Six monographs on wind stresses; wind pressure factors, specification requirements, mill-building stresses, rigid joint wind bracing for office buildings

WIND STRESSES

[FLEMING]

Six Jyfono&ra pAr on

~./- , —v' /

Wind

WIND PRESSURE FACTORS
SPECIFICATION REQUIREMENTS
MILL-BUILDING STRESSES
RIGID JOINT • WIND BRACING
FOR OFFICE BUILDINGS

BY ROBINS FLEMING
Engineer, American Bridge Company , New York

REVISED AND ENLARGED REPRINTS FROM
ENGINEERING NEWS

ENGINEERING NEWS

HILL BUILDING, NEW YORK

1915

Copyright, 1915,

by
Hill Publishing Co.

PREFACE

Wind is everywhere. It affects all structures. Every
engineer, or even every person who ever sees an engineer,
has a personal interest in the effect of wind on structures.
That is the subject of the present book.

Ignorance is not always bliss. If it be true — as seems
very likely — that wind is preeminently a matter concern-
ing which no one knows he knows not, then this book
deserves to have many readers.

There is a fresh touch to what the author says. His
main argument throughout is common sense. In this
respect his frame of mind is catching; the reader will
find himself saner and sounder for having read the book.
When the author refers to intricate studies of wind
action, claimed to show the need for radical changes
in building practice, he leads us to notice the practical
fact that these intricate studies are based on tests made
in mild breezes, and can hardly be safe guides as to
what happens in storms.

Six articles which appeared in ENGINEERING NEWS,
most of them in the early months of 1915, make up
this book. One of the six, however — No. 6 — is so
changed from the form in which it was printed March
13, 1913, that it is new. And this subject, the stress
calculation for tier-building frames without diagonals, is
so far without any literature.

The many slow hours of work which the author con-
sumed in searching out and studying the material re-
quired for writing this book merit the reader's apprecia-
tion.

EDITOE Engineering News.

382055

CONTENTS

Page

I Wind Pressure Formulas and Their Experi-
mental Basis

II Wind Stresses in Steel Mill Buildings . . 13

III Wind Stresses in Eailroad Bridges • • • ^7

IV Wind Stresses in Highway Bridges . . .

V Windbracing Kequirements in Municipal

Building Codes 53

VI Windbracing without Diagonals for Steel-
Frame Office Buildings 61

Wind Pressure Formulas and
Their Experimental Basis

SYNOPSIS — A discussion of the current formu-
las for relation between wind pressure and velocity,
relation between pressure on normal planes and
planes inclined to the wind, and several other
phases of wind pressure. The author brings out
strikingly how inadequate is the experimental basis
for the formulas and figures commonly employed.

The purpose of this article is to give the basis from
which some of the commonly used formulas for wind
pressure are derived. Even the engineer who wishes to
know only the wind pressure in pounds per square foot
for which he shall make provision in his structure will be
better equipped for designing if he is acquainted with the
foundations on which ordinary practice rests.

KELATION BETWEEN WIND PBESSUBE AND VELOCITY

In view of the extent of the literature on the subject it
might reasonably be supposed that the elementary prin-
ciples of wind pressure are determined, at least theoretic-
ally. How near this is to being the case may be inferred
from the following extracts taken from two modern
American textbooks, each of which is regarded as an
authority. Marburg, in his Framed Structures and
Girders, under ''Wind Pressure," writes:

Theoretically the pressure p, in Ib. per sq.ft., on a plane
surface normal to the direction of flow of a fluid having a
relative velocity v, in ft. per sec., is equal to the weight of
a vertical column of the fluid having a cross-section of 1
sq.ft. and a height h, in ft. equal to that through which a
freely moving body must fall to acquire the velocity v. If
w denotes the weight of the fluid, in Ib. per cu.ft.,

wv2

p = Wh = _ (1,

For air at a temperature of 32° F. and at a barometric
pressure of 760 mm., w = 0.081. Letting g = 32.2,

p = 0.00126 v« (2)

[i]

If V denotes the velocity of the wind in miles per hour,
v =. 1.47 V, whence equation (2) becomes

p — 0.0027V2 (3)

Burr and Falk, in The Design and Construction of
Metallic Bridges, under "Stresses due to Wind" write:

If the wind were directed as a finite stream against an
infinitely large surface, so that the direction of the air is
completely changed, an equation expressing the force against
that surface may be obtained from the laws of mechanics.
Let

W == the weight of air directed against any normal

surface in a given time;

w = the weight in pounds of one cubic foot of air;
v = the velocity of wind in feet per second;
a == the area of cross-section of the wind stream,

Then W = wav.
Let

M = the mass of air of the weight W;
g = the acceleration due to gravity = 32.2 feet per

second;
P = the force acting on the area a,

Wv wava

Then F = Mv = = (1)

g g

If a be taken at 1 sq.ft., and w at 0.0807 Ib. per cu.ft. for
a temperature of 32° F. and a barometric pressure of 760
mm., and if v be replaced by V, the velocity in miles per
hour, then

P = 0.0054 V2 (2)

The reader will observe that starting with the same as-
sumptions one author finds the resultant pressure to be
twice that of the other. Both authors make haste to write
that the theoretical conditions upon which their formula
is* based do not exist. A cushion of air is formed in front
of the plate and a partial vacuum at the back ; there is a
certain amount of air friction and the change of direction
is not complete. The student facing such conflicting
theories on the very fundamentals of wind pressure may
well raise the question of authority.

It is almost impossible to give undue credit to Sir Isaac
Newton for his work in the realms of science and mathe-
matics. His great book was the Philosophia Naturalis
Principia Mathematica, or "The Mathematical Principles
of Natural Philosophy," commonly called the Principia.
Originally published in 1686, revised editions were is-
sued in 1713 and 1726. Modern hydrodynamics had its

[2]

origin in the second book, treating of Motion of Bodies in
Resisting Mediums. Section VIII of this book is entitled
''Of Motion Propagated through Fluids." A translation
of Prop. XLVIII (Newton wrote in Latin) reads:

The velocities of pulses propagated in an elastic fluid are
in a ratio compounded of the subduplicate ratio of the elastic
force directly, and the subduplicate ratio of the density in-
versely; supposing- the elastic force of the fluid to be pro-
portional to its condensation.

This means that the velocity v varies as -7—, or p varies

V a

as dv2. For wind pressure, the density of the air being
constant, we have the law that the pressure varies di-
rectly as the square of the velocity, which has remained
almost undisputed since Newton's day.

Furthermore, according to Newton, for an area of

v2
unity, p = dh, in which h = ^— is the distance through

which a heavy body must fall to acquire the velocity v,
g being the coefficient of gravity or 32.2. This may be
called the Newtonian theory, and has been followed by
a host of writers, including Marburg (quoted above).

W. J. M. Rankine was one of the master mathema-
ticians of the nineteenth century. In his fifteenth year
his uncle presented him with a copy of Newton's Prin-
cipia, which he read carefully. He remarks, "This was
the foundation of my knowledge of the higher mathe-
matics, dynamics and physics." But the pupil did not
blindly follow the master. In his Applied Mechanics,
he has a section devoted to "Mutual Impulse of Fluids
and Solids." A jet of fluid A, striking a smooth sur-
face, is deflected so as to glide along the surface in that
path which makes the smallest angle with its original di-
rection of motion. Let v be the velocity of the particle
of fluid, q the volume discharged per second equal to Av,
d the density, and 0 the angle by which the direction of

motion is deflected; then — — is the momentum of the

y

quantity of fluid whose motion is deflected per second.
With these notations the general equation for the force

[3]

Fx perpendicular to the plane in question is found to be

For the particular case of the plane at right angles to the
jet or B = 90°,

9 9

This may be called the impact theory, and is followed in
some textbooks, including that of Burr and Falk.

From the time of Newton until this day a long line of
investigators have sought by experiment to obtain the
value of Tc in the formula P = kV2f in which P = pres-
sure in Ib. per sq.ft. and V = velocity in miles per hour.
As before noted, according to the Newton formula Ic is
0.0027 and with the same assumptions according to Ran-
kine Tc is 0.0054. What is known as the Smeaton for-
mula held almost universal sway for 150 years and is still
in use. It is very simple, P = 1/200 V2. In the Philoso-
phical Transactions of the Royal Society, England, for
the year 1759 is a lengthy paper entitled, An Experi-
mental Enquiry Concerning the Natural Power of Water
and Wind to Turn Mills, and Other Machines, Depend-
ing on a Circular Motion. By Mr. J. Smeaton, F. R. 8.
Part III is "On the Construction and Effects of Wind-
mill-Sails/' For his experiments Smeaton constructed
an elaborate machine or whirling-table in which fixed
sails revolved through the air about a given axis and their
velocities were measured by the weights lifted. A foot-
note reads:

Some years ago Mr. Rouse, an ingenious gentleman of
Hasborough in Leicestershire, set about trying experiments
on the velocities of the wind, and force thereof upon plain
surfaces and windmill sails.

It is presumed, though not so stated, that Mr. Rouse
used a whirling-table similar to that described by
Smeaton. Further on in the paper a table "containing
the velocity and force of wind, according to their common

appellations," is found introduced with :

The following table which was communicated to me by
my friend Mr. Rouse, and which appears to have been con-
structed with great care, from a considerable number of

[4]

facts and experiments, and which having relation to the sub-
ject of this article; I here insert as he sent it to me; but at
the same time must observe that the evidence for those num-
bers where the velocity of the wind exceeds 50 miles an hour, do
not seem of equal authority with those of 50 miles an hour
and under. It is also to be observed, that the numbers in
column 3 are calculated according to the velocity of the
wind, which in moderate velocities, from what has been be-
fore observed, will hold very nearly.

From this introduction it is impossible to tell where ex-
periment ended and theory began. The coefficient of V*
according to the figures given in the third column of the
table is found to be 0.00492, or V2oo nearly. It is hard
to understand how a formula resting upon such a slender
foundation should have had such wide vogue.

The most careful experiments of recent years for the
pressure on flat plates of moderate size normal to the di-
rection of a uniform wind give a value of Tc from 0.0032
tc 0.004. Hence the formula P = 0.004 V2 may be
safely used. It is interesting to note that Weisbach, in
his monumental work, the Mechanics of Engineering,
followed Newton's method but multiplied the value of Tc
as found by this method by a coefficient 1.86, stating that
about two-thirds of the action is upon the front and about
one-third upon the rear surface. He based his coefficient
upon the experiments of Dubuat (about 1780) and Thi-
bault (1826).

The U. S. Weather Bureau uses the formula

P = 0.004 ^-F2
oO

in which B = height of barometer in inches. This for the

Tt

engineer is an unnecessary refinement as ^ varies but

oU

little from unity. Wolff in his book The Windmill as a
Prime Mover takes into account also the effect of tem-
perature in determining wind pressure. At sea level for
a wind velocity of 40 miles per hour he finds pressures
of 8.6 Ib. per sq.ft. for 0° F. to 7.08 Ib. for 100° F. For
a velocity of 80 miles per hour he finds pressures of
34.98 Ib. per sq.ft. at 0° F. to 28.86 Ib. at 100° F.
WIND-PRESSURE COEFFICIENT FOR INCLINED SURFACES
For the intensity of wind pressure on inclined surfaces
we have a wide range of values from which to choose.

[ 5 ]

Tiberius Cavallo, F. E. S., etc., in 1803, published a four-
volume treatise on The Elements of Natural or Experi-
mental Philosophy. The writer has never seen the treatise
quoted, but Chapter IV of Book II, "Of the Action of
^"onelastic Fluids in Motion," and Chapter X of the same
book, "Of Air in Motion, or of the Wind," are written
in a truly scientific spirit and are readable today. A
proposition of Cavallo's reads, "The forces of a fluid
medium on a plane cutting the direction of its motion
with different inclinations successively, are as the square?
of the sines of these inclinations." This, however, ia
implied by the great Newton in the Principia, Book II,
Prop. XXXIV. Among recent writers Spofford in "The
Theory of Structures" deduces the same theoretical re-
sults.

As these results differ widely from those obtained by
experiment, recourse must be had to empirical formulas.
Among such, Button's formula has been used in England
and the United States perhaps more than all others com-
bined. It is still found in the latest editions of many
technical books. The experiments upon which it is based
were decidedly crude. Tract XXXVI of Tracts on
Mathematical and Philosophical Subjects by Charles
Hutton, LL.D., F.E.S., Professor of Mathematics in the
Eoyal Military Academy of Woodwich, England, entitled,
"Eesistance of the Air Determined by the Whirling-
Machine," records his experiments. Hutton secured a
whirling-machine and during 1786 and 1787 experi-
mented with hemispheres and cones. Under date of July
23, 1788, he records:

Prepared the machine to make experiments with figures
of shapes different from the foregoing ones. Procuring a
thin rectangular plate of brass to fix on the arm of the ma-
chine; its weight 11^ oz. and its dimensions 8 in. by 4 in.,
consequently its area was 32 sq.in. ... It was adapted
for fitting on the end of the arm in both directions, . . .
It was also contrived to incline the surface in any degree
to the direction of motion, to try the resistance at all angles
of inclination. When fitted on with its length in the direction
of its arm, the distance of its center from the axis of mo-
tion was 53% in.; and the same distance also when fitted on
the other way.

Experiments were carried on at different inclinations
of plate with a velocity of 12 ft. per sec. or 8.2 miles per

[6]

hour. When attempting to bring the velocity up to 20
ft. per sec. or 13.6 miles per hour, the thread carrying
the weight broke. These experiments are recorded under
dates of July 24, 25, 31 and Aug. 11. The results ob-
tained were tabulated and the well known formula
Pn = P (sitfx)l-**co*x-i

was deduced. This is sometimes called Unwin's formula,
though for what reason is not clear, as Prof. Unwin
simply quotes Prof. Hutton's formula approvingly.
The Duchemin formula

P p 2 sin A
1 + sin* A

for inclined surfaces may be said to represent the best
knowledge on the subject and is considered the most re-
liable formula in use. The pressures obtained are greater
than those from the Hutton formula. Col. Duchemin, a
French army officer, made his investigations in 1829 and
the results were published in 1842 (Bixby).* Consider-
able weight has been attached to the work of Col. Duche-
min. Weisbach quotes it, as well as most writers since
his time. The Duchemin formula was verified by S. P.
Langley in 1888. He had erected at the Allegheny
(Penn.) Observatory a whirling-table consisting of two
symmetrical wooden arms, each 30 ft. long, revolving in
a plane 8 ft. above the ground. The motion thus ob-
tained was nearly rectilinear, quite in contrast with that
from Button's machine of less than 5-ft. radius. He also
used velocities up to 100 ft. per sec., or nearly 70 miles
per hour. He writes:

At the inception of the experiments with this apparatus
it was recognized that the Newtonian law, which made the
pressure on an inclined surface proportional to the square
of the sine of the angle, was widely erroneous. Occasional
experiments have been made since the time of Newton to
ascertain the ratio of the pressure upon a plane inclined at
various angles to that upon a normal plane, but the published

*The writer, while obtaining his information first hand
from the sources quoted, acknowledges an obligation to a
valuable report: Appendix C of the Report of Sept. 29, 1894,
of the Special Army Engineer Board as to the Maximum Span
Practicable for Suspension Bridges. By W. H. Bixby, Captain
(now General) of Engineers, U. S. A. It is really a treatise
on wind pressure in engineering construction. It is said only
500 copies were issued. This valuable paper may be found
reprinted entire in "Engineering News," Mar. 14, 1895.

experiments exhibit extremely wide discordance, and a series
of experiments upon this problem seemed therefore, to be
necessary before taking up some newer lines of inquiry.

It is remarkable that Langley obtained results varying
less than 3% from those derived from the Duchemin for-
mula. Regarding this he writes :

Only since making these experiments my attention has
been called to a close agreement of my curve with the
formula of Duchemin, whose valuable memoir published by
the French War Department, "Memorial de 1'Artillerie" No.
V, I regret not knowing earlier.

Attention is called to the monographs by Langley,
Experiments in Aerodynamics and The Internal Worlc
of the Wind, being Numbers 801 and 884 of the "Smith-
sonian Contributions to Knowledge."

WIND PEESSUKE ON NONPLANAR SURFACES

When the wind blows on nonplanar surfaces the pres-
sure on the projected area depends upon the form of the
surface. This is important in the case of the cylinder
(standpipes, chimneys and similar objects). Rankine
states in his Applied Mechanics, "The total pressure of
the wind against the side of a cylinder is about one-half
of the total pressure against a diametral plane of that
cylinder." A theoretical value of two-thirds is found in
some treatises, but in engineering practice one-half is
generally used.

Goodman in his Mechanics Applied to Engineering,
London, 1904, gives the following ratios of pressure:

Plat plate 1.0

Sphere 0.36 to 0.41

Elongated projectile 0.5

Cylinder 0.54 to 0.57

Wedge (base to wind) 0.8 to 0.97

Wedge (edge to wind) 0.6 to 0.7

Vertex angle 90°

Cone (base to wind) 0.95
Cone (apex to wind)

Vertex angle 90° 0.69 to 0.72

Vertex angle 60° 0.54

Lattice girders about 0.8

WIND PRESSURE ON PARALLEL PLATES
The pressures upon parallel plates or bars with an open
space between them are important in application to plate-
girder bridges, the trusses in a truss bridge, or parallel
bars in the same truss when one bar is behind another.

[8]

The Committee of the National Physical Laboratory,
England, having decided that one of the first researches
to be undertaken in the Engineering Laboratory should
be the investigation of the distribution and intensity of
the pressure of wind on structures, an elaborate series of
experiments was conducted by Thomas Edward Stanton
and the results embodied in two papers contributed by
him to the Institution of Civil Engineers: "On the Ke-
sistance of Plane Surfaces in a Uniform Current of Air"
and "Experiments on Wind Pressure." For circular
plates 2 in. in diameter at 1% diameters apart, he found
the value of the total pressure was less than 75% of the
resistance on a single plate; at 2.15 diameters apart the
total pressure was equal to that on a single plate; while
at a distance of 5 diameters apart the total pressure was
1.78 times that on a single plate. Stanton's first experi-
ments were criticized because they were conducted with
such small models. For his second series he built a tower
and used larger surfaces, but found little to change his
previous conclusions.

Baker's experiments at the Forth Bridge led him to
the conclusion that in no case was the area affected by the
wind in any girder which had two or more surfaces ex-
posed more than 1.8 times the area of the surface directly
fronting the wind. The Board of Trade regulations
under which the Forth Bridge was built required that a
wind pressure of 56 Ib. per sq.ft. should be used in cal-
culations, and this twice over the area of the girder sur-
face exposed.*

MEASURING WIND PRESSUBE AND VELOCITY

It has been assumed by experimenters that the pressure
of the wind on a given shape with a certain velocity is the
same as that of the shape moving through the air with an
equal velocity. This seems to follow from Newton's
Corollary V to his Laws of Motion, "The motions of bod-
ies included in a given space are the same among them-
selves, whether that space is at rest or moves uniformly
forward in a right line without any circular motion."

*Engineers regard the requirement of 56 Ib. as needless
and excessive.

[ 9 ]

Perhaps the only dissonant voice is that of T. Claxton
Fidler, who in his Bridge Construction writes: "But it
has not yet been ascertained that the pressure of the wind
is the same thing as the resistance offered by the air to
a moving body."

The pressure of the wind has been measured direct and
independently of the velocity. The methods of doing this
are so limited in their application that the pressure is
almost universally determined in terms of the velocity.
Hence, the prime importance of measuring the velocity
of the wind correctly. Attempts to do this have been
made by all manner of means for the past two centuries.
The science of Anemometry has a literature of its own.
The velocities obtained by all methods are more or less
in error — some of them very much so. At present the
Kobinson Cup Anemometer or some modification of it is
used pretty generally throughout the meteorological world
for measuring wind velocities.

In the Transactions of the Royal Irish Academy, Vol.
XXII, part III (1852), is a paper: "Description of an
Improved Anemometer for Registering the Direction of
the Wind, and the Space Which it Traverses in Given In-
tervals of Time. By the Rev. Tfhomas] R[odney] Rob-
inson, D.D., Member of the Royal Irish Academy, and of
other Scientific Societies. Read June 10, 1850." Dr.
Robinson, who was connected with the observatory at
Armagh, Ireland, writes :

After some preliminary experiments I constructed in 1843
the essential parts of the machine, a description of which
I now submit to the Academy, and I added in subsequent
years such improvements as were indicated by experience.
It was complete in 1846, when I described it to the British
Association at Southampton.

He found "from sixteen experiments made in four days
with winds from a moderate breeze to a hard gale,

£-4.011

or, in round numbers, the action on the concave is four
times that on the convex." From this he found the
theoretic value m of the ratio of the velocity of the wind
to that of the cup center to be m = 3.00. Dr. Robinson
concluded that no matter what the size of the cups or the

[10]

lengths of the arms, "the centers of the hemisphere move
with one-third of the wind's velocity, except so far as they
are retarded by friction." This has been disproved. As
a necessary result, many published velocities are in error.
The U. S. Weather Bureau prescribes that each pat-
tern of anemometer should have its particular law of ro-
tation determined by special experiment. Its stand-
ard instruments in use throughout the United States have
hemispherical cups 4 in. in diameter on arms 6.72 in.
long from the axis to the center of the cups. To the ob-
served velocity the correction Log. V = 0.509 + 0.912
Log. v is applied in which V is the actual velocity of the
wind and v is the linear velocity of the cup centers, both
expressed in miles per hour.

EFFECT OF VABIATIONS WITHIN THE WIND
Measurements of either wind velocity or wind pressure
are complicated enormously by the variations in the wind.
This is illustrated by two observed facts, both of which
are vitally important to the structural engineer :

1. Wind pressures are less per unit of area for large
surfaces than for small ones. On the Forth Bridge two
pressure boards were set up, one 20 ft. long by 15 ft.
high, and 8 ft. from it a circular plate of 1% sq.ft. area.
The maximum pressure registered on the small plate dur-
ing the years 1884 to 1890 was 41 Ib. per sq.ft. The large
board showed at the same time a pressure of 27 Ib. per
sq.ft. The readings for the large board never exceeded
80% of those recorded for the small plate at the same
time, and generally were 50 to 70%. A technical journal
of the time hastily drew the inference from these experi-
ments that pressure per square foot varies inversely as
area, the velocity remaining the same — another illus-
tration of generalizing from insufficient data !

2. Wind velocity increases with the distance from the
ground. Thomas Stephenson from his experiments writes
the equation

or

[11]

A limiting unit of height must be established for this
equation to be of any use. An anemometer placed at the
top of the Eiffel Tower, an elevation of 994 ft., and
another in the meteorological office at an elevation of 69
ft., showed for light winds velocities nearly four times
as great at the top of the tower as at the office. For
higher winds the velocities came nearer together.

CONCLUSION

Cavallo, previously quoted, wrote, "a great many more
experiments must be instituted by scientific persons be-
fore the subject can be sufficiently elucidated." More than
a hundred years after Cavallo's writing, the U. S.
Weather Bureau in its monograph on Anemometry,
after giving values for pressures and velocities with all
the refinements at its command, says :

Great dependence cannot be placed in these values for
indicated velocities beyond 50 or 60 miles per hour, as thus
far direct experiments have not been made at the higher
velocities, though it is probable the corrected values are
throughout much more accurate than values computed from
older formulas and uncorrected wind velocities.

Structures have long been designed with satisfactory
results to withstand wind pressure. The bracing at times
may have been excessive, but in the absence of better
knowledge on the subject, engineers cannot radically de-
part from present practice.

II

Wind Stresses in Steel Mill-
Buildings

SYNOPSIS — Discusses the distribution of wind
pressure on a sloping roof, referring to the experi-
ments of Irminger, Kernot, Stanton, Smith and
others. Analyses of stresses in Fink roof trusses
show that a uniform vertical excess load is suffi-
cient to take care of wind stresses if rigid mem-
bers are used. In kneebraced mill-building bents,
wind corrections are necessary. Suction effects
are to be neglected except as regards anchorage.
Recommends wind pressures and unit stresses, and
discusses special bracing.

In designing ordinary mill-buildings it is common
practice either (1) to neglect the wind stresses or (2) to
calculate them in accordance with some textbook method
and then tone down the results. In doing the latter, the
general practice of designing buildings is followed, in
conformity to which structures have been built that have
rendered excellent service for many years. To bridge the
gap between theory and practice, recourse is being had
by some to what might be called a new school, which has
advanced new methods and new experimental results. In
the present article this school will be briefly reviewed, its
conclusions negatived, and textbook assumptions made
to agree as near as possible with actual conditions — the
object being to present a safe, sane, workable method of
determining and making provision for the wind stresses
in steel mill-buildings.

AMOUNT AND DISTRIBUTION OF WIND STRESSES
A recent writer1 of the new school states the case thus :

In a high wind the maximum pressure against the roof
is at the windward eaves. The pressure decreases upward
on the windward slope, and is zero, it is claimed, at a point

^'Insurance Engineering," August, 1912.

[ 13 ]

three-fourths the distance to the ridge. Beyond the zero
point, up to the ridge and down the leeward slope, the pres-
sure is negative. The wind deflected upward by the wind-
ward surface of the roof rarefies the air over the leeward
surface, which allows the air inside the building to exert an
upward pressure in excess of the downward pressure on the
roof. In other words, there is direct or inward pressure on
the windward slope of the roof, center of pressure below
middle of slope, and at ridge and on all of leeward slope,
there is outward pressure or suction.

SUCTION ON EOOF

In 1894, J. 0. V. Irminger, manager of the Copen-
hagen Gas Works, made a number of experiments on wind
pressure, the description and results of which he em-
bodied in a paper2 to which reference is often made. A
rectangular opening about 6%xll in. was made in a
chimney 5 ft. in diameter and 100 ft. high. Into this
opening was inserted a conduit 4%x9 in., polished on
the inside to reduce friction. Currents of air were made
to strike plates and models placed in this conduit and the
resultant pressure registered. A model of a pitched roof
with 45° slopes showed a normal uplift on the leeward
side due to suction three times as great as the normal
pressure on the windward side. The conclusion drawn
was "if the author's experiments on models represent the
facts with regard to buildings, the methods with which
roof principals are commonly calculated for wind-pres-
sure need revision." An enthusiastic admirer of Irminger
writes,3 "It will be due to him that we surely in the
future shall save tons of material in our roofs."

In 1891-94, Prof. W. C. Kernot, of the University of
Melbourne, made the experiments connected with his
name.4 By means of a gas engine and propeller, he dis-
charged a jet of air 12 in. by 10 in., placing into this jet
the plates and models he wished to test. He concluded
that the usual method of calculating wind stresses in
roofs applied only to roofs supported by columns under
which the air could blow freely. With roofs of a low

2"Engineering News," Feb. 14, 1895; "Engineering," Dec.
7, 1895; Proc. Inst. Civ. Engrs., Vol. CXVIII, p. 468.

•Theodore Nielsen, "Engineering," Oct. 9, 1903.

*"Engineering Record," Feb. 10, 1894; Proc. Inst. Civ.
Engrs., Vol. CLXXI, p. 218; Australian Association for the
Advancement of Science, Vol. V (1893), p. 573, Vol. VI (1895),
p. 741.

[14]

pitch resting on walls having parapets, he found a tend-
ency to an uplift.

In 1893 and later, T. E. Stanton, of the National Phys-
ical Laboratory, England, made the experiments which
have become widely known from the papers he contrib-
uted to the Institution of Civil Engineers.5 From ob-
servations on models of roofs the sides of which were 3
in. by 1 in. and sloped at 30°, 45° and 60°, placed in a
current of air having velocities of 10.0, 13.6 and 16.8
miles per hour, he writes, "The experiments appear to
indicate beyond question the importance of a consider-
ation of a negative pressure on the leeward side of roofs/'
From later experiments on pressure boards 5x5 ft. to
10x10 ft., he found the coefficients of wind pressure to be
as follows :

STANTON'S COEFFICIENTS k IN FORMULA Pn = kV2

(a) Roof mounted on columns through which air can pass

60° 45° 30°

Windward side +0.0034 +0.0028 +0.0015
Leeward side negligible

(b) Roofs of buildings in which the pressure on the interior

may be affected by the wind.

60° 45° 30°

Windward side +0.0034 +0.0028 +0.0015

Leeward side —0.0032 — —0.0022

This coefficient gives the normal pressure on roof sur-
face in Ib. per sq.ft., if V is the wind velocity in miles
per hour, the wind blowing horizontal.

Prof. Albert Smith in a paper read before the West-
ern Society of Engineers, November, 1910, entitled
<rVVind Loads on Mill Building Bents,"6 among his con-
clusions advocates "placing the wind loads equally on the
two walls, and inward and outward on the windward and
leeward roofs respectively, as giving important changes
of stress in members of the roof truss, as giving less stress
in the kneebraces and columns, and as permitting the
rational design of the girts." In 1912, he made a num-
ber of observations on a model building 6 ft. wide by
15 ft. long, with wall heights of 4, 5 and 6 ft. In a
paper "Wind Pressure on Buildings,"7 he writes:

•Proc. Inst. Civ. Engrs., Vol. CL.VI, p. 78, Vol. CLXXI, p. 175.
'Journal Western Soc. Engrs., February, 1911.
Mournal Western Soc. Engrs., December, 1912.

[ 15 ]

The ordinary methods of assuming wind loads on mill
buildings ought to be somewhat revised. For the case of roof
trusses on masonry walls, or on steel bents with long diag-
onals, a suction effect in the neighborhood of 0.4 of the unit
wind pressure should be placed on the leeward roof of all
closed buildings, and a pressure or suction derived from the
curves drawn from the observations placed on the windward
roof. The resulting stresses will not only be different in
amount from those computed on the present basis, but will
in many members differ as to sign. Wind loads on purlins
might in most cases be entirely omitted. * * * * In
buildings with kneebraced bents, in addition to the preceding
points, the suctions on the leeward wall should be considered.

Prof. Boardman, University of Nevada, in 1911 made
experiments on a model roof 10 ft. long, each slope 6 ft.
wide, resting on walls 4 ft. high. His conclusions are
similar to those of Prof. Smith.8

An English textbook, Brightmore's Structural Engi-
neering, first issued in 1908, quotes the Stanton experi-
ments as authority and the stress diagrams for the roof
truss given are made with the wind forces so acting. The
heading of the section is significant: "Stresses Due to
Wind Pressure and Wind Suction."

Another English textbook, Andrews' The Theory and
Design of Structures, in an appendix to the last edition,
1913, calls attention to Stanton's conclusions and gives
a stress diagram for a truss with the wind loading in ac-
cordance with these conclusions. In mentioning the
stresses due to suction on the leeward side the author
writes, "Few designers appear to have allowed for this
in their calculations for roofs, but the question is of con-
siderable importance and the results of these experiments
should either be disproved, or allowance should be made
for them in design."

Marburg in Framed Structures and Girders alludes to
the experiments of Kernot, Irminger and Stanton and
reproduces one of the Irminger sketches. His practical
conclusion is:

The experiments of Kernot, Irminger and Stanton were
made on much too small a scale to admit of quantitative de-
ductions applicable to conditions in practice. They are val-
uably suggestive, however, in calling attention to conditions
which were previously not generally or adequately recognized.

With this conclusion the writer is in thorough accord.

8Journal Western Soc. Engrs., April, 1912.

[ 16 ]

SELECTING A WIND PKESSUEE FOE DESIGN

Our knowledge of wind pressures is very imperfect. It
is generally agreed that the fundamental equation P =
kV2 is correct for horizontal wind. There is little dispute
that for wind with a uniform velocity and normal to
plates of moderate size, the value of k is from 0.0032 to
0.004. Of the formulas for wind pressure on inclined
surfaces our best knowledge indicates that of Duchemin
as the most accurate. It is

2 sin A
I + sin* A

There remains to be assigned a value to V. Average
wind velocities for a day or a month or a year are use-
less. Shall the highest wind velocity on record be taken?
Is this likely to occur again?

It is useless to attempt to make provision for torna-
does or violent hurricanes "against which neither care,
nor strength, nor wisdom, can avail."* Such storms are
limited in area and come but seldom, perhaps once in a
century. The endeavor to make a mill-building strong
enough to resist them would not only add greatly to the
cost but would be ineffective, f

The highest wind velocity recorded in New York City
since 1871 by the U. S. Weather Bureau was 96 miles
per hour sustained for a period of five minutes. During
one minute of that time the velocity was 120 miles per
hour. This was in Feb. 22, 1912, a Robinson anemom-
eter being used in the same location as at present, about
20 ft. above the roof of the 33-story building at 17 Bat-
tery Place. A recorded velocity of 80 to 90 miles is not
uncommon. A recorded velocity of 90 miles per hour
corrected by the Weather Bureau formula gives an actual
velocity of 69.2 miles per hour. With this value in the
formula P = kV2, k = 0.004, the normal pressure is
19.2 Ib. per square foot on a vertical surface. Wind pres-

*This is the way it is stated in the Foreword of a little
volume issued by the Home Insurance Co., of New York, advo-
cating windstorm and tornado insurance. More than a
hundred photographs in this volume of wrecks caused by
windstorms illustrate the truth of the Foreword.

fEditor's Note — This argument in its terms applies Just as
much to office buildings and all other structures as it does to
mill buildings. The author probably means to emphasize the
cost limitation, for mill-buildings alone.

[17]

sure increases with the distance from the ground and
decreases per square foot as the area becomes larger.
When it is remembered that the instrument above men-
tioned is about 400 ft. from the ground and the cups
are only 4 in. in diameter, the assumptions that will be
made of a horizontal wind force of 20 Ib. per sq.ft. in de-
signing the trusses of mill-buildings, and 15 Ib. in de-
signing columns and kneebraces, seem to be ample and
fully warranted.

WIND STRESSES IN KOOF TRUSSES

Eoof trusses resting on brick walls will first be con-
sidered. The example taken will be a roof truss as in
Fig. 1, with pitch of 6 in. to 1 ft., and span of 60 ft.
c. to c. of bearing plates. Trusses are 16 ft. apart on cen-
ters. For a horizontal wind from the left, with pressure
of 20 Ib. per sq.ft. on a vertical surface, the normal pres-
sure on a surface inclined 6 in. to 1 ft. will be (by Du-
chemin's formula) 14.9 Ib. per sq.ft.

The following cases will be considered:

(1) Wind load of 15 Ib. per sq.ft. or 2012 Ib. per
panel, normal to one slope of roof, both ends of truss
fixed.

(2) Loads as in (1), left end fixed, right end on
rollers.

(3) Loads as in (1), left end rollers, right end fixed.

(4) Load of 15 Ib. per sq.ft. exposed surface or 2012
Ib. per panel on both sides of the roof, the loads ap-
plied vertically.

The stresses for these four cases are tabulated below :

It is seen at a glance that Case 4 is sufficient to cover

wind stresses. The slight excess in a few members found

in the other cases is negligible, especially when they are

considered with the combined stresses due to all loads.

With the same wind velocity as before, according to
Stanton, the pressure on the windward slope is about
n/2 Ib. per sq.ft. and 22/15 times 7^ or 11 Ib. per square
foot negative pressure or suction on the leeward side.
The forces acting upon the truss are as in Fig. 2 (reac-
tions are for both ends fixed, wind shear equally divided),
while Fig. 3 is the stress diagram for both ends fixed.

[18]

The tabulation of stresses given below is for

(5) Both ends of truss fixed.

(6) Left end fixed, right end on rollers.

(7) Left end rollers, right end fixed.

It might be stated here that all the above cases with
one end on rollers are hypothetical, as roof trusses under
100-ft. span are seldom built with other than fixed ends.*

EECOMMENDED DESIGN LOAD — Maximum wind load-
ing comes seldom and lasts but a short time. The work-
ing stresses used for this loading may therefore be in-
creased 50% above those used for ordinary live- and
dead-loads. A wind load of 15 Ib. per sq.ft. is thus equiv-
alent to a load of 10 Ib. using the working stresses for
other loads.

The snow load varies from 20 Ib. per sq.ft. horizontal
projection in the latitude of New York City to 30 Ib. in
parts of New England. This is equivalent to 16.6 up to
25 Ib. vertical load per sq.ft. surface of a 6-in. pitch
roof.

For combined snow and wind a load of 25 Ib. per sq.ft.
over entire surface, acting vertically, is ample for roofs
in the latitude of New York City. If to this is added the
weight of trusses, purlins, and roof covering, reduced to
square foot of exposed surface, we have the total load
for which the ordinary roof truss should be designed.
However, not less than 40 Ib. should be used except in
tropical climates with no snow, where the minimum load-
ing should be 30 Ib. Where snows are severe 5 to 10 Ib.
should be added to the 40 Ib.

No ALLOWANCE FOR SUCTION — Turning to the tabu-
lation of stresses found by the Stanton assumptions, and
taking into account the total stresses from all loads, the
saving due to reduced wind stresses is small. A serious
objection to taking advantage of even this saving is that
with a monitor along the ridge, or openings in the build-
ing and roof, the closed roof may become a partly open
roof, thus changing the conditions for which the assump-

*Editor's Note — The wind shear may, however, come wholly
on one or the other wall, due to unequal bedding of the
anchor bolts or to temperature movement. The condition
then, as regards the present calculation, is identical with one
end on rollers.

[ 19 ]

tions were made. For a truss resting on brick walls the
tendency to an uplift can be met by firmly anchoring it
at the ends. The tendency to reversals of stress can be
sufficiently met by using stiff shapes for all members;
flats and rounds have no place in an ordinary roof truss.
The writer believes that the assumption of a total uni-
form load per square foot of exposed surface applied ver-
tically at the panel points, with the same working stresses
used throughout, is specially well adapted to the design
of roof trusses.

WIND STRESSES IN KNEEBRACED BENTS

KNEEBRACED BENTS — The case of an intermediate
transverse bent of a kneebraced mill-building will now
be considered. The example taken will be that shown in
Fig. 4; span 60 ft., roof pitch 6 in. to 1 ft, height 14 ft.
to foot of kneebrace and 20 ft. to bottom chord. Trusses
are 16 ft. apart c. to c.

The wind pressure will be taken at 15 Ib. per sq.ft.
perpendicular to the sides of the building and the cor-
responding normal component on the roof at 11.2 Ib.
(For buildings over 25 ft. to the eave line the normal
component of a wind load of 20 Ib., or 14.9 Ib., would
be used for the roof.) The columns are assumed par-
tially fixed at the lower end, with the point of contraflex-
ure at one-third the distance between the lower end and
the foot of the kneebrace; the upper ends are considered
supported. The wind shear is divided equally between
the two columns. Fig. 5 is the stress diagram.

Bending moments in the columns are as follows :

At the foot of windward column 12,320 ft.-lb.

At foot of leeward column 14,940 ft.-lb.

At foot of windward kneebrace 19,410 ft.-lb.

At foot of leeward kneebrace 29,870 ft.-lb.

It is seen that the maximum bending moment is at the
foot of the leeward kneebrace.

RECOMMENDED METHOD — For mill-building bents the
writer first determines the stresses in the truss due to a
total uniform load and then proportions it for the same.
The ordinary working values for medium steel are gen-

[ 20 ]

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[21]

erally used — 16,000 Ib. per sq.in. in net tension and (re-
duced by formula) for gross compression. If the wind
stresses in any member from Figs. 4 and 5 are greater
than the wind stresses from the uniform wind loading of
10 Ib. per sq.ft. applied vertically, that member is pro-
portioned for the maximum wind stress plus the stresses
from the uniform loads other than wind, using working
stresses 50% more than in the first calculation; but in
no case is a less section used than that first obtained. The

v^

FIGS. 4 AND 5. KNEEBRACED BENT or A MILL-BUILDING ;
STRESS DIAGRAM FOR WIND LOAD

(Equal shears; contraflexure one-third height to kneebrace)

members be and fr^ will generally need be increased;
often cd and c^; occasionally gd, gf, gf± and g^. A
reversal of stresses is noted in certain members, particu-
larly in ~bc and the lower chord. The diagonals "be and
biC^ can be made of two angles instead of one as wher*
designed for tension alone. The compressive stresses in
the lower chord are overcome by the tensile stresses due

[ 22 ]

to the dead-load. The kneebraces have wind stresses only,
end are proportioned for the larger working stresses.

The column is first proportioned for carrying the di-
rect stress due to the total uniform load from the truss,
noting the flange area required. From the maximum
bending moment due to the wind, as in Fig. 4 and 5, the
sectional area required for the flanges is found using the
larger working stresses and considering the column as
a beam. If this flange area is not more than one-third
of that first found no change is made; if more than one-
third, the excess is added. The compressive stress due
to overturning need not be considered unless it exceeds the
stress from the wind portion of the uniform roof load.

GIKTS — The side and end girts are proportioned as
beams supported at each end with a uniform horizontal
load of 15 Ib. per sq.ft.; an extreme fiber stress of 24,000
Ib. per sq.in. is used.

The girts are apparently the simplest portion of the
building to design, but if observation and experience
count they are the most difficult. Side and end girts of
3%x2%x}4-iii. or ^-in. angles, 16 to 20 ft. long and
5 ft. apart, are still in use after 20 years' service, in de-
fiance of all figures. Notwithstanding this, such design-
ing practice is reprehensible.

SPECIAL CASES OF MILL-BUILDING BRACING

Traveling cranes running through a building often bar
the use of kneebraces. The gussets connecting the trusses
to the columns should then be as large as possible and
calculations made accordingly. An ideal way is to trans-
fer the transverse thrust from the wind as well as that
from the cranes to the ends of the building by means of
diagonal bracing in the plane of the lower chords of the
trusses, and thence by diagonals in the ends of the build-
ing to the ground. Openings in the ends often interfere
with this expedient. Neither is it feasible in buildings
so long as to require provision for longitudinal expan-
sion and contraction due to changes in temperature.

In all cases diagonal bracing should be introduced into
the planes of both top and bottom chords for stiffness as
well as to take calculated stresses. This applies also to

[ 23 ]

roof trusses resting on brick walls. Adjustable rods can
be used for top-chord bracing, but the bracing of the
bottom chord should be entirely of angles or other rigid
shapes, with bolted or riveted connections.

The ends of a building, the gables in particular, are
more liable to be severely strained from wind than any
other portion of the building. Generally diagonals in
the planes of the chords of each end panel, and in each
end side bay to the ground will be sufficient to take care
of the induced stresses. If not, the shear may be divided
with other braced bays.

Special types of buildings should be considered in ref-
erence to their own requirements. Open sheds, especially
if the gables are closed, may have an uplift as well as a
vertical load.

COMMENTS ON PRIOR KECOMMENDATIONS

The leading textbook on the subject of mill building!,
is Ketchum's Steel Mill-Buildings. In this book a knee-
braced mill bent is considered for four cases:

(1) A horizontal wind load of 20 Ib. per sq.ft. on the
side and vertical projection of the roof, with the columns
Mnged at the base.

(2) Same wind load as in Case 1, with columns fixed
at the base.

(3) A horizontal wind load of 20 Ib. per sq.ft. on the
side, and the normal component of a horizontal wind load!
cf 30 Ib. per sq.ft. on the roof, with columns hinged at
the base.

(4) Same wind load as in Case 3, with columns fixed
at the base.

The writer believes that the loads of 20 and 30 Ib. are
larger than need be used. The columns are seldom if
ever rigidly fixed at the base, neither are they hinged.
That they are partially fixed and the point of contra-
iiexure is at one-third the distance from base to foot of
kneebrace is believed to be nearer correct than either as-
suming it one-half the distance or assuming the columns
supported at the base. There seems no good reason for
assuming a normal component of a horizontal wind load
of 30 Ib. on the roof while a horizontal wind load of 20

t 24]

Ib. is taken on the sides. It is not clear why the Hut-
ton formula is used to find the normal component. Near
the beginning of the book we read, "Button's formula is
based on experiments which were very crude and probably
erroneous. Duchemin's formula is based on very care-
ful experiments and is now considered the most reliable
formula in use." The specifications near the close of the
book call for the Duchemin formula to be used in com-
puting the normal wind pressure; by this formula, for a
30-lb. load, the 18-lb. normal pressure in Cases 3 and
4 would be 22 A Ib. The only increase of the usual work-
ing stresses allowed is 25% for laterals and 50% for
combined direct and flexural stress due to wind. This in-
crease does not apply to the combination of wind with
other loads though with the maximum wind load a min-
imum snow load of 10 Ib. per sq.ft. is allowed. (For
the purpose of aiding those who wish to make compari-
sons the same roof truss and bent have been taken in
this article as found in Ketchum.)

The chapter on "Iron and Steel Mill-Building Con-
struction" by G. H. Hutchinson in Johnson, Bryan &
Turneaure's Modern Framed Structures, considers three
cases of a mill-building bent, arriving at conclusions sim-
ilar to those of Ketchum. The method of obtaining re-
actions and moments is quite abstruse and difficult to
follow. No mention is made in the chapter of working
stresses to be used.

Smith, in "Wind Loads on Mill-Building Bents,"6 as-
sumes a total horizontal wind force of 30 Ib. per sq.ft.
on the bent considered in this article. The pressure on
the sides is divided equally between the two columns.
One-third of the normal component of the total pressure
on the roof, found by Duchemin's formula, is taken by
the windward slope and two-thirds as suction or an out-
ward pressure on the leeward slope. The bases of the
columns are considered hinged. Comparing his results
with those obtained by Ketchum, he shows reduced
stresses but is unfortunate in the example selected for
comparison: Ketchum's stresses are taken and 50% is
added to them for a 30-lb. load; but Ketchum calculate?
his roof for the normal component of a horizontal wind

[ 25 ]

of 30 Ib. and the side for 20 lb., so that Smith is actually
comparing his results with those obtained from a bent
having a pressure on the sides of 30 lb. per sq.ft. and
on the roof the normal component (by the Hutton for-
mula) of a horizontal force of 45 lb. per sq.ft.

However, with the same wind force, the Smith method
does give reduced stresses, especially in the columns,
kneebraces and girts. The important point is whether
these reductions are permissible. In a modern mill-build-
ing the sides are from one-fourth to one-half or more of
glass, a large proportion of which can be opened to permit
of ventilation. If opened on one side only, Smith's as-
sumption that the pressure on the inside of a mill-build-
ing is a mean between the windward pressure and the lee-
ward suction disappears. In a high wind the windows on
the leeward side are liable to be open and those on the
windward side closed; there is then little suction. In a
building the sides of which are covered with sheet metal
there is always a probability of the covering on one side or
end being removed for 8 ft. or more from the ground,
thus completely doing away with the suction theory. For
these reasons it is unwise to take advantage of a theory
based upon assumptions which are destroyed by a prob-
able change of conditions.

In conclusion, while the methods advocated for treat-
ing wind stresses may not be thoroughly scientific, they
are easily workable, and experience proves that they art
safe and sane. The load of 15 lb., the working stress of
24,000 lb., and the assumed point of contraflexure, may
all be criticized, but for the ordinary mill-building it is
more rational to use these assumptions and make strict
provision for them than to follow the present method of
giving an intellectual assent to the theories of the text-
book and ignoring them in actual practice.

Ill

Wind Stresses in Railroad
Bridges

SYNOPSIS— The Tay Bridge failure reviewed.
English practice in the 70's ignored wind stresses,
while American engineers used methods nearly
equal to those of today. Empirical development
is the basis of practice. Modern specifications
show a great number of variations in detail, but
may be brought nearer uniformity in the future.
Lateral-oscillation forces should be specified sepa-
rate from wind pressure.

The purpose of this article is to review past and pres-
ent practice of the treatment of the wind forces acting on
railroad bridges.

THE TAY BKIDGE

On the evening of Dec. 28, 1879, occurred the "Tay
Bridge Disaster." During a violent gale, 11 spans of
245 ft. and two of 227 ft., with the train passing over
them at the time, fell into the river. This failure of what
was at the time the largest bridge in the world after a
service of less than two years marked an epoch in bridge
building in Great Britain. "Wind stresses in railroad
bridges had previously been almost neglected; from that
time they have been fully considered, if not magnified. A
Court of Inquiry was appointed by the English Board of
Trade to report on the causes of the disaster. Today the
testimony taken regarding the provision made in the de-
sign of the bridge for wind stresses is interesting reading.

Sir George Airy, Astronomer Eoyal, testified that about
seven years previously he had been consulted on the sub-
ject of the provision which should be made for wind pres-
sure on the plans prepared by Sir Thomas Bouch of a
bridge of two spans of 1600 ft. over the Forth. He gave
as his opinion that the greatest wind pressure that might
be expected over the whole extent of such a surface was
10 Ib. per sq.ft.

[27]

Sir Thomas Bouch, the designer of the Tay bridge, tes-
tified that he did not specially make any allowance for
wind pressure, but he had seen the report on the Forth
Bridge; he thought the greatest pressure would be about
10 Ib.

The majority report of the Court of Inquiry ends :

In conclusion, we have to state that there is no require-
ment issued by the Board of Trade respecting wind pressure,
and there does not appear to be any understood rule in the
engineering profession regarding wind pressure in railway
structures; and we therefore recommend that the Board of
Trade should take such steps as may be necessary for the
establishment of rules for that purpose.

A minority report was submitted by the third member
of the Court. f An extract is:

It is said that Sir Thomas Bouch must be judged by the
state of our knowledge of wind pressure when he designed
and built the bridge. Be it so; yet he knew or might have
known that at that time the engineers in France made an
allowance of 55 Ib. per sq.ft. for wind pressure, and in the
United States an allowance of 50 Ib.

In the engineering literature of 1880 and 1881, a
paper often referred to is "The Tay Bridge," by Edgar
Gilkes, a member of the firm building the bridge. It
was read before the Cleveland Institution of Engineers,
Nov. 6, 1876. The special paragraph that must have
plagued the author reads:

A consideration of the action of the wind on this bridge
will dissipate the often-advanced theory that at some period
it will be blown over. The exposed surface of one large pier
is about 800 sq.ft., and of the superstructure which depends
upon it, about 800 more, and so, giving 800 ft. for a train

tThe majority of the Court of Inquiry reported that in
their opinion the cross bracing at the pier and its fastening
by lugs was the first part to yield. The evidence, however,
was ample to justify the language of the minority report,
"that this bridge was badly designed, badly constructed, and
badly maintained, and that its downfall was due to inherent
defects in the structure which must sooner or later have
brought it down."

The piers which failed carried two adjoining trusses and
consisted of a hexagonal group of six cast-iron columns
filled with Portland cement, two 18 in. and four 15 in. in
diameter. Each column in case of the higher columns was
made of seven lengths 10 ft. 10 in. long, united by flanges.
These columns were braced vertically on the exterior sides
by struts of two 6-in. channels and diagonals of 4%x%-in.
flats fastened to cast-iron lugs with 1%-in. bolts. Horizontal
bracing connected the four interior columns. It will readily
be seen that such a system is weak throughout.

As a matter of interest it may be noted that during the
progress of construction on the night of Feb. 2, 1877, two of
the 245-ft. spans were blown into the river. To this accident
"Engineering" of Feb. 9, 1877, devoted just 14 lines.

above, we have 2400 ft. Twenty-one pounds per sq.ft. is
the force of a very strong gale, but it would take no less
than 96 Ib. per sq.ft. on the surface given to overturn the pier.
Even the most severe hurricane on record would equal only
one-half this resultant power.

C. Shaler Smith, after a careful calculation in accord-
ance with American rules, found the exposed surface of
the superstructure to be 2576 sq.ft. instead of 800, while
the London Engineering shows the exposed train surface
was 1630 sq.ft. instead of 800.

EAKLY ENGLISH PRACTICE

It is surprising how little is found in the English
technical books and papers of those days regarding the
force of the wind on structures. Humber, in his volum-
inous "Complete Treatise on Cast- and Wrought-Iron
Bridge Construction," published in 1861, does not mention
it. TJnwin's "Wrought-Iron Bridges and Roofs," 1869,
was a far better textbook than any that had preceded it.
What he writes regarding wind pressure on roofs is still
quoted; yet he says nothing of wind stresses in bridges.
The article on Bridges, by Prof. Jenkin, in the ninth
edition of the "Encyclopedia Britannica" (1876), after-
ward issued as a separate treatise, fills 58 closely written
pages, but not a line is found concerning wind bracing.
Thomas Cargill, in his "The Strains upon Bridge Gird-
ers and Eoof Trusses," 1873, writes :

No allowance is made in the theoretical calculation for the
violent shock, concussion and consequent vibration that attend
the passage of a heavy train over a bridge. This must be
allowed for by experience, by the introduction of such addi-
tional bracing as the skill of the engineer suggests. These
are points which cannot be learned from books.

To the effect of the wind on a bridge he makes no al-
lusion, though in the chapter "Curved Roof Trusses," he
says:

Some writers lay great stress upon providing a large
margin of strength for wind pressure, but there is more
theoretical than practical knowledge displayed in such state-
ments.

Rankine, in his "Manual of Civil Engineering," in the
early 60's, gives a formula for the effect of wind on tubular
girders, and in a footnote states that the greatest pres-
sure of wind ever observed in Britain was 55 Ib. per sq.ft.,

[29]

but we have no record that this observation ever entered
into the consideration of bridge engineers.

The first German edition of Hitter's "Elementary The-
ory and Calculation of Iron Bridges and Roofs," was is-
sued in 1862. An English translation was published in
1879. In this book the lateral force is taken as a per-
centage of the combined vertical live- and dead-loads. In
one particular bridge under consideration, it is assumed
to be one-seventh.

The outcome of the agitation following the fall of the
Tay Bridge was a commission appointed by the Board
of Trade to consider the question of wind pressure on rail-
way structures. This committee made its report in 1881.
The substance of its five recommendations was: (1)
That for railway bridges and viaducts a maximum wind
pressure of 56 Ib. per sq.ft. should be assumed for the
purpose of calculation. (2) That the area of exposed sur-
face should be taken at once to twice the front surface,
according to the extent of the openings in the trusses or
lattice-girders. (3) That a factor of safety of 4 should
be used for strains caused by wind pressure, and for the
whole structure overturning as a mass a factor of safety
of 2 should be used. These recommendations became law
in Great Britain.

EARLY AMERICAN PRACTICE

Not less interesting is the historical development of
wind bracing in the United States. In 1851 was pub-
lished, "General Theory of Bridge Construction," by
Herman Haupt, A.M., General Superintendent of the
Pennsylvania R.R., formerly professor of Mathematics
in Pennsylvania College. The pioneer book in which
bridge trusses are correctly analyzed is "A Work on
Bridge Building," by Squire Whipple, published at Utica,
N. Y., in 1847. Whipple's book was little known for a
ong time after its publication, while Haupt's book, written
without any knowledge of the existence of Whipple's, soon
became widely circulated and for years was regarded as
an authority. In Part 1 of Haupt's book we read :

The use of lateral bracing is principally to guard against
the effects of wind, and other disturbing causes, tending to
produce lateral nexure in the roadway * * * The greatest

[30]

lateral strain is that produced by the action of a high wind;
assuming the force of wind at 15 Ib. per sq.ft., as a
maximum, * * *

In Part II, written some time after Part I, we read,
"The heaviest locomotives in use weigh about 23 tons,
and their length is 23 ft.," and further on :

The greatest strain upon the lateral bracing of a bridge
would be that caused by the action of the wind in a violent
tornado. It is probable that this force is far greater than
it is usually estimated. The observations of the writer at
the Susquehanna Bridge, during the tornado which caused
the loss of six of the unfinished spans, led him to believe that
the direct effect of the storm was increased by reflection from
the surface of the water. * * * If we suppose a storm
could be so violent as to cause a pressure of 30 Ib. per
sq.ft., * * *

The tornado alluded to occurred Mar. 27, 1849. A
viaduct across the Susquehanna River, near Harrisburg,
was being built for the Pennsylvania R.R. It was sup-
ported on 22 piers, 160 ft. center to center. The trusses
were of the Howe type, with the addition of wooden
arches. After the fourteenth span had been raised, the
storm came and carried off six spans. The contractor was
busy at the time putting in the arches, and as the diagonal
braces could not be fastened until after the arches were
in place, they had been omitted except over the piers and
in the middle of the spans. The wind came at right angles
to the bridge and the six spans without lateral bracing
gave way.

As late as the early 70's American textbooks had little
or nothing to say on wind bracing. De Yolson Wood de-
votes less than one-half a page to the subject in his
"Theory on the Construction of Bridges," while Greene
in "Bridge Trusses" spares only a page. Col. Merrill, in
his "Iron-Truss Bridges for Railroads," makes no men-
tion of wind bracing. Shreve, whose "Treatise on the
Strength of Bridges and Roofs" was translated into
French, finds vertical strains, horizontal strains, chord
strains, brace strains, but the word wind does not occur in
the book, nor is any mention made of bracing in a hori-
zontal plane. Nearly the same might be written of Roeb-
ling's "Long and Short Span Railway Bridges/' 1869.

American practice, however, was ahead of the teaching
profession. C. Shaler Smith, on Dec. 15, 1880, presented

[31 ]

a masterly paper to the American Society of Civil Engi-
neers, entitled, "Wind Pressure upon Bridges." He
gives specifications which he had used in constructing a
number of bridges, some of them high and in exposed lo-
calities. He specifies :

The portal, vertical and horizontal bracing shall be pro-
portioned for a wind pressure of 30 Ib. per sq.ft. on the
surface of a train averaging- 10 sq.ft. per lin.ft., and on
twice the vertical surface of one truss. The 300 Ib. pressure
per lin.ft. due to the train surface shall be treated as a mov-
ing load, and the pressure on the trusses as a fixed load.
Trusses of less than 200 ft. span shall also be proportioned
for a pressure of 50 Ib. per sq.ft. where unloaded, and the
greatest strain by either method of computation shall in
each case be used in determining the sectional area of the
bracing.

Several leading railway companies at that time were us-
ing practically these specifications. From this same paper
the following is significant :

Many engineers prefer to express wind force in pounds
per lineal foot of bridge instead of per square foot of exposed
surface. Using a 200-ft. span as an example, the specifications
in question can be condensed as follows:

Fixed load in plane of roadway, 210 Ib. per lin.ft.

Fixed load in plane of other chord, 130 Ib. per lin.ft.

Moving load in plane of roadway, 300 Ib. per lin.ft.

It is refreshing to see C. Shaler Smith quoted as the
exponent of American practice for wind bracing in the
article on Bridges, by Unwin, in the eleventh edition of
the "Encyclopedia Britannica."

The rules in the Erie Specifications, formulated in
1878 by Theodore Cooper, were:

To provide for wind strains and vibrations, the top lateral
bracing in deck bridges and the bottom lateral bracing in
through bridges shall be proportioned to resist a lateral force
of 450 Ib. for each foot of the span, 300 Ib. of this to be
treated as a moving load.

The bottom lateral bracing in deck bridges and the top
lateral bracing in through bridges shall be proportioned to
resist a lateral force of 150 Ib. for each foot of the span.

It is thus seen that in the early days of iron railway
bridges, the American engineers were far in advance of
their English brethren in the recognition of wind forces.

FACTORS IN THE PROBLEM

"A Practical Treatise on Bridge Construction/' by T.
Claxton Fidler, was published in London in 1887. Chap-

[ 32 ]

ter XXIV is "On Wind-Pressure and Wind-Bracing." In
1894, Captain (now General) Bixby, U. S. A., in a mono-
graph reviewing the literature on wind pressure, writes:
"The chapter is perhaps the best single, short, concise,
comprehensive and practical review of the whole sub-
ject yet in print." This characterization in a large
measure still holds true. Some concluding sentences from
the chapter are:

We have seen, for example, how large a proportion of the
metal in a long-span bridge is required for the purpose of
resisting wind-pressure and for the purpose of carrying the
metal that resists wind-pressure. But we have also seen
that it is really impossible to estimate the wind stresses
within 100% of their real value. * * * In this state of un-
certainty, the responsible engineer will generally be disposed
to err on the safe side; but it must be remarked that this
will be a very expensive proceeding. * * * On the other
hand, he knows that an error in the opposite direction might
be attended with still more disastrous results.

The sting of these sentences is in their truth. Our
knowledge of the wind is uncertain, especially regarding
the higher velocities. Although there are many unknown
quantities in the problem of wind stresses in a bridge,
the main questions to be considered are two :

(1) What is the pressure to be assumed per unit of
area?

(2) What shall be taken as the area exposed to the ac-
tion of the wind?

Wind pressure is generally measured in terms of the ve-
locity. According to the best information we have, an in-
dicated velocity by the ( Weather-Bureau standard) ane-
mometer of 100 miles per hour denotes an actual velocity
of 76 miles, which is equivalent to a pressure of 23 Ib.
per sq.ft. on a surface at right angles to its direction. A
pressure of 30 Ib. per sq.ft., which corresponds to an
indicated velocity of about 120 miles per hour, will over-
turn empty freight cars, the ordinary passenger car,
and acting over an extended area of land would sweep
from it all trees. No engine driver could take his train
upon a bridge with such a pressure, though it is possible
that the train during a sudden gust might be caught there.
A man could not keep his feet with such a pressure, no
matter at what angle his legs were inclined to the ground.

[33]

It would seem that 30 Ib. per sq.ft. is ample for assumed
wind pressure.

The second question to be considered is even more diffi-
cult to answer than the first. In a bridge composed of two
or more trusses several feet apart, and each truss made
up of members which may shelter other members, the case
is far different from that of wind on a plate or on a solid
body. Our actual knowledge of the subject is slight.
Baker's experiments at the Forth Bridge* and Stanton's
experiments at the National Physical Laboratory f are
generally quoted. Bridge engineers and writers on the
subject vary in their methods. C. Shaler Smith, as pre-
viously noted, uses an exposed area of "twice the vertical
surface of one truss." In estimating the vertical surface
of one truss he adds to the elevation of the upper chord
and posts, as seen on the drawing, 1% times the surface of
the ties, and twice the surface of the lower chord. J Du
Bois, in his "The Stresses in Framed Structures," gives
as a rule this method for finding the area of surface of a
single truss. "In preliminary estimates," he writes,
"we may take the exposed surface for both trusses at 10
sq.ft. per lin.ft."

Johnson, Bryan and Turneaure, in "The Theory and
Practice of Modern Framed Structures," use "the ex-
posed surface of all trusses and the floor as seen in ele-
vation." Merriman and Jacoby, in "A Text Book on
Eoofs and Bridges," Heller in "Stresses in Structures,"
and a number of other writers do the same. "Structural
Engineering," an English textbook by Husband and
Harby, says "The area of the bridge exposed to the higher
pressure will be from once to about three times the area
as seen in elevation, depending on the type of construc-
tion." Another English textbook, Anglin, "The Design
of Structures," says, "In double-webbed lattice girders, the
area of both webs should be taken, or double the web area
as seen in elevation, . . . . If a bridge consists of
two such main girders, the wind pressure must be taken
as acting on an area equal to four times that as seen in

* "Engineering-," Sept. 5, 1884.

f'Proc. of Inst. of C. E.," Vol. CLVI and Vol. CLXXI.
t"Trans. Am. Soc. C. E.," Vol X, pp. 170. (Private letter
to O. Chanute.)

[ 34]

elevation." This same textbook adds, "American engi-
neers assume a wind pressure of 30 Ib. per sq.ft. upon
the loaded, and 50 Ib. upon the unloaded structure."

From the foregoing it is readily seen that specifications
that simply give the load per square foot of exposed sur-
face to be used do not fully specify. Descriptions of
bridges which state the lateral pressure per square foot
used in the calculations without defining the extent of ex-
posed surface intended by the designer are incomplete
in their description.

It is to be remembered that there are stresses due to lat-
eral forces other than the wind. A considerable lateral
force is developed by a rapidly moving train, or the lurch-
ing of a locomotive when it first strikes a bridge. This
lateral vibration appears to be much more accidental in
its character than the vertical vibration.* Even were there
no wind, rigidity would have to be maintained against
this lateral vibration, which in short spans is probably a
greater factor than the wind pressure itself. We have
nothing to determine a relation between lateral vibration
and wind strain.

Further, the compression chords of bridges must be held
in alignment by the lateral bracing. The amount of ma-
terial required to do this is not, with our present knowl-
edge, a matter of exact calculation.!

In some specifications provision for all lateral forces,
except the centrifugal force when the track is on a curve,
is included in that for wind pressure without being so
stated. In others, "for lateral forces" or "for wind loads
and lateral vibration" are the words used and more clearly
express what is intended.

Giving the lateral force in terms of pounds per lineal
foot of bridge (rather than in pounds per square foot)
has a decided advantage in the preparation of designs for
competition, as all bidders are working upon the same
basis. Theoretically, for the wind itself the pressure
per square foot is to be preferred and the force that pro-
duces lateral vibration is best represented by a percentage

*Robinson, "Vibration of Bridges." Trans. Amer. Soc.
C. E., Vol. XVI, p. 42.

fReichman, "Journal of the Western Soc. of Eng's," Vol.
29, p. 93.

[ 35 ]

of the moving load. As engine weights and car loads are
increased, provision is thus made for the increased ten-
dency to vibration. Again, a different lateral force for
spans under 200 ft. from that for spans over 200 ft. is as-
sumed by some engineers.

While the wind pressure on a moving train should be
treated as a moving load, engineers are divided in their
opinions as to the wind load on the structure itself ; some
considering it uniform and some moving.

In regard to end anchorage, the following will be quoted
from Waddell's "De Pontibus" : "No matter how great
its weight may be, every ordinary fixed span should be
anchored effectively to its support at each bearing on
same." (Principle XXVI, in chapter "First Principles of
Designing.")

In passing, a criticism will be launched at the Eng-
lish bridges of "an early Victorian type,"* having an
arched portal strut at every post and no top laterals.
Some of these are of late date. All are wasteful in mater-
ial, and there is great ambiguity in regard to the lateral
stresses.

PRESENT SPECIFICATIONS

The specifications of the American Eailway Engineer-
ing Association, 1910, read :

All spans shall be designed for a lateral force on the loaded
chord of 200 Ib. per lin.ft. plus 10% of the specified train load
on one track, and 200 Ib. per lin.ft. on the unloaded chord;
these forces being considered as moving.

The American Bridge Co. or Schneider specifications
assume the wind pressure :

First, at 30 Ib. per sq.ft. on the exposed surface of all
trusses and the floor as seen in elevation, in addition to a
train of 10 ft. average height, beginning 2 ft. 6 in. above
base of rail, moving across the bridge. Second, at 50 Ib.
per sq. ft. on the exposed surface of all trusses and the floor
system. The greatest result shall be used in proportioning
the parts.

The Cooper specifications call for provision to be made
to resist a lateral force of 600 Ib. per lin.ft. on the loaded
chord, of which 450 Ib. is to be treated as a moving load
acting on a train of cars at a line 6 ft. above base of rail.

*The Tugela Bridge, "Engineering," Jan. 26, 1900.

[36]

The unloaded chord is to resist a lateral force of 200 Ib.
per lin.ft. for spans up to 200 ft., and 25 Ib. for each ad-
ditional 50 ft.

The specifications of the railroads mentioned below are
selected from a larger number to show the varying assump-
tions made of the amount of wind and lateral forces to be
used in the design of railroad bridges. The wind is as-
sumed to act horizontally at right angles to the bridge.
Pounds per lineal foot means lineal foot of bridge.

Baltimore & Ohio R.R. Co. — A moving lateral force of 600
Ib. per lin.ft. against the loaded chord, and 200 Ib. per lin.ft.
against unloaded chord.

Buffalo, Rochester & Pittsburgh Ry. Co. — (a) On the

loaded structure, 30 Ib. per sq.ft. on the exposed surface of
all trusses and the floor system as seen in elevation, and on
a moving train surface of 10 ft. average height beginning
2 ft. 6 in. above base of rail, (b) On the unloaded structure,
50 Ib. per sq.ft. (instead of 30). In no case shall a lateral
force of less than 200 Ib. fixed and 300 Ib. moving per lin.ft.
be used for the loaded chord and less than 150 Ib. per lin.ft.
fixed for the unloaded chord.

Canadian Pacific Ry. Co. — Same as the Schneider specifica-
tions.

Chesapeake & Ohio Ry. Co. — Against the unloaded chord
a fixed force of 200 Ib. per lin.ft. for all spans of 200 ft.
and under, and an additional force of 10 Ib. per lin.ft. for
every 25 ft. increase in span over 200 ft. Against the loaded
chord same as above with an additional force of 500 Ib.
per lin.ft. acting 8 ft. above base of rail and treated as a
moving load.

Chicago, Milwaukee & St. Paul Ry. Co. — A lateral force of
750 Ib. per lin.ft. against the loaded chord, and 200 Ib. per
lin.ft. against the unloaded chord, these forces being consid-
ered as moving.

Delaware & Hudson Co. — For the loaded chord 300 Ib. per
lin.ft. moving load and 200 Ib. per lin.ft. dead-load. For the
unloaded chord, 200 Ib. per lin.ft. dead-load. For double-track
bridges these loads shall be increased one-half.

Delaware, Lackawanna & "Western R.R. — A moving load
of 300 Ib. per lin.ft. against the loaded chord, and a uniform
load of 300 Ib. per lin.ft. divided equally between loaded and
unloaded chords.

Grand Trunk Railway System has "Private" printed on the
title page of its specifications and hence they can not be
quoted.

Harrimnii Lines — Same wording as Buffalo, Rochester &
Pittsburgh Ry. Co. above.

Lehigh Valley R.R. Co. — A moving load of 700 Ib. per lin.ft.
against the loaded chord and a moving load of 300 Ib. per
lin.ft. against the unloaded chord.

Long Island R.R. Co. — (1st) A load of 30 Ib. per sq.ft.
"on the exposed surface of entire surface as seen in elevation"
(but never less than 200 Ib. per lin.ft. at the unloaded chord),
and on a moving train 10 ft. high beginning 2 ft. 5 in. above
base of rail; (2d) 50 Ib. per sq.ft. on "the exposed surface of
the entire structure as seen in elevation."

Mexican International R.R. Co. — Six hundred pounds per
lineal foot against the loaded chord and 200 Ib. per lin.ft.
against the unloaded chord, both forces considered as moving.

National Lines of Mexico — On the unloaded structure 50 Ib.
per sq.ft. "on the geometrical elevation of the completed
structure and track." On the loaded structure, "30 Ib. per
sq.ft. of said elevation," plus the moving surface of train 10

[37]

ft. high, beginning 2% ft. above the base of rail. In no case
shall the fixed wind pressure be less than 150 Ib. per lin.ft.
for each chord of any bridge.

New York Central Lines— (1st) A moving load of 30 Ib.
per sq.ft. on 1% times the vertical projection of the structure
on a plane parallel with its axis (but never less than 200 Ib.
per lin.ft. at the unloaded chord), and a moving load of 360
Ib. per lin.ft. applied 8 ft. above the base of the rail. (2d) A
moving load of 50 ft. per sq.ft. on 1% times the vertical pro-
jection of the unloaded structure on a plane parallel with its
axis.

New York, New Haven & Hartford R.R. Co. — Same as the

A. R. E. Assn.

New York, Ontario & Western Ry. Co. — Same as the A. R.

B. Assn. For double-track bridges the constants are increased
50% but the percentage of live-load remains the same.

Norfolk & "Western Ry. Co. — Same as the Schneider speci-
fications, but omitting "beginning 2 ft. 6 in. above base of
rail."

Pennsylvania R.R. Co. — Same as the Schneider specifica-
tions.

Pennsylvania Lines West of Pittsburgh — A uniform load
of 150 Ib. per lin.ft. against the unloaded chord and 200 Ib.
per lin.ft. against the loaded chord. A moving load of 300
Ib. per lin.ft. against the loaded chord acting at a line 6 ft.
above the base of rail.

Philadelphia & Reading: Ry. Co. — A uniform load of 200
Ib. per lin.ft. against each chord and a moving load of 400
Ib. per lin.ft. against the loaded chord with its point of appli-
cation iy2 ft. above the rail.

Piedmont & Northern Lines — Same as A. R. E. Assn.

Seaboard Air Line Ry. — Same as A. R. E. Assn.

Southern Ry. Co. — Same as A. R. E. Assn.

Western Maryland Ry. Co. — Dead-load, 150 Ib. per lin.ft.
against the unloaded chord, and 200 Ib. per lin.ft. against the
loaded chord. Moving load, 400 Ib. per lin.ft. against the
loaded chord, applied at a distance of 6 ft. above the base
of rail.

Western Pacific Ry. Co. — Same as Western Maryland.

The wide range of requirements demanded in exist-
ing specifications shows the difficulty of uniting on a com-
mon standard. At present an increasing number of
railroad engineers is following the specifications of the
American Eailway Engineering Association. In Europe,
bridges are built in accordance with rules and regulations
prepared by the respective governments. This at times is
an advantage, at other times it is not. Unwin writes:
'English bridge builders are somewhat hampered in adopt-
ing rational limits of working stresses by the rules of the
Board of Trade."

WORKING STRESSES

The required material in a bridge depends upon as-
sumed unit stresses as well as upon assumed loadings.
Some ten years ago, the late Professor Heller* found that
for the same live- and dead-load stresses in a bottom-

*"Engineering News," Nov. 19, 1903.

[38]

chord member of a 134-ft. span, there was a variation
from 11.4% below to 18.6% above the average section of
25.4 sq.in. required by the 28 specifications he examined.
In the specifications of the 25 railroads mentioned above,
with the total stresses assumed by Heller, the variation
is from 11.65% below to 9.33% above the average of
24.97 sq.in. required. There is nearly a unanimity in
using for the combined stress due to lateral forces, plus
live- and dead-loads, a unit-stress 25 or 30% greater
than that due to the live- and dead-loads alone.

In this connection attention is called to the bending
stresses in the end posts due to portal bracing; and the
stresses induced in different members when the bridge
is figured for overturning moments. These are not to
be neglected, nor are centrifugal stresses when track is
on curve.

LONG SPANS

What has been written and the specifications quoted
apply primarily to railroad bridges of noncontinuous truss
spans. When the Ohio Eiver bridge between Cincinnati
and Covington was finished in 1889 with a center span
of 545 ft. and two spans of 486 ft., it had the distinction
of having the longest and heaviest simple truss that had
been built either in the United States or in Europe. The
specifications called for a wind pressure of 30 Ib. per sq.ft.
on the exposed surface of both trusses and the vertical
projection of the floor system, and on a moving-train sur-
face averaging 10 sq.ft. per lin.ft.

The St. Louis Municipal Bridge has three spans, each
of 668 ft. center to center of end pins, at present the
longest simple truss spans in the world.* The permissible
lengths of the spans are explained by 58% of the metal
being nickel-steel. The wind loads assumed were 300
Ib. per lin.ft. for the upper lateral system, and 600 Ib. per
lin.ft., one-half moving and one-half fixed, for the lower
lateral system.

*Merriman and Jacoby in the last edition of their "Roofs
and Bridges" enumerate 31 railway bridges and 6 combined
railway and highway bridges which have simple truss spans
of 400 ft. and over in length. Of these 15 are over 500 ft.
and two, including the St. Louis bridge, are over 600 ft.
The new Ohio River Bridge at Metropolis, recently contracted
for, has a noncontinuous channel span of 700 ft. clear distance
between piers.

[ 39 ]

The Hell Gate Bridge, now building, will have the long-
est arch in the world — a span of 977^ ft. The para-
graph in the specifications relating to wind pressure reads :

Wind, pressure shall be assumed as a moving load of 500
Ib. per lin.ft. in the plane of the tracks, plus 30 Ib. per sq.ft.
on such vertical surface of the unloaded bridge as shall be
exposed at any angle between 20° above or 20° below the
horizontal or at an angle of 45° from the axis of the bridge,
but not less than 200 Ib. per lin.ft. on any chord.

For 25 years the Forth Bridge of cantilever design,
in Scotland, has remained the greatest bridge in the
world. Its spans of 1700 ft. exceed in length and magni-
tude any other now standing. The wind loads and unit
stresses used in the design were those of the English Board
of Trade Eegulations, which most engineers regard as ex-
cessive and needlessly severe. The table below, made by
Sir Benjamin Baker from his calculations of stresses due
to the separate loadings, will show the important part
wind forces played in the design.

Dead Live

Load Load Wind Total

Stresses Stresses Stresses Stresses

Bottom member . 2282 1022 2920 6224

Top member 2253 997 544 3794

Vertical member 1550 705 1024 3279

Diagonal struts 802 167 414 1383

Diagonal ties 754 186 194 1134

Horizontal wind bracing. . 80 5 265 350

Vertical wind bracing 42 169 108 319

Central girder— top 337 303 182 822

Central girder — bottom . . . 330 301 247 878
Stresses are given in tons of 2240 Ibs.

The Quebec Bridge, also of cantilever design, now
building, will, when finished, eclipse the Forth Bridge,
its enormous channel span being 1800 ft. long. The as-
sumed wind loads are:

A wind load normal to the bridge of 30 Ib. per sq.ft. of the
exposed surface of two trusses and 1% times the elevation
of the floor (fixed load), and also 30 Ib. per sq.ft. on travelers
and falsework, etc. during erection.

A wind load on the exposed surface of the train of 300
Ib. per lin.ft. applied 9 ft. above base of rail (moving load).

A wind load parallel with the bridge of 30 Ib. per sq.ft.
acting on one-half the area assumed for normal wind pressure.

CONCLUSION

The writer has no intention of passing judgment upon
the specifications of engineers who have carried American
bridge building to such a marked success. Standard speci-
fications, as far as wind stresses are concerned, may not

[40 ]

be practicable, but it should be possible to come nearer to
points of agreement than at present. As an instance, the
Lehigh Valley, the Philadelphia & Heading, and the Lack-
awanna railroads, all in the same territory, must have
practically the same lateral forces ; but the assumed forces
vary nearly 75%. A discussion of the reasons for these
variations would be interesting.

In no specifications that the writer has ever read is
there an attempt to separate the stresses due to wind
from those due to other lateral forces. The 10% of the
weight of the train often specified for the lateral force
on the loaded chord includes the wind pressure on the
train. The wind pressure of 30 Ib. per sq.ft. on a mov-
ing train, sometimes called for, includes the lateral force
due to vibration. When the assumed loading is given in
Ib. per lin.ft., the total pressure due to all lateral forces
is intended.

Perhaps in the future some engineer may be able to
assign definite amounts to the different items that make
up the total lateral force on a bridge. This would be one
of the first steps to be taken to secure any degree of uni-
formity in proposed requirements for lateral stresses. As
a beginning in this direction, the writer suggests that the
lateral force on the loaded chord due to oscillation of
the train be taken at 4% of the train load.

[41]

IV

Wind Stresses in Highway
Bridges

SYNOPSIS — A review of the varying assump-
tions that have been made regarding the wind
stresses in highway bridges. Problem complicated
by lateral forces due to traffic. Present-day spec-
ifications, and variation of practice.

EARLY AMERICAN WRITERS

WHIPPLE — In the early part of 1847 there appeared
a pamphlet of 48 pages with the title, "An Essay on
Bridge Building, containing analyses and comparisons
of the principal plans in use, with investigations as to
the best plans and proportions, and relative merits of
wood and iron, for bridges. By S. Whipple, C. E., Mathe-
matical and philosophical instrument maker. Utica, N. Y.
H. H. Curtiss, printer, Devereux Block, 1847." After dis-
tributing 50 or 60 copies among friends, the author bound
the remainder of the edition with "Essay No. II on
Bridge-Building Giving Practical Details and Plans for
Iron and Wooden Bridges/' which he had written and
printed later in the year. This little book of 120 pages
and 10 plates was the pioneer in the mathematics of
bridge construction. To Squire Whipple, its author, the
inventor of the Whipple bridge, belongs the honor of
being the first to publish a correct analysis of the stresses
in a simple truss. His work did not become widely
known. In 1869 he took the copies remaining of his
original edition and bound them "with an appendix, con-
taining Corrections, Additions & Explanations, Sug-
gested by Subsequent Experience : to which is annexed an
Original Article on the doctrine of Central Forces." This
addition of about 150 pages the author prepared and
printed with his own hands.

In 1872 an enlarged and rewritten edition was pub-
lished by the D. Van Nostrand Co. In 1873 a chapter

[ 43 ]

of 35 pages on Drawbridges was added. From a copy
of this 1873 edition, the following quotations regarding
swaybracing are taken.

The primary and essential purpose of a bridge is to with-
stand vertical forces which are certain and, to a large extent,
determinate in amount But the lateral or trans-
verse forces to which a bridge superstructure is liable, are of
a casual nature, depending upon conditions of which we have
only a vague and general knowledge; .... But in ar-
ranging his system for securing lateral stability and steadi-
ness, science can lend him but little assistance He

knows the wind will blow against the side of his structure,
but whether with a maximum force of one hundred pounds, or
as many thousands, he has no means of knowing with any
considerable degree of certainty or probability .... No
attempt will be made here to assign specific stresses as liable
to occur in sway rods or braces, based upon calculations from
the uncertain and indeterminate elements upon which the
lateral action upon bridges depends. But judging from ex-
perience and observation, it may be recommended that iron
sway rods be made of iron not less than % inch in diameter,
for bridges of five panels or under, %-in. from six to ten
panels inclusive. For twelve and fourteen panels, %-in. for
ten middle panels and %-in. for the rest; and for sixteen the
same as last above, with the addition of a pair of 1-in. rods in
the end panels.

These are opinions from the father of modern bridge
building, written only 42 years ago.

BOLLER — Boiler's "Iron Highway Bridges/' first pub-
lished in 1876, which has passed through several editions,
says,

The horizontal or sway bracing may consist of very light
rods, if the floor is well laid, forming as it does a very effec-
tive system of bracing against lateral movement. Rods from
%- to 1-in. round will cover all but extreme requirements, and
they are attached by any convenient means to the floor-
beams near their point of support.

In modern textbooks calculation has taken the place of
speculation. Most of what has been written about the
wind stresses in railroad bridges* applies to highway
bridges. The same questions of the intensity of wind
pressure per unit of area exposed, and the amount of area
to be considered as exposed surface, are to be met. In-
duced stresses, load uniform or moving, and lateral forces
other than wind are also to be considered.

*In the preceding article.

[44]

CHANGED TRAFFIC KEQUIBEMENTS
The whole subject of loadings on highway bridges is
being revised. This is the day of heavy concentrated
loads. Many present bridges are seriously overloaded
by the traffic coming upon them, especially in the floor-
beams and joists. They were often built to carry uni-
form live-loads of, say 125 Ib. per sq.ft. for the floor-beams
and 80 or 100 Ib. for the trusses. Sometimes a road roller
was mentioned in the specifications. Manufacturers are
constantly increasing the weight of road rollers and trac-
tion engines, and with the good-roads movement many
bridges are called upon to carry rollers and engines for
which they were not designed. Then there is the automo-
bile, often run at a speed of 30 mi. per hr.

But the severest tests to which some of our highway
bridges are being put are those from the auto trucks.**
The traffic of towns and cities now reaches far out into the
country. The road roller runs slowly, while the auto
truck may be driven at a speed of 12 mi. per hr. and two
trucks may meet or pass each other on the same bridge.
A load of 10 tons is often carried and the weight of
the truck adds another 6 tons. (In New York City a load
of 75 tons has been carried on a truck weighing 10 tons,
most of the load being on the two rear wheels.)! Trucks
are being made heavier and with increased capacity.
Greater impact stresses are induced and the tendency to
both vertical and lateral vibration becomes greater. Some-
times centrifugal forces are introduced. AH this is par-
ticularly true of the auto truck when fully loaded and
with a driver ignorant or indifferent to loadings, speed,,
and the strength of bridges. One writer,J however, does
not think the vibration effects greater than those produced
by a horse and wagon. Anyone who has stood on a coun-
try bridge of 150-ft. span while a horse drawing a light
buggy was crossing at a trot may have felt a decided jolt-
ing of the whole structure, a condition largely remedied
by rigid connections and stiff members.

**Motor Truck Loading on Highway Bridges "Entr
News," Sept. 3, 1914.

tSeaman, Proceedings, Am. Soc. C. E., December, 1911.
JNeff (Am. Assoc. for Advancement of Science), "Enerineer-
ing and Contracting," Jan. 22, 1913.

[45]

Electric-car lines are being extended, and cars are be-
ing increased in weight and run at greater speed. When
a highway bridge carries electric cars it becomes in real-
ity a miniature railroad bridge. City or county officials
who, without examination by a competent engineer, will
sanction the use of existing bridges to carry electric cars,
belong to the class of undesirable citizens.

LATERAL FORCES OTHER THAN WIND PRESSURE

The assumed wind load in bridge specifications includes
all the lateral forces whether so stated or not. The writer
believes that this is sufficient (in nearly all present speci-
fications) to take care of the increased lateral forces due
to changed traffic requirements. With the exception of
the electric car, it is improbable that the full wind load
will be acting at the same time that the lateral vibration
occurs, due to the moving load. It should be remembered
that, if by any means a highway bridge is blown over,
there is not likely to be any loss of life, neither will traf-
fic be seriously interrupted. The actual loss to the au-
thorities is little more than the cost of the structure it-
self. Hence, excessive bracing in all bridges to guard
against a remote possibility in a single one is unneces-
sarily expensive. With a railroad bridge it is differ-
ent; provision must there be made for remote possi-
bilities.

The weakness of lateral systems of highway bridges in
the past has not been so much in the assuming of loads
as in the abominable details used. Witness the common
practice of 25 years ago and still prevalent in some quar-
ters of fastening the lower laterals in a nondescript way
to the floor-beams, which, in turn, are suspended from the
pins by U-bolt hangers; or, the top laterals having bent
eyes taking the top-chord pins and pulling against struts
attached to the same pins by bent plates. It is better to
design for a safe and sane wind loading, taking care
of induced stresses, and with all details fully up, than to
proportion the body of the lateral members for larger
stresses and use inefficient details.

In high-truss bridges the compression chord is kept in
alignment by the top lateral system. In the pony truss,

[46]

recourse is often had to doubtful expedients. "One has
only to shake the top chord of a pony truss to see how
loosely it is secured laterally and to demonstrate its lack
of fixity at intermediate points."* With the moving loads
now coming into use, the pony truss is doomed. In some
specifications it is prohibited altogether.

The wind is generally assumed to blow horizontally, but
it may vary greatly from the horizontal. For high bridges
in exposed localities, the upward pressure should be taken
into account; the end anchorage should provide for any
possible uplift and against the structure being moved off
its seats either by wind pressure or by a blow from a
passing object. A study of the wreck of the High Bridge
over the Mississippi River at St. Paulf is interesting.

PRESENT SPECIFICATIONS

SCHNEIDER — Passing to well known specifications, the
American Bridge Co. or Schneider specifications for steel
highway bridges read :

The wind pressure shall be assumed acting in either di-
rection horizontally:

First. At 30 Ib. per sq.ft. on the exposed surface of all
trusses and the floor as seen in elevation, in addition to a
horizontal live-load of 150 Ib. per lin.ft. of the span moving
across the bridge, but not less than 300 Ib. per lin.ft. shall
be used for bracing of loaded chord nor less than 150 Ib. per
lin.ft. of unloaded chord.

Second. At 50 Ib. per sq.ft. on the exposed surface of all
trusses and the floor system.

The greatest result shall be assumed in proportioning the
parts.

COOPER — Probably more highway bridges have been
built in accordance with the specifications of Theodore
Cooper than any other. The paragraphs stating amount
of lateral forces are:

To provide for wind and vibrations, the top lateral brac-
ing in deck bridges and the bottom lateral bracing in through
bridges shall be proportioned to resist a lateral force of 300
Ib. for each foot of the span; 150 Ib. of this to be treated as a
moving load.

The bottom lateral bracing in deck bridges and the top
lateral bracing in through bridges shall be proportioned to
resist a lateral force of 150 Ib. for each foot of the span.

For spans exceeding 300 ft., add in each of the above cases
10 Ib. additional for each additional 30 ft.

Johnson, Bryan & Turneaure; Merriman & Jacoby;
Ketchum; and others in their textbooks follow Cooper's
specifications regarding wind pressure. Others, as Mar-

*Smith, Proceedings, Indiana Eng. Soc., 1911, p. 209; "En-
gineering Record," Jan. 21, 1911.

tTurner, Trans. Am. Soc. C. E., June, 1905, Vol. LJV, p. 31.

[47]

burg, and Burr & Falk, quote both the Schneider and the
Cooper specifications.

WADDELL — Waddell in his "Ordinary Highway
Bridges" assumes a wind pressure of 40 Ib. per sq.ft. for
spans 100 ft. and under, 35 Ib. for spans 100 to 150 ft.,
and 30 Ib. for spans greater than 150 ft. ; these pressures
to be increased 10 Ib. for bridges in unusually exposed lo-
cations. The loads are considered moving.

The total area opposed to the wind is to be determined by
adding together the area of the vertical projection of the floor
and joists, and twice the area of the vertical projection of
the windward truss, hub plank, guard rail, and ends of floor-
beams.

In his "Specifications for Steel Highway Bridges,"
1906, the wind loads per lineal foot of span for both the
loaded and unloaded chords are taken from curves shown
on a diagram. The diagram was figured (for a clear
roadway of 20 ft.) with intensities varying from 40 Ib.
for very short spans to 25 Ib. for very long ones. For
spans up to 600 ft., the curves show loads from 200 to 355
Ib. per lin.ft. of bridge on the loaded chord and 100 to
265 Ib. on the unloaded chord, according to the length
of span and the class of the bridge. For wider struc-
tures, the wind loads are to be increased 2% for each
foot of width in excess of 20 ft.

GREINEK — The "Specifications for Steel Stationary
Bridges," by Greiner, require that

for city, interurban and country bridges the lateral force
against unloaded chords shall be assumed not less than
150 Ib. per lin.ft. plus 10% of the uniform load on one car
track or on a width of 12 ft., and for the unloaded chords 150
Ib. per lin.ft. In cases where a lateral force of 30 Ib. per
sq.ft. on 1% times the vertical projection of the structure
produces greater stresses than the above loads, it shall be
considered. All lateral loads shall be treated as moving.

OSTRUP — Ostrup, in his "Standard Specifications for
Highway Bridges/' calls for wind bracing to be designed
to resist one of the following lateral loadings, whichever
produces the greater stress: (a) Structure unloaded, 50
Ib. per sq.ft. on the exposed surface of all trusses and the
floor as seen in elevation; or (b) Structure loaded,
bridges (of all classes) carrying highway traffic only, 30
Ib. per sq.ft. on the exposed surface of all trusses and
the floor as seen in elevation in addition to a uniform

[48 ]

load of 150 Ib. per lin.ft. of structure applied on the
loaded chord; or (c) Structure loaded, bridges of all
classes carrying electric-railway traffic, the same loading
as under (b) except that the additional uniform load is
300 Ib. per lin.ft. of structure and is applied 7 ft. above
the base of rail. The minimum value of the pressure is
to be 250 Ib. per lin.ft. for the loaded and 150 Ib. for the
unloaded chord of the structure.

BOWSER — Bowser, in a "Treatise on Eoofs and
Bridges," gives 30 Ib. per sq.ft. of exposed surface of both
trusses as the maximum wind load upon a highway bridge.
To estimate the 30-lb. pressure when the surface is not
known, he writes, "it is customary to use the following
rule : Take 150 Ib. per lin.ft. per truss, or 75 Ib. per lin.
ft. for each chord."

MEREIMAN — In the earlier editions of Merriman's
work, "A Textbook on Eoofs and Bridges/' are found the
sentences :

For a highway bridge the surface exposed to wind action
is usually taken as double the side elevation of one truss. If
the area of this be not known, an approximation to its value
may be found by taking it as many square feet as there are
linear feet in the skeleton outline of the truss.

A number of the states, through highway commission-
ers or otherwise, have issued specifications for steel high-
way bridges. Some of them are incomplete and written
by men without a clear knowledge of the subject. Below
are given quotations from these and some other sources,
as to horizontal wind pressure.

COLORADO — 300 Ib. per lin.ft. on the loaded chord and
150 Ib. per lin.ft. on the unloaded chord.

ILLINOIS — Cooper's Specifications for Highway Bridges,
ed. of 1909, "except as hereinafter specified or as may be
specially indicated on the drawings."

MICHIGAN — No mention made of wind loads but they may
be covered by the paragraph, "Any questions that may arise
as to the quality of material and labor shall be settled in
accordance with the provisions of Theodore Cooper's Specifi-
cations for Steel Highway Bridges, under Class B-l.

NEBRASKA— 300 Ib. per lin.ft. on the loaded chord and
150 Ib. on the unloaded chord.

OHIO — Same as the Cooper Specifications, ed. of 1909.

VIRGINIA — 300 Ib. per lin.ft. on the loaded chord, 150 Ib.
of which is to be treated as a moving load, and 150 Ib. per
lin.ft. on the unloaded chord.

MASSACHUSETTS— The Massachusetts Railroad Commis-
sion, George F. Swain, Consulting Engineer, specifies that, for

[ 49 ]

bridges carrying electric railways "a lateral force of bO 11). per
sq.ft. on the unloaded structure, or of 30 Ib. per sq.ft. on the
loaded structure, shall be provided for. The surface of the un-
loaded structure shall, in the case of a truss, be taken as
twice the area of the vertical elevation of one truss, plus
that of the floor; and in the case of a girder, as IS times the
vertical surface. The surface of the loaded structure shall
be that of the unloaded structure plus a vertical surface 10
ft. in height and 50 ft. long, the pressure on which is to be
considered a moving load upon a car."

NEW YORK — The Department of the State Engineer and
Surveyor of New York specifies: "The intensity of the wind
pressure shall be assumed at: First, 30 Ib. per sq.ft. on the
exposed surface of all railings, trusses, trestle posts, bracing
and the floor in addition to a load of 150 Ib. per lin.ft. applied
at 4 ft. above the floor line for all bridges which do not carry
electric cars, and 300 Ib. per lin.ft. applied 8 ft. above the
floor line for all bridges which do carry electric cars. Second,
50 Ib. per sq.ft. on all exposed surface of the unloaded struct-
ure. All parts shall be proportioned for that one of these
loads which gives the greater results, but in no case shall
the wind pressure be assumed at less than 100 Ib. per lin.ft. at
the unloaded chord, or less than 250 Ib. per lin.ft. at the
loaded chord. All wind loads shall be considered as moving-
loads."

PHILADELPHIA— The Department of Public Works of the
City of Philadelphia specifies for its bridges a wind pressure
of 30 Ib. per sq.ft. against the side area of all trusses, railings,
and the end area of the floor construction. In no case is less
than 150 Ib. per lin.ft. to be used. In addition the system at-
tached to the floor is to carry a moving load of 150 Ib. per
lin.ft. of bridge.

HARRIMAN LINES — A number of railway companies have
specifications for highway bridges attached to or a part of
their specifications for railroad bridges. The Harriman Lines
issue separate specifications for highway bridges in which the
wind pressure is taken: (a) On the loaded structure at 30
Ib. per sq.ft. on the exposed surface of all trusses and the
floor system as seen in elevation, together with a moving load
of 150 Ib. per lin.ft. of bridge, (b) On the unloaded struct-
ure at 50 Ib. per sq.ft. on the exposed surface taken as in (a).

U. S. ROADS— The Office of Public Roads, U. S. Depart-
ment of Agriculture, issues "Typical Specifications for the
Fabrication and Erection of Steel Highway Bridges." The Di-
rector of the Office states that they are prepared "with the
view of furnishing a suitable guide for local highway offi-
cials in fixing requirements to which bridge structures must
conform." He further writes, "In the past many steel bridges
have been very poorly constructed, and it is believed that lack
of information on the part of highway officials concerning
proper specifications for this class of work has been in a large
measure responsible for the unsatisfactory results." It may be
remarked that unless the highway officials are reinforced by
competent engineers, the use of these specifications will not
prevent "unsatisfactory results." The wind loads assumed are
a load of 300 Ib. per lin.ft. on the loaded chord, one-half of

[50]

this to be treated as moving, and 150 Ib. per lin.ft. on the un-
loaded chord.

ONTARIO — The "General Specifications for Steel Highway
Bridges," of the Canadian province of Ontario are quite de-
tailed in their provisions for wind and lateral stresses. For
Class A (bridges suitable for main county roads) in spans of
200 ft. or less, a uniform load of 150 Ib. per lin.ft. per span is
used on the unloaded chord, and the same with the addition
of 150 Ib. per lin.ft. moving load on the loaded chord; for
spans exceeding 200 ft. the uniform load in each system is to
be increased 10 Ib. for each 30 ft. of span. For Class B
(bridges carrying light rural traffic), same as Class A. For
Class C (bridges for heavy traffic in towns and cities), for
spans of 200 ft. and less, a uniform load of 200 Ib. per lin.ft.
of span on the unloaded chord and a uniform load of 250 Ib.
per ft. in addition to a moving load of 250 Ib. per ft. on the
unloaded chord; for spans over 200 ft. the uniform load in
each system is to be increased 10 Ib. for every 30 ft. increase
of span.

TYRRELL — Merriman & Jacoby in their enumeration of
noncontinuous bridges of 400-ft. span and over include 21
which are exclusively highway. Of these 21 the longest span
is that over the Miami River at Elizabethtown, Ohio (de-
stroyed by flood in March, 1913). This structure was pro-
portioned "for a wind load of 30 Ib. per sq.ft. acting on the
exposed surface of both trusses, and all bracing that is like-
wise exposed to wind pressure."*

UNIT-STEESSES

In the specifications mentioned, the values allowed for
stresses due to combined dead- and live-load and wind
are 20 to 30% greater than that allowed for combined
live- and dead-loads. The proviso is attached that the sec-
tion used must not be less than that required for the
combined dead- and live-loads. One exception is that
of the IT. S. Department of Agriculture: these specifica-
tions require that the wind stresses be proportioned with
the same values as other stresses without allowance for
any combination with other loads. This may not be in-
tended, but there is no doubt of the literal interpretation.
Another exception is the Waddell specifications, where in
highway bridges no reduction of working stress is allowed
for any combination of loads. Unless the structure car-
ries an electric railway, it is assumed that the live-load
and wind-load cannot act together, "for the reason that no
person would venture on the bridge when even one-half
of the assumed wind-pressure is acting."

*Tyrrell, The Elizabethtown Bridge.

[51]

CONCLUSION

It will be seen from the above that the current require-
ments regarding lateral bracing vary greatly. A num-
ber of states have already legislated upon the subject of
highway bridges and others will soon follow. As far as
lateral bracing is concerned it might be well to divide
highway bridges into three classes, those which carry elec-
tric cars, those which carry heavy loads other than cars,
and ordinary country bridges. A different lateral load-
ing should be assigned to spans over 150 ft. than to those
under. It is better to state the wind pressure in pounds
per lineal foot of bridge rather than in pounds per square
foot of exposed surface, because contracts for highway
bridges are almost invariably let by competition, and if
wind loadings are given in pounds per lineal foot, the de-
signs of different bidders are on the same basis, which may
not be the case when given in pounds per square foot.

After a study of many specifications, the writer sug-
gests the following :

RECOMMENDED SPECIFICATIONS

For bridges carrying- electric-railway traffic the lateral
system shall be designed to resist a lateral force of 300 Ib.
per lin.ft. on the loaded chord and 150 Ib. per lin.ft. on the
unloaded chord, for spans of 150 ft. and under. An additional
allowance of 10 Ib. for every 30 ft. of span shall be made to
the loaded chord and 5 Ib. to the unloaded chord for spans
of more than 150 ft.

For bridges not carrying electric cars, but subject to heavy
loads such as auto-trucks, road rollers, and traction engines,
the lateral force shall be assumed at 250 Ib. per lin. ft. on the
loaded chord and 150 Ib. per lin.ft. on the unloaded chord, for
spans of 150 ft. and under. An additional allowance of 5 Ib.
for every 30 ft. of span shall be made to each chord for spans
of more than 150 ft.

Ordinary country bridges shall be designed for a lateral
force of 225 Ib. per lin.ft. on the loaded chord and 150 Ib. on
the unloaded chord with an additional force on the loaded
chord of 5 Ib. for every 30 ft. of span exceeding 150 ft.

All lateral loads are to be considered as moving loads.

In members subject to stresses from lateral forces alone
the unit-stresses may be increased 25% over those assumed
for live- and dead-loads. In bridges carying electric cars the
unit-stresses in chords and floor-beams for the stresses due to
lateral forces combined with those from the vertical forces
may be increased 25% over those assumed for dead- and live-
loads. If the track is on curve the centrifugal force shall be
added to the lateral live-load. For bridges not carrying elec-
tric traffic, unit-stresses of 50% increase may be used instead
of 25%. In no case shall the section be less than that re-
quired for the live- and dead-loads.

Provision shall be made for reversal of stress in any mem-
ber due to any combination of wind with other loads. The
end seats shall in all cases be firmly anchored against lateral
movement and uplift. In bridges in unusually exposed situa-
tions or at a great height above the water the amount of
anchorage shall be determined by calculation.

All details shall be designed to carry the stresses in the
main members.

[ 52 ]

Wind-Bracing Requirements in
Municipal Building Codes

SYNOPSIS— How 120 American cities specify
wind pressure for the design of buildings. Great
range of pressures and working stresses. Recom-
mendation that 20 Ib. per sq.ft., and for combined
stress 50% increase in working stress, be adopted
as standard.

The assumptions that are made for wind pressure and
working stresses due to wind loads play an important part
in the design of a many-storied hotel or office building.
These are seldom left to the judgment of the designer,
but are determined by the building code of the city in
which the building is located.

According to the census of 1910 there were in the
United States 50 cities each having a population over
100,000. The building codes of 45 of these cities, to-
gether with those of about 75 cities below 100,000, have
been examined with respect to their requirements for
wind bracing. The purpose of this article is to show
the wide variation in requirements in these codes, and to
make a plea that assumptions be made more nearly uni-
form.

The present Building Code of the City of New York,
affecting more building operations than that of any other
city on the continent, was adopted in 1899. The Board
of Aldermen passed a new code in 1909, after extended
discussion and bitter controversy, but the Mayor vetoed
it. The present code is archaic in some of its provisions
and is inadequate for present needs. It has been used
as the basis for the codes of a host of other cities. Some-
times it has been copied with but little change, and in
other cases some sections have been modified or rejected.

Regarding wind pressure the New York code requires
that all structures exposed to the wind (except those

[53]

under 100 ft. in height in which the height does not ex-
ceed four times the average width of the base) be designed
to resist a horizontal wind pressure of 30 Ib. in any di-
rection for every square foot of surface exposed from the
ground to the top, including the roof. Regarding unit-
stresses the code reads :

In calculations for wind bracing, the working stresses set
forth in this code may be increased by 50%.

This sentence is ambiguous as it does not state whether
the high unit-stress is applicable to the combined stresses
due to wind and other loads or whether it is to be used
for the wind stress only. There is considerable differ-
ence between the two interpretations as to the amount of
material required in bracing a high and narrow building.
The Chicago code removes all doubt by specifying:

For stresses produced by wind forces combined with those
from live- and dead-load, the unit-stress may be increased
50% over those given above; but the section shall not be
less than that required if wind forces be neglected.

It may be said that the practice in New York and else-
where is to interpret the 50% as applying to combined
stresses.

Another sentence in the New York code reads :

In all structures exposed to wind, if the resisting moments
of the ordinary materials of construction, such as masonry,
partitions, floors and connections, are not sufficient to resist
the moment of distortion due to wind pressure, taken in any
direction on any part of the structure, additional bracing
shall be introduced sufficient to make up the difference in
the moments.

Good practice does not permit and it is not common
to carry the wind stresses in steel buildings either in whole
or in part to the ground by walls or partitions. The
Bridgeport code has a clause which should be followed,
reading :

In buildings of skeleton construction the frame must be
designed to resist this wind pressure.

Manchester, Albany, Utica, Jersey City, Paterson, Terre
Haute, Kalamazoo, Milwaukee, St. Paul, Minneapolis,
Louisville, Tampa, Atlanta, Dallas and Tacoma all fol-
low the New York code regarding wind bracing except
for an occasional variation for buildings under 100 ft.
in height.

[54]

In Philadelphia a pressure of not less than 30 Ib. per
sq.ft. is called for on all buildings erected in open spaces
or on wharves. On tall buildings erected in built-up
districts the wind pressure is not to be figured for less
than 25 Ib. at tenth story, 2y2 Ib. IGSS on each succeeding
lower story, and 2% Ib. additional on each succeeding
upper story to a maximum of 35 Ib. at the fourteenth
story and above. In proportioning members subject to
stresses due to wind loads the working stresses may be
increased 30%. In Washington buildings are practically
limited to twelve stories in height. The prescribed wind
pressure is the same as in Philadelphia, but no mention
is made of any increase of working stresses. Lowell,
Bridgeport, Baltimore, Buffalo and Sioux City assume
wind pressure at 30 Ib. per sq.ft. and are also silent on
the subject of working stresses being increased.

Pittsburgh calls for 25 Ib., Detroit and Jacksonville
30 Ib. per sq.ft. wind pressure, and each allows the work-
ing stresses to be increased 25%.

Cincinnati requires provision to be made for a pressure
of 20 Ib. per sq.ft. for the surface exposed above surround-
ing buildings; working stresses may be increased 25%.
St. Louis assumes a pressure of 30 Ib. per sq.ft. and al-
lows an increase of 20% to working stresses. The St.
Louis code has this provision :

"Where there are buildings immediately adjoining, the wall
surface covered by such buildings will be considered as not
exposed to wind pressure.

The question might be asked concerning buildings in
Cincinnati and St. Louis as to what would take the wind
pressure if the surrounding buildings were removed.

Chicago, San Francisco, Covington and Akron call for
20 Ib. per sq.ft. wind pressure. An increase of 50% to
the working stresses is allowed in Chicago and San Fran-
cisco, 25% in Covington and none in Akron.

Poughkeepsie, Evansville and Chattanooga call for 30
Ib. per sq.ft. horizontal wind pressure, and state as follows :

The additional loads caused by the wind pressure upon
beams, girders, walls and columns must be determined by
calculation and added to other loads for such members.
Special bracing shall be employed wherever necessary to
resist the distorting effect of the wind pressure.

[ 55 ]

No mention is made of higher unit-stresses for wind
loads.

Syracuse, Erie, Cleveland, Duluth, Denver, Macon,
Birmingham and Portland (Oregon) for all buildings
whose heights exceed 1% times the width of the base fol-
low the wind pressures given in the Philadelphia code.
The Syracuse code alone allows an increase of working
stresses — 25%. Each code has this provision:

Every panel in a curtain wall shall be proportioned to re-
sist a wind pressure of 30 Ib. per sq.ft.

The code of Grand Rapids copies the Schneider "Spe-
cifications for Structural Work of Buildings." The wind
pressure is assumed as acting horizontally in any direc-
tion, as follows:

First — At 20 Ib. per sq.ft. on the sides and ends of buildings
and on the actual exposed surface, or the vertical projection
of roofs.

Second — At 30 Ib. per sq.ft. on the total exposed surfaces
of all parts composing the metal framework. The framework
shall be considered an independent structure, without walls,
partitions or floors.

For bracing and the combined stresses due to wind and
other loading, the permissible working stresses may be
increased 25%, or to 20,000 Ib. for direct compression or tension.

The code of Memphis has the same provisions though
differently worded.

The code of Oakland is unusually explicit in the treat-
ment of wind bracing. For buildings of Class A over
100 ft. high, or where the height exceeds three times the
least horizontal dimension, or for buildings of Class B
over 80 ft. high where the height exceeds two times the
least horizontal dimension, it provides :

The steel frame shall be designed to resist a wind force of
30 Ib. per sq.ft. acting in any direction upon the entire
exposed surface. All exterior wall girders shall have knee-
brace connections to columns. Provision shall be made for
diagonal, portal or kneebracing to resist wind stresses, and
such bracing shall be continuous from top story to and
including basement.

An increase of 50% above the allowed dead- and live-load
stress shall be used for wind stress. Columns subjected to
cross-bending by wind or eccentric loading shall have addi-
tional area to provide for the stresses, the eccentric loading
being calculated as dead-load and the wind provided above.
The area of metal thus obtained for wind, cross-bending and
eccentric loading shall be added to the area provided for
dead- and live-load to obtain the total metal in column.

[ 56 ]

In the case of reinforced-concrete buildings where pro-
vision must be made for wind pressure, there is this pro-
vision :

The reinforcing rods of columns shall be connected by
threading the rods and by threaded sleeve nuts or threaded
turnbuckles, or methods equally effective and satisfactory to
the Bridge Inspector.

In Salt Lake City for buildings over 102 ft. high, or
where the height exceeds three times the least horizontal
dimension, "the steel frame shall be designed to resist a
wind force of 20 Ib. per sq.ft. in any direction upon
the entire exposed surface." As in Oakland, it is re-
quired that the exterior wall girders shall have knee-
brace connections to the columns and that diagonal, por-
tal or kneebracing to resist wind pressure shall be used
from the top story to and including basement. Unlike
Oakland no increase of working stresses for wind loads
is mentioned.

The code of Waltham, Mass., has the provision :

All buildings exposed to the wind shall be calculated to re-
sist a pressure on either side so exposed, and upon the roof, if
pitched, amounting to 10 Ib. per sq.ft. of vertical projection
of roof between the ground and a height of 40 ft. above
the ground, a pressure of 15 Ib. per sq.ft. on parts between
40 and 60 ft. above the ground, and 20 Ib. per sq.ft. on parts
60 ft. above the ground.

No increased working stresses for wind are mentioned.

The code of Columbus, Ohio, adopted ten years ago,
reads the same on wind pressure as the New York code
except that working stresses may be increased 25%
instead of 50%. There is added the sentence:

In buildings constructed of structural steel the wind pres-
sure shall be allowed for as follows: Ten Ib. per sq.ft. of ex-
posed surface for buildings 20 ft. or less to the eaves; 20 Ib.
per sq.ft. of exposed surface for buildings 60 ft. to the eaves;
30 Ib. per sq.ft. of exposed surface for buildings over 60 ft.
to the eaves.

The codes of Boston, Cambridge, Haverhill and New
Orleans have the sentence: "Provision for wind bracing
shall be made wherever it is necessary." This is indefin-
ite and tends to put a premium on ignorance. If all
designers were experts there would still be enough differ-
ence of opinion as to the amount of wind bracing neces-
sary. But a design with little or no wind bracing is
also entitled to consideration if the maker gives assur-

[ 67 ]

ance that he is furnishing bracing "wherever it is neces-
sary." The same might be said concerning the codes of
New Haven, Providence, Worcester, Springfield, Wheel-
ing, Youngstown, Toledo, Omaha, Lincoln, Montgomery,
Fort Worth, Los Angeles and others, which while giving
loads and stresses for structural steel generally say noth-
ing on the subject of wind pressure. Indianapolis and
Seattle allow an increase of 50% to the working stresses
but do not state the amount of pressure.

The codes of Fall Eiver, Pawtucket, Elizabeth, Allen-
town, Altoona, Fort Wayne, Dubuque and Topeka are
very meager or altogether silent on the whole subject of
loads, stresses, and structural steel.

Codes often contain blanket clauses which might be
used to cover a wide range of omissions — thus, Cleveland,
Duluth, Little Eock, Fort Worth and others say:

The allowable factor or units of safety or the dimensions
of each piece or combination of materials required in a
building- or structure, if not given in this ordinance, shall
be ascertained by computation according to the rules pre-
scribed by the modern standard authorities on strength of
material, applied mechanics and engineering practice.

Erie, Pa., has the sentence: "In general all stresses
shall be figured in accordance with the standard speci-
fications of the American Society of Civil Engineers."

The New Haven code reads :

The dimensions of each piece or combination of materials
required shall be ascertained by computation according to the
rules and data given in Haswell's Mechanics' and Engineers'
Pocket Book, Trautwine's Engineers' Pocket Book, or Kid-
der's Architects' and Builders' Pocket Book, except ad may
be otherwise provided in this title. Stresses for materials
and forms of same not herein mentioned shall be those
determined by the best modern practice.

The last code from which quotations will be made is
that of the largest city in the world. The London Coun-
ty Council (General Powers) Act, 1909, in Section 22,
"Provisions with respect to Buildings of Iron and Steel
Skeleton Construction," requires:

All buildings shall be so designed as to resist safely a wind
pressure in any horizontal direction of not less than 30 Ib.
per sq.ft. of the upper two-thirds of the surface of such
buildings exposed to wind pressure.

Working stresses exceeding those specified "by not more
[ 58 ]

than 25% may be allowed in cases in which such excess
is due to stresses induced by wind pressure."

CONCLUSION

It might seem from the foregoing that our American
municipalities have exhausted the combinations of wind
pressure and wind stress that can be made. The fact
that one code differs from another is not in itself a cause
for criticism, but a code is decidedly at fault when it
contains absurd or needless requirements or when its
requirements are not clearly expressed. To assume wind
pressure over a large area at 30 Ib. per sq.ft. and then
to add the sectional area necessary to resist wind stresses
to that required for live- and dead-loads is needless.
Where this is specified in a code it is evaded in practice.
It would be far better to make rational assumptions and
insist on a rigid adherence to them, than to insert in a
code improbable loadings or working stresses that will
be ignored in actual construction.

That the need of revision in our building codes is be-
ing felt by the public is evidenced by the number now
being revised. Although our knowledge of wind action
is limited we should be able to come nearer to a common
ground of requirement for wind bracing than we have at
present. As a basis for uniformity the writer suggests
the building ordinances of Chicago. The paragraph on
Wind Eesistance reads :

All buildings shall be designed to resist a horizontal wind
pressure of 20 Ib. per sq.ft. for every square foot of exposed
surface. In no case shall the overturning moment due to
wind pressure exceed 75% of the moment of stability of the
building due to the dead load only.

The paragraph relating to Wind Stress, previously
quoted, reads:

For stress produced by wind forces combined with those
from live- and dead-loads, the unit-stress may be increased
50% over those given above; but the section shall not be
less than required if wind forces be neglected.

[59]

VI

Windbracing Without Diag-
onals for Steel-Frame
Office-Buildings

SYNOPSIS— Exact elastic analysis of rigid
square-panel tier-building frames being impossible
in practice, approximate methods based on certain
arbitrary assumptions are used. The first summar-
ized statement of these methods was given by the
author in ENGINEERING NEWS, Mar. 13, 1913. The
present article — an enlarged revision of that arti-
cle— gives four methods, and compares their re-
sults for a specific example. Method II-A of this
article has been added, and the treatment of the
other three revised and corrected.

If an apology is needed for adding to the literature of
the above subject, it may be found in the fact that many
of the methods given in technical papers for determining
stresses due to wind loadings are not workable. That
is, the average engineer to whom falls the lot of designing
the average office-building has neither the time nor
the ability to handle the cumbersome equations involved.
One paper published a few years ago and now before
the writer has for its purpose "to develop the exact theory
of framework with rectangular panels, and then to sug-
gest such short-cuts as may be of use in actual designing/'
This is an elaborate paper in which the theorem of four
moments is used. A bent of two unequal bays, three col-
umns and two girders, is considered and by the "short-
cuts" seven equations are found from which the values
of all the moments for the floor in question may be found.
Whatever may be the merit of this and similar papers,
it has not been recognized sufficiently to be followed to
any appreciable extent. It is to be regretted that the
treatment of the subject in our textbooks is not more
complete and adequate.

[61]

Buildings like the Trinity, the Fuller, the Singer, the
Woolworth, or the Metropolitan Tower, in New York
City, are each in a class by itself, and of necessity care-
ful study is given to the windbracing. For another and
a large class of office-buildings, little or no attention is
given to the matter of bracing for wind, either in the
proportioning of main members or in details.

Without further introduction the writer gives four
methods in current use of calculating wind stresses and
moments in office-buildings where diagonals are not per-
missible. Bach method has its own advocates.

Considering a single bent: It will be assumed that all
columns in any given story have the same sectional area
and the same section modulus, that all girders of the same
floor have the same section modulus, and that the joints
are perfectly rigid. It is obvious that if the forces in
the several members of the frame are small in relation
to the stiffness of the members, the longitudinal distor-
tions may be neglected; hence the adjacent joints oc-
cupying the corners of a rectangle will after distortion
occupy the corners of an oblique parallelogram.

It is assumed that the point of contraflexure of each
column is at midheight of the story. The first method
described further involves the tacit assumption that the
girders have their points of contraflexure at midlength.
Specific assumptions as to the distribution of column
shears and direct stresses are made in the several methods.
In only one of the four methods are the assumptions
strictly consistent. For example, in Method I the as-
sumption as to location of points of contraflexure would
make the distorted shape of panel constant in any given
story, and from this would follow that the column shears
must be equal; but the calculation gives column shears
of different amount.

The resistance to overturning will cause a direct stress
in tension on the windward side of the neutral axis, taken
by all or some of the columns on that side according to
the method used, and a direct stress in compression on
the leeward side taken by the columns on that side.

Figs. 1, 7, 9, and 12, give results obtained from calcu-
lations according to Methods I, II, II-A and III respec-

[63]

tively. Loads and stresses are given in thousands of
pounds and bending moments in thousands of foot-
pounds. Direct stresses are given in parentheses ().

METHOD I

This may be called the Cantilever Method and is
a restatement with some modifications of an arti-

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METHOD I tn« «eW»

FIG. 1. EECTANGULAR BUILDING-FRAME: DIRECT AND

BENDING STRESSES CALCULATED BY APPROXIMATE

METHOD I

144.0 = Moment of 144,000 ft.-lb.
(4.0) = Direct stress of 4000 Ib.

[63 ]

cle entitled "Windbracing with Kneebraces or Gus-
set-plates," by A. C. Wilson, in The Engineering Record,
Sept. 5, 1908. A section or bent of the building is con-
sidered similar to a beam loaded as a cantilever.

If a beam of rectangular section be loaded as a cantilever
with concentrated loads, it is possible by the theory of flexure
to find the internal stresses at any point. If, however, rec-
tangles be cut out of the beam between the loads, there will
then be a different condition of stress. What was the hori-
zontal shear of the beam will now be a shear at the point of
the contraflexure of the floor girders, causing bending, and,
as in the beam, the nearer the neutral axis the greater the
shear. The vertical shear in the beam would be taken up by
the columns as a shear at the points of contraflexure and the
amount of this shear taken by each column would, as in the
beam, increase toward the neutral axis. The direct stresses
of tension or compression in the beam would act on the col-
umns as a direct load of either tension or compression, and
as in the beam would decrease toward the neutral axis.

Each intersection of column with floor girders would be
held in equilibrium by forces acting at the points of contra-
flexure; and to find all the forces acting around a joint at any
floor the bending moments of the building at the points of
contraflexure of the columns above and below the floor in
question are found as will be explained later,

It is assumed that if a beam of constant, symmetrical
cross-section and homogeneous material is fixed at both ends,
and that if forces tend to move those ends from a position
in the same straight line to a position to one side with the
ends still parallel, reversed bending will occur with the point
of contraflexure in the center of the unsupported span. And
since this condition exists in all columns and floor girders
it will be necessary to find the shears at the points of con-
traflexure as well as the direct stresses in all members.

4 ; 7 "FLOOR

6000

6V FLOOR

5VFLOOR
t. \

METHOD I

FIG. 2. COLUMN SHEARS AND GIRDER MOVEMENTS

AT SIXTH FLOOR, CALCULATED BY

METHOD I

Fig. 1 gives stresses and maximum moments in all
members of a section of the building in accordance with
the above statement.

[ 64]

The calculation of stresses and bending moments in
members about the sixth floor will be given in detail. The
direct stress in any column is assumed to be proportional
to its distance from the neutral axis of the cross-section
of the building. In the cross-section considered, the
neutral axis coincides with the center line of the build-
ing. The total moment of the wind loads above the
sixth floor about the line of inflection of the sixth-story
columns must equal the moment of the direct stresses in
these columns about the neutral axis. Let SX be the
direct stress in each of the sixth-story columns B and C,
then 24X will be the direct stress in each of the sixth-
story columns A and D. Hence we have

(4000 X 30) + (6000 X 18) + (6000 X 6) =
(24X X 24) + (SX X 8) + (8Z X 8)

+ (24X X 24)
From which SX = 1650 and 24X = 4950.

In the same way for the fifth-story columns we have
the equation

(4000 X 42) + [6000 X (30 + 18 + 6)] =

[(24X X 24) + (SX X 8)] X 2

From which 8Z == 3075, the direct stress in the fifth-
story columns B and (7; and 24JT = 9225, the direct
stress in the fifth-story columns A and D.

The total horizontal shear on any line across the build-
ing is the sum of the wind loads above that line. The
shear taken by any column in any story is proportional to
the total horizontal shear in that story.

In Fig. 2, if X = shear of any fifth-story column at

1 £* f\r\f\ Q

its point of inflection, then 0 ' n X or ^ X = shear at

point of inflection of the sixth-story length of the same

6,000 T- 3

column, and ^-7^7: X 01 ~^ X = increment of shear

11

taken by the column at the floor girder.

We are now ready to consider the forces about the first
joint, or the intersection of Col. A with the sixth-floor
girder, sketched separately as Fig. 3.

The difference between 9225 and 4950 = 4275 is
taken up as a shear in the floor girder between Cols.
A and B. The moments of the shears must hold the

[ 65 ]

joint in equilibrium. Taking moments about the lower
point of inflection we have

(A ^ X 12) + (T3T X X 6) = 4275 X 8
from which X = 3300, T8T X = 2400 and T8T X = 900.
The bending moment M± for the floor girder is 4275 X 8
= 34,200 ft.-lb. The bending moment for the fifth-
story column is 3300 X 6 = 19,800 ft.-lb., and that for
the sixth-story column is 2400 X 6 = 14,400 ft.-lb. The
direct thrust on the floor girder is 6000 — 900 = 5100.
Proceeding to the second joint, sketched in Fig. 4 : The
difference between 3075 and 1650 = 1425 acts as a
shear in the girder between Cols. B and C. This added to
the 4275 shear continued from the girder between A and
B makes a total shear of 5700 in the girder. The equa-
tion of moments is

(A X X 12) + (A X X 6) = (4275 X 8) + (5700 X 8)
From which X = 7700; T8T3T = 5600, and T8T X =

5100*"

FIG.3

FIG.-4

3000

6V FLOOR A (*900)

3000-j* 900

FI6. 5

FIG. 6

FIGS. 3-6. SIXTH-FLOOR JOINTS OF BUILDING-FRAME,
WITH STRESSES CORRESPONDING TO METHOD I

2100, are the shears taken by Col. B to hold the joint
in equilibrium.

The bending moment M 2 of the girder from A to B at
Col. B is the same as at Col. A with an opposite sign;
Ms, of the girder from B to C, is 5700 X 8 = 45,600
ft.-lb. The bending moment of the fifth-story column is
7700 X 6 = 46,200 ft.-lb., and that of the sixth-story
column is 5600 X 6 = 33,600 ft.-lb. The direct thrust
on the girder between B and C is 5100 — 2100 = 3000.

At the third joint, Fig. 5, the shear taken by the
girder between C and D is 5700 — (3075 — 1650) =
4275. From the equation of moments
(A X X 12) + (T\ X X 6) = (5700 X 8) + (4275 X 8)
whence

X = 7700, ^ X = 5600, ^ X = 2100
As expected, the moments in Col. C are numerically equal
to those in Col. B, and the girder moments M4 = M&,
and M5 = M2. The compression in the floor girder
between C and D is 3000 — 2100 = 900.

At the fourth joint, Fig. 6, we have

(T\ X X 12) + (A X X 6) = (4275 X 8)
the same equation as at the first joint, and hence the same
numerical values for moments and shears.

The designer in following this method for the various
floors will find many short-cuts. A relationship between
the floors can soon be established. If the distances between
columns are not even spaces, or the columns have differ-
ent sectional areas, the direct stresses vary both in pro-
portion to their distances from the neutral axis and their
sectional areas. It will be necessary to first find the
neutral axis of the cross-section in question and then the
direct stresses. With these the shears and bending me
ments can be obtained.

METHOD II

This may be called the Method of Equal Shears. It is
assumed that the horizontal shear on any plane is equally
distributed among the columns cut by that plane. The
stresses and maximum bending moments for a cross-sec-
tion of the building are as given in Fig. 7.

[ 67 ]

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METHOO H

FIG. 7. RECTANGULAR BUILDING-FRAME: DIRECT AND

BENDING STRESSES CALCULATED BY APPROXIMATE

METHOD II

120.0 = Bending moment of 120,000 ft.-lb.
(4.0) = Direct stress of 4000 Ib.

Taking any aisle we find the direct stress in the fifth-

X 42'

story columns to be

\ + (^,X 30\

pf9 X 6)

16 . 10,^50

The direct stresses coming upon any interior column
[68]

from the adjacent aisles are equal in amount but op-
posite in direction. Hence their algebraic sum is zero

i i

B C

METHOD H

FIG. 8. COLUMN-SHEARS AND GIRDER MOMENTS AT
SIXTH FLOOR, CALCULATED BY METHOD II

and only the outside columns have direct stresses. This
may be found directly for any story, say the sixth,
(4000 X 30) + (6000 X 18) + (6000 X 6)
divided by 48 = 5500

Considering in detail, as in Method I, the sixth floor,
we have in Fig. 8 the direct stresses and shears in the
columns.

The shear in each girder is 10,250 - - 5500 = 4750.
The equations for bending moments in the girders can
be written as follows :

M, = [(4000 X6)X (5500X6)
M3 = [(4000 X6) +(5500 X6)
M3 = [2(4000 X6) +(5500 X6)
M4 = [2(4000X6) +(5500X6)
M5 = [3(4000 X6) +(5500 X6)
M6 = [3(4000 X6) +(5500 X6)

—[(10,250—5500) X16
—[(10,250—5500) X16
—[(10,250—5500) X32
—[(10,250—5500) X32
—[(10,250—5500) X48

= +57,000 ft.-lb.
= —19,000 ft.-lb.
= +38,000 ft.-lb.

38,000 ft.-lb.

= +19,000 ft.-lb.
= —57,000 ft.-lb.

The bending moment at the sixth-floor girder of each
sixth-story column is 4000 X 6 = 24,000 ft.-lb., and of
each fifth-story column is 5500 X 6 = 33,000 ft.-lb.

The compression in the floor girders is 6000 — 1500 =
4500 between Cols. A and 5, 4500 — 1500 = 3000 be-
tween B and C, and 3000 — 1500 = 1500 between C
and D. General equations can easily be deduced which
will simplify the calculation of stresses and moments for
other floors. If the spaces between columns are unequal,
the direct stresses from adjacent aisles will be unequal.
This difference is a direct stress in the column between
the two aisles considered. If the columns have differ-

[69]

ent sectional areas, the horizontal shear taken by each
column will be in proportion to its moment of inertia.

METHOD II-A
This is a special case of Method II and may be called

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t . is FLOOR

METHOD Z-A

FIG. 9. EECTANGULAK BUILDING-FEAME : DIRECT AND
BENDING STRESSES CALCULATED BY APPROXI-
MATE METHOD II — A

120.0 = Bending moment of 120,000 ft.-lb.
(4.0) = Direct stress of 4000 Ib.

[70]

the Portal Method. The structure is regarded as equiva-
lent to a series of independent portals. The total hori-
zontal shear on any plane is divided by the number of
aisles instead of by the number of columns as in II. An
outer column thus takes but one-half the shear of an in-
terior column. The stresses and maximum bending mo-
ments for a cross-section of the building are as given in
Fig. 9.

For equal spacing the direct or vertical axial stress due
to the overturning moment of the wind is all taken by the
outside columns and is the same in amount as in
Method II.

Considering in detail the sixth floor, we have in Fig. 10
the direct stresses and shears in the columns.

1^ FLOOR

16000^
6000^

7,333

5333

£333

£667
6r*FLOOR

$,667

r SV FLOOR

A B <_

METHOD 3-A

FIG. 10. COLUMN-SHEARS AND GIRDER MOMENTS AT
SIXTH FLOOR, CALCULATED BY METHOD II-A

The shear in each girder is 10,250 -- 5500 = 4750.
The equations for bending moments in the girders are as
follows :

Mt = [(2,667 X 6) 4- (3,667 X 6)] = 438,000

M, = [(2,667 X 6) 4 (3,667 X 6) — (10,250 — 5,500) X 16] = —38,000
M, = [(2,667 X 6) 4 (3,667 X 6) 4 ( 5,333 X 6) + (7,333 X 6)

— (10,250 — 5,500) x 16] = 4 38,000
M4 = [(2,667 X 6) + (3,667 X 6) + ( 5,333 X 6) 4 (7,333 X 6)

— (10,250 — 5,500) X 32] = — 38,000
M, = [(2,667 X 6) 4 (3,667 X 6) 4 2( 5,333 X 6) 4- 2(7,333 X 6)

— (10,250 — 5,500) X 321 = 4 38,000
M6 = 1(2,667 X 6) 4 (3,667 X 6) + 2( 5,333 X 6) 4 2(7,333 X 6)

— (10,250 — 5,500) X 481 = — 38.COO

The bending moment at the sixth-floor girder of each
outer sixth-story column is 2667 X 6 = 16,000 ft.-lb.,
and of each inner sixth-story column is 5333 X 6 =
32,000 ft.-lb. At the fifth-floor girder the bending mo-
ment of each fifth-story outer column is 3667 X 6 =
22,000 ft.-lb. and of each fifth-story inner column is 7333
X 6 = 44,000 ft.-lb.

[71]

The compression in the floor girders is 6000 — 1000 =
5000 between Cols. A and B, 5000 — 2000 = 3000 be-
tween B and C, and 3000 — 2000 = 1000 between C
and D.

H H

FIG. 11. CROSS-SECTION OF COLUMNS IN TRANSVERSE

BENT

It is noted from the above that the bending moment in
an outer column is one-half that in an interior column;
that the point of contraflexure of each girder is at its
center; and the bending moments due to wind for all
girders of any transverse bent on the same floor are alike.
This is an ideal condition for the detailer and the shop.
The designer finds this method very simple and his work
easily checked. The bending moment in a girder is the
mean between the bending moments in the interior col-
umn above and below the girder. The width of the aisle
does not affect the value of the bending moment.*

Methods I and II-A are specially adapted to transverse
bents when the columns are turned as in Fig. 11; also
when the outer columns carry floor loads only and the
stresses are but one-half those of the inner columns.

METHOD III

This may be called the Continuous Portal Method. The
direct stresses in the columns are assumed to vary as
their distances from the neutral axis, and the horizontal
shear on any plane is equally distributed among the
columns cut by that plane. Stresses and maximum bend-
ing moments for a cross-section of the building are as
given in Fig. 12.

The direct stresses in the columns are found the same
way and are the same in amount as in Method I.

*Burt, "Steel Construction" Section, Wind Bracing.

Considering in detail the sixth floor, we have in Fig.
13 the direct stresses and shears in the columns. The
shear in the girder A to B and the girder C to D is 9225
— 4950 = 4275. The shear in the girder B to C is
(9225 — 4950) + (3075 — 1650) = 5700.

4.0

6.0

6.0'

6.0

6.0

6.0

6.0-

8.0'

6.0

•48

6.0

(3.0)

(2.0)

M

•5f

^f\

q

o

|

£

o

^O

21.0

16.8

zt.o

(4.5)

(3.0)

(1.5)

s

£

Q

uj

39.0

3I.Z

390

(4.5)

(3.0)

(l.5)

?

1

s

0

57.0

45.6

57.O

75.0

(3.0)

(1.5)

£s

0

^

O

K

600

75O

(45)

0

(f.5)

"^

^S

6

V

<VJ

93.0

93.0

(4.5)

(30)

(1.5)

^0

K-

0

O

s<\3

K

«5

«H

tt/.O

88.8

l/t.O

180.0

(3.0)

(>•*)

""^T

Ci

o

i

i

t

/44.O

I6O.O

(4.0)

(2.0)

o

0

!

<-.-,&'-o'~-

s

§

Jg°V ^

2±.)LJ5WaL.

^

METHOD Ht

FIG. 12. EECTANGULAR BUILDING-FEAME : DIEECT AND

BENDING STRESSES CALCULATED BY APPROXIMATE

METHOD III

144.0 = Bending moment of 144,000 ft.-lb.
(4.0) = Direct stress of 4000 Ib.

The equations for bending moments in the girders can
be written as follows :

Mj = [(4000 X6) +(5500 X6) = +57,000 ft.-lb.

M, = [(4000X6) +(5500X6)1— [(9225^950) X16] = —11,400 ft.-lb.

M, = 2[(4000X6) +(5500X6)]— [(9225— 4950) X 16] = +45,600 ft.-lb.

2[(4000X6) +(5500X6)]— [(9225-^950) X32]— [(3075— 1650) X16] =

— 45,600 ft.-lb.

3[(4000X6) +(5500X6)]— [(9225— 4950) X32]— [(3075— 1650) X16] =

+ 11,400 ft.-lb

&

M8

B.

3[(4000X6) +(5500X6)]— [(9225— 4950) X48]— [(3075— 1650) X32] +
[(3075—1650) X16] = —57,000 ft.-lb.

The bending moment at the six-floor girder of each
sixth-story column is 4000 X 6 = 24,000 ft.-lb., and of

6000

5500 §
to

7* FLOOR

6 r-« FLOOR

•A

i

«B 1C

METHOD 3H

&

fvnoo*
!D

FIG. 13. COLUMN-SHEARS AND GIRDER MOMENTS AT
SIXTH FLOOR, CALCULATED BY METHOD III

each fifth-story column is 5500 X 6 = 33,000 ft.-lb. The
compression in the floor girders is 6000 — 1500 =
4500 Ib. between Cols. A. and B, 4500 — 1500 = 3000
between B and C, and 3000 — 1500 = 1500 between C
and D.

If the columns are unequally spaced or their sectional

LOAD JUV£&DZAD)

6VFLOOR

FIG. 14. GRAPHICAL COMBINATION OF MOMENTS FROM

VERTICAL LOADS AND WIND LOADS IN FLOOR

GIRDER

areas are different, the location of the neutral axis must
first be found. The direct stresses in the columns will
vary both as their distances from the neutral axis and

[ M]

their sectional areas. The horizontal shears taken by the
columns will vary as their moments of inertia.

CONCLUSION

It can be said of each of the above methods of calculat-
ing wind stresses that it is easily workable; and to quote
Prof. W. H. Burr : "So long as the stresses found by one
legitimate method of analysis are provided for, the sta-
bility of the structure is assured." At the present time
Method I is probably more used than any of the others,
though Methods II and II-A have been used quite exten-
sively. In the 36-story Equitable Building of New York
City, the largest office building in the world, Method I
was followed. In its near neighbor, the 32-story Adams
Express Building, Method II-A was used. Method III
is found in some text-books; it has been used but little
about New York, and only to a limited extent elsewhere.
The writer personally prefers Method I, though during
the past ten years he has used I, II, and II-A. In a 20-
story building in Philadelphia built in 1914-1915 he used
I. In an 18-story building in Atlanta, designed in 1912,
he used II-A. To Method III he objects not only because
of its practical limitations but because in theory it seems
farther from the truth than any of the others — especially
when it comes to distributing the shear for bents in build-
ings more than four aisles wide.

The practice of the writer in calculating wind stresses,
using Methods I or II-A (preferably I), is first to find
the distance of each column from the neutral axis of the
transverse bent to which it belongs, and then to assume
the moments of inertia of the inner columns in that bent
to be the same and of the outer columns to be one-half
that of the inner. The columns are proportioned for all
stresses coming upon them, including both direct and
cross-bending due to wind. It is seldom that corrections
are made for moments of inertia that differ from the as-
sumptions.

It is often convenient to assume the wind loads on the
basis of using the same unit-stresses as for live- and dead-
loads. A number of building codes call for a horizontal
wind pressure of 30 Ib. per sq.ft. and allow unit-stresses

[75 ]

to be increased 50% for wind-bracing. A wind load of 30
Ib. per sq.ft. with unit-stress of 24,000 Ib. per sq.in. is
equivalent to a load of 20 Ib. per sq.ft. with a unit-stress
of 16,000 Ib. per sq.in. — the working stress generally used
for live- and dead-loads. The diagrams of moments for
any floor girder can easily be combined in one figure (see
Fig. 14), and the total moment at any point read by scal-
ing. Fig. 14 is drawn for beam with ends supported. If
the ends were considered fixed the beam would be re-
strained and the diagram for both wind and floor loads
would show smaller bending moments. Any saving thus
made is doubtful economy as in actual practice it is un-
certain to what extent the beams are fixed (under vertical
load).

The building should be examined for wind in a longi-
tudinal direction as well as transversely and calculations
made if necessary. This is a simple thing to do but in
some marked instances it has been neglected.

Special attention should be given the column splices,
and the connection of floor girders to columns. It is folly
to add material to columns or floor girders to meet stresses
and moments due to wind, and then neglect their connec-
tions. Care should be taken that in all cases the connec-
tions are made strong enough for the bending moments
coming upon them. Many buildings have main members
sufficient to meet wind stresses without efficient connec-
tions. In such cases it matters little what particular
theory of wind distribution had been adopted.

[ 70

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