POCKET COMPANION
, OF
USEFUL INFORMATION
APPERTAINING TO^THEXUSE OF
PITTSBURGH, PA.
FOR
ENGINEERS, ARCHITECTS AND BUILDERS,
BY
C. L. STROBEL, C. E.
M.A.S. C. E.
Electrotype Edition, Price $1.SO.
WM. G. JOHNSTON & CO. PRINT. PITTSBURGH.
Entered according to Act of Congress, in the year 1881, by
CARNEGIE BROS. & CO. LIMITED,
In the Office of the Librarian of Congress, at Washington.
S3-
PREFACE.
THE present electrotype edition of the Pocket Companion is
a new work throughout. It is intended to supply such special
information and tables as, it was thought, would prove valuable
to workers in wrought iron in general, and the patrons of
the publishers, the firm of Carnegie Bros. & Co., Limited, in
particular.
The tables, with a few exceptions, were computed expressly
for this work, and some of them are original in both matter and
form.
The author hopes that they will be found to possess the
qualities of accuracy and reliability.
Such of the tables a$ were not Calculated for this work were
obtained from two or more works of presumably independent
origin, which were compared for the detection of errors.
The table of weight of a cubic foot of substances was derived
mostly from Trautwine, while for the table of linear expansion
of .substances by heat, Rankine is authority.
The list of shapes rolled by the Union Iron Mills will be found
increased in number, and some of the sections improved in
form. All angle irons are now made with flanges of uniform
thickness ; the range between the minimum and maximum
weight for a number of the shapes has been increased, and a new
and more rational system of numbering adopted.
CONTENTS.
PAGE.
Lithographed Sections of Eyebeams,
Shapes Nos. 1 to 13 1-4
" Sections of Deck Beams,
Shapes Nos. 20 to 22 4
" Sections of Channel Bars,
Shapes Nos. 25 to 45 5-8
" Section of Car Truck Channel,
Shape No. 46 8
" Sections of Angles with Equal Legs,
Shapes Nos. 50 to 63 9
" Sections of Angles with Unequal Legs,
Shapes Nos. 65 to 76 10
" Sections of Square Root Angles,
Shapes Nos. 80 to-93 .11
" Sections of Cover Angles,
Shapes 95 and 96 . .12
" Section of Obtuse Angles,
Shape No. 98 12
" Sections of Star Irons,
Shapes Nos. 100 to 105 12
" Sections of Keystone Octagon Columns,
Shapes Nos. 110 to 113 13
" Sections of Piper's Patent Rivetless Columns,
Shapes Nos. 115 to 118 14
" Sections of Corrugated Columns,
Shapes Nos. 120 and 121 15
Lithographed Sections of Patent Post Irons, PAGE.
Shapes Nos. 125 and 126 15
" Sections of Half T's
Shapes Nos. 127 and 128 15
" Sections of T Irons,
Shapes Nos. 130 to 178 16-20
" Section of Roof Iron,
Shape No. 180 20
" Sections of Hand Rails,
Shapes Nos. 195 and 196 21
Sections of Grooved Irons,
Shapes Nos. 200 to 209 21
Sections of Sash Irons,
Shapes Nos. 215 to 221 22
" Sections of Fence Irons,
Shapes Nos. 225 to 227 22
" Section of Beveled Flat,
Shape No. 230 22
" Sections of Ice Slides,
Shapes Nos. 231 and 232 '. .22
Section of Dove Tail,
Shape No. 233 22
" Section of Z Iron,
Shape No. 235 22
" Illustrations of Beams and their connections,
and Girders 23
" Illustrations of Beam supporting Wall, of Sepa-
rators, and of Fire-proof Floors 24
" Illustrations of Fire-proof and other Floors. . . .25
" " " Columns and Struts, and Dia-
grams of Pratt and Whipple Trusses 26
" Sections of Additional Shapes 27-30
Explanation of Tables on Eyebeams 31, 32
~~y[ " -
PAGE.
Tables on Eyebeams, giving Safe Load, Deflection and
Proper Spacing 33-35
Explanation of Tables on the Properties of Beams, Chan-
nels, Angles, Stars and Tees, also General Formulae
on the Flexure of Beams. 56-61
Properties of Eye and Deck Beams 62, 63
" Channel Bars 64, 65
" " Angle Irons 66, 67
Angle Irons, weights corresponding to thicknesses varying
by T V' 68
Properties of T Irons 69
" " Star Irons 69
Explanation of Table on Riveted Girders 70, 71
Table on Riveted Girders 72
Explanation of Tables on Columns and Struts 73-76
Keystone Octagon Columns, Thicknesses and corresponding
Areas and Weights per foot 77
Piper's Patent Rivetless Columns, Thicknesses and correspond-
ing Areas and Weights per foot .78
Ultimate Strength of Cast and Wrought Iron Columns 79
" " Wrought Iron Columns 80
Rectangular Timber Pillars 81
General Notes on Floors and Roofs 82-84
Corrugated and Galvanized Iron .' 85, 86
Illustration of Application of Tables on Flat Rolled Iron,
and Decimal Parts of a Foot for each ^jth of an inch. . .87
Weights of Flat Rolled Iron per Lineal Foot. 1 88-93
Areas of Flat Rolled Iron 94-99
Decimal Parts of a Foot for each ^ of an inch 100-103
Weights and Areas of Square and Round Bars of Wrought
Iron, and Circumferences of Round Bars 104-109
Sheet Iron, by Birmingham Gauge 110
" " American " , Ill
VII
PAGE.
Areas and Circumferences of Circles 112-124
Weights of Rivets and Round-headed Bolts 125
Upset Screw Ends for Round and Square Bars 126, 127
Standard Screw Threads, Nuts and Bolt Heads, by Franklin-
Institute Standard 128
Whitworth's Standard Screw Thread 129
Wood Screws, Tacks and Wrought Spikes 129
Sizes and Weights of Hot Pressed Square Nuts 130
" " Hexagon Nuts 131
Wrought Iron Welded Tubes, for Gas, Steam or Water 132
Explanation of Tables on Rivets and Pins 133, 134
Shearing and Bearing Value of Rivets 135
Maximum Bending Moments to be allowed on Pins 136
Bearing Value of Pins 137
Wooden Beams, Safe Load for 138
Explanation of Tables on Maximum Stresses in Pratt and
Whipple Trusses. 139, 140
Maximum Stresses in Pratt or Single Quadrangular Trusses . . 141
" " Whipple or Double Quadrangular
Trusses 142, 143
Natural Sines, Tangents and Secants 144-152
Logarithms of Numbers 153-155
Weight of a Cubic Foot of Substances 156-158
Window Glass, No. of Lights per Box 159
Linear Expansion of Substances by Heat .160
Mensuration 161-163
Weights and Measures, United States and British 164, 165
Comparative Tables of United States and French, and
French and United States Measures 166, 167
Strength of Materials 168-170
Decimals of an Inch for each J ? th 171
Index 172-177
_ . >
CARNEGIE BROTHERS & CO.
PITTS BURG H,
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31 1 / 2 to45!bs.
Ill
LL 0> Cr'O
01
CARNEGIE BROTHERS & CO. LIMP
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CARNEGIE BROTHERS . &,
i.i M ITI-: ix
to
i w
o
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4dto6o'lbs. ~
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v
PITTSBURGH, PA.
If *F
1' :1 ie
CARNEGIE BROTHERS & GO.LIM?
PITTSBURGH, PA.
CARNEGIE BROTHERS & CO.
ANGLES WITH EQUAL LEGS.
.. .
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0.9 to 18 Ibs.
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PITTSBURGH, PA.
ANGLES WITH UNEQUAL LEGS.
IS 1 ? 65.
13,9 to EGA IBs
10
CARNEGIE BROTHERS & CO.LIM?.
SQUARE ROOT ANGLES.
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COVER ANGLES.
N 9 6.
B7to8.3lbs
OBTUSE ANGLE
..
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CARNEGIE BROTHERS & CO.LIM^
KEYSTONE OCTAGON COLUMN.
13
PIPER'S PATENT RIVETLESS COLUMN.
CARNEGIE BROTHERS & CO.
CORRUGATED COLUMN.
127
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PITTSBURGH, PA.
T IRON.
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1.9 Ibs -
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PRATT OR SINGLE QUADRANGULAR TRUSS.
D J F <i If
A
\
WHIPPLE OR DOUBLE QUADRANGULAR TRUSS.
B c 1) K F cv H I K I. M X p P
X
Y
b c d e f cj li i k 1 m n o p q
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ADDITIONAL SHAPES
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ADDITIONAL SHAPES.
EXPLANATION OP TABLES ON UNION
IRON MILLS' EYEBEAMS.
Pages 33 to 55, inclusive.
These tables are calculated for the lightest and heaviest weights
to which each shape or size can be rolled, the term shape being
meant to include the variable sections which are rolled in the
same grooves by increasing or reducing the distance between the
rolls. Each shape is designated by a single number.
These tables give :
I. In second column, the load which a beam will carry safely,
distributed uniformly over its length, for the distances between
supports, (or lengths of span,) given in first column ;
II. In fifth to eleventh columns inclusive, the distances be-
tween centers at which beams should be placed in floors, to carry
safely loads of 100, 125, 150, 175, 200, 250 and 300 Ibs. per square
foot (including the weight of the beams), for the distances between
supports given in first column ;
III. In third column, the deflection of the beams at center
under these loads.
IV. In fourth column, the weight of the beam itself, for a
length equal to the distance between supports.
To determine the load which a beam will carry exclusive of
its own weight, the figures in fourth column must be subtracted
from the figures in second column.
It is assumed in these tables that proper provision is made for
preventing the compression flanges of the beams from deflecting
sideways. They should be held in position at distances not
exceeding twenty times the width of flange, otherwise the
strain allowed should be reduced.
If the deflection of beams carrying plastered ceilings exceeds
!^th of the distance between supports, or J^th of an inch per
foot of this distance, there is danger of the ceiling cracking, as
has been found by practical tests. This limit is indicated in the
following tables by a cross line, beyond which the spans and
loads must not be used for beams intended to carry plastered
ceilings. It may generally be assumed, both for rolled and
m a
SB-
built beams, that the above limit is not exceeded so long as the
depth of beam is not greater than 2 ] f th of the distance between
supports, or j inch per foot of this distance.
Inasmuch as the carrying capacity of beams increases largely
with their depth, and it is therefore economical to use the greatest
depth of beam consistent with the other conditions to which it is
necessary to conform, (as clear hight, etc.,) the above cases of
extreme deflection will rarely be met with in practice.
EXAMPLES OF APPLICATION OF TABLES.
I. What size and weight of beam 19'-G" long in clear be-
tween walls, and therefore say 20'-0" long between centers of
supports, will be required to carry safely a uniformly distributed
load of 15 tons, the weight of the beam included ? .
Answer : A 15" beam, No. 1, heavy, 65 Ibs. per foot, will be
sufficient, since the safe load, as per table, for 20 ; length ,= 16.38 1.
It is evident, however, that a beam intermediate in weight
between 50 Ibs. and 65 Ibs. can be used, to ascertain which,
proceed as follows :
The safe load for a 15" beam 50 Ibs. per foot = 14.12 t. Since
therefore an increase in the carrying capacity of beam, of 2.26 1.,
(16.38 1. 14.12 1.,) requires an increase of its weight of 15 Ibs.,
(65 Ibs. 50 Ibs.,) therefore an increase of its carrying capacity
of 0.88 t., (15t. 14.12 t.,) will require -||j- X 15 = 6 Ibs.
increase of weight of beam., i. e., the beam should weigh 56 Ibs.
per foot.
II. A fire-proof floor 24'-6" in clear between walls, weighing,
inclusive of beams, 70 Ibs. per square foot, (assumed,) is to be
proportioned to carry an additional load of 130 Ibs. per square
foot; what size and weight of beams will be required, and how
far apart should they be placed ?
Answer : The total load = 200 Ibs. per square foot, and the
distance between supports = 25', z. e. 6" greater than the distance
in clear between walls. By referring to tables, it will be seen
that either light 12" beams weighing 42 Ibs. per foot, spaced
2.9 ft. between centers, or light 15" beams, 50 Ibs., spaced 5.8 ft.
between centers, will answer the purpose, but since the 12"
beams for this span and load are beyond the cross-line, they
must not be used, if intended to carry a plastered ceiling.
_ , _
S3
UNION IRON MILLS'
15-INCH EYEBEAM, No.
1, LIGHT,
50
LBS. PER FOOT.
Depth, 15". Width of Flanges, 5.03".
Thickness of Web, 0.47".
Maximum fiber
strain = 12000 1
bs. per square inch.
g -U
ti^s
J3
la
Proper distance,
in feet, center to center
s Js
|lli
jl
i | J
of b<
jams, for Safe Loads of
8 5
-JfiS
I-S
?5
100
125
150
175
200
250
200
"
J_,
. '&'
j 5 M
Ibs.
Ibs.
Ibs.
Ibs.
Ibs.
Ibs.
Ibs.
.s & 1
~-~ &o
d-s
! 'S P J
per
per
per
per
per
per
per
314!.s.s
r^-
s<i. ft.
sq. ft.
54. ft.
<1. ft.
s<l. ft.
sq. ft. | f q. ft.
10
28.24
0.09
10.25
56.5
45.2
37.7
32.3
2si
22.6 1S.8
11
25.67
0.11
!0.28
46.7
37.4
31.1
26.7
23^3
18.7 15.6
23.53
0.13
10.30
39.2
31.4
26.1
22.4
19.6
15.7
13.1
13
21.72
0.16
S0.33
33.4
26.7
22.3
19.1
16.7
13.4 11.1
14
20.17
0.18
0.35
28.8
23.0
19.2
16.5
14.4
11.5 j 9.6
15
18.83
0.21
0.38
25.1
20.1
16.7
14.3
12.6
10.0 1 8.4
16
17.65
0.24
0.40
22.1
17.7
14.7
12.6 11.0
8.8 7.4
17
16.61
0.27
0.43
19.5
15.6
13.0 ! 11.1
9.8
7.8
6.5
18
15.69
0.30
10.45
17.4
13.9
11.6
9.9
8.7
7.0
5.8
19
14.86
0.33
0.48
15.6
12.5
10.4
8.9
7.8
6.2
5.2
20
14.12
0.37
0.50
14.1
n.3
9.4
8.1
7.1
5.6
4.7
21
13.45 0.41
0.53
12.8
10.2
8.5
7.3
6.4
5.1
4.3
22
12.84 !0.45
0.55
11.7
9.3
7.8
6.7
5.8
4.7
3.9
23
12.28
0.49
0.58
10.7
8.6
7.1
6.1
5.3
4.3
3.6
24
11.77
0.53
0.60
9.8
7.8
6.5
5.6
4.9
3.9 3.3
25
11.30
0.58
0.63
9.0
7.2
6.0
5.1
4.5
3.6
3.0
26
10.86 0.62
0.65
8.4
6.7
5.6
4.8
4.2
3.4 j 2.8
27
10.46
0.67
0.68
7.7
6.2
5.1
4.4
3.9
3.1 i 2.6
28
10.09
0.72
0.70
7.2
5.8
4.8
4.1
3.6
2.9 2.4
29
9.74
0.78
0.73
6.7
5.4
4.5
3.8
3.4
2.7 2.2
30
9.41
0.83
0.75
6.3
5.0
4.2
3.6 3.1 2.5 2.1
31
9.11
0.89
0.78
5.9
4.7
3.9
3.4 2.9
2.4 2.0
32
8.83
0.94
0.80
5.5
4.4
3.7
3.2 2.8
2.2
1.8
33
8.56
1.00
0.83
5.2
4.2
3.5
3.0 2.6
2.1 1.7
34
8.31
1.07
0.85
4.9
3.9
3.3
2.8
2.4
2.0
1.6
35
8.07
1.13
0.88
4.6
3.7
3.1
2.6
2.3
1.8
1.5
36
7.84
1.19
0.90
4.4
3.5
2.9
2.5
2.2
1.7
1.5
37
7.63
1.26
0.93
4.1
3.3
2.7
2.4
2.1
1.6
1.4
38
7.43
1.33
0.95
3.9
3.1
2.6
2.2
2.0
1.6
1.8
39
7.24
1.40
0.98
3.7
3.0
2.5
2.1
1.9
1.5 1.3
88
UNION IRON MILLS'
15-INCH EYEBEAM, No. 1, HEAVY,
65 LBS. PER FOOT.
Depth, 15". Width of Flanges, 5.33". Thickness of Web, 0.77".
Maximum fiber strain = 12000 Ibs. per square inch.
Ja
till
II
a
g~~
Proper distance, in feet, center to center
of beams, for Safe Loads of
^
J 5
55
100
125
150
175
200
250
300
ji ^
S m
Ibs.
Ibs.
Ibs.
Ibs.
Ibs.
Ibs.
Ibs.
.2 *
- <D -^ ko~^ < .3
'^3
per
per
per
per
per
p3r
per
IS 41 .S .5
si. ft.
si. ft. 4 ft i si. ft.
1. ft.
si. ft,
tfft.
10
32.76 0.09
0.33
65.5
52.4
43.7
37.4 32.8
26.2
21.8
11
29.78 1 0.11
0.36
54.1
43.3
36.1
30.9
27.1 21.7
18.0
12
27.30
0.13
0.39
45.5
36.4 30.3
26.0
22.8 18.2
15.2
13
25.20
0.16
0.42
33.8
31.0 25.8
22.2
19.4 ! 15.5
12.9
14
23.40
0.18
0.46
33.4
26.7
22.3
19.1
16.7 13.4
11.1
15
21.84
0.21
0.49
29.1
23.3
19.4
16.6
14.6 11.6
9.7
16
20.48 iO.24
0.52
25.6
20.5
17.1
14.6
12.8
10.2
8.5
17
19.27 0.27
0.55
22.7
18.1
15.1
13.0
11.3
9.1
7.6
18
18.20 0.30-
0.59
20.2
16.2
13.5
11.6
10.1
8.1 1 6.7
19
17.24 0.33
0.62
18.1
14.5
12.1
10.4
9.1
7.3 6.0
20
16.38
0.37
0.65
16.4
13.1
10.9
9.4
8.2
6.6 5.5
21
15.60
0.41
0.68
14.9
11.9
9.9
8.5
7.4 5.9 i 5.0
22
14.89
0.45
0.72
13.5
10.8
9.0
7.7
6.8
5.4) 4.5
23
14.24
0.49
0.75
12.4
9.9
8.3
7.1
6.2
5.0 4.1
24
13.65
0.53
0.78
11.4
9.1
7.6
6.5
5.7
4.6 1 3.8
25
13.10
0.58
O.P1
10.5
8.4
7.0
6.0 5.2.
4.2 j 3.5
26
12.60
0.62
0.85
9.7
7.8
6.5
5.5
4.8
3.9 i 3.2
27
12.13
0.67 0.88
9.0
7.2
6.0
5.1
4.5
3.6; 3.0
28
11.70
0.72 1 0.91
8.4
6.7
5.6
4.8
4.2
3.3
2.8
29
11.30
0.78
0.94
7.8
6.2
5.2
4.4
3.9
3.1
2.6
30
10.92
0.83
0.98
7.3
5.8
4.9
4.2
3.6
2.9
2.4
31
10.57
0.89 i 1.01
6.8
5.5
4.5
3,9 3.4 2.7
2.3
32
10.24
0.95
1.04
6.4
5.1
4.3
3.7
3.2 2.6
2.1
33
9.93
1.01
1.07
6.0
4.8
4.0
3.4
3.0
2.4
2.0
34
9.64
1.07
1.11
5.7
4.5
3.8
3.2 2.8
2.3
1.9
35
9.36
1.13
1.14
5.3
4.3
3.6
3.1 2.7 2.1
1.8
33
9.10
1.20
1.17
5.1 4.0
3.4 2.9 2.5 2,0
1.7
37
8.85
1.26
1.20
4.8 3.8 3.2 2.7 2.4 1.9 i 1.6
38
8.62
1.33
1.24
4.5 3.6
3.0
2.6
2.3 1.81 1.5
39
8.40
1.40
1.27
4.3 3.4
2.9
2.5
2.2
1.7 ! 1.4
i
! i c
:<
UNION IRON MILLS'
15-INCH EYEBEAM, No.
2, LIGHT,
67
LBS. PER FOOT.
Depth, 15". Width cf Flanges, 5.55".
Thickness of Web, 0.67".
Maximum fiber
strain = 12000 Ibs. per square inch.
g^
ti?^
3
rt
Proper distance,
in feet, center to center
"
licl
11
Ig
of b
earns,
forSa
e Loads 01
s i
5ri?
s "
'o'~
o
100
125
150
175
200
250
300
.3 .
0,0 'S g
Ibs.
Ibs.
Ibs.
Ibs.
Ibs.
Ibs.
Ibs.
I i*
s'-i bL^
<i .2
be
per
per
per
per
per
per
per
3l^.2.2
*"
sq. ft
sq.ft.
sq. ft. sq. ft.
q. ft.
sq. ft.
sq. ft.
i_
I
.
10
36.12
0.09
0.34
72.2 57.8
48.2
41.3
36.1
28.9
24.1
11
32.84
0.11
0.37
59.7 47.8
39.8
34.1
29.9
23.9
19.9
12
30.10
0.13
0.40
50.2
40.1
33.4
28.7
25.1
20.1
16.7
13
27.78
0.16
0.44
42.7
34.2
28.5
24.4
21.4
17.1
14.2
14
25.80
0.18
0.47
36.9
29.5
24.6
21.1
18.4
14.7
12.3
15
24.08
0.21
0.50
32.1
25.7
21.4
18.3
16.1
12.8
10.7
16
22.58
0.24
0.54
28.2
22.6
18.8
16.1
14.1
11.3
9.4
17
21.25
0.27
0.57
25.0
20.0
16.7
14.3
12.5
10.0
8.3
18
20.07
0.30
0.60
22.3
17.8
14.9
12.7
11.2
8.9
7.4
19
19.01
0.33
0.64
20.0
16.0
13.3
11.4
10.0
8.0
6.7
20
18.05
0.37
0.67
18.1
14.4
12.0
10.3 ! 9.0
7.2
6.0
21
17.20
0.41
0.70
16.4
13.1
10.9
9.4
8.2
6.6
5.5
22
16.42
0.45
0.74
14.9
11.9
10.0
8.5
7.5 6.0
5.0
23
15.70
.0.49
0.77
13.7
10.9
9.1
7.8
6.8 5.5
4.6
24
15.05
i 0.53
0.80
12.5 10.0
8.4
7.2
6.3 5.0
4.2
25
14.45
0.58
0.84
11.6
9.2
7.7
6.7
5.8 4.6
3.9
26
13.89
10.62
0.87
10.7
8.5
7.1
6.1
5.3 4.3
3.6
27
13.38
J0.67
0.91
9.9 7.9
6.6
5.6
5.0
4.0
3.3
28
12.90
:0.72
0.94
9.2 7.4
6.2
5.3
4.6
3.7
! 3.1
29
12.46
10.78
0.97
8.6 6.9
5.7
4.9
4.3
3.4
2.9
30
12.04
!o.83
1.01
8.0
6.4
5.4
4.6
4.0
3.2
2.7
31
11.65
!0.89
1.04
7.5 |. 6.0 5.0 1 4.3
3.8
3.0
i 2.5
32
11.29
0.95
1.07
7.1 5.6
4.7
4.0
3.5
2.8
! 2.4
33
10.95
1.01
1.11
6.6 5.3
4.4
3.8
3.3
2.7
; 2.2
34
10.62
1.07
1.14
6.2 5.0
4.1
3.6
3.1
2.5
; 2.1
35
10.32
1.13
1.17'
5.9 4.7
3.9
3.4
2.9
2.4
2.0
36
10.03
1.20
1.21
5.6 4.5
3.7
3.2
2.8
2.2
1.9
37
9.76
:i.26
1.24
5.3 4.2
3.5
3.0
2.6
2.1
1.8
38
9.51
1.33
'1.27
5.0 4.0
3.3
2.9
2.5
2.0
1 1.7
39
9.26
1.40
1.31
4.7 3.8
3.2
2.7
1.9
, 1.6
'A
J
s:
UNION IRON MILLS'
15-INCH EYEBEAM, No. 2, HEAVY,
80 LBS. PER FOOT.
Depth, 15". Width of Flanges, 5.81". Thickness of Web, 0.93".
Maximum fiber strain = 12000 Its. per sojiare inch.
ji?* a *
S3
Proper distance, in fee
~ center to center
| <!
jjUjlg "fe-g
H"s2
of beams, for Safe Loads of
to &
a '-^"g H i 13 .2
rO t ~~- 1
r~
^ rt
s
ICO 125
175
200
2CO
soo
1 a
3:2 1 1
iif
g>3
Us.
Ibs.
Its.
Ibs.
Ibs.
Ibs.
Ibs.
& 3
. Jjg"^ ^ ,3
'G _g
per
per
per
per
per
par
per
tg:a.s.s
^
ai.fi,
El.ft sq.ft.
sq. ft.
Bl.it
s:q. ft.
^. ft
10
40.00 0.09
0.40
80.0
64.0 53.3
45.7
40.0
32.0
26.7
11
33.36 ! 0.11
0.44
66.1
52.9 44.1 37.8
33.1
26.4
22.0
12
33.33
0.13
0.48
55.6
44.4
37.0 31.7
27.8
22.2
18.5
13
30.77
0.16
0.52
47.3
37.9
31.6
27.1
23.7
18.9
15.8
14
28.57
0.18
0.56
40.3
32.6
27.2
23.3
20.4
16.3
13.6
15
28.67
0.21
0.60
35.6
28.4
23.7
20.3
17.8
14.2
11.9
16
25.00
0.24
O.C4
31.3
25.0
20.8
17.9 15.6
12.5
10.4
17
23.53
0.27
O.C8
27.7
22.1
18.5
15.8 j 13.8
11.1
9.2
18
22.22
0.30
0.72
24.7
19.8
16.5
14.1
12.3
9.9! 8.2
19
21.05 0.33
0.76
22.2
17.7
14.8
12.6
11.1
8.9
7.4
20
20.00 0.37
0.80
20.0
16.0
13.3
11.4
10.0
8.0
6.7
21
19.05
0.41
0.84
18.1
14.5
12.1 10.4
9.1
7.3
6.0
22
18.18 0.45
0.88
16.5
13.2
11.0
9.4
8.3
6.6
5.5
23
17.39 0.49
0.92
15.1
12.1
10.1
8.6
7.6
6.0
5.0
24
16.67
0.53
0.96
13.9
11.1
9.3
7.9
6.9
5.6
4.6
25
16.00
0.58
1.00
12.8
10.2
8.5
7.3
6.4
5.1
4.3
26
15.38
O.C2
1.C4
11.8
9.5
7.9
6.8
5.9
4.7
3.9
27
14.81
0.67
1.08
11.0
8.8
7.3 6.3
5.5
4.4
3.7
23
14.29 0.72 1.12
10.2
8.2 6.8! 5.8 j 5.1
4.1
3.4
29
13.79
0.78 i 1.16
9.5
7.6 6.3 5.4
4.8
3.8
3.2
30
13.33
0.83 1.20
8.9
7.1 5.9 5.1
4.4
3.6
3.0
31
12.90
0.89 1.24
8.3
6.6' 5.5 4.8
4.2
3.3
2.8
32
12.50 0.9511.28
7.8
6.2 5.2 ; 4.5
3.9
3.1
2.6
83
12.12 1.01 1.82
7.3
5.9^ 4.9 4.2
3.7
2.9
2.4
84
11.76 ! 1.07 1.36
6.9 5.5; 4.6; 3.9
3.5
2.8
2.3
35
11.43 1.13 1.40
6.5 5.2 ' 4.3 3.7
3.3
2.6
2.2
86
11.11 1.20 1.44
6.2 4.9; 4.1 3.5
3.1
2.5
2.1
37
10.81 1.26 1.43
5.8; 4.7 3.9, 3.3
2.9
2.3
1.9 '
38
10.68
1.33 ! 1.52
5.5 i 4.4
3.7 3.2
2.8
2.2
1.8
39
'4
10.28 1.40 1.56
5.3 4.2
3.5 3.0
2.6' i 2.1
1.8
c
f.
UNION IRON MILLS 1
12-INCH EYEBEAM, No. 3, LIGHT,
42
LBS. PER FOOT.
Depth, 12". Width of Flanges, 4.64". Thickness of Web, 0.51".
Maximum fiber strain = 12000 Ibs. per square inch.
CJ +3
li^s
1 o3
a
Proper distance, in feet, center to center
{I
t. ^0 33
|1
JS
of beams, for Safe Loads of
fi ^
f=g
<*-!
100
125 1 150 175 200
250
300
|
15
ili
Ibs.
Ibs. Ibs.
Ibs.
Ibs.
Ibs.
Ibs.
a &
If
A
per
sq. ft.
par
sq. ft.
per
sq. ft.
per
sq.ft.
per
sq.ft.
per
sjft.
10
18.36
0.12
0.21
36.7 29.4
24.5
21.0
18.4
14.7
12.2
11
16.69
0.14
0.23
30.3
24.3
20.2
17.3
15.2
12.1
10.1
12
15.30
0.17
0.25
25.5
20.4
17.0
14.6
12.8
10.2
8.5
13
14.12
0.20
0.27
21.7
17.4
14.5
12.4
10.9
8.7
7.2
14
13.11 J0.23
0.29
18.7
15.0
12.5 10.7
9.4
7.5
6.2
15
12.24
0.26
0.32
16.3
13.1
10.9
9.3
8.2
6.5
5.4
16
11.48
0.30
0.34
14.4
11.5
9.6
8.2
7.2
5.7
4.8
17
10.80
0.33
0.36
12.7
10.2
8.5
7.3
6.4
5.1
4.2
18
10.20 i 0.37
0.38
11.3
9.1
7.6
6.5
5.7
4.5
3.8
19
9.66 0.42
0.40
10.2
8.1
6.8
5.8
5.1
4.1
3.4
20
9.18
0.46
0.42
9.2
7.3
6.1
5.2
4.6
3.7
3.1
21
8.74
0.51
0.44
8.3
6.7
5.5
4.8
4.2
3.3
2.8
22
8.35
0.56
0.46
7.6
6.1
5.0
4.3
3.8
3.0
2.5
23
7.98
0.61
0.48
6.9
5.6
4.6
4.0
3.5
2.8
2.3
24
7.65
0.68
0.50
6.4
5.1
4.2
3.6
3.2
2.6
2.1
25
7.34
0.72"
0.53
5.9
4.7 1 3.9
3.3
2.9
2.4
2.0
26
7.06
0.78
0.55
5.4
4.3 3.6
3.1
2.7
2.2
1.8
27
6.80
0.84
0.57
5.0
4.0 3.3
2.9
2.5
2.0
1.7
28
6.56
0.90
0.59
4.7
3.7
3.1
2.7
2.3
1.9
1.6
29
6.33
0.97
0.61
4.4
3.5
2.9
2.5
2.2
1.7
1.5
30
6.12
1.04
0.63
4.1
3.3
2.7
2.3
2.0
1.6
1.4
31
5.92
1.11
0.65
3.8
3.1
2.5 2.2
1.9
1.5
1.3
32
5.74
1.18
0.67
3.6
2.9
2.3 2.0
1.8
1.4
1.2
33
5.56
1.26
0.69
3.4
2.7
2.2
1.9
1.7
1.3
1.1
34
5.40
1.34
0,71
3.2
2.5
2.1
1.8
i.6
1.3
1.1
35
5.25
1.42
0.74
3.0
2.4
2.0
1.7
1.5
1.2
1.0
36
5.10
1.50
0.76
2.8
2.2
1.9
1.6
1.4
1.1
0.9
37
4.96
1.58
0.78
2.6 2.1
1.8
1.5
1.3
1.1
0.9
38
4.83
1.67
0.80
2.5 2.0
1.7
1.5
1.3
1.0
0.8
39
5r~~
4.71
1.76
0.82
2.4
1.9
1.6
1.4
1.2
1.0
0.8
5
E
UNION IRON MILLS'
12-INCH EYEBEAM, No.
3, HEAVY,
60 LBS. PER FOOT.
Depth, 12". Width of Flanges, 5.09". Thickness of Web, 0.96".
Maximum fiber strain = 12000 Ibs. per square inch.
rt *
|| P 1 .
2
Proper distance,
in feet, center to center
| J
bl
fs
of beams,
for Safe Loads of
2 J
I'-^si 1-2
1
-|2
"."3 ,3 = ^ 2
~
100
125
150
175
200
250
300
jf
-ill If
-*
-a 01
Ibs.
Ibs.
Ibs.
Ibs.
Ibs.
Ibs.
Ibs.
a 1
JI.2.S 1
ll
per
rq. ft.
per
sq. ft.
per
sq.ft.
per
sq. ft.
per
sq.ft.
per
sq.ft.
per
sq.ft.
10
22.68 0.12
0.30
45.4 36.3
30.2
25.9
22,7
18.1
15.1
11
20.62
0.14 0.33
37.5
30.0. 25.0
21.4
18.7
15.0
12.5
12
18.90 0.17 0.36
31.5
25.21 21.0
18.0
15.8
12.6
10.5
13
17.45
0.20 | 0.39
26.8
21.5 i 17.9
15.3
13.4
10.7
8.9
14
16.20
0.23 0.42
23.1
18.5 i 15.4
13.2
11.6
9.3
7.7
15
15.12
0.26 ! 0.45
20.2
16.1 ' 13.4
11.5
10.1
8.1
6.7
16
14.18
0.30 1 0.48
17.7
14.2 ! 11.8
10.1
8.9 7.1
5.9
17
13.34
0.33 ! 0.51
15.7
12.6 10.5
9.0
7.8 6.3
5.2
18
12.60
0.37 0.54
14.0
11.2 i 9.3
8.0
7.0
5.6
4.7
19
11.94
0.42 i 0.57
12.6
10.1 8.4
7.2
6.3
5.0 4.2
20
11.34
0.46 0.60
11.3
9.1
7.6
6.5
5.7
4.5 3.8
21
10.80
0.51 0.63
10.3
8.2 6.9
5.9
5.2
4.1
3.4
22
10.31
0.56
0.66
9.4 7.5 6.2
5.4
4.7
3.7
3.1
23
9.86
0.61
0.69
8.6 i 6.9 5.7
4.9
4.3
3.4
2.9
24
9.45
0.66
0.72
7.9
6.3 5.3
4.5
3.9
3.1
2.6
i
25
9.07
0.72
0.75
7.3
5.8
4.9
42
36
29
2.4
26
8.72
0.78
0.78
6.7
5.4
4.5
3^9
3^3
27
2.2
27
8.40
0.84
0.81
6.2
5.0
4.2
3.6
3.1
2.5
2.1
28
8.10
0.90 0.84
5.8
4.6
3.9
a.3
2.9
2.3
1.9
29
7.82
0.97 i 0.87
5.4
4.3
3.6
3.1
2.7
2.1
1.8
30
7.56
1.04
0.90
5.0 4.0
3.4
2.9
2.5
2.0
1.7
31
7.32
1.11
0.93
4.7
3.8
3.2
2.7
2.4
1.9
1.6
32
7.09
1.18
0.96
4.4
3.5
3.0
2.5
2.2
1.8
1.5
33
6.87
1.26
0.99
4.2
3.3
2.8
2.4
2,1
1.7
1.4
34
6.67
1.34
1.02
3.9
3.1
2.6
2.2
2.0
1.6
1.3
35
6.48
1.42
1.05
3.7
3.0
2.5
2.1
1.9
1.5
1.2
36
6.30 1.50 1.08
3.5
2.8
2.3
2.0
1.8
1.4
1.2
37
6.13
1.58
1.11
3.3
2.6
2.2
1.9
1.7
1.3
1.1
38
5.97
1.67
1.14
3.1
2.5
2.1
1.8
1.6
1.3
1.0
39
5.82
1.76
1.17
3.0
2.4
2.0
1.7
1.5
1.2
1.0
G
B 38
*
rz
UNION IRON MILLS'
10K-INCH EYEBEAM,
No.
4, LIGHT,
313-2
LBS. PER
FOOT.
Depth, 10K". Width
of Flanges, 4.54"
. Thickness of Web, 0.41".
Maximum fiber
strain = 12000 Ibs. per square inch.
g -g
l^?2
t3 ;
A.
Proper dis
>tance, in feet, center to center
1 3
Ifli
I
of b<
jams, for Safe Loads of
42"
?'"o
(S -- 1
o . ( t
100 ' 125
150
175 ! 200
250
300
3 1
Ssi 1
j3
Ibs. i Ibs.
Ibs.
Ibs. Ibs.
Ibs.
Ibs.
s 1*
=2^ bD
<~
ifj
per i per
per
per per
per
per
ji^.s.s
*
sq. ft. j sq. ft.
sq. ft.
sq. ft. sq. ft.
sq.ft.
sq. ft.
.
10
12.56
0.13
0.16
25.1 1 20.1
16.7
14.4 12.6
10.0
8.4
11
11.42
0.16
0.17
20.8 i 16.6
13.8
11.9 10.4
8.3
6.9
12
10.47
0.19
0.19
17.5 14.0
11.6
10.0 8.7
7.0
5.8
13
9.66
0.22
0.21
14.9 1 11.9
9.9
8.5 7.4
5.9
5.0
14
8.97
0.26
0.22
12.8 i 10,2
8.5
7.3 6.4
5.1
4.3
15
8.37
0.30
0.24
11.2; 8.9
7.4
6.4: 5.6-
4.5
3.7
16
7.85
0.34
0.25
9.8 i 7.8
6.5
5.6; 4.9
3.9
3.3
17
7.39
0.38
0.27
8.7' 7.0
5.8
5.0 4.3
3.5
2.9
18
6.98
0.43
0.28
7.8; 6.2
5.2
4.4 3.9
3.1
2.6
19
6.61
0.48
0.30
7.0; 5.6
4.6
4.0 3.5
2.8
2.3
20
6.28
0.53
0.32
6.3 5.0
4.2
3.6 3.1
2.5
2.1
21
5.98
0.58
0.33
5.7 4.6
3.8
3.3 2.8
2.3
1.9
88
5.71
0.64
0.35
5.2 4.2
3.5
3.0 2.6
.2.1
1.7
23
5.46
0.70
0.36
4.8 3.8
3.2
2.7 2.4
1.9
1.6
24
5.23
0.76
0.38
4.4 3.5
2.9
2.5 2.2
1.7
1.5
25
5.02
0.82
0.39
4.0 3.2
2.7
2.3 2.0
1.6
1.3
26
4.83
0.89
0.41
3.7 3.0
2.5
2.1 1.9
1.5
1.2
27
4.65
0.96
0.43
3.4 2.8
2.3
2.0 1.7
1.4
1.1
28
4.49
1.03
0.44
3.2; 2.6
2.1
1.8 1.6
1.3 1.1
29
4.33
1.11
0.46
3.0; 2.4
2.0
1.7; 1.5
1.2
1.0
30
4.19
1.19
0.47
2.8' 2.2
1.9
1,6: 1.4
1.1
.9
31
4.05
1.27
0.49
2.6; 2.1
1.7
1.5 1.3
1.0
.9
32
3.93
1.35
0.50
2.5 2.0
1.6
1.4 1.2
1.0
.8
33
3.81
1.44
0.52
2.3 1.8
1.5
1.3! 1.2
.9
.8
34
3.69
1.53
0.54
2.2; 1.7
1.4
1.2 1.1
.9
.7
35
3.59
1.62
0.55
2.1 1.6
1.4
1.2 1.0
.8
7
36
3.49
1.71
0.57
1.9; 1.6
1.3
1.1 1.0
.8
.6
37
3.39
1.80
0.58
1.8 1.5
1.2
1.1 ! .9
.7
.6
38
3.31
1.90
0.60
1.7; 1.4
1.2
1.0 , .9
.7
.6
39
'4
3.22
2.01
0.61
1.7! 1.3
1.1
.9 ; .8
.7 .6
H
UNION IRON MILLS'
10^-INCH EYEBEAM, No.
4, HEAVY,
45 LBS. PER FOOT.
Depth, 10}^". Width of Flanges,
4.92". Thickness of Web, 0.79".
Maximum fiber strain = 12000 Ibs. pe
r square inch.
a ^
ti^s
1.9 ! ft
i ^ - i :.-
Proper distance,
in feet, center to center
11
jj'gj^g
of beams, for Safe Loads of
i*
if
Jit's
1 a ** <*-.
175
100
125 ICO
200
250
300
*8fj|lf Hi
Ibs.
Ibs. : Ibs.
Ibs.
Ibs.
Its.
Ibs.
Q w
iirfr I 1
per
apt
per per
sq. ft. i Eq. ft.
per
sq^lt.
per
Eq ft.
La
per
Eq. ft.
i
10
15.32
0.13 i 0.23
30.6
24.5 20.4
17.5
15,3
12.3
10.2
11
13.93
: 0.16 I 0.25
25.3
20.3 16.9
14.5
12.7
10.1
8.4
12
12.77
: 0.19 i 0.27
21.3
17.0 ! 14.2
12.2
10.6
8.5
7.1
13
11.78
! 0.22 ! 0.29
18.1
14.5 12.1
10.4
9.1
1 7.2
6.0
14
10.94
1 0.26 j 0.32
15.6
12.5 10.4
8.9
7.8
6.3
5.2
15
10.21
!0.30 0.34
13.6
10.9 l 9.1
7.8
6.8
5.4
4.5
16
9.58
10.34 0.36
12.0
9.6 8.0
6.8
6.0
4.8
4.0
17
9.01
0.88 0.38
10.6
8.5 7.1
6.1
5.3
4.2
3.5
18
8.51
10.43 0.41
9.5
7.6 6.3
5.4
4.7
3.8
3.1
19
8.06
0.48 0.43
8.5
6.8 5.7
4.8
4.2
3.4
2.8
20
7.66
i 0.53 ! 0.45
7.7
6.1 5.1
4.4
3.8
3.1
2.5
21
7.30
iO.58 0.47
7.0
5.6 4.6
4.0
3.5
2.8
2.3
22
6.96
10.64 0.50
6.3
5.1: 4.2
3.6
3.2
2.5
2.1
23
6.66
I 0.70 : 0.52
5.8
4.6 3.9
3.3
2.9
2.3
1.9
24
6.38
0.76 0.54
5.3
4.2 3.6
3.0
2.7
2.1
1.8
25
6.13
1 0.82 i 0.56
4.9
3.9 3.3
2.8
2.5
1.9
1.6
26
5.89
0.89 0.59
4.5
3.6 3.0
2.6
2.3
1.8
1.5
27
5.67
0.96 ; 0.61
4.2
3.4 2.8
2.4
2.1
1.7
1.4
28
5.47
1.03 : 0.63
3.9
3.1 ! 2.6
2.2
2.0
1.6
1.3
29
5.28
1.11 0.65
3.6
2.9 2.4
2.1
1.8
1.5 I 1.2
30
5.11
1.19 ! 0.68
3.4
2.7 2.3
1.9
1.7
1.4
1.1
31
4.94
1.27 0.70
3.2
2.6 2.1
1.8
1.6
1.3
1.1
32
4.79
1.35 : 0.72
3.0
2.4 2.0
1.7
1.5
1.2
1.0
33
4.64
1.44 0.74
2.8
2.2! 1.9
1.6
1.4
1.1
.9
34
4.51
1.53 . 0.77
2.7
2.1 1.8
1.5
1.3
1.1
.9
35
4.38
1.62 0.79
2.5
2.0i 1.7
1.4
1.3
1.0
.8
36
4.26
1.71 ; 0.81
2.4
1.91 1.6
1.4
1.2
.9
.8
37
4.14
1.80 i 0.83
2.2
1.8 1.5
1.3
1.1
.9
.7
38
4.03
1.90 i 0.86
2.1
1.7, 1.4
1.2
1.1
.8
.7
39
3.93
2.01 ; 0.88
2.0
1.6; 1.3
1.2
1.0
.8
.7
1
i
UNION IRON MILLS'
10-INCH EYEBEAM, No. 5, LIGHT,
30 LBS. PER FOOT.
Depth, 10". Width of Flanges, 4.32". Thickness of Web, 0.32".
Maximum fiber strain = 12000 Ibs. per square inch.
II
it*!
-2^
i.
b-9
fl
Proper distance, in feet, center to center
of beams, for Safe Loads of
ft
w
i.s
r 9
100
125
150
175
200
250
300
J &
IJfl
i'f
ILs
Ibs.
Ibs.
Ibs.
Ibs.
Ibs.
Ibs.
Ibs.
s S
sSH
tS M
per
per
per
per
per
per
per
=3:3.2.2
^~
sq.ft.
sq.ft. sq.ft.
sq.ft.
sq.ft. sq.ft.
sq.ft.
10
12.00
0,14
0.15
24.0
19.2
16.0
13.7
12.0
9.6
8.0
11
10.91
0.17
0.17
19.8
15.9 ! 13.2
11.3
9.9
7.9
6.6
12
10.00
0.20
0.18
16.7
13.3 ! 11.1
9.5
8.3
6.7
5.6
13
9.23
0.23
0.20
'14.2
11.4
9.5
8.1
7.1
5.7
4.7
14
8.57
0.27
0.21
12.2
9.8
8.2
7.0
6.1
4.9
4.1
15
8.00
0.31
0.23
10.7
.5
7.1
6.1
5.3
4.3
3.6
16
7.50
0.35
0.24
9.4
7.5
6.3
5.4
4.7
3.8
3.1
17
7.06
0.40
0.26
8.3
6.6
5.5
4.7
4.2
3.3
2.8
18
6.67
0.45
0.27
7.4
5.9
4.9
4.2
3.7
3.0
2.5
19
6.32
0.50
0.29
6.7
5.3
4.4
3.8
3.3
2.7
2.2
20
6.00
0.55
0.30
6.0
4.8
4.0
3.4
3.0
2.4
2.0
21
5.71
0.61 0.32
5.4
4.4
3.6
3.1
.2.7
2.2
1.8
22
5.45
0.67 0.33
5.0
4.0
3.3
2.8
2.5
2.0
1.7
23
5.22
0.73 0.35
4.5 ! 3.6
3.0
2.6
2.3
1.8
1.5
24
5.00
0.80 0.36
4.2 3.3
2.8
2.4
2.1
1.7
1.4
25
4.80
0.87
0.38
3.8 3.1
2.6
2.2
1.9
1.5
1.3
26
4.62 i 0.94
0.39
3.6 I 2.8
2.4
2.0
1.8
1.4
1.2
27
4.44 1.01 0.41
3.3 2.6
2.2
1*9
1.6
1.3
1.1
28
4.29 1 1.09 0.42
3.1 2.4
2.0
1.7
1.5
1.2
1.0
29
4.14
1.17
0.44
2.9 2.3
1.9
1.6
1.4
1.1
.9
30
4.00
1.25
0.45
2.7 2.1
1.8
1.5.
1.3
1.1
.9
31
3.87
1.33 0.47
2.5
2.0
1.7
1.4 1.2
1.0
.8
32
3.75
1.42 ! 0.48
2.3
1.9
1.6
1.3 1.2
.9
.8
33
3.64 1.51 : 0.50
2.2
1.8
1.5
1.3 1.1 .9 i .7
34
3.53 1.60 i 0.51
2.1
1.7
1.4
1.2 1.0 ; .8
.7
35
3.43 1.70 ! 0.53
2.0
1.6 1.3
1.1
1.0 .8
.7
36
3.33 1.80 0.54
1.9
1.5 1.2 1.1
.9 .7
.6
37
3.24 1.90:0.56
1.8
1.4 1.2
1.0 .9
.7
.6
38
3.16 2,01 i 0.57
1.7
1.3 1.1
.9 .8
.7
.6
39
3.08 2.11 0.59
1.6 1 1.3 1.1 .9
.8 .6
.5
R
1 '
]
UNION IRON
r.
MILLS'
10-INCH EYEBEAM, No.
5, HEAVY,
45
LBS. PER FOOT.
Depth, 10". Width of Flanges, 4.77".
Thickness
of Web, 0.77".
Maximum fiber strain = 12000
Ibs. per square inch.
I!
1-ili
J|
Si
Proper distance,
of beams,
in feet, center to center
for Safe Loads of
1 if
ft?
1-9
?5
100 125
150
175
< 200
250
300
E,
,~'f3
t -=?
i 5 M
Ibs. Ibs.
Ibs.
Ibs.
! Ibs.
Ibs.
Ibs.
.2 *
ilL J
I- 2
.|Fg
per
per
per
per
per
cg^.S.S
5
*
cq. ft.
Jft
*fft.
sq. ft.
sq.ft.
10
15.00
0.14 i 0.23
30.0 24.0
20.0
17.1
! 15.0
12.0
! 10.0
11
13.64
0.17 i 0.25
24.8
19.8
16.5
14.2
!12.4
9.9
8.3
12
12.50
0.20
0.27
20.8 16.7
13.9
11.6
10.4
8.3
6.9
13
11.54
0.23
0.29
17.8 14.2
11.8
10.1
: 8.9
7.1
5.9
14
10.71
0.27
0.32
15.3
12.2
10.2
8.7
: 7.7
6.1
5.1
15
10.00
0.31
0.34
13.3
10.7
8.9
7.6
6.7
5.3
: 4.4
16
9.38
0.35
0.36
11.7 9.4
7.8
6.7
5.9
4.7
3.9
17
8.82
0.40
0.38
10.4 8.3
6.9
5.9
i 5.2
4 2
3.5
18
8.33
0.45
0.41
9.3 7.4
6.2
5.3
: 4.6
3.7
3.1
19
7.89
0.50
0.43
8.3: 6.6
5.5
4.7
i 4.2 3.3 2.8
20
7.50
0.55
0.45
7.5
6.0
5.0
4.3
1 3.8
3.0
2.5
21
7.14
0.61
0.47
6.8
5.4
4.5
3.9
3.4
2.7
2.3
22
6.82
0.67
0.50
6.2 5.0
4.1
3.5
i 3.1
2.5
2.1
23
6.52
0.73
0.52
5.7 4.5
3.8
3.2
2.8
2.3
1.9
24
6.25
0.80
0.54
5.2 4.1
3.5: 2.9
2.6
2.1
1.7
25
6.00
0.87
0.56
4.8
3.8
3.2
2.7
2.4 1.9
1.6
26
5.77
0.94
0.59
4.4 3.6
3.0
2.5
2.2! 1.8
1.5
27
5.56
1.01
0.61
4.1 i 3.3
2.8
2.4
2.1
1.6
1.4
28
5.36
1.09
0.63
3.8 3.1
2.6
2.2
1.9
1.5
1.3
29
5.17
1.17
0.65
3.6 2.9
2.4
2.0
1.8
1.4
1.2
30
5.00
1.25
0.68
3.3 2.7
2.2
1.9
1.7
1.3
1.1
31
4.84
1.33
0.70
3.1 2.5
2.1
1.8
1.6
1.2
1.0
32
4.69
1.42
0.72
2.9 2.3
1.9
1.7
1.5
1.2
1.0
33
4.55
1.51
0.74
2.8! 2.2
1.8
1.6
1.4
1.1
.9
34
4.41
1.60
0.77
2.6
2.1
1.7
1.5
1.3
1.0
.9
35
4.29
1.70
0.79
2.4
2.0
1.6
1.4
1.2
1.0
.8
36
4.17
1.80
0.81
2.3
1.9
1.5
1.3
1.2
.9
.8
37
4.05
1.90
0.83
2.2
1.8
1.5
1.3
1.1
.9
.7
38
3.95
2.01
0.86
2.1
1.7
1.4
1.2
1.0
.8
.7
39
3.85
2.11
0.88
2.0
1.6
1.3
1.1
1.0
.8
.7
SB
UNION IRON MILLS'
9-INCH EYEBEAM, No. 6, LIGHT,
23^
LBS. PER FOOT.
Depth, 9". Width of Flanges, 4.01". Thickness of Web, 0.26".
Maximum
fiber
strain = 12000 Ibs. per square inch.
a H-s
^?^
.2
"3 eft
.*
Proper distance, in feet, center to center
II
JlMs
bl
f
of beams, for Safe Loads of
if
35*5
la
5i
100
125
150 175
200
250 800
.2 a
j=.o'| g
iif
fls
Ibs.
Ibs.
Ibs.
Ibs.
Ibs.
Ibs. | Ibs.
s S
ll.s.s
Ji Jj
|f
per
sq. ft.
per
sq.ft.
per
sq.ft.
per
sq.ft.
per
sj.ft.
per ! per
sq. ft. j sq. ft.
10
8.68
0.15
0.12
17.4
13.9 11.6
9.9 i 8.7
6.9! 5.8
11
7.89
0.19
0.13
14.4
11.51 9.6
8.2| 7.2! 5.7 4.8
12
7.23
0.22
0.14
12.1
9.6
8.0 6.9 6.0 4.8 4.0
13
6.68
0.26
0.15
10.3
8.2
6.9 5.9! 5.1 4.1 3.4
14
6.20
0.30
0.16
8.9
7.1
5.9, 5.1 4.4
3.5 | 2.9
15
5.79
0.35
0.18
7.7
6.2
5.1 4.4 3.9 3.1 1 2.6
16
5.43
0.40
0.19
6.8
5.4 4.5 3.9 3.4 2.7 2.3
17
5.11
0.45
0.20
6.0
4.8 4.0 3.4 3.0 2.4 2.0
18
4.82
0.50
0.21
5.4
4.3 3.6 3.0
2.7 2.1
1.8
19
4.57
0.56
0.22
4.8
3.8 3.2 2.7
2.4 1.9 1.6
20
4.34
0.62
0.24
4.3
3.5
2.9
2.5
2.2 1.7
1.4
21
4.13
0.68
0.25
3.9
3.2
2.6 2.2 2.0 1.6
1.3
22
3.95
0.75
0.26
3.6
2.9
2.4 2.0 1.8, 1.4
1.2
23
3.77
0.82
0.27
3.3
2.6
2.2 i 1.9 1.6 1.3
1.1
24
3.62
0.89
0.28
3.0
2.4
2.0
1.7
1.5
1.2
1.0
25
3.47
0.96
0.29
2.8
2.2
1.9
1.6
1.4
1.1
.9
26
3.34
1.04
0.31
2.6
2.0
1.7
1.5
1.3
1.0 i .9
27
3.21
1.12
0.32
2.4
1.9 1.6
1.4
1.2
1.0
.8
28
3.10
1.20
0.33
2.2
1.8
1.5 1.3
1.1
.9
.7
29
2.99
1.29
0.34
2.1
1.6
1.4
1.2
1.0
.8
.7
30
2.89
1.39
0.35
1.9
1.5 1.3
1.1
1.0
.8
.6
31
2.80
1.48
0.36
1.8
1.4 1.2
1.0
.9 .7
.6
32
2.71
1.58
0.38
1.7
1.4 1.1
1.0
.9 .7
.6
33
2.63
1.68
0.39
1.6
1.3 i 1.1
.9
.8
.6
.5
34
2.55
1.78
0.40
1.5
1.2 1.0
.9
.8 .6
.5
35
2.48
1.89
0.41
1.4
1.1 .9
.8
.7
.6
.5
36
2.41
2.00
0.42
1.3
1.1
Q
.y
.8
.7
.5
.4
37
2.35
2.11
0.43
1.3
1.0
.8
.7 .6
.5
.4
38
2.28
2.22
0.45
1.2
1.0
.8 .7 .6
.5
.4
39
2.23
2.34
0.46
1.2
.9
.8 .7 .6
.5
.4
x?
,
^
UNION IRON MILLS'
9-INCH EYEBEAM, No. 6, HEAVY,
33
LBS. PER FOOT.
Depth, 9". Width of Flanges, 4.33".
Thickness of Web, 0.58".
Maximum fiber
strain = 12000 1
bs. per square inch.
rt -*s
tif^l-i-
.3
-J
Proper distance,
in feet, center to center
11
|j
K.2
a^
of b
earns,
for Safe Loads of
j.a
i'^s
f.a
Ja t= ~ >
g -2"
^3 "^ CM
ng-S-gjO
c4
""
* <*-!
ICO
125
150
175
200
250 300
il ^*
J;g'| |
g-^"
2a w
Ibs.
Ibs.
Ibs.
Ibs.
Ibs.
Ibs.
Ibs.
3 f
-*5 w feJD^*
JJ
sj
per
per
per
per
per
per
per
&
=
Eq. ft.
sq.ft.
sq. ft.
sq. ft.
sq.ft.
sq. ft. sq. ft
10
10.40
0.15
0.17
20.8 16.6
13.9
11.9
10.4 8.3' 6.9
11
9.45
0.19
0.18
17.2 13.8
11.5
9.8
8.6
6.9: 5.7
12
8.67
0.22
0.20
14.5 11.6
9.6
8.3
7.2 5.8 I 4.8
13
8.00
0.26
0.22
12.3 9.8
8.2
7.0
6.2 4.9 4.1
14
7.43
0.30
0.23
10.6 8.5
7.1
6.1
5.3 4.2
3.5
15
6.93
0.35
0.25
9.2 7.4
6.2
5.3
4.6 3.7
3.1
16
6.50
0.40
0.26
8.1 6.5
5.4
4.6
4.1 3.3 2.7
17
6.12
0.45
0.28
7.2
5.8
4.8
4.1
3.6 2.9 2.4
18
5.78 0.50
0.30
6.4
5.1
4.3
3.7
3.2
2.6 2.1
19
5.47
0.56
0.31
5.8
4.6
3.8
3.3
'2.9 2.3
1.9
20
5.20 0.62
0.33
5.2
4.2
3.5
3.0
2.6 2.1
1.7
21
4.95 ! 0.68
0.35
4.7! 3.8
3.1
2.7
2.4
1.9
1.6
22
4.73 0.75
0.36
4.3 3.4
2.9
2.5
2.2 1.7
1.4
23
4.52
0.82
0.38
3.9 3.1
2.6
2.3
2.0
1.6
1.3
24
4.33
0.89
0.40
3.6 2.9
2.4
2.1
1.8
1.4
1.2
25
4.16
0.96'
0.41
3.3 2.7
2.2
1.9
1.7
1.3
1.1
26
4.00
1.04
0.43
3.1 2.5
2.1
1.8
1.5
1.2
1.0
27
3.85
1.12
0.45
2.9 2.3
1.9
1.6
1.4
1.1
.9
28
3.71
1.20
0.46
2.7i 2.1
1.8
1.5
1.3
1.1 .9
29
3.59
1.29
0.48
2.5
2.0
1.6
1.4
1.2
1.0 1 .8
30 v
3.47
1.39
0.50
2.3 1.8
1.5
1.3
1.2 .9 .8
31
3.35
1.48
0.51
2.2 1.7
1.4
1 2
1.1 .9
.7
32
3.25 ! 1.58
0.53
2.0
1.6
1.4
1.1
1.0 .8 .7
33
3.15 : 1.68
0.55
1.9
1.5
1.3
1.1
1.0 .8 .6
34
3.06 1.78
0.56
1.8
1.4
1.2
1.0
.9 .7 .6
35
2.97
1.89
0.58
1.7
1.4
1.1
1.0
.9 .7 .6
36
2.89 2.00
i 0.59
1.6
1.3
1.1
.9
.8
.6 .5
37
2.81 2.11
0.61
1.5
1.2
1.0
.9
.8
.6
t
38
2.74 2.22
0.63
1.4
1.21 1.0
.8
.7
.6
39
2.67
2.34
0.64
1.4 U
.9
.8
.7 .5
.5
UNION IRON MILLS'
8-INCH EYEBEAM, No. 8, LIGHT,
22 LBS. PER FOOT.
Depth, 8". Width of Flanges, 3.81 ". Thickness of Web, 0.31 ".
Maximum fiber strain = 12000 Ibs. per square inch.
| rf -,:
Proper distance, in feet, center to center
I *
ills
il
2 .3
|s
of beams, for Safe Loads of
tS ~
5]f:3g
2 -a
""M
ICO
125
150 175
200
250
300
j?'S f.
- ij i ;2
Ibs.
Ibs.
Ibs.
Ibs.
Ibs.
Ibs.
Ibs.
1 1*
~Z'B fl-2
J> J> j -|f 1
per
per
per
per i per
per j per
<i.s.s
| =~
sq. ft.
sq.ft.
q. ft. sq. ft.
sq. ft.
sq. ft. i sq. ft.
5
14.00
0.04 0.06
56.0
44.8 1 37.3 32.0
28.0
22.4 18.7
6
11.67
0.08 I 0.07
38.9
31.1 25.9
22.2
19.5
15.6 13.0
7
10.00
0.08 0.08
28.6
22.9 19.0
16.3
14.3
11.4
9.5
8
8.75
0.11
0.09
21.9
17.5 14.6
12.5
10.9
8.8
7.3
9
7.78
0.14
0.10
17.3
13.8
11.5
9.9
8.6
6.9
5.8
10
7.00
0.17
0.11
14.0
11.2
9.3
8.0
7.0
5.6
4.7
11
6.36
0.21 i 0.12
11.6
9.2
7.7
6.6
5.8
4.6
3.9
12
5.83
0.25 0.13
9.7
7.8
6.5
5.8
4.9
3.9
3.2
13
5.38
0.29 0.14
8.3
6.6
5.5
4.7
4.1
3.3
2.8
14
5.00
0.34
0.15
7.1
5.7
4.8
4.1
3.6
2.9
2.4
15
4.67
0.39
0.17
6.2
5.0
4.2
3.6
3.1
2.5
2.1
16
4.38
0.44
0.18
5.5
4.4
3.7
3.1
2.7
2.2
1.8
17
4.12
0.50
0.19
4.9
3.9
3.2
2.8 2.4
1.9 1.6
18
3.89
0.56
0.20
4.3
3.5
2.9
2.51 2.2
1.7 1.4
19
3.68
0.62
0.21
3.9
3.1
2.6
2.2
1.9
1.5
1.3
20
3.50
0.69
0.22
3.5
2.8
2.3
2.0
1.8
1.4
1.2
21
3.33
0.76
0.23
3.2
2.5
2.1
1.8
1.6
1.3
1.1
22
3.18
0.84
0.24
2.9
2.3
1.9
1.7
1.4
1.2
1.0
23
3.04 1 0.92
0.25
2.6
2.1
1.8
1.5
1.3
1.1
.9
24
2.92 1.00
0.26
2.4
1.9
1.6
1.4
1.2
1.0
.8
25
2.80 1.08
0.28
2.2
1.8
1.5
1.3
1.1
Q
.7
26
2.69 1.17
0.29
2.1
1.7*
1.4
1.2
1.0
8
.7
27
2.59 ! 1.26
0.30
1.9
1.5
1.3
1.1
i.b
!s
.6
28
2.50 i 1.36 0.31
1.8
1.4
1.2
1.0
.9
.7
.6
29
2.41 1.46
0.32
1.7
1.8
1.1
.9
.8
.7
.6
30
2.33
1.56
0.33
1.6
1.2
1.0
.9
.8
.6
.5
31
2.26
1.67
0.34
1.5
1.2
1.0
.8
.7
.6
.5
32
2.19
1.78
0.35
1.4
1.1
.9
.8
.7
.5
.5
33
2.12
1.89
0.36
1.3
1.0
.9
.7
.6
.5
.4
34
2.06
2.00
0.37
1.2
1.0
.8
.7
.6
.5
.4
4
!
i
UNION IRON MILLS'
8-INCH EYEBEAM, No. 8, HEAVY,
35 LBS. PER FOOT.
Depth, 8". Width of Flanges, 4.29". Thickness of Web, 0.79".
Maximum fiber strain = 12000 Ibs. per square inch.
g -g
fA?J*|j
.a .
Proper distance, in feet, center to center
II
111 1 j|
jj
of beams, for Safe Loads of
11
3^2 *rt
100
125
150
175
200
250 300
1 1
,2^'S ft &
3 M
Ibs.
Ibs. Ibs.
Ibs.
Ibs. Ibs. Ibs.
-* ^ S ^ < C3 ^
"fi o
per
per per
per
per per
psr
l^.a.a
a
^
sq.ft.
sq. ft. q. ft. sq. ft. sq. ft. sq. ft.
sq. ft.
5
18.08
0.04 0.09
72.3 57.9 48.2 41.3 36.2 28.9
24.1
6
15.07
0.06
0.11
50.2 40.2 83.5 28.7 125.1 1 20.1
16.7
7
12.91
0.08
0.12
36.9 129.5 24.6 21.1
18.4 14.8
12.3
8
11.30
0.11
0.14
28.3122.6 18.8 16.1
14.1 ; 11.3 9.4
9
10.04
0.14
0.16
22.3 : 17.8 14.9
12.7
11.2 8.9
7.4
10
9.04 0.17
0.18
18.1
14.5 12.1 10.3
9.0 7.2
6.0
11
8.22
0.21
0.19
14.9
12.0
10.0 8.5 7.5 ' 6.0
5.0
12
7.53
0.25
0.21
12.6
10.0
8.4 7.2 6.3 5.0
4.2
13
6.95
0.29
0.23
10.7
8.6 7.1 6.1
5.3 4.3
3.6
14
6.46
0.34
0.25
9.2
7.4
6.2
5.3
4.6 3.7
3.1
15
6.03
0.39
0.26
8.0
6.4 5.4
4.6
4.o! 3.2
2.7
16
5.65
0.44
0.28
7.1
5.6
4.7
4.0
3.5 2.8
2.4
17
' 5.32
0.50
0.30
6.3
5.0 4.2
3.6 3.1 2.5
2.1
18
5.02
0.56
0.32
5.6
4.5
3.7
3.2 2.8
2.2
1.9
19
4.76
0.62
0.33
5.0
4.0
3.3
2.9
2.5
2.0
1.7
20
4.52
0.69
0.35
4.5
3.6 3.0
2.6
2.3
1.8
1.5
21
4.30
0.76
0.37
4.1
3.3 2.7
2.3
2.0
1.6
1.4
22
4.11
0.84
0.39
3.7
3.0 2.5
2.1
1.9 1.5
1.2
23
3.93
0.92 0.40
3.4
2.7 2.3
2.0
1.7
1.4
1.1
24
3.77
1.00
0.42
3.1
2.5 2.1
1.8
1.6
1.3
1.0
25
3.62
1.08
0.44
2.9
2.3
1.9
1.7
1.4
1.2
1.0
26
3.48
1.17
0.46
2.7
2.1
1.8
1.5
1.3
1.1
.9
27
3.35
1.26
0.47
2.5
2.0
1.6
1.4
1.2
1.0
.8
28
3.23
1.36
0.49
2.3
1.8
1.5
1.3
1.2
.9
.8
29
3.12 1.48
0.51
2.2
1.7
1.4
1.2
1.1
.9
.7
30
3.01
1.56
0.53
2.0
1.6
1.3
1.1
1.0
.8
.7
31
2.92
1.67
0.54
1.9
1.5
1.2
1.1
.9
.8
.6
32
2.83
1.78
0.56
1.8
1.4
1.2
1.0
.9
.7
.6
33
2.74
1.89 1 0.58
1.7
1.3
1.1
.9
.8
.7
.6
34
2.66
2.00 0.60
1.6 1.2
1.0
.9
.8
.6
.5
46
UNION IRON MILLS'
7-INCH EYEBEAM, No. 9, LIGHT,
18 LBS. PER FOOT.
Depth, 1". Width of Flanges, 3.61". Thickness of Web, 0.23".
Maximum fiber strain = 12000 Ibs. per square inch.
g
l^^j .1^ . SM .
Proper distance, in feet, center to center
1 *
iici la
J
of beams, for Safe Loads of
1 "^
^ ^ i S "~*
8*
100 125
150 175
200 250
300
1 1
j=jTg g -^^- ^ M
Ibs. Ibs.
Ibs.
Ibs.
Ibs.
Ibs.
Ibs.
=2 -S t,^ <S -3 '3 <=
per 1 per
per
per
per
per
per
JB^.S.2 =~
sq. ft. sq. ft.
sq.ft. sq.ft.
sq. ft.
sq.ft.
sq. ft.
5
10.48 0.05 ''0.05
41.9 33.5 27.9
24.0
21.0
16.8
14.0
6
8.73
0.07 0.05
29.1 23.3 19.4
16.6
14.6
11.6
9.7
7
7.49
0.10 0.06
21.4
17.1 14.3
12.2
10.7
8.6
7.1
8
6.55 0.13 0.07
16.4
13.1 10.9
9.4
8.2
6.6
5.5
9
5.82 | 0.16
0.08
12.9
10.3 8.6 7.4
6.5
5.2
4.3
10
5.24 0.20
0.09
10.5
8.4
7.0
6.0
5.2
4.2
3.5
11
4.76
0.24
0.10
8.7
6.9
5.8
4.9
4.3
3.5
2.9
12
4.37
0.28
0.11
7.3
5.8
4.9
4.2
3.6
2.9
2.4
13
4.03
0.33
0.12
6.2
5.0
4.1
8.5
3.1
2.5
2.1
14
3.74
0.39
0.13
5.3
4.3
3.6
3.1
2.7
2.1
1.8
15
3.49
0.45
0.14
4.7
3.7
3.1 2.7
2.3
1.9
1.6
16
3.28
0.51
0.14
4.1 i 3.3
8.7 2.3
2.1
1.6
1.4
17
3.08
0.57
0.15
3.6
2.9
2.4
2.1
1.8
1.4
1.2
18
2.91
0.64
0.16
3.2
2.6
2.2
1.8
1.6
1.3
1.1
19
2.76
0.71
0.17
2.9
2.3
1.9
1.7
1.5
1.1
1.0
20
2.62
0.79
0.18
2.6
2.1
1.7
1.5
1.3
1.0
.9
21
250
0.87
0.19
2.4
1.9
1.6
1.4
1.2
1.0
.8
22
2.38
0.96
0.20
2.2
1.7
1.4
1.2
1.1
.9
.7
23
2.28
1.05
0.21
2.0
1.6
1.3
1.1
1.0
.8
.7
24
2.18
1.14
0.22
1.8
1.4
1.2
1.0
.9
.7
.6
25
2.10
1.24
0.23
1.7
1.3
1.1
1.0
.8
.7
.6
26
2.02
1.34
0.23
1.6
1.2
1.0
.9
.8
.6
.5
27
1.94
1.44
0.24
1.4
1.2
1.0
.8
.7
.6
.5
28
1.87
1.55
0.25
1.3
1.1
.9
.8
.7
.5
.4
29
1.81
1.66
0.26
1.2
1.0
.8
.7
.6
.5
.4
47
TV CT
UNION IRON
MILLS'
7-INCH EYEBEAM, No. 8, HEAVY,
25 LBS. PER FOOT.
Depth, 1". Width of Flanges, 3.91".
Thickness of Web, 0.53".
Maximum fiber strain = 12000
Ibs. per square inch.
^
ti^s" 1
.3 M .
Proper dis
tance, in feet, center to center
Jpi
|I|| l|
Jfj
oft
earns, for Safe Loads of
^
vrfS*- ^'2
100 125
150
175
200
250
300
. <
3|f|
"3 S m
Ibs.
Ibs.
Ibs.
Ibs.
Ibs.
Ibs.
Ibs.
Jj.2
3$
per
per
per
per
per
per
per
l^.a.2
A
&
sq.ft.
sq. ft.
sq.ft. sq.ft. sq.ft. sq.ft.
sq. ft.
.
5
12.40
0.05 0.06
49.6 39.7
33.1 28.3 24.8 19.8
16.5
6
10.33
0.07 0.08
34.4
27.5
123.0 19.7 17.2 13.8
11.5
7
8.86
0.10
0.09
25.3
20.2
;16.9 14.5 12.7 10.1 8.4
8
7.75
0.13
0.10
19.4
15.5
12.9
11.1 9.7, 7.8 6.5
9
6.89
0.16
0.11
15.3
12.2
10.2 8.7
7.71 6.1
5.1
10
6.20
0.20 0.13
12.4 9.9
8.3 ' 7.1 6.2 5.0 4.1
11
5.64
0.24
0.14
10.3 8.2
6.8 5.9 5.1 4.1 3.4
12
5.17 0.28
0.15
8.6 6.9
5.7 4.9 4.3 3.4 2.9
13
4.77
0.33 0.16
7.3 5.9
4.9 4.2 3.7 2.9 2.4
14
4.43
0.39 0.18
6.3 5.1
4.2 3.6 3.2 2.5 2.1
15
4.13
0.45
0.19
5.5 4.4
3.7! 3.1 2.8 2.2
1.8
16
3.88
0.51
0.20
4.9 3.9
3.2 2.8
2.4
1.9
1.6
17
3.65
0.57
0.21
4.3 3.4
2.9 2.5
2.1
1.7
1.4
18
3.44
0.64
0.23
3.8
3.1
2.5 2.2
1.9
1.5
1.3
19
3.26
0.71
0.24
3.4
2.7
2.3 ! 2.0
1.7
1.4
1.1
20
3.10
0.79
0.25
3.1
2.5
2.1
1.8
1.5
1.2
1.0
21
2.95
0.87 . 0.26
2.8 2.2
1.9
1.6
1.4
1.1
.9
22
2.82
0.96
0.28
2.6
2.0
1.7
1.5
1.3
1.0
.9
23
2.70
1.05
0.29
2.4
1.9
1.6
1.3
1.2
.9
.8
24
2.58
1.14
0.30
2.2
1.7, 1.4
1.2
1.1 .9
.7
25
2.48
1.24 0.31
2.0
1.6
1.3
1.1
1.0 .8
.7
26
2.38
1.34 0.33
1.8
1.5
1.2
1.0
.9
.7
.6
27
2.30
1.44
0.34
1.7
1.4
1.1
1.0
.9
.7
.6
28
2.21
1.55
0.35
1.6
1.3
1.1
.9
.8
.6 .5
29
2.14
1.66
0.36
1.5
1.2
1.0
.8
.7
.6
.5
48
-.A:
5
UNION IRON
MILLS'
6-INCH EYEBEAM, No. 10, LIGHT,
13^ LBS. PEE,
FOOT.
Depth, 6". Width of Flanges, 3.24".
Thickness of "Web, 0.24".
Maximum fiber strain = 12000
Ibs. per square inch.
||
ill
Si
||
Proper distance,
of beams,
in feet, center to center
for Safe Loads of
i -J
li^c
|s
O ^
100
125
150
175
200
250
300
1 1
gj-s'g
_3 T3
-t-3 O
Ibs.
Ibs.
Ibs.
Ibs.
Ibs.
Ibs.
Ibs.
llfj
j-
fl
per
sq, ft.
per
sq.ft.
per
sq.ft.
per
per
sq. ft.
per
sq. ft.
per
sq.ft.
5
6.53
0.06
0.03
26.1
20.9
17.4
14.9
13.1
10.4
8.7
6
5.44 0.08
0.04
18.1
14.5
12.1
10.4
9.1
7.3
6.0
7
4.66 0.11
0.05
13.3
10.6
8.9
7.6
6.7
5.3
4.4
8
4.08 0.15
0.05
10.2
8.2
6.8
5.8
5.1
4.1
3.4
9
3.63 0.19
0.06
8.1
6.5
5.4
4.6
4.0
3.2
2.7-
10
3.26 0,23
0.07
6.5.
5.2
4.4
3.7
3.3
2.6
2.2
11
2.97 0.28
0.07
5.4
4.3
3.6
3.1
2.7
2.2
1.8
12
2.72
0.33
0.08
4.5
3.6
3.0
2.6
2.3
1.8
1.5
13
2.51
0.39
0.09
39
3.1
2.6
2.2
1.9
1.5
1.3
14
2.33
0.45
0.09
3^3
2.7
2.2
1.9
1.7
1.3
1.1
15
2.18
0.52
0.10
2.9
2.3
1.9
1.7
1.5
1.2 \ 1.0
16
2.04
0.59
0.11
2.6
2.0
1.7
1.5
1.3
1.0 .9
17
1.92
0.67
0.11
2.3
1.8
1.5
1.3
1.1
.9 .8
18
1.81
0.75
0.12
2.0
1.6
1.3
1.11 1.0
.8 .7
19
1.72
0.83
0.13
1.8
1.4
1.2
1.0 ! .9 .7
.6
|
20
1.63
0.92
0.14
1.6
1.3
1.1
.9 ! .8 .7
.5
21
1.55 1.01
0.14
1.5
1.2
1.0
.8 .7 ! .6
.5
22
1.48 1.11
0.15
1.8
1.1
.9
.8 .7 .5
\5
23
1.42 1.22
0.16
1.2
1.0
.8
.7 .6 ' .5
]4
24
1.36 1.33
0.16
1.1
.9
.7
.6 j .6 .5
.4
25
1.31 , 1.45
0.17
1.0
.8
.7
.6
.5
.4
.4
26
1.26 11.56
0.18
1.0
.8
.6
.5
.5
.4
.3
27
1.21 il.68
0.18
.9
.7
.6
.5
.4
.4
.3
28
1.17 1.81
0.19
.8
.7
.0
.5
.4
.3
.3
29
1.13 1.95
0.20
.8
.6
.5
4
.4
.3
.3
K
UNION IRON MILLS'
6-INCH EYEBEAM, No. 10, HEAVY,
18
LBS. PER FOOT.
Depth, 6". Width of Flanges, 3.46". Thickness of Web, 0.46".
Maximum fiber
strain = 12000 Ibs. per square inch.
g *5
ti^s
a*
JS '
Proper distance,
in feet, center to center
1 !
o'g Jjo
ll
J^^
of beams,
for Safe Loads of
"S .s
3 '*~ f * 4 - 1 <==>
8
If
-3-^4?
ijjj
5
100
125
150
175
200
250
300
_i .
'5
3 s
Ibs.
Ibs.
Ibs.
Ibs.
Ibs.
Ibs.
Ibs.
M e
<*H W 00
.2
'S 5
per
per
per
per
per
per '
per .
wS^S.2.2
^
sq. ft.
sq. ft.
sq. ft.
sq. ft.
sq.ft.
sq.ft.
sq. ft.
5
7.58
0.06
0.05
30.3
24.3
20.2
17.3
15.2
12.1
10.1
6
6.32
0.08
0.05
21.1
16.9
14.0
12.0
105
8.4
7.0
7
5.42
0.11
0.06
15.5
12.4
10.3
8.9
7.7
6.2
5.2
8
4.74
0.15
0.07
11.9
9.5
7.9
6.8
5.9
4.7
4.0
9
4.21
0.19
0.08
9.4
7.5
6.2
5.3
4.7
3.7
3.1
10
3.79
0.23
0.09
7.6
6.1
5.1
4.3
3.8
3.0
2.5
11
3.45
0.28
0.10
6.3
5.0
4.2
3.6
3.1
2.5
2.1
12
3.16
0.33
0.11
5.3
4.2
3.5
3.0 2.6 2.1
1.8
13
2.92
0.39
0.12
4.5
3.6
3.0
2.6
2.2
1.8
1.5
14
2.71
0.45
0.13
3.9
3.1
2.6
2.2
1.9
1.5
1.3
15
2.53
0.52
0.14
3.4
2.7
2.2
1.9
1.7
1.3
1.1
16 .
2.37
0.59
0.14
3.0
2.4
2.0
1.7
1.5
1.2
1.0
17
2.23
0.67
0.15
2.6
2.1 1.7
1.5
1.3
1.0
.9
18
2.11
0.75
0.16
2.3
1.9 1.6
1.3
1.2
.9
.8
19
2.00
0.83
0.17
2.1
1.7 1.4
1.2
1.1
.8
.7
20
1.90 0.92
0.18
1.9
1.5 1.3
1.1
1.0
.8
.6
21
1.81
1.01 | 0.19
1.7
1.4 1.1
1.0
.9
.7
.6
22
1.72
1.11
0.20
1.6
1.2
1.0
.9
.8
.6
.5
23
1.65
1.22
0.21
1.4
1.1
1.0
.8
.7
.6
.5
24
1.58
1.33
0.22
1.3
1.1
.9
.8
.7
.5
.4
25
1.52
1.45
0.23
1.2
1.0
.8
.7
.6
.5
.4
26
1.46
1.56
0.23
1.1
.9 .7
.6
.6
.4
.4
27
1.40
1.68
0.24
1.0
.81 .7 .
.6
.5
.4
.3
28
1.35
1.81
0.25
1.0
.8 .6
.5
.5
.4
.3
29
1.31
1.95;
0.26
.9-
.7 .6
.5
.5
.4
.3
1
y >
UNION IRON MILLS'
r.
5-INCH
EYEBEAM, No. 11, LIGHT,
10
LBS. PER FOOT.
Depth, 5". Width of
Flanges, 2.73". Thickness of Web
, 0.225".
Maximum fiber
strain = 12000 Ibs. per square inch.
Distance between
supports, in feet.
Safe load, uniformlv
distributed, (includ-
ing weight of beam,)
in tons of 2000 Ibs.
F> i Daflection under this
^ load, in inches.
a
a
j
s~
-*.
i
|i
0.03
Proper distance, in feet, center to center
of beams, for Safe Loads of
100
Ibs.
per
sq. ft.
15.8
125
Ibs.
per
Eft.
12.6
150
Ibs.
&
175
Ibs.
per
sq. ft.
200
Ibs.
per
sj.ft.
7.9
250
Ibs.
per
sq. ft.
300
Ibs.
per
sq.ft.
5
3.95
10.5
9.0
6.3
5.3
6
3.29
0.10
0.03
11.0 8.8
7.3 6.3 5.5
4.4
3.7
7
2.82 '
0.14
0.04
8.1 6.4 5.4 4.6 j 4.0
3.2
2.7
8
2.47
0.18
0.04
6.2 4.9 4.1 3.5! 3.1
2.5 2.1
9
2.20 !
0.23
0.05
4.9 3.9 3.3 2.8 2.4
2.0 1.6
10
1.98 ;
0.28
0.05
4.0
3.2 2.6 2.3 2.0
1.6
1.3
11
1.80
0.34
0.06
3.3
2.6
2.2 1.9
1.7
1.3 I~U
12
1.65
0.40
0.06
2.8
2.2
1.8 1.6
1.4
1.1
.9
13
1.52
0.47
0.07
2.3
1.9
1.6 1.3
1.2
.9
.8
14
1.41
0.55
0.07
2.0
1.6
1.3
1.1
1.0
.8
.7
15
1.32
0.63
0.08
1.8
1.4
1.2
1.0
.9
' .7
.6
16
1.24
0.71
0.08
1.6 1.2
1.0 .9
.8
.6 .5
17
1.16
0.80
0.09
1.4 1.1
.9
.8
.7
.5 .5
18
1.10
0.90
0.09
1.2 1.0
.8
.7
.6
.5 .4
19
1.04
1.00
0.10
1.1 i .9
.7
.6
.5
.4 .4
20
21
.99
.94
1.11
1.22
0.10
0.11
1.0
.9
.8
.7
.7
.6
.6
.5
.5
.4
A
A
A
.3
.3
22
.90
1.34
0.11
.8
.7 .5
.5
.4
.3
.3
23
.86
1.47
0.12
.7
.6
.5
.4
.4
.3
.2
24
.82
1.60
0.12
.7
.5
.4 .4
.3
.3
.2
UNION IRON MILLS'
5-INCH EYEBEAM, No. 11, HEAVY,
13 LBS. PER FOOT.
Depth, 5". Width of Flanges, 2.91". Thickness of Web, 0.405".
Maximum fiber strain = 12000 Ibs. per square inch.
Distance between
supports, in feet.
:pl
ijl
Deflection under this
load, in inches.
Weight of beam, in
tons of 2000 Ibs.
Proper distance, in feet, center to center
of beams, for Safe Loads of
100
Ibs.
par
sq.ft.
125
Ibs.
150
Ibs.
per
sq.ft.
175
Ibs.
per
sq.ft.
200
Ibs.
per
sq.ft.
9.1
250
Ibs.
per
7.3
300
Ibs.
per
sq. ft.
6.1
5
4.55
0.07
0.03
18.2
14.6
12.1
10.4
6
3.79
0.10
0.04
12.6
10.1
8.4
7.2
6.3 5.1
4.2
7
3.25
0.14
0.05
9.3
7.4
6.2
5.3
4.6
3.7
3.1
8
2.85
0.18
0.05
7.1
5.7
4.8 4.1
3.6
2.9
2.4
9
2.53
0.23
O.OG
5.6
4.5
3.7 3.2
2.8
2.2
1.9
10
2.28
0.28
0.07
4.6
' 3.6
3.0 2.6
2.3
1.8
1.5
11
12'
13
2.07
1.90
1.75
0.34
0.40
0.47
0.07
0.08
0.08
3.8
3.2
2.7
3.0
2.5
2.2
2.5
2.1
1.8
2.1
1.8
1.5
1.9
1.6
1.3
1.5
1.3
1.1
1.3
1.1
.9
14
1.63
0.55
0.09
2.3
1.9
1.6
1.3
1.2
.9
.8
15
1.52
0.63
0.10
2.0
1.6
1.4
IwB
1.0
.8
.7
16
1.42
0.71
0.10
1.8
1.4
1.2
1.0
.9
.7
.6
17
1.34
0.80
0.11
1.6
1.3
1.0
.9
.8
.6
.5
18
1.26
0.90
0.12
1.4
1.1
.9! .8
.7
.6
.5
19
1.20
1.00
0.12
1.3
1.0
.8 .7
.6
.5
.4
20
1.14
1.11
0.13
1.1 .9
.8
.7
.6
.5
.4
21
1.08
1.22
0.14
1.0
.8
.7
.6
.5
.4
.3
22
1.03
1.34
0.14
.9
.8
.6
.5
.5
.4
.3
23
.99
1.47
0.15
.9
.7
.6
.5
.4
.3
.3
24
'4
.95
1.60
0.16
.8
.6
i
.5
.5
.4
.3
.3
i
UNION IRON MILLS 1
4-INCH EYEBEAM, No. 12, LIGHT,
8 LBS. PER FOOT.
Depth, 4". Width of Flanges, 2.48". Thickness of Web, 0.23".
Maximum fiber strain = 12000 Ibs. per square inch.
jl
II
till
fei
'a .2
ii
i~~
Proper distance, in feet, center to center
of beams, for Safe Loads of
100
Ibs.
par
sq. ft.
125
Ibs.
per
sq. ft.
150
Ibs.
per
sq.ft.
175
Ibs.
per
sj.ft.
200
Ibs.
250
Ibs.
300
Ibs.
per
sq.ft.
I
I
5
2.48 0.09 0.02
9.9
7.9 6.6
5.7
5.0
4.0
3.3
6
2.07
0.13 0.02
6.9
5.5
4.6
3.9
3.5
2.8
2.3
7
1.77 0.17
0.03
5.1
4.0
3.4
2.9
2.5
2.0
1.7
8
1.55 0.22
0.03
3.9
3.1 2.6
2.2
1.8
1.9
1.6
1.3
1.0
9
1.38 0.28
0.04
3.1
2.5
2.0
1.5
1.2
10
11
1.24
1.13
0.35
0.42
0.04
0.04
2.5
2.1
2.0
1.6
1.7
1.4
1.4
1.2
1.2
1.0
1.0
.8
.8
.7
12
1.03
0.50
0.05
1.7
1.4
1.1
1.0
.9
.7
.6
13
0.95
0.59
0.05
1.5
1.2
1.0
.8
.7
.6
.5
14
0.89
0.68
0.06
1.3
1.0
.8
.7
-6
.5
.4
15
0.83
0.78
0.06
1.1
.9
.7
.6
.6
.4
.4
16
0.78
0.89
0.06
1.0
.8
.6
.6
.5
.4
.3
17
0.78
1.01
0.07
.9
.7 .6 .5
.4
.3
.3
18
0.69
1.13
0.07
.8
.6 .5
.4
.4
.3
.3
19
0.65
1.26 0.08
.7
t
.5 .4
.3
.3
.2
2
53
I
UNION IRON MILLS'
4-INCH
EYEBEAM, No. 12, HEAVY,
10 LBS. PER FOOT.
Depth, 4". Width of Flanges, 2.63". Thickness of Web, 0.88".
Maximum fiber strain = 12000 Ibs. per square inch.
5^-jj
I
a
Proper distance, in feet, center to center
Jl
fill
1
of beams, for Safe Loads of
If
^15
5-2
"o ,_
100
125
150
175 200
250
300
ISff
'llf
3
Ibs.
Ibs.
Ibs.
Ibs. Ibs.
Ibs.
Ibs.
1 1*
sill
1
||
5,
per per
sq.ft. sq.ft.
per per per per
sq. ft. sq. ft. sq. ft. j sq. ft.
5
2.80
0.09
0.03
11.2
9.0 7.5
6.4
5.6
4.5
3.7
6
2.33
0.13
0.03
7.8
6.2: 5.2
4.4
3.9 3.1
2.6
7
2.00
0.17
0.04
5.7 4.6
3.8
3.3
2.9 2.3
1.9
8
1.75
0.22
0.04
4.4
3.5 2.9
2.5
2.2 1.8 1.5
9
1.56
0.28
0.05
r
3.5 2.8 2.3| 2.0
1.7 1.4 1.2
10
1.40
0.35
0.05
2.8 2.2
1.9
1.6
1.4
1.1
.9
11
1.27
0.42
0.06
2.3 1.8
1.5
1.3
1.2
.9
.8
12
1.17
0.50 0.06
2.0
1.6
1.3
1.1
1.0
.8
.7
13
1.08
0.59
0.07
1.7
1.3
1.1
.9
.8
.7
.6
14
1.00
0.68
0.07
1.4-
1.1
1.0
.8
.7
.6
.5
1
15
0.93
10.78 0.08
1.2
1.0
.8
.7
.6
.5
.4
16
0.88
0.89 i 0.08
111
.9
.7
.6
.6
.4
.4
17
0.82
1.01 0.09
1.0
.8
.6
.6
.5
.4
.3
18
0.78
1.13
0.09
.9
.7
.6
.5
.4
.3
.3
19
0.74
1.26
0.10
,8
.6 .5
.4
.4
.3
.3
54
UNION IRON MILLS'
3-INCH EYEBEAM, No. 13, LIGHT,
7 LBS. PER FOOT.
Depth, 3". Width of Flanges, 2.32". Thickness of Web v 0.19".
Maximum fiber strain = 12000 Ibs. per square inch.
M
J .3
1
M IT
Safe load, uniformly
distributed, (includ-
ing weight of beam,)
in tons of 2000 Ibs.
P P 1 Deflection under this
Q to 1 l<> a( i, in inches.
a
"s
5
S3
_
Pro
100
Ibs.
per
sq. ft.
per dis
of b
125
Ibs.
41
tance,
earns,
150
Ibs.
per
sq.ft.
4.4
3.0
2.2
1.7
1.4
1.1
.9
.8
.6
.6
in fee
forSa
175
Ibs.
per
4. ft.
, cente
? e Loa
loo
Ibs.
per
sq.ft.
r to c<
Is of
250
Ibs.
per
sq.ft.
mter
~300
Ibs.
per
sq.ft.
5
6
1.65
1.37
0.02
0.02
6.6
4.6
5.3
3.7
3.8
2.6
3.3
2.3
2.6
1.8
T3
1.0
.8
.7
.5
.5
: 4 s
2.2
1.5
1.1
n
\7
.5
.5
.4
.3
.3
7
8
9
10
11
12
13
14
1.18
1.03
0.92
0.82
0.75
0.69
0.63
0.59
0.23
0.29
0.37
0.46
0.56
0.67
0.78
0.91
0.02
0.03
0.03
0.04
0.04
0.04
0.05
0.05
3.4
2.6
2.0
1.6
1.4
1.2
1.0
.8
2.7
2.1
1.6
1.3
1.1
.9
.8
.7
1.9
1.5
1.2
.9
.8
.7
.6
.5
1.7
1.3
1.0
.8
i
i
UNION IRON MILLS'
3-INCH EYEBEAM, No. 13, HEAVY,
9 LBS. PER FOOT.
Depth, 3". Width of Flanges, 2.52". Thickness of Web, 0.39".
Maximum fiber strain = 12000 Ibs. per square inch.
Distance between
supports, in feet.
Safe load, uniformly
distributed, (includ-
ing weight of beam,)
in tons of 2000 Ibs.
Ij
a
11
a
JJ
^5
ILi
s*
Proper di
oft
stance, in feet, center to center
earns, for Safe Loads of
100
Ibs.
per
sq. ft.
125
Ibs.
per
sq. ft.
150
Ibs.
per
sq. ft.
175
Ibs.
per
sq.ft.
200
Ibs.
per
sq. ft.
3.8
2.6
1.9
1.5
1.2
.9
.8
.7
.6
.5
250
Ibs.
per
sq.ft.
300
Ibs.
Sq P \
5
6
1.89
1.57
0.12
0.17
0.02
0.03
7.6
5.2
3.9
3.0
2.3
1.9
1.6
1.3
1.1
1.0
6.0
4.2
5.0
3.5
4.3
3.0
3.0
2.1
2.5
1.7
7
8
9
10
11
12
13
. 14
1.35
1.18
1.05
0.94
0.86
0.79
0.73
0.67
0.23
0.29
0.37
0.46
0.56
0.67
0.78
0.91
0.03
0.04
0.04
0.05
0.05
0.05
0.06
0.06
3.1
2.4
1.9
1.5
1.2
1.1
.9
.8
2.6
2.0
1.6
1.3
1.0
.9
.7
.6
2.2
1.7
1.3
1.1
.9
.8
.6
.5
1.5
1.2
.9
.8
.6
.5
.4
.4
1.3
1.0
.8
.6
.5
.4
.4
.3
8 55
EXPLANATION OF TABLES ON THE
PROPERTIES OF UNION IRON MILLS'
EYE AND DECK BEAMS, CHANNEL
BARS, ANGLE, STAR AND
TEE IRONS.
Pages 62 to 69, inclusive.
The tables on I Beams, Deck Beams and Channel Bars are
calculated for the minimum and maximum weight to which the
various shapes can be rolled. The lithographed plates indicate
the manner in which the enlargement of the section takes place,
and column 7 in tables gives the increase of thickness of web
for each pound increase of weight of beam or channel. The
width of flanges is increased the same amount as the thickness
of web.
Angle Irons are increased in weight in the manner indicated
by Fig. 4 on page 23, the size corresponding with the least
thickness, and increasing somewhat with the increase of thick-
ness, but some of the heavier weights of a few of the shapes
are rolled in special finishing grooves, whereby the exact size is
obtained for a thickness greater than the minimum. In the
tables, for the sake of uniformity, it was assumed generally that
the size corresponds with the least thickness only,, and the
increase of weight is obtained in the manner indicated by the
above mentioned Fig. 4, page 23.
Beams, Channels and Angle Irons, may be rolled to any
weight intermediate between the minimum and maximum
weights given. Each shape of Star and T Iron, however,
can be rolled to one weight only.
Columns 11 and 13 in the tables for beams and channels give
coefficients, by the help of which the safe uniformly distributed
load for any beam or channel, and for any span length, can be
readily and quickly determined. To do this, it is only necessary
to divide the coefficient given by the span or distance between
supports, in feet, and multiply by 1000. If the weight of the
beam or channel is intermediate between the minimum and
B 5g
maximum weights given, add to the coefficient for the minimum
weight, the value given in columns 12 or 14 (for one pound
increase of weight) multiplied by the number of pounds the beam
or channel is heavier than the minimum.
If a beam or channel is to be selected, (as will usually be the
case,) intended to carry a certain load for a length of span
already determined on, it will be most convenient to ascertain
the coefficient which this load and span will require, and refer to
the table for a beam or channel having a coefficient as large as
this. The coefficient is obtained by multiplying the load, in
pounds uniformly distributed, by the span length in feet, and
dividing by 1000.
In case the load is not uniformly distributed, but is concen-
trated at the middle of the beam or channel, multiply the load
by 2, and then consider it as uniformly distributed. The deflec-
tion will be y^jths of the deflection by this load.
If the load is neither uniformly distributed nor concentrated
at the middle, obtain the bending moment. This, multiplied by
0.008 will give the required coefficient.
If the loads for which the beams or channels are to be pro-
portioned, are quiescent, the coefficients for a fiber strain of
12000 Ibs. per square inch should be used ; but if moving loads
are to be provided for, the coefficients fo*r 10000 Ibs. fiber strain
should be taken. Inasmuch as the effects of impact may be
very considerable, (the strains produced in an unyielding inelastic
material by a load suddenly applied, being double those produced
by the same load in a quiescent condition,) it will sometimes be
advisable to use still smaller fiber strains than 10000. The co-
efficients for these can readily be determined by proportion.
Thus, for a fiber strain of 8000 Ibs. per square inch, the coefficient
will equal the coefficient for 10000 Ibs. fiber strain multiplied
by ^-ths.
The table on the properties of Union Iron Mills' Angle Irons
requires explanation only relative to the angles with unequal
legs, to which the latter half of the table applies. It will be
observed that two values are given, in the case of each angle,
for the distance of center of gravity from outside of flange, the
moment of inertia, the moment of resistance and the radius of
67
gyration of the section. The first or larger value invariably
refers to a neutral axis parallel to the smaller flange, and to the
distance between the center of gravity and the outside of this
flange, and the second or smaller value to a neutral axis parallel
to the larger flange, and to the distance between the center of
gravity and the outside of this flange. For each position of the
neutral axis there will be two moments of resistance, since the
distance between the neutral axis and the extreme fibers has a
different value on one side of the axis from what it has on the
other. The moment of resistance given in table is the smaller
of these two values, and the fiber strain calculated from it, will
therefore give the larger of the two strains in extreme fibers,
(since these strains are equal to the bending moment divided by
the moment of resistance of the section). The left hand figures
in each column refer to the minimum weight of angle, and the
right hand figures to the maximum weight, throughout the table.
The table on the properties of Union Iron Mills' T Irons
is modeled after the foregoing, and will therefore scarcely
require explanation. The horizontal portion of the T is called
the flange and the vertical portion the stem. In the case of the
neutral axis parallel to the flange, there will be two moments of
resistance, and the least is given; but in the case of the neutral
axis coincident with stem, there is only one moment of resistance.
In calculating the table, the flange and stem of the T's were
considered as rectangles of equal area as the actual section, and
the figures given are therefore approximations only, though very
close ones.
No approximations have entered into the calculations of any
of the other tables, and the figures given may be relied upon as
accurate.
The use of the radii of gyration will be explained in connec-
tion with the table on the strength of wrought iron columns.
The moment of resistance is used to determine the fiber strain in
a beam or other shape iron subjected to bending or transverse
strains, by simply dividing the same into the. bending moment,
expressed in inch pounds.*
The 15th column in 'the table on the Properties of Union Iron
Mills' Channels, giving the distance of the center of gravity of
58
channels from outside of web, is used to obtain the radius of
gyration for columns or struts consisting of two channels latticed,
as represented by Fig. 1, page 26, in the case of the neutral axis
passing through the center of the section parallel to the webs of
the channels. This radius of gyration is equal to the square root
of the distance between the center of gravity of the channel and
the center of the section.
EXAMPLES OF APPLICATION OF TABLES.
I. What load, uniformly distributed, will a 10" beam 'carry,
weighing 40 Ibs. per foot, and measuring 14 feet between sup-
ports, allowing a fiber strain of 12000 Ibs. per square inch ?
Answer : By table, C, for a 10" beam, 40 Ibs., = 240 -f 10 X
4 = 280, therefore L = )0 * 28 = 20 000 Ibs., including
weight of beam.
II. What beam will be required to carry 36000 Ibs., uniformly
distributed over a span of 16 feet between supports, same fiber
strain ?
1L 16 X 36000 K - c , . ,
Answer: C required = -^ = -^ = 576, which
calls for a 15" beam, 52 Ibs. per foot.
III. A light 4" X 3" angle iron, weighing 8.3 Ibs. per foot,
spanning 4 feet, is loaded with 1000 Ibs. at center : what will be
the maximum fiber strain if the 4 /; flange is in a vertical position ?
Answer: By table, moment of resistance = 1.46. Bending
moment = 12000 inch pounds. Therefore maximum fiber strain=
120 ^ Q = 8220 *lbs., occurring in the fibers furthest from the
1.46
neutral axis, i, e., at the end of the long flange.
SPECIAL CASES OF LOADING.
I. Beam loaded at a point distant "-a" feet from the left
hand and "b" feet from the right hand support, by a single
load P.
1 = length of beam between supports = a -|- b.
59
Maximum bending moment, neglecting dead weight of beam,
occurs at point of application of the load and =
I 2
P = load given in tables X
8ab
Pressure or reaction at left hand support = P , and at right
hand support == P -p
II, Beam unsupported at one end and held horizontally at
the other, 1 representing the length of beam from end to support.
If loaded by a uniformly distributed load W :
W 1
bending moment occurs at support and = ^
W= load given in tables X X and tne deflection = that of
the tables X 2.4.
If loaded with a single load P at its extremity :
Maximum bending moment occurs at support and = PI.
P = load given in tables X ^> an d the deflection that of
tables X 3.2.
GENERAL FORMULAE ON THE FLEXURE OF BEAMS
OF ANY CROSS-SECTION.
Let A = area of section,
1 = length of span,
W = load, uniformly distributed,
M = bending moment,
d = depth of beam, out to out,
n = distance of center of gravity of section, from top or
from bottom,
s = strain per square inch in extreme fibers of beam, either
top or bottom,
D = maximum deflection,
I = moment of inertia of section,
R = moment of resistance,
r = radius of gyration,
E = modulus of elasticity,
(assumed = 2600QOOO for wrought iron in tables.)
Then R =
~~r~ R
8 =T 8 Q
w=-
_ Win _ w i_
81 8 R
5 Wl 3 for beam supported at both ends and uni-
384 El formly loaded,
_ PI 3 for beam supported at both ends and loaded
~ 48 El by a single load P at middle,
_ Wl 3 for beam held horizontally at one end only
8 El and uniformly loaded,
PI 3 for beam held horizontally at one end only
3 El and loaded with a single load P at the other.
VALUES OF / AND Jt FOR USUAL SECTIONS.
Rectangle ; h = hight, b = base ; for neutral axis through
center of gravity, parallel to base, I = , R = ^ - ; for
bh 3
neutral axis coincident with base, I = ^ .
o
Triangle ; h = hight, b = base ; for neutral axis through center
of gravity (i. e., distant ^ h from base), parallel to base, I =
- -, R = - ; for neutral axis coincident with base, I =
OD min. fA.
bh 3 bh 3
-. -.; for neutral axis through apex, parallel to base, I =
4
Circle ; d = diameter, TT = 3.1416; for neutral axis through
7T (\ 3
center, I = - = 0.0491 d*, R =-=- = 0.0982 d.
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CO CO
X X
IO 1C
CO CO
<M N d rH
X X X X
rr co csi <M
67
3 f.
UNION IKON MILLS' ANGLE IRONS.
Weights per Foot corresponding to thicknesses varying by T y".
One cubic foot weighing 480 Ibs.
Size.
Inches.
%" h"
&"
iVK"
A"
K"
T'
%"
tt"
&"it"i%"
Equal Legs.
6 x6
4 X4
3^x3>
3KX3K
3 x3
2%x2%
2> 2 / x2^
2^x2,^
2 x2
l^xlK
l#xl>I
l&xljj
IX x ii
1 xl
MX X
19.2
12.9
11.2
10.4
9.7
88
21.7
14.5
12.7
11.7
10.9
24.2
16.2
14.1
13.1
12.2
26.7
17.9
15.6
14.4
29.2
19.5
17.0
15.8
31.7
..
34.2
....
..
9.5
8.3
7.7
7.2
6.5
5.9
5.4
4.8
4.3
36
11.2
9.7
9.0
8.4
7.7
7.0
6.4
56
2.1
.. 1.8
1.0 1.5
0.9 1.4
0.8 1.2
06i 09
3*5
8.1
2.8
2.4
2.0
1.8
1 6
5.9
5.4
4.9
4.5
4.0
3.5
3.0
8.0
7.3
. . j . .
50
j
j
i
UnequalLegs
6 x4
5 x4
5 x3X
5 x3 "
4 x3>
4 x3
3>^x3
3>4X2
3 x2^
3 x2
2X x 2
2 "xl%
,.
....
10.8
10.2
9.5
13.9
12.7
11.9
11 ?,
16.0 1.8.1
14.5 16.4
13.7 15.5
12.9 14.5
20.222.324.4
18.3 20.2 22.0
17.2 19.0 20.8
16.2 17.9 19.5
15.2 1^7 1C.3
14.1 15.6 17.0
13.1 14.4 15.8
26.4
. . 1 . .
8.910.5 12.0
8.3| 9.7 11.2
7.7 9.010.4
6.4 7.4 8.5
6.7 7.8 9.0
6.0 7.1 ' 8.1
5.4 6.4 7.3
40
13.6
12.7
11.7
4.2
4.4
4.0
3.5
2.6
5.3
5.5
5.0
4.5
3.3
| 1
. if
<5
8
PROPERTIES OF UNION
IRON MILLS'
T IRONS.
The moments of
inertia and resistance, and radii of gyration, in this
table, are close approximations only.
The table does not include all sizes manufactured.
w
|
ij
|J
111
f 3
s| :|| 5
1-1*5*1!
all
I'glJl |a
gll
sT
m
1*1^1-
II?
111
5 X3
13
3.90 ! 0.73
2.5 1.1
0.80
5.7 ! 2.3
1.21
5 X25
101*
3.08 0.58
1.4 0.71
0.66
4.6 i 1.8
1.21
-4)^X33-2
15
4.50 1 1.13
5.2 2.18
1.07
3.9 ; 1.7
0.93
4 X5 14
4.20 1.57
10.5 3.05
1.57
2.7 | 1.4
0.80
4 X4X 13j^
4.05 i 1.37
7.8 2.48
1.39
2.7 1.4
0.82
4 X4 " 12
3.60 ! 1.18
5.4 i 1.91
1.22
2.6 1.3
0.84
4 X3 ^
2.78 , 0.80
2.1 | 0.96
0.87
2.3 1.1
0.90
4 X%% ly 2
2.25 ; 0.62
1.1 : 0.60
0.70
2.0 1.0
0.93
4 X2 6K
1.95 l 0.46
0.54 0.35
0.53
1.8 1 0.91
0.96
3lX4 11)
3.38 1.24
5.15 i 1.87
1.23
1.8 1.00
0.72
3)^X3^ 10
8.00 ! 1.04
3.34 ! 1.36
1.05
1.6 0.93
0.73
3^X3 9>^
2.78 | 0.85
2.14 1.00
0.88
1.6 0.93
0.77
3 X4 1214 3.68 ! 1.35
5.55 '12.10
1.24
1.8 ! 0.87
0.60
3 X3^' 11%
3.53 j 1.15
3.93 1.67
1.06
1.4 0.92
0.62
3 X3 7.6
2.28 i 0.90
1.89 0.90
0.91
0.94 0.63
0.64
3 X2> 6
1.80 ! 0.69
0.96 ; 0.53
0.73
0.77 0.51
0.66
2^X3 : 6^
1.95 ! 0.96
1.66 0.81
0.93
0.50 0.40
0.51
2KX2%- 6.6
1.98 0.86
1.39 ! 0.74
0.84
0.55 0.44
0.53
2)^X2^ 5.4
1.62 0.75
0.91 0.43
0.75
0.46 0.37
; 0.53
2^>Xl*4i 3
0.90 i 0.30
0.09 0.10
0.32
0.33 0.26
0.61
PROPERTIES OF UNION
IRON MILLS'
STAR IRONS.
Size.
Inches.
Weight Thickness in \ Inertia Moment of Radius of
perfoot. If^sat Area. | neutral ^ ; Resistance, Gyration,
r Lb ? End and Root i Sq. In. ! +;,,.' M t. neutral ans neutral axis
of Flange. | I ^
gravity as Before. as before.
4 X4
12
M T 9 u ! 3.60 ,
2.32 1.16
0.81
3% X3^
9 1
4 % I A 2.85 ;
1.49 0.85
0.72
3 X3
7
4 T 5 6-M i 2.18
0.82 0.55
0.61
2M X2^
4 A -H I.
0.45 0.36
0.52
2 ><2
3^
4 U'M 1.13
0.20 i 0.20
0.43
O
&.
3 tV A > 0.69 i
0.065 0.087
0.31 .
69
^
EXPLANATION OF TABLE ON RIVETED
GIRDERS.
Riveted girders are used in cases where rolled I Beams are
insufficient to carry the load. On page 23 of the lithographed
plates will be found illustrations of various forms of riveted
girders. The sections with single webs are more economical
than those with double webs (box girders), but the latter are
stiffer laterally, and should always be used where the proportion
of length of span to width of top flange is great and the girder
is not held in position sideways. This proportion of length to
width should not exceed twenty, without making provision for
such increase by an addition of metal in the compression flange
beyond that required by the table.
The web of the girder must be made of such thickness that
there will be no tendency to buckle, and that the vertical shearing
stress per square inch will not exceed 9000 Ibs. This shearing
stress is obtained by dividing half the load upon the girder by
the web section. The first condition is attained when this
10000
shearing stress does not exceed d 2 in which d repre-
h ~~^
sents the depth of web of girder and t its thickness, both in
inches. Ordinarily this formula gives a lower strain per square
inch than 9000 Ibs., so that both conditions are usually attained
when the first is. Instead of increasing the thickness of the
web, it may be stiffened also by means of vertical angle irons
riveted to it at proper intervals. These should always be less
than the depth of the girder, at least for the end panels, but
towards the middle of the girder the stiffeners may be placed
further apart or entirely omitted. Stiffeners ' should always be
used at or near the supports, and at any other points where there
is a concentration of heavy loads.
The rivets should be ^", unless the girder is light, when $"
may be sufficient. The spacing ought not to exceed 6" and
should be closer for heavy flanges, but in all cases it should be
close at the ends, say 3" for a distance of 18" to 24" at each end.
The following table furnishes a ready means of determining
the section of girder necessary to carry a certain load, for any
span length from 10 to 39 feet, inclusive.
It will be noticed that the table is calculated for an allowed
fiber strain of 10000 Ibs. per square inch, while the tables on
rolled beams are calculated for a fiber strain of 12000 Ibs. per
square inch. This reduction in the allowed strain is intended to
cover the loss in strength, (somewhat greater than the loss in sec-
tion,) due to the rivet holes, and the riveted girders proportioned
by this table, will be found to be of about the same strength
as the rolled beams, proportioned by the tables applying to them.
The transverse strength of the web is neglected in the table.
The term flange, as applied to riveted girders, embraces all
the metal in top or bottom of girder exclusive of web plate;
or, in the case of a rolled beam or channel, with top and bottom
plates, all the metal exclusive of web between fillets.
Girders intended to carry plastering, should be limited in depth,
out to out, to J T th of the span length or y 2 " per foot of this
length, otherwise the deflection is liable to cause the plastering
to crack.
EXAMPLE OF APPLICATION OF TABLE.
A 20 ;/ box girder is to carry a 13" brick wall equivalent to a
weight of 30 tons over a space 20' in the clear. What size of
girder is required?
Answer : The value of the coefficient for 20' span and 20 /7
depth, as per table, = 300, and for 21' span and 20" depth =
315. The span, in this case, may be assumed at 20M5", and the
coefficient therefore at 307. Consequently *, = 9.21
will be the area required in each flange. Making the top and
bottom plates 12" X &"> = 4.5 sq. in., there remain 4.7 sq. in. for
the two angles, = 8 Ibs. per foot apiece. Making the webs
*
20" X X", the shearing stress = ~ g g ^ /2 = 3000 Ibs.
per square inch, which is also safe against buckling, since
10000 10000
d 2 = (20) 2 = 3200 Ibs., allowed.
h 3000 t 2 3000 (X) 2
71
RIVETED
a
GIRDERS.
Coefficients for determining the area required in flanges, allow-
ing 10000 Ibs. per square inch of
gross section fiber strain :
Multiply the load, in tons of 2000
Ibs.,
uniformly distributed,
by the coefficient, and divide by
1000; the quotient will be the
gross area, in square inches, required
for each flange.
|t|
Depth of Girder, Out
to Out of Web, in Inches.
J3 S^
12 14
i
i ;
&% ~
16
18 20 22
24
26
28 30
32 34 36
10
250
214
188
167 150 136
125
115
107 100
94 88; 83
11
275
:236
206
183 165 150
138
127
118 110
103 97 92
12
300
|257
2251200 180 164
150
138
129 120
113 106 100
13
325
279
2441217 195 177
163
150
139 130
122:115 108
14
350
300
263
233 210 191
175
162
150 140
131 124 117
|
15
375
321
281
250 225 205
188
173
161 150
141 : 132 125
16
400
343
300
267:240 218
200
185
171 160
150 i 141 1 133
17
425
364
319
283 255 232
213
196
182 ! 170
159 150 ! 142
18
450
386
338
300 270 245
225
208 i 193 i 180
169 159 150
19
475
|407
356
317 285 259
238
219 204 190
178 168 158
20
500
429
375
333 300 273
250
231
214 200
188 176 167
21
525
450
394
350 315 286
263
242
225 210
197 185 175
22
550
471
413
"367 330 300
275
254
236 220
206 194 183
23
575
493
431
383 345 314
288
265
246 i 230
216 203 192
24
600
514
450
400 360 327
300
,277
257 240
225 212 200
I
1
25
625
536
469
417 375 341
313
! 288
268 250 :
234 221 208
26
650
557
488
433 390 355
325
300
279 260 '
244 '229 217
27
675
579
506
450 405 368
338
312
289 j 270
253 238 i 225
28
700
600
525
467 420 382
350
323
300 280
263 247 233
29
725
621
544
483 435 395
363
335
311 290
272 256:242
30
750
643
563
500 450 409 :
375
346
321 300
281 265 250
31
775
664
581
517 465 423
388
358
332 310
291 274 258
32
800
686
600 533 480 436
400
369
343 320
300 282 267
33
825
707
619
550 495 450
413
381 :
354 330
309 291 275
34
850
729 638
567 510 464
425
392
364 340
319 300 283
35
875
750 656
583 525 l 477
438
404'
375 ' 350 !
328 ' 309 : 292
36
900
771
675
600 540 491
450
415
386 360
338 318 300
37
925
793
694;
617 555 505'
463
427
396 370'
347 326 308
38
950
814 713!
633 570 518
475
438
407 380
856 335 317
39
r/,._.
975
836
731
650:585 532
488
450
418 390
366 344 325
72
COLUMNS AND STRUTS.
Explanation of tables, pages 77 to 81, inclusive.
The tables on Keystone Octagon and Piper's Patent Rivetless
Columns give the areas and weights corresponding to different
thicknesses of metal. Sections of these columns will be found
'on pages 13 and 14.
As it is .impossible to repaint the inner surface of closed
columns, or, at best, this is attended with much difficulty and
expense, such columns should preferably be used only in the
interior of buildings, where the changes in temperature are not
considerable and the air is comparatively dry. In places exposed
to the extremes of temperature and unprotected from the rain, the
paint on the inner surface of the columns will, sooner or later,
cease to be a protection to the iron from the moisture of the
atmosphere, corrosion will set in, and, once begun, will continue
as long as there is unoxidized metal left in the column.
Figures 1, 3 and 4, on page 26, represent types of columns with
open sections, which admit of repainting at any time, and are
therefore suitable for out-door work.
The table on the Ultimate Strength of Hollow Cylindrical
Cast and Wrought Iron Columns gives the strains per square
inch of section at which columns will fail, for various propor-
tions of length of column to diameter.
To facilitate the use of the table, the length (=1) is ex-
pressed in feet, and the diameter ( = d ) in inches. The
diameter to be assumed is the mean between the outside and
inside diameters of the section.
Wrought iron columns fail either by deflecting bodily out of
the straight line, or by the buckling of the metal between rivets
or other points of support. Both actions may take place at the
same time, but if the latter occurs by itself, it is an indication
that the rivet spacing or the thickness of metal is insufficient;
provided, however, that the length of column is greater than
twelve diameters, as columns of shorter length fail generally
by the buckling of the metal. The rule has been deduced
from actual experiments, that the distance between centers of
_
rivets in columns should not exceed, in the line of stress, sixteen
times the thickness of metal of the parts joined, and that the
distance between rivets or other points of support at right angles
to the line of stress, should not exceed thirty times the thickness
of metal.
The table on the Ultimate Strength of Wrought Iron Columns
gives the strain per square inch of section at which columns will
fail, for various proportions of length, in feet, to least radius of
gyration, in inches. This table should be used for columns and
struts which are not cylindrical, such as those represented by
Figures 1, 2, 3, 4 and 5, on page 26.
If the column or strut is a single rolled beam, channel or other
shape, the radius of gyration will be found in the foregoing
tables on the properties of Union Iron Mills' Beams, Channels, etc.
If the column is composed of two channels latticed, as
represented by Fig. 1, on page 26, the channels are usually
placed far enough apart so that the column will be weakest in
the direction of the webs, i. e., with neutral axis at right angles
to the webs; for which case the radius of gyration of the
column section is the same as that of the single channel. But if
the radius of gyration is wanted for the neutral axis through
center of section parallel with web, obtain first the distance
between center of gravity of channel and center of section, by
the help of column 15 in table on the properties of Union Iron
Mills' Channel Bars; the square root of this distance will be the
radius of gyration of the section.
For a column section consisting of two channels with a beam
between them, as in Fig. 3, on page 26, it is necessary to obtain
first the moment of inertia of the section, whence the radius of
gyration is found as the square root of the quotient of the moment
of inertia divided by the area of the section. This moment of
inertia, for a neutral axis through center of beam coincident with
web, is equal to the sum of the moments of inertia of the beam
and channels, as per tables on the properties of these shapes.
The moment of inertia with neutral axis through center at right
angles to web of beam, is found by adding the moment of inertia
of the beam for this position of the axis, as per tables, to the
product of the area of both channels multiplied by the square
m
of the distance of the center of gravity of the channel from
the center of the section. The moment of inertia, thus obtained,
is approximate, being too small by the value of the moment of
inertia of the channels with reference to a neutral axis through
their centers of gravity parallel to the web, but the error is small
and on the safe side.
For a section composed of three beams, as represented by
Fig. 4, page 26, the correction for this approximation can be
made, since the moments of inertia of beams with reference to
an axis through their centers of gravity parallel to (coincident
with) web is given in table for beams. In all other respects,
proceed for this form of section as in the previous case.
If two channels are connected by means of two plates instead
of a beam, as shown by Fig. 2, on page 26, the moment of inertia
of the plates must be obtained instead of the beam. This
moment 'of inertia, for a neutral axis through center of section
perpendicular to the plates, is equal to the cube of the width of
plate multiplied, by T ^th of the thicknesses of the two plates
added; and for a neutral axis parallel to plates, is equal to the
area of the two plates multiplied by the square of the distance
between the center of the plate and the center of the section.
A column is square bearing when it has square ends which
butt against or are firmly connected with an immovable surface,
such as the floor of a building; it is pin and sqttare bearing
when one end only is square bearing and the other presses against
a close fitting pin, and it is pin bearing when.both ends are thus
pin-jointed, (for example, the posts in pin-connected bridges.)
With regard to the table on the Safe Resistance of Wooden
Pillars, it should be said that comprehensive tests establishing
the constants to be used in the formula have not been made to
date, but it is believed that the values given in table err on the
side of safety.
EXAMPLES OF APPLICATION OF TABLES.
I. W T hat is the ultimate strength of a square bearing 10"
octagon column, ^" thick and 20' long?
Answer : The area of a 10" X YZ" column, as per table on
page 77, is 21.3 square inches. The mean diameter is 10", very
75
1 20
nearly, so that ~-r-= -v = 2, for which the ultimate strength,
as per table on page 79, = 33560 Ibs. per square inch. Conse-
quently the ultimate strength of the column = 33560 Ibs. X 21.3
= 714800 Ibs. The safe resistance for quiescent loads would be
= X X 714800 = 178700 Ibs., and for moving loads = i X
714800 = 143000 Ibs.
II. Required the ultimate strength of a 30 Ib. 10" beam
used in the form of a strut, riveted at its ends so as to be firmly
fixed, and measuring 10' between the points where it is held in
position.
By reference to table on page 64, the least radius of gyration
of a 30 Ib. 10" beam is found to be = 0.94, (neutral axis
coincident with web,) so that ==-_ g = 10.6, for which the
ultimate strength, as per table on page 80, =27600 Ibs. per square
inch. The area of the beam being = 9 square inches, its
ultimate strength will, therefore, = 9 X 27600 = 248400 Ibs.
III. What is the radius of gyration of a column section
composed of two 9", 18 Ib. channels, and a 6", 13>^ Ib. beam,
riveted together in the manner shown by Fig. 3, on page 26 ?
Answer, if neutral axis coincident with web of beam :
Moment of inertia of beam ^= 2.0
" channels = 129.6
" " " section = 131.6
Area of section = 14.85 square inches. .Therefore radius of
131.6
gyration = ~\,
Answer, if neutral axis at right angles to web of beam :
Moment of inertia of beam = - - . - 24.5.
Moment of inertia of channels = area of channels X
distance of center of gravity from center of section
squared = 10.8 square inches X 3.68 = - - 146.3
Moment of inertia of section = .... 170.8
Therefore radius of gyration = y / "TToc' == 3.39.
^
v v or
3- ~*
KEYSTONE OCTAGON COLUMNS.
Thicknesses and Corresponding Areas and "Weights per Foot.
^Wa |
** HS* ** -B*
,
1
i
4
!
CON OC5 001>
C0 1010 i>
o co NI> coca
coco oco t>o
HiH NN NCO
ij
iH 00 1C N O t>
05Oi OrH NN
CO ^ C01> 00 05
i
3
CD
&
l>0i NO OOiH COCO
H^uj t^-QO 05rH NCO
rH iHtH
1
{d
t** 00 05 C^ rH C^3 CO ^^
rH N NCO CO ^H ^ IO
ft
CO COO COCO 05 N
rH CO N t^ N C** CO
1Q t^* 00 ^^ rH CO ^H CO
3
O
00
Hi*
N OOlO N05 CON O5 CD
00 05rH CO^ COOO 05iH
iH rHrH rHrH rH N
!
1*
CO COO OOUD N05 CO^
N 05CO NO5 CON 05 CD
CO CO"* O1O CO1> I>00
I> 0000 0000 0000 0005
05 rHCO IOI> 05rH COIO
rHrH rH rH rH N NN
o
iH
1
sis
05 00 00 00 t^ t** ^Q c^ co if^j
rHCO* IO1> 05 rH CO'lO t>05
rHrH rH rH rH N NN NN
j*
I>10 COrH 00 CO* ^N OOO
v$\Q C01> l>00 O5O rHrH
rH i 1 rH
ii
N Sw COS
T^CO OOrH COCO OOO COlO
rHrH rH N NN NCO COCO
sswnpiqj; |
-ex 2 ^ <* ** **
77
ULTIMATE STRENGTH
OF
HOLLOW CYLINDRICAL CAST AND
WROUGHT IRON COLUMNS,
For different proportions of length in feet ( = 1 )
To least diameter in inches (= d).
Ultimate Strength in Ibs. per
square inch =
Cast Iron.
Wrought Iron.
Square Bearing : Pin & Square : Pin Bearing :
Square Bearing : Pin & Square : Pin Bearing :
80000 80000 80000
40000 40000
40000
(121
) 2 1 , 3(12 1) 2 (1!
I 2 M600 d 2 '40
21) 2
(12 1) 2 (12 1) 2 (12 1) 2
"^800 (
Od 2
"^OOOd 2 '20004^ ' 1500 d 2
To obtain Safe
Resistance :
For quiescent loads (buildings) divide bjr{ J f ^oughTiron.
For moving- loads (bridges) divide by < ? r r ?'
' (5 for wrought iron.
Cast Iron.
"Wrought Iron.
1 Ultimate Strength in Lbs. per sq. in.
Ultimate Strength in Lbs. per sq.in.
Square.
Pin and p .
Square. ; Pm '
Square.
Pin and
Square.
Pin.
1.0 ' 67800
62990 58820
38170
37310
36500
1.1 65690 -
60300 55730
37800
36790
35840
1.2 63530
57600
52690
37410
36240
35140
1.3
61340
54930 49740
37000
35660
34420
1.4
59140
52310
46900
36560
35050
33670
1.5
56940
49770
44200
36100
34420
32890
1.6
54760
47300
41630
35620
33770
32110
1.7
52620
44940
39210
35130
33110
31320
1.8 '
50530
42670
36930
34620
32430
30510
1.9
48490
40510
34790
34090
31750
29710
2.0
48510
38460
32790
33560
31060
28900
2.1
44600
38520
30920
38010
30360
28100
2.2
42750
34680
29180
32460
29660
27310
2.3
40980
32940
27540
31900
28970
25530
2.4 39280
31310
28030
31340
28270
25760
2.5 1 37650
29770
24620
30770
27590
25000
2.6 ! 38090
28320 23300
30200
26900
24260
2.7
34600
26950 22070
29630
26230
23530
2.8
33180
25670
20930
29060
25570
22820
2.9
31820
24460
19
860
28500
24910
22130
3.0
30530
23320
18870
27930
24270
21460
3.1
29310
22250 i 17940
27370
23640
20810
3.2
28140
21250 17070
26820
23020
20170
3.3
27030
20300 ! 16260
26270
22420
19560
, 3.4 25970
19410 15500
25730
21830
18960 ,
79
ULTIMATE STRENGTH OF WROUGHT
IRON COLUMNS,
For different proportions of length in feet ( = 1 )
To least radius of gyration in inches (= r).
Ultimate Strength in Ibs. per square inch =
Column
Square Bearing :
40000
,
(121)*
36000 r 2
Column
Pin and Square Bearing
40000
(121)*."
24000 r 2 "
Column
Pin Bearing :
40000
14
IJL
18000 r 2
To obtain Safe Resistance :
For quiescent loads, as in buildings, divide by 4.
For moving loads, as in bridges, divide by 5.
Ultimate Strength in Lbs.
Ultimate Strength in Lbs.
1 per square inch.
3.0
3.2
3.4
3.6
3.8
4.0
4.2
4.4
4.6
4.8
5.0
5.2
5.4
5.6
5.8
6.0
6.2
6.4
6.6
6.8
7.0
7.2
7.4
7.6
7.8
38610
33430
38230
38030
37820
37590
37360
37120
38870
36620
36360
36090
35820
35540
35260
34970
34870
34370
34060
33750
33440
33130
32810
32490
32170
37950
37680
37400
37110
36810
36500
36170
35840
35500
35140
34780
34420
34050
33670
33280
32890
32500
32110
31710
31310
80910
30510
30110
29710
29310
37310
36970
36610
36240
35860
35460
35050
34640
34210
33770
33330
32890
32440
31980
31520
31060
30590
30130
29670
29200
28740
28270
27820
27360
26910
8.0
8.2
8.4
8.6
8.8
9.0
9.2
9.4
9.6
9.8
10.0
10.2
10.4
10.6
10.8
11.0
11.2
11.4
11.6
11.8
12.0
12.2
12.4
12.6
12.8
per square inch.
Square.
Square!'
Pin.
31850
28900
26460
31520
28500
26010
31190
28100
25570
30870
27700
25130
30540 ;
27310
24700
30210 :
26920 :
24270
29880
26530 '
23850
29550
26140
23430
29230 ;
25760 i
23030
28900 ;
25370 |
22620
28570 !
25000 '
22220
28250 I
24630
21830
27920 i
24260
21440
27600 1
23890
21060
27270 I
23530
20690
26950
23170
20330
26640
22820
19960
26320
26000
25690
25380
25070
24770
24470
24170
22470
22130
21800
21460
21130
20810
20490
20180
19610
19270
18930
18590
18260
17940
17620
17310
80
^
ULTIMATE STRENGTH OF
RECTANGULAR TIMBER PILLARS, WELL
SEASONED,
For different proportions of length in feet (= 1)
To least
diameter or side in inches (= d).
Ultimate Strength in Ibs. per square inch =
Pillar
Pillar Pillar
Square Bearing: Pin and Square Bearing : Pin Bearing:
5600
5600 5600
(121)'
" 550 d^
1.5(121)*
1 , (121) 2
550 d^
275
The above formula for Square Bearing Pillars is based upon
Lemande's experiments on French oak, and agrees fairly with
Hodgkinson's
formula
for French oak pillars of 30 diameters
and over.
The strength of pillars of French oak, Red deal and Dantzig
oak, is given
by Hodgkinson as proportional to the ratio, 6.9:
7.8: 10.95.
It is believed the above formulae for French oak and the fol-
lowing table calculated
from them, will also apply to American
white
pine of best quality.
Green timber has only about half the strength of dry.
To obtain the Safe Resistance, divide by 6.
Ultimate Strength
in Lbs.
Ultimate Strength in Lbs.
1
per square inch.
1
per square inch.
T
Square.
Pin and
Square.
Pin.
d
Square.
Pin and
Square.
Pin.
1.0
4440 -
4020
3680
2.5
2120
1620
1310
1.1
4250
3800
3430
2.6
2020
1530
1230
1.2
4070
3580
3190
2.7
1930
1450
1160
1.3
3880
3370
2970
2.8
1830
1370
1100
1.4
3700
3160
2760
2.9
1750
1300
1040
1.5
3520
2970
2570
3.0
1670
1230
980
1.6
3350
2790
2390
3.1
1590
1170
930
1.7
3190
2620
2230
3.2
1520
1120
880
1.8
3040
2470
2080
3.3
1450
1060
840
1.9
2890
2320
1940
3.4
1390
1010
790
2.0
2740
2180
1810
3.5
1330
960
760
2.1
2600
2050
1690
3.6
1270
920
720
2.2
2470
1930
1580
3.7
1220
880
690
2.3
2350
1820
1490
3.8
1170
840
650
2.4
2230
1720
1400
3.9
1120
800 620
81
GENERAL NOTES ON FLOORS and ROOFS.
On page 23 will be found examples of floor joists and their
connections. When two beams are placed side by side, as in
Fig. 1, they should be connected together by means of bolts and
cast-iron separators, fitted closely between the flanges of the
beams. The office of these separators is to hold in position the
compression flange of the beams, preventing side deflection or
buckling, and to firmly unite the two beams, so that they will
act in unison. Separators should be used near the supports and
at distances of five or six feet. They are shown by Figs. 2 and 3,
on page 24. Their weight will range from 19 Ibs. for the heavy
15" beams, to 5 Ibs. for 6" beams.
Figures 1, 2 and 3 show the methods of connecting beams
with each other. In Figs. 1 and 2 the lighter beam is coped
into the heavier one, the weight being carried by the lower flange
of the latter. The angle with which the webs are connected,
serves only to hold the beams in position, in this case. In Fig.
3 the load of the smaller beams is transferred to the larger by
means of angles riveted to the webs, and in case this is not
sufficient, an angle may be riveted to the web of the larger
'beam underneath the smaller, as shown, to assist in carrying the
load.
Figures 5, 6, 7, 8, 9 and 10, on page 23, are illustrations of
various forms of girders, such as it is often necessary to use in
the front of buildings, to carry walls, or in the interior, to support
the joists. Where these girders rest upon the wall, cast or wrought-
iron bed plates should be used, to distribute the pressure over a
greater surface, and thereby prevent the crushing of the brick
directly under the girder. In some cases a tough, large size
stone will answer without the plates, but where the pressure is
heavy, both plates and stone should be used. Figs. 5, 6, 9 and 10,
are illustrations.
On page 24, Fig. 1, is represented a girder composed of two
beams, carrying a brick wall, in position. In case of failure of the
girder, only a part of the wall above it would drop down, the
line of rupture for brick-work making an angle of about 30
with the vertical, called the angle of repose. The weight to be
82 "
carried by the girder may, therefore, be considered to be only that
part of the wall between the lines of rupture, provided, that in
building the wall, the center of the girder was supported tem-
porarily with a wooden prop, preventing deflection. Several
courses should, however, be laid before this is done.
If /= the clear span of girder, and h = the hight of wall
above it, the superficial area of the trapezoid between the lines
of rupture, is expressed by h (2 1 1.2 h), but deductions must,
of course, be made for windows or other openings in the wall,
if there are any.
In order to be entirely on the safe side, and also for the sake
of simplicity, the weight of wall between vertical lines directly
over the girder, is frequently adopted as the load to be carried
by it.
Weight of Brick-ivork per Superficial Foot, for a
9" wall = 84 Ibs., 13" wall = 121 Ibs., 18" wall = 168 Ibs.,
one cubic foot weighing 112 Ibs.
There are various fire-proof floors in use; one of the most
common is that represented by Fig. 1, on page 23. Four-inch
brick arches are built between beams spaced not over 5 feet apart,
and tied together by rods %" to 1" diameter, at intervals of 4'
to 6', so as to take the thrust of the arches off the walls. Tee or
angle irons are inserted in the wall, so as to hold it firmly in line
between the points held by the rods. The top of the arches is
leveled off with concrete, allowing space, however, for wooden
strips, to which the floor timber is nailed. The plastering for
ceiling usually covers the arches only, so that the ceiling will
appear curved and show the lower flanges of the iron beams.
A convenient device for centering the arches is shown in
Fig. 4. The centers are suspended by iron hooks from the lower
flanges of the beams, and can be moved forward and back, and
removed at pleasure.
Figure 4, on page 24, and Fig. 3, on page 25, are examples of
flush, plastered ceilings, the laths in the latter case being held by
light castings. Fig. 3, on page 24, is an example of an iron
ceiling, composed of sheet iron pressed to suitable form, laid
upon the lower flanges of the beams; . and Figs. 2 and 5 are
_
illustrations of corrugated iron ceilings. Both are open to the
objection that the condensed moisture of the air will collect
upon the iron and fall into the rooms below. Particularly is this
the case in rooms filled with people, and such ceilings should,
therefore, be restricted in their use, or the iron should be covered
in such manner from below, that the access of the air is effectually
cut off, as by plastering.
The weight of a fire-proof floor, consisting of four-inch brick
arches between beams, with concrete filling above the arches and
flooring, will generally average about 70 Ibs. per square foot,
exclusive of the weight of the beams. The following are average
weights of some other constructions, and the usual assumptions
made for superimposed load:
Iron roof of 100 feet span, with corrugated iron laid directly
upon purlins, will weigh
Approximately, - - - - - - -10 Ibs. ^ sq. ft.
If boarded, add 3 "
For lathed and plastered ceiling, allow - - 10 " "
For snow and vertical component of wind force,
allow 30
For superimposed load on
Floors of dwellings, assume - - - 60 " "
" " churches, theaters and ball rooms, 125 " "
" " warehouses, - 250 " "
Weight of snow, freshly fallen, - - 5 to 12 " cub. ft.
" " saturated, (slush,) - 40 " "
Crowd of people, closely packed, - 80 " sq. ft.
Wind pressure (violent hurricane,) - 50 " "
Rule for finding the sectional area of a bar of wrought iron,
given the weight per foot :
Multiply by 3 and divide by 10.
Rule for finding the weight per foot, given the area :
Divide by 3 and multiply by 10.
84
CORRUGATED AND GALVANIZED IRON.
Corrugated Iron is used for roofs and sides of buildings. It is
usually laid directly upon the purlins in roofs, and held in place by
means of clips of hoop iron, which encircle the purlin and are
placed in distances of about twelve inches apart. Special care
must be taken that the projecting edges of the corrugated iron,
at the -eaves and gable ends, of the roof, are well secured, other-
wise the wind will loosen the sheets and fold them up.
The corrugations are made of various sizes ; the smaller
present a more pleasing appearance to the eye, while the larger
are stiffer and will span a greater distance, thereby permitting the
purlins to be placed further apart. The sizes of sheets generally
used for both roofing and siding, are No. 20 and 22.
The corrugated iron which will be described in the following,
is manufactured by the Keystone Bridge Company, of Pittsburgh.
It is of medium size, presenting both a good appearance and
being of sufficient strength for usual requirements.
By one corrugation is meant the double curve between corre-
sponding points, and by depth of corrugation, the greatest deviation
from the straight line, measured between the concave surfaces of
the corrugated sheet.
The Keystone Bridge Company's corrugations are 2.425" long,
measured on the straight line ; they require a length of iron of
2.725 /; to make one corrugation, and the depth of corrugation
is |4". One corrugation is allowed for lap in the width of the
sheet and ft" in the length, for the usual pitch of roof of two to
one. Sheets can be corrugated of any length not exceeding
ten feet. The most advantageous width is 30^ /; , which
(allowing y 2 " for irregularities) will make eleven corrugations
= 30", or, making allowance for laps, will cover 24^" of the
surface of the roof.
By actual trial it was found that corrugated iron No. 20,
spanning 6 feet, will begin to give a permanent deflection for a
load of 30 Ibs. per square foot, and that it will collapse with a
load of 60 Ibs. per square foot. The distance between centers
of -purlins should therefore not exceed 6 feet, and, preferably,
be less than this.
KEYSTONE BRIDGE CO.'S CORRUGATED
IRON.
The following table is calculated for sheets 3C
y^ 11 wide before
corrugating.
I J^
Weight per Square of 100 square
feet,
||
when
laid, allowing 6" lap in length and
or one corrugation in width of
.O.SJf JSJ3 Jjp 2 jjjf'l
she 4 et
for sheet lengths of:
'Ijf3
Lbs. Lbs.
5'
6'
7' 8'
9'
10'
LbT
16 .065 2.61 3.28
365
358
353 350
348
346
2.95
18 .049 1.97 2.48
275
270
267 264
262
261
2.31
20 .035 1.40 1.76
196
192
190 188
186
185
1.74
22 .028 1.12 1.41
156
154
152 150
149
148
1.46
24 .022 .88 1.11
123
121
119 118
117
117
1.22
26 .018 .72 .91
101
99
97 97
96
95
1.06
RESULTS OF TEST
of a corrugated sheet No. 20,
2/_0" wide, 6'-0" long between
supports, loaded uniformly with fire clay.
Load
per Square Foot.
Lbs.
Deflection
at Center under Load.
Inches.
Permanent Deflection,
Load Removed.
5
/2
10
X
15
1
20
1
25
1
30
]
H
%
35
2
Vt
Yz
40
2
1 /o
K'
45
3/2
]
-/&
50
4
]
Y*
55
C
#
Not
Noted.
60
Broke
Down.
"
a
86
ILLUSTRATION OF APPLICATION
OP TABLES ON FLAT ROLLED IRON.
Pages 88 to 99, inclusive.
What is .the weight per foot of a bar 5" X IjV' in section?
Answer : In the column for 5" width, and in the line for 1 j 1 ^"
thickness, will be found the value 17.71, which is the weight
desired.
What thickness of 4^" bar will be required to give an area
of 5.3 square inches? Answer: In the column for 4^" width
will be found 5.34, which is the area nearest to that required ;
the corresponding thickness being IfV ' tne ^ ar should be 4^"
X W-
ILLUSTRATION OF APPLICATION
OP TABLES ON DECIMAL PARTS OP A
FOOT FOR EACH th OP AN INCH.
Pages 1OO to 1O3, inclusive.
What is the value of 5' 7^ \" , expressed in feet and decimals
of a foot? Answer : 5.5977; found by looking in column for 7",
and in line for \\".
What is the value of 11.6838', expressed in feet, inches and
fractions of an inch? Answer: The value nearest to the
decimal .6833, to be found in table, is .6836, which is = 8$f ",
therefore 11.6838' = 11' 8JJ", nearly.
87
WEIGHTS OF FLAT ROLLED IRON
PER LINEAL FOOT.
For Thicknesses from -y^ in. to 2 in. and Widths
from 1 in. to 12% In.
Iron weighing 480 Ibs. per cubic foot.
Thickness
in Inches.
1"
i //]
IK"
2"
2)i"
2K"
2fc"
12"
*
.208
.260 .313
.365
.417
.469 .521
.573
2.50
.417
.521 .625 .729
.833
.938 1.04 .
1:15
5.00
A
.625
.781 .938
1.09
1.25
1.41
1.56
1.72
7.50
i
.833
1.04
1.25
1.46
1.67
1.88
2.08
2.29
10.00
TS
1.04
1.30
1.56
1.82
2.08
2.34
2.60
2.86
12.50
f
1.25
1.56
1.88
2.19
2.50
2.81
3.13
3.44
15.00
A
1.46
1.82-
2.19
2.55
2.92
3.28
3.65
4.01
17.50
I
1.67
2.08
2.50
2.92 3.33
3.75
4.17
4.58
20.00
j\
1.88
2.34
2.81
3.28
3.75
4.22
4.69
5.16
22.50
1
2.08
2.60
3.13
3.65
4.17
4.69
5.21
5.73
25.00
e
2.29
2.86
3.44
4.01
4.58
5.16
5.73
6.30
27.50
2.50
3.13
3.75
4.38
5.00
5.63
6.25
6.88
30.00
it
2.71
3.39 ! 4.06
4.74
5.42
6.09
6.77
7.45
32.50
2.92
3.65 4.38
5.10
5.83
6.56
7.29
8.02
35.00
it
3.13
3.91 4.69
5.47
6.25
'7.03
7.81
8.59
37.50
1
3.33
4.17 5.00
5.83
6.67
7.50
8.33
9.17
40.00
i-V
3.54
4.43 5.31
6.20 7.08
7.97
8.85
9.74
42.50
li-
3.75
4.69
5.63
6.56 7.50
8.44
9.38
10.31
45.00
ly 3 ^
3.96
4.95
5.94
6.93 I 7.92
8.91
9.90
10.89
47.50
H
4.17
5.21
6.25
7.29 8.33
9.38
10.42
11.46
50.00
IA
4.37
5.47 i 6.56
7.66 1 8.75
9.84
10.94
12.03
52.50
4.58
5.73 6.88
8.02 9.17
10.31 11.46
12.60
55.00
IJZg.
4.79
5.99
7.19
8.39 9.58 10.78 11.98
13.18
57.50
11
5.00
6.25
7.50
8.75 10.00
11.25
12.50
13.75
60.00
1 T 9 ^
5.21
6.51 7.81
9.11 ! 10.42
11.72
13.02
14.32
62.50
If
5.42
6.77 8.13
9.48 10.83
12.19
13.54
14.90
65.00
ift
5.63
7.03 8.44
9.84 111.25
12.66
14.06
15.47
67.50
If
5.83
7.29
8.75
10.21 111.67
13.13
14.58
16.04
70.00
113
6.04
7.55
9.06
10.57 12.08
13.59
15.10
16.61
72.50
1?
6.25
7.81
9.38
10.94
12.50 (14.06
15.63
17.19
75.00
6.46
8.07 9.69
11.30
12.92 14.53
16.15
17.76
77.50
2
6.67
8.33 10.00
11.67
13.33 15.00
16.67
18.33
80.00
'4
j
i
WEIGHTS OF FLAT ROLLED IRON
PER LINEAL FOOT.
(CONTINUED.)
Thickness
in Inches.
3"
3K"
3^"
g3/// 4//
4H
4K"
12"
625
.677
.729
.781
.833
.885
.938
.990
2.50
?
1.25
1.35
1.46
1.56
1.67
1.77
1.88
1.98
5.00
A
1.88
2.03
2.19
2.34
2.50
2.66
2.81
2.97
7.50
i
2.50
2.71
2.92
3.13
3.33
3.54
3.75
3.96
10.00
_5_
3.13
3.39
3.65
3.91
4.17
4.43
4.69
4.95
12.50
3.
3.75
4.06
4.38
4.69
5.00
5.31
5.63
5.94
15.00
^
4.38
4.74
5.10
5.47
5.83
6.20
6.56
6.93
17.50
\ 6 5.00
5.42
5.83
6.25
6.67
7.08
7.50
7.92
20.00
Ar I 5.63
6.09
6.56
7.03
7.50
7.97
8.44
8.91
22.50
f
6.25
6.77
7.29
7.81
8.33
8.85
9.38
9.90
25.00
H
6.88
7.45
8.02
8.59
9.17
9.74
10.31
10.89
27.50
7.50
8.13
8.75
9.38 110.00
10.63
11.25
11.88
30.00
it
8.13 8.80
9.48
10.16
10.83
11.51
12.19
12.86
32.50
1
8.75
9.48
10.21
10.94
11.67
12.40
13.13
13.85
35.00
It
9.38
10.16
10.94
11.72
12.50
13.28
14.06
14.84
37.50
1
10.00
10.83 11.67
12.50
13.33
14.17
15.00
15.83
40.00
JTC
10.63
11.51 12.40
13.28
14.17
15.05
15.94
16.82
42.50
l 1 !
11.25
12.19 13.13
14.06
15.00
15.94
16.88
17.81
45.00
11.88
12.86 13.85
14.84
15.83
16.82
17.81
18.80
47.50
H
12.50
13.54 14.58
15.63
16.67
17.71
18.75
19.79
50.00
i
JL
13.13
14.22 15.31
16.41
17.50
18.59
19.69
20.78
52.50
f 13.75 14.90 16.04
17.19
18.33
19.48
20.63
21.77
55.00
T V .14.38 15.57 16.77
17.97
19.17
20.36 21.56
22.76
57.50
.V 15.00
16.25 17.50
18.75
20.00
21.25
22.50
23.75
60.00
A 15.63
16.93 18.23
19.53
20.83
22.14
23.44
24.74
'62.50
4 16,25 17.60 18.96
20.31
21.67 23.02
24.38
25.73
65.00
m 16,88 18.28 19.69
21.09
22.50 123.91
25.31
26.72
67.50
1 f 17.50
18.96 20.42
21.88
23.33 J24.79
26.25
27.71
70.00
Hf 18.13 19.64 21.15 |22.66
24.17 25.68 27.19 28.70
72.50
1 1 18.75 '20.31 21.88 23.44
25.00 26.56 i28.13 29.69
75.00
U| 19.38 ;20.99 22.60
24.22
25.83 27.45 J29.06
30.68
77.50
2 20.00 21.67 23.33
25.00
26.7 28.33 ! 30.00 31.67
80.00
WEIGHTS OP FLAT ROLLED IRON
PER LINEAL FOOT.
(CONTINUED.)
Thickness
in Inches.
5"
6
m
5K"
6"
6* 6X
6X
12"
Te"
1.04
1.09
1.15 1.20
1.25
1.30 i 1.35
1.41
2.50
2.08
2.19
2.29J 2.40
2.50
2.60
2.71
2.81
5.00
A
3.13
3.28
3.44 3.59
3.75
3.91 4.06
4.22
7.50
V
4.17
4.38
4.58
4.79
5.00
5.21 5.42
5.63
10.00
T 5 6
5.21
5.47
5.73
5.99
6.25
6.51 6.77
7.03
12.50
6.25
6.56
6.88
7.19
7.50
7.81 8.13
8.44
15.00
ft
7.29
7.66
8.02
8.39
8.75
9.11 9.48
9.84
17.50
i
8.33
8.75
9.17
9.58
10.00
10.42
10.83
11.25
20.00
T 9 *
9.38
9.84
10.31
10.78
11.25
11.72
12.19
12.63
22.50
5.
10.42
10.94 11.46
11.98 12.50
13.02
13.54
14.06
25.00
ft
11.46
12.03 12.60 '13.18 13.75
14.32 14.90
15.47
27.50
3
4
12.50
13.13
13.75
14.38
15.00
15.63 16.25
16.88
30.00
M
13.54
14.22
14.90
15.57
16.25
16.93 17.60
18.28
32.50
14.58
15.31
16.04
16.77 17.50
18.23 18.96
19.69
35.00
it
15.63
16.41
17.19 17.97 18.75 19.53 j 20.31
21.09
37.50
1
16.67
17.50
18.33:19.17 20.00 20.83
21.67
22.50
40.00
! T V
17.71
18.59
19.48 ' 20.33 21.25 22.14
23.02
23.91
42.50
1|
18.75
19.69 20.63 jgl.56 22.50 j 23.44
24.38
25.31
45.00
19.79
20.78
21.77 1 22.76 23.75
24.74
25.73 1 26.72
47.50
1?
20.83
21.88
22.92123.96 5.00
26.04
27.08
28.13
50.00
IJL
21.88
22.97
24.03 25.1 6 ! 26.25
27.34 28.44
29.53
52.50
If
22.92
24.06
25.21
26.35 ; 27.50
28.65 29.79
30.94
55.00
4
23.96
25.16
26.35 27.55 28.75 29.95 31.15
32.34
57.50
U
25.00
26.25
27.50 28.75 30.00
31.25 32.50
33.75
60.00
1 T ^
26.04
27.34
28.65
29.95 31.25
32.55
33.85
35.16
62.50
H
27.08
28.44
29.79 31.15 32.50
33.85
35.21
86.56
65.00
m
28.13
29.53
30.94 : 32.34 33.75
35.16 : 36.56
37.97
67.50
if
29.17
30.63 i 32.08 33.54 35.00
36.43 37.92
39.38
70.00
Ht
30.21
31.72
33.23 84.74
36.25
37.73
39.27
40.78
72.50
i?
31.25
32.81 34.38 35.94 37.50
39.08 40.63
42.19
75.00
lit
32.29
33.91
35.52 37.14 38.75
40.36 41. 98! 43.59
77.50
2
i
33.33
35.00
36.67 38.33
40.00
41.67
43.33
45.00
80.00
WEIGHTS OF FLAT ROLLED IRON
PER LINEAL FOOT.
. (CONTINUED.)
Thickness
in Inches.
1"
7M"
7 l o" 7%"
8"
8X W
12"
T6
1.46
1.51
1.56; 1.61
1.67
1.72
1.77
1.82
2.50
2.92
3.02
3.13; 3.23
3:33
3.44
3.54
3.65
5.00
A
4.38
4.53
4.69
4.84
5.00
5.16
5.31
5.47
7.50
f*
5.83
6.04
6.25
6.46
6.67
6.88
7.08
7.29
10.00
jV
7.29
7.55
7.81
8.07
8.33
8.59
8.85
9.11
12.50
8.75
9.06
9.38! 9.69
10.00
10.31
10.63
10.94
15.00
i
10.21
10.57 i 10.94 11.30
11.67
12.03
12.40
12.76
17.50
i
11.67
12.08
12.50 12.92
13.33
13.75
14.17
14.58
20.00
Kl
13.13
13.59
14.06
14.53
15.00
15.47
15.94
16.41
22.50
V
14.58
15.10
15.63
16.15 16.67
17.19
17.71
18.23
25.00
A
16.04
16.61
17.19
17.76
18.33
18.91 19.48
20.05
27.50
i
17.50
18.13
18.75
19.38
20.00 i 20.63
21.25
21.88
30.00
It
18.96
19.64
20.31
20.99
21.67
22.34
23.02
23.70
32.50
7
20.42 21.15
21.88
22.60
23.33 24.06
24.79
25.52
35.00
ff 21.88
22.66
23.44 24.22 25.00 25.78
26.56
27.34
37.50
i
23.33 24.17 25.00
25.83 26.67 27.50
28.33
29.17
40.00
IT*
24.79 25.68 26.56^7.45
28.33 29.22
30.10
30.99
42.50
1?
26.25
27.19 28.13 29.06
30.00 30.94
31.88
32.81
45.00
27.71
28.70 i 29.69 30.68
31.67 32.66
33.65
34.64
47.50
H
29.17
30.21 i 31.25
32.29
33.38 34.38
35.42
36.46
50.00
IA
30.62
31.72
32.81
33.91
35.00
36.09
37.19
38.28
52.50
1 -^
32.08
33.23
34.38
35.52
3C.67 1 37.81
38.96
40.10
55.00
l- 7 r
33.54
34.74
35.94 37.14 38.33 39.53
40.73
41 93
57.50
H
35.00
36.25
37.50
38.75
40.00
41.25
42.50
4^.75
^ A .00
JJL
36.46 ! 37.76
39.06
40.36
41.67
42.97
44.27
45.57
62.50
i.f
37.92 39.27 40.63 41.98
43.33 44.69 146.04
47.40
65.00
39.38 '40.78 42,19
43.59 ' 45.00
46.41
47.81
49.22
67.50
If" 140.83 42.29
43.75
45.21
46.67
48.13
49.58
51.04
70.00
lif
42.29 43.80
45.31
46.82
48.33
49.84
51.35
52.86
72.50
1 i
43.75! 45.31 46.88
48.44 50.00
51.56
53.13
54.69
75.00
HI
45.21 I 46.82 i 48.44
50.05 51.67
53.28
54.90
56.51
77.50
2
46.67
48.33 ! 50.00
51.67 i 53.33
55.00
56.67
53.33
80.00
3
~Ti
WEIGHTS OP PLAT ROLLED IRON
PEK LINEAL FOOT.
(CONTINUED.)
Thickness
in Inches.
9" \9%"
&A"
9%"
10"
1<H"
10*"
10f"
12"
rV
1.88
1.93
1.98
2.03
2.08
2.14
2.19
2.24
2.50
|
3.75
3.85
3.96
4.06
4.17
4.27
4.38
4.48
5.00
A
5.63
5.78
5.94
6.09
6.25
6.41
6.56
6.72
7.50
i
7.50
7.71 7.92 8.13
o oo
o.oo
8.54
8.75
8.96 <
10.00
A
9.38
9.64
9.90
10.16
10.42
10.68
10.94
11.20
12.50
1
11.25
11.56
11.88
12.19
12.50
12.81
13.13
13.44
15.00
A
13.13
13.49
13.85
14.22
14.58
14.95
15.31
15.68
17.50
f
15.00
15.42
15.83
16.25
16.67
17.08
17.50
17.92
20.00
T 9 6
16.88
17.34
17.81
18.28
18.75
19.22
19.69
20.16
22.50
1
18.75
19.27
19.79
20.31
20.83
21.35
21.88
22.40
25.00
e
20.63
21.20
21.77
22.34
22.92
23.49
24.06
24.64'
27.50
i
22.50
23.13
23.75
24.38
25.00
25.62
26.25
26.88
30.00
it
24.38
25.05
25.73
26.41
27.08
27.76
28.44
29.11
32.50
i
26.25
26.98
27.71
28.44
29.17
29.90
30.63
31.35
35.00
it
28.13
28.91
29.69
30.47
31.25 1 32.03
32.81
33.59
37.50
i
30.00
30.83
31.67
32.50
33.33
34.17
35.00
35.83
40.00
i_i_
31.88
32.76
33.65
34.53
35.42
36.30
37.19
38.07
42.50
i -
33.75
34.69
35.63
36.56
37.50
38.44
39.38
40.31
45.00
l~V
35.63
36.61
37.60
38.59
39.58
40.57
41.56
42.55
47.50'
H
37.50
38.54
39.58
40.63
41.67
42.71
43.75
44.79
50.00
ifV
39.38
40.47
41.56
42.66
43.75
44.84 1 45.94
47.03
52.50
H
41.25
42.40
43.54
44.69
45.83
46.98 ! 48.13
49.27
55.00
IA
43.13
44.32
45.52
46.72
47.92
49.11
50.31
51.51
57.50
H
45.00
46.25
47.50
48.75
50.00 51.25
52.50
53.75
60.00
1 T 9 6
46.88
48.18
49.48
50.78
52.08
53.39
54.69
55.99
62.50
If
48.75
50.10
51.46
52.81
54.17
55.52
56.88
58.23
65.00
IH
50.63
52.03
53.44
54.84
56.25
57.66
59.06
60.47
67.50
11
52.50
53.96
55.42 56.88
58.33
59.79
61.25 62.71
70.00
HI
54.38
55.89 57.40 58.91
60.42
61.93
63.44
64.95
72,50
11
56.25
57.81 59.38 60.94
62.50
64.06
65.63
67.19
75.00
HI
58.13
59.74 61.35 62.97
64.58
66.20
67.81
69.43
77.50
2
60.00
61.67 63.33
65.00
66.67
68.33
70.00
71.67
80.00
4
i
WEIGHTS OF FLAT ROLLED IRON
PER LINEAL FOOT.
(CONTINUED.)
Thickness
in Inches.
11" 11"'11$" llf 12"
12|"
12$"
12f"
11
I , 1 i
A *
T V 2.29 2.34 2.40
2.45
2.50
2.55
2.60
2.66
p^ Ne0
.3 X
i : 4.58 4.69 4.79
4.90
5.00
5.10
5.21
5.31
r^ ^
-A 6.88: 7.03^ 7.19
7.34
7.50
7.66
7.81
7.97
CO
i 9.17' 9.38 9.58
9.79
10.00
10.21
10.42
10.63
a
T V 11.46 11.72 11.98
12.24
12.50
12.76
13.02
13.28
1!
V 13.75 14.08 14.38
14.69
15.00
15.31
15.63
15.94
J |
T V 16.04 16.41 16.77
17.14
17.50
17.86
18.23
18.59
>-,_
i 18.33 18.75 19.17
19.58
20.00
20.42
20.83
21.25
|.g
A 20.63 ! 21.09 ' 21.56
22.03
22.50
22.97
23.44
23.91
||
f 22.92
23.44 23.96
24.48
25.00
25.52
26.04
26.58
- "^
4-1 125.21 25.78! 26.35
26.93
27.50
28.07
28.65
29.22
i| J
I 127.50 28.13
28.75
29.38
30.00
30.63
31.25
31.88
j
.*
i*
29.79 30.47 31.15
31.82
32.50
33.18
33.85
34.53
**
1
32.08 32.81 i 33.54
34.27
35.00
35.73
36.46
37.19
I J
44 34.38 35.18 35.94
36.72
37.50
38.28
39.06
39.84
3s
1 ' 38.67 ; 37.50 | 38.33
39.17
40.00
40.83
41.67
42.50
|-s
|V
38.96 39.84
40.73
41.61
42.50
43.39
44.27
45.16
|x
1?
41.25
42.19
43.13
44.06
45.00
45.94
46.88
47.81
I 3 *
Ij 3 r
43.54
44.53
45.52
46.51
47.50
48.49
49.48
50.47
^\?
1 1.
45.83
46.88
47.92
48.96
50.00
51.04
52.08
53.13
Sis
g^
1 T 5 -
48.13
49.22
50.31
51.41
52.50
53.59
54.69
55.78
tiu
If
50.42
51.56 i 52.71
53.85
55.00
56.15
57.29
58.44
H
52.71
53.91 1 55.10
56.30
57.50
58.70
59.90
61.09
So 5 ?
1?
55.00
56.25
57.50
58.75
60'.00
61.25
62.50
63.75
38
1 9
57.29
58.59
59.90
61.20
62.50
63.80
65.10
66.41
IsS
H
59.58
60.94
62.29
63.65
65.00
66.35
67.71
69.06
^ g-
61.88
63.28
64.69
66.09
67.50
68.91
70.31
71.72
" & +
if
64.17
65.63
67.08
68.54
70.00
71.46
72.92
74.38
S f oo
Ht
66.46
67.97
69.48
70.99
72.50
74.01
75.52
77.03
f rt B
if
68.75
70.31
71.88
73.44
75.00
76.56
78.13
79.69
jgJS
lit
,71.04
72.66
74.27
75.89
77.50
79.11
80.73
82.34
*" M x
2
73.33
75.00
76.67
78.33
80.00
81.67
83.33
85.00
'^ ~
f
93
1
a
AREAS OP PLAT ROLLED IRON,
For Thicknesses from T ^ in. to 2 in. and Widths
from 1 in. to 12% in.
Thickness
2K" 2K"
in Inches.
~\." l/^ ;/ IV" \y n 2"
2^
12"
TV
.063 .078 .094 .109
.125 .141
.156
.172
.750
f
.125
.156 .188 .219
.250
.281
.313
.344
1.50
A
.188
.234 .281
.328
.375
.422
.469
.516
2.25
i
.250
.313 .375
.438
.500
.563,
.625
.688
3.00
iV -313
.391 .469 .547
.625
.703
.781
.859
3.75
f i .375
.469
.563 .656
.750
.844
.938
1.03
4.50
A -438
.547
.656 .766
.875
.984
1.09
1.20
5.25
i i .500
.625
.750 .875
1.00 1.13
1.25
1.38
6.00
T V .563
.703
.844
.984
1.13 1.27
1.41
1.55
6.75
f ; .625
.781
.938 1.09
1.25 1.41
1.56
1.72
7.50
-}-;, .688
.859
1.03 1.20
1.38 1.55
1.72
1.89
8.25
f .750
.938
1.13 1.31
1.50 1.69
1.88
2.06
9.00
it ' -813
1.02
1.22
1.42
1.63 1.83
2.03
2.23
9.75
1 .875
1.09
1.31 1.53
1.75
1.97
2.19
2.41
10.50
f| .938
1.17
1.41 1.64
1.88
2.11
2.34
2.58
11.25
1 1.00
1.25
1.50 jl.75
2.00
2.25
2.50
2.75
12.00
IrV 1-06
1.33
1.59 il.86
2.13
2.39
2.66
2.92
12.75
H
1.13
1.41
1.69
1.97
2.25
2.53
2.81
3.09
13.50
1.48
1.78 2.08
2.38 2.67
2.97
3.27
14.25
if 1JB5
1.56
1.88 2.19
2.50
2.81
3.13
3.44
15.00
I_P T ! i 31
1.64
1.97 2.30
2.63
2.95
3.28
3.61
15.75
If 1.38
1.72
2.06
2.41
2.75
3.09
3.44
3.78
16.50
IjV ! !- 44
1.80
2.16
2.52
2.88 3.23
3.59
3.95
17.25
1 1 1.50
1.88
2.25
2.63
3.00 3.38
3.75
4.13
18.00
IT?
1.56
1.95
2.34
2.73
3.13
3.52
3.91
4.30
18.75
If
1.63
2,03
2.44
2.84
3.25
3.66
4.06
4.47
19.50
144
1.69
2.11
2.53 2.95 3.38 3.80
4.22
4.64
20.25
If
1.75
2.19 i 2.63 3.05 3.50
3.94
4.38
4.81
21.00
lit
1.81
2.27
2.72 3.17 3.63
4.08
4.53
4.98
21.75
H
1.88
2.34
2.81
3.28
3.75
4.22
4.69
5.16
22.50
VH
1.94
2.42
2.91
3.39
3.88
4.36
4.84
5.33
23.25
2
2.00
2.50
3.00
3.50
4.00
4.50
5.00
5.50
24.00
i ,
j
tir
AREAS OP PLAT ROLLED IRON.
(CONTINUED.)
Thickness
in Inches.
8"
SH"
m
m
4"
4V
w
4%"
12"
A
.188
.203
.219
.234
.250
.266
.281
.297
.750
.375
.406
.438
.469
.500
.531
.563
.594
1.50
ft
.563
.609
.656
.703
.750
.797
.844
.891
2.25
.750
.813
.875
.938
1.00
1.06
1.13
1.19
3.00
Jj
.938
1.02
1.09
1.17
1.25
1.33
1.41
1.48
3.75
3.
1.13
1.22
1.31
Ml
1.50
1.59
1.69
1.78
4.50
1
1.31
1.42
1.53
1.64
1.75
1.86
1.97
2.08
5.25
i
1.50
1.63
1.75
1.88
2.00
2.13.
2.25
2.38
6.00
_ 9 ^
1.69
1.83
1.97
2.11
2.25
2.39
2.53
2.67
6.75
T
1.88
2.03
2.19
2.34,
2.50
2.66
2.81
2.97
7.50
ft
2.06
2.23
2.41
2.58
2.75
2.92
3.09
3.27
8.25
2.25
2.44
2.63
2.81
3.00
3.19
3.38
3.56
9.00
if
2.44
2.64
2.84
3.05
3.25
3.45
3.66
3.86
9.75
2.63
2,84
3.06
3.28
3.50
3.72
3.94
4.16
10.50
A
2.81
3.05
3.28
3.52
3.75
8.98
4.22
4.45
11.25
3.00
3.25
3.50
3.75
4.00
4.25
4.50
4.75
12.00
i y ,y
3.19
3.45
3.72
3.98
4.25
4.52
4.78
5.05
12.75
i i
3.38
3.66
3.94
4.22
4.50
4.78
5.06
5.34
13.50
4
3.56
3.86
4.16
4.45
4.75
5.05
5.34
5.64
14.25
u
3.75
4.06
4.38
4.69
5.00
5.31
5.63
5.94
15.00
IA
3.94
4.27
4.59
4.92
5.25
5.58
5.91
6.23
15.75
l 1 !
4.13
4.47
4.81
5.16
5.50
5.84
6.19
6.53
16.50
4.31
4.67
5.03
5.39
5.75
6.11
6.47
6.83
17.25
if
4.50
4.88
5.25
5.63
6.00
6.38
6.75
7.13
18.00
l- 9 -
4.69
5.08
5.47
5.86
6.25
6.64
7.03
7.42
18.75
1.1
4.88
5.28
5.69
6.09
6.50
6.91
7.31
7.72
19.50
5.06
5.48
5.91
6.33
6.75
7.17
7.59
8.02
20.25
i?
5.25
5.69
6.13
6.56
7.00
7.44
7.88
8.31
21.00
lit
5.44
5.89
6.34
6.80
7.25
7.70
8.16
8.61
21.75
11
5.63
6.09
6.56
7.03
7.50
7.97
8.44
8.91
22.50
1ft
5.81.
6.30
6.78
7.27
7.75
8.23
8.72
9.20
23.25
2
6.00
6.50
7.00
7.50
8.00
8.50
9.00
9.50
24.00
AREAS OF PLAT ROLLED IRON.
(CONTINUED.)
Thickness
in Inches.
5"
5*
5K
w
6"
w
ey,
6^
12"
.313
.328
.344
.359
.375
.391
.406
.422
.750
1
.625
.656
.688
.719
.750
.781
.813
.844
1.50
.938
.984
1.03
1.08
1.13
1.17
1.22
1.27
2.25
1
1.25
1.31
1.38
1.44
1.50
1.56
1.63
1.69
3.00
1.56
1.64
1.72
1.80
1.88
1.95
2.03
2.11
3.75
I
1.88
1.97
2.06
2.16
2.25
2.34
2.44
2.53
4.50
A
2.19
2.30
2.41
2.52
2.63
.73
2.84
2.95
5.25
2.50
2.63
2.75
2.88
3.00
3.13
3.25
3.38
6.00
JL
2.81
2.95
3.09
3.23
3.38
3.52
3.66
3.80
6.75
1*
3.13
3.28
3.44
3.59
3.75
3.91
4.06
4.22
7.50
H
3.44
3.61
3.78
3.95
4.13
4.30
4.47
4.64
8.25
i
3.75
3.94
4.13
4.31
4.50
4.69
4.88
5.06
9.00
is
4.06
4.27
4.47
4.67
4.88
5.08
5.28
5.48
9.75
'
4.38
4.59
4.81
5.03
5.25
5:47
5.69
5.91
10.50
1 5
4.69
49?,
516
5.39
563
586
609
6.33
11.25
1
5.00
5.25
5.50
5.75
6.00
6.25
6.50
6.75
12.00
IJL
5.31
5.58
5.84
6.11
6.38
6.64
6.91
7.17
12.75
lj
5.63
5.91
6.19
6.47
6.75
7.03
7.31
7.59
13.50
5.94
6.23
6.53
6.83
7.13
7.42
7.72
8.02
14.25
H
6.25
6.58
6.88
7.19
7.50
,7.81
8.13
8.44
15.00
1?8
6.56
6.89
7.22
7.55
7.88
8.20
8.53
8.86
15.75
If
6.88
7.22
7.56
7.91
8.25
8.59
8.94
9.28
16.50
iA
7.19
7.55
7.91
8.27
8.63
8.98
9.34
9.70
17.25
H
7.50
7.88
8.25
8.63
9.00
9.38
9.75
10.13
18.00
1 T 9 ,
7.81
8.20
8.59
8.98
9.38
9.77
10.16
10.55
18.75
If
8.13
8.53
8.94
9.34
9.75
10.16
10.56
10.97
19.50
8.44
8.86
9.28
9.70
10.13
10.55
10.97
11.39
20.25
If
8.75
9.19
9.63
10.00
10.50
10.94
11.38
11.81
21.00
l-U.
9.06
9.52
9.97
10.42
10.88
11.33
11.78 '
12.23
21.75
if
9.38
9.84
10.31
10.78
11.25
11.72
12.19
12.66
22.50
9.69
10.17
10.68
11.14
11.63
12.11
12.59
13.08
23.25
.&
10.00
10.50
11.00
11.50
12.00
12.50
13.00
13.59
24.00
r, .. ,
AREAS OP FLAT ROLLED IRON.
(CONTINUED".)
Thickness
in Inches.
7//
7> 4 '"
1%"
7&"
8"
aw
8K"
\*X"
12"
-
A
.438
.453
.469
.484
.500
.516
.531
.547
.750
i
.875
.906
.938
.969
1.00
1.03
1.06
1.09
1.50
3
1.31
1.36
1.41
1.45
1.50
1.55
1.59
1.64
2.25
1.75
1.81
1.88
1.94
2.00
2.06
2.13
2.19
3.00
A
2.19
2.27
2.34
2.42
2.50
2.58
2.66
2.73
3.75
I
2.63
2.72
2.81
2.91
3.00
3.09
3.19
3.28
4.50
TS
3.06
3.17
3.28
3.39
3.50
3.61
3.72
3.83
5.25
i
3.50
3.63
3.75
3.88
4.00
4.13
4.25
4.38
6.00
A
3.94
4.08
4.22
4.36
4.50
4.64
4.78
4.92
6.75
B
8
4.38
4.53
4.69
4.84
5.00
5.16
5.31
5.47
7.50
4.81
4.98
5.16
5.33
5.50
5.67
5.84
6.02
8.25
3
i
5.25
5.44
5.63
5.81
6.00
6.19
6.38
6.6
9.00
H
5.69
5.89
6.09
6.30
6.50
6.70
6.91
7.11
9.75
6.13
6.34
6.56
6.78
7.00'
7.22
7.44
7.66
10.50
16
1 G
6.56
6.80
7.03
7.27
7.50
7.73
7.97
8.20
11.25
1
7.00
7.25
7.50
7.75
8.00
8.25
8.50
8.75
12.00
IrV
7.44
7.70
7.97
8.23
8.50
8.77
9.03
9.30
12.75
H
7.88
8.16
8.44.
8.72
9.00
9.28
9.56
9.84
13.50
IA
8.31
8.61.
8.91
9.20
9.50
9.80
10.09
10.39
14.25
11
8.75.
9.06
9.38
9.69
10.00
10.31
10.63
10.94
15.00
1&
9.19
9.52
9.84
10.17
10.50
10.83
11.16
11.48
15.75
U
9.63
9.97
10.31
10.66
11.00
11.34
11.69
12.03
16.50
i*
10.06
10.42
10.78
11.14
11.50
11.86
12.22
12.58
17.25
10.50
10.88
11.25
11.63
12.00
12.38
12.75
13.13
18.00
iA
10.94
11.33
11.72
12.11
12.50
12.89
13.28
13.67
18.75
if
11.38
11.78
12.19
12.59
13.00,
13.41
13.81
14.22
19.50
IH
11.81
12.23
12,66
13.08
13.50
13.92
14.34
14.77
20.25
if
12.25
12.69
13.13
13.56
14.00
14.44
14.88
15.31
21.00
HI
12.69
13.14
13.59
14.05
14.50
14.95
15.41
15.86
21.75
u
13.13
13.59
14.06
14.53
15.00
15.47
15.94
16.41
22.50
1M
13.56
14.05
14.53
15.02
15.50
15.98
16.47
18.95
23.25
2
i
14.00
14.50
15.00
15.50
16.00
16.50
17.00
17.50
24.00
AREAS OP FLAT ROLLED IRON.
(CONTINUED.)
Thickness
in Inches.
9"
w
9K
9%"
10"
1CH"
10i'
'iOf
:
12"
1
1
rV
.563
.578
.594
.609
.625
.641
.651
)' .672
75(
i
1.13
1.16
1.19
1.22
1.25
1.28
1.31
1.34
1.50
j
I 1.69
1.73
1.78
1.83
1.88
1.92
1.97
2.02
2.25
i
2.25
2.31
2.38
2.44
2.50
2.56
2.63
2.69
3.00
A
2.81
2.89
2.97
3.05
3.13
3.20
3.28
3.36
375
3.38
3.47
3.56
3.66
3.75
3.84
3.94
4.03
4.50
A-
3.94
4.05
4.16
4.27
4.38
4.48
4.59
4.70
5.25
4.50
4.63
4.75
4.88
5.00
5.13
5.25
5.38
6.00
*
5.06
5.20
5.34
5.48
5.63
5.77
5.91
! 6.05
675
5.63
5.78
5.94
6.09
6.25
6.41
6.56
' 6.72
7.50
A
6.19
6.36
6.53
6.70
6.88
7.05
7.22
7.39
8.25
i
6??5
6.94
7.13
7.31
7.50
7.69
7.88
1 8.06
9.00
it
7.31
7.52
7.72
7.92
8.13
8.33
8.53
! 8.73
9.75
7.88
8.09
8.31
8.53
8.75
8.97
9.19
: 9.41
10.50
M
8.44
8.67
8.91
9.14
9.38
9.61
9.84
10.08
11.25
i "
9.00
9.25
9.50
9.75
10.00
10.25
10.50
10.75
12.00
H-
9.56
9.83
10.09
10.36
10.63
10.89
11.16
11.42
12.75
i 1 !
10.13
10.41
10.69
10.97
11.25
11.53
11.81
12.09
13.50
IA
10.69 !
10.98
11.28
11.58
11.88
12.17
12.47
'12.77
14.25
11.25 ;
11.56
11.88
12.19
12.50
12.81
13.13
,13.44
15.00
I A
11.81
12.14
12.47
12.80
13.13
13.45
13.78
'14.11
15.75
if
12.38
12.72
13.06
13.41
1375
14.09
14.44
1478
16.50
12.94
13.30
13.66 :
14.02
14.38 '
14.73
15.09
15.45
17.25
H
13.50 |
13.88
14.25 i
14.63
15.00
j
15.38
15.75
16.13
18.00
IA
14.08
14.45
14.84 i
15.23
15.63 !
16.02
16.41
16.80
18.75
if
14.63 !
15.03
15.44
15.84
16.25 !
16.66
17.06
17.47
19.50
M*
15.19
15.61
16.03
16.45
16.88
17.30
17.72
18.14
20.25
it
15.75
16.19
16.63 i
17.06
17.50
17.94 .
18.38
18.81
21.00
HI
16.31 i
16.77
17.22
17.67
18.13
18.58
19.03
19.48
2175
1?
16.88 i
17.34 i
17.81 !
18.28
18.75 :
19.22 !
19.69
20.16
22.50
17.44 11
t7.92 !
18.41
1S.89
19.38
19.86 i
20.34
20.83
23.25
2 16
13.00
8.50
19.00
19.50
20.00
20.50
21.00
21.50
24.00
ft
|
i
5
SQUARE AND ROUND BARS.
(CONTINUED.)
Thickness
or Diameter
in Inches.
2
A
: Weight of ; Weight of
[j Bar O Bar
: One Foot long. : One Foot long.
13.33 10.47
14.18 11.14
15.05 11.82
15.95 12.53
Area of
QBar
in sq. inches.
4.0000
4.2539
4.5156
4.7852
Area of
O Bar
in sq. inches.
Circumference
of O Bar
in inches.
6.2832
6.4795
6.6759
6,8722
3.1416
3.3410
3.5466
3.7583
A
,1
16.88 1 13.25
17.83 14.00
18.80 14.77
19.80 i 15.55
5.0625
5.3477
5.6406
5.9414
3.9761
4.2000
4.4301
4.6664
7.0686
7.2649
7.4613
7.6576
l
1
11
20.83 16.36
21.89 ! 17.19
22.97 1 18.04
24.08 ! 18.91
6.2500
6.5664
6.8906
7.2227
4.9087
5.1572
5.4119
5.6727
7.8540
8.0503
8.2467
8.4430
3
1
1 .!
25.21 19.80
26.37 20.71
27.55 : 21.64
28.76 22.59
7.5625
7.9102
8.2656
8.6289
5.9396
6.2126
6.4918
6.7771
8.6394
8.8357
9.0321
9.2284
3
A
30.00 23.56
31.26 24.55
32.55 25.57
33.87 26.60
9.0000
9.3789
9.7656
10.160
7.0686
7.3662
7.6699
7.9798
9.4248
9.6211
9.8175
10.014
T
"3
35.21 27.65
36.58 28.73
37.97 29.82
39.39 I 30.94
10.563
10.973
11.391
11.816
8.2958
8.6179
8.9462
9.2806
10.210
10.407
10.603
10.799
1
I
I
40.83 i 32.07
42.30 33.23
43.80 34.40
45.33 35.60
12.250
12.691
13.141
13.598
9.6211
9.9678
10.321
10.680
10.996
11.192
11.388
11.585
A
w
i
46.88 36.82
48.45 38.05
50.05 39.31
51.68 4O.59
14.063
14.535
15.016
15.504
11.045
11.416
11.793
12.177
11.781
11.977
12.174
12.370
TV fT
SQUARE AND ROUND BARS.
(CONTINUED.)
Thickness
or Diameter
ill Inches.
Weight of
[jBar
One Foot long.
Weight of
O Bar
One Foot long.
Area of
QBar
in sq. inches.
Area of
O Bar
in sq. inches.
Circumference
of O Bar
in inches.
4
i
A
53.33
55.01
56.72
58.45
41.89
43.21
44.55
45.91
16.000
16.504
17.016
17.535
12.566
12.962
13.364
13.772
12.566
12.763
12.959
13.155
!
60.21
61.99
63.80
65.64
47.29
48.69
50.11
51.55
18.063
18.598
19.141
19.691
14.186
14.607
15.O33
15.466
13.352
13.548
13.744
13.941
f
H
67.50
69.39
71.30
73.24
53.01
54.50
56.00
57.52
20.250
20.816
21.391
21.973
15.904
16.349
16.800
17.257
14.137
14.334
14.530
14.726
I
if
75.21 59.07
77.20 60.63
79.22 62.22
81.26 63.82
22.563
23.160
23.766
24.379
17.721
18.190
18.665
19.147
14.923
15.119
15.315
15.512
!
83.33
85.43
87.55
89.70
65.45
67.10
68.76
70.45
25.000
25.629
26.266
26.910
19.635
20.129
20.629
21.135
15.708
15.904
16.101
16.297
|
91.88
94.08
96.30
98.55
72.16
73.89
75.64
77.40
27.563
28.223
28.891
29.566
21.648
22.166
22.691
23.221
16.493
16.690
16.886
17.082
|
100.8
103.1
105.5
107.8
79.19
81.00
82.83
84.69
30.250
30.941
31.641
32.348
23.758
24.301
24.85O
25.406
17.279
17.475
17.671
17.868
1
A
110.2
112.6
115.1
117.5
86.56
88.45
90.36
92.29
33.063 25.967
33.785 26.535
34.516 27.109
35.254 27.688
18.064
18.261
18.457
18.653
106 ^
*15 C
SQUARE AND ROUND BARS.
(CONTINUED.)
Thickness Weight of Weight of
Area of
Area of
Circumference
' or Diameter! Q Bar Q Bar
[jBar
O Bar
of O Bar
in Inches. ; One Foot long.
One Foot long.
in sq. inches.
in sq. inches.
in inches.
6
120.0
94.25
36.000
28.274
18.850
iV
122.5
96.22
36.754
28.866
19.046
Y 125.1
98.22
37.516
29.465
19.242
& 127.6
100.2
38.285
30.069
19.439
i 130.2
102.3
39.063
30.680
19.635
TV 132.8
104.3
39.848
31.296
19.831
f 135.5 106.4
40.641 31.919
20.028
7
T
138.1
108.5
41.441
32.548
20.224
1
140.8
110.6
42.250 33.183
20.420
A 143.6
112.7
43.066 33.824
20.617
f
146.3
114.9
43.891 34.472
20.813
li-
149.1
117.1
44.723 35.125
21.009
f
151.9
119.3
45.563 35.785
21.206
154.7
121.5
46.410
36.450
21.402
?
157.6
123.7
47.266
37.122
21.598
160.4
126.0
48.129
37.800
21.795
7
163.3
128.3
49.000
38.485
21.991
T V
166.3
130.6
49.879
39.175
22.187
i
169.2
132.9
50.766
39.871
22.384
A 172 - 2
135.2
51.660
40.574
22.58O
T%
175.2
178.2
137.6
140.0
52.563
53.473
41.282
41.997
22.777
22.973
3
f
181,3
142.4
54.391
42.718
23.169
TV
134.4
144.8
55.316
43.445
23.366
187.5 147.3
56.250
44.179
23.562
190.6 149.7
57.191
44.918
23.758
|
193.8
152.2
58.141
45.664
23.955
11
197.O
154.7
59.098
46.415
24.151
i
200.2
157.2
60.063
47.173
24.347
It
203.5
159.8
61.035
47.937
24.544
}
206.7
162.4
62.016
48.707
24.74O
11 210.0
T i
164.9
63.004
49.483
24.936
SQUARE AND ROUND BARS.
(CONTINUED.)
Thickness
or Diameter
in Inches.
Weight of
QBar
One Foot long.
Weight of
O Bar
One Foot long.
Area of Area of
[J Bar O Bar
in sq. inches, in sq. inches.
Circumference
of O Bar
in inches.
8
!
213.3 167.6
216.7 170.2
220.1 172.8
223.5 175.5
64.000
65.004
66.016
67.035
50.265
51.054
51.849
52.649
25.133
25.329
25.525
25.722
i
226.9
230.3
233.8
237.3
178.2
180.9
183.6
186.4
68.063
69.098
70.141
71.191
53.456
54.269
55.088
55.914
25.918
26.114
26.311
26.507
I
240.8
244.4
248.0
251.6
189.2
191.9
194.8
197.6
72.250
73.316
74.391
75.473
56.745
57.583
58.426
59.276
26.704
26.900
27.096
27.293
it
it
255.2
258.9
262.6
266.3
200.4
203.3
206.2
209.1
76.563 60.132
77.660 6O.994
78.766 61.862
79.879 62.737
27.489
27.685
27.882
28.078
9
t
270.0
273.8
277.6
281.4
212.1
215.0
218.0
221.0
81.000 63.617
82.129 64.504
83.266 65.397
84.410 66.296
28.274
28.471
28.667
28.863
A
285.2
289.1
293.0
296.9
224.0
227.0
230.1
233.2
85.563
86.723
87.891
89.066
67.201
68.112
69.029
69.953
29.060
29.256
29.452
29.649
I
300.8
304.8
308.8
312.8
236.3
239.4
242.5
245.7
90.250
91.441
92.641
93.848
70.882
71.818
72.760
73.708
29.845
30.041
30.238
30.434
it
, *
316.9
321.0
325.1
329.2
1
248.9
252.1
255.3
258.5
95.063
96.285
97.516
98.754
74.662
75.622
76.589
77.561
30.631
30.827
31.023
31.220
SQTJAKE AND ROUN^&ff&ST
(CONTTOTED.) HUKIVBRS!
Thickness
Weight of Weight of
Area of ^^Dj
m$$
or Diameter
[~] Bar O Bar
Q Bar O^
StEJac^
in Inches.
One Foot long, i One Foot long.
in sq. inches. \ in sq. inches.
in inches.
10
333.3
261.8
100.00
78.540
31.416
TtT
337.5
265.1
101.25
79.525
31.612
341.7
268.4
102.52
80.516
31.809
I
346.0
271.7
103.79
81.513
32.005
l
350.2
275.1
105.06
82.516
32.201
A
354.5 278.4
106.35
83.525
32.398
358.8 281.8
107.64
84.541
32.594
rV
363.1 285.2
108.94
85.562
32.790
}
367.5
288.6
110.25 86.590
32.987
T 9 T
371.9 i 292.1
111.57 87.624
33.183
I
376.3
295.5
112.89 88.664
33.379
a
380.7
299.0
114.22 | 89.710
33.576
| 385.2
302.5
115.56 90.763
33.772
if
389.7
306.1
116.91
91.821
33.968
i
394.2
309.6
118.27
92.886
34.165
ft 398.8
313.2
119.63
93.956
34.361
11 403.3
316.8
121.00
95.033
34.558
407.9
320.4
122.38 96.116
34.754
412.6
324.0
123.77 97.205
34.95Q
417.2
327.7
125.16 98.301
35.147
i
~r
421.9
331.3
126.56
99.402
35.343
A
426.6 335.0
127.97
100.51
35.539
1
431.3 338.7
129.39 101.62
35.736
TV
436.1 342.5
130.82
102.74
35.932
440.8
346.2
132.25
103.87
36.128
445.6
350.0
133.69
105.00
36.325
f
450.5
353.8
135.14
106.14
36.521
tt
455.3
357.6
136.60
107.28
36.717
i
I
460.2
361.4
138.06
108.43
36.914
if
465.1 365.3
139.54 | 109.59
37.110
1
470.1 369.2
141.02 110.75
37.306
it
475.0 373.1
142.50 111.92
37.503
WEIGHT OF SHEETS OF WROUGHT IRON,
STEEL, COPPER AND BRASS. (From Haswell.)
Weights per Square Foot. Thickness by Birmingham Gauge.
2SE ^on. | Steel. Copper.
Brass.
0000 i .454
18.22 18.46 20.57
19.43
000 .425
17.05 17.28 19.25
18.19
00 .38
15.25
15.45 17.21 16.26
.34
13.64
13.82 15.40
14.55
1
.3
12.04
12.20 13.59 12.84
2
.284
11.40
11.55 12.87 12.16
3
.259
10.39
10.53
11.73 11.09
4
.238
9.55
9.68 10.78 10.19
5
.22
8.83
8.95 9.97
9.42
6
.203
8.15
8.25 9.20
8.69
7
.18
7.22
7.32 8.15
7.70
8
.165
6.62
6.71
7.47
7.06
9
.148
5.94
6.02
6.7O
6.33
10
.134
5.38
5.45
6.07
5.74
11
.12
4.82
4.88
5.44
5.14
12
.109
4.37
4.43
4.94
4.67
13
.095
3.81
3.86
4.30
4.07
14
.083
3.33
3.37
3.76
3.55
15
.072
2.89
2.93
3.26
3.08
16
.065
2.61
2.64
2.94 2.78
17
.058
2.33
2.36 2.63 i 2.48
18
.049
1.97
1.99
2.22 2.10
19
.042
1.69
1.71
1.90 1.80
20
.035
1.40
1.42
1.59 1.50
21
.032
1.28
1.30 1.45 1.37
22
.028
1.12 1.14 1.27 1.20
23
.025
1.00 1.02 1.13 1.07
24
.022
.883
.895 1.00 .942
25
.02
.803
.813 .906 .856
26
.018
.722
.732 .815 1 .770
27
.016
.642
.651 .725 .685
28
.014
.562
.569
.634 .599
29
.013
.522
.529 .589 .556
30
.012 .482
.488 .544 .514
31
.01 .401
.407 .453 .428
32 .009 .361
.366 .408 .385
33 .008 .321 .325
.362 .342
34 .007 .281 .285
.317 .300
35 .005 .201 .203 .227 .214
Specific Gravity,
7.704
7.806
8.698
8.218
Weight Cubic Foot,
481.25
487.75 543.6 513.6
. " " Inch,
.2787 .2823 .3146! .2972
WEIGHT OF
SHEETS OF WROUGHT IRON,
STEEL, COPPER AND BRASS. (From Haswell.)
"Weights per Sq. Foot.
Thickness by American (Browne & Sharpe's) Gauge.
No. of Thickness
Gauge. in inches.
Iron.
Steel. Copper.
Brass.
OOOO .46
18.46
18.70
20.84
19.69
000 .4096
16.44
16.66
18.56
17.53
00 .3648
14.64
14.83
16.53
15.61
.3249
13.04
13.21
14.72
13.90
1 .2893
11.61
11.76
13.11
12.38
2
.2576
10.34
10.48
11.67 11.03
3
.2294
9.21
9.33
10.39
9.82
4 .2043
8.20
8.31 9.26
8.74
5 .1819
7.30
7.40 8.24 7.79
6 .1620
6.50
6.59 7.34 6.93
7 .1443
5.79
5.87 6.54 6.18
8 .1285
5.16
5.22
5.82 5.50
9 .1144
4.59
4.65
5.18 4.90
10 .1019
4.09
4.14
4.62 4.36
11 .0907
3.64
3.69
4.11
3.88
12 .0808
3.24
3.29
3.66
3.46
13 .0720
2.89
2.93
3.26
3.08
14 .0641
2.57
2.61
2.90
2.74
15
.0571
2.29
2.32
2.59
2.44
16 .0508
2.04
2.07
2.30
2.18
17 .0453
1.82
1.84
2.05
1.94
18 .0403
1.62
1.64
1.83
1.73
19
.0359
1.44
1.46
1.63
1.54
20
.0320
1.28
1.30
1.45
1.37
21
.0285
1.14
1.16
1.29
1.22
22
.0253
1.02
1.03
1.15 1.08
23
.0226
.906
.918
1.02 .966
24
.0201
.807
.817
.911 .860
25
.0179
.718
.728
.811 i .766
26
.0159
.640
.648
.722
.682
27
.0142
.570
.577
.643
.608
28
.0126
.507
.514
.573
.541
29
.0113
.452
.458
.510
.482
30
.0100
.402
.408
.454
.429
31
.0089
.358
.363
.404
.382
32
.0080
.319
.323
.360
.340
33
.0071
.284
.288
.321
.303
34
.O063
.253
.256
.286
.270
35
.0056
.225
.228
.254
.240
As there sre many gauges in use differing from each other, and even the thicknesses of a
certain specified gauge, ss the Birmingham, are not assumed the same by all manufacturers,
orders for sheets ana wire should always state the weight per square foot, or the thickness
^ in thousandths of an inch.
AREAS and CIRCUMFERENCES OF CIRCLES.
For Diameters from -fe to 100, advancing by Tenths.
Diam.
Area.
Circum.
Diam.
Area.
Circum.
0.0
4.0
12.5664
12.5664
.1
.007854
.31416
.1
13.2025
12.8805
.2
.031416
.62832
.2
13.8544
13.1947
.3
.070686
.94248
.3
14.5220
13.5088
.4
.12566
1.2566
.4
15.2053
13.8230
.5
.19635
1.5708
.5
15.9043
14.1372
.6
.28274
1.8850
.6
16.6190
14.4513
.7
.38485
2.1991
.7
17.3494
147655
.8
.50266
2.5133
.8
18.0956
15.0796
.9
.63617
2.8274
.9
18.8574
15.3938
1.0
.7854
3.1416
5.0
19.6350
15.7080
.1
.9503
3.4558
.1
20.4282
16.0221
.2
1.1310
3.7699
.2
21.2372
16.3363
.3
1.3273
4.0841
.3
22.0618
16.6504
j
1.5394
4.3982
.4
22.9022
16.9646
.5
1.7671
4.7124
.5
23.7583
17.2788
.6
2.0106
5.0265
.6
24.6301
17.5929
.7
2.2698
5.3407
.7
25.5176
17.9071
.8
2.5447
5.6549
.8
26.4208
18.2212
.9
2.8353
5.9690
.9
27.3397
18.5354
2.0
3.1416
6.2832
6.0
28.2743
18.8496
.1
3.4636
6.5973
.1'
29.2247
19.1637
.2
3.8013
6.9115
.2
30.1907
19.4779
.3
4.1548
7.2257
.3
31.1725
19.7920
.4
4.5239
7.5398
.4
32.1699
i 20.1062
.5
4.9087
7.8540
.5
33.1831
20.4204
.6
5.3093
8.1681
.6
34.2119
20.7345
.7
5.7256
8.4823
.7
35.2565
21.0487.
.8
6.1575
8.7965
.8
36.3168
21.3628
.9
6.6052 1
9.1106
.9
37.3928
| 21.6770
3.0
7.0686
9.4248
7.0
38.4845
21.9911
.1
7.5477
9.7389
.1
39.5919
I 22.3053 .
.2
8.0425
10.0531
.2
40.7150
22.6195
.3
8.5530
10.3673
.3
41.8539
! 22.9336
.4
9.0792
10.6814
43.0084
! 23.2478
.5
3.6211
10.9956
.5
44.1786
1 23.5619
.6
10.1788
11.3097
.6
45.3646
23.8761
.7
10.7521
11.6239
.7
46.5663
: 24.1903
.8
11.3411
11.9381
.8
47.7836
24.5044
r - 9
11.9459
12.2522
.9
49.0167
> 24.8186 .
s
1
12
JLJ ""- a
AKEAS and CIRCUMFERENCES OF CIRCLES.
(CONTINUED.)
Diam.
Area.
Circum.
Diam.
Area. Circum.
8.0 50.2655 25.1327
12.0
113.0973
37.6991
.1 51.5300 25.4469
.1
114.9901
38.0133
.2 52.8102 25.7611
.2
116.8987
38.3274
.3 54.1061 26.0752
.3
118.8229
38.6416
.4 55.4177 26.3894
.4
120.7628
38.9557
.5 56.7450
26.7035
.5
122.7185
39.2699
.6
58.0880
27.0177
.6
124.6898
39.5841
.7
59.4468
27.3319
.7
126.6769
39.8982
.8
60.8212
27.6460
.8
128.6796
40.2124
.9
62.2114
27.9602
.9
130.6981
40.5265
9.0
63.6173
28.2743
13.0
132.7323
40.8407
.1
65.0388
28.5885
.1
134.7822
41.1549
.2
66.4761
28.9027
.2
136.8478
41.4690
.3
67.9291
29f2168
.3
138.9291
41.7832
.4
69.3978
29.5310
.4
141.0261
42.0973
.5
70.8822
29.8451
.5
143.1388
42.4115
.6
72.3823
30.1593
.6
145.2672
42.7257
.7
73.8981
30.4734
.7
147.4114
43.0398
.8
75.4296
30.7876
.8
149.5712
43.3540
9,
76.9769
31.1018
.9
151.7468
43.6681
10.0
78.5398
31.4159
14.0
153.9380
43.9823
.1
80.1185
31.7301
.1
156.1450
44.2965
.2
81.7128
32.0442
.2
158.3677
44.6106
.3
83.3229
32.3584
.3
160.6061
44.9248
.4
84.9487
32.6726
.4
162.8602
45.2389
.5
86.5901
32.9867
.5
165.1300
45.5531
.6
88.2473
33.3009
.6
167.4155
45.8673
.7
89.9202
33.6150
.7
169.7167
46.1814
.8
91.6088
33.9292
.8
172.0336
46.4956
.9
93.3132
34.2434
.9
174.3662
46.8097
11.0
95.0332
34.5575
15.0
176.7146
47.1239
.1
96.7689
34.8717
.1
179.0786
47.4380
.2
98.5203
35.1858
.2
181.4584
47.7522
.3
100.2875
35.5000
.3
183.8539
48.0664
.4
102.0703
35.8142
.4
186.2650
48.3805
.5
103.8689
36.1283
.5
188.6919
48.6947
.6 105.6832
36.4425
.6
191.1345
49.0088
.7 107.5132
36.7566
.7 193.5928
49.3230
.8 109.3588 37.0708
.8 196.0668
49.6372
.9 111.2202 i 37.3850
.9 198.5565 49.9513 c
1
3 ^
8
AREAS and CIRCUMFERENCES OP CIRCLES.
(CONTINUED.)
Diam. Area.
Circum.
Diam.
Area.
Circum.
16.0 201.0619
50.2655
20.0
314.1593
62.8319
.1 203.5831
50.5796
.1
317.3087
63.1460
.2 206.1199
50.8938
.2
320.4739
63.4602
.3 , 208.6724
51.2080
.3
323.6547
63.7743
.4 ! 211.2407
51.5221
.4
326.8513
64.0885
.5 213.8246
51.8363
.5
330'.0636
64.4026
.6 216.4243
52.1504
.6
333.2916
64.7168
.7 219.0397
52.4646
.7
336.5353
65.0310
.8 221.6708
52.7788
.8
339.7947
65.3451
.9
224.3176
53.0929
.9
343.0698
65.6593
17.0 226.9801
53.4071
21.0
346.3606
65.9734
.1 ; 229.6583
53.7212
.1
349.6671
66.2876
.2 232.3522
54.0354
.2
352.9894
66.6018
.3 i 235.0618
54.3496
.3
356.3273
66 9159
.4 ! 237.7871
54.6637
.4
359.6809
67.2301
.5
240.5282
54.9779
.5
363.0503
67.5442
.6
243.2849
55.2920
366.4354
67.8584
.7
246.0574
55.6062
369.8361
68.1726
.8
248.8456
55.9203
!s
373.2526
68.4867
.9
251.6494
56.2345
.9
376.6848
68.8009
18.0
254.4690
56.5486
22.0
380.1327
69.1150
.1
257.3043
56.8628
.1
383.5963
69.4292
.2
260.1553
57.1770
.2
387.0756
69.7434
.3
263.0220
57.4911
.3
390.5707
70.0575
.4
265.9044
57.8053
.4
394.0814
70.3717
.5
268.8025
58.1195
.5
397.6078
70.6858
.6
271.7164
58.4836
.6
401.1500
71.0000
.7
274.6459
58.7478
.7
404.7078
71.3142
.8
277.5911
59.0619
.8
408.2814
71.6283
.9
280.5521
59.3761
411.8707
71.9425
19.0
283.5287
59.6903
23.0
415.4756
72.2566
.1
286.5211
60.0044
.1
419.0963
72.5708
.2
289.5292
60.3186
.2
422.7327
72.8849
.3 292.5530
60.6327
.3
426.3848
73.1991
.4 295.5925
60.9469
A
430.0526
73.5133
.5
298.6477
61.2611
.5
433.7361
73.8274
.6 301.7186
61.5752
.6
437.4354
74.1416
.7 304.8052
61.8894
.7
441.1503
74.4557
.8 ! 307.9075
62.2035
.8
444.8809
74.7699
.9 311.0255
62.5177
.9
448.6273
75.0841 .
11
'>L
? "
AREAS and CIRCUMFERENCES OF CIRCLES.
(CONTINUED.)
Diam.
Area. Circum.
Diam.
Area.
Circum.
24.0
452.3893 75.3982
28.0
615.7522
87.9646
.1
456.1671 75.7124
.1
620.1582
88.2788
.2
459.9606 76.0265
.2
624.5800
88.5929
.3
463.7698 76.3407
.3
629.0175
88.9071
.4
467.5947 76.6549
.4
633.4707
89.2212
.5
471.4352 76.9690
.5
637.9397
89.5354
.6
475.2916 77.2832
.6
642.4243
89.8495
ry
479.1636 77.5973
.7
646.9246
90.1637
is
483.0513 77.9115
.8
651.4407
90.4779
.9
486.9547 78.2257
9
655.9724
90.7920
25.0
490.8739 ' 78.5398
29.0
660.5199
91.1062
.1
494.8087 78.8540
.1
665.0830
91.4203
a
498.7592 79.1681
.2
669.6619
91.7345
Is
502.7255 79.4823
.3
674.2565
92.0487
- .4
506.7075 79.7965
.4
678.8668
92.3628
.5
510.7052 80.1106
.5
683.4928
92.6770
.6
514.7185 80.4248
.6
688.1345
92.9911
.7
518.7476 80.7389
.7
692.7919
93.3053
.8
522.7924 81.0531
.8
697.4650
93.6195
.9
526.8529 81.3672
.9
702.1538
93.9336
26.0
530.9292 81.6814
30.0
706.8583
94.2478
.1
535.0211 81.9956
.1
711.5786 94.5619
.2
539.1287 82.3097
.2
716.3145 94.8761
.3
543.2521 82.6239
.3
721.0662 95.1903
.4
547.3911 82.9380
.4
725.8336 95.5044
.5
551.5459 83.2522
.5
730.6167 95.8186
.6
555.7163 83.5664
.6
735.4154 96.1327
.7
559.9025 83.8805
.7
740.2299 96.4469
.8
564.1044 84.1947
.8
745.0601 96.7611
.9
568.3220 84.5088
.9
749.9060 97.0752
27.0
572.5553 ! 84.8230
31.0
754.7676 97.3894
.1
576.8043 85.1372
.1
759.6450 97.7035
.2
581.0690 85.4513
.2
764.5380 98.0177
.3
585.3494 85.7655
.3
769.4467 98.3319
.4
589.6455 ; 86.0796
.4
774.3712 98.6460
.5
593.9574 86.3938
.5
779.3113 98.9602
.6
598.2849 86.7080
.6
784.2672 99.2743
.7
602.6282 87.0221
.7
789.2388 99.5885
.8
606.9871 87.3363
.8
794.2260 99.9026
9 -9
611.3618 87.6504
.9
799.2290 100.2168 ,
! I
AREAS and CIRCUMFERENCES OF CIRCLES.
(CONTINUED.)
Diam.
Area.
Oircum.
Diam. Area.
Oircum.
32.0 804.2477
100.5310
36.0 1017.8760 .
113.0973
.1
809.2821
100.8451
.1
1088.6887
113.4115
.2
814.3322
101.1593
.2
1029.2172
113.7257
.3
819.3980
101.4734
.3
1034.9113
114.0398
.4
824.4796
101.7876
.4
1040.6212
114.3540
.5
829.5768
102.1018
.5
1046.3467
114.6681
.6
834.6898
102.4159
.6
1052.0880
114.9823
.7
839.8185
102.7301
.7
1057.8449
115.2965
.8
844.9628
103.0442
.8
1063.6176
115.6106
.9
850.1229
103.3584
.9
1069.4060
115.9248
33.0
855.2986
103.6726
37.0
1075.2101
116.2389
.1
860.4902
103.9867
.1
1081.0299
116.5531
.2
865.6973
104.3009
.2
1086.8654
116.8672
.3
870.9202
104.6150
.3
1092.7166
117.1814
.4
876.1588
104.9292
.4
1098.5835
117.4956
.5
881.4131
105.2434
1104.4662
117.8097
.6
886.6831
105.5575
.6
1110.3645
118.1239
.7
891.9688
105.8717
.7
1116.2786
118.4380
.8
897.2703
106.1858
1122.2083
118.7522
.9
902.5874
106.5000
.9
1128.1538
119.0664
34.0
907.9203
106.8142
38.0
1134.1149
119.3805
.1
913.2688
107.1283
.1
1140.0918 ' 119.6947
.2
918.6331
107.4425
.2
1146.0844
120.0088
.3
924.0131
107.7566
.3
1152.0927
120.3230
.4
929.4088
108.0708
.4
1158.1167
120.6372
.5
934.8202
108.3849
.5
1164.1564
120.9513
.6
940.2473
108.6991
.6
1170.2118
121.2655
.7
945.6901
109.0133
.7
1176.2830
121.5796
.8
951.1486
109.3274
.8
1182.3698
121.8938
.9
956.6228
109.6416
.9
1188.4724
122.2080
35.0
962.1128 -
109.9557
39.0
1194.5906
122.5221
.1
967.6184
110.2699
.1
1200.7246
122.8363
.2
973.1397
110.5841
.2
1206.8742
123.1504
.3
978.6768
110.8982
.3
1213.0396
123.4646
.4
984.2296
111.2124
.4
1219.2207
123.7788
.5
989.7980
111.5265
.5
1225.4175
124.0929
.6
995.3822
111.8407
.6
1231.6300 ' 124.4071
.7
1000.9821
112.1549
.7
1237.8582 124.7212
.8
1006.5977
112.4690
.8
1244.1021 125.0354
.9
1012.2290 112.7832
.9 1250.3617 ! 125.3495
AREAS and CIRCUMFERENCES OF CIRCLES.
i (CONTINUED.)
Diam.
Area.
Circum.
Diam.
Area.
Circum.
40.0
1256.6371
125.6637
44.0 1520.5308
138.2301
.1
1262.9281
125.9779
.1 1527.4502
138.5442
.2
1269.2348
126.2920
.2 1534.3853
138.8584
.3 I 1275.5573
126.6062
.3
1541.3360 139.1726
.4 1281.8955
126.9203
.4
1548.3025 ; 139.4867
.5 1288.2493
127.2345
.5
1555.2847 139.8009
.6 1 1294.6189
127.5487
.6
1562.2826 140.1153
.7 1301.0042
127.8628
.7
1569.2962 140.4292
.8
1307.4052
128.1770
.8
1576.3255 140.7434
.9
1313.8219
128.4911
.9
1583.3706 141.0575
41.0
1320.2543
128.8053
45.0
1590.4313 141.3717
.1
1326.7024
129.1195
.1
1597.5077 | 141.6858
JB
1333.1663
129.4336
.2
1604.5999 142.0000
.3
1339.6458
129.7478
.3
1611.7077 142.3142
4
1346.1410
130.0619
.4
1618.8313
142.6283
.5
1352.6520
130.3761
.5
1625.9705
142.9425
.6
1359.1786
130.6903
.6
1633.1255
143.2566
.7
1365.7210
131.0044
.7
1640.2962
143.5708
.8
1372.2791
131.3186
.8
1647.4826
143.8849
.9
1378.8529
131.6327
.9
1654.6847
144.1991
42.0
1385.4424
131.9469
46.0
1661.9025
144.5133
i
1392.0476
132.2611
.1
1669.1360
144.8274
J8
1398.6685
132.5752
.2
1676.3853
145.1416
.3
1405.3051
132.8894
.3
1683.6502
145.4557
.4 1411.9574 .
133.2035
.4
1690.9308
145.7699
.5 1418.6254
133.5177
.5
1698.2272
146.0841
.6
1425.3092
133.8318
.6
1705.5392
146.3982
.7
1432.0086
134.1460
.7
1712.8670
146.7124
.8
1438.7838
134.4602
.8
1720.2105 147.0265
.9
1445.4546
134.7743
.9
1727.5697
147.3407
43.0
1452.2012
135.0885
47.0
1734.9445
147.6550
.1
1458.9635
135.4026
.1
1742.3351
147.9690
.2
1465.7415
135.7168
.2
1749.7414
148.2832
.3
1472.5352
136.0310
.3
1757.1635
148.5973
.4
1479.3446
136,3451
.4
1764.6012
148.9115
.5
1486.1697
136.6593
.5
1772.0546
149.2257
.6
1493.0105
136.9734
.6 1779.5237 149.5398
.7
1499.8670
137.2876
.7
1787.0086 149.8540
.8 1506.7393
137.6018
.8
1794.5091 150.1681
.9 ! 1513.6272
137.9159
.9 1802.0254 150.4823 .
v l,
AREAS and CIRCUMFERENCES OP CIRCLES.
(CONTINUED.)
Diam.
Area. Circum.
Diam.
Area. Circum.
48.0
1809.5574
150.7964
52.0
2123.7166 163.3628
.1
1817.1050
151.1106
.1
2131.8926 i 163.6770
.2
1824.6684
151.4248
.2
2140.0843 : 163.9911
.3
1832.2475
151.7389
.3
2148.2917 164.3053
.4
1839.8423
152.0531
.4
2156.5149 164.6195
.5
1847.4528
152.3672
.5
2164.7537 164.9336
.6
1855.0790
152.6814
.6
2173.0082 i 165.2479
.7
1862.7210
152.9956
.7
2181.2785 i 165.5619
.8
1870.3786
153.3097
.8
2189.5644 165.8761
.9
1878.0519
153.6239
.9
2197.8661 166.1903
49.0
1885.74C9
163.9380
53.0
2206.1834 : 166.5044
.1
1893.4457
154.2522
.1
2214.5165 : 166.8186
.2
1901.1662
154.5664
G)
2222.8653 j 167.1327
.3
1908.9024
154.8805
]3
2231.2298 167.4469
.4
1916.6543
155.1947
.4
2239.6100 167.7610
.5
1924.4218
155.5088
.5
2248.0059 i 168.0752
.6
1932.2051
155.8230
.6
2256.4175 168.3894
.7 1940.0042
156.1372
.7
2264.8448 168.7035
.8 ! 1947.8189 1 156.4513
.8
2273.2879 : 169.0177
.9
1955.6493
156.7655
.9
2281.7466 169.3318
50.0
1963.4954
157.0796
54.0
2290.2210 169.6460
.1
1971.3572
157.3938
.1
2298.7112 169.9602
.2
1979.2348 157.7080
.2
2307.2171 170.2743
.3
1987.1280 158.0221
.3
2315.7386 170.5885
A
1995.0370 158.3363
.4
2324.2759 170.9026
.5
2002.9617 158.6504
.5
2332.8289 171.2168
.6 2010.9020 158.9646
.6
2341.3976 171.5310
.7 2018.8581 ! 159.2787
.7
2349.9820 171.8451
.8 2026.8299 159.5929
.8
2358.5821 172.1593
.9 2034.8174 159.9071
.9
2367.1979 172.4735
51.0 2042.8206 i 160.2212
55.0
2375.8294 ! 172.7876
.1 2050.8395 \ 160.5354
.1
2384.4767 173.1017
.2 2058.8742 160.8495
.2
2393.1396 173.4159
.3 2066.9245 161.1637
.3
2401.8183 173.7301
.4 2074.9905 161.4779
.4
2410.5126 , 174.0442
2083.0723 161.7920
.5
2419.2227 ! 174.3584
.6 i 2091.1697 162.1062
.6
2427.9485 174.6726
.7 I 2099.2829 162.4203
.7
2436.6899 174.9867
.8 i 2107.4118 162.7345
.8
2445.4471 \ 175.3009
.9 ! 2115.5563 163.0487 .9
2454.2200 ' 175.6150 ,
<
AREAS and CIRCUMFERENCES OF CIRCLES.
(CONTINUED.)
Diam.
Area. Circum.
Diam. Area. Circum.
56.0 2463.0086 175.9292
60.0 ; 2827.4334 188.4956
.1 2471.8130
176.2433
.1 2836.8660 188.8097
.2 2480.6330
176.5575
.2 2846.3144 189.1239
.3 2489.4687
176.8717
.3 2855.7784 ; 189.4380
.4
2498.3201
177.1858
.4
2865.2582 189.7522
.5
2507.1873
177.5000
.5
2874.7536 | 190.0664
.6
2516.0701
177.8141
.6
2884.2648
190.3805
.7
2524.9687
178.1283
.7
2893.7917
190.6947
.8
2533.8830
178.4425
.8
2903.3343
191.0088
.9
2542.8129
178.7566
.9
2912.8926
191.3230
57.0
2551.7586
179.0708
61.0
2922.4686
191.6372
.1
2560.7200
179.3849
.1
2932.0563
191.9513
.2
2569.6971
179.6991
.2
2941.6617
192.2655
.3
2578.6899
180.0133
.3
2951.2828
192.5796
.4
2587.6985
180.3274
.4
2960.9197
192.8938
.5
2596.7227
180.6416
.5
2970.5722
193.2079
.6
2605.7626
180.9557
.6
2980.2405
193.5221
.7
2614.8183
181.2699
.7
2989.9244
193.8363
.8
2623.8896
181.5841
.8
2999.6241
194.1504
.9
2632.9767
181.8982
.9
3009.3395
194.4646
58.0
2642.0794 182.2124
62.0
3019.0705
194.7787
.1
2651.1979 182.5265
.1
3028.8173
195.0929
.2
2660.3321 182.8407
2
3038.5798
195.4071
.3
2669.4820 ! 183.1549
.3
3048.3580
195.7212
.4
2678.6476 183.4690
.4 3058.1520
196.0354
.5
2687.8289 183.7832
.5 3087.9616
196.3495
.6
2697.0259
184.0973
.6 3077.7869
196.6637
.7
2708.2386
184.4115
.7 3087.6279
196.9779
.8
2715.4670 184.7256
.8 3097.4847
197.2920
.9 2724.7112 185.0398
.9 3107.3571 i 197.6062
59.0 2733.9710 185.3540
63.0 3117.2453 197.9203
.1 2743.2466 185.6681
.1 : 3127.1492 198.2345
.2 2752.5378 i 185.9823
.2 3137.0688 I 198.5487
.3 2761.8448 186.2964
.3 3147.0040 ! 198.8628
.4 2771.1675 186.6106
.4 3156.9550 199.1770
.5 2780.5058 186.9248
.5 3166.9217 199.4911
.6 2789.8599 , 187.2389
.6 3176.9043 l , 199.8053
.7 1 2799.2297 , 187.5531
.7 3186.9023
200.1195
.8 2808.6152 ; 187.8672
.8 3196.9161
200.4336
.9 2818.0165 188.1814
.9 3206.9456
200.7478 ,
119 *-
AREAS and CIRCUMFERENCES OP CIRCLES.
(CONTINUED.)
Diam.
Area.
Circum.
Diam.
Area. Circum.
64.0 3216.9909 201.0620
68.0
3631.6811 j 213.6283
.1
3227.0518 201.3761
.1
3642.3704 , 213.9425
.2
3237.1285
201.6902
.2
3653.0754 214.2566
.3
3247.2222
202.0044
.3
3663.7960
214.5708
.4
3257.3289
202.3186
.4
3674.5324
214.8849
.5
3267.4527
202.6327
.5
3685.2845
215.1991
.6
3277.5922
202.9469
.6
3696.0523
215.5133
.7
3287.7474
203.2610
.7
3706.8359
215.8274
.8
3297.9183
203.5752
.8
3717.6351
216.1416
.9
3308.1049
203.8894
.9
3728.4500
216.4556
65.0
3318.3072
204.2035
69.0
3739.2807
216.7699
.1
3328.5253
204.5176
.1
3750.1270
217.0841
.2
3338.7590
204.8318
.2
3760.9891
217.3982
.3
3349.0085
205.1460
.3
3771.8668
217.7124
.4
3359.2736
205.4602
.4
3782.7603
218.0265
.5
3369.5545
205.7743
.5
3793.6695
218.3407
.6
3379.8510
206.0885
.6
3804.5944
218.6548
.7
3390.1633
206.4026
.7
3815.5350
218.9690
.8
3400.4913
206.7168
.8
3826.4913
219.2832
.9
3410.8350
207.0310
.9
3837.4633
219.5973
66.0
3421.1944
207.3451
70.0
3848.4510
219.9115
.1
3431.5695
207.6593
.1
3859.4544
220.2256
.2
3441.9603
207.9734
.2
3870.4736
220.5398
.3
3452.3669
208.2876
.3
3881.5084
220.8540
.4
3462.7891
208.6017
.4
3892.5590
221.1681
.5
3473.2270
208.9159
.5
3903.6252
221.4823
.6
3483.6807
209.2301
.6
3914.7072
221.7964
.7
3494.1500
209.5442
.7
3925.8049
222.1106
.8
3504.6351
209.8584
.8
3936.9182
222.4248
.9
3515.1359
210.1725
.9
3948.0473
222.7389
67,0
3525.6524
210.4867
71.0
3959.1921
223.0531
.1
3536.1845
210.8009
.1
3970.3526
223.3672
.2
3546.7324
211.1150
.2
3981.5289
223.6814 t
.3
3557.2960
211.4292
.3
3992.7208
223.9956
.4
3567.8754
211.7433
.4
4003.9284
224.3097
.5
3578.4704
212.0575
.5
4015.1518
224.6239
.6
3589.0811
212.3717
.6
4026.3908
224.9380
.7
3599.7075
212.6858
.7
4037.6456
225.2522
.8
3610.3497
213.0000
.8
4048.9160
225.5664
. .9
3621.0075
21&3141
.9
4060.2022
225.8805 ,
AREAS and CIRCUMFERENCES OP CIRCLES.
(CONTINUED.)
Diam.
Area.
Circum.
Diam.
Area.
Circum.
72.0
4071.5041
226.1947
76.0
4536.4598
238.7610
.1
4082.8217
226.5088
.1
4548.4057 239.0752
.2
4094.1550
226.8230
.2
4560.3673
239.3894
4105.5040
227.1371
.3
4572.3446
239.7035
'.4
4116.8687
227.4513
.4
4584.3377
240.0177
.5
4128.2491
227.7655
.5
4596.3464
240.3318
.6
4139.6452
228.0796
.6
4608.3708
240.6460
.7
4151.0571
228.3938
.7
4620.4110
240.9602
.8
4162.4846
228.7079
.8
4632.4669
241.2743
.9
4173.9279
. 229.0221
.9
4644.5384
241.5885
73.0
4185.3868
229.3363
77.0
4656.6257
241.9026
.1
4196.8615
229.6504
.1
4668.7287
242.2168
.2
4208.3519
229.9646
.2
4680.8474
242.5310
.3
4219.8579
230.2787
.3
4692.9818
242.8451
.4
4231.3797
230.5929
.4
4705.1319
243.1592
.5
4242.9172
230.9071
.5
4717.2977
243.4734
.6
4254.4704
231.2212
.6
4729.4792
243.7876
.7
4266.0394
231.5354
"7
4741.6765
244.1017
.8
4277.6240
231.8495-
4753.8894
244.4159
.9
4289.2243
232.1637
.9
4766.1181
244.7301
74.0
4300.8403
232.4779
78.0
4778.3624
245.0442
A
4312.4721
232.7920
.1
4790.6225
245.3584
9
&
4324.1195
233.1062
.2
4802.8983
245.6725
.3
4335.7827
233.4203
.3
4815.1897
245.9867
.4
.4347.4616
233.7345
.4
4827.4969
246.3009
.5
4359.1562
234.0487
.5
4839.8198
246.6150
.6
4370.8664
234.3628
.6
4852.1584
246.9292
.7
4382.5924
234.6770
.7
4864.5128 247.2433
.8
4394.3341
234.9911
.8
4876.8828 247.5575
.9
4406.0916
235.3053
.9
4889.2685 1 247.8717
75.0
4417.8647
235.6194
79.0 4901.6699 248.1858
.1
' 4429.6535
235.9336
.1 i 4914.0871 ! 248.5000
.2
4441.4580
236.2478
.2 ! 4926.5199 248.8141
.3
4453.2783
. 236.5619
.3 4938.9685 249.1283
.4
4465.1142
236.8761
.4 i 4951.4328 249.4425
.5
4476.9659
237.1902
.5 4963.9127 249.7566
.6
4488.8332
237.5044
.6 4976.4084 , 250.0708
.7
4500.7163
237.8186
.7 4988.9198 250.3850
.8
4512.6151
238.1327
.8 5001.4469 250.6991
.9
4524.5296
238.4469
.9 5013.9897 251.0133
J E
AREAS and CIRCUMFERENCES OF CIRCLES.
(CONTINUED.)
Diam.
Area.
Circum.
Diam. Area.
Circum.
80.0 5026.5482
251.3274
84.0 5541.7694
263.8938
.1 5039.1225
251.6416
.1 5554.9720
264.2079
.2 5051.7124
251.9557
.2 5568.1902
264.5221
.3 5064.3180
252.2699
.3 5581.4242
264.8363
.4 5076.9394
252.5840
.4
5594.6739 285.1514
.5 5089.5764
252.8982
.5
5607.9392 265.4646
.6 5102.2292
253.2124
.6
5821.2203
265.7787
.7 5114.8977
253.5265
.7
5634.5171
266.0929
.8 5127.5819
.253.8407
.8
5647.8296
266.4071
.9 5140.2818
254.1548
.9
5661.1578
266.7212
81.0 5152.9973
254.4690
85.0
5874.5017
267.0354
.1 5165.7287
254.7832
.1
5687.8614
267.3495
.2 5178.4757
255.0973
.2
5701.2367
267.6637
.3 | 5191.2384
255.4115
.3
5714.6277
267.9779
.4 5204.0168
255.7256
.4
5728.0345
268.2920
.5 ! 5216.8110
256.0398
.5
5741.4569
268.6062
.6 5229.6208
256.3540
.6
5754.8951
268.9203
.7 5242.4463
256.6681
.7
5768.3490
269.2345
.8 5255.2876
256.9823
.8
5781.8185
269.5486
.9 5268.1446
257.2966
.9
5795.3038 269.8628
82.0
5281.0173
257.6106
86.0
5808.8048 270.1770
.1
5293.9056
257.9247
.1
5822.3215 270.4911
.2
5308.8097
258.2389
.2
5835.8539 270.8053
.3
5319.7295
258.5531
.3
5849.4020 j 271.1194
.4
5332.6650
258.8672
.4
5862.9659 : 271.4336
.5
5345.6162
259.1814
.5
5876.5454 ! 271.7478
.6
5358.5832
259.4956
.6
5890.1407 : 272.0619
.7
5371.5658
259.8097
.7
5903.7516 1 272.3761
.8
5384.5641
280.1239
.8 5917.3783 1 272.6902
.9
5397.5782
260.4380
.9 5931.0208 i 273.0044
83.0
5410.6079
260.7522
87.0 i 5944.6787 ' 273.3186
.1
5423.6534
261.0663
.1 ' 5958.3525 i 273.6327
.2
5436.7146
261.3805
.2 5972.0420 ! 273.9469
.3
5449.7915
261.6947
.3 5985.7472 ; 274.2610
.4
5462.8840
262.0088
.4 5999.4681 274.5752
.5
5475.9923
262.3230
.5 6013.2047 274.8894
.6 5489.1163
262.6371
.6 6026.9570 275.2035
.7 5502.2561
262.9513
.7 i 6040.7250 ! 275.5177
.8 5515.4115
263.2655
.8 i 6054.5088 ! 275.8318
.9 5528.5826
263.5796
.9 6088.3082 : 276.1460 .
AREAS and CIRCUMFERENCES OF CIRCLES,
(CONTINUED.)
Diam.
Area.
Circum.
Diam.
Area.
Circum.
88.0 6082.1234
276.4602
92.0
6647.6101
289.0265
.1
6095.9542
276.7743
.1
6662.0692
289.3407
.2
6109.8008
277.0885
.2
6676.5441
289.6548
.3
6123.6631
277.4026
.3
6691.0347
289.9690
.4
6137.5411
277.7168
.4
6705.5410
290.2832
.5
6151.4348
278.0309
.5
6720.0630 290.5973
.6
6165.3442
278.3451
.6
6734.6008
290.9115
.7
6179.2693
278.6593
.7
6749.1542
291.2256
.8
6193.2101
278.9740
.8
6763.7233 291.5398
.9
6207.1666
279.2876
.9
6778.3082 ! 291.8540
89.0
6221.1389
279.6017
93.0
6792.9087 I 292.1681
.1
6235.1268
279.9159
.1
6807.5250 292.4823
.2
6249.1304
280.2301
.2
6822.1569 292.7964
.3
6263.1498
280.5442
.3
6836.8046 293.1106
.4
6277.1849
280.8584
.4
6851.4680 293.4248
.5
6291.2356
281.1725
.5
6866.1471 293.7389
.6
6305.3021
281.4867
.6
6880.8419 294.0531
.7
6319.3843
281.8009
.7
6895.5524
294.3672
.8
6333.4822
282.1150
.8
6910.2786
294.6814
.9
6347.5958
282.4292
.9
6925.0205 294.9956
90.0
6361.7251
282.7433
94.0
6939.7782
295.3097
.1
6375.8701
283.0575
.1
6954.5515
295.6239
.2
6390.0309
283.3717
.2
6969.3106 295.9380
.3
6404.2073
283.6858
.3
6984.1453 i 296.2522
.4
6418.3995
284.0000
.4
6998.9658
296.5663
.5
6432.6073
284.3141
.5
7013.8019
296.8805
.6
6446.8309
284.6283
.6
7028.6538
297.1947
.7
6461.0701 284.9425
.7
7043.5214
297.5088
.8
6475.3251 285.2566
.8
7058.4047
297.8230
.9
6489.5958
285.5708
.9
7073.3033
298.1371
91.0
6503.8822
285.8849
95.0
7088.2184
298.4513
.1
6518.1843 '
286.1991
.1
7103.1488
298.7655
.2
6532.5021
286.5183
.2
7118.1950
299.0796
.3
6546.8356
286.8274
.3
7133.0568
299.3938
.4
6561.1848
287.1416
.4
7148.0343
299.7079
.5
6575.5498
287.4557
.5
7163.0276
300.0221
.6
6589.9304
287.7699
.6
.7178.0366
300.3363
.7
6604.3268
288.0840
.7
7193.0612
300.6504
.8
6618.7388
288.3982
.8
7208.1016
300.9646
n - ' 9
6633.1666
288.7124
.9
7223.1577
301.2787 .
AREAS and CIRCUMFERENCES OF CIRCLES.
(CONTINUED.)
Diam.
Area.
Circum.
Diam.
Area.
Circum.
96.0
7238.2295
301.5929
98.0
7542.9640
1 307.8761
.1
7253.3170
301.9071
.1
7558.3656
, 308.1902
.2
7268.4202
302.2212
.2
7573.7830
! 308.5044
.3
7283.5391 -
302.5354
.3
7589.2161
308.8186
.4
7298.6737
302.8405
.4
7604.6648
309.1327
.5
7313.8240
303.1637
.5
7620.1293
309.4469
.6
7328.9901
303.4779
.6
7635.6095
309.7610
.7
7344.1718
303.7920
.7
7651.1054
310.0752
.8
7369.3693
304.1062
.8
7666.6170
310.3894
.9
7374.5824
304.4203
.9
7682.1444
i 310.7035
97.0
7389.8113
304.7345
99.0
7697.6893
311.0177
.1
7405.0559
305.0486
.1
7713.2461
1 311.3318
.2
7420.3162
305.3628
.2
7728.8206
311.6460
.3
7435.5922
305.6770
.3
7744.4107
311.9602
.4
7450.8839
305.9911
.4
7760.0166
312.2743
.5
7466.1913
306.3053
.5
7775.6382
312.5885
.6
7481.5144
306.6194
.6
7791.2754
312.9026
ty
7496.8532
306.9336
.7
7806.9284
313.2168
.'s
7512.2078
307.2478
.8
7822.5971
313.5309
.9
7527.5780
307.5619
.9
7838.2815
313.8451
100.0
7853.9816
314.1593
To compute the area or circumference of a diameter greater
than 100 and less than 1001 :
^Takeout the area or circumference from table as though the
m^H&erliacl one decimal, and move the decimal point two places
to the right for the area, and one place for the circumference.
EXAMPLE Wanted the area and circumference of 567. The tabular area for 56.7
is 2524.9687; and circumference 178.1283. Therefore area of 567 = 252496.87 and
circumference = 1781.283.
To compute the area or circumference of a diameter greater
than 1000:
Divide by a factor, as 2, 3, 4, 5, etc., if practicable, that will
leave a quotient to be found in table, then multiply the tabular
area of the quotient by the sqtiare of the factor, or the tabular
circumference by the factor.
EXAMPLE Wanted the area and circumferenee of 2109. Dividing by 3, the quotient
is 703, for which the area is 388150.84 and the circumference 2208.54. Therefore area
of 2109 = 388150.84 X 9 = 3493357.56 and circumference = 2208.54 X 3 = 6625.62.
124
WEIGHT OF RIVETS, and ROUND HEADED
BOLTS WITHOUT NUTS, PER 100.
Length from under head. One cubic foot weighing 480 Ibs.
Length.
yi,
1 A" V %" W '' 1" l}" 1^"
Inches.
Dia.
Dia. Dia. Dia.
Dia.
Dia. Dia. Dia.
Ijf
5.4
12.6 21.5
28.7
43.1
65.3 91.5 123.
1/12 ;
6.2
13.9 23.7
31.8
47.3
70.7 98.4
133.
IX
6.9
15.3
25.8
34.9
51.4
76.2 105.
142.
2
7.7
16.6
27.9
37.9
55.6
81.6 112.
150.
2^ ^
8.5
18.0
30.0
41.0
59.8
87.1
119.
159.
2^1
9.2
19.4
32.2 44.1
63.0
92.5
126.
167.
10.0 20.7
34.3 47.1
68.1'
98.0
133.
176.
3 4
10.8 i 22.1
36.4 j 50.2
72.3
103.
140.
.184.
3J4
11.5 23.5
38.6 53.3
76.5
109.
147. 193.
3X
12.3 24.8 40.7 56.4 80.7 114.
154. I 201.
3%
13.1 i 26.2 42.8 59.4 84.8 120.
161. i 210.
4
13.8 27.5 ; 45.0 62.5 \ 89.0 , 125.
167. ! 218.
4^
14.6 i 28.9 ' 47.1
65.6 ! 93.2 131.
174. 227.
41^
15.4 30.3 i 49.2
68.6 ! 97.4 136.
181. ; 236.
4%
16.2 31.6 51.4
71.7
102.
142.
188. 244.
5
16.9 33.0 53.5
74.8
106.
147.
195.
253.
5M
17.7
34.4
55.6
77.8
110.
153.
202.
261.
5)-^
18.4
35.7
57.7
80.9
114.
158. ! 209.
270.
5%
19.2
37.1
59.9
84.0
118.
163.
216.
278.
6
20.0
38.5
62.0 87.0
122.
169.
223.
287.
6j
21.5 41.2
66.3
93.2
131.
180.
236.
304.
7 "
23.0 43.9
70.5
99.3
139.
191.
250.
321.
7/12
24.6
46.6
74.8
106.
147.
202.
264.
338.
8
26.1 49.4
79.0
112.
156.
213.
278.
355.
S 1 ^
27.6
52.1
83.3
118.
164.
223.
292.
372.
9"
29.2
54.8
87.6
124.
173.
234.
306.
389.
9}<2
30.7
57.6
91.8
130.
181.
245.
319.
406.
10
32.2
60.3
96.1
136.
189.
256.
333.
423.
1()1
33.8
63.0
101.
142.
198.
267.
347.
440.
11
35.3
65.7
105.
148.
206.
278.
361.
457.
ll/^
36.8
68.5
109.
155.
214.
289.
375.
474.
12
38.4
71.2
113.
161.
223.
300.
388.
491.
Heads.
1.8
5.7
10.9
13.4'
22.2
38.0
57.0
82.0
v
I
"Yj
UPSET SCREW ENDS FOR
ROUND AND
SQUARE BARS.
Standard Proportions of the Keystone Bridge Company.
Dia. of
Round or
Side of
Square
Bar.
Inches.
ROUND BARS.
SQUARE BARS.
Dia. of
Upset
Screw
End.
Inches.
Dia. of
Screw at
Root of
Thread.
Inches.
Threads
per Inch.
No.
Excess of
Effective
Area of
Screw End
over Bar.
Per Cent.
Dia. of
Upset
Screw
End.
Inches.
Dia. of
Screw at
Root of
Thread.
Inches.
Excess of
Threads i ^J
0< t over Bar.
j Per Cent.
A
X .620 i 10
X -620 10
54
21
I
.620
.731
10 21
9 33
If
% .731 9 37
1 .837 8 48
i
i
.837 8 41
.837 8 17
it
1 .837 8
1M .940 i 7
25
34
W
.940 7
1.065 7
23
35
i!
IK ! 1.065 7
W ! 1.065 7
48
29
1
1.160 6
1.160- 6
38
20
i
IA
IK 1-160 6
1% 1-160 6
35
19
!
1.284 6
1.389 5^
29
34
j
1)1
1.284
1.284
6
6
30
17
IS
1.389 5^
1.490 5
20
24
IA
}|
1.389
1.490
5 2
23
29
11
1.615
1.615
5
5
31
19
}g
i
1.490
1.615
5
5
18
26
2
1.712
1.837
*&
22
28
IA
2
2
1.712
1.712
$
36
20
1!
1.837
1.962
*&
18
24
iff
%
1.837
1.837
$
28
18
If
2.087
2.087
4K
80
20
Iff.
3$
1.962
1.962
*%
26
17
9 1/
673
2.175
2.300
4
4
21
26
i
S*
2,087
2.175
4 2
24
26
i
2.300
2.425
4
4
18
23
2
If
2.175 i 4
2.300 4
18
24
2%
2.550
2.550
4
4
28
20
1
2.300
2.425
j
4
17
23
fc.
2.629
2.754
1
20
24
^TJ
UPSET SCREW ENDS.
(CONTINUED.)
Dia. of
ROUND BARS.
SQUARE BARS.
Round or
Side of
Square
Bar.
Inches.
Dia. of Dia. of
Upset Screw at
Screw Root of
End. ; Thread.
Inches. Inches.
Threads
per Inch.
No.
Excess of
Effective
Area of
Screw End
over Bar.
Per Cent.
Dia. of
Upset
Screw
End.
Inches.
Dia. of
Screw at
Root of
Thread.
Inches.
Threads
per Inch.
No.
Excess of
Effective
Area of
Screw End
over Bar.
Per Cent.
~2K~
2 7
2.550
4
28
m
2.754
3K
18
2fV
2%
2.550
4
22
3%
2.879
3/1
22
gS/
3
2.629
3^
23
3%
3.004
3K
26
gJL
3)8
2.754
3>2
28
3.004
3jl>
19
l%
3^5
2.754
21
3M
3.100
3^ I 21
3}^ 2.879
3J
26
3^
3.225
3K 24
2%
3i/
2.879
3>
20
3%
3.225
314 19
3K
3.004
3K
25
8g
3.317
3
20
2%
3/8
3.004
3/
19
3K
3.442
3 ,
23
3>
3.100
3^
22
%
3.442
3
18
2%
3%
3.225
3^f
26
4
3.567
3
21
3.225
3K
21
413
3.692
3
24
3
32/
3.317
3
22
4 3 8 '
3.692
3
19
3%
3.442
3
21
3.923
2%
24
3L/ !
4
3.567
3
20
4%
4.028
2%
21
3M
4>8
3.692
3-
20
4%$
4.153
19
3^
414
'3.798
2%
18
3%
4/i>
4.028
23
3K
w
4.153
2%
23
3% .
K
4.255
m
21
EEMARKS. As
upsetting reduces the strength of iron, bars
having the same diameter at
root of thread as that of the bar, in-
variably break in the screw end, when tested to destruction, without
developing the full strength of the bar. It is therefore necessary to
make up for this loss in strength by an excess of metal in the upset
screw ends over that
in the b
ar.
The above table ii
! the ree
tilt of numerous tests on finished bars
made at the Keystone Bridge Company's Works in Pittsburgh, and gives
proportions that will cause the bar to break in the body in preference
to the upset end.
The screw threads in above table are the Franklin Institute standard.
To make one upset end for 5" length of thread allow 6" length of
rod additional.
197 4
STANDARD SCREW THREADS, NUTS AND
BOLT HEADS. Recommended by the Franklin Institute.
SCREW THREADS.
Nuts and Bolt Heads
A?/ ^ ^ ,m
are determined by the fol-
/^ll^a .0 /^ll^ o j //|l||k.
lowing rules, which apply to
" ^ /^HlK.
Square and Hexagon Nuts
both :
^^^^^^J^^^^^^^^^^^^^^^^^^^^
Short diameter of rough nut
Angle of Thread 60. Flat at Top and Bottom^ % of pitch.
= IJ^ x dia, of bolt - y 3 in.
Dia. of
Dia. at Root Threads
Short diameterof finished nut
Screw.
of Thread. per Inch.
= V :< dia. of bolt + 1-18 in.
Inches.
Inches. No.
Thickness of rough nut
i/
.185 20
= diameter of bolt.
5
.240 18
Thickness of finished nut
%
.294 16
= diameter of bolt 1-16 in.
T^ff
.344
14
Short diameter of rough head
y
.400
13
= 1^ X dia. of bolt -f %in.
^
.454
12
Short dia. of finished head
%,
.507
11
=1% x dia. of bolt - 1-16 in.
%
.620
10
Thickness of rough head
%
.731
9
= y 2 short dia. of head.
I
.837
8
Thickness of finished head
.940
7
= dia. of bolt 1-16 in.
1%
1.065
7
The long diameter of a
1%
1.160
6
hexagon nut may be obtained
\y
1.284
6
by multiplying the short
\y
1.389
diameter by 1.155, and the
1 3/
1.490
5
long diameter of a square
10
1.615
5
nut by multiplying the short
2
1.712
diameter by 1.414.
1.962
4 1/
The above standards for
23^
2.175
4 /2
screw threads, nuts and bolt
fc>/2
2.425
4
heads, were recommended by
/4
the Franklin Institute in
3
2.629
aorrrk
3K
Dec. 1864. The standard for
3/^
.879
31 r\/\
3/2
screw threads has been very
i|
.100
3.317
3 4
generally adopted in the
United States, but the pro-
4
3.567
3
portions recommended for
4M
3.798
2
nuts and bolt heads have not
4f^
4.028
found general acceptance be-
4%
4.255
*&
cause of the odd sizes of bar
5 4.480
2>
not usually rolled by the
5^ 4.730
2M
mills which they would re-
5K 5.053
m
quire from which to make
5% 5.203
the nut.
. 6 ! 5.423 2M X
WHITWORTH'S STANDARD ANGULAR
SCREW THREADS.
Angle of Thread 55.
Depth of Thread = pitch of
screw.
Y & of depth is rounded off at
to and bottom.
p
Number of threads to the
inch in square threads = ^ the "number in angular threads.
Dia, of ; Threads
Screw, to the Inch.
In. No.
Dia. of
Screw.
In.
Threads
to the Inch.
No.
Dia. of
Screw.
In.
Threads
to the Inch.
No.
Dia. of
Screw.
In.
Threads
to the Inch.
No.
1-4 20
1
8
2
4 1-2
4
3
5-16 i 18
1 1-8
7
2 1-4
4
4 1-4
2 7-8
3-8 16
1 1-4
7
2 1-2
4
4 1-2
2 7-8
7-16 : 14
1 3-8
6
23-4
3 1-2
4 3-4
2 3-4
|
1-2 i 12
11-2
6
3
3 1-2
5
2 3-4
5-8 11
1 5-8
5
3 1-4
3 1-4
5 1-4
2 5-8
3-4 10
1 3-4
5
3 1-2
3 1-4
5 1-2
2 5-8
7-8 9
1 7-8
4 1-2
3 3-4
3
5 3-4
2 1-2
6
2 1-2
WOOD SCREWS.
Diameter = number X 0.01325 -f 0.056.
No.
Dia.
No.
Dia.
No.
Dia.
No.
Dia.
No.
Dia.
1
2
3
4
5
.056
.069
.082
.096
.109
.122
6
7
8
9
10
11
.135
.149
.162
.175
.188
.201
12
13
11
16
17
.215
.228
.241
.255
.268
.281
18
19
20
21
22
23
.293
.308
.321
.334
.347
.361
24
25
26
27
28
29
30
.374
.387
.401
414
.427
.440
.453
TACKS.
Title.
fe
Length.
In.
No.,
per Ib.
Title.
Oz.
Length.
In.
No.
perlb.
Title.
Oz.
Length.
In.
No.
perlb.
Title.
Oz.
Length.
In.
No.
perlb.
i
1 1-2
2
21-2
1-8
3-16
1-4
5-16
16000
10666
8000
6400
3
4
6
8
3-8
7-16
9-16
5-8
5333
4000
2666
2000
10
12
14
16
11-16
3-4
13-16
7-8
1600
1333
1143
1000
18
20
22
24
15-16
1 -
1 1-16
1 1-8
888
800
727
666
WROUGHT SPIKES.
Number to a keg of 150 Ibs.
In.
/ in.
No.
3 2250
3 1-2 1890
4 i 1650
4 1-2 1464
5 1380
6 1292
n.
o.
1135
1064
742
570
Length.
In.
v-
1161
in.
635
573
455
424
391
445
384
270
249
256
240
322
129
? r.
SIZES AND WEIGHTS OF HOT PRESSED
SQUARE NUTS.
As manufactured by Charles & McMurtry, Pittsburgh, Pa. The sizes are the usual manufacturers',
not the Franklin Institute Standard. Both weights and sizes are for the unfinished Nut.
Size of 1 Weight of Rough
Thickness Side of n: i 1 No. of Nuts in
Bolt. 1 One Nut. Hole.
of Nut.
Square. 100 Ibs. .
K -014
.7
H
K
.71
6900
A
H
.029
.048
ft
Ps
1
.88
1.06
3450
2080
A
.078
H
_7_
K 1.24
1280
P
.088
&
y*
1.24 1140
.116 T V
%
1 1.41
860
1
_9
.161
%
i
IK
1.59
620
y%
.172
9
%
1/8
1.59
580
H
.22
ft
%
ik
1.77
460
%.
.31
H
%
IX
1.94
320
%
.38
f 1
H
2.12
260
i/
.56
If
IM
2.30
180
%
.63
If
H
IX
2.47
160
1
.69
%
i
IK
2.47
144
l
.91
Js
i
2
2.83
110
IK
1.00
It
l/'S
2
2.83
100
1.43
it
1)1
2^
3.18
70
1&
1.54
lyV
IK
2^
3.18
65
lx^
1.79
ly 1 ^
IK
2/^
3.54
56
1>8
2.4
I*
2^ .
3.89
42
IK
3.1
1ft
'i 1 ^
3
4.24
32
4.0
ift
i|S
31^
4.60
25
i|
5.0
5.9
iii
L P
ii
4.95
5.30
20
17
2
7.1,
iff
2
4
5.66
14.
7.4
1%
4
5.66
13.5
2^
8.1
2
2^
4^
6.01
12.3
2%
8.3
2K
2%
41^
6.01
12.0
2y z 10.9
2/2
2/^
4^
6.36
9.14
2% 13.2
2 T V
2^
4^
6.72
7.55
3 14.9
aj|
3
5
7.07
6.72
3^ ! 17.5
31^
5j^
7.78
5.70
: SK-. 121.1
3/8
3K 6
8.49
4.75.
iS '
SIZES AND WEIGHTS OP HOT PRESSED
HEXAGON NUTS.
As manufactured by Charles & McMurtry, Pittsburgh, Pa. The sizes are the visual manufacturers',
net the Franklin Institute Standard. Both weights and sizes are for the unfinished Nut.
M Size of
* Belt.
Weight of
One Nut.
Rough Thickness
Hole. of Nut.
Short
Diameter.
Long
Diameter.
No. of Nuts in
100 Ibs.
~77
.013
,',
H
I./
.58
8000
A
.026
"K
A
^
.72
3840
3>
.042
M
K
.87
2400
A
.071
P
TV
%
1.01
1400
I/
.069
&
1 /
Js
1.01
1440
k
.100
M
1
1.15
1000
A
.161
}l
A
iNf
1.30
620
M
.147
9
^
1?8 '
1.30
680
/N}
.200
T 9 G
M
1'4
1.44 500
5/
ts&
li
y
lx^
1.44
53
7
'23
%
.26
f?
3 4
1^8
1.59
380
3/
.33
%
11^
1.73
300
7X
.45
J5/
1.88
220
%
.53
25
3 2
i ,
1M
1.88
190
1
.59
J
i
IK
2.02
170
1
.63
]_?8
2.02
160
1 L 3
.95
it
1M
2 /4
2.31
105
l 1 ^
1.43
IT a
1^8
2^
2.60
70
13/
1.64
JJL
l 1 ^
2^
2.89
61
1&
2.4
1&
1M
2%
3.18
42
1 5 8
3.0
i'A
IK
3
3.46
33
1/4
3,7
1A
1/8
3M
3.75
27
U-8
4.8
IT!
2
4.04
21
2
4.5
Iff
2
31 /
4.04^
22
5.1
1%
3/1
4.33*
19.5
2>4
5.4 2
2K
3%
4.33
18.4
2 3
6.3 2^
2%
4
4.62
15.84
2'4 7.6 2K'
4 1 4
4.91
13.11
2% , 9.3 2^
2^,
4)^
5.20
10.80
3 11.8
2|-i
3
4%
5.48
8.46
3*4 15.9
2tf
31^
5
5.77
6.30
3!<C 23.8
3^'
3K
5 1 ^
6.06
4.20
131
xxx^?
IN-OOOO-^^^-iT-iT-iT-^OGOOOOOOOOOOOOOOOOOOOO
CV} ,_ ,-H ,_,,_, ,_ ,-H .^H _
5 O2 1O OS OO OO ^> CC OO
T IT IT-" GvJCOlOCOJN-
'^is.aS, .looc^-co
=^^'a?"-;iOo
" C ,g \ "** ^
,3o^> r -<ce^ao}t-o,-| : * i o ^gg^ogg
<^ -T}< |>- -^f lO T-< CO I s - IN- CO
^ 10 co oq <o co co>os cooqo<oio < io
'
EXPLANATION OF TABLES ON RIVETS
AND PINS.
Pages 135 to 137, inclusive.
In transmitting stress by means of rivets, it is customary to
disregard the friction between the parts joined, as too uncertain
an element to be relied upon to any extent. The rivets must
then be proportioned for the entire stress which is to be trans-
mitted from one plate, or group of plates, to the other, and they
must be of sufficient size and number, to present ample resistance
to shearing and afford sufficient bearing area, so as not to cause a
crushing of the metal at- the rivet holes. This latter condition,
while generally observed for pins, is very often entirely over-
looked in riveted work. Its observance, in most cases of
riveted girders with single webs, determines the size and number
of rivets to be used, and frequently makes it necessary to adopt a
greater thickness of web than would otherwise be required.
Thus, if the web is -f^" thick, the rivets connecting the same
with the flange angles have a bearing value of only 3520 Ibs.
for a %" rivet, .while their shearing value is = 2 X 3310 =
6620 Ibs. per rivet, the rivets being in double shear. Con-
sequently, while the usual thickness of web of floorbeams for
railway bridges is ffi f , it sometimes becomes necessary, for
shallow floorbeams, to increase this thickness to )4 ff and even
$ rf , in order that the pressure of the rivets upon the semi-intrados
of the rivet holes be not excessive, between the points of support
of floorbeam and of application of the load, (in which space the
transmission of stress from web 19 flanges takes place.)
The pressure usually allowed upon rivet-bearing is 15000 Ibs.
per square inch, as assumed in table, the bearing area being the
diameter of hole multiplied by the thickness of metal. This
'" 133
pressure is somewhat greater than is generally allowed for pins,
in consideration of the neglect of the friction between plates
in riveted work.
Pins must be calculated for shearing, bending and bearing
stresses, but one of the latter two only, in almost every case,
determines the size to be used. The stress allowed upon pin-
bearing in bridges proportioned to a factor of safety of five,
is usually 12500 Ibs., and the maximum fiber strain by bending,
15000 Ibs. per square inch. Where groups of bars are connected
to the same pin, as in the lower chords of truss bridges, the size
of bars must be so chosen and the bars so placed that at no
point on the pin will there be an excessive bending strain, on the
presumption that all the bars are strained equally per square inch.
The following examples will illustrate the use of the tables -.
A pin in the bolster or end shoe of a bridge has to carry a
load of 40000 Ibs. between two points of support; what size
of pin is required, presuming the distance between points (i. e.,
centers) of support of bolster plates and centers of pressure of
end post plates = 2>"?
Anstver : Bending moment = 20000 Ibs. x 2> == 50000 inch
Ibs., therefore %% pin required for 15000 Ibs. fiber strain, since
the allowed moment for 3>(" = 50600, as per table.
Required the thickness of metal in the top chord or in a post
of a bridge, that will give sufficient bearing area to a 3^ ;/ pin,
having to transmit a stress of 63300 Ibs., the allowed pressure per
square inch on bearing being 12500 Ibs. maximum.
The bearing value of a 3^ /x pin for \" thickness of plate =
42200 Ibs., therefore the thickness of metal required
l/^'j r each of the two plates in the chord or post will have to
be " thick.
134
o ;
-3
ooo
t>CO
CO-^
IOI> (M
(MOO lOi-H
10
(M
10
(MOO lOi-H C^CO CD (MOO
COCO l>00 0005 OO rHiH
135
MAXIMUM BENDING MOMENTS TO BE AL-
LOWED ON PINS TOR MAXIMUM FIBER
STRAINS OF 15000, 20000 AND 22500 LBS.
PER SQUARE INCH.
Diam.
of
Pin.
Inches.
Moment
for
8 = 15000.
Lbs. in.
Moment
for
S = 20000.
Lbs. in.
Moment
for
S = 22500.
Lbs. in.
Diam.
of
Pin.
Inches.
Moment 1 Moment Moment
for for for
S = 15000. S = 20000. S = 22500.
Lbs. in. j Lbs. in. Lbs. in.
1
1470 1960
2210
4
94200 125700 14140O
1
2100 2800
3140
4M
103400 137800 155000
1#
2880 3830
4310
4 1 4 H13000 150700 169600
IK
3830 5100
5740
4%
123300 164400 18500O
IX
4970 663O
7460
4*
134200 178900 201300
1%
6320 8430
9480
4*
14570O 194300 21850O
i%
7890 10500
11800
4%
157800 21O400 23670O
i%
9710 12900
14600
4^
170600 227500 255900
2
11800 15700
17700
5
184100 245400 276100
2#
14100 18800
21200
5M
198200 264300 29730O
2^
16800 2240O
25200
5#
213100 284100 319600
2%
19700 26300
29600
5%
228700 304900 34300O
2#
23000 30700
34500
&x
245000 326700 367500
2%
26600
35500
40000
5%
262100 349500 39310O
2M
30600
40800
45900
5%
280000 373300 419900
2%
35000
46700
52500
5%
2986OO 398200 44790O
3
39800
53000
59600
6
318100 424100 477100
3^
44900
59900
67400
8M
338400 451200 507600
3^
50600
67400
75800
8
3595OO 479400 53930O
3%
56600
75500
84900
6%
381500 5087OO 572300
33^
63100 84200
94700
Q 1 A
404400 539200 606600
3%
70100 93500
105200
6%
428200 57090O 64230O
3M
77700 103500
116500
6M
452900 603900 679400
3%
85700114200128500
m
478500 638000 71780O
REMARKS The following is the formula for flexure applied to pins:
M= moment of forces for any section of the pin. %
S = strain per sq. in. in extreme fibers of pin at that section.
A=area of section.
d= diameter.
7T=3.14159.
The forces are assumed to act in a plane passing through the axis
of the pin.
The above table gives the values of M for different diameters of pin,
and for three values of S.
If M max. is known, an inspection of the table will therefore show
what diameter of pin must be used, in order that <S does not exceed
15000, 20000 or 22500 Ibs., as the requirements of the case may be.
For Railroad Bridges proportioned to a factor of safety of 5, it is
customary to make S max. = 1500Q Ibs. in iron and= 20000 Ibs. in steel.
136
BEARING VALUE OF PINS FOR ONE INCH
THICKNESS OF PLATE.
( Dia. of Pin X 1" X strain per sq. inch.)
Diameter of
Pin.
Inches.
1
IX
$
1#
Area of Bearing Value at Bearing Value at
Pi u> 12500 Ibs. 15000 Ibs.
square In'ches. per square inch. ; per square inch.
Lbs. Lbs.
.785
.994
1.227
1.485
1.767
12500
14100
15600
17200
18800
15000
16900
18800
20600
22500
! 5 /8
i
2
2.074
2.405
2.761
3.142 |
20300
21900
23400
25000
24400
26300
28100
30000
2#
2M
2&
2#
3.547
3.976
4.430
4.909
26600
28100
29700
31300
31900
33800
35600
37500
2^
2%
2%
3
5.412
5.940
6.492
7.069
32800
34400
35900
37500
39400
41300
43100
45000
3' 8 '
3%
3%
3J 8 X
7.670
8.946
10.32
11.79
39100
42200
45300
48400
46900
50600
54400
58100
4 1 8
m
m
4 7 8 x
13.36
15.03
16.80
18.67
51600
54700
57800
60900
61900
65600
69400
7310O
5M
m
5H
SH
20.63
22.69
24.85
27.11
64100
67200
70300
73400
78900
80600
84400
88100
8? B X
6M
6%
6. 7 ' 8
29.46
31.92
34.47
37.12
76600 91900
79700 95600
82800 99400
85900 103100
WOODEN BEAMS.
Safe Load, Uniformly Distributed, for Rectangular
White or Yellow Pine Beams one inch thick,
allowing 1200 Ibs. per square
inch fiber strain.
To obtain the safe load for
any thickness, multiply the
safe
load given in table, by the thickness of beam.
To obtain the required thickness for any load, divide by the
safe load for 1 inch, given in table.
a
"* -^s
DEPTH OF BEAM.
6"
7//
8" 9"
10"
11"
12"
13"
14//
15"
16"
Feet.
Lbs.
Lbs.
Lbs.
Lbs.
Lbs.
Lbs.
Lbs.
Lbs.
Lbs.
Lbs.
Lbs.
5
960
1310 1710 2160
2670
3230
3840
4510
5230
6000
6830
6
800
1090 1420
1800
2220
2690
3200
3760
4360
5000
5690
7
690
930
1220 1540
1900
2300
2740
'3220
3730
4290
4880
8
600
820
1070 1350
1670
2020
2400
2820 3270
3750
4270
9
530
730
950
1200
1480
1790
2130
2500 2900
3330
3790
10
480
650
850
1080
1330
1610
1920
2250
2610
3000
3410
11
440
590
780
980
1210
1470 j 1750
2050 2380
2730
3100
12
400 540
710
900
1110
1340 1600
1880
2180
2500
2840
13
370 500
660
830
1030
1240
1480
1730
2010
2310
2630
14
340
470
610
770
950
1150
1370
1610
1870
2140
2440
15
320
440
570
720
890
1080
1280
1500
1740
2000
2280
16
300
410
530
680
830
1010
1200
1410
1630
1880
2130
17
280
380
500
640
780
950
1130
1330
1540
1760
2010
18
270
360
470
600
740
900
1070
1250
1450
1670
1900
19
250
340
450
570
700
850
1010
1190 1 1380
1580
1800
20
240
330
430
540
670
810
960
1130
1310
1500
1710
21
230
310
410
510
630
770
910
1070
1240
1430
1630
22
220
300
390
490
610
730
870
1020
1190
1360
1550
23
210
280
370 470
580
700
830
980 1140
1300
1480
24
200 270
360 ; 450
560
670
800
940 1090
1250
1420
25'
190
260
340
430
530
650 770
900
1050
1200
1370
26
180
250
330
420
510
620 740
870
1010
1150
1310
27
180' 240
320
400
500
600 710
830
970
1110
1260
28
170! 230
300
390
480
580 690
800
930
1070
1220
29
1701 230
390
370
460
560 660
780
900
1030
1180
'4
Si
EXPLANATION OF TABLES ON MAXIMUM
STRESSES IN PRATT AND WHIPPLE
TRUSSES.
Pages 141 to 143, inclusive.
These tables give the stress in each member of a Pratt (single
quadrangular) or Whipple (double quadrangular) truss, for any
number of panels not exceeding twelve in the former, and twenty
in the latter case, on the assumption that the load is uniform per
foot, and the panels are all of the same length. The stresses are
given in terms of the truss-panel dead and moving loads, repre-
sented respectively by W and L. These are obtained by multi-
plying the dead load per foot of bridge, in the case of W, and
the moving or live load per foot of bridge, in the case of L, by
half the panel length.
The letters W and L are placed at the top of column, in tables,
and not next to the figures to which they belong, for want of space.
The stress in aB, for example, in a twelve panel Pratt truss,
= 5.5 W X 5.5 L, and in Be = 4.5 W X f | L, both multi-
plied by the quotient specified in the last column.
The system of lettering employed is shown by Figs. 7 and 8,
on page 26 of the lithographs, and, it is believed, is the best in
use. By making a sketch of the truss under consideration and
lettering the vertices in the manner shown, the truss members to
which reference is had in the tables, can be readily identified.
In the following tables, "the dead load is assumed as concen-
trated at the lower vertices of the trusses, for through bridges,
and at the upper vertices, for deck bridges. For through bridges
of very large span, the stresses thus obtained for the posts must
be increased by the truss-panel weight of the upper portion of
the truss, including the lateral bracing; but in small spans, the
increase of stress on this account is so inconsiderable that it is
usually neglected.
Note : In order to calculate the stresses in a Whipple or double
quadrangular truss by statical methods, it is necessary to consider
the truss as the combination of two Pratt trusses or single systems
of bracing, and assume that each of these two systems is strained
in the same manner as if one were independent of the other. If
the number of panels is odd, each of the two systems is unsym-
metrical, which has the effect of making the stress in the middle
panel of the lower chord slightly smaller than the stress in the
corresponding panel of the top chord. To avoid this peculiarity
and obtain equal stresses in these members, a division into sym-
metrical systems is sometimes assumed for the dead load stresses
and for the full load, by considering the counter ties canceled. For
the live load stresses obtained by partial loading, however, it is
again necessary to divide into unsymmetrical systems, so that,
while there appears to be no good reason in favor of this method,
it has the objection of inconsistency. The difference in the
resulting stresses obtained by the two methods is so small as not
to be of practical consequence. Each of the two systems is
assumed to carry one-half of the panel load at the top of the
inclined end posts.
ILLUSTRATION OF APPLICATION OF TABLES, ALSO
OF THE USE OF TABLE OF NATURAL SINES,
TANGENTS AND SECANTS.
A Pratt truss of 135' span and 18' depth, is divided into nine
panels of 15' each. Required the stress in first main tie Be, and
in middle panel DE of top chord, for a dead load of 1200 Ibs.
and a moving load of 3000 Ibs. per lineal foot of bridge.
1900
W = ~- x .15 = 9000 Ibs.
-^i x 15 = 22500 Ibs.
Q / /> -IO
DE=(10W + 10 L)-j|-
The factor -^r- , or panel length divided by depth of truss, is
lo
the tangent of the angle, for which the length Be, divided by
depth of truss, is the secant. By table of natural sines, tangents
and secants, for tangent = - = 0.833, the secant = 1.302;
lo
therefore
Be == 97000 X 1.30 = 126100 Ibs.
DE = 315000 X -j|~ = 262500 Ibs.
140
:5
MAXIMUM STRESSES UNDER
DEAD
AND
MOVING LOADS IN PRATT OR SINGLE
QUADRANGULAR TRUSSES
With inclined end posts and equal panel
3, for Through and Deck Bridges.
W = deac
1 load and L = moving load per truss and per panel.
Member.
12 Panel 11 Panel
Truss. Truss.
10 Panel
Truss.
9 Panel 8 Panel
Truss. , Truss.
Multi-
ply by:
W+L W+L
W+L
W+L W+L
aB
5.5+5.5 5+5
4.5+4.5
4_1_4 3.5+3.5
1
Be
4.5+f! 4+ff 3.5+3.6
8+Vi 2.5+ V
Cd
3.5+fl 3+ff 2.5+2.8
2+V; 1.5+ V
6*
De
2.5+f| ! 2+ff-
1.5+2.1
1+V 5 | 0.5+ V
'a s
Ef
1.5+|4 1 H
-ff
0.5+1.5
O+io -0.5+f
Pg
0.5+f| I 0+H
-0.5+1.0 -1+ f
-1.5+ f
Gh
-0.5-1
-15, ! _1_|
~TT
-1.5+0.6 -2+ 1
-&
Hi
-1.5-
-[H -2H
-TT
I
abc
5.5+ 5.5
5+ 5
4.5-|
- 4.5
4H
- 4
3.5H
-3.5
o
BO, cd
10.0+10.0
9+ 9
' 8.0-
- 8.0
7-
- 7
6.0-
-6.0
|f .
CD, de
13.5+13.5 12+12
10.5-
-10.5
9-
- 9
7.5-
-7.5
DE, ef
16.0+16.0; 14+14
12.0-
-12.0
10-
-10 8.0H
-8.0
1^"^
EF, fg
17.5+17.5
15+15
12.5-
-12.5
<:i
FG
18.0+18.0
Thro'. Deck.
Cc
4.5-|
-ff
44
-f
3.5-
h3.6
3H
r
2.5+ V
Cc, Dd
3.5-
4
2.5-
-2.8
-V
1.5+ V
Dd, Ee
2.5-
_3.i 2-1
4
1.5-
-2.1
1-
rV
0.5+ V
>
Be, Ff
1.5-
rl!
1+1
0.5-
-1.5
o+v
-0.5+ |
ti
Ff; Gg
0.5-
4i
o+l-
-0.5-
-1.0
-0.5+M
Member.
7 Panel
Truss.
6 Panel
Truss.
I 5 Panel
Truss.
4 Panel
Truss.
3 Panel
Truss.
Multi-
ply by:
W+L
W+L
W+L
W+L
W+L
aB
3+3
2.5-1
-2.5
2+2.0
1.5+1.51 1+1
Jui
Be
24 -v
1.5-
rV
1+1.2
0.5+ |
i
s^^
Cd
1_|
-V
0.5-
-1.0
0+0.6
-0.5+ J
1 o-3' s
De
0-
_ 6.
-0.5-
-0.5
-1+0.2
tf
Ef
-1-
-f
g *
abc
3+3
2.5+2.5
2+2
1.5+1.5
1+1
f-^i
BC, cd
5+5
4.0+4.0
3+3
2.0+2.0
1+1
3 "2?
CDE,de
6+6
4.5+4.5
Thro'. De&k.
Cc
2H
-
1.5+ V
1+1.2
0.5+f
Cc, Dd
1-
-V
0.5+1.0
0+0.6
-0.5+ i
jj
r, Dd
2+|
-0.5+0.5
'3
MAXIMUM STRESSES UNDER DEAD AND
MOVING
LOADS IN WHIPPLE OR
DOUBLE QUADRANGULAR
TRUSSES
With inclined end posts
and equal pane
.s, for Through and Deck Bridges.
W = dead load and L = moving
ioad per truss and per panel.
TUT 1.
20 Panel
19 Panel
18 Panel ! 17 Panel
16 Panel
a^
Member.
Truss.
Truss.
Truss.
Truss.
Truss.
^a
W+L
W+L
W+L
W+L
W+L
aB
9.5+9.5
9+9
8.5-1
-8.5 8+8
7.5+7.5
Be
4.5-
- 9^5 -
.0 _j_8^5
-W ff+W
3.5+ T G ,f
^
Bd
4.0-
"JKi
t+W
3.5-
-w
5.6. +5^
3-0+ *i
"S
Ce
3.5-
f- e r
3.0-
-W
16. -j-' 1 ^"'
2.5H
hW
f
Df
3.0-
~^t'
' <; -
_565
2.5-
- 4 ft 5
H+W
2.0-
-W
^ |
Eg
2.5-
-w
r- -
-W
2.0-
-y -g- j y y | 3 Ty-
1.5-
_3_05
J^
Fh
2.0-
_4J^5
1.-
1.5-
_ 35.5 1 2. _j_ 3^0 fr 5
1.0-
-W
S
S _ca
Gi
1.5-
-W
-f-
-w
1.0-
- 3 r
1.2 _[_ 2 4^5
0.5H
-20.5
II
Hk
1.0-
-w
i+j T
0.5-
-t 5
fV ~l~ 2 f*"
0.0+ W
11
0.5-
-S
0.0-
-w-^v+w
-0.5+ W
Km
0.0-
\ + ? T ir
-0.5-
-W-if+W
-1.0+ -J-f
3
Ln
-0.5+ ^
41 4- W
-1.0-
-Wrff+4'f
Mo
-1.0+ i}t 5
-ft+ l r
abc
9.5+ 9.5
9+9
8.5+ 8.5
8-f
-8
7.5+7.5
cd
14+14
WH
~w
12.5+12.5 WH
-W
11+11
^>
BC, de
22-
-22
\
-3_9^5
19.5+19.5 3 T V-
-w
17+17
-a
CD, ef
29-
-29
5 TV^
- 5 T y
25.5+25.5 W-
22-
-22
| |
DE, fg
35-
-35
6 T
^-4
- 6 T
30.5+30.5 W-
-w
26-
-26
^C^
EF, gh
40-
-40
w-
-W
34.5+34.5 5 T 3 7 9 -
_5_39
29-
-29
^^
FG, hi
44-
-44
w-
-W
37.5+37.5 W+W
31-
-31
J &
GH, ik
HI, kl
47-
49-
-47
-49
W J
w-
"S*
39.5+39.5 6 T y+TV*
40.5+40.5 W+ 6 T y
32-
HI=
-32
=GH
r
IKL
50-
-50
VM
,1
IK=HI
^k
Thro'. Deck.
ii
T+W
W+7 7
Cc
4.5H
hW
-
.0 _j_ 8^5
4.0+ W
ff -
~6ft 5
3.5H
- 5 -r
Dd
4.0-
-W
f + ^V 5 3.5+fift 5
if ~
~ ft 5
3.0-
-w
Cc, Be
3.5-
-w
i+W 3.0+ 5f ^
ff ~
-'ft 5
2.5-
Dd, Ff
3.0-
-8fjS
1 _j_ 5^
2.5-f
f 7 ~
'-ft 5
2.0-
" S T
^
Ee, Gg
2.5-
_5j>^5
t+ 4 T
~7 -
_3_5.5
1.5-
_30.5
'"a
Ff| Hh
2.0-
~~M
f+W
1.5-|
_3^?5
T7~
- 3 ft 5
1.0+ 4
3
Gg, li
1.5-
I+W
i.o+ 3 f?
T7~
-w
0.5+ W
Hh, Kk
1.0-
-4v
il+W
^ +2^
0.0+ i t
li, LI
0.5-
-w
T\+ 3 T
o!o+w
-^-[-IfyS
-0.5+ W
Kk
0.0-
-W-iV+W
-1^^5
.LI
-0.5+ S
;
MAXIMUM STRESSES UNDER DEAD AND
MOVING LOADS IN WHIPPLE OR
DOUBLE QUADRANGULAR
TRUSSES
With inclined end posts and equal panels, for Through and Deck Bridges.
W = dead load and L = moving load per truss and per panel.
Member.
15 Panel
Truss.
W+L
14 Panel
Truss.
W+L W+L
6.5+6.5
2.0+^!
1.5+2
1.0+
0.5+1
0.0+ J
7+7
W+W
W+W
W+W
; V+^ 3
6.5+ 6.5 6+6
9.5+ 9.5; W+W
14.5+14.5 n *
18.5+18.5
21.5+21.5
23.5+23.5, ,
24.5+24.5! W+ 2 T V
~ - ~~=FG
4.24.5 It5 i
15.0+16.0 W+
17.0+17.0! "
18.0+18.0' W+
FG=EF
2.5-[_30 y5
2.0+ wi
W+W
2^5 1.0+1
__^s 0.5+1
--W o.o-
-r 4 T+4-f -0.5+-'
143
+-W 1
NATURAL SINES
, TANGENTS AND SECANTS ,
Advancing by 1O min.
Beg.
Min.
00
10
20
Sine. Tangent.
Secant.
Deg.
Min.
Sine.
Tangent. ! Secant.
! 4
.0000 .0000
.0029 .0029
.0058 .0058
1.0000
1.0000
1.0000
5
00 .0872
10 .0901
20 .0929
.0875
.0904
.0934
1.0038
1.0041
1.0043
30
4fc
50
.0087 .0087
.0116 .0116
.0145 .0145
1.0000
1.0001
1.0001
30
40
50
;0958
.0987
.1016
.0963
.0992
.1022
1.0046
1.0049
1.0052
1
00
10
20
.0175 .0175
.0204 .0204
.0233 .0233
1.0002
1.0002
1.0003
6
00
10
20
.1045
.1074
.1103
.1051
.1080
.1110
1.0055
1.0058
1.0061
30
40
50
.0262 .0262
.0291 .0291
.0320 .0320
1.0003
1.0004
1.0005
30
40
50
.1132
.1161
.1190
.1139
.1169
.1198
1.0065
1.0068
1.0072
2
00
10
20
.0349 .0349
.0378 i .0378
.0407 | .0407
1.0006
1.0007
1.0008
7
00
10
20
.1219
.1248
.1276
.1228
.1257
.1287
1.0075
1.0079
1.0082
30
40
50
.0436 .0437
.0465 .0466
.0494 .0495
1.0010
1.0011-
1.0012
30
40
50
.1305
.1334
.1363
.1317
.1346
.1376
1.0086
1.0090
1.0094
3
00
10
20
.0523 .0524
.0552 .0553
.0581 .0582
1.0014
1.0015
1.0017
8
00
10
20
.1392
.1421
.1449
.1405
.1435
.1465
1.0098
1.0102
1.0107
30
40
50
.0610 .0612
.0640 .0641
.0669 .0670
1.0019
1.0021
1.0022
30
40
50
.1478
.1507
.1536
.1495
.1524
.1554
1.0111
1.0116
1.0120
4 : 00 ' .0698 .0699
; 10 ; .0727 .0729
| 20 .0756 .0758
1.0024
1.0027
1.0029
9 00
10
20
.1564
.1593
.1622
.1584
.1614
.1644
1.0125
1.0129
1.0134
30 .0785 .0787
40 i .0814 .0816
| 50 i .0843 .0846
ft. -1 '
1.0031
1.0033
1.0036
30
1 40
50
.1650 I .1673 1 1.0139
.1679 i .1703 1.0144
.1708 i .1733 1.0149
>
NATURAL SINES, TANGENTS AND SECANTS.
Min. Sine.
(CONTINUED.)
Deg.
10
Tangent. Secant.
Deg. Min.
Sine.
Tangent. Secant.
00 .1736
10 .1765
20 .1794
.1763 1.0154
.1793 1.0160
.1823 1.0165
15
00
10
20
.2588 .2679 1.0353
.2616 .2711 1.0361
.2644 .2742 1.0369
i 30 .1822
! 40 .1851
; 50 .1880
.1853 1.0170
.1883 1.0176
.1914 1.0181
30
40
50
.2672 ! .2773 1.0377
.2700 .2805 1.0386
.2728 .2836 1.0394
11
00 .1908
10 .1937
20 .1965
.1944 1.0187
.1974 1.0193
.2004 1.0199
16
00
10
20
.2756
.2784
.2812
.2867 1.0403
.2899 : 1.0412
.2931 1.0421
*
30 .1994
40 .2022
50 .2051
.2035 1.0205
.2065 1.0211
.2095 1.0217
30
40
50
.2840
.2868
.2896
.2962
.2994
.3026
1.0429
1.0439
1.0448
12
00 .2079
10 .2108
20 .2136
.2126 1.0223
.2156 1.0230
.2186 1.0236
17
00
10
20
.2924
.2952
.2979
.3057
.3089
.3121
1.0457
1.0466
1.0476
30 .2164
40 .2193
50 .2221
.2217 1.0243
-.2247 .1.0249
.2278 1.0256
30
40
50
.3007
.3035
.3062
.3153
.3185
.3217
1.0485
1.0495
1.0505
13
00 .2250
10 .2278
20 .2306
.2309 1.0263
.2339 1.0270
.2370 1.0277
18
00
10
20
.3090
.3118
.3145
.3249
.3281
.3314
1.0515
1.0525
1.0535
30 .2834
40 .2363
50 .2391
.2401 1.0284
.2432 1.0291
.2462 1.0299
30
40
50
.3173
.3201
.3228
.3346
.3378
.3411
1.0545
1.0555
1.0566
14 00 .2419
10 .2447
20 .2476
30 .2504
40 i .2532
50 : .2560
i
.2493 1.0306
.2524 1.0314
.2555 1.0321
.2586 1.0329
.2617 1.0337
.2648 1.0345
19
00
10
20
30
40
50
.3256
.3283
.3311
.3338
.3365
.8393
.3443
'.3476
.3508
.3541
.3574
.3607
1.0576
1.0587
1.0598
1.0608
1.0619
1.0631
c
14
& '*
NATURAL SINES, TANGENTS AND SECANTS.
(CONTINUED.)
Deg.
Min.
Sine.
.3420
.3448
.3475
Tangent. Secant.
I
Deg.
Min.
00
10
20
Sine. Tangent.
Secant.
20
00
10
20
.3640
.3673
.3706
1.0642
1.0653
1.0665
25
.4226 .4663
.4253 .4699
.4279 .4734
1.1034
1.1049
1.1064
30
40
50
.3502
.3529
.3557
.3739
.3772
.3805
1.0676
1.0688
1.0700
30
40
50
.4305
.4331
.4358
.4770
.4806
.4841
1.1079
1.1095
1.1110
21
00
10
20
.3584
.3611
.3638
.3839
.3872
.3906
1.0711
.1.0723
1.0736
26
00
10
20
.4384
.4410
.4436
.4877
.4913
.4950
1.1126
1.1142
1.1158
30
40
50
.3665
.3692
.3719
.3939
.3973
.4006
1.0748
1.0760
1.0773
30
40
50
.4462
.4488
.4514
.4986
.5022
.5059
1.1174
1.1190
1.1207
22
00
10
20
.3746
.3773
.3800
.4040
.4074
.4108
1.0785
1.0798
1.0811
27
00
10
20
.4540
.4566
.4592
.5095
.5132
.5169
1.1223
1.1240
1.1257
30
40
50
.3827
.3854
,3881
.4142
.4176
.4210
1.0824
1.0837
1.0850
30
40
50
.4617
.4643
.4669
.5206
.5243
.5280
1.1274
1.1291
1.1308
23
00
10
20
.3907
.3934
.3961
.4245
.4279
.4314
1.0864
1.0877
1.0891
28
00
10
20
.4695
.4720
.4746
.5317
.5354
.5392
1.1326
1.1343
1.1361
30
40
50
.3987
.4014
.4041
.4348
.4383
.4417
1.0904
1.0918
1.0932
30
40
50
.4772
.4797
.4823
.5430
.5467
.5505
1.1379
1.1397
1.1415
24
00
10
20
.4067
.4094
.4120
.4452
.4487
.4522
1.0946
1.0961
1.0975
29
00
10
20
.4848
.4874
.4899
.5543
.5581
.5619
1.1434
1.1462
1.1471
30
40
50
.4147
.4173
.4200
.4557
.4592
.4628
1.0989
1.1004
1.1019
30
40
50
.4924
.4950
.4975
.5658
.5696
.5735
1.1490
1.1509
1.1528
c
y
NATURAL SINES
, TANGENTS AND SECANTS.
(CONTINUED.)
Deg. Min.
Sine.
Tangent.
Secant.
Deg. Min.
Sine.
.5736
.5760
.5783
Tangent.
Secant.
30 00
10
20
.5000
.5025
.5050
.5774
.5812
.5851
1.1547
1.1566
1.1586
35
00
10
20
.7002
.7046
.7089
1.2208
1.2233
1.2258
30
40
50
.5075
.5100
.5125
.5890
.5930
.5969
1.1606
1.1626
1.1646
30 .5807
40 .5831
50 .5854
.7133
.7177
.7221
1.2283
1.2309'
1.2335
31 00
10
! 20
.5150
.5175
.5200
.6009
.6048
.6088
1.1666
1.1687
1.1707
36
00 .5878
10 .5901
20 .5925
.7265
.7310
.7355
1.2361
1.2387
1.2413
30
40
J50
.5225
.5250
.5275
.6128
.6168
.6208
1.1728
1.1749
1.1770
30
40
60
.5948
.5972
.5995
.7400
.7445
.7490
1.2440
1.2467
1.2494
32 00
10
20
.5299
,5324
.5348
.6249
.6289
.6330
1.1792
1.1813
1.1835
37
00 ! .6018
10 .6041
20 .6065
.7536
.7581
.7627
1.2521
1.2549
1.2577
30
40
50
.5373
.5398
.5422
.6371
- .6412
.6453"
1.1857
1.1879
1.1901
30
40
50
.6088
.6111
.6134
.7673
.7720
.7766
1.2605
1.2633
1.2661
33 00 ' .5446
10 .5471
20 .5495,
.6494
.6536
.6577
1.1924
1.1946
1.1969
38
00
10
20
.6157
.6180
.6202
.7813
.7860
.7907
1.2690
1.2719
1.2748
30 .5519
40 .5544
50 .5568
.6619
.6661
.6703
1.1992
1.2015
1.2039
30
40
50
.6225 .7954
.6248 ; .8002
.6271 i .8050
1.2778
1.2808
1.2837
34 00 .5592
10 .5616
20 .5640
.6745
.6787
.6830
1.2062
1.2086
' 1.2110
39
00
10
20
.6293 j .8098
.6316 .8146
.6338 .8195
1.2868
1.2898
1.2929
30
40
50
< -
.5664
.5688
.5712
.6873
.6916
.6959
1.2134
1.2158
1.2183
30
40
50
.6361
.6383
.6406
.8243
.8292
.8342
i 1.2960
1.2991
1.3022
i
NATURAL SINES, TANGENTS AND SECANTS.
(CONTINUED.)
Deg. Min. Sine.
Tangent. Secant.
Deg. Min.
Sine. Tangent.
Secant.
40 00 .6428
10 .6450
20 .6472
.8391 1.3054
.8441 1.3086
.8491 1.3118
45 00
10
20
.7071 1.0000
.7092 1.0058
.7112 1.0117
1.4142
1.4183
1.4225
30 .6494
40 .6517
50 .6539
41 00 .6561
10 .6583
20 .6604
.8541 1.3151
.8591 1.3184
.8642 1.3217
.8693 1.3250
.8744 I 1.3284
.8796 1.3318
30
40
50
46 00
10
20
.7133 ; 1.0176
.7153 i 1.0235
.7173 1.0295
.7193 l 1.0355
.7214 1.0416
.7234 1.0477
1.4267
1.4310
1.4352
1.4396
1.4439
1.4483
30 .6626
40 .6648
50 .6670
.8847 1.3352
.8899 1.3386
.8952 1.3421
30
40
50
.7254 1.0538
.7274 1.0599
.7294 1.0661
1.4527
1.4572
1.4617
42 00 .6691
10 .6713.
20 .6734
.9004 1.3456
.9057 1.3492
.9110 1.3527
47 , 00
: 10
20
.7314 1.0724
.7333 1.0786
.7353 1.0850
1.4663
1.4709
1.4755
30 .6756
40 .6777
50 .6799
.9163 1.3563
.9217 1.3600
.9271 1.3636
30
40
50
.7373 1.0913
.7392 1.0977
.7412 1.1041
1.4802
1.4849
1.4897
43 00 .6820
10 .6841
20 I .6862
.9325 1.3673
.9380 1.3711
.9435 1.3748
48 00
10
20
.7431 1.1106
.7451 1.1171
.7470 : 1.1237
1.4945
1.4993
1.5042
30 .6884
40 ! .6905
50 .6926
.9490 1.3786
.9545 1.3824
.9601 '1:3863
30
i 40
50
.7490 1.1303
.7509 1.1369
.7528 1.1436
1.5092
1.5141
1.5192
44 00 .6947
10 .6967
20 .6988
.9657 1.3902
.9713 1.3941
.9770 1.3980
49 00
10
20
.7547 1.1504
.7566 1.1571
.7585 1.1640
1.5243
1.5294
1.5345
30 ! .7009
40 .7030
50 .7050
'4
.9827 1.4020
.9884 1.4061
.9942 1.4101
30
40
50
.7604 1.1708
.7623 1.1778
.7642 1.1847
1.5398
1.5450 1
1.5504
NATURAL SINES
, TANGENTS AND SECANTS.
Tangent.
(CONTI
Secant.
VUED.)
Deg. Min.
Deg. :Min. Sine.
Sine.
Tangent.
Secant.
50 00 .7660
' 10 .7679
: 20 .7698'
1.1918
1.1988
1.2059
1.5557
1.5611
1.5666
55
00
10
20
.8192
.8208
.8225
1.4281
1.4370
1.4460
1.7434
1.7507
1.7581
30 ' .7716
40 .7735
i.50 .7753
1.2131
1.2203
1.2276
1.5721
1.5777
1.5833
30
40
50
.8241
.8258
.8274
1.4550
1.4641
1.4733
1.7655
1.7730
1.7806
51 00 .7771
; 10 .7790
20 .7808
1.2349
1.2423
1.2497
1.5890
1.5948
1.6005
56
00
10
20
.8290
.8307
.8323
1.4826
1.4919
1.5013
1.7883
1.7960
1.8039
30 .7826
i 40 .7844
; 50 .7862
1.2572
1.2647
1.2723
1.6064
1.6123
1.6183
30
40
50
.8339
.8355
.8371
1.5108
1.5204
1.5301
1.8118
1.8198
1.8279
52 00 .7880
i 10 .7898
20 .7916
1.2799
1.2876
1.2954
1.6243
1.6303
1.6365
57
00
10
20
.8387
.8403
.8418
1.5399
1.5497
1.5597
1.8361
1.8443
1.8527
30 .7934
, 40 .7951
50 .7969
1.3032
.1.3111
1.3190'
1.6427
1.6489
1.6553
30
40
50
.8434
.8450
.8465
1.5697
1.5798
1.5900
1.8612
1.8699
1.8783
53 00 ' .7986
! 10 ' .8004
20 .8021
1.3270
1.3351
1.3432
1.6616
1.6681
i 1.6746
58
00
10
20
.8480
.8496
.8511
1.6003
1.6107
1.6213
1.8871
1.8959
1.9048
' 30 .8039
40 .8056
50 : .8073
54 i 00 .8090
10 .8107
20 .8124
1.3514
1.3597
1.3680
1.3764
' 1.3848
1.3934
1.6812
i 1.6878
1.6945
I
: 1.7013
i 1.7081
1 1.7151
50
30
40
50
00
10
20
.8526
.8542
.8557.
.8572
.8587
.8601
1.6319
1.6426
1.6534
1.6643
1.6753
1.6864
1.9139
, 1.9230
1.9323
i
1.9416
1.9511
1.9606
30 .8141
40 .8158
50 .8175
2u
1.4019
! 1.4106
' 1.4193
1.7221
1.7291
1.7362
30
40
50
.8616
.8631
.8646
1.6977
1.7090
1.7205
i
1.9703
1.9801
1.9900
'4
NATURAL SINES, TANGENTS AND SECANTS.
(CONTINUED.)
Deg.
Min.
00
10
20
Sine. Tangent. Secant.
Deg. Min.
65 00
10
20
Sine.
Tangent.
2.1445
2.1609
2.1775
Secant.
60
.8660 1.7321 2.0000
.8675 1.7437 2.0101
.8689 1.7556 2.0204
.9063
.9075
.9088
2.3662
2.3811
2.3961
30
40
50
.8704 1.7675 , 2.0308
.8718 1.7796 2.0413
.8732 1.7917 2.0519
30 .9100
40 .9112
50 .9124
2.1943
2.2113
2.2286
2.4114
2.4269
2.4426
61
00
10
20
.8746
.8760
.8774
1.8040 2.0627
1.8165 2.0736
1.8291 2.0846
66
00
10
20
.9135
.9147
.9159
2.2460
2.2637
2.2817
2.4586
2.4748
2.4912
30
40
50
.8788
.8802
.8816
1.8418 ! 2.0957
1.8546 2.1070
1.8676 2.1185
30
40
50
.9171
.9182
.9194
2.2998
2.3183
2.3369
2.5078
2.5247
2.5419
62
00
10
20
.8829 1.8807
.8843 1.8940
.8857 1.9074
2.1301
2.1418
2.1537
67
00
10
20
.9205
.9216
.9228
2.3559
2.3750
2.3945
2.5593
2.5770
2.5949
30
40
50
.8870
.8884
.8897
1.9210
1.9347
1.9486
2.1657
2.1786
2.1902
30
40
50
.9239
.9250
.9261
2.4141
2.4342
2.4545
2.6131
2.6316
2.6504
63
00
10
20
.8910
.8923
.8936
1.9626
1.9768
1.9912
2.2027
2.2153
2.2282
68
00
10
20
.9272
.9283
.9293
2.4751
2.4960
2.5172
2.6695
2.6888
2.7085
30
40
50
.8949
.8962
.8975
2.0057
2.0204
2.0353
2.2412
2.2543
2.2677
30
40
50
.9304
.9315
.9325
i 2.5386
2.5605
; 2.5826
2.7285
2.7488
2.7695
64
00
10
20
30
40
50
.8988
.9001
.9013
.9026
.9038
.9051
2.0503
2.0655
2.0809
2.0965
2.1123
2.1283
2.2812
2.2949
2.3088
2.3228
2.3371
2.3515
69
00
10
20
30
40
50
.9336
.9346
.9356
.9367
.9377
.9387
2.6051
2.6279
2.6511
2.6746
! 2.6985
2.7228
2.7904
2.8117
2.8334
2.8555
2.8779
2.9006
NATURAL
SINES
r
, TANGENTS AND SECANTS.
Deg. Min.
Sine.
Tangent.
2.7475
2.7725
2.7980
(CONTl
Secant.
NUED.)
Deg. Min
. Sine.
Tangent.
Secant.
70 00
! 10
20
.9397
.9407
.9417
2.9238
2.9474
2.9713
75 00
10
20
.9659
.9667
.9674
3.7321
3.7760
3.8208
3.8637
3.9061
3.9495
30
40
50
.9426
.9436
.9446
2.8239
2.8502
2.8770
2.9957
3.0206
3.0458
30
40
50
.9681
.9689
.9696
3.8667
3.9136
3.9617
3.9939
4.0394
4.0859
71 00
10 i
20
.9455
.9465
.9474
2.9042
2.9319
2.9600
3.0716
3.0977
3.1244
76 00
10
20
.9703
.9710
.9717
4.0108
4.0611
4.1126
4.1336
4.1824
4.2324
30
40
50
.9483
.9492
.9502
2.9887 ,
3.0178
3.0475 !
3.1515
3.1792
3.2074
30
40
50
.9724
.9730
i .9737
4.1653
4.2193
4.2747
4.2837
4.3362
4.3901
72 00
10
|20
i
30
40
50
.9511
.9520
.9528
.9537
.9546
.9555
3.0777
3.1084 i
3.1397
3.1716
3;2041
3.2371
3.2361
3.2653
3.2951
3.3255
3.3565
3.3881
77 00
10
20
30
40
50
1 .9744
.9750
.9757
.9763
.9769
.9775
4.3315
4.3897
4.4494
4.5107
4.5736
4.6382
4.4454
4.5022
4.5604
4.6202
4.6817
4.7448
73 00
10
'20
.9563
.9572
.9580
3.2709
3.3052
3.3402
3.4203
3.4532
3.4867
78 00
10
20
.9781
.9787
.9793
4.7046
4.7729
4.8430
4.8097
4.8765
4.9452
30
40
50
.9588
.9596
.9605
3.3759
3.4124
3.4495
3.5209
3.5559
3.5915
30
40
50
.9799
.9805
.9811
4.9152
4.9894
5.0658
5.0159
5.0886
5.1636
74 00
10
20
.9613
.9621
.9628
3.4874
3.5261
3.5656
3.6280
3.6652
3.7032
79 00
10
20
: .9816
.9822
.9827
5.1446
5.2257
5.3093
5.2408
5.3205
5.4026
30
40
,50
.9636
.9644
.9652
3.6059
3.6470
3.6891
3.7420
3.7817
3.8222
30
40
50
.9833
.9838
.9843
5.3955
5.4845
5.5764
5.4874
5.5749
5.6653
i5 1
NATURAL SINES, TANGENTS AND SECANTS.
(COiNTINUED.)
Deg. Min.
Sine.
Tangent. 1 Secant.
Deg. <Min.
Sine.
Tangent.
Secant.
;
80 00
.9848
5.6713 5.7588
85 00
.9962
: 11.430
11.474
10
.9853
5.7694 5.8554
10
.9964
11.826
11.868
20
.9858
5.8708 5.9554
! 20
.9967
; 12.251
12.291
30
.9863
5.9758 6.0589
30
.9969
12.706
12.745
40
.9868
6.0844 6.1661
40
.9971
13.197
13.235
50
.9872
6.1970 6.2772
50
:9974
13.727
13.763
81
00
.9877
6.3138 6.3925
86 00
.9976
14.301
14.336
10
.9881
6.4348 6.5121
10
.9978
14.924
14.958
20
.9886
6.5606 6.6363
20
.9980
15.605
15.637
j
30
.9890
6.6912 6.7655
30
.9981
16.350
16.380
40
.9894-
6.8269 6.8998
40
.9983
17.169
17.198
50'
.9899
6.9682 7.0396
50
.9985
18.075
18.103
82
00
.9903
7.1154 7.1853
87 00
.9986
19.081
19.107
10
.9907
7.2687 7.3372
10
.9988
20.206
20.230
20
.9911
7.4287 7.4957
20
.9989
21.470
21.494
30
.9914
7.5958 7.6613
30
.9990
22.904
22.926
40
.9918
7.7704 7.8344
40
.9992
24.542
24.562
50
.9922
7.9530 8.0156
50
.9993
26.432
26.451
83
00
.9925 =
8.1443 8.2055
88 00
.9994
28.636
28.654
10
.9929
8.3450 8.4047
10
.9995
31.242
31.258
! 20
.9932
8.5555 8.6138
20
.9996
34.368
34.382
30
.9936
8.7769 8.8337
30
.9997
38.188
38.202
40
.9939
9.0098 9.0652
40
.9997
42.964
42.976
50
.9942
9.2553 9.3092
50
.9998
49.104
49.114
84 00
.9945
9.5144 9.5668
89 00
.9998
57.290
57.299
10
.9948
9.7882 9.8391
10
.9999
68.750
68.757
20
.9951
10.0780 10.1275
20
.9999
85.940
85.946
30
.9954
10.3854 10.4334
30
1.0000
114.589
114.593
40
.9957
10.7119 10.7585
40
1.0000
171.885
171.888
50
.9959
11.0594 11.1045
50
1.0000
343.774
343.775
.!
90 00
1.0000
Infinite.
Infinite.
1
)2 '*"
LOGARITHMS OP NUMBERS.
No.
1
2
3
4
5
6
7
8
9
Diff.
10
0000
0043
0086
0128
0170
0212
0253 ! 0294
0334
0374
40
11
0414
0453
0492
0531
0569
060710645
0682
0719
07551 37
12
0792
0828
0864
0899
0934
0969
1004
1038
1072
1106; 33
13
1139
1173
1206
1239
1271
1303
1335
1367
1399
14301 31
14
1461
1492
1523
1553
1584
1614
1644
1673
1703
1732 29
15
1761
1790
1818
1847
1875
1903
1931
1959
1987
2014 i 27
16
2041
2068
2095
2122
2148
2175
2201
2227
2253
22791 25
17
2304
2330
2355 ! 2380
2405
2430
2455
2480
2504
2529! 24
18
2553
2577
2601
2625
2648
2672
2695
2718
2742
2765! 23
19
2788
2810
2833
2856
2878
2900
2923
2945
2967
2989 21
I
20
3010
3032
3054 3075 3096
3118
3139
3160 3181
3201 21
21
3222
3243
3263
3284 3304
3324
3345 3365
3385
3404
20
22
3424
3617
3444
3636
3464
3655
348313502
3674 3692
3522
3711
3541
3729
3560
3747
3579
3766
3598
3784
19
18
24
3802
3820
3838 3856
3874
3892
3909
3927
3945
3962
17
25 3979
3997
4014
4031
4048
4065
4082
4099
4116!
4133
17
26 4150
4166
4183 4200
4216
423214249
4265
4281
4298
16
J
27 14314
4330
4346 4362
4378
4393
4409
4425
4440
4456
16
28 4472
4487
4502 451
4533
4548
4564
4579
4594
4609
15
29
4624
4639
4654
4669
4683
4698
4713
4728
4742
4757 14
i
30
4771
4786
4800
4814
4829
4843.4857
4871
4886 ;
4900 1 14
31
4914
4928
4942
4955
4969
4983 4997
5011
5024
5038 13
32
33
5051
5185
5065
5198
5079
5211
5092
5224
5105
5237-
5119)5132
525015263
5145 j 5159
527615289
5172
5302
13
13
34
5315
5328
5340
5353
5366
5378 5391
5403
5416
5428 13
35
5441
5453
5465 15478
5490
5502 j 5514
552715539
5551
12
36
5563
5575
5587 5599
5611
5623 5635
5647 15658
5670
12
37
5682
5694
5705 5717
5729
5740
5752
5763
5775
5786
12
38
5798
5809
5821 5832
5843
5855
5866
587715888
5899
IB-
39
5911
5922
5933 ! 5944
5955
5966
5977
5988
5999
6010
11
j
.
No.
1
2
3
4
5
6
7
8
9
Diff.
y 153
LOGARITHMS OF NUMBERS Continued.
No.
1 2
3
4
5
6
7
8
9 Diff.
40
41
42
43
6021
6031 6042
6053
6064
6075
6085
6096
6201
6304
6405
6107
6212
6314
6415
6117
6222
6325
6425
11
10
10
10
6128
6232
6335
6138 6149
6243 6253
6345 6355
6160
6263
6365
6170
6274
6375
6180
6284
6385
6191
6294
6395
44
45
46
6435
6532
6628
6444 6454
6542 6551
6637 6646
6464
6561
6656
6474
6571
6665
6484
6580
6675
6493
6590
6684
6503
6599
6693
6513
6609
6702
6522
6618
6712
10
10
9
47
48
49
50
51
52
53
6721
6812
6902
6730 6739
6821 6830
6911 6920
6749
6839
6928
6758
6848
6937
7024
6767
6857
6946
6776
6866
6955
6785
6875
6964
6794
6884
6972
6803
6893
6981
9
9
9
9
8
8
8
6990
7076
7160
7243
6998 7007
7084 7093
7168 7177
7251 7259
7016
7101
7185
7267
7033
7042
7050
7059
7067
7152
7235
7316
7110
7193
7275
7118
7202
7284
7126
7210
7292
7135
7218
7300
7143
7226
7308
54
55
56
7324
7404
7482
7332 7340
741217419
7490 7497
7348
7427
7505
7356
7435
7513
7364
7443
7520
7372
7451
7528
7380
7459
7536
7388
7466
7543
7396
7474
7551
8
8
8
57
58
59
60
61
62
63
7559
7634
7709
7566 '7574
76427649
7716 7723
7582
7657
7731
7589
7664
7738
7810"
7597
7672
7745
7604
7679
7752
7612
7686
7760
7619
7694
7767
7627
7701
7774
7'
8
8
7
7
6
7
7782
7789 7793
7803
7818
7889
7959
8028
7825
7832
7903
7973
8041
7839
7846
7853
7924
7993
7860 7868
7931 7938
8000 8007
7875
7945
8014
7882
7952
8021
7898
7966
8035
7910 7917
7980 7987
804818055
64
65
66
8062
8129
8195
8069 8075
8136 8142
8202 8209
8082
8149
8215
8089
8156
8222
8096
8162
8228
8102
8169
8235
8109
8176
8241
8116
8182
8248
8122
8189
8254
7
6
7
67
68
69
8261
8325
8388
8267 8274
8331 8338
8395 8401
8280
8344
8407
8287
8351
8414
8293
8357
8420
5
8299
8363
8426
8306 8312
8370! 8376
8432:8439
8319
8382
8445
6
6
6
No.
I 2
3
4
6
7
8
9
Diff.
^ 154
23 |i
LOGARITHMS OF NUMBERS Continued.
No.
1
2
3
4
8476
8537
8597
8657
5
8482
8543
8603
8663
6
7
8
9
Diff.
7
6
6
6
70
71
72
73
8451 8457
8463
8470
8531
8591
8651
8488
8494 8500
8506
8513 : 8519
8573 8579
8633 8639
8525
8585
8645
8549 1 8555
8609 ! 8615
8669 j 8675
8561
8621
8681
8567
8627
8686
74
75
76
8692 8698
.8751 8756
8808 8814
8704
8762
8820
8710
8768
8825
8716
8774
8831
8722
8779
8837
8727
8785
8842
8733
8791
8848
8739
8797
8854
8745
8802
8859
6
6
6
. 77
78
79
80
81
82
83
8865 8871
8921 8927
8976 8982
9031 9036
8876
8932
8987
8882
8938
8993
8887
8943
8998
8893
8949
9004
9058
9112
9165
9217
8899
8954
9009
8904
8960
9015
8910
8965
9020
9074
8915
8971
9025
6
5
6
6
5
5
5
9042 9047 9053
9063
9117
9170
9222
9069
9079
9085 9090
9138 9143
9191 9196
9096
9149
9201
9101
9154
9206
9106
9159
9212
9122
9175
9227
9128
9180
9232
9133
19186
9238
84
85
86
9243 ] 9248
9294 9299
9345 9350
9253
9304
9355
9258
9309
9360
9263
9315
9365
9269
9320
9370
9274
9325
9375
9279
9330
9380
9284
9335
9385
9289
9340
9390
5
5
5
87
88
89
90
91
92
93
9395 9400
9445 9450
9494 9499
9405
9455
9504
9410
9460
9509
9415
9465
9513
9420
9469
9518
9425
9474
9523
9430
9479
9528
9435
9484
9533
958l"
9440
9489
9538
5
5
4
4
5
5
4
9542 9547
9552
9557
9562
9566
9614
9661
9708
9571
9576
9586
9590 9595
9638 9643
9685 9689
9600
9647
9694
9605
9652
9699
9609
9657
9703
9619
9666
9713
9624
9671
9717
9628
9675
9722
9633
9680
9727
94
95
96
9731 9736
9777 9782
9823 ! 9827
9741
9786
9832
9745
9791
9836
9750
9795
9841
9754
9800
9845
9759
9805
9850
9763
9809
9854
9768
9814
9859
9773
9818
9863
4
5
5
97
98
99
9868 9872
9912'9917
9956 9961
9877
9921
9965
2
9881
9926
9969
9886
9930
9974
9890
9934
9978
9894
9939
9983
9899
9943
9987
9903
9948
9991
9908
9952
9996
4
4
4
No.
| 1
3
4
5
6
7
8
9
Diff.
** 155 '*
WEIGHT OF
A CUBIC FOOT OF SUBSTANCES.
Average
NAMES OF SUBSTANCES. Weight
LBs.
Anthracite, solid, of Pennsylvania, 93
" broken, loose, 54
" " moderately shaken, 58
" heaped bushel, loose, (8O)
Ash, American white, dry, 38
Asphaltum, 87
Brass, (Copper and Zinc,) cast, - - 504
rolled, 524
Brick, best pressed, 150
" common hard, 125
" soft, inferior, 100
Brickwork, pressed brick, 140
" ordinary, 112
Cement, hydraulic, ground, loose, American, Rosendale, 56
" " " " " Louisville, 50
" " " " English, Portland, - 90
Cherry, dry, . - 42
Chestnut, dry, - 41
Coal, bituminous, solid, 84
" " broken, loose, 49
" " heaped bushel, loose, - - - (74)
Coke, loose, of good coal, 27
" " heaped bushel, - (38)
Copper, cast, 542
rolled, 548
Earth, common loam, dry, loose, - - - 76
" " " " moderately rammed, - - 95
" as a soft flowing mud. - 108
Ebony, dry, 76
Elm, dry, 35
Flint, - 162
Glass, common window, - - - 157
156
WEIGHT OF SUBSTANCES Continued.
Average
NAMES OF SUBSTANCES. Weight.
Lbs.
Gneiss, common. _______ 1Q&
Gold, cast, pure, or 24 carat, _____ 1204
" pure, hammered, ______ 1217
Granite, _ 170
Gravel, about the same as sand, which see.
Hemlock, dry, ---_.._. 25
Hickory, dry, -__-__. 53
Hornblende, black, - - 203
Kce, - - '- - - - - - - 58.7
Iron, cast, -----_-__ 450
i< wrought, purest, - - - - - 485
average, - 480
Ivory, 114
Lead, - 711
Lignum Vitae, dry, _______ 83
Lime, quick, ground, loose, or in small lumps, - - 53
" " thoroughly shaken, - 75
" " " " per struck bushel, - *. (66)
Limestones and Marbles, - - - - _ - 168
" " loose, in irregular fragments, - 96
Mahogany, Spanish, dry, ' - - - - 53
" Honduras, dry, - - - - - 35
Maple, dry, - - - - - - - _ 49
Marbles, see Limestones.
Masonry, of granite or limestone, well dressed, - 165
" mortar rubble, 154
" " dry " (well scabbled,) - - 138
" " sandstone, well dressed, - 144
Mercury, at 32 Fahrenheit, - - ... 849
Mica, - - _ 183
Mortar, hardened, - - - - - - 103
Mud, dry, close, - - - - - - 80 to 110
" wet, fluid, maximum, - - - - 120
Oak, live, dry, -- - _-_ _ _ . 59
WEIGHT OF SUBSTANCES Continued.
Average
NAMES OF SUBSTANCES. Weight.
Lfe.
Oak, white, dry, ------- 52
" other kinds, - - - - - - 32 to 45
Petroleum, ____--_- 55
Pine, white, dry, _______ 25
" yellow, Northern, _.-___ 34
" " Southern, -____- 45
Platinum, 1342
Quartz, common, pure, - - - - - -165
Rosin, 69
Salt, coarse, Syracuse, N. Y. -.-.-. 45
" Liverpool, fine, for table use, - 49
Sand, of pure quartz, dry, loose, - 90 to 106
" well shaken, 99 to 117
" perfectly wet, - 120 to 140
Sandstones, fit for building, _____ 151
Shales, red or black, - ... - 162
Silver, - - 655
Slate, . - 175
Snow, freshly fallen, 5 to 12
" moistened and compacted by rain, - - 15 to 50
Spruce, dry, __---_-- 25
Steel, 490
Sulphur, 125
Sycamore, dry, --------37
Tar, 62
Tin, cast, --------- 459
Turf or Peat, dry, unpressed, - - - - 20 to 30
Walnut, black, dry, ___-_-_ 38
Water, pure rain or distilled, at 60 Fahrenheit, - 62 1 / 3
" sea, 64
Wax, bees, .-- 60.5
Zinc or Spelter, --_-__-- 437
Green timbers usually weigh from one-fifth to one-half more
than dry.
-*- 158 8
WINDOW GLASS.
Window Glass is sold by the box, which contains, as nearly as
may be, 50 square feet, whatever may be the size of panes.
The thickness of ordinary or "single thick" Window Glass is
about 1-16 of an inch, and of "double thick " nearly 1-8 of an inch.
'I
"he tensile strength of common glass varies from 2000 Ibs. to
3000 Ibs. per square inch, and its crushing strength from 6000 Ibs.
to 10000 Ibs.
The following is the list of the Pittsburgh City Glass Works,
Cunninghams & Co., Proprietors. Other sizes may be made to
order.
Sizes.
In.
Lights
per Box
No.
Sizes.
In.
Lights
perBoi.
No.
Lights
Sl T zes - perBoi.
Itt - No.
Sizes.
In.
Lights
perBoi
No.
Lights
No.
6X 8
150
11 X 24 27
14 X 18 29
18 X 18
22
24 X 30
10
7X 9
115
26 25
20 26
20
20
32
10
8X 10
90
28
23
22
24
22
18
34 9
12
' 75
30
22
24
22
24
17
36 9
13
69
32
20
26
20
26
16
38 8
* 14
64
34
19
28
19
28
14
40 8
15
60
36
18
30
17
30
14
42 7
16
56
38
17
32
16
32
13
44
7
18
50
46 16
34
15
34
12
46
7
20
45
42 15
36
14
36
11
48
6
9X U
73
12 X 12 50
38
14
38
11
26 X 26
11
12
67
13
46
40
13
40
10
28
10
13
62
14
43
42
12
42
10
30
9
14
57
15
40
44
12
44
9
32
9
15
53
16! 38
46
11
46
9
34
8
16
50
18 | 34
15 X 15
32
20X 20
18
36
8
18
44
19
32
16
30
22
17
38
7'
20
40
20
30
18
27
24
15
40
7
22
36
22
27
20
24
26
14
42
7
10 X 12
60
24
25
22
22
28
13
44
6
13
55
26
23
24
20
30
12
46
6
14
52
28
22
26
19
32
11
48
6
15 i 48
30
20
28
17
34
11
28X28
9
16
45
32
19 -
30
16
36
10
30
9
18
40
34
18
32
15
38
10
32
8
19
38
36
17
34
14
40
9
34
8
20
36
38
16
36
13
42
9
36
7
22
33
40
15
38
13
44
8
38
7
24
30
42
14
40
12
46
8
40
7
26
28
13 X 15
37
42
11
22 X 22
15
42
6
28
25
16
35
44
11
24
14
44
6
30
24
18
31
16 X 16
28
26
13
46
6
32
22
20
28
18
25
28
12
48
5
34
21
22
25
20
23
30
11
30X30
8
36
20
24
23
22 21
32
10
32' 7
38
19
26
21
24 19
34
10
34 7
40
18
28
20
26
17
36
9
36
7
42
17
30
18
28
16
38 9
38
7
11 X 12
55
32
17
30
15
40
8
40
6
14
47
34
16
32
14
42
8
42
6
15
44
36
15
34
13
44
7
44
6
16
41
38 15
36
13
46
7
46
5
18
37
40 14
38
12
48
7
48
5
19
34
42 13
40
11
24X 24
12
50
5
20
33
14 X 14 37
42
11
26 12
22
30
16 32
44
10
28 11
c
LINEAR EXPANSION OP SUBSTANCES
BY
HEAT.
To find the increase in the
length of a bar of any material clue
to an increase of temperature, multiply the number of degrees
of increase of temperature by the coefficient for 100 degrees and
by the length of the bar, and
divide by 100.
NAME OF SUBSTANCE.
Coefficient for 100 Coefficient for 180
Fahrenheit. Fahrenheit, or 100
Centigrade.
Baywood, (in the direction of the J
.00026
TO
.00046
TO
grain, dry,)
I
.00031
.00057
Brass, (cast,) -
-
.00104
.00188
" (wire,)
.O0107
.00193
Brick, (fire,) -
-
.0003
.0005
Cement, (Roman,) -
-
.0008
.0014
Copper,
.0009
.0017
Deal, (in the direction of the grain, J
dry,) - - -{
.00024
.00044
Glass, (English flint,) -
-
.00045
.00081
" (French white lead,)
-
.00048
.00087
Gold..
-
.0008
.0015
Granite, (average,)
-
.00047
.00085
Iron, (cast,) -
-
.0006
.0011
" (soft forged,)
-
.0007
.O012
" (wire,) -
-
.0008
.0014.
Lead,
-
.0016
.0029
.00036
.00065
Marble, (Carrara,) -
TO
TO
.0006
.0011
Mercury,
.0033 .0060
Platinum,
-
.0005 .0009
{
.0005 .0009
Sandstone, -
TO TO
f
.0007 .0012
Silver,
.0011 .002
Slate, (Wales,)
.0006 .001
Water, (varies considerably
wlthf .0086 .0155
the temperature,)
i .
MENSURATION.
LENGTH.
Circumference of circle = diameter X 3.1416.
Diameter of circle = circumference X 0.3183.
Side of square of equal periphery as circle = diameter X 0.7854.
Diameter of circle of equal periphery as square = bide X 1.2732;
Side of an inscribed square = diameter of circle X 0.7071.
Length of arc = No. of degrees X diameter X 0.008727.
Circumference of circle whose diameter is 1 =
TT = 3.14159265.
log.7r=0.4971499.
-,/ 7r=1.772454.
TT 2 =9.869604.
c 2
0.318310.
= 0.101321.
0.564190.
2v
or, very nearly, = -
AREA.
Triangle = base X half perpendicular hight.
Parallelogram = base X perpendicular hight.
Trapezoid = half the sum of the parallel sides X perpen-
dicular hight.
Trapezium, found by dividing into two triangles.
Circle = diameter squared X 0.7854 ; or,
= circumference squared X 0.07958.
Sector of circle = length of arc X half radius.
161
MENSURATION Continued.
Segment of circle = area of sector less triangle ; also, for
4 v i/ c~2~
Hat segments very nearly = -r 0.388 v- -\ j
Side of square of equal area as circle = diameter X 0.8862 ;
also, = circumference X 0.2821.
Diameter of circle of equal area as square = side X 1.1284.
Parabola = base X /i hight.
Ellipse = long diameter X short diameter X 0.7854.
Regular polygon = sum of sides X half perpendicular distance
from center to sides.
Surface of cylinder = circumference X hight X area of both
ends.
Surface of sphere = diameter squared x 3.1416;
also, = circumference X diameter. %
Surface of a right pyramid or cone = periphery or circumference
of base X half slant hight.
Surface of a frustrum of a regular right pyramid or cone = sum
of peripheries or circumferences of the two ends X half
slant hight -j- area of both ends.
The following formulae are used to obtain the areas of
irregular plane surfaces which are bounded by a base line, "cc"
and two ordinates, "" and "," as per figure.
The formulae are given in the order of their accuracy, be-
ginning with the most accurate.
The sift-face is divided into any number (n} of parallel strips
having the same widths, d, and whose middle ordinates are
represented by h h h h and //.
123 n 1 n
162
88
MENSURATION Continued.
I. Area = d X S h +(8 a + ly-9 h ) + 8b + t^j
(Francke's rule.)
II. Area = d X S h + ^ --(a - h) + -A- (b - hj
(Poncelet's rule.)
III. Area = d X h.
These formulae are more convenient for use than Simpson's
rule, and I and II give generally and III sometimes more
accurate results.
^ stands for sum of.
SOLID CONTENTS.
Prism, right or oblique, = area of base X perpendicular hight.
Cylinder, right or oblique, = area of section at right angles to
sides X length of side.
Sphere = diameter cubed X 0.5236.
also, = surface X l /6 diameter.
Pyramid or cone, right or oblique, regular or irregular, = area
of base X / perpendicular hight.
PRISMOIDAL FORMULA.
A prismoid is a solid bounded by six plane surfaces, only
two of which are parallel.
To find the contents of a prismoid, add together the areas of the
. two parallel surfaces and four times the area of a section
taken midway between and parallel to them, and multiply
the sum by i/th of the perpendicular distance between the
parallel surfaces.
WEIGHTS AND MEASURES.
AVOIRDUPOIS OR ORDINARY COMMERCIAL WEIGHT.
UNITED STATES AND
BRITISH.
Ton.
Owts.
Poandi.
Ounces.
1.
0.050
20.
1.
0.0089
2240.
112.
1.
0.0625
35840.
1792.
16.
1.
1 pound = 27.7 cubic inches
density, (39 Fahrenheit.)
of distilled water at
its maximum
LONG
MEASURE.
UNITED STATES AND
BRITISH.
Miles.
Rods. Yards.
Feet.
Inches.
1.
0.003125
0.000568
0.0001894
0.0000158
320. 1760.
1. 5.5
0.1818 1.
0.0606 0.3333
0.005051 0.02778
5280.
16.5
'3.
1.
0.08333
63360.
198.
36.
12.
1.
The British measures are shorter than those of the U. S. by
about 1 part in 17230 or 3.677 inches in a mile.
A fathom = 6 feet. A Gunter's surveying chain = 66 feet
or 4 rods, 80 chains making a mile.
SQUARE OR LAND
MEASURE
UNITED STATES AND BRITISH.
Sq. Miles. 1
Lores. Sq. Rods.
Sq. Yards. Sq. Feet.
Sq. Inches.
1. C
40. 102400. 3097600. 27878400.
1. 160. 4840. 43560. 6272640.
1. 30.25 272.25 39204.
0.0331 1. 9.0 1296.
0.111 1. 144.
0.00694 1.
" 164 r *
WEIGHTS AND MEASURES Continued.
CUBIC OR SOLID MEASURE.
UNITED STATES AND BRITISH.
1728 cubic inches = 1 cubic foot.
27 cubic feet = 1 cubic yard.
A cord of wood = 4' X V X 8' = 128 cubic feet.
A perch of masonry = 16.5' X 1.5' X 1' = 24.75 cubic feet,
but is generally assumed at 25 cubic feet.
DRY MEASURE..
UNITED STATES ONLY.
Struck Bush I Pecks.
Quarts.
Pints.
Gallons.
Cubic Inch.
1
\
32.
8.
1.
0.5
4.
64
16
2
1
8
8.
2.
0.25
0.125
1.
2150.
537.6
67.2
33.6
268.8
A gallon of liquid measure = 231 cubic inches.
A heaped bushel = 1 14' struck bushels. The cone in a heaped
bushel must be not less than 6 inches high.
A barrel of U. S. hydraulic cement = 300 to 310 Ibs., usually,
and of genuine Portland cement = 425 Ibs.
To reduce U. S. dry measures to British imperial of the same
name, divide by 1.032.
NAUTICAL MEASURE.
A nautical or sea mile is the length of a minute of longitude
of the earth at the equator at the level of the sea. It is assumed
= 6086.07 feet == 1.152664 statute or land miles by the United
States Coast Survey.
3 nautical miles = 1 league.
165
COMPARATIVE TABLE OF
UNITED STATES AND FRENCH MEASURES.
MEASURES. No.
One grain = gramme, O.0648
One pound avoirdupois = kilogramme, - - O.4536
One ton of 2240 Ibs. = tonnes, - - 1.0160
One ton of 2000 Ibs. = tonne, - 0.9071
One inch = millimetres, - 25.40O
One foot = metre, - O.3048
One mile = kilometres, 1.6094
One square inch = square millimetres, - - 645.2
One square foot = square metre, 0.09291,
One acre = are (100 square metres), - 40.47
One square mile = square kilometres, 2.590
One cubic inch = cubic centimetres, - 16.39
One cubic foot = cubic metre, O.02832
One cubic yard = cubic metre, - - 0.7646
One quart dry measure = litres, 1.1O1
One quart liquid or wine measure = litre, - O.9465
One foot pound = kilogrammetre, - 0.1383
One pound per foot = kilogrammes per metre, - 1.488
One thousand pounds per square inch = kilogramme
per square millimetre, 0.703
One pound per square foot = kilogrammes per
square metre, 4.882
One pound per cubic foot = kilogrammes per
cubic metre, 16.02
One degree Fahrenheit = degree centigrade, O.5556
166
3 ?
COMPARATIVE TABLE OF
FRENCH AND UNITED STATES MEASURES.
MEASURES.
No.
One gramme = grains,
15.433
One kilogramme = pounds avoirdupois, -
2.2047
Oncxtonne = tons of 2240 Ibs.
0.9843
One tonne = tons of 2000 Ibs.
1.1024
One millimetre = inch,
0.0394
One metre = feet,
3.2807
One kilometre = mile,
0.6213
One square millimetre = square inch,
0.00155
One square metre = square feet,
10.763
One are (100 square metres) = acres,
0.02471
One square kilometre = square mile,
0.3861
One cubic centimetre cubic inch,
0.0610
One cubic metre or stere = cubic feet,
35.3105
One cubic metre = cubic yards, -
1.3078
One litre (one cubic decimetre) = cubic inches,
61.017
One litre = quarts, dry. measure, -
0.908
One litre = quarts, liquid or wine measure, -
1.0566
One kilogrammetre = foot pounds,
7.2331
One kilogramme per metre = pounds per foot,
0.6720
One kilogramme per square millimetre = pounds
per square inch, -
1422
One kilogramme per square metre = pounds per
square foot,
0.2048
One kilogramme per cubic metre = pounds per
cubic foot,
0.0624
One degree centigrade = degrees Fahrenheit, -
1.8
STRENGTH OF MATERIALS.
ULTIMATE RESISTANCE TO TENSION
IN LBS. PER SQUARE INCH..
METALS.
Average.
Brass, cast, - - - - -- - - 18000
" wire, - 49000
Bronze or gun metal, ______ 36000
Copper, cast, _______ 19000
sheet, 30OOO
" bolts, 36000
" wire, 60000
Iron, cast, 13400 to 29000, ----- 16500
" wrought, round or square bars of 1 to 2 inch
diameter, double refined, - 50000 to 54000
" wrought, specimens % inch square, cut from large
bars of double refined iron, _ 50000 to 53000
" wrought, double refined, in large bars of about
7 square inches section, - - 46000 to 4700O
" wrought, plates, angles and other shapes, 48000 to 5100O
" " plates over 36" wide, - 46000 to 50000
Wrought iron, suitable for the tension members of bridges,
should be double refined, and show a permanent elongation of
20 per cent, in 5", when broken in small specimens, and a re-
duction of area of 25 per cent, at point of fracture.
The modulus of elasticity of Union Iron Mills' double refined
bar iron is 25000000 to 26000000, from tests made on finished
eyebars.
Iron, wire, 70000 to 1OOOOO
" wire-ropes, - 9000O
Lead, sheet, - - _____ 33OO
Steel, 65000 to 1200OO
Tin, cast, __.._. 4600
Zinc, _______ 7000 to 8000
168
STRENGTH OF MATERIALS-Continued.
TIMBER, SEASONED, AND OTHER ORGANIC FIBER.
Average.
Ash, English, - - 17OOO
" American, - 11000 to 14000
Beech, " 15000 to 1800O
Box, 20000
Cedar of Lebanon, ------- 11400
" American, red, - - - - - - 10300
Fir or Spruce, - 1000O to 13600
Hempen Ropes, - - - - 12000 to 1600O
Hickory, American, - 12800 to 180OO
Mahogany, 80OO to 2180O
Oak, American, white, - ----- 1800O
" European, ----- 10000 to 19800
Pine, American, white, red and pitch, Memel, Riga, - 1OOOO
" " long leaf yellow, - 12600 to 19200
Poplar, - - - - 700O
Silk fiber, 52000
Walnut, black, 1600O
STONE, NATURAL AND ARTIFICIAL.
Brick and Cement, - - - 280 to 300
Glass, - 9400
Slate, - - 9600 to 1280O
Mortar, ordinary, 5O
ULTIMATE RESISTANCE TO COMPRESSION.
METALS.
Brass, cast, 10300
Iron, " - - 82000 to 145000
" wrought, 36000 to 40000
169
STRENGTH OF MATERIALS Continued.
TIMBER, SEASONED, COMPRESSED IN THE
DIRECTION OF THE GRAIN. Average.
Ash, American, 4400 to 5800
Beech, " 5800 to 6900
Box, 10300
Cedar of Lebanon, - 5900
" American, red, - 6000
Deal, red, 6500
Fir or Spruce, 5100 to 6800
Oak, American, white, - - 720O to 9100
" British, 10000
" Dantzig, - - - 770O
Pine, American, white, - 5000 to 5600
" " long leaf yellow, 8000
Spruce or Fir, 5800 to 6900
Walnut, black, - 7500
STONE, NATURAL OR ARTIFICIAL.
Brick, weak, - - - - - - - 55O to 800
" strong. - 1100
" fire, 1700
Brickwork, ordinary, in cement, - 300 to 450
best, - - 1000
Chalk, 330
Granite, - - - 5500 to 11000
Limestone, - - 4000 to 11000
Sandstone, ordinary, ____-- 4000
ULTIMATE RESISTANCE TO SHEARING.
METALS. -
Iron, cast, - - 27700
" wrought, along the fib'er, - 45000
TIMBER, ALONG THE GRAIN.
White Pine, Spruce, Hemlock, - 500 to 800
Yellow Pine, long leaf, 630 to 960
Oak, European, - - - 2300
Ash, American, - - 2000
PAGE.
Cast iron columns, and wrought iron, ultimate strength of ____ 79
Channel bars, lithographed sections of ................... 5-8
" " explanation of table on properties of ....... 56-61
" " table on properties of .................... 64, 65
Circumferences of circles, and areas .................. 112-124
Columns, corrugated, lithographed sections of .............. 15
" Keystone octagon, lithographed sections of ........ 13
" " " thicknesses and corresponding
areas and weights ........................... 77
" Piper's patent rivetless, lithographed sections of. ... 14
" " " " thicknesses and correspond-
ing areas and weights of ..................... 78
" explanation of tables on ..................... 73-76
" cast and wrought iron, ultimate strength of ........ 79
" wrought iron, ultimate strength of ....... ........ 80
" wooden, ultimate strength of .................... 81
Comparative table of United States and French, and French
and United States measures ..................... 166, 167
Corrugated and galvanized iron ....................... 85, 86
Cover angles, lithographed sections of ..................... 12
Decimal parts of a foot for each g'jth of an inch ...... ...... 87
Decimals of, an inch for each ^th ................ . ...... 171
Deck beams, lithographed sections of ...................... 4
" " properties of ......................... ..... 63
Deflection of rolled eyebeams under load ............... 33-55
" formulas for special cases ...................... 61
Dove tail, lithographed section of ...................... , .22
Elasticity, modulus of, assumed in tables .................. 60
" for eyebars ....................... 168
Expansion, linear, of substances by heat .................. 160
Eyebeams ........................ ........... See Beams.
Fence Iron, lithographed sections of. .... ................. 22
Fire-proof floors .................................... 83, 84
Flat, beveled, lithographed section of .............. '. ...... 22
Flat rolled iron, weights per lineal foot of ............... 88-93
" areas of ............................. 94-99
fit
PAGE.
Flexure of beams of any cross-section, general formulae on, 60, 61
Floorbeams of bridges 133
Floors and roofs, general notes on 82-84
Floors, lithographed illustrations of 23-25
Foot, decimal parts of, for each -^th of an inch 100-103
French and United States measures, comparative table of. . . .167
Galvanized iron 86
Gas pipe, sizes and weight of 132
Gauge, American, for sheet iron Ill
" Birmingham, " " , 110
Girders, riveted, table on .' 72
Glass, window, number of lights per box 159
Grooved irons, lithographed sections of 21
Half T's, lithographed sections of 15
Handrails, " " 21
Ice slides, " 22
Inertia, moments of, for usual sections 61
See also tables on properties of beams, channels, angles, etc.
Keystone Bridge Co.'s corrugated iron 86
" " " standard proportions for upset
rods 126, 127
" octagon columns, lithographed sections of 13
" " " thicknesses and corresponding
areas and weights 77
Linear expansion of substances by heat 160
Loads per square foot, for floors, roofs, etc 84
Logarithms of numbers 153-155
Materials, strength of 168-170
Measures, and weights, United States and British 164, 165
" " " comparative table of United States
and French, and French and United States 166, 167
Mensuration 161-163
Modulus of elasticity, assumed in tables 60
-_
PAGE.
Modulus of elasticity for eyebars 168
Moments, maximum bending, to be allowed on pins 136
Natural sines, tangents and secants 144-152
Notes, general, on floors and roofs 82-84
Nuts, sizes and weights of hot pressed square 130
" " " " " hexagon 131
Obtuse angle, lithographed section of 12
Octagon columns, lithographed sections of 13
" " thicknesses and corresponding areas and
weights 77
Patent post iron, lithographed section of 15
Pillars, timber, ultimate strength of 81
Pins, bearing value of, for one inch thickness of plate 137
" maximum bending moments to be allowed on 136
Pipe, wrought iron, for gas, steam or water 132
Piper's patent rivetless columns, lithographed sections of 14
" " - " " thicknesses and correspond-
ing areas and weights of 78
Plastered ceiling, weight of 84
Plastering, limit of deflection to allow for 31
Post irons, patent, lithographed sections of 15
Posts See Columns.
Pratt trusses, maximum stresses in 141
" truss, diagram of 26
Properties of U. I. M.'s eye and deck beams 62, 63
" " channels.... 64,65
" " " angle irons 66,67
" " " tee irons 69
" " " star irons 69
" explanation of tables on 56-61
Riveted girders, explanation of table on 70, 71
" " table on 72
Rivetless columns, lithographed sections of 14
" " thicknesses and corresponding areas and
weights of 78
'< 7^ )
175
PAGE.
Rivets and round-headed bolts, weight of 125
Roof iron, lithographed section of 20
Roofs, loads and weights per square foot for 84
Round bars, and square, of wrought iron, weights and areas,
and circumferences of round bars 104-109
Rule for finding the area of a bar of wrought iron, given the
weight, and vice versa 84
Sash Irons, lithographed sections of 22
Screws, wood 129
Separators, between beams, lithographed illustrations of 24
" " " weight of 82
Shearing and bearing value of rivets 135
Sheet iron, by Birmingham gauge 110
" " American " Ill
Sines, tangents and secants, natural 144-152
Spacing of beams in floors 33-55
Spikes, wrought 129
Square root angle irons, lithographed sections of 11
Square and round bars of wrought iron, weights and areas,
and circumferences of round bars 104-109
Standard screw threads, nuts and bolt heads, recommended
by the Franklin Institute 128
Star irons, lithographed sections of 12
" " properties of 69
Strength of cast and wrought iron columns 79
" " wrought iron columns 80
" " timber pillars 81
" " materials 168-170
Stresses, maximum, in Pratt trusses 141
" in Whipple trusses 142, 143
" explanation of tables on 139, 140
Struts See Columns.
Substances, weight of a cubic foot of 156-158
linear expansion of, by heat 160
Tacks 129
Tee, half, lithographed sections of 15
Tee irons, " 16-20
176 *
08
PAGE.
Tee irons, properties of 69
Threads, screw, Franklin Institute standard 128
" " Whitworth standard 129
Tie rods, for brick arches in floors / 83
Timber beams, safe load for 138
" pillars, ultimate strength of 81
Tubes, wrought iron welded, for gas, steam or water 132
Upset screw ends for square and round bars 126, 127
Weights of a cubic foot of substances 156-158
angle irons, corresponding to thicknesses vary-
ing b y TV'-. 68
" brick-work, walls of 83
" flat rolled iron 88-93
nuts, hot pressed, square and hexagon 130, 131
" separators and bolts 82
sheet iron 110, 111
" square and round bars of wrought iron 104-109
tubes, of wrought iron, for gas, steam or water. . .132
wrought iron, rule for finding, given the area 84
" spikes, wood screws and tacks. ...'..... 129
Weights and measures, United States and British 164, 165
" " " comparative table of United States
and French, and French and United States 166, 167
Whitworth standard screw thread. 129
Window glass, number of lights per box 159
Wooden beams, safe load for 138
Wood screws 129
Wrought spikes 129
Z iron, lithographed section of 22
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