THE LIBRARY
OF
THE UNIVERSITY
OF CALIFORNIA
LOS ANGELES
GIFT OF
John S.Prell
'
MACHINE DESIGN
PART I.
FASTENINOS
BY
WILLIAM LED YARD CATHCART
ADJUNCT PROFESSOR OF MECHANICAL ENGINEERING, COLUMBIA UNIVERSITY; MEMBER
AMERICAN SOCIETY OP MECHANICAL ENGINEERS; MEMBER OP THE AMERICAN
SOCIETY OF NAVAL ENGINEERS; MEMBER OF THE SOCIETY OF
NAVAL ARCHITECTS AND MARINE ENGINEERS.
NEW YORK
D. VAN NOSTRAND COMPANY
23 MURRAY AND 27 WARREN STS.
1903
JOHN S. PRELL
Civil & Mechanical Engineer.
SAN FRANCISCO, CAL.
COPYRIGHT, 1903, BY
D. VAN NOSTRAND COMPANY
Eagiwerug
Library
TJ
Y.I
PREFACE.
THE main purpose of this book is to present, in compact lorm
for the use of the student and designer, modern American data
from the best practice in the branch of Machine Design to which
the work refers. The theoretical treatment of the subject has
also been given fully ; but this has been done for completeness
only, since that field has been covered exhaustively by able writers-
Scientific analysis and the records of practice are both essential
to success in the design of machine members, but neither alone is
trustworthy. The former predicts only those stresses which pre-
vail under normal conditions arid ignores the overload, the rough
handling, or the slight accident which the machine may meet and
against which it should not fail. Practical data, on the other
hand, show only the proportions which constructors have given
in specific cases of stress and service and empirical formulae
founded upon them may give results wide of the mark, if the
inherent limitations of these formulae be exceeded. The problem
of design is one whose many elements vary continually in num-
ber, character, and magnitude, and, for its solution, theoretical
analysis, precedent, and the ripened judgment of the designer
are required.
Elsewhere acknowledgment has been made of the courtesy of
the many officials and companies who have furnished information.
^ The author's thanks are due especially to Rear Admiral George
W. Melville, Engineer-in-Chief, U. S. Navy ; Professor Philip R.
Alger, U. S. Navy ; Professor J. Irvin Chaffee ; Leo Morgan, Esq.;
J. M. Allen, Esq., President the Hartford Steam Boiler Inspection
and Insurance Company ; C. C. Schneider, Esq., Vice President
the American Bridge Company ; Messrs. William Sellers and
a Company ; the Baldwin Locomotive Works ; and the Newport
News Shipbuilding and Dry Dock Company. The author desires
£3 also to express his deep indebtedness to Stevenson Taylor, Esq.,
Ci President of Webb's Academy and Vice President of the W. and
A. Fletcher Co., whose examination of, and additions to, the text
have added materially to the value of this work.
COLUMBIA UNIVERSITY, NEW YORK,
IO February, 1903.
733412
CONTENTS.
CHAPTER I.
PACK.
SHRINKAGE AND PRESSURE JOINTS :...... i
i. General formulae. 2. Proportions of the joint. 3. Metals.
4. Forcing pressures. 5. Shrinkage temperatures. 6. Shrinkage
vs. pressure fits. 7. Stationary engines, data from practice. 8.
Marine engines, data from practice. 9. Railway work, data from
practice. 10. Shrinkage in gun construction.
CHAPTER II.
SCREW FASTENINGS : . . . . . . . .42
ii. Triangular vs. square threads. 12. Requirements of the
screw-thread. 13. Elements of the screw-thread. 14. The U. S.
standard (Sellers) thread. 15. Modifications of the Sellers system.
16. The sharp V thread. 17. The Whitworth thread. 18. The
sharp V, Sellers, and Whitworth threads. 19. The French Stand-
ard thread. 20. The International Standard thread. 21. The
British Association Standard thread. 22. The square thread. 23.
The |--V thread. 24. Special threads. 25. Machine and wood
screws. 26. Pipe threads. 27. Stresses in screw-bolts. 28.
Stresses in nuts. 29. Efficiency of the screw. 30. Types of
screw fastenings. 31. Methods of manufacture. 32. Materials.
33. Nut -locks. 34. Wrenche s.
CHAPTER III.
RIVETED JOINTS : THEORY AND FORMULAE : . . . .127
35. Rivets. 36. Proportions of rivets. 37. Rivet and plate
metals. 38. Rivet-holes. 39. Boiler-seams : longitudinal, cir-
cumferential, and helical. 40. Forms of riveted joints. 41. The
elements of a riveted joint. 42. The theoretical strength of riveted
joints. 43. General formulae for boiler-joints. 44. The thickness
of shell sheets. 45. The stresses in riveted joints. 46. The fric-
tion of riveted joints.
v
vi CONTENTS.
CHAPTER IV.
RIVETED JOINTS : TESTS AND DATA FROM PRACTICE : . . .192
47. Tests of multiple-riveted, double-strapped butt joints. 48.
Riveting machines. 49. Riveted joints, marine boilers. 50. Riv-
eted joints, locomotive boilers. 51. Riveted joints, stationary
boilers. 52. Riveted joints, structural work. 53. Riveted joints,
hull plating.
CHAPTER V.
KEYED JOINTS: PIN-JOINTS: . 251
54. Forms of keys. 55. Proportions of keys. 56. Stresses on
keys. 57. Through-keys: forms. 58. Through-keys: stresses.
59. Pin-joints.
TABLES.
I. Shrinkage vs. Pressure Fits (Wilmore) . . - . 15
II. Pressure Fits (Lane and Bodley Co.) B'.. . . . 17
III. Shrinkage and Pressure Fits (Russell Engine Co.) . 17
IV. Pressure Fits, Stationary Engines . . . . .18
V. Shrinkage and Pressure Fits (Buffalo Forge Co.) . .18
VI. " " " " (B. F. Sturtevant Co.) . . 18
VII. " " " " Summary of Practice . . 19
VIII. " " " " (Union Iron Works) . . 23
IX. " Fits (Am. Railway Master Mechanics' Asso'n) 25
X. U. S. Standard (Sellers) Bolts and Nuts . . . .50
XL Standard Bolts and Nuts, U. S. Navy (Bureau of Steam
Engineering) . . . . . . . 52
XII. Manufacturers' Standard Dimensions of Bolt-heads (Am.
Iron and Steel M'f g Co.) 53
XIII. Manufacturers' Standard Dimensions of Hot-pressed Nuts
(Am. Iron and Steel M'f'g Co.) . . . . -53
XIV. Round Slotted Nuts (Newport News Shipbuilding and Dry
Dock Co.) 54
XV. Whitworth System, Bolts and Nuts 55
XVI. French Standard Screw Threads 58
XVII. International Standard Screw Threads . . . -59
XVIII. British Association Standard Thread 60
XIX. Standard Square Threads (William Sellers and Co.) . . 61
XX. Standard Square Threads (Newport News S. B. and D.
D. Co.) .62
XXI. X-v Screw Thread (William Sellers & Co.) ... 63
XXII. Standard Bastard Screw Threads (Newport News S. B. &
D. D. Co.) 64
XXIII. Acme Standard (29°) Screw Thread 65
XXIV. Proportions of Armor Bolts, U. S. Navy . . . .66
XXV. Machine Screws (Tyler) 69
XXVI. Wrought Iron Welded Tubes (Briggs' Standard) . .71
XXVII. Ratio of Bearing Pressure to Tensile Stress (Sellers
Threads) ......... 74.
XXVIII. " Grooved " Specimens (Howard) 76
XXIX. Threaded and " Grooved " Specimens (Martens) . . 77
XXX. Coefficients of Friction for Square Threads (Kingsbury) . 88
Coefficients of Friction With Various Lubricants (Kings-
bury) . , . . . . . . .88
vii
viii TABLES.
XXXI. Steel Studs for Cylinder Covers (U. S. Navy) ... 94
XXXII. Approximate Efficiencies of Square Threaded Screws (Good-
man) .......... 97
XXXIII. Safe Loads for U. S. Standard Bolts (Williams) . . .103
XXXIV. Tap-bolts and Set-screws (Newport News S. B. and D. D.
Co.) 105
XXXV. Eye-bolts (Union Iron Works) 107
Dimensions and Conditions of Stay-Bolts (Sprague and
Tower) 108
XXXVI. Collar Nuts with Locking Screws (Union Iron Works). . 121
XXXVII. Engineers' Wrenches, Single Head (J. H. Williams & Co.) 124
XXXVIII. Check-Nut Wrenches (J. H. Williams & Co.) . . .125
Wrenches, International Standard Nuts . . . .126
XXXIX. Proportions of Rivet-Heads (Am. Iron and Steel M'f g Co.) 128
XL. Proportions of Rivet-Heads (Champion Rivet Co.) . .129
Tests of Drilled and Punched Plates (Kirkaldy) . . .137
Efficiencies of Butt Joints, Double-Strapped (Traill) . .163
XLI. Tests of Multiple Riveted, Double-Strapped, Butt-joints (U.
S. Navy) . 196
XLII. Boiler Rivets (U. S. Navy) ... . . .207
Proportions of Joints, Cylindrical Boilers (U. S. Navy) . 208
Weight of Boiler Rivets (U. S. Navy) . . . .209
XLIII. Locomotive Boilers, Single Riveted Longitudinal Seams
(Baldwin Locomotive Works). . . . . .211
XLIV. Locomotive Boilers, Double Riveted Seams (Baldwin Loco-
motive Works) 212
XLV. Locomotive Boilers, Quadruple Butt-joint Seams with Welded
Ends (Baldwin Locomotive Works). . . . .212
XLVI. Sextuple Butt-joint Seams with Welded Ends (Baldwin Loco-
motive Works) . . .213
Locomotive Boilers, Location and Proportions of Seams
(Baldwin Locomotive Works). . . . . .214
XLVH., XLVIII., XLIX., L. Stationary Boilers, Riveted Joints (Hart-
ford Steam Boiler Inspection and Insurance Co.). 218, 219
LI. Proportions of Rivet-Heads (American Bridge Co.) . . 220
Weight of Rivets, Structural Work 221
LII. Staggering of Rivets (American Bridge Co.) . . . 222
LIII. Rivet Spacing in Angles (Am. Bridge Co.) . . . 223
LIV. Shearing and Bearing Values of Rivets (Am. Bridge Co.) . 225
LV. Angles, Sectional Area (Am. Bridge Co.) . ' . . .230
LVL, LVII. Riveted vs. Bolted Joints (Berlin Iron Bridge Co.) . 234
LVII-A, LVIII. Proportions of Seams and Rivets, Torpedo-boat and
Ship-work (U. S. N.) ..... 240, 241
LIX. Diameter of Rivers, Hull-work (U. S. N.) . . . . 242
LX. Allowance for Rivet-Points, Hull-work (U. S. N.) . . 243
TABLES. ix
LXI. Breadth of Laps and Straps, Hull-work (U. S. N.) . . 243
LXII. Spacing of Rivets, Hull-work (U. S. N.) . . . .244
LXIII. Minimum Thickness of Outside Plating and Flat Plate Keel
(American Bureau of Shipping) 246
LXIV. Diameter of Rivets, Breadth of Laps, Lapped Butts, Width
of Butt-straps, and Breadth of Edge Strips on Plate Seams,
Hull-work (American Bureau of Shipping) . . . 247
Plating and Transverse Seams (Am. Bu. Shipping) . . 250
LXV. Square Keys (Richards) . . . . . . .257
LXVI. Flat " " 257
LXVII. Feather " " 257
LXVIII. Keys for Shafting (William Sellers and Co.) . . .258
LXIX. " Machine Tools (William Sellers and Co.) . . 258
LXX. Key-ways for Milling Cutters (Brown and Sharpe M'f'g Co.) 259
LXXI. Stationary Engines, Crank and Wheel Keys . . -259
LXXII. Marine Engines, Keys and Key-ways (Newport News S. B.
and D. D. Co.) 260
Taper-Pins (Morse Twist Drill and Machine Co.) . . 268
LXXIII. Stationary Engines, Connecting Rod Ends, Bolted Strap . 269
LXXIV. Maximum Bending Moments on Pins (American Bridge Co.) 280
LXXV. Pins with Lomas Nuts (Am. Bridge Co.) .... 282
LXXVI. " Cotters " "".... 283
LXXVII. Eye-Bars (Am. Bridge Co.) 284
AUTHORITIES QUOTED.
Alger, Prof. Philip R., U. S. N., 29
Allen, J. M., 134, 192
American Boiler Manufacturers' Asso-
ciation, 215
" Bridge Company, 219, 220,
222, 223, 225,
to 284, inc.
230, 280
Bureau of Shipping, 245 to
250, inc.
" Engineer and Railroad Jour-
nal, 134, 266
Iron and Steel M'fg Co.,
53, 78, 128
Machinist, 104, 105, 203
" Railway Master Mechanics'
Asso'n, 25
Bach, Prof. C., 181, 187, 188, 189,
191
Bailey, F. H., Lieut. Com'd'r, U. S.
N., 261
Baldwin Locomotive Works, 192, 210
to 214, inc.
Barr, Prof. John H., 100
Bauschinger, Prof., 133
Berlin Iron Bridge Co., 234, 235
Birnie, Major Rogers, U. S. A., 28,
29
Bond, Geo. M., 50, 68
Box, Thos., 78
Briggs, Robert, 69, 70
Broomall, 14
Brown and Sharpe M'fg Co., 258,
259
Bryan, C. W., C.E., 227, 233
Buffalo Forge Co., 16, 18
Bulletin Soc. d'Encour, 59
Bureau of Construction and Repair,
Burr
20, 51, 73, 94, 114,
196, 205, 207, 277
Prof. W. H., 4, 13, 227
134.
U. S. N., 66, 109, 237 to 244, inc.
Bureau of Ordnance, U. S. N., 66, 67 McBride, Jas., 99
" Steam Engineering, U. S. N., i Meier, E. D., 215
x
Canaga, Com'd'r A. B., U. S. N.,
148
Champion Rivet Co., 129, 132
Chief of Ordnance, U. S. A., 36, 67,
192
Cramp, Edwin S., 236
Wm. S. and E. B. Co., 192
Clavarino, 6
Colby, A. L., 131
Cotterill, Prof. J. H., 4, 277
Goodman, Prof. John, 97
Harlan and Hollingsworth Co., 24
Hartford Steam Boiler Insp. and Ins.
Co., 216 to 219, inc., 275
Howard, Jas. E., 75
Johnson, Prof. J. B., 76, 133, 227
Jones, Prof. F. R., 255
Kennedy, Prof., 165
King, Major W. R., U. S. A., 78
Kingsburg, Prof. Albert, 87, 88
Kirkaldy, 75, 78, 137
Lame, 6
Lane and Bodley Co. , 17
Lanza, Prof. G., 101, 105, 106
Lewis, Wilfred, 89, 98
Lineham, Prof. W. J., 14
Linnard, Naval Constructor J. H.,
U. S. N., 236
Marks, W. D., C.E., 264
Martens, Prof. A., 76, 79, 91
AUTHORITIES QUOTED.
Melville, Rear Admiral Geo. W., U.
S. N., 112
Merriman, Prof. M., 6, 79
Midvale Steel Co., 22
Morse Twist Drill and Machine Co.,
268
New York Shipbuilding Co. , 24
Newport News Shipbuilding and Dry
Dock Co., 54, 62, 64, 105, 260
Niles Tool Works Co., 25
Porter, H. F. J., 19
Rankine, Prof. W. J. M., 4, 182
Reuleaux, Prof. F. , 6, 13, 74, 166,
168, 254
Richards, John, 257, 263
Rivet-Dock Co., 113
Russell Engine Co., 17
Schell, Lieut. Com'd'r, U. S. N., 171
Seaton, A. E. , 170
Seaton & Rounthwaite, 102
Sellers, William, & Co., 61, 63, 2-58
Smith, Prof. A. W., 82
Sprague, Chief Eng'r Jas. W., U. S.
N., 108, 277
Sternbergh, J. H., 114, 128
Stoney, B. B., 127, 130, 165, 181
Stromeyer, C. E., 186
Sturtevant, B. F., Co., 17, 1 8
Sweet, Prof. J. E., 82
Thurston, Prof. R. H., 14
Thury, Prof., 59
Tower, Chief Eng'r Geo. E., U. S. N.,
108, 277
Townsend, David, 112, 136
Traill, Thos. W., F. E. R. N., 134,
163, 170, 171, 210
Union Iron Works, 23, 107, 121
Unwin, Prof. W. C., 86, 145, 185
U. S. Board of Supervising Inspectors
of Steam Vessels, 209
Weisbach, Dr. Julius, 74, 118, 119
Whitney M'f g Co., 253
Williams, H. D., 101, 102
Williams, J. H., & Co., 124, 125
Wilmore, Prof., 150
Wood, R. D., & Co., 202
JOHN S. PRELL
Civil & Mechanical Engineer.
SAN FRANCISCO, CAL.
MACHINE DESIGN.
CHAPTER I.
SHRINKAGE AND PRESSURE JOINTS.
Rigid connections of this character between members of a ma-
chine or structure are of frequent application. The inner member
of the pair to be united is made cylindrical or slightly conical in
form ; the corresponding portion of the outer member is bored so
that it is of the same shape, but less in diameter throughout.
When, therefore, the latter is made to encircle the former, the re-
sulting radial pressure, acting at the contact-surfaces, produces a
frictional resistance to relative motion of the parts. In a Shrinkage
Fit or joint, the outer member is expanded by heating, slipped in
place, and held therein by the subsequent contraction in cooling. In
a Pressure ("Press" or "Forced") Fit, the parts are driven together
by hydraulic pressure. Joints of the latter type are, as a rule,
restricted to members of moderate size — crank-pins, cranks, and
the wheels and axles of engines and cars being familiar examples.
The shrinkage fit is applied, not only in the union of large mem-
bers in which maximum resistance to relative motion is desired,
as in the crank-shafts of engines of high power ; but, as well,
in modern ordnance, where results of extreme accuracy are es-
sential in order to obtain the desired inward pressure required to
withstand the outward force of the gases generated in the powder-
chamber.
i. General Formulae.
The final diameter of a joint made by shrinkage or pressure is
intermediate between those of the parts before union, i. e., the
inner member has been compressed and the outer expanded.
These changes and the elasticity of the metal produce a radial
compressive stress acting upon both members at the contact-sur-
faces and a consequent circumferential stress or " hoop-tension "
MACHINE DESIGN.
fyS
SHRINKAGE AND PRESSURE JOINTS. 3
within the outer member. The latter stress is a maximum at the
joint and decreases rapidly toward the exterior.
i. THIN BANDS. — When the outer member is thin, as a band or
tire, and the inner is, relatively, of large diameter, the compres-
sion of the latter is so small as, frequently, to be negligible in
practice. The stress of the shrinkage or forcing may then be
considered as expended wholly in the expansion of the band.
Assume then, as in Fig. I, an incompressible hub upon which is
shrunk such a band, the stress upon the latter being within the
elastic limit.
Let:
R0 = original radius of interior of band ;
R = radius of hub ;
t = tensile unit stress within band ;
et = unit elongation due to t ;
E = modulus of elasticity of band-metal = — ;
/ = unit radial pressure ;
b = breadth (axial) of band ;
T= thickness (radial) of band, expanded ;
/= coefficient of friction.
Then:
Increase in length, interior of band = 2r:(R — R^) ;
Original length, interior of band = 27rR() ;
r> 7p
Elongation per unit of length = et = — ~ — ° ;
-"-o
/? — /?
Unit tensile stress = t = Eet = E ^ — -. (l)
-^•o
This tensile stress, t, acts throughout the band, tending to re-
sist rupture of the latter on any diametral plane, as A-B. The
total resistance opposed thus at A and B =
2(6 x Tx t). (2)
The unit radial pressure, /, acts outward, equally at all points
upon the band. The latter is, therefore, virtually in the condition
of a thin cylinder, of length b and thickness T, subjected to in-
ternal fluid pressure. In Fig. I the vertical component of the
pressure / is that which tends to part the band on the horizontal
4 MACHINE DESIGN.
plane A-B. For an elementary strip of the band, of length Rdd,
and of breadth b, we have :
Radial force on elementary strip = Rdd x b x p ;
Parting force, elementary, on plane, A-B = Rdd x b x / sin 6;
Parting force, total, on band = bpR I sin 6dd = 2bpR. (3)
Equating (2) and (3) :
Tt (R-R^T
P~ R- RR0
The resistance to movement at the contact-surface is equal to the
product of the area of that surface, the radial pressure, and the
coefficient of friction, /. e. :
r> rj
Resistance to slip = E -= — - • 2~bTf. (5)
2. THICK CYLINDERS. — The method, as above, disregards the
compression of the inner member, assumes the stress of forcing
or shrinkage as expended wholly in expanding the band, and con-
siders the unit-stress within the latter as uniform throughout the
cross-section. The inner member cannot be incompressible and,
therefore, the circumferential stress given by (i) is greater than
that which would exist. The method is hence applicable only
within the limits noted. In an outer member whose walls are rel-
atively thick, the stresses at various radial distances differ widely
in intensity ; and, for the determination of their magnitude, recourse
must be had to the complex formulae deduced for the investigation
of thick, hollow cylinders, subjected to internal fluid pressure. Of
such formulae, those founded on the method of Lame * give, with-
out the assumptions of Barlow or Brix, the character and intensity
of the various stresses at any point within the cylinder walls.
Thus, consider, as in Figs. 2 and 3, a horizontal hollow cylin-
der, open at the ends, the latter being faced off in a plane normal
the axis. Let this cylinder be filled with fluid, which is forced
inward by two expanding plungers A, A, the result being the
production of a fluid pressure upon the internal surface of the
wall. From the construction and operation it is clear that, as the
ends are free, the cylinder will remain a cylinder under stress ;
*Rankine, "Applied Mechanics," 1869, p. 290. Burr, " Elasticity and Resist-
ance," etc., 1897, p. 36. Cotterill, " Applied Mechanics," 1895, p. 408.
SHRINKAGE AND PRESSURE JOINTS. 5
that a transverse section, taken normal to the axis "when at rest,
remains thus normal under stress ; and that, on such a section,
the resultant longitudinal stress is zero, both over the whole area
and at every point thereof. Assume that the material is isotropic
and that no stress, at any point, exceeds the elastic limit.
Consider any point O within the cylinder wall. Let :
Ry and Rl = inner and outer radii of cylinder ;
P0 and Pl = inner and outer pressures upon cylinder ;
t = circumferential stress at point 0 ;
p = radial pressure at point 0 ;
/ = longitudinal stress = zero at point O ;
r = radius of point 0.
Then, from the deduction in § 10:
(23)
.
R? - R* R? - R* ' r*
f~~ <X°-*>' + °K?-V
It will be observed that the circumferential stress / varies in-
versely as r2 and is therefore a maximum at the cylinder-bore.
This condition prescribes the useful limit of thickness for cylinders
which are not under exterior compression. No such cylinder can
be made sufficiently thick to withstand an internal pressure per
sq. in. greater than the ultimate tensile strength per sq. in. of the
metal, as is shown by equation (19). Since the working pressure
of modern ordnance exceeds considerably the elastic limit in ten-
sion of the material used, the necessity for the " built-up " system
is apparent. With regard to formulae (23), it will be observed
also that t may be either tensile or compressive, as the relations
of the radii and pressures determine ; that / is always compres-
sive ; and that both p and t are " apparent " and not " true "
stresses, since the factor of lateral contraction has not been intro-
duced with respect to them. Considering this factor :
True Circumferential Stress = /_J/_(_ J^). (6)
In a gun, the layer in which the breech-plug houses is under a di-
rect longitudinal stress /, arising from the pressure upon the plug.
This stress is a maximum at the face of the plug and diminishes
rapidly toward the muzzle. If the apparent values of /, / and /
6 MACHINE DESIGN.
be substituted in (6), the working equation for true circumferential
stress will be obtained, which equation is Clavarino's principal
formula for the investigation and design of guns.*
3. THICK HUBS. — Professor Reuleaux, in The Constructor,^ gives,
largely without deduction, certain working formulas, based upon
those of Lame as above, which are especially applicable to the
shrinkage or cold forcing of large machine members, such as
cranks and wheel-hubs. Thus, consider Fig. 4, which represents a
shaft or pin A, forced into a ring or hub B. The deduction applies,
theoretically, to either shrinkage or forcing. The notation is :
Sv = radial compressive stress at r ;
S2 = circumferential tensile stress at r ;
p = unit radial pressure upon contact-surfaces = Sl ;
E^ = modulus of elasticity, inner member ;
E2 = modulus of elasticity, outer member ;
r^ = radius of pin before forcing ;
r2 = radius of hole before forcing ;
r = radius of fit ;
/ = length of fit ;
d = thickness, outer member, after forcing ;
3 , _ri~r2 _Si
r ' rz ^2'
Q = maximum forcing pressure required ;
f = coefficient of friction = 0.2.
Under the conditions shown in Fig. 4, the notation of equation (23)
giving the value of t, when translated into that of The Constructor
should be changed thus :
ttoS2', P0 to 5, ; Pl to zero ; 7?n to r ; R^ to r -f o ; r remains as r.
(a) Stresses and Allowances. — Transforming the equation for t,
in accordance with the above :
(7)
*Merriman, " Mechanics of Materials," 1899, p. 318.
f Suplee's Translation, 1895, pp. 17, 18, 45-47.
SHRINKAGE AND PRESSURE JOINTS.
In Fig. 4 :
Unit deformation (strain}, inner member = —
r — r.
Unit deformation (strain), outer member = — ; — -.
From the definition of the modulus of elasticity :
S, r.-r Sz r — rz
p = and T=r = -. (9)
Adding :
rS± + r^ = r-r (10)
Whence :
By definition and from (10) :
From (n) and (12) :
vSj and vS2 are mutually dependent, their relation being expressed
by (7) and (8). In view of this and by definition :
Si-Sf. (64,O
From (36, C~) and (64, £") :
s, SL s s*
The second term of each denominator is so small as to be negli-
gible. Hence :
* For convenience of reference, numbered formulae from The Constructor are given
the same numeral, with " C" added.
» MACHINE DESIGN.
If the value of the ratio -, be assumed or known, it may be sub-
stituted in (7), thus giving that of the ratio, -„- = p, i. e. :
If:
d
— = 0.500, i.ooo, 1.500, 2.000, 3.000 ;
then
p = 0.385, 0.600, 0.724, 0.800, 0.882.
Since Ev £2 and the allowable value of S2 are known quantities,
the values of <p and Sl may be found from (38, C) by substitut-
ing the value of p.
(b] Forcing Pressure. — The force necessary to press a cylindrical
pin into a hole by continuous motion may be taken as nearly pro-
portional to the rate of progress, since that force must overcome
a resistance which is largely due to sliding friction, and the latter
depends upon the unit pressure on, and the area of, the surfaces
in contact. The force will be a maximum just as the pin reaches
the end of the hole. From Fig. 4 we have :
Maximum Forcing Pressure = Q = 2xr x / X Sl x f. (62, C)
Radial Pressure = S^=p = rfr. (63, C)
(c) Resistance to Slip, either axial or rotary, is given by the value
of Q in (62, C).
(d} The Thickness of Hub required to withstand the bursting
pressure corresponding with the slip resistance Q, as above, may
be found by combining (62, 64, C}. Thus :
Q^27irlfS2x p, (13)
in which Q is given in terms of the circumferential stress at the
contact-surface. From (7), (13) and (64, C) :
whence / 8\2 2iirlfS2 + Q
SHRINKAGE AND PRESSURE JOINTS.
and Thickness _8 _ \2xrlf S2 + Q
Radius ~r~ \2zrt/St -Q~1'
from which the required thickness d may be found.
(e) Slip-resistance vs. Rotating Force. — In (66, C) Q is the resist-
ance opposed by the fit to slipping at the contact-surfaces; its
leverage at the latter is r. Assuming the hub to be a part of a
wheel or crank of effective radius R, and the external, rotating force
at that radius to be P, we have, as the moment of the latter P x R,
.-.Qxr^PxR. (14)
(/) Coefficients of Friction in Forcing and Slip. — Assuming that
the resistance is wholly frictional, it is apparent that, for continu-
ous forcing, the coefficient of friction for motion should be used.
Slipping of the hub, however, must occur always from a state of
relative rest of the members. Therefore in (13) and (66, C\ the
coefficient for rest applies. With the high radial pressures which
prevail, there is a marked difference between the two coefficients.
2. Proportions of the Joint.
Economy of material prescribes that S0 shall be the maximum per-
missible tensile stress. For any given fit, S2, £} and £2 are therefore
constants, while the radius r is fixed by other considerations and the
length / is known approximately or accurately. The total grip Q
required would determine by (66, C) the value of the thickness d,
if the coefficient / were known ; but experiments indicate that the
value of this coefficient, as given ordinarily for the friction of motion
between the clean metallic surfaces considered, is not a safe measure
of the resistance of shrinkage and pressure fits, the latter especially.
Such investigation, however/with regard to the value of f'm these
fits, has been limited. In determining d, therefore, there should be
used, preferably, formulae which do not include this coefficient.
From (38, C] we have:
Total allowance / i p \
Diameter ** S*\E^ EJ (I5)
In the right-hand member all quantities are known except p.
From (7) and (64, C) it will be seen that, with increased thick-
ness, f) becomes larger. Therefore, if, with the same diameter
and metals, the hub be made thicker, the total allowance, the
radial pressure, and the grip per unit of surface may be increased.
IO MACHINE DESIGN.
Again, consider two hubs, one of steel, the other of cast iron,
both on the same steel shaft, with p and, therefore, d the same in
each case. In the former, as compared with the latter, the cir-
cumferential stress S2, the radial stress Sv and the unit grip pres-
sure may be larger and the allowance may be increased, although
not proportionately. Therefore, to obtain the same grip in both
cases there should be, as shown by (15), a decrease in the value
of d, p, and the allowance with the steel hub.
i. ALLOWANCE. — With regard to the relative values of shrinkage
and forcing in producing grip, the meager experiments available
indicate that, with equal allowances, fits of the former type are the
more effective in resisting both torsional and axial stresses. This
permits, apparently, for the same unit grip, a decreased allowance
in shrinkage. The differences in grip lie, doubtless, in the methods
of making the two joints. In shrinkage, there is, in cooling, sim-
ultaneous contact over the entire area of clean metallic surfaces,
without relative axial movement of the latter except that due to
contraction, while, in a pressure fit, surfaces lubricated originally
to a greater or less extent, are not only abraded, but the passage
of the inner member produces a longitudinal stress within the in-
ner layers of the hub.
If, in (15), the quantities in the right-hand member be kept
constant, there will be, for the same radial pressure and grip, a
uniform allowance per inch of diameter for shrinkage or forcing.
This uniformity, while by no means universal, is the practice of
many large companies, a frequent allowance for steel being one
one-thousandth of an inch (o.ooi in.) per inch of diameter. Since
the value of p depends upon that of the thickness, there must be
also with increasing diameter a proportionate growth in thickness.
When, as in Table IV., there is a decreasing unit-allowance with
increased diameter, there will be lessened grip, which reduction
must be met by an augmented length of hub. In any case, with
diameters of 2 inches and upward, keys should be fitted between
the shaft and hub as an assurance against slip.
2. LENGTH. — Let P x R — driving moment, ^ = polar modu-
lus of section, St = maximum shearing stress. Then, for a solid,
cylindrical shaft of diameter, d :
P x R = S. x Jc r = Ss x ~. (16)
SHRINKAGE AND PRESSURE JOINTS. II
From (62, C) :
(17)
Taking St and 5X as constant and equating (16) and (17) :
l=Kd, (i 8)
where Kisa. constant. Therefore, with a constant radial stress, the
hub-length should vary as the diameter, in order to make the grip
equal to the full strength of the shaft in torsion.
3. THICKNESS. — Let Fig. 5 represent the transverse section of
a closed, hollow cylinder (of inner and outer radii R0 and ^),
initially unstressed but subjected to the internal radial pressure
P0. For these conditions, equation (23) for the stress t at radius
R0 becomes :
/? rr~, D~
(19)
from which it appears that, if t = P0 = ultimate tensile strength,
7?j becomes infinite, i. e., no thickness whatever will prevent rup-
ture. Further, from (64, C), P0 = / x p, and, as p, in an initially
unstressed cylinder, is always less than unity, the ultimate tensile
stress t, as above, will be reached before P0 attains the same in-
tensity.
Again, for one side :
Area of Load Diagram O-d-e-f •= P^R^ ;
/•*
Area of Resistance Diagram, a-b-c-d = I tdr = P0J^0,
J£0
in which r = radius of any point within the wall and / = tensile
stress at that point, as given by (23). It is apparent, therefore, that,
for any given values of P0, R0, and the ultimate tensile strength, there
is but one value of ^ which will satisfy the equality of the areas, as
above, which value may be found from (19) by taking t at, or
within, the elastic limit, making P0 < /, and solving for Rr With
regard only to adequate strength, no useful purpose will be served
by increasing the value of ^ thus obtained. Finally, by substi-
p
tuting p = y° and Sl = />„ in (38, C), there will be obtained the
total allowance for the prescribed diameter.
12 MACHINE DESIGN.
4. FORM. — With regard to the form of the contact-surfaces, a
slightly tapering hole and corresponding inner member have ad-
vantages over the plain cylindrical shape, in that, with the latter,
the entrance of the hole must withstand the strain of abrading
and compressing the pin or shaft throughout the length of the fit.
The tapered member, on the contrary, enters without contact for a
considerable distance and is thus well guided ; the compression,
upon engagement, is distributed over a greater area ; the parts are
separated readily when a renewal of the fit is desired ; and the
drawings may be marked : " Fit pin — inches from the end of the
hole," which is the most trustworthy way of measuring the allow-
ance. The disadvantage of this form lies in the difficulty of secur-
ing, with the accuracy required, the same taper in both members.
3. Metals.
From (9) it will be seen that the radial stress of the inner mem-
ber and the circumferential stress within the outer, depend directly
upon the modulus of elasticity E of each material so stressed.
This follows since E is a measure of the stiffness of a metal, i. e.y
the stiffer the latter, the less will be the deformation (strain) under
a given stress and the larger the modulus. The following are
general values :
ELASTIC LIMIT.
Cast Iron. Wrought Iron. Steel.
Tension 6,000 25,000 50,000
Compression 20,000 25.000 50,000
MODULUS OF ELASTICITY.
Cast Iron. Wrought Iron. Steel.
Tension 15,000,000 25,000,000 30,000,000
Compression . 15,000,000 25,000,000 30,000,000
The circumferential stress of the outer member is the important
element, especially when that member is of cast iron, a metal which
has, in tension, a very low elastic limit, as compared with that, in
compression, of the steel or wrought iron of the inner member.
Cast iron is also, in tension especially, a very uncertain metal,
owing to differences in composition, in the size and form of the
SHRINKAGE AND PRESSURE JOINTS. 13
casting, and in the intensity of the original shrinkage strains.
Professor J. B. Johnson gives E for cast iron as varying from —
" 10,000,000 to 30,000,000 ; but, for ordinary foundry iron, it may be taken at from
12,000,000 to 15,000,000. * * * The modulus of cast iron is approximately the same
in tension, compression and cross-bending." *
Professor Burr, in commenting upon certain tensile tests of cast
iron, says :
"The metal is seen to be very irregular and unreliable in its elastic behavior. A
large portion of the material can scarcely be said to have an elastic limit, although no
apparent permanent set takes place under a considerable intensity of stress. In other
words, although perhaps all tested specimens resume their original shape and dimen-
sions for small intensities of stress, yet the ratio between stress and strain is seldom
constant for essentially any range of stress."!
4. Forcing Pressures.
The pressure required, at any given time during the process, of
making the joint, depends, approximately, upon the radial stress,
the character and area of the surfaces in contact, and the coeffi-
cient of friction.
1. CHARACTER OF SURFACES. — This will vary with different
metals and with the standard of workmanship. If the surfaces are
smooth but not accurately of the same form, the radial and forcing
pressures will be irregular in intensity. With rough surfaces the
frictional resistance will be increased ; and, in extreme cases, longi-
tudinal cutting, uneven bearing, and lessened grip may follow.
2. COEFFICIENTS OF FRICTION. — In a pressure fit there is not
only surface abrasion but the material of the outer member must
be forced aside by the forward part of the advancing inner mem-
ber ; and, if the elastic limit of the softer metal be exceeded, some
flow of the latter occurs. The resistance is not, therefore, purely
frictional and the usual coefficients of friction do not give an ac-
curate measure of its amount. In discussing shrinkage and pres-
sure fits, Reuleaux takes /= 0.2 which is the value used by Wei s-
bach for the usual metals in a dry state. The results of experiments
presented in Table I. show, as a rule, much lower values of/
than that quoted above. On the other hand, Rennie, from ex-
periments upon solids usually unlubricated, gives, for pressures
* " Materials of Construction," 1898, p. 476.
f " Elasticity and Resistance of Materials of Engineering," 1897, p. 279.
14 MACHINE DESIGN.
per sq. in. ranging from i86| to 560 Ibs., results, for the coeffi-
cient of rest, as follows : *
Wrought iron on wrought iron, _/"= 0.25 to 0.41 ;
Wrought iron on cast iron, /= 0.28 to 0.37 ;
Steel on cast iron, /= 0.30 to 0.36.
Abrasion occurred in the first case at 672 Ibs. pressure ; and, in the
latter case, at 784 Ibs. Broomall f gives, for static friction, as above :
Cast iron on cast iron, dry, f= 0.3 1 14;
Steel on cast iron, dry, /= 0.2303 ;
Steel on steel, dry, 7=0.4408.
Since the value of the coefficient is affected by conditions as to
motion and rest, temperature, lubrication, and speed of rubbing,
reported results vary considerably. Both shrinkage and forced
fits have higher radial pressures than those which prevail in the
usual friction tests ; the resistance in forming a pressure fit is not
purely frictional ; the force required to break such a joint may
be less than that of making, if the elastic limit has been exceeded ;
and pressure fits may be lubricated only to the extent of wiping
the surface with oiled waste, although a lubricant of white-lead
and oil, mixed to the consistency of paint, is frequently used to
prevent cutting. In view of these conditions the application to
these joints of the usual coefficients for unlubricated metals, is
inadvisable.
5. Shrinkage Temperatures.
Let e= unit diametral or circumferential deformation ; « = coeffi-
cient of linear expansion for a change of one degree F.; /= number
of degrees of change. Assume an outer member of steel with an
allowance of o.ooi in. per inch of diameter of fit. Then (Fig. 4) :
e=r^ = a.xt- t=€-. (20)
Substituting :
0.0000065
i. e., a raise in temperature of this amount would give the mem-
bers the same diameter. The usual shrinkage-temperature of
wrought iron and steel is about 600°, the increase providing for
greater allowance, for clearance in assembling, or for both. The
value of a for cast iron is 0.0000062 per degree F.
*Thurston, "Friction and Lost Work," 1898, p. 215.
fLineham, " Mechanical Engineering," 1898, p. 868.
SHRINKAGE AND PRESSURE JOINTS.
6. Shrinkage vs. Pressure Fits.
Table I. gives the results of comparative tests made under the
supervision of Professor Wilmore * upon cast-iron discs which
were either forced or shrunk upon steel spindles, the latter being
pulled from the discs in the " tension " tests or twisted in the holes
in measuring the grip in torsion.
TABLE I.
No.
Fit.
Test.
Q
*
Si
s,
f
I
P
Tension
1,000
O.OOI
9,700
10,116
0-033
2
S
"
5,320
"
"
"
0.170
3
S
"
5,820
"
"
a
0.190
4
S
Torsion
2,200
"
II
a
0.072
5
P
Tension
2,150
0.0015
14,516
15,275
0.047
6
P
Torsion
2,200
«
0.048
7
P
"
2,800
"
II
a
0.061
9
S
"
9,800
"
'I
a
O.2IO
10
P
Tension
2,570
O.OO2
19,355
20,366
0.042
ii
S
"
7,500
«
"
O.I 2O
12
S
«
8,100
"
"
«
0.130
13
P
Torsion
4,200
«
«
•i
0.069
14
P
Tension
4,000
O.OO25
24,^194
25,458
0.053
15
S
"
9,340
"
O.I 20
16
s
«
9,710
II
"
ii
O.I3O
17 ! P
Torsion
4,600
II
"
a
O.06 1
18 S
"
13,800
II
'I
"
O.igO
19 S
"
17.000
0.003
29,000
30,550
0.190
The discs were 6 in. in diameter and I in. thick, with, on one
side, a boss 2 in. in diameter, projecting ^ in., giving a bore i^
in. long and I in. in diameter. The spindles of machinery steel
were \\ in. in diameter, turned at the contact-surface to I in.
plus allowance for a length of i^ in., which length was reduced
by a taper at the extremity and a shallow groove at the top, each
^ in. long, making the bearing surface I in. in length.
The number of spindles tested was 19. The diameter of the
various sets differed by 5 ten-thousandths of an inch, the finished
dimensions being i.ooi in., 1.0015 in., 1.002 in., 1.0025 in. and
1.003 m- The pressure fits were made without lubrication, other
than that from wiping the surfaces with oiled waste. The spindles
and holes were found to be in good condition after the tests. The
maximum force required to move each spindle is given as Q in the
table. After movement had occurred, a less force was required
to continue it or begin it anew. Columns Nos. I to 5, inclusive,
* American Machinist, Feb. 16, 1899.
16 MACHINE DESIGN.
of the table were taken from the data of the tests ; the values in
the remaining columns were computed from formulae (15), (38, C),
(62, C) and (64, C).
Accuracy in calculating the intensities of the stresses ^ and S2,
and the coefficient f, is to some extent prevented by the boss,
groove, and taper described above. The approximation given
should be, however, sufficiently close for service. The value of
— was made = — — = 5, whence/-* = 0.946. Since both the length
and diameter of the contact surface = I in., (/> = allowance in each
case. The coefficients El and Ev were taken as 30,000,000 and
15,000,000 respectively. Shrinkage and pressure fits are marked
respectively " S" and " P," in the second column of the table.
The calculated results show very low coefficients of resistance
and very high circumferential stresses. Since the ultimate tensile
strength of cast-iron ranges between 15,000 and 35,000 Ibs. per
sq. in. and the discs were of good quality, rupture of the inner
layer of the bore did not occur ; but the elastic limit, in the ma-
jority of the tests, was exceeded. The superiority of the shrinkage
fit is marked, as is also that of both types in torsion. Excluding tests
Nos. 4 and 8, the results give average ratios of strength, as follows :
Tension: Shrinkage to Pressure = 3.66;
Torsion: Shrinkage to Pressure = 3.20;
Shrinkage: Torsion to Tension =1.50;
Pressure : Torsion to Tension —- 1.30.
7. Stationary Engines : Data from Practice.
Prevailing practice, with regard to diametral allowances in
shrinkage and forced fits and the pressures required for the latter,
varies considerably, owing to differences in the sizes of the mem-
bers, the qualities of the metals, the workmanship upon, and lubri-
cation of, the contact-surfaces, etc. There are given below, in tabular
form, through the courtesy of leading manufacturers of stationary
engines and similar machinery, records of allowances as follows :
Table II., the Lane and Bodley Company ; Table III., the
Russell Engine Company ; Table IV., a prominent stationary en-
gine building company ; Table V., the Buffalo Forge Company;
Table VI., the B. F. Sturtevant Company ; Table VII., summary
of Tables II. to VI.
SHRINKAGE AND PRESSURE JOINTS.
TABLE II.*
0
2
a.°^
O^S
l>~
8
Length of Fit
un.).
Mean Diameter
of Hole
(in.).
Total
Allowance
S.
j!
<
1 .
&
ft
Volume within
Fitted Surface
(cu. in.).
Pressure to
Enter Pin
(tons).
Pressure at
Mid-position
(tons).
Maximum Pres-
sure (tons).
___
1.8798
6.125
1.8767
.0031
.0017
36
I6.7
2
10
2O
2
1.8819
6.I2S
1.877
.0042
.0022
36
I6.7
2
15
23
3
1.8774
4-375
1.8764
.001
.00052
24.4
13-7
/2
I
4
2-7455
4-5
2.7387
.0068
.00247
38.7
26.5
3
12
25
2.7465
4-5
2.7437
.0028
.001
38.7
26.5
5
12
23
6
3.261
5
3-2542
.0068
.0021
51
41-5
5
2O
45
7
3.2625
5
3-2555
.007
.002
51
41-5
5
IS
30
8
3.267
5
3.261
.006
.0018
51
41-5
5
15
20
9
4-2505
6
4.2402
.0103
.OO24
79.8
85.1
5
22
44
io
4.2388
6.625
4.2478
.0091
.OO2I
78.1
93-4
12
30
60
ii
4 2303
6.5
4.2224
.co79
.OOI9
95-8
91
10
60
125
12
5-9343
4.0625
5.9216
.0127
.OO22
75-7
II2.2
6
16
25
13
5-9381
4
5-9252
.0129
.OO22
74-4
IIO.4
3
18
35
14
5-9294
4-125
5-9I94
.01
.OOI7
76.7
II3.8
5
15
25
15
6.8829
5-125
6.8697
.0132
.002
110.7
I9O.I
8
20
42
16
6.889
5
6.8785
.0105
.0015
108
185.9
5
22
45
X?
6.8692
4-875
6.855
.0142
.O02I
104.8
180.4
5
35
65
18
7.8884
5-5
7.873
.0154
.CO2
135-9
267.3
5
32
64
>9
7.8715
6-5
78575
.014
.0018
160.5
3*5-9
5
25
50
20
7.862
5-625
7.846
.016
.OO2
138.2
272.8
8
40
80
21
8.924
6.125
8.905
.019
.OO2I
170.8
378.9
20
45
68
22
8.9
6-75
8.8848
.0152
.OOI7
188.4
419.9
5
47
96
23
8.878
6-5
8.8669
.OII2
.0013
180.7
401
IO
45
92
TABLE III.*
CAST-IRON CRANKS.
Total Allowance, In.
In.
Shrinkage.
1'ressure.
4 to 5
0.0045
o.o' 90
5 ' 7^
0.0030
O.O060
7/2 ' 9
0.0027
0.0055
10 ' 12
0.0025
O.0050
12 ' l6
0.0020
o. 0040
16 « 18
O.OOI5
0.0030
The practice of the B. F. Sturtevant Company is as follows :
(«•) Shaft couplings are bored 0.003 in- less than the shaft. The forcing pres-
sure ranges from 6 tons for a 2lI3g-in. shaft to 12 tons for a 5~in. shaft.
(3) Crank-pins for cast-steel crank-plates are turned 0.005 m- large. The forc-
ing pressure ranges from 25 to 28 tons for a 5-in. pin to 10-15 tons for small pins.
(c) Crank-pins for cast-iron crank-plates are turned 0.009 m- too.on in. large.
The forcing pressure is as in (/>).
(J) Cast-iron Counter-balance Plates shrunk on Steel Crank- Discs. For diameters
of 9 in. to II in., the total allowance is 0.007 m- With increased diameters, this
allowance decreases, i. <?., for 13-in. diameter, total allowance — 0.006 in.
* Machinery, May, 1897.
iS
MACHINE DESIGN.
TABLE IV.
(A)
(B)
Diam., Shaft, In.
Allowance. In. of Diam.
Diam., Shaft, In.
Allowance, In. of Diam.
4
0.003
12
O.OOI
5
0.0024
13
0.0009
6
O.OO2
15
0.0008
7
O.OOI7
17
0.0007
8
0.0015
18
0.0006
9
O.OOI3S
19
0.00055
10
O.OOI3
22
0.0004
ii
0.0012
23
0.00035
12
O.OII
24
0.0003
13
O.OOI
26
0.00025
14
O.OOI
27
O.OOO2
15
O.OOI
16
0.0009
18
o 0008
20
0.00075
(A) Steel shaft and pin to cast-iron cranks. Average pressure required = 12 5
tons (2,000 Ibs ) per in. of diam.
(B) Steel shaft to cast-iron wheel hubs. Average pressure required = 10 tons
(2,000 Ibs.) per in. of diam.
TABLE V.
Pressure Fits.
Shrinkage Fits.
Diam., In.
Total Allowance, In.
Diam., In.
Total Allowance, In.
I to 2
O.OOI
I to 2
0.009
2
3 0.002
2
4
O.OIO
3
5
0.003
4
6
I/64
= .0156
5
7
0.005
6
9
3/128
= -0234
7
10
0.008
9
12
1/32
= -0313
10
12 ! O.OIO
12
18
3/64
= .0469
From the practice of the B. F. Sturtevant Company, with regard
to crank-plates and discs, we have :
TABLE VI.
Metal.
Diameter.
Allowance Per Inch.
Type.
Cast steel.
5 in.
o.ooioo in.
Pressure.
" iron.
5 "
O.OO2OO "
<*
« «
ii "
0.00064 "
Shrinkage.
" "
13 "
0.00046 "
"
In Table II. the outer member of No. 1 1 was a crank-disc of
cast steel, which, with less allowance, required twice the maximum
forcing pressure used with No. 10. In about 75 per cent, of the
fits, the maximum pressure was twice that at mid-position. The
allowance for shrinkage in Table II. is one-half that for pressure
(§ 2, Allowance), and, in both types, the unit-allowance decreases
with increased diameter. The latter is true also of the fits re-
SHRINKAGE AND PRESSURE JOINTS.
TABLE VII.
SUMMARY.
Diameter,
Total Allowance, In.
Members.
Shrinkage.
Pressure.
Table 11.
1.8798
0.0031
Shaft, steel ; hub, cast iron.
"
4.2505
0.0103
« «
«< <i «
"
8.9000
0.0152
« «
« « «
III.
4 to 5
0.0045
O.OOgO
Crank, c.
st iron.
»
7-5 " 9
0.0027
0.0055
"
'
«
16 " 18
0.0015
0.0030
"
'
IV.
4
O.OI20
"
' shaft, steel.
"
8
O.OI2O
M
< « «
V.
16
I " 2
O.009O
0.0144
O.OOIO
"
4 « 6
0.0156
11
5 " 7
O.OO5O
"
9 " 12
0.0313
«<
10 " 12
O.OIOO
VI.
5
0.0050
Shaft, steel; crank, cast steel.
II
5
O.OIOO
n «
" " iron.
I
ii
13
0.0070 \
0.0060 J
Cast-iron counter-balance
plates on steel crank discs.
corded in Table IV., in which, further, the allowance differs with the
outer member, being less for a wheel hub than for a crank, owing
doubtless to a difference in the thickness of the metal surrounding
the shaft. The allowance and length of hub are so proportioned
that the forcing pressure per inch of diameter is about uniform
throughout the range of each type. In Table V., the allowances for
pressure fits are practically uniform per inch of diameter, while those
for shrinkage fits decrease with increased diameter. The latter
also exceed considerably the corresponding pressure-allowances.
Table VI. gives double the allowance for cast iron as compared
with steel and a decreasing allowance with increased diameter.
8. Marine Engines : Data from Practice.
In marine practice, shrinkage fits are used in assembling " built-
up " crank-shafts and in securing the bronze casing of propeller-
shafts. Pressure fits are employed occasionally with crank-shafts
and frequently with smaller work. With regard to shafts, Mr.
H. F. J. Porter says :
" In the built-up type, the various parts are small and can be carefully worked,
and, if necessary, bored and oil-tempered. The physical properties of the metal can,
therefore, be raised to the highest possible limit. The forcing or shrinking process,
however, always puts a strain on the metal which will act as an initial load, approach-
ing possibly close up to the elastic limit. In the solid type, on the contrary, a very
large ingot would be required; and, as such a crooked forging cannot always be oil-
20
MACHINE DESIGN.
tempered with safety, the physical properties of the metal cannot usually be raised by
heat -treatment. The metal, however, can be relieved of all strains by annealing; and,
if properly designed, should work satisfactorily against externally applied stresses for a
very long time. ' ' *
When it is possible to make the crank-shaft in sections of
moderate length, interchangeable or otherwise, each section con-
taining one or more pairs of cranks, these sections may be forged,
each from a single ingot, bored and oil-tempered, thus obtaining high
physical characteristics without the initial stresses due to building up.
The necessity for casing the after, or propeller, section of a
marine shaft with non-corrodible material lies in the exposure of
that section to the action of sea-water, both in the " stern -tube "
and, sometimes, beyond the latter when the shaft extends through
the water to the strut-bearing and propeller. Within the tube the
bearings are of lignum vitae and the lubricant is, as a rule, sea-
water, the forward end of the tube being closed by a stuffing box.
To prevent corrosion the practice, for years, has been (Fig. 6, a,
b] to encase the after section of the shaft in a bronze sleeve, made
in short (3 -ft.) lengths, shrunk on, with lapped and recessed joints,
the latter being sealed on the outside with soft solder. Since the
torsion of the shaft tends to
loosen the casing, the latter is
secured further by pins or tap-
rivets. The casing should be
recessed within the propeller-hub
and should make an absolutely
water-tight joint with the latter.
As a rule, a protecting ring of
zinc is fitted also as an additional
precaution against galvanic action
between the casing and shaft. A
less usual practice than the use
of the bronze sleeve, as above, is to leave the shaft uncovered, to fit
a gland at the after end of the stern-tube and to keep the latter
filled with oil or tallow. In U. S. Protected Cruisers, Nos. 20 to 22,
the diameter of the propeller-shaft is 18 in. and the casing thick-
nesses are I in. at forward and i^g- in. at after bearing, | in. at the
laps (i in. long), and |- in. elsewhere. The following data are
given through the courtesy of leading builders of marine work.
*" Fatigue of Metal," &.c.,Jour. Franklin Institute, Dec., 1897.
SHRINKAGE AND PRESSURE JOINTS.
2L
AC.C
fy. «
22 MACHINE DESIGN.
I. The practice of the Midvale Steel Company, Philadelphia,
Pa., is as follows :
(#) Shaft Casings. — A new stern-tube shaft for the American
Liner New York was made recently at these works. It was 40
ft. long, 20^ in. diameter, and was cased partially with two bronze
sleeves, each 8 ft. long, fitted by shrinkage, the total allowance
for the latter bring 0.013 in. = 0.000634 in. per inch of diameter.
To secure uniform expansion, the casing was set vertically and
heated internally by gas, the latter issuing from a pipe a little
longer than the sleeve, inserted within the latter, and perforated for
the flow. When the bore as gauged showed sufficient expansion for
a free fit, the sleeve was slipped in place, held firmly at one end, and
cooled by water at the latter until contraction and grip occurred.
(£) Crank-shafts. — An allowance of o.ooi in. per inch of diam-
eter is made for steel. The method of building up is shown in
Figs. 7 to 1 6, inclusive. The crank-pin is finish-machined and a
cross-piece (Fig. 9), for guiding it when inserted, is secured by
screws at one end. The holes in the crank-webs for pin and shaft
are bored in a vertical machine to within % in. of finished diameter,
the tool (Fig. 7) being circumferential and two-bladed. If the web
is less than 7 in. thick, the cut is made from one side in one setting ;
otherwise, it is run half way through from each face. Then the
two webs which form a pair are bolted to a portable surface-plate
(Fig. 8), the latter is set on a horizontal machine, and the holes are
bored to the diameter of the pin, less the shrinkage-allowance.
The setting on the plate, with regard to parallelism and distance,
is that required for the pin when the latter is in place.
The webs are then heated in a sheet-iron furnace (Fig. 10), pro-
vided with a burner of perforated gas-pipe (Fig. 1 1), sliding doors,
and covered holes for occasional measurement of the bores by a
gauge (Fig. 12) made to the exact diameter of the pin, the gauge
being cooled in water after each test. When the expansion is
sufficient for a free fit, the webs are removed from the furnace and
the pin is pushed home, being guided by the cross-piece so that
the key-ways come flush, the latter being ensured by a loose false
key (Fig. 13) which is inserted as soon as the pin enters the web.
The pin is slung from a crane-hook, the sling being shifted, if the
pin is solid, when the latter has traversed one hole. If the pin is
hollow, it rides on a heavy gas-pipe, passing through the bores
and suspended by slings at the ends.
SHRINKAGE AND PRESSURE JOINTS.
The webs and pin are cooled with water, the false key is taken
out, and the permanent key driven home. The construction is
then removed from the surface-plate and set in a horizontal machine,
where the holes for the shaft are bored to the finished diameter,
less shrinkage-allowance. The webs are then set with the bores
vertical and one is heated as before. When the furnace is re-
moved, a planed plate (Fig. 14) is placed under the heated web, a
paper liner — which does not project into the bore — is laid between,
and the plate is forced against the web by three or four screw-jacks.
The shaft is then slung vertically over the bore and lowered until
it meets the plate, the downward projection due to the liner being
sufficient to make the end of the shaft and the face of the web
flush, when cooled by water. False and permanent keys are fitted,
as with the pin. While lowering, the shaft is guided by a wooden
frame (Fig. 15).
The remaining portion of the shaft is then shrunk into the other
web ; the completed section is set in a lathe ; the shaft and pin are
tested for parallelism ; and the centers of the shaft are drawn to cor-
rect any error. The section is then finish-machined and joined
by shrinkage with others. The entire shaft is then placed in a line
of V-blocks (Fig. 16), accurately set on a bed, for the final tests
in calipering, parallelism of center-lines, faces of webs and coup-
lings, and to determine whether the two latter are square with
the center-lines. Any errors detected are corrected by hand-
work.
2. Examples of the practice of the Union Iron Works, San
Francisco, Cal., are given in Table VIII.
TABLE VIII.
Members.
Diam. Ins.
Total Allowance.
Forcing Pres-
sure, Tons.
Shrinkage.
Pressure.
Steel Crank to Steel Shaft.
14
0.01562$
0.00938
loo to 150
Wro't-iron Crank to Wro't-iron Shaft.
8
0.0125
0.007
80 " 100
Cast-iron Crank to (hard) Steel Shaft.
8
0.00938
80
" « » « (soft) « •«
8
0.00938
20
Wheel Hub (C. I. hard) " "1
Length of Fit, 36-in.; Mean Dia'r. J
17-63/64
0.003125
80
As above ; hub of soft cast iron.
0.003125
3°
Cylinder-Liner, cast iron, hard.* "^
In Cylinder " " medium, j
80
O.O2I9
As above.
60
0.015625
40 to 60
« «
30
0.0125
Pressure fits now discontinued.
24 MACHINE DESIGN.
3. The practice of the New York Shipbuilding Company,
Camden, N. J., is as follows :
(a) Allowances. — These, in shrinkage or pressure fits in iron or
steel, are one one -thousandth of an inch (o.ooi in.) per inch of
diameter of fit, plus one one-thousandth of an inch (o.ooi in.).
Thus, on a 2-in. diameter, the allowance is 0.003 in.; on a lo-in.
fit, o.o 1 1 in., etc.
(V) Form. — With large fits, both the inner and outer members
have a taper of Jg in. to the foot, the allowances being as above,
If the conditions are such that it is more convenient to ream the hole
with standard parallel reamers, the inner member is tapered one half
thousandth of an inch (0.0005 in.) per inch of length, unless the fit
is so long that this taper would reduce the allowance at the small
end to less than one half that at the other extremity of the joint.
(c) Drive Fits. — For these, the allowance is one half that for
shrinkage or pressure joints.
(d) Shaft-Casings. — The allowance is one half that for a shrink-
age fit on heavy work.
4. The Harlan and Hollingsworth Company, Wilmington, Del.,
give, in built-up shafts, a shrinkage allowance of one one-thou-
sandth of an inch (o.ooi in.) per inch of diameter; and, in shaft-
casings, one half of this amount, i. e., 0.0005 m-
9. Railway Work: Data from Practice.
In railway work pressure fits are used in securing wheels to
axles and crank-pins to driving wheels while the tires of the lat-
ter are shrunk in place. A pair of drivers consists of the axle of
wrought iron or steel, the wheel-centers of cast iron, the tires of
TABLE IX.
Total Allowance, Tire, In.
A
B
38
0.040
0.0312=1/32
44
0.047
0.0469 = 3/64
So
0-053
0.0625 = 1/16
£
O.o6o
O.o66
0.0625 = 1/16
0.0781 = 5/64
66
0.070
0.0781 = 5/64
steel, and the crank-pins of the latter metal. In assembling these
parts, the wheel-centers are first driven on the axles and keyed.
SHRINKAGE AND PRESSURE JOINTS.
The tires are then shrunk on, the holes bored for the crank -pins
and the latter pressed in. Finally, the tires are turned to the fin-
ished size.
1. TIRES. — In 1886-7 the American Railway's Master Me-
chanics' Association recommended and adopted the diameters and
allowances printed, through the courtesy of that Association, in
the first and second columns of Table IX. These allowances
have not met universal use ; and, in column B the practice of a
prominent road, for the same diameters, is presented. The fit is
cylindrical between the wheel-center and the tire. The latter is
heated usually by gas-jets set about its circumference ; and, when
expanded, is placed on the wheel-center and allowed to cool.
Tires thus secured resist the lateral thrust and rolling action until
they are worn considerably, when they may become loose and
require liners or refitting.
2. WHEEL-FITS. — The joint is cylindrical. The pressure re-
quired for mounting the wheel is usually 9 to i o tons per inch of di-
ameter of fit; for removal, the total pressure may be 100 to 150
tons, depending on the condition of the joint as to rust, etc. The
FIG. 17.
mechanism used in these operations is shown by Figs. 17 and 18,
which represent the 4<DO-ton wheel-press made by, and illustrated
herein through, the courtesy of the Niles Tool Works Company,
Hamilton, Ohio.
The press consists essentially of a hydraulic ram ; a resistance
head, or abutment, sliding on tension-bars to which it may be
keyed at the required distance from the ram-head ; and supporting
26
MACHINE DESIGN.
hooks for the axle, depending from the upper bar. The resistance-
head has a central bearing for the axle, to enable the latter to lie in
the line of pressure. In mounting wheels, the axle, with each wheel
started on its fit, is hoisted into the hooks and resistance-head, and
the ram, acting on the hub next to it, drives both wheels home.
In dismounting, the resistance-head is moved nearer to the ram,
the stop-block shown in the head is removed, and the axle is laid
within the latter. The ram then engages the axle and forces it
out of the wheel, after which the axle is reversed and the remain-
ing wheel removed in a similar way.
FIG. 18.
The ram R is a solid iron casting, provided, at the rear, with
cupped leather packing. The cylinder is of strong and dense cast
iron, lined with \ in. copper, the latter being spun into place
and beaded over the counterbore. Water from the pumps en-
ters at d; a release-valve f, operated by a hand-wheel, permits
the fluid to escape, when desired, into the tank ; a safety-valve, e,
limits the pressure to 6,000 Ibs. per sq. in.; and the chains and
counter-weight retract the ram when the release valve is opened.
The pump is provided with two plungers, if in. and I in. diam-
eter, respectively, each operated by an eccentric on the driving
SHRINKAGE AND PRESSURE JOINTS. 2/
shaft. The plunger chambers are separate, each being provided
with suction and discharge valves. Through the suction pipe to
each chamber a tripping rod, c, passes, which, when elevated, lifts
the suction valve from its seat and thus stops the delivery from
that chamber while the shaft still rotates. The rod, c, is connected
externally to a lever and link, a support holding the latter in place
when the suction-valve is operating. It will be seen that the trip-
ping rods provide a very quick method of throwing either or both
pumps out of operation — an action which is essential, since, when
the wheel has reached the end of the fit, the inflow to the cylinder
should cease at once.
In starting the press, the belt is shifted to the tight pulley, the
trip-rods are lowered and both plungers operate until such a pres-
sure has been obtained as the belt permits. Then the suction
valve of the larger chamber is tripped and the work continues
with the smaller plunger until the limit of the fit is reached, when
the remaining suction valve is raised and further movement of
the ram is prevented.
10. Shrinkage in Gun Construction.
The stresses to which a gun is subjected upon the explosion
of the charge are : First, a radial pressure tending to split it on
an axial plane ; and second, a longitudinal stress acting to rupture
it on a plane transverse to the axis. There must be considered
also in design the radial compression of the bore — due to the
shrinkages of the exterior cylinders — which, when the system is
at rest, the inner layer must withstand.
To secure equal strength throughout without undue weight, the
material should be so arranged that every portion does its full
share in resisting the pressure from within. Fig. 5 shows the
rapid reduction in stress toward the exterior of a homogeneous
cylinder, the tension in the outer layer being but two fifths of that
in the inner, when ^ = 2R0. This uneconomical distribution of
the metal and the fact that the elastic strength of the latter is, in
such cylinders, the limit of the allowable internal pressure PQ, led
to the abandonment of cast guns, although some measure of com-
pressive, reinforcing stress upon the bore may be obtained, during
casting, by cooling the inner wall first, thus producing tension in
the outer layers.
28 MACHINE DESIGN.
Maximum economy of material will be attained when the
stresses throughout the walls are, at all points, upon the explosion
of the charge, not only approximately equal but also the greatest
permitted by the elastic strength. This condition can be ap-
proached only by placing the outer metal in a state of initial ten-
sion, the result being, when the system is at rest, a compression
and reinforcement of the inner layer, the latter being given thus
additional strength, since the initial compression must be over-
come by the pressure of the gases before tensile stress in the
fibers will be produced. In order to develop these initial stresses,
the gun is built of separate concentric cylinders shrunk one upon
the other, the unit diametral allowance or relative shrinkage of the
outer cylinders being such that, while these cylinders are thus
normally in tension, they have still a margin of strength, within
their elastic limits, to withstand the added tensile stress upon ex-
plosion. The stress-diagrams for such a construction are shown
approximately in Fig. 5, a, which represents a portion of a trans-
verse section of a tube with superposed cylinder. The area,
a-b-c-d, is the diagram of tangential stress for a single cylinder of
the maximum radius and combined thickness, subjected to the
internal pressure, P0. The area, e-g-f-c, represents the initial
tension in the outer cylinder, and its equivalent, d-e-h-k, the initial
compression in the tube. The areas, d-l-g-e and e-m-n-c, show,
respectively, the tangential stresses in the tube and cylinder when
under the internal pressure, P0. It is obvious that the latter
areas are together equal to the original diagram, a-b-c-d, less that
of initial compression, and plus that of initial tension. The
possibility of reducing the stress at the bore is apparent.
Since both radial and circumferential stresses change with each
increment of radius, the greater the number of superposed
cylinders in a given thickness, the more equable will be the
disposition of stress under internal pressure. In practice (Fig.
19), the number of such cylinders is, in large guns, four, viz. :
the tube, a single forging, the length of the bore ; the jacket,
encircling the tube from the breech-end about half way to
the muzzle ; two layers of hoops, superposed upon the jacket,
the chase-hoop extending to the muzzle ; and tapering and
locking bands. With regard to the radial and circumferential
stresses in a gun thus assembled, Major Rogers Birnie, U. S. A.,
says :
SHRINKAGE AND PRESSURE JOINTS. 29
" The accepted theory of this mode of construction is to assemble the several rows
of cylinders so that :
" In whatever state the system may be considered, none of the fibers of any cylinder
in the structure shall be elongated or contracted beyond the elastic limits determined
for such displacements by the free tests of the metal.
" With the system at rest this applies especially to the tube which, ordinarily, has to
support alone, or without other assistance than the atmospheric pressure, the accumu-
lated stress due to the shrinkages of all the outside cylinders. Under these circum-
stances, the surface of the bore undergoes the greatest change of form by compression,
so that the shrinkages of the outer cylinders must be limited to retain uninjured the
elastic properties of the metal at the surface of the bore of the tube. (It is, perhaps,
an open question whether the compression of the bore may not, with advantage, be
carried beyond this limit ; but, for the purposes of theoretical discussion, we assume
that it should not be. )
" With the system in action, that is, subjected to the maximum interior pressure which
it can support with safety, the cylinders or hoops composing each layer of the structure
should work together to the elastic limit of their metal. Here, again, it is the interior
fibers which undergo the greatest change of form in general by circumferential exten-
sion in the outer cylinders and by radial compression in the inner cylinders. The theo-
retical resistance of the gun must then be limited to retain uninjured the elastic proper-
ties of the metal at the interior of any of the cylinders composing the structure. This
involves the following considerations, viz. : As many of the cylinders as practicable
should work together to the elastic limit of their material under extension ; but, when
other cylinders are endangered from radial compression of their walls, the theoretical
interior pressure must be curtailed to provide against such over-compression, and the
working tensions of the first-named parts will be correspondingly reduced. However,
the wall of the tube (or part of the structure next to the bore) has always to support
the greatest normal pressure with the system in action ; hence, frequently, in this state
of the system also, the theoretical resistance of the gun will be limited by the strength
of the tube to resist compression, in this case radial instead of tangential, as in the
other extreme state of the system." *
Major Birnie considers that the longitudinal tension developed
in firing may, without noteworthy error, be neglected in deducing
the equations of equilibrium, expressing the relations between the
tangential and radial resistances for any state of the system.
i. SHRINKAGE FORMULA. — For the deduction which follows
the author is indebted to Professor Philip R. Alger, U. S. N.,
formerly of the Bureau of Ordnance, U. S. Navy, now head of
the Department of Mechanics, U. S. Naval Academy. Practically
all of the guns in the U. S. Navy were assembled with shrinkages
calculated by the formulae given below.
In this deduction it is assumed :
i. That there is no longitudinal stress on any layer. This
would be true only in the case of a hollow cylinder under fluid
* Ordnance Department U. S. A., "Notes on the Construction of Ordnance," No. 35.
30 MACHINE DESIGN.
pressure and having both ends free, and is not true for a gun ; but,
even with the latter, only the layer in which the breech-plug houses
is under direct longitudinal stress and that stress diminishes rapidly
as we go forward from the breech -plug face.
2. That a transverse section of the cylinder when at rest re-
mains a plane normal to the axis of the cylinder when the latter is
under strain — in other words, that the longitudinal strain is uniform
over the whole section. This would be a natural result of the
condition of free ends, but can be considered as only approximately
true for a gun.
3. That the total strain, in any direction, due to all the stresses
is the measure of the tendency to yield in that direction, so that
the limit of safety is reached, not when the stress in any direction
equals the elastic strength of the material, but when the strain in
any direction equals the strain which would be caused by the direct
action of a single stress equal to that elastic strength.
4. The ratio of strain, in the direction of the stress producing
it to the accompanying strain at right angles to that direction, is
taken to have the value 3.
(a) Stresses and Strains. — Let a hollow cylinder of radii R0 and
7?j be under pressure P0 from within and Pl from without, and
let T0 and 7^ be the resulting circumferential tensions at the
inner and outer surfaces. Also, let / and / be the circumferential
tension and radial pressure at any point of radius r within the
cylinder-wall and let et, er and et be the tangential, radial and
longitudinal strains at the same point. Also, let E be the modulus
of elasticity of the material. Then :
and since, by hypothesis, et is constant, we have
/ — p = constant = k.
But
'A>
and, assuming /=//(r), this gives,
SHRINKAGE AND PRESSURE JOINTS.
whence
f(r)=-pr- and so, t=f'(r)=-p-r^.
Thus, we have t — p = k and / -f p = — r -r* whence
dp
the integration of which gives 2p + k = -\t where kv is a constant
fcZ
of integration. Combining with t —p = k, we have t+p=^\.
These, then, are the fundamental equations which express the
relation between circumferential tension and radial pressure at all
points within the cylinder :
t-p=k=T0-PG=Tl-Pl I
(/ + py = ** = (TO + />x* = (T. + piW 1
Eliminating 7j between the last parts of these equations, we have :
and substituting this in the first parts of the same equations, we
have, after combining :
,
-R02
(23)
Substituting these values in the first part of (21), we have, for
the tangential strains at the inner and outer surfaces, where r = R0
and r = Rv respectively :
(24)
Suppose now the pressure Pl to be caused by a second cylinder
(radii Rl and /?,) embracing the first and itself under the external
MACHINE DESIGN.
pressure Py Let the circumferential tension at its inner surface
be designated as Zj' (to distinguish it from Tv the tension of the
outer surface of the inner cylinder, which is under the same radial
pressure Pv but not at the same tension as the surface in contact
with it) and that at its outer surface as T2. Then, applying
formula (24) to this second cylinder, we have, for the circumferen-
tial strains at the inner and outer surfaces :
(25)
Finally, assuming P2 to be caused by a third cylinder (radii, R2
and R^) whose outer surface is under no pressure, we have, for the
circumferential strain at its inner surface :
tr.
(26)
Now let -£, -£. , and ^ be the values fixed for the maximum
strains of the three cylinders respectively, when under the action
of the system of pressure P0, /*, and Py Substituting these values
for eTo, eTl,, and eTz, in (24), (25), and (26), we have
(27)
22 -f 2R?
the last of which equations gives the internal pressure which the
built-up cylinder will stand, if its parts have been so assembled
that the inner surface of each reaches at the same instant the con-
dition of maximum circumferential strain assigned to it. This, of
course, implies a definite shrinkage for each cylinder, which shrink-
age remains to be determined.
(&) Relative Shrinkages. — Observe now that equations (24), (25)
and (26) give the tangential strains resulting from the pressures P0,
SHRINKAGE AND PRESSURE JOINTS. 33
Pv and P2, and that if we substitute for these pressures any simul-
taneous changes in their values as pQ, pv and /2, the same equations
will give the corresponding changes of strain. But the surfaces of
contact of the cylinders must contract and expand together and so
the change of strain at the outer surface of each cylinder must equal
that simultaneously occurring at the inner surface of the cylinder
embracing it. Hence equating the second part of (24) to the first
part of (25) and the second part of (25) to (26), after replacing
P0, Pv and P2 by pv /, and pv we have :
- R* (R* - R*)fi + R>(R> - R^ = 0 1
R? (R? - Rfip, - R; (X* - R?}pz =o J '
the first of which gives the relation between simultaneously occur-
ring changes in the pressures at the radii, Rti, Rv and Rv and the
second, the relations between such changes at the radii, R^ and Rr
If, now, in the first equation of (28), we make p0 = — P0 and
P2 = — P2, we find :
R? (R* - X*) P9 + R* (X* - Rf).Pj
l~ ^i2W-^o2)
and this is the change of pressure at the radius Rlt which would
result from the simultaneous removals of the outer cylinder
which causes P2 and of the internal pressure P0 itself. There-
fore, substituting this value of p{ for Pl and — P2 for P2 in the
second equation of (25), we have, for the change of outer diameter
of the middle cylinder, due to removing the outer cylinder and
suppressing the internal pressure, the expression :
But, by hypothesis, the strain at the inner surface of the outer
/i
cylinder, before the change just referred to, was -£, and, there-
fore, the relative shrinkage of the outer cylinder must have been :
To find <pv the relative shrinkage of the middle cylinder, put
— P0 for P0 and — Pl for Pl in the second equation of (24) which
34 MACHINE DESIGN.
gives, for the change in outer diameter of the inner cylinder, due
to removing the outer cylinders and suppressing the internal pres-
sure, the expression :
whence
By the term relative shrinkage is meant the difference of diameter
per unit length of diameter of the surfaces to be superposed, so
that the actual differences of diameter are zR2<p2 and 2Rly>l.
(c) The Method of Procedure, then, is to calculate Pv P1 and P0 by
formulae (27) and then determine the shrinkages by formulae (29)
and (30). It may be, however, that the shrinkages thus found
would cause excessive compression of the bore of the inner cyl-
inder, when at rest ; and, if so, smaller values of 6l and 62 must
be used. To ascertain whether this is the case, eliminate p2 be-
tween the parts of equation (28) which gives :
'A J
and, making /0 = — P0 in this, the resulting value of p^ is the
change of pressure at the outer surface of the inner cylinder due
to the suppression of PQ. Therefore, pv + Pl must be the pressure
on that outer surface when the system is at rest ; and this must
not exceed
since, if it does, the tangential compression of the bore will ex-
ceed 00.
As a matter of fact, however, experience seems to show that
there is no objection to compressing the bore beyond the elastic
limit of the material under tension, presumably because the elas-
tic resistance to compression is really considerably greater than
that so-called elastic limit of tension.
It is also to be noted that no account has been taken of the fact
that the radial strain at the inner surface of a cylinder may, and
SHRINKAGE AND PRESSURE JOINTS. 35
indeed sometimes does, exceed the tangential strain, while our
formulae assume that it is only the latter which must not exceed a
fixed limit. This, too, can only be justified by the assumption
that the material really has a higher limit of elasticity under com-
pression than under tension.
In assembling U. S. naval guns with shrinkages calculated by
the foregoing formulas, #0, dl and 02 were taken as the lowest
elastic limit given by any specimen from the particular forging
considered, excepting where the resulting compression of bore
considerably exceeded #0, in which case 0t and 02 were some-
what reduced. The formulae as given herein are, of course,
easily extended to cover cases where there are more than
three layers.
The tangential strain is really the change of length per unit
length of the circumference and, so also, the change of length per
unit length of diameter. An alternative nomenclature of the
strains is as follows: Take a circle of radius 'r in the cylinder
walls when at rest and suppose that, when the pressures act, each
point of the circle moves outwardly Jrand axially Ah, then the tan-
Jr dAr
gential strain is — , the radial strain is -j-, and the longitudinal
strain is --,, , these strains being what have been called et, er and ev
(d} Radii. — If only the tangential resistance to internal pressure
is to be considered, the maximum value of P0 will be obtained by
making the radii increase in geometrical progression from that
of the chamber outward, provided the several cylinders have the
same elastic strength and the same modulus of elasticity. Thus,
for the case of one cylinder superimposed upon another, make P0,
formula (27), a function of Rl (R0 and R2 being constant and
6l = 0Q), differentiate, and make -^ = o. After cancellation, we
have R* = R0R2, showing that the maximum value of elastic re-
sistance for a given total thickness of a given material occurs when
the radius of the common surface is a mean proportional between
the inner and outer radii. For example, with the 6-inch gun of
4-inch chamber-radius and 8-inch thickness of chamber-wall, the
maximum resistance against tangential bursting stress would be
secured by making R0 = 4-inch ; /?t = 4^3 ; R2 = 4^9 ; and
^3=4^27= 12.
36 MACHINE DESIGN.
In practice, however, other considerations than tangential
stress prevent complete conformity with theory. In the first
place, it is necessary to make that layer which takes the longitu-
dinal strain of sufficient cross-section. In United States guns, the
breech-block houses in the jacket or second layer and the area
~(R£ — T^2) must be adequate, being, in naval guns, about three
times that of the rear end of the chamber, so that the longitudinal
stress on the jacket, if uniformly distributed, is one third of the
chamber pressures. In French guns, the breech-block usually
houses in the tube or inner layer, thus making Rl much greater
than is necessary for resistance to the maximum tangential stress.
Again, the tube thickness over the enlarged chamber should not be
too small to prevent lining the bore with a thin tube, after the erosion
of the powder gases has cut away the rifling and rendered the gun
inaccurate. Finally, the necessity for keeping down weight, which
prescribes a decreasing exterior diameter to correspond with the
diminishing pressure toward the muzzle, together with the need
for avoiding sudden or great changes of section in the various
forgings, sometimes dictates dimensions not otherwise desirable.
2. GUN CONSTRUCTION. — The 1 6-inch Breech-loading Rifle
(Type, Model 1895), completed — except as to the final boring,
rifling, and the hoops engaging the mount — during the year 1900
by the Ordnance Department, U. S. A., at the Watervliet Arsenal,
N. Y., is not only the most powerful gun yet built, but is also the
largest construction ever assembled by shrinkage. The general
data * are as follows :
Weight of gun 126 tons (252,000 Ibs.), of armor-piercing pro-
jectile, 2,400 Ibs., of powder-charge (smokeless), 576 Ibs.; powder-
pressure, 37,000 to 38,000 pounds per sq. in.; muzzle-velocity,
2,300 ft. per second ; muzzle-energy, 88,000 ft.-tons ; penetration
in steel at muzzle (De Marre's formula, normal impact), 42.3 in. ;
range, 20,978 miles; height of trajectory, 30,51 6 ft. (about 5^
miles) ; length of projectile, 5 ft. 4 in. ; cost per round, powder
and shot, $1,000.
(a) Description. — The gun is shown in section in Fig. 19. Its
total length is 590.9 in.; external diameter at rear, 60 in., at
muzzle, 28 in.; length of main bore, 448.5 in., diameter, 16 in. ;
rifling, 96 lands, 96 grooves ; depth of groove, 0.06 in. ; the
* Ordnance Department, U. S. A., "Notes on the Construction of Ordnance," No. 78.
SHRINKAGE AND PRESSURE JOINTS.
37
38 MACHINE DESIGN.
rifling curve is a semi-cubic parabola, ranging from one turn in 50
calibers to one in 25 at the muzzle. The cylindrical part of the
powder-chamber is 90.7 in. long, and 18.9 in. diameter, and is con-
nected with the bore by a conical slope 24 in. long. The volume
of the chamber is 29,385 cu. in. The recess for breech-block is
24.4 in. long, with a diameter at top of thread of 24.86 in. The
breech-mechanism is after the " Stockett System." The gun is
built up of parts, as follows :
The tube, 566.5 in. long, with a maximum outside diameter of
29.3 in.; two C-hoops shrunk upon the tube from the forward end
of the jacket to the muzzle ; the jacket, 304.65 in. long, shrunk
upon rear of tube, and overhanging the latter by 24.4 in. to form
the breech-recess; the D-koop, 144.5 m- l°ng> encircling forward
end of jacket and rear of (7-hoop, and having two locking
shoulders in its bore which engage corresponding projections on
jacket and £T-hoop, thus preventing any sliding backward of the
former or forward of the latter, from the shock of firing ; three
A-hoops, A-i covering the joint between the Z>-hoop and the
jacket, and A-2, A-j, being shrunk over the outer surface of the
latter ; four B-hoops, encircling the ^4-hoops.
Weights (Ibs.).
Rough.
Finished.
Tube with (7-hoops.
Jacket.
Hoop D.
' A-i.
' A-2.
' A-3.
' *B,
• *B-i, B-2, B-S.
124,351
90,058
26,965
19,859
16,137
20,163
58,620
100,260
73,900
23,900
14,910
15,120
19,940
The tube and jacket were each made from a nickel-steel ingot,
not fluid-compressed, and octagon in section. After removing the
discards, a longitudinal, axial hole was bored through the remain-
ing block and the tube or jacket was then forged hollow on a
mandrel under a hydraulic press. The completed forging was
then rough-turned, bored, tempered in oil, and annealed. The
hoops were made of fluid-compressed steel containing no nickel.
Excepting that the ingots were round, the general process was
similar to that for the tube and jacket. The hoop-metal was the
harder, i. e., having the greater elastic limit and tensile strength.
* Awaiting decision as to carriage.
SHRINKAGE AND PRESSURE JOINTS. 39
All forgings were of sufficient total length to provide test- metal.
The specimens for tube and jacket were 0.564 in. diameter and 3
in. long. The average physical qualities obtained in all tests are :
Tube.
Jacket.
Hoops.
Elastic limit, Ibs. per square inch. 5^,375
52,250
57,125
Tensile strength, Ibs. per s
quare inch.
84,350
87,800
107,050
Elongation, per cent.
20.38
22.16
IQ.28
Contraction, " "
41-93
48.32
45-52
(£) Shrinkage Furnace. — The furnace used in expanding the
parts for assemblage is shown in Fig. 20. It consists of a
wrought-iron "cage" or frame-work A, surrounding immediately
a cylindrical wall B of fire-brick, the whole resting upon solid
rock, at the 3O-ft. level, in a corner of the shrinkage-pit (Fig. 21).
The thickness of the wall is 13 in. and its internal diameter is 8 ft.
4 in. A cylindrical muffle C, built of ^2 -in. boiler steel, sur-
rounds the hoop to be heated. The outer diameter of the muffle
is 6 ft. 6 in., there being, thus, an annular space, 1 1 in. wide, which
forms a combustion-chamber for the burning gases. The furnace is
27 ft. 9 in. high ; its top is 2 ft. 3 in. below the floor-level ; it is
closed by a removable cover D, which confines the steam and
gases ; and the products of combustion are drawn off through a
flue connecting the top of the chamber with the main chimney.
Fuel oil is supplied through a 3 -in. pipe from a 5,ooo-gallon
tank and enters the furnaces through 20 burner-openings E, set
in five tiers F, of four burners each. The burner consists of an
internal steam-pipe of /^-in. bore, the latter being reduced at the
end to -Jg in. Surrounding this is a J^-'m. oil-pipe, the forward
end of which is plugged and a y^ -in. hole drilled therein, opposite
the Y6"^n- °Penmg m the internal pipe. The steam issuing at high
velocity through the latter opening, carries the oil with it as a
spray ; and its oxygen, combining with the oil, gives an intensely
hot flame. The burners are so directed that the flame strikes the
muffle at a tangent approximately, thus giving a rapid spiral move-
ment to the gases. The muffle transmits the heat to the hoop
and the circulation of air within it tends to make the temperature
equal at all points of the hoop. The furnace-temperature is
governed by a damper in the flue, by the number of jets burning,
and by the amounts of oil and steam admitted. Each burner is
surmounted by an observation opening, closed by a mica door.
MACHINE DESIGN.
Uniformity of heating is secured by the tangential direction of the
gases and by the intervention of the muffle, the latter keeping the
flames from impinging directly upon the hoop and thus causing local
heating in excess.
(<r) Shrinkage-Pit. — Within the same excavation which contains
the shrinkage-furnace, the shrinkage -pit (Fig. 21) is located, the
latter being 60 ft. deep and
cut from the solid rock.
To hold the gun during
the shrinkage processes,
a cast-iron chuck G is
anchored in the concrete
foundation at the bottom
of the pit and an interme-
diate chuck H is placed at
the 35-ft level. Upon this
level, also, there is con-
structed a heavy platform
or " tipping rest" K, for
supporting the lower end
of the gun while it is lying
in an angular position, after
having been brought to,
and partly lowered within,
the pit by two cranes. The
platform enables one of the
latter to lift the gun to a
vertical position and set it in
the chucks. In order to
handle the gun, when thus
within the pit, two steel
FIG 2I plugs, connected by a rod 7
in. in diameter and screwed
into each, were fitted within the bore of the tube, the plug at the
upper end being arranged for connection with the bail on the crane-
hook. A steam-pump to free the pit from the water used to cool
hoops after assembling completes the equipment.
(d} Assembling. — In preparation for the shrinkage of the jacket,
the tube was placed in the pit, muzzle-end down, and water con-
nections were made for interior cooling and for cooling the jacket
SHRINKAGE AND PRESSURE JOINTS. 41
when seated. The latter was then heated for 30 hours and its
bore calipered three times during that period to determine the ex-
pansion. Upon removal from the furnace, it was measured,
centered, and lowered in place and water was applied at the
muzzle-end. The cooling continued for nine hours, the number
of the encircling " water-rings " or pipes varying from four, as a
maximum, to two at the close of the operation. The shrinkage
of the C- and D-hoops was effected in a similar manner. The
A-hoops were assembled with the gun in a horizontal position in
the lathe. The hoists of a crane were attached to straps secured
to the hoop after heating and the latter was carried to the gun,
seated in place, and cooled by water from the forward end.
During contraction, the hoop was under the constant pressure of
two 3O-ton hydraulic jacks, one on each side, acting in the hori-
zontal plane through the axis of the gun. It is proposed to effect
the seating of the .5-hoops in a similar manner.
(e) Expansion, Shrinkage, and Clearance. — The expansion of
the metal, per inch of diameter for each degree of temperature,
was 0.000007 in. Thus, for an exterior diameter of hoop of 64
in., the total expansion for i ° of temperature = 0.000448 in., and,
for 800°, = 0.358 in. Measured exterior diameters at several
points on the surface of a hoop, if uniformly increased by ex-
pansion, indicate uniform temperature and the amount of expansion
shows the degree of temperature. Calling the diameter of the
cold tube D, that of the cold hoop or jacket d, and the shrinkage ^:
Expansion = 0.000007 (D — s}= E ;
Shrinkage = D — d= s ;
Clearance = E + (D — s) — D ;
Diameter of jacket heated = E -f (D — s}.
CHAPTER II.
SCREW FASTENINGS.
A screw-surface or helicoid is described by a right line, A-B,
Fig. 22, revolving about and advancing along an axis, Y-Y, as
directrix, one extremity, A, of the line remaining upon -the axis
and the angle of advance, a, between the latter and the line or
generatrix being constant. The base-angle, /?, is the complement
Y
of the angle of advance. In the screw-thread, the generating line
is replaced by a plane figure — as the triangle, B-E-F, a rec-
tangle, or a trapezoid — maintained always in an axial plane and
in contact with, and traversing a helical path upon, the surface of
a cylinder, as G-H-K-L.
42
SCREW FASTENINGS. 43
The nominal, or outer diameter, D, of a screw is that of the
outside or top of the thread. The effective diameter, d, is that of
the base or root of the thread and of the cylinder or core upon
which the latter is described. The depth of the thread is the radial
D — d
distance between its base and top, i. e., "£\v& pitch, p, is the
axial distance between adjacent convolutions of the same thread,
/. e., the axial distance which the nut traverses during one revolu-
tion. The pitch-angle, d, of any helix of the thread, is the inclination
between that helix and a plane perpendicular to the axis of the
cylinder. While, in a normal screw, the pitch of all helices is the
same, the pitch-angle of each depends upon its diameter. Cal-
culations with regard to stresses within the thread are referred
to the mean thread-diameter, d0, (of pitch-angle <50), at which all
forces are assumed to be concentrated. This diameter may be
taken also, with sufficient accuracy, as that of the mean helix,
equally distant from the helices at base and top of thread. The
projected area of the thread is used in computations for bearing
pressure.
In addition to differences in the forms of the threads, screws
are distinguished further as right- or left-handed and single- or
multiple-threaded. In a right-handed screw, the thread ascends
contra-clockwise from left to right. Screw-fastenings have usually
a single, right-handed, approximately triangular thread. A mul-
tiple (double, triple) threaded screw is one in which the cylinder
is traversed by two or more threads, parallel and similar in all
respects. Such screws, having ample bearing surface, are used
for the transmission of power.
The screw and its nut form, kinematically, a pair ; the relative
motion of whose two elements consists of rotation about an axis
and translation along the latter. If the material of the nut be
relatively inelastic, as metal, the requirement for motion as above,
is that the ratio between translation and rotation shall be constant,
i. e., that there shall be uniform pitch. When, however, the screw
revolves in a mobile medium or nut, as water, its surface may
have a varying pitch throughout. The marine propeller is a
transverse section of a multiple-threaded screw, the pitch of whose
blade-surface may be either constant or expand in either or both
of two ways — radially outward or from the leading to the follow-
ing edge of the blade.
44
MACHINE DESIGN.
ii. Triangular vs. Square Threads.
The form of the thread is determined by the character of its
service. The more important differences between the square
thread and the full or modified triangular type lie in the relative
strengths of these forms and the friction of operation. The load
in a bolt is usually axial. It is transmitted to the bolt-thread and
supported by the reaction of the nut-thread. The load-action and
the nut-reaction must be, for equilibrium, equal. These mutual
actions are, disregarding friction, normal to the contact surfaces,
i. e., to the threads. Considering friction, the reactions are di-
verted from the normal by the angle of friction, <p.
Fig. 23 represents sec-
tions of triangular and
square-threaded bolts of
the same pitch. Let W
and W^ be the axial
loads respectively, n the
number of threads in
W
each nut. and w = —
n
W,
and wl = — , the respec-
tive loads per thread.
Disregarding the small
angle, y, the lines of ac-
tion, a-b and e-f of the
pressures due to the loads will be normal to the respective thread-
surfaces. Consider the threads with regard to :
1. FRICTION. — This is directly proportional to the normal pres-
sure upon the contact-surfaces. With the square thread, the unit-
pressure upon the nut = e-f and 2. 'e-f = wl ; but, with the trian-
gular form, this unit-pressure = a-b, whose components are a-c
and b-c. The latter acts to burst the nut while 2a-c = w. Since
a-b ;> a-c, there is, other things equal, greater friction with the
triangular thread.
2. STRENGTH. — In the triangular thread, the section at the root
is the full length of the nut, while, in the square form, the sec-
tion is but one half this length. Against shearing and flexure
at the root, the latter thread is, therefore, proportionately the
weaker.
FIG. 23.
SCREW FASTENINGS. 45
3. NUT. — As noted, the triangular type has a bursting action
upon the nut, which action, disregarding friction, does not exist
with the square thread.
In general, the triangular form is more suitable for screw-fasten-
ings, owing to its greater strength, its increased frictional holding
power which prevents backing off under load, and the finer pitches
permissible by the full section at the base of the thread. On the
other hand, the square thread is better adapted for power-trans-
mission, since it has less friction and its bursting effect upon the
nut is so small as to be negligible.
12. Requirements of the Screw-Thread.
The screw is used as a detachable fastening in joining the mem-
bers of a structure or machine; in producing pressure or tension, as
in the screw-jack and testing-machine ; and for the transmission of
power and conversion of motion, as in the worm-gear and screw
propeller. Its requirements for these uses are :
1. POWER. — This depends upon the pitch and form. The effect
of the latter upon the strength and power of thread has been dis-
cussed. With a given applied force, the less the pitch, the greater
the axial load may be, since the pitch fixes the angle of the inclined
plane upon which the load virtually moves.
2. STRENGTH. — This is governed by the pitch, form and depth
of the thread. With constant load, the steeper the pitch, the
greater must be the applied power and the consequent normal
pressure upon the thread. For the same load and nominal diam-
eter, the deeper the thread, the less its mean bearing-pressure will
be ; but the moment of the load upon the root will be larger and
the effective diameter of the bolt to resist tension, will be reduced.
3. DURABILITY. — The most durable thread is one whose form
produces the least friction, whose depth gives minimum bearing
pressure, and which is most accurately fitted.
13. Elements of the Screw-Thread.
The requirements of the screw-thread make its elements inter-
dependent. Consider :
i. EFFECTIVE DIAMETER. — This depends upon the axial load
and the torsional stress produced by friction between the threads
in setting up the nut. The magnitude of the latter stress is gov-
46 MACHINE DESIGN.
erned by the applied power, and that of the power by the axial
load and pitch.
2. PITCH. — The relations between pitch and diameter in the
prevailing systems of screw-threads are the outcome less of log-
ical analysis than of long experience. For screw-fastenings, the
limit in one direction lies in the fact that, with an excessively
coarse pitch, the depth will be too great and the effective diameter
will be reduced unduly. Again, that component of the pressure
which is parallel to the thread -surfaces will exceed the force of
friction between the latter, and, owing to this excess, the nut will
back off. On the other hand, with an unduly small pitch-angle,
the surface-friction will form too large a proportion of the total
work of setting up the nut, the torsional action upon the bolt will
be excessive, and the latter may be sheared. In general, fine
pitches are unsuitable for soft metals and coarse pitches for shal-
low holes.
3. FORM. — As stated, the square thread is the form best adapted
for power-transmission. For large fastenings requiring to be read-
ily and frequently removed and which are strained heavily, but
in one direction only, as the breech-block of a gun, the trapezoidal
thread (Fig. 30) is most suitable. This thread has the acting face
normal to the axis, the rear face at an angle thereto, and combines
the greatest strength and least friction attainable.
For screw-fastenings in general, the triangular thread, with
blunt top, straight sides, and filled-in base-angle, was adopted
through various considerations with regard to strength, friction,
durability, ease of manufacture, and conformity with general prac-
tice. Thus, in strength and frictional holding power, this form is
superior ; its straight sides give even wear and maximum bearing
surface ; the angle between them is fixed, in the various systems,
by compromises between the conditions as to strength, friction,
bursting action upon the nut, and facility of verification and pro-
duction ; the flat or rounded top reduces the liability to injury ;
and the filling in of the reentrant base angle increases the effec-
tive diameter of the bolt and, in the Seller's system, the resilience
of the latter also.
4. NUT. — The nut may yield either by the shearing or rup-
ture of its threads or by bursting from the action of the outward
component of the pressure upon the thread. The latter, both on
bolt and nut, acts as a cantilever beam, fixed at the root and loaded
SCREW FASTENINGS. 47
uniformly over the bearing surface. When worn, the area of
the latter is reduced, the bearing becomes irregular, the load is
practically concentrated, and the bending moment at the root may
be increased. If the nut is of a metal materially weaker than that
of the bolt, its depth should be greater than the normal. In any
event, this depth should be sufficient to give ample strength
against flexure and shear at the root of the thread, to provide
sufficient bearing surface to prevent abrasion, and to afford a good
hold for the wrench.
5. MULTIPLE THREADS. — In power-transmission screws of large
pitch, a single thread will provide adequate bearing surface only
by having a depth so great as to give an unduly small effective
diameter of bolt. When the pitch is sufficient to permit it, the
use of two or more parallel threads of usual proportions will
secure the required surface with a normal effective diameter. Such
threads are usually of square or trapezoidal form.
14. The United States Standard (Sellers) Thread.
It would be difficult to overestimate the services to English-
speaking engineers of Mr. William Sellers and of his predecessor
in the same field, the late Sir Joseph Whitworth, in the investiga-
tions and efforts which led to the wide adoption of the respective
systems of screw threads which bear their names. The two sys-
tems are in essentials almost identical. That of Sellers was orig-
inally presented by him before, and recommended by, the Frank-
lin Institute in 1864. It was adopted later, with trifling modifica-
tion, by the U. S. Navy and War Departments and by the Master
Mechanics' and Master Car Builders' Associations and is now
known as the U. S. Standard System of Screw Threads.
The thread, as shown in Fig. 24, is triangular with flat sides in-
clined at an angle of 60°, the apex being cut off and the base
filled in to a radial distance in each case of one eighth the height
of the primitive triangle making "flats,"/", at these points each
one eighth of the pitch, />, in length. The Sellers system provides
dimensions for bolts from one fourth inch to six inches nominal
diameter. The notation and formulae are :
D = nominal (outside) diameter of bolt, inches ;
d= effective diam., ins. = D — 2s = D — \.-ip = D ;
3r n
48 MACHINE DESIGN.
D-d
s
depth of thread, ins. = — — p x 0.65 ; (31)
p = pitch of thread, ins. = 0.24 VD + 0.625 — 0.175 ; (32)
n = number of threads per inch = - ;
/= width of flat = ^ ; (3 3)
H = depth of nut, rough = D ;
h = depth of head, rough = ^ dh ;
dn = short diam., hex. or square nut, rough = ^ D -\- -|" ;
dh = short diam. of head, rough = |- D + -|/r ;
The equation for the pitch, as above, is an empirical formula con-
structed to cover diameters within the scope of the system. To
avoid impracticable fractions, the number of threads, as thus de-
duced, is modified to secure a convenient aliquot value. Thus,
for a 2 -in. bolt :
/ = 0.241/2 -f 0.625 — 0.175 = 0.2138 in.;
1/0.2138 =±= 4.68 = n = say, 4.5 threads per in.
The depth of the thread is obtained from the equation :
s = \p cos 30° = 0.65^,
deduced from the diagram, Fig. 24. The formula for the short
diameter, dn, of the nut is empirical and was derived from success-
ful practice. The values of the depths, H and //, of the nut and
head respectively were based upon considerations as to adequate
bearing surface, shearing stress, and provision for an efficient hold
for the wrench. The long diameters of hexagon and square fig-
ures may be obtained by multiplying the corresponding short
diameters by 1.155 and MH, respectively. The finished dimen-
sions for the depths and short diameters are :
H finished = Z? —
The U. S. Navy Department adopted the Sellers system with
the single exception that no difference was made in the size
SCREW FASTENINGS.
49
- — J> -J
G- O. 6SJO
f- /*-
' o.aeejtr.
fnternat'L
y.
• o.ejo
MACHINE DESIGN.
of finished and unfinished bolt-heads and nuts, in order that the
same wrench might be used for both. The size adopted was that
given by Sellers for rough work.
The formula for " the exact diameter of the tap-drill with no
allowance for clearance is :
1.2990381
n
d=D-
" The usual allowance (for clearance) above exact bottom diam-
eter is from 0.004 f°r /^ mcn to o.oio for 2-inch taps." *
TABLE X.
U. S. STANDARD (SELLERS) BOLTS AND NUTS.
Bolt.
Nut.
Head.
Nut and
Head.
Diameter. Area.
Threads.
Depth.
Depth.
¥
t
fr
p
w
If'
|f
i
-!
l|l
A
0.185 0.049
0.240 0.077
0.027
0.045
20
18
0.0063
0.0069
I
|
A
1
0.294
O.I 10
0.068
16
0.0078
i
i
tt
A
0-345
0.150
0.093
ii
0.0089
?
1
§i
\
0.400
0.196
0.126
13
0.0096
"s
i
A
0-454
0.249
0.162
12
0.0104
ft
I
H
0.507
0.307
0.2O2
II
0.0114
i
i
i ft
j
0.620 0.442
0.731 0.60 1
0.302
0.420
10
9
0.0125
0.0139
i
§
i!
0.838 0.785
0.550
8
0.0156 i
fl
JA
0-939 0.994
0.694
7
0.0179 H
it
1.064 1 1-227
0.893
7
0.0179 T¥
i
2
I-I59
1.284
1.485
1.767
1-057
1.295
6
6
0.0208 if
0.0208 1 1
i
2f
1.389
2.074
I.5I5
5i
0.0227 if
2T95
1.490
2.405
1.746
5
0.0250 1 1
|¥
2 f
I.6I5
2.761
2.051
5
0.0250 ' 1 1
2r|
I.7II
3.142
2.302
4
\
0.0278
2
IT95
3
I.96l
3-023
4
\
0.0278 ~2\
I*
3
2.175
4.909
3.7I9
4
0.0313 2£
IT!
3
2.425
5-940
4.620
4
0.0313 2f
2i
4
3
2.629
7.069
5428
3
\
0.0357 j 3
2ft
4
3*
2.879
8.296
6.510
3
]
0.0357 3*
2 ^
5
32
3.100
9.621
7.548
Si
0.0385 3'
2ri
5:
3l
3-3I7
11.045
8.641
3
0.0417 i 3 1
5:
4
3.567 12.566
9.963
3
0.0417 4 3ft
6
4
3.798 ! 14.186
11.329
2
r
0.0435 A 3 \
6
4
4.028
15.904
12.753
0.0455 ! 4* 3rV
6
4
4-255
17.721
14.226
0.0476 41 1 3t
7
5
4.480
19.635
15.763
0.0500
5 ! 3if
7
5
4-73°
21.648
17.572
0.0500 5£ 4
8
5
4-953
23.758
19.267
0.0526 si- ! 4ft
84
I
5-203
5423
25.967
28.274
21.262
23.098
0.0526 s| 4f 8f
0.0556 6 4ft 9!
* "Standards of Length," G. M. Bond, 1887, p. 169.
SCREW FASTENINGS. 51
The Sellers system was investigated exhaustively by a Board of
U. S. Naval Engineer officers in 1868. This Board * found as to
i. Pitch. The relations of pitch and diameter did not differ
materially from the average proportions dictated by good practice.
2. Form. The thread, as compared with that of ordinary V form,
gave with equal pitches a greater effective diameter and was less
liable to injury. Further, in the most unfavorable case — that of
the one-fourth-inch bolt — where the inclination of the thread and
the torsional stress are maxima, the tendencies of the bolt to yield
to tension or torsion are, with clean and well-lubricated surfaces,
about equal. 3. Nut. To resist shearing (stripping) of the thread,
the depth, H = D, gives a marked excess of strength for perfect
threads, since, for the latter, but 0.357^ is required. With regard
to bearing surface for fastenings, the depth, H, provides as much
or more than nuts were given ordinarily. The diameter, dn, was
found to give ample security against bursting action, since, neglect-
ing the resistance of the thread and taking the entire section of
the bolt as effective, the required diameter, dn= i^D. 4. Head.
The depth, h, was sufficient to provide fully against shearing and
to afford an efficient hold for the wrench.
The proportions of the Sellers system are given in Table X.
15. Modifications of the Sellers System.
Experience with the proportions of this system has resulted in
modifications as to :
1. PITCH AND DIAMETER. — For nominal diameters ranging
from 2^ ins. to 6 ins., equation (32) gives the corresponding
numbers of threads per inch as ranging from 4 at 2^ in. to 2^
at 6 in. These proportions, theoretically, should be such as will
give a bolt equally strong in all respects. In naval practice and in
that of many large companies, it is now customary to make the
number of threads per inch 4 for all diameters from 2 y2 in. to 6 in.,
inclusive, thus increasing materially the effective diameter of the
bolt. The proportions of bolts and nuts now prescribed by the
Bureau of Steam Engineering, U. S. Navy, are given in Table XI.
2. BOLT-HEADS AND NUTS. — The proportions of nuts and
bolt-heads, as given in the Sellers system, require odd sizes of
bar-metal, not usually rolled by the mills, for the nuts and addi-
* " Report of Board to Recommend a Standard Gauge for Bolts, Nuts, and Screw-
Threads for U. S. Navy." May, 1868.
MACHINE DESIGN.
tional upsets in order to obtain sufficient metal for the standard
head. Tables XII. and XIII. give dimensions which are without
these disadvantages.
3. CIRCULAR NUTS. — The Sellers system gives the dimensions
of hexagonal and square nuts only. The former are lighter, their
long diameter is less, and, where the movement of the wrench is
restricted, they are more readily screwed home. The circular,
grooved nut is a form applicable for use in a confined space and
is of especial value where very large sizes are required as, for ex-
ample, on the end of a propeller shaft. The outside diameter of
the circular nut is equal to the short diameter of the other types,
TABLE XI.
STANDARD DIMENSIONS OF BOLTS AND NUTS FOR U. S. NAVY.
(BUREAU OF STEAM ENGINEERING.)
Dia
IB.
Eff. Diam.
Threads
Long
Diam.
Short
De
3th.
L
>B
D — d.
Per Inch.
Hex.
Sq.
Diam.
Head.
N
,
1
t'
065?
.072
20
18
if
If
V
A"
c
-
.081
16
II
B
1
||
t
f
•093
14
if
II
II
(
J
f
.100
13
I £
1
JL
f
J
1
.108
12
1
I f
H
1?
5
k
.118
II
ft
I £
iA
n
1
\
.130
IO
fi
I |
i ^
§
-
•144
9
fi
2TV
IT\
ft
r
.162
8
l
2JL
i f
13.
.186
7
A
2T\
iH
II
.186
7
T5.
2|£
2
i "
.217
6
H
3A
2T3^
133*
.217
6
1
3«
2j
JtV
.236
Si
H
IT9J
i.
.260
.260
5
5
3^
4A
2|"
2r?
I*
i
.289
31!
4H
3*
IT9jJ
r
.289
4?
4A
4rw
3*
I f
I
.
.325
4
4|f
5H
3*
IT!
;
|
4
6
4
2 i
i
3
4
sH
6H
4
2f\
3
3
4
5tt
7A
5
2 5
3
r
3
4
6^
7H
5
2T5
3
;
3
4
8i
5
3
f
4
4
7A
SH
6
4
4-
;
4
9r3i;
6
3i
4
|
4
7H
9lt
6
3A
4
4
4
8f
10 i
7
31
4
5
4
8$
lOff
71
3«
5
1
4
4
9l
9«
"A
S?
8
8}
4A
5
5
5
6
4
4
I0?f
io{j
I2ff
y
4|
6
E
SCREW FASTENINGS.
53
plus twice the depth of the groove. In large sizes, this diameter
is less than the long diameter of the hexagonal form. Good pro-
portions for circular nuts are given in Table XIV.
TABLE XII.
MANUFACTURERS' STANDARD DIMENSIONS OF BOLT HEADS.
(AMERICAN IRON AND STEEL MANUFACTURING COMPANY.)
Diameter, Bolt.
Square and Hexagon
Heads,
Diameter, Bolt.
Square and He;
Heads,
cagon
Width and Thickness.
Width and Thickness.
A
i XA
MX i
A X A
I
I]
I
1
I* X i
IUX
IT X i
F
i
MX f
IXA
fix i
8x§
III
•
i
iiX f
2}fX 1
•
i
iAX f
2
3 Xii
TABLE XIII.
MANUFACTURERS' STANDARD DIMENSIONS OF HOT-PRESSED NUTS.
(AMERICAN IRON AND STEEL MANUFACTURING COMPANY.)
SQUARE.
HEXAGON.
A
Short Dia. Thickness. Hole. Size, Bolt
54
MACHINE DESIGN.
TABLE XIV.
ROUND SLOTTED NUTS.
(NEWPORT NEWS SHIPBUILDING AND DRY DOCK COMPANY.)
Diameter of
Bolt.
Diameter of
Bolt.
r
16. The Sharp "V" Thread.
This thread has been superseded very largely in the United
States by that of Sellers. As shown in Fig. 25, the sides are in-
clined to each other at an angle of 60° and have a sharp apex and
base. A section of the thread forms, therefore, an equilateral tri-
angle, each side of which is equal to the pitch of the screw.
Using previous notation :
s=p cos 30° = 0.866/;
d= D— 2s = D— 1.732/5
The pitch is usually that of the Sellers system.
SCREW FASTENINGS.
55
17. The Whitworth System of Screw-Threads.
In 1841 the late Sir Joseph Whitworth brought forward, in a
communication to the Institution of Civil Engineers, the system
of screw-threads which bears his name. This system, modified
slightly in 1857 and 1861, has met universal adoption in Great
Britain and extended use upon the continent of Europe. The
range of diameters was originally, as in the Sellers system, from
one quarter inch to six inches.
TABLE XV.
WHITWORTH SYSTEM. BOLTS AND NUTS.
Bolt.
Hexagon.
Diameter.
Area.
Pitch.
Threads.
Head.
Nut and Head.
Nominal,
D.
Effective,
d.
Effective.
P-
Per Inch,
Depth,
Short Diam.,
dn and </A.
\
•
0.186
0.0272
0.0500
20
0.2187
0.525
i
I
0.241
0.0456
0.0555
18
0.2734
0.6o I
i
0.295
0.0683
0.0625
16
0.3281
0.709
T
V
0.346
0.0940
0.0714
14
0.3828
0.820
j
•
0-393
O.I2I3
0.0833
12
0-4375
0.920
-
•
0.508 0.2035
0.0909
II
0.5468
1. 100
0.622 0.3038
0.1000
10
0.6562
1.300
1
r
0.732
0.4219
O.IIIO
9
0.7656
1.480
0.840
0.5542
0.1250
8
0.8750
1.670
0.942
0.6969
0.1428
7
0.9843
1. 860
1.067
0.8942
0.1428
7
1.0937
2.050
1.161
1-0597
0.1666
6
I.203I
2.210
1.286
1.3009
0.1666
6
1.3125
2.410
1.368
I.47I9
O.2000
5
I.4I28 2.570
Ij
1.494
1-7530
0.2000
5
I-53I2 2.750
I:
1-590
I.9855
0.2222
4*
1.6406
3-020
2
I.7I5
2.3101
0.2222
44
1.7500
3.I50
2;
•
1.930
2.9255
0.2500
4
1.9687
3-540
2
2.180
3.7325
O.250O
4
2.1875
3.890
2:
2.384
44637
0.2857
3
2.4062
4.180
3
2.634
5-4490
0.2857
3
2.6250
4-530
s
1
2.856
3-105
3-320
6.4063
7.5769
8.6726
0.3077
0.3077
0-3333
3
3
3
2.8256
3.0624
3.2812
4.850
5.I70
5-550
4
3-573
10.0270
0-3333
3
3.5000
5-950
4^
•
3.804
11.3710
0.3478
3.7046
6.370
4^
•
4-054
12.9140
0.3478
3^9374
6.820
•
4.284
I44HO
0.3636
4-1562
7-300
5
4-534
16.1460
0.3636
4-3750
7.800
11
•
4.762
5-012
17.8100
19.7290
0.3809
0.3809
4.5936
4.8124
8.350
8.850
si
•
5.240
21.5490
0.4000
5-0312
9-450
6
5-487
23.6540
0.4000
5-2500
IO.OOO
As shown in Fig. 26, the thread is triangular in section, the
angle between the sides being 55°. The primitive triangle
$6 MACHINE DESIGN.
is rounded off at the top and bottom by an amount equal, in
each case, to one sixth of its height, making the depth of the
thread two thirds of the altitude. The relation between di-
ameter and pitch, the angle of the sides, and the depth of the
thread were determined by taking the mean of the variations in
these respects of a large collection of screw-bolts gathered from
the principal machine-shops throughout England. The one quar-
ter inch, one half inch, one inch, and one and one half inch bolts
were examined particularly and taken as the fixed points of a
scale by which intermediate sizes were regulated, deviation from
the exact average being made only to avoid small fractional parts
in the number of threads per inch. The formulae are :
s = y^p -i- tan 27° 30'= 0.64 / ;
d=D—2s=D—
p = — = 0.08 D + 0.04 approximately ;
r = radius of rounding = o. I373/.
The dimensions of the system are given in Table XV. The
depth of the nut is equal to the nominal diameter of the bolt.
18. The Sharp V, Sellers, and Whitworth Threads.
Consider bolts of the same nominal diameter in these systems
with regard to :
. i. TENSILE STRENGTH. — The effective diameters are :
V Thread, d=D— 1. 732/1
Sellers, </= D — 1.3/5
Whitworth, d= D — I.28/.
2. STRIPPING OF THREAD. — The section, at base of thread, to
resist shear in :
V and Whitworth Threads = / ;
Sellers Threads = O.875/.
3. BEARING SURFACE. — This is a maximum in the V thread
with its straight sides from apex to root and a minimum in the
Whitworth form owing to the rounding. The Sellers thread
holds an intermediate place.
SCREW FASTENINGS. 57
4. FRICTION. — The normal pressure and, therefore, the friction
are less in the Whitworth thread than in the other types, owing to
the smaller angle of the sides.
5. RESILIENCE. — The section of least diameter is but a line in
the V thread and is a flat, \p in length, in the Sellers system.
The rounded base gives the Whitworth form an intermediate posi-
tion. While the Sellers type seems thus to be superior, the
sudden change in section at the bottom of its thread is a source
of weakness.
6. DURABILITY. — The sharp tops of the V thread are very
liable to injury. In this and the Sellers form, the normal pressure
is uniform over the entire surface, while, in the Whitworth thread,
it is uniform upon the sides and varying and greater over the
curved surfaces. The wear of the Sellers type will be, therefore,
less than that of the Whitworth.
7. REPRODUCTION. — The 60° angle can be reproduced and
verified more readily than one of 55°. The curves in the Whit-
worth form vary in radius with the pitch and cannot be made with
the same degree of precision as the flats of the Sellers system.
The taps and dies used in the making of the V thread soon lose
their fine cutting edges, thus causing constant variations in fitting.
19. French Standard Screw-Thread.
(Sy steme Unifie Frangais^
To the Societe d' Encouragement pour r Industrie Nationale is
due the credit for the adoption of a standard thread in France.
The thread form is practically that of Sellers based on metric
units. The section is an equilateral triangle whose base is equal
to the pitch, the top of the triangle being cut off and the root of
the thread filled in to form flats, situated one eighth the height of
the triangle from its apex and base respectively. As in the
Sellers system :
Angle = 60° ;
Depth s = 0.65 / ;
Width of flat, f =-0.
o
The proportions of the system are given, in millimetres, in Table
XVI. It has been extended to a nominal diameter of 148 mm.
(5.82 in.) and a pitch of 10.5 mm. (0.4133 in.). At nominal
MACHINE DESIGN.
diameters of 80, 96, 106, 1 16, 126, 136 and 148 mm., the pitches,
respectively, are: 7, 8, 8.5, 9, 9.5, 10, 10.5 mm. The standard
screws adopted by the French Navy include the extended series
as above with certain others intercalated to. meet the requirements
of the service.
TABLE XVI.
FRENCH STANDARD SCREW-THREADS.
Diameter.
Thread.
Pitch.
Nominal,*
D.
Effective,
d.
Depth,
s.
/•
mm.
mm.
mm.
mm.
6
4.70
0.650
I.O
10
8.50
0-975
1-5
14
11.40
1.300
2.0
18
14-75
1.625
2-5
24
20. 10
1-950
3-0
30
2545
2.275
3-5
36
30.80
2.600
4.0
42
36.15
2.925
4-5
48
41.50
3.250
5-0
56
48.85
3-575
5-5
64
56.20
3.900
6.0
72
63.55
4.225
6-5
80
70.90
4-550
7.0
20. International Standard Screw-Thread.
(Systeme Internationale, S. /.)
This system was adopted by the Congres International pour
r Unification des Filetages, held at Zurich, October 3-4, 1898. Its
proportions differ from those of the French Standard only in the
pitches of the screws of 8,9, 12 and 1 3 mm. diameter, and in the
insertion in the series of the odd numbered diameters 27, 33, 39,
45 mm., which were not included in the French system.
The rules formulated by the Congress apply only to screw-
bolts of a nominal diameter of 6 mm. and upward. The form of
the thread is practically that of the Sellers system, excepting that
a serious defect in the latter is avoided by providing clearance at
the bottom of the thread. This clearance must not exceed one
sixteenth the height of the primitive triangle. The top of the
thread is flat in order to facilitate production and to reduce the
liability to injury. The shape of the bottom may be flat or
rounded, the latter being recommended to avoid reentrant angles
which aid rupture. The dimensions prescribed by the Congress
* Dimensions given only for bolts at which change of pitch occurs.
SCREW FASTENINGS.
59
are given in Table XVII. The pitch of any size intercalated be-
tween those of standard diameters is to be the same as that of the
next smaller diameter. The thread, with the full clearance and
curved bottom recommended, is shown in Fig. 27. The formulae
are :
Altitude, a, primitive triangle = O.866/ ;
d= D — 2 x & = D —
D-d
s (maximum) = -- = 0.703 5/ ;
/ = width of flat = ^ ;
Clearance, C (max.) = — .
TABLE XVII.
INTERNATIONAL STANDARD SCREW-THREADS.*
Nominal
Diameter,
D.
Pitch,
/•
Nominal
Diameter,
D.
Pitch,
P-
Nominal
Diameter,
D.
Pitch,
P-
mm.
mm.
mm.
mm.
mm.
mm.
6
.00
20
2-5
48
5-o
7
.00
22
2-5
52
5-0
8
•25
24
3-0
56
5-5
9
10
•25
•50
27
30
3-o
3-5
60
64
ii
ii
•50
33
3-5
68
6.0
12
1-75
36
4.0
72
6.5
14
2.00
39
4.0
76
6-5
16
2.00
42
4-5
80
7-0
18
2.50
45
4-5
21. The British Association Standard Thread.
This thread was taken, with a slight modification, directly from
the Swiss system of Professor Thury whose work, for the small
screws used in watches and scientific instruments, was similar to
that of Sellers and Whitworth for screw-bolts. Thury's investi-
gation was undertaken in 1876 at the instance of the Geneva
Society of Arts. His system, like those which preceded it, was
formulated from data obtained by measuring the dimensions of
many screws accepted as well proportioned. The form of the
* Bulletin Soc. d'Encour., March, 1899.
6o
MACHINE DESIGN.
British Association thread is shown in Fig. 28. It is similar to
that of Whitworth. The angle is 47.5°. The formulae are :
P = °-9" 5
o.6p ;
In these equations the quantities are expressed in millimetres.
For screws characterized as No. o, No. I, No. 2, etc., the index
n has the values o, 1,2, etc., respectively. The equation for /
gives thus a gradually decreasing series, each pitch being 0.9 of
its predecessor. The values of the pitches thus obtained, substi-
tuted in the equation for D, give the corresponding diameters in
millimetres, two significant figures only being taken. Table XVIII.
gives the proportions of this system.
TABLE XVIII.
BRITISH ASSOCIATION STANDARD THREAD.
N,
Exact Dimensions,
Millimetres.
Approximate Dimensions,
Inches.
Diameter,
Nominal,
D.
Pitch,
P-
Diameter,
Nominal,
D.
Pitch,
p.
Threads
Prr Inch,
n
0
6.00
1. 00
0.236
0.0394
254
I
5-30
0.90
0.209
0.0354
28.2
2
4.70
0.81
0.185
0.0319
31-4
3
4.10
°-73
0.161
0.0287
34-8
4
3-6o
0.66
0.142
0.0260
38.5
5
3.20
0-59
0.126
0.0232
43-0
6
2.80
0-53
O.I 10
0.0209
47-9
7
2.50
0.48
0.098
0.0189
52.9
8
2.20
0-43
0.086
0.0169
59-i
9
1.90
0-39
0.075
0.0154
65.1
10
1.70
0-35
0.067
0.0138
72.6
ii
1.50
0.31
0.059
0.0122
81.9
12
1.30
0.28
0.051
O.OIIO
90.7
13
1.20
0.25
0.044
0.0098
IOI.O
M
1. 00
0.23
0.039
0.0091
1 1 0.0
J5
0.90
0.21
°-°35
0.0083
I2I.O
16
0.79
0.19
0.031
0.0075
134.0
17
0.70
0.17
0.027
0.0067
149.0
18
0.62
0.15
0.024
0.0059
169.0
19
0.54
0.14
0.021
0.0055
181.0
20
0.48
O.I2
0.019
0.0047
212.0
21
0.42
O.I I
0.017
0.0043
231.0
22
0-37
0.098
0.015
0.0039
259.0
23
o-33
0.089
0.013
0.0035
285.0
24
0.29
0.080
o.on 0.0031
317.0
25
0.25
0.072
o.oio 0.0028
353-0
SCREW FASTENINGS.
61
In 1900, a committee of the British Association, appointed to
consider modifications in this thread, recommended, as to the
screws and nuts from No. o to No. 1 1 inclusive, that the exist-
ing proportions remain unchanged, excepting that the top and bot-
tom of the thread be made cylindrical, showing " flats " in section ;
and that, to provide clearance, the depth of the thread be increased
by one tenth of the pitch, thus reducing the effective diameter by
one fifth the pitch. Thus, for screw No. o, the nominal and
effective diameter, as modified, would be 6 and 4.6 millimetres
respectively, while the corresponding diameters of the nut thus
modified would be 6.2 and 4.8 mm.
22. The Square Thread.
The relative advantages and disadvantages of this form of thread
have been discussed in §n. It is used for the transmission of
power as in screw-jacks, the leading screw of lathes, etc. It is
more costly than the triangular thread since it must be cut in the
lathe. The proportions have not been standardized. The practice
of two prominent companies is given in Tables XIX. and XX.
The corners of the thread are slightly rounded and occasionally
a small angle is given its sides, although the thread-form is prac-
tically square.
TABLE XIX.
STANDARD SQUARE THREADS.
(WILLIAM SELLERS & COMPANY.)
Nominal
Diam.,
D.
Threads
Per In.,
Effective
Diam.,
d.
Nominal
Diam.,
D.
Threads
Per In.,
n.
Effective
Diam.,
d.
\"
10
.1625"
if
3
1.0834"
A
9
•2153
if
3
1.2084
A
7
.2658
.3125
l|
!
1.307
1.4
A
?
.3656
.4167
2
\
1.525
1.612
A
51
5
.466
•512
3
2
2
1.862
2.0626
i
5
4|
4|
4
ill
.6806
.7188
2|
i
2
I-
I
I
['
2.3126
2-5
2-75
2.962
i
4
.7813
3!
I
3.168
«|
3i
.875 4"
I
34l8
1}
3^
I !
62
MACHINE DESIGN.
TABLE XX.
STANDARD SQUARE THREADS.
(NEWPORT NEWS SHIPBUILDING AND DRY DOCK Co.)
°s
Diar
Nomii
neter,
lal, D.
Diameter,
Effective, d.
Area, Effective,
irar*-^4.
Threads per In.,
Nut, Depth,
H.
•
//
0-3333"
0.0870
6
/'
i
0.4250
0.1418
5
0.5500
0.2376
5
[
0.6530
0-3349
4-5
0.7500
0.4418
4
0.8750
0.6013
4
|
0.9640
0.7300
3-5
|
I.O900
0.9331
3-5
2
1.1670
1.0700
3
2}
1.2900
1.3070
3
2|
I.4I70
1-5770
3
2|
1-4750
1.7090
2-5
4
1. 600O
2.0106
2-5
3
r
1.8500
2.6880
2-5
3l
1
2.0000
3.I4I6
2
3f
"
<
2.2500
3.9760
2
4|
3
2.5000
4.9087
2
42
23. The |-V Screw-Thread.
This thread is a modification of the square and triangular forms
designed to combine some of the advantages of both types. The
sides are inclined at a moderate angle and there are wide flats at
the top and bottom. As compared with the square thread, the
various |-V forms are stronger, being relatively wider at the root;
they can be cut with a die, which is not possible with the square
thread ; the fit in the nut can be made closer ; the angularity of
the sides facilitates the engagement and disengagement of the
divided nuts used with such screws in the lathe and permits also
the wear of the thread to be taken up by closing the nut ; and
finally the thread is cleaned more readily. These advantages are
obtained without an excessive increase in friction. It is difficult,
however, to keep the cutting tools to the exact angle of the thread.
SCREW FASTENINGS.
i. SELLERS. — Table XXI. gives the dimensions of the Sellers
thread of this type. The formulas are :
Angle = 15° on side ;
Nominal diameter = D.
TABLE XXI.
J-V SCREW-THREAD.
(WILLIAM SELLERS AND COMPANY.)
vT*
Diam.
Nominal,
D.
Pitch,
Threads,
No. Per In.
Depth of
Thread,
Width
of Flat at
Root,
A.
Width
of Flat at
Top,
Angle of Thread
for Tools.
1
A
10
.0438
.038
.0385
7° 15' 22"
1
i
8
.0548
•0475
.0481
6 3 24
i
6
\ '
.0674
•0585
.0592
5 35 37
T95
6
.0731
.0641
5 23 26
|
5
r
.0797
.0691
.07
5 17 28
ii
5
.0877
.076
.077
5 17 25
f
5
.0877
.076
.077
4 5i 6
if
4^
r
.0974
.0844
.0855
4 58 32
I
4
f
.0974
.0844
.0855
4 37 18
\\
4
.1096
•095
.0962
4 5i 6
4
.1096
.095
.0962
4 33 o
\
3
r
•1253
.1086
.11
4 37 18
3!
•
•1253
.1086
.11
4 9 40
1
i
3
.1461
.1266
.1283
4 24 45
|
I
3
.1461
.1266
.1283
4 2 46
T4T
1
•1594
.1382
.14
4 4 33
f
f
1
•
•1754
.152
.154
4 9 41
|.
i
•
•1754
.152
.154
3 53 5
:
•
.1948
.1688
.171
4 2 46
i
•
;
•
.1948
.1688
.171
3 35 52
\
.2192
•19
.1924
3 38 33
f
.2192
•19
.1924
3 18 44
3
.2505
.2172
.22
3 28 ii
3|
.2505
.2172
.22
3 12 ii
.2698
.234
.2368
3 12 ii''
3f
1
.2923
.2532
.2566
3 14 20
4
2
.2923
•2532
.2566
3 2 12
4i
H
T
s
•3049
.2643
.268
2 58 57
4$
4f
f
T;
,
.3188
•3340
.2764
•2895
.28
•2933
2 56 41
2 55 22
5
•3507
.304
.308
2 55 56
5i
1
.3507
.304
-308
2 46 36
64
MACHINE DESIGN.
Pitch, / = 0.48 V D -f 0.625 — 0.35 ;
Depth, s = 0.43 84/5
Flat at root, A = 0.38/5
Flat at top, B = 0.385/5
Clearance = o.oip.
2. NEWPORT NEWS SHIPBUILDING AND DRY DOCK COMPANY. — >
The proportions of this thread are given in Table XXII.
TABLE XXII.
STANDARD BASTARD SCREW-THREADS.
(NEWPORT NEWS SHIPBUILDING AND DRY DOCK COMPANY.)
Diameter,
Nominal,
D.
Diameter,
Effective,
d.
Area,
Effective,
ltd* -r- 4.
Threads
Per In.,
ft.
Width
of Flat,
Nut,
Depth,
I//
0-3333"
0.0870
6
0.0420
K
|
0.4250
O.I4I8
5
0.0500
i
I
0.5500
0.2376
5
0.0500
|
0.6530
0-3349
4-5
0.0560
0.7500
0.4418
4
0.0625
0.8750
0.6013
4
0.0625
0.9640
0.7300
3-5
0.0714
1.0900
3-5
0.0714
If
1.1670
1.0700
3
0.0833
2
1.2900
1.3070
3
0.0833
2\
I.4I70
1-5770
3
0.0833
2f
1.4750
1.7090
2-5
O.IOOO
22
1. 6000
2.0106
2.5
O.IOOO
2|
L
1.8500
2.6880
2-5
O.IOOO
3
\
2.0000
3.1416
2
0.1250
3}
|
2.2500
3.9760
2 0.1250
3f
3
2.5000
4.9087
2
0.1250
4
3. ACME STANDARD (29°) THREAD. — This form has the same
depth as the similar square thread and its sides are at the same
inclination as is now adopted generally in cutting worm gears.
The formulae are :
Angle of sides = 14.5° = 29° included angle ;
SCREW FASTENINGS.
Number of threads per inch = n ;
Width of flat at top, B = °'37°7 ;
Depth of thread, s = h o.oi ;
2n
Nominal diameter = D ;
Effective diameter = D — i — + 0.02 J.
TABLE XXIII.
ACME STANDARD (29°) SCREW-THREAD.
k-.
A « <?*
No. ofThds.
per in. Linear,
Depth
of Thread,
Width at Top
of Thread,
Width at Bottom
of Thread,
A.
Space at
Top of Thread,
Thickness at
Root of Thread,
D.
I
.5100
.3707
.3655
.6293
.6345
ij
.3850
.2780
.2728
•4720
.4772
2
.2600
.1853
.l8oi
.3147
•3199
3
.1767
•1235
.1183
.2098
.2150
4
.1350
.0927
.0875
•1573
.1625
5
.1100
.0741
.0689
•1259
.1311
6
.0933
.0618
.0566
.1049
.nor
7
.0814
.0529
.0478
.0899
•0951
8
.0725
.0463
.0411
.0787
.0839
9
.0655
.0413
.0361
.0699
•0751
10
.0600
.0371
.0319
.0629
.0681
24. Special Threads.
1. THE KNUCKLE THREAD, Fig. 29, may be considered as formed
from the square type by rounding the top and root of the latter
in curves which unite. The curvature increases the strength and
friction of the thread and reduces its liability to injury in service.
Its advantage lies solely in its fitness for rough usage.
2. THE BUTTRESS THREAD, Fig. 30, is a trapezoidal form suit-
able for producing pressure in one direction only. The driving
66
MACHINE DESIGN.
side is normal to the axis of the screw as in the square thread
the angle between the sides is usually 45° ; and the width of
the flat at top and bottom is one eighth of the pitch. For maxi-
FIG. 29.
FIG. 30.
mum effort in one direction, the thread has the greatest strength
and least friction attainable.
3. MODIFIED BUTTRESS THREAD. — This thread meets extended
and important use in the breech-blocks of modern ordnance and
also in securing armor-plate to the hulls of war vessels. The
profile of armor-threads as used by the U. S. Navy, is shown in
Fig. 31, the proportions of various sizes being given in Table
I—
— *
XXIV.* One side of the thread makes an angle of I 5° with the
normal to the axis of the bolt, the similar inclination of the other
side is 45°, and the top and root are rounded with ample curves.
TABLE XXIV.
PROPORTIONS OF BOLTS FOR SIDE, DIAGONAL, AND BELT-ARMOR, U. S. NAVY.
Outboard End.
Inboard End.
Thread.
Armor,
Thickness.
Diameter,
D. '
Diameter,
Effective,
d.
Diameter,
Nominal,
A-
Diameter,
Effective,
</,.
Depth,
s.
Pitch,
P-
Radius of
r.
2.o8o"
2.68o
3.200
3.680
4.2l6
i.8o//
2.40
2.88
3.36
3-84
1. 780"
2.28o
2.720
3.120
3.576
i. So"
2.00
2.40
2.80
3.20
0.1414"
0.1414
0.1604
0.1604
0.1885
\
0.030"
0.030
0.035
0.035
0.040
to 5" inc.
6" 9 "
10 "13 "
I4"i7 "
l8"2I "
* " Report of Chief of Bureau of Construction and Repair, U. S. Navy," 1896.
SCREW FASTENINGS.
67
4. MODIFIED TRIANGULAR THREAD. — In modern ordnance,
the breech-block is secured by the " Interrupted Screw " method,
i. e., the outer surface of the cylindrical block is threaded to form
a screw which engages an internal thread in the breech. Neither
thread is continuous, each being divided into sectors, 12 in large
guns, 6 threaded and 6 blank, the surface of the latter being just
below the root of the thread in the former. Each sector is 30° in
length and all correspond with similar sectors in the breech-recess
of the gun. In closing the breech, the block is placed so that its
threaded parts are opposite the blanks of the recess. It is then
moved axially home, turned through 30°, and thus locked by the
engagement of the threads.
In U. S. naval guns the breech-block thread is of the modified
buttress type used upon armor-bolts. Fig. 32 shows in profile
the thread of the 1 6-inch U. S. Army rifle. While the sides of
the thread are symmetrical in their inclination to the normal to
the axis, the angle between them is large and there is a full
rounding at top and root. In this gun the maximum powder-
pressure is taken as 37,000 to 38,000 Ibs. persq. in. The dimen-
sions of the block are :
Diameter of breech-block, D == 25.96" ;
Diameter at root of thread, d = 24.82 ;
Depth of thread, s = 0.57 ;
Pitch of thread, p = 1.71 ;
Radius of rounding, top, r = o. 1 7 ;
Radius of rounding, bottom, r^ = o. 1 1 ;
Length of threaded portion = 19.89 ;
Length of threaded sectors
30°— 0.05'
08 MACHINE DESIGN.
25. Machine and Wood Screws.
1. MACHINE SCREWS are those from J^-in. diameter downward,
used in metal work. The head is slotted and is either "round"
(spherical), "flat" (conical frustum), or "fillister" (cylinder with
spherical top). The nominal diameters of these screws are desig-
nated by screw-gauge numbers. That of the number o screw is
0.05784 in. and the difference between consecutive numbers is
0.01316 in. Therefore, the nominal (outside) diameter (D) of any
number (N) may be found from the formula :
D = 0.01316 N+ 0.05784.
An assortment of pitches is given for each diameter of screw, in
order to provide for the use of the same number with either
thick or thin pieces, the latter having shallow holes and re-
quiring finer pitches. These screws are described therefore by
both the number and pitch. Thus, a " 16-18 machine screw"
means one of size (screw-gauge number) 16 and 1 8 threads per inch.
At the meeting of the American Society of Mechanical Engi-
neers, held in May, 1902, Mr. Charles C. Tyler presented a paper
on " A Proposed Standard for Machine Screw Sizes." As to
present practice, Mr. Tyler states that there are no recognized
basic reference standards having a generally accepted form of
thread and diameter ; that the pitches are apparently stand-
ardized only for the sizes having even numbers, although screws
and taps are furnished for a number of different pitches for
each size ; and that the form of the thread varies with differ-
ent manufacturers. He recommends the adoption of the Sel-
lers form of thread and the computation of the pitch by the
formula :
/ = o.23 VD + 0.625 —0.175,
which formula was proposed by Mr. George M. Bond* in 1882,
and differs from that of the U. S. Standard only in the coefficient
being 0.23 instead of 0.24. The change in this increases the
number of threads per inch more rapidly as the diameter decreases.
Table XXV., taken from Mr. Tyler's paper, gives present practice
and the modifications suggested by him.
2. WOOD-SCREWS. — The maximum diameter of any size of
wood-screw is measured by the screw-gauge given in the preced-
*" Standards of Length," G. M. Bond, 1887.
SCREW FASTENINGS.
69
TABLE XXV.
MACHINE SCREWS.
(PRESENT PRACTICE AND SUGGESTED CHANGES.)
Present Diameters and Threads per Inch of Small Machine Screws.
The Difference Between Consecutive Sizes is .01316.
Suggested Diameters and
Threads per Inch
of Small Machine Screws.
|rf
fcl-g
-I-
2 S'D .
$T°*
^1-s
li
in g
O
. 1 J
IS
Threads also Furnished.
til
IP1
E'gtS
J«-
«'!!
Pitch.
.050
72
.013889
.060
64
.015625
I
56,60,64,72.
rV
.07100
.070
60
.016667
ij
56.
A
.07758
.080
56
.017857
2
56
48,64.
A
.08416
.090
52
.019231
3
4
36
40,44,48,56.
30,32,40,42,44,48.
%
.09732
.11048
.100
.110
44
.020833
.022727
5
30,32,36,40,44,48.
1
.12364
.125
40
.025000
6
32
30,36,38,40,44,48.
A
.13680
.135
40
.025000
7
24,28,30,32,36,40.
.14996
.150
36
.027778
8
32
24,30,36,40,44.
A
.16312
.165
32
.031250
9
10
24
24,28,30,32.
20,22,28,30,32,36.
s
.I7628\
.18944 /
.180
32
.031250
ii
22,24,28,30.
13.
.20260
.200
3°
.033333
12
13
24
20,22,26,28,30,32,34,36.
20,22,24,32.
ff
•21576)
.22892 /
.220
28
•035714
14
15
20
16,18,22,24,26.
18,20,22,24.
.24208 I
.25524 j
.250
24
.041667
16
18
16,20,22,24,26.
6
.26840
11
18
l6,l8,20.
16,20,22,24,26.
ft
.28156
.29472
.28125
22
•045455
19
20
16
16,18,20,22,24.
18,20,22,24.
ft
.307881
.32104 f
.3125
20
.050000
22
16 18.
II
.34736
•34375
20
.050000
24 16 14,18,20,22,24.
f
.37368
•375
IS
.055556
26
16 14.
M
.40000
.40625
18
.055556
28 i 14
16.
If
42632
•4375
16
.062500
30
14
1 6.
II
.45264
46875
16
.062500
.500
14
.071429
ing table. These screws differ from those used in metal -work for
two reasons : The screw forms its nut as it enters the wood and
the material of the nut is much weaker than that of the screw.
Therefore, the latter is gimlet-pointed, its body tapers, the threads
are thin and sharp, and the space between them is relatively wide
in order to provide a wooden nut-thread of sufficient strength.
26. Pipe Threads.
The standard system of pipe -threads now used in the United
States was formulated by Mr. Robert Briggs from the average
usage of good practice. It was reported upon favorably in 1886
70
MACHINE DESIGN.
by a committee of the American Society of Mechanical Engineers,
was adopted by various associations of manufacturers, and recom-
mended by the American Railway Master Mechanics' Association.
The following extract is taken from a paper presented by Mr.
Briggs in the Proceedings of the Institution of Civil Engineers of
Great Britain, Vol. LXXI.:
" The taper employed for the conical tube-ends is an inclination of I in 32 to the axis.
... A longitudinal section of the tapering tube-end, with the screw-thread as actu-
ally formed, is shown in Fig. 33 for a nominal 2^-in. tube, /. e., a tube of about 2\ in.
internal diameter and 2^ in. actual external diameter.
, w »'
FIG. 33.
" The thread employed has an angle of 60°; it is slightly rounded off both at the top
and bottom, so that the height or depth of the thread, instead of being exactly equal to
the pitch, is only § of the pitch or o.8/w, if n be the number of threads per inch. For
the length of tube-end throughout which the thread continues perfect, the empirical
formula used is :
(o.8Z> + 4.8)/«, (34)
where D is the actual external diameter of the tube throughout its parallel length and
is expressed in inches.
"Further back, beyond the perfect threads, come two having the same taper at the
bottom but imperfect at the top. The remaining imperfect portion of the screw-thread,
furthest back from the extremity of the tube, is not essential in any way to this system
of joint and its imperfection is simply incidental to the process of cutting the thread at
a single operation. From the foregoing, it follows that, at the very extremity of the
tube, the diameter at the bottom of the thread is :
" The thickness of iron below the bottom of the thread, at the tube extremity, is taken
empirically to be :
o.oi75Z> + 0.025. (36)
" Hence, the actual internal diameter, J, of any tube is found to be in inches :
.9)/» — 2 (o.oi75Z> -f 0.025)
— o.o5Z>/«— i. 9/« — 0.05." (37)
The proportions of the Briggs thread are given in Table XXVI.
As compared with the Sellers system, the depth of the thread is
SCREW FASTENINGS.
measured by a greater fraction of the pitch ; but the latter is much
finer for a given outside diameter and the thread is therefore shal-
lower and more suitable for the thin walls of a tube.
TABLE XXVI.
WROUGHT-IRON WELDED TUBES.
( Briggs Standard. )
TAPER OF CONICAL TUBE END % INCH PER FOOT, OR i IN 32 TO Axis OF TUBE.
Diameter of Tube.
Screwed Ends.
Thickness
of
Length
Diameter
Diameter
Nominal
Actual
Actual
Metal
Number
of Perfect
of Bottom
of Top of
Inside,
Inside,
Outside,
Inches.
of Threads
Thread
of Thread
Thread at
Inches.
Inches.
Inches.
per Inch.
at Bottom,
at End of
End of Pipe,
Inches.
Pipe, Inches
Inches.P
i
0.270
0.405
0.068
27
0.19
0-334
0-393
f
0.364
0.540
0.088
18
0.29
0-433
0.522
g
0.494
0.675
0.091
18
0.30
0.567
0.656
0.623
0.840
0.109
14
0-39
0.701
0.815
|
0.824
1.050
O.II3
14
0.40
0.911
1.025
I
1.048
I-3I5
0.134
ii J
0.51
1.144 1-283
l|-
1.380
1. 660
0.140
n|
0-54
1.488
1.627
l|
I.6IO
1.900
0.145
n|-
0.55
1.727
1.866
2
2.067
2-375
0.154
lli
0.58
2.200
2-339
2V 2.468
2.875
0.204
8
0.89
2.62O
2.820
3" 3.067
3-500
0.217
8
0-95
3-24I
3-441
3*
3.548
4.OOO
0.226
8
1. 00
3.738
3.938
4
4.026
4.500
0.237
8
1.05
4-235
4-435
4.508
5.000
0.246
8
1. 10
4-732
4-932
5"
5-045
5.563
0.259
8
1.16
5-29I
5-491
6
6.065
6.625
0.28o
8
1.26
6.346
6.546
7
7.023
7.625
0.301
8
1-36
7-340
7-540
8
7.982
8.625
0.322
8
1.46
8-334
8-534
9
8-937
9.625*
0.344
8
i-57
9-328
9-528
10
10.019
10.750
0.366
8
1.68
10.445
10.645
27. Stresses in Screw-Bolts.
The body of a screw-bolt may be regarded as a cylindrical bar,
subjected in various services either to simple tension or compres-
sion or to one of these stresses combined with torsion, or, as in
the flanged coupling, to tension and cross-shear. The thread may
be considered as a cantilever beam whose section is that cut by a
plane passing through the axis, as O-A, Fig. 34. The length of
this assumed beam is the depth of the thread, s; its depth at the
support is p — f, where p = pitch and/~= width of flat at root; and
its breadth at the root is the developed distance through which the
axial section B-C-E extends. This distance, for one convolution
= ltd and for the threads engaged by a nut of depth H ins. and'
* Originally, 9.688.
72 MACHINE DESIGN.
having n = Up threads per inch = nd x Hn. Let the total axial
load on the bolt = W\ the load per convolution engaged = W/Hn
= w ; and the permissible tensile and shearing stresses per sq. in.=
St and S, — o.SSt, respectively. Consider the assumed beam with
regard to :
i. SHEARING OF THE THREAD, i. e., "stripping" at the root.
The shearing force = W and is opposed by the section of metal at
the support or root. The area of this section = breadth x depth of
beam
. • . Resistance to Stripping = W= irdffn( p — /)£,. (3 8)
Equating this, for equal strength throughout, to the tensile resist-
ance of the bolt :
Tensile Resistance = W=T--d'LS = ~dHn( p-f)S. (39)
4
c J $pd
"^ = 7^77 T\ • (4°)
In the Sellers system, / = //8. Substituting:
^=0.357^.
2. RUPTURE OF THREAD by bending at the root. Theoretically,
the load is uniformly distributed over the surface, which assump-
SCREW FASTENINGS. 73
tion could be true only of new and perfect threads ; practically it
may be considered as concentrated at the mean thread diameter.
Therefore : s
Moment of Load = W x - = M= S//c ;
Section-Modulus at Root = - = - 5 5
Resistance to Rupture = W = — — ^ - - — ' x -. (41)
Equating (41) and (39) : pds
ti-*u=rr (42)
which expression assumes the tensile stress in the bolt and that
in the thread due to flexure to be of the same intensity. Substi-
tuting the values for the Sellers system :
y/= 0.637^.
3. BEARING PRESSURE UPON THE THREAD. — The allowable
pressure upon the area of the engaged threads, as projected upon
a plane normal to the axis, depends upon the service of the screw,
being much greater with fastenings than with screws for the trans-
mission of power, since, with the latter, friction and wear should
be as small as possible. The projected area of the threads engag-
ing the nut is (Fig. 34) :
_ (& _ d*) x Hn.
4
Letting Sb = permissible bearing stress per sq. in. :
Permissible Load in Bearing = W = - (LP — d2) HnSb. (43)
Equating (43) and (39) :
(a) Fastenings. — Letting a = effective area of bolt and A = ag-
gregate projected area of engaged threads :
aS, = AS, and § = -. •
St A
This stress-ratio, the reciprocal of that in (44), is given for the
Sellers system (H = D) in Table XXVII. * It will be seen that,
* " Report of the Board to Recommend a Standard Gauge for Bolts, Nuts and Screw-
Threads for the U. S. Navy," May, 1868.
74
MACHINE DESIGN.
in this system, as the nominal diameter increases, there is an in-
crease also in the bearing pressure, the latter varying from 0.242
to 0.331 of the permissible tensile stress per sq. in. Thus, for a
2-in. bolt of metal whose ultimate tensile stress is 60,000 Ibs.
per sq. in., the permissible tensile stress, allowing for torsion = St
= 7,000 Ibs. per sq. in. From the table, Sb / St= 0.3046, whence Sb
= 2132.2 Ibs. per sq. in., which pressure is about the maximum
allowable for fastenings.
TABLE XXVII.
RATIO OF BEARING PRESSURE TO TENSILE STRESS.
(SELLERS SYSTEM.)
•a
^
"3
r
1
•3
"3 II
I
'o
•81
V
It
i*
Jl
||
i$
*k
R
51
pi
11
< §
II
1
1
h
«N
11
12
§S
W
IE
§
i
II
*
i
fc
i
i
n.
.02688
.11105
.242
2 in.
2.3019
7-5573
•3046
A
«
.04524
.17696
.2556
2i «
3.0232
9.6471
.3134
*
"
.06789
•09347
.25536
.34826
.266
.2684
2| «
3.7188
4.6224
11.8990
14.4881
•3125
.3190
H
.12566
•45949
.273
3 "
5.4283
17.2221
•3150
/•,.
"
.16189
•58461
.2769
3i "
6.5009
20.4158
.3188
f
"
.20174
.30190
.72222
1.0470
.2795
.288
3l "
8^416
23-5849
27.0337
.3200
•3196
1
"
.41969
1.4303
.293
4
9.9929
30.8820
•3235
"
•55024
1.8813
.3112
11.328
34.9236
•3244
ij
11
•69399
2.2877
•3033
!<
12.743
40.3586
•3157
•
"
.89082
2.94245
.3027
«
14.250
43-2728
.3288
i
"
1.0568
3-5310
.2993
5 |
15.763
48.4000
.3260
"
1.2948
4-2507
•3051
17.572
53-4950
.3290
«
I-5I52
4.9925
•3035
5| |
19.267
58.6676
.3280
"
1.7460
5-7750
.3023
21.262
62.7850
-3286
"
2.0510
6.6572
.3081
6 '
23.098
69.8540
•3310
(<£) Screws for Transmitting Power — In such screws, the bear-
ing pressure varies within fairly wide limits, being determined
by the character and duration of the work. Reuleaux gives 700
pounds per square inch of projected area for square and trape-
zoidal threads, which pressure is given also by Weisbach for
square threads. Unwin states that for screws constantly in motion
this pressure should not exceed 200 pounds, and that with no
power-screw should it be more than 1,000 pounds.
4. TENSION UNDER STATIC LOAD. — Under this stress, the body
of a screw-bolt has a higher elastic limit and a greater ultimate
SCREW FASTENINGS. 75
strength than a cylindrical bar of the same metal and of diameter
equal to that at the root of the thread. These gains are due to :
(a) The Reinforcing Action of the Thread. — When a cylindri-
cal bar is subjected to simple tension only, it is increased in length
and contracted in sectional area. The contraction is gradual, ex-
tends over a considerable portion of the specimen, and reaches a
minimum at the point where rupture occurs finally. To permit
the gradual tapering of the specimen in unrestricted contraction,
the bar should be originally of the same diameter throughout the
section subject to elongation.
If, now, there be turned in the bar one or a series of parallel
grooves of any form but of the same depth, the tensile stress and
the tendency to elongation and to contraction of area will be
greater in the portions of lessened diameter. This reduced sec-
tion is, however, insufficient in length to permit considerable con-
traction ; and, further, the latter is resisted by the metal under
less stress in the ridges of the grooves. In other words, in addi-
tion to the lessened distance of least diameter through which
stretching occurs, the ridges oppose the contraction of area and
the consequent elongation of the reduced section and therefore
add to the strength of the latter. As a result, the " grooved
specimen " is stronger under static tensile load than a cylindrical
bar having the same diameter as that at the base of the grooves.
Mr. Kirkaldy * was the first to emphasize the effect of the form
of a specimen upon its ultimate strength. In his report upon the
Essen and Yorkshire iron plates, he says :
"When the breadth of a specimen is reduced to a minimum at one point, a greater
resistance is offered to its stretching than when formed parallel for some distance ; and,
as the stretching is checked, so will also be the contraction of area and with it will
be an increase in the ultimate stress."
Table XXVIII. gives the results of tests made by Mr. James
E. Howard f upon six specimens from the same i^-in. steel bar, to
illustrate the effect of turning a reduced section or " stem," 0.798
in. in diameter on each specimen. Nos. I, 2 and 3 had cylindrical
stems, I in., 0.5 in., 0.25 in. long, respectively, connected by full
fillets to the body ; in specimens Nos. 4 and 5, the stems were
semicircular grooves of 0.4 in. and 0.125 in. radius, respectively;
a V-shaped groove was formed in specimen No. 6.
*" Experiments on Wrought Iron and Steel," 1862, p. 74.
t "Proceedings International Engineering Congress," 1893.
MACHINE DESIGN.
TABLE XXVIII.
GROOVED SPECIMENS.
No.
Elastic Limit,
Pounds Per Sq. In.
Tensile Strength,
Pounds Per Sq. In.
Contraction of Area,
Per Cent.
2
3
4
!
64,900
65,320
68,000
75,000
86,000, about.
90,000 "
94,400
97,800
102,420
116,380
134,960
117,000
49-0
43-4
39-6
31-6
23.0
Indeterminate.
In Table XXIX. there are given the results of tests made by
Professor Martens which show that a screw-bolt under static ten-
sile load is practically equivalent to a specimen with grooves
turned in it of the same form as the thread-groove and also that
there was an average increase of 14 per cent, in strength for the
specimens tested over that of the cylindrical bar having the same
diameter as that of the root of the thread. The table and the
following particulars are taken from Professor J. B. Johnson's
abstract of Professor Martens' paper : *
"Two grades of mild steel were used for these bolts, all of which were cut from
round bars originally 35 mm. (1.4 in. ) in diameter. The softer material, having a
tensile strength of 53,500 Ibs. per sq. in., was used for screw-bolts approximately i in.
in diameter, and the harder material having a tensile strength of 62,000 Ibs. per sq. in.
was used for the bolts which were reduced to approximately £ in. in diameter. Four
such bolts were made of each of these sizes of the four styles of thread (sharp V, angle
55°; Whitworth ; Sellers, and German Society of Engineers. The latter having an
angle of 53° 8' with flats whose height is one eighth that of the primitive triangle),
making in all 32 bolts with screw-threads which were tested. Two of each of these
sets were tested in plain tension, the pulling force being applied to the inner face of the
nut at one end and increased until rupture occurred.
" The other two bolts of each set were tested also in tension, but under a torsional
action resulting from the continuous turning of the nut as the load increased to rupture.
In this case the distortion resulting from the permanent elongation of the bolt was
nearly all taken up by the movement of the testing machine, the distortion taken up by
the turning of the nut being the least possible to maintain a continuous torsional action
at this point.
"The same bars were also tested as plain tension-test specimens with cylindrical
bodies and again with grooves turned into them of the same shape as the corresponding
screw-threads, leaving the same diameter at the bottom of the groove as obtained at the
base of the threads."
The ratio fsa -*-fg, given in Table XXIX., is practically unity
showing that the grooved and threaded specimens are equal in
strength. The ratio, fsa -7- test bar, ranges between no and 119
and averages 114, giving thus a mean excess of strength of 14
* Zeits, d. Ver. Deuts. Ing., April 27, 1895. Abstract by Professor Johnson in
" Digest of Physical Tests," July, 1896.
SCREW FASTENINGS.
^ a
X >
X 8
I!
Ml O C^ I-* HH ^
S^ Nfr « O ON ro
^> I ^ ^ H M M
•^•vO O "5
Too" <
10^
t^L\O t^v£>
q ts <>vq
0 M' ^£> CO
CO t^CO t^
rtCO ON M M
« « o"
vo v£>^5 vO
: «
. .0
77
;S MACHINE DESIGN.
per cent, for the threaded rods as compared with cylindrical bars
of the same net area of cross-section. These results apply only
to static or gradually applied loads.
It will be noted that the tensile load upon the cross-section of a
bolt at the root of the thread is not uniform throughout, since the
metal of the latter opposes the elongation of the section imme-
diately adjacent at the root, thus increasing its stress beyond that
existing at the axis. It is apparent that, other things equal, the
finer the pitch the more equable will be the distribution of the
stress upon the minimum cross-section and the greater the resili-
ence or internal work of the bolt before final yielding. Thus,
Major W. R. King, U. S. A., in experimenting with gradually
applied loads upon wrought-iron bolts of one and one half inch
nominal diameter, U. S. standard, but of varying pitch, obtained
results as follows : *
Threads per Inch, 6 12 18
Relative Tensile Strength, I 1.21 1.23
Elongation, 0.025 0.06 0.08
Relative Internal Work, I 2.9 4
The U. S. standard pitch for one and one half inch nominal diam-
eter gives 6 threads per inch. The bolts with 1 8 threads per inch
were the stronger. They yielded finally, neither by stripping nor
by fracture at the root, but by lateral contraction, so that the
threads of bolt and nut became disengaged.
(&) Increased Density of Threaded Section. — Mr. Kirkaldy f
found that, when the thread was cut with new dies, the strength
of the threaded section averaged 72.5 per cent, of that of a cylin-
drical bar whose diameter was that of the outside of the thread.
When, however, old and worn dies were used, the average strength
was increased to 85 per cent. In the latter case the tendency of
the tool is to force aside and compress the metal rather than to
remove it by clean cutting, thus increasing the density and strength
of the thread and adjacent parts.
Again, in bolts threaded by the "cold-pressed" method, no
metal is removed but the thread is raised or spun above the body
of the bolt so that the diameter of the shank is intermediate be-
tween those of the top and root of the thread. In frequent
tests \ of mild steel bolts threaded by this method, fracture, under
* 'Trans. Am. Inst. Mining Engineers, 1885.
f Box : " Strength of Materials, " 1883, p. 12.
J Catalogue Am. Iron and Steel Mfg. Co., 1899.
SCREW FASTENINGS. 79
a gradually applied tensile load, occurred in every instance in the
shank, leaving the threaded portion intact. The normal reinforcing
action of the thread is, by this process, aided doubtless through the
compression and increased density of the thread and adjacent metal.
(c) Resume. — The experiments of Professor Martens show
that, for static or gradually applied loads, the ultimate strength
of the section at the root of the thread is 14 per cent, greater
than that of a cylindrical bar of the same metal and cross-section.
This increase in strength is due to the reinforcing action of the
thread, and, in some degree, to the greater density of the metal.
Under sudden and repeated stresses, however, the results would
probably be less favorable, owing to the appreciable concentration
of the stress about the bottom of the groove which would produce
fracture at the reentrant angle. The increase in strength of the screw
from these causes is, therefore, not considered in designing bolts.
5. TENSION UNDER SUDDEN LOADS OR IMPACT-. — In both ma-
chinery and structures a bolt may be required to withstand not
only the tensile stress of a gradually applied or static load but
also that produced by a suddenly applied load or by impact.
Examples of such requirements may be found in bridge work, in
marine machinery, in rock drills, etc.
Let the static or gradually applied load, P, produce in the bolt
a total stress, P, and elongation, /. Then, the same load, if sud-
denly applied, will produce a maximum, momentary, total stress,
2P, and elongation, 2X, which, after a series of axial oscillations of
the bolt, will be reduced, when the latter comes to rest, to the
final stress, P, and elongation, ),, due to P as a static load. In
impact, the load, P, is assumed to act as if it were not only sud-
denly applied but in motion with a velocity, v, such as would be
acquired by fall through a height, h. Under these conditions,
P produces a maximum, momentary, total stress, Q, and elonga-
tion, y, which, when -the bolt after oscillation comes to rest, are
reduced to P and ^, respectively. Disregarding the weight and
consequent inertia of the bolt, we have : *
y*l\i + <
r~* \
sl2i+I>
(45)
(46)
*Merriman, "Mechanics of Mechanics," 1900. Art. 93.
80 MACHINE DESIGN.
When h = o, these formulae become :
Q=2P and y = 2).,
i. e., the values for a load suddenly applied but without im-
pact.
In the three cases cited, the total final stress is P. For this
stress, the absolute requirement is that the area, a, of the mini-
mum cross-section of the bolt shall be such that the unit stress,
Pja, shall not exceed the working stress of the metal. The
strength of this minimum section is therefore practically the
measure of the resistance of the bolt to safe static stress.
Work is the product of a resistance by the distance through
which the latter is overcome. The external work of impact,
P(1i-\-y), is resisted by the elastic resilience or internal work,
YZ Q X y, of the bolt. The same internal work may be the prod-
uct of a high average, total stress, y2Q, and a small elongation
y, or, conversely, of a low stress and a large elongation.
Under the conditions given, it is apparent that the elastic resilience
is the measure of the resistance of the bolt to sudden or impul-
sive stress.
In order to secure maximum total elongation under sudden load
and therefore the least value of <2,the sectional area of the unthreaded
portion of the bolt should be the minimum permissible, i. c., that
at the root of the thread, which minimum area is determined by
the static load. The minimum section should extend through
as great a portion of the bolt as possible, since the total elonga-
tion depends upon its length. When the area at any point is
greater than the minimum, the unit stress over that area is less
than over the latter and the elongation of that part and therefore
of the bolt will be reduced proportionately and there will be an
increase in the average stress.
Equating the external and internal work, we have for a bar of
sectional area A, length L, and maximum total and unit stresses,
Q and q, respectively : 2
K=\qE-AL, (47)
on which K is the internal work or elastic resilience and E is the
modulus of elasticity for tension.
Consider two bolts of the same total length, length of shank,
and area, a, at the root of the thread. In :
SCREW FASTENINGS.
81
Bolt No. i : Let the length of threaded portion be / and its
minimum sectional area and maximum unit stress be a and q, re-
spectively. Let the length of shank be kl and its sectional area be
na. Then, the maximum unit stress in the shank will be : .
«.?_z.
an n
Bolt No. 2 : As before, total length = / + kl = I (i + k\ Let
the uniform sectional area throughout screw and shank (disregard-
ing thread ridges) =a and the maximum unit stress throughout=^r
The elastic resilience of each bolt will be the sum of the internal
work of its threaded portion and shank. From (47), we have for :
Bolt No. i :
2EK n
Bolt No. 2 :
(h
K=y^
(48)
(49)
2EK
al i -f k
\2hK n
= \ a/ ' «T
nk'
Assuming the total work, K, as the same in each case, it will be
seen that ql<.g, i- c., that, by making the shank of the same
sectional area as that at
the root of the thread,
the maximum unit stress
upon the bolt has been re-
duced. The equations dis-
regard the increase of area
due to the thread ridges,
which increase, for accur-
acy, should be included.
When there is no impuls-
ive load and a rigid connec-
E
FIG. 35.
tion is required, there is no advantage, possibly the reverse, in
increasing the elastic resilience of the bolt by decreasing the cross-
section of the shank.
82 MACHINE DESIGN.
In reducing its section, the shank may be turned down on the
outside to the diameter at the root of the thread or it may be
drilled axially from the head inward to the point where the thread
begins, both as in Fig. 35. The latter method is preferable, since
it leaves a section which is the stronger of the two in torsion.
The shearing stress at any point of a section varies directly as the
distance of that point from the axis, but the resisting moment of
that stress with respect to the axis varies directly as the square
of that distance. Therefore, a given area of section is most
economically used with regard to torsion by so disposing it that
its fibres shall be remote from the axis.
Professor Sweet,* in testing solid and drilled bolts, i^ in. nom-
inal diameter and 12 ins. long, found that, under gradually ap-
plied load, the undrilled bolt broke in the thread with an elonga-
tion of ^ in., while the drilled bolt was fractured in the shank after
a total elongation of 2\ ins. Assuming the same mean load in
each case, the ultimate resilience of the drilled bolt was 9 times
that of the other. " Drop tests," i. e., those producing tensile
shock, gave similar results.
6. FRICTION OF THE SCREW. — The screw-thread is essentially
an inclined plane wrapped around a cylinder, as on the bolt, or
within a hollow cylinder, as in the nut. If the bolt be vertical,
the wrench engages the nut in a horizontal plane and the axial
load upon the bolt may be assumed as raised vertically by move-
ment along the inclined plane of the nut-thread, the force acting
horizontally. The efficiency of the screw, per se, and that of the
inclined plane are the same. Sliding friction is generated between
the bolt and nut threads as they move upon each other. The
resistance or force of this friction acts along the contact-surfaces in
opposition to the direction of relative motion of the latter. The
magnitude of this force is measured by the product of the coeffi-
cient of friction and the total normal pressure between the surfaces.
Thread -friction not only reduces the useful work and efficiency
of the screw, but also adds to the torsional stress within the body
of the bolt produced by the component of the load which is nor-
mal to the axis. Therefore, the bolt is subjected, in screwing up,
to torsion due to the nut and to tension or compression from the
axial load. The combined stress thus developed, exceeds mate-
rially the simple axial stress when the nut is screwed home and at
*A. W. Smith, "Machine Design," 1895, P- 135-
SCREW FASTENINGS. 83
rest. This torsional action is of especial importance in small screws,
which may readily be sheared by excessive force upon the wrench.
In addition to the friction of the threads, the efficiency of the
screw is reduced further by the friction of the rotating member of
the pair — the nut or screw, as the case may be — upon its sup-
port. Again if, as is usual, the turning moment is applied at one
side only and not as a couple, there is a lateral thrust upon the
support with a frictional resistance similar to that of a journal.
(a) Torsion due to Thread Friction. — The pressure upon the
FIG. 36.
threads in computations respecting friction, may be taken as con-
centrated upon the mean helix or the circumference of the mean
thread-diameter, d^ of pitch-angle, <50 (Figs. 22 and 36). Each
element of the thread-surface is regarded as sustaining an equal
elementary portion of the total axial load or stress, W, and each
element has, therefore, a frictional resistance of the same magnitude.
84 MACHINE DESIGN.
Since the conditions for all elements are thus identical, the total ex-
ternal forces and thread-resistances may be assumed to be concen-
trated at a single point upon the circumference of diameter, dy
In Fig. 36, taking the nut as the turning member, let A-B-C
be the inclined plane formed by developing one convolution of the
nut thread of diameter, d^. Let A-B be that thread and E-G a
portion of the bolt-thread. The base of the plane is xd0, the
height is the pitch, /, and the pitch-angle, o0 = B-A-C. Consider
the external rotating force as applied in a plane normal to the
axis and as tangent to the mean thread-circumference. Let :
W = total axial load or tension in bolt ;
P0 = external force to raise W without friction ;
P= external force to raise Wwith friction ;
Pl = external force to lower W with friction ;
N = direction of thread -pressure, without friction ;
R = direction of thread-pressure, raising, with friction ;
Rl = direction of thread-pressure, lowering, with friction ;
JJL = coefficient of thread-friction = tan <p ;
(f = angle of repose or of friction ;
F •=. total force of thread -friction in raising W '= N tan <p ;
F^ = total force of thread-friction in lowering W = N tan <f.
Square Threads. — Consider the force upon, and the resist-
ance of, the nut-thread, A-B. To raise W, the latter must move
to the left ; to lower it, to the right. The resistances of the
thread to these movements are the components normal to the
axis of ^Vand /''and N and Fl respectively, which resistances must
be equal to the corresponding and parallel applied forces, P and Pr
In raising W without friction :
N is normal to the thread. The resistance is its component
normal to the axis and opposing P0, which component is
a-b — o-a tan SQ = If7 tan d0 = Py (50)
In raising Wwith friction :
The resistances are the components, normal to the axis, of N
and F. The latter = pN= N tan c. The resultant of N and F
is R, making the angle <p with N. The component of R, normal
to the axis and opposing P is
a-c = O-a tan (<p + ofl) = W tan (<p + d0) = P. (51)
SCREW FASTENINGS.
From (50) and (5 1) it will be seen that the resistance of friction is
equivalent to increasing the angle fi-A-Cof a frictionless plane by <p°.
In lowering W with friction :
The resistance are the components, normal to the axis, of N and
Fr The latter = pN = N tan <f>. The resultant of N and Fl is
Rv making the angle <p with, and lying to the left of, N. If
<p > 30, the angle between R^ and the axis is <p — d0, and the com-
ponent of Rl normal to the axis and opposing Pv is
a-d = o-a tan (<p — OQ) = W tan (<p — dQ) = Pr (52)
In " overhauling " screws, the pitch is so coarse that the load
is capable of reversing and lowering the screw. If, in (52),
30 = (f, then will tan (y> — <J0) = o /. Pl = o. The pitch-angle is
then equal to the angle of repose and no force will be required
either to lower the load or to hold it in equilibrium. If, as in Fig.
36, a, o0 > <p, then Rv the result-
ant of N and Flt will lie to the
right of the axis and its compo-
nent normal to the axis will be e-a,
which acts in the direction of the
lowering force, Pr Therefore, the
screw, if not sustained by a force,
P, will overhaul, with a torque
equal to the product of W tan
(<J0 — <p) by its leverage, dj 2.
Screws of this type are met infre-
quently and, as a rule, in light
mechanisms only. Usually, JJL lies
between o. 10 and 0.20, giving val-.
ues of if of about 5° 45' and 1 1°
30', respectively. In Table XIX.,
for ^-in. and 4-111. screws, d0 is about 8° 45' and 3° 15', respec-
tively. These values are for square-threaded, power-screws whose
pitch is twice that of corresponding screws of the U. S. Standard.
Triangular Threads. — In Fig. 37, let N and N' be the normal
pressures upon square and triangular threads, respectively. Then
N' = N sec /9, in which /? is the base-angle. Letting F1 = the
frictional resistance of a triangular thread, we have, since for the
square thread, F= pN:
F' = pN' = (JJL sec fi}N=F sec /?.
FIG. 37.
86 MACHINE DESIGN.
As compared with the square thread of the same pitch-angle,
the friction, F' , is, therefore, sec ft times greater. Hence, the re-
sisting component, normal to the axis, will be increased propor-
tionately; and, in the formulae leading to equations (51) and (52),
we may replace // by p sec ft. From these equations, we have :
P== W. ten P + tan *o = W. P + ten *o = W. ^d* + P.
I — tan (p tan 30 i — p. tan d0 xd^ — pp'
and, similarly, p = w fwd0 - /
1 '*< + /'/
Replacing fj. by p sec ft :
p_wP**cfad*+P ( ,
V ro/0->sec#'
pace fad, -fi
^- r^0 + ^sec^'
These are the equations for the raising and lowering forces, P
and Pv respectively, which, considering friction, require to be ap-
plied tangentially to the mean thread circumference of a triangular-
threaded screw. The form of the equations is that given by Unwin.
In the Sellers system, ft = 30° and sec ft = 1.15. Substituting :
p=w.^J^±±
K- i.is &'
Pi=W.^^~P, (56)
7r^0-f 1.15^
Thus, the ^-in. bolt has, in this system, the maximum inclination
of the thread and hence the greatest tendency to be sheared by
torsion. For this bolt,
D -(- d 0.25 + 0.185
p = 0.05 and d0 = = -= 0.2175.
Taking // = o. 1 24 :
P=0.22W.
With an ultimate tensile strength of bolt-metal of 60,000 Ibs.:
red'1
W = x 6o,OOO = 1,613 Ibs.;
4
P= 1613 x 0.22 = 355 Ibs.,
i. e., a force of 355 Ibs. applied, under the conditions as above, to
a J-in. screw-fastening will rupture the latter by tensile stress.
SCREW FASTENINGS. 8/
The assumed value of ft is suitable only for accurately fitting, well-
lubricated threads. Owing to viscidity of the lubricant, the pres-
ence of foreign matter, or rough surfaces from abrasion, the coeffi-
cient will be usually much higher with a corresponding increase
in friction and torsional stress.
(£) Coefficients of Friction for Screw -Threads. — In average cases,
the value of // is taken as 0.15. This assumes fair conditions of
surface and lubrication. Under other circumstances the coefficient
may reach 0.40 or more. Professor Albert Kingsbury * has con-
tributed to the meager knowledge available upon this question,
the results of valuable experiments conducted by him and apply-
ing especially to slow-moving power-screws.
The tests were made upon a set of square-threaded screws and
nuts of materials as given in Table XXX. and of dimensions as
follows :
Outside Diameter of Screw ... . . 1.426 inches.
Inside Diameter of Nut 1.278 "
" Mean Diameter " of Thread I-352 "
Pitch of Thread 333 "
Depth (effective) of Nut 1.062 "
The nuts fitted the screws very loosely, so that all friction was
excluded except that on the faces of the threads directly supporting
the load. Four sets of tests were made. The maximum total load
was 14,000 pounds in all tests excepting No. 4, in which it was
4,000 pounds. Readings were taken at pressures given in the
table. The total bearing area of thread was approximately one
square inch, so that the total axial load was equal to the pressure
per square inch upon the thread.
The lubricants were a purely mineral " Heavy Machinery Oil "
of specific gravity, 0.912, and "Winter Lard Oil" of sp. gr.,
0.919. The former, in test No. 3, was mixed, in equal volumes,
with graphite, the brand being Dixon's " Perfect Lubricator."
The screws and nuts were flooded with lubricant immediately
before the tests.
The threads were carefully cut in the lathe and had been worn
down to good condition by previous trials. Screw No. 5 was not
quite so smooth as the others. The speed was very slow, being
about one revolution in two minutes and the motion, in tightening
especially, was also somewhat irregular, so that the action between
* Trans. Am. Soc. Meek. Engs., Vol. XVII.
88
MACHINE DESIGN.
screw and nut was quite similar to that occurring when machine-
bolts are set up in comparatively unyielding material. The re-
sults are given in Table XXX. Each figure in test No. i is the
average of eight readings ; in the remaining tests, of four readings.
TABLE XXX.
COEFFICIENTS OF FRICTION FOR SQUARE THREADS.
Screws.
Nuts.
6
Mild
Steel.
Wr/ught
8
Cast
Iron.
cast
Brass.
I. Mild Steel.
2. Wrought Iron.
3. Cast Iron.
4. Cast Bronze.
5. Mild Steel, Case Hardened.
O.I4I
0.139
0.125
0.124
0.133
0.16
0.14
0.139
0.135
0.143
0.136
0.138
O.II9
0.172
O.I3
0.136
0.147
O.I7I
0.132
0.193
TEST No. i.
Heavy Machinery
oil.
Pressure, 10,000
Ibs. per sq. in.
2.
3-
4-
5-
0.12
O.II25
0.10
0.115
0.1175
0.105
0.1075
O.IO
0.10
0.0975
O.IO
O.IO
0.095
O.I I
0.105
O.II
0.12
O.II
0.1325
0.1375
TEST No. 2.
Lard oil.
Pressure, 1 0,000
Ibs. per sq. in.
2.
3-
4-
5-
O.I 1 1
0.089
0.1075
0.071
0.1275
0.0675
0.07
0.071
0.045
0.055
0.065
0.075
0.105
0.044
0.07
0.04
0.055
0.059
0.036
0.035
TEST No. 3.
Heavy Mach'y oil
and Graphite.
Pressure, 10,000
Ibs. per sq. in.
2.
3-
4-
5-
0.147
0.15
0.15
0.127
0.155
0.156
0.16
0.157
0.13
0.1775
0.132
0.15
0.14
0.13
0.1675
0.127
O.II7
O.I2
0.14
0.1325
TEST No. 4.
Heavy Machinery
oil.
Pressure, 3,000
Ibs. per sq. in.
Professor Kingsbury's conclusions are :
" That, for metallic screws in good condition, turning at extremely slow speeds, under
any pressure up to 14,000 Ibs. per square inch of bearing surface and freely lubricated
before application of the pressure, the following coefficients of friction may be used :
COEFFICIENTS OF FRICTION.
Lubricant.
Minimum.
Maximum.
Mean.
Lard Oil,
0.09
0.25
O.II
Heavy Machinery Oil (Mineral),
O.II
0.19
0.143
" and I
graphite in equal volumes, /
0.03
0.15
0.07
With regard to the value of the coefficient to be used in design-
ing power-screws, Professor Kingsbury says :
" That (the value) depends upon the object of the design. If the screw is to be made
so that it could not overhaul under the most favorable conditions, with either lard oil or
SCREW FASTENINGS.
89
FIG. 38.
heavy machinery oil, probably 8 per cent, would be the highest allowable coefficient ;
and, for a certain margin of safety, a somewhat lower figure. If the driving mechan-
ism is to be designed with a view to making the screw turn, even if perfectly dry, prob-
ably 30 or 40 per cent, would be the figure. If the amount of power likely to be lost
in the long run is what is wanted, probably 15 per cent, would be a safe coefficient for
everyday work. This might be reduced to 10 per cent, with lard oil under the best
conditions and at the speeds used in these experiments. ' '
Mr. Wilfred Lewis states that, " for feed screws which turn
slowly, [JL = o. 1 5 may be taken as a good gen-
eral average."
(c) Friction of the Support. — The thrust of a
power-screw may be taken by the end of the
screw itself upon a plane step-bearing whose
maximum diameter is equal to the effective
diameter, d, of the screw or the thrust may be
borne by an annulus forming a collar-bearing
at the end of the threaded portion. Both types of
bearing are indicated in Fig. 38. In fastenings,
the thrust and force of friction act between the
under surface of the nut and the washer, the
leverage of the force being about two thirds
the nominal diameter, D, of the bolt. Let :
W = total axial load ;
p.' = coefficient of friction ;
Wfjf = force of friction j
r •= radius of plane step bearing of diameter, d\
Rl and R2 = outer and inner radii, respectively, of collar-bearing ;
R = 2^ D = leverage of Wfi! in nut.
Then, the moment of the friction in the :
Step Bearing = W/JL'- %r; (57)
E> 3 r> 3
Collar Bearing = Wa'- % • - ~ ^ ; (58)
K\ — Ki
Nut — Wpr •% D. (59)
The reduction of the moment by the use of a step-bearing is ap-
parent. This form, however, produces the most uneven wear
and usually the greatest unit pressure.
In addition to the vertical load there is usually a sidewise
thrust on the screw-support, since the power is generally applied
as a single force and not as a couple. This produces lateral pres-
90 MACHINE DESIGN.
sure and friction between the threads or shank of the screw and
the support or nut and connected parts. The action resembles that
of a shaft journal. Views as to the distribution of friction in the
latter are somewhat conflicting. In practice, the total pressure is
assumed to be divided uniformly over the projected area of the
bearing surface.
7. COMBINED TORSIONAL AND TENSILE OR COMPRESSIVE
STRESSES. — The axial load upon a screw produces a tensile or
compressive stress and the external force applied to the nut in
order to raise the load, develops a shearing stress. Disregard-
ing the reinforcing action of the thread, both stresses may be
assumed as acting upon the effective area only of the bolt. Then,
the unit tensile stress will be equal to the total load divided by
the effective area and the unit shearing stress at the outer.circum-
ference of the area — where that stress is a maximum — will be
equal to the twisting moment divided by the polar modulus of
the section. Referring to Fig. 36, the twisting moment is P x
4/2. Then :
Unit tensile stress = W -±- - — = S ; (60)
4
Unit shearing stress = P^.~ = ~^ = St. (6 1 )
These stresses coexist and combine to produce a maximum, unit
tensile stress upon a plane whose angle with the axis depends
upon their relative magnitude. Similarly, they combine to pro-
duce a maximum unit shearing stress upon a plane whose angle
differs from that of the first but is governed by similar conditions.
Evidently, the required effective area will depend upon the inten-
sity of these resultant stresses, the formulae for which are :
Maximum tensile unit stress = |- St + V -S* + ^^2 = St max.; (62)
Maximum shearing unit stress = y S* + ^St2 = Ss max. (63)
When a screw which is so short that it may be treated as a strut,
is under compression, the maximum compressive and shearing unit
stresses may be found by replacing St in (62) and (63) by the unit
compressive stress. In designing a screw for a given load, the
maximum stresses, as above, must not exceed the elastic strength
of the metal. The usual practice, as given in § 29, is to assign a
reduced working stress to the material as the diameter decreases.
SCREW FASTENINGS.
The experiments of Professor Martens — the results of which
are given in Table XXIX. — show the weakening of the effective
section of the bolt to axial tensile load which results from the
torsional action of the nut. His conclusions, from these tests,
are :
" The weakening effect of the turning of the nut under stress at rupture, is much less
than might have been predicted, when the distortion of the screw below the nut by per-
manent elongation is taken into consideration. The tests indicate, for this case, a
strength of the I -in. bolts about 20 per cent, less than that of the plain bars and of the
^-in. bolts about 15 per cent, less than that of the plain bars. In general, it may be
said that the turning of the nut upon the bolt at rupture reduces the strength of the nut
section of the bolt by about 30 per cent."
8. CROSS SHEAR. — In the flange coupling shown by Fig. 39,
the bolts transmit the torsional stress from one section of the shaft
to the next, and, if accurately
fitted to the bolt-holes, are
exposed practically to cross
shear only, there being no
bending stress and the tensile
load, due to drawing the
flanges together, being rela-
tively slight. The usual
method of design is to assume
FIG. 39.
the diameter of the bolt circle and equate the resistances to shear-
ing of the shaft and bolts, the result being an equation in terms of
the diameter and number of the latter. Let :
R = radius of centre of bolt-holes ;
D = diameter of shaft ;
d = diameter of bolts ;
n = number of bolts ;
T. M. = maximum twisting moment on shaft ; (force, 7!jP.)
R. M. = resisting moment of shaft ;
T.'M.' = twisting moment at bolt centres ; (force, T.'F.')
R.S. = aggregate resistance of bolts to shearing.
The resisting moment to shearing of a circular section is equal
to the product of the shearing stress, Sf, at its periphery by the
polar modulus of the section, ~d3/i6, where d is the diameter.
T.F. is expressed in terms of the unit radius and will be to T.'F.'
inversely as their respective radii. We have :
92 MACHINE DESIGN.
T.M. = R.M. = r~ - S '
ID
T.'F' : T.F. :: i : R .: T.'F.' = = ~D • S ;
K IDA.
-d2
R,S. = -- x n x Sf
Equating the values of T.'F.' and R.S.:
To allow for inaccurate fitting and, therefore, for slight bending,
the shearing stress on the bolts is usually made three fourths of
that on the shaft. Introducing this fraction :
R is usually 0.75 to O.8 times D. The number and diameter of
the bolts are interdependent. If it be desired that the outside
diameter of the coupling shall be as small as possible, n should
be increased and d decreased, n is usually a multiple of the num-
ber of duplicate sections of the crank-shaft. The bolts may be
either headless taper bolts or " body-bound " and cylindrical with
heads, as shown in Fig. 39. With the former type the weight of
the head is saved and a rigid joint ensured. The objections to it
are the accurate fit required, and, owing to the tapering hole, the
impossibility of making the sections of a crank-shaft interchangeable.
It will be noted that the analysis assumes the shearing stress to be
distributed uniformly over the cross section of the bolt. While
this assumption has sufficient practical accuracy, the stress upon the
bolt-section varies in intensity, being greatest upon that side of the
section which is most remote from the centre of the shaft.
9. STRESS IN CYLINDER-HEAD STUDS. — The stress in bolts used
in securing steam-cylinder covers and in other joints requiring to
be tight against fluid pressure, is affected by somewhat complex
conditions. The joint may be made metal to metal and ground
or a gasket may be interposed between the flanges. The ma-
terial of the latter depends upon the steam pressure and the cor-
responding temperature. Rubber and sheet asbestos, plain or in
combination, and copper in corrugated sheets, wire, or wire-gauze,
are used for this purpose.
SCREW FASTENINGS.
93
w
The bolts, the flanges, and the gasket (if any), are all more or
less elastic. The bolts are set up with an initial tension which is
opposed by the force due to the compression of the flanges and
gasket. Later, steam is admitted to the cylinder placing an addi-
tional tensile load upon the bolts,
which load elongates the latter
still further and thus reduces
the compressive force, as above.
Referring to Fig. 40, let :
St = initial unit stress in bolt ;
Sc = initial unit force on bolt
due to compression of gasket and
flanges.
Then : S, = S .
FIG. 40.
When the steam enters the cylin-
der, the forces acting unon the bolts are the maximum load, W,
due to the steam and the reduced compressive force between the
flanges. These forces are opposed by the tensile stress within
the bolt. Let :
Sw = unit force on bolt corresponding with external load, W\
Sc' = unit force on bolt corresponding with reduced compres-
sion between flanges ;
Stf = unit tensile stress in bolt when load, W, is applied.
Then : S/ = Sw + Ser.
If the bolt stretches by an amount equal to the initial compres-
sion of the other members, St' = Sv, and the joint will open. On
the other hand, with a short, rigid bolt, connecting ground flanges
without gasket, the elongation will be relatively small and, with
high initial stress, the value of St' approaches Sw, plus the initial
compressive force, Se. In any event, for a tight joint, the intensity
of Stf must exceed S^ and Scf must be greater than zero. In
Table XXXI., there are given the numbers, diameters, working
stresses, and ultimate unit strengths of the cylinder-head studs for
the high-pressure cylinders of some of the later vessels of the U. S.
Navy. The area under load includes that of the cylinder and
counterbore plus, in some cases, a portion of that over the ports.
When a cylinder liner is used, the counterbore may be only ^
inch deep.
94
MACHINE DESIGN.
TABLE XXXI.
STEEL STUDS FOR CYLINDER COVERS. U. S. NAVY.
H. P. Cylinder.
Studs.
Diameter,
Ins.
Initial Press.
Gauge, Ibs.
per sq. in.
Total Area
Inside of
Flange,
Total Load
at Initial
Press., Ibs.
Number.
Diameter.
Stress per
sq. in. of
Eff. Area at
Initial
Material of
Tensile
Strength
(Minimum)
sq. ins.
Press., Ibs.
Ibs. per
sq. in.
H
250
153
38,250
18
:
7036
8o,OOO
20*
250
342.25
85,562
28
7240
8o,OOO
30
200
921.3
184,260
24
I
7264
8o,000
35
250
1484
371,000
38
I
7539
75,000
38*
250 1 1720
430,000
38
I
7469
75,000
28. Stresses in Nuts.
i. SHEARING, RUPTURE, AND BEARING PRESSURE upon the
thread. The conditions as to these stresses are similar to those
which exist with the bolt-thread, excepting that, as the diameter
at the root of the nut-thread is the nominal diameter, D, plus the
clearance spaces, the total section at the root to resist shearing
and rupture and the projected area of the thread are slightly
greater than those of the bolt.
2. BURSTING STRESS. — In Fig. 41,* let:
- W= axial load upon the bolt ;
* ' ' Report of Board to Recommend a Standard Gauge for Bolts, Nuts, and Screw-
Threads, U. S. Navy," May, 1 868.
SCREW FASTENINGS. 95
N— normal pressure upon one half the thread, resolved in a
direction perpendicular to any single element of its heli-
coidal surface ;
B = component of N acting in a direction perpendicular to the
axis of bolt ;
/5 = base-angle of thread ;
<p = angle of repose or friction.
Then, without friction :
W
W= 27V cos B.:N
- —5
2 COS /? '
W sin /? W
B = N sin /? = - --- ^ == — -tan /?.
2 COS ft 2
Considering friction, the true direction of pressure, R, is inclined
to the normal, N, by the angle <p ; and, as the tendency of Wto
resist and reverse the nut is opposed by the friction, the bursting
effect of W will be reduced and the angle between W and R be-
comes 3 — (D. Then :
W
*-Ttan<0-f). (65)
In the Sellers system /? = 30°. Taking fj. = tan ^ = 0.124,
<p = 7° 04' and /9 — ^ = 22° 56'. Hence,
W
£= — tan 22° 56' =0.2115 W7.
A given axial load, W7, produces, then, a bursting pressure, B
= 0.2 W; and, therefore, the vertical section, through the short
diameter of the nut — the stress upon which section resists B —
should be two tenths the effective bolt-area, since the stress upon
the latter sustains W.
The total width of the resisting section of the nut is dn — D,
where dn = short diameter of nut and D = nominal diameter of
bolt ; the height of the section is that, ff=D, of the nut. For
convenience, assume the nominal area of the bolt as effective in
sustaining W. Then
H(dn - D) = D(dn - U) = - -D2 x 0.21 15,
4
.-. d = i.i66D.
96 MACHINE DESIGN.
Since, in this system, dn= i.$D -f -J^ in. for finished nuts, there is
a considerable excess of strength to resist bursting.
29. Efficiency of the Screw.
Consider the screw with regard to :
i. Loss OF POWER. — The efficiency is the ratio between the
useful and total work. Disregard journal friction, as absent or
uncertain.
(a] Square Threads. — From Fig. 36 and equations (50) and
(51), we have, for the thread only, per revolution, in raising W
with friction :
Useful Work P0.7id0 W ten 30~d0
Total Work ~ P.xdQ ~ ~W tan (<50 + (f].^d^
(66)
tan o,,
~ tan (<50 + p) ~
which expression gives the efficiency, E, of the screw-thread for
any given pitch-angle, d0, of the mean helix and any angle of repose,
(f. When the screw is employed solely for transmitting power,
the pitch-angle of maximum efficiency should be used, if practi-
cal considerations do not prevent. Differentiating (66) and put-
ting the first derivative equal to zero :
dE cot (dn + v} tan 3n
: o;
whence OQ = 45° — <p / 2, which value of 30 will make E a maxi-
mum. Substituting in (66) :
tan (45°- f)
E(max.} = N—
tan I 45° +
If ^ = 0.105, <f> = 6°, o0 = 42°, and £=o.8i. Good practical
reasons make it undesirable to use so large an angle. Multiple
threaded screws, however, owing to their ample bearing surfaces,
permit relatively steep pitches.
For the friction of the support, we have, for a screw whose
thrust-collar has a mean friction-diameter, D' , a work of collar-
friction per revolution equal to the force of friction multiplied by
its circumferential path = Wp'.nD' = W 'tan' <p* .xD1 '. This work
SCREW FASTENINGS.
97
must be added to that expended on the thread in order to find the
total work. Hence, including thread and collar-friction :
W tan (£0 + <p) xdQ + W tan <p' .
tan
D'
(67)
Assuming the same coefficient of friction for thread and collar,
tan <f>' = tan <p = ft and E' becomes a maximum when
cot
>l
D>
I +-y-
In the table relating to square-threaded screws which follows,
the efficiencies have been calculated, but, in several cases, they
have been checked by experiment and found to be fair average
values. The efficiency of any screw will, of course, vary widely
with the amount of lubrication. The same coefficient of friction
— p= 0.15, (f> — 8° 30' — is taken for both thread and thrust-
collar. The diameter of the latter is assumed to be that of the
thread. E = the efficiency per cent, when there is no friction be-
tween the thrust-collar and its bearing; E' = the efficiency per
cent, allowing for thrust-collar friction.
TABLE XXXIL*
APPROXIMATE EFFICIENCIES OF SQUARE THREADED SCREWS.
Angle of Thread, S0
E
^
2
19
ii
3
26
14
4
32
17
5
36
21
10
55
36
20
67
48
45° -|
79
52
The efficiency of a square-threaded screw in lowering IV may
be found from the values of the useful and total work by a process
similar to that given for the efficiency in raising the weight.
* Goodman : " Mechanics Applied to Engineering," 1899, p. 204.
98 MACHINE DESIGN.
(&) Triangular Threads. — From equation (66), we have for the
efficiency of a square thread :
tan d0 + tan y
Replacing tan <p by // sec /?, we have, in raising W with friction
in triangular-threaded screws, for the thread only, the efficiency :
*-*"*•• ItZ/*.T^?' (68)
For the friction of the nut on its washer or boss — assuming the
mean friction diameter of the nut as % of D, the nominal diameter
of the bolt — we have a work of nut-friction per revolution of
£Ftan <pr • %xD, which work must be added to that expended on
the thread. Hence, including thread and nut friction, as in (67) :
Wtan30.iui0
J0 -f <p)xdQ + W tan <p ' •
tan fi
(69)
0 "*: Y + 4./%.tan »'.
i — tan ^0 tan y *
Replacing tan <p by fi sec /9 and tan <p' by // ' :
tan 3n
£' =
0
tan
In the Sellers system, sec /? = 1.15. Hence :
tan d0 + 1.15 ft ^
(7.)
tan
The efficiency of a triangular-threaded screw in lowering W may
be found by a similar process.
Mr. Wilfred Lewis gives the following approximate formulae
for the external force and efficiency of triangular-threaded screws,
which formulae he states are applicable with a close degree of ac-
curacy to most of the cases which occur in practice. Let :
SCREW FASTENINGS. 99
p = pitch of screw ;
D = outside diameter of screw ;
P= force applied at circumference (of screw) to lift a unit of
weight ;
E' = efficiency of screw in lifting.
Then: P = f-±^ and E' - ^ (72)
Experiments,* conducted by Mr. James McBride to deter-
mine the efficiency of a screw, gave results in accord with
the formulae given above. The test was made with an ordinary
2-inch screw-bolt, not especially prepared. The thread was of the
standard V-shape and of 0.2 2 -inch pitch. The nut was not faced
and had the flat side to the washer, the latter being of malleable
iron, not faced. The contact-surfaces of nut and washer and the
threads of nut and bolt were well lubricated with lard oil. The
axial, tensile load upon the bolt was 7,500 Ibs. The nut was a
good fit, and, when not loaded, was easily run up and down the
bolt with the fingers. Wrenches of different lengths were applied
to the nut and a known force which would just move the latter,
exerted upon each wrench. The ratio between the useful work of
lifting the weight and the total work expended upon the nut, gave
the efficiency, which, for 5 tests, averaged 10.19 per cent.
The effective diameter of a 2-inch bolt = 1.712 in. The mean
thread diameter, d^ is therefore 1.856 in. The pitch = 0.2222 in.
and tan 30 = pfxd^ = 0.038 in. Assuming // = o. 1 5 and //' = o. 10,
and substituting in formula (71), we find E' = 10.7 per cent.
Again, substituting the values of / and D in formula (72), we
find E' = 10 per cent. The theoretical and experimental results
are hence practically the same.
2. Loss OF AXIAL STRENGTH. — In screwing up a nut, the bolt
is subjected to the tensile or compressive stress corresponding with
the axial load produced and to the torsional stress developed
through the action of the nut-thread on the bolt-thread. The
torsional action results from thread-friction and from that com-
ponent of the axial load which must be overcome in order to move
the latter up the inclined plane of the screw.
The measure of torsion is the twisting moment, T.M., the latter
being the product of the force, P, Fig. 36, by its lever-arm dQJ2
* Trans. Am. Soc. Meek. Engrs., Vol. XII.
100 MACHINE DESIGN.
= /. For equilibrium, the twisting moment must be equal to the
resisting moment. The latter, for a circular section, is the product
of the unit shearing stress Sa, at the periphery of the section by
the polar modulus of the section, which is /r^3/i6, where d is the
diameter. Taking, for convenience, dQ — dt we have / = dJ2 and :
TM.-Pt-S.~.-.P-S.~, (73)
i. e., if St be the greatest allowable shearing stress in all bolts, the
turning force P, which may be applied as above with safety, varies
as the square of the diameter. This condition prevails also with
the axial load, since that load by (60) is
in which St is the greatest allowable tensile unit stress.
The relation between the twisting force and the axial load is
given by (51) as :
P
<p is here a constant for all screws under similar conditions of sur-
face and lubrication. The angle, 30, is, however, in the Sellers
system, variable, being a maximum at the smallest diameter. For
example, it is 4° 11' for the ^-inch screw and i° 45' for the 3-
inch screw. Replacing IV in (51) by its equivalent :
P-S,~.ton(39 + <p),
in which <p may be regarded as simply a constant addition to d0.
It will be seen that, while P produces a shearing stress which varies
as dz, it develops a tensile stress varying not only as d2 but also
as tan (dQ -f <p). Since tan d0 increases with decreased diameter, it
is evident that, with the same tensile stress in two bolts of different
diameters, the shearing stress will be larger in the smaller bolt.
The disadvantage of this increased shearing stress in setting up
the nuts of small bolts, is aggravated by the tendency of the aver-
age mechanic to put excessive force upon the wrench in such cases.
As a result of a series of tests made at Cornell University, Pro-
fessor Barr * concludes :
" (a) That the initial tensile load due to screwing up for a tight joint varies about as
the diameter of the bolt — that is, a mechanic will graduate the pull on the wrench in
* "Notes on Machine Design," 1900, p. 106.
SCREW FASTENINGS. IOI
about that ratio, (b) That the load produced maybe estimated at 16,000 Ibs. per
inch of diameter of bolt, or
P^ = 16,000 d,
in which Pl is the initial load in pounds due to screwing up, and d is the nominal (out-
side) diameter of the screw thread. * * * If the initial load due to screwing up be
divided by the cross-sectional area of the bolt at the bottom of the thread, the initial in-
tensity of the tensile stress is obtained. The above experiments indicate that this in-
tensity of stress varies, approximately, inversely as the nominal diameter (d} of the
bolt ; and that it may frequently equal or exceed :
30,000
/= d Ibs. per sq. in.
In addition to this tensile stress, there is a considerable twisting action on the bolt."
Mr. Harvey D. Williams * has calculated the efficiency of the
U. S. Standard bolts whose proportions are given in Table XL,
on the basis of the ratio between the useful fibre stress — or that
portion which would be required for the support of the safe axial
load only — and the total fibre stress produced in screwing up the
nut. His results are given in Table XXXIII.
The method of computing the efficiencies given, is as
follows :
From (55) the value of Pis found in terms of W, p and dQ be-
ing known for any given bolt and /j. being taken as 0.15. Then,
P= K'W, where A' is a numerical factor. Also :
Twisting Moment = T.M. = P x -£ ;
from (7 3): \6T.M.
from (60):
S<=^2'
Then : _
Maximum tensile stress = f= | St + \\/S? + 4$* ; f (74)
w
But, to support the load, W, there is required only per sq. in. the
A.W
Useful tensile stress =f' = St = —-&
The load, W, must be reduced below the amount which the
*Jour. Am. Soc. Naval Engineers, Vol. XIII., No. 2.
t Lanza: "Applied Mechanics," 1897, p. 892.
102 MACHINE DESIGN.
screw would carry, if under direct tension only, in order that the
load produced by the stress,/, shall not exceed the strength of
the bolt. Hence, in this respect — considering the thread-friction
only — the efficiency of the bolt in raising the weight W, is :
in which W is the useful axial load in pounds, T. M. is the torque
in inch-pounds, and d is the effective diameter in inches. Equa-
tion (74) is similar to (62), the former being the formula deduced
by Grashof and the latter that by Rankine.
Referring to the table, Mr. Williams says :
"The factor of safety equals the direct load factor 7, divided by the efficiency;
and the safe loads given in the body of the table correspond to the factor of safety
in the same horizontal line and the ultimate strength at the head of the column. To
facilitate the computation of bolts having threads which are finer or coarser than the
standard, the column headed "Relative Fineness of Thread" is given, in explana-
tion of which it need only be remarked that the relative fineness of thread equals the
number of threads per inch multiplied by the diameter and that bolts of different
sizes but having the same relative fineness of thread will have the same efficiency and
the same factor of safety. As the thread is made relatively finer and finer beyond the
limits of the table, the corresponding efficiency approaches 88.06 per cent, as a limiting
value, beyond which it cannot go. The factor of safety meantime approaches the limit-
ing value, 7.95. The efficiency of a hollow bolt is always greater than that of a solid
bolt of the same diameter and number of threads, the limiting efficiency for a very fine
thread on a very thin tube being 96.48 per cent., as against 88.06 per cent, for a solid
bolt. The error will therefore be always on the safe side, if we use the efficiencies and
factors of safety given in the table in computing hollow bolts. ' '
Seaton and Rounthwaite * give a table for the effective strength
of Whitworth screws in which the torsional stress is allowed for
by assuming progressively lower values for the working stress as
the bolts diminish in size. The table is based on the relation :
Working Stress per sq. in. = (Effective Area)& x C,
where C = 5,000 for iron or mild steel and 1,000 for muntz or
gun-metal. For iron or steel bolts above 2 inches in diameter
and gun-metal or bronze ones above 3^ -inch diameter, the
moment of the twisting stress is small, proportionately, and is
neglected in the table, the working stresses in Ibs. per sq. in.,
for all sizes above those noted being uniformly 7,000 and 2,500,
respectively.
* "Pocketbook of Marine Engineering Rules and Tables," 1899, p. 73.
SCREW FASTENINGS.
I03
TABLE XXXIII.
SAFE LOADS FOR U. S. STANDARD BOLTS.
Ultimate Strength.
•o
i
£
20,000
40,000
50,000
6O,OOO
65,000
80,000
95,000
8
•S
c
S.
dt
"o
M
"8
S
I
•s
1
1
|
E
1
Q
c
p
1
Efficiency.
7
1
1
Is
22
B Bolt Mat.
A Bolt Mat.
G Q
if
Grade Mac!
gings
1
1
zL
?
f
Cu, 8$$
I
Is
0
I
U
jl
S
5
\
20
74.68
9-4
57
115
143
172
186
229
272
A
18
76.56 9-1
99
198
247
297
322
396
470
6
1
16
77-49
Q
150
301
376
451
488
601
A
14
78.38
8.9
207
415
519
623
675
830
986
6.5
F
13
78.48
8.9
282
564
704
845
915
1,125
1,340
12
78.92
8.9
365
730
912
1,095
1,186
1,460
1,730
i
II
79.11
8.8
456
1,140
1,370
1,480
1,820
2,170
7-5
I
10
80.00
8.8
690
1,380
1,725
2,070
2,240
2,760
3,280
£
Q
80.48 8.7
964
I,93°
2,410
2,900
3,!40
3,86o
4,580
8
8
80.61 8.7
1,265
2,530
3,i7o
3,800
4,120
5,060
6,010
7
80.48 8.7
i,595
3,190
3,990
4,790
5,180
6,380
7,570
7
81.37 8.6
2,070
4,140
5,180
6,210
6,73°
8,280
9,830
6
80.92 8.7
2,440
4,890 6,110
7,330
7,940
9,780
n, 600
9
6
8i.6i!8.6
3,020
6,040
7,540
9,060
9,800
12,050
14,300
5^
81.56 8.6
3,530
7,060
8,820
10,600
11,500
14,100
16,75°
5
81.37; 8.6
4,060
8,120
10,150
12,200
13,200
16,200
19,250
5
81.92 8.5 4,800
9,600
12,000
14,400
15,600
19,200 22,800
9
,
Ji
81.61 8.6
82.43 8.5
5,360
7,120
10,750
14,200
13,400
17,800
16,100
21,400
I7,4oo
23,100
21,500
28,500
25,500
33,8oo
10
.]
4
82.351 8.5
8,750
17,500
21,900
26,300
28,400
35,ooo
41,500
II
•|
4
83.20 8.4 11,000
22,000
27,50°
33,000
35,7oo
44,000
52,200
12
3
4
83.42:8.413,400
26,800
33,5oo
40,200
43,600
53,6oo
63,600
13
4
83.8818.316,100
32,200
4o,2ooj 48,400
52,400
64,400
76,400
14
3i
4
84.20
8.319,000
38,100
47,600
57,2oo
61,900
76,200
90,400
15
3f
4
84.47
8.3:22,200
44,500
55,600
66,700
72,300
89,000
105,500
16
4
4
84.71
8.325,700
51,400
64,200
77,000
83,400
102,800
122,000
17
18
4\
4f
4
4
84.91 8.2 29,350
85.09 8.2 33,300
58,700
66,600
73,400
83,200
88,100
100,000
95,4oo
108,000
117,400
133,000
139,300
158,000
19
20
41
5
4
4
85.26' 8.2 37,400
85.44 8.2 41,900
75,ooo
83,800
93,700
105,000
112,000
126,000
122,000
136,000
150,000
167,500
178,000
199,000
21
5-V
4
85.55 8.2 46,600
93,2oo
116,500
I4O,OOO
151,000
186,000
221,000
22
5j
4
85.68; 8.2 51,500
103,000
129,000
154,500
167,000
206,000
244,500
23
sl
4
85.8o! 8.2 56,700
113,500
142,000
170,000
l84,000
227,000
269,000
24
6
4
85.92 8.1:62,000
124,000
155,000
186,000
202,000
248,000
295,000
30. Types of Screw Fastenings.
Screw fastenings have forms as numerous as their uses are
varied. Brief reference will be made to a few types.
I. BOLTS, TAP BOLTS, STUDS. — The proportions of Machine
Bolts have been given in preceding tables. When employed to
104
MACHINE DESIGN.
FIG. 42.
join flanges, as in Fig. 40, this form, if short and tightly fitted,
gives a most rigid connection. For steam cylinder heads, they
are somewhat objectionable, since, if a bolt breaks, the lagging
must be removed to replace it.
With the Stud, on the contrary, the broken
part may be drilled out readily from the
flange. The stud has further advantages in
its use when through bolts are inadmissible
and in the fact that, once set in the weak
threads of cast metal, it need not be removed,
as the tap-bolt must be, to disconnect the
parts. The threaded portion which enters
the casting should be longer than that for
the nut and the unthreaded shank should be shorter than the
flange through which it passes. Fig. 42 * gives good general
oroportions, as follows :
D = diameter of stud ;
F= \.2$D = depth of hole ;
G •= i . 1 5/? = length of stud to be screwed in ;
H = 1.30/2 = length of thread on nut-end ;
J = F = length of thread on opposite end.
The Tap-Bolt, Fig. 43, is practically a machine-bolt without a
nut, the shank passing through a flange or other member and the
threaded section screwing into the remaining part connected.
Like the stud, it is liable to stick fast and it has
the further disadvantage that its frequent removal
to break the joint will wear the weak threads of
a casting. For this reason, the depth of the tapped
hole should be from 1.5 to twice the diameter.
The proportions of counter-sunk and round and
button-head tap-bolts and screws are given in
Table XXXIV.
2. SET-SCREWS are fastenings which are suit-
able only for light work. They find most fre-
quent use in securing pulleys, etc., to shafting.
Their chief advantage is that no key-way is necessary and that,
therefore, the connected piece may be readily shifted. The
disadvantages are the liability to slip, the burring of the shaft,
* American Machinist, June 6, 1901.
FIG. 43-
SCREW FASTENINGS.
ICK
TABLE XXXIV.
TAP-BOLTS AND SET-SCREWS.
(NEWPORT NEWS SHIPBUILDING AND DRY DOCK Co.)
Suit on Head Scrntf
Ji
HeaJles* &t tScrmt
Tap Bolts.
Round Heads. Button Heads.
meter
B
Diameter
B
Depth of
Head,C
the radial stress in the hub, and the uneven bearing and slight
eccentricity of the latter, if a free fit. The points of set-screws
are made flat, conical, rounded, or cupped. A shallow hole is
sometimes bored in the shaft to receive the point. In light work,
however, the screw is set up sufficiently to make its own indenta-
tion. A relatively strong fastening may be made by interposing a
thin steel plate between the set-screw and a " flat " filed on the
shaft, the plate fitting into a recess in the hub.
Professor Lanza * tested the holding power of points of various
forms upon a ^|-in. shaft, the screws being of wrought iron, f -in.
diameter, 10 threads to the inch, and set up with a force of 75
* Trans. Am. Soc. Mech. Engs., Vol. X.
106 MACHINE DESIGN.
Ibs. at the end of a lo-in. monkey wrench. The shaft was of steel
and the points made but little impression upon it. Two screws
were used to secure a pulley to the shaft and then the circum-
ferential load required to make the pulley slip was found, from
which load the resistance of the screws was determined. The
shapes of the points were :
A. Ends perfectly flat, T9^ in. diameter.
B. Ends rounded, radius \ in.
C. Ends rounded, radius \ in.
D. Ends cup-shaped and case-hardened.
The holding power in pounds was :
Lowest. Highest. Average.
A. 1412 2294 2064
B. 2747 3079 2912
C. 1902 3079 2573
D. 1962 2958 2470
Professor Lanza states as to :
A. The set-screws were not entirely normal to the shaft ; hence they bore less in
the earlier trials before they had become flattened by wear.
B. The ends of these set-screws, after the first two trials, were found to be flattened,
the flattened area having a diameter of about \ in.
f. The ends were found, after the first two trials, to be flattened, as in B.
D. The first test held well because the edges were sharp ; then the holding power
fell off till they had become flattened in a manner similar to £, when the holding power
increased again.
3. EYE-BOLTS. — Good proportions for eye -bolts are given in
Table XXXV. Since the bolt when screwed home is without
load, the torsional effect is negligible and the same working stress
may be used for all sizes. Owing
to bending action, the sides of the
eye are subjected to greater stress
than the body of the bolt, and
their combined cross-sectional area
is made greater than that of the
FIG. 44.
weakest section at G, the excess
being about 200 per cent, in the |-inch bolt and decreasing rap-
idly with the larger sizes.
4. STAY-BOLTS. — These bolts are used to brace the flat sur-
faces of boilers. They vary in details of form and manufacture.
Good practice is shown by Fig. 44. The bolt is threaded at each
end, turned down in the shank to the diameter at the base of the
thread, screwed into both sheets, and riveted over cold with shallow
spherical heads. Minimum general proportions are : diameter,
SCREW FASTENINGS.
lO/
TABLE XXXV.
EYE-BOLTS.
(UNION IRON WORKS.)
Capacity Based on 10,000 Ibs.
per sq. Inch Strain.
767
1,104
I>963
2,485
3.712
5,135
6,903
7,854
9,940
12,270
13,520
16,210
19,150
22,340
-| inch ; threads per inch, 1 2 ; spacing, centre to centre, 4 inches.
The stress at root of thread should not exceed 6,000 Ibs. per
sq. in. A " detector " hole — at which leakage will show when the
bolt is broken — is drilled or punched, preferably the former, from
the outer end of the bolt inward to the beginning of the shank.
Flexibility is a most important requirement of these bolts. In
some cases, various combinations of the ball-and-socket joint have
been applied at one end. In the ordinary type, this quality de-
pends upon the material, the reduced shank, and the form and
method of driving the heads. As material, the best grade of
wrought iron is preferred.
The Falls Hollow Staybolt is rolled with a central hole through-
out, thus avoiding later drilling or punching. The bolt is also
threaded through its full length with, therefore, uniform strength at
all points. The size of the hole is usually -| inch or y3^ inch. It
serves not only as a " detector " but also, if desired, as an inlet for
the admission of air to aid combustion.
The data and results of tests of these bolts at McGill University are :
io8
MACHINE DESIGN.
Material, double-refined charcoal stay-bolt iron, i inch diameter,
•j3g inch hole; length, 25^ inch ; mean diameter, outside, 1.014
inch ; yield-point, 32,000 Ibs. per sq. in. ; ultimate tensile strength,
49,300 Ibs. per sq. in.; equivalent elongation in 8 inches,
per cent. ; reduction of area, 45.7 per cent.
Chief Engineers Sprague and Tower, U. S. Navy, in 1879,
exhaustive experiments upon the strength of boiler-bracing. From
their report * the following data are taken with regard to the re-
sistance of screw stay-bolts in flat surfaces :
"In reference to iron and low steel bolts, andiron and low steel plates, and copper
plates and iron bolts, after a careful examination of the results of these experiments in
particular, we are satisfied that the following formulae will correctly and safely repre-
sent the working strength of good material in flat surfaces, supported by screw stay-bolts
with riveted button-shaped heads or with nuts, when the thickness of the plates forming
said surfaces and the screw stay-bolts are made in accordance with the dimensions and
conditions given in Table Y. W= safe-working pressure ; T= thickness of plate ;
*/= distance from centre to centre of stay-bolt :
T2
For iron plates and iron bolts W= 24000 —
Tl
For low steel plates and iron bolts W— 25000 —
For low steel plates and low steel bolts.
For iron plates and iron bolts, with nuts
'=28°°°£
'= 40000 Z?
For copper plates and iron bolts
= 14500
" To obtain the ultimate bursting pressure, multiply the results of the above formulae
by 8, which is the factor of safety used.
TABLE Y.
DIMENSIONS AND CONDITIONS FOR MAKING IRON AND Low STEEL SCREW STAY-
BOLTS FOR FLAT SURFACES SUBJECT TO INTERNAL PRESSURE FOR DIS-
TANCES RANGING FROM FOUR TO EIGHT INCHES (INCLUSIVE)
FROM CENTRE TO CENTRE OF STAY-BOLT.
Nuts.
ills m 5
(«« 155 ; K
*" Experiments in Boiler Bracing," U. S. Navy Dep't, 1879.
SCREW FASTENINGS.
I09
" The rivet-heads to be a segment of a sphere, formed by first upsetting the end of the
bolt with a few quick, sharp blows of the hammer, then finished to shape with the ham-
mer and button-head set. Where nuts can be used instead of riveted heads, they should
be of the standard size, suited to trie diameter of the bolt, faced on the side bearing on
the plate, and dished out so as to form an annular bearing surface of as large a diameter
as the nut will allow, aud of a breadth and depth given in the table. Before securing
the nut in place the dished portion should be filled with red-lead putty made stiff with
fine iron borings."
The regulations (January, 1901) of the U. S. Board of Supervis-
ing Inspectors of Steam Vessels, prescribe for plates, ^ inch thick
and under, used in boilers as " flat surfaces fitted with screw stay-
bolts riveted over, screw stay-bolts and nuts, or plain bolt with
single nut and socket, or riveted head and socket," a working
pressure determined by the formula :
*-*£. 04
where P =. working pressure in Ibs., C — 112, / = number of six-
teenths in plate thickness (i. e., for -j^-inch plate, /= 7), and d =
distance between stays in inches. For plates above -j^-inch thick
C ' = 1 20. The pressures, as above, refer to fire-box plates. Also,
FIG. 45-
" on other flat surfaces there may be used stay-bolts with ends
threaded, having nuts on same, both on the outside and inside of
plates." For these surfaces, formula (76) is used with C = 140.
5.. ARMOR BOLTS. — The proportions of threads for these bolts,
as used in the U. S. Navy, have been given in § 24. The method
of their application with side, diagonal, and belt-armor, is illustrated
in Fig. 45. The armor-plate is fitted snugly to a backing of teak,
the latter being secured to the backing plates of the hull by bolts
countersunk in the wood. After the armor-bolt is screwed down
no
MACHINE DESIGN.
to a bearing in the plate, the space around the shank is calked
solidly with oakum and the nut is screwed up against a lead
washer until it embeds itself in the latter, thus causing the lead to
flow into the thread. As an additional precaution against leakage,
the backing plates and washer are coated with red lead, all inter-
stices in the backing are filled with red lead under pressure, and
the joint between the backing plates is calked. Turret-armor is
secured by similar bolts which have, however, a solid head instead
of a nut. The spacing, in all cases, is such as to provide one bolt
for each 5 sq. ft. of armor surface.
3i. Methods of Manufacture.
Bolts are headed hot from round stock ; then threaded and
pointed. Nuts are pressed or forged hot, or pressed and punched
cold, and tapped.
i. BOLT-BLANKS. — The round stock is sheared into lengths
containing enough material for shank and head. Each blank is
then heated and the head
formed in a forging ma-
chine. Figs. 46 and 460.
give a view, plan, and
details of the I 3^ -inch
Heading and Forging
Machine built by the
Acme Machinery Co.,
Cleveland, O., and illus-
trated herein through
the courtesy of that
FIG. 46. company.
" There are two sets of tools : the stationary or gripping dies, A, which hold and re-
lease the blank and the heading die, B, and finishing punch, C, which form the head
and are carried by a tool-holder fixed to a reciprocating plunger. The latter is driven
from the shaft which is actuated by a fly-wheel with clutch-connection controlled by a
pedal. The plunging or upsetting mechanism is omitted from the plan ; it moves on
the line marked "centre of heading slide."
"The dies, A, are divided and open vertically on the centre-line of the lower cylin-
drical groove, Z>, and the upper groove, E, also cylindrical but having a square or
hexagonal recess for the bolt-head. The opening and closing of the dies is done by the
toggle-joint mechanism shown. The latter is operated, through an intervening spring,
by an adjustable connecting rod driven from the shaft. The bolt-blank is upset while
in groove, Z>, by the heading die, B. It is then shifted to E where the head is finished
by punch, C. The grooves, D and E, are concentric respectively with die, B, and
SCREW FASTENINGS.
I I I
punch, C. The latter die holds a die-plug and the punch has a head, both suitably
shaped for upsetting square, or with other forms, hexagonal heads.
" In forging a bolt-head, the operator places a heated blank in groove, D, and touches
the pedal. The machine makes a "plunge" and the gripping dies close, remaining
thus while die, £, advances and forms the head and until the plunger has travelled
about 3 inches. When the machine has passed its forward centre, the plunger has re-
ceded about $£ inch and the gripping dies open. The operator now removes the bolt
to the upper groove, E, and again touches the pedal, upon which the finishing punch
enters the die at E, presses against the head, and removes the slight draught formed
during the first stroke. At the same time, the side pressure of the dies drives all ' fins '
back into the head. The bolt is really made during the first stroke, while the heated
metal is at its best for working. The second stroke simply removes the slight taper of
the head and smooths the sides of the latter.
" The toggle-joint gives maximum pressure when the gripping dies are closed. Until
its joints are in line, it is acted upon by an elastic force in the spring, so that if the dies
become obstructed, the mechanism will yield and the machine will not meet undue
FIG. 460.
strain. In addition to its action as an automatic relief, the spring forms also, with the
connecting rod of adjustable length, a device to regulate the time and duration of closure
of the gripping dies with regard to the advance of the heading dies on the plunger, as
may be required for various sizes of work."
The machine described above is of the " grip-and-plunge " type.
In the " hammer-header" form of heading machine, there are, for
a square head, five hammers, one striking on the top and one on
each of the four faces of the head, simultaneously. In this ma-
chine, the head is molded by a succession of relatively light blows
while it is cooling. An objection urged against this form is that
112 MACHINE DESIGN.
the -bond between the head and shank may be destroyed by a
" cold-shut " at the point of juncture.
2. NUT- BLANKS are made by several processes. In the " hot
pressed " machine, the nut is formed in a die, pierced, and crowned,
and is then placed in the holder of a " burring machine " in which
revolving cutters remove the rough edges. In " hot forging ma-
chines," the nut is forged smooth by hammers automatically oper-
ated ; and, in " cold pressing," the flat bar is fed between the rolls
of the machine, cut into blanks, and a nut made complete at each
revolution. Finally, if desired, the nut is faced and chamfered in
a facing machine.
While the cold-punched nut meets extensive service in struc-
tural and other work, the rigid specifications of the Bureau of
Steam Engineering, U. S. Navy, permit the use of hot-pressed
nuts only. With regard to this question, the Engineer-in-chief says :
" In making a cold-punched nut, either of wrought iron or steel, the fibre of the metal
is injured and its full strength can be restored only by bringing the nut to a welding
heat and finishing it under the hammer, as with the hand-made forged nut. The hot-
pressed nut, on the contrary, although not so perfect as that made by hand forging, ap
preaches the latter so nearly that it can be reamed, tapped, finished, and used with
fair degree of safety."
The injurious effects upon boiler-plate of punching rivet-holes
will be discussed in the succeeding chapter. In 1878, Mr. David
Townsend * made some experiments which show the flow of metal
in nuts punched cold under the conditions of his test. He found
that both the top (nearest the punch) and bottom faces of the nut
were depressed ; that the lower diameter was increased, making
the sides tapering ; and that a portion of the blank punched from
the hole had flowed into the body of the nut throughout a zone
nearly half as deep as the nut and beginning almost at the top
face of the latter. The original depth of the nut was 1.75 in. ;
that of the core removed was 1 .063 in. The density of the latter
was found to be the same as that of the metal before punching.
Therefore, a volume of metal, whose sectional area was that of the
core and whose length was 1.75 — 1.063 = 0.687 ins. was forced
into the body of the nut. It is apparent that the stress was
severe.
3. THREADING AND TAPPING. — Bolts are threaded in the lathe,
or by hand-operated dies, or in the bolt-cutter, the latter being
* Jour. Franklin Institute, March, 1878.
SCREW FASTENINGS. 113
practically but a set of revolving dies into which the bolt-blank is
fed at the required axial speed. The bolt-cutter produces usually
a full thread at one cut with, in consequence, greater stress in the
bolt metal and greater pressure upon the lead-screw than in the
lathe where the same thread would be made in several cuts.
Square threads or those requiring unusual accuracy of workman-
ship require lathe-work. The merits
of the bolt-cutter lie in the rapidity
and cheapness of execution and the
fact that its product is sufficiently
accurate for all ordinary purposes.
Fig. 47 shows a threading tool
which is illustrated herein through
the courtesy of the Rivet-Dock*
Company, Boston, Mass. The dis-
advantages of the single-point thread
tool used in lathe work are : the
difficulties of keeping the exact
angle in grinding, of setting with FIG
the small thread-gauge, the suc-
cession of cuts, necessarily light, to prevent burning the point, and
the repeated stops to test with a limit-gauge or master-nut.
The thread-cutter shown, is a simple disc of tool steel having
ten teeth, each of the latter being longer radially than the one pre-
ceding. In operation, a cut is run with each tooth. There are
thus, in effect, ten cutting tools, the leading ones suitably shaped
for roughing out and the final tooth proportioned for finishing with
accuracy. The single-point tool both roughs and finishes, while
the final tooth of the cutter does finishing work only. The cutter
is mounted on a steel slide, the latter having a movement to and
from the work by means of an eccentric stud in the hub of the
lever. The lever, in moving the slide, engages the pawl and
rotates the cutter one tooth for the next cut. The heel of the
tooth in action rests upon a stop, which takes the strain of cutting.
The stud extends through the lever-hub and is secured on the
back by an arm with pin-stop engaging ten holes so spaced that
changing the stop from one hole to another moves the slide and
cutter a fraction of a thousandth of an inch forward, thus giving
the necessary adjustment for fine fits and provision for exact dupli-
cation.
MACHINE DESIGN.
Bolt-threads are produced also by cold rolling. For the de-
scription of this process which follows, acknowledgment is due to
J. H. Sternbergh, Esq., President of the American Iron and Steel
Manufacturing Company.
" The machine is horizontal and of simple construction. It has a stationary die with
threads cut on the face of the latter at a certain angle. Another die, having threads
cut on its face also, is held in a reciprocating cross-head. The bolt-blank is placed
perpendicularly between the two dies and the thread is produced by compression in
rolling the blank between the latter. The distance between the apices of the dies is the
same as the diameter of the bolt at the root of the thread. For a bolt of, say, |^-inch
diameter, the dies are about ten inches long and the blank is rolled throughout nearly
the whole length of the die, one operation producing the thread. A portion of the latter
is actually raised above the external circumference of the bolt and no metal whatever is
cut away. Great accuracy, however, is required as to the diameter of the blank bolt in
order to produce uniform and perfect threads."
There are various types of machines for threading nuts. In one
well-known automatic nut-tapper, the blank nuts are placed in a
receptacle on the top, from which they are conveyed to the taps
by means of guide-ways. After being threaded, the nuts are
ejected automatically. It is stated that one operator can attend
ten machines and produce about 1 80,000 nuts per day.
32. Materials.
The specifications (1901) of the Bureau of Steam Engineering,
U. S. Navy, for bolts and nuts of steel and iron are as follows :
RODS FOR BOLTS, STUDS, AND RIVETS.
I. The physical and chemical characteristics of rods for bolts, studs, and rivets are
to be in accordance with the following table :
Class.
Material.
Minimum
Tensile
Strength.
Minimum
Elastic
Limit.
Minimum
Elongation.
Maximum
Amount of —
P.
S.
Lbs.fer
Lbs.per
Per cent.
sq. in.
sf. in.
in 8 Inches.
Class A.
Open-hearth
75,000
40,000
23
.04
•03
Cold and quench
nickel or
bend about an
carbon
inner diameter
steel.
equal to the
thickness of the
test piece in
each case.
Quenching
temperature
80° to 90° F.
Class B.
Open-hearth
58,000
30,000
28
.04
.03 I Inner diameter
carbon
: equal to one
steel.
j half the thick-
1 ness.
SCREW FASTENINGS. 115
If the contractor desires, and so states on his orders, the Bureau will direct that the
inspection of the rods be made at the place of manufacture of the bolts, studs or rivets
instead of at the place where the rods are rolled.
2. Kind of Material. — The steel shall be made by the open-hearth process, shall
contain not more than four one-hundredths of I per cent, of phosphorus, nor more than
three one-hundredths of I per cent, of sulphur.
3. Surface and other Defects. — The rods must be true to form, free from seams,
hard spots, brittleness, injurious sand or scale marks, and injurious defects generally.
4. Test Pieces. — If the total weight of rods, all of the same diameter, and rolled
from the same heat, amounts to more than 6 tons, the inspector shall select at random
six tensile test pieces, three cold-bending test pieces and three quench-bending pieces ;
but if the weight is less than 6 tons, one half of that number of test-pieces will suffice.
If, however, the rods in one heat are not of the same diameter, then the inspector will
take such additional test pieces as he may consider necessary according to the number
of different sizes of rods in the heat. All of the test pieces shall be taken from rods
finished in the rolls and, when practicable, but one piece will be cut from each rod
selected for test. Should any test piece be found too large in diameter for the testing
machine, the piece may be prepared for test in the manner prescribed for forgings.
The tensile tests for rounds fy inch in diameter and less, shall be made on the largest
sizes available and the elongation measured on a length equal to eight times the diam-
eter.
5. Bending Tests. — The cold and quench test pieces of Class Ai rods shall stand
bending through an angle of 1 80° around a curve, the inner diameter of which is equal
to the diameter of the rod. The cold and quench bends of Class A2 rods shall stand
bending through an angle of 1 80° around a curve, the inner diameter of which is equal
to one half the diameter of the rod. The quench test piece shall be heated to a dark
cherry red in daylight, and plunged into fresh clean water at a temperature between
80° and 90° F. No bending test will be satisfactory if any cracks are to be seen on
the outside of the bent portion.
FINISHED BOLTS, STUDS, AND RIVETS, CLASSES A AND B.
After the rods to be made up into bolts, studs, and rivets have been tested as pre-
viously described, the finished articles shall be tested by lots of 500 pounds or fraction
thereof, one piece being taken to represent the lot. The failure of 10 per cent, of the
lots of 500 pounds to stand the specified tests in a satisfactory manner will render the
whole of any delivery liable to rejection.
Salts and Studs. — When the bolts or studs are of sufficient length in the plain part
to admit of being bent cold, they must stand bending double to a curve of which the
inner radius is equal to the radius of the bolt or stud, without fracture.
When bolts or studs are not of sufficient length in the plain part to admit of being
bent cold, the threaded part must stand bending cold without fracture as follows :
If of l/2 inch diameter or less 35°
If above % inch diameter and under I inch 3°°
If I inch diameter or over . 25°
Where the bending tests can not be applied, the two following hammer tests must be
substituted :
(a) The test piece to stand flattening out cold to a thickness equal to one half its
original diameter without showing cracks.
(t>) The test piece to stand flattening out, while heated to a cherry-red heat, to a
thickness equal to one third its original diameter without showing cracks.
n6
MACHINE DESIGN.
Surface Inspection. — ( i) All bolts and studs shall be free from surface defects.
(2) All bolts are to be headed hot, and the heads made in accordance with the U.
S. standard proportions unless otherwise specified. The head must be concentric with
the body of the bolt.
(3) The threads must be of the U. S. standard unless otherwise specified, and must
be clean and sharp. The threads of Classes A and B bolts may be either chased or cut
with a die, but the threads of body-bound bolts must be chased and must extend far
enough down so that when the nut is screwed home there will be not more than one
and one half threads under it. The plain part of body-bound bolts must be turned in a
lathe to fit accurately in the bolt hole.
STEEL AND IRON NUTS.
( To be used with class A and B bolts and studs. )
1. One tensile and one bending test bar from each lot of 1,000 pounds of
material or less from which nuts are to be made shall be selected by the inspector for
test.
2. The material (whether steel or iron) shall show a tensile strength of at least
48,000 pounds per square inch and an elongation of at least 25 per cent, in 8 inches.
A bar y2 inch square or % inch in diameter shall bend back cold through an angle of
180° without showing signs of fracture.
3. The nuts must be free from surface defects and the threads clean, sharp, and well
fitting.
4. The dimensions of threads must be in conformity with the United States standard
unless otherwise specified.
5. The nuts must be hot-pressed and reamed before threading, the holes to be cen-
tral and square with the faces. All nuts must fit on the bolts without shake.
FORCINGS.
i . The physical and chemical characteristics are to be in accordance with the fol-
lowing table :
Class.
Material.
Treatment.
Minimum' Minimum
Tensile Elastic
Strength, j Limit.
Minimum
Elonga-
tion.
Maximum
Amount of —
Cold Bend
About an
Inner Diam
eter of—
P.
S.
Lbs.per
*/. in.
Lbs.per
sq. in.
Per crnt.
in a in.
High
Grade,
Open-hearth
nickel steel.
Annealed
and oil
95,000
65,000
21
.06
.04
One inch
through
tempered.
180°.
Class A.
Open-hearth
Annealed.
80,000
50,000
25
.06
.04
One inch
either nickel
Oil tem-
through
or carbon
pered op-
180°.
steel.
tional.
Class B.
Open-hearth
Annealed.
60,000
30,000
30
.06
.04
Half inch
carbon steel.
through
180°.
6. Nuts to be used about machinery must fit so tight that it will be necessary to use
a wrench to turn them. All other nuts must be at least thumb tight.
7. For the purpose of test all nuts which fulfill the preceding requirements will b<
divided into lots of 500 pounds or less, and two nuts from each lot selected by the in
specter for test as follows :
SCREW FASTENINGS. 117
(a) One of the two shall stand flattening out cold to a thickness equal to one half its
original thickness without showing cracks.
(/>) The other shall stand flattening out (when heated to a cherry red in daylight),
to a thickness equal to one third of its original thickness without showing cracks.
8. The failure to stand these tests will subject the lot represented by them to rejec-
tion. The failure of 10 per cent, of the lot to pass the tests will render the whole order
liable to rejection.
For bolts requiring unusual strength, the metals described under
" Forgings " are specified. Thus, connecting rod bolts are made
from " High Grade " forgings as above.
For wrought iron and various alloys and bronzes, the maximum
tensile strength per sq. in. of cross section is taken as :
Wrought Iron 50,000 Ibs.
Alloy: Cu88%, Sn 10%, Zn 2% 2o,ooo '<
Phosphor Bronze, rolled 40,000 "
Muntz Metal, rolled 40,000 "
Manganese Bronze, rolled 50,000 "
Tobin Bronze 50,000 "
Naval Brass .... 50,000 "
The specifications (1900), of a prominent railroad company fix
requirements for stay-bolt iron, as follows :
" The material desired is fagoted iron, free from admixture of steel and preferably box
piled, the rilling of the box being small rods. It shall show when nicked on either
side and then broken, a fracture with long fiber with sound welds. The iron must be
smoothly rolled, free from slivers and depressions, and shall be truly round within .01
of one inch. It shall not be more than .005 of one inch above and not more than .010
of an inch below nominal size. This to insure freedom from jamming in the thread-
ing dies.
" Sample bars will be required to meet the following physical test: They shall show
when tested in full size as rolled, a tensile strength of not less than 48,000 pounds per
square inch, with an elongation of not less than 25 per cent, in 8 inches. One piece from
each of the two sample bars shall be subjected to tensile test and one piece from each of
them shall be threaded in dies with a sharp "V" thread 12 to one inch and firmly
screwed through two holders, having a clear space between them of 5 inches. One of
the holders shall be of such form and length that the bolt shall be rigidly held, so as to
prevent rocking. This holder will be rigidly secured to the bed of a suitable machine
and the holder at the other end will be vibrated in a direction at right angles to the
axis over a space of }£ of an inch, so that the end of the specimen shall be deflected
alternately ^ of an inch on each side of the center line. When thus tested acceptable
iron should show not less than 2,200 double vibrations before breakage.
" If the test of either of the bars shows a tensile strength of less than 48,000 pounds
per square inch in an original section or an elongation less than 25 per cent, in a sec-
tion originally 8 inches long, or if either bar stands less than 1,700 double vibrations, or
if the two give an average of less than 1,900 double vibrations before breakage, the pile
represented by such two bars will be rejected and returned to the maker. In addition,
those bars which fail to meet the requirements as to rolling will also be rejected and
returned."
MACHINE DESIGN.
33. Nut-Locks.
As has been shown previously, the pitch-angle of screw-fasten-
ings is so small that the screw cannot possibly "overhaul," i. e.,
no static axial load, however great, will cause the nut to back off.
On the other hand, on such a screw, when exposed to shock or to
repeated, even though small, vibrations, the nut will loosen inevitably.
Dr. Weisbach * has discussed fully and clearly the effect upon the
nut of these external forces. When the joint is subjected to shock
or vibration, work is done upon all of its parts. The work trans-
ferred to the nut, expends itself in producing elastic oscillations in
the material of the latter, with corresponding stresses of tension
or compression, and, therefore, at any instant, a resultant stress.
When the moment of this resultant is equal to the moment of nut-
friction, any further shock or vibration will cause the nut to yield.
It is evident, therefore, that the force with which the nut is screwed
home, fixes the magnitude of the shock which will loosen it.
Hence, nuts which can be set up with but moderate pressure, as
on shaft bearings, especially need locking arrangements. Again,
the effect of small vibrations, if they follow each other with sufficient
frequency, seems to be cumu-
lative, so that, even when nuts
are set up with the greatest per-
missible force on solid supports,
as the fish-plates of rails, they
will, if unlocked, back off under
these conditions. The usual de-
vices for locking a fastening nut
are the check-nut, set-screws,
spring-washers, and lock-plates.
The nut itself is sometimes
made elastic or the thread self-
locking.
i. CHECK-NUTS. — A check-
nut is essentially a friction -brake
for the fastening nut. Assume,
as in Fig. 48, a bolt, A, with
fastening and check nuts, B and C, respectively. Let the lower
nut be held and the upper be screwed against it as tightly as
*" Mechanics of Engineering," Vol. III., Parti., Sec. II., 1896, p. 605.
FIG. 48.
SCREW FASTENINGS. 1 19
the strength of the bolt permits. There will be developed a
pressure, P, between the adjoining nut-faces, and the nuts B and
C will transmit this pressure to the lower and upper surfaces, re-
spectively, of the bolt threads. Hence, a unit tensile stress,/,
will exist within the bolt section, D-E, included between the limits
of action of the nuts upon the bolt. This stress will not be present
elsewhere. If now the bolt be subjected to shock, the fastening
nut, B, cannot back off unless either its own thread-friction and
that of the lower nut be overcome and the two withdraw together,
or the nut, B, have a sufficient impulse to move independently, de-
spite the friction between the nut-faces. In either case, the check-
nut acts as a brake upon the fastening nut.
Again, assume, as in the left-hand half of the figure, that the
bolt is used for securing the cap, F, of a shaft-bearing. Let the
lower nut, C, be first screwed down until the required pressure, Pv
is produced upon the cap and then the upper nut, B, be screwed
home as before, developing the pressure, P, between the nut-faces.
The nut, C, is now subjected to a downward force, P, and an up-
ward force, Pv with a resultant, P — Pv acting on the bolt-threads.
There are three possible cases :
(a) If Pl > P, the resultant force is upward, the lower nut bears
on the lower surfaces of the bolt-threads and aids in sustaining the
axial load, Pv upon the bolt.
(b) If Pl = P, the resultant force is zero. Hence the lower nut
is unloaded and has no pressure on either the upper or lower sur-
faces of the bolt threads.
(c) If Pl < P, the resultant force is downward, the lower nut
bears on the upper surfaces of the bolt-threads, does not aid in
sustaining the axial load, and produces an additional tensile stress,
as at D-E.
In both (a) and (c), thread-friction exists with the lower nut and
the latter acts as a brake ; in (a) only this nut aids in sustaining
the axial load, Pv upon the bolt, which load in (&) and (c) is borne
wholly by the upper nut. The fastening and check-nuts are
frequently of different thicknesses. The discussion as above —
adapted largely from Weisbach — shows that the upper nut may
bear the entire load and should be the thicker of the two, although,
in the absence of a thin wrench, the reverse is often the case. In
practice, the lower nut is screwed down and home and the upper
nut almost entirely so. Then, the latter is held with the wrench
120
MACHINE DESIGN.
and the nut, C, is forced backward through a slight angle until it
binds on the upper nut.
FIG. 49.
FIG. 50.
FIG. 51.
2. SET-SCREWS. — The set-screw, bearing upon a cylindrical
prolongation of the nut, is the most effective locking device for
heavy nuts requiring to be frequently removed as, for example,
those on the connecting rods and main bearing caps of marine
engines. Fig. 35 shows a bolt for the former which is fitted with
a "collar-nut" and two set-screws — one for locking the nut, the
other for holding the bolt when backing off the nut. Table
XXXVI. gives the proportions of such collar nuts and of the
dowelled stop-ring into which the set-screw is tapped. Fig. 49
shows a similar nut, omitting the stop-ring and groove, the pro-
portions for typical sizes of which, in inches, are :
Diameter
Least Value of H for
of
Bolt.
A
B
C
D
E
F
G
Wrought Iron or
Brass.
Cast Iron.
1
2
4
f
4
1
I
If
1
i
I
Ij
I
ft
!
i
I \
6
9
6
2
If
I*
I Ij-
if
if
3. ELASTIC NUTS. — Fig. 50 shows the nut made by the Na-
tional Elastic Nut Company. The blank is cut from a flat steel
bar, bent into a ring with a lap on the side, pressed in a die into
the shape of a finished nut, and finally tapped with special minus
taps, -jj-g- under size. When screwed on the bolt, the split side is
forced open about -^-^ of an inch, giving the nut a constant grip.
The Wiles lock-nut, shown in Fig. 51, has a slot milled half
way through of a width equal to the pitch. When the nut is in
place, the walls of the slot are brought slightly together by a set-
screw, thus gripping the bolt-thread.
SCREW FASTENINGS.
121
TABLE XXXVI.
COLLAR-NUTS WITH LOCKING SCREWS.
(UNION IRON WORKS.)
Nut
Set-Screw.
Dowel.
4. SELF-LOCKING THREADS. — In the " Harvey Grip " thread,
the bolt has a ratchet-thread, under cut on the bearing side at
about 5 degrees less than a right angle to the axis of the bolt and
the apex of the thread is cut to a knife-edge. The nut also has a
ratchet-thread, the bearing side of which is about 5 degrees greater
than a right angle to the axis of the nut. There is thus a cavity
122 MACHINE DESIGN.
of about 10 degrees between the bolt and nut-threads ; and, when
the nut is screwed home, the axial pressure upon it forces the thin
bolt-threads out into the nut-threads, thus filling the cavity and
locking the nut.
In another locking device of this class, the thread is triangular
with the V cut off at % of its height from the top and filled in at
*<i the height from the bottom. The thread is thus about yz the
height of the sharp V type and has broad flats. The threaded
portion of the bolt has a taper of I in 48 to the axis, while the
nut has the usual thread and is tapped straight. Hence, as the
latter moves up the conical surface of the bolt, the metal of the
broad-topped bolt-threads flows into the narrower nut-spaces caus-
ing the threads to lock tightly. The fibre of the metal displaced in
screwing the nut on, is broken when the nut is unscrewed.
5. SPRING- WASHERS. — A spring-washer, such as is shown in
Fig. 52^, is used frequently as a locking device. It is, in effect,
one convolution of a helical spring which is interposed between
the nut and the member to be secured. The nut is screwed home
upon the washer and the elasticity of the latter produces a pres-
sure upon the nut and, therefore, increased frictional resistance of
the threads.
Fig. *)2.b represents one form of the Verona nut-lock, a spring
washer which is not curved helically as a whole, but has the
points thrown out, thus giving added power and cutting edges
which engage the abutting surfaces. The tail-piece extension is
used in railway construction in keeping the lock clear of the oval
holes punched in fish-plates.
The National Lock Washer, shown in Fig. 52^, has a sharp rib
on its inner circumference and next the nut-face. When the nut
is set up, it meets the rib, which, being harder than the nut, pro-
gressively upsets and forces some of the metal of the latter into
the bolt-threads. Hence, the nut is held not only by spring pres-
sure but by a partially locked nut-thread.
SCREW FASTENINGS.
I23
Fig. 53 illustrates the Excelsior Double Nut Lock as applied to
a fish-plate. It is of serpentine form with two loops and out-
thrown points, and is bent into a shallow elliptic curve. Since it
embraces two bolts, it cannot rotate with the nuts.
FIG. 53.
6. LOCK-PLATES. — The nut may be kept from reversing by a
lock-plate fastened at one side of it, as in Fig. 54. The plate is
held by a cap-screw tapped into the flange to be secured and is
essentially but a thin wrench engaging the nut. The form shown
will hold the nut in either of two positions, i. e., with a side of the
nut parallel or perpendicular to the centre-line, B-C. Lock -plates,
single or double, are used frequently for the nuts of studs which
join propeller-blades to the hub. The plate shown in Fig. 54 may
have a slot for the screw, C, concentric with the bolt-centre. In
that case, the plate may be shifted and the nut locked in any position.
\A
FIG. 54.
FIG. 55.
The Jones Tie-Bar Lock is shown in Fig. '5 5. It is a square
washer with one end, A, flanged upward against the bar and the
other extremity, B, bent downward against the side of the nut.
The latter flange, B, is turned after the nut is in place.
7. SPLIT PINS. — Nuts not requiring frequent removal, as those
of piston follower-bolts, are sometimes fitted with split pins.
After the nut is in place, a hole is drilled through the bolt so that
the pin when inserted will bear upon, and prevent axial move-
ment of, the nut. Such a lock serves for but one position of the
parts.
124
MACHINE DESIGN.
34. Wrenches.
i. U. S. STANDARD. — Table XXXVII. and Fig. 56 — which
are reproduced herein through the courtesy of Messrs. J. H. Wil-
liams and Company, Brooklyn, N. Y. — give the proportions of
Engineers' Wrenches, Single Head, drop-forged, for the nuts of
bolts ranging in diameter from ^ inch to 3^ inches.
FIG. 56.
TABLE XXXVII.
ENGINEERS' WRENCHES, SINGLE HEAD.
(MESSRS. J. H. WILLIAMS & Co.)
Number.
For U.S. Standard
Nut; Size Bolt.
Opening Finished.
Extreme
..ength.
Thickness Head.
OO
0
A
ft
2i
2
f
l\
I
j
£
3!
I
2
_5
4t
3
4
A
li
¥
5
A
7^
\A
6
T97
H
8
xV
7
£
I-jJjr
9
li
8
9
!'
ijt
III
13
'
ft
10
I £
14^
f
ii
^
l}|
16
If
12
i
2
18.
~ T
X3
|
»&
20;
'
ff
14
|
2|
22^
'
rV
15
|
2T9^
24
16
f
2 f
2*
•
if
2
$
2*
29}
•
'
18
2 i
3 1
33
H
19
2 J
sl
37
|^
19*
2 I
4}
37
i
20
3
A 4
44
X
20*
3*
5 1
44
1
SCREW FASTENINGS.
I25
The length and thickness of similar wrenches — excepting that
the handle tapers in the opposite direction — are given as, respec-
tively, 59 inches and 2\ inches. It will be observed that . the
opening of these wrenches is at an angle of 1 5 degrees with the
handle. This inclination permits the turning of a hexagon nut
completely around in positions where the swing of the handle is
limited to 30 degrees — an important improvement which origi-
nated with this firm. The proportions given in Fig. 56 are those
of a wrench of medium size, the unit being the bolt-diameter.
These proportions are modified somewhat as the wrenches become
very large or very small, although the general design remains the
same. Check-nut wrenches are shorter and, of course, thinner.
Their dimensions are given in Table XXXVIII.
TABLE XXXVIII.
CHECK-NUT WRENCHES.
(MESSRS. J. H. WILLIAMS & Co.)
Number.
For U. S. Standard
Nut ; Size Bolt.
Opening, Finished.
Extreme Length.
Thickness Head.
602
. A
19
4i
H
603
1
\\
5&
-h
604
If
A
o
605
\
£
4
i
607
|
iJj
8|
A
608
|
I £
10
I
609
610
I
:t
11}
I3i
f
2. INTERNATIONAL STANDARD THREAD (S. I.). — The origin
and proportions of this system of screw-threads have been de-
scribed in § 20. A special committee of delegates from the As-
sociation of German Engineers, the Society for the Encourage-
ment of National Industry at Paris, and the Swiss Union of
Mechanical Manufacturers met at Zurich, October 20, 1900, to
formulate an auxiliary standard system of wrench openings for
nuts and bolt-heads. A conference of delegates from these socie-
ties, on October 30, 1900, adopted and recommended for interna-
tional use the system whose rules * follow :
The standard openings are considered as limiting dimensions which the nut is not to
exceed nor the wrench fall short of.
To each diameter of the standard series corresponds a particular wrench opening.
* American Machinist, April 4, 1901.
126
MACHINE DESIGN.
The same openings should be employed for diameters specially intercalated, between
the standard ones. (This evidently means that where a bolt of special diameter is
made, it should be given a head and nut of a standard size. )
The opening of the wrench is the same for the nut and for the head of the bolt and
the screw of the same diameter.
The same opening is applicable to rough nuts and machined nuts.
It is recommended that the height of the nut be equal to the diameter, and of the
head to seven tenths of the diameter.
The following table gives these openings for all the standard diameters :
Diameter of pitcij
the Screw.
Opening of
the Wrench.
Diameter of
the Screw.
Pitch.
Opening of
the Wrench.
mm. mm.
mm.
mm.
mm.
mm.
6
I
12
33
3-5
50
7
I
13
36
4
54
8
1-25
15
39
4
58
9
1-25
16
42
4-5
63
10
1-5
18
45
4-5
67
ii
1-5
19
48
5
7i
12
1-75
21
52
5
77
\i
2
2
11
t
5-5
5-5
82
88
18
2-5
29
64
6
94
20
2-5
32
68
6
100
22
2-5
72
6-5
105
24
3
38
76
6-5
no
27
3
42
80
7
116
30
3-5
46
The wrench openings in the above table approximate those deduced from the formula
.4 diameter (in millimeters) -\- 4 mm.
CHAPTER III.
RIVETED JOINTS. THEORY AND FORMULA.
35. Rivets.
RIVETS are permanent fastenings used in joining the parts of
metallic structures, such as the framing of buildings and bridges,
the hulls of ships, the shells of steam boilers, and the plating of
tanks, gasometers, etc. They are made in a forging machine
(§ 3 1), the dies of which form under pressure, from the heated bar,
a rivet-blank composed of the head and the shank or body. When
the blank is reheated and set in the joint, a second head or point is
made by hand or power from the metal of the protruding extrem-
ity of the shank.
36. Proportions of Rivets.
i. HEAD AND POINT. — The shape of the head is usually spher-
ical or that of a frustum of a cone ; that of the point may be
spherical, conoidal, or conical, the latter being the usual form with
hand-work. Either the head or point or both may be counter-
sunk and recessed in the plate, having then the form of an inverted,
conical frustum.
In the United States, riveted joints are designed without regard
to the resistance to yielding opposed by the friction between the
plates, the rivet being assumed to have practically the same func-
tion as that of a bolt subjected only to cross-shear. In effect,
however, the rivet has an initial tension due to its contraction in
cooling ; and, further, from the same cause, the shank is smaller
than the hole through which it passes. Therefore, when the joint
is loaded, bending stress precedes shearing in the rivet, and, in
service, the latter thus meets compound stress of which tension is
a factor.
While, therefore, the rivet is not intended for, and is untrust-
worthy in, tension, that stress acts in service within the shank,
producing a consequent compression and tendency to shear
within the head and point and to rupture at the junctions of
these features with the shank, especially if slight fillets are not
made at these places. In experiments made by Stoney on the
127
128
MACHINE DESIGN.
strength of iron rivets in tension, he found that, with |-inch rivets
with pan heads and hand-made snap-points, in punched holes, the
heads or points flew off under an average tensile stress of 12.32 tons
per sq. in. of rivet cross-section. It is apparent that the contour
and strength of these features of the rivet are important, not only
because of the stresses met, but, as in marine work, bridges, etc.,
where minimum weight is desirable.
Good practice, with regard to the proportions of rivet-blanks
for general service, is given by Table XXXIX. and Fig. 57, which
FIG. 57.
illustrate cone or "pan-head," spherical or "button-head," and
countersunk -head types, as designed by J. H. Stern bergh, Esq.,
President of the American Iron and Steel Manufacturing Com-
pany.
TABLE XXXIX.
PROPORTIONS OF RIVET-HEADS.
.(AMERICAN IRON AND STEEL MANUFACTURING COMPANY.)
Shank,
Diameter.
Head.
Form.
Diameter,
Least.
Diameter,
Greatest.
Height.
Angle.
D
G
K
Cone.
Button.
Countersunk.
B = D
c
F
II
= 1-75 D
= 1-75 G
A = .875 D
E = 0.75 G
35°
K
H
1
ft
i
ftll
ftlJt
4J
.LULU
if ill
It
2
Similar proportions of Victor Steel Rivets, as made by the
Champion Rivet Company, are shown in Table XL. and
Fig. 58.
RIVETED JOINTS.
— 2D
I29
*__
FIG. 58.
The button-head form, Fig. 59^, is widely used for points and,
in structural work especially, for heads as well, excepting where,
from lack of space, the countersunk type, Fig. $c)b, is required.
TABLE XL.
PROPORTIONS OF RIVET- HEADS.
(CHAMPION RIVET COMPANY.)
Diameter.
Form.
Diam. Least.
Diam. Greatest.
Height.
Angle.
D
D
D
D
Cone.
Button.
Steeple.
Countersunk.
tt»
2 D
\D
D
40°
The former is much more trustworthy than the conical or steeple
point, Fig. 59<:, usual with hand-work.
YP
d
FIG. 59.
The pan-head, Fig. 59, c, d, is much employed in boiler and ma-
rine work generally. The form is one of great strength. The
objections to it are its weight and the fact that unless its shortest
diameter is equal to that of the rivet-shank, it is difficult to make
the latter and the head concentric.
130 MACHINE DESIGN.
The countersunk head or point, Fig. 59^, adds no weight to the
joint and, when properly closed, its wedge-like form gives rigidity
and produces maximum plate -friction. There is, however, a de-
crease in the strength of the plate, owing to the additional metal
removed and an increase in cost from the countersinking required.
It is essential that countersunk heads shall fit the holes exactly
when the rivet is driven home. The angle of countersink varies
from 15 to 45 degrees.
2. SHANK. — The shank is cylindrical throughout the greater
part of its length but tapers slightly toward the end. Its length
is equal to the grip (i. e., the combined thicknesses of the plates
through which it passes) plus" that of the additional metal required
to fill the rivet-hole and to form the point. To permit the inser-
tion of the heated and expanded rivet-blank, the rivet holes are
usually jJg in. larger in diameter than the blank when cold.
Again, in machine-riveting, the pressure upon the hot and plastic
metal of the rivet is more continuous and severe than in hand-
work, thus forcing more metal into the hole.
Hence, the required length of shank, additional to the grip, de-
pends upon the form of the head, the length and clearance of the
rivet-hole, and the character of the riveting process. In aver-
age proportions, the total length of the shank is equal to the grip
plus 1.5 times the diameter, with an increase, fixed by experiment,
for machine-riveting. The length of shank required to make a
countersunk point is about that of the shank-diameter.
The slight tapering of the shank under the head, Fig. 59^, adds
strength at their junction and gives a better form for the conical
hole made in punching. In drilled holes a short countersink is
advantageous at this point in removing sharp edges left by the
tool.
3. RIVET-HEADS AND PLATE- FRICTION. — The results of Pro-
fessor Bach's extensive experiments upon pi ate -friction will be
given in § 46. With regard to the magnitude of the friction be-
tween the plates produced by the pressure of different forms of
rivet-heads, Stoney * gives the following results from tests made
with steel rivets and steel plates, the joint being composed of a
middle plate between two others, all united by three rivets in one
row, the rivets being thus in double shear. The i-inch rivets
'Strength and Proportions of Riveted Joints," 1885, p. 75.
RIVETED JOINTS. 131
were used in ^-inch plates and the ^-inch rivets in i^-inch plates.
With hand- riveting, the mean frictional resistances, per rivet in
tons, were :
I-IN. RIVET. ^-JN. RIVET.
Snap head and point 6.40 4.72
Pan head, boiler point. 7.36 4.52
Pan head, countersunk point 8.55 6.25
Countersunk head and point 9- 04 4-95
As a whole, these tests show the greatest friction for counter-
sunk rivets, whose wedge-shaped heads, when properly driven,
produce great pressure as the rivet contracts. In other experi-
ments with snap-heads and points, but with machine- riveting, the
mean friction per rivet was 9.6 tons for i-inch rivets and 5.9 tons
for j^-inch rivets.
37. Rivet and Plate Metals.
i . STEEL has very largely superseded wrought iron for rivets,
plating, shapes, etc., in all structural, ship, and boiler-work. The
following extracts, with regard to chemical and physical properties,
are taken from " The American Standard Specifications for Steel,"*
adopted August, 1901, by the American Section of the Interna-
tional Association for Testing Materials :
STRUCTURAL STEEL FOR BUILDINGS.
1. Steel may be made by either the open-hearth or Bessemer process.
2. Each of the two classes of structural steel for buildings shall not contain more
than o. 10 per cent, of phosphorus.
3. There shall be two classes of structural steel for buildings, namely : RIVET STEEL
and MEDIUM STEEL, which shall conform to the following physical qualities :
Tensile strength, Ibs. per sq
Yield point, in Ibs. per sq. i
Elongation, per cent, in eight
inch,
n. , shall not be less than
ins., shall not be less than
50,000-60,000
JT S.
26
60,000-70,000
JT.S.
22
STRUCTURAL STEEL FOR BRIDGES AND SHIPS.
1. Steel shall be made by the open-hearth process.
2. Each of the three classes of structural steel for bridges and ships shall conform to
the following limits in chemical composition :
Steel Made by | Steel Made by
the Acid Process, the Basic Process.
Per cent. Per cent.
Phosphorus shall not exceed
Sulphur shall not exceed
0.08 0.06
0.06 0.06
American Standard Specifications for Steel," A. L. Colby, 1902.
132
MACHINE DESIGN.
3. There shall be three classes of structural steel for bridges and ships namely :
RIVET SEEEL, SOFT STEEL, and MEDIUM STEEL, which shall conform to the following
physical qualities :
Rivet Steel.
Soft Steel.
Medium Steel.
Tensile strength, Ibs. per sq. in.
Yield point, in Ibs. per sq. in., shall
not be less than
Elongation, per cent, in eight inches,
shall not be less than
50,000-60,000
JT.&
26
52,000-62,000
£T.S.
25
60,000-70,000
JT.&
23
OPEN-HEARTH BOILER PLATE AND RIVET STEEL.
1. Steel shall be made by the open-hearth process.
2. There shall be three classes of open-hearth boiler-plate and rivet-steel, namely :
FLANGE OR BOILER STEEL, FIRE-BOX STEEL, and EXTRA SOFT STEEL, which shall
conform to the following limits in chemical composition :
Flange or Boiler Steel.
Per cent.
Fire- Box Steel.
Per cent.
Extra Soft Steel.
Per cent.
Phosphorus shall not ex-
ceed
Sulphur shall not exceed
Manganese.
( Acid, 0.06
\ Basic, 0.04
0.05
0.30 to 0.60
{ Acid, 0.04
\ Basic, 0.03
0.04
0.30 to 0.50
0.04
0.04
0.30 to 0.50
4. The three classes of open-hearth boiler-plate and rivet-steel, namely : FLANGE
OR BOILER STEEL, FIRE-BOX STEEL, and EXTRA SOFT STEEL, shall conform to the
following physical qualities :
Flange or Boiler
Steel.
Fire-Box Steel.
Extra Soft Steel.
Tensile strength, Ibs. per sq. in.
Yield point, in Ibs., per sq. in., shall
not be less than
Elongation, per cent, in eight inches,
shall not be less than
55,000-65,000
JT.S.
25
52,000-62,000
JT.S.
26
45,000-55,000
JT. S.
28
In all of the steels described above, modifications are made, for
thin and thick material, in the required elongation.
In general, steel rivets should be made by the open-hearth pro-
cess, be low in sulphur and phosphorus, and be of a soft, ductile
character. The following table gives the average of a number of
analyses of Victor Steel Rivets :
Phosphorus, per
Manganese, "
Sulphur, "
Silicon, "
Carbon, "
0.015
0.460
0.032
0.005
o. no
With steel, there is practically no change in tenacity when tested
with or across the direction of rolling. The results of numerous
RIVETED JOINTS. 133
experiments indicate that the ultimate shearing strength of mild
steel may be taken generally as 80 per cent, of the ultimate tensile
strength. The allowable bearing stress upon the rivet or the sur-
rounding metal ranges usually from 12,000 Ibs. to 24,000 Ibs.
per square inch of the projected semi-intrados (diameter x thick-
ness), although considerable latitude is given this stress by various
designers.
2. WROUGHT IRON. — Iron plates, rods, etc., differ widely in
quality, owing to the nature of the processes through which the
material passes in manufacture. In the puddling furnace, there
appear globules of wrought iron whose centres consist of excess
carbon and impurities. These, when passed through the rolls, are
stretched into fibres whose outer surfaces are of soft iron, while
the interiors contain foreign material as above. As a result of
this lack of homogeneity, the fracture in some cases appears
fibrous ; in others, from 30 to 40 per cent, crystalline.
The ultimate tensile strength with the grain, i. e., parallel to the
direction of rolling, ranges from 45,000 to 55,000 Ibs. per square
inch. Across the grain, this strength is less, being, according to
Bauschinger's experiments, about 78 per cent, of that with the grain.
With regard to the shearing strength of wrought iron, Professor
J. B. Johnson * gives the following summary of Bauschinger's
elaborate experiments :
" In general, we may say that the shearing strength across the thickness of the plate,
either with or across the grain, is about 80 per cent, of the tensile strength, while, il
the external forces lie in the plane of the plate and be applied on the planes of shear
perpendicular to the plane of the plate, the shearing strength is about the same as the
tensile strength. The shearing resistance on a plane parallel to the plane of the plate,
is less than 45 per cent, of the tensile strength. ' '
The allowable bearing stress for pins and rivets upon the surface
of the projected semi-intrados is usually taken in structural work
as 12,000 pounds per square inch.
Despite the widespread introduction of steel, the use of wrought-
iron rivets still finds favor, especially in locomotive work. It is
stated that, for the sizes used in locomotives, steel rivets, machine-
driven, are not so trustworthy as first-class iron rivets, the reason
given, being that :
"A rapid distortion at one operation of the steel formed head is more than liable to
reduce the tensile strength of the head. In other words, were the steel rivet driven by
*" Materials of Construction, " 1898, p. 486.
134 MACHINE DESIGN.
hand, the head would be stronger than when driven by machine and the contrary would
be the case with the iron rivet. This is well recognized in conditions where snap-
riveting is required and a leakage of the rivet in service requires calking. Under these
conditions the steel rivet will stand more calking than the iron rivet, for the reason that
the working due to hard driving has a refining effect on the steel and seems to improve
its toughness, whereas the distortion and twisting of the grain of the iron rivet in driv-
ing, seems to weaken instead of strengthen it. " *
3. SHEARING STRENGTH OF RIVETED JOINTS. — For iron rivets
in steel plates, Traill f gives ^ as the ratio, in single shear, be-
tween the mean shearing strength per sq. in. of the rivet and the
mean tensile strength per sq. in. of the plate. For steel rivets in
steel plates, this ratio becomes ||. A rivet in double shear he as-
sumes to have 1.75 times its strength in single shear. Mr. J. M.
Allen | takes 38,000 Ibs. per sq. in. as the strength in single
shear of an iron rivet in steel plates and assumes, in double shear, an
increase of 85 per cent., or a total strength of 70,300 Ibs. per sq. in.
4. COPPER, when used for the fire-box plates or stay-bolts of
locomotive boilers, should have a minimum tensile strength of
30,000 Ibs. per sq. in. and an elongation of at least 20 per cent,
in a section originally 2 ins. long.
38. Rivet-Holes.
1. MODERN PRACTICE, as to punching or drilling, varies some-
what, although the tendency toward the drilled hole, with its
greater accuracy and small liability to injury of the metal, grows
steadily. In boiler-work, the U. S. Naval specifications require all
rivet-holes to be drilled with the plates in position. The rules of
the American Boiler Manufacturers' Association permit punched
holes in steel plate up to ^ inch thick ; in thicker plate, the holes
may be either drilled or be punched and reamed. In stntctural-
work the holes are punched, as a rule. For field-rivets, they are
drilled to templet or reamed with the connected parts in place.
In hull-work, rivet-holes are generally punched from the faying
surfaces of the parts to be connected.
2. ULTIMATE TENSILE STRENGTH OF PERFORATED PLATES. —
If a plate be perforated with a row of holes, as for riveting, by
methods, as drilling, which produce no molecular disturbance
within the metal immediately surrounding the hole, leaving that
* Am. Engineer, Car Builder, and Railroad Journal, May, 1898.
•f " Boilers : Marine and Land," 1896, pp. 44, 45.
JSibley College Lectures, 1890-1.
RIVETED JOINTS.
135
metal unchanged in structure, the plate will break, when tested to
destruction, in the line of the reduced section remaining through
the rivet-holes ; but the ultimate tensile strength of that reduced
section will be found to exceed materially that of the unperforated
metal. In other words, if two plates of the same dimensions and
material be thus treated, one solid throughout, the other perforated
as above, they will rupture at different total loads, but the ultimate
tensile strength, per square inch, of the net section along the line
of holes will be greater than that of the metal in the solid plate.
This apparent paradox is analogous to that which occurs with the
"grooved specimens" discussed in § 27. The reduction in sec-
tional area of metal along the holes lessens the space for the flow
of that metal and checks its tendency to stretch. Hence, the con-
traction of area is hindered and opposition «to contraction gives in-
crease in tensile strength. When the holes are punched, the speci-
men is still "grooved" in type, but the condition that the metal
surrounding the hole shall be uninjured by the perforation, holds
no longer. Therefore, the gain in tensile strength is, in very thin
plates, nullified ; and, in thicker plates, reduced by the loss in
quality of the material.
3. PUNCHES AND DIES. — In punching, as shown in Fig. 60,
the plate rests on a die the bore of which is conical with the smaller
diameter toward the punch. The
base of the latter may be flat, givinp-
a full circumference of cutting surface
in action on contact, or the cutting
edge may be slanting or spiral (Fig.
6oa) so that, on contact, only part of
the circumference is cutting and, for a
time, shearing proceeds in detail.
With the spiral form, there is a
saving in power when the thickness
of the plate is less than f the di-
ameter of the hole to be punched.
For plates beyond that thickness, the flat-faced punch is better.
In order to reduce the stress in the plate-metal, the die is made
conical, as above, and its diameter is greater than that of the
punch by 10 to 15 per cent. The general practice is to make
the diameter of the die equal to that of the punch, plus o.i to 0.3
times the thickness of plate.
FIG. 60.
136 MACHINE DESIGN.
The punch is subjected to crushing stress. The resistance to
punching may be taken generally as that of shearing a section
equal to the circumference of the hole multiplied by the thickness
of the plate. Since a punch cannot withstand more than the total
crushing force corresponding with its cross-section, it is apparent
that there is a fixed limit to the thickness of plate which it will pierce.
4. EFFECTS OF PUNCHING. — On contact, the punch shears the
circumference of the blank to be removed, thrusting, in its ad-
vance, upon the body of the latter so that there is not only de-
trusion but a lateral, plastic flow of a portion of the metal of the
blank into the walls of the hole. The blank, when ejected, is, as
the experiments of Townsend (§31) show, no denser than the
original plate but its volume is less than that of the hole.
The lateral flow produces molecular disturbance within the
metal immediately around the hole, and a portion of this metal
becomes dense and hard with a decrease in ductility and rise in
elastic limit. There is also a loss in ultimate strength which may
possibly arise from minute cracks in the affected metal. Since the
thickness of the plate determines the allowable pressure upon the
punch, the injury is less with thin plates. It is also smaller with
ductile material, mild steel being stressed less than wrought iron.
Some experiments indicate that the flow and hardening are
greater on the die side of the plate, while others show that the af-
fected zone lies nearer the upper surface. In any event, the in-
jured metal appears to be included wholly within an annular cylin-
der, Jg inch or less in thickness around the hole. The remedy,
therefore, is to punch the hole ^ inch smaller in diameter than de-
sired and ream to finished size or else to anneal the plate. Either
of these methods will remove the ill effects of punching.
The loss of tenacity in punched plates not subsequently reamed
or annealed, is with plates | inch thick and upward, from i o to 25
per cent, in iron plates and from 10 to 35 per cent, in steel, the loss
in the latter increasing with the thickness. The excess tenacity of
a drilled plate is usually toto 12 per cent., although its maximum
range may be double this, since this gain depends upon the propor-
tions of the " grooved " specimen and the character of the metal.
5. DRILLED HOLES have none of the disadvantages of those
made by punching. The metal about the hole is uninjured since
there is little pressure upon it and no lateral flow exists. The
blank is removed from the hole in detail by cutting instead of be-
RIVETED JOINTS.
ing forced out bodily by pressure and shearing. The drilled hole
should be slightly countersunk to remove the sharp edge, which,
when the joint is loaded, would aid in shearing the rivet.
6. TESTS OF DRILLED AND PUNCHED PLATES. — The number of
such tests with joints, is large. The following tables * give, in
summary, the results of experiments by Mr. Kirkaldy to deter-
mine the ultimate tensile strength of steel plates : (a) drilled ; (S\
punched; (c} punched and afterward annealed. Plates 12 inches
wide were used. In the J-inch, i-inch, and a part of the |-inch
thicknesses, the number and diameter of the holes in each half of
the specimen were, respectively, 6 inches and 0.79 inch. In the re-
mainder of the |-inch and in the i-inch plate, the number and diam-
eter were 6 inches and i .08 inches, respectively. The results were :
(^4) Ultimate Stress per square inch of Gross Area at Holes. The stresses are
given in tons and are calculated with reference to the total sectional area of the plate,
including therein the part removed by perforation :
Thickness,
Jin.
Jin.
fin.
I in.
Drilled,
21.90
19.60
I9-65
18.30
Punched,
" and annealed,
19.30
20.15
16.65
18.55
I5.8o
18.70
1345
17.80
Mean Stress in tons per sq. in. of Net Section between Holes :
Thickness,
}in.
Jin.
Jin.
I in.
Drilled,
36.21
32-44
31.64
29.42
Punched,
31-94
27-53
24.60
21.02
" and annealed,
33-41
30-75
30.05
27.82
Solid Plate,
3I-65
29.15
29.70
27.70
(C) Stresses in per cent, per sq. in. of Net Section compared with Solid Plate :
Thickness,
}in.
Jin.
fin.
I in.
Drilled,
113.8
in. I
106.4
106.1
Punched,
IOI.O
94-2
82.5
75-8
" and annealed,
105.6
105.6
IOI.O
100.3
(D) Difference in per cent, between the Ultimate Stress per sq. in. of Net Section
of Perforated and Unperforated Plates :
Thickness,
Jin.
Jin.
fin.
I in.
Drilled,
Gain, 13.8
Gain, n.i
Gain, 6.4
Gain, 6.1
Punched,
" I.O
Loss, 5.8
Loss, 17.5
Loss, 24.2
" and annealed,
" 5-6
Gain, 5.6
Gain, i.o
Gain, 0.3
From (A} it will be seen that the punched plates have the least
ultimate strength and the drilled plates the greatest. (D) shows,
* Merchant Shipping, "Experiments on Steel," 1881, pp. 12-14.
138 MACHINE DESIGN.
for the drilled plates, a gain in ultimate strength over that of the
solid plate of 6.1 to 13.8 per cent., and a loss, in the punched
plates from ^-inch upward, of 5.8 to 24.2 per cent. The punched
and annealed plates occupy an intermediate position, having a
gain which is materially less than that of the drilled plate. The
manner in which the ductility of the steel was affected by its treat-
ment is indicated by :
(£) Elongation in per cent, of Holes at Ultimate Stress:
Thickness,
Jin.
Jin.
J in. ; i in.
Drilled,
24-3
37-0
37-6 33-5
Punched,
11.7
18.5
II. i
4-3
" and annealed,
27.1
35-1
33-o
29.8
As stated previously, the strength of a grooved specimen de-
pends upon its form, the quality of the metal, and the method of
" grooving " or, in these tests, of perforation. Hence the results
given apply, quantitatively, only to the specimens tested, although
the general principles which are indicated, hold true in all cases.
\ 4.262
\*
\-e
i!
n a
FIG. 61.
7. RIVETED JOINTS WITH PUNCHED OR DRILLED HOLES. — Joints
in which the holes are punched or drilled give, under test, similar
differences in strength, although the range of variation will not be
the same as in the unriveted plates since the joint is a built-up
structure and the load is transmitted from one plate to another in a
complex manner. For example, in the double-butt-strapped joint
shown in Fig. 61,* the plate and straps were -jV mc^ thick and
*Jour. Am. Soc. Naval Engineers, XII., p. 4.
RIVETED JOINTS.
139
had a tensile strength of 5 5, OCX) Ibs. per square inch; the rivets
were |^| inch diameter, and their strength was 40,000 Ibs., and
70,000 Ibs. per square inch of section in single and double shear,
respectively. The ultimate strengths of the joint, with the rivet
holes made as below, were :
Breaking Load in Lbs.
Holes punched 261,600
" " and reamed 286,800
" drilled 308,200
39-
Boiler-Seams: Longitudinal, Circumferential, and
Helical.
In the shell of a cylindrical boiler, circumferential or girth seams
are perpendicular to longitudinal seams, and the latter are parallel
to the axis. Helical, in place of longitudinal, seams have been
used to a slight extent for shells, and are employed in riveted pipe.
In Fig. 62, let :
FIG. 62.
R = radius of boiler-shell ;
t = thickness of boiler-shell ;
p = steam-pressure per gauge ;
C = length considered of circumferential seam ;
L == length considered of longitudinal seam ;
H = length of helical seam equivalent to L ;
St = unit tensile stress on circumferential seam ;
S/ = unit tensile stress on longitudinal seam ;
S" = unit tensile stress on helical seam.
140 MACHINE DESIGN.
Assume all joints as having the full strength of the plate, i. e.,
as if welded. The total load on the circumferential seam is that
on the boiler-head, or ~R2 x p. The resistance of the entire seam
is the product of its length, thickness, and the permissible unit
stress, or 2xR x t x St, Equating the load and resistance :
From equation (4) and Fig. I :
S/=f = 2S,, (78)
i. e., the longitudinal have double the unit stress of the circum-
ferential seams. Expressing C, L and H in the same units :
Normal load on length, C = C.St;
Normal load on length, L = L.S' = 2L.St.
The normal load, N, on the helical seam is the sum of the
components of the loads on seams C and Z, which are normal to
seam H.
Component of C.St, normal to H = C.St-cos a ;
Component of 2L.St, normal to H= 2L.St-sm a.
N= C.St-cos a -f 2L.St sin a.
L C
.'.N:
The unit tensile stress on the helical seam will be equal to the
total normal load on the seam divided by the length of the
latter, or: .
(79)
If C=L, St"=i.sSt;
if C=2L, St"=i.2St;
if C= $L, St" = i.iSt.
The stress on the longitudinal seam is 28 t in all cases. It is
apparent that the stress on the helical seam decreases as C grows.
If L = o, the helical seam becomes circumferential and St" = St.
If C= o, the seam is longitudinal and St" = 2St.
RIVETED JOINTS.
141
The strength required in the seam is decreased by the helical
form but its cost is increased by the greater length of the joint and
by the necessity for the use in all but small boilers of plates with
inclined sides, as shown in Fig. 62, laid in circumferential bands
or courses. This waste of metal is avoided in Root's spiral riveted
pipe, which is made of single strips, joined by welding to any de-
sired length and wound and riveted helically to form the pipe.
The thickness of the plate varies from No. 28 to No. 12, B. W.
G., and the approximate bursting pressures are given as ranging
from 900 to 1,300 Ibs. per sq. in. at 3 ins. diameter to 1 10 to 335
Ibs. at 24 ins. diameter. The pipe is used for water, exhaust
steam, etc.
40. Forms of Riveted Joints.
The function of a riveted joint may be simply that of resisting
direct stresses upon it, as in structural work ; or there may be
f\ ©
added to this the requirement that the joint shall be also tight
against fluid pressure. The latter is, in steam boilers, high and
internal ; in hull and gasometer plating, moderate or light and
142 MACHINE DESIGN.
external and internal, respectively, to the joint. The duty of the
latter affects materially its proportions.
The plates are, in the simplest form of joint, united by being
overlapped and riveted ; in stronger but more complex forms
they abut, the seam being covered infrequently by one, but usu-
ally by two, external and internal butt straps or cover plates,
which are riveted to the plates and to each other. Lap Joints are
shown in Fig. 63. One plate rests upon the other and rivets con-
nect them. Fig. 64 illustrates Double- Strapped Butt Joints. In
this form, the main plates do not overlap, but remain in the same
plane, the straps being above and below the latter. Fig. 61
shows a similar joint with straps unequal in width ; Fig. 65 a Sin-
gle-Strapped Butt Joint ; and Fig. 66 a Single-Strapped Lap Joint.
Joints differ also with regard to the number and arrangement
of the rows of riveting which are placed parallel to the plate-edges
in a lap-joint or on each side of the seam in a butt-joint. There
may be from one to four rows, giving a single, double, treble, or
quadruple-riveted joint. In chain-riveting (Fig. 63, b, d) the
rivets in adjacent rows are set one behind the other on a line per-
pendicular to the seam. In staggered (zigzag) riveting (Fig. 63,
c, e) the rivets are en echelon, being placed on a line which meets
the seam at an angle. In both of these forms, alternate rivets in
the outer or inner rows or in both may be omitted. Group rivet-
ing, as shown in Fig. 67, is sometimes employed in structural
work. The rivets are disposed usually in arithmetical series, pro-
ceeding from the centre outward with an increasing pitch.
41. The Elements of a Riveted Joint.
In order to allow for the expansion of the heated rivet-blank,
rivet-holes of average size are made -fa inch larger in diameter
than the rivet when cold. In calculating the strength of a joint,
the diameter of the hole, not that of the unheated rivet-blank,
should be considered, since the latter is upset in riveting so that it
fills the hole excepting for the slight contraction in cooling. The
pitch, /, Fig. 63, a, is the distance parallel to the seam between
consecutive rivets in the same row. Where alternate rivets are
omitted in any row, as in Fig. 64, d, the pitch of the joint and that
used in calculation, is the greatest pitch in the several rows, since
lines, as m-n and o-r, drawn through the centres of its bound-
ing rivets and normal to the seam, will include a section of the
RIVETED JOINTS. 143
joint which forms a repeating pattern throughout the whole extent
of the latter, so that such a section represents fully the construc-
tion and strength of the joint.
The transverse pitch, or distance between the centre-lines of
adjacent rivet-rows in a direction normal to the seam, as V, Fig.
64, c, d, differs in magnitude in chain and staggered riveting. The
diagonal pitch, pd, in the same figures, is the distance between the
centre of a rivet and that of the one nearest it diagonally in the
I Z
IT JT T TTHT
\ \ !
! /K 1
;! i <P
?!
i i A
(T\ \£gf (N ' fK
f rt? i
6 CD
E
~vJ LJr:
i ! V
i \ \
A cb T !
i V T i i
FIG. 67.
/
^\
FIG. 68.
|
1 \
V
1 1
FIG. 69.
next row. The margin is the width of plate or strap between the
centre of the outer row of rivets and the edge, as E, Figs. 63, a,
and 64, c. The lap, in lap-riveting, is the amount by which one
plate overlaps the other ; in butt-riveting, it is the extent by which
the strap overlaps one plate. In both cases it is equal to 2E, plus
the distance between rivet-rows. Before discussing these various
elements of the seam in detail, consider
i. THE MANNER OF FAILURE OF A JOINT. — Take the simplest,
case — that of the single riveted lap-joint, Fig. 63, a. This joint,
when tested to destruction, may fail by :
(a) Rupturing the plate between the rivet-holes, as in Fig. 68 ;
(£) Shearing the rivets, as in Fig. 69 ;
(c) Rupturing the margin, as in Fig. 70;
(d) Shearing the margin, as in Fig. 7 1 ;
(i) Crushing the plate or rivet, as in Fig. 72.
In staggered riveting, rupture as in (a) may proceed along the
diagonal pitches, if the latter are weak as compared with the
longitudinal pitch. The same action, under the same conditions,
may take place in chain-riveting with alternate rivets omitted in
the outer row. In staggered riveting with alternate rivets omitted
144
MACHINE DESIGN.
in the outer row, as in Fig. 73, (a) may occur along the pitch,
A-D, or along two diagonal pitches and the semi-pitch, as A-B-
C-D. In double butt-strap joints, (b) cannot take place unless
the main plate shears each rivet at two sections.
In complex joints, failure may be due to both shearing and rup-
ture, thus a lap-joint riveted as in Fig. 64, h or k, may give way
FIG. 70.
FIG. 71.
FIG. 72.
by shearing the rivets in the outer row and tearing the plate along
the rivet-holes of the central row. Each form of joint requires
separate investigation with regard to each possible manner of
failure. In design, the desire is usually to make the joint, as
nearly as possible, equal in strength throughout. Its efficiency is
measured by the ratio of the tensile strength of the net section of
plate-metal left along the line of the greatest pitch, as compared
with that of a similar section, one pitch long, of the solid plate.
FIG. 73.
An excess of strength, within reasonable limits, in other elements
of the joint is not material, if that of the net section as above be
fully utilized and yet be slightly less than those of the seam in
other respects, so that rupture will occur along that line, since,
especially in joints for tightness, an unnecessarily wide pitch not
RIVETED JOINTS. 145
only gives surplus metal and inequality of strength but adds to
the difficulty of making the joint tight.
2. RIVET-DIAMETER. — In a single-riveted lap-joint, let :
d = diameter of rivet ;
/ = pitch of rivet ;
t = thickness of plate ;
5, = unit ultimate tensile strength of plate ;
Sc = unit ultimate crushing strength of plate or rivet ;
Sa = unit ultimate shearing strength of rivet.
Then, considering a section of the joint one pitch wide :
Tensile strength, net section of plate = (p — d)t • St ;
Crushing strength, plate or rivet = d • t • Sc ;
red*
Shearing strength, rivet = • S .
4
For equality of strength throughout :
d-fSe = —'St.'.d=^'^-t = Ct (80)
d-t-Sc = (p-d}t-St.'.d=^-^-^p = Kp (81)
in which C and K are constants.
It will be seen that, for equal strength throughout, the 'maximum
permissible diameter of the rivet is fixed by the thickness of the
plate ; that, for that maximum diameter, there is but one pitch
which is suitable under these conditions ; and that, if a less diam-
eter than the maximum be used, the pitch, for equal strength,
changes with it.
Again, if the holes are punched, the permissible rivet-diameter
for a given thickness of plate is limited also, as stated previously,
by the ultimate strength of the punch, which, for crushing, is
?r^2/4 • Sc. The minimum shearing resistance of the plate is the
area of the sheared section x the unit ultimate shearing strength,
or Tid-t- St. Equating :
^Sc = ^.^.-.</=^<. ; = £•/,*
4 ^e
in which k is a constant.
In structural work, the rivet-diameter is usually f in. or | in.
With cylindrical steam-boilers, the shell-diameter, steam-pressure,
*Unwin : "Machine Design," 1901, I., 122.
146
MACHINE DESIGN.
type of longitudinal seam, and factor of safety determine the thickness
of the shell -sheets. From that thickness, the diameter and pitch
for equal strength throughout, may be found from formulae similar
to (80) and (81). In hull-work, the diameter of the rivet varies
from \ in. to I \ ins., depending upon the thickness of the plating.
3. MULTIPLE RIVETING. — The efficiency of the single-riveted lap
joint is but little more than 50 per cent., i.e., (p — d}t -± p /= 0.5,
about. Hence, only about one half of the full strength of the
connected plates is utilized. This seam is employed only where,
FIG. 74.
owing to caulking, corrosion, or other reasons, a sheet relatively
so thick is used that the fractional strength, as above, will suffice
to resist the load upon the joint.
Assume a single-riveted lap-joint just capable of bearing, with a
proper factor of safety, a given load and let it be desired to aug-
ment this load without increasing the thickness of the plate. It is
evident that the strength of the joint must be made greater in ten-
sion, shearing and bearing to resist stresses (a), (^), and (e), disre-
garding, for the time, the stresses (<:) and (d} within the margin.
To provide for the rise in stress (#), the net plate-section must be
greater, i. e., there must be a wider pitch. This extended pitch
will, from (81) and the increase in shearing load, (ft), per rivet,
necessitate a larger rivet-diameter. The latter, however, is lim-
RIVETED JOINTS. 147
ited, for equal strength, by (80) and, in practice, by the growth
in the pressure required for forming the rivet-point, which pres-
sure increases with the size of the rivet, but is restricted by the
thickness of the plate. Again, the pitch, in steam -joints is lim-
ited by the necessity for tightness. For these reasons, multiple
(double, triple) riveting must be adopted in such a case. There is
a marked gain from multiple riveting, owing to the better distri-
bution of the material of the joint.
Graphically, this distribution is shown in Fig. 74, in which the
boiler plate is assumed, with regard to shearing and tensile stresses
only, to be divided into tension-links and redundant material, the
latter being shaded in the diagrams. The width, b, of the link-
bars is so proportioned that the total strength of the link in ten-
sion, 2b-t-St, is equal to the shearing strength, ncl2/^.- Ss, of one
rivet, the latter being in single shear. To provide for bearing
stress, the width of the link at the head should be I ^ to i ^
times b. In (c) and (i), p and d are the same, the former be-
ing relatively greater and the latter relatively less than in (a).
Hence, the net-plate-section, (p — d)t, and the efficiency, (p — d)t
-r- p-t are greater in the double-riveted joints and the proportion
of redundant material is less.
4. PITCH. — The minimum pitch permissible is governed by
several considerations. If the distance between adjacent edges of
rivet-holes, is less than the diameter of the rivet, the stress in
punching or the lateral pressure of the plastic rivet-blank in
riveting, may crack the plate between the rivet-holes. Again,
the maximum diameter of the rivet-point is usually 1.75 times
that of the hole, so that a pitch of two diameters gives barely
enough space for the riveting dies. In practice, the minimum
pitch is generally from 2.$d to $d in various classes of work.
The minimum pitch permissible depends upon the service of
the joint. If the latter is to be steam-tight, the pitch should be
equal to, or less than, that demanded by equality of strength.
In such a case, the steam tends to enter between the laps or
straps and the plates of a joint ; and the strip of metal between
two rivets is, very approximately, in the condition of a beam fixed
at its ends and loaded uniformly. The maximum deflection of
such a beam is :
148
MACHINE DESIGN.
in which w= unit pressure, /= span, i. e., pitch, £= modulus ol
elasticity, and / = moment of inertia of the section of the beam.
Since the deflection thus varies as the fourth power of the pitch,
the latter, to prevent leakage, should be as small as possible.
In structural riveting, this requirement as to fluid pressure
does not exist, but the rivets must not be spaced too widely or
the joint may open sufficiently for moisture to enter, thus causing
rusting and eventually bursting the joint. Again, when the joint
is in compression, the strip between two rivets is essentially a col-
umn and is, therefore, subject
to flexure. In the direction of
the stress, the pitch should not
exceed, as a rule, 6 inches or 16
times the thinnest outside plate
connected. Transversely to the
stress, the pitch may be 32 to
40 times that thickness.
5. DIAGONAL PITCH. — In
tension -joints, the stress along
the line of the pitch, p, is ten-
sile only, while in the direction
of the diagonal pitch, pd, there
are both tensile and shearing
components. Hence, the resistance of the metal along pd is, with
regard to tension normal to the seam, less than that of the same
section if located parallel to /. From Fig. 75,* we have:
Total load on \ pitch, A- C = W=(p — d}t- St.
This load must be borne also by the metal along the diagonal
pitch, A-B. Resolving W parallel and perpendicular to A-B :
Shearing component of W along A-B = (p — d}t- St • sin 6 ;
Tensile component of W, normal to A-B = (/> — d}t • St • cos 6.
The unit shearing stress, Ss, on the net section along A-B
will be equal to the total shearing load on that section, divided by
the area of the section, i. e.,
FIG. 75.
* Commander A. B. Canaga, U.S.N.,/o«r. Am. Soc. Naval Engrs., VIII., 2.
RIVETED JOINTS. 149
Similarly, the unit tensile stress, Sf, on the net section along
A-B will be equal to the total tensile load on that section, di-
vided by the area of the section, i. e.,
For steel plates, the unit shearing stress on any section should
not exceed T8-g- of the unit tensile stress. Hence :
St = 0.8 S/,
(p-d)t-St-smO _R (p-d)t-St-cosd
(pd-d)t -*'• (pd-d)t ;
sin 6 = T87 cos 0; tan 6 = 0.8 .-. 0 = 38° 40'. (82)
Also :
tan 6= V-±- = 0.8, .-. V= 0.4 /. (83)
The value of V depends thus upon that of 6 and the latter is
determined by the assumption that St = 0.8 Stf. As a general
rule, Traill takes the available resistance of the metal along the
diagonal pitch, for tension normal to the longitudinal pitch, as |
of that of the same section along the latter pitch.
6. TRANSVERSE PITCH. — The value, V, of this pitch has been
calculated in the preceding section for staggered riveting with no
rivets omitted in the outer row (Fig. 64 c] and for chain riveting
with alternate rivets omitted in the outer row (Fig. 64 d~]. When,
in staggered riveting, alternate rivets are omitted in the outer of
several rows, the values of Ffor the outer and the next rows are
different, since, as shown in Fig. 73, rupture may occur along the
pitch, A-D, or along two diagonal pitches and a semi-pitch, as
A-B-C-D. The calculation for the value of Fmust be based,
therefore, on an equality of strength in these two directions. The
method will be given later in the deduction of Traill's formulae.
In simple chain riveting, the minimum value of V\s fixed by the
same considerations which govern the minimum pitch, /. e., to pre-
vent cracking the plate and to provide room for making the rivet-
point, V, minimum, should not be less than 2d and is preferably
2.5^/in boiler-joints and ^d in structural work.
7. MARGIN AND LAP. — To avoid cracking the plate in punch-
ing or riveting, the distance from the nearest edge of the nearest
rivet-hole to the edge of a plate or strap should not be less, as
150 MACHINE DESIGN.
experience has shown, than the diameter of the rivet-hole. The
margin is measured from the centre of the hole. The least value
of the margin is therefore :
E=i.$d. (84)
The width of the lap depends upon the form of the joint. Thus,
in Fig. 63 a, it is 2E\ in Fig. 63 b, 2E -f V\ in Fig. 64 k, 2E -f 2 Vr
As noted previously, the rivet tends to rupture the margin, as
in Fig. 70, and to shear it, as in Fig. 71. In designing the margin
for rupturing stress, the portion of the plate included between the
rivet and the edge may be taken, approximately, as a rectangular
beam, fixed at the ends and loaded in the middle, since the rivet
is slightly less in diameter than the hole and has, theoretically,
but a line bearing on the walls of the latter. For such a beam,
the general formulae give :
M=\-W-l=S'- and - = ^-,
' c c 6
in which M= maximum bending moment, W= total load, / =
span, /= gravity moment of inertia of the cross-section of the
beam, c = distance of most remote fibre of the cross-section from
the neutral axis, b = breadth, and d= depth of beam. In the
assumed beam :
Span = diameter of rivet = d ;
Breadth = thickness of plate = / ;
Depth = E-dl2 (Fig. 70) ;
Distance c=\ depth = \ (E— dj 2);
^ _
C ~ O
Let F= factor of safety and St-^F= allowable working stress.
Substituting :
It is assumed — necessarily, but practically without warrant — that
the load on any pitch-section, as m-n-o-r, Fig. 64 d, is divided
RIVETED JOINTS. I5!
equally among the rivets in that section. Thus, in the figure re-
ferred to, the total permissible load on the section is :
and, since there are three rivets in the section, the load per rivet is :
3 *
In general, let n = the number of rivets in the section. Then :
(p-d}t St
n ' F'
Substituting in (85):
n F S~ F' 6
which equation applies to both lap and butt joints. In a good
design, it gives a close approximation to E = i.$d, as in (84).
The shearing and crushing of the portion of the plate between
the edge and the rivet, as in Fig. 71, remain to be considered.
For equal strength of margin with regard to these stresses, we
have :
Resistance to shearing = 2 ( £ )/ • £, ',
Resistance to crushing = d- 1- Sc.
Assuming ^, = f <Se and equating :
£= 1.2$ d.
Hence, if, as in (84), E= i.$d, that width will be more than
sufficient to withstand all stresses in the margin.
8. CHAIN AND STAGGERED RIVETING. — If the diagonal pitch
be properly proportioned, there is, theoretically, no difference in
strength between chain and staggered riveting, although some
tests have shown a slight advantage in favor of the former. The
practical advantage of staggered riveting is that pressure joints
may be made tighter, owing to the reduced width of the lap. The
152 MACHINE DESIGN.
breadth of the latter depends upon that of the margin, £, and of
the transverse pitch, V. In chain riveting, V= 2 to 2.$d = mini-
mum pitch, / ; in staggered riveting, as shown, V= o.4p, theo-
retically, although practically it is greater.
For example, in double-riveted lap joints, Fig. 63 b, c, in boiler-
work, with steel plates and steel rivets, with plate -thickness, t= 0.75
ins., rivet-diameter, d ' = 1.125 ins., and pitch, p = 3.30 ins. :
Staggered. Chain.
E=i.5<J= 1.69 1.69
r= 1.78 2.75
2E+ F=Lap= 5.16 6.13
9. BUTT-JOINT, SINGLE STRAP. — This seam, Fig. 65, consists
essentially of two abutting lap-joints. Theoretically, it has, in
tension and shear, no more strength than the latter, and, to resist
these stresses only, the strap need be no thicker than the con-
nected plates. Its practical advantage lies in the fact that the
plates are in the same plane and the bending to which they are
subjected in lap-joints is largely removed. The tension on the
plates will, however, tend to bend the strap ; and, for this reason,
the latter should be thicker than the plates, the increase depend-
ing upon the form of the riveting but being, as a minimum, ^ the
thickness of plate, when no rivets are omitted. The sole advan-
tage of this form of joint lies in the resistance to bending stress
offered by the thick strap. Its relative cost, as compared with
that of stronger joints of the double-strap type, warrants its use in
exceptional cases only.
i o. BUTT -JOINTS, DOUBLE STRAP. — The advantages of this
joint, Fig. 64, are that, not only are the connected plates in the
same plane, thus transferring bending stress from them to the
straps ; but the rivets, with regard to the plates, are in " double
shear," i. e., neither plate can withdraw from the joint without
shearing, across two sections, each rivet passing through it. The
efficiency of each rivet is, therefore, as compared with the lap or
single butt-joint, apparently doubled in shearing, although, as will
be shown later, the strength in double shear is not twice, but about
1.75 times that in single shear.
The progressive increase of efficiency of this joint with multiple
riveting, is limited by the fact that the resistances of the plate and
rivet to bearing stress are not doubled with that to shearing. For
RIVETED JOINTS. 153
example, consider a i^-in. rivet passing through |-in. steel plate.
Take St = 44,000 and Se = 70,000. Then :
Single Shear. Double Shear.
Ultimate bearing load = d • t • Sc = 59,o8o S9,o8o
" shearing " =-Kd2l^-Ss= 43,736
" = m/l/4- AX 1-75 = 76,538
In single shear, the rivet has an ultimate strength of 43,736 Ibs.;
in double shear, of 76,538 Ibs. The bearing strength is the same
in both cases, leaving, in double shear, a surplus shearing strength
of 17,458 Ibs., which is unavailable, since the limit in bearing has
been reached. The data, as above, will be regarded simply as
an indication of the principle involved.
The double-strap joint has also, and in greater degree, the ad-
vantage of the single-strap joint in relieving the plates of bending
stress. With regard to tension and shear only, the thickness of
the straps need be but one half that of each connected plate.
Owing to bending stress, however, as in the single-strap joint, each
strap should have, as a minimum, | the thickness of the plate,
when no rivets are omitted.
1 1. BUTT-JOINT, UNEQUAL STRAPS. — The butt-joint with double
straps unequal in width, Fig. 61, is stronger than a joint with
equal straps of the narrower width, owing to the added rivets of
wider pitch in the outer row. A properly designed joint of any
type is so proportioned as to take full advantage of the tensile
strength of the net section of metal along the pitch section. In
double shear, the shearing resistance, as shown, grows more
rapidly than the tensile and bearing resistances of the joint.
Hence, by increasing the width of the inner strap and adding two
rivets, doubly spaced, as at A and B, Fig. 61, the length of the net
plate-section becomes p — d, instead of pJ2 — d, as at C-D, and the
bearing resistance is increased also, without adding more shearing
strength than that given by one rivet in single shear. The main pur-
pose of this type of joint is to enlarge the net plate-section, as at A-B.
This joint has met wide adoption in stationaiy and locomotive
boilers. It has a practical advantage in that, as the wider strap
is always placed inside, there is a section of metal within the shell-
sheet and back of the calking edge on the outer strap. If, through
bad calking, the shell-sheet be indented on the outside, the inner
strap acts as a support instead of providing an edge over which
154 MACHINE DESIGN.
the shell-sheet may bend and crack. The half-pitch, at C-D
ensures tightness.
12. LAP-JOINT, SINGLE STRAP. — This joint, Fig. 66, consists
usually of an ordinary single-riveted lap-joint with, on the inside,
a butt-strap or welt-strip covering its whole length. There are
three rows of rivets. Those in the centre pass through both plates
and the strap ; those in one outer row extend through the strap
and one plate ; and those in the other row, through the strap and the
other plate. The pitch of the outer rows is twice that in the centre.
This joint is intermediate between the lap and butt types. Its
narrow central pitch ensures tightness while the wide pitch of the
outer rows gives increased length of net plate-section. The inner
edge of the main seam is inaccessible ; but the joint is stronger
than the lap-form in tension and shearing and the strap makes it
stiffer against bending. The strap, when below the water-line in
a boiler, prevents in a lap-joint the action known as " furrowing,"
i. e., the corrosion in grooves of the plate-metal near the joint.
13. GROUP RIVETING, Fig. 67. — This form of joint is applicable
especially in structural work for splicing narrow plates, etc. The
stresses in the net section of plate decrease from Row No. II. on-
ward and, in a lap-joint, efficiencies varying with the number of
rows and ranging from 80 per cent, upward are obtained. The
rivets are disposed in groups according to an arithmetical series,
the number in the rows being :
i, 2, i ;
or» i, 2, 3, 2, i ;
or, i, 2, 3, 4, 3, 2, i, etc.
42. The Theoretical Strength of Riveted Joints.
The riveted joint is a structure whose character and methods of
manufacture forbid extreme refinement of design. The plates are
not only exposed in various parts to direct tension, compression,
and shear, and the rivets to the latter two stresses in addition to their
initial tension ; but there is also, in service, bending action on the
rivets and on the plates or straps. Even on the assumption of
perfect workmanship throughout, the relation of the various
stresses, with regard to any element of the joint, is so complex
that a fair approach to the value of the resultant stress could be
obtained only by intricate calculation. Again, assuming such a
RIVETED JOINTS. 155
calculation as possible in practical design, its results would be af-
fected materially by the process of manufacture of the joint, which
process is essentially of such a nature as to exclude the accurate
fitting and alignment which are required for the correct distribu-
tion of the total load among the rivets, plates, and straps.
The many tests of joints give information of much value. That
information is, however, conclusive only in revealing the apparent
stress at which certain elements of that particular joint yielded.
The actual stress which existed within those elements at destruc-
tion is, owing to hidden components, unknown ; and the rearrange-
ment of stresses which occurs at various stages of a test renders
impossible an accurate determination of anything more than the
apparent load on any element at any time.
Furthermore, the majority of published tests have been made
upon thin plates which develop, as a rule, maximum ultimate re-
sistance ; the bulk of the test specimens have been narrow sections
of the joint ; and the method of testing is direct tension on a plane
specimen. In practice, on the other hand, the plate is, in boiler-
work, if thin, of small diameter and great curvature ; or, for high
pressures, may be of large diameter and less curvature but of maxi-
mum thickness. Again, in structures, a joint — for example, that
in the web of a plate -girder — may be in tension at one end and in
compression at the other ; or, as in the multiple plate form of
chord construction, it may present conditions which differ widely
from those of the simple joint tested in tension.
While, therefore, actual experiments upon joints give the only
available knowledge of their final strength, the use in designing
of the results thus obtained should be governed by the conditions
of the specimen tested and of the joint required. As a rule, prac-
tical designing regards only the simple stresses in plates and rivets ;
neglects, except in the added thickness of butt-straps, the bending
action within the joint ; allows for these omitted stresses by the
use of a fair factor of safety ; and accepts the efficiency of the
joint as thus computed.
i. NOTATION. — In the discussion of joint-strengths which fol-
lows :
d = diameter of rivet ;
n = number of rivets in the pitch-section, i. e., a strip of joint
of length / ;
156 MACHINE DESIGN.
t = thickness of plate ;
/j = thickness of single butt-strap = i-|^;
tz = thickness of double butt-strap = |7 ;
p = pitch, longitudinal, greatest ;
pd = pitch, diagonal ;
V= pitch, transverse, in staggered riveting, with no rivets omit-
ted, and in chain riveting, when alternate rivets are omit-
ted in outer row ;
V^ = distance between outer and next row of rivets in staggered
riveting, when alternate rivets are omitted in outer row ;
E= width of margin =1.5^;
c = shearing constant = I for lap and single butt-strap joints
and 1.75 for double butt-strap joints ;
R = ultimate resistance in tension of a strip of solid plate, the
width of the greatest pitch, / ;
Rt = ultimate resistance, in tension, of joint ;
Rx = ultimate resistance, in shearing, of joint ;
Rc = ultimate resistance, in bearing, of joint ;
Rm — ultimate resistance of joint, with alternate rivets in outer
row omitted, when joint yields by tearing the plate
along the central row and shearing one rivet in the outer
row ;
St = ultimate unit tensile stress of plate ;
St = ultimate unit shearing stress of rivet ;
Se = ultimate unit bearing stress of rivet and plate ;
Et = tensile efficiency, per cent, of joint = RJR X 100 ;
Et = shearing efficiency, per cent., of joint = RJR X 100 ;
Ec = bearing efficiency, per cent., of joint = RcjR X 100 ;
Em = efficiency, per cent., corresponding with the ultimate re-
sistance, Rm, or Em = RnJR x 100.
2. LAP-JOINT, SINGLE RIVETED. — Fig. 63 a. In this joint,
# = I. We have :
Rt=(p-d}t-St't
p-t-St.
RIVETED JOINTS. 157
For equal strength throughout :
^•Ss = d-t-S, (88)
From (87) :
p=*jjd+d. (89)
From (88) :
'•I '57554 (90)
(*?)
100 = 100
loo ;
(Sc d\
=(-.-)
A = # x I0° = I V ' -i ) I0°-
^ \s* f/
It will be noted that (89) and (90) are derived by equat-
ing the bearing strength of the joint to its tensile and shear-
ing strengths. As will be shown later, the ultimate compressive
or bearing strength of a rivet in its hole or of the walls of the hole
itself, is a somewhat uncertain quantity, since the confined situa-
tion of the metals restricts their plastic flow. The exact manner in
which the " bearing pressure " acts upon the surface of the rivet or
of the hole is unknown. It is assumed, with some warrant, to be
equivalent to a total pressure uniformly distributed over the pro-
jected semi-intrados, or d x /. Owing to the uncertainty in this
matter, some designers assume, from experience, a ratio djt and
find p by equating Rt and Rt, thus :
Rt = Rs= (p — d}t-St = 0.7854 dz- St;
In this equation, t is known from prior considerations ; d\t is as-
sumed, giving the value of d ; St ISt is ascertained from tests of the
metals. The value of/ can be found, therefore, by substitution.
158 MACHINE DESIGN.
Example: Steel plate and rivets; t = % in.; .£, = 65,000; St
= o.SSt = 52,000 ; Sc = 70,000.
From (90) :
70 0.375 21
d~ V
From (89) :
/> = ~- x 0.656 + 0.656 = 1.363, say 1 1 in.
Substituting the values of d and/ in the equations for efficiencies :
Et= 52.27 percent;
.£ = 52.44 per cent. ;
Ec = 5 1.39 per cent.
Efficiency of Joint = 51.39 per cent., the least of the three effici-
encies, as above.
3. LAP JOINT, DOUBLE RIVETED, NO RIVETS OMITTED. — Fig.
63, b, c. In this joint, n =2. We have :
Rt=(p-d}t.St;
R=p-t-St.
For equal strength throughout :
.'.(p-d}t-St=n-dtSc; (92)
n x 0.7854^5, *=n-dtS, (93)
From (92) :
(94)
Equation (93) gives equation (90) as before.
oo, (95)
R (S 0.7854^ , ^
= -£* x 100 = n( ^ . 'f] 100, (96)
= §xioo = «(|.|)ioo. (97)
RIVETED JOINTS. 159
Example. — Double-riveted seam, chain or staggered; steel
plate and rivets; t = -^ in.; St, Ss, Sc are, respectively, 65,000,
52,000, 70,000.
From (90):
From (94):
— X 2 x 0.75 + 0.75 = 2.366, say 2| in.
—
Substituting in (95), (96), (97):
Et = 68.42 per cent;
£= 68.01 per cent;
E0 = 68.02 per cent
Efficiency of Joint = 68.01 per cent., a gain of 68.01 — 51.39
= 16.62 per cent, over the single-riveted seam.
It will be observed that equations (90), (94), (95), (96), (97)
are general.
The double-riveted seam, with alternate rivets omitted in the
outer row, is not used with lap-joints.
4. LAP JOINT, TREBLE RIVETED, NO RIVETS OMITTED, chain
or staggered, as in Fig. 63 d, e. In this joint, n = 3.
Example. — Steel plate and rivets ; t== ^ in.; St, Ss, Sc are, re-
spectively, 65,000, 52,000, 70,000.
From (90) :
J-
From (94) :
+ = 3-432, say
From (95), (96), (97) :
.£,= 76.36 per cent;
Et = 72.22 per cent;
Ee= 76.25 per cent
Efficiency of 'Joint = 72.22 per cent., a gain of 72.22 — 68.01 =
4.21 per cent, over the double-riveted seam. Compare with
160 MACHINE DESIGN.
5. LAP JOINT, TREBLE RIVETED, ALTERNATE RIVETS OMITTED
IN OUTER Rows. — In this case, the grouping of the rivets is that
shown, on each side of the seam, in Fig. 64, h or k. In this joint,
0 = 4.
Example. — Data, the same as in the previous case. Since (90)
does not include n, we have, as before, d= i| in. From (94) :
70 13 13
^ = 67 X 4 X T6 + 16 = 4'3 ' ' say 4* * in"
From (95), (96), (97) :
Et = 81.16 per cent.;
Es = 76.74 per cent.;
Ee = 8 1 .42 per cent.
With regard to this form of riveting, a further efficiency must
be considered. Since there are twice as many rivets on the central
as on either outer row, the net plate-section on the central row is
less and the plate might tear along that line. Before total yield-
ing can occur in this manner, however, one rivet in the outer row
must be sheared for each pitch-section. Hence, with regard to
rupture in this manner, the total resistance, Rm, of the joint is equal
to that in tension of the net section along the middle row, plus
that in shearing of one rivet in the outer row. We have for these
conditions :
Rt (central row) = (p — 2d}t- St ;
Rt (one rivet, outer row) = 0.7854^ • St ;
Rm = Rt + Ri = (p- 2d)t-St + 0.7854^' Sf (98)
Similarly to (95), etc., the efficiency under these conditions is :
R \p-2d St 0.7854^1
Em = -R x wo.|t^- + 3J — J 100. (99)
Substituting in (99) :
Em= 81.5 per cent.
Comparing this with the efficiencies deduced previously, Effi-
ciency of Joint = 7<5-7/ per cent., a gain of 76.74 — 72. 22 = 4. 52
per cent., by omitting alternate rivets in the outer rows.
RIVETED JOINTS. l6l
The elements of the two joints are with :
t d 11 p (middle) p (outer]
No rivets omitted \ \\ 3 3^ 3_7.
Alt. rivets omitted 1 i| 4 2^ 4^
The plate-thickness and rivet-diameter are the same in both
cases. In the modified joint, one rivet has been added and the
pitch of the outer rows made greater and that of the central row
less. The addition of the rivet increases the strength in shearing
and bearing, since the outer pitch has not been increased propor-
tionately. The extended outer pitch augments the net plate-sec-
tion and, hence, the tensile strength. The reduced pitch and ten-
sile strength of the central row are more than balanced by the
added resistance of one rivet in shearing before rupture can occur
along that row. Hence, the modified joint is, in every respect, the
stronger. Its only disadvantage lies in the lessened tightness, due
to wider pitch, on the outer rows, to offset which there is a re-
duced pitch in the centre.
6. BUTT- JOINT, SINGLE STRAP, Fig. 65. — This joint is, in effect,
composed of two abutting lap-joints, one between the strap and
each plate. Hence, with regard to the plates, the methods of de-
sign used for lap-joints, apply. This is true also of the strap, since
the increased thickness given it is intended solely to resist bending
stress, which stress analysis does not consider. Under these con-
ditions, there is, theoretically, no gain in efficiency over the lap-
joint, except that the bearing and tensile stresses in the strap are
less. The increased strength against bending action is more than
offset by the additional cost of the strap and of calking one more
seam. This joint, therefore, is seldom used.
7. BUTT-JOINTS, DOUBLE STRAPS OF EQUAL WIDTH, Fig. 64. —
This joint is the strongest form for any purpose. The straps, one
on each side of the plates, reduce the bending action to a minimum
and the rivets are in double shear. The single-riveted type, Fig.
64 «, is seldom used for boiler work, since, with but one row of
rivets, the latter must be, for strength, of relatively large diameter
and therefore so widely spaced as to interfere with tightness. The
efficiency of such a joint is only about 65 per cent., or less than
that of the double-riveted lap form, with usual proportions in both
cases.
1 62 MACHINE DESIGN.
The butt-joint with double straps consists essentially of two
double shear joints with regard to the plates and of four single
shear lap-joints with regard to the straps. Each strap is assumed
to bear one half of the total load upon the plates and is, as stated
previously, made | the thickness of the plate, as a minimum, when
no rivets are omitted, in order to provide for bending stress. The
relations between the loads and strengths of the plate and either
strap are :
Plate. Strap.
Load, I \
Strength, tensile, i f
" shearing, 1.75 I
" bearing, I £
With one half the load of the plate, the strap has five eighths
the strength of the latter in tension and bearing and its shearing
strength exceeds its load in the proportion of i to 0.875. Hence,
if the joint be designed properly for the plates, its strength will be
ample for the straps.
The general formulae deduced previously for lap-joints were
founded solely upon the size and grouping of the rivets with re-
gard to the seam. Precisely the same conditions hold in butt-
joints, double-strapped, with the additional consideration that the
factor, c= 1.75, is introduced, since, with regard to the plates,
the rivets are in double shear. Therefore, for the plates of such
joints, we have :
Rc=(d-t-Sc}n-
Rt = (0.7854 d2- 5.x 1.75)*;
R =-t-S
r2-5,= ndt-Sc\
whence :
/ = -^ • nd + d\
^t
-; (100)
-374
RIVETED JOINTS. 163
o; (95)
* -
- X 100 = n - - I00. (101)
(97)
Where alternate rivets are omitted in the outer row, the plate may
tear along the central row ; but, before yielding occurs, one rivet,
in double shear, must be sheared in the outer row. We have for
these conditions :
^(central row) = (/ — 2d}t- St ;
Rs (one rivet, outer row) = i.^j^d2 • St ;
Rm = Rt + Ra=(p- 2d)t. St +
From the equations given above — if the thickness of the plate
and physical characteristics of the metal be known — the diameter
and pitch of the rivets and the various efficiencies of any required
butt-joint with double straps, may be obtained. When alternate
rivets in the outer row are omitted, the butt-strap must be thicker
than when no rivets are omitted, in the ratio (/ — d) H- (/ — 2d),
as will be shown later in the deduction of Traill's formulae.
The efficiencies of butt-joints, double-strapped, with steel rivets
and plates, as computed by Traill * for cylindrical boilers, with vari-
ous thicknesses of plates and diameters and pitches of rivets, are :
Single-riveted, 59.35 to 65.00 per cent.
Double " 73-39 " 78.00 " "
« «
each alternate rivet in 1
outer row omitted j
(• 79-68
"82.32 " "
Treble "
79.68
" 82.32 " «
" "
each alternate rivet in 1
both outer rows omitted j
^83.24
" 841.66 " "
<« it
each alternate rivet in
the outer row omitted
[84.95
" «
Quadruple "
83.24
« 84.66 " "
Boilers: Marine and Land," 1896, pp. 306-318.
i64
MACHINE DESIGN.
Example. — U. S. Cruiser Raleigh; diameter of cylindrical boilers,
14 ft., 6 ins.; steam -pressure, 160 IBs., gauge; longitudinal seam,
butt-joint, double-strapped, treble riveted, alternate rivets in outer
rows omitted (Fig. 64 k] ; St = 65,000 ; Se = 70,000 ; 5s = 44,000 ;
factor of safety = 4. 5. From the considerations as to the shell
(§ 44), the plate-thickness, t= i-j3g in. In this joint, n = 4.
From (100) :
From (94) :
44 1.374
1-375
fins.
7.298 = say,
The corresponding particulars of this joint, as built, were :
/ = i \\ in. ; d = iT5g in. ; / = J\ in.,
an allowance of -^ in. for corrosion having been made on the
calculated thickness, /.
8. BUTT-JOINT, DOUBLE STRAPS OF UNEQUAL WIDTHS, Fig. 61.
This joint, as designed for locomotive boilers, is shown in Fig. 76.
i*0
i
i
O
i '
i
i
o*i o
• J"
\St"
©* o
;*$
| !
^s:
/^\
FIG. 76.
The rivets are I in. in diameter and of wrought iron. The plates
and straps are of steel. The thickness of plates and of outer strap is
| in. ; of inner strap, Jg in. Take S, = 60,000 and Ss = 48,000.
Disregard resistance to crushing. In this joint, n = 3. Failure
may occur by :
(a) Rupture of plate along outer row of rivets, (b) Shearing
one rivet, outer row (single shear) and two rivets, inner row
RIVETED JOINTS. 165
(double shear). (V) Rupture of plate along inner row and shear-
ing one rivet, outer row (single shear).
For these conditions :
Rs= o.;854^2(i + 2 x 1.
Rm=(P~ 2d)t-St + 0.7854^-5.;
R=p-t-S,
Equating Rt and Rm : d = 0.995, Sa7 I in-
Equating Rt and Rt : p = 5.52, say sj in.
The efficiencies are :
n
£t = -g X 100 = 81.82 per cent. ;
R
ha = -g 9 x 100 = 82.25 Per cent. ;
zp
^m = R X I0° = 8l-92 Per cent-
With regard to crushing, failure may occur by :
(d} Rupture of plate along inner row and crushing one rivet in
outer row and inner strap ; (e) crushing two rivets in inner row
in plate or outer strap and one rivet in outer row and inner strap.
The total resistances of the joint are :
For conditions (d) :
For conditions (^) :
2(1 X f)S. + (I X
Investigation of these resistances shows that Sc must have a
value of about 100,000 Ibs. per sq. in. in order to make the effi-
ciency of the joint about equal to those already deduced. The
moderate value (70,000) used previously with steel rivets will not
serve, therefore, in this case. Since the destructive limit of metal
wholly free to flow, differs from that of the same metal when
plastic flow is restricted, as in a riveted joint, considerable varia-
tions in the value of Sc may be expected. Professor Kennedy
recommends 96,000 Ibs. per sq. in., and Mr. Stoney 50 tons per
sq. in., for the plates in butt-joints, double-strapped.
166 MACHINE DESIGN.
Failure of the lap-seams of the straps of this joint may occur
(disregarding crushing stress), as follows :
Inner Strap :
(/) By shearing 3 rivets in single shear ;
(gf) By shearing I rivet in single shear and tearing the plate
along the inner row of rivets.
Outer Strap :
(/«) By shearing 2 rivets in single shear ;
(k) By tearing the plate along the inner row of rivets.
From (/) and (Ji) it is clear that, in shearing, the seam of the
inner strap is necessarily the stronger in this form of joint. With
straps of equal thickness, this seam is also the stronger with re-
gard to (g) and (£). Hence, for equality in resistance to these two
methods of failure, the thickness of the inner strap may be made
less than that of the outer, as in Fig. 76.
The purpose, in extending the inner strap so that another row
of rivets in double pitch may be added, is that the net plate-section
— which is then taken along the added row — may be increased,
thus giving greater tensile efficiency. The latter, with this type, is
relatively high. Thus, the joint shown in Fig. 76 is, as compared
with butt-joints having straps of equal width, stronger than the
double-riveted and but little weaker than the treble-riveted forms,
no rivets being omitted in either of the latter cases.
9. SINGLE-STRAPPED LAP JOINT, Fig. 66. — The analysis of this
joint is given briefly in Reuleaux's Constructor* The joint con-
sists of an ordinary single-riveted lap-seam with an inside strap
riveted to the shell plates at, and on each side of, the seam. The
pitch of the outer rows is twice that of the central line of rivets.
The central rivets pass through the strap.
Against stress normal to the seam, three rivets act — two in the
lap-joint and one passing through the strap. The assumption is that
the total load, P, upon the pitch-section is divided equally among
the three rivets and that, hence, the strap withstands one third of
that load and the joint the remaining two thirds. Therefore, if
the strap and plates be of equal thickness and St be the ultimate
unit tensile stress in the plate beyond the joint, the corresponding
stress in the unperforated plate, within the joint and between the
rivet-rows, will be %St and, in the strap, ^St. Again, although
the rivets at the lap-seam pass through the strap, the latter is, at
*Suplee's translation, 1895, P- 43'
RIVETED JOINTS. 167
that seam, pulled in opposite directions by equal forces and hence
transmits no stress to the central row of rivets.
Assuming equal thicknesses and tensile strengths throughout,
the ultimate unit resistance of the plate, within and without the
joint, and of the strap would be equal under similar conditions ;
but, in this type of joint, the conditions are such that the pitch-
section beyond the joint bears the total load, P, the unperfo rated
plate within the joint bears f P, and the strap ^P. Hence, with
equal thickness, the plate within the joint and the strap — as com-
pared with the plate beyond the joint — are equivalent, respec-
tively, to metal, i -=- f = | and 1-7-^=3 times as strong. We
have, then, for the ultimate tensile resistances and efficiencies :
R (plate beyond joint) = / • / • St ;
Rt (plate within joint) = f (p — 2d)tSt ;
Rt (strap) = 3 (p - 2d)tSf
E, (strap) .
The efficiency of the strap-metal will depend upon its resistance
on the central row, along which line it will tend to part.
In shearing stress, in order that the right hand plate may with-
draw from the joint, it must shear one strap and two lap rivets,
all in single shear. For the strap the conditions are the same.
Hence, taking St = 0.8 St :
ltd*
R , xd2
^-^-loo-l-— -ioa
Comparing the efficiencies with those of an ordinary double-riveted
lap-joint, as in (95), (96) :
EI -^
p — 2d ndz
Single-strapped lap-joint: f •*— - — • 100 ; f • — • 100 ;
p-d , nd*
Double-riveted lap-joint : — — — • 100; f • — • 100.
108 MACHINE DESIGN.
10. GROUP RIVETING, as shown in the lap-joint, Fig. 67, is an
arrangement of the rivets in an arithmetical series, which grouping
— on the assumption of an equal division of the load among the
rivets — gives a gradually reducing tensile stress in the plate from
one side to the other of the group. The substance of the follow-
ing analysis is taken from Reuleaux's Constructor.*
Referring to Fig. 67, let Pbe the total load on the pitch-section,
p ; m, the number of rivets in the central row ; and a, the pitch of
that row. Then p = m x a. From the properties of an arith-
metical series, the total number of rivets in the group = w2. In
Fig. 67, m = 4.
(a) Shearing and Greatest Tensile Stresses. — To find the ratio
between pitch, /, diameter, d, and thickness, /, which shall give
equality between the tensile strength of the net plate-section in the
first, or outer, row and the shearing strength of the joint, let St be
the unit tensile stress in the plate beyond the joint and StT that in
the outer row. Then :
Rt (outer row) = (ma — d}t- Stf;
R (joint) = »z2- — -5.
4
Equating and taking Ss = O.8S* :
(So, C)
From which, / = ma may be found.
(b) Tensile Stress in any Row. — To find the stress on the net
plate-section in any given row, there must be deducted — on the
assumption of an equal division of the load among the rivets —
the fraction of the total load, P, which is borne by preceding rivets.
Thus, in Fig. 67, the net plate-section of Row I. carries the full
p
load, P; that of Row II., P minus the load, — 2, on the single rivet
*Suplee's translation, 1895, P- 41-
- d
RIVETED JOINTS. 169
of Row I. ; that of Row III., P minus loads on Rows I. and II,
or ^-2, etc.
m
The fractions of the total loads borne by the net plate-sections
of the various rows will then be :
P- III, ^.P- IV,
411* *
• P, etc.
Let the unit stresses in the net plate-sections, beginning with
the outer, be S/, Sta, Stni, StIV, etc. Then, equating the loads
and resistances :
P= (ma-
Row I. :
Row II. :
m2 - i
m2
T?nw TTT •
m2 — 3
£\.OW 111* •
m2
m2 — 6
Row IV. :
(ma- 2d)t-Stn;
— • P= (ma -
; etc.
(Si, Q
Now, let a bear such a proportion to d that Str = Stn. To find
the value of this ratio in terms of m, equate the values of P from
the first and second equations, as above :
(ma — d)t = (ma — 2d^t-—l —
(S2, Q
which equation holds only for the condition that St* = Stn.
Equating the value of P for each succeeding row with that for the
first row and substituting the value of -% :
Stm_ttf-$ Stir m2-6
-5 - w^2 ' ^ ~ ^^ ; 3
ttr — 10
m2 — 4
; etc.
With m = 4, these ratios are, respectively, if, \%, and T6^,
showing that, from the second row inward, there is a gradually
decreasing stress in the plate.
17° MACHINE DESIGN.
In order to compare the results for any given ratio between
diameter and thickness with varying values of m, assume in (50, C)
any convenient value for this ratio, as :
d 5
= -= i. 59i6= say 1.6
(53, C)
Also, since St is the unit tensile stress in the unperforated plate and
St* the greatest unit tensile stress in any net plate-section of the
joint :
EI (joint) _--i-
<VJ ' St ma
Again, for the unit bearing stress, Sb, we have :
(54, C)
(55, C)
Substituting various values of m in equations (50, 52, 53, 54, C) :
m =
,.
3-
4.
5-
d\t =
ab/=
a\t =
1.6
2.50
4.00
0.80
1.6
3.33
5.32
0.90
1.6
4-25
6.80
0.94
1.6
5-20
8.32
0.96
These efficiencies are based upon the assumptions that the load is
divided equally among the rivets ; that a bears such a proportion
to d that St'= Stn; that S, = o.8S/ ; and that df t = 1.6.
In butt-joints, with single or double straps, there will be two
groups, one on each side of the seam. Such a joint has, practically,
a further advantage in the increased thickness of the strap.
43. General Formulae for Boiler- Joints.
The formulae deduced in this section are given in Boilers : Marine
and Land, by Thomas W. Traill, F.E.R.N., in Foley's Mechanical
Engineers' Reference Book, and in Seaton's Mamial of Marine
Engineering (1890). In the work referred to, Traill gives a com-
plete series of tables calculated from these formulae, from which the
RIVETED JOINTS. \-ji
proportions of a joint for any given boiler-diameter and steam-
pressure can be selected at once without preliminary computation.
These tables are of much value and have met extensive use by
designers in the United States and Great Britain. No deduction
of the formulae is given in the works noted above. That which
follows is, in substance, that prepared by Lieutenant Commander
F. J. Schell,* U. S. Navy, for the use of midshipmen at the U. S.
Naval Academy.
The notation used by Traill is :
/ = pitch (greatest) of rivets in inches ;
d = diameter of rivets in inches ;
c = a shearing constant whose value is i for lap or single
butt-strap, and 1.75 for double butt-strap joints ;
A = area in sq. ins. of cross-section of one rivet ;
;/ = number of rivets in section of length, p ;
Jo = percentage of plate left between rivets in greatest pitch ;
<jol = percentage of rivet-section as compared with solid
plate ;
fi2 = percentage of combined plate and rivet-section when alter-
nate rivets are omitted in outer row ;
pd = diagonal pitch ;
E = distance from centre of nearest row of rivets to edge of
plate ;
V •=• transverse distance between rows of rivets in ordinary zig-
zag (staggered) riveting and in chain riveting with al-
ternate rivets omitted in outer row ;
V^ = distance between outer and next row of rivets in zigzag
riveting with alternate rivets omitted in outer row ;
T = thickness of plate in inches ;
T'j = thickness of single butt-strap in inches ;
T2 = thickness of double butt-strap in inches ;
i. ASSUMPTIONS. — (a) That the mean tensile strength of steel
plate is 28 tons per square inch of net section ; (&) that the mean
shearing strength of steel rivets is 23 tons per square inch of cross-
section ; (c) that a rivet in double shear offers 1.75 times the re-
sistance to shearing opposed by a rivet in single shear ; ((£) the
bearing stress is not considered.
* Jour. Am. Soc. Naval Engineers, IV., 403.
172 MACHINE DESIGN.
2. PERCENTAGE STRENGTH OF JOINT. — The net plate-section
along the greatest pitch is (p — d}T; the sectional area of the
same length of solid plate is / x T. Hence :
p-d
100-. (103)
The resistance to shearing offered by the rivets in one pitch
section is 23 x A x n x c ; the tensile strength of the solid plate
of length / is 28 x / X T. Hence :
Consider now the case in which alternate rivets are omitted in
the outer row, as in Fig. 73. In the next row, the net plate-
section will be (/ — 2d)T and ioo-(/ — 2d^jp will be the per-
centage strength of this row as compared with the solid plate.
Suppose, however, that the plate tears along this row, as at K.
Then, before total failure of the joint occurs, one rivet, for each
pitch-section, must be sheared in the outer row. The percentage
strength of this single rivet is, from (104), ^kl -+• n. Hence :
|fp fc-ioo-^ + l- (-5)
The lowest of the values obtained from (103), (104), (105) is
the percentage strength of the joint. An examination of these
equations shows that, for double-strapped butt-joints, so long as
d is not less than T, fi2 is always greater than fi or cjol. This is
also the case with lap-joints, so long as d is not less than
T T
If x 7854 -64515
Since both of these conditions hold usually, the use of formula
(105) will seldom be necessary.
3. DIAMETER AND PITCH. — The usual cases are :
(#) To find d so that Jfe = %l (i. e., equal tensile and shearing
strengths of joint), when /, c, n, a"nd T are given, equate (103)
and (104):
p — d 2-i.A-n-c
Ioo.^- = ioo--T. (106)
RIVETED JOINTS. 173
Substituting A = xd2/^ and simplifying :
(*) '
(io6):
^-2p)-^c~' (I°7>
To find /, when d, c, n, and T are given, we have from
+ -d. (108)
(c] To find d and /, when n, c, T, and 56 = <fol are known, we
have, from (103) :
100
Substituting this value of/ and A = '- — = — • — in (104) :
4 74
100 x 23 x 22 x d2-n-c
~ = 7>i = 7>;
Substituting this value of «? in (109) :
As a rule, it will be found simpler to substitute the numerical
value of d, as found from (no), in (109), thus obtaining a value
for/ directly, without using equation (ill).
4. DIAGONAL PITCH AND WIDTH OF BUTT -STRAPS. — The resist-
ing value of the net plate-section along the diagonal pitch, pd, with
regard to tensile stress normal to the joint, is usually — owing to
the shearing component (§ 26) along the diagonal pitch — about |
of that of the same section, if located parallel to the joint, as in the
pitch, p. Hence, the diagonal net section should be | longer than
174 MACHINE DESIGN.
that part of the longitudinal section to which it should be equiva-
lent in transverse tensile strength. In any event, the diagonal
pitch should not be less than that found by the following formulae :
(a) Ordinary Zigzag Riveting and Chain Riveting with Alternate
Rivets Omitted in the Outer Row. Fig. 64 c, d. Reference to Fig.
64 c, shows that the same reasoning applies to both cases, since,
in each, the net section of two diagonal pitches must be made equiv-
alent in strength to the net section contained in the greatest longi-
tudinal pitch, p. The liability of the plate to tear along A-B and
B-D should be the same as along A-D or B-F. The net section
along A-B-D is 2(pd — d} Tand that along A-D or £-Fis (p—d] T.
Hence :
*-• <«»)
From the right-angled triangle, A-B-C, we have, for the distance
between the rows of rivets :
10
The authors mentioned previously state that, for chain riveting the
distance, V, should not be less than
and, as this result is greater than that obtained from (113), it is
the one which, usually, is found tabulated.
The distance, £, from the centre of the nearest rivet-row, to the
edge of plate, should not be less than 1.5 d. Hence, the minimum
lap of plates in a lap joint or the half-width of butt-strap is :
2E+ V. (114)
(£) Zigzag Riveting with Alternate Rivets Omitted in Outer Rcnv.
Fig. 73- The joint may fail by rupture of plate along A-B-C-D
RIVETED JOINTS. 175
or along A-D. For equality of strength, the resistances of the
two net sections to tensile stress transverse to the seam, must be
equal. The net section on B-C is (//2 - d)T '• that on A-D is
(p - d}T- that on A-B or C-D is (pd - d)T. The section, to
which the metal left along A-B and C-D must be equivalent, is :
Pd = °-lP + d> (IIS)
In the right-angled triangle, A-F-E, the base, F-E = //4. For
the distance, Vv between the rows of rivets, we have :
_
1- 20
As before, the lap or half-breadth of butt-strap is, with two
rows of rivets :
2E + Vr (117)
Since the riveting in all ordinary cases is of the form shown in
Fig. 64, c, d, or Fig. 73, or a combination of those forms, formulae
(112), (113), (i 14), (115), (i 1 6) have a general application. For
example, consider a double-strapped butt-joint, treble-riveted, zig-
zag, with alternate rivets omitted in the outer row. The distance,
Vv between the outer and second row is obtained from (i 16) ; the
distance, V, between the second and third rows is obtained from
(113); and the half-breadth of butt-strap is :
2E+ V^ + V. (118)
5. THICKNESS OF BUTT-STRAPS. — To ensure strength and tight-
ness, the aggregate thickness of the butt-straps should be more
than that of the plate, since thin straps will bend and the joint
will work and leak. For single butt-straps, 7i = f Tt and, for
1/6 MACHINE DESIGN.
double straps, T2 = f T, are taken arbitrarily as the minimum
values allowed, when no rivets are omitted.
When alternate rivets in the outer row are omitted, the empiri-
cal minimum thicknesses, as above, should be increased. Thus,
with regard to joints shown in Figs. 64 b, d, let :
T2 = thickness of each butt-strap, no rivets omitted ;
T2f = thickness of each butt-strap, alternate rivets omitted.
With no rivets omitted, the plate can tear from the strap or
strap from plate in but one way, i. e., along the net section of
length, p — d. Hence, the ratio of strap-strength to plate-
strength is :
With alternate rivets omitted, the strap may tear from the plate
along the inner and weaker half-pitch line but the plate cannot be
ruptured along that line without also shearing one rivet in the
outer row for each pitch -section. Hence, with the previous thick-
ness, Tv the strap would be weaker than the plate. The ratio of
strap-strength to plate-strength, with thickness, T2f, is :
2Tj(p-2d)
T(p-d)
Equating the ratios and taking T2 = ^T:
(no)
r -
Hence, when alternate rivets are omitted, the butt-straps must
be thicker than when no rivets are omitted, in the ratio,
p-d
p — 2d
Under the same conditions, the thickness of a single butt-strap is
6. JOINTS BETWEEN PLATES UNEQUAL IN THICKNESS. — In gen-
eral, it is customary to proportion the joint as for two plates of
RIVETED JOINTS. 177
the smaller thickness. If the disparity be great, the proportions
may be a mean proportional between those for the thick and those
for the thin plate.
44. The Thickness of Shell Sheets.
The thickness of the shell plates of a cylindrical boiler depends
upon the diameter, steam-pressure, tensile strength of plate, factor
of safety, percentage strength of longitudinal joint, and allowance
for corrosion. The shell is treated as a "thin cylinder" and its
thickness is governed by the principles given in formulae (i) to
(4), §i- Let:
t= thickness of plate, ins.;
r = internal radius of shell, ins.;
P= steam pressure, gauge, Ibs. per sq. in.;
St = ultimate unit tensile strength of plate, Ibs. per sq. in.;
/ = factor of safety ;
ty = percentage strength of longitudinal joint ;
^/ioo = strength of longitudinal joint as compared with solid
plate.
If the shell were seamless and a factor of safety were not used,
we would have by (4) :
P x r = t x St and t = —=- •
°i
The shell, however, is as strong only as its weakest part — the
longitudinal joint. The strength of that joint is fi/ioo times t.
Hence, the thickness must be increased in inverse ratio over that
required for a seamless shell and for / there must be substituted
/ X ioo/fi. Again, the working strength of the plate is equal to
its ultimate strength, divided by the factor of safety. Therefore
St must be replaced by 5, -T-/. Making these substitutions ;
t x ioo /
jy— Pxrx^;
P-r-f
IOO
1/8 MACHINE DESIGN.
If the joint be designed, as is usual, so that it will yield along the
<y i _ »
net plate-section of greatest pitch, we have, by (95), -— =^—
and the equation becomes :
P-r-f _ P-r-f-p
p-d (p-d)S* (122)
'
For any given conditions, the value of ft is known in close ap-
proximation or can be taken from Traill's tables. This value, sub-
stituted in (121), gives t at once.
The thickness may also be computed from (122) by substituting
the value of/ and d. Thus, assuming that the longitudinal seam
is a butt-joint with double straps of equal width, we have from
§42:
(94)
Substituting the values of/ and p — d in (122) :
(I23)
in which n will be known from the type of joint and Se and Se by
the tests of the plate. To provide for corrosion, Jg inch is usually
added to the value of /, as calculated, for the thick sheets of marine
boilers.
45. The Stresses in Riveted Joints.
The riveted joint is not homogeneous and rigid, but is a built-up
and, under stress, a comparatively yielding structure. The rivets,
through which the load is transmitted, are not at first in contact
with the walls of the rivet-holes, and the metal of both rivets and
plates is not only elastic but will become, under excessive stress,
plastic. " Lost motion," elasticity, and plasticity cause, with in-
creasing pressure upon the joint, a continuous change in the load,
form, and relative position of each element of the structure.
RIVETED JOINTS.
179
Thus, in the lap-joint, Fig. 77, when first riveted, the plates are
pressed together by the axial contraction of the rivet in cooling,
while the radial shrinkage of the latter leaves a slight annular space
between its shank and the walls of the hole. The tension on the
plates forms a couple whose arm is approximately t. When such
FIG. 78.
a joint is loaded, the couple tends to bring the plates into the same
plane, thus bending the lap and inclining the rivet, as shown in
Fig. 78. This action is opposed by the resistance of the plates to
bending and by their friction at the contact-surfaces. When this
friction is overcome, the plates slip on each other, the rivet bears
at diagonal corners of the hole, and crushing pressure upon the
walls of the latter, and shearing and bearing actions on the rivet
are added to the tensile and bending stresses already existing in
the plates and rivets. With an increasing load, these conditions
grow in intensity but are modified in their local effect by the elas-
ticity of the metal. Finally, in more or less of the elements of the
joint, the plastic stage is reached and the rearrangement of stresses
becomes more marked. At any time during these stages, failure
may occur, if any element be strained beyond its ultimate strength.
FIG. 79.
FIG. 80.
Similarly, in the double -strapped butt-joint, Fig. 79, there is at
first no bearing of the rivet-shank upon plate or straps. The gradu-
ally applied load expends its force first in overcoming the frictional
resistances between the plates and straps and between the latter and
the rivet-heads. When slip at these surfaces occurs, the condi-
tions are as in Fig. 80. The rivet is bent, it bears at one side on
the plates and at the other upon the straps, and it is subjected to
1 80 MACHINE DESIGN.
double shear, while a bending moment, similar to that in a lap-
joint, acts upon the straps. All stresses now prevail ; and, with
increasing load, the elasticity and ultimate plasticity of the metal
will cause, until destruction, a continuous change in the stress upon
any given element of the joint.
i . TENSILE STRESS IN RIVETS. — This stress is due to the con-
traction in cooling. Its magnitude — if the plates be tightly
clamped during riveting — depends upon the coefficient of linear
expansion, the modulus of elasticity, and the temperature at which
riveting is completed. Let :
A = sectional area of rivet-shank ;
/ = length of rivet-shank ;
E = modulus of elasticity ;
r = difference between temperature of cold rivet-blank and that
at which riveting is completed ;
/ = increase, total, in length for change of r° ;
s = increase, per unit of length, for change of r° ;
St = unit tensile stress produced by contraction ;
a = coefficient of linear expansion for a change of I ° F.
Then:
St = E-s = a-r-E* (124)
The total tensile load on the shank = A x St. Equation ( 1 24)
shows that this load is independent of the length of the shank.
The deduction holds only while St lies within the elastic limit of
the metal.
For steel in general, a = .0000065 and E= 30,000,000 ; and,
for soft rivet steel, St at the elastic limit = 30,000 Ibs. per sq. in.
These values, substituted in (124), give r= 154°. In practice,
however, the range of temperature greatly exceeds this. Hence,
it follows that, with good workmanship, the cooling and attempted
contraction strain the shank considerably beyond the elastic limit.
The actual tension in the shank is uncertain, since permanent set
is produced and the elasticity of the metal is impaired. Mr.
Stoney, in experiments quoted previously (§36), gives the contrac-
tile strength of iron rivets with hand-made points as 12.32 tons
per sq. in. of rivet-section, at which stress the points or heads
*Merriman: " Mechanics of Materials," 1899, p. 145.
RIVETED JOINTS. l8l
flew off. He gives also, from his experiments, 0.6 as the coef-
ficient of friction of ordinary steel plates. For the latter, with
rivets as above, the frictional resistance to slip would then be
12.32 x 0.6 = 7.39 tons = 16,553 Ibs. Per sq- in. of rivet-section.
Professor Bach's experiments * show, for good single lap-riveting,
similar values ranging from 14,000 to 25,000 Ibs. per sq. in.
2. BENDING STRESS ON RIVETS, Figs. 77 to 80, inclusive. In
lap-riveting, this stress is a maximum as soon as the plates engage
the rivet, which position is approximately that shown in Fig. 77.
The rivet, in the lap-joint, acts as a cantilever, the distance be-
tween load and reaction being t ; in the double-strapped butt-joint
this distance is (/ + T2}/2 and the rivet is a simple beam, loaded in
the middle. The classification and distances are approximate and
must be regarded as simply an indication of the principle involved.
Let:
P= total load on rivet ;
/ itd*
- = section-modulus of nvet = ;
c 32
6" = maximum stress, tensile or compressive, due to bending ;
M= maximum bending moment ;
t+T,
in butt-joints, double-strapped ;
4
= P- 1 in lap-joints ;
S-- = resisting moment.
Equating the bending and resisting moments, we have for :
Lap-joints : S =
Butt-joints : S = SP ^pr-
In the lap-joint, as the plates bend, the bending moment de-
creases.
3. SHEARING STRESS ON RIVETS. — When failure by shearing
occurs in lap and single-strapped butt-joints, but one cross-section
of the rivet-shank is sheared, while, in double-strapped butt-
* " Die Maschinen-Elemente," 1901, p. 170.
1 82 MACHINE DESIGN.
joints, the shank must be sheared in two places. In the former
case, the rivet is said to be in single, in the latter in double, shear.
The resistance to shearing is the product of the area sheared by
the mean ultimate shearing stress ; or, in the case of a rivet,
7Td?z/4 X St, for each rivet-section.
In double-strapped joints, as shown in Fig. 80, the shearing
force, P, is always approximately normal to the rivet. Hence, the
shearing resistance of the latter is 2(>zY/2/4' ^.)- In the lap-joint,
Fig. 78, as the laps bend, the force, P, does not remain normal and,
hence, has both shearing and tensile components with regard to the
axis of the rivet. The mean ultimate shearing strength of steel
is taken as 0.8 of its mean ultimate tensile strength. Therefore,
the division of the force, P, in single shear, into tensile and shear-
ing components diverts a portion of it to the stress against which
the rivet's resistance is greater. As a consequence, the ultimate
strength, in joints, of a rivet in single shear is to that of one in
double shear, not as 1:2, but as 4 : 7 or I : 1.75, approximately.
For each rivet in a joint, then :
Ultimate strength, single shear = - • 5 ;
4
Ultimate strength, double shear = - • S x 1-75,
4
in which d is the diameter of the shank and St is the mean ulti-
mate unit shearing stress.
The shearing stress varies in intensity throughout the cross-sec-
tion. In a solid of circular section, as a rivet-shank, the maxi-
mum is % the mean shearing stress.* Taking the maximum shear-
ing unit stress, 5/max.), as ^ of the ultimate unit tensile stress,
St, the mean ultimate shearing stress,
While this is the theoretical ratio between the maximum and mean
shearing stresses of a solid circular section, the common practice
is to take St = o.8St for steel rivets, the discrepancy, if any, being
covered by the factor of safety.
4. BEARING STRESS ON RIVETS and on the walls of rivet-holes.
*Rankine: "Applied Mechanics," 1869, p. 340.
RIVETED JOINTS. 183
In a new joint, the rivet-shank, owing to contraction in cooling, is
not in contact with the plate, and, further, its initial tension pro-
duces frictional resistance to movement between the plates, straps,
and rivet-heads. This friction, when the joint is first loaded, re-
duces the pressure upon the rivet and it must be overcome wholly
before the full bearing stress can exist. In fact, if it be assumed
that each rivet carries the same load, there would be, in service
and with the customary factor of safety, no bearing pressure what-
ever upon the rivets of a new joint. Thus, taking the mean ulti-
mate shearing stress of rivet-metal as 44,000 Ibs. per sq. in., the
factor of safety as 4.5, the elastic limit as 30,000 Ibs. per sq. in.,
and the coefficient of friction of steel plates as 0.5, we have, per
sq. in. of rivet-section :
Allowable shearing load = 44,000 -4-4.5 = 9,778 Ibs.;
Frictional resistance at elastic limit = 30,000 x 0.5 = 15,000 Ibs.,
i. e., even if the elastic limit were not exceeded, the resistance of
the plates to slip would be 50 per cent, greater than the permissible
shearing load. In view of these considerations, high authorities in
France and Germany (§46) contend that riveted joints should be
designed with regard to their frictional resistance and not with
reference to the ultimate strength of their elements.
On the other hand, owing to the elasticity of the plate, the ir-
regularity of workmanship, the bending of plates or straps, and
their actual and relative movement, especially in pressure-joints,
during expansion and contraction, it seems probable that frictional
resistance is modified greatly in service. Furthermore, experi-
ment shows that, in multiple riveted joints, the outer lines of the
rivets in test-specimens bear a wholly disproportionate share of
the load, owing doubtless to the elasticity of the plate between
them and the inner rows. Hence, their load probably exceeds
the frictional resistance they produce and the latter may be over-
come in detail throughout the joint.
In considering bearing pressure, assume for simplicity, as in
Fig. 8 1 , that the rivet is incompressible, that the elastic limit of
the metal is not exceeded, and that the rivet axis remains parallel
to the walls of the hole. The total load, P, upon the rivet will
force the latter into the plate the distance, 0-0'= A- A', since the
1 84
MACHINE DESIGN.
displacement, parallel to the line of action of P, will be the same
for all compressed parts of the plate in front of the rivet. The
elasticity and reaction of the plate produce on any element, B, of
the circumference a bearing pressure, b, which is a maximum, b' , at
C and varies as the cos 6 throughout the quadrant, being zero at D.
The summation of the vertical components of b equals P.
The rivet, however, is compressible and its section under
pressure is no longer circular. Again, Figs. 78 and 80 show that
the pressure on the axial plane is not uniform throughout. Finally,
under excessive stress, the plastic stage is reached and the in-
tensity and distribution of the pressure depend upon the free-
dom of flow of the metal. These unknown elements make an
analysis of the problem impossible without assumptions so broad
as to render the results valueless. With regard to an empirical
formula, it may be noted that, in summation by the calculus of
the vertical components of b, the normal pressure upon the ele-
mentary arc, ds = r'dd, must be considered and that the radius,
rf=r = dl2, approximately. Again, with a given load,/3, the
resulting unit bearing pressure depends, in some degree, upon the
thickness, /. These conditions warrant the introduction of d and
t in such a formula, the latter becoming :
P=SC x d x t,
(125)
RIVETED JOINTS. 185
in which P= safe load on one rivet and Sc = a mean working
bearing stress determined by experiment. Professor Unwin* says :
From experiments on indentation, it is known that the resistance to indentation of a
plastic material does not much depend on the form of the indenting body, but only on
the projected area normal to the direction of indentation. Hence, it is not an arbitrary
rule, but one based on experiment, to take the resistance to indentation of a plate of
thickness, /, by a rivet of diameter, d, to be proportional to the projected area, d X '•
5. BENDING STRESS IN PLATES. — In a lap-joint, the stress will
be a maximum when the parts are in the position shown in Fig.
77. For example, in plate, A, there acts at the left a force, P,
which produces a direct unit tensile stress, St, and, at the right, an
opposing force, P, with leverage, /, which tends to bend the plate
and to produce a further tensile stress, Sb, in its upper fibres.
The breadth of the section thus bent is p — d and its depth is /.
The stresses are :
Lap-joint (Fig. 77) :
Tensile load on section = P\
Resistance of section = S^p — d}t ;
P
Equating load and resistance : St = /v,__^w '
Bending moment of load = P x t ;
(p - dy
Modulus of section =? - ^ - ;
Resisting moment of section = Sb -- g - ;
6P
Equating the moments : Sb = / _ ^. •
Total maximum unit tensile stress = St + Sb ;
Double-strapped Butt-joint (Fig. 80) :
Tensile load on strap = — ;
*" Elements of Machine Design," Part I., p. 131,
1 86 MACHINE DESIGN.
Resistance of strap = S((p — d)T2 ;
Equating load and resistance : St =
Bending moment of load =
Modulus of section = — — g-t-*- ;
Resisting moment = Sb • 6 2 5
Equating the moments : Sb = ^P- -, - . /L2 •
Total maximum unit tensile stress
These calculations will be regarded as general, giving maximum
results. In lap-joints especially, the moment of the load is re-
duced rapidly by the bending of the plates.
6. BEARING, SHEARING, AND TENSILE STRESSES IN PLATES. —
The bearing pressure between the rivet and the walls of the rivet-
hole, is, of course, mutual. The metal in front of the rivet is, as
indicated in § 4 1 , in the condition, approximately, of a beam fixed
at the ends, with, in consequence, a shearing stress at the latter
since, at those points, the stress due to the resistance of the rivet
is communicated to the net section of plate along the pitch-line.
The distribution of the tensile stress in this net section is affected
by several conditions and presents a complex problem which Mr.
C. E. Stromeyer * contends is treated most adequately by regard-
ing the metal surrounding the rivet as part of a section of a thick-
walled cylinder.
It is possible to gain from experiments some knowledge of the
conditions which prevail. Thus, when a rectangular specimen of
unperforated plate is tested to rupture, the fracture is of crescent
form and, if the separated parts be brought together, they will
touch at the sides, leaving a gap in the middle. Evidently, then,
the stress is a maximum in the centre of the specimen. Again,
* "Marine Boiler Management and Construction, "1893, P- Io<>-
RIVETED JOINTS. 187
as shown in §38, the perforation of a plate, as for rivets, causes a
restriction of the flow of metal, a change in stress-distribution, and
an increase in ultimate tenacity, owing apparently to the partial
removal of stress from the centre of the net plate-section to the
portions adjoining the holes. Furthermore, when such a plate
forms part of a loaded joint, it is the rivets which produce stress
in it. If the plate be considered, very generally, as made up of
simple beams, each loaded in the centre by one rivet, the stress
would be a maximum at the walls of the hole and reach its mini-
mum at the centre of the net plate-section.
46. The Friction of Riveted Joints.
Many tests to determine the resistance to slip of riveted joints
of various types, have been made at the U. S. Arsenal, Water-
town, Mass., the results of which will be found in the various
annual reports to the Secretary of War. M. Dupuy,* also, has
conducted extensive experiments with regard to the magnitude
and effect of the friction of the joint. The researches of Professor
C. Bach, of Stuttgart, have been exhaustive and he has presented
strong argument in favor of the theory which bases the design of
riveted joints upon their frictional resistance alone. The review
of his conclusions which follows, has been summarized from the
matter, as set forth in his work on Machine Design^
The effect, upon the frictional resistance, of the temperature, the
length of the shank, the number of rivet-rows, etc., is considered
separately. Unless otherwise stated, the joint was not calked.
Consider :
i. THE TEMPERATURE AT RIVETING, either cherry -red or rose-
red. Notation : t = thickness of plate, d = diameter of rivet,
/= length of shank. One kilogramme (kg.) — 2.20462 Ibs.,
avoirdupois ; one millimetre (mm.} ==• 0.03937 in. ; one square
centimetre (qcm.) = 0.155 sq. in.
(a) Lap-joint; /= 13 mm., d = 19 mm., 1=26 mm. The
lower (cherry-red) temperature gave sometimes a greater friction
than the higher, averaging 1,199 to l>ll$ kS- Per 4*™- of rive*
cross-section.
* An. d. Fonts et Chauss6es.
f " Die Maschinen-Elemente," 1901, pp. 165-170.
1 88 MACHINE DESIGN.
(d) Lap-joint with inside and outside welt-strips ; /= 13 mm.,
d = 19 mm., /= 52 mm., t (each welt) = 13 mm. Owing to the
doubled length of shank, there was given, at the higher tempera-
ture, a greater friction, averaging 1,769 to 1,305 kg. per qcm. of
rivet cross-section.
Experiments by Considere confirm (a) and apparently contradict
(b\ He found, that, at a riveting temperature of 600° to 700°
C., the friction reached a maximum, being then greater than when
the rivet was at a rose-red heat, say 1000° C. Prof. Bach con-
cludes that it is not the temperature of the rivet at insertion which
is important but that at the moment of finishing the point. Also,
in machine-riveting, his experiments showed, that, within limits,
the friction increased with the duration of the pressure upon the
rivet. The resistance was affected further by the temperature, at
finishing, of the portions of plate adjacent to the rivet.
2. LENGTH OF RIVET-SHANK. — The shank of greater length
produced the higher resistance. Thus :
(a) Lap joint ; /= 7.5 mm., d= 16 mm., 1= 15 mm. Resist-
ance, 846 kg. per qcm. of rivet cross-section.
Lap joint ; / = 7.5 mm., d= 16 mm., I = 31 mm. Resistance,
1,037 to 1,1 1 1 kg. per qcm. of rivet cross-section.
(&) Lap joint; /= 13 mm., ^=19 mm., 1= 26 mm. Resist
ance, 1,115 kg. per qcm. of rivet cross-section.
Lap joint; t= 13 mm., ^=19 mm., I •= 52 mm. Resistance,
1,769 kg. per qcm. of rivet cross-section.
The slip with varying loads is shown by the following experi-
ments :
(a) Single-riveted lap-joint; ^=13 mm., d = 19 mm., 1—26
mm., pitch =/ = 48 mm., number of rivets = n — 3, diameter of
rivet-hole = 20 mm.
Load. Load on Rivet Area. Slip.
10,000 kg. I,1 74 kg. per gem. o
11,000 " 1,291 " 0.0125 mm.
15,000 " 1,761 " o.i "
20,000 " 2,348 " 1.175 "
(fr) Same joint as (a), excepting that length of shank = 52 mm.,
a plate, 13 mm. thick, having been laid on each side of the seam.
It will be seen that the resistance of (&) was 15,000 kg., while
that of (a) was 10,000; but that, with (b\ the slip increased far
more rapidly, and, at 20,000 kg. load, was much greater.
RIVETED JOINTS. 189
Load. Load on Ri
15,000 kg. 1,761 kg. pe
l6,OOO
17,000
18,000
19,000
2O,OOO
i,995
2,"3
2,230
2,348
SKp.
o.
0.004 '
0.009
O.202
1-255
1.405
The breaking strengths of these joints were :
Kg. per gem., Rivet-section.
(«) 3,522
(*) ' • • • 3,404
Prof. Bach's conclusions as to the greater length of rivet-shank
giving the greater resistance are, apparently, at variance with the
theory of contractile stresses, as given in § 45. Assuming abso-
lutely the same conditions throughout, excepting dissimilar aggre-
gate plate-thicknesses and shank-lengths, the contractile-stress,
pressure, and frictional resistance per sq. in. of rivet-section
should be the same in all cases, since St = a-r-E'm (124). The
explanation of this seeming discrepancy lies probably in the fact
that, with the shorter shank, the expansion, while the same per-
centage of the length, is a less amount actually ; and, therefore,
in riveting, will be more affected by the same looseness of plates
or other defect, than the expanded length of the longer shank.
3. NUMBER OF Rows OF RIVETS. — The frictional resistance
to slip does not increase proportionately in passing from single to
multiple riveting, owing to the fact that the elasticity of the plate
prevents the regular and proportionate distribution of the load
upon the joint Thus, in a lap-joint, chain-riveting, 6 rows,
t= 12 mm., d= 19 mm., diameter of rivet-hole = 20 mm., width
of plate = 1 50 mm., in the plane of the cross-section of the rivets
slip, was observed at
6,000 kg., load in 1st and 6th rows.
8,000 " " 2d " 5th "
11,000 " " 3d " 4th "
The slip, therefore, was greater in the outside rows, owing to the
unequal distribution of the load.
4. DOUBLE-STRAPPED BUTT-JOINTS. — The single-riveted butt,
as compared with the single-riveted lap-joint, gives a somewhat
less resistance. Thus, /(plate) = 13 to 14 mm., /(strap) = 9 mm.,
190 MACHINE DESIGN.
d= 19 mm., resistance = 906 kg. per qcm., while, in the single-
riveted lap-joint, with t = 12.5 mm. and ^=19 mm., the resist-
ance = i, 1 86 kg. per qcm. This difference arises from the ab-
sence of plate-bending in the butt-joint, the plates and load being
in the same plane, while, in the lap-seam, the eccentricity of the
load, in bending the plates, clamps them more closely and gives
greater friction. Multiple riveting, in butt-joints, is affected by
the elasticity of the plate in a manner similar to that which has
been described for multiple lap-riveting.
5. MACHINE RIVETING. — In machine-riveting, the magnitude
of slip-resistance depends greatly upon the duration of pressure
upon the rivet. With rapid work, the friction may be less than
in hand-riveting. With sufficient pressure and duration the re-
verse is true, especially when thick plates and, consequently,
large rivets are employed.
6. INFLUENCE OF CALKING. — The effect of calking is shown,
in detail, by the results, as follows, of experiments upon 25 lap-
joints, in each of which /= 12 mm., d= 19.5 mm., diameter of
holes = 20.5 mm. The holes were drilled and the joints hand-
riveted.
Plates. Rivet-Heads.
(a) 5 Joints. Not Caulked. Not Calked.
(3) 5 " Caulked both sides.
(c) 5 " " one side. Calked one side.
(d) 5 " " both sides. " " "
(e) 5 " " " " " both sides.
The results, in kg. per qcm. of rivet cross-section, were :
Resistance to Slip. Breaking Load.
(«) 88 1 3,397
(*) 1,238 3,413
(O i,327 3,3"
(d) 1,572 3,178
(e) 1,617 3,258
Other things being equal, a greater proportional advance in fric-
tional resistance will be made by calking the heads of a short,
then a long, rivet, since that resistance depends also upon the
length of the rivet-shank.
7. RESUME. — Prof. Bach's experiments show that, (#) in good
single lap-riveting, there will be a frictional resistance ranging
from 1,000 to 1,800 kg. per qcm. of rivet cross-section, or even
RIVETED JOINTS. 191
more, according to length of shank and width of specimen tested ;
(<£) the age of the joint has an appreciable effect upon the amount
of resistance ; (c) the magnitude of the resistance is fully adequate
to transmit the load generally placed upon a riveted joint ; (d]
calking increases considerably the resistance, a fact which is of
importance, not only in pressure-joints but also in structural work
in cases where inaccessibility makes good riveting difficult.
CHAPTER IV.*
RIVETED JOINTS: TESTS AND DATA FROM PRACTICE.
47. Tests of Multiple-Riveted, Double-Strapped Butt-joints.
The tests whose records follow were conducted under the
supervision of the Ordnance Department, U. S. Army, at the
Watertown Arsenal in 1887, for the Bureau of Steam Engineer-
ing, U. S. Navy. They are of especial value, since the specimens
were unusually wide, the plates thick, and multiple riveting was
used, the conditions thus corresponding with those of boiler-joints
for moderate pressures. The plates were of open-hearth steel
with drilled holes and sheared edges and the joints were riveted by
steam. The strips tested to show the quality of the metal were
of the same grade, although not from the same sheets, as the
joints. The mean tensile strength of three such specimens for
each thickness was used in computing the efficiencies of the joints.
The plate -thickness varied somewhat at different edges. After
testing, the rivet heads were planed from a number of the joints,
the rivets driven out and butt-straps removed, and the elongation
of the rivet-holes measured. Owing to the absence of tensile
tests of the unperfo rated plate, the efficiencies of joints Iv /2, /3
were not computed.
The unequal distribution of the load among the various rows
of rivets is shown clearly by the elongations of the rivet-holes.
Thus, in the joint, B2, Fig. 82 (f-in. plate, |-in. steel rivets) which
failed by rupture at 50,200 Ibs. apparent tension on net plate sec-
tion, the average elongations on the right of the seam were, in the
outer row, 0.284 in.; in the central row, 0.173 in.; and, in the
inner row, 0.054 in. Again, the average elongation of the two
*For the data from practice given in this chapter, the author is indebted to the
Bureau of Steam Engineering, U. S. Navy ; the Baldwin Locomotive Works ; Messrs.
R. D. Wood and Company; J. M. Allen, Esq., President, The Hartford Steam Boiler
Inspection and Insurance Company ; E. D. Meier, Esq., of the American Boiler Manu-
facturers' Association; the Editor of the American Machinist; C. C. Schneider, Esq.,
Vice-President, American Bridge Company ; the Bureau of Construction and Repair,
U. S. Navy ; Edwin S. Cramp, Esq., Vice-President, the William Cramp Ship and
Engine Building Company; and W. Irving Comes, Esq., Secretary, the American
Bureau of Shipping.
I92
RIVETED JOINTS. 193
end holes in the outer row was 0.31 in.; that of the middle hole,
same row, was 0.26 in. Similar values for the central row were
0.22 in, and 0.145 in.; and, for the inner row, 0.065 m- and 0.05 in.
The stress in the joint section was, therefore, greatest at the edges.
.0 ! 0
iO O
FIG. 82.
As shown in Fig. 82, the metal drew down in thickness, in diag-
onal and zigzag lines between the rivet-holes of adjacent rows,
although the space thus traversed was greater than that along the
pitch-line. All riveting, through two butt-straps, was zigzag with
no rivets omitted.
In the tables which follow, tests No. 905 and 909 are sample
records of the strips tested to show the quality of the metal. The
succeeding tables give tension tests of metal from the fractured
ends of the joints, the tests of the joints, and data as to the mode
and appearance of fracture. The widths of the various classes of
joint-specimens tested, were :
A, B, K, 20 ins.; D, 17 ins.; E, 16.5 ins.; G, 15.75 ins-; -^
20.12 ins.; /, 14.39 ins.
TEST No. 905. — SPECIMEN C2. — THICKNESS, FIVE EIGHTHS INCH.
Gauged length, 15 inches ; cross section, 12" X •^>39// > area, 7-668 square inches.
Applied Loads.
In Gauged Length.
Remarks.
Total.
^inT"6
Elongation.
Set.
Pounds.
Pounds.
Inches.
Inches.
7,668
I.OOO
0.0000
o.oooo Initial load.
38,340
5,000
.0017
o.oooo
76,680
10,000
.0042
o.oooo
115,020
15,000
.0065
o.oooo
^
153,360
20,000
.0089
o.oooo
M
161,028
21,000
.0094
^"
168,696
22,000
.0098
n
176,364
23,000
.0103
-
184,032
24,000
.0108
^b
191,700
25,000
.0112
— .0001
6
194,000
.0113
^ "3
196,000
.0115
« i
198,000
*OIl6
v~ ^
200,000
.0118
lo
2O^ OOO
.OI2O
_ -s
204,000
.0123
o> So
206,000
.0125
Tt- 'O
208,000
.0127
&f^
210,000
.0130
212,000
•OI33
^ ^ oo
.214,000
.0136
S5^?
2l6,OOO
.0140
3 °°. -
2l8,OOO
.0144
* £5-0
220,000
.0150
%~ c 's
222,000
28,950
.0154
Elastic limit. % . 2 tj
224,000
.0162
- rt c
226,000
.0170
V* •» JL
228,000
.0183
^ c§ «
230,000
.0213
%• ^
232,000
.0277
• it *S
234,000
.0480
%" ^ £
236,000
•0995
^ ^
237,708
31,000
•2175
1 '« u'
245,376
32,000
•23
V a €
253,044
33,000
•25
°1 o* g
260,712
34,000
.28
v" <» -2
268,380
35,ooo
•31
g £ >.
276,048
36,000
•33
- •* S
283,716
37,000
•37
^ || ^
291,384
38,000
•41
**' ^) "•>
299,052
39,000
•45
ui 't ^
306,720
40,000
•5o
0 X ^
314? 3&^
41,000
•54
"•2 ^ 1)
322,056
42,000
•59
81 vS 3
329,724
43,000
.66
"a ^ 2
337,392
44,000
•71
C ^7 **^
345,060
45,000
.78
*S 2 "o
352,728
46,000
.86
Cgo
360,396
47,000
•95
•2 ^^ ^
368,064
48,000
1.07
M ^ S
375,732
49,000
I.2I
§ I §:
383,400
50,000
1.47
s < <
391,068
51,000
1.58
398,736
52,000
i. 80
406, 404
53,ooo
2.08
414 072
54,000
2.98
414,800
0
54,ioo
0
3-42
o
5-52
Tensile strength.
= 36.8 per cent.
(p. 194)
RIVETED JOINTS.
195
TEST No. 909. — SPECIMEN Fs.— THICKNESS, SEVEN EIGHTHS INCH.
Gauged length, 15 inches; cross section, 8.5io// X $&l" > area, 7.378 square inches.
Applied loads. In gauged length.
Remarks.
Total. Per square Elongation.
| me .
Set.
Pounds.
Pounds.
Inches.
Inches.
7,378
I,OOO
O.OOOO
0.000
Initial load.
36,890
5,000
.OO2O
O.OOO
73,780
10,000
.0045
o.ooo
110,670
15,000
.0070
o.ooo
147,560
20,000
.0097
o.ooo
154,930
21,000
.0103
162,316
22,000
.0108
169,694
23,000
.0115
172,000
.0120
174,000
.0122
176,000
.0124
I78.0OO
.0127
l8o,OOO
.0130
l82,000
•0134
184,000
.0137
l86,000
.OI42
188,000
190,000
25,750
.0147
•0153
Elastic limit
192,000
.0165
194,000
.0182
196,000
•1775
206,584 28,000
•23
213,962 29,000
.26
221,340 30,000
.28
228,718 31,000
•32
236,096
32,000
•35
243,474
33,000
.38
250,852
34,ooo
•43
258,230
35,ooo
•47
265,608
36,000 .52
272,986
37,000 .57
280,364
38,000
.63
287,742
39,ooo
.69
295,120
40,000
•74
302,498
41,000
.84
309,876
42,000
•92
317,254
43,000
I.OI
324,632
44,000
1.16
332,010
45,000
1.28
339,388
46,000
1.47
346,766
47,000
1.67
354,H6
48,000
1.98
361,524
365,700
0
49,000
49,570
0
2.48
3-3*
5.31
Tensile strength.
= 35.4 per cent
Elongation of inch sections: .17", .20* 22", .25", .29", -36", •49//, *Ml
VJ", .29", .25*, .21", .\l", .12".
Area at fracture, 6.43" X &* = 3-73 square inches. Contraction 494 per cent
Appearance of fracture, silky, lamellar. Fracture open at the middle, .40" ; edges
closed.
196
MACHINE DESIGN.
TABLE XLI.
TESTS OF RIVETED JOINTS FOR BUREAU OF STEAM ENGINEERING,
,
I
Sectional Area of
Plate.
i
"8
8
Style of Joint.
fa
Size and Kind of Rivets
and Holes.
I
1
1*
Gross.
Net.
fc
Inch.
Sq inches. &7 inches.
910
912
J
(Double riveted ; dou-
ble butt straps £ in.
thick ; 3 in. pitch.
I!
}\ inch steel rivets;
|| inch drilled
holes.
f 13.22
13.08
I 12.41
10.12
IO.OI
9-50
913
914
915
Bi
B2
Treble riveted ; dou-
- ble butt straps £ in.
thick ; 3T9^ in. pitch.
II
)£ inch steel rivets ;
|f inch drilled
holes.
'12.81 10.31
- 12.69 10.21
12.691 10.21
Ql6
Dj
1 Double riveted ; dou-
$ j ~) i inch steel rivets ; I
( 14.671 10.09
917
D2
ble butt straps f in.
| 1 \ i A inch drilled
-^ 14.646 10.07
918
Ds
thick ; 3| in. pitch.
[ I J holes.
(14.705 io.ii
919
920
921
1
1 Treble riveted ; dou-
ble butt straps J in.
thick ; 4T9^ in. pitch.
£ ^| I inch steel rivets ;
• \ I i-j-1^ inch drilled .
| i J holes. ;
14.322 10.63
- 14438 10.72
. 14.256 10.58
Leavitt joint ; double
butt straps ; one of
usual width for dou-
ble riveting and £
inch thick ; other, f
3 plates ; ITV inch
iron rivets ; I \
922
G,
inch thick and ex-
|
in. drilled holes.
I3.78I
10.93
923
G2
t- tended far enough
£
}-2 plates; i}
j 13.852 10.985
924
G8
on each side to re-
£
in. iron rivets ;
I3.74I
10.90
ceive five additional
ij inch drilled
rivets in two rows.
holes.
Pitch of double rivet-
ing on inner rows,
2| inch.
,'
1
1 Leavitt joint ; same
925
926
927
H;
arrangement as in G
series except that
wide butt strap has
six rivets on each
side beyond narrow
strap. Pitch of dou-
ble riveting, 7.\
1
3 plates ; I inch
iron rivets ; ly1^
in. drilled holes.
2 plates ; I \ inch
iron rivets ; I J j
inch drilled holes.
1
13.252
•! 12.776
1 12.81
10.537
10.154
10.186
inch.
Leavitt joint ; same
f
arrangement as in G
928
i,
series except that the
five rivets in ends of
A
T| inch iron rivets ;
8.287
6.820
929
i
wide butt strap are
• K
\- i inch drilled
•( 8.21 1
6-755
930
i»
differently spaced.
S
holes.
8.28
6.81
Pitch of double riv-
eting on inner rows,
2£ inch.
931
KI
(Treble riveted ; dou-
| ; ) f inch iron rivets; ("12.36 9.94
932
933
i
ble butt straps \ in.
thick ; 3T9^ in. pitch.
- | I || inch drilled
Jyj holes.
4 12.93 i I0-4o
( 12.98 10.44
* No figures given because no tests were made of this thickness of metal for tensile
strength.
RIVETED JOINTS.
TABLE XLI. — Continued.
UNITED STATES NAVY DEPARTMENT.
I97
^8*
Maximum Stress on Joint per Square Inch.
Bearing
Shearing:
Sal
Surface
of Rivets.
Area ot
Rivets.
«5 «5
p*
H
Tension
on Gross
Section
of Plate.
Tension
on Net
Section
of Plate.
Compression
on Bearing
Surface of
Rivets.
Shearing
on Rivets.
Efficiency
of Joint.
Sq. inches.
6.72
6.64
6.30
Sq.inches.
12.46
12.46
12.46
Pounds.
53.710
53.710
53.710
Pounds.
42,860
40,960
42,720
Pounds.
tss
55,800
Pounds.
84,320
80,690
84, 140
Pounds.
45,470
43,ooo
42,540
Percent.
79.8 a
76.2 b
79-5 c
8.01
7-93
7-94
15-34
15-34
15-34
53.710
53.710
53.7'Q
43,460
40,390
44,290
54,040
50,200
55,050
69,560
64,630
70,790
36,320
33,4io
36,640
80.9 d
75-2 e
82.5 f
8.25
8.23
8.27
15-96
15-96
15.96
5LI90
51,190
5LI90
35,l8o
36,190
35,780
51,1.50
52,640
52,050
62,560
64,410
63,630
32,340
33,2io
32,970
68.7 g
70.7 h
69.9 i
10.15
10.23
I9-5J
19-51
5LI90
51,190
37,910
38,400
51,080
51,720
53,500
54,190
27,830
28,420
74-1 J
75.0 k
10.10
19-51
51,190
37.950
51,130
53,560
27,730
74-1 1
16.30
16.38
16.26
28.00
28.00
28.00
5LI90
51,190
51,190
40,8lO
41,740
40,120
51,460
52,640
50,580
34,500
35,300
33,910
20,090
20,650
19,690
79-7 m
81.5 n
78.4 o
14-045
13.548
30.41
30.41
53,710
53,710
42,820
45.300
53,860
51,000
40,410
42,720
18,660
19,030
79-7 P
84-3 q
I3.576
30.41
53.710
46,070
57,940
43.470
I9,4io
85.8 r
8.057
1 8.06
*
42,250
51,330
43,450
19,380
* s
7-994
1 8.06
*
40,800
49,590
41,910
18,550
* t
8.05
1 8.06
*
40,720
49,520
41,890
18,670
* u
7-773
8.08
8.ii
15-34
15-34
15-34
53.710
53.710
53.710
43,600
43,260
43,000
54,220
53,780
53.46o
69,720
69,220
68,820
35,130
36,460
36,390
81.2 v
80.5 w
80.1 x
Figures in heavy-faced type indicate manner of failure.
For explanation of reference letters in last column, see next page.
I98 MACHINE DESIGN.
MODE OF FRACTURE AND APPEARANCE OF FRACTURED SURFACES.
a. Sheared the rivets in one plane in Plate A ; started a fracture at side of one rivet
hole in outside row of riveting.
b. Fractured Plate A along outside row of rivet holes. Appearance of fractures,
silky, lamellar.
c. Fractured Plate A along outside row of rivet holes ; sheared ( double shear ) six
rivets in Plate B. Appearance of fractures, silky, slight lamination.
d. Fractured Plate A along outside row of rivet holes. Appearance of fractures, silky.
e. Fractured Plate A along outside row of rivet holes. Appearance of fractures,
silky, slightly lamellar.
f. Fractured Plate A along outside row of rivet holes. Appearance of fractures,
silky, lamellar.
g. Fractured Plate B along outside row of rivet holes ; tore apart from one edge. Frac-
tures also started in Plate A at opposite edge. Appearance of fractures, silky, lamellar.
h. Fractured both plates along outside row of rivet holes. The separation of Plate
A was complete ; Plate B fractured through four sections. Appearance of fractures,
silky, slightly lamellar.
i. Fractured both plates along outside row of rivet holes. Plate B did not separate
at one edge. Appearance of fractures, silky, slightly lamellar ; metal well drawn down.
j. Fractured Plate B, taking zigzag course through two outside rows of rivet holes.
Appearance of fractures, silky in part, granular in part ; the metal in the silky sections
well drawn down, the granular sections not much reduced in thickness, the extremes
of thickness after fracture being .665" in the silky and .840" in the granular metal.
A loud report accompanied the fracture of the granular metal.
k. Fractured Plate A, taking a zigzag course through two outer rows of rivet holes.
Appearance of fracture, silky, slightly lamellar.
/. Fractured Plate B, taking a zigzag course through two outside rows of rivet
holes. Fracture silky, slightly lamellar.
m. Fractured Plate A along outside row of rivet holes. Fracture silky, slightly
lamellar. Mean thickness at fracture, .56 inch.
«. Fractured Plate A along outside row of rivet holes. Fracture silky, slightly lamellar.
o. Fractured Plate A along outside row of rivet holes. Fracture silky, lamellar.
One seam in fractured surface $£ff wide.
p. Fractured Plate A along outside row of rivet holes. Fracture, silky lamellar.
q. Fracture in same place as Hr Appearance, silky, slightly lamellar.
r. Fractured Plate B along outside row of rivet holes. Appearance, silky, slightly
lamellar. Plates open at butt joint ^ inch.
s. Fractured Plate B along outside row of rivets, beginning the fractures at edges
and extending from rivet holes toward middle of plate. Fracture silky, slightly
lamellar ; metal well drawn down.
t. Fractured Plate A along outside row of rivets. Appearance of fracture, silky,
slight lamination.
u. Fractured Plate A along outside row of rivets. Appearance of fracture, silky,
slightly lamellar ; metal well drawn down.
v. Fractured Plate B ; followed outside row of rivet holes in part, and thence,
through inside rows, to end of plate ; sheared two end rivets. Fractures silky,
slightly lamellar.
w. Fractured Plate A along outside row of rivet holes, except end sections and one
middle section. Appearance, silky, lamellar.
x. Sheared every rivet in the joint in both plates. The under butt strap dropped
to the floor. Double shear in Plate A, .three rivets ; single shear in Plate B, with the
exception of one rivet, which sheared in two planes.
RIVETED JOINTS.
I99
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200 MACHINE DESIGN.
TENSION TESTS OF STRIPS CUT FROM FRACTURED ENDS OF RIVETED JOINTS.
These strips were taken from the middle of the width of the joint plates and parallel
to the direction the joints were pulled.
Two strips were taken from each ; one was annealed by heating bright red and cool-
ing in the open air ; the duplicates were not annealed and were tested as taken from the
fractured joint.
When the annealed specimens were at the maximum temperature, centre-punch
marks, 10" apart, were stamped on one edge, and about the time the color had left
them they were marked again on the other edge. After cooling to 70° Fahr. the dis-
tances between these marks were measured.
The amount of contraction, therefore, indicates approximately the heat at which the
strips were annealed.
48. Riveting Machines.
Rivets are driven either by a succession of relatively light blows,
as in hand-work and by pneumatic hammers, or by heavy and
sustained pressure, as in hydraulic machines. In the latter pro-
cess, the continuous and powerful compression of the hot rivet-
blank upsets the shank, fills the hole, and closes the plates, while
in hammering, especially if the blows are light, the head may be
formed before the shank is upset fully, the rivet may be more or
less loose in its hole, and the impact tends to crystallize the metal.
Owing, however, to the extremely rapid action of the pneumatic
hammer, excellent results in hull and structural work have been
obtained by its use. When, as in marine cylindrical boilers, the
plates are thick and the rivets large, hydraulic riveting is necessary
in order to secure tight joints.
Riveting machines may be " fixed " and powerful, as for steam
boilers and shop-riveting in general, or light and portable, as in
the types used for hull work and field-rivets. The essential parts
of any machine are a stationary "stake" holding the die which
engages the rivet-head and a piston or ram driving a second die
which upsets the shank and forms the point. The stake or its
equivalent forms part of the framing of the machine. In the pneu-
matic hammer, it is replaced by an air-pressure mechanism known
as the "pneumatic holder-on." In portable riveters, the riveting
plunger may be direct-acting or be operated through linkage from
the piston rod. An auxiliary cylinder, actuating a plate-closing
device, has been used for clamping the joint before the rivet is upset.
Either steam, hydraulic, or pneumatic power is used in riveting
machines. All are applied to drive by pressure and the latter, in
the pneumatic hammer, by impact as well. Steam has the ad-
vantages of familiar mechanism and the absence of an accumulator
RIVETED JOINTS.
201
or compressor-plant ; but its relatively low pressure makes large
cylinders necessary, and, owing to its condensation, expansibility,
and the leakage inevitable with piston-valves, the pressure de-
veloped is not uniform and is delivered largely in the form of a
blow which tends to crystallize the rivet. These objections, ex-
cept with regard to condensation, apply in the main to pneumatic
machines, although their portability gives them a wide field. In
hydraulic riveting, a pressure of 1,500 Ibs. per sq. in. is used.
This gives a small cylinder requiring, relatively, but little fluid,
while the practically incompressible and inexpansible character of
the latter makes the driving stroke a powerful and uniform
squeezing of the metal which fills the hole and forms the point
without impact. The high pressure, however, necessitates strong
and accurately made joints, and, with careless handling in winter
weather, waste water in cylinders or pipes may freeze. Since
FIG. 83.
2O2
MACHINE DESIGN.
the fluid in the driving line is under 1,500 Ibs. pressure, its
liability to freezing is slight. A mixture of one third crude
glycerine and two thirds water is used with success in Canada
and northern Russia.
Riveting machines, in their power, form, and fixed or portable
character, present a wide variety of types. The descriptions given
below refer to the two which may be considered as the extremes
of this range.
i. HYDRAULIC FIXED RIVETER. — Fig. 83 shows in elevation
the riveter of this type built by Messrs. R. D. Wood and Company.
It is of "triple power," i. e., it exerts any one of three pressures upon the rivet,
thus fitting it not only for work of the heaviest character, but also for that upon light
plates which would be crushed by the pressures required for rivets of large diameter.
The powers and sizes of the standard machines of this type are :
No. i— 50, 35 or 15 tons power 5', 6', 7', 8', 9/6", IO'D" and 12' gaps.
" 2— 60, 40 " 20 " " 5', 6', T, 8', 9'6", io'6" " 12' "
" 3— 75, 5o " 25 " " T, 8', io'6", 12' " 17' "
" 4—100, 67 " 33 " " 8', io'6", 12' " 17' "
" 5 — 150, 100 " 50 " " 8', 9/6//, io'6", i2/ " 17' "
« 6— 180, 120 " 60 " " 8', 9'6", lo'W, 12' " \T "
Usual working pressure, 1,500 pounds per square inch.
The frame is a single casting to which the cylinder is bolted, the joint being tongued
and grooved to ensure absolute rigidity. The cylinder, glands, rams, the framing, and
hence the stakes, are made from open-hearth steel castings, having an ultimate tensile
strength of 70,000 Ibs. per sq. in., an elastic limit of 40,000 Ibs. per sq. in., and an
elongation of 20 per cent, in an 8-in. test-piece.
FIG. 84.
Fig. 84 gives a vertical section through a riveting head, with rams having inside
packing of leather. The section in Fig. 85 is similar, excepting that the n>ms are
packed outside with flax. In the latter arrangement, the packing in the three stuffing
boxes is held in place by outside glands and is, hence, accessible readily for repacking
or adjustment.
RIVETED JOINTS.
203
ca
FIG. 85.
The operation of the ram is the same in each case. Referring to Fig. 85, it will be
seen that there are tandem cylinders, A and B, in which the duplex ram, CD, carrying
the riveting head, E, reciprocates. In the additional cylinder, F, the "pull-back
ram," G, moves. The riveter is fitted with a distributing valve and an operating valve.
The former is practically a double-stop valve and may be adjusted in any one of three
positions, viz. : With the water passage to the small cylinder, A, open and that to the
large cylinder, B, closed ; with the passage open to B and closed to A ; with the pas-
sages open to both cylinders. The ram-areas upon which the accumulator-pressure acts
are : With the first adjustment, that of cylinder, A ; with the second, that of the dif-
ference in area between cylinders B and A ; and, with the third, the full area of cylin-
der, B. The operating valve is of the balanced piston type with leather packing. The
accumulator-pressure is led directly to the pull-back ram without passing through either
of the valves as above. This ram is, hence, always in action and its back pressure must
be overcome by that in the driving cylinders before the ram, CD, can advance. In
riveting, the operator first sets the distributing valve for the pressure desired ; then
moves the plates until the rivet is opposite the dies and throws the operating lever.
Until the latter is withdrawn to its original position, the pressure remains upon the
rivet. Since the operation of the type shown in Fig. 84 is the same as that just
described, the reference-letters for similar parts in both are identical.
FIG. 86.
2. PNEUMATIC RIVETING HAMMER. — Fig. 86 * gives a longi-
tudinal section of the Boyer " Long-Stroke Pneumatic Hammer."
Compressed air is admitted to the hammer through a hose coupled at the lower ex-
tremity of the handle. The admission is controlled by a main throttle valve of the
American Machinist, April 25, 1901.
204 MACHINE DESIGN.
balanced piston type. This valve is closed by a spring and is depressed and opened
by the throttle-lever, /, which is pressed by the thumb of the operator. The riveting
die, a, is held in position by the light clip, b, only. Hence, if it is not pressed against
the rivet, the first blow of the hammer, r, would discharge it like a bullet. To prevent
this, an auxiliary spring-pressed throttle or stop- valve, c, is fitted, which valve is oper-
ated by two rods, as d, which extend through the body of the hammer and have their
outer ends resting upon the ring e, against which the die-shank abuts. When, there-
fore, the die is not forced firmly against a rivet — although the main throttle- valve may
be open — the auxiliary valve c will be seated by air and spring pressure and the rods
d, ring e, and die a, will be moved slightly to the right. Since both valves must be
open before the piston, r, will act, the auxiliary valve, c, forms a safeguard.
The valves which control the air in its pasage to and from the ends of the cylinder
are shown at/and^. They are hollow and of short stroke. Rods, as h, similar to
d, lie between the valves in the walls of the cylinder. As one valve moves toward
the centre of the cylinder to admit air at its end, it, through the rods, pushes the other
valve away from the centre, so that the exhaust is open at that end.
In the position shown, the air enters the inner end of the cylinder, as indicated by
the arrow i, and drives the piston, r, outward, the exhaust escaping as shown at j.
When the outer end of the piston enters the valve, g, it compresses the air before it,
forming a cushion which, acting upon the annular end of g, pushes the latter to the left
and hence valve /also through the rods, h. In this position, the ports which were
open previously are closed, port k is open to live air, and exhaust occurs through port
/. The holes in which the rods, d, lie, serve also as passages for air to the port k. On
the completion of the return stroke, the piston enters the inner valve, _/) and the valves are
driven to the right.
FIG. 87.
This hammer weighs about 17 Ibs. and is made for driving
rivets from I in. to \\ in., diameter. It is stated that it requires
20 cubic feet of free air per minute. The air-pressure which de-
termines the force of the blow, ranges from 90 to 100 Ibs. per
sq. in., The hammer may be used without a supporting frame.
RIVETED JOINTS. 205
Its operation, with such frame and with the pneumatic holder-on,
is illustrated by Fig. 87.
49. Riveted Joints, Marine Boilers.
Marine cylindrical boilers are of the internally fired type. Fig.
88 shows one half of a longitudinal and one half of a transverse
section of the double-ended boilers of the U. S. Battleship Kear-
sargc. The diameter is 15 ft., 8 in.; the length, 21 ft. As
FIG.
shown, the shell, A, is made of three courses of four plates each ;
the front and back heads, B, are each built up of three plates, the
upper of which is curved backward to meet the shell ; the furnaces
are cylindrical and are corrugated to give strength ; the combus-
tion chamber, C (one to each pair of furnaces and two to each
end), is built of flat plates throughout, except at the outer side
which is curved so that it is concentric with the shell. The boiler
is braced by stays, JD, in the steam and water spaces, girders, E,
upon the tops of the combustion chambers, screw-stays at the sides
and backs of the latter, and by stay -tubes.
206
MACHINE DESIGN.
The longitudinal seams of the shell are double-strapped butt-
joints, treble-riveted ; the circumferential seams (central) are lap-
joints, treble-riveted ; the joints of heads with shell are lapped and
double-riveted, except with the curved plates which are treble-
riveted ; the head plates are united by lapped seams — the upper,
quadruple, the lower, double-riveted ; all joints in furnaces and
combustion chambers are single-riveted lap seams.
i. RIVET AND PLATE METALS. — The physical and chemical
characteristics of rivet-metals, as prescribed in the specifications
(1901) of the Bureau of Steam Engineering, U. S. Navy, have
been given in § 32. The tests for rivets, as laid down in these
specifications, are :
Rivets. — Samples from each lot are to stand the following tests without fracture,
test (a) being applied to one lot, and (6) to a second, etc. :
(a) Bend double cold to a curve of which the inner diameter is equal to the diameter
of the rivet.
(3) Bend double hot through an angle of 180° flat back.
(c) The head to be flattened when hot without cracking at the edges until its
diameter is two and one half times the diameter of the shank.
(a ) The shanks of sample rivets to be nicked on one side and bent cold to show the
quality of the material.
Surface Inspection. — Rivets shall be true to form, concentric, and free from in-
jurious scale, fins, seams, and all other injurious defects. If the material is found to be
very uniform and none of the tests made of a series of lots fail, the inspector may discon-
tinue the tests after he has made enough to satisfy himself that the whole of the material
on the order is satisfactory.
Note. — In measuring the diameter of rivets the inspector will allow for the trade
custom of making rivets with an actual diameter slightly (about y1^ of an inch) less than
the nominal diameter.
Class.
Material.
Mini-
mum
Tensile
Strength.
Mini-
mum
Elastic
Limit.
Elon-
gation.
Maximum
Amount of.
Cold Bend about an
Inner Diameter.
P.
S.
Class A.
Class B.
Class C.»
Open-hearth
steel.
Open-hearth
steel.
Open-hearth
or Besse-
mer.
Lbs. per
sg. in.
70,000
6o,OOO
To be ir
the /
Struct
Lbs. per.
sq. in.
37,000
32,000
accorda
Lssociatioi
ural Steel
Per ct. in
8 inches.
22
25
ace with
i of Am
," revisec
.04
.04
the «
erican
ljuly
.03
•03
Stanc
Stee
1896
Equal to thick-
ness of plate and
through I 80°.
Flat back through
1 80°.
ard Specifications of
Manufacturers for
* Class C plates, shapes, etc., will be inspected at the building yard and not at the
place of manufacture except upon special request of the contractor. No physical or
chemical test will be made unless from the appearance of the plates giving evidence of
overheating, cold-rolling, etc., or for other reasons, the inspector has doubts as to their
fitness for the purpose for which they are intended.
RIVETED JOINTS.
207
The physical and chemical characteristics of steel boiler-plate,
as similarly prescribed, are :
1. The physical and chemical characteristics of steel boiler-plate are to be in
accordance with the table on page 206.
2. Kind of Material. — Steel for boiler-plates of all grades (except Class C) shall
be made by the open-hearth process, and shall contain not more than four one-hun-
dredths of I per cent, of phosphorus, and not more than three one-hundredths of I per
cent, of sulphur.
2. PROPORTIONS OF RIVETS. — The standard boiler rivet for the
U. S. Navy is of the "pan-head," or conical frustum, type. The
head and point are alike. Table X LI I. gives the proportions. In
this table, a is the diameter of the rivet, b the greatest and d the
least diameter of the head, and c is the height of the latter. The
angle of the sides is about 65° in the i-in. rivet, a and d are
equal.
TABLE XLII.
(BOILER RIVETS, U. S. NAVY.)
a
3
c
^
Wt. of
lo-Heads.
r
jl"
1"
f
.331 Ibs.
•531
•713
i
|
A
f
1.007
il
J
f
$
1-373
|
A
1
f
I-55I
it
A
ii
i.t
2.032
^
A
ii
^.
2.258
it
i
|
if
ilf
2.871
3.584
i_i
it
it
iA
3-91
i £
- it
ii
4.761
t,
i
iA
5-17
i
if
i?
6.215
£A
i
i
TA
7-391
The rivet-heads used for boilers at the Union Iron Works are
" button -head " or spherical. The proportions are :
Diameter of shank = d ;
head = f</+Ty;
Depth " =\d.
3. PROPORTIONS OF JOINTS. — The following tables give the
proportions of the principal seams of typical cylindrical boilers
of the U. S. Navy. The plates and rivets are of steel, d is the
diameter of the rivet-hole, / is the greatest pitch, V is the
208
MACHINE DESIGN.
distance between the rivet- rows in staggered riveting, and P\ the
similar distance between the outer and the next row, when alter-
nate rivets in the outer row are omitted. The general dimensions
and thickness of sheets are :
t
%
I
a
3
!!
180
180
180
Diameter.
II
i
1
Thickness of Sheets.
I
Head.
fa
!«'
H£
P
Butt Straps.
1
2
S
|
§
i
15' 8"
10 6
7 9t
20' 10"
10 6
9 9t
"A
I
if
1
|
I
1
|
1
t
1
The proportions of the joints are :
ll
Seam.
Kind of Joint.
d
/
V
^
*
I
Shell, longitudinal.
Double strapped, butt, triple riveted,
zigzag, alternate rivets, outer row,
If
8&
2f
sA
.
omitted.
Double strapped, butt, triple riveted,
2
<« «
zigzag, alternate rivets, outer row,
I&
7
If
2ii iJL
omitted.
Double strapped, butt, triple riveted,
3
« «
zigzag, alternate rivets, outer row,
1
54
I 1
2 i
I 1
omitted.
i
Shell, circumferential.
Lap, triple riveted, zigzag.
i i 1 4A
2 3
2 \
2
" "
Lap, double riveted, zigzag.
if
3t
2
2A
3
a tt
tt tt tt tt
I_3
I
I— w-
I
Head to shell.
tt tt if tt
iX
4?
2
I |
2
" "
" " " "
i \
3A
I
l}£
3
tt n
tt tt tt tt
IT^T
I
I i
i
Front head, upper.
Lap, quadruple riveted, zigzag.
V, lower row = 2iV
I&
5
2f
II
Lap, triple riveted, zigzag ; alter-
2
tt n
nate rivets, middle row omitted ;
IrV
3l
If
pitch, outer rows, 3^, inner, 7^.
3
i
i
Front head, lower.
Furnace to tube sheet.
Lap, triple riveted, zigzag.
Lap, double riveted, zigzag.
Lap, single riveted.
i
3i
3j
:A
ii
2
ft ct
" " "
2
a
3
if tt
tt tt tt
2 ^
1 1
Tube-sheet to combus-
*
i
tion chamber and com-
it a tt
15
2i
ITS
bustion chamber seams.
16
4
Tube-sheet to combus-
2
tion chamber and com-
tt tt tt
I
2 3
i i
bustion chamber seams.
TS
4
Tube-sheet to combus-
3
tion chamber and com-
it tt tt
15
2 -J-
I T
bustion chamber seams.
8
5
RIVETED JOINTS.
209
4. WEIGHT OF RIVETS. — The total weight and the weight of
rivets are given below for three cylindrical boilers of large size for
the U. S. Navy. The weight given is that of the boiler simply
without fittings, such as grate-bars, valves, lagging, etc. The
plates and rivets are of steel.
Working Pres-
sure, Ibs.
Diameter.
Length.
Total Weight
of Boiler, Ibs.
Weight of
Rivets, Ibs.
Rivet-percen-
tage of Total
Weight.
160
160
135
I5'o"
I5'3"
I4'8"
1 8V
21 '3"
19/2"
135,793
149,634
108,128
5,788
6,218
5,39i
4.26
4.16
4.98
5. THE U. S. BOARD OF SUPERVISING INSPECTORS OF STEAM
VESSELS. — The regulations (Jan., 1901) of this board give the
following formulas for the proportions of single- and double-rivetod
lap-joints for both iron and steel boilers. Let :
p =r greatest pitch of rivets, ins. ;
n = number of rivets in one pitch-section ;
pd = diagonal pitch, ins. ;
d= diameter of rivets, ins. ;
T-=. thickness of plate, ins. ;
F= distance between rows of rivets, ins. ;
E = distance from edge of plate to centre of rivet, ins.
For iron plates and iron rivets :
+ d.
For steel plates and steel rivets :
For all joints :
For double ^/Jam-riveted joints, V should not be less than zd\ but it is more desirable
that V should not be less than— -^ . For ordinary, double, az^za^-riveted joints :
For double, zigzag-riveted lap joint, iron and steel :
*±4*
10
For single-riveted lap joints :
Maximum pitch = (i.3iX T) + l\-
For double-riveted lap joints :
Maximum pitch = (2.62 X T} -j- if.
210 MACHINE DESIGN.
These formulae are equivalent to those of the British Board of
Trade and are similar in many respects to those given in Traill's
handbook (§ 43). From the latter, tables of single- and double-
riveted lap joints, for both iron and steel, are quoted in, and
authorized for use by, these regulations.
6. PROCESS OF RIVETING. — U. S. Naval specifications for
boilers require that " hydraulic riveting shall be used wherever
possible. In parts where hydraulic riveting cannot be used, the
rivet-holes shall be coned and conical rivets used. Seams will be
calked on both sides in an approved manner."
50. Riveted Joints, Locomotive Boilers.
The following data refer to the practice of the Baldwin Loco-
motive Works.
i . RIVET AND PLATE METALS. — The specifications are :
Boiler and Fire- Box Steel. — All plates must be rolled from steel manufactured
by the open-hearth process, and must conform to the following chemical analysis :
BOILER STEEL.
FURNACE STEEL.
Carbon, between
o. 15 and 0.25 per cent.
1. 15 and 0.25 per cent
Phosphorus, not over
0.05 per cent.
0.03 per cent.
Manganese, "
0.45 «
0-45 "
Silicon,
0.03 "
0.03 "
Sulphur, "
0.05 "
0.035 "
No sheets will be accepted that show mechanical defects. A test strip taken length-
wise from each sheet rolled and without annealing should have a tensile strength of
60,000 pounds per square inch, and an elongation of 25 per cent, in section originally
8 inches long. Sheets will not be accepted if the test shows a tensile strength of less
than 55)000 pounds, or greater than 65,000 pounds per square inch, nor if the elonga-
tion falls below 20 per cent.
Fire-Box Copper. — Copper plates for fire-boxes must be rolled from best quality
Lake Superior ingots ; they must have a tensile strength of not less than 30,000 pounds
per square inch, and an elongation of at least 20 per cent, in section originally 2 inches
long.
Stay-Bolt Iron. — Iron for stay-bolts must be double-refined, and show an ultimate
tensile strength of at least 48,000 pounds per square inch, with a minimum elongation
of 25 per cent, in a test section 8 inches long. Pieces 24 inches long must stand bend-
ing double, both ways, without showing fracture or flaw. Iron must be rolled true to
gauges furnished, and permit of cutting a clean, sharp thread.
Copper Stay- Bolts. — Copper stay-bolts must be manufactured from the best Lake
Superior ingots ; they must have an ultimate tensile strength of not less than 30,000
pounds per square inch, and an elongation of at least 20 per cent, in section originally
2 inches long.
The general practice of this company is to use iron rivets of
the quality required as above for stay-bolts.
RIVETED JOINTS.
211
2. PROCESS OF RIVETING. — All parts of the boiler which can
be reached by fixed or portable machines are riveted by hydraulic
pressure. The latter for iron or steel rivets is :
i^ in. diameter, 100 tons.
'i " 75 "
i " 66 "
I « 50 •«
! " 33 "
f " 25 «
For copper rivets, a pressure ranging from 25 to 33 tons — never
exceeding the latter — is used. The driving head of the rivet is
made the same in height as the diameter of the shank.
3. PROPORTIONS OF JOINTS. — Tables XLIII., XLIV., XLV.,
XLVI. give the size and arrangement of rivets for various thick-
nesses of sheets in single- and double-riveted lap seams and quad-
ruple- and sextuple-riveted butt joints, with double straps unequal
in width.
TABLE XLIII.
SlNGLE-RlVETED LONGITUDINAL SEAMS. ( FOR ALL PRESSURES.) FOR OUTSIDE
FIRE-BOX SEAMS OF RADIAL STAY BOILERS.
(BALDWIN LOCOMOTIVE WORKS. )
PL
ite.
^
£
J
Thickness.
Material.
if
Iron.
1"
\"
2-
-"
Steel.
|
I
2}
•
Iron.
|
2
Steel.
3
2
Iron.
|
2
Steel.
|
2
Iron.
5
i
2
Steel.
5
i
2
Iron.
1
i
I]
•
Steel.
i
2,
'- "
i
3
"
i
3
«
i
3
ft
"
i\
.
3
i
212
MACHINE DESIGN.
TABLE XLIV.
DOUBLE-RIVETED SEAMS.
(BALDWIN LOCOMOTIVE WORKS.)
fit
te.
B
d
£>
.£
Per cent,
of solid
Thickness.
Material.
plate.
3//
Steel.
!//
2//
//
I //
^
^
62
TV
2J
A
4-
65
I
24
A
4i
65
rV
I
2f
\
4^
63
I
I
2|
i
41
63
U
H
3
iU
9i
62
i
4
3i
2
if
5i
64
TABLE XLV.
QUADRUPLE BUTT-JOINT SEAMS WITH WELDED ENDS.
(BALDWIN LOCOMOTIVE WORKS.)
Plate.
A
B
C
z>
^
F
C
H
/
^
Thickness.
Material.
r
Steel.
r
2//
2^
2I
2^
i/x
ft
f
r
8
s
3
r
t
r
81.2
82.5
82.5
o
I
2|
3
6
9 12
A
si.8
4
I
2^-
3
6
9 12
if
JLf
81.8
|
H
i
1
3i
3i
3i
6*
7
7
w|
13
14
14
f
1
81.2
80.7
80.7
RIVETED JOINTS.
TABLE XLVI.
SEXTUPLE BUTT- JOINT SEAMS WITH WELDED ENDS.
(BALDWIN LOCOMOTIVE WORKS.)
2I3
Thickness. Material.
Steel.
87
86.5
85.7
85.7
85.0
84.0
84.0
85.0
4. LOCATION OF JOINTS. — Fig. 89 gives a longitudinal section,
omitting tubes and braces, of a Radial Stay, Wagon-top, locomo-
214
MACHINE DESIGN.
tive boiler, as built by this company. In Fig. 90 there is shown
a transverse semi-section through the fire-box. The barrel is built
of three courses of one sheet each,
the thicknesses, beginning at the
furnace tube-sheet, being ^ in., ^
in., and i| in., respectively. The
remaining shell sheet is ^ in. thick.
The thicknesses of the tube-sheets,
crown-sheet, and fire-box front and
side-sheets are, respectively, y2 in.,
T/% in., and ^ in. The longitudinal
and circumferential seams of the
barrel are, respectively, quadruple-
riveted butt (unequal straps) and
double-riveted lap joints ; the re-
maining seams are single-riveted lap
joints. Since rivet-heads in the fur-
nace are liable to be burned off, the
rivets are counter-sunk in fire-box
and side sheets for 36 ins. from the
bottom upward. The proportions
of the principal seams are given in
the following list, the notation being
that of the joint-tables previously
given and the locations being num-
FIG. 90. bered in Figs. 89 and 90.
Seam.
Plate.
No.
Kind.
Thick.
I
Quadruple, butt.
ir
ft
3"
31//
if
6*"
13"
H"
I//
2
|
3i
3?
1 1
7
14
^
^
5.
Vr
3?
1 1
7
14
3
1
•4
Double-riveted lap.
ti> 1
3
'U
Si
i
i «
if
2
Tf
:f
sl
4f
7
Single-riveted lap.
i> H
2
4
9
Iu
II
; «
&
!
•
•
2
2
2
K> »v> K> O>
*Hi-*)-'H«
RIVETED JOINTS. 21$
51. Riveted Joints, Stationary Boilers.
Cylindrical boilers for stationary service are usually of the ex-
ternally fired type, the shell containing only the bracing and the
tubes or flues.
1. AMERICAN BOILER MANUFACTURERS' ASSOCIATION. — The
following extracts from the Uniform American Boiler Specifications
adopted in October, 1898, by this association are given through
the courtesy of E. D. Meier, Esq., chairman of the committee
which formulated these specifications.
2. Steel. — Homogeneous steel made by the open hearth or crucible processes,
and having the following qualities, is to be used in all boilers :
Tensile Strength, Elongation, Chemical Tests. — Shell plates not exposed to the
direct heat of the fire or gases of combustion, as in the external shells of internally fired
boilers, may have from 65,000 to 70,000 pounds tensile strength ; elongation not less
than 24 per cent, in 8 inches ; phosphorus not over .035 per cent. ; sulphur not over
.035 per cent.
Shell plates in any way exposed to the direct heat of the fire or the gases of combus-
tion, as in the external shells or heads of externally fired boilers, or plates on which any
flanging is to be done, to have from 60,000 to 65,000 pounds tensile strength ; elonga-
tion not less than 27 per cent, in 8 inches ; phosphorus not over .03 per cent. ; sulphur
not over .025 per cent.
Fire-box plates or such as are exposed to the direct heat of the fire, or flanged on the
greater portion of their periphery, to have 55,000 to 62,000 pounds tensile strength ;
elongation 30 per cent, in 8 inches ; phosphorus not over .03 per cent. ; sulphur not
over .025 per cent.
For all plates the elastic limit to be at least one half the ultimate strength ; per-
centage of manganese and carbon left to the judgment of the steel maker. * * *
3. Rivets to be of good charcoal iron, or of a soft, mild steel, having the same
physical and chemical properties as the fire-box plates, and must test hot and cold by
driving down on an anvil with the head in a die ; hy nicking and bending, by bending
back on themselves cold, without developing cracks or flaws. * * *
10. Riveting. — Holes made perfectly true and fair by clean-cutting punches or
drills. Sharp edges and burrs removed by slight countersinking and burr reaming
before and after sheets are joined together.
Under side of original rivet head must be flat, square and smooth. For rivets ^ inch
to \\ inch diameter allow i ^ diameters for length of stock to form the head, and less for
larger rivets. Allow 5 per cent, more stock for driven head for button set or snap
rivets. Use light regulation riveting hammers until rivet is well upset in the hole ;
after that snap and heavy mauls. For machine riveting more stock to be left for driven
head to make it equal to original head, as fixed by experiment.
Total pressure on the die about 80 tons for i^-inch to i^-inch rivets ; 65 tons for
i -inch ; 57 tons for ||-inch ; 35 tons for ^f-inch rivets.
Make heads of rivets equal in strength to shanks by making head at periphery of
shank of a height equal to y£ diameter of shank and giving a slight fillet at this point.
Approximately, make rivet holes double thickness of thinnest plate ; pitch three times
rivet hole ; pitch lines of staggered rows % pitch apart ; lap for single-riveting equal to
pitch, for double-riveting i^ pitch, and % pitch more for each additional row of
216
MACHINE DESIGN.
rivets ; exact dimensions determined by making resistance to shear of aggregate rivet
section at least 10 per cent, greater than tensile strength of net or standing metal.
11. Rivet Holes punched with good sharp punches and well-fitting dies in A. B. M.
A. steel up to $ inch thickness ; in thicker plates punch and ream with a fluted reamer,
or drill the holes.
12. Drift Pin to be used only with light hammers to pull plates into place and
round up the hole, but never to enlarge or gouge holes with heavy hammers. * * *
25. Rivet Seams when proportioned as prescribed in Section 10 with materials tested
as per Sections 2 and 3 shall have 4^ as factor of safety ; when not so tested, but in-
spection of materials indicates good quality, a factor of safety of 5 is to be taken, and at
most 55,000 Ibs. tensile strength assumed for the steel plate and 40,000 Ibs. shear
strength for the rivets, all figured on the actual net standing metal.
2. THE HARTFORD STEAM BOILER INSPECTION AND INSURANCE
Co. — The following data refer to the practice of this company.
The specifications for horizontal tubular steam boilers require that
the material for shell plates and heads shall be Open Hearth Fire-
box Steel and best Open Hearth Flange Steel, respectively ; that
the longitudinal and girth seams shall be, respectively, of the butt-
FIG. 91.
joint type with double-covering strips and the single-riveted lap-
joint type ; and that the rivet-holes shall be drilled in place, i. e.,
holes punched at least \ in. less than full size, then courses rolled
up, covering plates and heads bolted to courses with all holes to-
gether perfectly fair, rivet-holes drilled to full size, and finally
plates taken apart and burrs removed. No rivets shall be driven
in unfair holes ; such holes must be brought in line with a reamer
RIVETED JOINTS. 2 1/
Tables XLVIL, XLVIIL, XLIX., L. and Figs. 91 and 92 give
the proportions of longitudinal and circumferential or girth seams.
The inner covering strap of the butt joints is wider than the outer.
I .±c*I
FIG. 92.
The inner row or rows of rivets have half the pitch of the outer
row. The rivets of the latter pass through the plate and inner
covering strap only and are thus in single shear. The joints are
proportioned for steel plates and iron rivets. The tensile strength
of plates is taken as 60,000 Ibs. per sq. in. of section and the
shearing resistance of rivets (single shear) as 38,000 Ibs. per sq. in.
of section. The diameter of rivet holes is Jg in. greater than the
diameter, d, of the rivets. The notation of the tables is :
C = circumferential or girth seam ;
L = longitudinal seam ;
T = thickness of plate, ins. ;
/ = thickness of outer butt-strap, ins. ;
tl = thickness of inner butt-strap, ins. ;
d = diameter of rivet, ins. ;
p = greatest pitch of rivets, ins. ;
218
MACHINE DESIGN.
V= distance between rivet-rows, staggered riveting, ins. ;
Pj = distance between outer and next row, staggered riveting,
when alternate rivets are omitted in outer row, ins. ;
E = distance from centre of nearest rivet to edge of plate or
strap, ins. ;
A = total width of outer butt-strap, ins. ;
B = total width of inner butt-strap, ins.
TABLE XLVII.
CIRCUMFERENTIAL SEAM, C, SINGLE-RIVETED LAP ; LONGITUDINAL SEAM, Z,
DOUBLE- (STAGGERED) RIVETED LAP.
(HARTFORD STEAM BOILER INSP. AND INS. Co.)
Plate Thickness.
Seam.
d
P
F
^
I//
C
\\"
2T8//
i|/7
^
L
\\
2 \
IH//
ij
i
C
3
2 |
|
L
C
L
C
L
i
2*
1
iH
1
i
C
i
2 \
^
L
i
3fVff
2tV
Jtf
TABLE XLVIII.
CIRCUMFERENTIAL SEAM, C, SINGLE-RIVETED LAP ; LONGITUDINAL SEAM, Z,
TREBLE- (STAGGERED) RIVETED LAP.
(HARTFORD STEAM BOILER INSP. AND INS. Co.)
Plate Thickness.
Seam.
d
p
y
JE
r
C
5 //
2h"
j ^
I
L
5
3
2//
j i
1
C
L
C
f
3
2 -
•A
ii
1
L
3
3-
2T%
rV
C
1
2
jl.3
T\
L
I
3
2 I.
ll|
1
C
L
»
2
3}
\
M
1!
RIVETED JOINTS.
219
TABLE XLIX.
DOUBLE- (STAGGERED) RIVETED BUTT JOINTS WITH UNEQUAL STRAPS. ALTER.
NATE RIVETS OMITTED IN OUTER Row.
(HARTFORD STEAM BOILER INSP. AND INS. Co.)
Efficiency.
4
9"
83.0^
82.9
82.0
80.0
TABLE L.
TREBLE- (STAGGERED) RIVETED BUTT JOINTS WITH UNEQUAL STRAPS. ALTER-
NATE RIVETS OMITTED IN OUTER Row.
(HARTFORD STEAM BOILER INSP. AND INS. Co.)
tt
14'
Efficiency.
87.5
86.0
86.6
52. Riveted Joints, Structural Work.
The tables and other data given in this section refer principally
to the practice of the American Bridge Company.
i. RIVET AND PLATE METALS. — General specifications for
structural steel have been given in § 37. For steel railroad
bridges this company requires :
All steel to be made by Open Hearth process. Per cent, of phosphorus : Acid, .08;
basic, .05.
Grades.
Rivet.
Soft.
Medium.
Lit. strength, Ibs. per sq. in.
Elongation, per cent.
Elastic limit.
48-58,000
26
\ ult. str.
52-62,000
25
\ ult. str.
60-70,000
22
\ ult. str.
For rivet and soft steel, test-piece to bend 180° flat on itself; for medium steel, 180°
to a diameter equal to thickness of piece — in all cases without fracture on outside of
bent portion. •
In general practice, field-rivets, i. e., those driven in course of
erection, are frequently of wrought iron, since its range of riveting
temperature is less affected than that of steel by cooling and delay.
2. RIVET PROPORTIONS. — The diameter ranges between | in.
and i in., the usual size being | in. or | in. The smaller diame-
220
MACHINE DESIGN.
ters are used with thin and narrow flanges and the I in. size only
when the thickness or stress requires it. Field-rivets should not
be over f in., if possible. The selection of the diameter is, to some
extent, a matter of judgment.
The form of the head and point is usually either spherical, coun-
tersunk, or flattened to f in. thickness. Table LI. gives the pro-
portions for spherical (button-head) and countersunk forms, the
formulae being :
Spherical. Countersunk.
D = \d + £", Angle of sides = 60°,
in which d = diameter of shank, D = diameter of head or point,
H = height of spherical or depth of countersunk head or point.
TABLE LI.
PROPORTIONS OF RIVET-HEADS.
(AMERICAN BRIDGE Co.)
Shank.
Spherical Heads.
Countersunk Heads.
Diam.
Diam.
Height.
Diam.
Height.
in.
liin-
A in.
r
t
lylg.
it
A
:
it
I
i!
i
The conventional Rivet-signs used to mark on the drawing the
character of the head and point are shown in Fig. 93. To save
SJuJ&rets.
Field favei
FltLtte.nt.il to £".
Countersunk
F%a.\n..
FIG. 93.
time in construction, but one size of rivet is used throughout each
piece, as a plate girder, and the diameter of the rivet-holes is noted
RIVETED JOINTS. 221
on the drawing. The heads of countersunk rivets project usually
about \ in. If they are required to be flush, they must be chipped.
The length of rivet-shank required for a given joint is equal to
the " grip " plus the metal required to fill the hole and form the
point. The grip is the aggregate thickness of the connected
plates plus an allowance for irregularity, of ^ in. for each place
where two plate-surfaces meet. The diameter of the rivet-holes
is Jg in. greater than that of the rivets. For, any given grip,
the length of shank and weight of spherical (button) head steel
rivets may be found from the following data :
WEIGHT IN POUNDS.
1"
V
S"
r
i"
I//
Shank, per in. of length.
Two rivet-heads.
.031
.037
.056
.116
.087
.222
•125
.273
.170
•453
.223
.780
3. THE SPACING OF RIVETS is determined mainly by the re-
quired strength at any given point, tightness, as in pressure joints,
not being essential. The conditions previously given for the lat-
ter, as to plate-rupture and room for the die, hold with regard to
the minimum margin and pitch. The maximum pitch in a compres-
sion member is fixed by the consideration that the plate in a pitch
section is practically a column. In general, also, the maximum
pitch must not be so great as to permit the entrance of moisture
which would rust and burst the joint. The rivets in the ends of a
compression member carry the full load on the member and are
spaced with this consideration in view. The specifications of this
company as to pitch and margin are :
The pitch of rivets, in the direction of the strain, shall never exceed 6 inches, nor
1 6 times the thickness of the thinnest outside plate connected, and not more than 40
times that thickness at right angles to the strain.
At the ends of compression members, the pitch shall not exceed 4 diameters of the
rivet for a length equal to twice the width of the member.
The distance from the edge of any piece to the centre of a riyet-hole must not be
less than 1.5 times the diameter of the rivet nor exceed 8 times the thickness of the
plate ; and the distance between centres of rivet-holes shall not be less than 3 diame-
ters of the rivet.
In structural work, the pitch of the rivets may vary between the
minimum limit, fixed by the possible cracking of the plate in punch-
ing or riveting and the clearance for tools, and the maximum limit
222
MACHINE DESIGN.
(6"), determined by the union of the parts so that they shall be
stressed as a whole and also by the necessity for excluding mois-
ture. Table LII. gives various pitches for double staggered
riveting and for the staggered spacing of two rows of rivets in the
two legs of an angle.
TABLE LII.
STAGGERING OF RIVETS. (AMERICAN BRIDGE Co.)
Distance c to c of Staggered Rivets.
3A
3t |3f 3A3A
NOTE : Values below or to right of upper zigzag lines are large enough for J rivets.
« " " " " " lower " " " " " "• "
Minimum Stagger for Rivets.
J" Dia
The rivet-spacing for various angles is given by Table LII I. for
both longitudinal and transverse pitches. In -a " crimped angle,"
as shown in Fig. 94, the distance, b, should be i J in. plus twice
RIVETED JOINTS.
223
the thickness of chord angles, but never less than 2 in. The clear-
ance required for |-in. and |-in. rivets is shown by Fig. 95.
FIG. 94.
TABLE LIII.
RIVET SPACING IN ANGLES. (AMERICAN BRIDGE Co.)
I
Leg.
G
Max. Rivets.
Leg.
c/
C2
Max. Rivets.
8"
7
6
4
3^
]
;"
8"
7
6
5
3/x
F
5
5
2
Jf
I
4
3*
2i
2
When 6" .£ exceeds j". .
3
6"
2£"
2\"
Y
2
If
i
I
A
•
•
MINIMUM RIVET SPACING.
Size of Rivet.
i"
I"
ir
*"
i"
J"
i"
i"
Minimum Distance.
I"
ir
2//
2i
2f
3X/
4. PUNCHING AND RIVETING. — The specifications of this com-
pany for steel railroad bridges are :
All riveted work shall be punched accurately with holes T\ in. larger than the size
of the rivet, and, when the pieces forming one built member are put together, the holes
224 MACHINE DESIGN.
must be truly opposite. No drifting to distort the metal will be allowed ; if the hole
must be enlarged to admit the rivet, it must be reamed.
All holes for field-rivets, excepting those in connections for lateral and sway bracing,
shall be accurately drilled to an iron templet or reamed while the connecting parts are
temporarily put together.
In medium steel over £ in. thick, all sheared edges shall be planed and all holes
shall be drilled or reamed to a diameter ^ in. larger than the punched holes, so as to
remove all the sheared surface of the metal.
The rivet-heads must be of approved hemispherical shape and of a uniform size for
the same size rivets throughout the work. They must be full and neatly finished
throughout the work and concentric with the rivet-hole.
All rivets when driven must completely fill the holes, the heads be in full contact
with the surface or countersunk when so required.
Wherever possible, all rivets shall be machine-driven. Power-riveters shall be
direct-acting machines, worked by steam, hydraulic pressure, or compressed air.
5. STRESSES IN RIVETED MEMBERS. — The built-up members
of framed structures are made of rolled shapes of various forms,
plates, angles, etc., joined by rivets which distribute and transfer
the stress developed by the load. Rivets should be subjected to
shearing and bearing stresses only. The connected parts resist
shear, tension, compression, or compound stress, as their location
with respect to the load determines.
Working Stresses. — The greatest permissible working stresses
for the parts of a member vary with the location of the part and
the character of its load. For wrought iron, general values in Ibs.
per sq. in. are : in tension, 7,500 ; in shear, 6,000. For steel, the
tensile stress ranges from 10,000 to 17,000 and the shearing
stress from 6,000 to 11,000. For compression members, the per-
missible stresses are those for tension, modified by the relation
between the length and least radius of gyration of the section.
One formula of this nature is quoted below.
The shearing resistance in Ibs. per sq. in. of cross-section for
rivets in single shear is : iron, 6,000 to 7,500 ; steel, 7,500 to 12,-
ooo. Corresponding values of the bearing pressure are : iron,
12,000 to 15,000 ; steel, 15,000 to 24,000 Ibs. per sq. in. upon the
projected area equal to diameter of rivet-hole x thickness of plate.
For field-riveting, the number of rivets as calculated is increased
by 10 to 50 per cent., as a margin for defective work. Table LIV.
gives the shearing and bearing values of rivets for resistances of
11,000 Ibs. (single shear) and 22,000 Ibs. per sq. in. respec-
tively.
RIVETED JOINTS.
225
i
ill
M N
88 8
a
10 VO t^ 00
O Q O Q O
p-c VO t^ vO HI
N M ro OO v£)
M C") CO -^- \O
rO OO 00 f>
10 o ^o O >o
t-. 0 M tr> t-.
rO up vq t^ 00
i!
II
M ^
•c ^
S j)
226
MACHINE DESIGN.
The following extracts from specifications refer to the require-
ments of this company as to working stresses in steel railroad
bridges :
All parts of the structure shall be so proportioned that the sum of the maximum
loads, together with the impact, shall not cause the tensile strain to exceed : on soft
steel, 15,000 Ibs. per sq. in.; on medium steel, 17,000 Ibs. per sq. in.
* * * For compression members, these permissible strains of 15,000 and 17,000
Ibs. per sq. inch shall be reduced in proportion to the ratio of the length to the least
radius of gyration of the section by the following formulae :
15,000
I1 '' (128)
For soft steel, p =
For medium steel,
17,000
u,ooor2
(129)
where / = permissible working strain per sq. in. in compression ; / = length of piece
in inches, centre to centre of connection ; r = least radius of gyration of the section in
inches.
* * * The shearing strain on rivets, bolts, or pins per sq. in. of section shall not
exceed n,ooo Ibs. for soft steel and 12,000 Ibs. for medium steel ; and the pressure
upon the bearing surface of the projected semi-intrados (diameter X thickness) of the
rivet, bolt, or pin hole shall not exceed 22,000 Ibs. per sq. in. for soft steel and 24,000
Ibs. for medium steel. In field-riveting, the number of rivets thus found shall be in-
creased 25 per cent., if driven by hand, but 10 per cent, if driven by power.
* The shearing strain in web-plates shall not exceed 9,000 Ibs. per sq. in. for
soft steel and 10,000 Ibs. per sq. in. for medium steel ; but no web plate shall be less
than Jljin. in thickness.
I
FIG. 96.
6. DISTRIBUTION OF STRESSES. — The character and distribution
of the stresses in a member depend upon the function of the latter.
The Plate-Girder is a fairly comprehensive example of the prin-
ciples of design in riveted structural work. As shown in Fig. 96,
RIVETED JOINTS. 22?
it consists essentially of a web-plate, W, and four angles, L, ex-
tending from end to end. To these may be added, at top and
bottom, a flange-plate, C, of partial or full length, and, if required,
one or more flange-plates, Cv traversing the section in which the
magnitude of the bending moment makes necessaiy the additional
flange-area. These plates are all of the same width, which is that
of the girder. The upper and lower flanges are similar, excepting
that one plate of the latter is usually thicker to make up for the
loss in net plate-section due to rivet-holes. The parts are joined
by rows of rivets, r, passing through web and angles and rows, rv
through angles and flange-plates. As a rule, these are single
rows. The method of design is indicated briefly below.*
Length, Width, Depth. — The length, /, is the distance between
the centres of the end -bearings. Since the upper flange is in com-
pression, it may buckle if weak. Hence, if the unsupported length
of the girder exceeds 1 6 to 20 times its width, b, the girder should
be given lateral support. The depth, h, is the distance between
the centres of gravity of the cross-sections of the flanges, each of
the latter being made up of two angles and the attached flange-
plates. The effective depth may be taken, without material error,
as that of the web-plate. To avoid excessive deflection, the least
depth should be Jfr to tV °^ t^ie sPan- ^or ^e economical depth,
with regard to weight, Mr. C. W. Bryan, C.E., gives the follow-
ing formulae : f
Neglecting moment of resistance of web to bending :
x= 1.27
Considering moment of resistance of web to bending :
x=i.46^~; (131)
in which,
x = depth of girder, ins. ;
tn= centre-moment, inch-lbs., from dead and live loads ;
f-= allowable fibre-stress on flanges, Ibs. per sq. in. ;
/ — thickness of web, ins.
* For detailed investigation, see Burr: " Elasticity and Resistance," etc., 1897, p.
578 ; Johnson, Bryan, Turneaure : "Modern Framed Structures," 1901, p. 292.
-(-"Modern Framed Structures," 1901, p. 299.
228 MACHINE DESIGN.
Moments, Vertical Shear, Flange-stress. — The external forces
acting on the girder are the loads and the reactions at the sup-
ports. These are transmitted directly to the web by vertical
angles, D, riveted to the web at the supports and under concen-
trated loads and by the rivets, r, of the compression flange. The
vertical shear produced in the web by the loads acts upon the
rivets, r, of both flanges with a leverage equal to the pitch of the
rivets, and thus develops bending stress in the flanges. Since
the parts are so bound together that the girder bends as a whole,
bending stress, in addition to shear, acts in the web. Two methods
of design are used : Either to assume that the web is subjected
to vertical shear only and proportion the flanges for the full bend-
ing stress; or — and correctly — to allow for the resistance to
bending of the web and design the flange-area for the remainder
of the load.
Let A be the sectional area of the angles and plates (web not
included'] forming one flange at any given point in the girder and
5 the mean unit working stress over that area. Then, A x S is the
total load or horizontal bending stress on the flange and A-S x - —
resisting moment of this stress about the neutral axis of the girder.
Assuming A and 5 as the same for both flanges and neglecting
the bending stress on the web, the external bending moment at
the given point = resisting moment of girder at that point ; or,
(132)
Flange-stress = A.S. = -j-\ ( * 3 3)
Flange-area = ^ = — . (134)
The web-section is that of a rectangular beam of depth, h, and
breadth equal to the thickness, t. Hence, its resistance to bend-
S.th*
ing is ~ To allow for the reduced section due to vertical
RIVETED JOINTS. 229
rows of rivet-holes the 6 is replaced by 8. Hence, considering
the resistance of the web to bending stress :
(135)
Flange -stress = A.S = - -- ~ ; (136)
M t.h
Flange-area = A = - - — • (137)
For steel girders in buildings, the usual unit flange-stress, S, is
15,000 Ibs. per sq. in. and the unit shearing-stress, Se, on the web
is 7,000 to 1 1,000 Ibs. per sq. in.
FLANGE-AREA, ANGLES, FLANGE-PLATES. — The required flange-
area at any given point in the girder may be found from (134) or
(137). The area found thus, serves for the compression flange
which is assumed as not weakened by the rivet-holes, since the rivets
should about fill the latter. The resistance of plates and angles
in the tension flange is that of their net section. The two rivet-
rows, rv are opposite each other ; but 1\ is staggered with regard
to r. Hence, the net section of a cover or flange-plate is (b — 2d)
x thickness and the net area of an angle = gross area — d x
thickness. The diameter, d, is that of the rivet plus ^ in., to allow
for enlarged hole and effects of punching. The increased area
required in the tension flange is added by thickening one of
the flange -plates or by calculating for the tension-flange and mak-
ing the area of both flanges the same. The flange-area may be
calculated for different points in the girder or it may be found
graphically as shown in Fig. c>6a, which is the bending moment
diagram for a concentrated load at the centre of the girder. The
maximum bending moment, M, should be equal to the sum of the
individual resisting moments R.L, R.C, R.CV of the angles, L, and
the flange -plates, C and Cv i. e., on the same scale, M= R.L +
R.C + R. Cr Hence, at a, the full section will be required ; at c,
that of L and C ; and at c that of L only. These theoretical lengths
of flange -plates are increased somewhat, as will be shown later.
In general, .not less than 50 per cent, of the maximum flange-area
should be in the angles, since the thinner the flange-plates, the
230
MACHINE DESIGN.
less their leverage through the rivets on the angles, both vertically
and with regard to the centre of gravity of the latter.
The sectional areas of various angles are given in Table LV.
The centre of gravity of a given flange-area should be as far as
possible from the neutral axis of the girder in order to give the
maximum resisting moment to bending and the maximum breadth
of the area should be as great as the conditions permit in order to
strengthen the girder against buckling or lateral yielding. Hence,
the angles should have unequal legs with the longer horizontal.
The thickness of the angle should be, approximately, that of the
web-plate.
TABLE LV.
ANGLES: SECTIONAL AREAS (SQ. INS.).
(AMERICAN BRIDGE Co.)
Size.
i"
A"
i"
A"
1"
A"
*"
A"
1"
ii"
J"
il"
i"
IB" | i"
8" X 8"
7.76 8.76
976
10.76
11.47
12.47
13-47
I4.50 15.53
6 X6
4-35
5-09
5-79 6.47
7.18 7.79 8.47
9.121 9.82 10.56
5 X5
3.62
4.21
4-79
5-35
5-91
6.47 7.00
7.53 8.06
8.65
4 X4t
2.41
2.88
3-32
3-76
4.21
4.65
5.06
5-47
2.09
2.50
2.88
3-26
3-65
4-03
2 X2*
1-44
1-79
2.12
2.44
2.76
3-06
3.38
1.32
1.65
1-94
2.26
2-53
2\ X 22
0.91
1. 21
1-47
1.74
2.03
2.29
2? X 2?
0.79
1.06
1.32
1-59
2 X 2
0.74
0.94
1.18
1.41
if X if
0.62
0.82
1.03 j 1.21
i\ X ij
0-35
0-53
0.71
0.85 1.03
I jf X IT
0.29
o.44
0.59
i Xi
0.24
Q.35
0.44
8 X6
1 6.76 7.59
"84!
9-32
~9^94
10.76 11.62 12.5013.41
7 X 3z
5-oo 15.59 6.18
6.76
7.29 7.85 8.41 8.97 9.56
6 X4
3-59
4.21
4-79
5-32
5.91
6.47
7.00 7.53; 8.06 8.65
6X3*
3-41
4.00
4.56
5-03
5.59 6.12
6.65 7.21
7-79
8.4I
5 X4
3-24
3.76
4-29
4.76
5-26 5.76
6.26
5 X3*
5 X3
2-56
2.41
3-03
2.85
3.53 4.00 4.47
3.29 3.76 4.18
4-94 j 5-41
4.62 5.06
5-88
5.50
4 X3i
2.26
2.68 3.09
3-5o
3-91
4-32 1 4JI
5-12
4xX3
2.09
2.50 2.88
3-26
3.65
4.06
1.94
2.29 j 2.68 j 3.03
3-41
3-79
3 i X 2i
1.44
1.79
2.12 1 2.44
2.76
3 X ^ij
1.32
1.62
1.94 2.26
2.56
2JX2
0.79
i. 06
1.32
i-59
1.82
2.06
2X4
0.62
0.85
1. 06
1.26
2 XI*
0.56
0.76
0.97
1. 15
-
In general, the aim in design should be to make the girder
as deep and the angles as heavy as possible in order to reduce
the thickness of the plates and their consequent leverage through
RIVETED JOINTS. 231
the rivets on the angles. In compression, one plate -is better
than two of the same aggregate thickness. To increase the re-
sistance to buckling, the plates of the compression flange may be
made the full length of the girder. Since the stress is transmitted
to the plates by the flange rivets, rv the width of the plates outside
of those rows is limited by the necessity for an approximately uni-
form distribution of stress.
Web-plate, Stiffeners. — The thickness of the web-plate, W, must
be such as to provide for the maximum vertical shear at the sup-
ports and to give sufficient bearing area for the rivets joining the
web and angles without making the pitch of the rivets smaller than
the minimum allowable. The minimum thickness of web is ^ in.
for light work. In railway bridges, no web less than f in. thick
should be used.
The load on the web not only produces vertical shear and bend-
ing stress but also tends to make the plate yield vertically by
buckling. The latter is prevented by pairs of vertical angles or
stiffeners, B, riveted to the web. If the thickness of the latter is
less than g1^ of its depth, the stiffeners are placed at intervals not
greater than the depth of the girder throughout the length of the
latter, with a maximum spacing of 5 ft. Angles for stiffening solely
may be made very light. They should bear against both upper
and lower flange angles and the web, being bent inward to the lat-
ter or left straight and a filling piece interposed.
At the supports and under concentrated loads, as at D, the stiff-
eners have the further function of transferring the external loads
to the web-plate. The rivets passing through them should have
a strength sufficient for this. Hence, in addition to the fitting and
bearing as above, these transferring stiffeners should be broad
enough to give space for the rivets and thick enough to prevent
the pressure on the rivets and of the stiffener on the lower flange-
angle from exceeding the allowable bearing stress.
Riveting. — The rivets r, and rv are in double and single shear
respectively and both are under bearing pressure which must be
computed for the least bearing surface in either direction of stress.
The strength, s, of a rivet is its least resistance under either of the
two stresses to which it is subjected. The vertical shear in the
web acts through the rivets, r, on the flanges, bending the latter.
Considering only bending stress, the required number of the rivets,
r, depends upon their diameter and the magnitude of the bending
232 MACHINE DESIGN.
moment. Let Me be the bending moment on the tension flange at
E. The flange-stress Af.S divided by the strength, s, will give
the number of rivets for Me from E to either support. Again,
the increase of moment between E and F is Mf — Me and the in-
crease of flange-stress is S(Af — Ae). The latter divided by s gives
the number of rivets to be added between E and F, the total num-
ber thus far being that on either side of F for the moment M .
In general, the number, N, of rivets required on each side for a
moment, M, is :
N~~ (138)
Again, from the relation between the bending moment and the
vertical shear, F, we have, for an elementary length, dx :
V=d~--> Fx dx=dM,
dx
i. e., the vertical shear at the left of dx acts with a leverage dx to
produce the increment of moment, dM. Let the length of the
section be the pitch, /, between two rivets, a at the left and b at
the right. Then, if Ma , Aa, Mb, and Ab be the respective moments
and flange-areas, we have, neglecting resistance to bending of web :
Vxp = Mb-Ma = h [AbS - AaS] = h.s •
h.s
/= F> (139)
since the rivet, b, must resist the increment of flange-stress
required in the distance, p.
In the upper or compression flange, in addition to the horizon-
tal bending-stress, the rivets, r, are subjected to vertical stress from
the loads transmitted by them to the web. These loads are : the
weight of the girder, the uniform load if any, and any concen-
trated load which is not provided for fully by transmitting angles,
D. Let w be the sum of these loads per inch of length of gir-
der at the section considered. Then / x w will be the vertical
load upon the pitch section and on one rivet. From (139) the
horizontal load due to any pitch, /, is -. - . The final stress upon
the rivet will be the resultant of these two loads which are normal
RIVETED JOINTS. 233
to each other and this resultant must not exceed the strength, s,
of the rivet. Hence, neglecting resistance to bending of web :
(I4o)
p and h being expressed in inches and s, V, and zv in Ibs.
From (139) and (140) the pitches in both flanges of rivets, r,
may be obtained. If the bending resistance of the web be con-
sidered, equations (139) and (140) must be modified in accordance
with the terms of (136). The shear is greatest and the pitch least
at the supports, both varying in some degree at every section. In
practice, the minimum pitch required is generally preserved until
the maximum (6 in.) can be used. The number of rivets in the
tension flange will be less than that in the upper angle, but, for con-
structive reasons, rivets inserted below should be in line vertically
with those above. When the moment of resistance of the web
to bending is considered, the pitch formulae should be changed to
include this factor.
The pitch of the rivets, rlt joining the flange-plates to the angles
is 6 in. excepting at the ends of the plates. The latter are ex-
tended beyond the theoretical limits sufficiently to provide space
for enough rivets in the two rows to carry the load on the plate
in each case, the pitch of these rivets being 4 diameters. Thus,
theoretically, the plate, C, ends at c. The load on this plate is ap-
proximately the product of its net cross-section and the working
stress. Dividing this load by the strength of one rivet, we have
the total number of rivets in both rows to be driven between e and
the end, ev of the plate.
The following extracts from the specifications of this company
for steel railroad bridges cover the points discussed above :
" Girders shall be proportioned on the assumption that £ of the gross area of the web
is available as flange-area. The compressed flange shall have the same sectional area as
the tension flange ; but the unsupported length of flange shall not exceed 16 times its width.
" In calculating shearing strains and bearing strains on web rivets of plate-girders, the
whole of the shear acting on the side next the abutment is to be considered as being
transferred into the flange angles in a distance equal to the depth of the girder.
"The web shall have stiffeners riveted on both sides, with a close bearing against
upper and lower flange angles, at the ends and inner edges of bearing plates and at all
*" Modern Framed Structures," 1901, p. 306.
234
MACHINE DESIGN.
points of local and concentrated loads ; and also when the thickness of the web is less
than -fa of the unsupported distance between flange-angles, at points throughout the
length of the girder generally not farther apart than the depth of the full web-plate,
with a maximum limit of 5 ft.
« * * * AH joints in riveted work, whether in tension or compression members must
be fully spliced.
« * * * Web-plates of girders must be spliced at all joints by a plate on each side of
the web, not less than f in. thick, capable of transmitting the full strain through splice
rivets.
"The flange-plates of all girders must be limited in width so as not to extend beyond
the outer lines of rivets connecting them with the angles more than 5 in. or more than
8 times the thickness of the first plate. Where two or more plates are used on the
flanges, they shall either be of equal thickness or shall decrease in thickness outward
from the angles."
TABLE LVI.
RIVETED vs. BOLTED JOINTS.
(LAP JOINTS.)
r*- 7 — »>
0
o— |
i
in/
Joints A.
Joints B.
Double Riveted.
Double Bolted.
Treble Riveted.
Treble Bolted.
Quadruple Riveted.
Quadruple Bolted.
Rivets or bolts, Diam.
\"
I"
\"
" " No.
2
3
4
" " Pitch.
3T/
3"
Plates, width.
tji"
1"
thickness.
I/?
i//
V
lap.
Y'
10"
'37'
tensile stress per sq. in.
at failure for :
Iron rivets.
26, 1 20 Ibs.
24,310 Ibs.
26,450 Ibs.
Steel rivets.
Iron bolts.
26,990 "
18,690 »
29,590 "
18,090 "
28,820 "
20,470 "
Steel bolts.
21,110 "
21,460 "
22,060 "
Failure, in all cases, by shearing rivets or bolts.
7. BOLTS. — For facility in erection or in cases where a rivet
would be in tension, bolts are used as permanent fastenings in some
parts of structural work. For full strength they require to be
finished and fitted accurately in drilled holes. Tables LVI. and
LVII. give comparative tests — made for the Berlin Iron Bridge
Co. at the Watertown Arsenal in 1896 — of riveted and bolted
single- and double-shear joints with punched holes. The plates
RIVETED JOINTS.
235
were of steel ; diameter of punch, i| in., of die, £ in. ; chain-rivet-
ing, the "pitch" in the tables being the distance between the
rows. The test-piece consisted of a section of the joint contain-
ing one rivet in each row. The joints were similar throughout,
excepting that the rivets in A and C were replaced in B and D by
through bolts and nuts.
TABLE LVII.
RIVETED vs. BOLTED JOINTS.
(ONE WEB AND Two COVER-PLATES.)
O G~
'T
/tv
Joints C.
Joints D.
Double Riveted.
Double Bolted.
Treble Riveted.
Treble Bolted.
Quadruple Riveted.
Quadruple Bolted.
Rivets or bolts, Diam.
I"
f"
f"
" " No.
2
3
4
" " Pitch.
•3"
3"
3"
PI es, width.
4"
V
8"
thickness.
| and f "
fandf"
| and \"
lap.
1"
10"
13"
tensile stress.
(web) per sq. in. at
failure for :
Iron rivets.
29,670 Ibs.
28,520 Ibs.
28,470 Ibs.
Steel "
29,540 "
31,040 "
28,970 "
Iron bolts.
18,000 "
17,720 "
18,990 "
Steel "
20,050 "
25,010 "
23,440 "
Manner of failure for :
Iron rivets.
Sheared rivets.
Sheared rivets.
Sheared rivets.
Steel "
Fractured web plate.
K «
Fractured covers
through rivet holes.
Iron bolts.
Sheared bolts, both
" bolts.
Sheared bolts.
planes.
Steel "
Sheared bolts, one
« «
K «
plane.
53. Riveted Joints, Hull Plating.
The hull of a ship is essentially a girder constructed to bear
a given maximum load with various modes of support. Hence
the principles which govern the design of structural work in
236 MACHINE DESIGN.
general apply to the proportion and connection of the members of
hull-framing. In the joints of the outside plating and those
of the double bottom, bulkheads, etc., there is the further re-
quirement of tightness against water-pressure. Since the lat-
ter is, in any event, but moderate, these joints hold an interme-
diate position, with respect to tightness, between those of general
structural work and the seams of steam boilers.
In outside plating, the longitudinal seams are lapped except
where flush work is required. The transverse seams are butt
joints with single straps. Rivet-points are countersunk and
chipped and all seams are calked. The riveting is done either by
hand-work, or by portable hydraulic or pneumatic machines car-
ried on a gantry which spans the ship, or by the pneumatic rivet-
ing hammer which, with its frame and pneumatic " holder-on,"
forms a readily portable combination operated by two men. The
latter method for hull-riveting is meeting wide adoption in the
United States. With regard to its cost and results as compared
with hand-work, Edwin S. Cramp, Esq., Vice President of the
William Cramp and Sons Ship and Engine Building Co., says :
" We have found that the use of these tools results in an increase of operating expenses
and a decrease in labor-charges, with a net saving of about ten per cent, over the cost
of hand-riveting. The quality of the work done and the speed with which it is done
are increased to a great extent."
Rivets are usually of steel. Up to | in. diameter they should
be riveted cold, since the rivet-blank of small size not only cools
very quickly but, proportionately, wastes much more rapidly by
oxidation and scaling. For cold-riveting, the steel should be soft
and ductile as the harder metal of higher tensile strength becomes
brittle and untrustworthy when thus worked. The countersunk
points used in shell plating, while more costly and giving a re-
duced net section of plate, have two great advantages : Their use
removes much of the metal injured in punching the holes and they
add no weight to that of the full plate, since they are chipped flush.
Weight-saving without reduction of strength is a matter of impor-
tance in ships, especially in men-of-war, since useless weight is
but so much unprofitable load to be transported during the life of
the ship. Rivets form a very considerable proportion of the total
weight of the hull. Naval Constructor J. H. Linnard, U. S. Navy,
gives,* for the U. S. Armored Cruiser Brooklyn (9,270 tons), the
* Trans. Soc. Naval Architects and Marine Engineers, Vol. IV.
RIVETED JOINTS.
237
total weight of rivets driven as upward of 330,000 Ibs., of which
weight from ^ to ^ is in the rivet-heads and points. The rivet
blank will have a better fit in punched holes which are not counter-
sunk, if coned under the head as shown in Fig. 97.
Countersunk or- Plug ffeacls.
ClatsA ClnssR
Panffead.
Class A. Class B.
JButttm. //ecul. £uiton or S'nap Point.
Class A
Jeyo Rivet*.
Template fir Cmcnt
F;G. 97.
I . U. S. NAVAL PRACTICE. — The following extracts, relating to
hull-riveting in general, are taken from the Specifications (1899)
of the Bureau of Construction and Repair, U. S. Navy.
PLATE AND RIVET METALS :
SHIP PLATES AND SHAPES.
26. Kind of Material. — Plates and shapes shall be of steel or nickel steel, made
by the open hearth process, and must not show more than six one-hundredths (.06) of
one per cent, of phosphorus, nor more than four one-hundredths (.04) of one per cent.
238 MACHINE DESIGN.
of sulphur for acid steel; and not more than four one-hundredths (.04) of one per
cent, of phosphorus, nor more ihanfottr one-hundredths (.04) of one per cent, of sul-
phur for basic steel. The material shall be of the best composition in all other respects.
At the option of the manufacturer the material may be annealed.
The material will be classified in three standard grades according to its characteris-
tics and the purposes for which intended. These grades will be known as ( I ) soft or
flange steel, (2) medium steel and (3) hard steel.
The following are the minimum requirements of each grade of steel :
Grade.
Tensile Strength.
Elongation.
Cold Bend.
Quench Bend.
Soft or flange
50,000 Ibs.
30 per cent.
1 80° flat.
1 80° flat.
steel.
Medium steel.
60,000 Ibs.
25 per cent.
For plates below For plates below f
\ inch in thick-
inch in thickness;
ness : I 80° flat
1 80° to diameter
for longitudinal ;
of \\ thicknesses
1 80° to diameter
for longitudinal ;
of I thickness for
1 80° to diameter
transverse. For
of 2.\ thicknesses
plates above \
for transverse.
inch in thickness,
For plates above
the bends will be
f inch in thick-
1 80° to a diame-
ness, the bends
ter of I thickness
will be 1 80° to a
for longitudinal,
diameter of \\
and 2 thicknesses
thicknesses for
for transverse
longitudinal, and
specimens.
2\ thicknesses for
transverse speci-
mens.
Hard steel.
75,000 Ibs.
1 8 per cent.
1 80° to a diameter
No quench bend.
of ij thicknesses
for longitudinal ;
1 80° to a diameter
of 3 thicknesses
for transverse.
PROTECTIVE DECK PLATING.
38. The lower courses of plating for the protective deck will be of steel of the quali-
ties of ship plate, and shall be inspected accordingly.
39- The upper course of plating of protective deck shall be of nickel steel, contain-
ing about three and a quarter (3^) Per cent- °f nickel, not more than six one-hun-
dredths (.06) of I per cent, of phosphorus, nor more than four one-hundredths (.04)
of I per cent, of sulphur, and be of the best composition in all other respects. All
these plates shall be oil- or water-tempered and annealed.
All rivets are of steel whose characteristics are :
HULL RIVETS.
43. Kind of Material. — Steel for hull rivets shall be made by the open-hearth
process, and not show more than five one-hundredths (.05) of one per cent, of phos-
phorus, nor more than four one-hundredths (.04) of one per cent, of sulphur, and be
of the best composition in other respects.
RIVETED JOINTS. 239
44. A whole heat or part thereof may be rolled into rivet rods, and from each size
rolled six (6) tensile tests shall be taken at random, each from a different bar as finished
at the rolls. When lots smaller than five tons are rolled, one test piece shall be taken
from each size for every ton or fraction thereof.
45. Rods from which rivets are to be made of a diameter of one half (£) inch or less
shall be tested in the diameter of the finished rivet. These rods shall show a tensile
strength of not less than 58,000 pounds per square inch and an elongation of not less
than 28 per cent.
46. Rods from which rivets are to be made of a diameter above one half (£) inch
shall be tested with specimens of the same diameter as the finished rivet, when practic-
able, and shall show the same tensile strength as the smaller rivets and an elongation
of not less than 29 per cent. Specimens from these rods shall be of the maximum cross
section within the capacity of the testing machine.
47. From each lot of rivets kegged and ready for shipment there shall be taken at
random six (6) rivets, to be tested as follows :
(a) Three rivets to be flattened out cold under the hammer to a thickness of one
half (^) the diameter of the part flattened, without showing cracks or flaws. Rivets of
over an inch in diameter shall be flattened to three fourths (|) of the original diameter.
(b) Three rivets to be flattened out hot under the hammer to a thickness of at least
one third (|) of the original diameter of the part flattened, the heat to be the ordinary
driving heat.
(c) From each heat of rivet rods as finished at the rolls four cold-bending tests shall
be taken, which shall be bent over flat on themselves without showing any cracks or
flaws on the outer round.
48. Inspection for Surface and Other Defects. — Rivets must be true to form, con-
centric, and free from scale, fins, seams, and all other injurious or unsightly defects.
Tap rivets will be milled under the head, if necessary to obtain accuracy.
49. The style of rivet used will be determined by the Superintending Naval Con-
structor. As a general rule, countersunk heads will be used only where required by
mechanical or other special reasons. Wherever practicable, the pan-head rivet will be
used, with countersunk points where flush work is required, button or snap points for
finished appearance or where rivets are closed by power and hammered or mashed
points elsewhere. Where points are made with a snap-tool, or where riveting by
power is employed, care will be taken that the points are properly centered. In these
cases, and also in the case of hammered points, the aim must be to have the point of
adequate strength, following as nearly as possible the dimensions of points given in
Table LVIII. Care must be taken that snap points are not reduced from the standard
sizes by grinding down tools that have been chipped or burred. All pan-head rivets
not less than ^ inch diameter for punched holes should be coned under head, as shown
in Fig. 97, the rule for punching from the faying surface of plate being carefully ob-
served. If, however, the practice of punching the holes small and reaming to size by
power be employed, the coning under head may be omitted.
Proportions of Seams. — General proportions of plates, laps,
straps, rivets, and spacing are given in Table LVII, page 240.
Proportions of Rivets. — The approved types of head and points
for torpedo-boats and ship work are given in Fig. 97, page 237,
and Table LVIII, page 241.
240
MACHINE DESIGN.
1
I*
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I
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RIVETED JOINTS.
24I
dp
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•sjuioj dBug
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242
MACHINE DESIGN.
The diameters of rivets and rivet holes for torpedo-boat and ship
work are given in :
TABLE LIX.
DIAMETER OF RIVETS.
>v eigm 01 i laics.
V^UI I C5 pUUUlIlg
Rivets.
i^uircbpuiiumg
Rivet Holes.
FOR TORPEDO-BOAT WORK.
Inches.
Inches.
Up to 3 pounds, exclusive.
3 pounds to 6 pounds, exclusive.
\
1l
6 pounds to 7 5 pounds, exclusive.
7i pounds to 9 pounds, exclusive.
9 pounds to 1 1 pounds, exclusive.
I
II pounds to 13 pounds, exclusive.
I
II
FOR SHIP WORK.
Up to 3 pounds, exclusive.
3 pounds to 6 pounds, exclusive.
6 pounds, inclusive, to 8 pounds, exclusive.
1
1
8 pounds, inclusive, to 13 pounds, exclusive.
|
T5
13 pounds, inclusive, to 20 pounds, exclusive.
i
\\
20 pounds, inclusive, to 30 pounds, exclusive.
30 pounds, inclusive, to 40 pounds, exclusive.
40 pounds, inclusive, to 51 pounds, exclusive.
I
1
5 1 pounds, and above.
IT
31
NOTE. — The sizes of flanges of angles to which plates are connected in torpedo-boat
work may sometimes be such as to require a reduction in the size of the rivet to secure
satisfactory workmanship.
For connections between plates of different thicknesses and for
tap-rivets, the requirements as to diameter are :
II. In cases where rivets connect plates of different thicknesses, the size of rivet
indicated for the greater thickness, with corresponding spacing, will be used where
strength is required, and that indicated for the lesser thickness where water-tightness is
a special consideration, always provided that the greater thickness is not more than
double the lesser.
Where tap rivets must be used they should be \ inch larger than the corresponding
ordinary rivets for the same thickness, excepting taps into heavy forgings or castings,
such as stem and stern posts, which should be \ inch larger. Where strength is re-
quired tap rivets must not penetrate less than I diameter, and should penetrate 1 1 diam-
eters when the thickness of metal will allow it.
The following extract and Table LX. refer to the length of
rivet necessary to form the point :
19. Special care will be taken in riveting that rivets used are of sufficient length to
insure a proper point, the aim being to have the rivet a trifle long, if anything. Such
cutting as is necessary should be done while the rivet is still a dull red, and the point
finished after further cooling. Allowances for length over the thicknesses connected
are given in Table LX., below, the allowance being for two thicknesses only. An
additional allowance of J^ should be added to that given for each additional thickness
connected, unless the additional thickness is less than T3? inch, when gV inch additional
allowance should be sufficient. The allowances given in the table are based upon the
RIVETED JOINTS.
243
employment of hand riveting, and are not sufficient in the case of power riveting, for
which an added allowance — about \ inch — should be made in each case. This
table must be used judiciously and not absolutely depended upon.
TABLE LX.
ALLOWANCE IN LENGTH OF RIVETS FOR POINTS.
In.
In.
In.
In.
In
/».
In.
Ins.
Ins.
Diameter of rivet.
1
f
1
f
i
1
I
I|
Ik
Allowance for point, over 2 thicknesses connected.
Type of point :
Countersunk.
Hammered.
t
I
\
f
t
*
j
I
I
s
Button.
\
5
f
1
i
The allowances given above apply only to rivets which fit the holes neatly, as here-
inbefore described.
Laps and Straps. — The required thickness of single and
double butt straps is given in the following extracts and the
breadth of laps and straps in Table LXI.
TABLE LXI.
BREADTH OF LAPS AND STRAPS.
Diameters.
Breadth of laps for single riveting.
Breadth of laps for double chain riveting.
Breadth of laps for double zigzag riveting.
Breadth of double-riveted butt laps.
Breadth of laps for treble riveting.
Breadth of treble-riveted butt laps in outside plating.
Breadth of edge strip for single riveting.
Breadth of edge strip for double riveting.
Breadth of butt strap for double riveting.
Breadth of butt strap for treble riveting.
Breadth of double butt strap, double-riveted.
Breadth of double butt strap, treble-riveted.
5;
5
8
9
6
Hi
Hi
16
12
\
SINGLE STRAPS.
1 6. Single butt straps and edge strips, when single- or double-riveted, should be of
the same thickness as the plates connected, and where the plates connected are of
different thickness they should be of the same thickness as the lighter plate. Single
butt straps, when treble-riveted, should be i^ times the thickness of plates which
they connect.
DOUBLE BUTT STRAPS.
17. Double butt straps should not be used for water-tight work, owing to difficulty
in calking. They may be used to advantage, however, in connections requiring great
strength, but not water-tightness. The thickness of each strap should be one half the
244
MACHINE DESIGN.
thickness of plates connected for double-riveted straps and five eighths the thickness for
treble-riveted straps. * * * For double butt straps the size of rivet to be used
should be as follows :
For plates from 15 to 20 pounds, exclusive, f-inch rivets.
For plates from 20 to 25 pounds, inclusive, f -inch rivets.
For plates above 25 pounds, as per Table LIX.
Since double butt straps are, as a rule, used in hull work in
joints requiring strength but not tightness, the spacing of the rivets
in such joints is that required for maximum efficiency, the assump-
tions being : Tensile strength of plate, 63,000 Ibs. per sq. in.;
shearing strength of rivets, 50,000 Ibs. per sq. in. ; for single
straps, plate to be through-countersunk.
TABLE LXII.
SPACING OF RIVETS.
Number of
; Diameters from
Center to Center.
Single-riveted laps and straps.
Double-riveted laps and straps.
Treble-riveted laps.
Treble-riveted straps, with alternate rivets in third row omitted.
Longitudinal seams of plating required to be water-tight (excepting
single-riveted laps and straps).
Connections of transverse frames not water-tight to outside plating.
Connections of deck plating to beams ; of nonwater-tight longitudinals
to outside plating ; of the angles and stiffeners to bulkheads when '
entirely above the water line, and in general where special strength
is not required.
Connections of floor plates, brackets, lightened intercostals, etc., to
clips and angles ; of the vertical keel angles to the flat and vertical
keel plates and to the flat keelson plates beyond the limits of double
bottom, provided water-tightness is not required.
Connections of angles and other stiffeners to bulkheads at or below the
water line ; of boiler and engine bearings and foundations generally.
Connections of inner bottom plating to all frames and longitudinals.
Connections of angles of water-tight frames and longitudinals to all
plating, and in general where water-tightness is required between
shapes and plates.
Angles and other stiffeners to bulkheads forming supports to turrets,
barbettes, connections of armor shelf angles to plating, etc.
Connections between staple angles of water-tight floors and the floor
plates.
In special cases of intercostals, beam ends, etc., where strength is re-
quired in connections of limited extent, and in all other exceptional
cases, spacing to be as required by circumstances, except that the
rivets in the same line should never be spaced less than
Rivet-spacing. — General proportions for the spacing of rivets
are given in Table LXII. Where this spacing cannot be followed
exactly, it may be slightly closer for heavy plates and slightly
RIVETED JOINTS. 245
wider for light plates. The division between " light " and " heavy "
plates lies, with single-riveting, at 7^-lb. plates ; with double-
riveting at 15-lb. plates; and, with treble-riveting at 25-lb. plates.
15. When strength is required in laps and butted connections of plating, with the
spacing indicated, single-riveting is suitable only for plating under 12^ pounds and
double-riveting for plating under 25 pounds. * * * For maximum strength in connec-
tions of plating above 30 pounds it will generally be found that quadruple-riveting is re-
quired.
DISTANCE BETWEEN Rows.
1 8. Centers of rivets should be placed not less than if times the diameter from the
edges of plates connected. In double- and treble-riveting, for laps and single straps, the
distance from centre to centre of rows should not be less than z\ diameters ; in butt laps and
double butt straps the distance between centres of rows should be not less than 3 di-
ameters (butt laps should be at least double-riveted). For zigzag riveting the distance
between centres of rows should not be less than i| diameters for rivets spaced 4 di-
ameters apart in rows.
Punching, Drilling, Riveting. — The size of the rivet-hole for a
given diameter of rivet has been given previously.
4. All rivet holes through material i inch or more in thickness should be drilled, or,
if punched, should afterwards be reamed to finished size. The increase in diameter of
hole due to reaming should be equal to at least one eighth the thickness of the material.
In punching, where possible, holes will be punched from the side which will form the
faying surface.
5. Great care must be taken in punching to prevent holes from coming unfair. Any
unfair hole must be reamed out before riveting, and a rivet suitable to the increased size
of hole inserted.
In countersunk holes, where the depth, B, given in Fig. 97,
would extend through the plate, the countersink should be carried
to within ^ in. of the bottom. Power riveting is preferred for
torpedo-boat work. Rivets, in general, less than |-in. diameter
should be driven cold ; in torpedo-boat work, j^-in. rivets also
may be thus driven.
2. AMERICAN BUREAU OF SHIPPING. — In the rules of this
bureau for the building and classing of vessels, the character as-
signed to the latter is expressed by numerals ranging from A i to
A 3, the former being the highest grade and corresponding with
the grades A i of Lloyd's Register and 3/3 — i.i of the Bureau
Veritas. Vessels classified under the latter grades are regarded
as fitted for the carriage of all kinds of cargo on all voyages.
New vessels built in conformity with, or equal to, the rules of the
American Bureau are graded thus : 1st Class, A i for 17 years ;
2d Class, A i for 13 years ; 3d Class, A i for 10 years. If built
under inspection, these terms are increased by three years for the
246
MACHINE DESIGN.
1st and 2d classes and by two years for all others. The follow-
ing extracts are taken from the rules (1901) of this Bureau :
Outside {skin) Plating : of all (steel) steam vessels whose length does not exceed
TI times their depth to be, for half the vessel's length amidships, and at ends, the thick-
ness specified in Table LXIII. * * * Skin plates (in general) must not be less than
6 frame spaces in length. * * * Butts in adjoining strakes must be shifted clear of each
other not less than two frame-spaces. Butts in alternate strakes must have a clear shift
of not less than one frame-space. * * * The butts of all skin-plates must be planed and
close fitted and the butt-straps be drawn up iron to iron. * * * The edges of all skin
plates to be sheared from their faying surfaces and those of outside strakes to be planed
or chipped fair. All butts and seams to be efficiently calked. * * * The skin plat-
ing can be worked in out-and-in strakes or flush. If worked in out-and-in strakes, the
insides strakes must be fitted to frames, iron to iron, and solid liners must be fitted be-
tween the frames and the outside strakes. * * * If the skin plating is worked flush,
* * * continuous edge-strips, with their butts shifted well clear of the butts of the skin-
plating to which they are secured, must be properly worked on the plating seams.
TABLE* LXIII.
MINIMUM THICKNESS OF OUTSIDE PLATING AND FLAT PLATE KEEL.
17 Years Class. Thickness in Lbs., Per Square Foot.
Sheer
Strake.
Sheer to
Bilge.
Bilge and
Bottom.
Garboards.
Flat Plate
Keel.
Numerals.!
,c .
.e .
wC .
j3 .
j- .
If
Si
1
It
1
j
II
If
i
~5 B
rt c
P
w
!s|
||
2,000 and under 3,500
12
10
IO
9
II
10
12
12
16
12
5,000 6,500
16
14
13
II
14
12
16
l,S
18
14
8,000 10,000
19
16
15
12
16
13
18
16
22
18
14,000 16,500
24
19
17
14
19
16
21
19
28
22
I9,OOO 22,000
30,000 36,000
27
2Q
20
22
19
22
15
18
21
24
17
20
11
21
24
32
24
27
42,000 48,000
24
24
19
26
21
28
2S
37
28
56,000 64,000
31
26
21
28
22
30
27
39
29
72,000 80,000
26
28
22
30
24
32
29
31
IOO,OOO IIO,OOO
3<>
27
30
24
33
26 j 35
30
44
32
NOTE. — The following to be the minimum width of main sheer strake for f length
amidships for vessels of all grades. Numeral under 10,000, 33 inches ; numeral 10,000
and under 16,500, 36 inches ; numeral 16,500 and under 22,000, 40 inches ; numeral
22,000 and above, 45 inches.
The minimum width of garboards and flat-plate keels for f length amidships for
vessels of all grades to be as follows : numeral under 10,000, 30 inches ; numeral 10,000
and under 16,500, 33 inches ; numeral 16,500 and above, 36 inches.
*The table is reproduced in part and for the 17-year class only.
fThe numeral = (Depth -f- £ breadth -f | girth) in ft. X length, in ft.
RIVETED JOINTS.
24?
Butt-straps :
The widths for single-, double-, and treble-riveted butt-straps, suited to different
series of rivets, are specified in Table LXIV. * * * Butt straps must in no case be
less than 2 Ibs. thicker than the plates to which they are secured. Treble-riveted butt
straps must, in all cases, be at least 4 Ibs. thicker than the plates to which they are
secured.
TABLE LXIV.
FOR DIAMETER OF RIVETS, BREADTH OF LAPS, LAPPED BUTTS, WIDTH OF
BUTT STRAPS AND BREADTH OF EDGE STRIPS ON PLATE SEAMS.
Thickness of Plates in Ibs. weight
1
per square foot.
Diameter of Rivets in sixteenths
IO
"1
15
*7i
20
221
*5
27;
30
321
35
37*
40
of an inch.
9
IO
ii
12
12
12
14
14
16
16
18
iS
20
Size in inches of Countersink for
Rivets of Plating.
Breadth of Laps, in inches, for
I
I
iA
*A
'A
'A
iA
'A
iA
'A
i«
Iff
i«
Single Riveting.
2
at
*1
2f
H
2f
Breadth of Laps, in inches, for
Double Riveting.
Width of Butt Straps, in inches,
31
3*
4
41
41
41
5i
5k
6
6
7
7
71
Double Riveted.
Width of Butt Straps, in inches,
7
7*
81
91
91
91
ii
ii
"1
1*1
14
14
'5i
Treble Riveted.
Breadth of Edge Strips for Plate
IOJ
"1
I2f
14
14
14
i6i
i6J
18*
iSi
21
21
23
Seams, in inches, for Single
Riveting.
Breadth of Edge Strips for Plate
4
41
4f
51
51
51
6i
6*
71
71
81
81
9
Seams, in inches, for Double
Riveting.
Breadth of Double-riveted Butt
71
8
8*
9:!
9t
9f
ii
ii
13
13
141
Ul
15?
Laps.
41
4i
5
5
5
6
6
6
6
6
Breadth of Treble-riveted Butt
Laps.
71
7j
9
9
9
9
roj
roi
wj
The number and thickness of butt-straps varies with the ves-
sel's numeral for plating. The following specification applies to
the hull whose midship section is shown in Fig. 98.
Vessels whose numeral is 30,000 and under 48,000 to have the butts of sheer
strake, 2 strakes of plating at bilge and upper deck stringer-plate secured with treble-
riveted butt straps for J the vessel's length amidships. The butt straps of bilge and shear-
strakes, also deck stringer-plate if it is under 54 ins. wide, to be 7 Ibs. thicker than the
plate to which they are secured. The back row of rivets in foregoing butt straps to be
spaced similar to the other rows. In addition to above, the remaining skin-plates are
to be secured at their butts with treble-riveted butt straps 7 Ibs. thicker than the plates
to which they are secured for | the vessel's length amidships. If any of the foregoing
skin plates exceeds 54 ins. in width, the butts of same are to have butt straps IO Ibs.
thicker than the plates to which they are secured. * * * When the vessel's numeral
is, or exceeds, 16,500, the lapped butts of outside plating are to be treble-riveted
throughout.
248 MACHINE DESIGN.
Rivets and Rivet- Work :
I. The diameters of rivets for the different thicknesses of plates and angle bars are
specified in Table LXIV. 2. The longitudinal laps of skin plating, except main sheer
strake, worked in, out- and in-strakes, and which is sixteen pounds and above in thick-
ness, to be double-riveted. Main sheer strakes fourteen pounds and above to have the
lap at their lower edge double-riveted. 3. The longitudinal seams of skin plating that
is worked flush, and which is twenty pounds and above in thickness, to be secured
with edge strips having two rows of rivets on each side of seam. 4. The longitudinal
laps of skin-plating which is under the above specified thicknesses, for double-riveting,
to be single-riveted. 5. All double-riveting in longitudinal laps and edges to be chain
fashion, the distance between the rows in lap riveting to be not less than two and three
quarter times, nor more than three times the diameter of rivet, from centre to centre of
rivet and the laps are to be not less in width than six times the diameter of rivet.
Double riveted edge strips to be the width specified in Table LXIV., and the spacing of
rivets between rows to be similar to that hereafter specified for double-riveted butt
straps. 6. Single-riveted laps to be, in width, three and a half times the diameter of
rivet. Single-riveted edge strips to be the width specified in Table LXIV. 7.
Longitudinally the distance between rivets in laps and edges, of skin plating, and
the laps and seams of all plating required to be calked watertight, to be, from
centre to centre, four times the diameter of rivet, providing the plating does not exceed
twenty pounds in thickness ; if the plating exceeds twenty pounds in thickness, the dis-
tance may be four and a half times the diameter of rivet. 8. The rivets in all butts —
except the third row of a butt which is treble-riveted — are to be spaced apart, from
centre to centre, three and a half times the diameter of rivet ; and the distance between
rows of butt rivets to be from two and a half to three diameters of rivet, from centre to
centre of row. 9. The rivets in the third row of a butt, which is treble-riveted, may be
seven diameters of rivets apart, from centre to centre, except otherwise specified. 10.
The spacing of the rivets which secure the frames to skin plating, and to floor plates, to
be, from centre to centre, not more than seven and a half times the diameter of rivet,
except frames having watertight bulkheads secured to them, in which the spacing, from
centre to centre, must not exceed five times the diameter of rivet. * * * 15. When the
thickness of skin-plating amidships demands double-riveted laps or edges, the same is
to be continued right fore and aft. 16. The diameter of rivets for securing plates, or
plates and angle bars, of different thicknesses, to each other to be regulated by the
thicker of the two. 17. When three or more thicknesses are riveted together, the
thickest of the parts is to regulate the diameter of rivet. * * * 20. Rivet holes are to
be fairly and regularly pitched, and must in no case be nearer the edge of a plate or
angle bar than their diameter. 21. It is recommended that all rivet holes be punched
one sixteenth of an inch smaller than the diameter of rivet to be used, and the holes be
reamed to the size of rivet after the parts are in place. Any structure, or parts, where
more than two thicknesses of material are riveted together, and all longitudinals, floors
or brackets in double bottom, also keelsons and stringers in holds, to have their rivet
holes punched one sixteenth less than the size of rivet to be used, and the holes reamed
to size of rivet after the parts are in place. 22. Rivet holes are to be punched from
the faying surfaces of the different parts, and great care must be taken to have them,
in the different parts joined, truly opposite each other. When holes, in the parts joined,
are not truly opposite each other, heavy drifting must not be resorted to ; the holes
must be reamed or drilled fair and a larger size rivet used. 23. The rivet holes in
frames opposite skin-plate laps or edges to be drilled after the plates are fitted in place.
* * * 25. Rivets in skin plating * * * to have their necks beveled under the rivet-
heads so as to fill the countersink made in punching. 26. Rivet-heads should not be
thicker than f the diameter of rivet. The countersinking of all plates and angle-bars
RIVETED JOINTS.
249
to be made by drill and the countersink to extend right tnrough the piate or angle-bar
27. Each rivet to fill its hole, the heads of those for skin plating to be close laid up and
the rivets outside finished flush and fair, except in keel, stem, and stern-post, where
they must be slightly convex.
Fig. 98 is a midship section of a typical steel, 3 -deck, screw
steamer of the 17-year class. The principal data are: Length,
415 ft. ; breadth, 48 ft. ; depth, 32 ft. ; J girth to second deck,
43.5 ft. ; | breadth moulded, 24 ft. ; depth to upper deck, 32 ft. ;
numeral for outside plating = (43.5 -f 24 + 32)415 = 41,292.
Longitudinal Seams.
a. Lap, 6 in. wide, i in. rivets ;
b. Lap, 5 J in. wide, J in. rivets ;
c. Lap, 4-J in. wide, f in. rivets.
250
MACHINE DESIGN.
PLATING AND TRANSVERSE SEAMS.
Plating.
Thickness in Ibs. per sq. ft.
Seam.
|I-g«-d.
At ends.
Throughout.
Treble-riveted butt for.
A. Bulwarks.
10
B. Sheer strake.
33
23
J length.
C
D.
25
23
18
18
f length amidships,
f length amidships.
E.
30
20
\ length amidships.
F.
28
20
| length amidships.
G.
23
20
f length amidships.
H. Garboards.
25
f length amidships.
K. Keel, outer plate.
Keel, inner plate.
34
25
28
extends \ ICE
gth amid.
Throughout.
Throughout.
CHAPTER V.
KEYED JOINTS; PIN-JOINTS.
The term "key" is applied to two forms of removable fasten-
ings : The key proper, which is splined in a shaft to prevent relative
rotation and sometimes axial movement of an attached member,
as a pulley or gear-wheel ; and the "through-key" or " cotter"
which joins parts subjected to tensile or compressive stress or to
both, as the sections of a pump-rod, the strap and body of a con-
necting rod, etc. The key proper is purely a locking device de-
signed to resist shearing stress on the sectional area formed by its
breadth and length ; the cotter not only unites the parts, but, if
of suitable length, gives, through its taper, a limited range of axial
adjustment, while it withstands shearing at two transverse sections,
each the product of its breadth and depth. Both forms are made
generally of steel, although wrought iron finds infrequent use.
54. Forms of Keys.
Keys for shafting may be classified as : Sunk keys, i. e., those
which are fitted in key-seats cut in the shaft and in the attached
hub ; Friction keys, for which the key-seat in the shaft is omitted
and which drive, or are driven by, the latter through friction only ;
and Keys on the Flat which, in their action, are intermediate
between the two former classes.
i . SUNK KEYS are almost universally of the square or flat forms,
shown in Figs. 99 and 100, respectively.
Square Keys prevent relative rota-
tion only. They are approximately
square in section with opposite sides
parallel ; the width, W, is slightly
less than the depth, T, and the key
is sunk in the shaft a little more
than 1 T; the key bears only on
the sides of the key-seats in shaft
and hub, there being usually a slight clearance at top and bot-
tom. Such a key will not secure the attached hub against axial
movement. The latter must be prevented by set-screws pass-
251
252 MACHINE DESIGN.
ing through the hub and bearing on the key ; by making the
hub a shrinkage or forced fit on the shaft ; by splitting the
hub, boring it for a pressure fit, and drawing the split to-
gether with bolts ; by using loose collars with set-screws on the
shaft at the ends of the hub ; or, finally, if the hub be keyed at
the extremity of the shaft, by threading a nut on the latter. On
the other hand, the square key drives practically through its resist-
ance to shearing stress on a longitudinal section, and, therefore,
exerts no bursting pressure upon the hub and has no tendency to
force the latter into eccentricity with the shaft. Hence, while its
liability to tipping in its seat unfits it — unless secured by screws
or dowels — for heavy loads, it is suitable for machine tools or
other work in which accurate concentricity is required or in which
the parts may be disconnected frequently.
The Flat Key (Fig. 100) locks both axially and circumferen-
tially. Its section is rectangular and its sides are parallel, but
its top and bottom, while plane, are
inclined toward each other to form a
wedge. The key is fitted accurately
on all four surfaces. When driven
home, the compression and elasticity
of its metal and that of the hub, lock
FIG. 100. , . . .
the latter effectually against motion in
any direction. There are, however, a bursting pressure upon the hub
and a tendency to spring the latter out of truth, both with the axis
and with a plane normal to it. This key, as Mr. John Richards has
pointed out, drives as a diagonal strut rather than by pressure
normal to its face. If the angle, a, Fig. 100, be made about 30°,
fair proportions will be obtained with a reasonably low value for
the magnitude of the bursting element of the driving force. The
taper is usually ^-inch per foot. The key is suitable for heavy
or light work in which slight inaccuracy in adjustment is not
material.
The Feather Key is a square key fitted for relative axial move-
ment of the connected parts, as in a clutch-coupling. The key is
secured in a key-seat in either the shaft or hub and the other key-
way is made a working fit. The necessary surface to prevent wear
from sliding movement may be had by increasing the length and to
some extent the depth of the key. The latter is fastened to the seat
either by countersunk screws, or by dove-tailed ends, or, in the case
KEYED JOINTS; PIN-JOINTS.
253
FIG. 101.
of a hub, by gib (hooked) heads at the extremities of the feather.
When the required surface warrants their use, two feather-keys
set diametrically apart are better than one in equalizing the strain.
The Woodruff Key * (Fig. 101) may be of either the " square " or
" flat " types. It has one-milled key-seat with parallel sides, but
of circular outline at the bottom and hence
of varying depth ; the other key-seat is of
the usual form. The maximum depth of
the circular key -seat is considerably greater
than that of the ordinary type and the
shaft is, at that point, correspondingly
weaker. On the other hand, the key is so
firmly inset that it cannot possibly tip in
its seat as the usual key may ; and, further,
the circular key will rotate in its seat until accurate adjustment
with an angular spline is obtained, while the ordinary taper key
may bear at one point only, if not well fitted. In order to avoid
cutting too deeply into the shaft in securing a long hub, two or
more " square " Woodruff keys may be inset in axial alignment
with each other so as to engage the same key-seat in the hub.
"Quartering" Keys. — With large shafts, especially when the
hub to be secured is a loose fit, it is better to use two keys set 90°
apart on the shaft, since the second key will oppose the hub's
tendency to rock on the single key as a pivot. If two sunk keys
be thus used, the width, W, of each need be but one half that
required for a single key while the thickness, T, will also be less.
In some cases, a sunk key is used to
do the driving while a saddle-key or key
on the flat, set quartering, steadies the
hub and gives a rigid joint.
The Peters System of semi-sunk keys
is shown in Fig. 102. It is suitable es-
pecially for fastening members having a
reciprocating motion, either rotary or
rectilinear, as, for example, a rock-shaft
arm. There are two pairs of keys set
The keys of each pair have each one
The latter engage, while the parallel
FIG. 102.
preferably 135° apart,
parallel and one tapered side.
* The Whitney Manufacturing Co. , Hartford, Conn.
\
254
MACHINE DESIGN.
FIG. 103.
sides abut against those of parallel-sided key-seats. The seats are
normal to a radial and are partly in both shaft and hub, so that, for
motion in either direction, the system supplies a radial driving face.
The tapered sides enable the keys, when driven
home, to make a rigid joint.
Pin-Keys, Fig. 103, may be used when the hub
to be secured is on the end of the shaft. A cylin-
drical or taper hole is drilled and reamed at the
shaft circumference, parallel to the axis, and one
half each in shaft and hub. Into this hole a closely
fitting cylindrical or taper-pin is driven which thus forms a sunk
key. The method is accurate and cheap but is used only with
light work.
2. FRICTION KEYS. — With this form no key-seat is cut in the
shaft, the holding power of the key being due to friction only.
The Saddle Key is shown in Fig. 1 04.
The sides are parallel, the top tapered,
and the bottom concave, to fit the shaft.
When the key is driven home, the friction
causes it to grip the shaft. Its driving
power is small and the principal uses of
the key are to prevent rocking, when
set quartering with a sunk key, and in
temporary service, as in setting an eccentric. Locomotive eccen-
trics are sometimes secured permanently by two saddle-keys, fitted
90° apart, whose curved faces have
longitudinal grooves or teeth which
cut into the shaft when the keys
are driven home.
The Kernatil Key* Fig. 105,
drives only in one direction. The
key, K, is approximately a seg-
ment somewhat less than 90° in
extent, the inner face of which is
curved to the radius of the shaft,
the outer to that of an eccentric
slot, S, formed in the hub, H.
The inner surface of the key is left rough, the outer being finished
and smooth. Hence, when the hub is rotated in the direction of
FIG. 104.
FIG. 105.
*Reuleaux's "Constructor," Suplee translation, 1895, p. 49.
KEYED JOINTS; PIN-JOINTS. 255
the arrow, it slides over the key until the latter grips and revolves
the shaft. A set-screw at a is used to set up the key and a simi-
lar one at b to loosen it.
The Blanton Fastening* while not a friction-key, is, to some
extent, a modification of the Kernaul principle. If, in Fig. 105,
the key, K, be fixed on the shaft, it is evident that, with the circum-
ferential clearance shown in the slot, S, the hub, H, will drive the
shaft when rotated in the direction of the arrow ; but, when the
direction of rotation is reversed, the hub will become loose with
limited angular play, so that it may be slipped along the shaft and
removed readily. This is essentially the principle of the Blanton
fastening which is applicable especially to the lifting cams of ore
stamp-mills, largely because of the ease with which the cams may
be disconnected and others substituted. The surface of the shaft
is formed in a series of corrugations corresponding with a series of
keys, K, and the hub is slotted to fit, with clearance at the ends
of the slots, which ends are inclined and not radial, as in Fig. 105.
Roller Keys. — If, in Fig. 105, there be substituted for the key
a hardened steel cylindrical roller whose diameter is a little less
than the maximum radial width of the slot, S, it is obvious that
a slight rotation of the hub will cause the roller to bind and thus
drive the shaft. The connection is, like the Blanton, readily dis-
engaged but is suitable for light work only. In fitting it, the ends
of the hub are bored concentrically with the shaft and to the diam-
eter of the latter, while the central recess for the key is circular
but eccentric with the shaft.
The Cone-Key depends wholly upon friction for its driving power.
The hub of the pulley or other member to be secured, is bored
centrally with a tapered hole whose least diameter is greater than
that of the shaft. A cast-iron bushing, bored to fit the shaft and
turned to the taper of the hub-bore, is then split longitudinally
into three equal parts, giving thus three saddle-keys, each nearly
120° long circumferentially. These keys, forced between shaft
and hub, hold and drive the latter. The diameter of the shaft
may be varied, within limits, for the same hub, by using a cone-
key of the proper bore. Perhaps the most effective application
of this principle is the Sellers Double Cone Coupling for shafts,
patented and manufactured originally by William Sellers and
*F. R. Jones : "Machine Design," 1899, Part II., p. 205.
256
MACHINE DESIGN.
Company. As shown in Fig. 106, each shaft, as A, of the two to
be connected is surrounded by a hollow cone, B, split only in one
FIG. 1 06.
place. The cone is bored to fit the shaft and turned to a taper
corresponding with the bore of one end of the encircling shell
or " muff," C. The cone-bushings are bound to the shell and
shaft through friction due to the axial stress upon three bolts, D, of
square cross-section which lie in rectangular slots in both cones and
draw the latter together and into the shell. As an additional pre-
caution against slipping, each cone is attached positively to its
shaft by a sunk key, E. The taper of the cones is about I : 7^-.
FIG. 107.
3. KEYS ON THE FLAT. — This type, Fig. 107, is, in driving
power, intermediate between saddle and sunk keys, being recessed
in the hub and bedded on a flat planed on the shaft. The upper
KEYED JOINTS ; PIN-JOINTS.
257
side of the key is tapered. Fastenings of this character were used
formerly, as in Fig. 1070, in securing large hubs, as those of
paddle-wheels, on square shafts. In such cases, the keys not
only lock the hub in place, but may be used, within limits, to
align it with the shaft.
55. Proportions of Keys.
The proportions of keys and key -seats have not been standard-
ized and, in practice, show some variation.
i. GENERAL PROPORTIONS. — The following tables give the pro-
portions recommended for general work by Mr. John Richards.*
The notation refers to Figs. 99 and 100.
TABLE LXV.
SQUARE (STRAIGHT) KEYS.
(JOHN RICHARDS.)
Groove in shaft should be T9^ T in depth. Keys should not bear at top and bottom.
TABLE LXVI.
FLAT (TAPER) KEYS.
(JOHN RICHARDS.)
D
i
1}
i f
2
2*
3
4
5
6
7
8
W
A
A
ft
|
1
A
i
1
I*
if
H
1
if
i
For shafts larger than those given in the table, there should be two or more keys,
the width of which may be \D while the depth may be obtained by making angle
0 = 30°.
TABLE LXVII.
FEATHER (SLIDING) KEYS.
(JOHN RICHARDS. )
D
W
T
L
1
J
i f
4
*
5
3
1
9
3j
f
ii
t
13
4j
15
L — Maximum length. With feather fixed in hub, the shaft key- way should be a
little the deeper.
* "Manual of Machine Construction," 1889, p. 57.
258
MACHINE DESIGN.
2. SHAFTING. — Professor Coleman Sellers, E. D., gives * the
following proportions :
TABLE LXVIII.
KEYS (SQUARE) FOR SHAFTING.
(WILLIAM SELLERS & Co.)
Diameter of Shaft.
Size of Key.
A*
A
Length of key-seat for coupling = ij X nominal diameter of shaft.
3. MACHINE TOOLS. — The following tables are given herein
through the courtesy of Messrs. William Sellers and Company
and the Brown and Sharpe Manufacturing Company :
TABLE LXIX.
KEYS (SQUARE) AND KEY-SEATS FOR MACHINE TOOLS.
(WILLIAM SELLERS AND Co.)
Diameter of Shaft.
I" and under.
Over \»
I '-'and I?'
2
2
4
51
7
9
ii
13
Size of Key.
Size of Key-Seat
* " The Stevens Indicator," IX., 2.
KEYED JOINTS ; PIN-JOINTS.
TABLE LXX.
KEY-WAYS FOR MILLING CUTTERS.
(BROWN AND SHARPE MANUFACTURING Co.)
259
Diameter (D) of Hole.
Width ( W ) of
Key-way.
Depth (rf) of
Key-way.
Radius (tf).
r to Ty
A"
*3/
.020"
f I
H i i
A
ft
.030
•035
iA J 1
T5
A
.040
:(? |
2TV 2 i
I
t
•3°
.060
.060
*A 3
A
A
.060
4. STATIONARY ENGINES. — The following table gives the prac-
tice of one of the leading builders in the United States with regard
to the keys (square) for cranks and the flat (tapered) keys for the
fly-wheels of stationary engines :
TABLE LXXI.
ENGINE KEYS.
Diam. of
Shaft.
Width of
Key.
Thickness.
T*:«™, ~f
Width of
Key.
Thickness.
Crank
Key.
Wheel Key, Shaft.
Thin End.
Crank
Key.
Wheel Key,
Thin End.
3
I
A J5
16
2f
*f
1
3i
A
A
3
2\
|
4
8
20
Si
2f
5
22
3f
3
6
I 3^
24
3
7
jJL
26
4
3
I 1.
{ 28
3
9
I | j
30
3
10
I *
i 32
4
ii
ITS
i 34
4
3
12
2yV 1
1 36
5
4
3
13
2? !
1 38
5|
4
3
2|
if 4o
5f
4
3i
260
MACHINE DESIGN.
The practice of this company is, with regard to :
Crank- Keys :
(a) No taper for crank-keys.
(b ) Key to be \ in shaft and \ in hub, measured at edge of key -way.
(f ) Use 2 keys, set 90° apart, for cranks bored 23! inches diameter and above.
(d) Use keys for nominal diameter of shaft.
(e ) Keys in all counterbalanced cranks to be on the diameter passing through crank-
pin, but on the opposite side of shaft from the pin.
Fly -Wheels:
(a) Taper of key, ^-inch to I foot ; tapered side in hub.
(£) Thin end of key to be \ in shaft and £ in hub, measured at edge of key- way.
(f ) Use 2 keys, set 90° apart, for shaft 15 inches diameter and above.
(d) For sizes not given in table, use key for next smaller shaft.
5. MARINE ENGINES. — The following table is given herein
through the courtesy of the Newport News Shipbuilding and Dry
Dock Company. The notation (Fig. 100) is :
D = diameter of shaft, ins.
W = width of key and key-way, ins. = ^D + \".
T= thickness of key = -feD + \".
t = depth in shaft, measured at the side.
T — t = depth in hub, measured at the side.
Taper = ^ in. per foot.
TABLE LXXII.
KEYS (TAPERED) AND KEY-WAYS, MARINE ENGINES.
(NEWPORT NEWS SHIPBUILDING AND DRY DOCK Co.)
KEYED JOINTS; PIN-JOINTS. 261
Propeller Keys. — The hub or boss of a screw-propeller is bored
conically and fitted accurately to a corresponding taper on the
after -end of the shaft, the latter being threaded for a nut which
keeps the boss in place. The screw is driven by one or more
longitudinal keys or feathers set in the tapered part of the shaft
and fitting into suitable key -ways cut in the boss. These keys
meet exceptionally severe service in rough weather when the ship
is pitching and the position of the screw varies, in "racing," from
partial to deep immersion. The screw-propellers for U. S. naval
vessels are now made of manganese bronze or approved equivalent
metal. With regard to the proportions of keys for naval pro-
pellers, Lieutenant-Commander F. H. Bailey, U. S. Navy, in
charge of designs, Bureau of Steam Engineering, Navy Depart-
ment, says :
" These keys are properly feathers since they are not usually driven, although this
has been done in the case of some torpedo-boats. In our practice, the width of the key
is about one and a half times its thickness, the latter being such that the side-pressure,
calculated from the maximum turning moment on the shaft, shall not exceed about
25,000 Ibs. per sq. in. on the propeller-hub. Thus, if a key is 2 ins. x3 ins., bears
for 30 ins. of its length, and is half in hub and half in shaft, the bearing surface would
be 30 sq. ins. If the mean distance of the key from the centre of the shaft is 8 ins.,
the maximum turning moment on the shaft could be 30 X * X 2S>OO° X & =6,000,000
inch pounds which maximum moment should be from 1.3 to 1.4 times the mean turn-
ing moment calculated from the horse-power and revolutions. Usually, we design the
key so that the pressure on the key-way shall be about 22,000 Ibs. per sq. in. If this
pressure gives a key whose thickness is over £ of the shaft diameter, two keys set oppo-
site are preferable."
56. Stresses on Keys.
Keys for shafting are subjected to shearing stress on the longi-
tudinal cross-section and to crushing stress on the sides, or, when
the key acts as a strut, in the direction of an approximate diagonal
to the transverse section. As a general rule, it is better, in design-
ing, to follow the empirical proportions given in the various tables
which have been quoted, since keys with these dimensions, when
well fitted and driven, seldom fail by either shearing or crushing.
It is more probable that the shaft will be sheared or that the key
will become loose in its seat The latter action is soon fatal to
-the joint, since, through lost motion, vibration, and shock, the key,
if not secured, will back out, or its sides or those of the key-seat
will become so battered as to be useless. In work of an unusual
nature or requiring especial care, keys may be designed or empir-
262 MACHINE DESIGN.
ical proportions tested by the application of the principles given
below.
Shearing Stress on Key. — Let P be the load on the crank-pin
or pulley-rim ; R, the lever-arm of that load from shaft-centre ; D,
the diameter of the shaft ; L, the length, and W, the width of the
key ; and Ss, the working unit shearing stress on the longitudinal
cross-section. Then :
Shearing resistance of key =L x W x St ;
Moment of key-resistance = L • W- St x -£>/2 ;
Moment of load = P x R.
Equating the moments :
Since the length, L, of the hub is known, the minimum value of
l¥may be obtained from (141).
If the strength of the key against shearing is to be equal to
that of the shaft in torsion, the width, W, may be found by equat-
ing the resisting moments of both. Let SJ be the allowable
shearing unit stress at the circumference of a solid cylindrical
shaft, the polar modulus of the section being Jjc. Then :
Resisting moment of shaft = S' — = Sr • — ^- :
1 c 16 '
.
-=!•!•?• I
For a hollow shaft of outer and inner diameters, Dl and d, re-
spectively, Jjc becomes
16 Dl
and the leverage of the key is DJ2.
Crushing Stress on Key. — The total resistance of a key to side-
wise crushing is equal to the least area of the parts of the side
inset in shaft or hub, multiplied by the working unit crushing
KEYED JOINTS ; PIN-JOINTS.
263
stress, Sc. The leverage of this resistance is, as before, D/2, ap-
proximately. Assume that the key is inset one half the depth, T.
Then:
Crushing resistance of key = L x T/2 x S ;
Moment of key-resistance = L • T/2 • Sc x DJ2.
y
Equating this moment with that of a solid, cylindrical/shaft to
torsion :
Equating the values of L from (142) and (143):
*r> ^J_ TTT
(143)
('44)
which values apply to a key whose strength, in shearing and
crushing, is the same and is equal to that of its shaft (solid, cylin-
drical) in torsion. If Sc = 2St, we have T = W, which is approx-
imately true for square keys. For flat (taper) keys, which drive
as a strut and are therefore relatively shallow, Richard's propor-
tions (Fig. 100) give T = Wtan 30°. The crushing action on the
sides is, other things equal, greater in square keys and feathers.
The flat key is wedge-shaped, tends to drive on a diagonal to
the cross-section, to tip in the seat, and thus to relieve the sides
somewhat.
W *,
'"1
Shearing Stress on Shaft. — The load on a square key or feather
acts to shear the shaft on the plane of the base of the key-seat,
i. e., in the direction, M-N, Fig. 108. Assume that the unit
264 MACHINE DESIGN.
shearing resistances of shaft and key are the same, that the key is
sunk l Tin the shaft, and that M-N = 0-N = W. Then :
. T=2K-L=2(CK-CL\
Substituting the values of C- K and C-L, we have, with sufficient
approximation :
Neglecting the last term and under the conditions given, the
thickness of a key varies directly as the square of its breadth.
Hence, since the shearing resistance varies as the breadth, the use
of two or more keys in the place of one is attended, considering
shearing stress only, by a reduction in the total metal used in keys
and in the amount slotted out for key-ways.
The Grip of Friction Keys. — The holding power of these keys
cannot be calculated with accuracy. The cone-key, Fig. 109, is
driven home by a total maximum
£g^0^A force, Q, which, through the ex-
pansion of the hub and the com-
IJI pression of the cone-bushing, pro-
duces the normal unit pressure, N,
^4i at the contact-surfaces of hub and
r ^ key and the radial unit-pressure,
. ft, % \ p^ at the jomt between key and
T shaft. If 9 be the half angle of
f the cone, the component of N
FIG. 109. which is normal to the axis, will be
Pl = Arcos 6. Letting L = axial
length of bearing, R^ = mean radius of outer surface of cone,
R^ = radius of shaft, and JJL and // = coefficients of friction, the
resisting moment to circumferential slip will be, between :
Resistance. Moment.
Shaft and bushing: 2xR0L x /> '> ^~R^LP^ x ^0 '>
Bushing and hub : 2~RVL x />' ; 2-R^LPjt! x R^ ;
which moments should be = P.R, the turning moment on the shaft.
* Marks: "Relative Proportions of the Steam Engine," 1896, p. 97.
KEYED JOINTS; PIN-JOINTS.
265
In these expressions, the surface removed in dividing the bushing
is neglected. At the instant of driving home :
(2 (Max.)
I cos ^
in which F and Fl are the total frictional resistances acting along
the contact-surfaces. While Q may be measured, the values of p
and p.' ', as pointed out in §4, are uncertain in such cases. Again,
the magnitude of P0 is fixed by that of Pl and the action of the in-
tervening metal. Owing to the slots, the bushing cannot strictly be
treated as either a thick cylinder or a thin band. In fair approxi-
mation, the grip may be estimated by considering the cone as a
hollow cylinder of inner and outer radii, RO and Rv respectively,
subjected to the external pressure, Pv
57. Through-Keys : Forms.
The through-key (cross-key, cotter) is simply a tapered cross-
bar of rectangular or circular section driven through two members
to be joined, as the sections of a pump-rod, a piston-rod and piston,
a piston-rod and cross head, the strap and body of a connecting-
rod, etc. The joint may be designed to resist tension only, as in
foundation bolts ; but is usually adapted for both tensile and com-
pressive stresses. If the connected parts are movable axially and
the key is sufficiently long,- the latter
gives means for longitudinal adjustment
of the joint.
(a) Cross-keyed Joints. — Fig. 1 10
shows such a joint as used for connect-
ing the piston and rod of a locomotive
engine. The rod has a shoulder at A
against which the piston is driven and
on which it bears ; its end has a sharp
taper (J in. in 4 ins.) from the shoulder
to the extremity, B, and fits in a conical
hole of the same taper in the piston, C; and the rod and piston
are joined rigidly by a key, K, whose sides are parallel and
whose top has a taper of \ in. in 12 ins. The sharp taper on
the rod makes the parts readily detachable when the key is
backed out.
FIG. no.
266
MACHINE DESIGN.
In Fig. 1 1 1 * there are given two forms of a similar joint be-
tween the piston rods and crossheads of locomotive engines. In
FIG. in.
that to the left, the body of the rod is reduced for the taper and
the crosshead is held by tension upon the extremity and weakest
part of the rod, while, in
the other type, the taper
is made upon an enlarge-
ment of the rod and the
latter bottoms in the fit,
the joint being thus made
by compressive stress.
The latter method is much
more secure than the for-
mer, in which the tension
invites rupture.
In Fig. 112 a similar
connection between the
sections of a pump-rod is
shown. A socket, G, is
formed on the lower sec-
tion, E, in which the up-
per section, F, is re-
cessed. Through the
socket and the prolonga-
*-j *" tion of the upper rod a
FIG ii2 key -way is slotted. The
section, F, is held rigidly
by the collar, //", formed on it and the key, K, passing through it
and the socket.
* American Engineer and Railroad Journal, January, 1899.
KEYED JOINTS; PIN-JOINTS.
26;
(ff) Gib and Key (Pig. 113). — The brasses of the connecting-
rod end shown in this figure are secured in place by the key, K,
FIG. 113.
and gib, G, both of which pass through parallel-sided key-ways
slotted through the strap, S, and the body of the rod. The
abutting sides of gib and key have a taper of ^ in. to ^ in. in
12 ins.
As the key is driven home, the gib bears on the inner ends of the
strap-slots and the key presses against the outer side of the key-
way in the rod, thus drawing the brasses firmly together and
against the body of the rod. The hooked ends of the gib
overlap the strap and keep it from spreading. The location
of the center of the journal is regulated by the liners between the
brasses and by the position of the key. The latter gives,
therefore, a limited range of adjustment as to the length of
the rod.
In gib and key joints which are to be disconnected frequently or
in which the pressure is excessive, the key may be tapered on
both sides and pass between two gibs similar to G. This ar-
rangement provides increased surface of a durable character for
the key.
268
MACHINE DESIGN.
(V) Bolted Strap-Ends. — Fig. 1 14 and Table LXXIII. give the
proportions of good practice in bolted strap-ends for connecting
FIG. 114.
rods, a form which is more modern and in many respects more
satisfactory than that shown in Fig. 113. In this type, the strap
is secured by bolts, G, passing through it and the body of the
rod, while the key, N, becomes a wedge simply which forces the
brasses together and against the outer end of the strap. The
taper (8 degrees) of the key is considerable and the position of the
latter is regulated by the bolt, O, passing through it and through
both forks of the strap.
(d} Taper Pins. — In light work, taper-pins are frequently used
as cross-keys, as, for example, when driven into a diametrical
hole, drilled and reamed {p a corresponding taper, through the
hub and shaft of a gear-wheel. The dimensions of the standard
taper-pins made by the Morse Twist Drill and Machine Co., are :
Number.
0
i
2
3
4
5
6
7
8
9
10
Diameter at Large
End, Inches.
.156
.172
•193
.219
.250
.289
•341
.409
492
•591
.706
Approximate Frac-
tional Sizes.
A
tt
T3*
A
i
it
a
if
\
H
If
The taper is ^ in. per foot. The length ranges from | in. for
the No. o to 6 ins. for the No. 10, in increments of |- in.
0) Split Pins (Table LXXVL). —These pins may be used to
prevent endwise motion in a nut or a pin-joint. They are circu-
lar in section, cylindrical or tapering in form, and are either split
throughout, except at the head, or at the end only. When driven
home, the pin is locked by spreading the split end.
KEYED JOINTS; PIN-JOINTS.
269
X § 2
X <§£
- Is
3j*
Diam.
of Cylinder,
Inches.
CO O <N ^J-\O CO
\O CO O M Tj-vO OO O N -^"VO 03
>OVO vb vo"t^ t-CO &>' O^O* O
> lO^O VO VO t~* t~-00 ON OS O O M <->
CO -=fr -<t >O
O "-* CO ^ ^}" iO t^.GO ON O *-" CN rO ^" LO^O
MMMt-!l-ll-(MMI-((N<NCS<NMtS<N
J^JSHWHOHB.^-
Diam.
Cylinder,
Inches.
2/0 MACHINE DESIGN.
58. Through-Keys : Stresses.
i. TENSILE, SHEARING, AND BEARING STRESSES. — Assume the
joint, Fig. 112, to be stressed axially and alternately in opposite
directions. Failure may occur by :
Tensile Stress :
(a) On sections, E or F\ (ft) on section, Z, where reduced by
the keyway ; (c) on socket, G, where similarly reduced ; (d} on
the key, due to bending.
Shearing Stress :
(e) On the key at inner surface of socket, G ; (/) on socket, G,
above key; (g) on collar, H ; (/i) on section, L, below key.
Bearing Stress :
(fc) On key ; (/) on section, L ; (?#) on socket, G ; («) on
collar, H.
Take St, St = o.8^S(, and Sh as the permissible unit tensile, shear-
ing, and bearing stresses, respectively. The exact manner in
which the key is loaded, is unknown. Assume it to be a simple
beam, uniformly loaded with total stress, P. Then for condition :
(b)
(c)
0) P=2(b-h-St);
(/) P=2(D-d)hl.St
(g) P=xJ./is-S,;
(h] P=2(d-/i2-St);
(k) P=b-d-S,-
(»)
KEYED JOINTS; PIN-JOINTS. 271
It is evident that the more important of these stresses are shown
by (<*)» 00 and (0- Taking S. = o.SSt and equating (d) and (e) :
btf
%'~d° S<= I-6A&-S;;
h=l.2d. (I45)
Substituting in (e) and equating (ff) and (e) :
i.c>2bd-S = -d-
b = o.2?d, say 0.25^ (I46)
a ratio which conforms with good practice. The value of D in
terms of d may be found, for tensile stress, by equating (b) and (c)
and making b = o.2$d. This value, however, is less than that for
bearing pressure obtained by equating (/) and (in). From the
latter equations :
D=2d. (,47)
Equating the tensile and bearing resistances, (b} and (/), respec-
tively, of rod L :
.'.^=2.14, (148)
a ratio which is not excessive with good materials and fitting. The
depths, /^ and hv if calculated for shearing simply by (/) and (//),
are less than is required by good practice. Their value is usually
from d to 1.25^, with wrought iron. The diameter d2, of the col-
lar, H, should be greater proportionately in small rods, since the
fillets and rounding greatly reduce the bearing surface. Taking
the unit bearing pressure upon the collar as |5ft, we have, from
(/) and (n) with b = dJ4:
i.22d. (149)
2/2 MACHINE DESIGN.
Equating (e) and (g} and substituting the values of b and h :
z = o.2d, about,
(ISO)
a height which, considering the fillet of the collar, is sufficient.
2. DRIVING FORCE ON KEY. — Let A and B, Fig. 115, be two
members of the same material united by a through-key, C, one side
of the latter having the
angle of taper, 6. Take
IVas the axial load upon
the joint and /z and <p as
the coefficient of friction
and angle of repose,
respectively, of C and A
jf or B. Then, disregard-
ing the friction between
the members, A and B, in :
(a) Driving home the
key, the latter is acted
upon by the driving
force, P, and the reac-
tions, R and Rv devel-
oped at the contact-sur-
faces by the load, W.
The force, P, is opposed
by the horizontal com-
ponents of these reac-
tions.
At the contact-sur-
faces of B and C, the
load, W, taken as con-
centrated at 0, produces
the total normal pressure,
N, which pressure, when
the key moves, develops the force of friction, F — fjtA7 = N
tan<f. The reaction, R, is the resultant of N and F and is
hence inclined from N and toward P by the angle <p, and from the
vertical by the angle <p + 6. The horizontal component of this
reaction is R sin (<p + 0).
KEYED JOINTS; PIN-JOINTS. 2/3
The load, W, is divided between the two forks of member, A.
Consider it as concentrated at D, at which point it produces a total
normal pressure, Nv and, when the key moves, a force of friction,
Fl = pNl = NI tan <p, and a reaction, Rv inclined toward P and
from TVj and the vertical by the angle <p. The horizontal compo-
nent of this reaction is Rl sin if. Hence :
P=Rsin(y> + 0) + R^iny; (151)
but, R=Wj cos (<p + 6} and Rl = NJ cos y> = Wj cos <p
+ 0) + tanp]. (152)
(£) /# backing out the key, consider the load as concentrated
at 0 and E with regard to the members, B and ^4, respectively.
The conditions are as before, excepting that the forces of friction,
F' and F^ , act toward the backing force P' . Therefore, the reac-
tion, R' , is inclined from the vertical and toward P' by the angle
(<p — 0) and the reaction, R^ , by the angle (p. Hence, as in (i 52) :
/>'= JF[tan(ip-0) + tanp]. (153)
, (c) Maximum Taper. — If the angle 6 is so great that the key,
when driven home, is on the point of backing out, P' = O. Hence,
tan (<p — 6) -f tan <p = o
and
0= 2<p,
which is the limiting value for 0, when the key is not fitted with
set-screws or other locking devices.
(d} Friction of Members. — The preceding equations neglect
the friction between the members, A and B, and the value of W
is therefore greater than the given force, P and P', would over-
come in practice. Let Wf be the axial load, considering this fric-
tion. Then (Fig. 1 1 5) the reaction, R, will produce, between the
contact-surfaces of A and B, a force of friction,
which force will act downward in driving home. Hence, in raising
B, the vertical loads to be overcome are :
Wf + {Ji.fi sin (<p + 0),
2/4 MACHINE DESIGN.
which quantity must be substituted for W in preceding equations.
Hence, considering the friction between the connected members :
Wsm+e W
cos ( <p 4- 6) cos (<f> + 6) — fJLz sin (y + 6} '
(f +0)
1 cos tp
Substituting in (151) :
P= [ Wf + fjtyR sin (ip + 0)] [tan (p + (?) + tan
tan (p + 0) + tan y
in which /^2 is the coefficient of friction for the metal of A and ^.
In finding the value of P' by a similar method, the force of friction
is calculated from the normal pressure produced by R' and that
force acts upward, in opposition to Wf, and hence is subtractive.
(i) Double Taper. — Assume that both sides of the key have
the same angle of taper, 6, as shown by broken lines in Fig. 115.
Then, Rl and R^ are equal to R and R' ', respectively, and, from
(1 52) and (153):
6); (155)
6), (156)
which equations neglect the friction of the connected members.
The limiting angle of taper at which this key, when driven
home, is on the point of backing out, is found, as before, by
making P' = o. Hence :
tan (<p — 6) = o .-. 6 = tp.
Under customary conditions, with slightly oily metals and with-
out locking devices on the key, the latter will begin to back out
when its taper reaches about I -\ ins. per ft, i. e., a ratio of I to 8.
The taper for such keys is, in practice, much less, the ratio being
usually 5 or 6 times this limit.
59. Pin-Joints.
Pin-joints, i. e., those in which two or more members are united
pivotally by a cylindrical pin meet frequent use.
KEYED JOINTS; PIN-JOINTS.
275
I. BOILER BRACES. — The joint may be as shown in Fig. 116
or the member, B, may be replaced by a lug or curved strap pass-
e^d
FIG. 116.
ing over the pin and riveted to the head-plate. In such a joint,
if the parts be accurately fitted without lost motion between
members, A and B, or between the pin-bearing and pin, the latter
is subject only to double shear. The fit, however, is frequently
loose ; and, in any event, the pin and bearing will probably wear.
Hence, the pin is subject frequently to both shearing and bending
stresses and may fail as shown in Fig. 117.*
FIG. 117.
(a) Brace-body. — In general, let L be the length and B the
breadth in ins. of the area supported by the brace and let p be the
pressure per sq. in. upon that area. Then the total load on area
and brace is :
(157)
in which St is the working unit tensile stress of the brace.
* The Locomotive, August, 1901.
270 MACHINE DESIGN.
(ft) Shearing Stress on Pin. — Assuming accurate fitting through-
out, the pin will be subject only to double shear. Then, by §45,
3, and taking Ss, the mean unit shearing stress, as 0.8 St:
W= 1.75 --d2l4-Ss = i.4-xd2/4-St. (1S&)
Equating (157) and (158) :
(c) Bending Stress on Pin. — The distribution of the load upon
the pin, in its bearings both in B and in the forks of A, is unknown.
In any event, the pin acts as a supported beam of circular cross-
section, as in Fig. 118. In extreme cases, the load, Wt may be
FIG. 1 1 8.
concentrated at the centre of the length, and the distance, /,
between the supports maybe the total width, C-£, Fig. 1 16, of the
bearing. Assume / = i.$d and the load as concentrated, as above.
Then, the maximum bending moment is :
in which Ife is the modulus of the section. Then :
W=i~J*-Sf (159)
Taking the tensile stress due to bending as equal to that in direct
tension and equating (157) and (159) :
d= 1.2D.
For average practice, the diameter for shearing, as thus calculated,
is too small and that for bending is large. Taking the mean :
d = D.
KEYED JOINTS; PIN-JOINTS. 277
(d) Sides and Crown of Eye. — When the diameter of the pin is
such that the eye may be tested to destruction, the latter fails by
crushing at h, Fig. 116, and rupture at the two sections, b, the
metal flowing so that the thickness of the eye is increased consid-
erably at the inner limit of h and much decreased at those of b,
where fracture appears first.
The section at b is subjected not only to tensile stress due to its
share of the load, W, but also to an additional bending stress,
owing to the distance between the line of application of the load
and the centre of gravity of the section. With regard to the width
of the crown at h, the problem is, in general, one of indentation
(p. 184) and the stresses (§ 45, 46) resemble somewhat those in a
thick, hollow cylinder under internal fluid pressure.* The case is
also similar generally to that of the margin of a riveted joint, in
which, for ample strength E= i.$d (84), i. e., the distance from
edge of hole to edge of sheet is d. In practice the periphery of the
eye is concentric with the hole and h = b = o.$d to 0.7 $d.
(e) Member A. — The thickness, /, of the forks should be pro-
portioned for two thirds of the load to allow for inaccurate fitting
and irregular distribution. Generally,/= 0.66^ to 0.75^.
In good work, bosses for planing are formed on each side of the
eye and where the head and washer of the pin fit, with a conse-
quent increase of thickness at those points.
(/) Tests. — In 1879, Chief Engineers Sprague and Tower, U.
S. Navy, made exhaustive experiments upon boiler braces. Their
recommendations t are :
"The following is submitted for the proportions (with sufficient excess in the eye for
wear, etc.) of the ends of boiler braces made in the manner specified. In the same
bar, the section across the eye must be increased with each material increase of the
diameter of the pin. When the brace is round and the thickness of the eye and the
diameter of the bar are equal, let .r = areas.
" For ends made by drawing out the bar, bending it around and welding : x = width
of bar and the diameter of iron pin, ^ j- x = diameter of steel pin, | x = breadth of
(concentric) eye, thickness of eye to equal that of bar.
" For ends cut from flat bars, x= width of bar and diameter of iron pin, f x = di-
ameter of steel pin, f x = breadth across each side of eye, | x = depth through crown
of eye, thickness of eye = that of bar.
"For ends upset, and forged solid, holes drilled, x = area of bar and area of iron
pin, 1.48.*— area of section across the eye, .9^ = area through crown of eye."
*Cotterill: " Applied Mechanics," 1895, p. 368.
f" Report on Experiments to Ascertain Proportions for the Ends of Boiler Braces,"
Washington, 1880.
278
MACHINE DESIGN.
2. STRUCTURAL WORK. — Pin-joints are used for trusses and in
the lateral system. One such joint is shown in Fig. 119, which
-
f
1
1
f
f
\
T
J
I
|
3"
2.7.
ft
4 li
I
t/&yJ^.
Men\ber
i
i
1
-
FIG. 119.
has a compound member in the centre with four sets of eye-bars
in pairs, one bar of each pair being on each side of the centre.
Large pins have a nut at each end ; those of smaller diameter
may have a head at one end and a split-pin, serving as a cotter,
at the other. To allow for irregularities in thickness or fit, the
"grip," or length of pin between the inner faces of the nuts, is
increased, beyond the aggregate thickness of the connected mem-
bers, by ^g in. for each bar and ^ in. for the riveted member as a rule.
The stresses on the bars and pin may be horizontal, vertical,
or diagonal. Resolving the latter into horizontal and vertical
components, the pin-stresses may be divided into four classes :
Positive horizontal and negative horizontal stresses, acting toward
the left and right, respectively ; and positive vertical and negative
vertical stresses, acting upward and downward, respectively. The
pin, Fig. 119, may be considered as a beam, acted upon by various
stresses, as above, each at a distance from the next stress corre-
sponding with the thicknesses of the respective eye-bars and the
allowance for irregularities. The diameter of the pin must be
proportioned for bending, shearing, and bearing pressure.
(a) Bending. — If the maximum bending moment on the pin be
known, the diameter of the latter for bending stress may be found
from the fundamental formula :
J/(max) = 5-7 = 5. —
c 32 '
in which M is the maximum moment, 5 is the allowable working
unit stress, and d is the diameter required.
KEYED JOINTS; PIN-JOINTS. 279
To determine the maximum moment for any given manner of
loading, the moment at the centre of each member must be found,
each load being considered as concentrated at the centre of its
respective bar. This moment will be the resultant of all preceding
moments to the left. The principles of the resolution and com-
position of forces apply also to moments. Hence, the moment
upon any section will be the resultant of the horizontal and verti-
cal moments upon that section, i. e., the square root of the sum
of the squares of the latter moments.
Thus, assume in Fig. 1 19, stresses, />, />, Py />, upon the cor-
responding members, the lines of action being separated by the
distances, av a2, ay Let Pl be a positive horizontal stress ; Pv a
diagonal stress with vertical and horizontal components, + Pp
and — PJi, respectively ; Py a diagonal stress with vertical and
horizontal components, — P3v and — PJi, respectively ; and PI a
negative vertical stress. Then at :
Member No. ^ .•
Horizontal Moment = Pl x al
Vertical " = o ;
Resultant " = V H. M22 -f o = H.MV
Member No. j :
Horizontal Moment = Pl (a^ -f- a^) — PJi x tf 2 =
Vertical " = P2v X
Resultant " =
Succeeding resultant moments may be calculated similarly.
From a comparison of the results, the value and location of the
maximum bending moment upon the pin may be found. Table
LXXIV. gives the required diameters for various maximum mo-
ments and extreme fibre stresses per sq. in., as computed by the
fundamental formula for bending moment. It will be observed
that the calculations, as above, apply only to the pin before bend-
ing. When the latter occurs, the stress-leverages and maximum
moment are reduced.
280
MACHINE DESIGN.
TABLE LXXIV.
MAXIMUM BENDING MOMENTS ON PINS.
Pin.
Moments in Inch Pounds for Fibre Strains per Square Inch of
Diam. Area.
15,000
18,000
20,000 22,000
*S,ooo
I "
0.785
1,470
1,770
1,960
2,160
2,450
ij
1.227
2,880
3>45o
3,830
4,220
4,790
If
1.767
4.970
5,96o
6,630
7,290
8,280
l£
2.405
7,890
9-470
10,500
H,570
13,200
2
3-I42
11,800
14,100
I5,7oo
I7,28o
19,600
2i
3-976
16,800
20,100
22,400
24,600
28,000
•2\
4.909
23,000
27,600
30,700
33,700
38,400
2i
30,600
36,800
40,800
44,900
51,000
3
7.069
39,800
47,700
53,ooo
58,300
66,300
8.296
50,600
60,700
67,400
74,100
84,300
3i
9.621
63,100
75,800
84,200
92,600
105,200
3f
H.045
77,700
93,200
103,500
113,900 j 129,400
4
12.566
94,200
113,100
125,700
138,200 157,100
4*
I4.l86
113,000
I35,7oo
150,700
165,800
188,400
3
I5-904
17.721
134,200
157,800
161,000
189,400
178,900
210,400
196,800
231,500
223,700
263,000
5
I9-635
184,100
220,900
245,400
270,000
306,800
5t
21.648
213,100
255,700
284, 100
312,500
355,2oo
5*
23.758
245,000
294,000
326,700
359,3oo
408,300
1*
25-967
28.274
280,000
318,100
335,900
381,700
373,300
424, TOO
410,600
466,500
466,600
530,200
6J
30.680
359,500
431,400
479,400
527,300
599,200
6J
33-I83
404,400
485,300
539,200
593,ioo
674,000
6f
35.785
452,900
543>5oo
603,900
664,200
754,800
7
38.485
505,100
606,100
673,500
740,800
841,900
7i
41.282
561,200
673,400
748,200
823,000
935,300
7i
44-179
621,300
745,5oo
828,400
911,200
1,035,400
7!
47-173
685,500
822,600
914,000
1,005,300
1,142,500
8
50.265
754,000
904,800
1,005,300
1,105,800
1,256,600
8|
53456
826,900
992,300
1,102,500
1,212,800
1,378,200
8*
56.745
904,400
,085,200
1,205,800
1,326,400
1,507,300
8J
60.132
986,500
,183,800
1,315,400
1,446,900
1,644,200
9
63.617
,073,500
,288,200
1,431,400
i,574,5oo
1,789,200
9t
67.201
,165,500
,398,600
1,554,000
1,709,400
1,942,500
9i
70.882
,262,600
,5i5,ioo
1,683,400
1,851,800
2,104,300
9f
74-662
,364,900
,637,900
1,819,900
2,001,900
2,274,900
10
78.540
,472,600
,767,100
1,963,500
2,159,900
2,454,400
loj
82.520
,585,900
,903,000
2,114,500
2,325,900
2,643,100
loj
86.590
,704,700
2,045,700
2,273,000
2,500,200
2,841,200
lof
90.760
,829,400
2,195,300
2,439,300
2,683,200
3,049,100
ii
95.030
,960,100
2,352,100
2,613,400
2,874,800 3,266,800
ii \
99400
2,096,800
2,516,100
2,795,700
3,075,400 3,494,800
til
103.870
2,239,700
2,687,600
2,986,300
3,284,800 3,732,800
iif
108.430
2,388,900
2,866,600
2,185,200 3,503,700 : 3,981,500
12
II3.IOO
2,544,700
3,053,600
3,392,900 3,732,190 ; 4,241,200
(£) Shearing. — The vertical shear at any section of the pin is
the algebraic sum of the vertical stresses to the left of that section.
Similarly, the horizontal shear at the section considered is the
algebraic sum of the horizontal stresses to the left of that section.
Then, the resultant shear upon the section is the square root of
KEYED JOINTS; PIN-JOINTS. 28 1
the sum of the squares of the vertical and horizontal shears, as
above. Thus, the shears are at :
Member No. j :
Horizontal = /> - PJi = H.S3 ;
Vertical = o + P2v = V.S^\
Resultant = VH.S* + V.S*
While, in a cylindrical section, the maximum is £ the mean shear-
ing stress (p. 182), it is usual to consider the shearing stress on
pins as uniformly distributed over the cross-section. Again, since
the bars are in pairs, the pin may be considered as under double
shear. Hence, for one pair of bars :
in which R.S. is the maximum resultant shear, as above, d is the
diameter required to withstand that shear, and S^ is a unit work-
ing shearing stress which is low enough to permit, with safety,
the excess of maximum over mean stress.
(c) Bearing. — The ranges of permissible bearing pressure and
shearing stress have been given previously (p. 224).
(d} Proportions. — Table LXXV. gives the proportions of pins
with Lomas nuts and Table LXXVI. of pins with cotters. The
latter are used with pins of small diameters only. The former are
preferable, since the nut is recessed and bears only on its periph-
ery. This allows the body of the pin to enter it and enables it to
be set up tightly when the aggregate thickness of the members
with the allowances is not equal to the estimated grip of the pin.
(e) Eycbars. — The proportions of plain and adjustable eye-bars
are given in Table LXXVII.
(/") Specifications. — The following extracts, referring to pin-
joints, are taken from the specifications of the American Bridge
Company for steel railroad bridges. The specifications for rivet,
soft, and medium steel are given on page 219.
' ' Pins made of either of the above mentioned grades of steel shall, on specimen test-
pieces cut from finished material, fill the requirements of the grade of steel from which
they are rolled, excepting the elongation, which shall be decreased 5 per cent, from
that specified.
" Pins up to 7 inches diameter shall be rolled.
282
MACHINE DESIGN.
TABLE LXXV.
PINS WITH LOMAS NUTS.
(AMERICAN BRIDGE Co.)
P
la.
3
Mut.
11
Ii
Set
ew.
Di£
m.
•s
3*
1
Diam.
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41
NOTE. — To obtain grip G add TJ5 for each bar, together with amount given in table.
KEYED JOINTS; PIN-JOINTS.
283
" Pins exceeding 7 inches diameter shall be forged under a steel hammer striking a
blow of at least 5 tons. The blooms to be used for this purpose shall have at least
three times the sectional area of the finished pins.
"All pins shall be accurately turned to a gauge, and shall be straight and smooth.
" The clearance between pin and pin-hole shall be J% of an inch for all lateral pins ;
and for truss pins the clearance shall be ^ of an inch for pins y/2 inches in diameter,
which amount shall be gradually increased to ?V of an inch for pins 6 inches in diameter
and over. .
" All pins shall be supplied with steel pilot nuts, for use during erection.
" All pin-holes shall be reenforced by additional material when necessary, so as not to
exceed the allowed pressure on the pins. These reenforcing plates must contain enough
rivets to transfer the proportion of pressure which comes upon them, and at least one
plate on each side shall extend not less than 6 inches beyond the edge of the tie plate.
" Pin-holes shall be bored truly parallel with one another and at right angles to the
axis of the member unless otherwise shown in drawings ; and in pieces not adjustable
for length, no variation of more than -fa of an inch for every 20 feet will be allowed in
the length between centres of pin-holes.
The permissible shearing strain and bearing pressure are given
on page 226.
" The bending strain on the extreme fibre of pins shall not exceed 22,000 pounds per
square inch for soft steel and 25,000 per square inch for medium steel, when centres of
bearings of the strained members are taken as the points of application of the strains.
TABLE LXXVI.
PINS WITH COTTERS.
(AMERICAN BRIDGE Co.)
Pin.
Head.
Cotter.
Add to Grip.
Diam
of Pin.
P
Diam of
Pin-Hole.
at End,
Diam.
H
Thick-
ness,
T
Length,
Diam.
D
For Length
over All,
M
For Length
under Head,
I"
if
¥ ?"
¥ V
\H
!
*
If"
\
l//
!
i
2
$
]
!
i
3
I
2|
in
!
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A
I
4
5|
3
\
3i
5
I
3 A
III
\
: i!
s!
6
2;
2
i
NOTE. — Use pins
with Lomas nuts in preference to cotter pins whenever possible.
284
MACHINE DESIGN.
TABLE LXXVII.
EYEBARS.*
(AMERICAN BRIDGE Co.)
Oxo.
Width
Mi
D.
He
id.
Screv
rEnd.
Min.
oi
Bar.
0
Ba
r
r.
Diam
.
Ma
Pi
K.
1,
Additional Mat.
for Head.
Additional Mat.
for Upset.
Diam.
length.
Thicknesi
of Bar.
3
9J
4
L
1
8
i
4
3
6
I
4
5
10
8
3f
6J
IT35
H^
4
9
9
3t
6J
I
5
' 3
1
:
\
"'
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s
I
ii
9
ii
3|
7
8
;i
i
r
14^
6J
2
ii
4
8
f
16
6
3
3
4*
9
7
H
17
7
8
3
a
9
!
c
17
b
3
8
3
t
18
i8J
r
7i
10
*NOTE. — Eye-bars are hydraulic forged, and will develop the full strength of the bar,
under conditions given in the above table, when tested to destruction. The maximum
sizes of pins given in the above table allow an excess in sectional area of head on lines
" SS " over that of the body of the bar of 33 per cent, for diameter of pins, not larger
than the width of the bar and 36 per cent, for pins of larger diameter than the width
of the bar.
" Full size test of steel eye-bars shall be required to show not less than 10 per cent,
elongation in the body of the bar, and tensile strength not more than 5,000 pounds
below the minimum tensile strength required in specimen tests of the grade of steel from
which they are rolled. The bars will be required to break in the body, but should a
bar break in the head, but develop 10 per cent, elongation and the ultimate strength
specified, it shall not be cause for rejection, provided not more than one third of the
total number of bars tested break in the head ; otherwise the entire lot will be rejected.
" The heads of eye-bars shall not be less in strength than the body of the bar.
"The heads of eye-bars shall be made by upsetting, rolling, or forging into shape.
Welds in the body of the bar will not be allowed.
"The bars must be perfectly straight before boring.
" The holes shall be in the centre of the head and on the centre line of the bar.
" All eye-bars shall be annealed.
' ' Bars which are to be placed side by side in the structure shall be bored at the same
temperature, and shall be of such equal length that, upon being piled on each other,
the pins shall pass through the holes at both ends at the same time without driving. ' '
APPENDIX. 285
APPENDIX.
PAGE 20. In many shops, a custom — and a good one — obtains
of covering the exposed parts of shafts of twin-screw steamers
with ratline laid in paint, when the shafts are not cased with brass.
The use of pins or tap-rivets as an aid in holding shaft casings
does not meet with universal approval, the argument against them
being that, if the shrinkage of the casing does not fully secure the
latter, no pins will ; and, further, that often the putting in of the
pins tends to loosen the casing.
PAGE 34. The expression,
is simply the value of Pl obtained from the third equation of (27)
by making P0, in that equation, equal to zero.
PAGE 260. The " Flat Key" is the type used almost exclusively
in marine work.
INDEX.
Bach, experiments on joint friction, 187
lap-riveting, 181
length of rivet-shank, 189
riveting temperature, 188
Bands, thin, shrinkage formulae, 3
Boiler-braces, 275
seams, longitudinal, circumferential,
helical, 139
Bolt-blanks, no
-heads, stresses, 51
heading and forging machine, 1 10
heads, manufacturers' standard, 53
-threads, cold-rolling process, 114
Bolts and nuts, U. S. Standard (Sellers), 50
U. S. Navy, 52
Whitworth, 55
rods for, U. S. Naval Specifications,
114
stresses, 71
Braces, boiler, 275
tests, 277
Calking, effect on joint-friction, 190
Cone-coupling, Sellers, 255
Cotters, bolted strap end, 268
connecting rod, 267
crosshead, 266
driving force, 272
forms, 265
friction, 273
maximum taper, 273
piston, 265
pump-rod, 266
split-pins, 283
stresses, 270
taper-pins, 268
Crank-shaft, 22
Cylinders, thick, shrinkage and pressure
formulae, 4
Dies, 135
Drilled holes, 136
Drilling vs. punching, tests, 137, 138
Engines, marine, 19, 22, 23
shrinkage and pressure
joints, 19, 23
keys, 260
stationary, 259
keys, 260
Eye-bars, proportions, 281, 284
specifications, 281
stresses, 277
tests, 277
Friction, calking, effect on, 190
coefficients of, 9, 13, 87
cotters, 273
keys, 254, 264
of riveted joints, 187
of support, screws, 89
plate, 130
rivet-heads, 130
screw, 82
-threads, 44, 57, 82, 87, 89
Furnace, shrinkage, 39
Gib and key, 267
Grooved ' ' specimens, 75
Gun, breech-block, 67
-construction, 36
shrinkage in, 27
expansion, shrinkage, clearance,
41
i6-in. B. L. R., U. S. A., 36
radii of cylinders, 35
relative shrinkages 32
shrinkage formulae, 29
-furnace, 39
-pit, 40
Stockett system, breech-mechanism, 38
Heading and forging machine, 1 10
Hull-work, Am. Bureau of Shipping, 245
laps and straps, 243
plating, thickness, 246
proportions of seams, 239, 247
punching, drilling, riveting, 245
287
288
INDEX.
Hull-work, rivet-metals, 238
riveted joints, 235
rivets, proportions, 237, 241, 242
spacing of rivets, 244
U. S. Naval practice, 237
Key, gib and, 267
Keys, Blanton fastening, 255
cone, 255
crushing stress, 262
feather, 252, 257
flat, 252, 257
forms, 251
friction, 254
Kernaul, 254
machine-tools, 258
marine engine work, 260
on the flat, 256
Peters system, 253
pin-, 254
propeller-, 261
proportions, 257
quartering, 253
roller, 255
saddle, 254
shafting, 258
shearing stress, 262
square, 251, 257
stationary engine work, 259
stresses on, 261
from, 265
sunk, 251
through, see "Cotters"
Woodruff, 253
Key-ways, milling cutters, 259
Nuts, blanks, 1 12
bursting stress, 94
circular, 52
check, 118
cold-punched, 112
collar, 121
elastic, 1 20
forgings, U. S. N., 116
hot-pressed, manufacturers' standard
S3
lock-plates, 123
locks, 118
Excelsior double, 123
Harvey grip, 121
^uts, locks, Jones tie-bar, 123
self-locking threads, 121, 122
set screws, 120
split pins, 1 23
Verona, 122
Lomas, 282
materials, U.S.N., 114, 116
methods of manufacture, 1 1 2
round, slotted, 54
self- locking, 121
Sellers system, 5 1
stresses, 46, 51, 94
tapping machine, 114
threading and tapping, 1 12
washers, national lock, 122
spring, 122
Wiles lock, 120
Pin-joints, 274
Pins, bending moment, 280
stress, 276, 278
proportions, 281, 282, 283
shearing stress, 276, 280
split, 268, 283
structural work, 278
taper, 268
with Lomas nuts, 282
Pipe, spiral riveted, 141
-threads, Briggs' standard, 71
Pit, shrinkage, 40
Plate, boiler, 132, 207, 210, 215, 216
flange, 229
ship, 131, 237, 242, 246, 250
structural, 131
web, 231
girder, 226
perforated, tensile strength, 134
Pressure joints (press fits), B. F. Sturte-
vant Co., 17
Buffalo Forge Co., 18
character of surfaces, 13
coefficients of friction, 13
forcing pressure, 8, 13
form, 12, 24
Lane and Bodley Co. , 1 7
length, 10
marine engines, 19, 23
metals, 12
proportions, 9
railway work, 24
INDEX.
289
Pressure joints (press fits), resistance to
slip, 8
Russell Engine Co., 17
slip-resistance vs. rotating
force, 9
stationary engines, 16
stresses and allowances, 6,
10, 24
summary of practice, 19
thick cylinders, 4, 6
thickness, II
of hub, 8
wheel fits, 25
press, 25
Punches, 135
Punching, effect of, 136
vs. drilling, 137
Railway-work, shrink and press fits, 24
Riveted joints, Am. Boiler M'fr's Asso'n,
215
Baldwin Locomotive Works, 210
bearing pressure, 157
bending stress, 185
boilers, percentage strength of, 172
butt, 152, 161, 164, 190, 192
efficiencies, 163
straps, 173, 175
unequal straps, 153, 164
elements, 142
forms, 141
friction, 187
general formulae, 170
Hartford Steam Boiler Insp. and
Ins. Co., 216
hulls, 235
lap, 154, 156, I58> '59, i&>, 166
laps and straps, 243
location, 205, 213, 249
locomotive boilers, 210
manner of failure, 143
marine boilers, 205
plates, stresses upon, 186
bending stress, 185
of unequal thickness, 176
proportions, 207, 211
of seams, 239
punching vs. drilling, 138
U. S. Board of Supervising In-
spectors, 209
Riveted joints, shearing strength, 134
stationary boilers, 215
theoretical strength, 154
stresses, 171, 178
structural work, 219
tests, 192
U. S. N. practice, 237
Riveted members, stresses in, 224
Riveter, hydraulic, 202
pneumatic, 203
Riveting, chain and staggered, 151, 174
group, 154, 1 68
hand, frictional resistance in, 131
hydraulic, 202
machine, 190
machines, 200, 202
multiple, 146
pneumatic, 202
punching and riveting, 223
spacing, 221
structural, 231
temperature, 187
U. S. N. specifications, 245
Rivets, American Iron and Steel Manufac-
turing Company, 1 28
bearing value, 25
blanks, 128
diameter, 145, 172, 207, 219, 237, 242
heads, 127, 128, 129, 207, 2U, 215,
220, 237, 241
holes, 134, 136, 138, 142, 215
margin and lap, 149
metals, 114, 131, 206, 210, 219,
236, 237
number of rows, 189
proportions, 127, 207, 219, 237
pitch, 147, 149, 172, 173
diagonal, 147, 173
transverse, 143, 149
points, 127, 220, 237, 241
shank, 130, 188
bearing stress, 185
bending stress, 181
shearing stress, 182
tensile stress, 180
Victor, 128, 132
weight, 209
Screw-bolts, armor, 66, 109
combined stresses upon, 90, IO2
290
INDEX.
Screw-bolts, cross-shear, 91
efficiency, 101
eye, 106
friction of support, 89
as grooved specimens, 75
heading machine, no
loss of axial strength, 99
methods of manufacture, no
materials, 114, 117
resilience, 57, 81
safe loads, 103
shaft-couplings, 91
stay, 1 06, 1 08, 117
studs, 104
tap, 103, 104, 105
tension, static, 74
sudden load or impact, 79
threading, 112
tool, 113
types, 103
Screws, geometry of, 42
machine, 68
wood, 68
set, 104, 105, 120
Screw-threads, bearing pressure, 73
surface, 56
Briggs', 71
Bristol Association Standard, 59
buttress, 65
.-old-pressed, 78
density of, 78
diameter, 51
durability, 57
elements of, 45
forms, 43, 46, 51
French standard, 57
friction of, 44, 57, 82, 87, 89
friction, coefficients of, 87
international Standard, 59
interrupted, 67
knuckle, 65
lubricants, 87
modified triangular, 67
multiple, 47
pitch, 46, 51
reinforcing action of, 75
requirements, 45
rupture, 72
sharp V, 54
special, 65
Screw-threads, square, 6 1
Newport News S. B. and D. D.
Co., 62
Sellers, 61
strength, 44, 56
stress-ratio, 73
stripping, 56, 72
Swiss system, 59
tensile strength, 56
tests, 87
torsion, 83
triangular vs. square, 44
U. S. Standard (Sellers), 47
modified, 51
V, Sellers, Whitworth, compared, 56
#-V, 62
Acme standard, 64
Newport News S. B. and D. D.
Co., 64
Sellers, 63
Whitworth, 55
Sellers thread, 47
Shaft-casings, 20, 22, 24
-couplings, 91
Shafts, marine engine, 22
Shell-sheets, thickness, 177
Shrinkage, formulae, guns, 29, 41
thick cylinders, 4
thin bands, 3
guns, radii of cylinders, 35
in gun construction, 27
stresses and strains, guns, 30
vs. pressure fits, Wilmore, 15
tires, 25
Shrinkage joints (fits), B. F. Sturtevant
Co., 1 8
Buffalo Forge Co., 18
form, 12, 24
length, 10
marine engines, 19, 22, 23
crank-shafts, 22
metals, 12
Midvale Steel Company, 22
proportions, 9
railway work, 24
resistance to slip, 8
Russell Engine Company, 17
shaft-casings, 20, 22, 24
slip-resistance vs. rotating
force, 9, 15
INDEX.
29I
Shrinkage joints (fits), stresses and allow-
ances, 6, 10, 24
summary of practice, 19
thickness, 8, n
thin bands, 3
tires, 25
Union Iron Works, 23
Shrinkages, relative, guns, 32
Steel, American standard specifications, 131
boiler, 132, 194, 195, 215
bolts, 114
bridge, 131
nuts, 116
rivet, 114, 132, 206, 210, 219, 237
238
ship, 131, 237
structural, 131, 219
Stiffeners, web, 231, 233
Stresses and allowances, 6, 10, 24
strains, guns, 30
bolt-heads, 51
bolts, 71
bursting, nuts, 94
cotters, 270
eye-bars, 277
from keys, 263
in riveting, 168
nuts, 46, 5 1 , 94
on keys, 261
Stresses on keys, plates, 185
riveted joints, 171, 178
members, 224
rivets, 180, 181, 182, 183
screw-threads, 73
Structural work, bolts, 234
distribution of stresses, 226
flange-area, angles, flange-plates,
229
moments, vertical shear, flange-
stress, 228
riveting, 231
Stiffeners, 231, 233
web-plate, 231
Studs, 103
cylinder-head, 92, 94
metal, U. S. N., 114
Temperature, riveting, 187
shrinkage, 14
Tires, shrinkage, 25
Washers, 122
Web-plates, 231
Whitworth thread, 55
Wheel-fits, 25
press, 25
tires, 25
Wood screws, 68
Wrenches, loo, 124, 12$
Catalogue of the Scientific Publications
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