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 and Dia-
Struts,

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-

and Tees,
nels, Angles, Stars 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 TV' 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
_ .
>
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ANGLES WITH EQUAL LEGS.

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3.5to7,3 Ibs ',

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 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 length, for the distances between
its

supports, (or lengths of span,) given in first column ;

II. In fifth to eleventh columns inclusive, the distances be-
tween centers which beams should be placed in floors, to carry
at

and 300 Ibs. per square

safely loads of 100, 125, 150, 175, 200, 250
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-

builtbeams, 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. will require
14.12
-||j-
15
t.,) 6 Ibs. X =
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 =
per square foot, and the Ibs.

distance between supports =

6" greater than the distance
25', z. e.

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'

UNION IRON MILLS'
:<
J
5
H
UNION IRON
x?
UNION IRON MILLS'
UNION IRON MILLS'
UNION IRON MILLS'
TV CT
5
UNION IRON MILLS'
UNION IRON MILLS'
UNION IRON MILLS 1
 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.
 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 thesake of uniformity, it was assumed generally that
the sizecorresponds 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 givenby 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.
Thetable 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' Irons T
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
by simply dividing the same into the. bending moment,
strains,

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
the webs of
passing through the center of the section parallel to
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

= L = )0 * 28
= 20000
4 280, therefore 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 ?

Answer: C
1L
= -^ = 16 X 36000
= K -c ,
which
. ,

required
-^ 576,

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
^
1.46
= 8220 *lbs., occurring in the fibers furthest from the

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 =
2
P = load given in tables X I

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 :

bending moment occurs = W^

at support and
1

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,
= length of span,
1

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 per square inch
strain in extreme fibers of beam, either

top or bottom,
D = maximum deflection,
= moment of
I of inertia section,
R = moment of resistance,
= radius of
r gyration,
E = modulus of elasticity,

(assumed = 2600QOOO for wrought iron in tables.)

Then R=

~~r~ R
8 =T 8 Q
w=-
_ Win _wRi_
81 8

5 Wl 3 for beam supported at both ends and uni-

El formly loaded,
384
3 for beam supported at both ends and loaded
_~ PI
48 El by a single load P at middle,

_ Wl beam held
3 for 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

neutral axis coincident with base, I = bh ^

o
3
.

Triangle ; h = hight, b = base ;

for neutral axis through center
of gravity (i. e.,
distant ^ h from base), parallel to base, I =
- -, Rmin.= -
;
for neutral axis coincident with base, I =
OD fA.

bh 3 bh 3
-.
-.; for neutral axis through apex, parallel to base, I = 4

Circle ; = diameter, = 3.1416; neutral axis through

d TT for

center, I = -= d*, R =-=- = 0.0982 d.

0.0491
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67
3 f.

UNION IKON MILLS' ANGLE IRONS.

Weights per Foot corresponding to thicknesses varying by Ty".
One cubic foot weighing 480 Ibs.
<5
 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
isnot 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 d2 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. should always be

Stiffeners

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 be found to be of about the same strength
this table, will

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 JTth of the span length or 2 " per foot of this y
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

is required?
girder
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
d2 = (20)
2 = 3200 Ibs., allowed.
h 2 2
3000 t 3000 (X)
71
RIVETED
 COLUMNS AND STRUTS.
Explanation of tables, pages 77 to 81, inclusive.

The on Keystone Octagon and Piper's Patent Rivetless

tables
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

tableson the properties of Union Iron Mills' Beams, Channels, etc.
If the column composed of two channels latticed, as
is

represented by Fig. on page 26, the channels are usually

1,

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
necessary to obtain
26, it is

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,
the correction for this approximation can be
page 26,

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 a neutral axis through center of section
'of inertia, for

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
in pin-connected bridges.)
pin-jointed, (for example, the posts

With regard to the table on the Safe Resistance of Wooden

Pillars, should be said that comprehensive tests establishing
it

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 hat
T
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
nearly, so that
1
~-r-= -v
20
= 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

gyration =
131.6
~\,

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

= 10.8 square inches X = - -

146.3
squared
Moment of inertia of section =
3.68

.... 170.8

Therefore radius of gyration = y/"TToc' == 3.39.

^
v v or
 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 Column Column
Square Bearing : Pin and Square Bearing Pin Bearing :

40000 40000 40000

(121)* 14 (121)*."
,
"
IJL
36000 r
2
24000 r 2 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. per square inch.

Square.

3.0 38610 37950 37310 8.0

3.2 33430 37680 36970 8.2
3.4 38230 37400 36610 8.4
3.6 38030 37110 36240 8.6
3.8 37820 36810 35860 8.8

4.0 37590 36500 35460 9.0

4.2 37360 36170 35050 9.2
4.4 37120 35840 34640 9.4
4.6 38870 35500 34210 9.6
4.8 36620 35140 33770 9.8

5.0 36360 34780 33330 10.0

5.2 36090 34420 32890 10.2
5.4 35820 34050 32440 10.4
5.6 35540 33670 31980 10.6
5.8 35260 33280 31520 10.8

6.0 34970 32890 31060 11.0

6.2 34870 32500 30590 11.2
6.4 34370 32110 30130 11.4
6.6 34060 31710 29670 11.6
6.8 33750 31310 29200 11.8

7.0 33440 80910 28740 12.0

7.2 33130 30510 28270 12.2
7.4 32810 30110 27820 12.4
7.6 32490 29710 27360 12.6
7.8 32170 29310 26910 12.8
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. for6" 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
in
part of the wall between the lines of rupture, provided, that
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 the superficial area of the trapezoid between the lines
it,

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 by iron hooks from the lower

centers are suspended

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
composed of sheet iron pressed to suitable form, laid
ceiling,
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
" " - 250 " "
warehouses,
- - "
Weight of snow, freshly fallen, 5 to 12 cub. ft.

" " - 40 " "

saturated, (slush,)

Crowd of people, closely packed, - 80 " ft.

sq.

Wind - 50 " "

pressure (violent hurricane,)

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 isused 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 for a
permanent deflection
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.
 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 1j
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
 WEIGHTS OP FLAT ROLLED IRON
PER LINEAL FOOT.
(CONTINUED.)

Thickness
in Inches.
WEIGHTS OF FLAT ROLLED IRON
PER LINEAL FOOT.
.
(CONTINUED.)
3
1
 AREAS OP PLAT ROLLED IRON.
(CONTINUED.)

Thickness
in Inches.
 AREAS OF PLAT ROLLED IRON.
(CONTINUED.)

Thickness
in Inches.
 AREAS OP FLAT ROLLED IRON.
(CONTINUED".)

Thickness
in Inches.
 AREAS OP FLAT ROLLED IRON.
(CONTINUED.)

Thickness
in Inches.
5

SQUARE AND ROUND BARS.

(CONTINUED.)
TV fT
*15 C

SQUARE AND ROUND BARS.

(CONTINUED.)
SQUARE AND ROUND BARS.
(CONTINUED.)
SQTJAKE AND ROUN^&ff&ST
(CONTTOTED.) HUKIVBRS!
WEIGHT OF SHEETS OF WROUGHT IRON,
AREAS and CIRCUMFERENCES OF CIRCLES.
For Diameters from -fe to 100, advancing by Tenths.
JLJ
""-
a
AKEAS and CIRCUMFERENCES OF CIRCLES.
(CONTINUED.)
 "
?

AREAS and CIRCUMFERENCES OF CIRCLES.

(CONTINUED.)
! I

AREAS and CIRCUMFERENCES OF CIRCLES.

(CONTINUED.)
AREAS and CIRCUMFERENCES OF CIRCLES.
i

(CONTINUED.)
v l,

AREAS and CIRCUMFERENCES OP CIRCLES.

(CONTINUED.)
<

AREAS and CIRCUMFERENCES OF CIRCLES.

(CONTINUED.)
AREAS and CIRCUMFERENCES OP CIRCLES.
(CONTINUED.)
AREAS and CIRCUMFERENCES OP CIRCLES.
(CONTINUED.)
J E

AREAS and CIRCUMFERENCES OF CIRCLES.

(CONTINUED.)
AREAS and CIRCUMFERENCES OF CIRCLES,
(CONTINUED.)
AREAS and CIRCUMFERENCES OF CIRCLES.
(CONTINUED.)

Diam.
"Yj
^TJ
STANDARD SCREW THREADS, NUTS AND
BOLT HEADS. Recommended by the Franklin Institute.
 WHITWORTH'S STANDARD ANGULAR
SCREW THREADS.
Angle of Thread 55.
Depth of Thread = pitch of
screw.
Y& of depth is rounded off at
top and bottom.
= ^ the"number inNumber
of threads to the
inch in square threads angular threads.
Dia, of ;
Threads
Screw, to the Inch.
In. No.
? r.
 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.
 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,-| :* o ^gg^ogg i

<^ -T}< |>- -^f lO T-< CO Is- 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

10 10
IOI> (M (M
t>CO (MOO lOi-H C^CO CD (MOO
CO-^ 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.
BEARING VALUE OF PINS FOR ONE INCH
THICKNESS OF PLATE.
( X 1" X strain per sq.
Dia. of Pin inch.)
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
for any
quadrangular) or Whipple (double quadrangular) truss,
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
consider
quadrangular truss by statical methods, it is necessary to
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
by the two methods is so small as not
resulting stresses obtained
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.

W = ~-
1900
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 = -

lo
= 0.833, the secant = 1.302;

therefore
Be == 97000 X 1.30 = 126100 Ibs.

DE = 315000 X = 262500 Ibs.

-j|~

140
:5

MAXIMUM STRESSES UNDER

 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.

15 Panel 14 Panel
Member.
Truss. Truss.

W+L W+L W+L

6.5+6.5

2.0+^!
1.5+2
1.0+
0.5+1
J
0.0+

7+7 6.5+ 6.5 6+6

W+W
W+W
9.5+
14.5+14.5
9.5; W+W
n *

W+W 18.5+18.5
21.5+21.5
15.0+16.0
17.0+17.0!
W+
"

V+^
; 3
23.5+23.5, 18.0+18.0' W+
~ - W+
,

TV
24.5+24.5!
2
FG=EF
~~=FG
W+W
2.5-[_30 y5
2.0+
i
wi
4.24.5 It5

2^5 1.0+1
__^s 0.5+1
4
--W o.o- +-W 1

-r T+4-f -0.5+-'

143
NATURAL SINES
NATURAL SINES, TANGENTS AND SECANTS.
NATURAL SINES, TANGENTS AND SECANTS.
y

NATURAL SINES
NATURAL SINES, TANGENTS AND SECANTS.
NATURAL SINES
 '4

NATURAL SINES, TANGENTS AND SECANTS.

NATURAL
i5 1

NATURAL SINES, TANGENTS AND SECANTS.

(COiNTINUED.)
LOGARITHMS OP NUMBERS.
LOGARITHMS OF NUMBERS Continued.
23 |i

LOGARITHMS OF NUMBERS Continued.

 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
" 100
soft, inferior,

Brickwork, pressed brick, 140

"
ordinary, 112
Cement, hydraulic, ground, loose, American, Rosendale, 56
" " " " " 50
Louisville,
" " " "
English, Portland,
-
90
Cherry, dry, .
-
42
Chestnut, dry, -
41
Coal, bituminous, solid, 84
" "
broken, loose, 49
" " loose, - - -
heaped bushel, (74)
Coke, loose, of good coal, 27
" " -
heaped bushel, (38)
Copper, cast, 542
rolled, 548
Earth, common loam, dry, loose, - - -
76
" " " " - -
95
moderately rammed,
" 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.

Gneiss, common. _______

_____
Weight.
Lbs.

1Q&
Gold,
"

Granite,
pure, ______
cast, pure, or

hammered,
24 carat,

_
1204
1217
170

Hemlock,
Hickory, dry,
---_.._.
Gravel, about the same as sand, which see.

-__-__.
dry, 25
53
-
Hornblende, black, - 203
Kce,
Iron, cast,
i<
-

-----_-__
wrought, purest,
- '-

-
- - -

-
-

-
-

-
-

-
58.7
450
485
average, - 480
Ivory, 114
Lead,
Lignum Vitae, dry,

Lime, quick, ground,

_______
loose, or in small lumps, -
-

-
711
83
53
" "
thoroughly shaken, - 75
" " " " -
per struck bushel, *.
(66)
Limestones and Marbles, - - - - _ - 168
" " -
loose, in irregular fragments, 96
'
- - - - 53
Mahogany, Spanish, dry,
" - - - -
Honduras, dry, - 35
- - - - - - - _ 49
Maple, dry,
Marbles, see Limestones.
Masonry, of granite or limestone, well dressed, - 165
" mortar
rubble, 154
" " " - -
dry (well scabbled,) 138
" "

Mercury,
sandstone, well dressed,
at 32
-
Fahrenheit,
-
-

- - ... 144
849
Mica, _ 183
Mortar, hardened, - - - - - - 103
Mud, dry, close,
- - - - - - 80 to 110
" - -
maximum, - - 120
Oak,
wet, fluid,
live, dry,
-- - _-_ _ _ . 59
 WEIGHT OF SUBSTANCES Continued.

Average
NAMES OF SUBSTANCES.

Oak, white, dry, ------- 52

Weight.
Lfe.

" other kinds,

Petroleum, ____--_-
_______
- - - - - - 32 to45
55
Pine, white, dry,
"
"
yellow, Northern,
"
_.-___
-____-
Southern,
25
34
45
Platinum, 1342
Quartz, common, pure,
- - - - - -165
69
Rosin,
Salt, coarse, Syracuse,
"
N. Y. -.-.-.
-
45
49
Liverpool, fine, for table use,
Sand, of pure quartz, dry, loose, - 90 to 106
" well shaken, 99 to 117
"
perfectly wet,
Sandstones,
Shales, red or black,
fit
-

for building,
-
_____
...
120

-
to 140
151
162
- - 655
Silver,

Slate, .
- 175
Snow, freshly fallen, 5 to 12
"
__---_--
moistened and compacted by rain,
Spruce, dry,
Steel,
- - 15 to 50
25
490
Sulphur,
Sycamore, dry, --------37 125

Tar,
Tin, cast, --------- 459
62

Walnut, black, dry,

Water, pure rain or
___-_-_ /
Turf or Peat, dry, unpressed,

distilled, at 60
- -

Fahrenheit,
- - 20 to 30

-
38
62 31

"

Wax, bees,
sea,
.--
--_-__--
64
60.5
Zinc or Spelter, 437
Green timbers usually weigh from one-fifth to one-half more
than dry.

-*- 8
158
LINEAR EXPANSION OP SUBSTANCES
 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.
0.318310.

-,/ 7r=1.772454.

TT
2
=9.869604.
= 0.101321.
2
c

0.564190.

2v

or, very nearly, = -

AREA.
Triangle= base X half perpendicular hight.
= base X perpendicular hight.
Parallelogram
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 = length of arc X half radius.
circle

161
 MENSURATION Continued.

Segment of circle = area of sector less triangle ; also, for

Hat segments very nearly = 4 v i/

-r 0.388 v- -\
c~2~

Side of square of equal area as circle = diameter X 0.8862 ;

also, =circumference X 0.2821.

Diameter of of equal area
circle square = as X side 1.1284.
Parabola = base X /i hight.
Ellipse = long diameter X short diameter X 0.7854.

Regular polygon = sum of X half perpendicular distance

sides
from center to sides.
Surface of cylinder = circumference X hight X area of both
ends.
Surface of sphere = diameter squared x 3.1416;
= circumference X diameter.
also, %
Surface of a pyramid or cone = periphery or circumference
right
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

88
162
 MENSURATION Continued.

I. Area =d X Sh +(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 =

perpendicular hight. X
Cylinder, right or oblique, =
area of section at right angles to
sides X
length of side.
Sphere = diameter cubed X 0.5236.
= surface X /6 diameter.
also,
l

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 Continued.

CUBIC OR SOLID MEASURE.

UNITED STATES AND BRITISH.

= cubic
1728 cubic inches 1 foot.

= cubic yard.
27 cubic feet 1

A cord of wood = X V X = 128 cubic

4' 8' feet.

A perch of masonry = X X = 24.75

16.5' 1.5' 1' cubic feet,
but is generally assumed at 25 cubic feet.

DRY MEASURE..
UNITED STATES ONLY.

Struck Bush I
Pecks.
 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 = kilogrammes per metre,

foot - 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.
 STRENGTH OF MATERIALS.

ULTIMATE RESISTANCE TO TENSION

IN LBS. PER SQUARE INCH..

METALS.

Brass, cast, - - - - -- - -
Average.

18000
"
wire,
Bronze or gun metal,
Copper, cast,
______
_______
- 49000
36000
19000
sheet, 30OOO
"
bolts, 36000
"
wire,
Iron, cast, 13400 to 29000,
"
-----
wrought, round or square bars of 1 to 2 inch
60000
16500

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 1OOOOO

to
"
wire-ropes,
Lead, sheet, - - _____ - 9000O
33OO
Steel,
Tin, cast,
Zinc,
__.._.
_______
65000 to 1200OO
4600
7000 to 8000

168
 STRENGTH OF MATERIALS-Continued.

TIMBER, SEASONED, AND OTHER ORGANIC FIBER.

Average.

Ash, English, - - 17OOO

" 11000
American, - to 14000
" 15000
Beech, to 1800O
Box,
Cedar of Lebanon,
"
American, red,
-------- - - - - -
20000
11400
10300
Fir or Spruce, - 1000O to 13600
Hempen Ropes, -
- - - 12000 to 1600O
Hickory, American, - 12800 to 180OO
Mahogany,
Oak, American, white,
"
European,
- -----
-----
80OO

10000
to

to
2180O
1800O
19800
Pine, American, white, red and pitch, Memel, Riga, - 1OOOO
" " leaf - 12600 to 19200
long yellow,
Poplar,
- - - - 700O
Silk fiber, 52000
Walnut, black, 1600O

STONE, NATURAL AND ARTIFICIAL.

Brick and Cement, - - -

280 to300
Glass, - 9400
Slate, - - 9600 to 1280O
Mortar, ordinary, 5O

ULTIMATE RESISTANCE TO COMPRESSION.

METALS.
Brass, cast, 10300
" - - 82000 to 145000
Iron,
" 36000 to 40000
wrought,

169
 STRENGTH OF MATERIALS Continued.

TIMBER, SEASONED, COMPRESSED IN THE

DIRECTION OF THE GRAIN. Average.

Ash, American, 4400 to 5800

" 5800 to 6900
Beech,
Box, 10300
Cedar of Lebanon, - 5900
" - 6000
American, red,
Deal, red, 6500
Fir or Spruce, 5100 to 6800

Oak, American, white, - - 720O to 9100

" 10000
British,
" - - - 770O
Dantzig,
Pine, American, white, - 5000 to 5600
" " 8000
long leaf yellow,
5800 to 6900
Spruce or Fir,
Walnut, black, - 7500

STONE, NATURAL OR ARTIFICIAL.

Brick, weak, - - - - - - - 55O 800 to
" - 1100
strong.
" 1700
fire,

Brickwork, ordinary, in cement, - 300 to 450

best, - - 1000
Chalk, 330
Granite, - - - 5500 to 11000
Limestone, -

Sandstone, ordinary,
-

____-- 4000 to 11000

4000

ULTIMATE RESISTANCE TO SHEARING.

METALS. -

Iron, cast,
- - 27700
" - 45000
wrought, along the fib'er,

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
" and wrought
cast 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 each -^th of an inch
of, for 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

" " " 110
Birmingham, ,

on
Girders, riveted, table .' 72
Glass,window, number of lights per box 159
Grooved irons, lithographed sections of 21

Half T's, lithographed sections of 15

" " 21
Handrails,

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 for
proportions 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
" " " " " 131
hexagon

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, forone 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
"
diagram of
truss, 26
Properties of U. I. M.'s eye and deck beams 62, 63
" " channels.... 64,65
" " " irons angle 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
)