1^ tons per sq. ft.
Therefore, we conclude that the pressure on the sand will be at least as much as 6.8 — 1.5 — 2.6 = 2.7 tons per sq. ft,; and that it may possibly, but not probably, amount to 6.8 -|- 2.7 — 2.6 — 1.5 = 5.4 tons per sq. ft. The larger value was taken at the gi-eatest pos- sible one for the sake of establishing the conclusion stated in the last paragraph of § 581.
583. Oihej- BxanqjJes. At the St. Louis steel-arch bridge the greatest pressure possible on the deepest foundation (bed- rock) is 19 tons per sq. ft. The pressure at the base of the New York tower of the East Eiver suspension bridge is about 7:^ tons per sq. ft, upon a stratum of sand 2 feet thick overlying bed-rock ; and at the base of the masonry the pressure is about 11^ tons per sq. ft.* The corresponding quantities for the Brooklyn tower were a little over a ton less in each case. At the Plattsmouth bridge f the maximum pressure caused by the weight of train, bridge, and pier is 3 tons per sq. ft. At the Bismarck bridge f the pressure due to the direct weight is 3 tons per sq. ft. on clay.
Art. 2. Details of Construction.
584. Top Dimensions. The dimensions on the top will depend somewhat upon the form of the cross section of the pier, and also upon the style and span of the bridge; but, in a general way, it may be stated that, for trussed spans of 100 ft. or over, the dimensions under the coping will not be less than 5 ft. X 20 ft. ; for 250-ft. spans, 8 ft. X 30 ft.: and for 500-ft. spans, 10 ft. X 40 ft. Appar- ently 6 ft, X 22 ft. under the coping is the favorite size for spans of 100 to 200 ft.
* F. CoUingwood, assistant engineer, in Van Nostrand's Engin'g Mag., vol xyL p. 431.
t Report of Geo. S. Morison, chief engineer.
378 BRIDGE PIERS. [CHAP. XVI.
685. Bottom Dimensions. Theoretically the dimensions at the "bottom are determined by the area necessary for stability; but the top dimensions required for the bridge seat, together with a slight batter for the sake of appearance, gives suflBcient stability (§ 581). Only high piers for short spans — a combination not likely to occur in practice — are liable to fail by overturning or crushing.
586. Battee. The usual batter is 1 inch to a foot, although ^ an inch to a foot is very common. In high piers it is customary to use a batter of 1 to 24, and offset the masonry and introduce a water- table at the high-water line, so as to give an average batter of about 1 to 12. This construction very much improves the appearance, and does not add materially to the cost.
A corbel course, or "belt course," is sometimes introduced im- mediately under the coping for appearance's sake. For an exam- ple, see Fig. 85 (page 372), Fig. 87 (page 383), and Fig. 88 (page 384).
587. Ceoss Section. The up-stream end of a pier, and to a considerable extent the down-stream end also, should be rounded or pointed to serve as a cut-water to turn the current aside and to prevent the formation of whirls which act uj)on the bed of the stream around the foundation, and also to prevent shock from ice, logs, boats, etc. In some respects the semi-ellipse is the best form for the ends ; but as it is more expensive to form, the ends are usually finished to intersecting arcs of circles (see Figs. 85, 87, and Sd — pages 372, 383, and 385, respectively), or with semi-circular ends. Above the high-water line a rectangular cross section is as good as a curved outline, except possibly for appearance.
A cheaper, but not quite as efficient, construction is to form the two ends, called starlings, of two inclined planes. As seen in plan, the sides of the starlings usually make an angle of about 45° with the sides of the pier (see Fig. 90, page 386). A still cheaper construction, and the one most common for the smaller piers, is to finish the up-stream end, below the high-water line, with two in- clined planes which intersect each other in a line having a batter of from 3 to 9 inches per foot, and build the other three sides and the part of the up-stream face above the high- water line with a batter of 1 in 12 or 1 in 24. Of course the simplest construction is to make the pier rectangular in horizontal cross sections and give it the same batter on ill faces.
ART. 2.] DETAILS OF COXSTRUCTION. 379
Occasionally, for economy, piers, particularly pivot piers, are built hollow — sometimes with and sometimes without interior cross walls (see Fig. 86, page 380). The piers of the bridge across the Missouri River at Glasgow, Mo., are solid up to the high- water line, and above that each pier consists of two stone columns. The piers of the bridge over the Missouri at St. Charles, Mo., have a somewhat similar construction, except that the secondary piers are connected by a comparatively thin wall.
With piers subjected to a severe pressure from ice, it is customary to protect the edge of the nose with an angle-iron or a railroad rail.
588. Pivot Piees. These differ from the ordinary piers only in that they are circular, are larger on top, and have plumb sides. Pivot piers are about 25 to 30 feet in diameter, under the coping, for spans of 250 to 350 feet, respectively.
Fig. 86 shows the pivot pier for the Northern Pacific R. R, bridge over the Red River at Grand Forks, Dakota. The specifica- tions for the grillage were as follows: '*^ Fasten the first course of timbers together with |-inch X 20-inch drift bolts, 18 inches apart; fasten second course to first course with drift bolts of same size at every other intersection. Timbers to be laid with broken joints. Put on top course of 4-inch X 12-inch plank, nailed every 2 feet with ^''g^-inch X 8-inch boat spikes. The last course is to be thor- oughly calked with oakum."
Pivot piers are protected from the pressure of ice and from shock by boats, etc., by an ice breaker which is entirely distinct from the pier. The ice breaker is usually constructed by driving a group of 60 or 70 piles in the form of a V (the sharp end up stream), at a short distance above the pier. On and above these piles a strong timber crib-work is framed so as to form an inclined ridge up which the cakes of ice slide and break in two of their own weight. Between the ice breaker and the pier two rows of piles are driven, on which a comparatively light crib is constructed for the greater security of the pier and also for the protection of the river craft.
589. Quality of Masonry. Bridge piers are usually quarry- faced ashlar, /. e., first-class masonry (see § 207) backed with rubble. Good concrete, if made with reasonable care, is equally as good as ordinary rubble masonry, and is sometimes cheaper, — since it affords an opportunity to use up the refuse from the quarry.
380
BKIDGE PIERS.
[chap. XYI.
ART. 2.] DETAILS OF CONSTRUCTION. 381
For an illustrated description of the method of building concrete bridge piers, see Engineering News, vol. xix. pp. 443-44.
590. Specifications. The following specifications for the ma- sonry of the railroad bridge over the Missouri River near Sibley, Mo., (Octave Chanute, engineer) may be taken as an example of the best practice. *
591. General Requirements. " The stone to be used in these piers must be of what is known as the best quality of Cottonwood limestone, or other stone which, in the opinion of the engineer, is of equally good quality and in every way suitable for the purpose for which it is to be used. It must be sound and durable, free from all drys, shakes, or flaws of any kind whatever, and must be of such a character as will, in the opinion of the engineer, withstand the action of the weather. No stone of an inferior quality will be accepted or even permitted to be delivered upon the ground. The masonry in the bridge piers must be of the best and largest stones that the quarry will afford, and must be quarried in time to season against frost before being used.
" The face stones composing the starling, and the ends and sides of the river piers from the neat line about low water up for a distance of twelve (12; feet, and also the pedestal blocks of the main piers will be of Minnesota granite, or a granite of equal quality approved by the engineer.
" All masonry of the main piers shall be regular coursed ashlar of the best iescription, and must be laid in mortar of the proportions of sand and cement hereinafter specified.
" All stones must be so shaped that the bearing beds shall be parallel to the natural beds, and be prepared by dressing and hammering before they are brought on the walls, as tooling and hammering will not be allowed after the stones are in place. They are to be laid to a firm bearing on their natural beds in a full bed of mortar, without the use of chips, pinners, or levelers. No shelving projections will be allowed to extend beyond the under bed on either side. The stone and work are to be kept free from all dirt that will interfere with the adhesion of mortar. Stones must be sprinkled with water before being placed in position on the wall. In laying stone in mortar, their beds are to be so prepared that when settled down they may rest close and full on the mortar. In handling the stones care must be used not to injure the joints of those already laid; and in case a stone is moved after being set and the joint broken, it must be taken out, the mortar thoroughly cleaned from the beds, and then reset.
" Wherever the engineer shall so require, stones shall have one or two IJ- inch iron dowels passing through them and into the stones below. The holes for the dowels shall be drilled through such stones before they are put in position on the walls. After the stones are in place the holes shall be con- tinued down into the under stones at least six (6) inches ; the dowel pins will then be set in and the holes filled with neat cement grout. Cramps binding
* For specifications for first-class masonry, see § 207 ; see also Appendix I.
382 BRIDGE PIERS. [CHAP. XVI.
the several stones of a course together may be inserted when required by the engineer ; in such case they will be counter-sunk into the stones which they fasten together.
592. Face Stones. " The face stones must be accurately squared, jointed, and dressed on their beds and builds ; and the joints must be dressed back at least twelve inches (12) from the face. Face stones are to be brought to a joint, when laid, of not more than three quarters (f ) of an inch nor less than one half (i) inch. The courses shall not be less than eighteen (18) inches in thick- ness, decreasing from bottom to top of the wall. Courses to be well bonded. The face stones shall break joints at least twelve (12) inches. The face stones may be left rough, except the stones forming the starling, which must be care- fully dressed to a uniform surface. The edges of face stones shall be pitched true and full to line, and on corners of all piers a chisel draft one and a half (1+) inches must be carried up from base to the under side of the coping. No projection of more than three (3) inches from the edge of face stones will be allowed. No stone with a hollow face will be allowed in the work.
593. Stretchers. "Each stretcher shall have at least twenty (20) inches width of bed for all courses of from eighteen (18) to twenty (20) inches rise, and for all thicker courses at least as much bed as rise ; and shall have an average length of at least three and one half (3*) feet, and no stretcher shall be less than three (3) feet in length.
594. Headers. " Each header shall have a width of not less than eighteen inches (18) and shall hold, back into the heart of the wall, the size that it shows on the face. The headers shall occupy at least one fifth (^) of the whole face of the wall, and be, as nearly as practicable, evenly distributed over it, and be so placed that the headers in each course shall divide equally, or nearly so, the spaces between the headers in the course directly below. In walls over six feet (6) in thickness, the headers shall in no case be less than three and one half feet (3i) long; and in walls over nine (9) feet thick, the headers shall be equal in length to one third the thickness of the wall, except when this length of header exceeds six (6) feet, — no header over six (6) feet long being required.
595. Backing. " The headers must alternate front and back, and their binding effect be carried through the wall by intermediate stones — not less in length and thickness than the headers of the same course — laid crosswise in the interior of the wall. The stretchers and all stones in the heart of the wall shall be of the same general dimensions and proportions as the face stones, and shall have equally good bed and bond, but may have less nice vertical joints, — although no space greater than five (5) inches in width shall be left be- tween stones. All stones in the backing must be well fitted to their places, and carry the course evenly quite through the wall.
596. Coping. " The tops of the bridge piers, cap stones of the pedestals, and such other parts of the masonry as the engineer shall direct, shall be cov- ered with coping of such dimensions as prescribed. All coping stones shall be neatly bush-hammer dressed on the face, bed, top, and joints; and shall be well and carefully set on the walls, brought to one quarter (i) inch joints, and,.
ART. 3.] DETAILS OF CONSTRUCTIO]^-.
383
Fig. 87.— Shore Pier, Blair Bridgb.
384
BRIDGE PIERS.
[chap. XVI.
if required, be doweled, tlie dowels being well secured in and to the coping with grout. No coping stone shall be less than nine (9) square feet on top.
597. Pointing. " All masonry is to be pointed .so as to till the joints solid. The surface of the wall is to be scraped clean and the joints freed of all loose rnortar and refilled solid by using proper rauamiug tools. Joints must be well wet before being pointed. Mortar used in pointing is to be composed of one part Portland cement and one part sand.
598. Cement. " The cement used in the work shall be equal in quality to the best brands of Milwaukee or Louisville cement, and shall be ground so that at least 90 per cent, in weight will pass a standard sieve of 2,500 meshes to the square inch, and shall have a tensile strength — after being exposed one hour, or until set, in air, and the balance of the twenty- four hours in water not
jS'cale
J^ee-ir
(f-- - //' O"- -^
^
5:::±_
-^
30' O" J e 5' 5'^
/3' o" -J
— 7
-/<?' 6'-
FiG. 88.— Top OF Pier, Henderson Bridge.
below 60^ F. — of at least 40 pounds per square inch; and, after being exposed one day in air and six days in water, from 60 to 100 pounds per square inch.
" All cements shall be furnished by the contractor subject to approval by the engineer. The contractor shall provide a .suitable building for .storing the cement, in which the same must be placed before being tested. The engineer shall be notified of the receipt of cement at least three days before it is required for use, and the inspector may take a sample from each package for testing.
599. Mortar. " The mortar shall be composed of the above cement and ■clean, dry, sharp sand in the proportion of one part cement to two parts of ;sand by weight.* The sand and cement shall be thoroughly mixed dry, and, after adding sufficient water to render the mass plastic, shall be mixed and worked until of uniform consistency throughout.
" Mortar remaining unused so long as to have taken an initial set shall not 1)6 tised in the work.
* This is an unusual, but exact, method of specifying proportions ; they are usually stated in volumes.
.KT. U.]
DETAILS OF COXSTKUCTIOX.
385
600. Pedestal Masonry. " The pedestals shall be founded upon a bed of concrete or upon piles, as may be directed by the engineer. The masonry in the pedestals shall be of the best de- scription of coursed ashlar composed of the limestone and the mortar described above, the stones to be not less than twelve (12) inches thick, and to have horizontal beds and vertical joints on the face. When the walls do not ex- ceed three and one half (3i) feet in thickness, the headers shall run entirely through, or a single stone — square and of the proper thickness — may be used. In walls over three and one half (3i) feet in thickness, and not over seven (7) feet in thickness, headers and stretchers shall alternate, and there shall be as many headers as stretchers. The space in the interior of the walls shall be filled with a single stone cut to fit such space, and said stone shall be of the same height as the headers and stretchers of the course. In all the masonry of these pedestals the slope must be carried up by steps and in ac- cordance with the plans of the engineer. All the quoins must have hammer- dressed beds, builds, and joints, and draft corners."
601. Examples of Bridge PlEES. Fig. 85 (page 372) shows the channel pier of the Illinois Central K. E. bridge over the Ohio at Cairo, 111.
Fig. 86 (page 380) shows the pi'-ot pier of the Northern Pacific R. R. bridge over the Red River at Grand Forks, Dakota.
Fig. 87 (page 383) shows one of the two shore j^iers of the bridge over the Missouri River, near Blair, Neb.* This pier stands between two 330-ft. spans. * From the Report of Geo. 8. Morison, chief engineer of the bridge.
386
BRIDGE PIERS.
[chap, xvi*
Seise of Jiail.
wmm
;* .
n I I H I I I I I I I I I I I I I I ITTTnTTT
n n 1 1 1 1 1 1 iTTTi M 1 1 1 1 1 1 1 1 n
Fio. 80.— Pier of St. Croix River Bridge.
ART. 2.]
DETAILS OF CONSTRUCTIOX.
387
" The vertical joints are shown as they actually are in the struct- ure." The masonry is 145 i't. from top to bottom.
Fig. 88 (page 384) shows the top of the pier between two o25-ft. channel spans of the Louisville and Nashville R. R. bridge across the Ohio River at Henderson, Ky.
Fig. 89 (page 385) shows the actual arrangement of the stones in one of the courses of one of the channel piers (Fig. 85) of the Illinois Central R. R. bridge over the Ohio River, at Cairo, 111.
602. Fig. 90 (page 386) shows the river pier of the Chicago, Bur- 1 '.ngton and Northern R. R. bridge across the St. Croix River. This pier stands between a draw of 370 feet and a fixed span of 153 feet. The thickness of the courses is as follows, in order from the bottom up : Two courses, including the footing, 28 inches; two 26 inches ; one each 24, 22, 21, 19, and 17 inches ; two 15 inches ; four 14 inches ; one 13 inches ; one 12 inches ; and the coping 18 inches.
The following table gives tiie quantity of masonry in the pier and illustrates the manner of computing the contents of such structures. Notice tha^ the order in the table is the same as that in the pier ; i. e., the top line of the table relates to the uppermost masonry, etc.
TABLE 40. Contexts of the Pier shown in Fig. 90 (page 386).
Description.
Strinc-er Rests. Bridge Seats. . . Copiug
Keat Work
Ice Breaker. . . . Footing Course.
Dimensions.
3X 2.75 X 3.0' X 3.13' 3 X 2.75' X 3.0' X 1.46'. 7.0' X 24.0' X 1.5.'
i (3 X 6.5' + 8.6) 23' + (2 X 8.6' + 6.5') 25.1' |
25.17'
18.17'
(3x8.6' + 7.1') 3.8' X
(3.6'X3.6)(^- + l.o)
^(3.6' X 3.6'-f 4.3' X 4.3) 18.17'
9.6' X 29.4' X 2.33'
4.8' X4 8' X2.33'
Total = 230.39 cubic yards :
Cubic Feet.
51.6
24.1 270.0
,579.7 279.6
17.3
285.8
658.5
53.8
,220.4
603. Iron Tubular Piers. For a description of an iron tubular pier, see § 415 ; and for a description of a pier founded upon screw piles, see Engineering News, vol. xiii. pp. 210-12.
388 BRIDGE PIERS. [CHAP. XVI.
604. Timber Barrel Piers. The Chicago, Burlington and Quincy R. R. has constructed a few " barrel piers" as an experiment, the object being to reduce the cost of foundations, and also to find some cheap substitute for masonry. The barrels are cylindrical, 8 feet in diameter, and 20 to 30 feet in length. The staves are 10 inches thick, 8 inches wide on the outside, and are dressed to fit together to form a cylinder. The staves are bolted at the top and bottom to two inside rings made of I-beams, and are further held in place by strong outside hoops of iron. These caissons or barrels are sunk by excavating the soil from the inside. The bottom and top por- tions of the caisson are filled with concrete, and the intermediate portion with sand. On top of the wooden barrel, an iron frame is placed, upon which the truss rests. Two barrels constitute a pier. The advantages claimed for the wooden caissons are that they can be put in without interfering with traffic, or without loss of time in sinking by the passage of trains. Tlie objection to them is that they are not durable.
605. Contents of Bridge Piers. The table on page 380 gives the quantity of masonry in bridge piers having rectangular cross sections and such dimensions on top and batters as occur most frequently (see §§ 584-8T). The quantities in the first four columns cover most of the cases for highway and single track railway bridges; and the quantities in the last two columns are applicable to double track railway bridges. Since that portion of the pier below the water should have more or less pointed ends, and since there is likely to be an offset in the profile — particularly of high piers, — the quantities in the table (being for a rectangular cross section) are mainly useful in making preliminary estimat'^s.
The contents of piers of other dimensionsL than those in the table may be computed by the following formula : *
contents = thl+h{l + t) Ir + 1^ h^¥, in which / = the length on top under the coping,
/; = '' thickness on top under the coping, A = '' height to the under side of the coping, Jj — " batter—/, v., h = ^^ ^^ ii- The length on the bottom = I -\~2bh; and the thickness on the bottom = t -\- )lb]i. To illustrate the method of applying this for-
* See foot-note, page 3S9.
ART. 2.]
DETAILS OF CONSTRUCTION.
3S9
TABLE 41.
Contents of Bridge Piers having Rectangular Cross Section and THE same Batter on all Faces.
|
Height- |
Dimension oi |
' THE Pier ox top under |
THE Coping. |
|||
|
top OF Footing TO bottom |
5 ft. X |
20 ft. |
6 ft. X |
22 ft. |
6 ft. X |
S4ft. |
|
OF Coping. |
Batter 1 : 12 |
Batter 1 ; 24 |
Batter 1 : 13 |
Batter 1 : 24 |
Batter 1 : 12 |
Batter 1 : 24 |
|
fe€t. |
cu. yds. |
cu. yds. |
cu. yds. |
cu. yds. |
cu. yds. |
cu. yds. |
|
5 |
20.49 |
19.49 |
26.64 |
25.53 |
40.90 |
39.33 |
|
6 |
25.07 |
23.63 |
32.51 |
30.90 |
49.84 |
47.57 |
|
7 |
29.83 |
27.85 |
38.57 |
36.36 |
59.05 |
55.98 |
|
8 |
34.74 |
32.13 . |
44.81 |
41.90 |
68.52 |
64.43 |
|
9 |
39.84 |
36.52 |
51.34 |
47.55 |
78 23 |
73.04 |
|
10 |
45.09 |
40.97 |
57.86 |
53.28 |
88.23 |
81.80 |
|
11 |
50.53 |
45.51 |
64.67 |
59.09 |
98.50 |
90.68 |
|
12 |
56.14 |
50.14 |
71.69 |
65.02 |
109.02 |
99.68 |
|
13 |
61.93 |
54.85 |
78.89 |
71.02 |
119. !<3 |
108.83 |
|
14 |
67.91 |
59.64 |
86.31 |
77.13 |
130.90 |
118.09 |
|
15 |
74.07 |
64.52 |
93.93 |
83.33 |
142.25 |
127.49 |
|
16 |
80.40 |
69.48 |
101.72 |
89.61 |
! 153.88 |
137.03 |
|
17 |
86.93 |
74.53 |
109.75 |
96.00 |
105.79 |
146.69 |
|
18 |
93.65 |
79.66 , |
117.98 |
103.49 |
177.99 |
156.49 |
|
19 |
100.56 |
84.87 1 |
126.43 |
109.06 |
190.45 |
166.40 |
|
20 |
107.66 |
90.18 j |
135.07 |
115.73 |
203.22 |
176.47 |
|
21 |
114.96 |
95.57 1 |
143.94 |
132.49 |
216.28 |
186.67 |
|
22 |
122.46 |
101.06 : |
153.01 |
129.36 |
229.60 |
196.98 |
|
23 |
130.15 |
106.63 i |
163.33 |
136.34 |
243.24 |
207.45 |
|
24 |
138.04 |
112.27 ! |
171.84 |
143.39 |
257.17 |
218.05 |
|
25 |
146.14 |
118.03 |
181 . 56 |
150.53 |
271.39 |
228.79 |
|
26 |
154.45 |
123.86 |
191.53 |
157.79 |
i 285.91 |
239.65 |
|
27 |
162.96 |
129.79 |
201.74 |
165.17 |
300.74 |
250.67 |
|
28 |
171.69 |
135.81 |
212.16 |
173.63 |
315.87 |
261.82 |
|
29 |
180.62 |
141.93 |
233.79 |
180.18 |
i 331.27 |
273.09 |
|
30 |
189.77 |
148.12 |
233.68 |
187.85 |
1 347.01 |
284.51 |
|
32 |
208.72 |
160.81 |
256.15 |
203.47 |
379.43 |
307.78 |
|
34 |
228.54 |
173.86 |
279.58 |
219.52 |
413.06 |
331 . 59 |
|
36 |
249.26 |
187.30 i |
303.98 |
235.98 |
447.99 |
355.99 |
|
38 |
270.91 |
201.12 |
329.36 |
252.84 |
1 484.17 |
480.92 |
|
40 |
293.47 |
215.32 |
355.74 |
270.13 |
' 521.66 |
406.43 |
|
42 |
316.98 |
229.92 |
383.17 |
287.88 |
560.51 |
432.57 |
|
44 |
341.46 |
214.91 |
411.59 |
306.02 |
1 600.64 |
459.22 |
|
46 |
366.90 |
260.29 |
441.05 |
324.60 |
643.15 |
486.47 |
|
48 |
393.36 |
276.09 |
471.66 |
343.66 |
1 684.99 |
514.33 |
|
50 |
420.82 |
292.29 |
503.32 |
363.13 |
739.24 |
542.78 |
|
52 |
449.33 |
308.90 |
536.07 |
383.08 |
1 774.88 |
571.80 |
|
54 |
478.86 |
325.93 |
569.96 |
403.45 |
821.98 |
601.47 |
|
56 |
509.45 |
343.38 |
604.96 |
424.39 |
870.45 |
631.71 |
|
58 |
541.13 |
361.24 |
641.11 |
445.57 |
1 920.41 |
662.57 |
|
60 |
573.85 |
379.52 |
678.48 |
467.42 |
971.78 |
694.02 |
390 BRIDGE PIERS. [CHAP. XVI.
mula, assume that it is required to find the contents of a pier 4 feet thick, 20 feet long on top, and 30 feet high, having a batter on all four faces of 1 inch per foot. Then I = 20, t = 4:, b = y^, and the preceding formula becomes
contents = 4 X 20 x 30 + I'g (20 + 4) (30)= + f X ji? X (30)' =4^450 cubic feet.
606. Cost. For a general discussion of the cost of masonry, see §§ 226-38 (pp. 153-60) ; and for data on the cost of bridge pier masonry, see § 235 (p. 157).
CHAPTER XVII. CULVERTS.
Art. 1. Water Way Eequired.
607. The determination of the amount of water way required in any given case is a problem that does not admit of an exact mathe- matical solution. Although the proportioning of culverts is in a measure indeterminate, it demands an intelligent treatment. If the culvert is too small, it is liable to cause a washout, entailing possibly loss of life, interruptions of traffic, and cost of repairs. On the other hand, if the culvert is made unnecessarily large, the cost of construction is needlessly increased. Any one can make a culvert large enough ; but it is the province of the engineer tc design one of sufficient but not extravagant size.
608. The Factors. The area of water way required depends upon (1) the rate of rain-fall, (2) the kind and condition of the soil, (3) the character and inclination of the surface, (4) the condi- tion and inclination of the bed of the stream, (5) the shape of the area to be drained and the position of the branches of the stream, (6) the form of the mouth and the inclination of the bed of the culvert, and (7) whether it is j)ermissible to back the water up above the culvert, thereby causing it to discharge under a head.
1. It is the maximum rate of rain-fall during the severest storms which is required in this connection. This certainly varies greatly in different sections ; but there are almost no data to show what it is for any particular locality, since records generally give the amount per day, and rarely per hour, while the duration of the storm is seldom recorded. Further, probably the longer the series of observations, the larger will be the maximum rate recorded, since the heavier the storm the less frequent its occurrence ; and hence a record for a short period, however complete, is of but little value in this connection. Further, the severest rain-falls are of compara- tively limited extent, and hence the smaller the area, the larger the
391
392 CULVERTS. [chap. XVII.
possible maximum precipitation. Finally, the effect of the rain-fall in melting snow would have to be considered in determining the maximum amount of water for a given area.
2. The amount of water to be drained off will depend upon the permeability of the surface of the ground, which will vary greatly with the kind of soil, the degree of saturation, the condition of cultivation, the amount of vegetation, etc.
3. The rapidity with which the water will reach the water courses depends upon whether the surface is rough or smooth, steep or flat, barren or covered with vegetation, etc.
4. The rapidity with which the water will reach the culvert uepends upon whether there is a well-defined and unobstructed channel, or whether the water finds its way in a broad thin sheet. If the water course is unobstructed and has a considerable inclina- tion, the water may arrive at the culvert nearly as rapidly as it falls ; but if the channel is obstructed, the water may be much longer in passing the culvert than in falling.
5. Of course, the water way depends upon the amount of area to be drained ; but in many cases the shape of this area and the position of the branches of the stream are of more importance than the amount of the territory. For example, if the area is long and narrow, the water from the lower portion may pass through the culvert before that from the upper end arrives ; or, on the other hand, if the upper end of the area is steeper than the loAver, the water from the former may arrive simultaneously with that from the latter. Again, if the lower p)art of the area is better supplied with branches than the upper portion, the water from the former will be carried past the culvert before the arrival of that from tlie latter; or, on the other hand, if the upper portion is better supplied with branch water courses than the lower, the water from tlie whole area may arrive at the culvert at nearly the same time. In large areas the shape of the area and the position of the water -*,ourses are very important considerations.
6. The efficiency of a culvert may be materially increased by sc arranging the upper end that the water may enter it without being retarded (see § 639). The discharging capacity of a culvert can also be increased by increasing the inclination of its bed, provided the channel below will allow the water to flow away freely after
ART. 1.] WATER WAY REQUIRED. di)'6
having passed the culvert. The last, although very important, is frequently overlooked.
7. The discharging capacity of a culvert can be greatly increased by allowing the water to dam up above it. A culvert will discharge twice as much under a head of 4 feet as under a head of 1 foot. This can only safely be done with a well-constructed culvert.
609. Formulas. The determination of the values of the differ- ent factors entering into the problem is almost wholly a matter of judgment. An estimate for any one of the above factors is liable to be in error from 100 to 200 per cent., or even more, and of coui'se any result deduced from such data must be very uncertain. Fortunately, mathematical exactness is not required by the jiroblem nor warranted by the data. The question is not one of 10 or 20 per cent, of increase; for if a 3-foot pipe is insufficient, a 13-foot pipe will probably be the next size — an increase of 225 per cent., — and if aG-foot arch culvert is too small, an 8-foot will be used — an increase of 180 per cent. The real question is whether a 2-foot pipe or an 8-foot arch culvert is needed.
Numerous empirical formulas have been i^roposed for this and similar problems ; * but at best they are all only approximate, since no formula can give accurate results with inaccurate data. The several formulas, when applied to the same problem, give very discordant results, owing (1) to the sources of error already re- ferred to and (2) to the formulas' having been deduced for localities differing widely in the essential characteristics upon which the results depend. For example, a formula deduced for adi-y climate, as India, is wholly inapplicable to a humid and swampy region, as Florida ; and a formula deduced from an agricultural region is inapplicable in a city.
However, an approximate formula, if simple and easily applied, may be valuable as a nucleus about which to group the results of personal experience. Such a formula is to be employed more as a guide to the judgment than as a working rule; and its form, and also the value of the constants in it, should be changed as subse- quent experience seems to indicate. With this use in view, a few formulas will be referred to briefly.
There are two classes of these formulas, one of which purports
* For a general note on empirical formulas, see § .S&i.
394 CULVERTS. [chap. xtii.
to give the quantity of water to be discharged per unit of drainage area and the other the area of the water way in terms of the area of the territory to be drained. The former gives the amount of water supposed to reach the culvert; and the area, slope, form, etc., of the culvert must be adjusted to allow this amount of water to pass. There are no reliable data by which to determine the discharging capacity of a culvert of any given form, and hence the use of the formulas of the first class adds complication without securing any compensating reliability. Most of the formulas in common use for proportioning water ways belong to this class. Such formulas will not be considered here.
The two following formulas belong to the second class.
610. Myer's Formula. Of the formulas giving a relation be- tween the area of water way and the area to be drained, Myer's is the one most frequently used. It is
A7'ea of water way, in square feet = C \^ Drainage area, in acres,
in which C is a variable co-eflficient to be assigned. For slightly rolling prairie, C is usually taken at 1; for hilly ground at 1.5; and for mountainous and rocky ground at 4. For most localities, at least, this formula gives too large results for small drainage areas. For example, according to the formula, a culvert having a watei way of one square foot will carry the water from a single acre only. Further, if the preponderance of the testimony of the formulas for the quantity of water reaching the culvert from a given area can be relied upon, the area of water way increases more rapidly than the square root of the drainage area as required by this formula. Hence, it appears that neither the constants nor the form of this formula were correctly chosen; and, consequently, for small drainage areas it gives the area of waterway too great, and for large drain- age areas too small.
611. Talbot's Formula. Prof. A. N. Talbot proposed the fol- lowing formula, '^more as a guide to the judgment than as a work- ing rule :" *
Area of water way, in square feet = C \/ {Drainage area, in axyresf,
in which C is a variable co-efRcient. Data from various States gave values for C as follows: ''For steep and rocky ground, C varies
* Selected Papers of the Civil Engineers' Club of the University of Illinois. No, 2, pp. 14-17.
AKT. 1.] "WATER WAY REQUIRED. SS'o
from f to 1. For rolling agricultural country subject to floods at times of melting of snow, and with the length of valley three or four times its width, C is about -^; and if the stream is longer in proportion to the area, decrease C. In districts not affected by accumulated snow, and where the length of the valley is several times the width, \ or \, or even less, may be used. C should be increased for steep side slopes, especially if the upper part of the valley has a much greater fall than the channel at the culvert."
The author has tested the above formula by numerous culverts and small bridges in a small city and also by culverts under high- ways in the country (all slightly rolling prairie), and finds that it agrees fairly well with the exjDcrience of fifteen to twenty years. In these tests, it was found that water ways proportioned by this formula will probably be slightly flooded, and consequently be com- pelled to discharge under a small head, once every four or five years.
612. In both of the preceding formulas it will be noticed that the large range of the "■ constant " C affords ample opportunity for the exercise of good judgment, and makes the results obtained by the formulas almost wholly a matter of opinion.
613. Practical Method. Valuable data on the proper size of any particular culvert may be obtained (1) by observing the existing openings on the same stream, (2) by measuring — preferably at time of high water — a cross section of the stream at some narrow place, and (3) by determining the height of high water as indicated by drift and the evidence of the inliabitants of the neighborhood. With these data and a careful consideration of the various matters referred to in § 608, it is possible to determine the proper area of water way with a reasonable degree of accuracy.
Ordinarily it is wise to take into account a probable increase of flow as the country becomes better improved. However, in con- structing any structure, it is not wise to make it absolutely safe against every possible contingency that may arise, for the expen- diture necessitated by such a course would be a ruinous and un- justifiable extravagance. Washouts can not be jorevented altogether, nor their liability reduced to a minimum, without an unreasonable expenditure. It has been said — and within reasonable limits it is true — that if some of a number of culverts are not carried away
396 CULYERTS. [chap. XVII.
each year, tliey are not '^\'ell designed; that is to say, it is only a question of time when a properly proportioned culvert will perish in some excessive flood. It is easy to make a culvert large enough to be safe under all circumstances, but the difference in cost be- tween such a structure and one that would be reasonably safe would probably much more than overbalance the losses from the washing out of an occasional culvert. It is seldom justifiable to provide for all that may possibly happen in the course of fifty or one hundred years. One dollar at 5 per cent, compound interest will amount to $1147 in 50 years and to $131.50 in 100 years. Of course, the question is not purely one of finance, but also one of safety to human life; but even then it logically follows that, unless the engineer is prej^ared to s^^end $131.50 to avoid a given danger now, he is not justified in spending $1 to avoid a similar danger 100 years hence. This phase of the problem is very important, but is foreign to the subject of this volume.
614. In the construction of a new railroad, considerations of first cost, time, and a lack of knowledge of the amount of future traffic as well as ignorance of the physical features of the country, usually require that temjDorary structures be first put in, to be re- placed by permanent ones later. In the mean time an incidental but very important duty of the engineer is to make a careful study of the requirement of the permanent structures which will ulti- mately replace the temporary ones. The high-water mark of streams and the effect of floods, even in water courses ordinarily dry, should be recorded. With these data the proper j^^'oportioning of the water way of the permanent structures becomes a comparatively easy task. Upon the judgment and ability displayed in this depends most of the economical value of the improvements; for, as the road will have fixed or standard plans for culverts, abutments, piers, etc., the supervision of the construction will not be difficult.
Art. 2. Box axd Pipe Culverts.
615. Stone Box Culvert. This culvert consists of vertical side walls of masonry with flag stones on top from one wall to the other. Masonry box culverts were constructed much more frequently for- merly than at the present time. The lack of suitable stone in many parts of the West led to the adoption of vitrified pipes (§ 627) and iron pipes (§ 631) instead of masonry box culverts. However, in
ART. 2.] STOXE BOX CULVERTS. 397
many localities they are built frequently enough to warrant a brief discussion here.
616. Foundation. A common foundation for masonry box cul- verts is a stone pavement (§ 219) under the entire culvert, upon which the side walls rest (see Fig. 91«). This is not good practice ; for, since the paving is liable to be washed out, it endangers the
Fig. 91a. Fig. 916.
wall. The tendency of the pavement to undermine may be dimin- ished (1) by driving sheet piling or by setting deep curb-stones at both ends, or (2) by extending the paving to a considerable distance beyond bo+h ends. The first is the better method ; but usually these devices only postpone, and do not prevent, final failure. The water is nearly certain to carry the soil away from under the pave- ment, even if the curb-vstones or sheet piles remain intact.
Sometimes culvert foundations are paved by laying large stones flatwise. This practice is no better than ordinary stone paving, un- less the flags are large enough to extend under both walls ; but stones large enough for this can seldom be obtained.
A much better method is to give each side wall an independen/ foundation and to pave between the walls only (see Fig. 915). Ak important advantage of this method is that each wall can be placed separately, which facilitates the keeping of the water away from the foundation pit. Indeed, if the foundations are deep, or if there is not much current, the paving may be entirely omitted. If the cur- rent is only moderate, it is sufficient to build in, at each end of the culvert, between the ends of the side walls with solid masonry up to the bed of the stream ; but if the culvert is long, it is wtse to build one or more intermediate cross walls also. If the current is strong, the cross walls at the ends should be carried down deep, and the space between the side walls should be paved with large stones closely set and deeply bedded. The best job possible is se- cured by setting the paving in cement mortar. In this connection, see Figs. 94, 95, and 96 (pages 403, 404, and 406).
398
CULVERTS.
[CHAP. xvn»
The side walls and the cross walls (particularly at the end of the culvert) should have their foundations below the effect of frost.
617. End Walls. The ends of box culverts are usually finished either with a plane wall perpendicular to the axis of the culvert as shown in Fig. 95 (page 404), or by stepping the ends off as shown in Fig. 92. Either form is liable to become clogged and to have its effectiveness greatly decreased, and probably its own existence endangered, by drift collected at its upper end. This danger is
jELevaiion
'^^-"■■'^>ai ' ^_ -1^. i^'tf-'-.^.^.i-M-^i
' Lon^itudinaL ' Section.
Lion^itadinai Section
JPlan
Fig. 92.
Fig. 93.
considerably decreased by extending the side walls at the upper end as shown in Fig. 93 and in Fig. 94 (page 403). If the mouth of the culvert should become stopped with drift, the open top is a well into which the water may fall. In this way the full discharging capacity of the culvert can be maintained. The lower end may be stepped as shown in Fig. 92.
The wing walls may be made thinner at the outer end, thus pro- ducing to a small degree the same effect as is obtained in splaying the wings of arch culverts (see §§ 638-39).
In this connection, see also Fig. 96 (page 406).
618. Cover Stones. To deduce a relationship between the thick- ness of the cover stones and the load to be supported, let
T = the thickness, in inches ; S = the span, in feet ;
H = the height of bank, in feet, above the top of the culvert ; R = the modulus of rupture, in pounds per sqiiare inch ; C = the co-eflficient of transverse strength (§ 15) ; W = the total weight of the earth over the cover stone, iti pounds.
ART. 2.] STONE BOX CULVERTS. 39&
For simplicity, consider a section of the culvert only a foot long.
The cover stones are in the condition of a beam supported at the ends and loaded uniformly. By the principles of the resistance of materials, one eighth of the uniform load mnltijMed hy the span is equal to one sixth of the continued product of the modulus of rup- ture, the breadth, and the square of the thickness. Expressing this in symbols as above, and reducing, gives
T^VV-^ (1)
8 R
Ordinarily, earth weighs from 80 to 100 lbs. per cu. ft., but for convenience we will assume it at 100 lbs. per cu. ft., which is on the safe side ; then W = 100 US. The maximum moving load for railroad bridges may be taken at, say, 2 tons per foot of track.* This is distributed over at least 8 square feet ; and hence the live load is equal to one quarter of a ton, or 500 pounds, per square foot, i. e. the live load is equal to an embankment 5 feet high. Therefore, the maximum live load — a locomotive — is provided for by adding 5 feet to the actual height of the embankment. The table on page 12 shows that for limestone R = 1,500. Substituting these values in equation (1), above, gives for limestone
T = 0.20 S VH+T, (2)
By substituting the corresponding value of R from the table on page 12, we have for sandstone
T=0.2bSVH+b, (3)
For highways, it is sufficiently exact to drop the 5 under the radical, i. e., to neglect the live load ; and equation (1) then becomes for limestone
and for sandstone
T=0.20SVH, (4)
T= 0.25 SVH. (5)
The preceding formulas give the thickness which a stone of average quality must have to be on the point of breaking; and hence
400 CULVERTS, [chap. XVIL
in applying them it will be necessary to allow a margin for safety, either by selecting the stone or by increasing the computed thick- ness. If reasonable care is used in selecting the stones, it is probably safe to double the thickness found as above. To allow for any given factor of safety, multiply the thickness found by applying the above formulas by the square root of the factor of safety. Thus, to allow for a factor of 4, multiply the thickness found as above by 2 ; for a factor of G, multiply by 2| ; and for a factor of 9, multiply by 3.
-619. The thickness of the cover stones does not, however, de- pend alone upon the depth of the earth, the live load, and the span.
In the first place, the pressure on the cover stone does not vary directly as the depth of the earth above it. (a) The earth itself acts more or less as a beam to support part, at least, of the weight over the opening. That earth may act thus is proven by the fact that an excavation can be carried horizontally into an embankment or side hill without supporting the roof. The beam strength of the earth increases with the compactness and the tenacity of the soil and with the square of the height of the embankment above the roof. This effect would be zero with clean sand ; but, owing to the nature of that material, it would seldom be employed for filling over a culvert. Hence, under ordinary conditions, part of the load is supported by the beam strength of the earth itself. Therefore, a low embankment may produce a greater strain in the cover than a much higher one. (b) The prism of earth directly over the culvert will be partially supported by the adjacent soil ; that is to say, the particles of earth directly above the culvert will act more or less as arches resting upon the earth at the sides of the culvert, thus par- tially relieving the cover stones. This effect would be greater with sharp sand than with clay, but would be entirely destroyed by shock, as of passing trains, (c) The stones at the center of the culvert would be relieved of part of their load by an action similar to that mentioned above, whereby the weight over the center of the culvert is transferred towards its ends. However, the relief caused by this -action is but slight.
In the second place, the pressure due to the live load is trans- nnitted downward in diverging lines, thus distributing the weight over a considerably larger area than that assumed in deducing equa- tions (2) and (3) above.
In the third place, the cover must be thick enough to resist the
ART. 2. J STONE BOX CULVEETS. iOl
effect of frost, as well as to support the earth and live load above it. The freezing, and consequent expansion, of the earth is a force tending directly to break the cover stones. That this is an impor- tant consideration is proved by the fact that these stones break near the ends of culverts as frequently as near the middle, although the weight to be supported is greater at the latter place.
620. It is impossible to compute, even approximately, the effect of the preceding factors ; but experience shows that the thickness is indejDcudent of the height of the embankment, provided there is sufficient earth over the cover stones to prevent serious shock, — say 3 feet for railroads and 1 to 2 feet for higliways.
The thickness employed on the raih'oads in States along the fortieth parallel of latitude is generally about as follows, irrespec- tive of the height of the bank or of whether the cover is limestone or sandstone :
Span of Culvert. Thickness of Coyer.
2 feet 10 inches.
3 feet, 13 inches.
4 feet 15 inches.
On the Canadian Pacific R. R., the minimum thickness of cover stones for spans of 3 feet is 16 inches, and under 3 feet, 14 inches.
621. Quality of Masonry. Box culverts are usually built of rubble masonry (§ 213) laid in cement mortar. Formerly they were often built of dry rubble, except for 3 or 4 feet at each end, which was laid in mortar. It is now generally held that box culverts should be so built that they may discharge under a head without damage. It is usually specified that the cover stones must have a solid, well-leveled bearing on the side walls of not less than 15 inches. The most careful constructors close the joints between the cover stones by bedding spalls in mortar over them.
622. Specifications.* All stone box culverts shall have a water way at least 24 X 3 feet. The side walls shall not be less than two feet (2') thick, and shall be built of sound, durable stones not less than six inches (6") thick, laid in cement mortar [usually 1 part Rosendale cement to 2 parts sand]. The walls must be laid in true horizontal courses, but in case the thickness of the course is greater than 12 inches (12"), occasionally two stones may be used to make up the thickness. The walls must be laid so as to be thoroughly bonded, and at least one fourth of the area of each course must be headers going en-
* Pennsylvania Kaikoad.
40;<5 CULVERTS. [CHAP, XVII.
tirely through the wall. The top course must have one half its area of through stones, and the remainder of this course must consist of stone going at least one half of the way across the wall from the Inside face. The face stones of each course must be dressed to a straight edge, and pitched off to a true line. All of the coping stones of head walls must be throughs, and must have the upper surface hammer-dressed to a straight edge, and the face pitched off to a line with margin draft. Cover stones shall have a thickness of at least twelve inches (13") for opening of three feet (3), and at least 14 inches (14") for opening of four feet (4) ; and must be carefully selected, and must be of such length as to have a bearing of at least one foot (1') on either wall.
The beds and vertical joints of the face stones for a distance of S:ix inches (6") from the face of the wall shall be so dressed as to require a mortar joint not thicker than three fourths of an inch (f "). Joints between the cov- ering stones must be not wider than three fourths of an inch (f ';, and the bearing surface of cover stones upon side walls must be so dressed as to require not more than a one-inch (1") mortar joint.
The paving shall consist of flat stones, set on edge, at right angles with the line of the culvert, not less than twelve inches (13") deep, and shall be laid in cement mortar and grouted.
623. Examples. The box culvert shown in Fig. 94 (page 403), is presented as being on the whole the best (see § 617). The table accompanying the diagram gives the various dimensions of, and also quantities of masonry in, box culverts for different openings. The former data and the diagrams are ample for the construction of any box culvert ; while the latter data will be useful in making esti- mates of cost (§ 626). In the headings of the colums under " Size of the Openings," the first number is the span of the culvert, and the second is the clear height of water way. The quantities of masonry in the table were computed for a cross wall at each end of the culverts, of the section shown in Fig. 94 ; but in many cases, this should be 3 feet deep instead of 2, as shown. In using the table this correction is easily applied.
624. The box culvert shown in Fig. 95 is the one employed in the construction of the ''West Shore R. R."— New York City to Buffalo. The data in the table accompanying the diagram give tlie dimensions and quantities of masonry of various sizes. In the head- ings under " Size of the Openings," the first number is the span of the opening and the second is its height.
Box culverts of the general form shown in Fig. 95 are sometimes built double ; i. e., two culverts are built side by side in such a manner as to have one side wall in common. The following table
iRT. 2.]
STOKE BOX CULVERTS.
403
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404
CULVERTS.
[chap. XYII.
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ART. 2.]
STONE BOX CULVERTS.
405
gives the dimensions and quantities for such box culverts. The dimensions not given in the following table are the same as in the table accompanying Fig. 95.
TABLE 44. Dimensions and Contents of Double Box Culverts.
Items.
Dimensions:
End wall, length of
Center wall, thickness of
Contents:
Masonry in two end walls, in cu. yds
Masonry in trunk, per font of lengtli from in- side to inside of end walls, in cii. yds. Paving in trunk, per foot of lengtli from inside to inside of end walls, in cu. yds
Size oi' the Opening.
2X2J feet.
IC 6" •.>' 0"
13.16
0.864 0.407
ajx3
feet.
20' 0" 2' 0"
10.18 0.982 0.444
2J X 3J feet.
20' 0" 2' 0'^
21.50 1 .222
0.481
3X4 feet.
23' 0''
2' u"
32.18 1.778 0.592
4X5 feet.
30' 3' 3' 0-
53.25 2.565
0,703
The standard double box culvert employed in the construction of the Canadian Pacific E. E. differed from the form described above in having (1) shorter end walls, and wiugs at an angle of 30° with the axis of the culvert, and (2) a triangular cut-water at the upper end of the division wall.
625. The culvert shown in Fig. 96 is the standard on the Inter- colonial Eailway of Canada, and is very substantially constructed.
626. Cost. With the data accompanying Figs. 94 and 95 (pages 403 and 404), and the table of cost of masonry on page 160, it is an easy matter to make an estimate of the cost of a box culvert. For example, assume that it is proposed to build a culvert 30 feet long — out to out of culvert proper — having a water way 3 feet wide and 4 feet high, and that estimates of the cost of the general forms shown in Fig. 94 and also of that of Fig. 95 are desired.
Estimates for a 3 X 4/i!. Box Culvert oftJie General Form, shown in Fi^. 94,
Masonry in 2 end walls— 16.88 cu. yds ® S3.50 per cu. yd. = $59.08
" 25 feet of trunk (1 444x25=) 36.10 cu. yds. @ S3.50 " " = 126 35 Paving "25 " " " (0.111x25=) 2.78 " " @ $2.00 " " = 5.55
Total cost $190.98
Estimates for a 3 X 4/if. Box Culvert of the General Form shown in Fig. 95.
Masonry in 2 end walls— 24.20 cu. yds @ $3 ,50 per cu. yd. = $84.70
" 24 feet of trunk (24 x 1.148=) 27..55 cu. yds. @, $3 50 " " = 96.43 Paving "24 " " " (24x0.370=) 8.88 " " (^ $2.00 " " = 17.76
Total cost $198.89
406
CULVERTS.
[chap. XVIL
U 4JtJ M
A.KT. 2.] VITRIFIED PIPE CULVERTS. 407
If the price for the masonry does not include the expense for th,e necessary excavation, the above estimates should be increased by tJie cost of excavation, which will vary with the situation of the culvert.
To make a comparison of the relative cost of the two types of culverts just mentioned, we may proceed as follows : The cost per foot of the trunk of a 3 X 4 culvert of the form shown in Fig. 94 is (1.444 cu. yds. of masonry @ $3.50 j^^us 0.111 cu. yds. of paving @ $2.00) $5.28; and the corresponding cost for Fig. 95 is (1.148 cu. yds. of masonry @ $3.50 ji^/ms 0.370 cu. yds. of paving @ $2.00) $4.76. The difference in cost per foot is ($5.28 -$4.76) $0.52 in favor of Fig. 95. The cost of the end walls for Fig. 94 is (16.88 cu. yds. @ $3.50) $59.08; and the corresponding cost for Fig. 95 is (24.20 cu. yds. @ $3.50) $84.70. The difference is $25.62 in favor of Fig. 94. Since in the former the cross wall extends but 2 feet below the floor of the culvert, while in the latter the end walls extend 3 feet, the difference in cost should be decreased by the cost of the difference of the foundations. If the cross Avails of Fig. 94 be carried down another foot, the amount of masonry will be increased 2 cu. yds. and the cost $7.00; and the difference in cost of the end walls will be ($25.62 — $7.00) $18.62 in favor of Fig. 94. Under these conditions, for a culvert 40 feet long, the two types will cost the same; for lengths less than 40 feet Fig. 94 is the cheaper, and for lengths greater than 40 feet Fig. 95 is the cheaper. If the end walls of Fig. 95 are carried down only 2 feet, the amount of masonry will be decreased by 3.4 cu. yds. and the cost by $11.90; and then the difference of cost will be ($25.62 — $11.90) $13.72. Under this condition, for a culvert 30 feet long, the two types will cost the same; for lengths less than 30 feet Fig. 94 is the cheaper, and for lengths greater than 30 feet Fig. 95 is the cheaper. We may conclude, therefore, that for lengths under 35 or 40 feet the type shown in Fig. 94 is a little cheaper, while for greater lengths than 35 or 40 feet that in Fig. 95 is slightly cheaper. For the smallest size the length of equal cost is about 10 feet.
There is no material difference in the first cost of the two types; but the culvert shown in Fig. 94 is the more efficient.
627. Vitrified Pipe Culverts. During the past lew years vitrified sewer pipes have been extensively employed for small cul-
408 CULVERTS. [chap. XYIl
verts under both highways and railroads. The pipe generally employed for this purpose is that known to the trade as culvert pipe or "extra heavy" or "double strength" sewer pipe, which is 20 to 40 per cent, (varying with the maker and the size) heavier than the quality ordinarily employed for sewers.
Apparently the heavier pipe is used on the supposition that the lighter is not strong enough for culverts. In most cases, at least, tills is an erroneous assumption. 1. AVith the same depth of earth over the pipe, there is but little more pressure on the pipe when used as a culvert than when employed in a sewer. At most, tlie difference of pressure is that due to the live load, which can not exceed the weight of an additional 5 feet of earth (see § 618), and will generally be much less (see the second paragraph of § 619). 2. Experience demonstrates that the lighter pipes are not deficient in strength when used in sewers, however deep they are laid. According to experiments made by bedding the lower half of the pipe in sand and applying a pressure along a comparcdivcly narrow urea, the average crushing strength of ordinary sewer pipe was 2,400 lbs. per sq. ft. of horizontal section, and for culvert pipe 12,000 lbs. per sq. ft.* If the pressure had been applied more .nearly as in actual practice, the pipes would have borne consider- ably more. The first of the above results is equal to the weight of 24 feet of earth, and the second to that of 120 feet, although actual embankments of these heights would not give anything like the above pressures (see § 619).
There is a little difference between culverts and sewers in the exposure to frost; but no danger need be apprehended from this cause, provided the culverts are so constructed that the water is carried away from the lower end, since ordinary soft drain tile are not in the least injured by the expansion of the frost in the earth around them.
628. Construction. In laying the pipe, the bottom of the trench should be rounded out to fit the lower half of the body of the pipe, with proper depressions for the sockets. If the ground is soft or sandy, the earth should be rammed carefully, but solidly, io. and around the lower part of the pipe. On railways, three feet of earth between the top of the pipe and the bottom of the tie has been found sufficient. On highways pipes have stood from 10 to 15 years under heavy loads with only 8 to 12 inches of earth over * For additional data, see Note 7, page 547.
ART. 2.]
VITRIFIED PIPE CULVERTS.
409
them; but as a rule it is not wise to lay them with less than 12 to 18 inches of earth covering.
In many cases — perhaps in most — the joints are not calked. If this is not done, there is liability of the water's being forced out at the Joints and washing away the soil from around the pipe. Even if the danger is not very imminent, the joints of the larger pipes, at least, should be calked with hydraulic cement, since the cost is very small compared with the insurance of safety thereby secured. Sometimes the joints are calked with clay. Every culvert should be built so that it can discharge water under a head Vi^ithout damage to itself.
The end sections should be protected with a timber or masonry bulkhead, although it is often omitted. Of course a parapet wall of rubble masonry or brick-work laid in cement is best (see Fig. 97).
Fig. 97.
Fig.
The foundation of the bulkhead should be deep enough not to be disturbed by frost. In constructing the end wall, it is well to in- crease the fall near the outlet to allow for a possible settlement of the interior sections. When stone and brick abutments are too expensive, a fair substitute can be made by setting posts in the ground and spiking plank on as shown in Fig. 98. When planks are used, it is best to set them with considerable inclination towards the road bed to prevent their being crowded outward by the pressure of the embankment. The upper end of the culvert should be so protected that the water will not readily find its way along tlie out- side of the pipes, in case the mouth of the culvert should become submerged.
The freezing of water in the pipe, particularly if more than half full, is liable to burst it; consequently the pipe should have a sufficient fall to drain itself, and the outlet should be so low that
410
CULVEKTS.
[chap. XVII.
there is no danger of back-water's reaching the pijDe. If properly drained, there is no danger from frost.
When the capacity of one pipe is not sufficient, two or more may be laid side by side. Although two small pipes do not have as much discharging capacity as a single large one of equal cross section, yet there is an advantage in laying two small ones side by side, since then the water need not rise so high to utilize the full capacity of the two pipes as would be necessary to discharge itself through a single one of larger size.
629. Examples. Fig. 99 (page 411) shows the standard vitri- fied pipe culverts employed on the Kansas City and Omaha E. E. This construction gives a strong, durable culvert which passes water freely. The dimensions of the masonry end walls and of the con- crete bed for the intermediate sizes are nearly j)ro23ortional to those shown in Fig. 99. Table 46 (page 411) shows the quantities of masonry required for the principal sizes.
630. Cost. Prices of vitrified pipe vary greatly with the con- ditions of trade, and with competition and freight. Current (1888), non-competitive prices for ordinary sewer pipe, in car-load lots /. 0. h. at the factory, are about as in the table below. *
TABLE 45. Cost and Weight of Vitrified Sewer Pipe.
|
Inside Diameter. |
Price per Foot. |
Area. |
Weight per Foot. |
Amount in a Car Load. |
|
12 inclies. |
15 cents. |
. 78 sq. ft. |
45 lbs. |
500 feet. |
|
14 " |
23 " |
1.07 " " |
55 " |
400 " |
|
16 " |
30 " |
1.40 " " |
65 " |
350 " |
|
18 " |
38 " |
1.76 " " |
75 " |
300 " |
|
20 " |
53 " |
2.18 " " |
90 " |
260 " |
|
23 " |
57 " |
2.64 " " |
110 " |
230 " |
|
24 " |
87 " |
3.14 " " |
140 " |
200 " |
Culveift pipe costs about 20 to 25 per cent, more than as above, and second quality sewer pipe about 20 to 25 per cent. less. The latter differs from first quality in being less perfectly glazed, less perfectly burned, or not perfectly round, or in having fire cracks in the glazing, blisters on either surface, excrescences or pimples on the inside, or a piece broken out of the end. Frequently such pipe is as good for culverts as first quality sewer pipe.
ART. y.J
VITEIFIED PIPE CULVERTS.
ni
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Fig. 99.— Standard Vitrified Pipe Culvert.— K. C. «& O. R. R.
TABLE 46.
ll.j*ONRY Required for Vitrified Pipe Culverts of the General Form shown above.
|
Items. |
Diameter |
OF PlP3. |
||
|
14 inches. |
16 inches. |
20 inches. |
24 inches. |
|
|
iJoping, two ends |
cu. yds. 0.54 2.93 |
CM. yds. 0.71 4.45 |
cu. yds. 0.97 6.98 |
cu. yds. 1 07 |
|
I arapets, two ends |
8.47 |
|||
|
Total Masonry |
3.47 |
5.16 |
7.95 |
S.54 |
|
Concrete, per lineal foot.. |
0.070 |
0.102 |
0.136 |
0.180 |
412
CULVERTS.
[chap. XVII.
631. Iron Pipe Culverts. In recent years, iron pipes have been much used for culverts. In many localities good stone is not available, and hence stone box culverts {§§ 615-26) can not be used. In such localities vitrified stoneware j^ipes are used ; but as they are not made larger than 2 feet in diameter, iron or stone is the only material available for permanent culverts requiring a greater water way than that obtained by using one or two of the largest vitrified pipes. Apparently, stone culverts if well built should last forever; but, as constructed in the past, they have been found to last rela- tively only a short time. Hence, with the increasing cheapness of iron, there has been an increasing tendency to use iron pipe for even large culverts. Cast-iron pipes from 12 to 48 inches in diameter and 12 feet long are in common use by all of the prominent roads of the Mississippi Valley. Some of the roads cast their own, while others buy ordinary water pipe. The lightest water pipes made, or even siich as have been rejected, are sufficiently strong for use in culverts. The dimensions used on the Chicago, jVIilwaukee and St. Paul R. R. are about as follows:
TABLE 47. Dimensions of Cast-Iron Culvert Pipe.
|
Inside Diameter. |
Weight per Foot. |
Thickness. |
Weight per Lineal Foot PER SQ. ft. of Area. |
|
12 inches. |
60 lbs. |
y^^ inch. |
77 lbs. |
|
16 '• |
88 " |
i " |
63 " |
|
20 " |
118 " |
1 " |
59 " |
|
24 " |
175 " |
i " |
56 " |
|
30 " |
240 " |
f " |
49 " |
|
36 " |
320 " |
1 " |
46 " |
|
42 " |
400 " |
7 " |
42 " |
|
48 " |
510 " |
1 " |
41 " |
632. Construction. In constructing a culvert with cast iron, the points requiring particular attention are (1) tamping the soil tightly around the pipe to prevent the water from forming a chan- nel along the outside, and (2) protecting the ends by suitable head walls and, Avhen necessary, laying riprap at the* lower end. The amount of masonry required for the end walls depends upon the relative width of the embankment and the number of sections of. pipe used. For example, if the embankment is, say, 40 feet wide at the base, the culvert may consist of three 12-foot lengths of
ART. 2.] IRON PIPE CULVERTS. 413
pipe and a light end wall near the toe of the bank ; but if the embankment is, say, 32 feet wide, the culvert may consist of two 12-foot lengths of pipe and a comparatively heavy end wall well back from the toe of the bank. The smaller sizes of pij^e usually iome in 12-foot lengths, but sometimes a few 6-foot lengths are included for use in adjusting the length of culvert to the width of bank. The larger sizes are generally 6 feet long.
Fig. 100 (page 414) shows the method employed on the Atchi- son, Topeka and Santa Fe K. R. in putting in cast-iron pipe culverts. Table 48 (page 414) gives the dimensions for the end walls for the various sizes. The length of pipe is determined by taking the multiple of 6 feet next larger than the length given by the position slope as in Fig. 100. To allow for settling, the pij)e is laid to a vertical curve having a crown at the center of 1 inch for each 5 feet in vertical height from bottom of pipe to profile grade.
Where the soil is treacherous, it would be wise to lay the pipes on a bed of broken stone to prevent undue settling. In this con- nection, see Figs. 96 and 99 (pages 406 and 411).
633. Fig. 101 (page 415) shows the method employed on the Chicago, Burlington and Quincy R. R. of putting in cast-iron pipe culverts. This construction has given entire satisfaction.
The same road has recently commenced the use of iron for cul- verts up to 12 feet in diameter. For diameters greater than 4 feet, the pipes are cast in quadrants 2, 4, 6, and 8 feet long, which are afterwards bolted together, through outside flanges, to form a cylinder of any desired length. The different segments are so com- bined as to break joints around and also along the pipe. The body of the pipe was formerly 1| inches thick ; but is now 1^, stiffened on the outside by ribs. The sections are put together without any chip- ping, drilling, or other skilled labor. Between the different sec- tions is a recess in which a tarred rope smeared with neat cement mortar is placed before bolting the segments together, which makes t.e joints tight.*
634. Cost. The cost of cast-iron pipe varies greatly with com- petition and the conditions of trade. The price ranges from §26 to $36 per ton for first quality water pipes, /. o. h. at the foundry; or approximately, say, 1^ cents per pound.
* For illustration of details, see Railroad Gazette, vol. six. pp. 123-^4.
414
CULVERTS.
[chap. XVII,
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IRON PIPE CULVERTS.
415
Fie. 101.— Cast-Ihon Pipe Culvert.— C, B. & Q. E. B.
416 CULVERTS. [chap. XVII:
Table 47 (page 412) shows that the average weight of the pipe per foot per square foot of water way is about 60 pounds ; anu hence the cost of the trunk of a cast-iron pipe, exclusive of trans- portation and labor, is about (60 X 1|-) 90 cents j)er lineal foot per sq. ft. of area. The cost of sewer pipes is, from Table 46 (page 411), about 22 cents per foot per square foot of water way ; and for culvert pipe about 30 cents.
Assuming the cost of rubble masonry to be $3.50 per cubic yard and of paving to be $2.00 per cubic yard, the average cost of the niahonry in the trunk of the box culvert shown in Fig. 95 (page 404) is 40 cents per lineal foot for each square foot of >water way ; and the corresponding cost for the culvert of Fig. 94 (page 403) is 46 cents. The end walls required for these different forms of cul- verts are essentially the same ; and hence the above comparison sliows approximately t.ie relative cost of the different forms of cul- verts. According to this showing, cast-iron pipe is the most ex- pensive ; but this difference is partly neutralized by the greater ease with which the iron pipe can ])e put into place either in new work or in replacing a Avooden box-culvert.
635. The following figures give the cost of a 7-foot cast-iron culvert of the form referred to in § 633, which see.
42 ft. body @ $26.55 per foot (1.55 ceuts per pound) |], 114.83
8 ft. specials @ $29.43 " " " " " " 235.32
Bolts and washers 29.91
Unloading 1 7. 52
Putting iu place 14S.95
Stone for end walls, 70 cu. yds., @ $1..50 105.00
Stone for riprap f(niudation, 60 cu. yds., @, $1.00 60.00
Removing temporary bridge 235.63
Total $1,947. 15
Excluding the cost of removing the tem.porary bridge — which Is not a jDart of the culvert proper, — and of the riprap foundation — which the unusual conditions required, — the cost of the culvert was
■•$33.0.3 per foot, or 83 cents per lineal foot for each square foot of
\water way.
636. Timber Box Culverts. Timber box culverts should be nsed only where more substantial material is not attainable at a reasonable cost. Many culvertc are constructed of timber an^
ART. 2.] BOX AND PIPE CULVERTS. 417
periodically renewed with the same material, and many are con- structed of wood and replaced with stone, or sewer or iron pipe.
The latter is an example of what may be called the standard practice in American railroad building; /. e., constructing the road as quickly and cheaply as possible, using temporary structures, and completing with permanent ones later as the finances of the company will allow and as the requirements of the situation become better understood. After the line is open, the permanent structures can be built in a more leisurely manner, at ai^j^i'opriate seasons, and thus insufe the maximum durability at a minimum cost.
There is a great variety of timber box culverts in common use, but probably there are none more durable and eflBcient than those used on the Chicago, Milwaukee and St. Paul E. E., — shown in Pig. 103 (page 418).* On this road, it is the custom to rejilace the wooden boxes with iron pipes before the timber has seriously de- cayed. If experience has shown the size of the wooden box to be about right, the timbers are cut out a little and an iron pipe is placed inside of the box without disturbing the earth.
For timber box culverts of sizes larger than can be made of plank, the Atchison, Topeka and Santa Fe E. E. employs bridge- tie box culverts. These are made by laying Q> X 8 inch sawed bridge ties flatwise, in contact, to form a floor. These ties are gained at the ends so as to leave a shoulder 1 inch deep against which the inside of the side walls bears. Upon this floor, vertical side walls are constructed by laying ties flatwise, one on top of the other ; the lowest timber in each side wall is fastened to each tie in the floor by a drift-bolt 12 inches long, and each timber in the side wall is fastened to the one below it by a 12-inch drift-bolt every 3 feet. The lengths of the ties employed in the side Avails are so ad- justed as to make the exposed ends conform closely to the slope of the embankment. The roof consists of 6- X 8-inch ties set edgewise, in close contact, with a shoulder 1 inch deep on the inside, both ends of each piece being also drift-bolted to the side wall.
637. Timber Baerel Culverts. For a number of years past the Chicago, Burlington and Quincy E. E. has found it desirable, in view of the absence or poor quality of the stone along its lines, to use a timber '^barrel-culvert" when the opening is too large for a
* From Railroad Gazette.
418
CULVERTS.
[CIIAP. XVIL
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ART. 3.]
ARCH CULVERTS.
419
timber box-culvert. The staves are 10 or 12 inches thick, accord- ing to the size of tlie culvert, and 8 inches wide on the outside, dressed to form a circle 4|^ or 6 feet in diameter. Iron rings — made of old rails — spaced about 10 feet apart, are used as a form upon which to construct the culvert and also to give it strength. The staves break joints and are drift-bolted (§ 381) together. As soon as the timber is thoroughly seasoned, the culverts are lined with a single ring of brick, and concrete or stone parapet walls are built. If, at an}^ time, the timber fails, it is the intention to jnit iron pipe through the present opening.
The timber costs about 812 per thousand feet, board measure, at the Mississippi Eiver ; and the cost of dressing at the company's shops is about $1.50 per thousand.
Art. 3. Arch Culverts.
638. In this article will be discussed what may be called the theory of the arch culvert in contradistinction to the theory of the arch. The latter will be considered in the next chapter.
By the theory of the arch culvert is meant an exposition of the method of disposing a given quantity of masonry so as to secure (1) maximum discharging capacity, (2) minimum liability of being choked by drift, and (3) maximum strength. Attention to a few points, which are often neglected in the design of culverts, will se- cure these ends without additional cost.
639. General Form of Culvert. Splay of Wings. There are three common ways of disposing the Aving walls for finishing the ends of arch culverts. 1. The culvert is finished with a straight wall at right angles to the axis of the culvert (see Fig. 103). 2. The
L
Fig. 10.3.
Fig. 104.
wings are placed at an angle of 30° with (see Fig. 104). 3. The wing walls are axis of the culvert, the back of the wing and
Fig. 105,
the axis of the culvert
built parallel to the
the abutment
being in a straight line and the only splay being derived from thiu-
420
CULVEETS.
[chap. xvn.
ning the wings at their outer ends (see Fig. 105). The first method is shown on a kirger scale in Plate II, the third in Plate III, and the second in Plate IV.
The quantity of masonry required for these three forms of wings does not differ materially, Fig. 105 requiring the least and Fig. 103 the most. The most economical angle for the wings of Fig, 104 is about 30° with the axis.
The position of the wings shown in Fig. 104 is much the most common and is better than either of the otliers. Fig. 103 is ob- jectionable for hydraulic considerations which will be considered in the next section, and also because it is more liable to become choked than either of the others. Fig. 105 does not have splay enough to admit the natural width of tlie stream at high water, and does not give sufficient protection to tlietoe of the embankment. 640. Junction of Wings and Body. With a culvert of the
general form outlined in Fig. 104, there are two methods of joining the wings to the body of the cul- vert. The more common method is shown in Figs. lOG and 108; and the better, but less common, one is shown in Figs. 107 and 109.
The form shown in Figs. 106 aiid 108 is very objectionable because (1) the corners reduce the c^'pacity of the culvert, and (2) add to its cost..
Fig, lOG.
Fig. lor.
Fig. :08.
1. The sharp angles of Fig. 106 materially decrease the amount of <yater which can enter under a given head and also the amount
ART. 3.] ARCH CULVERTS. 421
Avhicli can be discliarged. It is a well-established fact in hydraulics that the discharging capacity of a pipe can be increased 200, or even 300, per cent, simply by giving the inlet and outlet forms some- what similar to Fig. 107. Although nothing h.<e this increase can be obtained with a culvert, one finished at both the upper and the lower end like Fig. 107 will discharge considerably more water than one like Fig. 106. The capacity of Fig. 107 decreases as the angle between the wing and the axis increases ; hence, the less splay the better, provided the outer ends of the wings are far enough apart to accommodate the natural width of the stream at high water. Also the less the splay, the less the probability of the culvert's being choked with drift. Fig. 106 is very bad for both the admission and the discharge of water, and also on account of the great liability that drift and rolling stones will catch in the angles between the wings and the end walls. In this latter respect Fig. 108 is slightly better than Fig. 106.
2. Every angle adds materially to the cost of the masonry. In a culvert like Fig. 106, there are four unnecessary corners. This form probably owes its prevalence to the desire to have a uniform batter on the face of the wing, and to have the face of the wing wall intersect the end wall back of the arch stones. Satisfying both of these conditions gives a culvert in ground plan like Fig. 106; and satisfying the second one only, gives Fig. 108. Practically there is but little difference between these two forms — both are objectionable, as already explained. If the wing of Fig. 108 is moved inward, and the corner of the wing, which would other- wise project into the water way, is rounded off to a gentle curve. Fig, 109 is obtained. This form is simple, efficient, and. on the whole, the best.
Plate III shows another method of joining the wing to the end wall without having an unnecessary angle. In this case, the face of the wing up to the springing line of the arch is a warped surface, which is in some respects undesirable, although it saves a little masonry. However, the face of the wing wall could be built vertical up to the springing line and then battered; or the wing could be moved forward and the corner be rounded off as in Fig. 109.
641. Semi-circular t'.y. Segmental Arches. There are two classes of arches employed for culverts, viz., the semi-circular and
422 C UL VEETS. [chap. XVII.
the segmental. The first is by far the more common; but neverthe- less the latter is, on the whole, much the better.
1. For the same span, the segmental arch requires a shorter in- trados (the inside curve of a section of the arch perpendicular to its axis). For example, the culverts shown in Plates IV and V have the same span, but the intrados of the semi-circular arch is 15.71 ft., Avhile that of the segmental arch is 10.72 ft.; that is, the intrados of the segmental is only 68 per cent, of the intrados of the semi-circular arch. This difference depends upon the degree of flatness of the segmental arch. The above example is an extreme case, since the segmental arch is unusually flat, the central angle being only 73° 44'. (The rise is one sixth of the span.) With a central angle of 120°, the intrados of the segment is 77 per cent, of the semi-circle.
Or, to state the above comparison in another and better form, for the same length of intrados the segmental arch gives the greater span. For example, a segmental arch on the same general plan as that of Plate V, but having an intrados equal to that of Plate IV, would have a span of 14.64 ft., which is 46 per cent, greater than the span of the semi-circular arch shown in Plate IV. A segmental arch with a central angle of 120° has a span 33 per cent, greater than a semi-circular arch having the same length of intrados. This difference constitutes an important advantage in favor of the seg- mental arch culvert, since the wider the span the less the danger of the culvert's being choked by obstructions, and because it will pass considerably more water for the same depth.
2. For the same length of intrados, the segmental arch gives the greater water way. The water way of the culvert shown in Plate IV is 87.6 square feet ; but the same length of intrados in a seg- mental arch culvert having 73° 44' central angle (the same as Plate V) would have a water way of 98.3 square feet; and with a central Angle of 120° would have a water way of 99.5 square feet. In both examples the increase is one eighth.
3. On the other hand, the segmental culvert will require a thicker arch. It will be shown in the next chapter that arches can not be proportioned strictly in accordance with mathematical formulas ; and hence the exact difference in thickness of arch which should exist between a semi-circular and a segmental arch can not be computed. According to established rules of practice, small
ART. 3.] ARCH CULVERTS. 423
segmental arches are from 10 to 25 per cent, thicker than semi- circular ones. This difference is not very great, and its effect upon the cosu of the culvert is, proportionally, still less, since the cost per yard of arch masonry is less for the thicker arches. Then, we may conclude that, since for the same span the intrados of seg- mental arches is from 20 to 40 per cent, shorter than the semi- circle, the segmental arch requires a less volume of arch masonry than the semi-circular, and also costs less per cubic yard. The arch masonry per foot of length of the segmental arch culvert shown in Plate V is only 71 per cent, of that in the semi-circular one shown in Plate IV. The dimensions and contents of arch culverts of the general forms shown in Plates IV and V are given in Tables 51 and 52 (pp. 430 and 431 respectively), from which it appears that the segmental arch contains only from 60 to 76 per cent, as much masonry as the semi-circular, the average for the six spans being almost exactly 70 per cent. The cost of these two classes is shown in Tables 56 and 57 (pages 437 and 438), from which it ajjpears that the average cost of segmental culverts 20 feet long and of different spans is only 59 per cent, of the cost of semi-circular ones of the same length and span; and the average cost of an additional foot in length for the segmental is only 86 per cent, of that for a circular one. The water ways of the semi-circular culverts are a little the greater, and hence the difference in cost per square foot of water way is not as great as above; but, on the other hand, the form of water way of the segmental culvert is the more eflficient, and hence the above comparison is about correct.
4. Will the segmental, /. e., the flatter, arch require heavier abut- ments (side walls)? Unquestionably the flatter the arch the greater the thrust, upon the abutment; but the abutment not only resists the thrust of the arch which tends to turn it over outwards, but also the thrust of the embankment, which tends to push it in- wards. It is impossible to compute, with any degree of accuracy, either the thrust of the arch or of the embankment; and hence it is impossible to determine either the relative value of these forces or the thickness which the two abutments should have. Experience seems to indicate that the thrust of the earth is greater than that of the arch, as is shown by the fact that nearly all semi-circular culverts have abutments of much greater thickness than are required to re- sist the thrust of the arch; and hence we may conclude that expe-
424 CULVERTS. [chap. XVII.
rience has shown that the thrust of the earth necessitates a heavier HDutment than does the thrust of the arch. If this be true, then the abutment for segmental arches may be thinner than those for semi-circular ones; for, since the thrust of the former is greater than the latter, it exerts a greater force outward, which counter- balances a larger part of the inward thrust of the embankment, and thus leaves a less proportion of the latter to be resisted by the mass of the abutment. Segmental arch culverts are not often built; and designers appear to have overlooked the thrust of the earth, since the side walls of segmental arches are generally thicker than for semi-circular ones (compare Plates IV and V).
The conclusions may, therefore, be drawn that segmental arch culverts are both cheaper and more eflficient than semi-circular ones.
642. As built, many semi-circular arches are 23i'actically seg- mental; that is, the side walls are built so high, or the backing is made so heavy, that practically the abutments are less than 120° apart, and hence the two lower ends of the arch are really only a part of the side wall, and should be built square.
Further, it is shown in §§ 681-82 that a true avch of more than about 90 to 120 degrees is impossible.
643. Examples. Under this head will be given a brief descrip- tion of four series of arch culverts which are believed to be repre- sentative of the best practice.
644. Illinois Central Arch Culverts. Plate II shows the gen- eral plan of the standard arch culvert employed in the construction (185"2-53) of the Chicago branch of the Illinois Central Railroad.* While the timber in the foundation is apparently still in good con- dition, the use of timber for such shallow foundations can not be considered as the best construction. However, many of the con- ditions, particularly drainage, have greatly changed since this road was built, and it is by no means certain that this use of timber was not good practice at that time (see § 636).
Table 49 (page 425) gives the dimensions and contents for the several spans of this form of culvert. The contents of the end walls were computed on the assumption that the off-set at tha back was 6 inches for each foot, counting from the top, until the full thickness at the bottom was obtained (see Section E-F, Plate II).
* Published by permission of J. M. Healey, Division Engineer.
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426 CULVERTS. [chap. XVII.
645. Example of the Use of Table 49. To illustrate the method of using the above table, assume that an estimate of the amount of material in an 8-ft. arch culvert of the preceding form is required. Assume that the top of the coj^ing is 3 feet below sub-grade, i. e., that there is 4.25 feet of earth above the crown of the arch. Assume also that the road bed is IG feet, and that the slojie of the embank- ment is li to 1. Then the length of the culvert from inside to in- side of the end walls will be 16 -f 2 (| X 3) = 10 + 9 = 25 feet; and from out to out of end walls, the length will be 25 + 2 X 2.5 = 30 feet.
Assuming that the timbers under the planking are 8 X 10 inches, the 205 sq. ft., as per the table, will require 1,422 ft. B. M. of tim- ber, or 9 pieces 24 ft. long. Notice, however, that in practice 10 pieces would be used — 5 at each end of the culvert. The length of the trunk of the foundation is 30 - 2 (4+ 1 + 1) = 19 ft. Hence the area under the trunk of the foundation to be covered with tim- ber is 19 X 8 (see table) = 152 sq. ft. ; and if 8 X 10-inch timbers are used, this will require 1,216 ft. B. M., or 12 pieces 14 feet long. The plank under the wings and in the sheet piling is 1,493 feet (see table), and that in the trunk is 32 (see table) X 19 = 608 ft. B. M. ; hence the total plank is 1,493 + 008 = 2,101 ft. B. M.
The masonry in the end wall is 32.97 cu. yds., as in table. The masonry in 1 foot of arch is (see table) 0.6T3 + 0.284 = 0.957; and in 30 ft. it is 0.957x30 = 28.71 cu. yds. The masonry in the side walls (abutments of the arch) is 0.444 (see table) X30 = 13.32 cu. yds. The coping is 117.0 cu ft. (see table) = 4.33 cu. yds.
Collecting and tabulating the preceding results, we have the following :
Timber:— 10 pieces, 8 X 10 inches, 24 ft. lone 1,600 ft. B. M.
13 '• " '• 14 '• "^ I.ISO " ••
2-inchplank 2,101" "
Total timber in culvert 25 ft. long... . 4,821 " "
Masonry: — 2 end walls 33 . 0 cu. yds.
coping 4.3 " "
side walls (abutments) 13.3 " "
arch masonry 28 . 7 " "
Total masonryin culvert 2-5 ft. long.. 79.3 " *'
AKT, 3. J ARCH CULVERTS. 4:27
646. Chicago, Kansas and Nebraska Arch Culverts. — The culvert shown in Plate III is the standard form employed on the Chicago, Kansas and Xebraska Railroad.* Xotice that the slope line inter- sects the inside face of the end wall at a considerable distance above the back of the crown of the arch (see Side View, Plate III). This is sometimes urged as an objection to this form of construction, on account of the stipposed liability of the. top of the end wall being pushed outward; but there is no danger of this method of failure, since the height of the end Avall above the crown of the arch is, ex- clusive of the coping, only equal to its thickness, and in iulu>:on it is buttressed on the outside by the wings. The advantage of this construction is that it requires less masonr}' and also less labor.
Concerning the manner of joining the wings to the body, see the last paragraph of § 640 (page 431).
Table 50 (page 428) gives the dimensions and contents for various spans. The contents of the wings above the springing line of the arch were computed for cotirses 1 foot tlnck and for an earth slope of 1^ to 1 (see §557).
647. Example of the Use of Table 50. Assume the same depth of earth over the crown of the arch as in the example in § G45, X. e., 4.25 ft.; and assume also that the slope line strikes the upper corner of the coping instead of the lower as shown in Plate III. The to^o of the coping will be 0.75 ft. below sub-grade; and, for a 16-ft. road-bed, the length of the arch — inside to inside of end walls— is 16 + 2(1 X 0.75) = 18.25 ft. With the above data and Table 50, we have the following for an 8 foot culvert :
Four wiug walls, including one footing course, . . 40.5 cu, yds.
Two head " " " " " . . 36.8 " "
Coping, 3.7 " "
Two side walls, 18i ft. @ 1.382 cu. yds. per foot, . . 25.2 " "
Arch masonry, " " " 1.184 " " " " . , 21.6 " " Paving, 23.58 ft. @ 0.272 cu. yd. per ft., .... 6.4 " '
Total masonry in culvert l&J ft. long, . . 134.1 " "
In attempting to make comparisons between the above total and that of § 645, notice that the culverts are of very difterent style (see §§ 638 and 639) and that the water ways are of different areas.
* Published by permission of H. A. Parker, Chief Engineer.
428
CULVERTS.
[CHAP. XVIL
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ART. 3.] ARCH CULVERTS. 429
648. Atchison, Topeka and Santa F6 Arch Culverts. Plates IV iiiid V show the standard semi-cireular aud segmental arch cul- verts used by the Atchison, Topeka and Santa Fe Eailroad.*
Tables 51 and 52 give the dimensions and contents for the several spans. Notice that the heights of the end walls do not vary uniformly, that for the 12-foot span being proportionately too great; and consequently the contents of the end walls and of the wings do not vary uniformly. The contents of the facing of the wings were computed for courses 18 inches thick (see § 557), and the backing was computed on the assumption that the back surface was a plane such that the dimension at the outer end 'and also where a plane parallel to the section E-F passes through the corner of the end wall is as in the diagram.
In computing the masonry in a given culvert, these tables are to be employed as already explained for Tables 49 and 50— see §§ 645 and G47.
649. Standard Arch Culvert. The culvert shown in Plate VI has been designed iu accordance with the principles laid down in the preceding discussion (§§ 638-41). The wings are joined to the body in such a manner as to offer the least possible resistance to the passage of water and drift. If the current is slow and not liable to scovir, the paving may be omitted, since the end walls, being continuous under the ends of the water way, will prevent under- mining of the side walls; or, iu long culverts, one or more inter- mediate cross walls may be constructed. But ordinarily the money paid for paving is a good investment. If the current is very rapid, it is wise to grout the paving, — and also to inspect the structure frequently.
The arch ring is amply strong to support any bank of earth (see Table 63, page 502, particularly Nos. 9, 12, 18, 53, 54, and 61). The strains in a masonry arch can not be computed exactly; but the best method of analysis (§ 688) shows that if the earth is 10 feet thick over the crown, the maximum pressure is not more than 55 pounds per square inch (comimre with §222 and also ,§§ 246-48). A greater thickness of earth at the crown would doubtless increase the maximum pressure in the arch; but proportionally the pressure would increase much less rapidly than the height of the bank (see
* Published by permission of A. A. Robinson, Chief Engineer.
430
CULVERTS.
[chap. XVII.
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ART. 3.]
ARCH CULVERTS.
431
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432 CULVERTS. [chap. XVII.
§ 619). The arch is also stable uitder any position of the moving load, with either a heavy or a light embankment. The joints of the abutment are radial, to prevent any possibility of failure by tlie sliding of one course on another (see § 674).
Table 53 (page 433) gives the dimensions and contents of various •sizes. In each case the rise is one fifth of the span, the central angle is 87° 12\ and the height of the opening is equal to half the span. The paving and coping were each assumed to be 1 foot thick; but for any other thickness it is only necessary to increase or de- crease the tabular numbers proportionally. The contents of the wings were computed on the assumption that all the courses were 1 foot thick (see § 557).
650. Quality of Masonry. The masonry of arch culverts is usually divided into two classes; the first consists of the masonry in the wings and end walls (parapet), and the second of the arch stones. The former is classified as first-class or second-class ma- sonry (see § 225). Only the masonry in the arch stones is called arch masonry. The arch stones which show at the end of the arch are called rmg stones, and the remainder of the arch stones the arch sheeting. The arch masonry proper is usually classified as first-class or second-class arch masonry. The distinction between these two classes is usually about as in the specifications below.
651. Specifications.* Foundations. "When the bottom of the pit is -common earth, gravel, etc., the foundations of arch culverts will generally <!onsist of a pavement formed of stone, not less than twelve inches (13") in .depth, set edgewise, and secured at the ends by deep curbstones which must be protected from undermining by broken stone placed in such quantity and position as the engineer may direct. When the bottom upon which a culvert is to be built is soft and compressible, and where it will at all times be covered with water, timber well hewn, and from eight (8) to twelve inches <12") in thickness, according to the span of the culvert, shall be laid side by side crosswise upon longitudinal sills; and when the position of the culvert is such that a strong ciu-rent will be forced through during floods, three courses of sheet piling shall be placed across the foundation — one course at each end, and one in the middle, — which shall be sunk from three (3) to six feet (6') l)elow the top of the timber, according as the earth is more or less compact, "f
652. First- Class Arcli Masonry. " First-class arch masonry shall be built in accordance with the speciticatioiis for first-class masonry [§ 225], with the exception of the arch sheeting and the ring stones. The ring stones shall be
* See also Specifications for Railroad Masonry, Appendix 1. ■f- Pennsylvania Railroad.
AKT. 3.]
AKCH CULVERTS.
433
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434 CULVERTS. [chap, xvil
dressed to such shape as the engineer shall direct. The ring stones and the arch sheeting shall be of stone not less than ten inches (10") thick on the inirados, shall be dressed with three eighths of an inch (f") joints, and shall be of the full depth specified for the thickness of the arch; and the jointa shall be at right angles to the surface of the iutrados. The face of sheeting stones shall be dressed to make a close centering joint. The ring stones and the sheeting shall break joints not less than one foot (1).
" The wings shall be neatly stepped with selected stones of the full width of the wing and of not less than ten inches (10") in thickness, which shall overlap by not less than eighteen inches (18"); or shall be finished with a neatly-capped newel at the free end, and a coping course on the wing. The parapets shall be finished with a coping course not less than ten inches (10") thick and of the full width of the parapet, which shall project six inches (6"). 653. Second-Class Arch Masonry. " Second-class arch masonry is the same as second-class masonry [§ 225], with the exception of the arch sheeting. The stones of the arch sheeting shall have a good bearing throughout, and shall be well bonded and of the full depth of the thickness of the arch. No stone -shall be less than four inches (4") in thickness on the intrados. Ring^ stones of all arches over eight feet (8) span shall be dressed according to specifications for first-class arch masonry [§ 651]." *
654. Paving. For specifications for Paving, see § 219 (page 148), and also Specifications for Railroad Masonr3^ Appendix I.
655. Cost. §§ 326-38 contain data on the cost of masonry, of which the last is a snmmary. Table 17 (page 159) contains a de- tailed statement of the actual cost of the masonry in an arch culvert; and below are the items of the total cost of that culvert.
613 cu. yds. of masonry @ $6.59, $4,036.85
Excavations — foundations and drainage, ...... 263.36
Sheet piling 19.69
Concrete, 43.75
Extra allowance on sheeting stones, 20.00
Total cost of culvert, $4,383.65
The total cost of the culvert per yard of masonry is $7.16, — which is unusually low.
Below is the total actual cost of the 8-ft. culvert (length out to out of end walls = 30 ft.) for which the quantities were estimated in § 645 (page 426).
* Atchison, Topeka and Santa F6 R. R.
ART. 3.]
ARCH CULVERTS.
435
Wall masonry— 48.7 cu. yds. @ $7.00, $340.90
Arch masonry— 28.7 " " " 8.50, 243.95
Timber— 5,247 ft., B M., @ $40.00, 209.88
Excavating foundations and straightening stream 158 cu.
yds. @ 50c., 79.00
Total cost of culvert $873.73
The total cost of this culvert per cubic yard of masonry is $11.29. The average total cost of a number of representative culverts of this style was 111.46 per cubic yard of masonry, being practically constant for all spans.
656. Illinois Central Culverts. Table 54 gives the cost of cul- verts 25 feet long — out to out of end walls — of various spans of the general plan shown in Plate II, and will be very useful in estimat- ing the cost of such culverts. The quantities of masonry necessary to compute Table 54 were taken from Table 49 (page 425). The prices are believed to be fair averages (see page 160) for the first- class masonry described in § 651. The prices are the same as actually paid by the Illinois Central Railroad, except for arch masonry and excavation, for which 68.50 and 50c. respectively were paid. The prices used in deducing the table are given therein, and hence the results can be modified for prices differing from those there employed by simply taking proportional parts of the tabulated
TABLE 54.
Cost of Illinois Central Arch Culverts 25 Ft. Long from Out to Out op End Walls, and also op each Additional Foot.
FOR description SEE PAGE 424.
|
Span. |
||||
|
6 ft. |
8 ft. |
10 ft. |
12 ft. |
|
|
Plain masonry @ SI'.OO per cu. yd Arch mason rv @ 8.IK1 •■ '• " |
$237.35 151.29 150.88 12.48 |
8325.29 191.29 188.12 15.85 |
8424.97 255.29 232.84 19.22 |
8455.98 362 82 |
|
Timber and plank at $40 per M. ft,, B. M ... Excavating foundation @ 25c. per cu. yd |
268.92 21.38 |
|||
|
Total cost of culvert 25 ft. long Cost of an Additional Foot of Length: Plain masonry @ $7.00 per cu. yd Arch masonry @ 8.00 " " " Timber and plank @ 840 per M ft., B. M Excavation @ 25c. per cu. yd |
»552.00 S;mi 6.05 3.36 .32 |
8720.55 83.11 7.65 3.84 .40 |
8932.32 83.11 10.21 5.04 .48 |
$1,109.10 83.63 14.51 5.88 .56 |
|
Total cost of 1 additional foot |
812.84 |
815.00 |
$18.84 |
$24.48 |
436
CULVERTS.
[chap. XVII.
quantities. The amount of excavation used in computing the table is the mean of the actual quantities for a number of representative culverts as constructed on the above road.
657. Chicago, Kansas and Nebraska Culverts. Table 55 is given to facilitate estimating the cost of culverts of the general form shown in Plate III. The prices are about the average for the respective kinds of work; but in case it is desired to determine the cost for other prices, it is only necessary to increase or decrease the tabular numbers proportionally. The quantities of excavation are, approximately, averages of the actual amounts for a number of similar culverts, and are equivalent to a pit 2 feet 2 inches deep and of an area equal to the area of the foundation. The table includes only one footing course, but in so doing it is not intended to imply that one is always, or even generally, enough. Notice that the cul- vert in Table 55 is 25| feet long from outside to outside of end walls, and hence is one third of a foot longer than that presented in Table 54.
658. A., T. and S. F. Semi-circular Culverts. Table 56 is similar to the two preceding ones, and shows the cost of the Atchison,
TABLE 55.
Cost op C K. and N. Arch Culverts 20 Ft. Long from Inside to
Inside of Coping, and also of each Additional Foot of Length.
for description see page 437.
This table includes one footing course.
|
Span. |
|||||
|
3 ft. |
4 ft. |
6 ft. |
8 ft. |
10 ft. |
|
|
Plain masonry @ $7.00 per cu. yd Arch masonry @ 8.00 " " " Paving @ 2.00 " " " Excavation @ .25 " " " |
$217.98 44.64 4.42 7.44 |
$397.04 79.03 6.32 9.33 |
$657.23 130.78 10.16 12.42 |
$703.43 2.39.92 13.96 13.95 |
$853.16 346.96 17.76 14.99 |
|
Total cost of culvert 20 ft. long . . . Cost of an Additional, Foot of Length: Plain masonry @, $7.00 per cu. yd Arch masonry © 8.00 " " " Paving @ 2.00 " " " Excavation @ .25 " " ". |
$274.48 $4.14 2.30 .17 .23 $6.84 |
$491.72 $6.17 4.06 .25 .27 |
$810.59 $9.33 6.72 .40 .35 |
$971.26 $9.67 10.06 .54 .39 |
$1,232.87 $10.9'> 14.55 .69 .46 |
|
Total cost of 1 additional foot |
$10.75 |
$16.80 |
$20.66 |
$26.66 |
ART. 3.]
AKCH CULVERTS.
437
Topeka and Santa Fe's standard semi-circular arch culvert as given in Plate IV and Table 51 (page 430). The excavation is only ap- proximate, and is computed on the assumption of a pit 2 feet 2 inches deep for the entire foundation including the paved area; /. e., the excavation is computed on the same basis as the two preceding. Notice that this culvert is 23 feet between the outer faces of the end walls, and hence is 1 foot shorter than that of Table 54 and 2^ feet shorter than that of Table 55.
TABLE 56.
Cost of A. T. and S. F. Semi-circulak Arch Culverts 20 Ft. Long FROM Inside to Inside of the Coping, and also of each Addi- tional Foot of Length.
FOR description SEE PAGE 429.
Thig table does not include the masonry in the footings.
|
Items. |
Span. |
|||||
|
6 ft. |
8 ft. |
10 ft. |
12 ft. |
14 ft. |
16 ft. |
|
|
Plain masonry @ $7.00 per cu. yd. Arch masonry " 8.00 " " " Paving " 2.00 " " " Excavation " .25 " " " |
$325.15 140.72 9.88 6.93 |
$766.42 197.28 13.15 13.51 |
$997.14 270.32 16.42 16.01 |
$1,071.42 356.04 19. 6S 18.21 |
$1,328.12 418.40 22.99 21.10 |
$1,785.91 516. 4& 26.26 24 44 |
|
Total cost of culvert 20 ft. long. Cost of an Additional Foot OF Length: Plain masonr\' @ $7.00 per cu. yd. Arch masonry " 8.00 " " •• Paving " 200 " " " Excavation " .25 "' " " |
$482.68 $5.44 6.12 .52 .28 |
$990.36 $8.49 8.58 .69 .32 |
$1,299.89 $11.66 11.75 .86 .40 |
$1,465.35 $12.44 15.48 1.04 .44 |
$1,790.61 $14.98 18.19 1.21 .48 |
$2,353.09 $19.48 22.46 1..38 .54 |
|
Total cost of 1 additional foot |
$12.36 |
$18.08 |
$24.68 |
$29.. 50 |
$34.86 |
$43.86: |
659. A., T. and S. F. Segmental Culverts. Table 57 is similar to- the three preceding, and is given to facilitate estimating the cost of segmental arch culverts of the standard form employed by the Atchison, Topeka and Santa Fe Eailroad, as shown in Plate V and Table 52 (page 431). The excavation is only approximate, and is computed on the assumption of a pit 2 feet 2 inches deep over the entire foundation, including the paved area. Notice that this culvert is 23 feet between the outer faces of the end walls, and is therefore the same length as that of Table 56.
438
CULVERTS.
[chap. XVII.
TABLE 57. Cost of A. T. and S. F. Segmental Auch Culverts 20 Ft. Long FROM Inside to Inside of the Coping, and also of each Addi- tional Foot of Length.
for description see page 429. This table does not include the masonry in the footings.
|
Items. |
Span. |
|||||
|
6 ft. 8 ft. |
10 ft. |
12 ft. |
14 ft. |
16 ft. |
||
|
Plain masonry @, $7.00 per cu. yd Arch masonry " 8.00 " '" " Paving " 2.00 " " " Excavation " .25 " " " |
$183.45 99.18 9.88 7.33 |
$470.34 150.33 13.15 11.75 |
$607.99 190.99 16.42 14.11 |
$657.83' $641.41 229. 12| 298.64 19.68 22.99 15.17, 16.45 |
$669.13 353 84 26.26 17.82 |
|
|
Total cost of culvert 20 feet long. . . . Cost of an Additional Foot of Length : Plain masonry © $700 per cu. yd Arch masonry " 8.00 " " " Paving " 2.00 ' Excavation " .25 " " " |
$299.84 $5.44 4.31 .52 .31 |
$645.57 $9.73 6.54 .69 .39 |
$829.51 $12.96 8.30 .86 .46 |
$921.80 $13.61 9.96 1.04 .50 |
$979.49 $14.47 12.98 1.21 .56 |
$1,067.05 $14.56 15.38 1.38 .62 |
|
Total cost of 1 additional foot |
$10.58 |
$17.35 |
$22.58 |
$25.11 |
$29.22 |
$31.94 |
660. Standard Arch Culvert. Table 58 is given to facilitate the estimation of the cost of culverts of the general form shown in Plate VI. The prices are about the average for the respective kinds of work ; but in case it is desired to determine the cost for other prices,
TABLE 58.
Cost of Standard Arch Culverts 20 Ft. Long from Inside to Inside OF THE Coping, and of each Additional Foot of Length.
FOR description SEE PAGE 429.
The masonry in the footings is not included in this table.
|
Items. |
Span. |
|||||
|
6 ft. |
8 ft. |
10 ft. |
12 ft. |
14 ft. 16 ft. |
||
|
Plain masonry @ $7.00 per cu. yd . . . Arch masonry " 8 00 " " " — Paving " 2.00 " " " .... Excavation '" .25 " " " |
$233.11 65.87 6.83 8.24 |
$3.30.88 92.72 9.84 9.53 |
$496.79 127.33 12.65 12.42 |
$683.55 184.00 15.47 15.42 |
$912.45 $1,193.35 238.64 305.62 18.281 20.09 18.33^ 20.61 |
|
|
Total cost of culvert 20 feet long . . . Cost of an Additional Foot of Length : Plain masonry @ $7.00 per cu. yd — Arch masonry " 8.00 '• " " Paving " 2.00 " " " .... Excavation " .25 " " " — |
$314.05 $3.88 2.86 .37 .21 |
$442.97 $6.56 4.03 .52 .26 |
$649.19 $9.85 5.54 .67 .31 |
$898.44 $14.00 8.00 .81 .36 |
$1,187.70 $18.75 10.38 .96 .41 |
$1,539.67 $24.28 13.29 1.11 .46 |
|
Total cost of 1 additional foot |
$7. 32 |
$11.37 |
$16.37 |
$23.17 |
$30.50 |
$39.14 |
AET. 3.] ARCH CULVERTS. 439
it is only necessary to increase or decrease the tabular numbers proportionally. The quantities of excavation are, approximately, averages of the actual amounts for a number of similar culverts, and are equivalent to a pit 2 feet 2 inches deep and of an area equal to the area of the foundation. Notice that the culvert in Table 58 ]s 23 feet between the outer faces of the end walls; and is therefore the same length as that in Tables 56 and 57, and is 1 foot shorter than that of Table 5-4 and 2^ feet shorter than that of Table 55. Notice also that in Table 58 the height of the opening is in each case half of the span (see Table 53, page 433), while in Tables 56 and 57 the height of the opening is nearly the same for all spans (see Tables 51 and 52, pages 430, 431).
CHAPTEE XVIII.
ARCHES.
661. Definitions. Parts of an Arch. Voussoirs. The wedge- shaped stones of which the arch is composed ; also called the arch- stone.s.
Keystone. The center or highest voussoir or arch-stone.
Soffii. The inner or concave surface of the arch.
Intrados, The concave line of intersection of the soffit, with a vertical plane perpendicular to the axis or length of the arch. See Fig. 110.
Extrados. The convex curve, in the same plane as the intrados, which bounds the outer extremities of the joints between the voussoirs.
Croivn. The highest part of the arch.
Skeioback. The inclined surface or joint upon which the end of the arch rests.
Abutment. A skewback and the masonry which sup- ports it.
Springing Line. The in- ner edge of the skewback.
Springer. The lowest voussoir or arch-stone
Hauncli. The part of the arch between the crown and th© skewback.
Spandrel. The space between the extrados and the roadway. The material deposited in this space is called the spandrel filling y and may be either masonry or earth, or a combination of them. In large arches it often consists of several walls running parallel with the roadway, connected at the top by small arches or covered with fiat stones, which support the material of the roadway.
440
Fig. 110.
KINDS OF ARCHES. 441
Span. The perpendicular iistaaoe '3etweeii the springing lines.
Rise. The vertical distance between the highest part of the intrados and the plane of the springing lines.
Bi7ig Stones. The voussoirs or arch-stones which show at the ends of the arch.
Arch Sheeting. The voussoirs which do not show at the end of the arch.
Backing. Masonry, usually with joints horizontal or nearly so, carried above the skewbacks and outside of the extrados.
String Course. A course of voussoirs extending from one end of the arch to the other.
Coursing Joint. The joint between two adjoining string courses. It is continuous from one end of the arch to the other.
Heading Joint. A joint in a plane at right angles to the axis of the arch. It is not continuous.
Ring Course. The stones between two consecutive series of heading joints.
662. Kinds of Arches. Circular Arch. One in which the intrados is a part of a circle.
Semi-circular Arch. One whose intrados is a semi-circle; also called a full-centered arch.
Segmental Arch. One whose intrados is less than a semi- circle.
Elliptical Arch. One in which the intrados is a part of an ellipse.
Basket-Handle Arch. One in which the intrados resembles a semi-ellipse, but is composed of arcs of circles tangent to each other.
Pointed Arch. One in which the intrados consists of two arcs of equal circles intersecting over the middle of the span. For ex- ample, see Figs. 115 and 117, page 447.
Hydrostatic Arch. An arch in equilibrium under the vertical pressure of water.
Geostatic Arch. An arch in equilibrium under the vertical pressure of an earth embankment.
Catenarian Arch. One whose intrados is a catenary.
663. Right Arch. A cylindrical arch, either circular or el-
442
AECHES.
[chap. XVIII.
liptical, terminated by two planes, termed heads of the arch, at right angles to the axis of the arch. See Fig. 111.
FiQ. 111.— Right Arch.
Fig. 112.— Skew Arch.
Skeio Arch. One whose heads are oblique to the axis. See Fig. 112. Skew arches are quite common in Europe, but are rarely employed in the United States ; and in the latter when an oblique arch is required, it is usually made, not after the European method with spiral joints as shown in Fig. 112, but by building a number of short right arches or ribs in contact with each other, each successive rib being placed a little to one side of its neighbor.
Groined and Cloistered Arches. Those formed by the in- tersection of two or more cylindrical arches. The spans of the intersecting arches may be different, but the rise must be the same in each; and their axes must lie in the same plane, but may intersect at any angle. The groined arch is formed by removing those portions of each cylinder which lie under the other and between their common curves of intersection, thus forming a projecting or salient angle on the soffit along these curves. The cloistered arch is formed by removing those portions of each cylinder which are above the other and exterior to their common intersection, thus forming re-entrant angles along the same lines.
Dome and Vault. If an arch revolves around a vertical through the keystone, a dome is produced ; and if it moves in a straight line on the springer, a vault is produced. Hence there are essentially the same kinds of domes and vaults as arches.
Only right arches will he considered in this chapter.
LIXE OF RESISTANCE.
443
664. Line of Resistance. If the action and reaction between each pair of adjacent arch-stones be replaced by single forces so situated as to be in every way the equivalent of the distributed pressures, the line connecting the points of application of tliese several forces is the line of resistance of the arch. For example, assume that the half arch shown in Fig. 113 is held in equilibrium by the horizontal thrust T — the reaction of the right-hand half of the arch — applied at some point a in the joint OF. Assume also that the
Fig. 113.
several arch-stones fit mathematically, and that there is no adhesion of the mortar. The forces F^, F^, F^, and F^ represent the result- ants of all the forces (including the weight of the stone itself) acting upon the several voussoirs. The arch-stone CIHF is in equilib- rium under the action of the three forces, T, F^ , and the reaction of the voussoir IHEG. Hence these three forces must intersect in a point, and the direction of i?, — the resultant pressure be- tween the voussoirs CIHF and IHEG — can be found graphically as shown in Fig. 113. The point of application of R^ is at b — the point where R^ intersects the joint HI. The voussoir GEHl
444 ARCHES. [chap. XVIII.
is in equilibrium under the action of R^, F,, and R^ — the resultant reaction between GEHI and GEDH, — and hence the direction, the amount, and the point of application (c) of R^ can be deter- mined as shown in the figure. R^ and R^ are determined in the same manner as R^ and R^ .
The points a, b, c, d, and e, called centers of pressure, are the points of application of the resultants of the pressure on the several joints ; or they may be regarded as the centers of resistance for the several joints. In the latter case the line ahcde would be called the line of resistatice, and in the former the line of pressure. Strictly speaking, the line of resistance is a continuous curve cir- cumscribing the polygon ahcde. The greater the number of joints the nearer the polygon ahcde approaches this curve. Occa- sionally the polygon imiop is called the line of resistance. The greater the number of joints the nearer this line approaches the line of resistance as defined above. For an infinite number of joints the polygons ahcde and tmiop coincide with the curved line of re- sistance, a, h, c, d, and e being common to all three.
Notice that if the four geometrical lines ah, he, cd, and de were placed in the relative position shown in Fig. 113, and were acted upon by the forces T, F^, F^, F^, F^, and R, as shown, they would be in equilibrium ; and hence the line ahcde, or rather a curve passing through the points a, b, c, d, and e, is sometimes called a linear arch.
Akt. 1. Theory of the Arch.
665. The theory of the masonry arch is one of great com- plexity. Numerous volumes have been written on this subject, and it still occupies the attention of mathematicians. No attempt will be made here to give an exhaustive treatise on the arch ; but the fundamental principles will be stated as clearly as possible, and tlie principal solutions of the problem which have been proposed from time to time will be explained and their underlying assumptions pointed out.
666. The External Forces. It is clear that before we can find the strains in a proposed arch and determine its dimensions, we must know the load to be supported by it. In other words, the strength and stability of a masonry arch depend upon the
ART. 1.] THEORY OF THE ARCH. 445
position of the line of resistance ; and before this can be deter^ mined, it is necessary that the external forces acting upon the arch shall be fully known, i. e., that (1) the point of application, (2) the direction, and (3) the intensity of the forces acting upon each voussoir shall be known. Unfortunately, the accurate determina- tion of the outer forces is, in general, an impossibility.
1. If the arch supports a fluid, the pressure upon the several voussoirs is perpendicular to the extrados, and can easily be found; and combining this with the weight of each voussoir gives the several external forces. This case seldom occurs in practice.
2. If the arch is surmounted by a masonry wall, as is frequently the case, it is impossible to determine, with any degree of accuracy, the effect of the spandrel walls upon the stability of the arch. It is usually assumed that the entire weight of the masonry above the soffit presses vertically upon the arch; but it is known certainly that this is not the case, for with even dry masonry a part of the wall will be self-supporting. The load supported by the arch can be computed roughly by the principle of § 250 (p. 168); but, as this gives no idea of the manner in which this pressure is distributed, it is of but little help. The error in the assumption that the entire weight of the masonry above the arch presses upon it is certainly on the safe side; but if the data are so rudely approximate, it is use- less to attempt to compute the strains by mathematical processes. The inability to determine this pressure constitutes one of the limi- tations of the theory of the arch.
Usually it is virtually assumed that the extradosal end of each voussoir terminates in a horizontal and vertical surface (the latter may be zero) ; and therefore, since the masonry is assumed to press only vertically, there are no horizontal forces to be considered. But as the extrados is sometimes a regular curve, there would be active horizontal components of the vertical pressure on this surface; and this would be true even though the spandrel masonry were divided by vertical Joints extending from the extrados to the upper limit of the masonry. Further, even though no active horizontal forces are developed, the passive resistance of the spandrel masonry — either spandrel walls or spandrel backing — materially affects the stability; of an arch. Experience shows that most arches sink at the crown and rise at the haunches when the centers are removed (see Fig. 116, p. 44?), and hence the resistance of the spandrel masonry will
446 AKCHES, [chap. XVITL
materially assist in preventing the most common form of failure. The eflBciency of this resistance will depend upon the execution of the spandrel masonry, and will increase as the deformation of the arch ring increases. It is impossible to compute, even roughly, the horizontal forces due to the spaiidrel masonry.
Further, in computing the strains in the arch, it is usually assumed that the arch ring alone supports the masonry above it ; while, as a matter of fact, the entire masonry from the intrados to the top of the wall acts somewhat as an arch in supporting its own weight.
3. If the arch supports a mass of earth, we can know neither the amount nor the direction of the earth pressure with any degree of accuracy (see Chap. XIV — Eetaining Walls, — particularly § 527, page 339). We do know, however, that the arch does not support the entire mass above it (see §§ 618-20). No one ever thinks of trying to make a tunnel arch strong enough to sustain the weight of the entire mass above it.
In the theory of the masonry arch, the pressure of the earth is usually assumed to be wholly vertical. That the pressure of earth gives, in general, active horizontal forces appears to be unquestion- able. An examination of Fig. 113 (page 443) will show how the horizontal forces add stability to an arch ring whose rise is equal to or less than half the span. It is clear that for a certain position and intensity of thrust T, the line of resistance will approach the extrados nearer when the external forces are vertical than when they are inclined. We know certainly that the passive resistance of the earth adds materially to the stability of masonry arches ; for the arch rings of many sewers which stand without any evidence of weakness are in a state of unstable equilibrium, if the vertical press- ure of the earth immediately above it be considered as the only external force acting upon it.
667. Method of Failtjee of Arches. A masonry arch may yield in any one of three ways, viz.: (1) by the crushing of the stone, or (2) by the sliding of one voussoir on another, or (3) by rotation about an edge of some joint. 1. An arch will fail if the pressure on any part is greater than the crushing strength of the material composing it. 2. Figs. 114 and 115 represent the second method of failure ; in the former the haunches of the arch slide
ART. 1.]
THEORY OF THE ARCH.
447
out and the crown slips down, and in the latter the reverse is shown. If the rise is less than the span and the arch fails by the sliding of one voussoir on the other, the crown will usually sink; but if the rise is more than the span, the haunches will generally
Fig. 114.
Fig. 115.
be pressed inward and the crown will rise. 3. Figs. 116 and 117 show the two methods by which an arch may give way by rotation
Fig. 116.
Fig. 117.
about the joints. As a rule the first case is most frequent for flat arches and the second for pointed ones.
However, more arches fail on account of unequal settlement of the foundation than because of a faulty design of the arch proper.
668. Ceiteria of Safety. There are three criteria, corre- sponding to the three modes of failure, by which the stability of an arch may be Judged. (1) To prevent overturning, it is necessary that the line of resistance shall everywhere lie between the intrados and the extrados. (2) To prevent crushing, the line of resistance should intersect each joint far enough from the edge so that the maximum pressure will be less than the crushing strength of the masonry. (3) To prevent sliding, the angle between the line of resistance and the normal to any joint should be less than the angle of repose (''angle of friction") for those surfaces; that is to say, the tangent of the angle between the line of resistance and the normal to any joint should be less than the co-efficient of friction (§ 489).
448 ARCHES. [chap. XVIII.
669. Stability against Rotation. An arch composed of incom- pressible voussoirs can not fail by rotation as shown in Fig. 116, unless the line of resistance touches the intrados at two points and the extrados at one higher intermediate point (see Fig. 120, page 454); and an arch can not fail by rotation as shown in Fig. 117, unless the line of resistance touclies the extrados at two points and the intrados at one higher intermediate point (see Fig. 120). The factor of safety against rotation about any point is equal to half the length of the joint divided by the distance between the center of pressure and the center of the joint ; that is to
1 I the factor of safety = —-, (1)
in which I is tlie length of the joint and d the distance between the center of pressure and the center of the joint. For example, if the center of pressure is at one extremity of the middle third of the joint, d =^ \ I ; and, by equation (1), the factor of safety is three. If the center of j^ressure is 5 ^ from the middle of the joint, the factor of safety is two.
It is customary to require that the line of resistance shall lie within the middle third of tlie arch ring, which is equivalent to specifying that the minimum factor of safety for rotation shall not be less tlian three.
670. Stability against Crushing. The method of determining the pressure on any part of a joint has already been discussed in the chapter on masonry dams (see pp. 320-26). When the total press- ure and its center are known, the maximum pressure at any part of the joint is given by formula (23), page 323. It is
P=^+^, . . . „)
in which P is the maximum pressure on the joint per unit of area ; W is the total normal pressure on the joint per unit of length of the arch ; I is the depth of the joint, i. e., the distance from intrados to extrados ; and d is the distance from the center of pressure to the middle of the joint. This formula is general, provided the
ART. l.J THEORY OF THE ARCH. 449
masonry is capable of resisting tension ; and if the masonry is assumed to be incapable of resisting tension, it is still general, pro- vided d does not exceed ^ /.
For the case in which the masonry is incapable of resisting ten- sion and d exceeds \ I, the maximum pressure is given by formula (24), page 324. It is
3(i/-f/) ^"•'
If the line of resistance for any arch can be drawn, the maximum pressure can be found by (1) resolving the resultant reaction per- pendicular to the given joint, and (2) measuring the distance d from a diagram of the arch similar to Fig. 113 (page 443), and (3) sub- stituting these data in the proper one of the above formulas (the one to be employed depends upon the value of d), and computing P.* This pressure should not exceed the compressive strength of the masonry.
It is customary to presci'ibe that the line of resistance shall lie within the middle third of each joint, and also that the result obtained by dividing the total pressure by the area of the joint shall not be more than one twentieth of the ultimate crushing strength of the stone. Under these conditions the maximum pressure is twice the mean, and hence using the above limits is equivalent to saying that the maximum pressure shall not be more than one tenth of the ultimate crushing strengtli of the stone. The mean pressure in arches is usually not more than one fortieth or one fiftieth, and sometimes only one hundredth, of the ultimate compressive strength of the stone or brick of which it is constructed.
671. Unit Pressure. In the present state of our knowledge it is not possible to determine the value of a safe and not extravagant unit working-pressure. The customary unit appears less extrava- gant, when it is remembered (1) that the crushing strength of masonry is considerably less than that of the stone or brick of which it is composed (see §§ 221-22 and §§ 246-47 respectively), and that we have no definite knowledge concerning either the ultimate or the safe crushing strength of stone masonry (§ 223) and but little
* For a numerical example of the method of doiag this, see 2, § 690.
450 ARCHES. [chap. XVIII.
concerning that of brickwork (§ 248) ; and (2) that all the data we have on crushing strength are for a load perpendicular to the pressed surface^ while we have no experimental knowledge of the effect of the component of the pressure parallel to the surface of the joint, although it is probable that this component would have some- what the same effect upon the strength of the voussoirs as a sheet of lead has when placed next to a block of stone subjected to com- pression (§ 12).
On the other hand, there are some considerations which still further increase the degree of safety of the usual working-j^ressure. (1) When the ultimate crushing strength of stone is referred to, the crushing strength of cubes is intended, although the blocks of stone employed in actual masonry have less thickness than width, and hence are much stronger than cubes (see § 15, paragraph 2 § 60, and § 273). To prevent the arch stones from flaking off at the edges, the mortar is sometimes dug out of the outer edge of the joint. This procedure diminishes the area under pressure, and hence increases the unit pressure ; but, on the other hand, the edge of the stone which is not under pressure gives lateral support to the interior portions, and hence increases the resistance of that portion (see § 273). It is imiDossible to compute the relative effect of these elements, and hence we can not theoretically determine the efficiency of thus relieving the extreme edges of the joint. (2) The preceding formulas (2 and 3) for the maximum pressure neglect the effect of the elasticity of the stone ; and hence the actual pressure must be less, by some unknown amount, than that given by either of the formulas.
672. Notice that the distance which the center of pressure may vary from the center of the joint without the masonry's being crushed depends upon the ratio between the ultimate crushing strength and the mean pressure on the joint. In other words, if the mean pressure is very nearly equal to the ultimate crushing strength, then a slight departure of the center of pressure from the center of the joint may crush the voussoir ; but, on the other hand, if the mean pressure is small, the center of pressure may de- part considerably from the center of the joint without the stone's being crushed. This can be shown by equation (2), page 448.
W If both P and -y are large, d must be small ; but if F is large and
mm/imm/m/mm/mi/i/m////ii/\
ART. ].] THEORY OF THE ARCH. 451
^ small, then d may be large. Essentially the same result can be
deduced from equation (3), page 449.
Even though the line of resistance approaches so near the edge of the Joint that the stone is crushed, the stability of the arch is not necessarily endangered. For example, conceive a block of stone resting upon an incompressible plane, AB, Fig. 118, and' assume that the center of pressure is at X Then the Jl^mmd^ pressure is applied over an area pro- i ?ctod in A V, such that AX=^ A V. The pressure at A is represented by « AK, and the area of the triangle Fi«- ^'^^■
AKV represents the total pressure on the joint. Assume that AK is the ultimate crushing strength of the stone, and that the center of pressure is moved to JV'. The pressure is borne on an area projected in A V\ The pressure in the vicinity of A is uniform and equal to the crushing strength ^^j and the total pressure on the joint is represented by the area of the figure A K G V, which has its center of gravity in the vertical through X'. Eventually, when the center of pressure approaches so near A that the area in which the stone is crushed becomes too great, the whole block will give way and the arch will fall.*
673. Open Joints. It is frequently prescribed that the line of - resistance shall pass through the middle third of each joint, " so that the joint may not open on the side most remote from Ibe line of resistance." If the line of resistance departs from the middle third, the remote edge of the joint will be in tension ; but since cement mortar is now quite generally emj^loyed, if the masonry is laid with ordinary care the joint will be able to bear considerable tension (see Table 13, page 94); and hence it does not necessa- rily follow that the joint will open.
* Rankine saj-s : " It is true that arches have stood, and still stand, in which the centers of resistance of joints fall be.vond the middle third of the depth of the arch ring ; but the stability of such arches is either now precarious, or must have been precarious while the mortar was fresh." The above is one reason whj- the stability of the arch is not necessarily precarious, and other reasons are found in § 666 and also in the subsequent discussion. A reasonable theory of the arch will not make a structure appear instable which shows every evidence of security.
452 ARCHES. [chap. XVIII.
If the line of pressure departs from the middle third and the mortar is incapable of resisting tension, the joint will open on the side farthest from the line of resistance. For example, if the center of pressure is at W, Fig. 118, then a jDortion of the joint AV {= 3 AN) is in compression, while the portion VB has no force acting upon it ; and hence the yielding of the portion A Fwill cause the joint to open a little at B. This opening will increase as the center of pressure approaches J, and when the material at that point begins to crush the increase will become comparatively rapid.
Notice that if there are open joints in an arch, it is certain tliat the actual line of resistance does not lie within the middle third of such joints. Notice, however, that the opening of a joint does not indicate that the stability of the arch is in danger. In most cases, an open joint is no serious matter, particularly if it is in the soffit. If in the extrados, it is a little more serious, since water might get into it and freeze. To guard against this danger, it is customary to cover the extrados witli a layer of puddle or some coating impervious to water (§ 204).
674. Stability against Sliding. If the effect of the mortar is neglected, an arch is stable against sliding when the line of resist- ance makes with the norma an angle less than the angle of friction. According to Table 36 (page 315) the co-efficient of friction of masonry under conditions the most unfavorable for stability — /. e., while the mortar is wet — is about 0.50, which corresponds to an angle of friction of about 25°. Hence if the hne of pressure makes an angle with the normal of more than 25°, there is a possibility of one voussoir's sliding on the other. This possibility can be elimi- nated by changing the joints to a direction more nearly at right angles to the line of pressure.
However, there is no probability that an arch will receive its full load before the mortar has begun to set ; and hence the angli^ of friction is virtually much greater than 25°. It is customar; to arrange the joints of the arch at least nearly perpendicular to the line of resistance, in which case little or no reliance is placed on the resistance of friction or the adhesion of the mortar.
675. Conclusion. From the preceding discussion, it will be noticed that the factors of stability for rotation and for crushing are dependent upon each other ; while the factor for sliding is independent of tlie other conditions of failure, and is dependent
AKT. 1.] THEORY OF THE ARCH. 453
only upon the direction given to the joints. A theoretically perfect design for an arch would be one m which the three factors of safety were equal to each other and uniform throughout the arch. As arches are ordinarily built, the factor for rotation is about three, or a little more ; the nominal factor for crushing is ten to forty ; and the nominal factor for sliding is one and a half to two.
It is evident that before any conclusions can be drawn concern- ing the strength or stability of a masonry arch, the position of the line of resistance must be known ; or, at least, limits must be found within which the true line of resistance must be proved to lie.
676. Location of the True Line of Resistance. Tlie de- termination of the line of resistance of a semi-arch requires that the external forces shall be fully knoAvn, and also that (1) the amount, (3) the point of application, and (3) the direction of the thrust at the crown shall be known. The determination of the external forces is a problem independent of the theory of the arch ; and for the present it will be assumed that they are fully known, although as a matter of fact they can not be known with any considerable degree of accuracy (see § 666).
Each value for the intensity of the thrust at the crown gives a different line of resistance. For example, in Fig. 113 (page 443), if the thrust T be increased, the point I — where R^ intersects the plane of the joint HI — will approach /; and consequently c, d, and e will approach G, H, and A respectively. If T be increased sufficiently, the line of pressure will pass through A or H (usually the former, this depending, however, upon the dimensions of the arch and the values and directions of F^, F^, and F^), and the arch will be on the point of rotating about the outer edge of one of these joints. This value of T is then the maximum thrust at a consistent with stability of rotation about the outer edge of a joint, and the corresponding line of resistance is the line of resistance for maxi- mum thrust at a. Similarly, if the thrust T'be gradually decreased, the line of resistance will approach and finally intersect the intrados, in which case the thrust is the least possible consistent with stabil- ity of rotation about some point in the intrados. The lines of resistance for maximum and minimum thrust at a are shown in Fig. 119 (page 454).
If the point of application of the force T'be gradually lowered and at the same time its intensity be increased, a line of resistance
454
ARCHES.
[chap. XVIIT.
may be obtained ■which will have one point in common with the intrados. This is the line of resistance for maximum thrust at the crown joint. Simi- larly, if the point of application of T be gradually raised, and at the same time its intensity be decreased, a line of resistance may be obtained which will have one point in common with the extrados. This is the line of resistance for minimum thrust at The lines of resistance the crown are shown in
Fig. 119.
Fig. 120.
the crown joint. for maximum and minimum thrust at Fig. 120.
Similarly each direction of the thrust T will give a new line of re- sistance. In short, every different value of each of the several factors, und also every combination of these values, will give a different position for the line of resistance. Hence, the problem is to determine which of the infinite number of possible lines of resistance is the actual one. This problem is indeterminate, since there are more unknown quantities than conditions (equations) by which to determine them. To meet these difficulties and make a solution of the problen;i possible, various hypotheses have been made ; but there is no unanimity of opinion among authorities regarding the position of the true line of resistance. Some of these hypotheses will now be considered briefly.
677. Hypothesis of Least Pressure. Some writers have assumed the true line of resistance to be that which gives the smallest abso- lute pressure on any joint. This principle is a meta-physical one, and leads to results unquestionably incorrect. Of the four hypo- theses here discussed this is the least satisfactory, and the least frequently employed. It will not be considered further.
For an explanation of Claye's method of drawing the line of pres'^ure according to this theory, see Van Nostrand's Engineering Magazine, vol. xv, pp. 33-36. For a general discussion of the theory of the arch founded on this hypothesis, see an article by Pro-
ART. 1.] THEORY OF THE ARCH. 455
lessor Du Bois in A"an Xostrand's Engineering Magazine, vol. xiii, pp. 341-46, and also Du Bois's '•Graphical Statics," Chapter XV.
678. Hypothesis of Least Thrust at the Crown. According to this iiypothesis the true line of resistance is that for which the thrust at the crown is the least possible consistent with equilibrium. This assumes that the thrust at the crown is a passive force called into action by the external forces ; and that, since there is no need for a further increase after it has caused stability, it will be the least possible consistent with equilibrium.
This principle alone does not limit the position of the line of resistance; but, if the external forces are known and the direction of the thrust is assumed, this hypothesis furnishes a condition by which the line of resistance corresponding to a minimum thrust can be found by a tentative process. The principle of least crown thrust was first proposed by Moseley,*' was amplified by Scheffler,f and has been adopted more generally
by writers and engineers than any jwj Wj [w/, I*"! other. . ^..^._x;^^=— r — |C
679. The portion of the arch shown \i^""'j^ ' \ ! 1 ! m Fig. 121 is held in equilibrium by (1) y<C j; VH""*^ : ii the vertical forces, w,, w^, etc., (2) by r/t \i^ • i \
the horizontal forces 7i J, /<„, etc., (3) by /^-^X/C.-.m j-, -: ^*-
the reaction R at the abutment, and (4) A)C— \—i, \
bv the thrust r at the crown. The !* -x,-—--->!
r . Fig. 121.
direction of R is immaterial in this
discussion. Let a and l represent the points of application of T and R, respectively, although the location of these points is yet un- determined. Let
7^= the thrust at the crown;
a'j = the horizontal distance from h to the line of action of ii\ ; x^ = the same for u\, etc. ;
* Philosophical Magazine, Oct., 1833 — see Moseley's Mechanical Principles of En- gineering, 2d American ed., p. 430.
t " Theorie der Gewolbe, Futtermauern, und eisernen Briicken.'' Braunschweig, 1857. A French translation of this work is entitled " Traits de la Stability des con- structions ; Ire partie, Theorie des Voutes et des Murs de Soutenement," Paris, 1864. Cain's " A Practical Theory of Voussoir Arches " — No. 12 of Van Nostrand's Science Series — New York, 1874, is an exposition of a theory of the arch based upon thia hypothesis.
4:^6 ARCHES. [chap. XVIII.
y = the perpendicular distance from b to the line of action of T; k^ = the perpendicular distance from b to the line of action of
h^- k^ = the same for h^; etc. Then, by taking moments about b, we have
Ti/ = w^ rr, + ii\ 2\ + etc. + h^ h^ + A, ^% + etc. ; . (4) hence
r^^^WX 2hh
y y
1. The value of T depends upon ^ h h — the sum of the moments of the horizontal component of the external forces; — but we know neither the nature of the material over the arch nor the value of ^hkiov any particular material (see §§ 527-31). In discussing and applying this principle, the term ^ h Tc is usually neglected. Ordinarily this gives an increased degree of stability; but this is not necessarily the case. The omission of the effect of the horizontal component makes the computed value of Tless than it really is, and causes the line of resistance found on this assump- tion to approach the infrados at the haunches nearer than it does in. fact ; and hence the conditions may be such that the actual line of resistance will be unduly near the cxtrados at the haunches, and consequently endanger the arch in a new direction.
2. For simplicity of discussion, and because the error involved in the discussion immediately to follow is immaterial, we will tempo- rarily omit the effect of the horizontal components of the external forces. If the horizontal forces are disregarded, equation (5) becomes
T=?^'^ (G)
y
From equation (6) we see that, other things remaining the same, the larger // the smaller T ; and hence, for a minimum value of 7', a should be as near c as is possible without crushing the stone (see §§ 670-72). Usually it is assumed that ac is equal to one third of the thickness of the arch at the crown ; and hence the average pressure per unit of area is to be equal to one half of the assumed unit working pressure ; or, in other words, twice the thrust T divided by tlie thickness of the crown is to be equal to the unit working pressure.
ART. 1.] THEORY OF THE ARCH. 457
3. To determine y. it is necessary that the direction of T should be known. It is usually assumed that T is horizontal. If the arch is symmetrical and is loaded uniformly over the entire span, this assumption is reasonable ; but if the arch is subject to heavy moving loads, as most are, the thrust at the crown is certainly not hori- zontal, and can not be determined.
4. If the joint A B is horizontal, then h is to be taken as near A as is consistent with the crushing strength of the stone, or at, say, one third of the length of the joint ^4 B from ^4. Xotice that if the springing line is inclined, as in general it will be (see last two paragraphs of § 682, p. 463), moving h toward A decreases .r, and will at the same time increase y. Hence the position of b cor- responding to a minimum value of T can be found only by trial. It is usual, however, to assume that Ah is one third of AB. what- ever the inclination of the joint.
680. Joint of Rupture. The joint of rupture is that joint for which the tendency to oj^en at the extrados is the greatest. The joint of rupture of an arch is analogous to the dangerous section of a beam. Practically, the joint of rupture is the springing line of the arch, the arch masonry below that joint being virtually only a part of the abutment.
That no joint may open at the extrados, the thrust at the crown must be at least equal to the maximum value of T as determined by equation (5), page 45G. If the thrust is less than this, the joint of rupture will open at the extrados ; and a greater value is incon- sistent Avith the hypothesis of minimum crown thrust. Since the moment of the horizontal components of the external forces is indeterminable, the position of the true joint of rupture can be found only by trial for assumed values and positions of tlie hori- zontal forces.
681. As an example, assume that it is required to determine the joint of rupture of the 16-foot arch shown in Fig. 122, which is the standard form employed on the Chicago, Kansas & Xebraska I\. R. (see page 427 and Plate III). Assume that the arch supports an embankment of earth extending 10 feet above the crown, and that the earth weighs TOO pounds per cubic foot and the masonry 100. For simplicity, consider a section of the arch only a foot thick periDcndicular to the plane of the paper. The half-arch ring and the earth embankment above it are divided into eight sections,
4'58
ARCHES.
[chap. XVIII.
■which for a more accurate determination of the joint of ruj^ture are made smaller near the supposed position of that joint. The weight of the first section rests upon the first joint, that of the first two upon the second joint, etc. The values and the positions of
Fig. 123.
the lines' of action of the weights of the several sections are given in the second and third columns of Table 59.*
* The center of gravity of the arch stone is found by the method explained in § 494 (page 318); and the center of gravity of the prism of earth resting upon each arch 6tone may, without sensible error, be taken as acting through its medial vertical line. The center of gravity of the combined weight of the arch stone and the earth resting upon it may be found by either of the two following methods, of which the first is the shorter and more accurate :
1. The center of gravity of the two masses may be found by the following well- known principle of analytical mechanics :
Wj Xi -\- u'2 a"j
(7)
in which x is the horizontal distance from any point, say the crown, to the vertical through the center of gravity of the combined masses, k', and u\ are the weights of the two masses, and z^ and x^ the horizontal distances from any point, say the crown, to the verticals through the centers of gravity of the separate masses respectively. The same method can be employed for finding the center of gravity of any number of masses, by simply adding the corresponding term or terms in the numerator and the denominator of equation (7).
2. Since the principles employed in the second method of finding the center of gravity of each arch stone and its load are frequently employed, in one form or
ART. 1.]
THEORY OF THE ARCH.
469
TABLE 59. To FIND THE Joint of Ruptuke of the Arch Ring shown in Fig. 122.
|
FOSITIO.N OF THE |
|||||||||
|
Data for Ver- |
Data for Hori- |
Center of |
|||||||
|
tical |
Forces. |
zontal Forces. |
Pressure for |
Thrust |
AT the Crown. |
||||
|
each |
Joint. , |
||||||||
|
55 |
|||||||||
|
<D |
tk« r^ |
(D |
-, •- * c |
||||||
|
^-c |
J3 |
■°ot |
JS |
gft5s |
|||||
|
si. |
0 3 D 0 U |
= 0 as 0 0 s 5'-s |
■s a 3 (6 0 0 as |
ertical distai f point of ap aiion from op of the crc oint. |
3 PI 1. H 0 0 e8 - |
%W X |
y |
Total thrust. |
|
|
55*- -^ |
<!'" |
m-oi- |
>'^« |
||||||
|
Lbs. |
Feet. |
Lbs. |
Feet. |
Feet. |
Feet. |
Lbs. |
Lbs. |
Lbs |
|
|
1 |
2.9.38 |
1.20 |
66 |
0.10 |
2.20 |
1.18 |
3.866 |
94 |
3.960 |
|
2 |
3.04.5 |
3.. 57 |
243 |
0.155 |
4 27 |
1.86 ' |
7.744 |
308 |
8.052 |
|
3 |
1.644 |
5.33 |
192 |
1.17 |
5.27 |
2.42 |
8,518 |
424 |
8,942 |
|
4 |
1.716 |
6.45 |
259 |
1,78 |
6.17 |
3.11 |
S.74.f |
662 |
Q.410 |
|
5 |
1.825 |
7.50 |
315 |
2.. 53 |
6.98 |
3.90 |
8,577 |
700 |
!i.277 |
|
6 |
1,888 |
8.47 |
415 |
3.40 |
7.71 |
4.81 |
8.407 |
941 |
9..S48 |
|
7 |
3,939 |
9.77 |
1,030 |
5.02 |
8.85 |
6.84 |
7.506 |
1.407 |
8,911 |
|
8 |
4,098 |
11.05 |
1,624 |
7.70 |
9.50 |
9.25 1 |
S,<?^ |
1,983 |
7,973 |
another, in discussions of the stabilitj- of the masonry arch, this method will be ex- plained a little more fully than is required for the problem in hand.
The first step is to reduce the actual load upon an arch (including the weight of the arch ring itself) to an equivalent homogeneous load of the same density as the arch ring. The upper limit of this imaginary loading is called the red need -load contour. For example, suppose it is required to find the reduced-load contour for the arch loaded as in Fig. 123. Assume that the weight of the arch ring is 160 pounds per
Fig. 123.
Fig. 124.
cubic foot ; that of the rubble backing, 140 ; and that of the earth, 100. Then the ordinate at a to the load contour of an equivalent load of the density of the arch ring
is equal to ab + bc
140
+ CI
100
= > say,gf. The value of ^/is laid off in Fig. 124.
160 ' ' " 160
Computing the ordinates for other points in the load contour gives the line E F, Fig. 124, which is the reduced-load contour for the load shown in Fig. 123. The area between the intrados and the reduced-load contour is proportional to the load on the arch. In a similar manner, a live load (as, for example, a train) can be reduced to an equivalent load of masonry,— in which case the reduced-load contour would con- sist of a line O H above and parallel to E I for that part of tbe spau covered by the
460 AKCHES. [chap. XVIII.
The value and position of the horizontal components of the external forces are somewhat indeterminate (see §§ 528-31). Ac- cording to Eankine's theory of earth pressure,* the horizontal
pressure of earth at any point can not be greater than — - — . — —
times the vertical pressure at the same point, nor less than
times the vertical pressure, — 0 being the angle of
1 -f- sin 0
repose. + If 0 = 30°, the above expression is equivalent to saying that the horizontal pressure can not be greater than three times the vertical pressure nor less than one third of it. Evidently the horizontal component will be greater the harder the earth spandrel-filling is rammed into place. The condition in which the earth will be deposited behind the arch can not be foretold, but it is probable that at least the minimum value, as above, will always be realized. Hence we will assume that the horizontal intensity is at least owe tliird of the vertical intensity ; that is to say, /i =z 1 e c? ?, in which e is the weight of a cubic unit of earth — which was assumed above at 100 pounds, — d the depth of the center of pressed surface below the top of the earth filling, and / the vertical dimension of the surface. The values and the positions of the horizontal forces acting on the respective sections of the arch ring are given in the second double column of Table 59.
To find the least thrust at the crown consistent with stability of rotation, assume that the center of pressure on any joint is at a distance from the intrados equal to one third of the IcDgth of the joint (see paragraph 4, page 45T). The co-ordinates to the several centers of pressures are given in the third double column of Table 59. Notice that the several values of x and h are simply the differ- ences between two quantities given in the table. The thrust at the crown is supposed to be applied at the upper limit of the middle third of the crown joint. The length of the crown joint is 1.25 feet; and hence the several values of y are the respective quantities in the
train : while for the remainder of the span, the line I F is the reduced-load contour. The second step is to draw the arch ring and its reduced-load contour on thick paper, to a large scale, and then, with a sharp knife, carefully cut out the area repre- senting the load on each arch stone. The center of gravity of each piece, as ij k I m a. Fig. 124, can be found by balancing it on a knife-edge ; and then the position of the center of gravity is to be transferred to the drawing of the arch.
* See ^ .544, page .348.
+ Rankine's Civil Engineering, p. 320.
»RT. 1.] THEORY OF THE ARCH. 461
seventh column of Table 59 minus ^ of 1.20 feet. The last three columns of the table contain the values of the crown thrust as computed by equation (5), page 456.
Au inspection of the results in the last column of Table 59 shows that the thrust is a maximum for joint 4. A repetition of the computations, using smaller divisions of the arch ring, might show that the absolute maximum occurs a little to one side or the other of this joint; but the uncertainty in the data for both the vertical and the horizontal forces is too great (see § G19 and §§ 527-31 respectively) to justify an attempt at absolute accuracy, and hence we will assume that joint 4 is the true joint of rupture. The angular distance of this joint from the crown is 45°, which quantity is termed the angle of rupture.
Any increase in the assumed intensity of the horizontal com- ponents increases the computed value of the angle of rupture. For example, if the quantities in the next to the last column of Table 59 be doubled, the thrust for joint 7 will be the maximum. Probably this condition could be realized by tightly tamping the earth spandrel-filling.
Notice that the preceding discussion of the position of the joint of rupture is for a uniform stationary load. The angle of rui)ture for a concentrated moving load will differ from the results found above; but the mathematical investigation of the latter case is too complicated and too uncertain to justify attempting it.
682. In discussions of the position of the joint of rupture, the horizontal components are usually neglected.* This phase of the subject will be considered only briefly. The following is the method usually employed f in investigating the position of the joint of rupture, and is based on the assumption that the crown thrust is correctly given by equation (6), page 456.
Let ir=the total weight resting on any joint; .t = the hori- zontal distance of the center of gravity of this weight from the origin of moments; and // = the arm of the crown thrust. Then equation (6) becomes
^=T" (')
*So far as observed, Rankine's investigation is the only exception; and it is, in fact, only an apparent exception (see paragraph 2, page 490).
tFor example, see Sonnet's Dictionnaire des Mathdmatique Appliqudes, pp. 1084-85.
^ - (9)
462 ARCHES. ^[CHAP. XVIIL
To determine the condition for a maximum, it is assumed that W, X, and i/ are independent variables. Differentiating equation (8),
dy ~ y dij y^ '
but d{ Wx) = Wdx -\- dW . ^ dx = Wdx, and then
dT_^dx_ Wx
dy ~ y dy y
Hence the condition for a maximum crown thrust is
'^=^- • . (10)
dy y ^ '
The usual interpretation of equation (10) is: " The joint of rup- ture is that joint at Avhich the tangent to the intrados passes through the intersection of T and the resultant of all the vertical forces above the joint in question."
The position of the joint of rupture can be found by the above principle only by trial. This method possesses no advantage over the one explained in the preceding section, and is less convenient to apply. The preceding investigation is approximate for the following reasons: 1. The effect of the horizontal forces is omitted. 2. ]]\ X, and ?/are dependent variables, and not independent as assumed. 3. In the interpretation of equation (10), instead of "the tangent to the intrados," should be employed the tangent to the line of resistance.
In applying this method, a table, computed by M. Petit, which gives the angle of rupture in terms of the ratio of the radii of the intrados and the extrados, is generally employed. The table in- volves the assumption that a, Fig. 121 (p. 455), is in the extrados and b in t]ie intrados; and also that the intrados and extrados are parallel According to this table, '' a semi-circular arch of which the thickness is uniform throughout and equal to the span divided by seventeen and a half is the thinnest or lightest arch that can stand. A thinner arch would be impossible." If the line of re- sistance is restricted to the middle third, then, according to this theory, the thinnest semi-circular arch which can stand is one whose span is five and a half times the uniform thickness. Many
AET. 1.] THEORY OF THE ARCH. 463
arches in which the thickness is much less than one seventeenth of the span stand and carry heavy loads without showing any evi- dence of weakness. For example, in arch No. 26 of Table 63 (pp. 502-3), which is frequently cited as being a model, the average thick- ness is 3.25 ft., or about one twenty-JiftJi of the sj^an; and since no joints open, the line of resistance must lie in the middle third, even though the thickness is only one fifth of that required by the table. Owing to the approximations involved, and also to the limi- tations to arches having intrados and extrados parallel, the ordi- nary tables for the position of the joint of rupture have little, if any, practical value. The only satisfactory way to find the angle of rupture is by trial by equation (5), as explained in § 681.
According to M. Petit's table, if the thickness is one fortieth of the diameter, the angle of rupture is 46° 12'; if the thickness is one twentieth, the angle is 53° 15'; and if one tenth, 59° 41'.
In conclusion, notice that the investigations of both this and the preceding section show that an arch of more than about 90° to 120° central angle is impossible.
683. Winkler's Hypothesis. Prof. Winkler, of Berlin,— a well- known authority — published in 1879 in the " Zeitschrift des Archi- telcten unci Ingenienr Vereins zu Hannover," page 199, the follow- ing theorem concerning the position of the line of resistance: "For an arch ring of constant cross section that line of resistance is approximately the true one Avhich lies nearest to the axis of the arch ring, as determined by the method of least squares." *
The only proof of this theorem is that by it certain conclusions can be drawn from the voussoir arch which harmonize with the accepted theory of solid elastic arches. The demonstration de- pends upon certain assumptions and approximations, as follows: 1. It is assumed that the external forces acting on the arch are vertical; whereas in many cases, and perhaps in most, they are inclined. 2. The loads are assumed to be uniform over the entire span ; whereas in many cases the arch is subject to moving con- centrated loads, and sometimes the permanent load on one side of the arch is heavier than that on the other. 3. It is assumed that the load included between the lines PGD and NHC, Fig. 122 (page 458), is equal in all respects to that included between PG2
* This theorem was first brought to the attention of American readers in 1880, by Professor Swain in an article in Van Nostrand's Engln'g Mag., vol. xxiii, pp. 26.5-74
464 ARCHES. [chap. XVIII.
and NIIl. The error thus involved is inappreciable at the crown, but at the springing of semicircular arches is considerable. 4. The conclusions drawn from the voussoir (masonry) arch only approxi- mately agree with the theory of elastic (solid iron or wood) arches. 5. Masonry arches do not ordinarily have a constant cross section as required by the above theorem; but it usually, and properly, increases toward the springing. 6. The phrase " as determined by the method of least squares " means that the true line of resist- aiice is that for which the sum of the squares of the vertical deviations is a minimum. Since the joints must be nearly perpen- dicular to the line of resistance, the deviations should be measured normal to that line. For a uniform load over the entire arch, the lines of resistance are comparatively smooth curves; and hence, if the sum of the squares of the vertical deviations is a minimum, that of the normal also Avould probably be a minimum. But for eccentric or concentrated loads it is by no means certain that such a relation would exist. 7. The degree of approximation in this theorem is le.-s the flatter the arch.
684. To apply Winkler's theorem, it is necessary to (1) con- struct a line of resistance, (2) measure its deviations from the axis, and (3) compute the sum of the squares of the deviations; and it is then necessary to do the same for all possible lines of resistances, the one for which the sum of the squares of the deviations is least being the " true" one.
Instead of applying Winkler's theorem as above, many writers employ the following principle, which it is asserted follows directly from that theorem: "If any line of resistance can be constructed within the middle third of the arch ring, the true line of resistance lies within the same limits, and hence the arch is stable." This assertion is disputed by Winkler himself, who says it is not, in geu- .eral, correct.* It does not necessarily follow that because one line of resistance lies within the middle third of the arch ring, the ■" true" line of resistance also does; for the " true" line may coin- cide very closely with the axis in one part of the arch ring and • depart considerably from it in another part, and still the sum of the squares of the deviations be a minimum. This method of applying "Winkler's theorem is practically nothing more or less than an appli-
* Prof. Swain's review of Winkler's Theorem — Van Nostrand's Engineering Magar zine, vol. xxiii. p. 275.
ART. 1.] THEORY OF THE ARCH. 465
cation of the conclusions derived from the hypothesis of least resistance (§ 677).
685. Navier's Principle. It is well known, from the principles of fluid pressure, that the tangential thrust at any point of a circle pressed by normal forces is equal to the pressure per unit of area multiplied by the radius. " The condition of an arch of any form at any point where the pressure is normal is similar to that of a cir- cular rib of the same curvature under a normal pressure of the same intensity; and hence the following principle: tlie thrust at any nor laalhj pressed point of a linear arch is the product of the radius of curvature by the intensity of the pressure at that point. Or, denoting the radius of curvature by p, the normal pressure per unit of length of intrados by ^;, and the thrust by T, we have
T=pp:' (11)
The above relation, due originally to Navier, has in itself nothing to do with the position of the line of resistance; but is employed by writers who assume that an arch is stable if a line of resistance can be drawn anywhere within the middle third of the arch ring, to determine the crown thrust. Xotice, however, that under these conditions the radius of curvature is known only within limits. An example of its application will be referred to later (§ 704; and 8, § 705; — pp. 482 and 486 respectively).
686. Theories of the Arch. Various theories have been proposed from time to time, which differ greatly in the fundamental principles involved. Unfortunately, the underlying assumptions are not usually stated ; and, as a rule, the theory is presented in such a wav as to lead the reader to believe that each particular method ''is free from any indeterminateness, and gives results easily and accurately." Every theory of the masonry arch is approximate, owmg to the uncertainty concerning the amount and distribution of the external forces (§ 666). to the indeterminateness of the posi- tion of the true line of resistance (§§ 676-85), to the neglect of the influence of the adhesion of the mortar and of the elasticity of the material, and to the lack of knowledge concerning the strength of masonry; and, further, the strains in a masonry arch are indeter- minate owincr to the effect of variations in the material of which the
466 ARCHES. [chap. XVIII.
arch is composed, to the effect of imperfect workmanship in dress- ing and bedding the stones, to the action of the center — its rigidity, the method and rapidity of striking it, — to the spreading of the abutments, and to the settling of the foundations. These elements are indeterminate, and can never be stated accurately or adequately in a mathematical formula ; and hence any theory can be at best only an approximation. The influence of a variation in any one of these factors can be approximated only by a clear comprehension of the relation which they severally bear to each other ; and hence a thorough knowledge of theoretical methods is necessary for the. intelligent design and construction of arches.
A few of the most important theories will now be stated, and the fundamental principles involved in each explained.
687. To save repetition, it may be mentioned here, once for all, that every theory of the arch is but a method of veritication. The first step is to assume the dimensions of the arch outright, or to make them agree with some existing arch or conform to some em- pirical formula. The second step is to test the assumed arch by the theory, and then if the line of resistance, as determined by the theory, does not lie within the prescribed limits — usually the middle third, — the depths of the voussoirs must be altered, and the design must be tested again.
688. Rational Theory. The following method of determining the line of resistance is based ujoon the hypothesis of least crown thrust (§ 678), and recognizes the existence of the horizontal com- ponents of the external forces. Unfortunately, the results found by this method, as well as those by all others, are rendered some- what uncertain by the indeterminateness of the external forces (§ 666).
689. Symmetrical Load. General Solution. As an example of the application of this theory, let us investigate the stability of the serai-arch shown in Fig. 125 (page 467). The first step is to determine the line of resistance. The maximum crown thrust was computed in Table 59 (page 459), as already explained (§ 681). To construct the force diagram, a line 7?0 is drawn to scale to represent the maximum thrust as found in the fourth line of the last column of Table 59. From 0, w, is laid off vertically upwards ; and from its extremity, li^ is laid off horizontally to the left. Then the line from 0 to the left-hand extremity of 7i, (not shown in this
ART. l.J
EATIOXAL THEORY OF THE ARCH.
467
particular case) represents the direction and amount of the external force F^ acting upon the first division of the arch stone ; and the line 7?j from B to the upper extremity of F^ represents the resultant pressure of the first arch stone upon the one next below it. Simi- larly, lay off u\ vertically upwards from the left-hand extremity of //,, and lay off h^ horizontally to the left; then a line F^ from the upper end of u\ to the left-hand end of li^ represents the resultant of the external forces acting on the second divisions of the arch, and a line E^ from the upper extremity of F„ represents the resultant pressure of the second arch stone on the third. The force diagram is completed by drawing lines to represent the other values of ii\ //, F^ and the corresponding reactions.
Fig. 125.
In f he diagram of the arch, the points in which the horizontal «nd vertical forces acting upon the several arch stones intersect, are marked 7, , g„ , etc., respectively ; and the oblique line through each of these points shows the direction of the resultant external force acting on each arch stone.
To construct tlie line of resistance, draw through U — the upper
468 ARCHES. [chap. XVIII.
limit of the middle third of the crown joint — a horizontal line to an intersection with the oblique force through g^ ; and from this point draw a line parallel to R^ , and prolong it to an intersection with the oblique force through g^. In a similar manner continue to the springing line. Then the intersection of the line parallel to i?, with the first joint gives the center of pressure on that joint ; and the intersection of R^ with the second joint gives the center of pressure for that joint, — and so on for the other joints. Each center of pressure is marked by a circular dot. A line connecting these centers of pressure would be the line of resistance; but the line is not shown in Fig. 125.
690. The next step is to determine the degree of stability.
1. Since the line of resistance lies within the middle third of the arch ring, and touches the inner limit of that third at two jjoiuts and its outer limit at an intermediate and higher point, the factor against rotation is 3 (see § 6G9).
2. The unit working pressure is found by applying equation (2),
2 W page 448. At the crown, d ■=^ \l, and hence P = -^— ; or, since
W = 9,400 pounds and I = 1.25 feet, P = 15,040 pounds per square foot = 104 pounds per square inch. At the springing, W = 21,700 pounds, / = 4,5 feet, and d — 0.10 feet ; and therefore
p 21.700 , 6 X 21,700X0.10 . q^. , . .„ . ..^ P = -~^-^- H ^y = 4,820 + 643 = 5,463.
That is, F = 5,463 pounds per square foot, or 38 pounds per squar^ inch. Except for a particular kind of stone and a definite quality of masonry, it is impossible even to discuss the probable factor of safety ; but it is certain that in this case the nominal factor is excessive (see § 223), while the real factor is still more so (see §§ G71-72).
If the maximum pressure at the most compressed joint had been more than the safe bearing power of the masonry, it would have been necessary to increase the depth of the arch stones and repeat the entire process. Notice that the total pressure on the joints increases from the crown toward springing, and that hence the depth of the arch stones also should increase in the same direc- tion.
3. To determine the degree of stability against sliding, notice
ART. 1.] RATIONAL THEORY. 46&
that the angle between the resultant pressure on any joint and the joint is least at the springing joint ; and hence the stability of this joint against sliding is less than that for any other. The nominal factor of safety is equal to the co-efficient of friction divided by tan (90° — 72°) = tan 18° = 0.33. An examination of Table 36 (page 315) shows that when the mortar is still wet the co-efficient is at least 0.50 ; and hence the nominal factor for the joint in question is at least 1^, and probably more, wliile the real factor is still greater. The nominal factor for joint 7 is at least 34, and that for joint 3 is about 5. There is little or no probability tiiat an arch will be found to be stable for rotation and crushing, and unstable for sliding. If such a condition should occur, the direc- tion of the assumed joint could be changed to give stability.* The actual joints should be as nearly perpendicular to the line of resist- ance as is consistent with simplicity of workmanship and with stability. For circular arches, it is ordinarily sufficient to make all the joints radial. In Fig. 125, the joints are radial to the intrados ; but if they had been made radial to the extrados or to an intermedi- ate curve, the stability against sliding, particularly at the springing joint, would have been a little greater.
691. Special Solution. The folloAving entirely graphical solution is useful when it is desired to find a line of resistance which will pass through two predetermined points.
For example, assume that it is desired to pass a line of resistance through ?7and «, Fig. 126 (page 470), the former being the upper extremity of the middle third of the crown joint and the latter the inner extremity of the middle third of joint 4.
The value and positions of the external forces, which are the same as those employed in Fig. 125, are given in Table 59 (page 459). Construct a load line, as shown in the force diagram, hy laying off iv^ and h^ , and w^ ^^^ ^'2 ? ^tc, in succession, and drawing F^, F^, etc. Since the load is symmetrical, we may assume that the thrust at the crown is horizontal ; and hence we may choose a pole at any point, say P', horizontally opposite 0. Draw lines from F' to the extremities of F^, F^, etc. Construct a trial equilibrium polygon by drawing through CT^aline parallel to the line F'O, of the force diagram, and prolong it to b where it intersects F^ . From
* Strictly any change in the direction of the joints will necessitate a recomputatioa of the entire problem ; but, except in extreme cases, such revision is unnecessary.
470
ARCHES.
[chap. XVIII.
b draw a line he parallel to R\ of the force diagram ; from r, the point where he intersects the line of F^, draw a line c d parallel to R\ ; from d, the point where c d intersects F^ , draw a line d e parallel to R\ ; and from e, the point where d e intersects F^ , draw a line ef parallel to R\ . Prolong the line fe to r/, the point in
Fig. 1-X.
which it intersects the prolongation of Ub ; and then, by the prin- ciples of graphical statics, ^ is a point on the resultant of the forces F^,F,, F^, and F^.
The section of the arch from the crown joint to joint 4 is at rest under the action of the crown thrust 7\ the resultant of the external forces, and the reaction of joint 4. Since the first two intersect at g, and since it has been assumed that the center of pressure for joint 4 is at a — the inner extremity of the middle third, — a line ag must represent the direction of the resultant reaction of joint 4; and hence the line R^, in the force diagram drawn from the upper extremity of F^ , parallel to a g, to an intersection with P' 0, reprasents, to the scale of the load line, the amount of the reaction of joint 4. Then PO, to the same scale, represents the crown thrust corresponding to the line of resistance passing through U and a ; and a line — not shown in Fig. 12G^from the upper
ART. 1.] RATIONAL THEORY. 471
eAtremity of F^ to the lower extremity of F^ , would represent, in both direction and amount, the resultant of F^, F^, F^, and F^ .
Having found the thrust at the crown, complete the force dia- gram by drawing the lines E^, R^, R^, etc. ; and then construct a new equilibrium polygon exactly as was described above for tlie trial equilibrium polygon. The construction may be continued to the springing line. Tlie equilibrium polygon shown in Fig. 126 by a solid lino was obtained in this way.
The amount of the pressure on any Joint is given by the length of the corresponding ray in the force diagram. The points in which the sides of tne equilibrium polygon cut the joints are the centers of pressure on the respective joints. The stability of the arch may be discussed as in § 690.
692. One of the most useful applications of the method described in the preceding section is in determining the line of resistance for a segmental arch having a central angle so small as to make it obvious that the joint of rupture (§§ 680-81) is at the springing.
For example, assume that it is required to draw the line of resistance for the circular arch shown in Fig. 127 (p. 472). The span is 50 feet, the rise 10 feet, che depth of voussoirs 2.5 feet, and the height of the earth above the summit of the arch ring'is 10 feet. The angular distance of the springing from the crown is 43° 45' ; and since the angle of rupture is nearly always more than 45°, it is safe to assume that the joint of rupture is at the springing.
The method of determining tlie line of resistance is the same as that explained in § 691, and is sufficiently apparent from an inspection of Fig. 127.
693. Unsymmetrical Load. The design for an arch ring should not be considered perfect until it is found that the criteria of safety (§§ 668-75) are satisfied for the dead load and also for ■every possible position of the live load. A direct determination of the line of resistance for an arch under an unsymmetrical load is impossible. To find the line of resistance for an arch under a symmetrical load, it was necessary to make some assumption con- cerning (1) the amount of the thrust, (2) its point of application, and (3) its direction ; but when the load is unsymmetrical, Ave neither know any of these items nor can make any reason;ible iiypothesis by which they can be determined. For an unsymmetri- cal load we know nothing concerning the position of the joint of
472
AECHES.
[chap. XVIII.
rupture, and know that the thrust at the crown is neither horizontal nor applied at one third of the deptli of that joint from the
Fig. 127
crown : and hence the preceding methods can not be employed. When the load is not symmetrical, the following method may be employed to find a line of resistance ; but it gives no indication as to which of the many possible lines of resistance is the true one.
Let it be required to test the stability of a symmetrical arch hav- ing a uniform live load covering half the span. Divide the arch and its load into sections, as shown in Fig. 128. The live load is a ver- tical force, and the earth pressure Avould give a horizontal compo- nent. The approximate reduced-load contour for the vertical forces is shown in Fig. 128, and the horizontal and vertical components are laid off in the force diagram. An equilibrium polygon can be made to pass through any three points ; and therefore we may as- sume three points for a trial equilibrium polygon, — as, for example, (1) the lower limit of the middle third of the joint at the abutment A, (2) the middle, C, of the crown joint, and (8) the upper limit of the middle third of the joint at B.
ART. 1.]
RATIONAL THEORY.
473
Construct a force diagram by laying off the external forces suc- cessively from 0 in the usual way (§ 689), selecting a pole, P', at any point, and drawing lines connecting F' with the points of division of the load line. Then, commencing at A, construct an equilib- rium polygon through A, C , and B' , by the method explained in §§ 091-92.
It is then necessary to move the pole of the force diagram in such a way that the equilibrium polygon will pass through b instead of B'. To do this, draw a line through the pole P' , parallel to A B' — the closing line of the trial equilibrium poh'gon, — and then tlirough H — the intersection of the preceding line with the load line— draw HP parallel to AB. The new pole, P. is at a point
Fig. 128.
on this line such that HP i.s to the horizontal distance from P' to the load line as CD' is to CD. From P draw lines to the points of division of the load line, and then construct an equilibrium polygon through A, C, and B. If the resulting line of resistance does not lie within the middle third, try some other position of the three points A, G, and B instead of as above. If a line of resistance can not be drawn (see § 694) within the prescribed limits, then the section of the arch ring must be changed so as to include tlie line of resistance within the limits.
694. Criterion. If the line of resistance, when constructed by any of the preceding methods, does not lie within the middle thn-d of the arch ring, the following process may be employed to deter- mine whether it is possible, or not, to draw a line of resistance in ihe middle third.
Assume, for example, that the line of resistance of Fig. 129 lies
474 ARCHES. [chap, xviii.
outside of the middle third at a and I, Next draw a line of resist- ance through c and d, the points where normals from a and h intersect the outer and inner boundary of the middle third respectively. To pass a line of resistance through c and d, it is necessary to deter- mine the value and point of application of the corresponding crown thrust. The condition which makes the line of resist- ance pass through c is: the thrust multi- FiQ. 129. PLIED BY the vertical distance of its point
of application above c is equal to the load on the joint at c multi- plied BY its horizontal distance from c. The condition that makes the line of resistance pass through d is: the thrust multiplied BY the sum of the distance its point of application is above c and of the vertical distance between c and d is equal to the load on the joint at d multiplied by its horizontal distance from d. These conditions give two equations which contain two unknown quanti- ties— the thrust and the distance its point of application is above c. After solving these equations, the line of resistance can be drawn by any of the methods already explained.
If this new line of resistance lies entirely within the prescribed limits, it is plain that it is possible to draw a line of resistance therein ; but if the second line does not lie within the prescribed limits, it is not at all probable that a line of resistance can be drawn therein. The possibility of finding, by a third or subsequent trial, a line of resistance within the limits can not, in general, be answered definitely, since such a possibility depends upon the form of the section of the arch ring.
If the line of resistance drawn through TJ and V goes outside of the arch ring beyond the extrados only, as at a, the second line of resistance should be drawn through c and F; and if, on the other hand, it goes outside below the intrados only, as at Z*, the second line should be drawn through TJ and d.
695. SCHEFFLER'S THEORY.* This theory is the one most fre- quently employed. It is based upon the hypothesis of least crown thrust (§§ 678-82), and assumes that the external forces are vertical.
* See the second foot-note page 455,
ART. 1.]
SCHEFFLER S THEORY.
475
This theory is frequently referred to as assuming that the arch stones are incompressible; but, fairly considered, such is not the case. Dr. Scheffler develops the theory of the position of the line of pressures for incompressible voussoirs; but subsequently states that the compressibiliiy of the arch stones causes the line of resist- ance to retreat within the arch ring at points where it would other- wise reach the edge. He also says that, if a line of resistance can be drawn within the arch ring, that nowhere approaches nearer the edges of the joint than one fourth of its depth, the stability of the arch is assured.
This theory will be illustrated by two examples.
696. First Example. Assume that it is required to determine, in accordance with this theory, the line of resistance for the circular segmental arcli shown in Fig. 130. The span is 50 feet, and th**
Fig. 130.
rise is 10 feet. The voussoirs are 2 feet 6 inches deep, and the spandrel wall rises 2 feet 10 inches above the summit of the arch ring. In this example we will follow the explanation used by Scheffler.*
The first step is to find the amount and the point of application of the resultant of the external forces acting on the portion of the arch above the successive joints. Divide the semi-arch and the spandrel wall into any convenient number of parts by vertical lines
* Cain's " Practical Theory of the Arch," pp. 38-44.
476
AECHES.
[chap. XVIII.
through F, G, H, I, J, and K, as shown. The positions of the act- ual joints are assumed to be not yet fixed; but, for temporary pur- poses, assume radial joints to be drawn through F, G, H, I, J, and A". Then the load on any part of the arch is assumed to be proportional to the area above it, — for example, the load on CHGR is assumed to be proportional to the area CNPD.*
Having determined the area representing the loads, it is then necessary to determine (1) the numerical values of the several loads and the distances of their centers of gravity from a vertical through the crown, and (2) the amount and the position of the center of gravity of the loads above any joint. The steps necessary for this are given in Table 60.
The quantities in column 2 of Table GO are the lengths of the medial lines of the several trapezoids. Column 6 contains the
* Notice that reallj' the load on the joint SH, for example, is SHXPGR, and not CJ^PD as above. The error is least near the crown of flat segmental arches, and greatest near the springing of semi-circular ones. The error could be eliminated (1) by finding the weights of GPNH and RGHS separately and combining them into a single resultant for the weight on the joint SH. as was done in §681; or ('2) by drawing the arch to a large scale on thick paper and cutting out the several six-sided figures which represent the loads, when the amounts of the several loads can be determined readily from the weights of corresponding sections of the paper, and the center of gravity of each section can be found by balancing it on a knife edge.
Scheffler gives the following empii-ical and approximate method of altering the position of the joints to correct this error. Let I)CG, Fig. 131, be the side of the trapezoid, and CH the uncorrected joint. From b, the middle point of GH, draw
Fig. 131.
Fig. 132.
bD ; and draw Gc parallel to bD, and ch parallel to CH. Then will ch be the corrected joint. Conversely, having given the joint CH, Fig. 133, to find the sid« of the trape- zoid which limits the portion of the load upon it, through Cdraw DG vertical, and draw Cii parallel to Db {b being the middle point of GH) ; then, from g, draw ay ver- tical, and 5ve have the desired side of the trapezoid.
,-,KT. 1."]
SCHEFFLER^S THEORY.
477
TABLE 60.
Application of Scheffler's Theory to the Arch Ring shown in Fig. 130, page 475.
|
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
|
0 n f. o H ns S o W « |
The Amount, and Position op the Center of Gravity, of the Several Loads |
To find the Amount, and the Center OP Gravity, of the Loads above the Several Joints. i |
||||||
|
Dimensions of the sections. |
Horizontal distance of centei' of gravity of eacli sectiou from U. |
1 6 1 S I 1^ 1.1 |
tn Is ©3 cS o 1* |
|S3 C 3 CS ill |
o (u .a . C OttJ - !0 ScDO®a -D ■" .-S ^ -^i |
|||
|
Height. |
Width. |
Area. |
© — >; C 3> 'c s 1- * u |
|||||
|
1 2 3 4 5 6 |
5.4 6.1 7.6 9.8 13.2 14.5 |
5 5 5 5 5 1.75 |
27.0 30.5 38.0 49.0 66 0 25.4 |
2.5 7 5 12.5 17.5 22.5 25.9 |
67. 50 228 75 475 00 857.. 50 1,485.00 657.86 |
27.0 .57.5 95 5 ]4t.5 210.5 2.35.9 |
67.50 296 25 771.25 1,628.75 3,113.75 . 3,771.61 |
2 5 5 1 8.1 11.3 14.7 16.0 |
products of the numbers ill columns 4 and 5. Column 7 contains the continued sums of the quantities in column 4. Column 8 con- tains the continued sums of the quantities in column 6. Column 9 is found by the principle of analytical mechanics : the distance of the center of parallel forces from any point is equal to tJie sum of the moments of the several forces about that point divided by the sum of the several forces ; and hence the numbers in column 9 are found by dividing the quantities in column 8 by the corre- sponding quantity in column 7.
697. The second step is to find the minimum thrust which applied at U ( UF ^ ^ FE) is sufficient to prevent the semi-arch from rotating. The origin of moments is considered as being i?j the successive joints at one third of the depth of each from the intrados.
li T = the thrust and y = its arms, and W = the load above any joint and x = its arm, then for equilibrium about any joint
T.
Wx
(12)
It is required to find the maximum value of T.
478
ARCHES.
[chap. XVIII.
The W — in terms of the weight of a cubic foot of the masonry — for each joint is the corresponding number in column 7 of Table 60, and is for convenience repeated in cohimn 2 of the table below. The X for each joint is the horizontal distance between the resultant of the load above each joint and the center of moments for that joint; and is equal to the horizontal distance from U to the points 1, 2, etc., minus the respective quantities in column 9 of Table 60. The first of these quantities is given in column 3 of Table 61, the second in column 4, and their difference in column 5. The /y for each joint is given in column 6 of Table 61. The value of the thrust, obtained by substituting the above data successively in equa- tion (12) and solving, is given in column 7 of Table 61.
TABLE 61.
Application of Scheffler's Theory to the Arch Ring shown in Fig. 130, page 475.
|
1 |
2 1 |
3 |
4 |
5 |
6 |
7 |
|
No. OF THE .TOINT, COUNTING FROM THE ONK NEXT TO THE Crown. |
i|ii |
Horizontal dis- tance from U to 1,2, 3, etc., re- spectively. |
Horizontal dis- tance from [7 to the center of fjravity of the loads above the successive joints. |
Arm of the load about the center of resistance of the successive joints ( — x). |
Arm of the thrust about the center of resistance of each joint ( = y) |
Horizontal thrust required to pi'e- vent rotation about tlie suc- cessive joints |
|
1 2 3 4 5 6 |
27.0 57.5 95.5 144.5 210.5 235.9 |
4.8 9.6 14.4 19.2 24.0 25.6 |
2.5 5.1 8.1 11.3 14.7 16.0 |
2.3 4.5 6.3 7.9 9.3 9.6 |
1.15 2.09 3.72 6.16 9.60 11.00 |
54.0 123.6 116.9 185.3 204 0 205.9 |
The horizontal thrust for joint 6 is the greatest, and hence that joint is the joint of rupture. This result might have been antici- pated, since the angle of rupture ordinarily varies between 45^ and 60° (see last paragraph of § 682, page 463), while the angular distance of joint 6 from the crown is only 43° 35'.
698. The second step is to construct the line of resistance.
To find the center of pressure on joint 1, Fig. 130, page 475, draw
a horizontal line through U, and lay off, to any convenient scale, a
distance Ua to the left equal to the first quantity in column 4 of
Table 61. a is a point through which the weight of DEQP*
* Assumed to be equal to REQPO (see foot-note, page 476).
ART. i , SCHEFFLER's THEORY. 479
acts. Lay off, vertically, a distance ab equal to the first quantity in column 2 of Table 61; this line represents the weight of the first voussoir and the load resting upon it. From h lay oflf, horizontally to the right, a distance he equal to the last quantity in column T of Table 61. This line represents the horizontal pressure at the crown. Then, by the principle of the triangle of forces, a line ca repre- sents the resultant pressure on the joint IIG\ and this line pro- longed intersects the joint RG 2X d, which is, therefore, the center of pressure on that joint.
To find the center of pressure on the second joint, lay off from JJ, horizontally to the left, a distance equal to the second quantity in column 4 of Table 61; erect a vertical equal to the second quan- tity in column 2; and from the point thus found lay off, horizon- tally to the right, a quantity equal to the last quantity in column 7. Then draw the third side of the triangle of forces, and prolong it until it intersects the joint at e.
By a similar construction, the centers of pressure for the several joints are determined to be U, d, e,f, g, h, and 6, as shown in Fig. 130. A line joining these points is the line of resistance (not shown in the figure).
699. The preceding method of drawing the line of resistance has two advantages : (1) The center of pressure on any joint may be found at once; and (2) any small error in draughting is confined to the joint where it first occurs. Notice, however, that the method is applicable only when the horizontal component of the pressure on the several joints is constant; that is, this method is applicable only when the external forces are assumed to be vertical.
Having determined the line of resistance by the above method, the stability of the arch can be discussed as described in § 690.
700. Second Example. Let us construct, according to this theory, the line of resistance for the semi-arch shown in Fig. 133, page 480, which is the same one discussed in § 681, where it was shown that joint 4 is the joint of rupture, and that, if the horizon- tal forces be disregarded, the maximum crown thrust is 8,748 pounds (see Table 59, page 459).
The crown thrust is laid off, to any convenient scale, from S to 0 ; and the loads as given in Table 59 are laid off, to the same scale, successively from 0 downwards. The remainder of the
480
ARCHES.
[chap. XVIII.
construction — shown by dash lines — is exactly similar to that described in § 689 in connection with Fig. 125, page 467.
I !
I I I i
tr V
! A.
I ui
h:-.
I !
14^
|
i \ ^' i / |
y / |
a |
|
• / '' / |
||
|
i ; / / |
||
|
1 // |
9 |
|
|
/ / / |
||
|
/ ^' / |
||
|
/ / / |
||
|
' / / ToporrooriNd |
||
|
10 |
|
0 |
C S i |
|
•^a^'^^'^y'^/Vn |
|
|
^*^ ^ y^y^y/ I] |
|
|
lX<^^%f/ I |
|
|
■■''■■<> |
'^''yX/f I |
|
yf/nl |
|
|
\.>^ ///a |
y /// / / |
|
^■■' ^/^ / |
//^■W J 1 1 |
|
A7 / |
|
|
A// / •■/ |
11 I |
|
' Y / / ■ / |
1 / |
|
H/.-/: /l |
|
|
/ / |
|
|
'T/l 1 1 |
' / |
|
''4^ // |
h? |
|
:\- 1 / |
1 |
|
i/^ |
/ |
|
7 .' \ 1 |
/ |
|
^ ■■'■ l\/ |
/ |
|
' •■ ■/'■'Y |
1 |
|
•■ ' \ |
1 |
|
■ / i v |
1 |
|
// i \ |
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•/ • \ / |
|
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:l ■ \ |
|
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i ■■ \ |
|
|
> : 7.. V |
Fig. 183.
701. Erroneous Application. Frequently the principle of the joint of rupture is entirely and improperly neglected in applying this theory; that is to say, the crown thrust employed in determin-
ART. 1.] SCHEFFLER's THEORY. 4S1
ing the line of resistance is that which would produce equilibrium of rotation about the springing line, instead of that which would produce equilibrium about the joint of rupture. For example,
instead of employing the maximnm value in the column of
y
Table 59, page 459, the last quantity in that column is used.
The line of resistance obtained by this method is shown in Fig. 133 (page 480) by the dotted line, the crown thrust (5,990, as com- puted in Table 59, page 459) being laid off from C to 0, to the scale employed in laying off the load line.
702. The error of this method is shown, incidentally, in §§ 678- 82 and §§ 688-701, and needs no further explanation.
The amount of the error is illustrated in Fig. 133. According to this analysis, the line of resistance is tangent to the intrados, which seems to show that the arch can not stand for a moment. However, many such arches do stand, and carry a heavy railroad traffic without any signs of weakness ; and further, any reasonable method of analysis shows that the arch is not only safe, but even extravagantly so (§ 690).
This method of analysis certainly accounts for some, and per- haps many, of the excessively heavy arches built in the past. For examjDle, compare 8 and 9, 17 and 18, 33 and 34, 52 and 54, etc., of Table 63 (page 502).
703. Reliability of Scheffler's Theory. For the sake of com- parisons, the line of resistance according to the Eational Theory (§§ 688-94), as determined in Fig. 125 (page 467), is shown in Fig. 133 by the solid lines. (K'otice that Fig. 133 gives the lines of re- sistance, and not the equilibrium polygons as in Fig. 125.) In this particular case, the difference between the two lines above the joint of rupture is not material ; but the difference below that joint has a very important effect upon the thickness of the arch at the spring- ing, and also upon the thickness of the abutment (§ 712).
If the maximum ratio of the horizontal to the vertical compo- nent of the external forces (see first paragraph on page 460) had been employed in determining the crown thrust and the line of resistance, there would have been a material difference in the posi- tion of both the joint of rupture and the line of resistance above that joint. Although the horizontal components of the external forces can not be accurately determined, any theory that disregards
482 AECHES. [chap. XVIII.
the existence of these forces can not be considered more than a loose approximation.
704. Rankine's Theory. Although this theory has long been, before the public and is in some respects much superior to the one in common use, it is comparatively but little employed in i)ractice. This is probably due, in part at least, to the fact that Eankine's discussion of the theory of the masonry arch is not very simjjle nor very clearly stated, besides being distributed throughout various parts of his works.*
Eankine determines the thrust at the crown by Navier's princi- ple (§ 685) ; but he makes no special assumption as to the point of application of this thrust, further than to assume that if a line of resistance can be drawn anywhere within the middle third of the arch ring, the arch is stable.
In that part of his books which precedes the discussion of arches, Rankine investigates the various curves which a cord will assume under different distributions of the load ; and subsequently adopts, these curves as the form which the line of resistance of an arch similarly loaded should have. The discussion of these curves con- stitutes the most valuable part of his investigations concerning the stability of the masonry arch.
705. Curvature of the Linear Arch. Tlio curves assumed by a cord under the various conditions of loading, can be ajDplied to linear arches (the line of resistance of actual arches) by imagining that the curve of the cord is reversed, and that the cord itself is replaced by a thin metal strip, which, like the cord, shall be prac- tically without transverse strength, but wliich, unlike the cord, shall be able at every point to resist a compressive force in the di- rection of its length. The amount and distribution of the external forces are the same in both cases ; but with the cord they act out- ward, while with the linear arch they act inward. The formulas and diagrams are essentially the same in both cases. The curves assumed by a suspended cord under various distributions of the load will now be briefly considered. In each case it will be assumed that the ends of the suspended cord and also of the corresponding linear arch are in the same horizontal line.
1. If the cord is acted upon by vertical loads distributed uni-
* "Civil Engineering," and " Applied Mechanics.''
ART. 1.] KANKINE's THEORY. 483
formly along the horizontal, it will assume the form of a parabola. This case does not occur with masonry arches.
2. If the load is vertical and distributed uniformly along the curve, the resulting curve is the common catenary, of which the equation is
y = y(^-+^ -], (13)
in which i/ is the ordinate to any point, w the ordinate to the apex, E the base of the Naperian logarithms, and x the abscissa corre- sponding to I/. Approximately, this case may occur with masonry arches, since the above law of loading is nearly that of an arch whose intrados is the common catenary and which supports a span- drel wall of masonry having a horizontal upper surface (see 3, page 445).
3. Three points fix the common catenary ; and hence, if the posi- tion of the springing lines and the crown are assumed, the depth of the load at the crown is fixed by the equation of the curve. This limitation would often interfere with the use of the common cate- nary in building arches. To meet this difficulty, Eankine trans- forms the common catenary by the principle of what he calls paral- lel projections, i. e., by increasing or decreasing one set of the rectangular co-ordinates to the curve without changing the other, and obtains the transformed catenary. The equation of the curve is
y = lI^\E^ + B-^\, (14)
in which ?/„ is the ordinate to the apex, and m is the modulus of the curve and is found by the formula
X
m =
hyp- log. 1-^- +
/^
(16)
I/O 2/o
The determination of values of y by equation (14) is not easy except with either a table of Naperian logarithms or a table of results deduced therefrom, and even then it is tedious.
With this curve we may assume the springing lines, the crown, and the depth of load at the crown, and then compute the curve of equilibrium. The transformed catenary differs from a circular arc between the same points only in being slightly (and frequently only
484 ARCHES. [chap. XVIII.
very slightly) sharper in the haunches ; and hence it is not neces- sary to discuss it further.*
4. If the load is uniform and normal at every point, the curve of equilibrium is plainly a circle. An example of this case would be an empty masonry shaft standing in water.
5. The ellipse is the form assumed by a cord under a load com- posed of horizontal and vertical components which are constant along the horizontal and vertical lines, but which differ from each other in intensity. There is no case in ordinary practice where the pressures upon an arch are strictly identical with those which give an elliptical curve of equilibrium. The curve of "equilibrmm of a tunnel arch through earth, wiien the depth below the surface is great compared with the rise of the arch itself, approximates to an ellipse. The load is nearly uniform along the horizontal, while the horizontal force at any point is some fractional part of the vertical one at the same point ; and therefore the horizontal forces are nearly uniform. It is readily shown that the intensity (the pressure per unit of area perpendicular to the force) of the vertical com- ponent is to that of the horizontal component as the square of the vertical diameter of the ellipse is to the square of its horizontal diameter ; f that is to say.
the horizontal axis _ . /intensity of horizontal component the vertical axis intensity of vertical component ' ^
6. If the forces acting on the linear arch are normal and increase in intensity in proportion to the distance of the points of application from a horizontal line, the curve is a hydrostatic arch. A tunnel under water is an example of this method of loading. The form of the curve is shown in Fig. 134, of which only the portion
ff ^^ 6^ is available in the construction of
arches. The equation of the curve is
p p = lojJo Po = a constant, . (17)
I ^ in which jt? is the normal pressure on a ^°- ^34. unit area at any point, p the radius of
* For two numerical examples of the method of employing the transformed cate- nary in the design of an arch, see an article by W. H. Booth in Van Nostrand's Engin'g Mag., vol. xxxi, pp. 1-10 ; and for another, see an editorial in Engineering News, vol. xviii, p. 372.
+ Rankine's Civil Engineering, p. 205.
ART. 1.] RAXKINE's THEORY. 485
curvature at the same point, y the distance from the line 0 (the surface) to any point, po and y^ the values of p and y for the point A, and lo the weight of a unit of volume of the loading.
" The true semi-ellipse of a given span and rise differs from the hydrostatic arch by being of somewhat sharper curvature at the crown and springing and of somewhat flatter curvature at the haunches, and by enclosing a somewhat less area. The application of the hydrostatic arch to practice is founded on the fact that every arch, after having been built, subsides at the crown, and spreads, or tends to spread, at the haunches, which therefore press horizon- tally against the filling of the spandrels ; from which it is inferred as probable that, if an arch be built of a figure suited to equilibrium under fluid pressure — /'. c, pressure of equal intensity in all direc- tions,— it will spread horizontally, and compress the masonry of the spandrels until the horizontal pressure at each point becomes of equal intensity to the vertical pressure, and is therefore sufficient to keep the arch in equilibrio." *
7. If the vertical and the horizontal comijoncnts of the normal force differ from each other but both vary as the distance of the point of application from a horizontal line, tlie curve of equilbrium is the geostatic arch. An arch in clean dry sand is the best example of this form of loading. The geostatic arch bears the same relation to the hydrostatic arch that the ellipse does to the circle. The geostatic curve can be produced from that of the hydrostatic curve by increasing or decreasing one set of ordinates without altering the other. If px be the horizontal intensity of the forces acting on the hydrostatic arch and 2^'x be that for the geostatic arch, then p^ z= cp'x ', and if X is the horizontal diameter at any point of the hydrostatic curve and x' the same for the geostatic, then x' = cx.\
8. Rankine next discusses the following more general problem : " Given the curve of a linear arch and the vertical components of a symmetrical load, to find the intensity and distribution of the horizontal components necessary to produce equilibrium.
* Rankine's Civil Engineering, pp. 419-20.
+ For a numerical example of the method of employing the geostatic curve for the intrados of tunnel arches, see an article—" The Employment of Mathematical Curves as the Intrados of Arches "—by W. H. Booth in Van Nostrand's Engin'g Mag., vol. XXX, pp. 335-60.
486
ARCHES.
[chap. XVIII.
"Let V = the vertical load on any arc DC, — represented in Fig. 135 by the line £0; Vi — the vertical load on the serai-arch A C; H = the horizontal load on any arc DC, — represented by
the line GF, Fig. 135 ; Hi = the horizontal load on the semi-arch A C; Ho = the compression at the crown C, — represented by the
line BC, Fig. 135 ; C = the compression on the rib at any point D, — rej^re- sented by FD, Fig. 135 ; = the intensity of the horizontal force, i. e., the force per unit of area perpendicular to its line of action; = the intensity of the vertical force; = the value of py at the crown C; = the radius of curvature at the crown C; = the angle that the tangent of the linear arch at any point makes with the horizontal, — that is, i = the angle BDG, Fig. 135.
Pv Po Po
Fig. 135.
"Then V =-- fj i\dx', (18)
(7= Fcosec i\ (19)
H-Vcoii', (20)
- ^ - _ ^(^CQtQ _ _ ^ v'd'y] ^'~ dy ~ dy ~ dy ' ' ' ^^ '
•* The integration constant for (21) is Hq ; and is found by equa- tion (11), page 465, which, in the above nomenclature, becomes
Ho=PoPo-" . . . . • (S2)
ART. 1.] RANKINE's THEORY. 487
However, before concluding this phase of tlie discussion of arches, it is well to state that the only arches in common use are tlie circular — cither semi-circular or segmental — and the elliptic.
706. Stability of any Proposed Arch. To apply the preceding principles in designing an arch, it is necessary to know both the vertical and the horizontal forces acting on the arch. Rankine assumes* (1) that the vertical force acting on any part is the weight of the masonry, earth, or other load vertically above the same; and (^)) that the horizontal pressure of earth is given by the formula
7 1 — sin 0 1
Px=iod^ , .,\ (23)
1 + sm 0 ^ '
in which p^ is the horizontal intensity at any point, w the weiglit of a unit of the earth, d the depth of earth over the point, and 0 the angle of repose. In the above nomenclature, the vertical inten- sity is
Pv=2ud (24)
By an application of these two principles are to be determined the amount and distribution of the vertical and the horizontal forces acting on the arch; and then the equilibrium curve corresponding to this form of loading (see § 705) is to be adopted for the intrados of the proposed arch.
For an example, take the case of an arch under a high bank of earth whose angle of repose is 30°. Strictly, the curve of equi- librium is the geostatic arch (see paragraph 7, § 705) ; but it will be more simple and sufficiently exact, if we assume it to be an ellipse, which is equivalent to assuming that the rise of the arch is inconsiderable in comparison with the depth of earth over it. The intrados is then to be an ellipse in which
the vertical axis _ a/~P^ _ i/l + sin 0 _ ^- tfie horizontal axis Px 1 — sin 0 "" • * v /
*' If the earth is firm, and little liable to be disturbed, the propor- tion of the half-span — or horizontal semi-axis — to the rise — or ver-
* Civil Engineering, p. 434.
+ Rankine states (Civil Engineering, p. 320) that the horizontal pressure can not
l+sin<^ , 1 - sin<i>
be greater than w h— -. — -, nor less than w h-— — : — -. Notice that the value employed
1-sin* l+siQ"* '
above is the minimum.
488 ARCHES. [chap. XVIII.
tical semi-axis — may be made (/rm^er than is given by the preced- ing equation, and the earth will still resist the additional horizontal thrust ; but that proportion should never be made less than the value given by the equation, or the sides of the archway will be in danger of being forced inwards.^' *
"There are numerous cases in which the form of the linear rib suited to sustain a given load may at once be adopted for the in- trados of a real arch for sustaining the same load, with sufficient _f exactness for practical purposes. The follow- -'' -], ing is the test whether this method is appli- cable in any given case. Let A CB in Fig. 136 be one half of the ideal rib which it is proposed to adopt as the intrados of a real arch. Draw A a normal to the rib at the /q crown, so as to represent a length not ex-
FiG. 136. ceeding two thirds of the intended depth of
the keystone. Draw a normal Bb at the springing of a length such that
Bb _ thrust along rib at ^ „ ,
^« ~ thrust along rib at iy* ' ' * • • v~ /
The thrust at A is found by equation (11), page 465 ; and the thrust at any other point is given by equation (19), page 486. Construct, a line acb such that its perpendicular distance from the intrados at any point, cC, is inversely as the thrust along the rib at that point. Then if acb lies within the middle third of the proposed arch ring, the ideal rib A CB is of a suitable form for the intrados.
707. Eankine's general method of determining the stability of a proposed arch is as follows : J
" The first step towards determining whether a proposed arch will be stable, is to assume a linear arch parallel to the intrados or soffit of the proposed arch, and loaded vertically with the same weight, distributed in the same manner. Then by equation (21), page 486, determine either a general expression, or a series of val- ues, of the intensity j^x of the conjugate pressure, horizontal or oblique as the case may be, required to keep the arch in equilibrio
* Rankine's Civil Engineering, p. 434. ^ Ibid., p. 417. X Ibid., pp. 421-22.
ART. l.J
RANKINE S THEORY.
489
imder the given vertical load. If that pressure is nowhere nega- tive, a curve, similar to the assumed arch, drawn through the middle of the arch ring will be, either exactly or very nearly, the line of pressure of the proposed arch; p^ will represent, either exactly or very nearly, the intensity of the lateral pressure which the real arch, tending to spread outwards under its load, will exert at each point against its spandrel and abutments; and the thrust along the linear arch at each j^oint will be the thrust of the real arch at the- corresponding joint.
" On the other hand, if ])x has some negative values for the assumed linear arch, there must be a pair of points in that arch where that quantity changes from positive to negative, and is ecpial to nothing. The angle of inclination i at that point, called the (Dujlc of rupture,!?, to be determined by placing the second member of equation (21), page 480, equal to zero and solving for cot i. The corresponding joints in the real arch are called the joints of i-up- ture ; and it is below those joints that conjugate pressure* from without is required to sustain the arch and that consequently the- backing must be built with squared side-joints.
"In Fig. 137, let BC'A represent one half of a symmetrica.* arch, KLDE an abutment, and C the joint of rupture — found by the method already described. The point of rupture, which is the center of re- sistance of the joint of rupture, is somewhere within the middle third of the depth of that joint; and from that point down to the springing joint B, the line of pressure is a curve sim- ilar to the assumed linear arch, and E^ parallel to the intrados, being kept in equilibrio by the lateral pressure between the arch, and its spandrel and abutment.
" From the joint of rupture C to the crown A, the figure of the true line of pressure is determined by the condition that it shall be
* A minus value oipx will correspond to an outward pull, and consequently tho- backing below the joint of rupture should be capable of resisting tension.
Fig. 137
490 AECHES. [CHAP. XYIII.
X linear arch balanced under vertical forces only ; * that is to say, tlie horizontal component of the thrust along it at each point is a constant quantity, and equal to the horizontal component of the thrust along the arch at the joint of rupture.
" The only point in the line of pressure above the joint of rupture which it is important to determine is that of the crown of the arch. A} and it is found in the following manner : Find the center of gravity of the load between the joint of rupture 6' and the crown A ; and draw through that center of gravity a vertical line. Then if it be possible, from any point, such as M, in that vertical line, to draAV a pair of lines, one parallel to a tangent to the soffit at the joint of rupture and the other parallel to a tangent to the soffit at the crown, so that the former of those lines shall cut the joint of rupture and the latter the keystone, in a pair of points which are both within the middle third of the depth of the arch ring, the stability of the arch will be secure ; and if the first point be the point of rupture, the second will be the center of resistance at the crown of the arch and the crown of the true line of pressures.
"When the pair of points, related to each other as above, do not fall at opposite limits of the middle third of the arch ring, their exact positions are to a small extent uncertain ; but that uncertainty is of no consequence in practice. Their most probable positions are equidistant from the middle line of the arch ring.
*' Should the pair of points fall beyond the middle third of the arch ring, the de])th of the arch stones must be increased."
708. Reliability of Rankine's Theory. 1. This theory is ap- proximate since it makes no attempt to determine the true line of resistance, but finds only a line of resistance wliich lies within the middle third of the arch ring.
2. The value of the radius of curvature to be used in finding the crown thrust is indeterminate. It is frequently, but erroneously, taken as the radius of the intrados at the crown.
3. The method of finding the center of pressure at the crown and also at the joint of rupture assumes that the portion CM A, Fig. 137, is acted upon by only three forces ; viz., the vertical load, the thrust at the crown, and the pressure on the joint of rupture.
* From this it appears that Rankine himself disregards, for that part of the areh above the joint of rupture, the principal characteristic of his theory, viz. : the recog- nition of the horizontal components of the external forces ; and hence this theory is, in fact, the same as Scheffler's (§§ 695-703).
ART. L] RAXKIXE'S THEORY. 491
This is erroneous (a) because it neglects the horizontal components; of the external forces, and hence the actual center of pressure at the joint of rupture is nearer the intrados than the position of 0 as found in Fig. 137 ; and (h) because it finds a new value for the thrust at the crown which, in general, will differ from that employed in finding the position of the Joint of rupture.
4. Rankine himself says that the method of § TOT is inapplical)le to a circular arch greater than 90°, and gives a complicated formula for that case.
Eankine's theory is more complicated and less accurate thau either Scheffler's (§ 695) or the rational theory (§ 688).
709. Other Theories of the Arch. There are several methods^ in more or less common use, of determining the stability of the vous- soir arch, many of which are but different combinations of the pre- ceding principles, while some have a much less satisfactory basis. It is not necess..ry to discuss any of these at length ; but there is one which, owing to the frequency with which it is employed, requires a few words. It is the same as Scheffier's (§§ 695-T03), ex- cept in assuming that the line of resistance passes through the m iddle of the crown Joint and also through the m iddle of the spring- ing Joint. The line of resistance is then determined in any one of a number of ways ; and the arch is said to be stable, if the line of resistance lies in the middle third of the section of the arch ring. This theory is much less satisfactory than Scheffler's and possesses no advantage over it.
710. Theory of the Elastic Arch. It has long been recognized that all theories for the voussoir arch are very unsatisfactory ; and hence it has been proposed to consider the masonry arch as an elastic curved beam fixed at its ends, and examine its stability by the principles employed in computing the strains in arches of iron or wood. There is no essential difference, as far as the theory is concerned, between the iron and the stone arch ; but there is great difficulty in applying the mathematical theory of elasticity to the masonry arch. The theory of elasticity when applied to the masonry arch has the following sources of error, in addition to those of the ordinary theory of the elastic arch : 1. There is great un- certainty as to the external forces (§ 666). 2. TVc have no definite knowledge concerning either the modulus of elasticity (§§ 16 and 146) or the ultimate strength of masonry (§§ 221-23, and §§ 246-
492
ARCHES.
[chap. XVIII.
49). 3. The stone arch is not homogeneous ; i. e., the modulus of elasticity is not constant, but varies between that of the stone and the mortar. 4. Slight imperfections in the workmanship — as, for example, a projection on the bearing surface of an arch stone or a pebble in the mortar — would break the continuity of the arch, and render the theory inapplicable. 5. The stability of the arch would be greatly influenced by the action of the center, — its rigidity, the method of loading it to prevent deformation, and the method and rapidity of striking it.
The application of the theory of elasticity to stone arches has been considerably discussed in late years ; but it is generally con- ceded that the results are, for the most part, illusory, since the much simpler methods give results equally reliable. The explana- tion of the theory of the elastic masonry arch as given by Professor Greene in Part III — Arches — of his ''' Trusses and Arches" is all that can be desired; and hence this theory will not be discussed here.
711. Stability of Abutments and Piers. The stability of the abutment is in a measure indeterminate, since it depends upon the position of the line of resistance of the arch. The stability of the abutment may be determined most easily by treating it as a part of the arch, i. e., by extending the load line so as to include the forces acting upon it and drawing the reactions in the usual way ; or its stability may be deter- mined as follows : Assume that it is re- quired to test the stability of the abutment shown in Fig. 138. Let qc represent the direction of the resultant pressure on the ]omt AB. g is the center of gravity of the section ABC of the abutment, and g.y that for the section ABED.* At a^the point Fig. 13S. where a vertical through g intersects qCi
prolonged — lay off, to scale, a line ad equal to the weight of ABC, and also a line ab equal to the pressure qc^ ; then r.^ — the point where the diagonal ea pierces A C — is the center of pressure on A C.
* For a method of finding the center of gravity when the section is a trapezoid, see the third paragraph of § 494 (page 318).
A.RT. 1.] STABILITY OF THE ABUTMENT. 493
In a similar manner, C3 is found to be the center of pressure on DE.
The amount of the pressure on ^ C is given by the length of the line ae ; and the stability of the joint against crushing can be de- termined as described in §§ 670-73 and paragraph 2 of § 690. The stability against rotation may be determined as described in § 669 and paragraph 1 of § 690. A line — not shown^connecting Ci, C2, C3, is the line of resistance of the abutment, to which the joints should be nearly perpendicular (see § 674 and division 3 of § 690).
712. In Fig. 133 (page 480) is shown the line of resistance for the abutment according to the rational theory of the arch (§§ 688- 94), and also that according to Scheffler's theory (§§ 695-703), — the former by the solid line and the latter by the broken one. Since to overestimate the horizontal components of the external forces would be to err on the side of danger, in apj^lying the former theory in Fig. 133, the liorizontal component acting against the abutment was disregarded on the assumption that the abutment might be set in a pit without greatly disturbing the surrounding earth. If the horizontal component had been considered, the dif- ference between the lines of resistance according to the two theories would have been still greater. Xotice that the analysis which recognizes the existence of the horizontal forces, i. e., the rational theory, permits a lighter abutment than the theory which assumes the external forces to be entirely vertical.
The omission of the horizontal components assumes that the only object of the abutment is to resist the thrust of the arch ; and that consequently the flatter the arch the greater the thrust and the heavier the abutment. Ordinarily the abutment must resist the thrust of the arch tending to overthrow it and to slide it outward, and must act also as a retaining wall to resist the lateral pressure of the earth tending to overthrow it and to slide it inward. For large arches the former is the more important ; but for small arches, particularly under high embankments, the latter is the more important. Hence, for large arches or for an arch having a light surcharge, the abutment should be proportioned to resist the thrust of the arch; but for small arches under a heavy surcharge of earth, the abutment should be proportioned as a retaining wall (Chap. XIV).
494 ARCHES. (chap. XVIII.
Although the horizontal pressure of the earth can not be com- puted accurately, there are many conditions under which the horizontal components should not be omitted. For example, if the abutment is high, or if the earth is deposited artificially behind it, ordinarily it would be safe to count upon the pressure of the eartii to assist in preventing the abutment from being overturned out- wards. Finally, although it may not always be wise to consider the earth pressure as an active force, there is always a passive resistance which will add greatly to the stability of . the abutment, and whose, intensity will increase raj^idly with any outward movement of the abutment (see last paragraph of § G6(J).
For empirical rules for the dimensions of abutments, see §§ 722-23.
Art. 2. Rules Derived from Practice.
713. In the preceding article it was shown that every theory of the arch requires certain fundamental assumptions, and that hence the best theory is only an approximation. Further, since it is prac- tically impossible, by any theory (§ 693), to include the effect of passing loads, theoretical results are inapplicable when the moving load is heavy compared with the stationary load. It was shown also that the stability of a masonry arch does not admit of exact mathematical solution, but is to some extent an indeterminate problem. At best the strains in a masonry arch can never be com- puted anything like as accurately as those in metallic structures. However, this is no serious matter, since the material employed in the former is comparatively cheap.
Considered practically, the designing of a masonry arch is greatly simplified by the many examples furnished by existing structures which afford incontrovertible evidence of their stability by safely fulfilling their intended duties, to say nothing of the history of those structures which have failed and thus supplied negative evidence of great value. In designing arches, theory should be interpreted by experience ; but experience should be studied by the light of the best theory available.
This article will be devoted to the presentation of current prac- tice as shown by approved empirical formulas and practical rules, and by examples.
ART. 2.] RULES DERIVED FROM PRACTICE. 495
714. Empirical Formulas. Numerous formulas derived from existing structures have been proposed for use in designing masonry arches. Such formulas are useful as guides in assuming propor- tions to be tested by theory, and also as indicating what actual practice is and thus affording data by which to check the results obtained by theory.
As proof of the reliability of such formulas, they are frequently accompanied by tables showing their agreement with actual struct- ures. Concerning this method of proof, it is necessary to notice that (1) if the structures were selected because their dimensions agreed with the formula, nothing is proven ; and (2) if the struct- ures were designed according to the formula to be tested, nothing is proven except that the formula represents practice which is probably safe.
At best, a formula derived from existing structures can only indicate safe construction, but gives no information as to the degree of safety. These formulas usually state the relation between the principal dimensions ; but the stability of an arch can not be de- termined from the dimensions alone, for it depends upon various attendant circumstances, — as the condition of the loading (if earth, upon whether loose or compact ; and if masonry, upon the bonding, the mortar, etc.), the quality of the materials and of the workman- ship, the manner of constructing and striking the centers, the spreading of the abutments, the settlement of the foundations, etc. The failure of an arch isa very instructive object lesson, and should be most carefully studied, since it indicates the least degree of stability consistent with safety. Many masonry arches are excessively strong ; and hence there are empirical formulas which agree with existing structures, but which differ from each other 300 or 400 per cent. All factors of the problem must be steadily borne in mind in comparing empirical formulas either with each other or with theo- retical results.
A number of the more important empirical formulas will now oe given, but without any attempt at comparisons, owing to the lack of space and of the necessary data.
715. Thickness of the Arch at the Crown. In designing an arch, the first step is to determine the thickness at the crown, i. e., the depth of the keystone.
496 ARCHES. [chap. XVlil.
Let d = the depth at the crown, in feet ;
p = the radius of curvature of the intrados, in feet ; r = the rise, in feet ; s = the span, in feet.
716. American Practice. Trautwine's formula for the depth of the keystone for a first-class cut-xtoiie arch, whether circular or elliptical, is
^^±ii+ifi + 0.3 (27)
''For second-class worh, this depth may be increased about one eighth part ; and for hiHck worh or fair rubble, about one third."
717. English Practice. Eankiue's formula for the depth of keystone for a single arch is
d = 4/0.13/3 ; (38)
for an arch of a sei'ies,
d = V 0.17 p ; (39)
and for tunnel arches, where the ground is of the firmest and safest,
= 1/0.134", and for soft and slipping materials,
d=y 0.12- , (30)
d= 1/0.48--
. (•")
The segmental arches of the Refinies and the Stephensons, which are generally regarded as models, ''have a thickness at the crown of from -jIq to -^^ of the span, or of from ^'g- to -5^ of the radius of the intrados.""
718. French Practice* Perronnet, a celebrated French engi- Jieer, is frequently credited with the formula,
d=li. + i^s, (32)
♦From "Proportions of Arches from French Practice," by E. Sherman Gould in Van Nostrand's Engin'g Mag., vol. xxix, p. 450.
ART. 2.] RULES DERIVED FROM PRACTICE. 497
as being applicable to arches of all forms — semi-circular, segmental, elliptical, or basket-handled, — and to railroad bridges or arches sustaining heavy surcharges of earth. '^Perronnet does not seem, however, to have paid much attention to the rule ; but has made his bridges much lighter than the rule would require." Other formulas of the above form, but having different constants, are also frequently credited to the same authority. Evidently Perronnet varied the proportions of his arches according to the strength and weight of the material, the closeness of the joints, the quality of mortar, etc. ; and hence different examples of his work give differ- ent formulas.
Dejardin's formulas, which are frequently employed by French engineers, are as follows :
For circular arches.
d =1 + 0.1 p; (33)
d = l-{-0.05p; .... (34) d = l-\- 0.035 p ; . . . . (35)
|
if |
r s |
= |
^> |
|
if |
r s |
= |
h |
|
if |
r s |
= |
i. |
r
if - = ^, d = 1 + 0.02 p; .... (36)
For elliptical and basket-handled arches,
if -= I, d =1+0.07 p (37)
Croizette-Desnoyers, a French authority, recommends the fol- lowing formulas :
if -> i, ^ = 0.50 + 0.28 VTp"; . . . (38)
r
if -= I, t? = 0.50 + 0.26 VTp; . . . (39) s
a -= ^, d = 0.50 + 0.20 V2p; . . . r40)
498
ARCHES.
[chap. XYIII.
719. Notice that in none of the above formulas does the char- acter of the material enter as a factor. Notice also that none of ihem has a factor depending upon the amount of the load.
Table 62 is given to facilitate the comparisons of the preceding formulas with each other and with actual structures. Values not given in the table can be interpolated with sufficient accuracy. It is remarkable that according to all formulas credited to Perronnat the thickness at the crown is independent of the rise, and varies only with the span. Notice that by Dejardin's formulas the thickness decreases as the rise increases, — as it should.
TABLE 63. Comparison of Empirical, Formulas for Depth of Keystone.
|
Proportion op Rise to Span. |
|||||||||
|
Semi-circle. |
Rise _ , Span " ' |
Rise Span ~ ^ |
|||||||
|
Formula. |
Span. |
Span. |
Span. |
||||||
|
10 |
50 |
100 |
10 |
50 |
100 |
10 |
50 |
100 |
|
|
Trautwine's, for flrst-class work " second " " " third •' |
.99 1.11 1.38 .77 1.51 1.50 1.38 |
1.9S 2.23 2.64 1.73 •3.26 3.50 2.48 |
2.70 3 04 3.60 2.45 5 43 6.00 3.30 |
1.11 1.25 1.48 1.00 1 51 1.42 1.56 |
2.23 2.51 2.97 2.25 3.26 3 07 2.86 |
3.09 3.43 4.12 3.16 5.43 5.17 3.85 |
1.26 1.44 1.68 1.25 1.51 1.26 1.62 |
2.57 2.89 3.42 2 79 3.26 2 30 3.01 |
3.55 4.00 4.73 3.95 |
|
5.43 |
|||||||||
|
2.60 |
|||||||||
|
Oroizette-Desnoyers's |
4.05 |
||||||||
720. Thickness of the Arch at the Springing. Generally the thickness of the arch at the springing is found by an application of theory ; and hence but few empirical formulas are given for this purpose.
Trautwine gives a formula for the thickness of the abutment, which determines also the thickness of the arch at the springing (see § 722).
''The augmentation of thickness at the springing line is made, by the Stephensons, from 20 to 30 per cent. ; and by the Kennies, ibout 100 per cent."
721. If the loads are vertical, the horizontal component of the compression on the arch ring is constant ; and hence, to have the mean pressure on the joints uniform, the vertical projection of the
AKT. 2.] RULES DERIVED FROM PRACTICE. 499
joints should be constant. This principle leads to the following formula, which is frequently employed : Tlie length, measured radi- ally, of each joint hetiveen the joint of rupture and the croivn should be such that its vertical projection is equal to the depth of the keystone. In algebraic language, this rule is
/ 1= fZsec a, (41)
in which / is the length of the joint, d the depth at the crown, and a the angle the joint makes with the vertical.
The length of the joint of rupture,* i. e., the thicknesss of the arch at the practical springing line, can be computed by the above formula. The following arc the values for circular and segmental arches :
If ^ > l: 1= 2.J00 d; (42)
''-=. i, l^lAOd; (43)
''-= h ^-1.24^: (44)
r
j\, l=l.ud; . . . . , (45)
r
1 = J^, l = l.lOd (46)
722. Thickness of the Abutment, t Trautwi7ie's toTmnla, is
^ =0.2p+0.1 /• + 2.0, (47)
in which t is the thickness of the abutment at the springing, p the radius, and r the rise, — all in feet. ''' The above formula applies equally to the smallest culvert or the largest bridge — whether cir- cular or elliptical, and whatever the proportions of rise and span — and to any height of abutment. It applies also to all the usual methods of filling above the arch, whether witli solid masonry to the level of the top of the crown, or entirely with earth. It gives a thickness of abutment which is safe in itself without any back' ing of earth behind it, and also safe against the pressure of the
* Concerning the method of determining the joint of rupture, see §§ 68Q-8L I- For a theoretical discussion of tliis subject, see §§ 711-12.
500
AECHES.
[chap. XVIII.
earth when the bridge is unloaded. It gives abutments which alone are safe when-the bridge is loaded ; but for small arches, the formula supposes that earth will be deposited behind the abut- ments to the height of the roadway. In small bridges and large culverts on first-class railroads, subject to the jarring of heavy trains at high speeds, the comparative cheapness with which an excess of strength can be thus given to important structures has led, in many cases, to the use of abutments from one fourth to one half thicker than those given by the preceding rule. If the abutment is of rough rubble, add 6 inches to the thickness by the above formula, to insure full thickness in every part."*
To find the thickness of the abutment at the bottom, lay off, in Fig. 139, 071= t as computed by the above equation ; vertically above
Fig. 139.
n lay off a7i = half the rise ; and horizontally from a lay off ab = one forty-eighth of the span. Then the line h)i prolonged gives the back of the abutment, provided the width at the bottom, sp, is not less than two thirds of the height, os. " In practice, os will rarely exceed this limit, and only in arches of considerable rise. In very high abutments, the abutment as above will be too slight to sustain the earth pressure safely."*
To find the thickness of the arch, compute the thickness ce liy equation (27), page 496, draw a curve through e parallel to tl e intrados, and from J draw a tangent to the extrad«s; and then will bfe be the top of the masonry filling above the arch. Or, instead of drawing the extrados as above, find, by trial, a circle which will pass through b, e, and b', the latter being a point on the left abut- ment corresponding to b on the right.
* Trautwine's Engineer's Pocket-book.
ART. 2.] EULES DERIVED FROil PRACTICE. 501
Trautwine's rule, or a similar one, for proportioning tlie abut- ment and the backing is frequently emploved. For examples, see Plates IV and V.
723. Rankine says that in some of the best examples of bridges the thickness of the abutment ranges from one third to one fifth of the radius of curvature of the arch at its crown.
The following formula is said to represent German and Russian practice,
i; = 1 + 0.04 (5 5 + 4/0, (48)
in which h is the distance between the springing line and the top of the foundation.
724. Dimensions of Actual Arches. Table G3 (pages 502-3) gives the dimensions of a number of actual structures, which, from their wide distribution and the frequency with which most of them are cited as examples, may be taken to represent average practice. Unfortunately the details concerning most of them are very meager, the following and those in the table being all that can be obtained.
No. 1 is the longest span ever built.
No. 2 is the longest span in existence.* The arch is a circular arc of 110°. It carries a conduit (clear diameter 9 feet) and a car- riage-way (Avidth 20 feet). The top of the roadway is 101 feet above the bottom of the ravine. The voussoirs are Quincy (Mass.) granite, and are 2 feet thick, 4 feet deep at the crown, and 6 feet at the springing. The spandrel filling is composed of Seneca sandstone, which, for a distance above the arch of 4 feet at the crown and 15 feet at the springing, is laid in regular courses with joints radial to the intrados ; and hence the effective thickness of the arch is about 8 feet at the crown and about 21 feet at the springing (see Fig. 159. page 525). The abutments are prevented from spreading by the bed-rock in the side-hills.
No. 9 is a remarkable bridge. It was built by an " uneducated '' mason in 1750; and although a very rude construction, is still in perfect condition. A former bridge of the same general design at the same place fell, on striking the centers, by the weight of the haunches forcing up the crown ; and hence in building the preseni structure the load on the haunches of the arch was lightened bt
* Concerning arched dams, see foot of page 330 and top of 331.
502
ARCHES.
[chap. XVIII.
TABLE Data Concerning
■Ref.
No.
Location and Description.
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
2.T
26 27 28 29 30 31 Si 33 34 35 36 37 3S 39 40 41 42 43 44 45 46 47 48 49 50 51 53 53 54 55 56 .57 58 59 60 61
Trezzo, Italy: built in 1380, destroyed in 1427; granite
Cabin John, Washington (D. C); aqueduct; granite (see § 724, p. 501)
Grosvenor bridge, Chester, England
Ballochmyle, over the Ayr, Scotland
London bridge, England; street; granite
Gloucester, England • . .
Turin, Italy
Alma bridge, Paris; small rough rubble in cement; railroad
Pont-y-Prydd, Wales; rough rubble in lime mortar (see § 724, p. 501)
Maidenhead, England; brick in cement; railroad
Neuilly, France; five spans (see page 504)
Bourbonnais Railway bridge ; France ; cut granite (see page 504)
Waterloo bridge, London, England; granite
Tongueland. England ; turnpike
Napoleon bridge, Paris; small rough rubble in cement; railroad
Mantes, over Seine, France
Etherow river, England ; railroad ; four spans
Bishop Auckland, England: turnpike; built in 1388
Wellington bridge, Leeds, England
Louis XIX
Dean bridge, near Edinburgh, Scotland ; turnpike
Licking Aqueduct, Chesapeake & Ohio canal
Dnrlaston
Over the Oise, France; railroad
Trilport, France : railroad
Conemaugh viaduct, Pennsylvania R. R. ; sandstone in lime (no sand)
Royal Border viaduct, England ; brick in cement
Posen viaduct. Germany: brick in cement
Orleans, Fi-ance : railroad
Hutcheson bridge, Glasgow, Scotland
Falls bridge, Philadelphia & Reading R. R
St. Maxeiice, over the Oise, France
Westminster bridge, London
Allentown, England; turnpike
Staines, England : turnpike.
Black Rock Tunnel bridge, Philadelphia & Reading R. R
Edinburgh ,
Swatara, Philadelphia & Reading R. R. ; brick ■
Brent R. R. viaduct. England ; brick in cement
Wellesley bridge at Limerick
Bow bridge. England ; turnpike
Houghton river, England ; railroad
Bewdly, England; turnpike
Chestnut Street bridge, Philadelphia; brick in cement
Carrollton viaduct, near Baltimore; railroad : granite
Llanwast, in Denbighshire, Wales; built in 1636; turnpike .
Monocacy viaduct, Chesapeake & Ohio canal
Over the Forth, at Stirling ,
Nemours. France
Abattoir Street, Paris; railroad
Dole, over the Doubs, France
Chateau Thierry, France
Avon viaduct, England; brick in cement. ....
Filbert St., Extension Pennsylvania R. R., Philadelphia; brick in lime mortar.
James River aqueduct. Virginia
Des Basses-Granges. Orleans a Tours, France
Over the Salat. France
Pesmes. over the Ougnon. France
Philadelphia & Reading R. R
Couturette, Arbois, France
Tonoloway culvert, under Chesapeake & Ohio canal; rubble in cement
* C = semi-circle ; E = elliptical ; B = basket-bandied.
ART. 2.]
RULES DERIVED FROM PRACTICE.
503
63
A-CTUAL Arches.
Engineer.
Meigfs
Hartley.. . Miller. ...
Rennie
Telford. .
Mosca
Darcel
Edwards. .
Brunei
Perronnet Yaudray. .
Rennie
Telford... Couche . . .
Haskoll. . .
Rennie
Perronnet, Telford.... Fisk
Stephenson
Perronnet..
Labelye
Stephenson
Rennie
Robinson. ..
Mylne
Osborne
Brunei
Walker
Haskoll
Telford
Kneass
Jones ,
Fisk
Perronnet..
Perronnet,. Vignoles
Ellet
Bertrand... Steele
Fisk
Curve
of
Intrados.
Span.
feet.
251
220
200
181
152
150
148
141
140
128
128
124
120
118
116
115
100
100
100
94
90
90
87
83
81
80
80
80
74 72 72 70 70 70 66 65 60 60 58 58 54 53 53 53 52 51 50 50 50 49 46 45 44 43 40
Rise.
feet. 88 57 42 90.5 29.5 35 18 28 35 24 32
6.92 32 38 14.8 34 25 22 15
9.75 30 15
13 5 11.75 28 40 40 16
26.3 13 25
6.40 38 11.50
9.25 16.5 36 25 17.6 17.5 13.75 32.5 20 18 29 17
9 10.25
3.75
5.11 17.50 17.0 15
24.5 6 27 3.83 8 6.13
15
Radius
at Crown.
feet. 133 134 140
90 162
98 160 103
88 169 159 281 112
65 120
43
119 38
44
28.3
Thickness.
Crown.
feet.
4.00
4 t
4.60
4 50
4.75
4.50
4.92
4.92
1.50
5.25
5.13
2.67
4.50
3.50
4.00
6.40
4.00
1.83
3.00
3.67
3.00
2. as
3 50 4.60 4.45 3.00 2.66
4 66 3.95 3.50 3.00 4.80 7.60 2.50 3.00 2.75 2.75 3.50 3.00 2.00 2.50 2.75 2.20 2.50 2.50 1.50 2.50 2.75 3.16 2.97 3,75 3.75 2.00
2 00 2.66
3 95 3.63
3. as
2. 50 2.97 2.00
Spring- ing.
feet.
7.00 6 00 9.00
1.50 7.16
3.60 8.00
4.00 1.83 7.00
3.50
4.50
14.00 3.00 6.00 2.75
3.50
2.75 2.50
t See § 720, and also Fig. 159, page 525.
604 ARCHES. [chap. XVIII.
leaving horizontal cylindrical openings (see third paragraph of § 730) through the spandrel filling. The outer, or showing, arch stones are only 2.5 feet deep, and that depth is made up of two stones; and the inner arch stones are only 1.5 feet deep, and but from 6 to 9 inches thick. The stone quarried with tolerably fair natural beds, and received little or no dressing. It is a wagon-road bridge, and has almost no spandrel filling, the roadway being dan- gerously steep. A strain sheet of the arch shows that the line of resistance remains very near the center of the arch ring (see § 730). The mean pressure at the crown is about 244 pounds per square inch. On the whole it is an example of creditable engineering.
No. 11, as designed, had a radius at the crown of 160 feet ; but the arch settled 2 feet on removing the center, and increased the radius to about 250 feet.
No. 12 is noted for its boldness. This design was tested by building an experimental arch — at Soujoes, France— of the propor- tions given in the table, and 12 feet wide. The center of the ex- perimental arch was struck after four months, when the total set- tlement was 1.25 inches, due mostly to the mortar joints, which were about one quarter inch ; and it was not injured by a dis- tributed load of 500 pounds per square foot, nor by a weight of 5 tons falling 1.5 feet on the key.
No. 46 is said to have " approached a horizontal line in conse- quence of the substitution of vehicles for pack-horses."
725. Table 63 affords some striking comparisons. For exam- ple, Nos. 8 and 9 have practically the same span ; and as the rise of the former is four fifths that of the latter, the thickness at the crown of the former should be only about one and a .quarter times that of the latter, while in fact it is 3.3 times as thick. How- ever, the former carries a railroad, and the latter a turnpike ; but, on the other hand, the former is laid in cement, and the latter in lime.
Nos. 11 and 12 have nearly the same#span, but the rise of the former is 4.7 times the latter ; and if the thickness at the crown were in like proportion — as it should be, — that of the former would be only 0.6 feet. Also compare No. 32 with No. 33 ; and No. 33 with Nos. 9 and 18.
726. Dimensions of Abutments. For examples of the abutments of railway culverts, see Tables 49-52 (pages 425-31). Table 64,
AET. 2.]
RULES DERIVED FROM PRACTICE.
505
below, gives the dimensions of a number of abutments represen- tative of French railroad practice.
TABLE 64. Dimensions of Abutments from French Railroad Practice.*
Designation of Bridge.
I Circular Arches.
De crochet, chemiti de fer de Paris k Chartres
De Lotifir-Sauts, chemin de fer de Paris ft. Cliartres.
D'Eiifcliien, cheiiiiii de fer du Nord
De Pantin, caual St. Martiu
De la Bastille, canal St. Martin
De Basses-Grauges, Orleans k Tours
Segmental Arches.
Des Fruitiers, chemiu du fer du Nord
De Paisia
De M6ry, chemin de fer du Nord.
De Couturette, at Arbois
Over the Salat
iDe la rue des Abattoirs, at Paris, chemin de fer de
Strasbourg
Over the Forth, at Stirling
St. Maxence, over the Oise
Over the Oise, chemin de fer du Nord
De Dorlaston
Elliptical or False-Elliptical Arches.
I De Charolles
I Du Canal St. Denis
j De Chateau-Thierry
De Dole, over the Doubs
Wellesley, at Limerick
D'Orleans, chemin de fer de Vierzon
De Trilport
I De Nantes, over the Seine
De Neuilly, over the Seine
feet. 13.3 16.5 24.4 27.0 36.3 49.4
13.2 16.5 25.2 42.9 46.1
52.9 53.5
77.2 82.7 87.0
19.8 39.5 51.3 52.4 70.0 79.5 80.7 115.2 128.0
feet.
2.31 2.64 2.97 6.13 6.27
5.11 10.25
6.40 11.75 13.50
7.55 14.85 17.10 17.50 17.50 26.30 27.80 34.40 32.00
5 >>
feet. 1.65 1.81 1.95 2.47 3.95 3.95
1.81 1.72 2.14 2.97 3.63
2.97 2.75 4.80 4.60 3.50
1.95 2.95 3.75 3.75 2.00 3.95 4.45 6.40 5.35
M;3
feet.
13.20 9.90 6 60
11.85
20.75 6.60
13.20 6.60
14.20 6.60
24.49
12.96 20.75 27.85 17.90 16.55
1.30 10.20 13.65 1.35 12.00 2.85 6.40 3.20 7.55
feet. 4 95 5.90 6.93
o.no
12.50
5.94 5.01 11.71 17.16 19.14
33.00 16.00 38.94 31.65 .32.20
5.25 12.35 15.00 11.85 16.50 IS. 40 19.30 28.90 35.50
727. Illustrations of Actual Arches.— For illustrations of stone arches for railroad culverts, see Plates II-V. Fig. 1-1:3 (page 509) shows a 50-foot stone arch on the Pennsylvania Railroad. For brick arches for sewers, see Figs. 148 and 149 (pages 513 and 514). For an example of a brick tunnel-arch, see Fig. 147 (page 512). Cabin John arch, the longest span in the world (see No. 2 of Table 63, page 502), is shown incidentally in Fig. 159 (page 525).
728. Minor Details. Backing. The backing is masonry of inferior quality laid outside and above the arch stones proper, to give additional security. The backing is ordinarily coursed or ran- dom rubble, but sometimes concrete. Sometimes the upper ends
* E. Sherman Gould, in Van Nostrand's Engin'g Mag., vol. xxix, i> 450.
50G
ARCHES.
[chap. XVIII.
of the arch stones are cut with horizontal surfaces, in which case the backing is built in courses of the same depths as these steps and bonded with them. The backing is occasionally built in ra- diating courses, whose beds are prolongations of the bed-joints of the arch stones ; but it usually consists of rubble, laid in horizontal courses abutting against the arch ring, with occasional arch stones extending into the former to bond both together. The radial joints possess some advantages in stability and strength, particu- larly above the joint of rupture ; but below that joint the horizon- tal and vertical joints are best, since this form of construction the better resists the overturning of the arch outward about tlie springing line. Ordinarily, the backing has a zero thickness at or near the crown, and gradually increases to the springing line ; but sometimes it has a considerable thickness at the crown, and is pro- portionally thicker at the springing.
It is impossible to compute the degree of stability obtained by the use of backing ; but it is certain that the amount ordinarily employed adds very greatly to the stability of the arch ring. In fact, many arches are little more than abutting cantilevers ; and it is probable that often the backing alone would support the struct- ure, if the arch ring were entirely removed.
729. Spandrel Filling. Since the roadway must not deviate greatly from a horizontal line, a considerable quantity of material is
required above the backing to bring the roadway level. Ordinarily this space is filled with earth, gravel, broken stone, cinders, etc. Sometimes, tc save filling, small arches are built ovei- the haunches of the main arch, as shown in Fig. 140. The interior longitudinal walls may be strengthened by transverse walls between them. To distribute the pressure uni- formly, the feet of these walls should be expanded by footings where they rest upon the back of the arch.
730. When the load is entirely sta- tionary— as in an aqueduct or canal Fia. 140. bridge — or nearly so — as in a long span
arch under a high railroad embankment, — the materials of the
ART. 3.]
EULES DERIVED FROil PRACTICE.
507
spandrel filling and the size and position of the empty spaces may be such as to cause the line of resistance to coincide, at least very nearly, with the center of the arch ring.
For example, A BCD, Fig. 141, represents a semi-arch for which it is required to find a disposition of the load that will cause the line of resistance to coincide with the center line of the arch ring.
Fig. 141.
Divide the arch and the load into any convenient number of divi- sions, by vertical lines as shown. From P draw radiating lines par- allel to the tangents of the center line of the arch ring at a, h, c, etc. ; and then at such a distance from P that 01 shall represent, to any convenient scale, the load on the first section of the arch ring (including its own weight), draw a vertical line through 0. The intercepts 0-1, 1-3, 3-3, etc., represent, to scale, the loads which the several divisions must have to cause the line of resistance to coincide with the center of the arch ring. Lay off the distances 0-1, 1-3, etc., at the centers of the respective sections vertically upwards from the center line of the arch ring, and trace a curve through their upper ends. The line thus formed — EF, Fig. 141— shows the re- quired amount of homogeneous load; i. e., EF is the contour of the homogeneous load that will cause the line of resistance to pass ap- proximately through the center of each joint.
Hence, by choosing the material of the spandrel filling and
508
ARCHES.
[chap. XVIII.
arranging the empty spaces so that the actual load shall be equiv- alent in intensity and distribution to the reduced load obtained as above, the voussoirs can be made of moderate depth. The vacant spaces may be obtained by tlie method shown in Fig. 140 (page 506) ; or by that shown in Fig, 142, in which .4 is a small empty cylindrical arch extending from the face of one end wall to that of the other. (See the description of arch No. 9, § 724, p. 501.)
Notice that the lines radiating successively from P, Fig. 141 (page 507), will intercej)t increasing lengths on the load-line ; and that, therefore, the load which will keep a circular arch in equilib- rium must increase in intensity per horizontal foot, from the crown towards the springing, and must become infinite at the springing of
a semi-circular arch. Hence it follows that it is not practi- cable to load a circular arch, beyond a certain distance from the crown, so that the line ol resistance shall coincide with the center line of the arch ring.
731. Drainage. The drain- age of arch bridges of more than one span is generally ef- fected by giving the top sur- FiG- 142. face of the backing a slight
inclination from each side toward the center of the width of the bridge and also from the center toward the end of the span. The water is thus collected over the piers, from whence it is discharged through pipes laid in the masonry.
To prevent leakage through the backing and through the arch sheeting, the top of the former should be covered with a layer of puddle, or plastered with a coat of best cement mortar (see § 141), or painted with coal tar or asphaltum (see § 264).
732. For an illustration of the method of draining a series of arches, and also of several minor details not mentioned above, see Fig. 143, which represents " Little Juniata bridge No. 12 " on the Pennsylvania Railroad.*
* Published by permission of Wm. H. Brown, chief engineer.
ART.
RULES DERIVED FROM PRACTICE.
509
610 ARCHES. [chap. XYIII.
733. Beick Arches. The only matter requiring special mention in connection with brick arches is the bond to be employed. When the thickness of the arch exceeds a brick and a half, the bond from the soffit outward is a very important matter. There are three principal methods employed in bonding brick arches. (1) The arch may be built in concentric rings ; i. c, all the brick may be laid as stretchers, with only the tenacity of the mortar to unite the several rings (see Fig. 144). This form of construction is frequently called roivlock bond. (2) Part of the brick may be laid as stretchers and part as headers, as in ordinary walls, by thickening the outer ends of the joints — either by using more mortar or by driving in thin pieces of slate, — so that there shall be the same number of bricks in
Fm. 144. Fig. 145. Fig. 14B.
each ring (see Fig. 145). This form of construction is known as header and stretcher bond, or is described as being laid with contmuous radial joints. (3) Block in course bond is formed by dividing the arch into sections similar in shape to the voussoirs of stone arches, and laying the brick in each section with any desired bond, but making the radial joints between the sections continuous from intrados toextrados. With this form of construction, it is custom* ary to lay one section in rowlock bond and the other with radial joints continuous from intrados to extrados, the latter section being much narrower than the former (see Fig. 146).
1. The objection to laying the arch in concentric rings is that, since the rings act nearly or quite independent of each other, the proportion of the load carried % each can not be determined. A ring may be called upon to support considerably more than its proper share of the load. This is by far the most common form of bonding in brick arches, and that this difficulty does not more often mani-
ART. 2.] RULES DERIVED FROM PRACTICE. 611
fest itself is doubtless due to the very low unit working pressure employed. The mean pressure on brick masonry arches ordinarily varies from 20 to 40 pounds per square inch, under which condition a single ring might carry the entire pressure (see Tables 19 and 20, pages 164 and 166). The objection to this form of bond can be partially removed by using the very best cement mortar between the rings.
The advantages of the ring bond, particularly for tunnel and sewer arches, are as follows : It gives 4-inch toothings for con- necting with the succeeding section, while the others give only 2-inch toothings along much of the outline. It requires less cement, is more rapidly laid, and is less liable to be poorly executed. It possesses certain advantages in facilities for drainage, when laid in the presence of water.
2. The objection to laying the arch with continuous radial joints is that the outer ends of the joints, being thicker than the inner, will yield more than the latter as the centers are removed, and hence concentrate the pressure on the intrados. This objection is not serious when this bond is employed in a narrow section between two larger sections laid in rowlock courses (see Fig. 146).
3. When the brickwork is to be subject to a heavy pressure, some form of the block in course bond should be employed. For economy of labor, the ''blocks" of headers should be placed at such a distance apart that between each pair of them there shall be one more course of stretchers in the outer than in the inner ring ; but a moment's consideration will show that this would make each section about half as long as the radius of the arch, — which, of course, is too long to be of any material benefit. Hence, this method necessitates the use of thin bricks at the ends of the rings.
734. Examples of Brick Arches. The method of bonding shown in Fig. 146 (page 510) is frequently employed — as, for example, in the 70-foot brick arch of the Swatara bridge (Philadelphia and Reading R. R.). The bonding employed in arching the Vosburg tunnel (Lehigh Valley R. R.) is shown in Fig. 147 (page 512).*
735. Fig. 148 (page 513) shows the standard forms of large brick sewers employed in the city of Philadelphia, f " They are
*From Rosenberg's " The Vosburg Tunnel," by permission. tR. Hering, in Trans. Am. Soc. of C. E., vol. Tii, pp. 252-57. The illustrations are reproduced from those in the original, the force diagrams being omitted here.
512
ARCHES.
[chap. XVIII.
designed for a maximum pressure on the brick-work of 80 pounds per square inch," which, considering the usual specifications for such work (see § 2G0, p. 176), seems unnecessarily small (see Tables 19 and 20, pages 164 and 166).
Fig. 149 (page 514) shows the standard forms of sewers in Washington, D. C* "The invert as shown is the theoretical form, although the concrete is rammed into the trench and nearly always extends beyond the limits shown." The largest sewers have a trap- rock bottom ; the intermediate sizes have a semi-circular vitrified
Fig. 1J7.— Bond and Center of Vosburg Tunnel.
pipe in the bottom ; and the smallest sizes consist of sewer pipes bedded in concrete.
736. Owing to their great number of joints, brick arches are liable to settle much more than stone ones, when the centers are re- moved ; and hence are less suitable than the former for large or fiat arches. Nevertheless a number of brick arches of large span have been built (see Table 63, page 503). Trautwine gives the following description of some bold examples. " On the Filbert Street exten- sion of the Pennsylvania R. R., in Philadelphia, are four brick arches -of 50 feet span, and with the very low rise of 7 feet. The arch rings :are 2h feet thick, except on their showing faces, where they are but 2 feet. The joints are in common lime mortar, and are about ^ inch
* Report of the Commissioners of the District of Columbia, for the year ending June 30, 1884, p. 175. For details of quantities of material required, and for esti- mates of cost, see report for preceding year, pp. 277-79.
ART. 2. J
RULES DERIVED FROM PRACTICE.
513
514
ARCHES.
[chap. XVIII.
Fia. 149.— Standard Forms of Brick sewers.— Washington, D. C.
ART. 3.] CEN-TERS. 515
thick. These four arches, about ^00 yards apart, with a large num- ber of others of 26 feet span, form a viaduct. The piers between the short spans are 4^ feet thick, and those at the ends of the oO-foot spans are 18j feet. The road-bed is about 100 feet wide, giving room for 9 or 10 tracks. The springing lines of all the arches are about 6 to 8 feet above the ground. One of the 50-foot arches settled 3 inches upon permanently striking the center ; but no further settle- ment has been observed, although the viaduct has, since built (1880), had a very heavy freight and passenger traffic at from 10 to 20 miles per hour.-"
737. Specifications for Stone Arches. The specifications for arch masonry employed on the Atchison, Topeka and Santa Fe Railroad are as follows : *
738. First-Class Arch Masonry shall be built in accordance with the speci- fications for first-class masonrj- [see § 207], with the exception of the arch sheet, iug and ring stones. The ring stones shall be dressed to such shape as the engineer shall determine. The ring stones and the arch sheeting shall be not less than ten inches (10") thick on the intrados, and shall have a depth equal tn the specified thickness of the arch. The joints shall be at right angles to the intrados, and their thickness shall not exceed three .eighths of an inch (f ). The face of the sheeting stones shall be dressed so as to make a close center- ing joint. The ring stones and sheeting shall break joints not less than one foot (1 ).
The wings shall be neatlj- stepped with selec>*'d stones of the full width of the wing, and of not less than ten inches (10") in thickness, overlapping by not less than one and one half feet (U'); or they shall be finished with a neatly capped newel at the end of each wing, and a coping course on the wing. The parapets shall be finished with a coping course of not less than ten inches (10 ■) in thickness, having a projection of six inches (6").
739. Second-Class Arch Masonry shall be the same as first-class masonry (see § 207). The stones of the arch sheeting .shall be at least four inches (4) in thick- ness on the intrados ; shall have a depth equal to the thickness of the arch ; shall have good bearings throughout ; and shall be well bonded to each other and to the ring stones.
740. Specifications for Brick Arches. See §§ 2G0-61 (pages lTG-77).
Art. 3. Arch Cexters.
741. A ce7iter is a temporary structure for supporting an arch while in process of construction. It usually consists of a number of frames (commonly called ribs) placed a few feet apart in planee
* For general specifications for raihroad masonry, see Appendix I.
516 ARCHES. [chap. XVIII.
perpendicular to the axis of the arch, and covered with narrow planks (called laggings) running parallel to the axis of the arch, upon which the arch stones rest. The center is usually wood — either a solid rib or a truss, — but is sometimes a curved rolled-iron beam. In a trussed center, the pieces upon which the laggings rest are called hack-pieces. The ends of the ribs may be supported by timber struts which abut against large timbers laid upon the ground, or they may rest upon a shoulder on the abutment.
The framing, setting up, and striking of the centers (§§ 752-55) is a very important part of the construction of any arch, particularly one of long span. A change in the shajje of the centei', due to insufficient strength or improper bracing, will be followed by a change in the curve of the intrados and consequently of the line of resistance, which may endanger the safety of the arch itself.
742. Load to be Supported. If there were no friction, the load to be supported by the center could be computed exactly ; but fric- tion between the several arch stones and between these and the center renders all formulas for that purpose very uncertain. Fortunately, the exact load upon the center is not required ; for the center is only a temporary structure, and the material employed in its construction is not entirely lost. Hence it is wise to assume the loads to be greater than they really will be. Some allowance must also be made for the accumulation of the material on the center and for the effect of jarring during erection. The following analysis of the problem will show roughly what the forces are and why great accuracy is not possible.
To determine the pressure on the center, consider the voussoir DEFG, Fig. 150, and let
a = the angle which the joint DE makes
with the horizontal ; fx = the co-efficient of friction (see Table ."'0. page 315), i. e., jj. is the tangent of the angle of repose ; 0 — the angular distance of any point from
the crown ; W = the weight of the voussoir DEFG ; N =■ the radial pressure on the center due to ^'°- ^^- the weight of DEFG,
If there were no friction, the stone DEFG would be supported
ART. 3;] CENTERS. 517
by the normal resistance of the surface DE and the radial reac- tion of the center. The pressure on the surface DE would then be W cos a, and the pressure in the direction of the radius W sin a. Friction causes a slight iiidetermination, since part of the weight of the voussoirs may pass to the abutment either through the arch ring or through the back-pieces (perimeter) of the center. Owing to friction, both of these surfaces will offer, in addition to the above, a resistance equal to the product of the perpendicular pres- sure and the co-efficient of friction (foot-note, page 276). If the normal pressure on the joint DE is IT cos a, then the frictional resistance is yu IF cos a. Any frictional resistance in the joint DE will decrease the pressure on the center by that amount ; and conse- quently, with friction on the joint DE, the radial pressure on the center is
N = ir (sin a — J.I cos a) (49)
On the other hand, if there is friction between the arch stone and the center, the frictional resistance between these surfaces will decrease the pressure upon the joints DE, as computed above ; and consequently the value of N will not be as in equation (49).
Notice that in passing from the springing toward the crown the pressure of one arch stone on the other decreases. Near the crown this decrease is rapid, and consequently the friction between the voussoirs may be neglected. Under this condition, the radial pres- sure on the center is
N=WcosO (50)
As a rough approximation, equation (50) may be applied for the first 30° from the crown, although it gives results slightly greater than the real pressures ; and for the second 30°, equation (49) may be employed, although it gives results less than the actual pressure ; and for the third 30°, the arch stones may be considered self-supporting.
743. The value of the co-efficient to be employed in equation (49) is somewhat uncertain. Disregarding the adhesion of the mortar, the co-efficient varies from about 0.4 to 0.8 (see Table 36,
518 ARCHES. [chap.' XVIII.
page 315) ; and, including the adhesion of good cement mortar, it may be nearly, or even more than, 1. (It is 1 if an arch stone remains at rest, without other support, when placed upon another one in such a position that the joint between them makes an angle of 45° with the horizontal.) If the arch is small, and consequently laid up before the mortar has time to harden, probably the smaller value of the co-efficient should be used ; but if the arch is laid up so slowly that the mortar has time to harden, a larger value could, with equal safety, be employed. As a general average, we will assume that the co-efficient is .58, i. e., that the angle of repose is 30°.
Notice that by equation (49) N = 0, if tan a = /u ; that is to say, N = 0, if a = 30°. This shows that as the arch stones are placed upon one another they would not begin to press upon the center rib until the plane of the lower face of the top one reaches an angle of 30° with the horizon.
Table 65 gives the value of the radial pressure of the several por- rions of the arch upon the center ; and also shows the difference between applying equation (49) and equation (50). Undoubtedly the former should be applied when the angle of the lower face of any arch stone with the horizontal does not differ greatly from 30°; and when this angle is nearly 90°, then equation (50) should be ap- plied. It is impossible to determine the point at which one equation becomes inapplicable and the other applicable ; but it is probably safe to apply equation (49) up to 60° from the horizontal.
744. Example. To illustrate the method of using Table 65, assume that it is required to find the pressure on a back-piece of a 20-foot semi-circular arch which extends from 30° to 60° from the horizontal, tlie ribs being 5 feet apart, and the arch stones being 2 feet deep and weighing 150 pounds per cubic foot. Take the sum of the decimals in the middle column of Table 65, which is 3.19. Tins must be multiplied by the weight of the arch resting on 2° of the center. (In this connection it is convenient to remember tliat an arc of 1° is equal to 0.0175 times the radius.) The radius to the middle of the voussoir is 11 feet, and the length of 2° of arc is 0.38 feet. The volume of 2° is 0.38x5x2 = 3.8 cubic feet; and the weight of 2° is 3.8x150 = 570 pounds. Therefore the pressure on the back-piece is 570x3.19 = 1,818 pounds.
ART. 3.]
CENTERS.
519
TABLE 65.
The Radial Pressure op the Arch Stones OP A Semi-Arch, on the Center.
|
Radial Pressure in Terms of the |
||
|
Angle of the Lower |
Weight of the Arch Stone. |
|
|
Face with the Horizontal. |
||
|
By Equation (49). |
By Equation (50). |
|
|
30° |
0.00 |
|
|
33° |
0.04 |
|
|
34° |
0.08 |
|
|
36° |
0.12 |
|
|
38° |
0.16 |
|
|
40° |
0.20 |
|
|
42° |
0.24 |
0.67 |
|
44° |
0.28 |
0.69 |
|
46° |
0.33 |
0.72 |
|
48° |
0 36 |
0.74 |
|
50° |
0.40 |
0.76 |
|
55° |
0.45 |
0.83 |
|
60° |
0.54 |
0.86 |
|
65° |
.... |
0.91 |
|
70° |
|
0.94 |
|
80° |
|
0.98 |
|
90° |
1.00 |
745. Outline Forms of Centers. Solid Wooden Rib. For
flat arches of 10-foot span or under, the rib may consist of a plank, a, a, Fig. 151, 10 or 12 inches wide and 1^ or 3 inches thick, set
Fig. 151.
f^dgewise, and another, b, of the same thickness, trimmed to the curve of the intrados and placed above the first. The two should r>e fastened together by nailing on two cleats of narrow boards as snown. These centers may be placed 3 or 3 feet apart.
520
ARCHES.
[chap. XVI II»
746. Built Wooden Rib. For flat arches of 10 to 30 feet span,
the rib may consist of two or three thicknesses of short boards, fitted and nailed (or bolted) together as shown m Fig. 152. An iron plate is often bolted on over the Joints (see Fig. 147, page 512), which adds materially to the rigidity of the rib. Centers of this form have an astonishing strength. Trantwine gives the two fol- lowing examples which strikingly illustrate this.
In the first of these examples, this form of center was employed for a semi-circnlar arch of 35 feet span, having arch stones 2 feet deep. " Each rib consisted of two thicknesses of 2-inch plank, in lengths of abont 6.5 feet, treenailed. together so as to break joint. Each piece of plank was 12 inches deejj at the middle, and 8 inches, at each end, the top edge being cut to suit the curve of the arch. The treenails were 1.25 inches in diameter, and 12 of them were used to each length. These ribs were placed 17 inches apart from center to center, and were steadied together by a bridging piece of 1-inch board, 13 inches long, at each joint of the planks, or about 3.25 feet apart. Headway for traffic being necessary under the arch, there were no chords to unite the opposite feet of the ribs. The ribs were covered with close board-lagging, which also assisted in steadying them together transversely. As the arch approached about two thirds of its height on each side, the ribs began to sink at the haunches and rise at the crown. This was rectified by loading the crown with stone to be used in completing the arch, which was then finished without further trouble."
The other example was an elliptic arch of 60 feet span and 15 feet rise, the arch stones being 3 feet deep at the crown and 4 feet at the springing. '^'^Eacli frame of the centre was a simple rib 6 inches thick, composed of three thicknesses of 2-inch oak plank, in lengths (about 7 to 15 feet) to suit the curve and at the same time to preserve a width of about 16 inches at the middle of each length and 12 inches at each of its ends. The segments broke joints, and were well treenailed together with from ten to sixteen
AET. 3.] CENTERS. 521
treenails to each length. There were no chords. These ribs were placed 18 inches from center to center, and were steadied against one another by a board bridging-piece, 1 foot long, at every 5 feet. When the arch stones had approached to within about 12 feet of each other, near the middle of the span, the sinking at the crown and the rising at the haunches had become so alarming that pieces of 12- X 12-inch oak were hastily inserted at intervals and well wedged against the arch stones at their ends. The arch was then finished in sections between these timbers, which were removed one by one as the arch was completed."
Although the above examples can not be commended as good construction — the flexibility of the ribs being so great as to endanger the stability of the arch during erection and to break the adhesion of the mortar, thus decreasing the strength of the finished arch, — they are very instructive as showing the strength attainable by this method.
747. The above form of center is frequently employed, partic- ularly m tunnels, for spans of 20 to 30 feet, precautions being taken to have the pieces break joints, to secure good bearings at the joints, and to nail or bolt the several segments firmly together. The centers for the 25-foot arch of the Musconetcong (N. J.) tun- nel (Lehign Valley R. R.) consisted of segments of 3-inch plank, 5 feet 8 inches long, 14 inches wide at the center, and 8 inches at the ends, bolted together with four -l^-inch and four f-inch bolts each, and 14- x 8-inch pieces of plate-iron over the joints. Where the center was required to support the earth also, a three-ply rib was employed ; but in other positions two-ply ribs, spaced 4 to 5 feet apart, were used. Centers of this form have successfully stood very bad ground in the Musconetcong and other tunnels;* and hence we may infer that they are at least sufficiently strong for any ordinary arch of 30 feet span.
Although not necessary for stability, it is wise to connect the feet of the rib by nailing a narrow board on each side, to prevent the end of the rib from spreading outwards and pressing against the masonry — thus interfering with the striking of the center, — and also to prevent deformation in handling it.
* Drinker's Tunneling, p. 548.
522
ARCHES.
[chap. XVIII.
748. Braced Wooden Rib. For semi-circular arches of 15 to 30 feet span, a coustruction similar to that shown in Fig. 147 (page 512) may be employed. The segments should consist of two thicknesses of 1- or 2-inch plank, according to span, from 8 to 12 inches wide at the middle, according to the length of the segments. The hori- zontal chord and the vertical tie may each be made of two thick- nesses of the plank from which the segments are made.
For greater rigidity, the rib may be further braced by any of the methods shown in outline in Figs. 153, 154, 155, or by obvious
Fig. 153.
Fig. 154.
Fig. 155.
modifications of them. The form to be adopted often depends upon the passage-way required under the arch. Fig. 153 is supported by a post under each end; in extreme cases, Fig. 154 may be supported at the middle point also; and Fig. 155 may be supported at both middle points as well as at the ends.
Since the arch masonry near the springing does not press upon the center, it may be laid with a template before the center is set up; and hence frequently the center of a semi-circular arch does not extend down to the springing line. For examples, see Figs. 147 and 158 (page 512 and 524).
Center frames are put together on a temporary platform or the floor of a large room, on which a full-size drawing of the rib is first drawn.
749. Trussed Center. When the span is too great to employ any of the centers described above, it becomes necessary to construct trussed centers. It is not necessary here to discuss the principles
Fig. 156
of trussing, or of finding the strains in the several pieces, or of determining the sections, or of joining the several pieces, — all of
ART. 3.] CENTERS. 533
wliich are fully described in treatises on roof and bridge construc- tion. There is a very great variety of methods of constructing such centers. Figs. 156 and 157 show two common, simple, and efldcient general forms.
750. Camber. Strictly, the center should be constructed with a cambi'r ju<t equal to the amou.nt it will yield when loaded with the arch ; but, since the load is indeterminate, it is impossible to compute what this will be. Of course, the camber depends upon the unit strain in the material of the center. The rule is frequently given that the camber should be one four -hundredth of the radius; but this is too great for the excessively heavy centers ordinarily used. It is probably better to build the centers true, and guard against undue settling by giving the frames great stiffness; and then if unexpected settling does take place, tighten the striking wedges slightly.
The two sides of the arch should be carried up equally fast, to prevent distortion of the center.
751. Examples of Actual Centers. For an examj^le of a center employed in a tunnel, see Fig. 1-47 (page 512).
Fig. 158 (page o2-4) shows the center designed for the 60-foot granite arches of the recently completed Washington bridge over the Harlem River, Xew York City.* The bridge is 80 feet wide, and fifteen ribs were employed. N"otice that the center does not extend to the springing line of the arch ; the first fifteen feet of the arch were laid by a template.
Fig. 159 f (page 525) shows the center employed in constructing the Cabin John arch, which carries the Washington (D. C.) aque- duct over a creek, and which is the largest masonry arch in the world (see No. 2, Table 63, page 502). The arch is 20 feet wide, and five ribs were emploved.
752. Striking the Center. The Method. The ends of the ribs or center-frames usually rest upon a timber lying parallel to. and near, the springing line of the arch. This timber is supported by wedges, preferably of hard wood, resting upon a second stick, which is in turn supported by wooden posts — usually one under each end of each rib. The wedges between the two timbers, as above, are used
* Published by permission of Wm. R. Hutton, chief engineer. + Compiled from photographs taken during the progress of the work (1856-60), by courtesy of Gen. M. C. Meigs, chief engineer.
524
ARCHES.
CHAP. XVITT.
ART. 3.]
CEIS^TEKS.
5:^5
526 ARCHES. [chap. XVIII.
in removing the center afier the arch is completed, and are known as striking wedges. They consist of a pair of folding wedges — 1 to 2 feet long, 6 inches wide, and having a slope of from 1 to 5 to 1 to 10 — placed under each end of each rib. It is necessary to remove the centers slowly, particularly for large arches ; and hence the striking wedges should have a very slight taper, — the larger the span the smaller the taper.
The center is lowered by driving back the wedges. To lower the center uniformly, the wedges must be driven back equally. This is most easily accomplished by making a mark on the side of each pair of wedges before commencing to drive, and then moving each the same amount.
753. Instead of separate pairs of folding wedges, as above, a compound wedge. Fig. 160, is sometimes employed. The pieces
Fig. 160.
A and B are termed striking plates. The ribs rest upon the former, and the latter is supported by the wooden posts before referred to. The wedge C is held in place during the construction of the arch by the keys. A", K, etc., each of which is a pair of folding wedges. To lower the center, the keys are knocked out and the wedge Cis driven back.
The piece C is usually as long as the arch, and supports one end of all the ribs ; but with large arches, say 80 to 100 feet span, it is customary to support each rib on a compound wedge running parallel to the chord of the center (jDcrpendicular to the axis of the arch). Instead of cutting the striking plates A and B as shown in Fig. 160, the compound wedge may play between tapered blocks gained into A and B. The piece C is usually made of an oak stick 10 or 13 inches square. The individual wedges are from 4 to 6 feet long.
For the larger arches, the compound wedge is driven back with a heavy log battering-ram suspended by ropes and swung back and forth by hand. The inclined surfaces of the wedges
ART. 3.] CEXTEKS. 527
should be lubricated when the center is set up, so as to facilitate the striking.
754. An ingenious device, first employed at the Pont d'Alma arcli — 141 feet span and 28 feet rise, — consisted in supporting the center-frames by wooden pistons or plungers, the feet of which rested on sand confined in plate-iron cylinders 1 foot in diameter and about 1 foot high. Xear the bottom of each cylinder there was a plug which could be withdrawn and rejDlaced at pleasure, by means of which the outflow of the sand was regulated, aud consequently also the descent of the center. This method is particularly use- ful for large arches, owing to the greater facility with which the center can be lowered. See Fig. 158, page 5.24:.
755. The Time. There is a great difference of opinion as to the proper time for striking centers. Some hold that the center should be struck as soon as the arch is completed and the spandrel filling is in jolace ; while others contend that the mortar should be given time to harden. It is probably best to slacken the centers as soon as the keystone is in place, so as to bring all the Joints under pressure. The length of time which should elapse before the centers are finally removed should vary Avith the kind of mortar employed (see Fig. 5, page 89) and also with its amount. In brick and rubble arches a large proportion of the arch ring consists of mortar ; and if the center is removed too soon, the compression of this mortar might cause a serious or even dangerous deformation of the arch. Hence the centers of such arches should remain until the mortar has not only set, but has attained a considerable part of its ultimate strength (see Fig. 5, page 89), — this depending somewhat upon the maximum compression in the arch. It is probable that a knowledge of the elasticity and of the ''set" of mortar would give some light as to the best time to strike centers ; but unfortunately our infor- mation on those topics is very limited (see § 146).
Frequently the centers of bridge arches are not removed for three or four months after the arch is completed ; but usually the centers for the arches of tunnels, sewers, and culverts are removed as soon as the arch is turned and, say, half of the spandrel filling is in plaee.
APPENDIX I.
SPECIFICATIONS FOE MASONRY.*
Contents.
General Railroad Masonry page 529
Masonry for Railroad Buildings " 534
Architectural Masonry " 5,39
Laying Masonry in Freezing Weather " 543
Railroad MASOXRT.f
General Provisions. All stone used for the different classes of masonry must be furnished from the best quarries in the vicinity, subject to the ap- proval of the engineer. Brick masonry shall at all times be substituted for stone, when so desired by the engineer.
Inspection. All materials will be subject to rigid inspection, and any that have been condemned must be immediately removed from the site of the work. The work will be done under the supervision of an inspector, whose duties will be to see that the requirements of these specifications are carried out; but his presence is in no way to be presumed to release in any degree the responsi- bility or obligation uf the contractor.
Laying Masonry. All classes of masonry laid in cement must be neatly pointed with cement mortar, finely tempered. No masonry of any kind must be covered until it has been inspected and accepted by the engineer. No ma- sonry will be allowed to be laid in freezing weather. [Many specifications omit this condition. See " Specifications for Laying Masonry in Freezing Weather," page 543.]
Measurement of Masonry. All masonry and brick-work will be built ac- cording to the plans and instructions furnished by the engineer, and will be estimated and paid for by the cubic yai-d, computing ouly'the actual solidity thereof. No constructive or conventional measurement will be allowed, any rule or custom in the section of the country through which the road passes to the contrarj- notwithstanding. The price per cubic yard paid for masonry and brick-work will include the furnishing of all material, scaffolding, cen- tering, and all other expenses necessary to the construction and compleHon of the masonry or brick-work. All " dressed " or "cut-stone" work— such as copings, bridge-scats, cornices, belt-courses, water-tables, brackets, corbels, etc — furnished under the plans of the engineer will be paid for b}' the cubic yard, imder the classification of the masonry in which they occur, with an iidditional price per square foot of the entire superficial surface of the stones " dressed." or " cut," or " bush-hammered."
Allowance for Extras. No allowance will be made for timber, or work on same, used in .scaffolding, shoring, or centering for arches, — excepting only timber, sheet-piling, or foundation plank, necessarily, and by order of the en- gineer, left in the ground. No allowance will be made to the contractor for
• See also the specifications in the body of the bo k. See " Specifications ' in Index.
+ These specifications are the same, except ip form, as those employed in the construction of the " West Shore" Railroad, but do not differ materially from those used in other roadSf and have frequently been accepted as the standard.
529
530 SPECIFICATIONS FOR MASONRY. [APP. I.
any damage he may sustain by reason of floods or other causes; but such draining, bailing, or pumping from foundations as the engineer may decide to- be necessary will be paid for at a price to be tixed by the engineer.
First-class Masonry will consist of quarrj^-faced ashlar [see §§ 200-07] laid in horizontal courses having parallel beds and vortical joints, of not less than ten inches (10") nor more than thirty inches (30") in thickness, — decreas- ing in thickness regularly from the bottom to the top of the wall, — laid Hush in cement mortar of the quality hereinafter speciiled. Each course must be thoroughly grouted before the succeeding one is laid.
Size of Stones. Stretcliers must be not less than two and one half feet(2i'> nor more than six feet (6') in length, and not less than one and one half feet (H') in width, nor less in width than one and one half (li) times their depth. Headers must not be less than three and one half feet (SV) nor more than tour and one half feet (4+) in length — where the thickness of the wall will admit of the same, — and not less than one and one half feet (U') in width, nor less in width than they are in depth of course.
Cutting. Every stone must be laid on its natural bed. All stones must have their beds well dressed, parallel and true to the proper line, and made al- ways as large as the stone will admit of. The beds and sides of the stone must be cut, before being placed on the work, so as to form joints not exceeding one half inch (^") in width. No hammering on a stone will be allowed after it is set; but if any inequalities occur, they must be pointed olf. The vertical joints of the face must be not less than eight inches (8") in from the face, and as much more as the stone will admit of. All corners and batter lines must be run with a neat chisel draft one and one half inches (1+") on each face. The projections of the quarry face beyond the draft lines must not exceed four inches (4"); and in the side-walls of tunnels this projection m^st not exceed two inches (2").
Bond. The masonry shall consist of headers and stretchers alternating. At least one fourth of it shall consist of headers extending entirely through the wall, and every header shall be immediately over a stretcher of the underlj'in* course. The stones of each course shall be so arranged as to form a proper bond — in no case less than one foot (1') — with the stones of the underlying course.
Backing^ The backing shall be of good-sized, well-shaped stones, laid so as to break joints and thoroughly bond the work in all directions, and leave no spaces between them over six inches (6") in width, which spaces shall be filled with small stones and spalls well grouted.
Coping. All bridge-seats and tops of walls will be finished with a coping course of such dimensions and projections as may be ordered bj" the engineer, dressed and cut to a true surface on top and front edges, in conformity with diagrams for same which will be furnished by the engineer.
Foundation Courses. All foundation courses must be laid with selected large flat stones; not less than twelve inches (12") thick, nor of less superficial surface than fifteen (15) square feet.
Second-class Masonry [^g 208-12] will consist of broken range rubble of superior qualit}^ laid with horizontal beds and vertical joints on the face, with no stone less than eight inches (8 ') in thickness — unless otherwise directed by the engineer, — well bonded, and leveled as well as can be without hammer- dressing. No mortar joint shall exceed three quarters of an inch (f ' ) in thick- ness. AH corners and quoins shall have hammer-dressed beds and joints; and all corners and batter lines shall be run with an inch-and-one-half (U") chisel draft. At least one fourth {\) of the stones in the face must be headers evenly distributed through the wall.
Bridge-seats and tops of walls shall be coped in the same manner as specified for first-class masonry. Stones in foundaLion courses shall be not less than twelve inches (12") thick, and shall contain not less than twelve (12) square feet of surface.
RAILROAD MASONRY. 531
Third-class Masonry will consist of good substantial rubble [§§213-1 7] laid in cement mortar. All stones shall be perfectly sound, and sufficiently large to make good, well-bonded, strong work; and shall be laid on their natural beds, in the most substantial manner, and with as much neatness as this description of work admits of. The stones in the foundations must be not less than ten inches (10 ') thick, and shall contain not less than ten (10) square feet of surface; and each shall be tirmlj', solidly, and carefully laid.
First-class Arch-culvert Masonry shall be built in accordance with the specitications for first-class masourj', with the exception of the arch sheeting and the ring-stones. The rings shall be dressed to such size and shape as the engineer shall direct. The ring-stones and sheeting-stones shall not be of less thickness than ten inches (10") on the intrados, and shall be dressed with three eighths inch (f ") joints, and shall be of the full depth speci- fied (by drawings or otherwise) for the thickness of the arch. The joints must be made on truly radial lines, and the face of the sheeting-stones must be dressed to make close joints with the center. The ring-stone and sheeting- stones shall break joints by not less than one foot (1').
The wing walls shall be neatly stepped, in accordance with the drawings furnished, with selected stones of the full width of the wing and of not le^s than ten inches (10 ') in thickness, no stone being covered less than eighteen inches (18 ) by the one next above it; or the wing shall be finished with a neatl}^ capped newel at the end, and a coping course, — as may be selected by the engineer. The parapet shall be finished with a coping course of full width of parapet, with such projection as may be directed by the engineer, the stone to be not less than ten inches (10") thick.
Second-class Arch-culvei't Masonry shall be of the same general character and description as second-class masonry, with the exception of the ring-stones and the arch sheeting. The former shall be dressed as specified for first-class arch-culvert masonry. The latter shall consist of selected stones of the full depth of the arch, and shall have a good bearing throughout the thickness of the arch, and shall be well bonded. No stone shall be less than six inches (6") in thickness on the intrados.
Box-culv^ert Masonry will be good rubble [see §g 313-17], neatly laid up with square-shaped stones of a size and quality satisfactory to the engineer. The end parapet walls and also the side walls for three feet (3) from the ends shall be laid in good cement mortar. "When box culverts are ordered to be laid up entirely in cement mortar [see § 214], they will be classified as third- class masonry, and must conform to the specifications for the same.
The covering-stone for all box culverts shall be not le.ss than ten inches (10") in thickness, and must have a good, solid, well-leveled bearing on the side walls of not less than fifteen inches (15").
Vitrified Pipe. In localities where but a small quantity of water passes, vitriMed pipe will be .substituted for culverts when so ordered by the engineer. Sizes of twelve (12"), fifteen (15"), or eighteen (18") inches in diameter may be used, and must be of the best qualitj' double strength, vitrified culvert pipe, subject to the approval of the engineer. Vitrified pipes must be well and care- fully bedded and laid [see Figs. 97-99, pages 409-10], in accordance with the instructions of the engineer.
Ketainins' Walls will be classified as second- or third-class masonry laitl dry, as nitiy be ordered in each particidar case.
Slope Walls will be of such thickness and slope as directed by the en- gineer. Tlie stones must reach entirely tlirough the wall, and be not less than four inches (4") thick and twelve inches (12") long, laid with close joints, and as free as possible from spalls. The foundations must be prepared and laid as directed by the engineer.
Stone Paviiig" shall be made by setting on edge stone from eight (8") to
532 SPECIFICATIONS FOR MASONRY. [APP. I.
fifteen inches (15") in depth, laid either dry or grouted with strong cement mortar, as may be directed by the engineer.
Riprap. When required by the engineer, the face of embankments and the foot of slopes shall be protected from the action of water bj' a facing of riprap stone, or of brush and stones, or by a retaining wall, as may be directed. The riprap, when used, shall be laid by hand by competent workmen, and shall be of such thickness and slope and of such undressed stone as the en- gineer may direct
Brick Masoury. The brick must be of the best quality [see ^ 57], well tempered, hard burned, and 8J X 4 X 2f inches.* No bats, ciueked, crooked, or salmon bricks will under any circumstances be allowed in the work. Tlie brick shall be well soaked in water before being laid, and shall be laid in hydraulic cement mortar of the quality hereafter specitied, with such thickness of joint and style of bond [§ 242 and ^' 783] as shall be presciibed by the engineer. Grout will be substituted for mortar when ordered by the engineer.
Brick arching must be covered on the back with a coat of strong cement mortar one inch (1") thick. In tunnel arching wherever a seam of water is met, the arch must be covered with rooting felt; or with a course of asphaltum (applied hot) of such thickness as may be directed by the engineer, and this covered with a plastering of cement mortar so as to make the arch impervious to water. A properly formed drainage channel shall be left in the backing of the arch and side walls, with suitable openings for the escape of the water, at such points and of such size as may be directed by the engineer. The keying of all arches shall be most carefully done, and in such manner as may from time to time be directed by the engineer. The packing between the arch and tunnel roof shall never be put in until at least forty-eight (48) hours after the section has been keyed.
Cement. The cement must be of the best quality of freshly ground hy- draulic cement [of tlie Rosendale type — see § 72], and be equal in quality to the best brands of . . . ... cement. It will be subject to test by the engineer or his
appointed inspector, and must stand a tensile stress of tifty (50) pounds per square inch of sectional area on specimens allowed a set of thirty (30) minutes in air and twenty-four (24) hours under water [see § 90, and art. 5 of Chapter III).
Mortar. The mortar shall in all cases be composed of one (1) part in bulk of the above specitied hydraulic cement to two (2) parts in bulk of clean, sharp sand, well and thoroughly mixed together in a clean box of boards, be- fore the addition of the water. It must be used immediately after being mixed; and no mortar left over night will, under any pretext, be allowed to be used. The sand and cement used will at all times be subject to inspection, test, and acceptance or rejection by the engineer.
Concrete. The concrete shall be composed of two (2) parts in bulk of hard, sound, and acceptable stone — broken to a size that will pass in any direc- tion through a two-inch (2") ring, thoroughly clean and free from mud, dust, dirt, or any earthy admixture whatever, — and one (1) part of freshly-made cement mortar of the quality above described. The concrete shall be quickly laid in sections, in laj'ers not exceeding nine (9) inches in thickness, and shall be thoroughly rammed until the water Hushes to the surface. It shall be al- lowed at least twelve (12) hours to set before any work is laid on it.
Foundations. Excavations. Foundations for masonry shall be excavated to such depths as may be necessary to secure a solid bearing for the masonry, — of which the engineer shall be the judge. The materials excavated will be
* Instead of the dimensions as above, the speciflcations of which these are a revision and also many others contain the term "standard size," but until recently that term could have had no special significance (see § 62, page 46).
RAILROAD MASONRY. 533
classified and paid for, as provided for in the Specifications for Grading. All materials taken from the excavations for foundations, if of proper quality, shall be deposited in the contiguous embankment; and any material uutit for such purpose shall be deposited outside the roadwa}-, or in such place as the engineer shall direct, and so that it shall not interfere with any drain or water course. In case of foundations in rock, the rock must be excavated to such depth and in such form as may be required bj- the engineer, and must be dressed level to receive the foundation course.
Artificial Foundations. When a safe and solid foundation for the masonry can not be found ut a reasonable depth (of which the engineer is to be the judge), the contractor shall prepare such artificial foundations as the engineer may direct.
Paving. Box culverts and small bridge abutments may have a paved foun- dation, if so directed by the engineer, by setting stones on edge, breaking joints, and extending across tlie entire width of the foundation.
Timber. Timber foundations shall be such as the engineer may by drawing? or otherwise prescribe, and will be paid for bj- the thousand feet, board meas ure. — the price to include the cost of material, framing, and putting in place. All timber must be sound, straight-grained, and free from sap, loose or rotten knots, wind shakes, or any other defect that would impair its streugth or durability. It must be sawed (or hewed) perfectly straight and to e.xact dimensions, with full corners and square edges. All framing must be done in a thoi'ough, workmanlike manner. Both material and workmanship will be subject to the inspection and acceptance of the engineer.
Piling. All piles shall be of youug, sound, and thrifty white oak, yellow pine or other timber equally good for the purpose, acceptable to the engineer. They must be at least eight inches (8 ') in diameter at the small end and twelve inches (12") in diameter at the butt when sawn off; and must be perfectly straight and be trimmed close, and have the bark stripped off before they are driven. The piles must be driven into hard bottom uutil they do not move more than one half inch (I") under the blow of a hammer weighing two thou- sand (3,000) pounds, falling twenty-five feet (25) at the last blow. They must be driven verticall}^ and at the di.stances apart, transversely and longitudinally, required by the plans or directions of the engineer. They must be cut off square at the butt and be well sharpened to a point; and when necessary, in the opinion of the engineer, shall be shod with iron and the heads bound with iron hoops of such dimensions as he may direct, — which will be paid for the same as other iron-work used in foundations.
The necessary length of piles shall be ascertained by driving test piles in different parts of the localities in which they are to be used. In case a single pile shall not prove long enough to reach hard bottom, two shall be spliced together as follows: The head shall be sawed off square, and a hole two inches (2) in diameter and twelve inches (12") deep shall be bored into it; and into this hole a circular white oak treenail twenty-three inches (23 ')in length shall be well driven. Then another pile similarly squared and bored, and of as large a diameter at the small end as can be procured, shall be placed upon the lower pile, brought to its proper position, and driven as before directed. All piles, when driven to the required depth, are to be cut off truly .square and horizontal at the height given by the engineer; and only the actual number of lineal feet of the piles left for use in the foundations after being sawed off, will be paid for.
Iron. All wrought and cast-iron work ordered by the engineer will be paid for by the pound, — the price to include the cost of material, manufac- ture, and placing in the work.
Coffer-dams. Where coffer-dams are, in the opinion of the engineer, re- quired for foundations, the prices provided in the contract for timber, piles, and iron in foundations, will be allowed for the material and work on same,
534: SPECIFICATIOIS^S FOR MASOXRY. [aPP. I.
which is understood as covering all risks from high water or otherwise, drain- ii.g, bailing, pumping, and all materials connected with the colfer-dams. Sheet-piling will be classed as plank in foundations; and if left in the ground will be paid for by the thousand feet (1,000), board measure.
Kailroad Buildings.^
Tools. All tools necessary for the execution of the contract, including mortar boxes, will be furnished by the contractor at his own expense.
Stag'iiig. All staging required for the execution of the work done under contract shall be furnished by the contractor at his own expense. The rail- way company will, however, upon the completion of any structure, purchase of the contractor such staging material as it can advantageously use, and pay the contractor for such material an amoimt which, in the opinion of the rail- way company's engineer, shall seem reasonable and just.
Excavations. Dry excavations, or excavations above water, will be made by the contractor when so ordered by the railway company. Wet exca- vations, or excavations below water, will be made by the railwaj'^ company, excepting when a special arrangement is made with the contractor. All exca- vations will be classified as either earth, loose rock, or solid rock.
When the excavation for any structure is made entirely by the contractor, it shall be measured in cubic yards, and paid for at the price per cubic yard specified in the contract. When an excavation is made in part by the railway company's force and is finished by the contractor's force, or when contractor's force assists railway company's force in making any excavation, contractor will be paid for the actual time that his force is employed, at laborer's current rate per da}' plus ten per cent. In case contractor furnishes a foreman for such work, time charged for foreman must not exceed one day for foreman for each ten days of laTjor, and contractor will be paid for the services of .such foreman at a rate per day not to exceed the current wages paid foremen of laborers plus ten per cent. lu case contractor uses masons, foremen of masons, or other skilled labor for the execution of the above "extra" or "time" work, the wages and time allowed will be the same as it would be if the work had been performed and supervised by laborers and foremen of laborers. When "extra" or " time" work is performed by contractor's force, and is supervised by contractor's foreman, who at the same time and place has charge of and is supervising "contract" work, no pay will be allowed contractor for such supervi.sion, except when, in the opinion of the railway company's engineer, it may seem reasonable and just.
All excavations shall be made strictly in accordance with the plans fur- nished by the railway companj' and the stakes set by the railway comjiany's engineer, and .shall be executed in a neat and workmanlike manner. Where excavations are made under the supervision of the contractor, his agent or foreman, any erroneous or unnecessary excavation, and any masonry conse- quent to such erroneous or unnecessary excavation, shall be entirely at the contractor's expense, unless the contractor can show that such unnecessary work was caused by errors in the plans furnished by the railway compan}', or by errors in the railway company's engineer's stakes or instruction!?.
When excavation is made for concrete, great care must be taken to make the pits or trenches, as the case may be, of the exact width and depth required for tiie concrete, and any unnecessary excavation made or concrete used on accouiit of lack of such care on the part of the contractor will be at his ex- pense. Excav^tiaQs for stone footing courses will be made, when not other-
* A)!tcbi80n, Topeka and Santa Fe Railroad.
EAILROAD BUILDINGS.
■wise ordered, eight inches (8") (four inches (4") on each side) wider than the footing course. Excavations for walls not having footing courses will be iiuule, when not otherwise ordered, twelve inches {V^") (six inches (6') on each side) wider than the wall is thick.
Before masonr}^ is built, excavations must be cleared of all loose earth, mud, or other objectionable material.
Stone. Stone will be furnished by the contractor at his own expense, and he of a qualitj' suitable for the dill'erent cla.sses of masonry beieinafter speci- tied, and be subject to the inspection and acceptance of the railway company's engineer. Stone will be loaded on cars and unloaded by the contractor at his own expen.se. Stone will be delivered by the railway company on the nearest available side track to the work, and no charges whatsoever will be allowed contractor for hauling .stone from cars to the work, except in extreme cases, where, in the opinion of the railway company's engineer, such charges may appear rea.sonable and just.
Sand. All sand for mortar or concrete will be furnished by the contractor at his own expense. When, in the opinion of the railway company's engineer, sand can not be secured by contractor within reasonable distance by wagon haul and at a reasonable price, transportation by rail will be furnished by the railway compan^^ it being optional with the railway company at what point saiul sliall be procured. When railway company furnishes transportation for sand, cars shall be loaded and unloaded by contractor at his own expense.
All sand furnished by contractor shall be clean and sharp, and subject to the inspection of, and rejection by, the railway company's engineer. When, in the opinion of the railw^ay company's engineer, sand requires screening, it shall be .screened by the contractor at his own expense.
Ceineiit and Lime. All cement and lime will be furnished by the railway company at its own expense; and will be delivered on cars on the nearest available side track to the work. It shall be unloaded by the con- tractor at his own expense, and shall be piled up in such manner by him as the railwaj' company's engineer may direct. Cement and lime shall be covered and protected from the weather by the contractor at his own expense, in such manner as seems suitable to the railway company's engineer; and the con- tractor will be held responsible for the value of any cement damaged on ac- count of unsuitable protection.
Water. Water required for all work done under contract shall be fur- nished l;y the contractor at his own expense. No charges made b}' contractor lor hauling water will be allowed. When, in the opinion of the railway com- pany's engineer, water can not be procured by the contractor within reason- able wagon haul, or at a reasonable expense, it will be furnished by the rail- way comjiany.
31<)rtar. Except when otherwise ordered, all mortar shall be thoroughly mixed in a box, in the foF-owing proportions: One (1) part cement, two (3) parts sand, with sufficient w^ater to render the mixture of the proper consist- ency. Care must be taken to thoroughly mix the .sand and cement drj', in the proportions specitied, before the introduction of water into the mixture. Mor- tar shall not be mixed except as it is u.sed, and no mortar must be allowed to stand over night in mortar boxes or elsew^here.
CoiM'iH'te. All concrete shall consist of one (1) part cement, two (2) parts sand, and six (i>) parts broken .stone, together with sufficient w'ater to mix the sand and cement to the consistency of good moi'tar for masonry. The pro- portion of .sand, cement, broken stone, and the quantity of water used in the mixture, may be varied at the option of th'e railway company's engineer.
Stone sliall be of a quality acceptable to the railway company's engineer, and be broken .so that seventy-live (75) \^ev cent, will pass through a two-inch (3') ring antl so that all wiil jia.ss through a two and one half inch {2^") ring. Broken stone shall be free from mud, dirt, and other objectionable
536 SPECIFICATIONS FOE MASONRY. [aPP. I.
material, and shall be subject to the inspection of, and rejection by, the rail- way company's engineer.
The sand and cement must be thoroughly mixed dry, in a clean, tight mortar box, before the introduction of water; and after water is apitlied to the mixture, the whole must be worked over with hoes until a good mortar of proper consistency is secured. After the mortar is made, the broken stone must be thoroughly drenched whh clean water, and then shall be added to the mixture in the proportion stated above — or in any other proportion which the railway company's engineer may specify. The concrete must then be worked over and mixed until each stone is completely covered with mortar and all spaces between the stones entirely -filled with same.
The concrete shall be deposited in horizontal layers not exceeding twelve inches (12 ') in depth, and shall be thoroughly tamped when so required by the railway company's engineer.
Kubble Masoui'y. Rubble masonry will be classified as either heavy rubble, foundation rubble, pier rubble, or uncoursed hammer-squared rubble. The latter will be called for convenience .squared rubble [see §§2U8-12].
J'-^avy Rubble. When not otherwise specihed or shown on the plans, foot- ing courses will be built of rubble masonry. When footing courses exceed thfrty inches cjO ) in width, the masonry will be classitied as heavy rubble; and when thirt}' inches (SO") or less in width, the masonry will be classitied as foundation rubble.
Heavy rubt)le footing courses shall be built of well-selected stone, which shall have a thickness not less than the height of the footing course. Each stone shall have a bottom bed of good surface over its entire area, which shall be horizontal when the stone is in po.sition. As much of the upper .surface of each stone as will be directly vmder the ma.sonry to be put above the footing course shall be uniform and parallel to the bottom bed. At least one third (i). of the length of the footing course shall be built of through-stone, and a larger proportion shall be furni.shed by the contractor when, in the opinion of the railway company's engineer, more through-stone are required to secure stability. No stone shall be used which will not bond or extend under the- masonry to be built above the footing course a distance equal to at least one third {^) the thickness or width of the masonry; and not more than two .stones shall be used at any section to make up the total width of the footing cour.se, and the exposed face of each stone shall he at least twelve inches (12 ) in length.
All stones must be roughly jointed with a hammer for a distance back from their faces equal to the projection or offset of the footing cour.se. No spaces to exceed forty (40) square inches in area shall he filled with spalls or chips, and the total area of all spaces must not exceed five (5) per cent, of the area of the footing course.
All stone when placed in position must be thoroughly rammed until firmly embedded in a bed of mortar, which shall first be placed in bottom of excava- tion or trench, and after stone are placed in position, all joints must be well grouted with mortar. When so required by the railway company's engineer, fooling courses shall be built exactly to the dimensions shown on drawings or specifications, or with their edges built to a line.
Foundation Bubble. In general, and when not otherwise specified, all masonry below the bottom of water table or below the top of rail for stone buildings, and all masonry below the sill of wooden buildings, will be classified as foiui- dation rubble, except footing courses more than thirty inches (30") in width, which will be classified as heavy rubble. Foundation rubble may be required, however, for any portion or for all the masonry in any structure, in which case no additional price shall be allowed, except when, in the opinion of the railway company's engineer, it shall seem reasonable and just.
In this class of masonry no stone having an exposed face shall be less, than one twentj'-fourth (^y of a foot in cubical contents nor less than two inches -(2") thick. Any stone smaller than this will be considered a spall;.
RAILKOAD BUILDINGS. 53?
and spalls are not to be used to exceed seven (7) per cent, of the entire mass. The contractor will not be required to furnish stone (except for through- stone) larger than one and one half feet (IV) in cubical contents, but the stone used shall not average less than one half (|) of a cubical foot in contents. No stone shall be used which does not bond, or extend into the wall, at least six inches (6"). One through-stone, whose face area shall not be less than one half (i) of a superHcial foot, will be required for each sixteen (16) superticial feet of face measurement of wall, and more than this may be required by the railway company when, in the opinion of its engineer, a larger proj)oriiou of tiiroiigh-stoue is required to secure stability; provided, however, that the con- tractor shall in no case be required to furnish through-stone to exceed ten (10> per cent, of the entire mass. At least twenty (20) per cent, of the entire ma- sonry shall consist of headers, or bond stones. In walls twenty-four inches (24 ') thick or less, these headers shall be at least two thirds (f ) the thickness of the wall in length; and in walls more than twenty-four inches (24) thick, they shall he of sufficient length and be so placed as, in the opinion of the railway compau3'^'s engineer, seems necessary to secure well-bonded and stable work.
Each stone shall be laid in its quarry bed, and any stone set on edge, or with the planes of its stratiricatiou vertical, will be rejected and ordered re- moved at the expense of the contractor. Stones shall be tirmly bedded in mortar, and all spaces and joints thoroughly grouted with same.
Pier Rubble. Piers or pedestals whose horizontal sectional area is nine (9) s(iuare feet or less will be classitied as pier rubble. When this area exceeds nine (9) square feet, the masonry will be classed as foundation rubble. Foot- ing courses for such piers, when not exceeding sixteen (16) square feet in area, will be classed as pier rubble; and when exceeding this area, they will be classitied as heavy rubble.
Footing courses must be built, so far as practicable, in accordance with the preceding specifications for heavy rubble masonry. iVIasonry in piers above footing courses must be carefully built of well-selected stone, having horizon- tal beds and vertical joints, and be thoroughly bonded; corners and facea must be built true and plumb. The specifications for foundation rubble, sa far as practicable, shall apply to this class of masonry.
Each pier or pedestal shall be furnished with a hammer-dressed cap-stone not less than six inches (6") thick, of same area as pier, which must be accu- rately set at the required level. The price of this cap-stone must be included in the contract price per cubic yard for this class of masonry.
Squared Rubble. When not otherwise specified, the walls of all stone build- ings above the bottom of the water-table wiU be built of uncoursed squared rubble.
In general the specifications for foundation rubble will apply to this class of masonry, the difference between the two classes being in the construction and finish of the outside face. The outside face of the wall will be built of well -selected stones, as nearly uniform in color as possible, which shall be neatly squared to rectangvilar faces, and which in all cases shall be laid on their natural or quarry beds. The beds of the stones shall be horizontal and the side joints vertical, and no joints to exceed three fourths (f) of an inch will be allowed. No stone having a face area of less than eighteen (l^<) square inches or a thickness less than three inches (3") shall be used; and the average face of all the stones shall not be less than seventy-two (72) square inches.
The inside face shall be built and finished in accordance with the specifica- tions for foundation rubble.
Corners of all buildings shall be built up with quoin stones, uniform in size and arrangement, for which no extra pay will be allowed contractor. Drafts will be cut on the corners when so specified or shown on plans. All joints shall be cleaned or raked out for a distance of three quarters of an inch (f"), and neatly pointed with a raised joint. The mortar used for pointing shall be composed of such material as the railway company's engineer may select.
538 SPECIFICATIO]Sl"S FOR MASOXRY. [aPP. I.
Openings for windows, doors, or for other purposes, will be made in walls when specified or shown on plans. The jambs of such openings shall be neatly cut to a true and smooth surface, and be drove tooled, craudalled, or tooth-axed [see pages 12.5-34, particularly 12ti and 133], as may be re(iuired by the railway company's engineer. Bed-joints of jamb-stones must be care- fully cut, so that no joint to exceed one half an inch (+ ) will appear on the exposed face of the jambs. Jamb-stones shall be uniform in height, and one half shall be through-stones. In general the arrangement of jamb-stones will be shown on drawings.
The contract price for any opening shall include the cost of cut-stone sills, lintels, arches, jamb-stones, or any other cut-stone work required for that opening. In case no contract price is made for any opening, the contractor will be paid such price as, in the opinion of the railway company's engineer, seems reasonable and just.
Cut stone shall be furnished and put in place by the contractor when so re- quired by the railway company. The stone furnished shall be of the quality required for the work, and acceptable to the railway company's engineer; and must be cut strictly in accordance with the plans and specitications in each case, and must be so cut as to lie, when in position, on natural or quarry beds. Cut stone will be paid for at the price specified in contract, and in case cut stone is furnished by the contractor for which theie is no contract price, a price will be paid which, in the opinion of the railway company's engineer, seems reasonable and just.
Cut stone, or dimension stone for cut-stone work, may be furnished by the railway company at its own expense, and the contractor required to set the cut stone in position, or to cut and .set the rough dimension stone, in which case the contractor will be paid for the work either as "extra" or "time" work, or at a price which, in the opinion of the railway company's engineer, may seem reasonable and just.
AVall Masonry. All walls shall be built to a line both inside and out- side, and both faces shall be finished with a smooth and uniform surface, which shall be flat-pointed with a trowel, in a neat and workmanlike manner.
The upper courses of all walls, when leveled or finished for the reception of superstructure, .shall be provided with a through-stone at each end, and also one through-stone for at least each five (5) linearfeet of wall. These through- stone shall be dressed on tlieir top beds and accurately set to a level one half inch a") below the level of the bottom of the supenstructure. Between these through-stone the walls must be carefully laid, with the upper beds of the stones brought up flush with the top of the above-described through-stones so as to secure a perfectly level surface for the top of the wall. In no case shall spalls or chips be used, except in vertical joints.
The contractor will make such openings in walls as are required for windows, doors, or other purposes. Ko additional pay will be allowed for such openings, except where jambs are to be cut, and cut-stone sills or lintels are required, in which case such price per opening will be allowed as, in the opinion of the railway couipanj^'s engineer, may seem reasonable and just. Cut or dressed dimen.sion-.stone will be furnished and set in position when so re- quired by plans or specifications, and will be paid for by the railway company at such price as may, in the opinion of its engineer, .seem reasonable and just. Wood, iron, or other material which may be required to be built into the ma- sonry shall be properly put into position by the contractor, and no extra pay shall be allowed for such work. The cubical contents of such material, how- ever, will not be deducted from the measurement of the masonry.
When so required, the contractor shall plaster the outside surface of base- ment or other walls with hydraulic mortar, composed of such materials as the railway company may select, and tor such work the railway company will pay the contractor a price per square yard in addition to the contract price ot the masonry.
ARCHITECTURAL MASOXRY. 539
Fouiidatioiis for Trestles. Foundations for trestle bents, such as are built for coal chutes, will he classihed as foundation rubble, and must be built wiih i,n-eat care. The lower footing course, when exceeding thirty inches (80") in width, will be classed as heavy mbble. The upper course shall have one hammer-dressed through-stone at each end of wall, and at least three such through-stones betweerTthe end through-stones; otherwise the top course will be tinl^shed in accordance with the second paragraph under "wall masonry" al)ove. This does not apply to bent foundations inside of coal-chute build- ing, which will be built in the same manner as foundation walls in general.
''Well-wall 3Ias<)ury. Well-walls will be classified as foundation rubble. "Well masonry will be built under the supervision of the well foreman who has. charg-e of the" well excavation, and contractor's foreman shall execute the work stricFly in accordance with instructions given by him. When well-walls are sunk, or settled, as the excavation is made great care must be taken to make the outside surface perfectly smooth and uniform; and as many headers, not to exceed the maximum heretofore specified, may be required as, in the opin- ion of the railway company's engineer or well foreman, are necessary to secure stability.
3Ieasiireiiient of Masonry. In measuring masonry paid for by the cubic yard, all openings will be deducted, and the number of cubic yards will be the actual cubical contents of the masonry built. The cubical contents of cut stone, iron work, timber or other material, built into the masonry by the contractor, will not be deducted from the cubical contents of the whole mass.
Architectural Masoxet.*
Permit. The contractor for the masonry shall take out a building per- mit, including water for himself and plasterer and all other contractors that may require water about the building during the progress of the work. This contractor shall also take out street and obstruction permit, and permit for building curb and retaining walls. The cost of the above permits is to be in- cluded in the estimate.
Cxrade. The inside grade at the building shall be such as the superintend- ent shall direct. At the time of starting an}- pier, this contractor shall ascer- tain from the superintendent the height the inside grade shall be set above the established outside grade, taking into consideration the settlement that may occur during the progress of the work.
Kxcavatioii. It is the intention that this contractor shall call at the building and examine for himself the exact situation of the building site. He shall remove from the premises all earth or debris, except that which the super- intendent maj' consider good for use in the grading required about the build- ing. This contractor shall complete such grading about the building as may be found necessary. All sidewalk stone that may be found in connection with the excavation shall be removed by the mason, the .said stone becoming his property. The same shall apply to any foundation stone or other material that may be found in excavating' although none of said material shall be used in connection with the new work about the building.
This contractor shall excavate, according to drawings, for all walls, piers, areas, etc., the intention being that the general level shall be excavated simply to the level of the finished basement floor. All trenches shall be excavated to the neat size as near as practicable; and each shall be leveled to a line on the bot- tom, ready to receive the foundation. At such time as the superintendent shall
* Except in form, these specifications are those employed by Burnham & Root, archi- tects. Chicago, for the Society of Savings Building, Cleveland, Ohio, and conform closely to the general form employed by these architects.
540 SPECIFICATIOXS FOR MASONRY. [APR I.
direct, this contractor shall level off the basement surfaces and floors of areas to a line finishing three inches (8) below the top of the level of the finished basement floors, and leave the surface ready to receive the work of other con- tractors. When considered necessary in the judgment of the superintendent, all earth shall be tamped solidly and then be wet.
If any pockets of quicksand are found, this contractor shall excavate the same, and fill in solidly with concrete composed of clean broken stone of a size that will pass through a two-inch (2") ring and English Portland cement, pro- portioned 1 to 3, rammed solidly into place in the pockets, in layers, as the superintendent may direct. None of the sand that may be found while ex- cavating shall be used in connection with any of the work about the building.
After all foundations or retaining walls are in and fixed, this contractor shall tamp the earth solidly around them, leaving it level to a line within eighteen inches (18") of the finished grade, and ready to receive the work of other contracU rs.
Bailing'. Tliis contractor shall do all bailing and draining of trenches or basement surfaces that may be found necessary during the progress of the work.
Shoring'. This contractor shall protect all walls of the adjoining buildings, underpin all walls that may be considered necessary — in the judgment of the superintendent — to place the new work or to prevent injury of the old work, make good all repairs, provide such cutting as may be found necessary to place the work, and leave the adjoining buildings as good as at the start. The cost of this work is to be included in his estimate. This contractor shall furnish and put in place any sheet piling that may be required to retain the earth while the footings are being put in, and include all costs of the same in his estimates.
Protection. This contractor shall use proper care and diligence in brac- ing and securing all parts of the work against storm, wind, and the action of frost. Every night during freezing weather, each pier or wall shall be covered on top with sail-cloth, and the covering shall extend down over the face of all green work.
Concrete Footing's. This contractor shall provide a frame of the area of the pier, composed of two-inch (2") plank, so arranged that the parts can be withdrawn and the pier left isolated after the concrete is set [see § 800]. All footings not otherwise indicated shall be constructed of concrete furnished by this contractor. The cement shall be first-quality, fresh Utica, or any other equally good quality approved by the architects. The contractor at the time of submitting his proposal shall state the kind of cement he intends using. The sand shall be clean and sharp. The stone shall be clean limestone, cru.shed to a size that will pass through a two-inch (2") ring, and screened. The con- crete shall be composed of these ingredients in the following proportions: one (l)part of hydraulic cement, one (1) part of sand, and two (2) parts of crushed limestone. The cement and sand shall be mixed dry, and the mixture wet with a quantity of water sufficient to reduce it to the consistency of mortar. The stone and mortar shall be thoroughly mixed and laid in trenches as soon as possible, in layers of not more than six inches (6') in thickness, and be rammed until the water rises freely to the top.
All concrete footings shall be carefully leveled or pitched with concrete, and be left ready to receive the piers, walls, or columns, in each case as par- ticularly indicated on the drawings.
Railroad-Rail Footing's. All railroad rails that may be required in connection with the foundations shall be of Bessemer .steel, weighing not less than sixt}'-five (65) pounds per yard, straight and sound, cut to the neat lengths indicated on the drawings. All railroad rails shall be furnished by this con- tractor, and by him set in place to centers and levels as indicated on the dia- grams. None of these railroad rails are to be painted.
The concrete used in connection with steel-rail footings shall be composed
AECHITECTURAL MASONRY. 541
of one (1) part of first-quality English Portland cement— or any other equally good quality approved by the architects, — one (1) part of clean sharp sand, and two (2) parts of clean limestone crushed to chestnut size. This concrete shall be mixed as for concrete footings, and shall be rammed in solidly between the rails; and each tier shall be neaily squared at the outer edge.
liubble Masonry. All piers colored blue on the drawings shall be classed as cut stone, and shall be furnished and set in place by another con tractor; but all walls colored blue on the drawings — referring particularly to foundation walls for boiler-house, foundation wall for staircase way in alley, area walls, curb walls, and curtain walls between piers— shall be classed as rub- ble masonry, and shall be furnished and set in place by the mason.
All stone used in connection with rubble masonry shall be of selected, large size, first-quality stone, laid to the lines on both sides, well fitted together and thoroughly pointed, frequent headers that extend through the wall being pro- vided. All stone shall be not less than two feet six Inches (2' 6") long, one foot six inches (1' 6") wide, and eight inches (8") thick, except sucli as may be found necessary to level up a course to the required height. The intention is that all walls shall be laid in courses about one foot six inches (1 6") in height, leveled off at each course. Each stone shall have hammer dressed beds and joints, and shall be firmly bedded and be well cushioned into place. All joints shall be filled with mortar. The facing of all walls .shall be laid ran- dom range, and the face of the stone shall becoar.se bush-hammered.
At the time of completing the retaining walls, this contractor shall excavate at least one foot (1') on the outside of the wall, and point up all joints on the outside; and then provide and apply a coat of firsl-quality Engli.sh Portland cement, notlessthan a half inch (i") thick, to the outside of the wall from top to bottom. No cement covering will be required on the curb walls. All joints showing inside the building shall be raked out and neatly pointed up with cement; and, in addition, the face of walls coming in connection with the area shall be squared up, the joints finishing not to exceed one half inch (^") thick.
All curb walls that may be required to receive the side-walks shall be brought to such levels as the superintendent shall direct, and shall be cemented on top and left ready to receive the sidewalks— which shall be furni.shed and set by another contractor. None of the screen walls shall be set in place until such time as the superintendent shall direct. The foundation for the staircase bay in the alley shall be set in place, after the building is partly completed, at such time as the .superintendent may direct. This contractor, at the time of starting this work, shall furnish such anchors as may be considered neces- sary, in the judgment of the superintendent, to attach his work to that already in place, and shall do all cutting and fitting that may be found neces- sar\' to properly place his work.
Mortar for Eubble Masonry. All rubljle masonry above referred to shall be laid in mortar composed of perfectly' fresh Utica cement— or other equally as good approved by the architects, — mixed in the proportion of one (1) part of cement to two (2) parts of clean sharji coarse .sand. The sand and cement shall be mixed in a box dry; then wet, tempered, and immediately used.
Coiniuoii Brick-work. All walls or sections colored red on the draw- ings or otherwise indicated to be of brick, shall be of selected, first-quality, hard-burned Chicago sewer brick — or other equally good quality approved by the architects. The above quality of brick shall be used throughout the entire work, except that hollow fire-clay brick shall be used in connection with all curtains between windows on elevations above the first story, and for the back- ing of all stone-work above the top of the eighth-story floor beams. No bats shall be used. No pressed or face brick will be required in connection with this work.
All brick shall be well wet, excejn in freezing weather, before being laid. Each brick shall be laid with a shove joint, in a full bed of mortar, all inter-
542 SPECIFICATION'S FOR MASONEY. [APR I.
Slices being thoroughly filled; and where the brick conies in connection with anchors, each one shall be "brought home" to do all the work possible. Up to and including the tifth story, every fourth course shall consist of a heading course of whole brick extending through the entire thickness of the walls; above the fifth story, every sixth course shall be a heading course. All mor- tar joints shall be neatly struck, as is customary for " tirst-^lass trowel work." All coursesof brick- work shall be kept level, and the bonds shall be accurately preserved. When necessary to bring any course to the required height, clip- ped courses shall be formed, as in no case shall any mortar joints finish more than one lialf inch (.V) thick. All brick-work shall be laid to the lines, and each tier kept plumb, the intention being that none of the window-frames shall be set in place until the roof is on.
All lintels over openings indicated in connection with brick partition walls in basement shall be of steel railroad rails, and shall be furnished and set in place by the mason. These rails shall be painted one coat of mineral paint be- fore being brought to the building.
All cut stone shall be backed as fast as the superintendent m:iy consider proper, and the mason shall build in all anchors that may be furnished by the contractor for the cut stone. When openings or slots are indicated in connec- tion with walls, the size and position of the same shall be such as the superin- tendent shall direct, unless otherwise shown. This contractor shall leave openings to receive all registers that may be required in connection with the heating or ventilating system, and shall also leave openings in connection with the corner vaults at such places in the floor and ceiling as the superintendent shall direct.
All masonry that may be required at the time of setting the boilers shall be furnished and set in place by the contractor for steam-heating apparatus.
Mortar for Brick-work. AH mortar used in connection with sewer brick, together with the mortar in the brick parapet walls and the chimney above the roof line, shall be composed of two (2) parts of lime mortar— made up very poor, — and one (1) part of first-quality Utica cement — or other equally good approved by the architects. Said mortar shall be used immediately after being mixed, and in no case shall any be used that has stood over night.
The remaining brick-work, including the fire-brick hereinafter referred to, shall be laid in mortar composed of best slaked lime and coarse sharp cleaa sand of approved quality.
Brick Arches. Where arches are indicated in connection with the first- story banking vault or in connection with roadway in the court on the north front of building, said arches shall be formed with common brick laid in row- lock courses, regularly bonded [see § 733]. The mortar for this work shall con- sist of one (1) part Portland cement and three (3) parts clean sharp sand. Each brick shall be laid with a shove joint; and each rowlock course shall be cemented on top at the time of laying the next course. The last course shall be cemented on top, and be left ready to receive the concrete floor or roadway — which shall be provided by another contractor.
All centers that may be required in connection with this work shall be furnished and set in place by the carpenter; and none of said centers shall be removed until such time as the superintendent shall direct. After the same have been removed, this contractorshall thoroughly clean down all face-work.
All iron indicated in connection with this work shall be furnished and set in place by the contractor for constructional iron work, — except the bearing plates, which shall be bedded by the mason.
Smoke Britehing'. The smoke britching indicated in connection with the main boiler-stack will be furnished and set in place by the contractor for constructional iron, although the mason shall back up the same at such time as the superintendent shall direct.
Fire-brick. The lining shown to stand alone in connection with the
ARCHITECTURAL MASONRY. 543
boiler cnimney in the lower stories sball be laid with first-quality fire-clay brick, laid iu stretcher courses, regularly bonded, with headers of whole brick sixteen inches (16 ) apart in every sixth course to stay the linings, care being taken to preserve the air-space indicated.
All tire-clay brick shall be laid in first-class fire-clay mortar, each brick being laid with a solid joint neatly struck on each side with a trowel.
Hollow Fire-clay Brick. All brick used in connection with the spandrels above the first story ou all elevations, together with all backing re- quired in connection with the stone work above the top of the eighth-story floor- beams, shall consist of first-quality, hard-burned, tire-clay, hollow brick, equal in quality to sample to be seen at tlae office of the architects. Each brick shall be laid with a shove joint. This contractor shall point up this work, and leave the surfaces of the walls smooth and ready to receive plastering.
Cutting' and Fitting-. This contractor .shall do, promptly and at the time the superintendent so directs, all cutting and fitting that may be required In connection with the masou-work by other contractors to make their work come right, and shall make good after them.
Setting Iron-work. It is the intention that all constructional iron- work shall be furnished and set in place by another contractor, and that all iron shall be hoisted from the outside of the building by means of a derrick. In setting the beams and columns in place, the mason shall keep pace with the contractor for constructional iron work, and at no time shall the mason be left one story behind the constructional iron-work. Each beam, girder, or column shown to rest on the masonrj' shall be provided with iron plates by the con- tractor for constructional iron, said plates being furnished to the mason at the sidewalk; and the mason shall set the same in place, firmly bedded in mortar, at such position or height as the superintendent shall direct.
All iron wall-plates that maj' be required to receive the fire-clay arches will be furnished at the sidewalk by the constructional-iron contractor: and this contractor shall set each in such position and at such height as the super- intendent shall direct.
Cut Stone. All parts colored blue on the drawings, or otherwise indi- cated to be of stone, or usually classed as cut stone, shall be furnished and set in place by the contractor for cut stone. The same shall apply for the terra- cotta roof-copings indicated. All mortar, staging, or hoisting apparatus that may be required in connection with this work shall be furnished by the con- tractor for cut stone. All cut stone will be set from the outside; but the mason shall back up all cut-stone work in a manner approved by the superintendent.
Lattng Masonry in Freezing Weather.
Masonry shall be laid in freezing weather only in case of absolute neces- sity, aud then only by permission of the engineer. When necessary, masonry maybe laid in freezing weather, provided (1) that the stone or brick while being laid are dry and perfectly free from snow or ice; (2) that there is added to the water used in mixing the mortar 1 per cent, of salt for each Fahrenheit degree below freezing ; and (3) that the mortar is mixed rather dry. Any masonry laid in freezing weather shall not be pointed until warm weather in the spring.*
* For additional precautions that may be prescribed, see §§ 141-143, pages 102-4.
APPENDIX II.
SUPPLEMENTAEY NOTES.
Note 1. Labor Required in Quarrying.* The following table shows the labor required in quarrying the stone [gneiss] for the Boyd's Corner dam on the Croton River near New York City. The stone to be cut was split out with plugs and feathers.
|
Labor Required |
IN Quarrying Gneiss. |
|||
|
Kind |
OF |
Labor. |
Days per Cubic Yard. |
|
|
Rough stone. |
Stone to be cut. |
|||
|
0.041 0..339 0.140 0.036 0.035 0.141 0.077 |
0.114 |
|||
|
Drillers |
0.917 |
|||
|
0 429 |
||||
|
0.102 |
||||
|
0.108 |
||||
|
0 620 |
||||
|
Labor loading teams |
0.284 |
Note '2. Cost of Cutting Granite. f " Below is given the cost of cutting several kinds of masonry for the New York Department of Docks, in 1874-5. Between December 1873 and May 1875 with an average force of 40 stone- cutters, 2,065 yards of granite of the following kinds were cut in the Depart- ment yard:
" 1,524 yards of dimension stone were cut into headers and stretchers. This stone was cut to lay ^-iuch beds and joints, the faces being pointed work, with a chisel draft l^-inches wide. The headers averaged 2 feet on the face by 3 feet in depth; and the stretchers averaged 6 feet long bj' 2 feet deep, the rise being 20, 22, and 26 inches for the different courses. The average time of stone-cutter cutting one cubic yard was 4.53 days of 8 hours; and the average cost of cutting was $27.54 per cubic yard ($1.02 per cubic foot).
" 310 yards of coping were cut to lay ^-inch beds and joints, pointed on the face with chisel draft same as headers and stretchers, and 8-cut patent- hammered on top, with a round of 3^ inches radius, the dimensions being 8 feet long, 4 feet wide, and 2^ feet rise. The average time of stone-cutter cutting one cubic yard was 6.26 days, and the average cost of cutting |38. 07 per cubic yard ($1.41 per cubic fool).
"231 yards of springers, ke}'stones, etc., for arched pier at the Battery,
were cut. These stones were of various dimensions, part being pointed work
.-and jmrt 6- cut patent-hammered. The average time of stone-cutter cutting
. one cu-i)ic j'ard was 6.88 days, and the average cost of cutting was $41.85 per
. cubic yard ($1.55 per cubic foot).
" The above cost of cutting includes, besides stone-cutter's wages, labor of -moving stone, all material used — such as timber for rolling stone, new tools, •etc. — sharpening tools, superintendence, and interest on stone-cutter's sheds, blacksmith shop, derrick, and railroad. The.se expenses, in per cents, of the total cost of cutting, are as follows: superintendence 5; sharpening tools 15; labor rolling stones 30; interest on sheds, derrick, and railroad 1; new
* J. James S. Croes, in Trans. Am. Soc. of C. E., Vol. III., page 363.
t From an article by Wm. VV. Maolay, in Trans. Am. Soc. of C. E., Vol. IV., pp. 310-11.
544
APP. II. J
SUPPLEMENTARY NOTES.
545
tools and timber for rolling stone 1; total 52 per cent., which, added to the wages paid stone-cutters, gives the total cost. During the last year stone- cutters were required to do at least 13 superficial feet per day of beds and joints, or its equivalent in pointed or fine cut work. The average day's work of each stone-cutter, during one year and a half in which 118,383 superficial feet of beds and joints were cut, was 13.6 square feet per day, for which he received $4.00.
" The following table shows the amount of granite that a stone-cutter can cut in a day of 8 hours.
Labor Required in Cutting Granite.
Kind op Work.
Number op Superpicial Feet
|
Constituting a |
Required as a |
|
day's worli of 8 |
minimum |
|
hours in stone- |
day's work |
|
yards and con- |
by the De- |
|
tract-workdone |
partment of |
|
in vicinity of |
Docks, New |
|
New York City. |
York. |
|
16 |
12 |
|
10 |
7.5 |
|
7.27 |
5.45 |
|
6.15 |
4.61 |
|
5 |
3.75 |
Averaged per dayof Shours by stone-cut- ters in the Departm e n t of D o ck s , New York.
Beds and joints
Pointed work with chiseled margin, lines
all round
Pean-hammered
6cut patent-hammered
8-cut " '•
13.6
8.5 6.15 5.22 4.34
Note 3. Cost of Cutting Granite.* The average day's work of a man in cutting the face of granite pitch-faced, range, squared-stone masonry (§ 197, page 137) of the Boyd's Corner dam, as deduced from three and a half years' work in which 5,200 cubic yards were cut, was 6,373 square feet, the dimensions of the stones being 1.8 feet rise, 3.6 feet long, and 2.7 feet deep; and the average day's work in cutting the beds to lay f-inch joints was 18.7 square feet. The granite coping, composed of two courses — one of 12-inch rise, 30-inch bed, and 3|-feet average length, and one of 24-inch rise, 48-inch bed, and 2|-feet average length, — the top being pean-hammered, the face being rough with chisel draft around it, and the beds and joints cut to lay ^-inch joints, required 6.1 days' work of the cutter per cubic yard.
' ' In cutting the granite for the gate-houses of the Croton Reservoir at Eighty- sixth Street, New York City, in 1861-2, the minimum daj-'s work for a cutter was fi.xed at 15 superficial feet of joint. This included also the cutting of a chi-sel draft around the face of the stone, which costs per linear foot about one fourth as much as a square foot of joint, making the actual limit equivalent to about 17.7 square feet of joint. On this work, the proportion to be added to the cost of the cutters to give the total cost was as follows, the average for 19 months' work: for superintendence 8 per cent.; sheds and tools 7; sharpen- ing tools 11; labor moving stone in j^ard 10; drillers plugging oS rough faces 4: making a total of 40 per cent, to be added."
Note 4. Cost of Laying Cut Stone, f Most of the cut stone was laid by one mason, more than two not being employed at any time. The mason's gang also shifted derricks. The cost of hauling stone to the work varied with the position of the blocks in the yard and whether they were assorted there into courses or lay promiscuously. The amount of labor required in laying the masonry was as follows:
* From an account of the construction of the Boyd's Corner dam on the Croton River Dear New York City, by J. James R. Croes, in Trans. Am. Soc. of C. E., "V^ol. III., pp. 3C3-^. + Ibid., p. 365.
546
SUPPLEMENTARY NOTES.
[APP. II.
Labor Required in Laying Cut-stone Masonry.
Kind of Labor.
Mason, days
Laborers, days
Mortar mixer, days
Derrick and car men, days.
Engine, hours .
Teams from yard, days
Labor loading teams, days.
Number of cubic yards laid.
Amount per Cubic Yard.
|
Hoisted by Hand. |
Hoisted by Steam. |
||
|
5 ft. |
10 to 20 ft. |
20 to 30 ft. |
30 to 50 ft. |
|
0.120 |
0.119 |
0.082 |
0.108 |
|
0.184 |
0.188 |
0 145 |
0.155 |
|
0.100 |
0.82 |
0.076 |
0.101 |
|
0.327 |
0.341 |
0.235 |
0.261 |
|
0.462 |
0.490 |
||
|
0.100 |
0.056 |
0.0.56 |
0.110 |
|
0.184 |
0.223 |
0.223 |
0.086 |
|
1,070 |
2,270 |
2,530 |
Note 5. Cost of Breaking Stone for Concrete.* " The stone [gneiss] for the concrete was broken to be not more than 2 inches in its largest dimension. A Blalte stone-breaker of 15-inch jaw, driven by a IShorse-power engine, was used. The stone, which was obtained from the surface and from old fence walls in the vicinity of the work, was tough, and used up the jaws very fast. A movable jaw ordinarily lasted 30 days. The stone was delivered 1o the breaker by carts, having been tirst sledged to the proper size — about 13 inches square by 6 inches thick. The machine, when running at f'liU speed, with one man feeding, two men supplying him with stone, one keeping the screen clear and helping to till barrows, two wheeling away the stone, and one on the dump, could break 144 cubic feet in an hour, or at the rate of 54.4 cubic yards per day of 10 hours. This excessive speed was kept up, however, only as long as it was known that an inspector was timing it. The average rate of breaking for the last year was 3.8 cubic yards per hour, which may be assumed as the economical rate for the 15-inch machine. The largest uuichine (20-inch) will break 8 cubic yards per hour, if fed to that capacity; but 6 cu])ic yards per hour is more economical. The following table gives the cost in time of breaking the stone:
Labor Required in Breaking Stone for Concrete.
|
« |
Days per Cubic Yard. |
|||
|
Kind op Labor. |
1867 |
1868 |
1869 1870 |
|
|
0.269 0.049 0.045 0.360 2,410 22.1 |
0 322 0.051 0.092 0.037 0.238 4.170 27.3 |
0.224 0.042 0.066 0.027 0.158 5,720 36.8 |
0.410 |
|
|
Laborers loading cartst Carts hauling Breaking: Engine and machine t |
0.087 0.118 0.026 0.174 |
|||
|
Total number of cubic yards broken Average number of cubic yards broken per day. . . |
3.6.50 38.0 |
* From an account of the construction of the Boyd's Corner dam on the Croton River near New York City, by J. James R. Croes. in Trans. Am. Soc. of C. E.. Vol. HI., pp. .356-58.
t " The difference in sledging is accounted for thus: In 1867 many fence-wall and cobble stones were used, which neeiled no sledging, but were hard to crush. In 180H refuse from the quarry which required sledging, was almost exclusively used. In 1869 stone-yard and quarry spalls were used. In 1870 the stone was quarried for the breaker; and consequently nearly liU 'if it was sledged. The carting and tending varied in the same way as above, for the same reasons." . . .in/Mr»
$ Includes cost of engine driver and helpers, fuel and repairs of e.igine— about 0.05 or the wages of a day laborer per cubic yard.
APP. II.]
SUPPLEMEXTARY NOTES.
547
iNote 6, Cost of Imbedding Large Stones in Concrete.* "The lars-e un- wrouirlit stone laid in the concrete, from the foundations to within 45 feel of the top of the dam, were set in full mortar beds and the surfaces plastered just before concrete was laid around them. The setting was done mosll}' by laborers, one mason superintending. The cost in day's work per cubic yard Tvas as follows :
Labor Required to Imbed Large Stones in Concrete.
Kind of Labor.
Foreman (mason)
Laborers setting
" plastering
mixing mortar
at derricK
loading teams
Teams transporting stone
Total quantity laid, cubic yards. Per cent, of whole mass
Days pkk Cubic Yard.
|
1867 1 |
1868 1 |
|
0.046 |
0.057 |
|
0.208 |
0.148 |
|
0.085 |
0.056 |
|
0.078 |
0.083 |
|
0.238 |
0.254 |
|
0.305 |
|
|
0.160 |
0.073 |
|
1,234 |
2..353 |
|
32.0 |
36.6 |
" The cost of the mass of concrete and large stone, as laid in 1867, was 89^ per cent, of the cost of the concrete alone; and in 1868 it was 84^ per cent, of such cost. If the large stones do not exceed 25 percent, of the mass, the cost of the mass is reduced about 10 per cent, below concrete cost, while its specific gravity is increased about 8 per cent."
Note 7. Crushing Strength of Sewer Pipe. Experiments made at Chicago in 1879 by W. D. llotchkiss, and reported to the author by Black- mer and Post, of St. Louis, gave the strength of ordinary sewer-pipe as fol- lows, when tested as described on page 408: one 12-inch and Uve 15-inch pipes failed at an average pressure of 8,504 lbs. per sq. ft. of horizontal sec- tion; and two 12-inch and two 15-inch were not crushed by an average pres- sure of 9,068 lbs. per sq. ft.
Note 8. Holding Power of Drift Bolts. According to experiments made under the author's direction, § the average holding power of a 1-inch round rod driven into a -i^-inch hole in pine, perpendicular to the grain, is 501 pounds per linear iucli (3 tons per linear foot); and under the .same con- ditions the holding power of oak is 1,300 pounds per linear inch (7.8 tons per linear foot). The holding power of a bolt driven imrallel to the grain is almost exactly half as much as when driven perpendicular to the grain. If the holding power of a 1-inch rod in a ||-inch hole be designated as 1, the holding power in a j;|-inchhole is 1.69, in a }f inch hole 2.13, and in a jf-iuch hole 1 .09. The holding power decreases very rapidly as the bolt is withdrawn.
Another series of experiments II using round and square drift-bolts in the same size holes shows that round drift-bolts have the ailvantage ovei' square ones, bulb in uliiuuite holding power and in holding power per pound of metal.
* J. James R. Croes in Trans. Am Soc. of C. E., Vol. IIL, p. 363. t Stone lowered an average of SO feet.
t One half lowered 5 feet: one quarter swung in level; one quarter hoisted 6 feet. § Selected papers of the Civil Engineers' Club of the University of Illinois, No. 4, prede» cesBor of The Technograph, pp. 53-5**.
D The Technograph, University of Illinois, No. 5, pp. 39-41.
PLATE I.
CAISSON, CRIB AND COFFER-DAM.
Havre de Grace Bridge.
FOR TEXT, SEE PAGE 286.
Plate I. PNEUMATIC CAISSON, CRIB, and COFFER-DAM.
FOR TEXT, SEE PAGE 286 SCALE OF FEET ' » »■ — —
PLATE II.
6-FOOT ARCH CULVERT.
Illlnois Central Standard
rOR TEXT, SEE PAGE 424.
FLA-TB II.
6-FOOT ARCH CULVERT.
ILLINOIS CENTRAL STANDARD.
PLAN OF TinBER UNDER FOUNDATION Flatted Surface +<= cover kalf the -fci-nrfnj-.on
PLATE m.
8-FOOT AKCH CULVERT.
C. K. AND N. Standard.
FOR TEXT, SEE PAGE 427.
CROS5 SECTION
jpx.a.t:ei III. 8-FOOT ARCH CULVERT.
C, K. & N. STANDARD.
FOR TEXT SEE PAGE 427.
SCALE OF FEET
PLATE IV.
lO-FOOT ARCH CULVERT.
SEMI-CIRCULAR.
A. T. AND S. F. Standard.
FOR T£ZT, SEE PAGE 429.
PLATE V.
10-FOOT ARCH Cl/LVERT.
SEGMENTAL.
A. T. AND S. F. Standard
FOR TEXT, SEE PAGE 429.
LONOrrUDINAX. SECTION-
lO-FooT Segmental Arch Culvert.,
PLATE VI.
12-FOOT STANDARD ARCH CULVERT.
FOB text: see pass 430.
INDEX.
ABIT— ARC
Abutments of arches, dimensions of exist- ine;, 505 stability, empirical formulas for, 499 theory of, 49^ Abutments of bridges, contents, 357, 361, 363 detailed plans, 356, 360, 362 foundation, 364 general form, 353 quality of masonry, 365, 385 T-abutment, 362 contents, 3G3 detailed plan, 362 U -abutment, 359 contents, 361 detailed plan, 360 wins' abutment, 355 contents, 357 detailed plan, 356 Air-cbamber, filling, 297 Air-lock, for pneumatic pile, 281 for pneumatic caisson, 2&4, 291, 299 position, 290 Arch, abutment of, stability, 492, 499 backing, 505 brick, 510
center, camber. 523 definitions, 515
examples. Cabin John arch, 525 stone bridges, tunnel arch. 512 AVasliin.Lrton bridge, 524 load sujiiHirted, 516 outline forms. 519, .5-JO, 523 striking, method, .523 time, 527 culvert, 419 cost, 434 examples. 424 Atchison, T. & S. F., segmental. 429 cost, 438 semi-circular, 429 cost, 437 Chicago, K. & N., semicircular, 427
cost, 436 Illinois Central, semi-circular, 424
cost, 435 standard segmental, 429 cost. 438 junction of wings to body, 420 masonry, cost of, 157, 1.59, 160
quality of, 4.32 specifications, foundations, 432, 533 masonry. 432, 531 paving, 148 segmental vx. semi-circular, 421 splay of wings, 419 definition, of kinds of arches, 441 of parts of an arch, 440
ARC
Arches, dimensions of abutments, 505 of arches, 502 rules derived from practice, 494 thickness of abutment, 499 thickness at crown, American prac tice, 495 English practice, 496 French practice, 496 thickness at springing, iSa drainage 508 elastic, theory of. 491 engravings, 505 inverted, for foundations. 212 joint of rupture, 457 line of resistance, definition, 443 location. 453 hypothesis of least preesure. 5.54 hypothesis of least cro\TO thrust, 465
joint of ruiJture, 4rj7 Navier's principle. 4C'i Winkler's hypothesis, 463 masonry, 432 backing, 605 cost. 157, 159, ICO specifications, brick, 176, 177 stone, 432, 51.5. 531 relieving arches for retaining walls, 35?
in spandrel filling, 506 spandrel, filling, q. v.. 506 stability, criteria of safety, 447 conclusion. 4.52 crushing, 448 open joints, 451 maximum pressure, 461 unit pressure, 449 rotation, 448 sliding, 4.52 theories, 405 elastic arch. 491 external forces. 444 method of employing, 466 method of failure. 446 rational theory, 466 criterion, 47-3 symmetrical load. 466 general solution. 466 special solution, 469 unsymmetrical load, 471 Schefflf r's theory, 474 algebraic solution, 475 erroneous solution, 480 gripiii'Ml solution, 479 rclialiility, 4S1 Rankincs 'theory, 482 curvjitiirc of huear arch, 482 met hod ofapplyiug, 487 relialiility. 490 various theories referred to, 491
549
550
INDEX.
ART— BEI
Artiflcial stone, 112
B6ton-Coignet, 113
Frear, 114
McMurtrie, 113
Portland, 113
Raiisome, 114
Sorel, 115 Ashlar, 138
backing, 140
bond, 139
definitions, 136
dressing, 138
mortar required per yard, 141
pointing, 141
specifications, 143
where employed, 142 Atchafalaya bridge, foundations, 273 Atchison, Topelja & Santa F6, bridge abut- ment, 359
culvert, iron pipe, 414
segmental arch. 429, 431, 438
semi-circular arch, 420, 430, 437 Ax, and Tooth-ax, 126
Batter, definition, 135
Bearing piles, 219
Bearing power, piles, q. v., 233
soils, q. v., 188 B6ton, see Concrete. B6tonCoignet, 113 Bismarck bridge, pressure on foundation,
377 Blair bridge, pier. 383 pneumatic foundation, caisson, 284 cost. 303
f lictional resistance, 297 rate of sinking, 295 Blasting in compressed air, 295 Brick, absorptive power, 21, 39, 45 arches, bond. 510
examples. 511, 513, 514 burning, 34 classification, 35 cost. 4^
flre-brick, how made, 35 elasticity, co-efflcient of , 14 masonry. 161 bond, 163 cost, 1.57, 160
data for estimates, brick required, 173 labor required, 174 mortar required, 174 impervious to water, 178 joir)ts, finishing, 162
thickness, 161 Streusith, 164 compressive, 164
pressure allowed, 167 transverse. 167 specifications, arches, 177 532, 542 buildings. 175, 541 sewers, 176 vs. stone masonry, 177 moulding. 34 requisites for good, 37 size, 46 strength, crushing, 41
condition of surface, 42 data, 43-46 form of specimen, 42 size of specimen, 41 transverse -40 data. 13. 45 weight, 46 Bridge abutment, see Abutment.
BRI— CEM
Bridge masonry, cost. 157, 160 Bridge piers, see Piers. Bond, brick arches, 510
brick masonry, 163
stone masonry, 139 Box-culvert masoin-y, cost. 1.57, 160 Brooklyn-bridge foundations, cost, 303
description, 298
pressure, 377 Bush-hammer, 126 Building-stones, classification, 24
requisites for good, 3
tests, 5 ; see also Stone. Buildings, data for computing weight of, 200
specifications for brick-work for, 541
Cain's profile for masonry dams, 329 Cairo bridge, frictional resistance of caisson, 297 pier, outline of, 372 pressure on foundation, 377 stability of. 371 stones in a course of, 385 Caisson, definitions, 266 diseas*'. 300 pneumatic. 284. 286 Blair bridge. 284 first use of, 280 guiding. 295
Havre de Grace bridge, 286 Canadian box culvert, 406 Cavil, 126 Cement, 51 amount required per yard of mortar, 88 burning, thoroughness of, 56 classification, 51 cost, 54
data for estimates, 86, 88 lime-cement mortar, 100 mortar, see Mortar, natiu'al. 52 definition. 52 specifications, 783 tests, see tests below, weight, per barrel, 54 Portland, constancy of volume, 7Sd cost, .54 description, 52
specifications, 78e. 78/, 78g. 787i strength, 67, 78a. 78rf, 78^^ 78/, 78h tests, see tests below, weigiit per barrel, 54 Rosendale, definition, 53 slag, 54
specifications, quality, American, 78^ English, 78e French, 78e German, 78d delivery and storage, 7Sh tests, 55 activfty, 57, 60
burning, thoroughness of, 50 chemical analysis, 68, 78e color, .55
constancy of volume, 78fi, 78e, 7Sfir. 78h fineness, 65, 66. 78d, 78e, 78/, 78gf,'78;i set, time of, 60 soundness. 60, 7Sd, 78e, 78(7
accelerated, tests of, 63 specific gravity, 50 strength, 67 age when tested. 76 data, 78a, 78d, 7He, 7S/, 78a, 78« form of briquette, 72
INDEX.
551
CEM— CUL
Cement tests, stieDgtli, mixing the mortar, 71 rapidity of applying the stress, 78 water required, 68 weight, 54, 56
Centrifugal pump, 364
Center of fuuiidation, proper position of,
Center of gravity of trapezoid, to find, 318 Center of pressure on foundation, 203 Channeling and wedging, quarrying by, 123 Chisel, pitching, 127 splitting, 128 tooth, 128 Chicago, K. & N. arch culvert, 427, 436 Co efficient of friction, foundations, 276
masonry, 315 Coffer-dam, definition, 258 construction, 258, 289 dovible, 261
Havre de Grace bridge, 289 iron, 261 leakage, 262 movable, 261
process, for foundations, 214, 258 Compressed air, physiological effect, 299 Compressed-air process for foundations,
see Foundations, pneumatic. Concrete, 106 aggregate, 107 cost, 11 2d, 157, 160, 265 depositing imder water, 112o estimates, data for, 112/ economics of, 113rt ingredients for a yard, 112fir, 112& laying, 112n mixing. 112/u
proportions, theory of, 109 strength, 112j) compressive, llSp transverse, 112m water required, 112j weight, 112v Concrete and piles for foundations, 254 Connecticut brown-stone, 30 1-,—^-, 13ti
Cost, see the article in question. Coulomb's theory of retaining wall, 341 Cover stones for box culverts, 398 theory for thickness. 398 formulas, 399 practical data, 401 Cramps, 136 Crandall. 127 Crib for coffer-dam, 260 Culvert, arch, see Arch, iron pipe, 412 construction, 413 cost. 410
dimensions of the pipe, 412 end walls, contents of, 414 e.xamples, 414, 415 Icirge. 416
weight of the pipe, 412 stone box. 396 Canadian, 406 contents, 403, 404, 405 cost, 405
CDver stones, q. v., 398 dimensions, 403, 404, 405 double, 405 end walls, 39S examples, 403. 404, 406 foundation, 397 masonry, quality of, 401 specifications, 401, 531
CUL— EFF
Culvert, stone box. Standard form, 402, 403 West Shore R. R., 402, 404 timber box, 417 timber barrel, 418 vitrified pipe, 407 construction, 408 cost of the pipe, 410 end walls. 409 examples. 411 material required, 411 strength of the pipe, 408 water-way required, 391 formulas, 393 for quantity of flow, 394 Meyer's for the area, 394 Talbot's for the area, 394 practical method of finding, 395 Cushing pile foundation, 255 Cylindrical surface, method of forming in stone, 129
Dam, arched vs. gravity, 330 bibliography, 334 curved gravity, 331 earth, 335 gravity, 311 masonry, 311 arched, 311 Cain's profile, 329 classification. 311
gravity, condition for stability of, 312 crushing, 320 maximum pressure, 392 tension in masonry, 324 limiting pressure, 325 nomenclature, 312 overturning. 317 by moments, 317 by resolution of forces, 320 plan, 329 arched vs. gravity, 330 curved gravity, 331 straight crest vs. straight toe, 399 pressure allowable, 325 profile. 326 Cain's, 329 Krantz's. 328 method of finding, 327 Quaker Bridge, 328 sliding, 313 quality of masonry. 333 when employed, 335 width on top, 326 rock-fill. 334 cost, 337
when employed, -336 stone-lilled timber crib, 335 Dimensiun stones. 136 Disk piles, described, 218
bearing power, 249 Dorchester sandstone, 30 Dowel, 136 Dredges, 271 Milroy. 272
Morris & Cumming's, 272 mud inmip. 292 Dredging thro' tul)es. 271 Drift bolts, described, 253
holding power, 253 Drills used in quarrying, 118 Dj-namite, 121 driving piles with, 227
Eads' mud-pump, 292 Efflorescence on brickwork, 181
UUli
INDEX.
ELA— FOU
Elastic arch, theory of. 491 Engravings, for list of, see Table of Con- tents. Estimates, data for, brick, 46, 47, 1T3, 174
ceiiient, 8G, 88
lime, 86
mortar, 88, 89
sand, r9^•, 88 Excavator, compressed-air, 272 ; see also
Dredges and Pumps. Explosives, 119
dynamite, r^l
gunpowder. 119
nitro-glycerine. 100, 124
quarrying by, 117 Extrados defined, 440
Face-hamm°r, 125 Facing, defined, 135 Feathers and Plug, described, 128 Figures, for list of, see Table of Contents. Footings, off-set for masonry, 208 steel rail. 212, 540 timber, 211 Forth bridge, pneumatic caisson, 298 Foundation, Atchafalaya bridge, 273 bearing power of clay, 190 bearing power of rock, 188 bearing power of sand, 192 bearing power of semi-liquid soil, 193
summary, 194 bed of, defined, 183 bridge piers, 255, 257; see also below. buildings, ISO area reqiiired, 201
bearing pnwer of soils, q. v. above, 188 consolidating the soil, 197 depth required, 195 drainage, 195 effect of wind. 204 examination of site, 186 footings, see Footings, grillage, q. v.. 215. 254 load to be supported, 199 piles, see Piles, piles and grillage, 253 piles and concrete, 254 preparing the bed, 213 sand piles, 197 sand in layers, 198 springs, 19B coffer-dam process, 214, 258 construction of the dam, 258 thickness, 259 puddle wall, 260 leakage, 262
pumps, q v.. 263 preparing the bed, 264 cost. 264 compressed-air process, see pneumatic
process, below, concrete, 103. 215, 265 cost of various processes compared, 310 crib and erect caisson process, 266 construction of the caisson, 267 construction of the crib, 269 excavating the site, 270 principle of the method, 267 definitions. 1S3 drainage, 195
dredging through wells, 271 dredges, q. v., 271 cost, 277 iron tubes, 278 timber cribs, 278
FOTJ
Foundation, examination of site, 186 examples, 272 Atchafalaya bridge, 273 brick cvlinders. 275 Hawkesbury bridge, 275 Pouglikeepsie bridge. 272 friciional resistance in sinking, 275 iron, cast, 276 wrought, 277 masonry, 277 freezing process, 307 advantages, 309 cost, 308 details, 307 history, 307 jirinciple, 307 footings, see Footings above, frictional resistance, 275 iron cylinders. 276 masonry cylinders. 277 pneumatic caissons, 297 wood piles, 247, 248 grillage. 215
Hawkesbury bridge. 275 independent. 204. 540 inverted arch. 212 lateral yielding, 255 pile, see Piles, piles and grillage. 253 piles and concrete, 254 preparing the bed. 213, 264 Point Pleasant bridge, cost, 265 Pouglikeepsie bridge, described, 273 pneumatic piles, 281 bearing power, 275, 283, 297 cost, 304, 305 pneumatic process, 278 advantages, 306 air-chamber, 284, 297, 298 air-lock construction, 281, 284, 290, 299'
position, 290 caisson. 284 Blair bridge. 284
Havre de Grace bridge, q. v., 286 coiiiiiressed-;iir process. 279 cost, Blair, 303 Brooklyn, 303
European examples, 304, 310 Havre de Grace. 302 Plattsmouth, 304 Philadelphia. 302, 304 definitions. 278 examples. Brooklyn, 298 Forth. 298
Havre de Grace, 286 St. Louis, 297 excavators. 291 blasting. 295 nuid-pump. 292 sand-lift. :iSl water-column, 294 filling Xhf air-chamber,' 297 frictional resistance, q. v., 275, 283, 297 guiding the caisson. 295 history. 2'; 9 phy.siological effect of compressed-air^
299 plenum process, 279 rate of sinking, 295 vacuum process, 278 sand in layers, 198 sand-piles", 197 steel-iail footings, 212 timber in, 209 timber footings, 211, 215
INDEX.
552
FOir— LIM
Foundation, under water, 257 vacuum process. 278 wind, effect of, 204 Freezing of mortar, 100 Freezing weather, specificatioa for laying
masonry in, 543 Freezing process for foundations, q. v., 307 Friction-clutch pile driver. 223 Friction, coefficient of, for foundations, 27S for masonry, 315 Fi'ictional resistance in sinking foundations,
q. v., 247, 248, 275, 297 Frost batter, 3t>4
Grand Forks pivot pier, 380 Grillage. 215 Groui, 89 Gunpowder, 119
cost. 120
efficiency in blasting, 120 Gunpowder pile-driver, 226
Hammer, bush, 126
face. 125
hand. 127
patent, 127 Haunch of an arch, defined. 440 Havre de Grace bridge, pneumatic founda- tions of, 286
air-lock, 291
caisson, 286
coffer-dam, 289
cost, 302
dimensions, 290
frictional resistance, 297
guiding the caisson, 295
machinery, 290
materials, quantity of, 290
mud-pump, 292
rate of sinking, 295 Henderson bridge, top of pier, 384 Hydraulic cement, see Cement. Hydraulic lime, 51, 82
Ice, effect on stability of pier, 368 Illinois Central arch culverts, 424, 435 Impervious brick-work, 178 Impervious mortar, 101 Independent piers for foundations, 204 Intrados, defined, 440 Inverted arch for foundation, 212 Iron coffer-dam, 261
Iron cylinders for foundations, bearing pow- er of, 283
cost. 302. 304
frictional resistance in sinking, 276
method of sinking, 274, 281 Iron piles, 216
Jet vs. hammer pile-driver. 229 Joint of rupture, defined, 457 method of finding, 457 Peiifs theory, 462
Krantz's profile for masonry dams, 328
Laitance. 112p Lake Superior sandstone, 31 Laieral yielding of foundations, 255 Leakage of coffer-dams, 262 Lime, cost, .50
data fi>r estimates, 86
described, 49
hydraulic, 51
LIM— MOR
Lime, preserving, 50
testing, 50
weight per barrel, 50 Lime mortar, 81
strength. 91 Lime-cement mortar, 100
Machines, pile-driving, 221 Masonry, ashlar, see Ashlar, brick, see Brick, co-efficient of friction, 315 cost, actual, arch culvert, 157, 160 bridge pier. 157. 160 railroad masonry, 157, 160 stone. 155
cutting. 156 summary. 100 tunnel masonry. 157 U. S. public buildings, cutting the stone. 156 mason r J" complete, 156 cost, estimated, 153 aslilar. 154 dressing, 153 quarrying, 153 rubble, 155 dressing. 153 quarrj'ing, 153 definitions of kinds, 136 footings, off -sets for, 208 general rules for. 138 measurement, brick. 172, 529
stone. 151, 529. 539 mortar required perjyard, 87 off-sets for footings. 208 pedestal, specifications for. 385 specificati 'ns, see Specifications, squared-stone. see Squared-stoue. stone, see Stone, strength of. 148 brick, compressive, 164
transverse, 167 stone, allowed pressure, 149 safe pressure, 150 rubble, see Rubble, weight of. 2U0 Measurement of masonry, brick, 172, 529
stone, 151, 529. 539 Medina sandstone. 31 Mortar, absor-ptive power, 21 amount ivquired per yard of masonry, 89 cement, change of volume in setting, 62, cement-lime. 100 [T8d, 78e, 78^
co-efficient of elasticity of, 14 compression of, 104 cost, 95
elasticity, 14, 104, estimates, data for, 86 freezing, effect of, 102 grout, 89
hydraulic cement, 83 hydraulic lime, 82 uigredieuits for a yard, 83 impervions to water, 101 lime, 81
lime-cement, 100 natural vs. Portland. 92, 95 Portland vs. natural, 92, 95 proportioning, method of, 83 re-tempering, 99 strength. 87 adhesive. 93 compressive. 92 increases with agt, 91 tensile, 90
554
IXDEX.
MOB,— PIL
Mortar, streiigtli, transverse, 13
water lequii-ed, 68 Mud-pump, 292
Nipper pile-driver. 223 Nit-ro-glyceriue, 120, 124
Open joints in an arch, 451
Patent hammer, 127 Paving, 148, 532 cost. 15T. 160
for foundations. 397, 432, .'iSS Philaitelpliia, pneumatic piles, cost at, 303
standaiil hriolf sewei's. 513 Physiological effect of compressed air, 299 Pick, 126
Piers, contents, 387, 388 cross section. 378
examples. 372. 383, 384, 385 Cushing's pile. 255 dimensions, bottom. 378 examples. 372, 380. 383-86 top, 377, 384 foundations, 257: see also Foundations, iron tubular, 274. 387 location. 366
masonry, cost of, 157, 160 qualtij' of, 379 specifications, 381, 537 pivot. 379 stability of, 367 crushing, theory of. 371
numerical example, 375 current, effect of. 367 foundation, pressure on, 376 ice, effect of, 368 overtui-ning. theory of. 369, 370
numerical example, 374 resisting forces. 369 " sliding, theory of, 367
numerical example, 371 wind, effect of. 367 timber-barrel, 388 Piles, bearing power of, disk, 249 screw, 249 wood, actual. 247 experiments on, 246 factor of safety, 249 formulas, empirical, 241 author's. 245 Beaufoy's, 243 Engineering News', 245 HaswelTs, 242 Mason s 243 Ny Strom s, 243 Sander's, 244 Trau twine's, 244 rational. 234 author's, 239 Rankine's, 241 Weisbach's, 241 frictioiiAl resistance of, 247, 248 load, safe, 248 ultimate, 247 butt rs top down, 251 *aps. 2-30 capping. 2.50
concrete and piles, in foundations, 254 cost, 230
definitions of kinds. 216 disk, described. 218 bearing power. 249
PIL— PUM
Pile foundations, 250 concrete. 254 cost. 310 grillage. 2.53 position of piles. 250 sawing off the piles, 252 iron, 216 cylinders. 274,281 cost. 304
sinking, frictional resistance, 273 method of, 274, 281 disk, q. v.. 218 screw, q. v.. 217 pneumatic. 281 ; see also Foundations,
pneumatic, sand, 197 sawing off, 252 screw. 217
bearing power, 249 sheet, 219 shoes. 220
specifications, 220, 533 splicing, 221 top vs. butt down, 251 used to consolidate soil, 197 wood. 219 bearing power.see bearing power, above specifications, 220, 533 Pile-il liver. 221 drop hammer, 222 friction clutch, 223 nipper, 223
steam vs. drop hammer, 225 dynamite, 227 friction clutch. 223 gunpowder, 22t; hammer vs. jet, 229 jet of water, 227 nipper, 223 steam, 224
drop hammer vs. steam, 225 water-jet, 227 hammer vs. jet, 229 Pile-driving, cost of, 230 bridge construction, 231 foundations, 232 harbor work, 233 railroad construction, 230 railroad repairs, 231 river protection, 233 Pitching chisel, 127 Pivot pier, 379 Plane surfaces, method of forming in stone,
129 Plates, for list of, see Table of Contents. Plattsmouth bridge, cost of concrete founda- tions at, 265 cost of pneumatic foundations, 304 pressure on foundations. 377 rate of sinking by pneumatic process, 295 Plug and feathers. 128 Pneumatic foundations, see Foundations.
pneumaiic. Point. 127
Pointing, 141 [265
Point Pleasant bridge, cost of foimdalion, Pouglikeepsie bridge, foundation described,
272 Pozzuolana. 53 Pressure allowed on masonry, bric'it, 166, 167
stone. 149, 151 Puddle. 260 Pulsometer, 264 Pumps, 263 hand, 263
INDEX.
555
PTJM— SEW
Pump«, centrifugal, 2u4 for water- jet pile-driver, 228 mud-pump, 292 piilsoineter, 264 steam siphon, 263
Quarrying, 116
by clianueling and wedging, lig3
by explosives, 117
by hand tools, 116 Quoin, defined, 136
Railroad masonry, classification, ^o2 cost, 157, 160 specifications, 529, 534 Rankine's theory of the arch, 482 Relieving arches for retaining walls, 352 Resistance, frictional, in sinking founda- tions. 247, 248, 275, 297 Retaining walls. Coulomb's theory, 341 definitions. 338 difficulties in theories. 339 dimensions, eniiiiricai rules for, Benj. Baker's, 349 English, 349 Trautwine's, 349 drainage, 350 failure, method of, 338 land-lies, 351 Rankine's theory, 348 stability, theory of, 339, 340 applicability of, 348 assumptions necessary, 340 Coulomb's theory. 341 surcharged wall, 343 reliability. 343 Rankine's theorj', 348 Weyrauch's theory, 343 general formula, 344 horizontal earth-surface, 346 surcharge, 345 reliability, "^46 Weyrauch's theory, q. v., 343 Riprap. 148. .532
cost, 157, 160 Rubble masonry, 145 cost, 157, 160 coursed, 137
mortar required per yard. 89, 146 specifications. 147, 531, o'^O, 541 uncoursed, 137
Sand, amount per yanl of mortar, 88 cost, 79/c
data for estimates. '^'^ foundations, used I ;':•;■, i!i8 requisites for gooG. .:«/ cleanness, 79c durability, 796 fineness, 79rf, 79/ sharpness, 79b voids, 797, 79t weight, 79/, 79fc Sand-lift, 291 Sand-pump, 292
Sandstones, those most frequently used, 31 Scheffler's theory of arch, 474 Schuylkill bridge.cost of pneumatic pile8,302 Screw-i>iles. described, 217
bearing power. 249 Seasoning of stone, 18 Sewers, brick arches for, Philadelphia standard, 513 Washington standard, 514
SEW— STE
Sewer-pipe, cost. 410 strength. 408, 547 weight, 410 Sibley bridge, guiding the caisson, 296
piers, specifications for, 381 Skew arch, defined, 442 Slope-wall masonry, 147 cost, 157. 160 specifications, 147, 531 Soap and alum wash for brick-work 178 Soffit, defined, 440 Soil, bearing power of, 188 clay, 190 rock, 188 sand, 192
semi-liquid soil, 193 summary, 194 testing, method of, 187 examining, method of, 186 improving, method of, 195 Spandrel, defined, 440 filling, arches in, 508 drainage of, 508 Specifications, arch culvert masonry, 432. 531 architectui-al masonry, 534, 539 ashlai-. 142, 530 bo.x culverts, 401, 531 brickwork, arches, 177, 532 buildings, 175, 541 sewers, 176 bridge piers, 381 cement, 7Sd, 78e, 78/, 78g, 78h concrete, 532. 535, 540 foundations, 432, 533 masonry, arch culvert, '432 ashlar. 142 brick-work, 175, 177 buildings, architectural, 539
railroad, 534 paving, 148 pedestal, 385 pier, 381,
rubtde, 147, 531, 536, 541 slope-wall, 147 squared-stone, 144 paving, 148 piers, .381, 539 piles. 220. 533
rubble masonry, 147, 531, 536, 541 slope-wall masonry, 147, 531 squared-stone masonry, 144, 530, 538 Splicing piles. 221 ' Squared-stoue masonry, 143 definitions. 137 pitched-face, 137 quarry-face, 137 range work, 137 mortar required per yard, 144 specifications. 144, .530, 5:38 Staiidard arch culvert, 249 contents, 433 cost, 438 dimensions, 433 Standard stone-box culvert, 402 contents, 403 cost, 405 dimensions. 403 St. Genevieve sandstone. 31 St. Louis bridge foundations, 297
maxinnim jiressure on, 377 Steam pile-driver, 224
drop-hammer vs. steam, 225 Steam siphon, 263
556
IXDEX.
STE— STO
Steel-rail footings, aiti, 540 Stone, absorbing power, 21 Stone, argillaceous, a6 artificial, 1136 calcareous, 2(5 cost, 155
crushing strength, 8 cushions, 9 data. 1 1
fracture, form of, 9 specimen, dressing, 13 form. 8 size, 8 slabs. 11 cut-stone, 132 axed, 133
brush-hammered, 134 crandalled, 133 diamond panel, 134 fine-pointed, 133 rough- pointed, 132 rubbed, 134 tooth-axed, 133 description, artificial, 112 granite, 27 limestone, 28 marble, 28 sandstone, 29 trap, 27 durability, 4, 15 destructive agents, 16 preserving, methods of, 23 resisting agents, 17 seasoning, effect of, 18 testing, metliod of, 20 artificial, 20 absorptive power, 21 acid, effect of, 23 atmosphere, effect of, 23 Brard's method, 23 crushing strength, 8 frost, effect of, 21 microscopical examination, 33 natural, 20 elasticity, 14 granite, 27 hardness, 7 limestone, 28 local names, 32 marble, 28 market price, 155 masonry, q. v., definitions, 135 measurement of, 151, 529, 539 requisites for good, 3 sandstones, description of principal, 29 siliceous, 2(J specific gravity, 6 squared, drafted, 132
STO— YAZ
Stone, squared, pjtcli-faced, 138 quarrj-faeed, 132
strength, cru!-hing, q. v., 6 transverse, 13
tests, bibliography of, 15
toughness, 7
vs. brick masonry, 177
weight, 7 Stone-cutting tools, described, 125 St(jne grinder, 129 Stone planer, 129 Stoue polisher, 129 Stone saws, 128 Surfaces, method of forming, 129
method of finishing, 131
Timber, barrel culvert, 419
box culvert, 417
footing, 211
foundations, 269 Tremie, 107
Vitrified pipe, cost, 410 strength, 408, 547 weight, 410
Wall, definitions of parts of a, 135 Warped surface, method of forming, 131 Washington brick sewers, 514 Water required for cement mortar, 68
concrete, H2j Water-jet pile-driver, 227
■ys. hammer pile-driver, 229 Water-way for culverts, 391
factors, 391
formulas, 393
Meyer's, 394
Talbot's, 394
Waverly sandstone, 31
AVeep holes, 351
West Shore stone-box culvert, 402, 404 Weyrauch's theory of retaining walls, 343 "White-wash" on brick-w'ork, 181 Wind, effect on foundation, 204
pressure, amount of, 201 Wood bearing-piles, see Piles. Weight, bricK, 46
buildings, 200
cast-iron pipe, 418
cement, barrel, 54 cubic foot, 56
lime, 50
masonry, 200
sand, 79/i;
stone, 7
vitrified-pipe, 410
Yazoo River bridge, guiding the caisson, 296
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Hayford's Text-book of Geodetic Astronomy Svo,
Howe's Retaining-walls for Earth TZmo,
Johnson's Theory and Practice of Surveying Small Svo,
" Statics by Algebraic and Graphic Methods Svo,
Kiersted's Sewage Disposal 12mo,
Laplace's Philosophical Essay on Probabilities. (Truscott and
Emory. ) 12mo,
Mahan's Treatise on Civil Engineering. (1873.) (Wood.) . .8vo,
• Mahan's Descriptive Geometry Svo,
Merriman's Elements of Precise Surveying and Geodesy. . . .8vo, Merriman and Brooks's Handbook for Surveyors. . . .16mo, mor.,
Merriman's Elements of Sanitary Engineering Svo,
Nugent's Plane Surveying Svo,
Ogden's Sewer Design 12mo,
Patton's Treatise on Civil Engineering Svo, half leather,
Reed's Topographical Drawing and Sketching 4to,
Rideal's Sewage and the Bacterial Purification of Sewage.. .Svo, Siebert and Biggin's Modern Stone-cutting and Masonry. . . .8vo, Smith's Manual of Topographical Drawing. (McMillan.) . .Svo,
• Trautwine's Civil Engineer's Pocket-book. ... 16mo, morocco. Wait's Engineering and Architectural Jurisprudence Svo,
Sheep, " Law of Operations Preliminary to Construction in En- gineering and Architecture 8to,
Sheep,
Wait's Law of Contracts Svo,
Warren's Stereotomy — Problems in Stone-cutting Svo,
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Webb's Problems in the Use and Adjustment of Engineering
Instruments 16mo, morocco, 1 25
• Wheeler's Elementary Course of Civil Engineering 8vo, 4 00
Wilson's Topographic Surveying 8vo, 3 50
BRIDGES AND ROOFS. Boiler's Practical Treatise on the Construction of Iron Highway
Bridges 8vo, 2 00
• Seller's Thames River Bridge 4to, paper, 5 00
Burr's Course on the Stresses in Bridges and Roof Trusses,
Arched Ribs, and Suspension Bridges 8vo, 3 50
Du Bois's Mechanics of Engineering. Vol. 11 Small 4to, 10 00
Foster's Treatise on Wooden Trestle Bridges 4to, 5 00
Fowler's Coffer-dam Process for Piers 8vo, 2 50
Greene's Roof Trusses 8vo, 1 25
" Bridge Trusses 8vo, 2 50
" Arches in Wood, Iron, and Stone 8vo, 2 50
Howe's Treatise on Arches 8vo, 4 00
" Design of Simple Roof-trusses in Wood and Steel . 8vo, 2 00 Johnson, Bryan and Tumeaure's Theory and Practice in the
Designing of Modem Framed Structures Small 4to, 10 00
Merriman and Jacoby's Text-book on Roofs and Bridges:
Part I.— Stresses in Simple Trusses 8vo, 2 60
Part II.— Graphic Statics 8vo, 2 50
Part III.— Bridge Design. Fourth Ed., Rewritten 8vo, 2 50
Part IV.— Higher Structures 8vo, 2 60
Morison's Memphis Bridge 4to, 10 00
Waddell's De Pontibus, a Pocket Book for Bridge Engineers.
16mo, mor., 3 00
" Specifications for Steel Bridges 12mo, 1 25
Wood's Treatise on the Theory of the Construction of Bridges
and Roofs 8vo, 2 06
Wright's Designing of Draw-spans:
Part I.— Plate-girder Draws 8vo, 2 60
Part II. — Riveted-truss and Pin-connected Long-span Draws.
8vo, 2 50
Two parts in one volume 8vo, 3 60
HYDRATJLICS. Bazin's Experiments upon the Contraction of the Liquid Vein
Issuing from an Orifice. (Trautwine.) 8vo, 2 00
Bovey's Treatise on Hydraulics 8vo, 5 00
Church's Mechanics of Engineering 8vo, 6 00
" Diagrams of Mean Velocity of Water in Open Channels
paper, 1 50
C5oflBn'8 Graphical Solution of Hydraulic Problems. .16mo, mor., 2 60
Flather's Dynamometers, and the Measurement of Power.l2mo, 3 00
Folwell's Water-supply Engineering , 8vo, 4 00
Frizell's Water-power 8vo, 6 00
Fuertes's Water and Public Health 12rao, 1 50
* Water-flltration Works 12mo, 2 50
Ckingnillet and Kutter's General Formula for the Uniform Flow of Water in Rivers and Other Channels. ( Ber- ing and Trautwine.) ~ 8vo, 4 00
Hazen's Filtration of Public Water-supply 8vo, 3 00
Hazlehurst's Towers and Tanks for Water-works 8vo, 2 60
Berschel's 115 Experiments on the Carrying Capacity of Large,
Riveted, Metal Conduits 8vo, 2 00
Mason's Water-supply. (Considered Principally from a Sani- tary Standpoint.) 8vo, 4 0
Merriman's Treatise on Hydraulics 8vo, 4 00
• Michie's Elements of Analytical Mechanics 8vo, 4 00
Schuyler's Reservoirs for Irrigation, Water-power, and Domestic
Water-supply Large Svo, 5 00
Turneaure and Russell. Public Water-supplies Svo, 5 00
Wegmann's Design and Construction of Dams 4to, 5 00
" Water-supply of the City of New York from 1658 to
1895 4to, 10 00
Weisbach's Hydraulics and Hydraulic Motors. (Du Bols.) . .8vo, 5 09
Wilson's Manual of Irrigation Engineering Small Svo, 4 00
Wolff's Windmill as a Prime Mover Svo, 3 00
Wood's Turbines Svo, 2 60
" Elements of Analytict. . ^chanics Svo, 3 00
MATERIALS OF ENGINEERING.
Baker's Treatise on Masonry Construction Svo, 6 00
" Roads and Pavements Svo,
Black's United States Public Works Oblong 4to,
Bovey's Strength of Materials and Theory of Structures. . . .Svo, Burr's Elasticity and Resistance of the Materials of Engineer- ing ,. .Svo,
Byrne's Highway Construction Svo,
" Inspection of the Materials and Workmanship Em- ployed in Construction 16mo,
Church's Mechanics of Engineering Svo,
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Johnson's Materials of Construction Large Svo,
Keep's Cast Iron Svo,
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Martens's Handbook on Testing Materials. {Henning.).2 v., Svo,
Merrill's Stones for Building and Decoration Svo,
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Part II. — Iron and Steel Svo,
Part III. — A Treatise on Brasses, Bronzes and Other Alloys
and Their Constituents Svo,
Thurston's Text-book of the Materials of Construction Svo,
Tillson's Street Pavements and Paving Materials Svo,
Waddell's De Pontibus. (A Pocket-book for Bridge Engineers.)
16mo, morocco,
" Specifications for Steel Bridges 12mo,
Wood's Treatise on the Resistance of Materials, and an Ap- pendix on the Preservation of Timber Svo,
* Elements of Analytical Mechanics Svo,
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KAHWAY ENGINEERING.
Andrews's Handbook for Street Railway Engineers. 3x5 in mor., 1 26
-Jerg's Buildings and Structures of American Railroads. . .4to, 5 00
Brooks's Handbook of Street Railroad Location.. 16mo, morocco, 1 60
Butts's Civil Engineer'a Field-book 16mo, morocco, 2 50
Crandall's Transition Curve 16mo, morocco, 1 50
" Railway and Other Earthwork Tables 8vo, 1 60
Dawson's Electric Railways and Tramways . Small 4to, half mor., 12 60
" " Engineering " and Electric Traction Pocket-book.
16mo, morocco, 4 00
Dredge's History of the Pennsylvania Railroad: (1879.) .Paper, 5 00
• Drmker's Tunneling, Explosive Compounds, and Rock Drills.
4to, half morocco, 25 00
Usher's Table of Cubic Yards Cardboard, 25
Gkxiwin's Railroad Engineers' Field-book and ikplorers' Guide.
16mo, morocco, 2 50
Howard's Transition Curve Field-book 16mo, morocco, 1 50
Hudson's Tables for Calculating the Cubic Contents of Exca- vations and Embankments Svo, 1 00
Molitor and Beard's Manual for Resident Engineers 16mo, 1 00
Nagle's Field Manual for Railroad Engineers 16mo, morocco, 3 00
Phfibriek's Field Manual for Engineers 16mo, morocco, 3 00
Pratt and Alden's Street-railway Road-bed Svo, 2 00
Searles's Field Engineering 16mo, morocco, 3 GO
" Railroad Spiral 16mo, morocco, 1 50
Taylor's Prismoidal Formulae and Earthwork Svo, 1 50
• iVautwine's Method of Calculating the Cubic Contents of Ex-
cavations and Embankments by the Aid of Dia- grams Svo, 2 00
• " The Field Practice of Laying Out Circular Curves
for Railroads 12mo, morocco, 2 60
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Webb's Railroad Construction Svo, 4 00
Wellington's Economic Theory of the Location of Railways. .
Small Svo, 5 00
DRAWING.
Bair's Kinematics of Machinery Svo,
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Coolidge's Manual of Drawing 8vo, paper,
Durley's Kinematics of Machines Svo,
Hill's Text-book on Shades and Shadows, and Perspective. . Svo, Jones's Machine Design:
Part I. — Kinematics of Machinery Svo,
Part n. — Form, Strength and Proportions of Parts Svo,
MacCord's Elements of Descriptive Geometry Svo,
" Kinematics; or, Practical Mechanism Svo,
" Mechanical Drawing 4to,
" Velocity Diagrams Svo,
•Mahan's Descriptive Geometry and Stone-cutting Svo,
Mahan's Industrial Drawing. (Thompson.) Svo,
Reed's Topographical Drawing and Sketching 4to,
l&eid's Course in Mechanical Drawing Svo,
" Text-book of Mechanical Drawing and Elementary Ma- chine Design Svo,
Robinson's Principles of Mechanism Svo,
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Drawing 12mo, 1 00
" Drafting Instruments and Operations 12mo, 1 26
" Manual of Elementary Projection Drawing. .. .12mo, 1 50 " Manual of Elementary Problems in the Linear Per- spective of Form and Shadow 12mo, 1 00
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" Elements of Descriptive Geometry, Shadows, and Per- spective 8vo, 3 50
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" Elements of Machine Construction and Drawing. .Bvo, 7 50 " Problems, Theorems, and Examples in Descriptive
Geometry Bvo, 2 50
Weisbach's Kinematics and the Power of Transmission. (Herr- mann and Klein.) 8vo, 6 00
Whelpley's Practical Instruction in the Art of Letter En- graving 12mo, 2 00
Wilson's Topographic Surveying Bvo, 3 60
Wilson's Free-hand Perspective Bvo, 2 5f
Woolf's Elementary Course in Descriptive Geometry. .Large Bvo, 3 00
ELECTRICITY AND PHYSICS.
Anthony and Brackett's Text-book of Physics. (Magie.)
Small Bvo, 3 00 Anthony's Lecture-notes on the Theory of Electrical Measur-
ments 12mo, 1 00
Benjamin's History of Electricity Bvo, 3 00
Benjamin's Voltaic Cell Bvo, 8 00
Classen's Qantitative Chemical Analysis by Electrolysis. Her-
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Crehore and Squier's Polarizing Photo-chronograph Bvo, 3 00
Dawson's Electric Railways and Tramways..Small 4to, half mor,, 12 60 Dawson's "Engineering" and Electric Traction Pocket-book.
16mo, morocco, 4 00
Flather's Dynamometers, and the Measurement of Power. . 12mo, 3 00
Gilbert's De Magnete. (Mottelay.) Bvo, 2 60
Hohnan's Precision of Measurements Bvo, 2 00
" Telescopic Mirror-scale Method, Adjustments, and
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Landauer's Spectrum Analysis. (Tingle.) Bvo, 3 00
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Tory and Pitcher. Manual of Laboratory Physics. .Small 8vo, 2 00
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LAW.
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Manual for Courts-martial 16mo, morocco, 1 60
Wait's Engineering and Architectural Jurisprudence 8vo, 6 00
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Sheep, 5 60
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" " The Iron Founder " Supplement 12mo, 2 60
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Eissler's Modern High Explosives Svo, 4 00
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Spencer's Handbook for Chemists of Beet-sugar Houses.
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Thurston's Manual of Steam-boilers, their Designs, Construc- tion and Operation Svo, 6 00
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10
Davie's Introduction to the Logic at Algebra 8vo, 1 60
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pap., 16
100 copies for 6 00
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MacCord's Kinematics; or, Practical Mechanism 8vo,
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•• " " " " Vol.n Small 4to, 10 00
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Durley's Kinematics of Machines 8vo, 4 00
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Merriman's Text-book on the Mechanics of Materials Svo, 4 00
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Reagan's Locomotive Mechanism and Engineering 12mo, 2 00
Reid's Course in Mechanical Drawing Svo, 2 00
" Text-book of Mechanical Drawing and Elementary
Machine Design Svo, 3 00
Richards's Compressed Air 12mo, 1 50
Robinson's Principles of Mechanism Svo, 3 00
Ryan, Norris, and Hoxie's Electrical Machinery. {In preparation.)
Sinclair's Locomotive-engine Running and Management. .12mo, 2 00
Smith's Press-working of Metals Svo, S 09
" Materials of Machines 12mo, 1 00
Spangler, Greene, and Marshall's Elements of Steam-engineering.
Svo, 3 GO Thurston's Treatise on Friction and Lost Work in Machin- ery and Mill Work Svo, 3 00
** Animal as a Machine and Prime Motor, and the
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Warren's Elements of Machine Construction and Drawing. .8vo, 7 60 Weisbach's Kinematics and the Power of Transmission.
(Herrman — Klein.) Svo, 6 00
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(man — KJein.) Svo, 6 00
Wood's Elements of Analytical Mechanics Svo, 3 00
" Principles of Elementary Mechanics 12mo, 1 26
" Turbines Svo, 2 56
The World's Columbian Exposition of 1893 4to, 1 00
METALLTTRGY. E^leston's Metallurgy of Silver, Gold, and Mercury:
Vol. I.— Silver Svo, T 60
Vol. n.— Gold and Mercury Svo, 7 §0
♦* Ees's Lead-smelting. . . . (Postage 9 cents additional) 12mo, 2 50
Keep's Cast Iron Svo, 2 50
Kunhardt's Practice of Ore Dressing in Lurope Svo, 1 60
Le Chatelier's High-temperature Measurements. (Boudouard —
Burgess.) 12mo, S 00
Metcalf's Steel. 'A Manual for Steel-users 12mo, 2 00
Smith's Materials of Machines 12mo, 1 00
Thurston's Materials of Engineering. In Three Parts Svo, 8 06
Part n.— Iron and Steel Svo, 3 6U
Part m. — A Treatise on Brasses, Bronzes and Other Alloys
and Their Constituents Svo, 2 M
14
MINERALOGY.
Barringer'g Description of Minerals of Commercial Value.
Oblong, morocco, 2 SO
Boyd'g Resources of Southwest Virginia 8vo, 3 00
" Map of Southwest Virginia Pocket-book form, 2 00
Brush's Manual of Determinative Mineralogy. (Penfield.) .8vo, 4 00
Chester's Catalogue of Minerals 8vo, paper, 1 00
Cloth, 1 26
" Dictionary of the Names of Minerals. Svo, 3 60
Dana'a System of Mineralogy Large Svo, half leather, 12 60
" First Appendix to Dana's New " System of Mineralogy."
Large Svo, 1 GO
" Text-book of Mineralogy Svo, 4 00
" Minerals and How to Study Them 12mo, 1 60
" Catalogue of American Localities of Minerals . Large Svo, 1 00
" Manual of Mineralogy and Petrography 12mo, 2 00
Egleston's Catalogue of Minerals and Synonyms Svo, 2 60
Huseak's The Determination of Rock-forming Minerals.
(Smith.) Small Svo, 2 00
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Mineral Tests Svo, paper, 60
Bosenbusch's Microscopical Physiography of the Rock-making
Minerals. (Idding's.) Svo, 6 00
•Tillman's Text-book of Important Minerals and Rocks. .Svo, 2 00
Williams's Manual of Lithology Svo, 3 00
MINING.
Beard's Ventilation of Mines 12mo, 2 60
Boyd's Resources of Southwest Virginia Svo, 3 00
" Map of Southwest Virginia Pocket-book form, 2 00
• Drinker's Tunneling, Explosive Compounds, and Rock
Drills 4to, half morocco, 25 0©
Eiseler's Modem High Explosives Svo, 4 00
Fowler's Sewage Works Analyses 12mo, 2 00
Groodyear's Coal-mines of the Western Coast of the United
States 12mo, 2 60
Ihlseng's Manual of Mining 8vo, 4 00
•* Iles's Lead-smelting 12mo, 2 50
Kunhardt's Practice of Ore Dressing in Europe Svo, 1 60
ODriscoll's Notes on the Treatment of Gold Ores Svo, 2 00
Sawyer's Accidents in Mines 8vo, 7 00
* Walke's Lectures on Explosives , Svo, 4 GO
Wilson's Cyanide Processes 12mo, 1 50
Wilson's Chlorination Process 12mo, 1 69
Wilson's Hydraulic and Placer Mining 12mo, 2 00
Wilson's Treatise on Practical and Theoretical Mine Ventila- tion 12mo, 1 26
SANITARY SCIENCE.
Fol well's Sewerage. (Designing, Construction and Maintenance.)
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Faertes's Water and Public Health 12mo, 1 60
" Water-flltration Works 12mo, 2 50
15
Gerhard's Guide to Sanitary House-inspection 16mo, 1 00
Goodrich's Economical Disposal of Towns' Refuse. . .Demy 8vo, S 50
Haven's Filtration of Public Water-supplies 8vo, 8 00
Kiersted's Sewage Disposal 12mo, 1 26
Leach's The Inspection and Analysis of Food with Special
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" Examination of Water. (Chemical and Bacterio- logical.) 12mo, 1 26
Merriman's Elements of Sanitary Engineering 8vo, 2 00
Nichols's Water-supply. (Considered Mainly from a Chemical
and Sanitary Standpoint.) (1883.) 8vo, 2 60
Ogden's Sewer Design 12mo, 2 00
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Richards'B Cost of Food. A Study in Dietaries 12mo, 1 Of
Richards and Woodman's Air, Water, and Food from a Sani- tary Standpoint 8vo, 2 00
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Rideal's Sewage and Bacterial Purification of Sewage Svo, 8 60
Tumeaure and Russell's Public Water-supplies 8vo, 6 00
Whipple's Microscopy of Drinking-water 8vo, 3 60
Woodhull's Notes on Military Hygiene 16mo, 1 60
MISCELLANEOUS.
Barker's Deep-sea Soundings 8vo, S 00
Emmous's Geological Guide-book of the Rocky Mountain Ex- cursion of the International Congress of Geologists.
Large Svo, 1 60
Ferrel's Popular Treatise on the Winds 8vo, 4 00
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Mott's Composition, Digestibility, and Nutritive Value of Food.
Mounted chart, 1 26
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Ricketts's History of Rensselaer Polytechnic Institute, 1824-
1894 Small 8vo, 8 00
Rotherham's Emphaaifled New Testament Large Svo, 8 00
Steel's Treatise on the Diseases of the Dog 8vo, 3 60
Totten's Important Question in Metrology 8vo, 2 60
The World's Columbian Exposition of 1893 4to, 1 00
Worcester and Atkinson. Small Hospitals, Establishment and Maintenance, and Suggestions for Hospital Architecture,
with Plans for a Small Hospital 12mo, 1 86
HEBREW AND CHALDEE TEXT-BOOKS.
Qreen's Grammar of the Hebrew Language 8vo, 8 00
" Elementary Hebrew Grammar 12mo, 1 26
" Hebrew Chrestomathy 8vo, 2 00
Ckeenius's Hebrew and Chaldee Lexicon to the Old Testament
Scriptures. (Tregellea.) Small 4to, hall morocco, 6 00
Letteris'B Hebrew Bible Svo, 2 26
16
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