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T H E D E S I G N IN G
OF ORDINARY
IRON HIGHWAY BRIDGES.
BY
J. A. L. WADDELL, C.E., B.A.Sc., MA.E.,
PROFESSOR OF CIVIL ENGINEERING IN THE UNIvºrs.Ty of tokro, JAPAN; consultſNG ENGINEER
For THE FIRM OF RAYMOND AND CAMPBELL, BRIDGE-BUILDERs of council, BLUFFS, IOWA;
MEMBER OF THE AMERICAN SOCIETY OF CIVIL ENGINEERs, RENSSELAER SOCIETY
OF ENGINEERS, ENGINEERs’ CLUB OF PHILADELPHIA, AND WESTERN
SOCIETY OF ENGINEERS; AND ASSOCIATE MEMBER OF THE
INSTITUTION OF CIVIL ENGINEERs, LONDON.
SECONWA) REVISED EDITION,
NEW YORK :
J O HN WILEY & SO NS,
I 5 AS TO R PLACE.
I886.
Jºva--af ~(~ ſº-
T &
3.C. C.
. Vaſ 2-
| 3 × 4
CoPYRIGHT, 1884,
By J. A. L. WADDELL.
ELECTROTYPED BY
RAND, AVERY, AND COMPANY.,
BOSTON, MASS.
PREF ACE.
THIS work is principally a compilation of the results of investigations
made by the author during the last three years, and presented in a
number of papers to the various American engineering Societies. Sev-
eral portions of the book, including many of the tables, are new, as
this is the first systematic treatment, by the author, of bridges for cities
and manufacturing districts; the previous papers having dealt especially
with those for country roads. In making this compilation, the author
has been governed by no blind adherence to what he has already writ-
ten, but has made changes wherever they have appeared to be advisable.
One of the chief objects of this work is to reduce the labor of iron
highway-bridge designing to a minimum, for which purpose every thing
that could be so arranged has been tabulated. Not only are the exact
sizes of hip verticals, joists, floor beams, beam hangers, lateral rods and
struts, portal rods and struts, vibration rods, intermediate struts, lattice
bars, stay plates, etc., given for all practical cases, but also the most
economic dimensions of panels and trusses, and dead loads, so exact
that by their use all necessity for a second trial is avoided. These
tables, it is hoped, will prove useful to those in the actual practice of
bridge designing, enabling them to greatly reduce the time required
to make diagrams of stresses and sections and estimates of cost. The
other tables, although they do not give final results, should also be of
Service.
The value of the book may appear to some readers to be limited, in
that it treats of only the Pratt and Whipple systems; but it must be
Ill
iv. AA’A.A.A. CAE.
remembered that at least ninety per cent of all American iron highway-
bridges are built on these systems. This fact alone ought to prove
conclusively that they are the best type of bridge. Moreover, the
author has demonstrated, in a paper entitled “Economy in Struts
and Ties,” published last year in the “Canadian Magazine of Science,”
and copied in the “American Engineer,” by a method entirely practical,
that for economy the web compression members of trusses should be
vertical, or nearly so ; thus showing, that, of all the ordinary types of
truss, the Pratt or Whipple is the best.
Through bridges and pony trusses, both having inclined end posts,
have alone been treated at length; for highway deck bridges are un-
common, and inclined end posts not only are more economical than
vertical ones, but are also superior to them because they produce tensile
stresses in the end panels of the bottom chords, thus adding to the
rigidity of the structure.
The work is written for engineers, students, and, to a certain extent,
county commissioners. It is not intended, though, to be used by itself
as a text-book on bridges, dealing, as it does, with only one general
style of truss, but to supplement the books generally used by classes
in engineering Schools. N
It is essentially a treatise upon bridge designing, and not one upon
stresses : nevertheless, it has been found necessary to discuss the latter
subject in order to make the work complete. The author would refer
those who wish to study concerning stresses to Burr's “Stresses in
Bridge and Roof Trusses,” Bovey's “Applied Mechanics,” and Du
Bois’ “Strains in Framed Structures.”
For county commissioners, Chapters IV., XIV., and XVII., Tables
I.—V., XV.-XXV., XXX.-XXXIII., and XXXVIII., and parts of Chap-
ter II., will be found very useful; containing, as they do, directions and
data for making estimates of cost, and means of proving whether either
designs or finished structures have or have not in many particulars
Sufficient strength.
Those portions of the “General Specifications” in Chapter II.,
relating to quality and tests of materials, workmanship, painting, etc.,
have been taken from standard specifications too numerous to permit
PREFACE. V
of their authority being here quoted: nevertheless, the author must
acknowledge that he has received considerable assistance from a paper
by Mr. P. F. Brendlinger published in No. 4, vol. iii., of the “Proceed-
ings of the Engineers’ Club of Philadelphia,” treating of some railroad-
bridge specifications prepared by Theodore Cooper, C.E. He wishes
to acknowledge also, with many thanks, the valuable aid rendered him
by his assistants, Messrs. Y. Nakajima and T. Fukuda, in preparing
drawings, and checking tables.
J. A. L. W.
Tokio, JAPAN, February, 1884.
PREFACE TO SECOND EDITION.
ALTHOUGH the first edition of this work was issued only three or
four months ago, it has had the opportunity for receiving a thorough
overhauling by a class of half a dozen students, who were requested
to take special pains to point out errors. A few were found; but
they are of small importance, being principally typographical or
numerical. It is thought that all have been discovered and corrected,
but it is possible that others may exist: So, if any reader find any, he
will confer a favor upon the author by informing him of the same.
The correctness of the weights of iron in Tables I., II., and III.,
has received additional confirmation from the same class of students,
each student having made a complete design for a bridge. The great-
est variation found was less than one-half of one per cent. As the
bridges varied in class, span, and width of roadway, one being on a
skew, and two having sidewalks, it is fair to conclude that the tables
may be relied upon as correct for all cases.
A slight change has been made in Chapter V., near the end, in respect
to a statement concerning stresses in the posts of deck bridges; but, for
reasons there stated, the formula has not been altered.
In a review of this treatise, by “Zhe American Engineer,” there was
mentioned the fact that double beam hangers are not a satisfactory
detail, because of the unequal distribution of the floor-beam load there-
on. In the addenda is described a detail which will remove the objec-
tion. There are given also in this part of the work, and on Plate VIII.,
several other details that will be found to be improvements upon those
previously described. Vii
viii PREAEA CE 7 O SECOM/D AED/7”/O/W.
About July 1, there will be issued by the University of Tokio, in the
form of the usual “Memoir,” a treatise of the author upon “A System
of Iron Railroad Bridges for Japan,” which will be found to contain a
number of important matters respecting the designing of railroad-
bridges, that have not hitherto received proper attention. The book is
not for sale; but there will be about two hundred copies distributed in
America among engineers, Colleges, public libraries, etc.
The author wishes to express his thanks to the profession for the
favorable reception given to his first edition.
J. A. L. W.
TOKIO, JAPAN, May 6, 1885.
CHAPTER.
II.
III.
IV.
VI.
VII.
VIII.
IX.
X.
XI.
XII.
XIII.
XIV,
XV.
XVI.
XVII.
XVIII.
XIX.
XX.
CONTENTS.
INTRODUCTION . ſº e © e Ç tº º tº ſº * ,
GENERAL SPECIFICATIONS . * > ſe e o * > © e
LIST OF MEMBERS ſº * tº tº * g * ſº se +º
LIVE AND DEAD LOADS. — WIND PRESSURE sº ſº © re
. STRESSES IN TRUSSES . *
STRESSES IN LATERAL SYSTEMS AND VERTICAL SWAY BRACING .
REMARKS CONCERNING MAIN MEMBERs . jº Hº * tº
PROPORTIONING OF MAIN MEMBERS OF TRUSSES, LATERAL SYS-
TEMS, AND SWAY BRACING * 4- * * te *
PROPORTIONING OF FLOOR SYSTEM . te g * tº g &
THEORY OF PIN PROPORTIONING . te * * wº º gº
PRACTICAL METHOD OF PIN PROPORTIONING . wº * tº
RIVETING $ § º tº § e sº º e º *
PROPORTIONING OF OTHER DETAILS. º †º tº { . ©
BILLS OF MATERIALS AND ESTIMATES OF COST . ſº tº
ECONOMY . º wº * tº º ge & *
CoMPLETE DESIGN FOR A BRIDGE * tº * &
BRIDGE LETTINGS tº ſº * ë * g ſº ſº *
WORKING-DRAWINGS . {e * tº tº
ORDER BILLS AND SHIPPING BILLS . e e º * * sº
ERECTION AND MAINTENANCE
APPENDIX I. A NEGLECTED CONSIDERATION IN HIGHWAY-BRIDGE
DESIGNING . jº © is & * * * *
APPENDIX II, DEMONSTRATION OF FORMULA FOR FLOOR BEAMs
APPENDIX III. METHOD OF FINDING THE LENGTH OF THE LONG
DIAGONALS IN A DouBLE-INTERSECTION BRIDGE . se e
ADDENDA . † gº ( ; o tº e e wº & ſº & º
GT,OSSARY OF TERM tº c (º e Q tº . * > * ©
INDEX * sº t tº º e iº vº © tº * & tº
48
55
67
76
85
93
II.4.
I 20
I26
I 57
I72
183
I96
2I 5
219
22I
225
233
247
INDEX OF TABLES.
I.-III.
IV., V.
VI.-VIII.
IX.
XIII., XIV.
XV.-XVIII.
XIX. —XXI.
XXII.-XXIV.
XXV.
XXVI., XXVII.
XXVIII.
XXIX.
XXX.
YXXI.
XXXII., XXXIII.
XXXIV., XXXV.
XXXVI, XXXVII.
XXXVIII.
XXXIX.
XL.
XLI.
XLII.
DEAD LOADS.
ECONOMIC DEPTHS AND PANEL-LENGTHS.
SIZES OF HIP VERTICALS.
WORKING TENSILE STRESSES AND INITIAL TENSIONS.
INTENSITIES OF WORKING-STRESSES FORCHANNEL STRUTS.
WoRKING BENDING-MoMENTS AND SHEARING-RESIST-
ANCES FOR PINS. -
WoRKING LOADS FOR WOODEN BEAMS.
AMoUNTs of LUMBER PER PANEL, SIZES OF JOISTs, ETC.
SIZES AND WEIGHTS OF FLOOR-BEAMS.
SIZES OF BEAM-HANGERS.
SIZES OF PORTAL, LATERAL, AND INTERMEDIATE STRUTS,
AND OF UPPER LATERAL, LOWER LATERAL, AND WIBRA-
TION RODS. -
THICKNESSES FOR PIN-BEARINGS.
DIMENSIONS OF UNION IRON MILLs” CHANNEL-BARS.
LENGTHS OF LATTICE-BARS, WEIGHTS PER FOOT OF SAME,
ETC.
SIZES OF LATTICE-BARS.
SIZES OF LACING-BARS.
SIZES OF STAY PLATES.
PERMISSIBLE PRESSURES ON ROLLERS.
WoRKING BENDING-MOMENTS AND BEARING-PRESSURES
FOR RIVETS.
LABOR IN ERECTION.
WoRKING LOADS FoR FALSEwork PILLARs.
WoRKING-LoADs For I-BEAM STRUTS.
STRESSES IN SINGLE-INTERSECTION TRUSSES.
STRESSES IN DOUBLE-INTERSECTION TRUSSES.
xi
I.
II.
III.
IV.
V.
VI.
VII.
VIII.
INDEX OF PLATES.
ISOMETRIC DRAWING OF A BRIDGE witH NAMES OF MAIN MEMBERS.
GENERAL DESCRIPTIVE PLATE OF DETAILS.
DETAILS FOR A PONY TRUSS-BRIDGE.
DETAILS FOR A SINGLE-INTERSECTION THROUGH CITY BRIDGE witH
Two SIDEWALKS.
DIAGRAM OF STRESSES AND SECTIONS.
WORKING-DRAWINGS FOR A BRIDGE.
WORKING-DRAWINGS FOR FALSEWORK.
DETAILs ILLUSTRATING THE ADDENDA.
THE DESIGNING
OF
ORDINARY IRON HIGHWAYBRIDGES.
CHAPTER I.
INTRODUCTION.
THAT many bridge designers will have fault to find with the
contents of this book goes without saying, but it will be found
that the principal objections will come from those who design
the lightest and poorest structures. The weights of iron in the
bridges here treated are probably from twenty to fifty per cent
greater than those in the bridges ordinarily built; but it is to
be remembered that most American iron highway-bridges are
not what they ought to be, and that the author has endeavored
to design structures first-class in every respect.
The principal differences between these bridges and those
ordinarily built are the stiffening of the end panels wherever
necessary; the use of C. Shaler Smith's formula, involving, as it
generally does, an increase of sectional area; the peculiar lower
lateral system, which avoids using the floor beams as lateral
struts; the large lateral rods employed; the allowance for initial
tension in all adjustable rods; the variation of the intensity
of working-stress for main diagonals; the assumption that all
stresses at joints in top chords and at upper ends of posts are
carried by the connecting plates and their rivets, no reliance
being placed upon the abutting ends of channels; the limiting
sizes of the sections of iron employed; and the unusual strength
I
2 ORDVAWAAC P VA’OAV HAGA WA P-BA*//XCE.S.
of the upper lateral and portal struts, especially when no verti-
cal sway bracing is used. *
On the other hand, those who wish to proportion bridges by
the latest theories may object to the employment of C. Shaler
Smith's formula (which fails to take into account the radius
of gyration of the section) and to the non-employment of the
results of Wöhler's and Weyrauch's recent investigations con-
cerning intensities of working-stresses. To the first objection,
the author would reply, that designers of ordinary highway-
bridges cannot afford the time to spend at least fifteen minutes
in obtaining the theoretically best intensity of working-stress for
each strut, but must have for this purpose tables which will give
the intensities without calculation : besides, the best theoretical
intensity is merely approximate. To the second objection, he
would reply, that the results of the investigations referred to
have not yet been generally adopted, and that the variation of
intensity of working-stress for the main diagonals used in this
treatise is, in his opinion, for ordinary highway-bridge design-
ing, a sufficient concession to the general correctness of the
theory of those writers. n
The units used throughout this work are as follows: the
American ton (two thousand pounds) for the units of weight
and stress, the foot for the unit of length, and the square inch
for the unit of area.
It is presupposed that the reader, if he intend to design, or
even study the designing of, iron bridges, has procured a copy
of Carnegie’s “Pocket-Companion,” the most useful little book
of its kind for bridge builders that has ever been printed: so
the tables therein are here referred to, instead of being repro-
duced. -
The sections of iron employed are those rolled at the Union
Iron Mills, for the reason that not only is there more iron rolled
in these mills than anywhere else in America, but the proper-
ties of the sections are tabulated in a much more convenient
form than are those of any other mills. The author intended
to prepare a table of channels rolled by the New-Jersey Steel
and Iron Company of Trenton, N.J., similar to Table XXVIII. ;
but the information in that company's pocket-book is not
ORD/MAA' P /ROAV HIGH WA P-BAe/DGE.S. 3
complete enough to enable him to tabulate the thicknesses of
the webs.
Any one intending to design bridges according to the method
herein proposed should thoroughly acquaint himself with the
numbers and uses of the different tables, so as to turn to the
one required without delay. He should also become posted on
the contents of Chapters VII.-XIII., so as not to have to refer
to that part of the book, turning to Chapter II. to refresh his
memory concerning intensities of working-stresses, limitations,
etc., while designing each main member and detail. After a
little practice, one will become acquainted with the method,
when it will be necessary to refer to the tables only.
If a designer be in doubt about how to proportion any main
member or detail, he can at once find out the method by look-
ing in the Index, under the head “Proportioning,” where he
will see the numbers of the pages on which the proportioning
of this member or detail is treated.
Any intelligent man who is not an engineer can make an
approximate estimate of what a first-class iron highway-bridge
ought to cost, by finding the required weight of iron from one of
Tables I., II., or III., modifying it, if necessary, in the manner
explained in Chapter IV. ; and the required amount of lumber,
from one of Tables XV., XVI., XVII., or XVIII., ascertaining
the prices of iron per pound, and lumber per thousand feet,
delivered at the nearest railway-station or seaport, and filling
out the form for an estimate of cost given on p. 116. By refer-
ring to the Index, under the heading “Cost,” he can ascertain
where approximate data for all bridge-building expenses can be
found.
No special treatment is here given for skew bridges; for none
is needed, the methods for designing them being precisely the
same as those for other bridges. On account of the obliquity,
the working drawings for the lateral bracing and sway bracing
are a little more complicated. Whenever it is convenient to do
So, the panel lengths should be arranged so that the shoe of
One truss comes opposite to the first panel point of the other
truss, in order that the floor beams may be at right angles
to the planes of the trusses, both for economical reasons, and to
4 ORDIAWARY IRO/W HIGH WA Pi—BRIDGES.
avoid using single beam hangers. This arrangement can often
be made by shortening the panel length a little, and, if it be
allowable, slightly changing the angle of the skew. Even if it
be impracticable to make this arrangement, it is usually better,
in skew bridges, to advance the ends of the floor-beams at one
side of the bridge, by one or even two panel lengths, if, by so
doing, the floor beams be shortened. -
ORDIMARY IROM HIGHWA Y-BAEIDGES. 5
CHAPTER II.
GENERAL SPECIFICATIONS.
THIS chapter, at first thought, may appear out of place; for it
is really a résumé of the whole subject of iron highway-bridge
designing. It is placed here in order to be of easy reference.
Students, and those unacquainted with bridge designing, are
advised to omit these specifications, and to return to them after
having read through Chapter XIII.
Classification. — Highway-bridges may be divided into three
classes; viz., Class A, which includes those for cities and their
suburbs that are subjected to the continued application of heavy
loads; Class B, which includes those for cities and their suburbs,
or manufacturing districts, that are subjected to the occasional
application of heavy loads; and Class C, which includes those
for country roads, where the traffic is lighter.
Live Load. — The live loads for bridges of the different
classes are to be taken from the following table:—

Moving LoAD PER Square Foot of FLOOR.
SPAN IN FEET.
Classes A and B. Class C.
o to 50 Ioo pounds 80 pounds
50 to I 5o 90 pounds 80 pounds
I 50 to 200 80 pounds 70 pounds
2OO to 3oo 70 pounds 60 pounds
3oo to 4oo 60 pounds 50 pounds
The live loads for joists, floor beams, beam hangers, and hip
Verticals, are to be one hundred (100) pounds per square foot of
floor for bridges of Classes A and B, and eighty (80) pounds per
6 OA’D/AWA A' V MA’OAV HIGH WA Y-ARA'ZZ) GAZ.S.
square foot for bridges of Class C, irrespective of the length of
bridge.
Dead Load. — The dead load is to include the weight of all
the iron and wood in the structure, excepting that of those por-
tions resting directly on the abutments, whose weights do not
affect the stresses in the trusses; also, if necessary, an allow-
ance for Snow, mud, paving, or any other unusual fixed load
that may ever be placed on the bridge.
Pine-lumber is assumed to weigh two and a half (23) pounds
per foot, board measure ; and oak-lumber, four and a third (4%)
pounds per foot, board measure.
Should, in any bridge of or below one hundred (IOO) feet
span, the calculated dead load differ more than eight (8) per
cent from that assumed, or in any bridge from one hundred
(IOO) to two hundred (2OO), feet span, more than six (6) per
cent, or in any bridge exceeding two hundred (200) feet span,
more than four (4) per cent, the calculations of stresses, etc.,
are to be made over with a new assumed dead load.
Wind Pressure. — The wind pressure per square foot is to
be assumed as forty (40) pounds for spans of one hundred (100)
feet and under, thirty-five (35) pounds for spans over one hun-
dred (IOO) and not greater than one hundred and fifty (150)
feet, and thirty (30) pounds for all greater spans.
For bridges in unusually exposed situations, these pressures
are to be increased by ten (IO) pounds per square foot.
The total area opposed to the wind is to be determined by
adding together the area of the vertical projection of the floor
and joists, and twice the area of the vertical projection of the
windward truss, hand rail, hub plank, guard rail, and ends of
floor-beams. **-
Zength of Span. — The length of span is to be understood
as the distance between centres of end pins for trusses, and
between centres of bearing-plates for all beams and girders.
Alimiting Zengths of Span for Different Clear Roadways. –
The greatest lengths of span for the different clear roadways
are to be one hundred and forty (140) feet for twelve (12) foot
roadways, one hundred and ninety (190) feet for fourteen (14)
foot roadways, two hundred and sixty (260) feet for sixteen
OA'D//WAA’ P ZAZOAV HIGH WA V–B/º/DGE.S. 7
(16) foot roadways, and three hundred and fifty (350) feet for
eighteen (18) foot roadways. By clear roadway is meant the
distance between the innermost portions of the opposite trusses,
measured in a direction perpendicular to their planes.
Limit of Clear Headway. — The least allowable clear head-
way is to be fourteen (14) feet, unless some local consideration
cause it to be increased. By clear headway is meant the ver-
tical distance between the upper face of the flooring and the
lowest part of the portal or overhead bracing.
Styles of Bridges for Different Sparts. – Spans of and below
twenty (20) feet are to consist of rolled beams; spans from
twenty (20) to forty (40) feet, of riveted plate girders or trussed
beams; spans from forty (40) to sixty-five (65) feet, of stiffened
pony trusses or stiffened deck bridges, unless the weight of
bridge be great enough to admit of the use of eye bars for the
bottom chords; and spans above sixty-five (65) feet, of pin-
connected through or deck truss bridges.
Limiting Depth of Pony Zºrusses. – The greatest allowable
depth, measured from centre to centre of chords, for pony
trusses without exterior side bracing, is to be six (6) feet; and
that for pony trusses with exterior side bracing, nine (9) feet.
For bridges with sidewalks, in which it is inconvenient to use
exterior side braces, the depth may be increased to eight (8)
feet, provided that the width of the top chord plate be double
the depth of the top chord channels, and that the channels
composing the posts and hip verticals be splayed outwardly so
as to be separated in the clear at their feet by at least twenty-
four (24) inches.
Limiting Slope for Batter Braces of Pony Trusses. – The least
allowable slope for batter braces of pony trusses is to be two
and a quarter (2}) horizontal to one (1) vertical.
Side Braces. – The least allowable batter for side braces in
pony-truss bridges is to be five (5) inches to the foot, and all
side braces are to be made to resist both tension and compres-
sion. In no case is a side brace to have less strength than that
of a 2;" × 2;" 5-lb. angle-iron.
Limiting Length of Span for Double Intersection Bridges. –
The least allowable length of span for double intersection
bridges is to be taken from the following table:–
8 O/CD//VA R P /ROM HIGH WA P-AEA’/DGES.

LIMITING LENGTHS.
CLEAR ROADWAY.
Class A. Class B. Class C.
I4' 165’ 175' I8o'
I6' I 55" 165’ 17o'
I87 I 50' I6o' 165’
2O' I45' I 55" I6o'
22' I40' - I 5o' I 55"
24! I4o' I45' I 5o'
Limiting Sizes of Sections. – No rods less than three-quar-
ters (3) of an inch in diameter are to be used in a bridge. No
channels less than five (5) inches in depth are to be used for
upper chords, batter braces, or posts, or less than four (4) inches
in depth for other members. No flat bars less than one-half (3)
inch thick, or one and a half (13) inches wide, are to be used
for diagonals or chord bars; nor any iron less than one-quarter
(#) of an inch thick anywhere in a bridge, excepting for filling
plates. -
Eapansion. — All spans are to be provided with some means.
of expanding and contracting longitudinally, with a variation in
temperature of one hundred and fifty (150) degrees Fahrenheit.
Spans of over seventy-five (75) feet are to have at one end nests
of turned wrought-iron friction rollers, running between planed,
surfaces.
Anchorage. — At least one end of every bridge must be
anchored to the foundations. If the overturning moment of
the greatest assumed wind pressure be more than half the
resisting moment of the weight of the bridge, the latter must
be anchored at the roller end also, but in such a manner as not
to interfere with the expansion.
Sliding. — At the roller end of a bridge, if the frictional
resistance to the sliding of the shoe in the direction of the axes
of the rollers be not more than double the tendency to slide
produced by the wind pressure, a resistance equal to the differ-
ence between this tendency and the frictional resistance with a
factor of safety of four (4) must be provided.
ORDIMARY IROM HIGH WA P-BRIDGE.S. 9
Continuous Spams. – Except in the case of swing bridges or
cantilevers, consecutive spans are not to be made continuous
over the points of support.
Camber. — The cambers for bridges of the different spans are
to be taken from the following table:– -

SPAN IN FEET. CAMBER IN INCHES. SPAN IN FEET. CAMBER IN INCHES.
40–60 I.O I8o–220 3.5
60–80 I.5 220–25o 4.O
8o—Ioo 2.o 250–280 4.5
Ioo—I4o 2.5 280–300 . 5.O
I40–180 3.O
Wertical Sway Bracing. — In all deck bridges, and in all
through bridges where the depth from centre to centre of
chords is twenty-four (24) feet or over, vertical sway bracing
is to be used.
Portal and Lateral Struts. – Portal and lateral struts are to
be proportioned to resist the compression produced by the
wind pressure and the initial tensions in all the rods meeting at
the end of the strut. If the strut be also subjected to bending,
then to the area necessary to resist compression must be added
sufficient area to resist the bending; the intensity of working
bending-stress being taken equal to six (6) tons.
Æffect of Wind on Posts and Batter Braces. – But the effect
of the wind on the posts and batter braces is not to be considered
to occur when the bridge is fully loaded: so, unless the stresses
produced thereby exceed the product of the live load stresses
by the ratio of seven and a half (7.5) to the intensity of working
tensile stress for the bottom chord, the effect of the wind on
these members may be neglected.
Effect of Wind Pressure on Bottom Chord Tension. — For the
Same reason, the sectional area of the bottom chord need not
be increased to resist the tension caused by the wind, unless
the latter exceed the product of the live load stress by the ratio
of seven and a half (7.5) to the intensity of working tensile
stress for chord bars.
IO OA' D/AVA R V ZAZOAV HIGH WA P-BA’//DGE.S.
Initial Tension. — To allow for the stresses caused in adjusta-
ble members by the screwing up of the turn buckles or sleeve
nuts, the stress in each such member is to be increased by the
amount given in the following table:–

DIAMETER of Rod. INITIAL TENSION. DIAMETER OF Rop. INITIAL TENSION.
3” O.50 ton I?" 2.25 tons
g” O.75 ton 13." 2.50 tons
Itſ I.OO ton 14" 2.75 tons
I?" I.25 ton 2” 3.oo tons
14" I.5o ton 2}” 3.25 tons
13." I.75 ton 23" 3.50 tons
I}" 2.OO tonS 2;" 3.75 tons
Square or flat bars are to receive the allowance for round rods
of equal sectional area.
Connection for Lateral Systems. – Whenever it be possible,
the lateral rods of both upper and lower systems are to be
connected directly to the chord pins. But, if the rods exceed
one and three-quarter (13) inches in diameter, bent eyes are not
to be employed. --
Lower lateral rods are not to be attached to the floor beams.
To make them clear the joists, wooden lateral struts resting
on the floor beams, and having wrought-iron jaws at their ends
attached to the chord pins, are to be employed for the joists to
rest upon.
These wooden struts are to be bolted about every two feet
through the upper flange of the floor beam by five-eighth (£)
inch bolts, care being taken to stagger the bolt holes, and to
avoid placing a bolt at the middle of the beam.
Should the sizes of the lateral rods be such as to prevent the
use of bent eyes, pins dropped vertically through the jaws are
to be employed.
Stresses in End Lower Lateral Struts. – In figuring the stress
in a lower lateral strut at the roller end of a bridge, the
stress caused by the wind pressure is to be added to the trans-
verse component of the initial tension in the end lateral rod,
ORD/AVA R P /ROAV HIGH WA P-B/C/DGAE.S. II
and from the sum is to be subtracted the product of the press-
ure on the windward shoe, when the bridge is empty and sub-
jected to the greatest wind pressure, by the co-efficient of iron
upon iron, which is about O.25 for this case.
Stiffened End Panels. – If, in the end panel of a bridge, the
longitudinal component of the greatest allowable working-stress
(including initial tension) in the lower lateral rod exceed the
tension in the lower chord of that panel, caused by the dead
load alone, when the bridge is subjected to the greatest wind
pressure, the bottom chord of that panel must be made to resist
both tension and the excess of compression. Where two chan-
nels are employed for the lower chord section, the effective area
of the webs alone must be counted on to resist tension. Where
the stiffening is obtained by trussing the inner chord bars, the
intensities of working tensile stress to be employed for the net
section of those bars are four (4) tons for bridges of Class A,
and five (5) tons for those of Classes B and C.
Top-Chord and Batter-Brace Sections. – The top chords and
batter braces shall consist of two channels, with a plate above,
and latticing or lacing below. The top plate must be of the
same section, and the chord channels of the same depth, from
end to end of span; the increase in chord section towards the
middle being obtained by thickening the webs of the chan-
nels. -
Post Sections. – Posts are to consist of two channels, with
latticing or lacing on each side. The upper ends may be either
rigidly attached to the chords, or may be hinged on the pins;
preference being given to the latter method.
Portal and Upper Lateral Strut Sections. – Portal struts and
upper lateral struts are to be formed of two channels, latticed or
laced, and rigidly attached at their ends to the batter braces or
chords. -
Working Tensile Stresses.— Except for the case of trussed
bars, mentioned under the divisions “Stiffened End Panels” and
“Stiffened Hip Verticals,” the intensities of working-stresses for
iron in tension in the various members are to be as given in the
following table:– - -
I 2 ORD/MARY ZROAV HIGH WA Y-BAIDGES.

INTENSITIES of Working-STREss.
MEMBERS. - -
- Class A. | Classes B and C.
Lower chord bars and end main diagonals . 5.00 tons 6.25 tons
Middle panel diagonals, counters, and hip -
verticals . . . . . . . . . . . . 4.00 tons 5.oO tons
Flanges of rolled beams . . . . . . . 5.00 tons 6.00 tons
Flanges of built beams (net section) . 4.00 tons 5.oo tons
Lateral and vibration rods . . . . . 7.50 tons 7.50 tons
Beam-hangers . 3.oo tons 4.00 tons
The intensities of working-stress for main diagonals inter-
mediate between the counters or middle panel diagonals and
the end diagonals lie between four (4) and five (5) tons for
bridges of Class A, and between five (5) and six and a quarter
(64) tons for those of Classes B and C; the amounts being
directly interpolated according to the position of the panel.
Working Compressive Stresses. – For struts composed of two
channels with plates, or lacing, or latticing, the following for-
mulas are to be used in finding the intensities of working
compressive stresses.
For chords, batter braces, and posts in bridges of Class A,
*z, -
I + a
4 + x;
and for all other cases,
- –4–
A”
- c
A E = 77.
4 + 3o
p being the intensity of working-stress, and
length of strut -
T least diameter of strut'
19.25 for two fixed ends . .
f = | 19.25 for one fixed end and one hinged end
18.90 for two hinged ends,
Aſ
ORD/MARY IRO/W HIGHWA P-B/C/DGES. I3
and
5820 for two fixed ends,
C = 3ooo for one fixed end and one hinged end
190o for two hinged ends.
Where I-beams are employed for intermediate struts or end
lower lateral struts, the working-stresses are to be taken from
Table XL. For the flanges of rolled beams, the intensities of
working compressive stress are to be taken equal to five (5) tons
for bridges of Class A, and six (6) tons for bridges of Classes B
and C. For the flanges of built beams, the corresponding inten-
sities are to be four (4) and five (5) tons respectively on the
gross section.
Working Bending-Stresses.—The intensities of working bend-
ing-stress on pins are to be seven and a half (7%) tons for bridges
of Class A, and nine and three-eighths (9%) tons for those of
Classes B and C. For pins belonging wholly to the lateral
systems of bridges of either class, the intensity of working
bending-stress may be taken equal to eleven and a quarter
(II*) tons. The intensities of working bending-stress for rivets
are to be seven and a half (73) tons for bridges of Class A, and
nine and three-eighths (9%) tons for those of Classes B and C.
The latter intensity is also to be used for the lateral systems of
bridges of Class A.
Where steel pins are employed, the intensity of working
bending-stress must not be taken greater than twelve (12) tons
for bridges of Class A, or fifteen (15) tons for those of Classes
B and C, unless special experiments on the steel used show an
ultimate bending resistance greater than sixty (60) tons per
square inch; in which case a factor of five (5) may be used for
bridges of Class A, and a factor of four (4) for those of Classes
B and C. As before stated, the intensity of working bending-
stress for channels in portal and lateral struts is to be six (6)
tons.
Working Bearing-Stresses. – The intensities of working bear-
ing-stress for pins and rivets, measured upon the projection of
the semi-intrados upon a diametral plane, are to be six (6) tons
for bridges of Class A, and seven and a half (73) tons for those
I4 OA’I)/AWAA' P. Z.A’OAV HIGH WA Y-BA’/DGE.S.
of Classes B and C. For pins and rivets belonging wholly to
the lateral system of a bridge of any class, the intensity is to
be taken equal to seven and a half (7%) tons.
Sizes of Upper Lateral Rods. – In bridges of less than two
hundred (200) feet span, the stresses in the upper lateral system
in through bridges, or the lower lateral system in deck bridges,
usually call for sections of rods which are practically too small:
therefore the inferior limits of the diameters of these rods in
such cases are to be taken from Table XXV.
Stiffened Hip Verticals. – Hip verticals in three or four panel
pony trusses are to be stiffened so as to resist compression. If
the section employed consists of two channels, the net section
of the webs alone is to be relied on to resist tension. If it con-
sists of two flat bars trussed, the intensities of working tensile
stress on the net section are to be reduced to three (3) tons for
bridges of Class A, and to four (4) tons for those of Classes B
and C.
Trussing. — Trussing is to be used only in the posts of pony
trusses, where there is a great excess of strength, in the hip
verticals of pony trusses, and in stiffening lower chord bars.
Opset Ends. – Middle panel diagonals, counters, lateral rods,
vibration rods, and all other adjustable rods, excepting beam
hangers that have an excess of section, are to have their ends
enlarged for the screw threads, so that the diameter at the bot-
tom of the thread shall be one-sixteenth (#) of an inch greater
than that of the body of the rod, square or flat bars being
figured as if of equivalent round section.
Threads. – All threads, except those on the ends of pins
must be of the United-States standard. * -
Minimum Dimensions of Chord and Batter-Brace Plates. –
The minimum dimensions for the top plate in top chords and
batter braces are to be taken from the following table. For five
(5) and six (6) inch channels, the thickness does not increase
with the width. For seven (7) inch channels, the thickness
should be increased to five-sixteenths (#) of an inch, should
the width exceed fifteen (15) inches. For the other channels,
should the width of plate exceed that given in the table by
from forty (40) to seventy (70) per cent, the thickness must be
ORD/AWA R P ZROAV HIGH WA P-BAZZOGAE.S. I5
increased by one-sixteenth (ſº) of an inch, while, if it exceed
by more than seventy (70) per cent, the thickness must be
increased by one-eighth (3) of an inch.

DEPTH of MINIMUM MINIMUM DEPTH OF MINIMUM MINIMUM
CHANNEL. THICKNESS. WIDTH. CHANNEL. THICKNEss. WIDTH.
// 1// // // // //
5 4. 7 9 +% II;
6” 4" 8ſt I o” #" I 2}"
8” #" Io” I 5” # Jy 19"
Stay Plates. – Sizes of stay plates are to be taken from
Tables XXXII. and XXXIII. Stay plates on latticed or laced
compression members are to be placed as near the pin holes as
possible. Latticing or lacing must never be used without stay
plates at the ends.
Latticing and Lacing Bars. — The sizes for lattice bars and
lacing bars are to be taken from Tables XXX. and XXXI.
The distance from the back of an end rivet hole to the end
of the bar must not be less than one-half the width of the bar.
The ends of the bars are to be semicircular, except when there
are two rivets at each end, in which case they should be cut
parallel to the channels.
Inclination of Latticing and Lacing Bars. — Lattice bars shall
make with each other, as nearly as circumstances will permit,
angles of ninety (90) degrees; and lacing bars, angles of sixty
(60) degrees.
Piameters of Rivets for Different Channels. – For attaching
plates and lattice or lacing bars to the flanges of channels, the
least diameters of the rivets to be used are to be taken from
the following table; and the greatest diameters must not exceed
those there given by more than one-eighth (#) of an inch.

4” 5” 6”
Depth of channel ſº
g $” #" $”
Diameter of rivets .
7” 8” e 9”
*" #" ##"
IO"
##"
I 2" | I 5"
3// 3 f/
4. #
Splice Plates. – The length of a splice plate is to be deter.
I6 OA’D/AWA R P ZAZO/W HZGA/WA P-AEAC/DGAZ.S.
mined by the number of rivets necessary to transfer the stress
from one main member to the other. The sum of the working
bearing resistances of all the rivets on either side of the joint
must not be less than the stress in the main member upon that
side. The rivets must also be figured for bending. When
practicable, a splice plate must be placed on each side of every
member where a joint occurs.
The transmission of compressive stresses shall be considered
as entirely through the medium of the rivets and connecting
plates, and these must be proportioned accordingly; so that the
area of the two splice plates connecting two channel bars must
be at least equal to that of the larger channel bar.
Re-enforcing Plates. – Simple re-enforcing plates, or plates
riveted to webs at pin holes in order to compensate for strength
lost there, or to provide additional bearing for the pins, must
have as many rivets to attach them to the webs as will give
bearing and bending resistances for the same, equivalent to at
least the greatest stresses that can come upon the re-enforcing
plates.
Cover Plates. – Cover plates for top chords or batter braces
are to have the same section as the chord or batter-brace plate,
the joints in which they cover, and enough rivets on each side
of the joint to take up the greatest stress that could ever come
upon the said chord or batter-brace plate.
Extension Plates. – Extension plates on the end of a strut,
for the purpose of hinging the latter, are to have at least twice
the sectional area of the strut from the pin-hole to the nearest
edge of the stay plate; and the thickness must be great enough
to give sufficient bearing upon the pin. The length of the
extension plates is to be such as to allow of the use of a suffi-
cient number of rivets to provide proper bearing and bending
resistances for the same.
Shoe Plates, Roller Plates, and Bed Plates.—No shoe plate
is to have a less thickness than three-quarters (3) of an inch,
and no roller plate or bed plate a less thickness than seven-
eighths (g) of an inch. When nine (9) or ten (IO) inch chan-
nels are used for the batter braces, the thickness of the shoe
plates is to be seven-eighths (g) of an inch. When twelve (I2)
ORDZAVA R P WRO/W HIGH WA P-BR/DGE.S. 17
inch channels are used for the batter braces, the thickness of
the shoe plates, roller plates, and bed plates, is to be one (I)
inch ; and, when fifteen (15) inch channels are used, it is to be
one and an eighth (I*) inches.
Bed plates must be of such dimensions that the greatest
pressure on the masonry shall not exceed two hundred (2OO)
pounds per square inch.
Every bearing upon masonry must be provided with either a
bed plate or a roller plate, well fastened to the masonry by bolts
not less than one (1) inch in diameter; but, if the shoe plate
be sufficiently large, it may act as a bed plate at the fixed end
of the span. {
Beam-Hanger Plates. – Beam-hanger plates are never to be
made less than three-quarters (#) of an inch thick, and their
areas are to be such that the hanger nuts will always have a full
bearing thereon. The necessary thickness for a beam-hanger
plate is to be determined by considering it as a beam uniformly
loaded by the whole weight that comes on the hangers; the
length of said beam being the distance between the centres of
the holes through which pass the ends of one hanger, and its
width being the extreme dimension of the plate, measured par.
allel to the floor beam. The intensity of working-stress for
bending in the plate is to be taken equal to that used in pro-
portioning the floor beam.
Riveting. — In riveted work, all joints are to be squarely and
truly dressed, and the rivet holes must be accurately spaced.
No rivets with crooked heads, or heads not formed accurately
on the shank, or rivets which are loose either in the rivet holes
or under the shoulders, will be allowed in a bridge.
Rivet holes in top-chord plates and batter-brace plates shall
be spaced as nearly as practicable two and a half (23) inches
centre to centre near the panel points, and four (4) inches centre
to centre elsewhere. -
No rivet-hole centre shall be less than one and a half (1})
diameters from the edge of a plate: whenever practicable, this
distance is to be increased to two (2) diameters.
The diameter of a hole shall never exceed that of the rivet by
more than one-sixteenth (#) of an inch.
I8 ORD//VARP WROM HIGH WA Pi—BRIDGES.
When two or more thicknesses of plate are riveted together
in compression members, the outer row of rivets shall not be
more than three (3) diameters from the side edge of the plate.
Rivet holes must never be spaced less than two and a half
(23) diameters from centre to centre: it is preferable that this
distance be increased to three (3) diameters when so doing will
not cause inconvenience in designing. -
All the rivet holes of the respective parts of any structure
must be made to exactly coincide, either by drilling the holes
full size through the connecting portions, after being put
together, or by sub-punching the pieces separately, and after-
wards reaming the combined rivet holes to proper size. In all
cases the burrs must be removed by slightly countersinking the
edges of the holes.
All rivets in splice or tension joints are to be systemati-
cally arranged, so that each half of a tension member or splice
plate will have the same uncut area on each side of its centre
line.
No rivet, excepting those in shoe plates, is to have à less
diameter than the thickness of the thickest plate through which
it passes, nor in any case less than half (#) an inch.
Built Members. — The several pieces forming one built mem-
ber must fit closely together, and when riveted shall be free
from twists, bends, or open joints.
Ose of Bolts. – The use of bolts instead of rivets is to be
avoided whenever practicable.
Lateral Bracing for Plate Girders. —When a span consisting
of plate girders is over fifteen (15) feet in length, the adjacent
girders are to be braced to each other by diagonal angle irons
attached to or near the lower flanges. There are to be, also,
light bracing-frames at each end between adjacent girders, so
placed as not to interfere with the expansion. When the span
is over twenty-five (25) feet in length, the upper flanges of
adjacent girders are also to be connected by diagonal angle-iron
braces.
In every case the joists are to be dapped at least an inch
onto the girders, and every third joist resting on any girder is
to be bolted through the upper flange.
OA’D/AWA R P /ROAW HMGA. WA P-BA’/DGE.S. I9
Formula for Built Floor Beams and Plate Girders.” — The
tension flanges of built floor beams and plate girders are to be
proportioned by the formula
WZ Aſ //
4 =#-F#4-4",
where A is the area of the flange, A’ that of the web, A" that
lost from the flange by a rivet hole, W the uniformly distributed
load in tons, L the length of the beam in feet between centres
of supports, D the depth in feet between centres of gravity of
flanges, and T the intensity of working tensile stress in tons.
The same formula will apply to the compression flanges by
making A" equal to zero.
Stiffemers. — Built floor beams and plate girders must be stiff-
ened by four (4) angle irons at each support, and by two (2)
angle-irons at several intermediate points; the distance apart
of the stiffeners being made no greater than twice the depth of
the beam when the ratio of thickness of web to depth of same
is not less than one-eightieth (sº), and no greater than one and
a half (13) times the depth when this ratio is one over one
hundred and twenty (#3). Distances for intermediate ratios
are to be interpolated.
Tee-irons are not to be used as stiffeners.
Stiffening angles, which must always be in pairs (one angle
on each side of the web), must extend from the upper leg of
the upper flange angle to the lower leg of the lower flange
angle, being made flush with the other legs of the flanges by
filling plates.
Web Splices in Floor Beams and Plate Girders. — Webs of
floor beams and plate girders must be well spliced at all joints
by a splice plate on each side of the web; and joints must be
located where the shear is not great.
Limiting Depths of Floor Beams and Plate Girders. — The
depth of the web of a floor beam or plate girder must never
exceed one hundred and twenty (I2O) times its thickness.
* For proof of this formula, see Appendix II. .
2O ORD/AVA A' P A ROAV HIGH WA Y-BR/DGE.S.
}
Rivets in Flanges of Floor Beams and Plate Girders. — In
spacing the rivets in the flanges of floor beams and plate gird-
ers, the flanges are to be divided into portions of about two (2)
feet in length, the stresses in the flanges are to be found at
each point of division, and there must be enough rivets between
any consecutive points of division to take up the difference
between the stresses at the points, providing that the rivets be
not spaced more closely than two and a half (23) diameters,
nor more than six (6) inches apart.
Eyes. – In welded heads, the length of metal behind the pin-
hole must be at least equal to the depth of the bar or diameter
of pin, whichever be the greater, unless the head be corre-
spondingly thickened; while in hammered heads the amount is
to be the same as that above or below the pin hole.
The least amount of metal in the heads across the pin holes
is to be as given in the following table : —

- METAL IN HEAD Across PIN.
WIDTH OF BAR. DIAMETER OF PIN.
Welded. Hammered.
I o.8o I.5O I.5o
I I.O4 I.5O 1.5o
I I. I 2 I.50 I.53
I I.2O I. So 1.56
I 1.28 I.5o I.60
I I.36 I.55 I.72
I I.43 I.6o 1.76
I I.5o 1.67 1.85
I I.64 1.67 I.95
I 1.77 1.70 2.05
I I,90 1.76 2.2 I
In loop eyes the distance of the inner point of the loop from
the centre of the pin must not be less than three (3) times the
diameter of the pin. The loop must fit closely to the pin
throughout its semi-circumference.
Pin holes in eye bars shall be bored to an exact size and dis-
tance, and to a true perpendicular to the line of stress. No
error in the length of bar exceeding one sixty-fourth (#1) of an
ORD/AWA R P VRO/V HIGH WA Y-AR/DGE.S. 2 I
inch will be allowed, nor any variation of more than one thirty-
second (º) of an inch between the centre of the eye and the
centre line of the bar.
Pins. – Pins are to be proportioned to resist the greatest
bending produced in them by the bars or struts which they
COnnect.
Steel pins are also to be proportioned for shearing.
No pin is to have a diameter less than eight-tenths (ſº) of
the depth of the deepest bar coupled thereon; nor shall it vary
from that of the eyes of the bars coupled thereto by more than
one-fiftieth (gº) of an inch.
The least allowable diameters for chord pins are two (2)
inches for bridges of Class A, and one and a half (13) inches
for those of Classes B and C. The least allowable diameter for
pins belonging wholly to the lateral systems of bridges of any
class is one and a quarter (1}) inches. -
Pin Bearings. – All pin holes through webs shall be re-en-
forced by additional material, so that the permissible pressure
upon the bearings shall not be exceeded. Where a pin bears
against a re-enforced channel bar, the web of the latter is not to
be assumed to take any bearing-stress, unless the re-enforcing
plates be riveted to it before the pin-hole be bored.
Chord Packing. — The lower chords are to be packed as
closely as possible, and in such a manner as to produce the
least bending-moments upon the pins. The various members
attached to any pin must be packed as closely as possible, and
all interior vacant spaces must be filled with wrought-iron
fillers.
Expansion Rollers. — Expansion rollers for bridges of Class A
are to be proportioned by the formula
A = o.25V.
and those for bridges of Classes B and C by the formula
A = o 3125V2.
where p is the working-load in tons per lineal inch of roller, and
d is the diameter of the roller in inches.
f
22 ORD//WAAP Y V ROAV HIGH WA P-BA’/DGES.
The least allowable diameters for rollers are one and three-
quarters (13) inches for bridges of Class A, and one and a half
(1}) inches for bridges of Classes B and C. The spaces between
rollers must never exceed three-quarters (3) of their diameter.
Turne Buckles and Sleeve Muts. – All turn buckles and sleeve
nuts must be made so strong, that they will be able to resist
without rupture the ultimate pull of the bars which they con-
nect, and without distortion, the greatest twisting-force to which
they could ever be subjected. U-nuts are not to be used in any
part of a bridge.
Sizes of Muts. – The dimensions of all square and hexagonal
nuts for the various diameters of rods are to be taken from
Carnegie’s “Pocket-Companion" (pp. 130, I31), excepting those
nuts on the ends of pins which are subject to but a slight ten-
dency to shear the thread: in this case, these dimensions may
be diminished, in direct proportion to this tendency, until the
thickness reaches the limit of one-half (#) of an inch.
Washers and Muts. – Washers and nuts must have a uniform
bearing. Cast-iron washers must be used under the heads and
nuts of all timber bolts, when the bearing is on the wood.
Beam Hangers. —Whenever possible, four (4) beam hangers
per beam are to be used. The screw ends are to be provided
with check nuts.
jaws. – Great care must be taken, in designing jaws for the
ends of any strut, that they be so strong in every respect, that,
when the strut is subjected to its ultimate load, it will fail near
the middle rather than at the ends. -
Brackets. – Brackets, or knees, must be used to connect each
overhead strut to the posts or batter braces. They should be of
straight tee, angle, or channel iron : if made curved, no depend-
ence is to be placed upon them, either for strength or stiffness.
When there is no vertical sway bracing, each intermediate
bracket must be proportioned to resist the compression induced
in it by the wind pressure concentrated at the windward and lee-
ward points of that panel of the top chords to which the bracket
belongs; and each portal bracket, to resist the compression
induced in it by one-half of the total wind pressure concentrated
at the panel points of the top chords.
ORDZAWAA' P IROM HIGH WA P-B/C/DGE.S. 23
Cutting off the Flanges of Channels. – The flanges at the ends
of channel bars must not be cut away, if it be practicable to
avoid doing so: if not, there must be sufficient re-enforcing
used to make the strut as strong as it would have been with
the flanges uncut.
Siges of Flooring and Şoists. – Pine flooring is to be at least
three (3) inches thick, and oak flooring at least two and a half
(24) inches thick. It is to be laid with close joints, and well
spiked to each alternate joist with two (2) seven (7) inch cut
spikes. Consecutive boards should not be spiked to the same
joists.
Joists are to be proportioned by the formula,
Åay3
W=#
where W is the safe uniformly distributed load in tons, & the
breadth of the joist in inches, d the depth of same in inches,
l the length in feet, and c = 16 for pine and II.5 for Oak.
Where the greatest load, is a concentrated one, it is to be
considered as supported equally between the joists directly
under the wheels and those contiguous to the same ; i.e., the
wheels on one side of a wagon are supposed to be placed
directly over a joist, which joist is assumed to take half their
load, the remaining half being equally divided between the two
adjacent joists. All concentrated loads must be reduced to
equivalent uniformly distributed loads in respect to deflection
by multiplying them by one and six-tenths (1.6) before applying
the formula.
Wooden Hand Rails, etc. —Wooden hand railing is to be
made of pine, the posts being 4" × 6" × 4, with two runs of
2" × 6" timbers—one on its flat, and the other below on edge to
support the first for a hand rail—and one run of 2" × 12" hub
plank. The latter and the lower run of 2" × 6" timber are to
be let into the posts to their full depth, and spiked to the same
with five (5) inch cut spikes; and the posts are to be halved
on the outer joists, to which each one is to be bolted by two
(2) three-quarter (#) inch bolts.
Guard rails are to be of 6" × 6" pine, bolted to each hand-
24 ORD/AWARY IRO/W HIGH WA Y-BRIDGE.S.
rail post, and to the floor once in, at most, every five (5) feet,
by three-quarter (#) inch bolts.
When there are no wooden hand-rail posts, the guard rails
must be bolted through joists placed symmetrically below them,
care being taken that there be no bolt within two (2) feet of the
middle point of any joist. -
The joints in the guard rails are to be lap joints, six inches
long, and are to have a bolt passing through the middle of each
lap.
About every eighth or tenth plank, there is to be a crack left
between flooring boards to let the water run through : this
crack should be less than a quarter (#) of an inch in width.
Should it be considered desirable to elevate the guard rails
in order to let the air and water pass beneath, it is to be accom-
plished by inserting hard-wood shims — one (1) foot long by two
(2) inches deep, and six (6) inches wide—beneath the guard rails
at each bolt hole; the bolt passing through the middle of the
shim, and each shim being fastened to the floor by four (4) five
(5) inch cut spikes.
Iron Hand Railing. — Bridges with sidewalks will not require
the wooden hand railing inside the trusses, but are to be pro-
vided with a neat, substantial iron hand rail on the exterior of
each sidewalk. It is to be rigidly attached to the floor beams
and exterior sidewalk joists.
Details not previously Mentioned. — Finally, as regards the
proportioning of any structure, if cases should occur which are
not covered by the preceding specifications, the following rule
is in all such cases to be adhered to : “Details must always
be proportioned so as to resist every direct and indirect stress
that may ever come upon them under any probable circum-
stances, without subjecting any portion of their material to a
stress greater than the legitimate corresponding working-stress.”
Cast-Iron. — No cast-iron is to be used except for washers
for timber bolts, and for ornamental work and name plates.
Mame Plates. – The names of the designer and the manu-
facturer of the bridge must be attached thereto in a prominent
position and in a durable manner. *
Field Riveting. — Field riveting must be done with the button
ORD/MARY ZRO/V HIGH WA Y-BRIDGE.S. 25
sett. The heads of the rivets must be hemispherical, and no
rough edges must be left.
Painting. — All finished work, before leaving the shop, shall
be thoroughly cleaned from all loose scale and rust, and covered
with one good coat of pure boiled linseed-oil well worked into
all joints and open spaces. In riveted work all surfaces coming
into contact shall be painted before being riveted together.
Bed plates, and all parts of the work which will not be acces-
sible for painting after erection, shall have two coats of paint.
Pins, bored pin holes, and turned friction rollers, shall be
coated with white lead and tallow before being shipped from
the shop.
After the structure is erected, the iron-work shall be cleansed
from mud, grease, or any other objectionable material that may
be found thereon, then thoroughly and evenly painted with two
coats of paint mixed with pure linseed-oil, of a color pleasing to
the eye; the tension members being generally of a lighter shade
than the compression members.
Wherever it be possible to so design it, the iron-work must
be made accessible to the paint-brush.
Timber. — All timber is to be of the best quality, free from
wind-shakes, large knots, decayed wood, sap, or any defect that
would impair its strength or durability.
Quality of Workmanship. — All workmanship is to be first-
class; abutting joints are to be truly planed and dressed, so
as to insure a perfect bearing ; the pin holes in chords, batter
braces, and posts, are to be bored as truly as is specified for the
eye bars; and there are no rough edges or corners to be left on
the iron-work.
Bars which are to be placed side by side, or in similar posi-
tions in the structure, shall be bored at the same temperature,
and of such equal length, that, upon being piled on one another,
the pins shall pass through the holes at both ends without
driving. Whenever necessary for the protection of the thread,
provision shall be made for the use of pilot nuts in erection.
Quality and Tests of Materials. – All wrought-iron must be
tough, fibrous, and uniform in character. It shall have a limit
of elasticity of not less than twenty-six thousand (26,000)
pounds per square inch.
26 ORD/AWARY IROM HIGH WA Pi—BRIDGES.
Finished bars must be thoroughly welded during the rolling,
and free from injurious seams, blisters, buckles, cinder spots, and
imperfect edges.
For all tension members the muck bars shall be rolled into
flats, and again cut, piled, and rolled into finished sizes.
They shall stand the following tests. Full-sized pieces of flat,
round, or square iron, not over four and a half (43) square inches
in sectional area, are to have an ultimate strength of fifty thou-
sand (50,000) pounds per square inch, and are to stretch twelve
and a half (12%) per cent of their whole length.
Bars of a larger sectional area than four and a half (43) square
inches are to be allowed a reduction of one thousand (1,000)
pounds per square inch for each additional square inch of sec-
tion, down to a minimum of forty-six thousand (46,000) pounds
per square inch.
Specimens of a uniform section of at least one (I) square
inch, taken from bars of four and a half (43) square inches sec-
tion, and under, are to have an ultimate tensile strength of
fifty-two thousand (52,000) pounds per square inch, and are to
stretch eighteen (18) per cent in eight (8) inches.
Similar specimens from bars of a larger section than four and
a half (43) square inches are to be allowed a reduction of five
hundred (500) pounds per square inch for each additional square
inch of section, down to a minimum of fifty thousand (50,000)
pounds per square inch.
Similar sections from angle and other shaped iron are to have
an ultimate strength of fifty thousand (50,000) pounds per
square inch, and are to stretch fifteen (15) per cent in eight (8)
inches.
All iron for webs of plate girders is to have an ultimate
strength of not less than forty-six thousand (46,000) pounds
per square inch of area of test-piece, and is to have a minimum
elongation of ten (IO) per cent in eight (8) inches.
Rivets are to be of the best quality of double refined iron.
The cast-iron must be of the best quality of soft gray iron.
Test of Structure. — On the completion of the entire struc-
ture, any bridge, after being in constant use for one day, may
be tested by a load equal to that for which it was designed
ORDVAWARP IRO/W HIGH WA P-AERIDGES. 27
remaining upon it for at least one hour, then removed, and
placed upon it again. The first removal of the load may show
a little permanent set; but, when the second load is applied,
the total deflection must not be any greater than it was for the
first loading, and upon its removal the bridge must return to
the exact position which it occupied after the removal of the
first loading.
28 ORD/AWARY IRO/W HIGH WA P-BRIDGES,
CHAPTER III.
LIST OF MEMBERS.
IN the following list of members will be found the names of
all the parts, both of wood and iron, in the bridges with which
this treatise deals. Its use will be explained in Chapter XIV.
It is inserted here so that those unacquainted with bridge
designing may inform themselves as to the names of all the
parts of a bridge before proceeding farther. This they can do
by consulting the Glossary, and referring to the plates there
indicated. The author would advise students, before proceeding
to Chapter IV., to study closely Plates I-IV., so as to obtain a
general idea of how bridges are constructed.
LIST OF MEMBERS IN A WROUGHT-IRON HIGHWAY-BRIDGE.
MAIN PORTIONS.
Channel Bars. — Top chords, batter braces, bottom chords,
posts, upper lateral struts, end lower lateral struts, upper portal
struts, lower portal struts, hip verticals in pony trusses.
Plates. – Top chords, batter braces. -
I-Beams. – Floor beams, intermediate struts, end lower lateral
struts, bottom chords.
Bars and Rods. – Main diagonals, counters, hip verticals,
upper lateral rods, lower lateral rods, vibration rods at portals,
vibration rods on posts, chord bars. .
Angle Iron. — Side bracing, end lower lateral struts.
Iron hand railing.
Floor beams.
DETAILS. º
Stay Plates. – Top chords, batter braces, ends of posts, mid-
ORDIWARY IROW HIGHWAP–BRIDGES. 29
dle of posts, bottom-chord channels, upper lateral struts, end
lower lateral struts, upper portal struts, lower portal struts.
Re-enforcing and Connecting or Splice Plates. – Hip inside, hip
outside, top-chord intermediate panel points inside, top-chord
intermediate panel points outside, bottom-chord struts at shoe,
bottom-chord struts at first panel points, shoe inside, shoe out-
side, lower ends of posts inside, lower ends of posts outside, mid-
dle of posts inside, middle of posts outside, lateral struts to top
chords, upper portal struts to batter braces, lower portal struts
to batter braces, portal struts to brackets and name plates,
intermediate struts to posts, side bracing to floor beams, end
lower lateral struts to pedestals.
Cover Plates. – Hip joints, joints at intermediate panel points
of top chords.
Filling Plates. – Hips, intermediate panel points of top chord,
over end floor beams, between pedestals and lateral struts.
Extension plates at upper ends of posts, shoe plates, roller
plates, bed plates, beam-hanger plates, name plates.
Lacing or Latticing. — Top-chord channels, batter-brace chan-
nels, bottom-chord channels, post channels, upper lateral strut
channels, end lower lateral strut channels, upper portal struts,
lower portal struts, hip verticals in pony trusses.
Trussing. — Hip verticals in pony trusses, lower-chord bars.
Pins. – Top chords, bottom chords, middle of posts, lower
lateral rod connection to jaws, vibration-rod connection to upper
portal and lateral struts, vibration-rod connection to lower portal
struts, between floor beams and beam-hanger plates.
Bolts. – Brackets to portal struts and lateral struts, brackets
to batter braces and posts, name plates to portal struts, vibra-
tion rods to lateral struts, vibration rods to intermediate struts,
bed plates to piers (anchor bolts), shoes to bed plates, expansion
pedestal connection to bed plates, portal struts to batter braces,
hand-rail posts to joists, lower lateral struts to floor beams,
lower lateral struts to jaws, felly planks to floor and hand-rail
posts. -
Brackets or Knee Braces. – Portal struts to batter braces,
upper lateral struts to posts, intermediate struts to posts.
Ornamental work at portals, beam hangers, expansion rollers,
3O ORDIWARP IROW HIGHWAP–BRIDGES.
roller frames, fillers for pins, turn buckles, sleeve nuts, connect-
ing-chord heads for bottom-chord channels, jaws for lateral and
portal struts.
Angle Iron. — Batter braces to shoe plates, sides of roller
plates, ends of roller plates.
Pieces of Channels. – Bearing for bent eyes of upper lateral
rods, bearing for bent eyes of lower lateral rods, batter-brace
connection :o shoe plates.
Rivet Heads. – Plate to chord and batter-brace channels, lat- .
ticing or lacing to channels, latticing to latticing, the various
stay plates to channels, the various connecting and re-enforcing
plates to channels, connecting plates to shoe plates, connecting
plates to intermediate struts, connecting plates to side bracing
and floor beams, connecting plates at pedestals to pedestals and
lateral struts, cover plates to chords, extension plates to posts,
trussing to hip verticals and posts, trussing to chord bars, orna-
mental work to portals, brackets to posts and batter braces,
brackets to portal, lateral, and intermediate struts, components
of jaws to each other, angle irons to shoe plates, angle irons to
roller plates, the various pieces of channels to the parts which
they connect.
Spikes. – Flooring to joists, hand rails to posts, hub planks
to posts, felly planks to flooring, joists to lower lateral struts,
jaws to lower lateral struts.
Washers. — Hand-rail post bolts, bolts connecting lateral struts
to floor beams, felly-plank bolts.
AVuts. – On pins, on bolts, on beam hangers, lock nuts on
beam hangers, pilot nuts.
Details for a Built Floor Beam. —Web, upper-flange angles,
lower-flange angles, top plate, bottom plate, stiffening angles,
filling plates, re-enforcing plates at beam-hanger holes, rivet
heads.
Details for a Trussed Beam. — Rolled I-beam for upper chord,
lower-chord bars, end diagonals, counters, I-beam posts, con-
necting plates for posts to beam, re-enforcing plates at feet of
posts, pin plates for end diagonal connection to beam, stiffeners
at supports, pins and nuts on same, fillers, turn buckles or.
sleeve nuts, rivet heads.
ORD//VAA' P IROM ºf IGHVA Pi—BRIDGE.S. 3 I
Lumber. —Joists, flooring, hand-rail pieces, hand-rail posts,
hub planks, felly planks or guard rails, lower lateral struts.
DETAILS FOR A SPAN COMPOSED OF PLATE GIRDERS.
Webs, upper-flange angles, lower-flange angles, top plates,
bottom plates, stiffening angles, filling plates, angles for lateral
braces, connecting plates for lateral braces, shoe plates, bed
plates, anchor bolts and nuts, rivet heads.
~
32 ORD//VARP IRO/V HIGH WA Y-BA’/DGES.
CHAPTER IV.
LIVE AND DEAD LOADS. – WIND PRESSURE.
As stated in Chapter II., highway-bridges are divided into
three classes, A, B, and C, which are respectively for locations
where the loads are heavy and of frequent occurrence, loca-
tions where the loads are occasionally heavy, and locations
where the loads are light.
After deciding upon the length of span, width of roadway,
and class of bridge for any location, the live load per square
foot of floor is to be taken from the table on p. 5. The reason
why long spans may be proportioned for lighter loads than short
ones is the very small probability of a long span ever being
covered by the maximum load, while there is a chance of such
an event taking place in case of a short span.
It can easily be seen, then, that, in all bridges of any length
of span, each panel should be proportioned to sustain the maxi-
mum load; for it is possible to load one panel heavily without
loading any of the others.
This panel excess will affect only the sizes of the joists, floor
beams, beam hangers, and hip verticals. Sometimes the panel
excess is supposed to exist when the bridge is partially or
wholly covered by the moving load, thus affecting all the main
members of the trusses; but this is too much refinement for
highway-bridge designing.
The dead load per lineal foot is to be taken from one of
Tables I., II., and III., if there be no special loading such as
that due to snow, if the style of hand railing, guard rail, etc.,
for the bridge to be designed, correspond with that adopted in
this work, if the width of roadway correspond with one of those
in the table, and if the length of the span be exactly divisible
ORDIWAR}^ IROM HIGH WA P -BRIDGE.S. 33
by ten. If either or both of the last two conditions be not
fulfilled, the dead load is to be directly interpolated; then if
there be any difference in the lumber, or any special loading,
the effect of the change or changes is to be calculated by the
method to be explained presently.
The weights of iron and lumber given in Tables I., II., and
III., are the results of calculations for the bills of materials of
sixty bridges, so chosen in respect to length of span, and width
of roadway, as to indicate the laws by which the weights vary
with these dimensions. All the bridges are of the most eco-
nomic depth and panel length, corresponding in these respects
with the dimensions given in Table IV. The figures in the
five columns under each roadway give respectively the weights
of iron per lineal foot in the trusses, lateral systems, and floor
system; the weight of lumber per lineal foot, not including
waste; and the dead load per lineal foot, corrected for the small
amount resting on the piers.
To find the dead load for any span where there is to be an
increased weight of flooring, or an additional load, find the new
value for the weight of lumber (proportioning the joists by the
method given in Chapter IX., remembering that pine lumber
weighs two pounds and a half per foot, board measure, and oak
lumber four pounds and a third), then that of the floor system
by the formula
F=#6 +1), º
where F is the weight per foot of the floor system required, F
that of the floor system given in the table, and r (greater than
unity) the ratio of total loads on floor beams in the two cases
considered. -
Next assume T', the new value for the weight T in the truss
column, and find the ratio r" (greater than unity) of total loads
per foot on trusses in the two cases; then
Z’’ = £g + 4r').
If the value of T' thus found agrees with that assumed, all right;
if not, it will be necessary to try again until it does agree.
34 ORDVAWARP IROM HIGH WA Pi—BRIDGES.
Next add together the differences between T’ and T, between
F' and F, and between the weights of lumber per lineal foot.
To the sum of these differences add the weight of snow or
other special loading per lineal foot of bridge, and the dead
load taken from the table. The final sum will be the dead load
required. - -
To find the dead load for a bridge with sidewalks, look in
the table of the class to which the bridge belongs, and find the
weights for a bridge of the same span and roadway without
sidewalks, then estimate the increments of these weights as
follows : — -
First, the weight of lumber per lineal foot on the sidewalks
is to be calculated; and from it is to be subtracted twenty-four
pounds, which is the weight per foot of the wooden hand rails,
hub planks, and hand-rail posts (lumber not required when there
are sidewalks). The difference will be the increment for the
“lumber" column.
The increment for the “lateral system ’’ column will be zero:
that for the “floor system ’’ column can be found approximately
by the formula
2/5A"
A = Taž’
where 7 is the increment required, F the weight per foot of
floor system taken from the table, & the sum of the widths
of the sidewalks, and B the clear width of main roadway.
The increment of the “truss” column is found by assuming
the dead load required, and calling it W.
Let
W. =: the dead load given in the table,
P. = the live load per lineal foot on the main roadway,
P = that on the sidewalks;
then
*#;" = the ratio of total loads.
Let
2. = the truss weight from the table,
Z} = the new truss weight;
ORDIAWAA’ V IROM HIGH WA Y-BAIDGE.S. 35
then
#( + 4 (P. -- P; + ro)
7-#( A., + W.
and the increment will be T. — T.
Next add W., the three increments found, and the weight
per lineal foot of the iron hand rails: the sum will be the dead
load required. If it agrees with the assumed load W., all right;
if not, another trial for the new truss weight is to be made.
There is one case in which this method would give too great
a result: it is that of a pony truss with side braces, of which
the only representative in the tables is the sixty-foot span. To
apply the method to this case, it will be sufficiently exact to
use the weight of floor system of the fifty-foot span, because the
floor beams of the sixty-foot span project beyond the trusses.
This change being made, the method can be otherwise followed
exactly.
The full double horizontal lines in Tables I., II., and III.,
divide the single from the double intersection trusses.
All the bridges in Table III, lying to the left of the double
vertical line which separates the twenty-two-foot and twenty-
four-foot roadways, have stiffened end panels. The correspond-
ing lines of division in Tables I. and II. separate the twenty-foot
and twenty-two-foot roadways. -
The weights of iron in Tables I., II., and III., do not include
the weight of the spikes. ~.
It is seldom necessary to make an allowance for snow load in
bridges of Class C, but it may be advisable to do so in bridges
of Classes A and B; for, after a heavy snow-storm, the travel
on country roads would be light, which would not necessarily
be the case in a city or its suburbs. The proper allowance
for snow load should be from ten (IO) to thirty (30) pounds
per square foot of floor; according to climate, locality, proba-
bility of greatest live load occurring simultaneously with the
Snow load, etc. s
As stated in Chapter II., the wind pressure assumed is forty
(40) pounds per square foot for spans of one hundred (IOO) feet
and under, thirty-five (35) pounds for spans between one hun-
dred (IOO) and one hundred and fifty (150) feet, including the
36 OA’D/AWA/C P VA’O/W Aſ/GA IVA P-AEA’ZZOGAE.S.
latter, and thirty (30) pounds for all greater spans. It is true
that actual wind pressures do occasionally exceed these amounts;
but in view of the fact that the chance of any one bridge ever
being subjected to such pressure throughout its whole length
is extremely small, and that it could receive once in a while
a far greater pressure without suffering material injury if the
bridge be properly designed, it seems legitimate to adopt the
pressures assumed.
Moreover, when a highway-bridge is blown down, the actual
loss is seldom much greater than the cost of a new bridge.
Travellers can cross the stream at the nearest bridge above or
below, until the structure be replaced. And the fall of the bridge
need involve no loss of life: for, in the first place, no human
being would be likely to be upon it in such a storm ; and, in
the second, if there were, he could not escape being dashed to
pieces or blown off, even if the bridge were sufficiently rigid
to withstand the pressure.
With railroad-bridges, of course, it is a very different matter.
The delay caused by the loss of such a bridge may be much
more expensive than the replacing of the structure. Besides,
railroad-bridges are subjected to the greatest wind pressure
when covered by a train; so that the fall usually involves the
loss of human life.
If the lateral systems of highway-bridges were to be made as
strong as those of railroad-bridges, unstiffened eye-bars could
be very seldom employed for the bottom chords; because the
compression there due to the wind pressure would be far in
excess of the tension due to dead load (vide Appendix I.).
Even with the pressures assumed, it is necessary to rely upon
the stiffness of the joists to prevent buckling the bottom chords
of at least two-thirds of the iron and combination highway-
bridges in the United States.
It is not necessary to add any area to the section of the bot-
tom chords to resist the tension due to wind pressure, unless
this tension exceeds that due to the live load multiplied by
the ratio of the intensity of working tensile stress in lateral
systems to that of working tensile stress in chords. Should it
so exceed, the chords should be proportioned to resist the wind
OA’/D/AVA A' P ZAZOAV AZGA/WA P-AEA’/ZOGAE.S. 37
stress plus the dead-load stress multiplied by the aforesaid
ratio, using an intensity of seven and a half (7%) tons, or, in
case of stiffened eye-bars, six and a half (63) tons. This ex-
cess should be looked for in narrow bridges in unusually
exposed situations, in the design for which the wind pressure
has been increased ten (IO) pounds per square foot.
For this same reason, of there being no probability of a live
load remaining upon a highway-bridge during a heavy storm,
the effect of the wind upon posts and batter braces may be
neglected, unless the stresses produced thereby exceed those
due to the live load multiplied by the ratio before mentioned;
in which case the wind stresses should be multiplied by the
reciprocal of this ratio, and to the product should be added
the dead-load stresses, in order to find the greatest stresses for
which to proportion these members. As before, this excess is
to be looked for when the assumed wind pressure has been
increased by ten (IO) pounds per square foot : it will probably
be only the lighter posts that will be so affected.
But the bending effect of the wind pressure upon portal and
lateral struts, when no vertical sway bracing except brackets is
used, should always be provided for.
The author believes, that, instead of designing highway-
bridges in ordinarily exposed situations to resist the greatest
recorded wind pressure in the district, it is better to run a
little risk of losing a structure than to make all the bridges
so much more expensive. Nevertheless, he wishes it to be
distinctly understood, that, in advocating the adoption of com-
paratively low wind pressures, he does not countenance the
building of such miserable apologies for lateral systems as one
finds in the majority of highway-bridges.
38 OA&ID//VA R P IRO/W HIGH WA Y-BA’/DGAE.S.
CHAPTER V.
STRESSES IN TRUSSES.
THE length of span having been decided by considerations of
both necessity and economy (vide Chapter XV.), and the width
of roadway by the requirements of travel, there remain to be
determined, before making out the diagram of stresses, only
the style of intersection, panel length, and depth of trusses.
These matters are fully treated in Chapter XV. Meanwhile,
the style of intersection may be settled by remembering that the
single is more expensive than the double, and that the inferior
limits of the latter for the different classes of bridges and differ-
ent clear roadways are given in the table on p. 8. The most
economic panel lengths and depths of truss for locations where
long timber is expensive, and, in fact, for nearly all locations,
are to be taken from Table IV. For locations where long tim-
ber is very cheap, there can be made a little saving in the
iron-work by using Table V. instead of Table IV.
As is customary in figuring stresses, uniformly distributed
loads are to be considered as concentrated at the panel points;
and the half-panel load at each end of the truss is not supposed
to produce any stress in any member of the truss. -
The first step in making a diagram of stresses is to fill out
one of the following tables of data: —
Double INTERSECTION. Double INTERSECTION.
SINGLE INTERSECTION. Even Number of Panels. - Odd Number of Panels.
72 = 72 > Ž -
d = d = d =
diag. = short diag. = short diag. =
sec 6 = long diag. = long diag. =
OA’D//WAA' P ZA’O/V HIGH WA P-B/º/DGES. 39
Double INTERSECTION. Double INTERSECTION.
SINGLE Intersection. Even Number of Panels. Odd Number of Panels.
tan 6 = SeC (X = Sec 0. =
Z09 = tan O. = tan (Z =
W = . sec/3 = sec (3 =
Wºr -: - 70) = 70) =
W’ = W. = W =
I py” - W/// -:
º 70/ :
72 W’ = W" =
I I I
-zey sec 6 = — 70) = — Z0) =
72 f Ž 72
W. Sec 6 = I I
1
–70) Sec 0. = - – W. =
# W, sec 6 = 72 zz" 1
// dº dº I
iſ...anº- W, seco = — Z2) Sec (Z =
# W’’ tan 6 = # W. Seco =
I I W.
;w sec 3 22 " " 1
– I
W, sec 8 = w sec (3 =
# W, sec 6 = 22
// smºs I
iſ...ana- – W, sec 6 =
# W’ tan & = Ž
I
n WZ" tan & =
where m is the number of panels in the span, l the length of
each panel, d the depth from centre to centre of chords, 6 the
inclination of the diagonal ties in the single-intersection truss
to the vertical, w the live panel load in tons on one truss (i.e.,
one-half the product of the live load per foot by the panel
length, or one-half the product of the clear roadway by the
panel length by the live load per square foot in pounds, all
divided by two thousand), W, the panel dead load on one truss,
W" = w -- W., W’ the portion of W, concentrated at the upper
panel point, & the inclination of the short diagonal ties in double-
intersection trusses to the vertical, and 8 the inclination of the
long diagonal ties in same to the vertical. The value of W’ is
usually between one-fourth and one-third of W.; by taking it
always equal to one-third of W, a small error on the side of
safety will be made in designing short spans,
Having filled out the table of data, the next step is to draw a
4O ORDIMARY IRoy HIGHWAP–BRIDGES.
skeleton diagram large enough to contain all the stresses and
sections. It is not necessary that the diagram be drawn to
scale; but the ratio of panel length to depth of truss on the
diagram, for the sake of appearance, should not vary too greatly
from the ratio of the actual values of these dimensions. A
panel length of an inch and a half, and a depth of two inches
and a half, are about as small dimensions as will be found ſcon-
venient. -
At each lower panel point write lightly in pencil, so that it
can be afterwards erased, the number of the panel point, begin-
ning with zero at the right-hand end of the span.
It is well known, and will be accepted here without proof,
that the greatest stresses in the chords and batter braces occur
when the bridge is entirely covered by the moving load; that
the greatest stress in any diagonal exists when the live load
extends to its foot from that end of the bridge towards which
the diagonal points in a downward direction; that the greatest
stress in any post occurs when the main diagonal (or, if there
be none, when the heaviest counter) attached to its upper end
receives its greatest stress; and that the two diagonals of a
panel cannot at the same time be subjected to the same kind
of stress, excepting, of course, the initial tension.
It is apparent that when the greatest stresses in all the
diagonals sloping upward in one direction, and in all the posts
and chord panels on one side of the central plane, are found, the
greatest stresses in the diagonals sloping in the opposite direc-
tion, and in the posts and chord panels on the other side of the
central plane, can be immediately written. This fact is so well
known, that, in making a diagram of stresses, it is usual to write
the stresses on only one-half of the members of the truss.
First let us take a single-intersection through-bridge.
The greatest stress in any diagonal sloping upward from right
to left can be found by the formula -
Ž — I
2
7–4 (n + Jºseco-(º- )w.ccº.
where m' is the number of the panel point at the foot of the
diagonal. This formula is applicable to counters as well as to
OA-AD/AWA R P IROM H ZGAſ WA P-BAC/DGE.S. 4. I
main diagonals. If the stress should come out negative, it
shows that no counter is needed in the panel considered. It is
also applicable to the batter brace by putting (n − 1) for m'.
The stress in any post can be found by the formula
c-tº-2.44 (2–º *)W,+W,
2 72 2
- 72\ . ~
where m' (not less than %) is the number at the foot of the post.
The stress in any panel of the top chord is given by the
formula ~ -
c=*Hºw” an 6,
where m' (not greater than %) is the number at the end of the
panel nearest to the centre of the bridge.
The stress in any panel of the bottom chord, except the one
at the end of the span, is given by the formula
Z’ = (n wº- I) (n — m +- 1) W” tan 9,
2
n' having the same value as in the last formula. For the end
panel, the stress is the same as for the second panel.
As the values of ; : Sec 6, and W, sec 6, are given in the
table of data, the substitution in these formulas is a very simple
matter. -
The stress in the hip vertical is w -- 3 (weight of floor beam
plus a panel weight of lumber), neglecting the weight of the
beam hangers, end lower chord bars, etc., which is not worth
considering. It is not necessary to calculate this stress; for
the section required, or the size of the square bars, if that
shape be employed, can be taken immediately from one of
Tables VI., VII., or VIII.
Some engineers may object to using formulas for figuring
stresses: if so, the following method will give the same results
for single-intersection bridges.
42 ORD/AWA R P IRON HIGH WA Y-BRIDGE.S.
Pass a vertical plane through the middle point of the bottom’
chord : all the dead loads to the right of this plane may be
considered to go to the right-hand pier, and all to the left of
the plane to the left-hand pier. Should there be a post at the
middle of the bridge, the weight at the foot is to be considered
as halved, one-half going to each pier. Then the stress in any
main diagonal of the left-hand half of the bridge is to be found
by commencing at the right-hand end, and adding the numbers
at the panel points until the foot of the diagonal considered is
reached, multiplying the sum by w sec 6, and to the product
adding the number of panel dead loads between the central
plane and the panel point at the foot of the diagonal considered
(including the one at this point) multiplied by W, sec 6.
For instance, in a ten-panel bridge, the stress in the end
main diagonal, the number at its foot being eight, will be
zey sec 6
IO
(1 + 2 + 3 + etc. . . . --8) + (; + 1 + 1 + 1) W, sec 6.
The stress in a counter on the right-hand half of the bridge
will be found by adding the numbers at the panel points
until the foot of the counter considered is reached, multiply-
ing the sum by ; w sec 6, and from the product subtracting the
dead-load stress of the main diagonal which crosses the coun-
ter. Thus, in the ten-panel bridge, the stress in the second
counter from the centre in the right-hand half of the span, or
the one at the foot of the third panel point, is
zy sec 6
IO
— (# + 1) W, sec 6.
(1 + 2 + 3)
The greatest stress in any post is found by adding W" to the
vertical component of the greatest stress in the main diagonal
attached to its upper end; thus, in the same bridge, the stress
in the first post from the left-hand end, or the one at the eighth
panel point, is
(1 + 2 + 3 + etc. . ... + 1) + (; + 1 + 1) W, 4. W.
OA’D//VARP WAZOAV HIGH WA P-B/º/DGAE.S. 43
For the case of a middle post, the stress in one of the coun-
ters at the upper end must be substituted for that of the main
diagonal; thus, in the same bridge, the stress in the middle
post is
(1 + 2 + 3 + 4) #–4W,+W.
The stresses in the chords are to be found by the following
method : —
Pass a plane through the foot of the post at or nearest to the
middle of the truss, and take the centre of moments at this
foot. From the moment of the re-action at the nearest end of
the bridge subtract the sum of the moments of the panel loads
(W") lying between the centre of moments and this end, and
divide the difference by the depth of the truss. The result will
be the stress in the panel of the top chord nearest the centre
of the bridge: it will be some multiple of W’’ tan 9.
The stress in the panel of the bottom chord immediately
below will be equal to the one found, less the horizontal com-
ponent of the main diagonal of the panel, when the bridge is
covered by the moving load. This horizontal component will
be zero for a truss with an odd number of panels, and 3 Wº tan 6
for a truss with an even number of panels.
The stress in the next panel of the bottom chord towards the
nearest end of the bridge is found by subtracting from the one
already determined the horizontal component of the stress in
the main diagonal at the panel point between the two panels
considered; the bridge, as before, being fully loaded. This com-
ponent is a multiple of W’’ tan 9. In this way can be found all
the stresses in the panels of the bottom chord, the correctness
of the work being checked by seeing if the stress in the end
panel be equal to the re-action multiplied by tan 6. If so,
the remaining upper-chord stresses may be at once written by
inspection; for the stress in the nth panel of the top chord,
counting from the nearest pier or abutment, and supplying
the missing panel at the end, is numerically equal to that in the
(n + i)th panel of the bottom chord.
It seems almost unnecessary to state, that the stresses in the
44 ORD/AVA R V /A’OAV HIGH WA P-BRIDGE.S.
top chords, batter braces, and posts, are compressive, and those
in bottom chords, main diagonals, counters, and hip verticals
tensile.
Next let us consider the double-intersection truss.
The formulas for this case are so complicated that it is better
not to employ them. The simplest method is to draw a skele-
ton diagram, and number the panel points, as in the single-inter-
section truss. The double-intersection truss really consists of
two trusses, as may be seen in the accompanying diagram.

> Eig.1
15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0
Fig.2
15 13 11 9 7 5 3 | 0
Fig. 3
15 14 12 10 8 6 4. 2 0
Such a division is necessary in order to calculate the chord
stresses when the truss contains an odd number of panels.
This is accomplished by finding, by the method of moments
already explained, the chord stresses in each of the trusses
shown in Figs. 2 and 3, and then combining them. Thus the
stress in panel 9–IO of the lower chord in Fig. I is equal to
that in panel 9–II of Fig. 2, plus, that of panel 8–IO of Fig. 3.
The live-load stress in any diagonal sloping upward from
right to left is found by noting whether the number at its foot
be odd or even, then taking the sum of the odd or even
numbers, from one or two up to the number at the foot of the
diagonal, and multiplying the sum by # sec o, Or : Sec 3, as
the case may be.
The stress due to the dead load is found by taking the sum
of the same numbers, and from it subtracting the sum of the
oddsor even numbers from one or two up to n – (n' + 2), where
m is the number of panels in the span, and n' is the number at
the foot of the diagonal considered. "Whether the odd or even
OA'D/AWA R P /A&O/W HIGH WA V-B/C/DGAE.S. 45
numbers should be taken can be ascertained by following out
towards the left the system to which the diagonal belongs: if
the system contain the short diagonal at that end, then the
even numbers are to be taken, otherwise the Odd ones.
W, seco. W, sec B
z-, or g-
as the case may be, will give the dead-load stress in the diagonal.
Thus, in the diagram, the dead-load stress in the main diago-
nal at the panel point IO is
The difference thus found, multiplied by
W, sec B
77 is
[(2 +4+ etc. + Io) — (1 + 3)]
As in the case of the single intersection, the stress in a main
diagonal is equal to the sum of the live and dead load stresses;
that in a counter, to the difference between its live-load stress
and the dead-load stress of the main diagonal crossing it at the
middle of its length; that in a post, by the sum of W’ and the
vertical component of the greatest stress in the main diagonal
(or, if there be none, that in the principal counter) attached to
its upper end. As the batter braces belong to both systems of
triangulation, their stresses are the sum of the stresses found
by each system, or by the formula
(w -- W.) seco.
73
C=[I + 2 + 3 + etc. . . . -- (n − 1)]
If the number of panels be even, the calculation for the dead-
load stresses may be much simplified by counting the number
of panel points on the system considered lying between the
central plane and the panel point at the foot of the diagonal,
including the latter, remembering that the load at the middle
panel is halved, and multiplying the result by W. Sec o, or
W, sec 3. -
The finding of the chord stresses is also simplified when
there is an even number of panels; for they can then be calcu-
lated by the method explained for the single-intersection truss.
In every double-intersection truss, there is necessarily a little
ambiguity; for it is possible that the whole of the load con-
46 ORD/AWA R P IRO/W HIGH WA P-BAZZZ)GAES,
centrated at the first panel point does not travel by the sys-
tem of odd numbers; but this ambiguity is a matter of small
moment.
The only difference between the stresses in a deck bridge
and those in a corresponding through bridge will be in the
posts, the stresses for which are to be found by letting the live
load extend from the farthest end of the bridge to the top of
the post; so that the post will no longer take its greatest stress
with the main diagonal attached to its top, but with the one
attached to its foot.
The formula for post stresses in single-intersection deck
bridges is, therefore,
c-º-º-te(?)-(–; ; )*, +w.
2 72 2
To find the stress in a post of a double-intersection deck
bridge, add w, W’, and the vertical component of the greatest
stress in the principal diagonal attached to its upper end.*
In designing bridges where there is an assumed snow load, the
counter stresses, and the post stresses produced by the counters,
should be figured without the snow load ; because, the greater
the dead load, the less the counter stresses.
In Carnegie’s “Pocket-Companion,” pp. 141–143, will be found
tabulated the numerical co-efficients for the stresses in single-
intersection trusses having from three to twelve panels, and in
double-intersection trusses having from eleven to twenty panels.
The panel dead loads are supposed to be concentrated on the
* This method of finding post stresses is not exact, but gives an error on the side of
safety, varying from : at the centre to zero at the ends of the span: it assumes the total
panel load w to pass down the post before being divided into the portions which pass to
right and left, when in fact the portion going to the farther end passes down the main diago-
nals as compression. The formula was originally obtained under the false assumption; but
it has been retained for the following reasons: —
Ist, There is a certain amount of shock accompanying the application of the panel live
load on the post; {
2d, The load w coming from the floor beam is applied to one side of the axis of the
post, and consequently tends to produce a slight bending thereon;
3d, The distribution of the excess of stress is favorable, being greatest for the light posts
near the middle of the span, and smallest for the heavy ones near the ends.
OAC/D/AWA R P /A2O/V AZGA/WA P-AEAC/DGA.S. 47
bottom chords in through bridges, which will cause an error on
the side of danger in the post stresses: this fact is pointed out
on p. 141. A slight difference will be found between the co-
efficients there given for the diagonal and chord stresses of
double-intersection trusses having an odd number of panels,
and those obtained by following the method indicated in this
chapter. The latter will give stresses slightly in excess of
those in the “Pocket-Companion;” but the difference is so
small, that it is scarcely worth mentioning. Had the engineer
who prepared the tables been a believer in the use of long
panels, he would have commenced his double-intersection trusses
with seven panels instead of eleven.
Tables XLI. and XLII. give the stresses for all bridges
treated in this work.
48 ORDINARY IRoy HIGHWAP–BRIDGES.
CHAPTER VI.
STRESSES IN LATERAL SYSTEMS AND SWAY BRACING.
THE wind loads concentrated at the panel points are deter-
mined by imagining a horizontal plane passing through the
middle of the truss, and supposing that the pressure on all
the exposed surface of the bridge above this plane is concen-
trated at the upper-panel points, and all below this plane at the
lower-panel points. This may be a correct assumption, or
may not ; but it is as likely to be correct as any other.
Where vertical sway bracing is used, the division of wind
pressure becomes still more ambiguous; but, as before, the
same assumption is as likely to be correct as any other.
In calculating the area opposed to the wind, the area of the
vertical projection of one truss, hand railing, including hub
plank, guard rail, and the rectangles described about the
windward ends of the floor beams, is to be doubled, and to this
is to be added the area of the vertical projection of the floor
and joists.
As the windward hand rail would probably fail under high
pressure, the total area thus found is somewhat in excess; but
such a failure should not be depended upon when the wind is
considered to strike the bridge suddenly. For spans of and
under two hundred, or sometimes even two hundred and thirty
feet, the sizes of the upper lateral rods are not to be determined
by the effect of the wind pressure, as this method would make
them smaller than experience would indicate to be necessary
for rigidity. The sizes to be used can be found in Table XXV.
The wind stresses on the lateral systems are to be calculated
for a moving load, instead of one upon the whole bridge; because
this method causes the rods towards the centre of the span to
ORDINARP IROM HIGH WA Y-BAIDGE.S. 49
be somewhat increased in diameter: besides, it is possible for
a portion only of a structure to be subjected to wind pressure;
the rest being protected by a hill, a building, or some other
neighboring object.
Without making any appreciable error, the wind pressure, for
the purpose of simplifying calculation, may be considered as
equally distributed between the two sides of the bridge, although
the windward side does receive the larger share.
The stress in any diagonal can be found by the formula
_ n' (n' + 1) w sec 6
* = 2 -a-,
7"
and that in any strut, except at the end of the lower lateral
system, by the formula
_z.'(n' – 1) + n
* = 272 tº
C
20,
where w is the sum of the pressures at a windward and leeward
panel point, m the number of panels in the wind bracing, count-
ing in the two lacking at the ends of the upper lateral bracing
in through bridges, m' (not less than º) the number at the lee.
ward end of the diagonal, or at either end of the strut, the
panel points being marked as directed in the last chapter, and
6 the angle that the diagonals make with the struts.
The stresses in the diagonals are to be increased for initial
tension, or, what is the same thing, the working-stresses are to
be taken from Table IX.
The effect of the initial tensions on the struts is also to be
added to the stresses in those members.
The method of calculating the stresses in the vertical sway
bracing is as follows. It is essentially that of Professor Burr, as
given in his treatise on “Stresses in Bridge and Roof Trusses.”
In Fig. 1, let P be the pressure supposed to be concentrated
at the upper panel point on one side of the bridge. It is that
which comes upon a panel length of top chord, one-half the
area of the diagonals meeting at the panel point and the por-
tion of the post above the plane A.B.
5O OA’D/AWA R V /A’O/V HIGH WA Y-B/C/DGAZ.S.
Let P be the pressure concentrated at one end of the inter-
mediate strut 7K. It is that which comes upon the portion of
the post between the planes AB and CD, the latter passing
halfway between the intermediate strut
“ and the bottom chords. If the interme-
diate strut be at the middle of the post,
and if the main diagonals and counters be
coupled on a pin at this point, it would
be necessary to divide the pressure upon
»->; H »-iH the diagonals between the upper, middle,
Fig. 1. and lower points of the posts; the middle
taking one-half, and the others one-quarter each.
Let
d = the depth of the truss,
f = the vertical distance between the upper lateral and interme-
diate struts, -
& = the perpendicular distance between centres of trusses,
G
and
6 = the angle made by the vibration rods with the vertical.
The pressures concentrated at the lowest points of the posts
do not affect the verticel sway bracing, so are not considered.
The total pressure, 2(P + P') = H, is assumed to be equally
resisted by the feet of the posts. It is possible that this
assumption is incorrect, for one foot may resist more than the
other; but, when it is remembered that perhaps the whole of
the force 2P passes through the upper lateral system to the
pedestals at the feet of the batter braces, it will be conceded
that the assumption is not upon the side of danger.
If the whole of 2(P + P') were to be resisted by the feet of
the posts, the functions of the upper lateral system would be
rather limited, the whole of the wind pressure upon the struc-
ture being carried by the lower lateral system, which is highly
improbable.
But, whether the wind pressure upon the upper part of the
trusses be carried by the upper or by the lower lateral bracing, it
is better, as far as the vertical sway bracing is concerned, to pro-
portion the latter under the supposition that the pressures at the
upper panel points are, carried thereby to the feet of the posts.


ORDVAWARY AROM HIGH WA V-BZPADGE.S. 5 I
Taking the centre of moments at E, the moment of the
pressure is
2Pd + 2 P'(d—f),
which can be resisted only by the moment of a released weight
Vupon the foot at F, thus,
2Pd + 2 P'(d—f) = Vå,
and ~,
2d(P+ P') — 2 Pf
TV = & tº
This release of weight V must pass up the vibration rod KG,
causing a tension therein equal to
2d(P+ P') — 2 Pf
& sec 6.
Vsec 6 =
To find the stress on the strut VK, pass a plane through the
sway bracing, cutting GH, GK, and JK (HV not being strained);
take the centre of moments at G, and consider the forces act-
ing on the left side of the truss; then the moment of the stress
in JK will balance the moments of P' and 3 H, thus,
Jo-º-º-ºp Po-2,
to which must be added the horizontal component of the initial
tension in VH. (JAT) represents the stress in J.A.
The stress in the upper lateral strut GH is that due to the
wind pressure, considering it as a portion of the upper lateral
system plus the sum of the horizontal components of the initial
tensions in the three rods meeting at one of its ends.
If GH be considered as a portion of the vertical sway bracing,
its stress may be found by passing a plane, as in the last case,
and taking the centre of moments at K, considering the external
forces acting on the left-hand half of the truss ; then the mo-
ment of the stress in GH will balance the moments of the
horizontal re-action at E and the pressure at G, the moment
of the increased weight at E balancing the moment of the
increased re-action ; thus,
#H(d–f) + Pf d &=
or equal to the stress in J.K.
(GH) =
52 ORD/AVA R V / ROM HIGH WA P-BRIDGE.S.
At first thought, it might appear that the two stresses found
for GH should be added together to obtain the total stress; but
such is not the case, for the wind pressures cannot pass by both
the vertical sway bracing and the upper lateral bracing: so the
greater stress must be taken. In all practical cases, the greater
stress will be found by considering GH as belonging to the
upper lateral system.
The bending moment on the post is
#H(d — f) = (P + P') (d — f);
and, if m be the distance between centres of gravity of post
channels, the stress on one channel produced by the bending
will be - & -
(P+ P) (2–7).
//?
C =
The released weight V, on the windward post, passes down the
leeward post, producing a stress equal toº on each channel,
making the total wind stress on one channel
17
C++.
According to the method given in Chapter IV., if twice this
stress, or 2C+ V, exceed the live-load stress on the post, mul-
tiplied by seven and a half (74), and divided by the intensity of
working tensile stress for lower chords, the post must be pro-
portioned for dead-load and wind stresses, instead of dead-load
and live-load stresses.
All these formulas, except that for the stress in GH, may be
made applicable to the portal bracing by putting for d the length
of the batter brace, for f the perpendicular distance between
centre lines of upper and lower portal struts, for P' the press-
ure on one-half of the batter brace, and for P one-fourth of the
sum of all the pressures concentrated at windward and leeward
panel points of the top chord.
If P, be the pressure at the leeward hip, then the stress on
the upper portal strut will be given by the formula
c=%2+ P') — P + P- P.
OA’D/AVA/º V ZA’O/W HZGA/MVA P-AEA2//OGAE.S. 53
The stresses on all vibration rods must be increased for initial
tension, or the rods must be proportioned by using Table IX. ;
and the stress on each portal strut is to be increased by the
sum of the components of the initial tensions in all the rods
meeting at one of its ends, taken in the direction of its length.
When there is no vertical sway bracing, stiffness is obtained
by the use of knee braces, or brackets (AB, CD, Fig. 2), making
angles of forty-five degrees with the vertical. Let the notation
be as shown in the figure; V being, as before, the release of
weight at F. P is the sum of the pressures at H and G.
Taking the centre of moments at E gives
Vă = P2 and v=#.
Again: taking the centre of moments at A gives the value of
the bending-moment M on the strut at that

point; thus, - #=: H
A7 £6 ^
M = V(3 — S) — ; P2 = . (3– 2S).
'S K 5
Let A equal the distance between the cen- Fig.2
tres of gravity of the two channels of which |
#x-P If »-3P
the upper lateral strut is composed, then the
bending-stress will be -
M A7
C = + = z:(6 – 2S). gº
The intensity of the working bending-stress being six tons,
the number of square inches to be added to the area of each
channel, in order to resist bending, will be
C A/
4 = , = 1.(? –
A
The stress in AB is found by taking the centre of moments
at G, and making the moment of its stress R equal to the
moment of the horizontal re-action at E.; thus,
ASV% = #P3,
2S).
and
AZ" A7
AC = #V. = o.707-s:
54 OA’D/AWA R P IROAV HIGH WA P-BA’//DGE.S.
As before, to make these formulas applicable to a portal,
make d equal to the length of the batter brace, and P equal to
one-half the sum of the pressures concentrated at all the upper
panel points of the bridge. *
To find the effect of the wind on posts and batter braces,
use the formula previously found, substituting in it S for f.
Finally, the stress in an end lower lateral strut, at the free
end of the span, may be obtained by the formula
272 — I 72 — I W
C. = 4 • z0 + / cos 6 + 4. ºw-4( 4 –7)
where m is the number of panels in the bridge, w the sum
of the windward and leeward panel wind loads for the lower
system, w the same for the upper system, I the initial tension
in the end lower lateral rod, 6 the angle between this rod and
the strut, W the total weight of the unloaded bridge, and V the
release of weight at a windward shoe.
Owing to the fact that the joists of the end panel rest on the
masonry, this formula will give a result slightly on the side of
safety.
One or two applications of this formula will convince the
most sceptical, that the general idea that any section is strong
enough for a strut between pedestals is a fallacy. Too great a
reliance has hitherto been placed upon the friction of the shoe,
the released weight there not having been considered; and the
pressure which comes from the upper panel points seems to
have been neglected.
ORD/MARY ZZºCAV HIGH WA P-B/C/DGAE.S. 55
CHAPTER VII.
REMARKS CONCERNING MAIN MEMBERS.
Top chords should nearly always be built of two channels,
with a plate on top, and latticing or lacing below. It is never
good practice to use a single I-beam for top chord or batter
brace, because of the great variation in stiffness in its two
principal rectangular planes and the difficulty in making neat
details for the connections. When the span becomes So short
that it appears to be economical to use such a section, it is short
enough to employ plate girders which are far superior, both as
regards strength and stiffness, to a bridge with I-beam chords.
The same objection applies to an I-beam post, a favorite
design of inferior bridge companies. If one were to take the
trouble, in passing over a few bridges where they are used, to
cast his eye along the posts, he would generally see that they
are bent to one side or the other, or to both ; the latter being
the case when there are employed what are termed out West
“Giasticutus rods,” or horizontal rods five-eighths or three-
quarters of an inch in diameter, passing from the middle of one
post to the middle of the next in the same truss. Such rods
are a noticeable feature in arch bridges, a class of structure that
ought to be universally condemned. The principal objections
to these bridges are their lack of rigidity, and their inability to
resist wind pressure, because of the absence of efficient lateral
bracing. But another grave fault is, that, being as a rule built
by companies of the lowest order, they are weak in section and
detail, and the workmanship is poor. They are, without doubt,
the cheapest kind of iron bridge that can be manufactured :
hence their general adoption throughout the West, where short-
sighted economy in building is the order of the day.
56 OA’D//VA R Y ZAZO/W HZGH WA P-B RAIDGAE.S.
The I-beam is more often found in upper lateral struts, where
its use is quite as objectionable. Even if strong enough, which
it seldom is, it is by no means the best section for that place,
owing to the difficulty in connecting to the top chord. Where
it rests on the chord plate, and is riveted thereto, the lateral
rods being attached to the chord pins, there is a great leverage
afforded to the wind stresses to distort the chord; and, where
connected to the pin by a jaw, the detail has to be either very
clumsy or very weak. Another objection to I-beams for lateral
struts is the little room which there is in the flanges for punch-
ing rivet holes. But the chief one is the small resistance that
they offer to the bending effect of the wind pressure when there
is no vertical sway bracing. What has been said of I-beams in
lateral struts can be said with much more effect concerning
I-beams in portal braces, for great stiffness and strength are
there necessary in order to carry the wind pressure upon the
upper half of the bridge to the foundations.
The proper function of an I-beam is to resist deflection in the
plane of its web : consequently it should be used as a floor
beam, in which place its depth should seldom be less than ten
inches, never less than nine inches. When one is debating about
using such small floor beams, he should figure them for a con-
centrated wheel load, as well as for a uniformly distributed load.
About the only places where a small I-beam can be legiti-
mately employed are between the pedestals, as a lateral strut
at the fixed end of a span, or at the free end if the bridge be
narrow and the span very short, and in vertical sway bracing as
an intermediate strut.
For upper lateral struts, iron gas-pipe was formerly often em-
ployed, and is so yet to a certain extent. Regarded as a section,
nothing could be better or more economical ; but the connec-
tions made with it are very weak. Then, again, there is the
objection that it is a closed column, and consequently inacces-
sible to painting. Notwithstanding the fact that two of the
leading bridge companies of the United States employ almost
exclusively closed columns, such columns are not, by engineers
in general, conceded to be so good as open ones, which are
always accessible to the paint-brush,
OA’D/AWA A' V //&O/V HZGA WA P-BAC/DGAE.S. 57
Some other common forms of upper lateral struts are the fol-
lowing: two tee-irons trussed, the upper resting on the chords,
and riveted thereto, the lower abutting against the same, and
attached by bent plates; two channels trussed and attached to
the chords in the same manner; a combination of a channel
and a plate, with trussing between ; and two tee-irons laced or
latticed, with a jaw plate at each end wider than their flanges,
screwed up to the chords by nuts on the ends of the chord pins.
Owing to their lack of both strength and rigidity, all these are
poor contrivances, two channels laced or latticed being the best
form of strut that can be designed for the upper lateral system.
As stated in the “General Specifications,” in no highway
bridge should the channels in chords, posts, or batter braces, be
less than five inches in depth, nor in any other part of the
structure less than four inches. One does hear occasionally of
such a thing as a three-inch channel top chord with two-inch
pins, for a sixty or seventy foot span. But, fortunately for the
public safety, such structures are few and far between. The
author once heard the senior representative of one of the most
flourishing highway-bridge companies in America contend that
two three-inch channels trussed make a very good centre post
for short through-spans, - strong enough, because the area
called for by the stress is less than three square inches. He
must either have forgotten, or been ignorant of, the fact that
stiffness is as important a factor in a bridge as simple strength.
In reality, strength is dependent upon stiffness; for where
vibration can occur, the stresses are increased, not only in the
members where stiffness is wanting, but in adjoining members
of the structure.
Light sections for compression members are more economical
than heavy ones, and it is generally preferable to use them.
But, if the situation be one where the members will be exposed
to excessive moisture, the webs should be thickened.
The top plate for chords and batter braces should generally
be from one-quarter to three-eighths of an inch thick. Any
thing below the inferior limit would be liable to distortion when
roughly handled, and to rust through too readily; and any thing
above the superior limit would usually be inconsistent with the
best distribution of area in the section.
58 ORDINARY IRON HIGHWA K-BRIDGES.
It used to be customary, and the practice is still followed
to some extent, to make the top plate of varying thickness, or to
vary the number of plates, increasing from the ends of the truss
to the centre, making the channels of the same dimensions
throughout. But this method is not advisable; for the proper
place for the larger part of the material in a chord like the one
under discussion is in the channels, and not in the plate. Simi-
larly, in any channel, the proper place for the larger part of the
material is in the flanges, and not in the web; the reason being,
in both cases, that the moments of inertia of the section in
respect to vertical and horizontal neutral axes are increased by
removing a portion of the area away from these axes, and the
strength of a strut increases with the moments of inertia of its
section. . '
Star iron should never be employed in an iron bridge, and
there is never any necessity for using tee-iron. Two of the
latter sections, latticed by a triple or quadruple intersection of
thin, narrow bars, are sometimes adopted for a portal brace;
but it is evident how weak such a strut must be, and it is in
the very place where a strong one is most needed.
Four angles with the legs turned in, and set at the corners of
a square, laced on the four faces thus formed, make an economi-
cal strut, as far as the section is concerned ; but it is probable
that the extra weight of detail and the increased cost of shop-
work will make it more expensive than another strut of larger
section. Two channels latticed or laced are the best form of
portal strut. Large, heavy cast-iron portals made in one or
two pieces look very well, and might be made strong enough,
but are not so neat and graceful as some other kinds of bracing,
besides adding unnecessary dead load to the structure. Cast-
iron is not to be depended upon, and should not be used in any
part of an iron bridge to resist stress. -
Channels in posts usually have their webs parallel to the direc-
tion of the plane of the truss, with their flanges turned outward:
sometimes they are turned inward; and, where the floor beams
are riveted to the posts, the webs are, or should be, placed at
right angles to the plane of the truss, the flanges turning out-
ward.
ORDVAWARP IROM HIGHWA P-BRIDGES. 59
Theoretically it is more economical, as far as the area of the
section is concerned, to turn the flanges in, for the moment
of inertia is greater; but, on the other hand, the difficulty en-
countered in riveting in a confined space more than equalizes
the advantage just mentioned.
Another advantage which can be claimed for channels turned
in, viz., avoiding cutting them off before reaching the upper
chord pin, is partially counterbalanced by the increased size of
pin, due to the larger leverage thus given to the stresses in the
diagonals. Notwithstanding the difficulty in riveting, it is often
found necessary, in swing bridges, to turn in the flanges of the
post channels in order to form a good connection with the chan-
nel bottom chords: otherwise, the channels of the bottom chords
may be turned in, and the post channels be allowed to bestride
them.
The objection to cutting away the flanges of channels at the
feet of posts has been shown by some experiments made by
the Chicago and Alton Railroad Company, as given in a paper
read before the Western Society of Engineers by Mr. E. J.
Ward, who shows that this cutting-away reduces the strength
of the strut about ten per cent.
Main diagonals, as will be demonstrated in Chapter X., should
have the proportion of width to depth of about one to four;
and the chord bars, the proportion of from one to four to one
to seven, according to the number of them in the panel.
It is preferable, for appearances, to make the counters of
square or round instead of flat bars, because of the unsightly
change that there would be in the diameter of the flat bars at
the upset ends. It is immaterial, except for the effect upon the
pins, whether the hip verticals be flat, square, or round; but
the preference is usually given to square iron.
Built floor beams in ordinary bridges should be formed of
solid plates and angles, and not made trussed; because, even if
the latter method permit of a saving of material, it is more
conducive to vibration. Where the panels are long and the
roadway is very wide, it would be permissible to use trussed
beams, provided that they be made very rigid in their details,
and not too slight in their sections.
6O O/º/D/AWA R Y YA’OAV HAGA WA P-AESA’ſ DGAZ.S.
CHAPTER VIII.
PROPORTIONING OF MAIN MEMBERS OF TRUSSES, LATERAI.
SYSTEMS, AND SWAY BRACING.
HAVING found all the stresses in the main members of the
truss and in those of the lateral systems and sway bracing, and
having written them alongside the respective members in the
diagrams, the next step is to calculate the sections required.
The diagrams for the lateral systems and sway bracing may be
roughly drawn in pencil; for they need not be preserved, as the
sizes of the members are to be written on the truss diagram.
For the tension members of the trusses, the sections required
can be found by dividing the stresses on the diagram by the
proper intensities of working-stress, as given on p. 12; remem-
bering that the intensities for main diagonals are to be inter-
polated. When found, the required areas for the sections
should be written on the diagram, after the stresses, prefixing
them with the letters S. R. (section required), as shown on
Plate V. Then, by using Carnegie's “Pocket-Companion,”
pp. 94–IO5, or some equivalent tables, can be found the sizes
necessary to give at least the section required, taking care that
the sections be in good proportion.
The stresses in the counters are to be increased for initial
tension by the amounts given on p. IO; or, what is the same
thing, the size required can be found from Table IX, by look-
ing down the column headed “Working-Stress = 4 tons per
square inch,” if the bridge belong to Class A, or down the one
headed “Working-Stress = 5 tons per square inch,” if it belong
to Class B or Class C, until a stress is reached which is equal
to or greater than one-half or the whole of the stress on the
diagram, according to whether double or single counters be
*
4
ORD//WAAC P VROAV HIGH WA P-B/C/DGAE.S. 6 I
employed; then, by following the horizontal line which con-
tains this stress, either to right or left, will be found the size
of the counters or counter required.
As previously mentioned, the sections required for, and the
sizes of, the hip verticals, can be found without calculation from
one of Tables VI., VII., or VIII. Should the joists and floor-
ing be of oak instead of pine, the section required for, and the
size of, hip verticals, can still be found from the table by sup-
posing an increase of one foot in the panel length.
The sizes of the lateral and vibration rods can be found from
Table IX. by looking in the column headed “Working-Stress
= 7.5 tons per square inch,” in the same manner as explained
for counters. If the panel length correspond with the one given
in Table IV., or if it do not differ greatly therefrom, there néed
be no calculations made for stresses in the lateral systems and
sway bracing; for the dimensions of all the struts and rods for
these systems are given in Table XXV. In that table the
dimensions in the column marked “Pan. I ?” are the sections
respectively of the upper portal struts, the portal vibration rods
(if any), the lower portal struts (if any), and the end lower lat-
eral rods. Those in the other columns are the sections
respectively of the upper lateral struts, the upper lateral rods,
the post vibration rods (if any), the intermediate struts (if any),
and the lower lateral rods. The portal struts are thus assumed
to belong to the first panel; the first upper lateral strut, with
its sway bracing, to the second panel, etc.; so that, when the
bridge has an odd number of panels, there is no lateral strut
or vertical sway bracing given for the middle panel. The forty-
foot, fifty-foot, and sixty-foot spans, being pony trusses, have
only lower lateral rods. Spans above one hundred and fifty
feet in length have vertical sway bracing.
If the counter stresses be large, it is preferable to use double
counters: sometimes both single and double counters are em-
ployed in the same truss. Where there is an odd number of
panels, the centre diagonals should be made double and adjusta-
ble. The number of main diagonals per panel is generally two ;
but, if the sections become so great as to necessitate excessively
large chord pins, it is better to employ four; placing two inside,
62 ORD/AWA R P /RO/W HIGH WA P-BA’/DGA.S.
and two outside, of the top chord and posts. The widths of the
main diagonals should, for the sake of appearance, increase
from the centre of the bridge to the ends. For the same rea-
son, it is well to have all the chord bars of the same, or nearly
the same, depth; the correct area of section being obtained for
each panel by varying the thickness and the number per panel.
In large bridges it is permissible to reduce the depth of the
chord bars towards the ends of the span in order to economize
on the pins. It is also permissible, when there are several
chord bars in the same panel, to employ depths varying by a
quarter of an inch, provided that the bars of smaller depth be
placed on the inside. -
As stated in the “General Specifications,” where chord bars.
are trussed to resist the buckling effect of the wind pressure,
the intensities of working-stress for the trussed bars on the met
section should be reduced to four tons for bridges of Class A,
and to five tons for those of Classes B and C. -
“Chord packing” is a term applied to the arrangement of the
chord bars, diagonals, posts, and beam hangers upon the bottom
chord pins. It is a matter of great importance, but is very
often neglected. The three principal considerations to be kept
in mind while arranging the packing are, that the bending-
moments on the pins are to be made as small as possible, that
the packing is to be made as close as circumstances will permit,
and that there be sufficient clearance to avoid all chance of
finding the space between the post channels too narrow when
the bridge is being erected.
The width of the packing is dependent, not only upon the
number and thickness of the bars, but also upon the width of
the top chord plate. The latter is often, in its turn, dependent
upon the chord packing. -
The usual arrangement is to pack the main diagonals, coun-
ters, and beam hangers inside of the posts, and the chord bars
outside; bringing the latter, however, within the batter braces.
at the shoes, unless the end panel contain four bars per truss,
when two should go outside, and two inside. It is not abso-
lutely necessary that the chord bars pull in the exact line of
the trusses; an inch or two of deflection in twenty feet being
OAC/D/AWAAC P VA’OAV HIGH WA Y-BAC/DGAE.S. 63
scarcely noticeable, and making no appreciable difference in the
length of the bar: nevertheless, it is better to make the bars as
nearly as possible parallel to the planes of the trusses. The
main diagonals should be placed next to the post, then the
beam hangers, and inside of all, the counters with a filler
between them long enough to permit of the screwing-up of the
turn buckles, or sleeve nuts.
The arrangement of the chord bars will be treated in Chap-
ter. X.
The sections of the top chords and batter braces are to con-
sist of two channels, with a plate on top, and latticing or lacing
below. The same depth of channel, and the same, width and
thickness of plate, are to be employed from one end of the chord
to the other; the difference in area being obtained by thicken-
ing the webs of the channels. On this account, there is often
an excess of section in the end panels of the top chord, and, in
long bridges, even in the next panels.
It is customary and better, but not necessary, to make the
depth of the channels in the batter braces the same as that of
the channels in the chord. The top plate for the batter brace
should be of the same size as that for the chord.
The width of the top plate is dependent upon the depth of
the channels; as the transverse distance between the centre lines
of the rivets which attach the channels to the plate should be
never less, and not (unless there be good reason) much greater,
than the depth of the channels. The least dimensions for such
plates for different channels are given on p. 15. The chord
channels are sometimes spread apart in pony trusses, so as
to increase the lateral stiffness; and in any bridge it may be
necessary to spread them a little to admit of a certain manner
of packing below: but, the more narrow the chord plate, the
more economy of material will there usually be.
To proportion the top chord or batter brace for a given stress,
assume the depth of the channels, and divide the length of the
panel or batter brace by it, both dimensions being expressed in
the same unit. Referring to Table X, or XI., according to the
class of bridge to be designed, look down the column marked
“Ratio of L to D,” until the ratio just found is reached: the
64 OA’D/AVA A' V /A’OAV AZZGAZ WA P-BAZZZOGAE.S.
number to the right, in the first of the three columns, is the
intensity of working-stress to be used. The three columns are
for the three cases, – both ends fixed, one end fixed and one
end hinged, and both ends hinged, marked EEE, iſ
respectively. The tables were calculated by the formula of
C. Shaler Smith, C.E. ; to whom the author is indebted for
its use, and for other valuable information in connection with
bridge work. Then, to find the area of the top chord or batter
brace, divide the stress given on the diagram by the intensity
of working-stress taken from the table; from the quotient
subtract the area of the top plate, and divide the remainder
by two : the final quotient will be the area of each channel.
This calculation should be made with both the stress in the
panel nearest the middle of the span and that in the end
one, or, in long spans, that in the one next to the end. If,
then, with the depth of channel assumed, it be found that
there is, in the table of channel sections employed, a light
channel that will not be much too heavy for the end, and a
heavier one suitable for the middle of the chord, all right :
if not, another trial must be made, with a channel of a dif-
ferent depth. The greater the depth of channel, the less
the ratio of length of strut to diameter, and consequently
the greater the intensity of working-stress, and the less the
sectional area required : So, generally speaking, it is well to
use the lightest and deepest channels possible, unless the
saving in section be small, when it will be more economical,
for other reasons, to use the next smaller depth. These rea-
sons will be given in Chapter XV. The dimensions of the
channels and plate should be written on the diagram of
stresses as shown on Plate V.
The sizes of the post channels are to be found in a similar
manner to the one just described, with these two exceptions, –
that the column for two hinged ends is to be used, and that
there is no plate. Some engineers prefer fixing the upper ends
of the posts by attaching them, through the medium of plates,
to the chord, thus saving a little in the section ; but, as will be
seen farther on, there is no true economy in so doing.
In high double-intersection bridges, where the diagonals are

ORD/AVAA' P ZA'O/V AZGA/WA P-AEAC/ZDGAE.S. 65
halved, and connected by pins passing through the middle of
the post channels, as shown in Fig. I5, Plate II., the post may
be proportioned for half-length with both ends hinged; but in
this case the counters must extend to the ends of the span,
although there be no stress in some of them, for the purpose of
preventing the posts from moving laterally at the middle.
The upper lateral struts and portal struts are to be propor-
tioned by using Table XI. for both ends fixed, and adding, if
necessary, to the section thus found, enough area to resist the
bending as determined in Chapter VI.
The ultimate strength of the intermediate struts, which are
I-beams, can generally be found from experiments made by the
manufacturers; a factor of safety of four being sufficient. In
default of such experiments, the approximate working-stresses
(not intensities) for I-beams used as pillars may be taken from
Table XL., which has been compiled from an old edition of
Carnegie’s “Pocket-Companion.” When the I-beam strut is
supposed to bend in a vertical plane, its length should be taken
equal to the distance between the points of attachment of the
brackets; but, when it is assumed to bend in a horizontal plane,
its length must be taken equal to the distance between opposite
posts of the trusses.
Brackets should extend inward and downward, from about
four feet in narrow bridges, to about six feet in wide ones. The
sway bracing given in Table XXV. was proportioned for brack-
ets of these dimensions. Brackets beneath intermediate struts
not only serve to stiffen the struts, but add to the appearance of
the bridge.
The intermediate lower lateral struts being of wood, it will
not be necessary to calculate their sections, which practical
considerations will always cause to be greater than the stresses
would demand.
The lower lateral struts between expansion pedestals should
consist of two channels laced or latticed, and attached to the
end chord pins by jaws. The size for the channels is to be
found by using Table XI. for one fixed and one hinged end, -
not that either end is really fixed or hinged, but because the
strength of a strut so attached is intermediate between that of
66 OAC/D/AVA R V /AOAV HIGH WA V-B/C/DGES.
one with fixed ends and that of one with hinged ends. It is
not positively necessary to use a lateral strut at the fixed end
of a span; but it is much better to do so, especially in long
spans, not only to distribute the horizontal re-actions, but also
to keep the chords in line, for there is necessarily a little play
in the anchor bolt holes. -
It is not unusual to make the struts between pedestals of the
same dimensions at both ends of the span, although the one at
the fixed end need not be so strong as the one at the free end.
Appendix I., the substance of which appeared as an editorial
in the “American Engineer” of July 20, 1883, shows the neces-
sity for stiffening, at least the end panels of many bottom
chords. This can be accomplished in several ways; one by
inserting a strut between the inner chord bars; another by
using channel bars, laced or latticed, instead of eye bars, in
which case the net section of the webs alone should be relied
on to resist tension; and another by trussing the inner chord
bars. The second of these methods is the most satisfactory,
but at the same time the most expensive. When stiffening
the end panel, it is well, though not perhaps essential, to
stiffen also the second panel, where the stress is the same as
in the one at the end. Such a practice is certainly conducive.
to the prevention of vibration of light bridges under rapidly
moving loads. +. - -
Hip verticals in three or four panel pony trusses are to be.
made to resist the compression which might be produced in
them by over-screwing the turn buckles of the counters. The
section to be employed is either that of two channels laced or
latticed, or two flat bars trussed : in the latter case, as pre-
viously stated in the “General Specifications,” the intensities
of working tensile stress on the net section are to be three tons
for bridges of Class A, and four tons for bridges of Classes B
and C. If two channels be used, the net area of the webs alone
is to be relied on to resist tension.
OA-D/AWA R P ZA'OAV HIGH WA P-B/C/DGE.S. 67
CHAPTER IX.
PROPORTIONING OF FLOOR SYSTEM.
THE wooden portions of the floor system are the joists, floor-
ing, hand railing, hub planks, and guard rails, or felly planks.
Of these, only the joists require calculation for strength. Pine
flooring is generally three inches thick, and oak flooring two
and a half inches. The hand railing, when of wood, should
consist of 4" × 6" × 4' posts, not more than ten feet apart,
2" × 6" rails, and 2" × 12" hub plank, all of pine, and built as
shown in Plate II., Fig. 13, and as specified on p. 23.
The guard rails should be of 6" × 6" pine, connected as speci-
fied in the same place.
To proportion the joists, first assume their number per panel
and their dimensions, in order to determine the total weight of
lumber per panel; to this add the total maximum panel live
load, or the product of the panel length by the clear roadway
by the live load per square foot, given on p. 5, the sum being
expressed in tons; then, referring to Table XIII. or Table
XIV., find, with the given panel length and the assumed depth
of joists, the safe load for a joist one inch wide, and divide this
number into the total load just found : the quotient will be the
total width of joists per panel, when laid side by side. Divide
this total width by the assumed width of one joist : the quotient
will be the number of joists per panel. If it agree approxi-
mately with the number assumed, and if the distance between
centres of joists, when in place, will be between eighteen and
twenty-four inches, all right; if not, another trial must be made,
with a different depth of joist, and a new assumed panel weight
of lumber. It may be well, in any case, to try two depths of
joists, in order to see which is the more economical. The
68 OA*/)/AWA R V /A’OAV HIGAZ WA Y-ARA'ſ DGA.S.
minimum size of pine joists should be 3" × Io": the maximum
size that it is advisable to figure on is 4" × 14", because deeper
joists cannot always be readily purchased. It is to be remem-
bered that pine lumber can be found in the market in only
certain sizes, usually even inches in depth, and always even feet
in length; i.e., timbers 3" × 8", 3" X IO", or 3" X 12" are readily
procured, while timbers 3" × 9" or 3" X II" are not ; also, if
one require joists eighteen feet six inches long, it will be neces-
sary for him to buy lengths of twenty feet, and cut off a foot
and a half. Timbers over eighteen feet in length cost more
per thousand than those of that and shorter lengths.
Tables XV., XVI., XVII., and XVIII. give not only the sizes
of joists, and number per panel, but also the total number of
feet, board measure, of pine and Oak per panel, including, when-
ever there is any, waste material. - *
The total load for a floor beam consists of the live load, the
weight of lumber which it supports, and the weight of the beam
itself. The latter must of course be assumed : this can always
be done with sufficient exactness to determine the floor-beam
load. The latter is assumed to be uniformly distributed be-
tween centres of bearings.
In calculating the dimensions of a floor beam to sustain a
given load, the section of the web is to be assumed; and the
beam is to be proportioned according to the formula given on
p. 19, and to the principles there enunciated. It may be neces-
sary to make two or three designs, in order to determine the
most economic depth ; but it will be often found that a variation
of several inches in the depth will not affect the weight per
foot.
The lower lateral strut, which is to be well bolted to the floor
beam, will add considerably to the strength and stiffness of the
latter. The joists should be dapped on to the strut at their
bearings, so as to offer a resistance to the lateral deflection of
both strut and beam.
The lower flange plate, if there be one, need not extend over
more than the middle half of the length of the beam. The
rivets attaching the plate to the lower flange angles should be
staggered, and should be spaced about four inches apart; and
OA’D/AVA R P ZAZOAV AZG H WA V-B/C/DGAZ.S. 69
the areas lost from the plate and angles by these rivet holes
should be deducted when figuring the net section.
In heavy beams, several plates are often used to vary the
section gradually from the centre of the beam to the ends; but
if one share Weyrauch's views upon rivet stresses, as expressed
in his “Structures of Iron and Steel,” he will avoid any such
practice. **
Many bridge companies reduce the depth of built beams at
the ends, in order to save a little weight of iron. This method /
may be advantageous to the company which pays for finished
bridges by the pound; but it is seldom so to the manufacturer,
for the triangular pieces cut from the web are often wasted : be-
sides, the extra work in cutting the web, bending the angles, and
making square rests for the beam-hanger nuts on the inclined
flanges, more than counterbalances any saving of material.
For a bridge with sidewalks, reducing the depth of the floor
beams at the ends adds to the appearance of the structure, and
need not interfere with the bearing of the hanger nuts.
Tables XIX., XX., and XXI. give the sizes of floor beams
for all cases ordinarily met with.
To illustrate the method of proportioning an ordinary floor
beam, let us take the case of a beam for a twenty-foot panel,
fourteen feet clear roadway, and fifteen feet between centres of
trusses, the bridge belonging to Class A.
The live load on the beam will be
I4 × 20 × 2% = 14 tons.
The weight of the lumber, from Table XV., is
2O85 × 2.5
2OOO
= 2.606 tons.
Let us assume the weight per foot of the beam to be fifty-five
pounds, the total weight of same will then be
55 × 16
F O. ton.
2OOO 44 ton
The total load on the beam is, therefore,
I4.OOO + 2.606 + O.44O = I 7.046 tons.
7o OR/D/AVA A' V ZAZOAV HAGH WA Y-BAZZZOGAE.S.
The most economic depth for the beam can be found by trial, or
by consulting Table XIX., which gives #" × 27" for the section
of the web. -
Let us assume these dimensions, and take the effective depth
D equal to 26"; then substituting in the formula given on p. 19,
omitting A", and remembering that T = 4 tons for bridges of
this class, gives
17.046 × 15 × 12 — 1 J: gº ºn a
A = 8 × 26 × 4 # × 3 × 27 = 2.56 D",
the half of which is 1.28 D", corresponding to a weight per foot
of 4.27 pounds, because a bar of wrought-iron one inch square
and three feet long weighs just ten pounds. Referring to Car-
negie's “Pocket-Companion,” p. 68, we find that a 24" × 3” 4.4%
angle will be required. Let us see if a 2"X3" 5:# angle will
do for the bottom flange. Assuming that the rivets are g”,
and the holes #", in diameter, the area lost by a rivet hole will
be 2 X #" × ##" = O.43 G", which, added to 2.56, gives 2.99 E",
corresponding to two angles, each weighing five pounds per
foot. The assumed angles will therefore be exactly what are
required. For stiffeners, let us use 2"X2" 3.1% angles. Four
of them at each end of the beam will be needed to take up the
compression produced by the stress in the beam hangers, leaving
a space between the inner angles equal to about fourteen feet.
I I
4 × 27 Troš
Referring to p. 19, we find, by interpolating, that the distance
between stiffeners should be 1.65 times the depth, or about
444". The number of spaces between stiffeners in the four-
I4 X I 2
44.5
each side of the web. The filling plates will have to be
#" X 2” X 22 #".
The method of finding the number and distribution of the
rivets in the flanges will be treated in Chapter XIII. : for
the present, it will be sufficiently accurate to assume that the
average spacing is two inches and a half.
The ratio of thickness of web to depth of same is
teen feet will be = 4, requiring six stiffeners, three on
ORDIVARP IROW HIGHWA K-BRIDGES.
74.
We are now ready to pass to the bill of iron for the beam,
the list of details for which is given on p. 30.
BILL OF IRON.3%

Web . we I f/ 27” I6' 360%
Upper flange . 2 24" × 3" | 4.4% L I6' 141 “
Lower flange . . 2 2" × 3” 5# L I6' I6o “
Stiffening angles. I4 2"x2" | 3.1# L 26;" 96 “
Filling plates . . . I4 #" 2” 22}" 55 “
Rivet heads . . . 22O pairs (a) o.16# 35 “
Total weight of beam . 847#
Dividing 847 by 16 gives 53 pounds as the weight per foot of
the floor beam.
Referring to Table XIX., we find that the beam there given .
agrees with the one just designed in every respect, except that
the weight is a pound and a half per foot greater. This is
owing to the fact that the weights in the tables of floor beams
were made large enough to cover a slight variation in the
designing.
There is no need for proportioning rolled beams, because in
Carnegie's “Pocket-Companion,” pp. 33–44, are given the work-
ing-loads for all the beams rolled at the Union Iron Mills.
These loads are directly applicable to bridges of Classes B and
C. For bridges of Class A, multiply the calculated load upon
the required beam by six (6), and divide by five (5), then search
in the “Companion” for a beam to sustain the resulting load.
Plate girders for short spans are to be designed according to
exactly the same principles as those laid down for the designing
of floor beams. The details, too, are the same, except that
there should be two inclined stiffening angles at each end of
the beam, one on each side of the web, their lower ends resting
over the edge of the bed plate nearest to the centre of the span,
as shown in Plate II., Fig. 17. -
The distance apart of plate girders should not exceed four-
* The method for preparing this table is explained in Chapter XIV,
.72 ORDINARP IRON HIGHWAP–BRIDGES.
teen (14) feet, on account of the difficulty in obtaining joists
large enough to support the concentrated wagon-loads. '
Trussed beams are sometimes made with one trussing-post,
and sometimes with two. To determine the relative length of
the part between the posts in the latter case, –
Let
A = length of an end division,
à, a length of the central division,
and
2 = 2 A+ 4 = length of beam between centres of supports.
The whole beam is now divided into three beams, two of which
may be considered fixed at one end, and supported at the other,
and the third fixed at both ends. If the moments of the loads
do not balance each other over the posts, the rigidity of the
connection there may be considered sufficient to insure fixed-
ness.
The greatest moment for a beam fixed at one end, supported
at the other, and subjected to a uniform load of w tons per
lineal foot, is
$zwl,” at the fixed end.
The greatest moment for a beam fixed at both ends is
Tºwl,” at either end.
Remembering the assumption of the fixedness of the beam over
the posts, it is evident, that, in order to make the moments
over these points a minimum, the two values found should be
made equal to each other, so that
2 — 2
#70A" = Hºwl,”,
Or
* = #4°,
and
* = 1.2244.
Again :
2 = 24 + 4 = 3.224A :
therefore
A = o.31%
and
A = A(I – 2 × 0.31) = o.38,
ORD/MARY IROAV HIGH WA P-BR/DGE.S. 73
or the length of the central portion should be about four-tenths
of that of the beam between supports.
To proportion the upper flange of a trussed beam having two
trussing-posts, such as shown in Plate II., Fig. I6, -
Let .
d = depth of beam proper,
1) = depth between centre line of beam proper and centre line of
bottom chord of trussing,
z0 = uniform load per foot on beam, -
A = }ºv(A + M) = load concentrated over one post,
and let &
l, A, and l, have the same values as before.
The area of the compression flange of the beam hecessary to
resist bending only is given by the formula
w/.” 1 A* *
º izia - $4,
where C is the intensity of working-stress upon the flange, to
be taken from the “General Specifications,” p. 13, and A' is
the area of the web.
The stress in either chord of the truss is
P,
A'- 75'
Let A" equal the area of one flange of the beam, supposing
that the loads P were really concentrated over the posts, instead
of being distributed, then . *
A' + 2A" = area of ideal beam,
and N
l Ž, g
Tºrº y
A.
” — 1 tº sº /
A = (# 4)
where C' is the intensity of working resistance to compression.
C’(A’ + 2A") = F =
* For proof of this formula, see Appendix II, which gives the demonstration for a similar
CaSC, t
74 ORD/AVA R Y IRO/V HIGH WA P-B RIDGE.S.
It should be about three (3) tons for bridges of Class A, and
four (4) tons for those of Classes B and C. The total area of
the lower flange of the beam should therefore be
'' – wl.” 1 A/ 1 P. ’ \ — wl.” P, 2 A/
A + A =#–14 +1(#–4 =ia + zaº-34.
If the beam be a rolled one, as it nearly always is, there is no
need of figuring upon the size of the upper flange; while, if it
were a built beam, it might be as well, for practical reasons, to
make the flanges of the same size, although theoretically a
slight reduction in the area of the upper one would be per-
missible.
For a beam with a single trussing-post, the bending-moment
over the post is
w!”
2
8
and the area of flange necessary to resist bending is, as before,
2
w/1
4 = 3;
1 A/
— #4'.
P, in this case, is equal to wh; making the re-action at each end
of the beam, under the supposition of concentrated loading,
I
#704.
The direct compression on the upper chord of the trussed beam
is, therefore, à.
1* = C((A + 2A"):
375
• " – iſ ºf A.
tº e A * =sº 1(, C’D A )
and the total area of the flange is
’’ — w/* — 1. 4' 1. wl.” gº /
4 + 4" = azā 144 (#, A
w!” P - f
= sāāa (CºP + 2 Ca') —#4'.
ORDIMARY IROM HIGHWAP–BRIDGES. 75
The author does not claim that these formulas are exact ; but
practically they will prove to be a great deal more useful than
others theoretically more correct, but also much more complex.
At the end of Chapter XIII., there is given a complete design
for a trussed floor beam with two posts. The reason why it is
not inserted here is, that it is necessary to understand the
contents of Chapters X.—XIII. inclusive, in order to properly
proportion the details.
The weight supported by the four hangers that usually sus-
tain a beam is that of a panel live load upon both trusses, that
of the lumber in one panel, and that of the beam itself. The
total load divided by eight times the intensity of working-stress
will give the area of the section of a hanger.
Square sections lie more closely to the pins than round ones,
and take up less room in the packing; but they must always be
upset, which, in short hangers, makes them more expensive than
round ones. •
Single beam hangers are allowable in skew bridges, where,
indeed, their use is often unavoidable, or in narrow bridges
with short panels, where there is not much weight to be sup-
ported. .
Tables XXII, XXIII., and XXIV. give the sizes of beam
hangers for nearly all bridges without sidewalks.
The most simple manner of finding the size of single beam
hangers for any roadway and panel length is to look in the table
of hip verticals of the same class for the section required, and
multiply it by one-half of the ratio of working-stresses for hip
verticals and beam hangers: the result will be the area in
square inches of the section of the hanger. -
If the floor and joists be of oak, the tables of floor beams and
beam hangers can still be employed by supposing an increase
of one foot in the panel length.
76 ORD/AWA R P ZROM HIGH WA P-B/C/DGES.
CHAPTER X.
THEORY OF PIN PROPORTIONING,
THE subject of “bridge pins” is one deserving of more con-
sideration than has been accorded it by engineers, and authors
of technical works. Until 1873, when Mr. Charles Bender, C.E.,
presented his paper on “Proportions of Pins used in Bridges” to
the American Society of Civil Engineers, very little was known
concerning it; the usual custom among engineers when propor-
tioning pins having been to allow one square inch of pin area
for every eight or ten thousand pounds of shear in the section
most subject to shearing-stress. As Mr. Bender states gener-
ally, and as will be shown farther on to be true for iron bridges,
it is not the shear, but the bending-moment, which causes the
greatest tendency to rupture; so that in any iron structure it
will be sufficient, in finding the sizes of pins, to calculate the
greatest moment induced in them by the various members
coupled thereon, and to proportion accordingly, due regard
being paid to the stresses in the eye-bar heads. Before making
any investigations, it will be well to review and summarize the
most important results of the investigations of others in this
subject.
The principal conclusions arrived at by Mr. Bender are, that,
for a well-fitting pin of large diameter, a pressure on the bearing-
surface of six tons per square inch is not too large; that for
simplicity it is well to assume that this pressure is uniformly
distributed over the diameter of the pin; that wrought-iron,
after millions of impacts, may break on the side where the
stress is tensile, but never on the side where it is compressive,
the ultimate resistance to crushing being about thirty tons per
square inch ; that the shearing-stress at the centre of a pin is
ORAD/WAA’ P WA’O/W AM/GA/MVA P-AE/º/DGAZ.S. 77
one and three-eighths times the average shear on the whole
section; that in iron and steel the ratio between the greatest
allowable tensile and the greatest allowable shearing-stresses
should be as 5 to 4, which would make the uniformly distributed
shear 2.91 tons per square inch, to correspond with a tensile
stress of 5 tons per square inch ; and that, owing to various con-
siderations, iron in pins may be strained much more than similar
iron in tension members. -
Mr. B. Baker, C.E., in “Beams, Columns, and Arches,” treats
of pins merely incidentally. He finds, that, for iron in solid
circular beams, the average value of q is #f, where f is the
ultimate resistance per square inch to rupture by tension, and
q, the difference between the apparent ultimate resistance per
square inch to rupture by bending and f, according to the equa-
tion F = f-- ſb, F being the apparent ultimate resistance per
square inch of the extreme fibre which first gives way; and,
that for steel, the value of $ varies between 1.7f and I.Qf.
Professor Burr devotes five pages of his work on “Stresses in
Bridge and Roof Trusses” to the subject of pins, and illustrates
the particular case of a suspension-bridge cable pin, and a gen-
eral case for ordinary truss-bridge pins.
Professor Du Bois, in “Strains in Framed Structures,” also
gives a mathematical discussion of how to find the maximum
bending-moment.
Table XII. gives the working bending-moments on all the
iron and steel pins, and the working-shear on all the steel pins,
which will ever be required for highway-bridges. Having cal-
culated the bending-moment, the requisite diameter for the pin
can be found by looking down the column for the class of bridge
considered, until a bending-moment at least equal to the one
found is reached. The diameter will be found at either end of
the horizontal row thus located. The use of the columns for
shear will be made apparent presently.
The upper and lower horizontal lines in the tables of bearings
(Tables XXVI. and XXVII.) give the diameters of the pins;
the extreme vertical lines, the necessary widths of bearing-sur-
face at each end of the pins, including both channel and re-
enforcing plates; and the other vertical lines, the permissible
78 OA’Z)/AWA A' P ZA’O/W HAGH WA P-AESA’/Z)GA.S.
pressure, on the bearings. The method of using these tables is
the following. The pressure which the pin is to carry is to be
taken from the diagram of stresses. A trial diameter is then
assumed. The vertical column in either Table XXVI. or Table
XXVII., headed by this diameter, is to be followed down, until
a number nearest the pressure to be carried is found. At either
end of the horizontal row thus located will be found the proper
width of bearing. Knowing the width of bearing, diameter and
pressure, the moment to which the pin is subjected may be at
once calculated. Turn, then, to Table XII, and see if this
moment agree with the working-moment corresponding to the
trial diameter. If it does, all right: if not, another trial is to be
made, with a new assumed diameter. After a little experience,
the first trial will be sufficient. A consideration of other de-
tails, such as widths and depths of eye bars, etc., will frequently
aid very much in these trials.
To find the least value of the ratio of the diameter of pin to
depth of eye bar in an iron bridge, by considering the tension
in the bar, and the pressure between the pin and bar, —
Let
zy = width of bar,
d = depth of bar,
d = diameter of pin,
C = intensity of working compressive stress,
Z" = intensity of working tensile stress;
then
wd,7" = tension in bar,
and
wd!C = Compression on pin and eye.
These, of course, are equal ; and, as C = 6 tons when T-5
tons, there results the equation,
d = #d, = o.833d, 3?
which shows that the diameter of the pin should never be less
than eighty-three per cent of the depth of the bar. It is possi-
ble, though, that good iron of twenty-five tons tensile strength
will resist more than thirty tons per square inch in compres-
OA'D/AWA R P WROAV HZGH WA P-BA’/DGE.S. 79
sion: consequently d may be taken at O.8d, as a matter of con-
venience.
To find the proportion between width and depth of bars for
the smallest allowable pin in an iron bridge, –
Let the notation be as before, and first let us suppose that
there be but one pair of bars acting at each end of the pin, and
that the total tension be a fixed quantity. The stress in one bar
is waſ, T, and its moment is wºd, T. This must be equal to the
resisting-moment of the pin, which is given by the well-known
equation
_ AZ
M = D
Here R = }T, I = }rrº, and D = r =; substituting which
gives
M = ºrt Złłº.
Equating the two values of the moments gives
wºd, T = ºrt Zä",
Or
2
3t dº
~ 64 a
Now, to make the diameter of the pin as small as possible,
the moment of the stress must be made as small as possi-
ble; and, as the stress is constant, the lever-arm w must be
made as small as possible. But the product of w and d is a
constant: So when w is smallest, d, must be greatest. But the
greatest value of d, is #d; substituting which gives
a – 37 - 94.22 – 2
209" = 64 X ** = o,754diº,
and -
z0 = O.2744,
or about one-fourth of the depth of the bars.
If there be two pairs of similar bars acting at each end of the
pin, instead of one pair, the equation of moments will be
2w°d, Z'- tºrt Złº,
8O ORD/AWA R P WROAV HIGH WA P-BA’/DGES.
Or
As before, to make d a minimum, w must be made a minimum,
or d, a maximum : therefore d = #d, which, substituted, gives
z0 =.o. 1944,
or about one-fifth of the depth of the bars.
For three pairs of similar bars at each end of the pin, the
equation of moments will be
370°d, T = #TTâ",
substituting in which #d, for d gives
z0 = O.I594,
or about one-sixth of the depth of the bars.
Finally, if there be four pairs of similar bars at each end of
the pin, the equation of moments will be
470°d, T = ſºrt Złº,
which gives
z0 = 0.1374,
or about one-seventh of the depth of the bars.
To find the greatest working shearing-stress (supposed to be
uniformly distributed) in terms of the working resistance to
tension, —
Let S = actual varying resistance to shearing, considered
uniformly distributed. The greatest value of S will correspond
to a value of w equal to O.274d, ; for suppose the moment to
remain at its maximum value, and the dimensions of the bar
to vary (consequently the stress therein also), the tension in
the bar will be greatest for the value of w corresponding with
the greatest value of d, : therefore the shear will also be great-
est for that value.
Equating the tension to the shear gives
Traº”.S
wd, 7– –H
OA’D/AWA R P Zºº’O/V AZG HTVA P-PA’AZOGAE.S. 8 I
Substituting #d for d, and O.274(#d) for w, gives
Traº”.S
9
o.274(#d)*Z" –
and
S = O.5457;
for T = 5 tons, S = 2.725 tons. But the greatest allowable
value for S is, according to Bender, 2.91 tons. This proves,
that, if an iron pin be properly proportioned for crushing and
bending, it will be strong enough to resist shear, and in fact,
that, before the pin could shear, it would either break by bend.
ing or crushing, or the eye of the bar would give way. A similar
investigation for steel bridges, where T = 8.35 tons, C = {T,
and R (the intensity of working bending-stress) = 1.87, gives
d = O. 57.14d, z0 = O. I816d, and S = 5.912 tons = the actual
intensity of shearing-stress when the pin is strained up to the
bending-limit, and the ratio # for that condition of stress is at
I
its minimum, and consequently the area of the bar, the tension
therein, and the shear on the pin, at their maxima. But the
greatest allowable shear is, according to Bender, 4 × # × T
= # X 8.35 = 4.858 tons; so that, for a pair of steel bars pull-
ing on a steel pin in opposite directions, or a single steel bar
against a steel bearing, the pin in certain cases will be liable
to rupture by shearing, and will therefore have to be propor-
tioned to resist that stress.
After making out the diagram of stresses, and proportioning
the main members of a bridge, comes the determination of the
sizes of the pins, -a matter that is liable to occupy more time
than did all the previous work. Knowing the sizes of all the
bars in the structure, the clear width between the inner faces
of the top chord channels (and consequently that between post
channels) can be found, after which the arrangement of all the
bars in the bridge can be decided on. Care must be taken in
performing the latter, that no two consecutive chord bars or
ties coupled on the same pin pull in the same direction, unless,
this arrangement reduce the bending-moments, as it can some-
times be made to do; that the lighter set of bars be so placed
82 OA'Z)/AVA R P ZAZOAV HIGH WA P-BA’/DGAE.S.
as to reduce the bending-moments; and that the diagonal ties
be placed close to the posts, and the beam hangers close to
the ties. Especial care is needed at the panel point where the
number of chord bars is different in the consecutive panels. It
is possible to arrange the bars there, so that there will be an
extremely large moment produced, or so that it will be smaller
than at any other panel point of the bottom chord. The neglect
of any of these precautions will cause an undue bending-moment
on the pin. »
The arrangement completed, the next questions to be decided
are, first, under what condition of loading will each pin take
its greatest bending-moment, and, second, at what point on
the pin will this be found. In large bridges, and in many well-
proportioned small ones, the bottom chord pins are subjected to
their greatest bending-moments when the bridge is fully loaded.
Under this condition, the stresses in the chord bars can be taken
from the diagram of stresses; but those in the main diagonals
must be calculated for the load covering the whole bridge, and
their horizontal and vertical components be ascertained.
After having had some practice, one will very often be able
by simple inspection to decide at what place the greatest
moment of flexure will exist; but, if not, it will be necessary
to calculate the values of both horizontal and vertical moments
at different points, and find where their combined result is a
maximum. As Professor Burr shows, the actual moment is
represented by the diagonal of a rectangle whose sides repre-
sent the vertical and horizontal moments. It is usually more
convenient to Square the component moments, add the results,
and extract the Square root of the sum, than to make out a
diagram.
The moments of the stresses can be easily recorded by draw-
ing two curved lines, as shown in the accompanying diagram,
representing the directions in which the
stresses tend to bend the pin, and writing
* each moment as calculated under one or
other of them, according to whether it would
produce positive or negative rotation. The
difference between the sums of each column will give the actual
ORD/AVA R Y IROAV HIGH WA Y-B/C/DGAE.S. 83
horizonal or vertical moment, as the case may be. The condi-
tion that a load covering the whole bridge may not produce the
greatest moment in the bottom chord pins is either when there
is a single counter coupled at the centre of the pin, or a main
diagonal coupled at a distance from the member that takes up
its stress. As a rule, single counters and single beam hangers
are to be avoided, on account of the unnecessarily large bend-
ing-moments they produce. The size of pin for the hip joint
depends greatly upon the arrangement of the bars which it
couples. In a double-intersection bridge, where there are two
hip verticals, two long diagonals, and two short ones, the best
arrangement is to put one pair of diagonals on the outside of
the chord, and the other pair inside, close to the bearing ; the
verticals coming next, and being kept apart by a filler. Some-
times it is not advisable to couple outside of the chord, in which
case the moment would become so great, that it would necessi-
tate the employment of a pin whose diameter would make the
heads of the eye bars too large for the space allotted them. In
such a case, a steel pin can be used to advantage. Hinged
ends at the hip joints require large pins, for the entire stresses
in both chords and batter braces come upon them with great
leverage, due to the necessarily large bearing-surface. Such
a connection is not advantageous : it is better to allow the
channels to abut. Such hinged ends are a great convenience
in erection, but usually necessitate an increase in the sizes of
the batter braces and the top chords at the end panels. A
detail to obviate this necessity will be given in Chapter XIII.
It is not necessary to consider the bending-effect of the
stresses in the lateral rods upon the chord pins, for the wind
and the live load are not supposed to act simultaneously.
Lateral rods should always be so connected to the chord pins,
that the effect of the stress in the outer one will be to diminish
the horizontal component of the moment on the pin ; i.e., if the
tendency of the chord and web stresses is to bend the pin con-
vex to the middle of the bridge, the outer lateral rod should
point towards the middle; but, if it be to bend the pin concave
to the middle of the bridge, the outer lateral rod should point
towards the nearest end of the span.
84 OA'ZD/AVA R P IRO/W HIGH WA P-BA’/DGE.S.
The ends of pins have to be reduced in diameter, so that the
nuts and pin pilots may be screwed thereon. Care must there-
fore be taken in proportioning small pins to see that sufficient
area be left under the root of the thread to resist the tension
on that section caused by the greatest transverse components
of the stresses in the lateral rods. The principal objection to
the use of large pins is not always the undue weight of the
pins themselves, but the increased size of the chord and tie-bar
heads, and the room that they take up. *
On the other hand, it is not always desirable to use the
smallest possible pin, as the width of the bearing is an inverse
function of the diameter of the pin : so if, owing to the neces-
sity of a large number of rivets, the re-enforcing plates be long,
it might be economical to increase the diameter so as to reduce
the width. Thickening the heads of eye bars has an injurious
effect on the pins, although a beneficial one upon the heads, for
the lever arms of the stresses are thereby increased.
Bridges with weak pins will not necessarily fail by the rup-
ture of the pins. The reason for this is thus stated by Professor
Burr: “The distortion of the pin beyond the elastic limit will
relieve the outside eye bars of a large portion (in some cases,
perhaps all) of the stress in them. This result will produce
a redistribution of stress in the eye bars, by which some will
be understrained, and the others correspondingly overstrained.
Thus, although the pin may not wholly fail, the safety of the
joint will be sacrificed by the overstrained metal in the eye
bars.”
ORD//VARK IRO/V H/GA/W/A Y-B/C/DGA.S. 85
CHAPTER XI.
PRACTICAL METHOD OF PIN PROPORTIONING.
THE ordinary method of pin proportioning is to figure the
diameters of a few principal pins, and to make the others of
the same sizes. Thus, by inspection, can be found which pin
near the middle of the bottom chord is subjected to the great-
est bending-moment. If there be an even number of panels in
the span, it will be the middle pin ; but, if there be an odd
number, it may be the first or second pin from the middle,
according to the number and arrangement of the chord bars.
The vertical component of the bending-moment on any one of
these pins is so small in comparison with the horizontal com-
ponent, that it may be neglected. For bridges with an even
number of panels, —
Let
T = tension in middle panels of lower chord,
and
w = the average thickness of chord bars in these panels;
then, approximately,
7%
4. = bending-moment on middle pin.
This formula may be applied, but perhaps with less accuracy,
to a bridge having an odd number of panels; and, if the chord
be properly packed, the error will be upon the side of safety.
With the exception of the chord pins at the shoes and at the
first panel points from the ends of the span, all the lower chord
pins may have a diameter corresponding to this maximum bend-
ing-moment.
86 OA’D//VA R Y ZAZOAV HAGH WA Y-AA/DGAES,
To find the size of the lower chord pin at the first panel
point, use the formula,
Aff = -
2
for the horizontal component of the moment, and the formula
_ £4(d+ d")
tº-ºº-ºº 4
W
for the vertical component; t being the intensity of working-
stress for the hip verticals, A their area (S. R.), to be taken
from one of Tables VI., VII., and VIII, d the diameter or thick-
ness of a hip vertical, and d" that of a beam hanger.
The moment given by the formula
M = V//* + Vº
applied to Table XII. will determine the diameter required.
This diameter is to be used also for the pin at the shoe.
To find the size of a hip pin, lay off the stresses in one hip
vertical and one end main diagonal to any convenient scale, and
find the value of their resultant by the parallelogram of forces.
This resultant will determine the thickness of the bearing, a
trial diameter being first assumed. It is possible that this bear-
ing will have to be increased, so that there will be enough iron
to transfer the stresses from the batter brace, hip verticals, and
diagonals to the chord, as will be explained in Chapter XIII.
An approximate test of the sufficiency of the bearing in this
respect may be obtained as follows:–
Let
A = the area of the section of the end panel of the top chord,
d = depth of chord channels,
# = thickness of web of an end chord channel;
*
then the bearing should not be less than that given by the
formula
A
B = x + i.
Next find the distance / between the centre of the bearing of
ORD/AWA R P IROM HIGH WA P-BRIDGE.S. 87
the chord and that of the diagonal, also the distance / between
the former and that of the hip vertical, the latter being on the
inside. Calling the stress in the hip vertical F, and that in
the diagonal S, the vertical moment will be Fl", and the inclined
one Sl. Next lay out these components to any convenient scale
in their proper directions, and find their resultant by the paral-
lelogram of moments. This resultant will determine the diame-
ter of the pin. &
If the diameter found agrees with the one assumed, or if it
does not agree, provided that the bearing was not determined
by the trial diameter, all right; but if the bearing were so
determined, and the two diameters do not agree, another trial
must be made.
Where there are more than two main diagonals coupled at
the hip, as is the case in double-intersection and in very heavy
single-intersection bridges, one pair is coupled on the outside
of the bearing, and the other on the inside; so that theoretically
the greatest bending-moment is equal to the stress in the outer
bar multiplied by the distance between the centre of the bar
and the centre of the bearing. But practically the moment may
be greater, for the distribution of stresses among the diago-
nals may not be as assumed : so it is well to determine the
moment by imagining the Outer bar not to exist, and proceeding
as explained above for the case of only two main diagonals at
the hip, excepting, of course, that the thickness of the bearing
must be ascertained by finding the resultant of the stresses in
the two diagonals and the hip vertical.
To calculate the size of an intermediate upper chord pin, the
widths of chord and post bearings are to be determined as shown
in Chapter XIII. The former is given approximately by the
last formula, where A is the section of the panel of the chord
on the side of the pin towards the middle of the bridge, and t
the thickness of the corresponding channel. The other is given
by the formula
where A, is the area of the section of the post, and h the depth
of one of its channels.
88 ORD//VA R Y WA’O/V HIGH WA Pi—BRIDGES.
Next resolve one-half of the diagonal stress vertically and
horizontally into P and P' respectively. Let / represent the
distance between the centre of the diagonal and that of the ex-
tension plate, and l’ the distance between the former and that
of the chord-bearing ; then
V = P,
A = P'/',
M = V/? -- 73.
If the bridge be a small one, it will be necessary to calculate
only the size of the pin at the top of the first vertical post from
the end of the bridge, and to make all the intermediate top
chord pins of the same size. But, if the bridge be a large one,
it will be better to calculate the diameter of the pin on the post
midway between the end vertical post and the middle of the
span, and to make all the pins between these places of this
diameter, and all the others of the same diameter as that at the
end of the first vertical post. After the diameters of the top
chord pins are determined, the post and chord bearings should
be tested by applying one of Tables XXVI. and XXVII., al-
though in most cases they will be found ample.
In double-intersection bridges, where the diagonals are halved,
and coupled on pins passing through the middle of the posts,
the size of any one of these pins may be found from the
moment
and
Sw
T 2
M
9
where S is the stress on the diagonals as given on the diagram
of stresses, and w the width of one of the main diagonals.
In all pin proportioning it must be kept in mind that the
diameter of the pin is never to be less than eight-tenths of
the depth of the deepest bar coupled thereon.
The author wishes to call attention to the superiority (in his
opinion) of the simple method given in this chapter for propor-
tioning lower chord pins by formula over the apparently more
accurate one given in the last chapter.
ORD//VA R P WA’O/V HIGH WA P-BA’/DGES. 89
In this method, when the proper proportion of width to depth
of bars is adhered to, the diameter of the pins will be almost
eight-tenths of the depth of the bars, and will be great enough
to resist the bending- moments produced by any legitimate
method of packing. Moreover, after the diameters of the pins
have been determined, the chord can be packed, if it be advisa-
ble, so as to reduce the bending-moments. This superabun-
dance of strength in the pins is obtained at the expense of a
slight increase in the weight of iron ; and the increased sizes
of heads for diagonals can do no harm, because they do not
enter any limited space, as do the heads at their other ends.
But if, by a skilful arrangement of the packing, we can so
reduce the bending-moments on the pins, that the diameters
may be made small, and the proportion of width to depth of
bars larger than that found in the last chapter, the pins may
not be as strong as we imagine them ; for we cannot be sure
that all the bars are going to pull as we have assumed that they
will. It may be that one of the outer bars is a trifle long, and
will not pull at all until the others are well stretched : what,
then, becomes of our calculated bending-moments 2
Any one of them may be so greatly exceeded, that the pin
will be strained beyond the elastic limit, and will bend percepti-
bly, so changing the distribution of stress in the panel that one
or more of the bars also may be strained beyond the elastic
limit.
But if the pin be large enough, or more than large enough,
it cannot bend perceptibly : consequently the distribution of
stress will be much more uniform, even if the bars be of slightly
unequal lengths.
90 OA'D//VAA’ Y /A’O/V HIGH WA Y-BA’/DGE.S.
CHAPTER XII.
RIVETING.
THE subject of riveting is one, which, like that of pin propor-
tioning, has never received its due amount of attention from
bridge designers. Many structures otherwise very strong are
extremely weak in detail, owing to the insufficient number
of rivets employed in the connections and to their improper
arrangement. The principal rules for riveting have been given
in Chapter II., pp. 17, 18.
Rivets should be proportioned for bending and for bearing
pressure ; i.e., for any given connection, the number of rivets
necessary to resist properly each of these stresses should be
determined, and the greater number chosen.
Tables XXXVI. and XXXVII. give the working bending-
moments and permissible bearing-pressures for bridges of Class
A and for those of Classes B and C. For the lateral systems of
both classes, Table XXXVII. is to be used. In these tables
the first and second horizontal lines of vulgar fractions and
decimals give the widths of bearings; and the other horizontal
lines in the portions pertaining to bearing give the working
bearing-stresses for rivets of different diameters. The rest of
the tables needs no explanation.
The sizes of rivets ordinarily employed for highway-bridges
are from five-eighths to three-quarters of an inch ; though half-
inch rivets are used for very light channels, and seven-eighths
inch rivets for very heavy ones.
The weight of a pair of rivet heads for any diameter can be
found in Table XXIX. It is well to memorize these weights.
Where two plates are riveted together, the rivets, driven
when hot, contract, or tend to contract, in length when cooled,
OA’/D/AWA A' P ZA'OAV AZZGAZ WA V-AAEMDGAE.S. 9I
thus drawing the plates together, and producing a friction, which
it is necessary to overcome before shear can come upon the
rivets. Whether this friction will continue indefinitely is doubt-
ful, for rivets occasionally become loosened when the structure
is subjected to oft-repeated loads: So it is not legitimate to
depend upon the friction in order to reduce the number of
rivets. Perhaps it is on account of this factor that rivets are
seldom, if ever, proportioned to resist the bending-moments
that come upon them, notwithstanding the fact that it is this
last consideration, which, in most cases, should determine the
number of rivets to be employed.
Again : if the friction were to be depended upon, it would be
only right to allow for the initial tension on the rivets, which
tension is sometimes great enough to force off the heads.
It will probably have been noticed by the reader, that shear-
ing-stress upon rivets has been omitted altogether from con-
sideration. The author would hesitate before making the broad
assertion that rivets cannot shear, although it is probable that
bending is the stress which ruptures rivets that are generally
considered sheared. This much, though, he will state as the
result of both theoretical investigation and many practical cases
of designing, that, when rivets are proportioned for Öending and
bearing, they will have more than sufficient strength to resist shear.
Sharp edges on rivet holes will certainly cut the rivets, but this
is not shear proper; and it may be possible that there is a cer-
tain kind of fixedness about a well-driven rivet which will make
the bending-moment less than its calculated value.
Should the reader wish to verify the statement concerning
bending and shearing stresses, he can do so by using an inten-
sity of shearing-stress of three tons for bridges of Class A, and
one of three tons and three-quarters for those of Classes B and C.
The theoretical proof is identical with the one for pins given in
Chapter X.
“Countersinking” is a term used to denote the sinking of
rivet heads into the plate so as to make them flush with its
surface. The least allowable depth for the countersinking is a
quarter of an inch, and the least thickness of plate used for this
purpose should be three-eighths of an inch : for rivets exceeding
92 OA’D/AWA R P WA’OAV HIGH WA P-BAZZOGE.S.
three-quarters of an inch in diameter, these dimensions should
be increased by an eighth of an inch. Rivets may be counter-
sunk at one or both ends.
Making parallel rows of rivets staggered avoids unnecessary
weakening of the parts riveted together.
There has been much discussion as to whether punched or
drilled holes are preferable; the general conclusion being, that
drilled holes weaken the plates less, and when slightly counter-
sunk, so as to avoid sharp edges, do not increase the shear upon
the rivets, but that punched holes are so much more economi-
cal as regards shop-work, that, when properly made, they are
preferable to drilled ones. The improvements made of late
years in riveting-machines have increased the efficiency of work
with punched rivet holes.
Should, for any reason, it ever be necessary, in bridge design-
ing, to put a rivet through a plate whose thickness is greater
than the diameter of the rivet, the rivet hole should be drilled.
Machine riveting is preferable to hand riveting, but there are
cases when the latter has to be employed.
Field riveting is nearly always inferior to shop riveting.
When a stress is transmitted from one plate, through one or
more plates, to another plate, the number of rivets must be
increased. The rule given by Weyrauch is, that, “for every
single shear connection, the indirect force transferrence requires
for m intermediate plates m + I times as many rivets as for
direct transferrence.” Keeping this in view, the designer will
avoid using more than one flange plate in floor beams, or more
than one plate for covering the channels of the top chord.
ORD//VA R P IROAV AZZGA/WA P-B/C/DGA.S. 93
CHAPTER XIII.
PROPORTIONING OF OTHER DETAILS.
THE sizes of stay plates used at the ends of systems of lat-
ticing or double-riveted lacing are given in Table XXXII., and
the sizes of those used at the ends of systems of single-riveted
lacing, in Table XXXIII. The headings of these tables fully
explain their use.
Stay plates are to be employed at the middle of posts (vide
Plate II., Fig. I5) when the diagonals are halved, and connected
by pins passing through the posts; their sizes being taken from
the before-mentioned tables. Stay plates, if they can be so
called, are also to be used on the lower portal struts, for the
purpose of attaching the knee braces.
Pin bearings are sometimes figured, counting in both re-en-
forcing plates and web; but the latter is often omitted. This
would be necessary when the holes in the web are bored inde-
pendently of those in the re-enforcing plates, for then it is very
improbable that the different holes will coincide; but, when the
re-enforcing plates are riveted to the web before boring, such
a precaution is not only unnecessary, but is a waste of material.
By consulting Table XXVIII. can be found at a glance,
accurately enough for all practical purposes, the thickness of
web of any Union Iron-Mills channel bar, when the weight is
given, or vice versa.
Where re-enforcing plates act also as splice plates, there
should be one on each side of the web in order to insure a good,
substantial joint; although the practice in the building of small
bridges is to omit the outer plate when the pin bearing does not
demand its use.
The length of a simple re-enforcing plate depends upon the
94 OA’D/AVA A' P ZAZOAV HIGH WA P-BA?AIDGES.
number of rivets required, and is thus determined. Find, by
dividing the stress given on the diagram of stresses between the
various thicknesses of iron which constitute the bearings, the
amount of stress which the plate considered is to carry. It is
well, though, to make a liberal allowance, say twenty per cent,
for the possibility that the stress may not be divided proport
tionately to the thicknesses. Next multiply the stress so ob-
tained by the perpendicular distance between the central plane
of the re-enforcing plate and that of the plate or web re-en-
forced : the product will be the moment of the stress upon the
re-enforcing plate Divide this moment by the working bend-
ing-moment, taken from Table XXXVI. or XXXVII., for a
rivet of the diameter to be employed for the connection: the
quotient will be the number of rivets required to resist bend-
ing. Next find, from one of the same tables, the working bear-
ing-stress for one of the rivets upon a plate of the thickness
of the re-enforced plate or web, and divide it into the stress
which the latter carries: the quotient will be the number of
rivets required to afford sufficient bearing. The greater of
the two numbers, thus obtained is the one to be employed.
Next make to scale a drawing of the re-enforcing plate, laying
out the rivets, if it be possible, symmetrically, and thus deter-
mine the length of the re-enforcing plate. In case of a re-
enforced pin hole, if the diameter of the hole exceed one-half
the width of the plate, it will be necessary to put more rivets
in front of the pin hole than behind it; the ratio of the num-
ber in front to the whole number being equal to that of the
diameter of the hole to the width of the plate.
The method of proportioning splice plates or connecting
plates is somewhat similar. For instance, let us take the plates
at a joint in the top chord; which joint, for reasons to be stated
in Chapter XVIII., is always to be placed a few inches to that
side of the pin hole farthest from the middle of the span. The
stress on the portions of the plates to this side of the joint is
that due to the stress in the panel where the joint occurs;
while that on the other portion of the plates is due to the stress
in the next panel towards the middle of the span. The number
of rivets on each side of the joint will be dependent upon the
OAC/D//WAA’ P //t’O/W HZGA/MVA P-AE/ø/ZDGAZ.S. 95
stresses carried by the channel bars of the two adjacent panels.
The simplest way to find the stress on any channel is to multi-
ply its area by the intensity of working-stress, which was found
from either Table X, or XI. This stress is then to be divided
equally, or otherwise, between the outer and inner plates which
splice the abutting channels; and the number of rivets neces-
sary to resist bending and bearing are to be ascertained in the
manner explained for re-enforcing plates.
To determine the length of a cover plate, find in the same
manner the number of rivets upon each side of the joint, which
will take up the stress carried by the chord plate, and lay out
the cover plate with the rivet spacing to scale. The stress car-
ried by the chord plate is equal to its sectional area multiplied
by the intensity previously found for the channels.
At the hip joint it is obvious, that, where the chord and batter
brace are hinged upon the pin, the resultant of the thrust in the
batter brace and the pulls in the diagonals and verticals must
equal the thrust upon the chord, and that the bearing must be
figured for this thrust; but, where they are not hinged, the
section of the splice plates must answer two requirements :
first, their area (neglecting, on account of its being bent, the
effect of the cover plate) must be sufficient to transfer to
the chord a stress equal to that in the first panel; and, second,
that the pin bearing be sufficient for the resultant of the ten-
sions in the diagonals and verticals meeting at the hip. The
length of the cover plate at the hip cannot be calculated; for
it carries no stress, simply adding to the rigidity of the joint,
and keeping the rain therefrom.
If the posts be figured for one fixed end, the inner splice
plate of the chord can be extended downward to act as a con-
necting plate for the post; and in this case there must be
enough rivets used in respect to bearing and bending to transfer
all the compression in the post to the chord by the connecting-
plate, under the supposition that the ends of the post channels
do not touch the flanges of the chord channels. If they do
touch, so much the better; but it would not be safe to count
upon their doing so. The thickness of the connecting-plate
should be such that it would not bend between the end of the
96 OA’D/AVA A' P ZAZOAV HAGATVA P-AEAe/DGAE.S.
post and the pin hole when the post would be on the point of
rupture by compression. Where the ends of the posts are
figured hinged, which is a decidedly better construction, the
extension plates pass inside the splice plates of the chord, and
are attached to the pins. As before, there must be enough
rivets to transfer the stress in the posts to the plate.
The thickness of the re-enforcing plates at the lower end of a
post is determined by the bearing required, and their length in
the manner already described. It is better to place these plates
on the inside of the posts; then, if the flanges of the channels
be partially cut away, an extra plate (at least three-eighths of an
inch thick) can be placed on the outside of each channel. The
reason for cutting away the bottoms of the post channels is
merely to pack the chord more closely, and thus reduce the
bending-moments on the pins. But, if the method of pin pro-
portioning given in Chapter XI. be adopted, the necessity for
cutting away the channels, to any extent, vanishes; for at the
middle of the span the web stresses are so small, that their
moments are neglected, and the pins at the feet of the other
posts have an excess of strength.
In high double intersection truss bridges with long panels,
the diagonals become so long, that it is convenient to halve
them, and connect the halves by pins. It is then advisable to
let these pins pass through the webs of the post channels where
the diagonals cross, for the latter then tend to stiffen the posts.
If intermediate struts also be used at the middle of the trusses,
the posts can be figured for half length, with both ends hinged.
On account of the stretch of the main diagonal, there would be
a tendency to deflect the post. If the diagonals were forty-two
feet long, the stretch of the upper half of them would be about
one-eighth of an inch ; so that, to avoid this objection, it will
be necessary to elongate the pin hole that amount on the lower
side, in the direction of the main diagonal. The pin holes
should, of course, be well re-enforced in order to compen-
sate for the material cut from the channels. The stretch of
the counters being less than that of the main diagonals, and the
posts crossed by the heavy ones generally having an excess of
strength, it is not necessary to elongate the pin holes in the
direction of the length of the counters.
ORD/MARY IRON HIGH WA Y-B/CIDGE.S. 97
In nearly all iron bridges the batter braces are made with
ends fixed at the pedestals (i.e., they are rigidly attached to the
shoe plates), although hinged pedestals are not unknown :
the advantage gained by their use is the certainty of a uni-
formly distributed pressure on the rollers, and the disadvantage
a great increase in the section of the batter braces.
The shoe plate can be attached to the batter-brace channels
by bent plates on the inside, the outside, or both, or by pieces
of channels, with one flange removed, placed on the inside, and
riveted through their webs to the webs of the batter-brace chan-
nels, and through their flanges to the shoe plate, as shown on
Plate IV. The lower end of the batter-brace plate should be
turned up horizontally, and riveted to the shoe plate.
The area of a section of the connecting channel or plate
made by a plane perpendicular to the direction of the batter
brace should be equal to the area of one batter-brace channel,
or greater if the shoe pin require greater bearing than this
would afford ; and there should be enough rivets to transfer the
stress from the batter-brace channel to the connecting channel
or plate. Should the batter-brace channels bear against the
shoe plates, as they ought to do, there will be more rivets than
necessary; but such a bearing should not be counted upon.
Details of shoes are shown on Plates II., III., IV., and VI.
The rules for proportioning shoe, roller, and bed plates, are
given on p. I6.
A very good connection for the hip joint is the one shown on
Plates III. and IV. The inner splice plate has five sides, the
under one passing entirely below the joint; and the outer splice
plate is cut to fit closely to the webs of the chord and batter-
brace channels, being made as wide as the flanges of the chan-
nels and the rivet heads therein will permit. The objection to
this detail is, that it requires a good deal of field riveting.
Another good detail for this joint is that shown in Fig. I4,
Plate II. Here there are two connecting-plates on the outside
of the chord, and two on the inside of the batter brace, through
all of which the pin passes. Those on the chord abut against
plates riveted to the outside of the batter-brace channels; and
those on the batter brace abut against plates riveted to the
98 OA’D/AVA A' V /A’O/V HIGH WA Pi—BA’/ZOGAE.S.
inside of the chord channels, all abutting surfaces being planed
to fit exactly ; so that, when the pin is driven into place, the
whole joint will be as rigid as if it were riveted. Of course this
detail demands neat workmanship, and is consequently some-
what expensive; but the satisfactory result attained more than
counterbalances the extra cost of the shop-work, and there is
no necessity for figuring on a hinged end at the hip when
proportioning the batter brace and the end panel of the top
chord.
A good method of attaching the upper lateral struts to the
chords is the following, which is illustrated on Plates II., IV.,
and VI. Let the web of the upper channel lie upon the cover-
plate of the chord, extending to its outer edge, and be riveted
thereto; and let the under face of the lower channel, its flanges
being turned downward, lie in the same horizontal plane as the
faces of the lower flanges of the top chord channels. The
length of the lower channel of the lateral strut should be a
couple of inches shorter than the clear roadway of the bridge.
The connection is made by a plate in the form of the letter T,
the head being riveted to the lower flanges of the inner chord
channels, and the stem passing between the flanges of the
lower channel of the lateral strut, to the web of which it is to
be riveted. The thickness of the T-plate should be five-eighths
of an inch, and the re-entrant angles should be rounded off with
a radius of an inch and a half or two inches. The width of
the stem should be made as great as the distance between the
flanges of the lateral strut will permit, and that of the head
equal to the width of the flanges of the chord channels.
The number of rivets for either stem or head must be calcu-
lated for bending and bearing resistances corresponding to the
greatest stress that could ever come upon the channel, which
stress is to be calculated by multiplying the area of the channel
by the intensity found in Table XI.
A good connection for the intermediate struts to the posts
is by means of two bent plates at each end of the strut (vide
Plates IV. and VI.). One leg of each plate is riveted to the
web of the inner channel of the post, and the other to the web of
the I-beam, which is placed horizontally. The vibration rods
OAA)/AWA R V /A’OAV HIGH WA P-B/C/DGAE.S. 99
are attached by bolts that pass through the two connecting-
plates and the web of the I-beam. The connection at the
upper ends of the vibration rod may be similar, if the width
of the T connecting-plate be great enough to permit of the
passage of a bolt.
At the intermediate strut connection, there should be enough
rivets used in respect to bending and bearing to transfer the
calculated stress upon the strut to the connecting-plates.
If there be but one portal strut at each end of the span, it
may be connected to the batter brace by two large bolts passing
through a jaw plate, as shown in Fig. I I, Plate II. These bolts
may have square heads placed so near the sides of the jaw that
they cannot turn, the nut having to be screwed up on the inside
of the batter brace. But, if there be two portal struts at each
end of the span, the channels are to be turned around ninety
degrees, and brought nearer together; so that it will be better
to use exterior bent plates attached to the flanges of the chan-
nels, as shown on Plates IV. and VI., in addition to a single
large bolt through the jaw.
Concerning the best method of connecting the lower lateral
rods, there is much diversity of opinion; although, in ninety-nine
cases out of a hundred, they are attached to the floor beams,
which are thus made to act as struts for the wind pressure.
. Some bridge designers put bent eyes on the lateral rods, and
run bolts through the web, usually near the middle, which is
very objectionable, for two reasons: First, the laterals take hold
of the weakest part of the beam ; and second, being attached at
such a distance from the pins, they permit of too much vibration.
Another detail is to rivet two 4 by 6 inch angles to the web, and
drop a pin through the six-inch legs: this is a little better detail,
but the same objections apply here. Another is to let the rods
pass through the webs, and through rods and plates bent so that
one face is perpendicular to the direction of the lateral rod,
another face parallel to it, and the other two end faces parallel
to the web of the beam, to which they are riveted. The same
objections apply to this, together with two which are still more
important; viz., that, as at each connection there are two such
plates and two lateral rods from adjacent panels crossing each
IOO OA*/O IAVA R Y /A’OAV HIGAZ WA P-AESA’ſ DGA.S.
other, the longitudinal components of the stresses in the latter
produce a moment tending to revolve the beam about the upper
edge of the web. Then, again, the bent plates must be made
so heavy that they would withstand, before buckling, the ulti-
mate pull of the lateral rods; and it is very seldom that such
a detail is made strong enough to stand the ultimate pull of an
inch and a half round rod. Another way is to rivet a plate across
the top of the beam, and two bent plates or large angles opposite
each other, just below the top flange, dropping pins through the
jaws thus formed. This is the best arrangement yet employed.
But in the author's opinion all these details are defective, for
the reason that the lateral rods all take hold of the floor beams,
which are simply suspended from the pins that are several
inches above them ; so that, unless the hangers be screwed up
very tightly, any wind stress in the lateral rod will cause a
rocking at the point of suspension, and, even if the hangers be
screwed up tightly, the tendency to rock still exists. The only
correct place to attach the lateral rods is to the chord pins, and
their stresses should not be transmitted through the floor beams.
Then come the questions, “How shall they be transferred 2"
and “How shall the rods be arranged so as to clear the joists 2 ”
The detail about to be described will answer these questions.
Upon the floor beam place a stick of square timber (about
eight inches for ordinary highway-bridges), and let the ends fit
into wrought-iron jaws, which screw up against the chord pins;
then fasten the timber every few feet on alternate sides of the
web, by half-inch bolts, to the flanges of the beam, and rest
the joists on the timber. The laterals can either be attached by
bent eyes to the chord pins (which would be preferable if their
diameters do not exceed an inch and three-fourths), or by ordi-
nary eyes to vertical pins passing through the wrought-iron
jaws. In this way the timber not only acts as a lower lateral
strut, but serves to give additional stiffness to the floor beam;
although the section of the latter should not be diminished on
that account.
Now, what objections can be raised to this method 2
Some may say that it is a clumsy contrivance, but that is a
matter of taste. Others may suggest that it reduces an iron
ORD/MARY IRO/V HIGH WA Y-BRIDGES. IOI
structure to a combination bridge. Not at all, - fio more than
the employment of wood for the floor and joists; because, at the
same time when the latter are renewed, the wooden struts can
be replaced. There is a slight objection for short through-
spans, viz., that it reduces the headway; but it would not
greatly increase the expense to add eight inches to the depth
of the trusses.
Another method of avoiding the difficulty is to rivet the floor
beams to the posts. But will not this be equally objectionable 2
Certainly such a connection is better for the beams, as it par-
tially fixes their ends; but what about the deflecting effects of
wind stresses and passing loads upon the posts 2 The trans-
verse components of the lateral rod stresses act with great
leverage, for the beams are always attached above the bottom
chords; and the weight of a heavy wagon coming suddenly
upon the beam must certainly cause the posts to vibrate trans-
versely to the planes of the trusses, but to what extent, and
with what injurious effect upon the posts, it is at present im-
possible to say. Even if there be but little known concern-
ing this attachment, it is certain that a floor beam should never
be riveted to only one of the channels of each post. Such an
arrangement would produce indirect stresses of a destructive
character: consequently the posts should be turned one-quarter
way round in order to let the beam pass between them.
Floor beams in deck bridges may either rest upon the chords,
be hung from the chord pins, or be riveted to the posts. In
neither case should they be used as lateral struts when the
lateral rods are attached to the chord pins, because of the lever-
age that would be afforded to the lateral stresses to produce
distortion.
It is not customary to calculate the thicknesses of beam-
hanger plates, for they are usually made from three-fourths of
an inch to an inch thick for ordinary highway-bridges; but
under certain assumptions their thicknesses can be calculated.
If the load on a plate be considered uniformly distributed over
the portion between the beam-hanger holes, and if the flange of
the beam be supposed to take up no bending-stress, the plate
may be considered as a beam supported at the ends, and uni-
I O2 OA’ZO/AWA A' V ZAZOAV HIGH WA Y-AA’//DGES.
formly loaded. For instance, take the case of a twenty-foot
panel and an eighteen-foot clear roadway, the re-action at each
end of the beam is about nine tons. Suppose the centres of
beam-hanger holes to be situated on the corners of a four-inch
square, and the plate to be seven inches square, then the bend-
ing-moment is
M = # WZ = } x 9 × 4 = 4.5 inch tons.
{ } a & . R/
The resisting moment is Tº where R = 5 tons, ſ = moment
l
* , º d G
of inertia = Hºbd” = Hººd", and d = 2. Equating the moments,
substituting, and solving, gives d = about seven-eighths of an
inch, a result agreeing with good practice. It is almost need-
less to say that this method is very approximate; for the plate
is greatly stiffened by the rigidity of the flange of the beam,
while, on the other hand, no reduction has been made for the
beam-hanger holes.
Lacing, or, as it is often improperly termed, single latticing,
is about the most common detail for keeping pairs of channel
bars in line: nevertheless, it must be inferior to latticing,
especially when the lattice bars are riveted together at their
intersection. By inspecting Tables XXXII. and XXXIII, it
will be seen that a system of lacing-bars with one rivet at each
end of a bar requires much larger stay plates at the ends than
does a corresponding system of latticing or double-riveted
lacing.
The actual sizes of lattice or lacing bars for any strut can be
determined only by experiment: it is thought that those given
in Tables XXX. and XXXI. are so strong, that the struts on
which they are employed would break in the channels rather
than in the bars, and yet not so heavy as to cause much un-
necessary use of material. It will be seen also in these tables,
that the requisite dimensions of latticing and lacing bars depend
not only upon the sizes of the channels which they connect, but
also upon the distance apart of these channels: this is due to
the fact that the bars are subject to compression as well as
to tension. The lengths and weights of latticing and lacing
ORDIAWAR}^ IRO/W HIGH WA P-B/º/DGE.S. IO3
bars can be found from Table XXIX. It must not be forgotten
that these lengths are to be used for estimates only; as they were
obtained from a diagram, and not checked by calculation.
The smallest trussing-bars used should be no less than a
quarter of an inch by three inches, and the bend for attach-
ment should be no less than three inches long, so as to permit
of the use of two staggered rivets. The heavier the trussed
bars, and the greater the distance between them, the greater
should be the section of the trussing-bars. At the ends of a
system of trussing, the bars should be turned and attached, as
shown on Plate II., Fig. 8, and on Plate VI.
The lightest bracket used should be no weaker than a 24"
× 24” 4.9% angle iron, which section is to be employed only
to attach intermediate struts to posts. Where there is no
vertical sway bracing, the stresses on the brackets are to be
calculated as shown in Chapter VI., and the sections are to
be proportioned by using the following table of approximate
intensities of working-stress.

INTENSITIEs of WoRKING-STREss.
LENGTH OF STRUT,
IN FEET.
2}^ X 2#’ L- 3” X 3” |-- 3#" X 3#’’ L.
4 3.O 3.5 4.O
6 2.5 3.O 3.5
8 2.O 2.5 3.O
The number of rivets that connect the bracket to the lateral
strut and post must be sufficient to transfer all the stress in the
bracket to each of these members.
To prevent the pedestal at the free end of a span from slip-
ping in the direction of the length of the rollers, the latter can
be notched about a quarter of an inch in depth, for a length of
about two inches at the middle, and the shoe plate and roller
plate be planed down so as to leave projections which will
exactly fill the notches. This detail is illustrated in Plate VI.
For short spans, a sliding-joint such as shown on Plate III.
is to be used.
IO4 OA’Z)/AVA R P ZA’O/V HAGH/WA P-AESR/DGE.S.
When it becomes necessary to anchor down the expanding
end of a bridge, it should be done in such a manner that the
shoe could not rise more than an eighth of an inch : thus the
projection on the under side of the shoe plate will be prevented
from being lifted out of the notches on the rollers.
Bed plates and roller plates should be anchored to the abut-
ments by rods with nuts. When the abutments are of stone, a
good method of attachment is to drill holes therein just below
the anchor bolt holes in the bed plates, enlarging them, if prac-
ticable, at the bottom. Split the ends of the anchor bolts several
inches, insert small iron wedges in the splits, drive the bolts
into place, so that the wedges force the split ends apart, thus
partially filling the enlarged bottoms of the holes, and pour in
molten sulphur.
In figuring lengths of fillers for pins, a clearance of from a
quarter to half an inch should be made, so as to allow for varia-
tion in thickness of eye-bar heads, re-enforcing plates, etc.: such
an allowance will save a good deal of trouble in erection. When
the end lower lateral strut is of such dimensions that it will not
fit, without being turned from the vertical between the flanges
of the batter-brace channels, filling-rings can be used between
the batter-brace webs and the ends of the strut. Such rings
will be necessary, if there be four chord bars in the end panel,
and the outer ones be not let into the channel flanges far enough
to lie against the webs.
In making turn buckles, a little expense can be saved by hav-
ing only one adjusting-end ; the other having a hole, through
which passes one end of the rod, which is enlarged into a head.
One advantage of this style is, that the turn buckle can never
be lost from the rod. Such a turn buckle should always be
used on portal vibration rods, for a reason that will be given in
Chapter XX.
Jaws are not a very desirable detail, although so convenient
that they are often employed. In the first place they have not
a pleasing effect to the eye; and in the second, on account of
the bent plates, are liable to be weaker than might be esti-
mated. If the flanges of the channels be cut away, as is some-
times unavoidable, the jaw plate, from the cut flanges to the
ORD/AWA R P /ROAV HIGH WA Y-BA’/DGE.S. IO5
bend, should be able to resist more compression than the rest
of the strut. Such a detail occurs often on the ends of the
struts which keep the pedestals apart. It is generally difficult
to make a satisfactory design for this member, as it interferes
with the joists; but, with the lower lateral system previously
described, all the difficulty vanishes.
Concerning the proportioning of eye-bar heads, there is a
variety of both opinion and practice. Many specifications call
for a section at the eye equal to one and a half times that of
the bar for welded bars, or one and a third times the same for
hammered eyes, not taking into account the effect which the
different ratios of diameter of pin to width of bar have upon
the strength of the eye. Specifications for the better class
of both railroad and highway bridges have of late made this
distinction ; but there seems to be some uncertainty as to what
is the exact effect of each ratio upon the strength. On p. 20 is
given a table for sizes of chord heads, prepared from actual
experiments by C. Shaler Smith, C.E., who is considered the
best American authority upon all matters connected with
the designing of bridge superstructures. The subject of chord-
head proportioning is further treated in Chapter XVIII.
Bent eyes do not make a very good detail, but are such a
convenience that they are often used by good designers. If
the diameters of the rods do not exceed one inch and three-
fourths, there is no objection to using such eyes. The principal
point to be raised against them is because of the eccentric pull
which they give upon the pin nut. This objection may be
removed by using either extra large nuts, or the detail shown in
the upper lateral rod connection of Plates II. and IV., in which
the bent eyes pull against a piece of channel riveted to the
strut. A still greater improvement is shown on Plate VI., in
which a piece of bent plate is substituted for the channel: this
permits of more rivets in the connection, and avoids the possi-
bility of having to insert a filling-plate between the channel and
the strut.
In connection with this detail, on Plate VI. is another and a
rather peculiar one. The plate, which was originally in the
form of the letter T, is bent so that the stem may be riveted to
IO6 OA’D//VA A' V /A’O/V HAGA/VVA P-BA’/DGE.S.
the strut channels, and the head may afford a bearing for the
vibration-rod pin. This connection is to be used when the lat-
eral strut channels are so small that there is no room for a
pin to pass through the connecting T-plate which attaches
the lower channel. When, because of their large diameter, the
lower lateral rods cannot be attached to the chord pins, but
must be connected by vertical pins passing through the lateral
strut jaws, they must be made to pull on the middle point of
each of the latter pins by using a double eye on one of the rods,
with a space between large enough to admit the eye of the
other rod. This is to avoid all tendency to rotate the lateral
strut about its axis. The rods can be retained in place by fillers
above and below. *
With this detail, there is a tendency to break the jaw through
the pin holes, because of the moment of the longitudinal com-
ponent of the lateral rod stress : the jaw plate must therefore
be made wide enough to properly resist this moment. The
easiest way to proportion the plate is to assume its dimensions,
and to find its resistance to bending, neglecting the area lost
by the pin holes (which area is close to the neutral surface),
and making up for the omission by providing a little extra
resistance.
To illustrate the method, let us take a two-inch lateral rod,
making an angle of forty-five degrees with the planes of the
trusses, and let the distance between centres of pin bearings be
six inches. The stress on such a rod is 3. I4 X 7.5 = 23.55
tons, and the bending-moment on the pin is 3 × 23.55 × 3
= 35.3 inch tons, corresponding (vide Table XII.) to a diame-
ter of three inches and a fourth. The distance from the axis
of the pin to the centre of the jaw bearing will be about
Ig” + 2* + 1" + 3" = 5". The longitudinal component of the
stress on the lateral rod is 2355 × O.7 = 16.5 tons, making
the moment on the jaw about 5 × 16.5 = 82.5 inch tons. The
thickness of the jaw plate should be g", and let us assume the
width to be 7". The resisting-moment is given by the well-
known formula, *
_ R/
M =#.
tº
ORD/AWARY IROM AſſCHWA V–BAE/DGES. Io/
where R = 11.25 tons, I = Hººd" = ſº, x * x (7)*, and d,=}.
Substituting, gives
I I.25 × 13 × 3 × 49 X 7 × 2
7
M = = 115 inch tons, nearly.
The difference between I I 5 and 82.5, or 32.5 inch tons, is greater
than the resisting-moment of the material lost by the pin hole:
so the dimensions assumed are ample.
U-nuts are objectionable in every case; for, if they are made
strong enough to resist without buckling the ultimate pull of
the rods, they will have a very clumsy appearance. The inser-
tion of a cast-iron washer will relieve the bending of the U, but
not the appearance: besides, it is better not to introduce cast-
iron into a wrought-iron structure.
It is now in order to take up the omitted portions of Chap-
ter IX.
First, to find the number and distribution of the rivets in the
flanges of the beam there designed, let us divide the fifteen feet
between centres of supports, as shown in the accompanying
diagram, and calculate the stresses at the points of division.
K 2’6” > K 2/o’’ × 2^o’’ X K I’o’y & I’o’y & 2/o’’ × 2^o’’ X.K 2’6” X

The re-action at each end is about 8.5 tons, and the uniformly
distributed load about O.O944 ton per lineal inch. The moment
at the first point of division from the support is
8.5 × 30 – O.O944 × 30 × 15 = 2f 2.5 inch tons.
At the next point of division the moment is
8.5 × 54 – O.O944 × 54 × 27 = 32 I.3 inch tons,
and at the next point it is
8.5 X 78 – O.O944 X 78 × 39 = 375.8 inch tons.
IO8 ORDIMARY IRON HIGHWA P-BRIDGES.
From the last equation of Appendix II. we have for the value
of the flange stress at any section,
M’
–7—TN.
In this case $
A’ - # × 27 )
P(, + #) {-º- *(· + #) – 36.7.
Dividing each of the moments by 36.7 gives, for the horizontal
stresses at the three points of division, respectively 5.8 tons,
8.74 tons, and Io.24 tons. Therefore, between the centre of
the support and first point of division, there must be enough
rivets to take up a horizontal stress of 5.8 tons; between the
first and second points, enough for a horizontal stress of
8.74 – 5.8 = 2.94 tons; and between the second and third
points, enough for a horizontal stress of IO.24 – 8.74 = I.5 tons.
The vertical pressure upon the rivets of the upper flange is
about 12 X O.O944 = I. I.33 tons per lineal foot, making the total
vertical stresses for the three divisions respectively 2.83 tons,
2.27 tons, and 2.27 tons. Combining these by the parallelogram
of forces with the horizontal stresses last found, gives the total
stresses for each division 6.45 tons, 3.71 tons, and 2.72 tons
respectively.
From Table XXXVI. we find the resisting bending-moment
of a five-eighth inch rivet to be o 18 inch ton, and the working
bearing-pressure on a quarter-inch plate, O.938 ton.
Let us first consider the stress of 6.45 tons. It is equally
divided between the two angles, making the stress on each 3.22
tons. The lever arm of this last stress is ; (4 + #) = **", and
the moment #: X 3.22 = O.906 inch-ton, dividing which by O. 18
gives five as the number of rivets required to resist bending.
Dividing 6.45 by O.938 gives seven as the number required for
bearing. If there be but seven rivets in two feet and a half,
the spacing will be five inches, which would be practically too
great. It is better to space the rivets two and a half inches near
the ends of the beam; and, if it be thought advisable, the distance
may be increased to four or even five inches near the middle.
S =
ORD/AWA R P IROM HAGH WA Y-BRIDGE.S. IO9
From the above, we may conclude that calculating rivet
spacing for flanges of floor beams is, as a rule, too much refine-
ment for highway-bridge designing.
If the depth of the beam be reduced near the ends, or if, by
reason of lack of headway beneath the bridge, shallow beams
be used, it might be well to go through the above investigation.
Next let us make the design for a trussed floor beam, taking
a twenty-foot panel and a twenty-four foot roadway of a bridge
belonging to Class A. Table XIX. gives the weight of an
ordinary built beam for these dimensions as ninety-four pounds
per lineal foot: so let us assume the weight of the trussed beam
to be eighty pounds per foot, also the length of beam between
centres of supports to be twenty-five feet. The live load will
be
24 × 20 × IOO
2OOO
= 24 tons.
Table XV. gives 3339 as the number of feet of pine lumber per
panel, the weight of which is
3339 × 5 e
.*.*... = 4.174 tons;
and the weight of the beam itself is
26 × 8o
2OOO
= I.O4 tons ;
making the total load equal to 29.214, or I. 1686 tons per lineal
foot. Let us use two posts. The central panel should be ten
feet long, and each of the others seven and a half feet. Let us
assume the beam to be a Io" 3O+ I, and the depth of the truss
five and a half feet centre to centre. Then in the formula
” – “... #7 – 2 a.
A + A = ºria + zap – #4
we will have w = 1. 1686, l, - Io, d = #, nearly, C– 5, P=
# X I. 1686 × 17.5 = I0.225, A = 7.5, C = 3, D = 5.5, and A’
about 8 × O.32 = 2.56. Substituting these values gives A + A"
= 3.21 as the area of one flange. The total area of the section
would then be 2 × 3.21 + 2.56 = 8.98 square inches, which cor-
responds almost exactly with the area of a thirty pound I-beam.
I IO OA'ZD/AWA R P ZAZOAV HIGH WA Pi—BR/DGE.S.
The design for the post agrees with that shown in Fig. 16,
Plate II., with the exception that the end diagonals are not
adjustable. The stress on a post is P = IO.225 tons ; that on
the bottom chord is
PA Io.225 × 7.5 g
ſ) T T5.5 = I3.944 tons ;
that on the end diagonals is
Psec 6 = 10.225 × 1.69 = 17.28 tons;
that on the counters is
#5 Psec 6' = o.3 × 10.225 × 2.16 = 6.625 tons.
The intensity for the tension members should be four tons,
making the sections required for the chord bars and main
diagonals respectively 3.48 and 4.32 Square inches. Referring
to Carnegie’s “Pocket-Companion,” p. 94, we find that two
g" × 23” bars will do for the former, and two g” × 24” bars for
the latter. From Table IX. we find that two one and a quarter
inch rods will be required for the counters. -
To the stress on a post must be added the vertical component
of the initial tension on the counters, which is about
2 × 1.5 × 0.46 = 1.38 tons;
making the total stress II.605. Before applying Table XL., we
must multiply this stress by about 1.5, the ratio of the factors
of safety for wind bracing and floor-beam struts; making the
total stress 17.407 tons. Using the column for one fixed and
one hinged end, we find that a 6' 15% I-beam will be required.
To find the thickness of the pin plate at the end of the beam,
let us assume it at five-eighths of an inch; then the lever arm of
the diagonal stress will be $(; + 3) = 3 inch, and the moment,
º = 6.48 inch tons.
# x
Consulting Table XII., we find that the necessary diameter of
pin is two inches and an eighth. Referring to Table XXVI.,
and looking down the column for a two and an eighth inch pin,
we find that the necessary bearing will be, for 8.64 tons, eleven-
sixteenths of an inch. It will be more economical to increase
the diameter of the pin to two inches and three-eighths than
the thickness of the plate to eleven-sixteenths.
ORD/AVA R P WAROM H ZGA WA Pi—BRIDGE.S. III
Next let us find the number of rivets necessary to attach the
plate to the I-beam. The horizontal and vertical components
of the end diagonal stress are respectively
17.28 × O.8 = 13.82 tons
and
I7.28 × O.6 = I.O.37 tons.
The first of these stresses produces bending; and the second,
direct tension on the rivets. The moment of the first stress is
about
13.82 × #(; + #) = 9.5 inch tons,
which, divided by O.493, the resisting-moment for a seven-eighths
inch rivet, found in Table XXXVI., gives twenty as the number
of rivets to resist bending. To resist tension the number re-
quired will be
IO.37
six.6 = 4.
making twenty-four rivets in all for the connection. Seven-
eighths inch rivets are rather large for the flanges of a ten-inch
beam, as there is not room for full heads: nevertheless, it is
better to use them, on account of the increased bending resist-
ance. Using twelve rivets on a side, and spacing them two
inches and a half apart, will make the length of the plate about
thirty-two inches. It is evident that there is no need of figuring
for bearing in this connection.
Next let us proportion the connecting-plate over a post,
assuming the thickness to be three-eighths of an inch, and using
five-eighths inch rivets. The moment on the rivets will be
II.605 × #(; + #) = 5.08 inch tons,
which, divided by O. 18 (the resisting-moment of a five-eighths
inch rivet), gives twenty-eight as the number of rivets required,
or fourteen for each lug. Using staggered rivets spaced two
inches apart will make the depth of each lug about fifteen inches.
The number of rivets necessary for attaching the plate to the
beam is partly dependent on the counter stress, and partly upon
the length of plate which we consider requisite for fixing the
end of the post. About eighteen inches ought to suffice for
II 2 ORD/AWA R P WROM H ZGA WA P-APA’AA)GAE.S.
this purpose. The horizontal component of the counter stress,
including initial tension, is 9.625 X O.89 = 8.566 tons, and its
moment on the rivets is
8,566 × #(§ -- #) = 4.82 inch tons,
which, divided by O.3 II (the resisting-moment for a three-
fourths inch rivet), gives sixteen as the number of rivets
required. Making them staggered, and spacing them two and
a quarter inches apart, would make the length of plate just
twenty inches. *
Let us assume the sections of the re-enforcing plates at the
feet of the posts to be "X 5"; then the lever arm for the chord
stress will be $(; + š) = # inch, and that for the vertical com-
ponent of the end diagonal stress #(; + 3 + 3) = #; making
the horizontal and vertical component moments on the pin
respectively,
# × * = 5.23 inch tons
and 3.
# X Io.225 4.79 inch tons.
2 ,
The resultant moment is
W(5.23)*-- (4.79)*= 7.09 inch tons.
It is evident, that, to obtain the lever arms used, the chord bars
must be packed on the outside and the end diagonals, between
the chord bars and the post. The diameter of pin correspond-
ing to 7.09 inch tons is 24"; but a 24" pin is the smallest that
can be used with a 23" bar. The post bearing is ample, and
needs no testing. -
If we divide the bearing-stress equally between the post and
the re-enforcing plates, there will come upon each of the latter a
stress of 2.9; making a moment upon the rivets equal to #x2.9
= 1.45 inch tons, which, divided by O. 18, gives eight as the num-
ber of five-eighths inch rivets required for each plate. Adding
two for safety, spacing the rivets two inches apart, and allowing
room for the eye-bar heads, will make the length of each re-
enforcing plate about sixteen inches.
ORDINARP IRON HIGHWA P-BRIDGES. II 3
The moment on a counter pin is 4.81 X #(§ + 1}) = 3.91 inch
tons, corresponding to a 14" pin. By examining Table XXVI.,
it will be seen that a 24" pin will be required to give sufficient
bearing.
Referring now to the list of details for a trussed beam, given
on p. 3O, so as to omit nothing, we can make out the bill of iron
as follows : — gº

Upper chord beam I io” 30% I 26' 780%
Lower chord bars. 2 #" 23" 13' 15o “
End diagonals . 4 4” 24” 13' 379 “
Counters . . . . 4 14" G) I 5’ 245 “
Posts . tº e 2 6't 15% I 5.3' 159 “
Connecting-plates . 2 // 14" 3' Io; “
Re-enforcing plates 4. fy 5" I6” 44 “
Pin plates. 2 // 15" 32" 167 “
Stiffeners . 4 2"x24" | 7.3% L 8” 30 “
Pins 2 23" G) Io" 25 “
Pins 2 24” O Io" 2O “
Pins . . 2 24” G) 13” 29 “
Fillers. 4. (3) 2#. each 8 “
Rivet heads . tºº gº wº about 5o “
Total weight of beam . . . . . . . . . . . . . . . 2, 191%
The weight of a plain beam for the same place would be
26 X 94 = 2,444, showing a saving of 253 pounds by using a
trussed beam. At five cents a pound, this would amount to
$12.65; which is considerably more than the cost of the field
riveting, and extra trouble in putting such a beam in place. A
similar investigation for a trussed beam with one post will show
that the weight of such a beam will exceed that of a corre-
sponding plain one: so there would be no economy in such a
design for this case.
II4 OA’ D//WAA’ P /A’O/V HAGH WA Y-BA’/DGE.S.
CHAPTER XIV.
BILLS OF MATERIALS, AND ESTIMATE OF COST.
IN making out bills of materials, the list of members given in
Chapter III. will prove of great assistance. By its use, one can
avoid an underestimate due to an omission of any of the parts
of the structure. A good way to make out a bill of material
is to prepare six vertical columns, in the first of which write
the name of the member; in the second, the number of pieces;
in the third and fourth, the dimensions determining their sec-
tion; in the fifth, their length ; and in the sixth, the weight
of all the pieces, or, if of wood, the number of feet, board meas-
ure, that they contain.
The following examples will serve to explain the method : —
BILL OF WIROUGHT-IRON.

Chord channels I 2 7" Ioğ [ 22' 2,772#.
Batter-brace channels 8 8" | 12# I 33' 9" | 3,375 “
Plate tº e I 4" 12// 262' 2,620 “
Post channels . . . 8 5” 6}# I 22' I, I44 “
Lateral struts 4. 4” 6# [ I5' 360 “
Lateral struts 4. 5" 6}# [ I 5’ 390 “
Main diagonals. . . 8 3” 13." 34' 1,020 “
Counters . 8
3” 3” 35' 525 46
Etc. gº * ſº * e * *
OA'D/AVA R P WA’OAV HIGA WA Y-MR/º/DGES. II 5
BILL OF LUMBER.

Joists . . . . . . . . 55 4” 14” 22' 5,647
Flooring . . . . . . . I Io 3" I2// I4' 4,620
Hand-rail caps . . . . . 20 21/ 6// 22' 44O
Hand-rail posts. . . . 30 4" 6” 4' 240
Hub planks . e 2 2// I 2// I Io' 44O
Felly planks. 2 6// 6// II 2' 672
Lateral struts . . 3 8// 8// 14' 224
Total number of feet, board measure . . . . . . . . . I2,283
It is to be noticed that it is often convenient, as in the case
of the “Plate” in the “Bill of Wrought-Iron,” or that of the
“Hub planks” in the “Bill of Lumber,” to combine several
lengths in one.
To the length of each chord bar, main diagonal, and hip ver.
tical is to be added three feet to allow for the weight of the
heads; and to that of each adjustable rod about five feet, for
the heads, upset ends, and sleeve nuts or turn buckles. Should
greater accuracy be required for the weight of an adjustable
rod, it will be necessary to ascertain what length will be needed
at each end for the heads, and how much for the upset ends
and adjusting-nuts by the following
TABLE OF EQUIVALENT LENGTHS OF RODS FOR UPSET ENDS,
NUTS, SLEEVE NUTS, AND TURN BUCKLES.

3" — 1" I upset end and I nut 14 feet of rod
I s”— 13" I upset end and I nut 13 feet of rod
I º'—2" I upset end and I nut 13 feet of rod
2}" —2}" I upset end and I nut I tº feet of rod
3" — 13" 2 upset ends and I sleeve nut 23 feet of rod
I #"—2}” 2 upset ends and I turn buckle 3 feet of rod
These equivalent lengths do not include the lengths of the
upset ends themselves: they represent simply the extra lengths
to be added to the bar to equalize the weight of the nuts,
sleeve nuts, or turn buckles, and the extra iron for enlarging
the ends, which are six or eight inches long.
II6 O/PD/AVA R Y NA’OAV HIGH WA Y-ARA'ZZOGAES.
It is not necessary in a preliminary estimate to find the exact
quantities of materials, so approximations to actual dimensions
can be made. This will be fully illustrated in Chapter XVI.
Before considering a bill of material as finished, it is well
to look it over to see that no mistake has been made in the
number of the pieces. It is not an uncommon error to put
down only half the correct number.
As soon as the bills of iron and lumber are made out and
checked, the dead load per foot should be calculated, to see
if it agree with the one assumed within the limit specified on
p. 6.
Estimates of cost should be liberal; for, as a rule, the actual
profits on bridges fall short of the amounts estimated. They
can be made very readily by using a blank similar to the fol.
lowing:—
Aſsºmate on.…- Bridge across
Length span, .......... ft. Height, ........... ft. Clear Roadway, ......... ft.
Static Load £er Zºneal ft., ........... lbs. Moving Load per lineal
ft., . . . lbs. AVo. Pane/s, ............. Length Panels, ... ... ft.
Wrought-iron, Zös. ..................... (3) . . . . $ Cts.
Cast-iron, /0s. . . ~~~~ (a).
Azemzóer, J7. ~~ @ .
Piles, J7. ~~~~~ @ .
Aſauºng, ..…. loads (3).
Areight . . . . . . . . . . . .
Framing.

Aaſsezvoz7% . . . . . .
Erection . . . . . . . . . .
Søðes . . . . . . . . . .
Painting. tº e g º O ſº ſº º
Blacksmithing. . . . . . . . . . .
Coal . . . . . . . . . . . . . .
Freight on tools . . . . . . . . .
Travelling expenses . . . . . .
Men's time travelling . . . . . . .
Aidding expenses . . . . . . . . .
Teaming during construction . .
Incidentals . . . . . . . . . . . .
Total cost of bridge . . . . . . . . .
Cost £er lineal foot . . . . . . . . .
OA’D/AVA R P /ROAV HIGH WA P-/3/ē/DGE.S. 117
On fair country roads, a load for a team of horses may be
taken to be a ton and a half of iron, a thousand feet of pine
lumber, or six hundred feet of oak lumber.
The designing of falsework will be treated in Chapter XX.
Its cost will include that of the piles in place, if any be required,
and that of the lumber, to which should be added about three
dollars per thousand for framing and raising, and a dollar or
more per thousand for taking down. Falsework timber can
generally be sold for something when the bridge is completed : *
so a reduction may be made in its cost when the estimate is to
be a close one.
The cost of erection can be found approximately for ordinary
conditions from Table XXXVIII., by multiplying the number
of days' labor there given by the average rate of wages for ordi-
nary bridge hands. It must not be forgotten that there is a
great variation in the cost of erection ; for it depends upon the
locality, weather, skill of laborers, efficiency of foreman, etc.
Those who feel inclined to question the correctness of this
table should make some allowance for the difficulty which the
author has experienced in getting any data whatsoever upon
the subject. Few bridge engineers care to part with the
knowledge which has cost them both time and money.
In regard to cost of painting, the same difficulty has been
encountered : so, for lack of more accurate data, the following
table will have to suffice. It has been prepared from a few
figures of cost of painting, obtained at a time when wages were
a dollar and a half a day.

SPAN. 12" roadway. 16 roadway 20 roadway, 24' roadway,
5o' $6.oo $7 oo $9.00 $1 I.oo
Ioo' 22.OO 25.OO 28.oo 31.OO
15o' wº 45.OO 5 I.OO 57.OO
2Oo' º 8o.oo 90.OO IOO.OO
25o' * - I25.OO I4O.OO I 55.OO
3oo' º - I7o.oo I90.OO
Before making an estimate on a bridge, one should endeavor
to obtain as many as possible of the following -
II 8 ORD/LVA A' V /A’OAV HIGH WA Y-BA’/DGE.S.
DATA FOR DESIGNING IRON HIGHWAY-BRIDGE SUPERSTRUCTURES,
AND EST IMATING THEIR COST.
Class of bridge required.
Length of span or spans.
Width of clear roadway.
Headway required in clear above floor.
Live load, if different from the ordinary.
Wind pressure per square foot, if different from the ordinary.
Any extraordinary load, such as paved flooring, heavy falls of
Snow, etc.
The velocity of passing loads.
Distance of bridge site from nearest railway-station or sea-
port.
Quality and condition of the roads between these places.
Nature of bed of river, and velocity of stream.
Height of lower chord above bed of river.
Cross section of stream at crossing, showing borings, if any
have been made.
Angle which the direction of bridge makes with axes of piers
or abutments.
Nature of the country at the site. º
Any special difficulty that may be anticipated for the raising.
Kind of falsework it would be advisable to use.
Cost of piles at various places in the neighborhood, if any be
required.
Cost of transport of same to site.
Cost of timber per thousand for falsework.
Probable value of falsework timber after bridge is finished.
Cost of withdrawing piles, if necessary.
Number of lineal feet of piles required.
Number of feet of lumber for falsework.
Cost of spikes, bolts, and nails for falsework.
Cost of driving piles.
Cost of transporting pile-driver to and from site.
Common laborer's wages.
Skilled laborer's wages.
Foreman's wages.
Wages for team and teamster.
ORD/AVA R P IROM HIGH WA Y-B/º/DGE.S. I IQ
Cost of superintendence by engineer or engineers.
Number of days' teaming on work.
Date when bridge must be finished.
Probable length of time it will take to raise and complete
bridge.
Chances of fair or foul weather during this time.
Chances of having falsework carried away by a sudden rise or
an ice-gorge.
Chances of a scarcity of laborers.
Chances of sickness among laborers.
Expenses attendant on same.
Cost of tents or other housing for laborers, if any.
Cost of iron at mill or foundry.
Cost of transport of same to nearest railway-station or sea-
port.
Cost of lumber per thousand at mill or market.
Cost of transport of same to nearest railway-station or sea-
port.
Probable expenses for blacksmithing and coal.
Cost of tools, if it be necessary to buy special ones.
Wear and tear of plant, and loss of tools.
Loss of bolts and timber.
Actual cost of raising similar structures under similar circum-
StanceS.
Travelling expenses of employees to and from site.
Bidding expenses, if any.
Office expenses in preparing plans, etc.”
Advisable allowance for contingencies.
* This is usually not considered, as it is a constant expense, and comes out of the annual
gross profits of the company.
I2O O/º/O/AWA R Y /ROAV HIGH WA P-B/CIDGE.S.
CHAPTER XV.
ECONOMY.
THE first point to be considered, when deciding upon the
style of bridge for a certain stream crossing, is the number of
spans. It is, in reality, a consideration of economy which
determines this ; for the best bridge to build, provided that the
water-way be not too much contracted, is the one for which
the sum of the cost of superstructure and the cost of founda-
tions is a minimum. If the water-way be too much interrupted,
the design would not be an economical one, even if its first cost
were the least, because of the risk of washout to which the
bridge would always be subject.
In most cases, there is not much choice concerning the num-
ber of spans, local considerations often determining it; but there
is occasionally a choice between two or even three numbers.
The only way, then, to decide is to make a rough estimate of the
cost of the superstructure and the foundations for each number;
then, if the choice fall about equally between two numbers, it is
better nearly always to adopt the longer spans, because the
actual expense for the foundations usually exceeds the amount
of the preliminary estimate.
Another preliminary point to be settled is whether it would
be most economical to build an iron, a combination, or a wooden
bridge. Although this work treats of iron bridges only, still
this is a point which ought to be considered.
The following mathematical treatment of the problem was
given by the late Ashbel Welsh, C.E., past president of the
American Society of Civil Engineers : —
ORDVAWA R V /A'O/V HIGH WA P-AE/?/DGE.S. I2 I
TO FIND THE COMPARATIVE ECONOMY OF TWO BRIDGES OF DIF-
FERENT COST AND DURABILITY, THAT WILL ANSWER THE SAME
PURPOSE EQUALLY WELL WHILE THEY LAST.
‘Let C be the cost and assumed real value of one of them, T
the time it will last, a the compound interest on one dollar for
that time, at whatever rate money is worth to the party paying
for the bridge, and L the loss on the bridge at the end of the
time T, or the amount which it would take to make it as good
as new. Let R be the real value of the other bridge, C' its cost,
7" its duration, aſ the compound interest on one dollar for that
time, and L’ the loss on the bridge at the end of the time T',
or the amount required to make it as good as new. And let V be
the real value of the bridge that would last forever if all cir.
cumstances should remain constant.
‘Now, supposing that the money required for building had
been borrowed for an indefinite time, the actual expense at the
end of the time T to the party paying for the bridge which
would last forever would be a l’; and the actual expense at the
end of the same time for the first bridge, after making it as
good as new, would be a C+ L. These two quantities are
equal : therefore the hitherto unknown value of Vis
c +4.
(Z
‘Similarly, at the end of the time T', the expense for the
bridge which would last forever would be a' l’; and that for
the second bridge, after making it as good as new, if the cost
had been the real value R, would be aſ R + L'. As before, these
two values are equal; and therefore,
A.'
V= A + i.
Equating the two values of V gives
A. A.”
and
J. C'
R = C++ -ā.
I 22 OA’D/ATA A' V ZA’O/V HIGH WA Y-BA’/DG E.S.
Now, if the value thus found for R be greater than the cost C",
the second bridge is more economical than the first; while, if it
be less, the first bridge will be the more economical.’
The next economic consideration is that of depth of truss,
Upon this subject much has been written, and many investiga-
tions have been made; the general conclusion being, that the
depth should be from one-seventh to one-tenth of the span:
some English writers say from one-tenth to one-fourteenth of
the span ; while only one, as far as the author knows, – Benja-
min Baker, C.E., in his treatise on “Beams, Columns, and
Arches,” — makes it from one fifth to one-seventh of the span.
Such investigations being purely mathematical, and involving
the use of the differential calculus, are of little practical value,
as they cannot take into account the numerous variables that
ought to be considered. Not only do the stresses in a truss
vary with the depth, but also the intensities of working-stress
in the compression members. These, again, vary with the
number of panels; and this variation is according to a law or
laws altogether too complicated to be handled by the calculus.
Again : the intensity of working-stress varies, or should vary,
according to the position and importance of the member.
In view of the complexity of the question, and wishing to
determine the most economic depths for Pratt and Whipple
trusses, the author, about a year ago, undertook to solve the
problem in a practical manner by assuming the most common
clear roadway (sixteen feet), and figuring out a number of dia.
grams of stresses, and bills of materials. At first he considered
that it would be necessary to calculate the total actual cost
for every case, but upon further investigation found that it
would be sufficient to figure out the sections and weights per
lineal foot of the different members of one truss, multiply these
by their respective lengths, and sum up the products, neglect-
ing all consideration of details, because the differences in the
weights of the latter balance each other. Thus, if the depth of
a truss be increased by one foot, there would be a little increase
in the weights of the lattice bars and rivets and a decrease in
that of the pins and eye-bar heads. These may be taken as
balancing each other, without making any appreciable error.
ORD/AVA R V ZAZOAV Aſ/GA/MVA P-AE/º/Z)GAE.S. I23
The most economic length of panel was at the same time
investigated, and was determined, without preparing complete
bills of materials, by considering only those portions of the
structure which are affected by the variation in the number of
panels.
Economy in pony trusses is an element which ought seldom
to influence the design, for a good bridge of this kind will gen-
erally require more iron than the ordinary calculations demand.
Instead of trying to avoid a little expense, regard should be
paid to obtaining a good distribution of plenty of material, in
order to partly compensate for the lack of rigidity which is
characteristic of the pony truss. In very wide pony-truss
bridges, especially when the length of span approaches its
superior economic limit, it might be well to make a few calcula-
tions concerning the economic depth; but the number of panels
should be regulated by the slope of the batter braces, which
should never be less than two and a quarter horizontal to one
vertical.
The superior economic limit of the pony truss is not a fixed
quantity, but decreases as the width of the bridge and the load
increase, and as the intensities of working stresses diminish.
For example, comparing a pony truss and a through bridge of
sixty-five feet span in four panels, sixteen feet clear roadway,
designed according to Class C, there is found a difference of
three hundred pounds of iron in favor of the pony truss; while
with the same span, for a twenty-foot clear roadway, and bridge
designed according to Class A, there is a difference of eleven
hundred and fifty pounds of iron in favor of the through bridge.
For a clear roadway of twelve feet, the superior economic limit
of the pony truss would reach as high as seventy-five feet; and,
for very wide bridges, the inferior economic limit of the through
bridge would reach as low as fifty-five feet : but, on account of
rigidity, the superior limit of the former may be placed at sixty-
five feet; and, on account of appearance, the inferior limit of the
latter at the same length.
After making out diagrams of stresses, and bills of materials,
for over one hundred spans, the author came to the following
conclusions : —
I24 ORD/AVA R Y IROM HIGH WA Pi—BRIDGES.
That if the economic depth be calculated for any span, where
the panel length is twenty feet, or the nearest length below
twenty feet, and if the economic depth for the same span, but
with one panel less, be calculated, the latter will exceed the
former by one or two feet.
That, in places where lumber is expensive, it will not be well
to make panels over twenty feet long, or, in places where it is
cheap, to make them over twenty-four feet long, because tim-
bers exceeding the latter length are not easily procured. Then,
too, in designing iron bridges, which are supposed to last indefi-
nitely, it must be remembered, that, as time goes on, long
timbers will become more and more expensive, and less easily
procurable, even in timber districts; so that panels exceeding
twenty feet in length should be employed very cautiously.
For appearance, through spans of one hundred feet and under
should have five panels.
The principal objections to the use of the double intersection
for short spans are, that, as the rods are long and slender, they
will vibrate more than the shorter and larger ones of the single
intersection. Any flaw in a small rod will have a proportion-
ately greater injurious effect than the same sized flaw in a larger
rod. Long and slender rods are difficult to transport, and are
liable to become twisted and bent; though this objection can
be partially removed by halving them, and, as the posts are
light, they will spring more under the shock of rapidly moving
loads.
As the width of roadway and the live load increase, and as
the intensities of working-stresses diminish, the inferior limit
of the double intersection may be lowered. The table on p. 8
gives the limits which the author would recommend.
The common idea among highway-bridge builders, that a
double-intersection bridge should, for economy's sake, have more
panels than a single-intersection bridge of the same span and
loading, is incorrect. -
The economic depth for a double-intersection truss is about
three feet greater than that for a single-intersection truss of
the same span, and number of panels.
Tables IV. and V. give the principal results of the before-
ORD/AWA R P /ROM HIGH WA Pi—BRIDGE.S. I 25
mentioned investigations. The first is the one to be ordinarily
used: the second may be employed for districts where the tim-
ber is large and plentiful.
There seems to be an unfounded prejudice in the minds of
county commissioners and bridge supervisors against long pan-
els. Practically they make a better bridge than do short panels;
for the members are fewer and larger, and therefore less affected
by flaws, besides less subject to vibration, and less liable to
inaccuracy of construction. The floor beams and joists being
larger, there is less probability of often receiving their maximum
working-loads. The only real objection to long panels is the
extra cost of the joist timbers when they are to be replaced.
In addition to what precedes, the following general economic
considerations should always receive attention.
Field riveting should be avoided as much as possible, and
designs should be made so that all the parts will come together
readily during erection.
Rivets should be spaced with regularity, so as to facilitate
the punching of the holes by riveting machines.
It is generally better, in through bridges, to pack all but the
end chord bars outside of the posts, and reduce the width of
top chord plate to a minimum. d
It is not always better to employ the apparently most economi-
cal depth of channels. For instance, if there be a choice of
using ten or twelve inch channels for the top chords and batter
braces, and if the sections alone would indicate a saving of say
three hundred pounds of iron by the use of the twelve-inch
channels, the others would be more economical ; for the twelve-
inch channels require larger stay plates, lattice bars, and
re-enforcing plates, besides a wider top chord plate, which would
increase the weights of the cover plates, chord pins, post lat-
ticing, post stay plates, shoe plates, etc., and even add a little
to the lengths of the floor beams. -
I26 ORDIAWA R Y IROM HIGH WA Y-BRIDGE.S.
CHAPTER XVI.
COMPLETE DESIGN FOR A BRIDGE.
LET the bridge to be designed have a span of one hundred
and sixty feet, and a clear roadway of fourteen feet with no
sidewalks, and let it belong to Class A. Referring to the table
on p. 8, we see that the trusses should be of single intersec-
tion. On p. 5 we find that the live load should be eighty
pounds per square foot of floor, which corresponds to eleven
hundred and twenty pounds per lineal foot of bridge.
Table I. gives the dead load as seven hundred and forty-two
pounds per lineal foot, say seven hundred and forty pounds.
Table IV. gives eight for the number of panels, and twenty-
four feet for the economic depth.
The diagonal upon 20 and 24 is 31.24, which divided by 24
gives I.3 for the secant; and 20 divided by 24 gives O.833 for
the tangent. -
The panel live load, w, is equal to
II 2 O X 2 O
- 2 OOO
I
2. = 5.6 tons.
The panel dead load, W., is equal to
74O X 20
# X 2000 = 3.7 tonS.
Let us assume that about a third of this is concentrated at
the upper panel point, making gº
W = 1.2 tons.
The sum of the live and dead panel loads, or W’’, is
5.6 + 3.7 = 9.3 tons.
OA’D/AVA R V ZAZOAV HIGH WA P-BR/DGAE.S. I27
One-eighth of w is o.7 ton, which multiplied by 1.3 gives
O.91 ton. Y.
The panel dead load multiplied by the secant is
3.7 × 1.3 = 4.81 tons.
W" multiplied by the tangent is
9.3 × O.833 = 7.747 tons. tº
The following table of data can now be written: —
72 = 8 - W" = 9.3
2 = 20 i W = 1.2
d = 24 .#20 = O.7
diag. = 31.24 #20 sec 6 = O.91
sec 6 = 1.3 W, sec 6 = 4.81
tan 6 = O.833 # W, sec 6 = 2.405
z0 = 5.6 - W” tan 6 = 7.747
W = 3.7 # W’’ tan 6 = 3.873
# W = 1.85 -
Next let us draw the skeleton diagram shown on Plate V.,
and number the panel points, commencing with zero at the right-
hand end. -
First let us find the stresses in the diagonals, using Table XLI.
The stress in the counter at the point 2 is -
#w sec 6 — #W, sec 6 = 3 × og I – 3 × 2.405,
a negative quantity, which shows that there is no stress on this
member. Let us mark it zero on the diagram.
The stress in the counter at the point 3 is
§w sec 6–3, W, sec 6 = 6 × og1 – 2.405 = 3.055.
Let us mark this and all succeeding stresses on the diagram.
The stress in the main diagonal at the point 4 is
*w-sec 0 + $ W, sec 6 = Io x o.91 + 2.405 = 11.505.
That in the next main diagonal is
lºw sec 6 + #W, sec 6 = 15 × 0.91 + 3 × 2.405 = 20.865.
I 28 OA’D/AWAA’ P ZAZOAV HIGH WA P-B RAZ)GE.S.
That in the end main diagonal is
*w sec 6 + 3 W, sec 6 = 2 I X o.91 + 5 × 2.405 = 31.135.
That in the batter brace is
*w sec 6 + 3 W, sec 6 = 28 × o.91 + 7 × 2.405 = 42.315.
That in the middle post is
§w – # W. -- W = 6 × o.7 — 1.85 + 1.2 = 3.55.
That in the next post is
*w -- # W. -- W’ = Io X o.7 -- 1.85 + 1.2 = Io.os.
That in the next is
*św + #W -- W = 15 × o.7 -- 3 × 1.85 + 1.2 = 17.25.
The stress in the top chord at the panel next to the centre is
g W" x ; — (1 + 2 + 3) w"; = 8 W’’ tan 6 = 61.976.
That in the next panel is
(8 – 3) W’’ tan 6 = 74 W’’ tan 6 = 58.103.
That in the next is
(74 – 1%) W" tan 6 = 6 W’’ tan 6 = 46,482. “
\
That in the lower chord at the panel next to the centre is the
same numerically as that in the top chord at the second panel
from the centre; viz., -
7% W’’ tan 6 = 58.103.
Similarly, that in the next panel of the lower chord is
6 W’’ tan 6 = 46.482.
That in the remaining panels is
(6 – 2%) W" tan 6 = 3% W" tan 6 = 27.114.
QRDINARY IRON HIGHWA V-BRIDGES. I29
A check by moments about the hip gives the stress in the
lower chord at the end panel 34 Wºtan 0, which shows that
the chord stresses are all right.
Next let us determine if any stiffening be required in the
end panels.
An examination of Table XXV. shows that the diameter of
the end lower lateral rod is one and eleven-sixteenths inches.
Consulting Table IX., we find that the greatest working-stress
that can ever come upon such a rod, including the initial ten-
sion, is
I4.399 + 2.375 = 16.774 tons.
The cosine of the angle which the rod makes with the planes
of the trusses is about O.8: therefore the component of its stress
in the direction of the chord is
I6.774 X o.8 = 13.419.
Referring to Appendix I., we see that it will be necessary to
assume values for Al, h, and c, in order to find the reduced dead
load W. From previous experience these values may be taken
as follows: A1 = IO, h = 9, and c = I, making
3O X IO X 9
W. = 37o — I5
= 190 pounds.
The reduced panel dead load will therefore be
I90 × 20
= I.Q. tons
2OOO 9 3.
and the stress on the end panel of the windward lower chord,
when the structure is subjected to a wind pressure of thirty
pounds per square foot of surface, will be
3% W, tan 6 = 4 × 1.9 × o.833 = 5.54 tons,
showing that stiffening is decidedly needed. This result could
have been predicted with certainty from what was stated in
Chapter IV. concerning Table I.
Next let us find the sections required for the tension mem-
bers.
I3O OA’D/AWA A' P //&O/V HIGH WA Y-BA’/DGAE.S. .
Dividing the stress in the counter at the point 3 by 2 gives
1.528; then, looking down the column marked “Intensity of
Working-stress = 4 tons,” we find the nearest number to be
the one corresponding to a diameter of seven-eighths of an inch:
so we will use two seven-eighth inch rods for this place. In
reality there is no counter needed in the third panel; but it will
be as well to use a single three-quarter inch rod there to aid in
adjusting the trusses, and to take up the shock of passing loads.
The intensities of working-stress for the main diagonal are
44, 43, and 5 tons. Dividing these into the respective stresses,
we find the sections required as marked on the diagram.
As the lower chords at the first and second panels are to be
stiffened, the intensity of working-stress for the inner bars at
these places will be 4 tons: the intensity for the rest of the
chords will be 5 tons. Dividing these intensities into the
stresses will give the sections required, which are marked on
the diagram. The section for the first and second panels was
obtained by supposing that there are four bars of equal size
used there; so that the average intensity is 4% tons.
These two trussed bars of the end panel will not be strong
enough to resist the difference between the compressive stress
of 13.42 tons and the tensile stress of 5.54 tons or 7.88 tons: so
we will have to use an I-beam between them, the trussing-bars
being attached to the web. This is a more economical arrange-
ment than two channels laced or latticed. Let us try a 4" I.
Consulting Table XL., we see that for two round ends the
strength of a 4” Io; I is 5 tons, because it is held by the truss-
ing from lateral deflection. Subtracting this from 7.88 leaves
2.88 tons to be resisted by the two bars, or O.88 ton per square
inch, which (vide Table XI.) is by no means excessive.
The stress in the top chord is probably so great that the
minimum width of top plate will determine the packing of
the bottom chord; so that the next step will be the proportion-
ing of the top chord.
Let us take first the stress, 58. IO3, and try nine-inch chan-
nels, which will give 263 as the ratio of length to least diameter.
Referring to Table X. for both ends fixed, we find 3.226 for 26}
diameters, so may use 3.222, which, divided into 58. IO3, gives
ORD/AWA R Y IROM HIGH WA Y-BR/DGE.S. I 3 I
18.03 square inches. From p. 15 we find that the minimum
size of top plate for nine-inch channels is #" X II.", corre-
sponding to an area of 3.59 square inches. Subtracting this
from 18.03, and dividing the remainder by 2, gives 7.22 Square
inches for the area of one channel, which corresponds to a
weight per foot of 24.07 pounds." Referring to Carnegie's
“Pocket-Companion,” p. 65, we find that nine-inch channels
vary in weight from eighteen to thirty pounds per foot; so the
nine-inch channels required will be procurable. This calcula-
tion is not final, for it is not improbable that ten-inch channels
will be found more economical.
The best way to settle the point is to ascertain the average
weight per foot of chord for both cases. Dividing, then, 46.482
and 61,976 by 3.222, subtracting 3.59 from each quotient, mul-
tiplying the remainders by IO, and dividing by 6, gives 18.07
and 26.08 as the weights of the channel bars for the second and
fourth panels; which weights are both procurable. The average
of the three sections will therefore be I7.23 square inches, cor-
responding to a weight per foot of 57.43 pounds.
If we employ ten-inch channels, the ratio of length to least
diameter will be 24, for which Table X. gives 3.369 as the in-
tensity of working-stress. Dividing this into each of the three
stresses gives 18.40, 17.25, and I3.80 as the sections required.
The minimum size of top plate (see p. 15) is #"X 123", cor-
responding to an area of 391 square inches. Subtracting this
from 13.80, and multiplying the remainder by '9, gives 16.48
pounds per foot as the weight of the channels in the end panels
of the top chord; but the lightest ten-inch channel procurable
(see Carnegie, p. 64) weighs seventeen and a half pounds per
foot : therefore the area of the section will have to be 14.41
square inches. .#
The average of the three sections will be 16.69 square inches,
corresponding to a weight of 55.63 pounds per lineal foot. The
difference between 57.43 and 55.63 is 1.8, which, multiplied by
* The reader may have forgotten that a bar of iron one square inch in cross-section and
three feet long weighs exactly ten pounds: consequently, when the area of a section is given
in square inches, multiply by ten, and divide by three, to find the weight per foot; and when
the weight per foot is given, multiply by three, and divide by ten, in order to find the area.
I 32 . O/P/D/AVA R P /ROA'ſ HZGA WA Y-B/C/DGAE.S.
240, the total length in feet of the two top chords, gives 432
pounds as the apparent saving of iron in the chords by using
ten-inch channels: to this must be added the saving in the
batter braces, which could be calculated in the same way. It
is, however, unnecessary to make this calculation; for we can
see, that, all things considered, it is better to adopt the ten-inch
channels.
The sections and weights of the top chord panels are now to
be entered on the diagram.
It is about time to look to the bottom chord packing, and see
if there be sufficient room inside the posts for the diagonals
and beam hangers; but we must first proportion the diagonals as
marked on the diagram by means of the table on pp. 94, 95, of
Carnegie's “Pocket-Companion,” and the hangers by referring
to Table XXII, which shows that $" square bars will be required,
square bars being adopted because there will be very little room
to spare inside the posts. Referring to Table XXVIII., we find
the width of flange for a 10" 24, 15% channel to be 2.63 inches.
Doubling this, and subtracting the product from the width of
plate, leaves 7.24 inches for the width between channels. The
thickness of the inner splice plate will be about seven-sixteenths
of an inch; doubling which, adding an eighth of an inch for
play, and subtracting the sum from 7.24, will leave 6.24 as the
distance between inner faces of post channels. The thickness
of each inner re-enforcing plate at the foot of a post cannot
exceed half an inch, which would leave 5.24 inches for packing
the diagonals and hangers. For the second and fourth panel
points this will be sufficient; but at the third there would be
room enough to let the counters in, and not enough to permit
of turning up the sleeve nuts. We can either substitute a single
counter, or widen the chord plate. The former will be prefera-
ble, as the counter stresses do not affect the sizes of the bottom
chord pins, and the central pin of the upper chord should have
an excess of strength in any case.
From Table IX. we find that the size of the counter required
will be 1+'s" square.
Next let us proportion the batter brace. The ratio of length
to least diameter is about 37}, for which Table X. gives 2.639
OA’D/AWAA’ P ZAZOAV HZGA/MVA V-E /º/Z)CA.S. I33
as the intensity of working-stress, which divided into 42.315
gives 16.03 as the section required. Subtracting 3.91, and mul-
tiplying the remainder by *, gives 20.2 pounds per foot as the
weight of each channel of the batter brace.
Next let us proportion the posts. We see immediately, from
the small stress in the centre post, that its section will be the
smallest ever used, viz., that of 5" 7# channels (vide p. 8): so
there is no need of calculating the section required. Let us
assume six-inch channels for the next post: the number of
diameters will then be forty-eight, and the intensity for two
hinged ends I.335. which, divided into IO.O5, gives 7.53 square
inches, corresponding to two 12 55-pound channels. These are
not so economical as seven-inch channels: so we will try the
latter. The ratio is 41%, and the corresponding intensity I.656,
which divided into IO.O5 gives 6 oz square inches, correspond-
ing to channels weighing Io. I2 pounds per foot. The smallest
procurable seven-inch channels weigh IO.5 pounds per foot,
which size we will therefore adopt.
Let us assume nine-inch channels for the next post, making
the ratio 32, and the intensity 2, 193, which divided into 17.25
gives 7.86 square inches, corresponding to channels each weigh-
ing I 3. I pounds per foot. As the lightest nine-inch channels
weigh 14.5 pounds per foot, it will be necessary to employ
these, unless eight-inch channels be more economical. Let us
try. The ratio is now 36, and the intensity 1.937; making the
area 8.91, and the weight of one channel I4.85 pounds per foot,
On account of the 'smaller sizes of lattice bars and stay plates.
the eight-inch channels will prove more economical, in spite of
their larger section : so we will adopt them.
Next let us proportion the bottom chord, recollecting, that, in
the two end panels, an allowance must be made for one rivet
hole in each inner bar, the rivets being half an inch in diameter.
It is to be noticed that the proportion of width to depth of
chord-bars in the centre panels is about one to five, because
there are four bars in a panel, and that the depth of the end
panel bars approaches the limit for stiffened bars.
From Table VI. we find the size of the hip verticals to be
IH's" square.
I 34 O/º/)//VA R P /ROAV HIGH WA P-BA’/DGES.
Next let us determine the sizes of the pins.
If we take the average thickness of one chord bar at the
centre of the span to be ##", we make a little allowance for
accidental thickening of the heads.
Substituting in the formula given on p. 85, viz.,
M = Zw,
2 $
we find the moment to be 23.56 inch tons, and, referring to
Table XII., determine the size of the pin to be 34". The least
allowable diameter of pin for a 33” bar is 3.75 × 0.8 = 3”: so
we will use 34" pins for the five middle panel points of the
bottom chords. The chord bars of the end panels being neces.
sarily out of proportion, we have to use at the pedestals and
first panel points pins 23" in diameter, the smallest that can
be used with bars 34” deep. It may be well to check the
size of these pins. The horizontal component of the moment
º . . . I . . 27. I º
on the pin at the first panel point is 2 £7.5 - 6.8 inch tons,
nearly. The stress in one hip vertical is equal to one-half of the
section required, as given in Table VI., multiplied by the inten-
sity of working-stress for hip verticals, or 4 × 2. I4 × 4 = 4.28
tons. This may be assumed without appreciable error as the
load on a hanger. The sum of the thicknesses of a hip vertical
and a hanger is almost 2 inches, making the lever arm I inch,
and the moment, about 4.3 inch tons. The total moment is,
therefore, V(6.8)*-F(4.3)” = 8 inch tons, which corresponds to a
2}" pin; so that the diameter previously determined is ample.
Next let us find the size of the hip pin. From the formula
on p. 86, and Table XXVIII., we find that the approximate
thickness of the bearing is about
T 4.4
2 X IO
+ O.3 = 1.02", say I".
The lever arm for the diagonal stress will be ##", say I", and,
for the hip-vertical stress, g” + 3 (1" + It's") = about 2", and the
corresponding moments respectively, I5.6 and 2 × 4.28 = 8.6
inch-tons. Laying out these moments in their respective direc-
tions, we find the resultant moment to be about 22.7 inch tons,
ORD/AVA R P IROAV HIGH WA Y-B/C/DGE.S. I35
which corresponds to a diameter of 34". The resultant of the
stress on one end diagonal and one hip vertical, found by dia-
gram, is about 19 tons. Looking in Table XXVI., we find that
a bearing of I" is sufficient.
Next let us find the size of the next chord pin from the hip.
From the formula on p. 86, and Table XXVIII., we find that
the approximate thickness of the chord bearing is
I7.25 gºsº gº
2 × Io + O.45 = 1.31 inches,
and that of the post bearing (p. 87),
º = I.II inches.
Allowing a little for play, the lever arms for the vertical and
horizontal components of the stress on a diagonal are respec-
tively I" and 2+": the components found by diagram are about
8 tons and 6.7 tons respectively, making the moments 8 inch
tons and I 5. I inch tons, the resultant of which is 17. I inch tons,
corresponding to a diameter of 24”. This is large enough for
a three-inch bar. There is no need of testing for bearing. A
similar investigation for the next panel point shows that a 24" pin
will be required, which size will also be used for the central pin.
By referring to Table XXV., we can write upon the diagram
the sizes of all the lateral and vibration rods and the sections
of the upper lateral, portal, and intermediate struts. It will be
sufficient to write the sizes of post vibration rods and interme-
diate struts on one post only, as they are of the same dimen-
sions throughout the bridge.
From p. 54 we take the formula
2% — I
C. =
witzeo,0++w-(º- )
4. 4.
to find the stress on the end lower lateral strut between expand-
ing pedestals. Here -
72 = 8 - w = 7.5 × 3° 2 * =
I = 2.375 (see p. Io) . *: 2OOO = 2.25
cos 6 = º: X 74O w = ** *...* 29 O.75
W= *** = 59.2
2OOO
I36 ORD/AWA R P IROM HIGH WA P-BRIDGES.
and V (vide Appendix I) = one-half the length of span multi-
plied by the release of pressure per lineal foot on the windward
trusS, Or
80 × 30 × Io X 9
I5 X 2000
= 7.2 tons.
Substituting these values gives C. = 9.2 tons. Assuming four-
inch channels, the ratio of length to least diameter will be 42,
for which, with one fixed and one hinged end, Table XI°gives
an intensity of 2.245: therefore the section required is 4. I
square inches, corresponding to two 6.83% channels. " It will
be more convenient for riveting to use 5" 7# channels. At the
fixed end of the span a 5" IO#I will answer for a strut between
pedestals. -
We are now ready to proceed with the “Bill of Iron,” in
making which, close approximations of lengths are allowable.
Let us prepare the blank form recommended in Chapter
XIV., then turn to the list of members given in Chapter III.,
and fill out the form, proportioning as we go any details whose
sizes have not been previously determined. The filling-out of
the part denominated “Main Portions” is a very simple matter,
and needs but little explanation. It is to be noticed that the
lengths of the chord bars and main diagonals have been in-
creased by three feet to allow for the weights of the heads, and
those of all adjustable rods by five feet to allow for the weight
of the eyes, upset ends, and adjusting-nuts. The intermediate
and portal struts are placed seven feet below the level of the
upper chord pins, so as to allow a clear headway of fifteen
feet.
The size of the floor beam is taken from Table XIX.
The grouping of members having some similar dimensions
is to be observed. It involves considerable economy of labor,
if one has to estimate on many bridges. In filling out the
last vertical column, the tables on pp. 88–93 and 104–109 of
Carnegie's “Pocket-Companion ” will be found very useful.
Let us employ latticing for the top chords, batter braces,
posts, and portal struts, and single-riveted lacing for the lateral
StrutS.
ORD//VA R P /RO/W HIGH WA Y-B/C/DGE.S. I37
Referring to Tables XXXII. and XXXIII., we find the size
of stay plates for the top chords and batter braces to be
#" × 8", since d = o.75D;
that for the middle posts,
4" × 5%", a being equal to 1.4D;
that for the next larger posts,
4" × 64", d being equal to D;
that for the largest posts,
* . #" × 64", d being equal to o,88D;
that for the portal struts,
#" × 4}", d being equal to 1.18D;
that for the upper lateral struts,
4" × 8", since d exceeds 2 D:
and that for the end lower lateral strut,
4" x 9", d being equal to about 1.5D.
If at the hip joint we make the thickness of each inner and
outer connecting-plate #", the cross section of the plates
through the pin hole by a plane perpendicular to the length of
the batter brace will be greater than either that of the batter
brace or that of the end panel of the top chord : moreover, the
bearing will be slightly in excess of that needed to resist
the stresses in an end diagonal and a hip vertical, so we may
conclude that these thicknesses will suffice.
Without committing any grave error, we may assume that the
total stress in the end panel of the chord is equally divided
between the four connecting-plates, making that on each plate
about I I.6 tons.
The thickness of the web of a Io" 17.5% channel is O.3"
(see Table XXVIII.): therefore the lever arm for the stress in
I38 ORD/AVA R Y YA’O/V HIGAZ VVA P-BA’/ZXGA.S.
a connecting-plate is #(O.3 + O.375) = 0.338 inch, making the
moment II.6 × O.338 = 3.92 inch tons, which divided by O.3 II,
the resisting-moment for a #" rivet, as given in Table XXXVI.,
gives thirteen as the number of rivets required to resist bend-
ing. From the same table we find by interpolation about 1.36
tons as the bearing-resistance for a #" rivet on a 0.3" plate.
The stress transferred to the channel is 2 X II.6 = 23.2 tons,
which divided by 1.36 gives seventeen as the number of
rivets required for bearing. It will be convenient to use
sixteen rivets, in four rows of four in a row. We can do so
legitimately, as the calculation calling for seventeen is merely
approximate.
It is evident, without calculation, that sixteen rivets will be
enough for the connecting plates on the batter-brace side of
the pin hole, for the stress is less and the thickness of web
slightly greater.
To make the outer plate fit between the flange rivet heads,
we cannot have it much more than seven inches wide, unless
the said rivet heads be countersunk.
Next let us lay out the hip to scale, as in the accompanying
figure, spacing the rivet holes according to the rules given in
Chapter II., and allowing three inches of length extra for the
part which connects with the batter brace, so as to provide for
the portal-strut connection. This approximation is accurate
enough for a bill of iron. The circles are those for the pin and
the limiting distance for non-countersunk rivets. The rivet
spacing is three inches along the horizontal lines.
To calculate the weight of an inner
plate, we may divide it into two parts
by the line AB in the figure. The
area of the lower part is equal to
the length of CD multiplied by the
perpendicular distance between AB
and GH, and that of the upper part
by one-half the product of AB and
EF. These dimensions are recorded approximately in the
“Bill of Iron.” The length of the outer connecting-plate is,
of course, measured along its centre line.
//

ORD/MARY IROM HIGHWA P-BRIDGES. I39
The area of a section of the four connecting-plates at the
first intermediate panel point of the top chord should equal
the area of a section of the two chord channels of the third
panel, or 13.34 Square inches. Let us use
two #" x 10" = 7.5
= 12.62 square inches.
and two ſº." × 7" = ă. 3.02 Sq
The stress carried by the channels of the third panel is equal
to their area multiplied by the intensity of working-stress, or
I3.34 × 3.369 = 44.94 tons; which may be divided equally
between the four plates, making the stress on each plate about
11.2 tons. Table XXVIII, gives the thickness of web of a 10"
22.23% channel as O.45 inch, which will make the lever arm
of the stress on the outer plate #(O.45 + 0.43) = 0.44 inch,
and the moment I 1.2 × 0.44 = 4.93 inch tons, which divided
by O.31 I gives sixteen as the number of rivets required to
resist bending. The web is so thick that there is no need for
figuring upon bearing.
For the other side of the joint the stress on the channels may
be taken as -
Io.5 × 3.369 = 35.37 tons,
or about 8.8 tons per plate. -
The lever arm is 4(O.3 + O.43) = 0.36 inch, making the mo-
ment 8.8 × 0.36 = 3, 17 inch tons, which divided by O.31 I gives
eleven as the number of rivets to resist bending. Dividing 17.6
by 1.36 gives thirteen as the number of rivets to resist bearing:
for convenience we can call it twelve, as the stress is not quite
so great as we assumed it. It is to be observed that at the hip
we suppose that all the chord stress is carried by the connect-
ing-plates, while at the next panel point we assume that the
connecting-plates carry only the portion of the stress trans-
ferred by the channels, the remainder being transmitted by the
Čover plate. The reason for this is, that the cover plate at
the hip, being bent, cannot be relied upon to carry stress.
At the next panel point the stress on one plate is
I4.49 × 3.369
4
= I 2.2 tons.
I4O OA’D//VA R P ZA’O/W HIGH WA P-BRIDGES.
The sections of the plates will have to be
two #5" × 10" = 8.75
= 14.88 square inches.
tWO #" X 7" -: ...} I4 Q I
The thickness of the web is found to be o 5" : therefore the
lever arm is #(O.5 + 0.43) = 0.46 inch ; and the moment, 12.2
X O.46 = 5.61 inch tons, which divided
rivets for bending.
To find the lengths of the connecting-
plates we must make, as before, a drawing to scale, as in the
accompanying diagram. We thus determine the length of
plates for the first intermediate connection to be thirty inches.
The length of the plates at the next panel point will be greater
by the space required for six rivets, or thirty-four inches and
a half, and that at the middle panel point greater by the space
required for eight rivets, or thirty-six inches.
Continuing down the “List of Members,” we come to the
re-enforcing plates on bottom chord struts. Let us make them
#" × 3" in section. It is not worth while to calculate the num-
ber of rivets required to connect them to the web of the
I-beam; because four five-eighths inch rivets will give an excess
of strength, making the length about ten inches. Next come
by O.3 II gives eighteen as the number of
the shoe connecting-plates. Let us employ the connection
illustrated in Plate VI. From Table XXVI. we find the thick-
ness of bearing for a 23" pin and a stress of 13.6 tons to be g”;
subtracting from which o 38", the thickness of web of batter-
brace channels, leaves 4" for the thickness of the re-enforcing
plate. Assuming the greatest width of plate in a direction
perpendicular to the length of the batter brace to be sixteen
inches, gives the sectional area of the connecting-plate equal
to sixteen square inches, or that of the batter brace: so, pro-
vided we have such a width, the half-inch plate will answer
the purpose.
The stress carried by the batter-brace channels is 12. 12
X 2.639 = 32 tons, nearly, or 16 tons on one channel. The
lever arm of this stress is 4(3 + 3) = H's", and the moment,
# X 16 = 7 inch tons, which divided by O.493, the resisting-
/

ORDIMARY IROM HIGHWAP–BRIDGES. I4I
moment of a seven-eighths inch rivet, gives fifteen as the num-
ber of rivets required to resist bending. It is better to use
seven-eighths inch rivets here, on account of their large bend-
ing-resistance. There is no need of calculating for bearing.
To determine the dimensions of the connecting-plate, we will
proceed as follows; the distance between the channels at the
shoe being 12.5” – 2 × 2.51" = 7.5".
In the accompanying diagram let us lay out a centre line
AB, and the two parallel lines CD and EF each at the distance
33" from AB. From any point A lay
off the lines ACG and AEH, making
angles with AB equal to the inclination Z
of the batter brace to the horizontal. Ž
Join CE. Draw the lines /K and LM As NT D
parallel to CG and EH, and ten inches A
therefrom : draw also the centre lines Ne e |S_F
AVO and PQ. To allow sufficient clear- \\
ance for the chord heads, the pin holes
should be five inches and a half above
the top of the shoe plate. By crowd-
ing the rivets as near as possible to the flanges of the channels,
we are able to use four rows. Laying out the circles for the
pin holes, and limiting distance for rivet centres, we determine
the height of the box plate to be about 14".
If the vertical sides KD and MF be adopted, the shoe plate
will be 28" long, which is probably too much. To ascertain,
let us find the number, size, and arrangement of the rollers.
The total pressure on one shoe is

B
H Q M
I86o
# x 160 ×
2OOO
= 37.2 tons.
Let us assume the dimensions of a roller to be 2"G) by 12".
Turning to Table XXXIV., we find the permissible pressure
on such a roller to be 4.24 tons, which divided into 37.2 gives
nine rollers. Spacing them 3" centre to centre, and allowing a
projection of 13" at each end, would make the shoe plate 29"
long. A plate 12}" X 29" is not a very good shape. Let us try
rollers 24" O by 15", the permissible pressure for one of which is
I42 OA&AED/AWAA’ P ZAZOAV HIGH WA Y-AR/ZDGAE.S.
5.63 tons; making the necessary number (37.2 + 5.63) seven.
Spacing them 34", and allowing the same projection as before,
will make the shoe plate I5;" × 25", a better shape. Allowing
the shoe plate to project 3" beyond the front end of the
channels will make the length of the connecting-plate 22",
which distance is laid off from C to R. The perpendicular
distance of R from AG exceeds 16”: so a plate of the shape
CGKRSMHEC, before bending, will fulfil all the require-
ments. To find its weight let it be divided into a rec-
tangle, two triangles, and two parallelograms, as indicated in
the “Bill of Iron.”
The next details on the “List of Members” are the re-enfor-
cing plates at feet of posts. From Table XXVI., we find that a
34" pin requires, for a stress of 8.6 tons, a bearing of less than
half an inch, but, in order to compensate for a slight trimming
of the flanges of the channels, there must be a plate on the
inside, and another on the outside, of each channel; and the least
thickness for one of these plates is three-eighths of an inch.
We will not trim the five-inch channels, so will not have to use
an outer re-enforcing plate: this is because there would be no
room for a 34" pin through such a plate. The requisite length
for these plates cannot be exactly determined; for it is impos-
sible to say how much of the bearing-stress is taken up by the
--~~~~, web, and how much by each plate. Let us assume
that the inner plate of the largest post channel
takes up half the stress on the channel, or 4.3

Sk f ! || | tons. Table XXVIII. gives the thickness of the
X f; | web as O.35 inch. Using #" rivets, and figuring
† ||# for bending and bearing, we find the number of
(D e g º g
\ rivets required to be nine. Laying out to scale
X | X the foot of the post, as in the accompanying dia-
gram, and allowing five inches and a half between
the centre of the pin hole and the foot of the channel, we find
that the required length of plate is sixteen inches. In the
same way, the lengths of the re-enforcing plates at the feet
of the other posts might be calculated : but it is hardly worth
while ; for, if we make them all of the same length, they will
be sufficiently strong without causing much waste of material.
ORD/AWA R P /ROM H ZGA WA Y-B/C/DGAE.S. I43
After entering these dimensions on the “Bill of Iron,” we
refer again to the “List of Members,” and, after omitting
re-enforcing plates at middle of posts, come to the connecting-
plates for lateral struts to top chords. The thickness of these
plates should be g", and the average width of the legs 24". The
area of a 4" 6% channel is 1.8 square inches, and the intensity of
working-stress for forty-two diameters with both ends fixed is,
by Table XI., 2.74 tons; making the greatest stress that could
ever come upon the channel I.8 × 2.74 = 4.93 tons. The lever
arm of the stress is ; (3 + 3) = H's inch, making the moment
# × 4.93 = 2.16 inch tons, which divided by O.389, the resist-
ing-moment for a #" rivet, as given in Table XXXVII., gives
six as the number of rivets required for attachment to the
lateral strut channel. Although the leverage is a little greater
for the attachment to the chord-channel flanges, still six rivets
will suffice, on account of the liberal estimate for stress, and
using rivet tables which have a surplus of strength for lateral
system connections. The length of each leg of the T will be
about eighteen inches, for various circumstances will necessitate
wide rivet spacing in this detail.
The stress and leverage being the same in the two attach-
ments, it is evident that six rivets will be required at each end
of the upper channel of the lateral strut for connection to chord.
There will be just room for this number; putting two through
the channel flanges, and four through the plate between the
channels. Were these not strong enough,
we could use seven-eighths inch rivets.
The next item upon the “List” is con-
necting-plates for portal struts to batter
braces. These should have a greater
strength than ordinary calculations would
indicate, in order to provide against the -
racking effect of the wind. If we use a jaw plate, as in the
first of the accompanying diagrams, and two bent plates, as
in the second, to attach to the flanges of the strut channels
and the web of the batter brace, we provide against all con-
tingencies. These plates are bent at right angles about the
lines AB, CD, and EF. It may be well to test the num-

I44. ORDINARP IROW HIGHWA K-BRIDGES.
ber of rivets for the jaw plate, because it has to act as a
re-enforcing plate also. First we must determine the size of
the pin which attaches the vibration rods. The diameter of
each rod being 14", the greatest working-stress thereon is 7.5
× 0.994 = 7.5 tons, nearly. The lever arm is 3(3 + 3 + 3) = 4",
making the moment g × 7.5 = 6.56 inch tons. Consulting
Table XII., we find Iſ" as the diameter required. Table XXVII.
shows that there is more than sufficient bearing. Assuming five
tons upon the re-enforcing plate, we find the number of eleven-
sixteenths-inch rivets required to resist bending to be
5 × #(+ + š) 6
O.299
5
so that the dimensions in the drawing are sufficient.
Let us assume the dimensions for portal connecting-plates to
brackets and name plates as #" × 8" X 18".
The section of a connecting-plate for an intermediate strut
should be #" × 3"; and we will use three rivets for the connec-
tion to the post, and four for that to the strut: it would be
useless to figure upon these numbers, as the stress is so small.
Owing to the peculiarity of the vibration-rod connection, each
plate will have to be about two feet long, as can be seen on
Plate VI. -
Omitting side-brace connection, the next item is the end
lower lateral strut connection to pedestal, which is by means
of a jaw plate #" × 5". The stress on the strut was found to be
9.75 tons, making 4.88 tons on each channel. The number of
three-fourths inch rivets required will therefore be
4.88 × #(3 + 3) 6
O.389 ſº
There is no need of figuring for bearing. This would make
the total length of jaw plate about three feet, as noted on the
“Bill.”
For the strut at the fixed end, a plate 4" × 5" × 2' will answer
the purpose.
The next item is the hip cover plate, which we will make of
the same section as the chord plate, and eighteen inches long.
ORD/AWA R P ZAZOAV HIGH WA P-B/C/DGE.S. I45
For the intermediate joints we must calculate the lengths
of the cover plate thus: the stress on the top plate is 3.91
× 3.369 = 13 tons nearly; making the moment on the rivets
13 × # = 4.06 inch tons, which divided by
o.3 II gives fourteen as the number of three- ſº 174—->
fourths inch rivets required to resist bend-
ing. For bearing, the number required will
be less. The arrangement of the rivets de-
termining the size of the plate is shown to
scale in the accompanying drawing. Next
come the filling-plates. Let us average
those for the top chord at #" thick. For
the thickness of the filling-plates over end floor beams, we
must subtract from the distance between centre of pin hole
and foot of post the half-depth of the chord heads in the end
panels, thus,

.
:
K
.
:
:
2.
K
É
:
É
5%" — #(33 × 3 + 23)” = 1%".
The width will be equal to the diameter of the pin, and the
length equal to that of the pin between shoulders.
Next come the extension plates. Let us make them in two
thicknesses, the shorter piece extending down to the stay-
plates. For the largest post, the total thickness will have to be
8.91" //
, or 13"; making that of each plate . . Neglecting the
effect of the stress on the outer plate, the moment He—82—-
on the rivets will be 8.6 X (O.35 + 0.56) = 3.91 ||x i < ||
inch tons, which divided by os II makes the num- |. (D . |
ber of three-quarter inch rivets to be employed x 4 x
equal to thirteen. For reasons advanced in Chap- f X X X t
ter XII., we must count in only one-half of those S$
- x | x ||
rivets which pass through the double portion of > f < ||
the plate and the web. Laying off the end of x f :
the post to scale, as in the accompanying dia- > f ≤ ||
gram, we determine the lengths of the plates to be L–--~~ f

twelve and twenty-four inches respectively. The
rivets above the line AB are to be countersunk: their use
is simply to make the two plates act as one. We might
I46 O/PD/AVA A' V /A’OAV HIGH WA V-BA’ſ DGA.S.
calculate the required lengths for the extension plates of
the other posts, but it would be unnecessary labor; for if, in
the posts with the seven-inch channels, we use two rows of
three-quarter inch rivets, instead of three, and in the posts
with the five-inch channels two rows of five-eighths inch
rivets, making the plates of the same length, we will provide
sufficient strength with very little waste of material.
The next on the list are the shoe plates, the area for which
we have determined to be 154" × 25"; their thickness (see
p. 16) should be g”.
To determine the size of the roller plate, we will adopt 3"
X 3" 5.9% angles to enclose the rollers, and allow for a motion
of two inches, which would make the area 214" × 33": the
thickness should be g”. The area of the plate in square inches
multiplied by two hundred pounds makes about seventy-one
tons, which is nearly double the greatest pressure on the shoe;
showing that the dimensions decided upon are large enough.
The area of the shoe plate multiplied by two hundred pounds
per square inch is equal to 38.75 tons; and, as the greatest
pressure on the shoe has been calculated to be 37.2 tons, it
is evident that we may use the shoe plate as a bed plate by
properly anchoring it to the masonry.
Next come the beam-hanger plates. It will not be neces-
sary to calculate their thickness, as the method was fully
illustrated by an example in Chapter XIII. ; and experience
would suggest a thickness of g”. From Carnegie's “Pocket-
Companion,” p. 126, we find that g’ square bars upset to I?";
and from p. 131 of the same book we see that the longest diam-
eter for the corresponding nut is 2.89", say 3"; so that, allowing
I” for clearance, the distance between centres of beam-hanger
holes will be 4", and the width of plate for full bearing 7". We
can average the lengths of the plates at 8".
The weight of a name plate need not exceed forty pounds.
Next come the latticing and lacing bars. Referring to
Tables XXX, and XXXI., we find for the top chords and
batter braces, *
where d = o'75 D, the bars should be ºs" x 24";
ORD/AVA R P IROM HIGH WA Y-B/C/DGE.S. I47
for the middle posts,
where d = I.4/9, they should be #" X 13";
for the next larger post,
where d = D, 4” x 13”;
for the largest posts,
where d = o.88D, 4” x 13”;
for the portal struts,
where d = 1.18 D, 4” x 13”;
for the upper lateral struts,
where d > 2 D, #" × 2;";
and for the end lower lateral struts,
where d = 1.5D, #" x 25".
The distance between centre lines of rivets in the chord and
batter-brace channel flanges is about ten inches; the space
per panel in chord over which the latticing extends is about
eighteen feet; the corresponding distance in the batter brace
is twenty-seven feet: so, if we space the rivet holes for the
latticing as nearly as possible ten inches apart, there will be
twice twenty-two lattice bars required for each chord panel
of one truss, and twice thirty-two bars for each batter brace,
making seven hundred and eighty-four bars in all. Their
length, from Table XXIX., is found to be I. 18' + O.2 I5' =
I.395', say 'I.4. - *
We can average the lengths of the lattice bars for the posts
thus: assuming a stretch of nine inches, a spread of eight
inches and a half, and I $" as the width of a bar, gives the total
length I.O34 + O. 18 = I.214, say Ił'. The average length of
space on the posts occupied by the latticing is about twenty
feet six inches; making the number of bars per post four times
twenty-seven.
The spread, or distance between centre lines of rivets in
channel flanges of portal struts, is about six inches and a half,
I48 OA'Z)/AWA R P ZAZOAV AZZGA/WA P-AEA’ZZOGAE.S.
and the latticing extends over about ten feet on the average,
after deducting for various plates; which would make the num-
ber of lattice bars per strut about four times nineteen. The
length will be about O.768′ + O. I45' = O.92' nearly.
The spread for the lateral strut rivet centres is eleven inches
and a half; and, as lacing-bars are used, the stretch must be
about six inches and three-quarters in order that the angle
between the bars may be sixty degrees. This distance is
most readily determined by diagram. The length of a bar
is, then, I. I I3' + O. 197' = I.31'. The extent of the lacing is
about eleven feet, making the number of bars per strut twice
nineteen. -
For the lacing-bars of the lower lateral strut, the spread of
the rivets is about nine inches and a half, and the correspond-
ing stretch about six inches. The length of the lacing is about
eleven feet, and the number of lacing-bars twice twenty-two.
The length of each bar is O.936 '+ O. 197' = I. I33", say Ił'.
Next on the “List” comes the chord trussing, of which we
will assume the section to be #" × 3". By a rough approxima-
tion, we can find the average length for one panel of one truss
to be about thirty-three feet. The lengths of the pins are cal-
culated so as to include the weights of the nuts by adding,
in most cases, an inch and a half for each nut. The diameter
of the intermediate vibration-rod pins is assumed to be I gº".
The lengths of the bolts include an allowance for heads and
nutS.
To find if there be any anchorage required at the roller
end of the bridge, we must compare the overturning and re-
sisting moments, or, what is the same thing, the release of
pressure on the shoe and the weight thereon when the bridge
is empty and there is no wind. In finding the stress on
the end lateral strut, we determined the release of pressure to
be 7.2 tons, and one-fourth the weight of the empty bridge
to be 14.8 tons. The latter being more than twice as great as
the former, no extra anchorage will be required at the expan-
sion pedestals.
As there is vertical sway bracing, the brackets may be light.
Let us make them of 24" × 24” 4.9% angle-iron, and let them
OAA)/AVA R V /A’O/V HIGH WA Y-A/º/DGAE.S. I49
extend vertically and horizontally four feet. Allowing six
inches at each end for attachment would make the total length
of a bracket about 6.7 feet.
An allowance of IOOH for ornamental work will be sufficient.
The equivalent length of a beam hanger can be thus approxi-
mately calculated: twice the distance from the centre of the
pin to the top of floor beam equals II"; twice the diameter of
pin equals about 6"; twice the depth of floor beam equals 54";
twice the length of hanger below the floor beam equals 6";
allowance for two upset ends and nuts equals 33"; total length
equals I IO" = say 9. *,
Let us average the diameters of the fillers at 34", and their
weight at Iok per foot. The average length of filler is not far
from 3”. Special fillers will be required at the free end of the
span, so as to keep the lateral strut clear of the batter-brace
channels, also similar fillers at each end of the span to lie
between the outer chord bars and the channels. Let us assume
that the channel flanges are notched out to a depth of one inch ;
then the thickness of the last-mentioned fillers will be 1;", and
that of the others say ". Let the external diameter be 7",
and the internal diameter 23": the weight per lineal foot will
then be (see Carnegie, pp. IO5–IO7) I28.3 — I4.8 = II 3.5.
Turn buckles and sleeve nuts have already been included,
and there are no connecting chord heads.
Next come the jaws for lower lateral struts. From the cen-
tre of the lower chord pin to the top
of the floor beam being 5...", the depth
of the wooden strut will have to be
9"; but the jaws need not be more
than 7" deep, as shown on the accom.
panying diagram. The width of the strut need not exceed 7",
nor that of the jaw plate 6”. The thickness of the latter
should be 4". The greatest stress upon any lateral strut, found
by resolving the stress upon the It's" lateral rod, is about 7 tons,
which stress has to be resisted by the rivets connecting the
inner and outer jaw plates. The number of rivets required is
7 × 4
o,389.
= 9, which will make the total length of the two jaw

I5O ORD/MARY ZROM HIGHWAP–BRIDGES.
plates about 5'. A piece of 6" 8.5% channel will be strong
enough for the bent eye bearing. It is not worth while to cal-
culate the number of rivets for the combined upper lateral strut
jaw and vibration rod bearing plate: So we will average the
dimensions as in the “Bill of Iron.”
Next on the “List” comes the angle iron around the edges
of the roller plates, which we will assume to be 3" × 3", weigh-
ing 5.9% per foot. The length on one side is 33", and at the
end say 44" on each side of the anchor bolt hole; making seven
feet in all for each plate.
Next come the pieces of channels, which we will assume to
be of the sizes marked on the “Bill,” and next the rivet heads,
for which we will make a separate bill, then enter the total
weight with the other items. Considerable approximation is
used in ascertaining the numbers ; and the floor-beam rivets are
omitted, for their weights are included in the weight of the
beams. The total length of top plate for chords and batter
braces is about 370': let us average the rivet spacing therein
at 34", making the total number 2 × 370 × 12 X # = 2537.
We may say that there is one rivet for each latticing or
lacing bar for attachment to channels, and one to every two
lattice bars for attaching latticing to latticing. Half-inch rivets
will be used for the latter purpose, so as not to weaken the bars
unnecessarily. Let us assume that half the stay plates are
attached by three-fourths inch, and half by five-eighths inch,
rivets, and that there are six or eight rivets per plate. Let
us average the number at each joint of the chord at sixty-four,
and at each pedestal, not including those through the shoe
plate, at thirty-two ; and let us assume eighteen rivets at the
foot of each post, six per bracket, and fourteen per jaw. The
following will then be the approximate
OA&DAVARP IROM HIGH WA Y-B/C/DGES. I5 I
BILL OF RIVET HEADS.

DIAMETERs.
CONNECTIONS.
#" #" #” g”
Plate to chords and batter braces . . - t- 2,537 º
Latticing and lacing to channels . . . * sº 784 wº-
Latticing and lacing to channels . . . - 432 - tº-º
Latticing and lacing to channels . . . - 648 - -
Latticing and lacing to channels , . . 3O4 <-- - *-
Latticing and lacing to channels . . . I90 * - º-
Latticing and lacing to channels . . . 44 sºme - -
Latticing to latticing . . . . . . . I,084 wº- - *-
Stay plates to channels . . . . . . - 44O 33O -
Connecting-plates to channels . . . . - * 896 I 28
Re-enforcing plates to channels . . . - I8o - sº-
Connecting-plates to channels . . . - 96 244 -
Connecting-plates to channels. . . . 96 6o - e-
Connecting-plates to channels and I . - cº- 8o *-*
Cover plates to chord plates . . . . - tº- 368 g-
Extension plates to posts . . . . . - sº 28o º-
Connecting-plates to shoe plates . . . - mº - 32
Trussing to bars . . . . . . . . 48o -º-º: - -
Brackets . . . . . . . . . . . - 84 - -
Jaws. . . . . . . . . . . . . - I4O 196 -->
Angle iron to roller plates . . . . . - tºº - 56
2,198 || 2,08o 5,715 216
2,198 (6) oo8# = 176#
2,080 (a) o.16 “ = 333 “
5,715 (3) o.25 “= 1,429 “
216 (6) o.40 “ – 86"
Total weight of heads = 2,024%, say 2,000$ after deducting for coun-
tersunk heads.
The number of spikes required will be ten per plank of floor
(each plank being 9" wide), six per post of hand railing, ten per
panel for felly plank to flooring, two per joist, and two per jaw;
in all, 2,612. The spikes should be #" square by 7” long.
I 52 ORD/AWA R P ZRO/V HIGH WA Y-BA’/ZDGE.S.
Consulting Carnegie's “Pocket-Companion,” p. 129, we find
that there are 662 spikes to a keg of 150*; so that we require
four kegs, or 600#.
With the exception of the bolts attaching the lateral struts to
the floor beams and jaws, each wood bolt must have two wash-
ers; making in all 385, say 4OO. Each washer weighs about a
pound.
The weights of most of the nuts have already been included:
let us add fifty pounds for lock and pilot nuts.
The total amount of lumber may be estimated in three ways:
first, as in the “Bill of Lumber;” second, by consulting Table
XV., which gives 2,085 as the amount per panel, multiplying
this by 8, and adding 515, the number of feet in the lateral
struts; and, third, by consulting Table I., which gives 269 as
the weight of lumber per lineal foot, and multiplying this by
160 × #3. The first two methods are accurate; the last,
approximate.
BILL OF IRON.

Top chord channels 8 Io’’ 24.15%
Top chord channels 8 || Io” 22.23% 2O’ IO,221
Top chord channels 8 || Io’’ I7.5%
Batter-brace channels. 8 || Io’’ 20.2% 32' 5,171
Post channels 4 5” 7#
Post channels 8 7” Io.5% 24' 5,539
Post channels * 8 8” I4.85%
Upper lateral strut channels IO 4” 6:# 15' 900
End lower lateral strut channels 2 5” 7# I4' 196
Portal strut channels . 8 4” 6:# 14.3' 686
Chord plate . 2 *” 12%." I2O.5. } 4,830
Batter-brace plate . 4. s” 12%." 32.5" y
Intermediate struts. 5 4” 8#I I4.4% 576
End lower lateral strut . I 5” Io:#I I4' I4O
Bottom chord struts 4 4” Io:#I 20.5' 82O
Main diagonals . 8 4” 23”
Main diagonals . 8 3" 3” | 34.25° 6,307
Main diagonals . 8 ſº 33”
Counters . 4. #" G) A
Counters . 4 IT’s” [...] } 36.25 7.59
Hip verticals. 8 I s” [T] 27' 813
ORDIAWA R P IRO/V HIGH WA P-BRIDGE.S. I53

Upper lateral rods . . . 4 I+" G)
Upper lateral rods . . . 4 14” G)
Upper lateral rods. 4 #” G)
Lower lateral rods . 4 1+}” G) 29.5’ 3,455
Lower lateral rods. 4. Iºs” G)
Lower lateral rods . . . 4 14” G)
Lower lateral rods . . 4 I// G)
Vibration rods at portals 8 I#" G) 2I’ 557
Vibration rods at posts . IO g” G) I9' 38o
Chord bars . . . . 8 3" 33”
Chord bars tº gº tº 8 #” 33” /
Chord bars . . . . . . I6 #" 33” 23 IO,459
Chord bars 32 #" 3}”
Floor beams . 7 27” 54}# b. b. I6' 6, IO4
Total weight of main portions 57,913
Stay plates on chords and bat-
ter braces . . . . . . 32 *" 8” 12%." 278
Stay plates on posts 8 #" 5}” Io;” 32
Stay plates on posts . . I6 +” 64” II// 76
Stay plates on posts . . I6 *" 6}” II” 99
Stay plates on upper lat. Struts. 20 #" 8” 13%" I 50
Stay plates on ldwer lat. Struts. 4 #" 9” II” 28
Stay plates on portal struts. I6 4” 43". 8” 42
Connecting-plates hip inside { 8 #" 9” 31” } 353
Connecting-plates hip inside 8 #" 4” 36”
Connecting-plates hip outside . . . 8 #" 7” 35” 2O4
Connecting-plates int. inside ‘8 #" Io” 30” 250
Connecting-plates int. inside 8 Y’s” Io” 34}" 335
Connecting-plates int. inside 4 Y's" IO// 36” I75
Connecting-plates int. outside. || 8 #" 7” 30” 2O4.
Connecting-plates int. outside . 8 #" 7” 34}” 23S
Connecting-plates int. outside. 4 Jºs” 7” 36” I23
Connecting-plates, b, ch, struts. 16 #” 3” IO// 42
- 4 4” 73" 22”
Connecting-plates at shoes . | 8 $" 9” 7” | 367
- U 8. 4" Io” 184” J
Re-enforcing plates, ft. of posts
inside tº e º is 8 #" 8” I6”
Re-enforcing plates, ft. of posts
inside . . . . . . . . 8 #" 7” I6”
Re-enforcing plates, ft. of posts
inside • - - - || 4 #" 5” 16" |} 380
Re-enforcing plates, ft. of posts
outside . vº º ve tº e 8 #" 6” I6”
Re-enforcing plates, ft. of posts
outside . 8 #" 5” 16" |
I54. ORD//VA R P / ROAV AZG H WA P-BA’ZZOGAE.S.

Connecting-plates, lateral strut
to chords . . . . . . . . Io #” 2}” 3' I56
Connecting-plates, portal strut
to batter braces . . . . . 8 #" 4” 3' I2O
Connecting-plates, portal strut
to batter braces . . . . . . I6 #" 8” 84” II3
Connecting-plates, portal strut
to brackets . . . . . . . 4 4” 8” I8” º
Connecting-plates, portal strut 6o
to name plate . . . . . . 2 4” 8” 18”
Connecting-plates, int. Strut to
posts . * * * • 2C) #" 3” 2’ I 50
Connecting-plates, end lower
lateral strut tº º º 2 #” 5” 3' 63
Connecting-plates, end lower
lateral strut 2 y” 5” 2? 33
Cover plates at hips 4. #" 12}” 18” 78
Cover plates at int. joints IO +s” 12%." 17” 185
Filling-plates at hips . 8 *" Io” I6” 22
Filling-plates at int. joints . I6 Ts” Io". I2” 33
Filling-plates over beams 4. 13." 2g". I2// 6I
Extension plates . . . . 8 *" 8” I2” } 360
Extension plates . . 8 *” 8” 24”
Extension plates 8 Ts" 7” I2// } 245
Extension plates . . 8 †s" 7” 24”
Extension plates . . . . 4 *" 5” I2// } 88
Extension plates 4 Ts” // 24”
Shoe plates 4 g” 15%" 25” 377
Roller plates . . . . . 2 g” 21%." 33” 345
Beam-hanger plates . 14 $” 7” 8” I9I
Name plates . gº ºn tº º 2 @ 40% each 8o
Lattice bars on chord and bat-
ter braces . . . . . . 784 *” 2}” I.4’ 2,572
Lattice bars on posts . . . . . 432 || #” 1;" I} 844
Lattice bars on posts . . . . . 432 4” 13” 14' 788
Lattice bars on posts . . . . . 216 4” I#” I}' 365
Lattice bars on portal struts . 304 4” I}” o.92/ 35O
Lacing-bars on upper lateral
Struts . . . • . . . . . I90 !" 2}" I.31' 44I
Lacing-bars on lower lateral
Strut . . . . . . . . 44 4” 24” I#’ 88
Chord trussing . . . . . 8 4” 3” 33' 66o
Pins, top chord . . . . 4 3}” G) I6” I47
Pins, top chord . . . . . 4 24” G) I8// I3O
Pins, top chord . . . . . 6 2}” G) 18” I2O
Pins, bottom chord . . . . IO 3}” G) 22// 507
Pins, bottom chord. . . 8 2#" G) 2O/ 24I
OA’A)/AVA R P WA’OAV HIGH WA P-B/C/DGAZ.S. I55

Pins, portal vibration . . 8 14" G) • I2” 74
Pins, post vibration . . IO 14” G) 8” 61
Bolts, name plates . . . 4 @ I# each 4
Bolts, vibration rods . IO (a) 5#. each 50
Bolts, anchor. tº e º 'º 8 14" G) 3' 98
Bolts, portal struts to batter-br. 8 @ 8#. each 64
Bolts, hand-rail . . 68 3" G) I2” IOO
Bolts, lower lat. strut to beams 49 g” G) 14” 58
Bolts, lower lat. strut to jaws . . 28 #" G) I2” 4I
Bolts, felly plank to floor 66 3" G) 15” I2 I
Bolts, felly plank to hand-rail
posts . we e º º 34 3" G) 18” 75
Brackets . . . . . I4 |2}”X2%"| 4.9% L 6.7' 460
Ornamental work . . . tº tº º e tº º tº IOO
Beam hangers 28 g” U 9' 643
Expansion rollers . I4 24” G) 15" 232
Roller frames, sides 4 4” 2” 22” I2
Roller frames, rods 6 !" G) 17” 6
Fillers . 4O (a) Io:# per ft. 3” IOO
Fillers . 8 || 7”G) |113.5% per ft. 14” } 97
Fillers . tº 2 7"G) |113.5% per ft. #”
Jaw plates . . . . . . . . . I4 y 6” 5' 7oo
Jaw plates. . . . . . . . IO #" 14” I2” I75
Angle iron on roller plates . 2 || 3'x3' 5.9% 7. 83
Pieces of channels . I4 6// 8.5% 6” 6o
Rivet heads . . . e tº º 2,OOO
Spikes . . . . . * 6oo
Washers 4OO
Nuts . 50
Total weight of details tº I9,850
Weight of main portions. tº º º 57,913
Total weight of iron e 77,763
BILL OF LUMBER,
Joists tº º º 8o 4” 14” 2O’ 7,467
Flooring (equivalent). I6o 3” I2” I4' 6,720
Hand rail . * 32 2” 6” 2O/ 640
Hand-rail posts . . 34 4” 6” 4' 272
Hub planks . . . . . I6 2” I2// 2O’ 64o
Felly planks . . . . . I6 6” 6// 2O’ 96o
Lateral struts. . . 7 7” 9” I4' SIS

Total number of feet, board
Iſle2SUll & . . . . .
I7,2I4
I 56 ORDIMARY IROW HIGHWAP–BRIDGES.
\
Table I. gives the weight of iron per lineal foot of bridge as
479 pounds, which multiplied by 16o gives 76,640; adding 6oo
pounds for the spikes, makes the total weight of iron 77,240
pounds. This indicates an error in the table of only seven-
tenths of one per cent, — a very satisfactory result.
If we deduct the weight of the end lower lateral struts, roll-
ers, roller plates, anchor bolts, etc., which really do not come
upon the bridge, in all about 1,400 pounds, the dead load per
lineal foot will be 1% + 269 = 746; which agrees within six
pounds with that assumed.
It may appear to the reader who has carefully followed out
all the calculations in this chapter, that the designing of iron
bridges, and estimating weights thereof, involve a great deal of
work, and demand considerable time: but such is not necessarily
the case; for an expert could have made this design in from two
to three hours, because his experience would have told him the
sizes of many of the details and the number of rivets to employ.
In this chapter everything has been figured out carefully enough
for making working-drawings, instead of merely an estimate of
weight; for the author considers that it is better to teach the
beginner exact methods in the first place, and leave him to
develop approximate ones as his practical experience increases. .
A useful deduction which can be made from the “Bill of
Iron’ in this chapter is the proportion which the weight of the
rivet heads bears to the weight of the rest of the iron, excluding
that of the floor beams, spikes, and washers. In this case the
ratio is about tº = 2.92 per cent. The average for a number
of estimates made by the author is 2.85 per cent, the greatest
being 3, and the least 2.4 per cent. The knowledge of this
fact will save considerable time for any one who has many esti-
mates of weight to make.
The author at one time, when in haste, used to figure out the
total weight of main portions, and divide by a certain quantity
less than unity, in order to determine the total weight of iron,
but has now abandoned the method as giving too loose an
approximation, finding that the correct divisor varies considera-
bly with the length of span and the class of bridge. Tables I.,
II., and III. give the weights of iron for all cases far more
accurately than will any such approximation.
OA’D/AWA R P IROAV HIGH WA Y-A/E/DGE.S. I57
CHAPTER XVII.
BRIDGE LETTINGS,
THE ordinary modus operandi of bridge lettings is by no means
the most perfect that could be devised.
A couple of months before the letting, advertisements are
inserted in some of the local newspapers, stating that on a cer.
tain day at noon, in the county town, at the court-house, there
will be let the contract for building a bridge, or several bridges,
in the county. The length of span and clear roadway are nearly
always given; and sometimes this is all, for the commissioners,
as a general rule, do not know whether they want an iron or a
combination bridge. Sometimes, even, they accept a wooden
one after advertising for an iron bridge. Occasionally a very
fair list of data is advertised, but such is not the rule. In addi-
tion to the local advertisements, circulars are often sent to the
various bridge companies, requesting them to send representa-
tives to attend the letting. Little do the commissioners think,
that in the end the county has to pay the travelling expenses
of each representative who attends, as well as for his time,
Instead, they say, “The more, the merrier,” and congratulate
themselves when they have a good attendance, thinking, that,
the more representatives, the greater the competition. It may
be so in certain cases; but ultimately some one has to pay each
traveller's expenses, and who but the counties is there to do it 2
It is true that mailed bids are received : but they are very sel-
dom accepted, even if the figures be the lowest; for the commis-
sioners are generally unable to resist the combined eloquence
of half a dozen bridge-men. It would be much better for all
parties concerned if bids were all sent by mail, and if the
awards were made by a competent engineer. It would permit
158 OAPD/AWAA’ P ZAZOAV HIGHTWA P-AE A*/A)GAE.S.
of the reduction of the staff of each bridge company, the less-
ening of cost to the counties, and, what is more important, the
building of better structures. When, by means of much com-
petition, the contract price for a bridge is reduced to cost, or
even below it, what does the successful (?) competitor generally
do 2 Lose money 2 Not at all if he can help it: that is not his
way of doing business. He puts up a cheap bridge, cutting
down weight on the details, and shaving as much as he dare on
the sections. The author does not wish it to be understood.
that such is the method of the better class of bridge companies.
They generally know better than to let their travelling men
take contracts for nothing; and when they do get bitten, as they
all do occasionally, they put up the bridge at a loss, and take it
out of the next county where they obtain a contract.
When remonstrated with for collecting a large crowd to
attend the letting of a little bridge, county commissioners have
been known to respond, “You see, we don't know exactly what
kind of a bridge would be best for the place, nor what style of
bridge the money at our disposal will pay for; and when we get
a lot of you bridge-men here, who know all about it, we are able
to find out exactly what we need.” Travelling bridge-men who
know all about it ! Bridge companies are not willing to send
their engineers travelling about the country to attend county
bridge lettings. They cannot afford to pay for this purpose
salaries of two or three thousand dollars per annum, when men
can be obtained to do the work for one-third of that amount.
When an engineer is found at a bridge letting, it is generally
because he has tired himself out at office-work, and needs a
little change.
It is surprising how little the average travelling bridge-man
really knows about bridges, and how incapable he is of giving
advice of any value to a commissioner. What he does know is
how much bridges will probably cost, and this knowledge he
obtains from the company's engineer. His forte is to do the
heavy talking, in which it is by no means necessary for him to
stick to the truth.
On the day of the letting, four or five honest farmers (they
are honest usually, though there have been and are exceptions)
ſº
ORD/AWA R P IRO/V HIGH WA V-B/ē/DGAE.S. I59
meet to determine upon who shall have the bridge. In some
cases, after the bids are opened, the contract is immediately let,
without discussion, to the lowest bidder. At other lettings,
each company's representative is allowed to hold forth, in turn,
before the assembly, and show in what way his bridge is supe-
rior to the rest.
Some of the arguments advanced are really amusing. One
will say “Mine is the best bridge, for it has the most iron in
the chords” (ignoring the fact that his bridge has a less depth
of truss than any of the others). Another says, “My bridge is
the best, because it has the most panels; and it is an acknowl-
edged fact, that, the greater the number of panels, the stronger
the bridge.” Another will point to the size of his floor beams,
forgetting that his bridge has one less panel than have any of
the others. With such nonsense are the minds of the poor
commissioners crammed, until they do not know the difference
between a counter and a batter brace (in fact, it is more than
probable that they never did know); and the result is, either
that the letting is broken up, or that the contract is let to the
one who has done the most talking, and has impressed the most
falsehoods upon the understandings of the honest farmers.
Sometimes the commissioners conclude to have the letting
done in style, so engage the services of an engineer. Their
acquaintance with the members of the engineering profession
being rather limited, they employ to decide for them the county
surveyor, whose technical knowledge is confined to the use of the
compass and transit, and whose mathematical education never
went much farther than arithmetic. Or perhaps they will find
some one much looked up to in the county as an engineer, who
has been plucked at some technical school, and returned home
to enjoy the honors of having been a college-man.
As Professor Vose, not long ago, stated in a very able article
published in the “Journal of the Association of Engineering
Societies" and “Van Nostrand's Magazine,” in order to insure
the building of none but good bridges, there must be a State
inspector, whose duty it would be to pass judgment on the
plans of all bridges, before permitting them to be erected in
the State. Such an inspector should be, not an ordinary engi-
I6O OA’ D/AVAA’ P ZA’OAV HIGH WA P-BA’ZZOGAE.S.
©
neer, but an expert in bridge designing. He should receive a
handsome salary, and be allowed enough assistance to enable
him to do his work in a satisfactory and efficient manner. His
tenure of office should be for life, or for a long term of years,
and should be beyond the reach of politics and politicians. As
long as his work be done efficiently, his position should be
assured to him; for a man of the requisite experience and ability
would not be willing to accept the position under other condi-
tions.
The letting of bridge contracts to the lowest bidder is the
worst method that could be adopted, even when plans and
specifications are on file; for the work generally goes to the most
unscrupulous bidder, who will secure his margin of profit by
diminishing the weight of the details. This weight should be
about twenty-five per cent of the total weight of iron-work in
the bridge, and it is quite possible to reduce it to one-half of this
amount.
If ignorant commissioners must have a rule for letting, it
would be better to award the contract to the highest bidder.
But the proper way would be to engage the services of a man
who knows something about bridge construction, and have him
figure out the probable cost of the bridge, allowing a fair margin
for profit. A margin of from fifteen to twenty per cent is not
excessive, even upon a liberal estimate of cost; for such a
margin by no means represents the contractor's actual profits.
From it must be subtracted, not only a portion of the annual
office expenses, including salaries of clerks, draughtsmen, and
engineers, but also the bidding expenses of several lettings
where the contractor has been unsuccessful. Then, too, there
is the risk of bad weather, high water, rise in price of iron,
delay in shop, etc., any one of which is liable to absorb the
whole calculated profit, to say nothing of the liability of losing
the bridge by a freshet during erection.
When the appropriation is small, it is much better to build
a good combination bridge than a poor iron one, because the
wood-work of the former can be replaced when it wears out ;
while the iron, if properly cared for, is as good as new. But a
used-up iron bridge is worth little more than the cost of taking
b
OA'D/AVA R P IRO/W HIGH WA Y-BA’/DGAE.S. I6 I
it down, and transporting it to where it can be sold for old
iron.
The method of having plans and specifications on file for
every competitor to bid upon is not a good one. In the first
place, it necessitates the sending of engineers to the letting, or
at least those who are capable of figuring out the weight of a
bridge, thus greatly increasing the bidding-expense; then, if
the plans are at all defective in design, a first-class company is
unwilling to bid upon them. It is much better to let each
company bid upon its own designs. “,
For most city bridges and for very large county bridges, it is
worth a bridge company's trouble to prepare special drawings;
but, for ordinary county lettings, standard drawings will answer
every purpose when accompanied by a diagram of stresses and
special specifications. If the letting is to be done by an engi-
neer, a plate of details similar to Plate III. or Plate IV. will be
sufficient; but the ordinary county commissioner does not under-
stand such plans, and generally wants to see what the bridge
will look like. Such a picture as the one given on Plate I.
would be very taking with county commissioners, but there is
a great deal of labor involved in making such a drawing. As a
general rule, a sheet showing side and end elevations, and
a plan of either the whole or one-half of the bridge, will be suffi-
cient when supplemented by a sheet of details.
It is not unusual for a fancy drawing to take a contract when
there are much better and even cheaper structures in competi-
tion.
The diagram of stresses should be filled out as shown on
Plate V. -
Specifications should be quite explicit without being long, or
confusing to a reader of ordinary intelligence. The author
would recommend the following or some similar form of blank
for the use of bidders. By a few erasures it may be made to
suit any case.
I62 ORD/AVA R P WA’O/V HIGH WA P-BA’/DGAE.S.
SMITH & WILLIAMS,
BRIDGE ENGINEERS AND BUILDERS,
PITTSBURGH, PENN.
SPECIFICATIONS FOR BUILDING A WROUGHT-IRON HIGHWAY-BRIDGE.
Length of Span. — To be .................... - feet …... inches between centres
of end pins
bearings.
Clear Roadway. — To be ....................... feet ..................... inches between innermost
portions of trusses.
Live Load. — To be ........................ pounds per lineal foot of bridge.
Dead Load. — To be ...................... pounds per lineal foot of bridge.
Depth of Truss. – To be ....................... feet … inches between centre
lines of chords.
Clear Headway. — To be ...................... feet --~~~~ - inches between floor and
lowest part of overhead bracing.
Upper Chords and Batter Braces. – To consist of two ....................... inch chan-
nels, with a plate ...................... - inch by … inches above, and lattice
bars … inch by … inches, riveted together at their mid-
dle points, below.
Splicing of Joints in Upper Chords. – Shall be made by a plate on each
side, as shown in the accompanying drawing. These plates shall be
of such thickness as to afford sufficient bearing for the pins, and their
combined sectional area shall not be less than that of the channels
which they connect. No splice plate to be less than three-eighths (;)
of an inch in thickness. These connections shall be designed under
the supposition that the entire stress is carried by the plates and
rivets, no reliance being placed on abutting ends of channels.
Cover Plates for Chords. – Shall be ..................... - inch by … inches by
tº e º sº sº e s = * * * * * * as a e s is sº inches, and shall contain as many rivets on each side of the
joint as will suffice to carry the greatest stress that can ever come
upon the chord plates.
O/PD/AVA R V /A’OAV HIGH WA P-AEA’/DGE.S. I63
Stay Plates for Chords and Batter Braces. – Shall be .............— inch by
sº is is a sº as a w sº º sº as a sºvºº we inches.
Posts. – Shall consist of two channels, of sizes as marked on the accompany-
ing diagram of stresses. The latticing for same shall vary from .................... •
inch by .........…. inches to ....................... inch by ....................... inches; the bars
being riveted together where they cross each other. The posts are to
be attached at their ends to the chord pins, and are proportioned for
both ends hinged. At the upper ends the connections are to be made
by extension plates, each of which is to have a sectional area between
the pin hole and stay plate equal to twice that of the channel to which
it is attached. The entire stress in the posts is to be considered as
carried by the extension plates and their rivets, no reliance being
placed on abutting ends of channels.
laced
atticed,
given on the diagram of stresses, rigidly attached to the chords.
lacing tº g *
The lattice bars for same shall vary in section from ..................... inch
Upper Lateral Struts. – Shall consist of two channels, I of sizes
by ~~~~ inches to ........................ inch by ....................... inches; and the
stay plates, from ....................... inch by ....................... inches by ......................
inches to … inch by … inches by ....................... inches.
One
two
each composed of two ....................... inch channels, as marked on the
Portal Bracing (at each end of the span). — Shall consist of struts,
l
diagram of stresses, º ced by bars …~~~ inch by ...................... ſº
inches in section, with stay plates ....................... inch by........................ inches
by ~~~~ inches; also four adjustable rods, each ....................... inches
in diameter. The struts are to be rigidly attached to the batter
braces.
Vertical Sway Bracing (between posts). — Shall consist of two vibration rods,
each … inch in diameter, and an intermediate strut of .......................
inch I-beam, weighing ...................... pounds per foot, rigidly attached to
the posts at a distance of ..............– feet … inches below the
level of the upper chord pins.
End Lower Lateral Struts. – Shall consist of
Intermediate Lower Lateral Struts. – Shall consist of ........................ inch by
*** * * * * * * * * * * * * * * * * * * * * inch pine timbers lying upon the floor beams, and well bolted
thereto, and attached by wrought-iron jaws to the chord pins.
I64 OA'D/AVA R V /A’OAV HIGH WA Y-BA’/DGE.S.
Side Bracing. — Shall consist of ....................... inch by … inch --~~~~
pound angle iron, well riveted to the top chord and to the floor beams,
which are prolonged ....................... feet … inches at each end be-
yond the trusses for this purpose, as shown on the accompanying
drawing.
Bottom Chords. – Shall consist of eye bars, as marked on the diagram of
stresses; those in the two panels next to each end of the span being
trussed.
Main Diagonals. – Shall consist of eye bars of the sections marked on the
diagram of stresses.
Counters. — Shall consist of adjustable rods with loop eyes, the sections
being as marked on the diagram of stresses.
Upper Lateral Rods. – Shall be from ....................... inch to ..…. inches
round iron, attached by bent eyes to the chord pins.
Lower Lateral Rods. – Shall be from ....................... inch to … inches
round iron, attached either to the chord pins by bent eyes, or to special
pins passing through the lateral strut jaws by loop eyes.
Floor Beams. – Shall be º beams … inches deep, weighing
As º a sº ºr e s a $ 5 & ºm m tº * * * * * * * * pounds per lineal foot; web ....................... inch by .......................
inches; upper flanges, two ....................... inch by … inch …
pound angles; lower flanges, two ...................... inch by ....................... inch
tº 8 º' & & & e º sº tº gº & © ºn 8 & 3 & 8 º' E & a pound angles. Stiffeners to be of ....................... inch by.....................
inch … pound angles, ....................... per beam, made flush with the
vertical legs of the flange angles by filling-plates.
B H A be of inch round . upset
eam Hangers. — Are to be of ........................ II].C Square Iron, not upset:
four
there are to be tWO of them to each beam.
Beam-Hanger Plates. – Are to be ...................... inch by................. inches by.….
inches.
inch
Shoe and Roller Plates. – Are to be ......................, inches
thick.
Pins.—Are to be of the sizes marked on the diagram of stresses. They shall
be turned so as to fit the pin holes within one-fiftieth (gº) of an inch.
Pin Bearings, – All pin bearings are to be properly re-enforced.
OAºA)/AWA R P WRO/W HIGH WA P-AER/DGE.S. I65
Brackets. – A straight bracket of ....................... inch by ....................... inch …
pound angle iron is to be used to connect each post to the overhead
strut. Those for the portals are to be of ..................... - inch by …
inch … - pound angle iron, They are to be connected by
sº º sº w w a tº a ºn tº *** * * * * * * * rivets at each end.
Chord Heads. – Shall be of standard shapes, and so strong that the bar will
break in the body rather than in the neighborhood of the eye.
Upset Rods. – All adjustable rods, unless otherwise specified. are to have
their ends enlarged for the screw threads; so that the diameter at the
bottom of the thread shall be one-sixteenth (Ps) of an inch greater
than that of the body of the bar, square or flat bars being figured as if
of equivalent round section. .*
Riveting.—Riveting shall in every respect be in accordance with standard
authorities; and all riveted connections shall be designed for the
rivets to resist the greatest shearing, bearing, and bending stresses
that can ever come upon them, no reliance being placed upon friction
between plates. Q
Expansion. — Shall be provided for by
Anchorage. — At one end of span, the superstructure is to be an-
the
each
chored to the foundations by ....................... bolts, each ...................... inches
in diameter, and at least .....................- feet …~~~~ inches long.
Camber. — Shall be at least ....................... inches when the bridge is empty, and
at least … inches when fully loaded.
Floor System. —Shall consist of ...................... runs of ..................... inch by ......................
ine
inch . joists, dapped and spiked on the lateral struts; and the
floor plank shall be of ....................... inch pine or oak plank laid diago-
nally or square across the bridge, as may be preferred, and well spiked
to the joists. A felly plank of ....................... inch by ....................... inch pine
is to be well fastened down on each side of the bridge, and at the
middle if required.
Hand Railing. — To consist of
I66 OA’D/AWAA’ P IRO/W HIGAZ WA Y-ARA'ZZOGAE.S.
Details of Construction. — All details of construction to be properly pro-
portioned with due regard to the various direct and indirect stresses
that may come upon them. All joints to be machine dressed and to
fit perfectly. Riveting in the field to be performed in a skilful man-
ner, using the button set. There shall be no loose rivets in the
bridge.
Quality of Materials. – Iron for tension members to have an ultimate
strength of ....................... pounds per square inch, and an elastic limit of
* * * * * * * * * * * * s tº e º is see s sº pounds per square inch. Iron for compression members to
have the usual correspondence of strength. All timber to be sound
and of good quality.
Workmanship. — All workmanship to be first class in every respect, and to
be performed to the satisfaction of the engineer or commissioner in
charge.
(Signed) º SMITH & WILLIAMS.
With the diagrams of stresses, plans, and specifications, there
should be handed in, or sent to the commissioner, a proposal in
the following or some similar form : —
To the County Commissioners of County,
State of
GENTLEMEN, - We the undersigned hereby agree to build, and put in con-
dition for travel, the superstructure of an iron highway-bridge of .............................
spans, across , in the County
of , State of , according
to accompanying plans and specifications, for the sum of
dollars cents ($ ).
SMITH & WILLIAMS.
, I88.
After the contract has been awarded, the successful com-
petitor and the commissioners must sign it, and a bond must
generally be given by the company as a guaranty that they will
complete the work according to the specifications. It is well
for the representative of each company to be provided with
ORD/wARY IRON HIGHWAP–BRIDGES. 167
blank forms for contract and bond. The author would recom-
mend the following for this purpose:–
BRIDGE CONTRACT.
This Agreement, made and entered into this day
of , A.D. 188....., by and between SMITH & WILLIAMS,
bridge builders, of the City of Pittsburgh, State of Pennsylvania, parties of
the first part, and
County of , State of
parties of the second part,
Witnesseth That the said parties of the first part hereby agree to furnish,
and erect complete and ready for travel, the Superstructure .......................................**
- of a - bridge
a CIOSS , in said county,
according to the plans and specifications hereunto attached, which are made
a part of this contract.
And the said parties of the first part hereby agree to have said structure
completed, and ready for inspection, on or before the day
of A.D., 188....., allowing a reasonable amount of time
in case of unavoidable delays in shipping, by reason of high water, or acci-
dents in construction.
And the parties of the second part agree to have the abutments for said
bridge completed by the * ........... day of
A.D. 188...... But in case the said abutments are not finished in the specified
time, and the parties of the first part have delivered the material for said
bridge at site of same, then the parties of the second part shall pay the
parties of the first part seventy-five per cent of the contract price.
And in consideration of the above presents, the said parties of the second
iº
z
I68 O/º/D/AVA R P YRO/V HIGH WA P-B RIDGE.S.
part contract, and agree to pay to the said parties of the first part the sum of
dollars, payable as follows:
In witness whereof the said parties do hereunto affix their seals and
signatures the day and year above written.
[SEAL.]
[SEAL.]
[SEAL.]
[SEAL.]
BOND FOR BRIDGE CONTRACT.
Know all men by these presents, That we, SMITH & WILLIAMs of Pitts-
burgh, Penn., as principals, and .
as sureties, are held and firmly bound to the
in the State of in the penal sum of
dollars, for the payment of which, well and truly to be made, we bind our-
selves, our heirs, executors, administrators, and assigns, jointly and severally,
firmly by these presents.
Dated at in the County of
and State of this day of , I88.......
The condition of this obligation is such, that if the said SMITH &
WILLIAMS Construct ................................... bridge in the aforesaid county, according
to the plans, specifications, and contract hereto attached
then this obligation to be void and of no effect, or otherwise to remain in
full force and virtue in law.
Principals.
Szereties.
OA'D/AWA R P WA’O/V AIGA WA P-BA’/DGAE.S. 169
The previous remarks concerning methods of bridge lettings
will probably not be altogether approved of by contractors.
Mr. A. P. Boller, C.E., in his treatise on “Iron Highway-
Bridges,” writes, “It will be noticed in the last clause of the
form for ‘Invitation,’ bidders are requested to be present at
the opening of the bids, and hearing them read. This is simple
justice. And when one considers the time required to make
plans and estimates, even for a small piece of work, to say
nothing of the expenditure of money incident thereto, with
probable travelling-expenses in addition, no fair-minded man
can object to rendering at least what satisfaction may be derived
from the public opening of tenders. Bids secretly opened
always lead, whether justly or unjustly, to the suspicion of
unfair practices, an imputation that can be readily removed by
the method of publicity suggested, a method which can be
objected to by no one, unless those whose mode of doing busi-
ness seeks darkness rather than light.” This is a clear and
well-stated argument, and it is difficult to propose a method
that will overcome every objection advanced. However, there
are some points in it that will bear criticising.
For a bridge worth, say, twenty thousand dollars, all that
Mr. Boller says is certainly correct. But is it so for a small
county bridge 2 The majority of county bridges do not exceed
one hundred feet in length, and they are very often let singly.
How long will it take, in a well-regulated office, to prepare
plans and estimates for an ordinary one hundred-foot county
bridge 2 Usually about thirty minutes; at any rate, no more
than two or three hours. The work consists in taking out of
their proper places a blue print of the diagram of stresses, a
sheet of details, a general plan, and blank forms of specification
and proposal, then filling out the two latter, and enclosing all
in an envelope for the post. The making out of the estimate
of cost should not take five minutes when the amounts of iron
and lumber, and a complete list of data, are at hand. If the
span be of unusual length, as sometimes happens when re-
placing an old structure, it may be necessary to make out a
new diagram of stresses, but not to prepare a bill of material ;
for every bridge company should have tables of weights of iron,
17o OA’D//VAA’ Y WA’O/V Aſ/GA/WA P-BA’AZOGA.S.
and amounts of lumber, for all ordinary cases. The actual
cost to the contractor, of an ordinary county bridge of one
hundred feet span and sixteen feet clear roadway, can be seen
from the following estimate : —
Wrought-iron, 27,900 lbs. at 5c. . . . . . . . . . $1,395. oo
Lumber, Io,880 ft. at $18 per M. . . . . . . . . . I95 84
Hauling, 20 loads, at $1.5o . . . . . . . . . . . 3o Oo
Framing . . . . . . . . . . . . . . . . . 7 oo
Falsework . . . . . . . . . . . . . . . . . 25 Oo
Erection . . . . . . . . . . . . . . . . . I 50 Oo
Painting . . . . . . . . . . . . . . . . . 25 OO
Blacksmithing . . . . . . . . . . . . . . . 5 Oo
Coal . . . . . . . . . . . . . . . . . . . 2 OO
Freight on tools . . . . . . . . . . . . . . . I 5 OO
Travelling-expenses . . . . . . . . . . . . . 30 OO
Men's time travelling . . . . . . . . . . . . . 2O OO
Bidding-expenses . . . . . . . . . . . . . . 4O OO
Teaming during construction . . . . . . . . . . IO OO
Incidentals. . . . . . . . . . . . . . . . . 5O OO
Total cost of bridge . . . . . . . . . . . . $1,999 84
Cost per lineal foot, say . . . . . . . . . . 2O OO
Adding twenty per cent for profit would make the bridge'
cost the county $2,400. Now, suppose there are ten other
bidders present, each of whose expense for time and travelling
is forty dollars; then there will be an additional four hundred
dollars to be added to the cost of this or some other bridge,
for, as before stated, some one must pay it. Eleven is by no
means an unusual number of bidders for a small span : there
are often as many as fifteen or sixteen. -
The estimate for forty dollars for time and travelling-expenses
is not excessive, as the author, who has attended a number of
lettings, can testify.
These four hundred dollars are worth saving, if it can be
done legitimately.
As for bids secretly opened always leading to the suspicion
of unfair practices, it is indeed true; and there is no way of
avoiding the difficulty, except by having them opened by a com-
mittee of public men who are above suspicion. These could be
ORD/AWA R V IRO/V HIGH WA P-B/C/DGAE.S. I71
government employees, and residents of the capital of the State,
to which bids for all county bridges should be sent. The duty
of the committee would be merely the opening of the bids, and
the recording of the amounts. The inspector of bridges, who
should also reside in the capital, should then examine the bids,
and report to the county commissioners, which, in his opinion,
is the best bridge for the money (i.e., which he would advise
them to accept), and which bridges are up to the specifications,
and which not, leaving the final decision to the commissioners.
A summary of his report should be advertised in certain of
the engineering-papers, say the two which have the greatest
circulation, so as to let the public see that there has been fair
play, and to clear the inspector of any imputation of unfair prac-
tice. The advertising of the report, including the price for each
bridge and the estimated weight of iron in same, would serve
to prevent any connivance between contractors and commis- .
sioners; because any decided departure from the recommenda-
tion of the inspector would immediately awaken suspicion.
No bids without an estimated weight of iron should be
received ; and, should the inspector doubt the genuineness of
the estimate, he could easily check it.
Then, too, the bridge should be weighed at the railway sta-
tion nearest the site; and, if the weight be found wanting more
than a certain per cent of the estimated amount, the contractor
should be fined.
In this way the only possibility of fraud would be an agree-
ment between a certain bridge company and all the members
of the committee for the latter to insert the contract price in
their bid so as to make it just a little lower than that of any
other competitor. Considering that the committee would be
composed of a number of the most prominent state officials, the
probability of such a fraud ever occurring reduces to zero.
I72 ORDIMARY IROM HIGHWA K-BRIDGES.
CHAPTER XVIII.
WORKING-T)RAWINGS.
THE first points to be determined before commencing a work-
ing-drawing are the scale and the size of the paper. The least
scale which it is convenient to use is one inch to the foot, and
the greatest scale for a whole drawing should seldom exceed an
inch and a half to the foot. If a smaller scale than one inch
be used, difficulty will be experienced in writing the rivet spacing
between the rivet holes. The width of the paper should be from
three and a half to four and a half, or even five feet: and, as
for the length, it is better to use roll-paper, and not to cut it
until the limits of the drawing be determined ; for it is a great
convenience to be able to make all the working-drawings for a
bridge upon a single sheet. *
The following is a draughtsman's equipment for making
working-drawings in a methodical and expeditious manner : a
table from four to five feet wide, from six to eight feet long,
and about three feet high ; a pair of steps each three or four
inches rise, and three feet long ; a bevelled steel straight-edge, at
least three feet long; a beam compass with tangent screw attach-
ment; a couple of small triangles (rubber ones are the best);
some four-H and six-H pencils; a little tracing-paper; a finely
divided duodecimal boxwood scale (the subdivisions being quar-
ters, eighths, and sixteenths); a good box of instruments, includ-
ing a protractor and a pair of hairspring dividers; and the usual
outfit of rubbers, tiles, pens, etc., that one finds in draughts-
men's offices. T-squares, large triangles, and parallel rulers
should never be used in making a working-drawing. The first
can never be depended upon, because of the impossibility of
having both board and T-square always perfectly true; no
ORD//WAA’ P IROAV HIGH WA Y-B/P/DGAE.S. I73
wooden ruler can be relied on not to warp; and parallel rulers
are a delusion. -
For a few inches it is permissible to turn right angles with
triangles, but for long distances the beam compass should be
used ; and parallel lines can be most accurately drawn by erect-
ing a perpendicular near each end of the original line, and
laying off on them equal distances. When distances are a little
too great for the triangles, and too small for the beam compass,
the large ordinary compasses can be used; but it will be found
that they are seldom required. The four-H pencils are to be
used for writing dimensions, etc., and the six-H ones for draw-
ing lines. The draughtsman should always have at least one
of the latter sharpened to a chisel edge for ruling, and another
to a point for sketching. He will find it to be greatly to his
advantage to keep his pencils always well sharpened, for an
error of the width of a pencil-line will often cause a great deal
of inconvenience. A piece of emery paper or a fine file will be
found useful for sharpening pencils. The tracing-paper will
be convenient in transferring drawings of similar chord heads,
etc. : its function is merely the saving of a little time.
It is generally better to have both a long and a short scale.
The long one may be divided into feet only, the inches and frac-
tions of inches being taken from a diagonal or other small scale.
If the draughtsman be not provided with a suitable scale, he
can easily prepare a very fair one for himself on a strip of the
roll of paper upon which the drawing is to be made.
The method of projecting one view of a piece from another
view will not do for working-drawings, owing to the liability of
the triangles to slip. All measurements should be transferred
by the dividers; and, if there be any probability of the points of
the dividers having been moved, the distance between them
should be tested by laying it off once more upon the original
length. There should be no more than a single transferrence
of any one distance, for errors often increase, instead of bal-
ancing. -
The general arrangement of a working-drawing consists
merely in laying out a plan and elevation of one-half of the
span, leaving at least a foot of space at each end, and six or
I74 ord/MARY IRoy HIGHWA K-BRIDGES.
eight inches above the elevation and below the plan, if there be
room to spare, with the same distance, or a little more, between.
As it is immaterial if different portions of the drawing cross
each other, provided that such intersection cause no conflicting
of the measurements, the various members may be shown in
several views alongside of their respective positions in plan and
elevation.
Thus the top chord may be represented in an under and an
upper view above the elevation of the truss, and the batter
brace may be shown in a similar manner above and to one side
of the elevation. Projections of the posts on planes transverse
to the bridge may be drawn alongside and a little below the
elevation of these members, the amount of lowering being
sufficient to bring the ends of the strut clear of the chords,
Attached to the projections of the posts can be shown the inter-
mediate struts and vibration rods, with their connections; and
shortened views of the chord bars and diagonals can be placed
alongside their elevations in order to represent the heads clear
of all other members. Passing to the plan, on one side is drawn
the packed lower chord, and attached thereto the lower lateral
rods and struts in half-length ; while alongside the latter can be
represented an elevation of the same with the floor beam's
beneath, and an end view of the beams near by. At the other
side of the plan, can be shown half-lengths of the upper lateral
rods and struts in two views, and a projection of the portal
bracing on the plane of the batter braces, and on planes at right
angles thereto. Each detail can be delineated to any required
extent in the neighborhood of its position in plan, elevation, or
both. If necessary, the panel points on one side of the plan
may be brought opposite the middle of the panels on the other
side, in order to avoid too much intersection.
This arrangement, although a good one, is by no means the
only one, and in some cases might not be the best. For instance,
in skew bridges it would be well to show the whole of the lower
lateral system in the plan, and the whole of the upper lateral
system above the elevation, in connection with the uppermost
view of the top chord, which should be the plan from above.
Then, again, if the bridge be a large one, the height may be so
OAQAD/AWAAC P VROAV HIGH WA P-BR/DGE.S. I75
great that it will be impossible to show the plan below the eleva-
tion; in which case it will be necessary either to make separate
drawings for the plan and elevation, or to place one alongside of
the other on the same sheet. In making tracings of the work-
ing-drawing, the tracing-cloth can be shifted about so as to
group similar parts and so as to avoid too much intersection of
different portions.
Provided that any piece be symmetrical about a plane cutting
it at the middle of its length and at right angles thereto, it will
be sufficient to show only one-half of the piece; and the meas-
urement may be referred to the end of the member, to the
central plane, or to both. Where the same detail is used in more
places than one, it is not necessary to show it more than once,
provided that it be exactly the same in every respect.
As an illustration of how to make a working-drawing, take
the case of the bridge treated in the last chapter, and assume
that the paper and table are each four and a half feet wide.
Using the scale of an inch to the foot, the depth of the eleva-
tion will be two feet, and the width of the plan one foot four
inches. Allowing six inches above the elevation, and as much
more between elevation and plan, will bring the lower side of
the plan within two inches of the edge of the paper: this
arrangement will do very well. The first step is to draw a line
with the steel straight-edge, as nearly as possible, without taking
too much trouble, parallel to the length of the paper, and at a
distance of two feet six inches below the upper edge. This
line should be very fine and perfectly straight. It can be made
so by prolonging it half the length of the straight-edge at a
time, and afterwards testing it in several places. On this line
take a point a foot or more from the left-hand end of the paper,
as the centre of the end lower chord pin. Lay off along this
line with the greatest possible accuracy the panel length, until
the centre of the bridge be reached; in this case twenty feet
must be laid off four times. At the panel points erect short
perpendiculars with the triangles, and on the perpendicular at
the centre lay off the camber, which in this case is three inches
(see p. 9). Had the bridge contained an odd number of panels,
it would have been necessary to draw the middle panel, and
176 OA’A)/AVA A' V /A2O/V AZZOAZ VVA P-BA’ZZOGAE.S.
lay off the camber of three inches at each end of this panel.
Then, assuming the curve of the chord to be a parabola, the
fall from the centre to any panel point is equal to the camber at
the centre multiplied by the square of the ratio of the distance
of the panel point considered from the middle of the span to
the half-length of span.
Thus in the case considered, the falls at the first, second, and
third panel points will be respectively 3(3)*, 3(3)”, and 3(4)”, or
#!", #", and #;", making the heights of these points above the
horizontal line respectively 3" — #4", 3" — #", and 3" — #", or
I Hºs", 2}", and 24;"; which distances are to be laid out upon the
perpendiculars so as to locate the centres of the lower chord pins.
The length of the panels as thus determined differ from those
of their horizontal projections by an inappreciable quantity. If
there be any lengthening of the chord, it may go against the
play of the pins in the eyes.
Next join the consecutive pin centres, producing them each
way a little more than a panel length, so as to facilitate the
erection of perpendiculars thereto. Then at each of the differ-
ent centres erect a perpendicular to each centre line meeting
there, and bisect the angle between the perpendiculars : the
line of bisection will be the centre line of the post. Great caré
must be exercised in turning these right angles with the beam
compasses, two points on each of the perpendiculars being
found, so that if these two points and the centre be in exact
line, the perpendicular may be relied on as correct. On each
of these centre lines lay off the depth of the truss, and complete
the skeleton diagram.
A partial check on the accuracy of the construction may be
had by measuring the panel length of the top, chord, which
should agree with the length calculated as follows. Let
£ = the increase in the panel length of the top chord above that
of the bottom chord,
c = the camber at the centre of the span,
s = length of span,
d = depth of truss,
and
n = number of panels.
ORDAVARY FROM HIGH WA Y-BRIDGE.S. 177
Then, according to the method given in Trautwine's “Pocket-
8ac
sn'
and p in inches. The panel length of the top chord will then
be / = 1 + p, where 2 is the panel length of the bottom chord.
This is not a certain proof of the accuracy of the work. Two
consecutive post centre lines might be equally inclined from
their correct positions, and on the same side, though this would
be shown in the next panel. A certain check must be obtained
by measuring the lengths of the diagonals, which should be
equal to each other, and agree with that found by the formula
2
p-Va-(+),
where D is the length required.
For double-intersection bridges, the length of the long diago-
nals can be found by the method given in Appendix III. The
length of the diagonal as manufactured should be one sixty-
fourth of an inch less than that calculated, so as to allow for
the play of the pins in the eyes. As a slightly greater allow-
ance for play is permissible, it is better to take the next smallest
sixty-fourth, if, after making the reduction just indicated, the
length should not come out on an exact sixty-fourth. Because
of the play in the pin holes of the bottom chord bars, the panel
length of the manufactured top chord should exceed the calcu-
lated length by about a thirty-second of an inch.
Next fill out the elevation of the chords, posts, diagonals,
and batter brace, without showing details. Alongside of each
tension member show the heads with their dimensions, and on
the shortened distance mark the size of the bars, the number
of them, and the length from centre to centre, as shown on
Plate VI.
At the right-hand end of the drawing, or on a separate sheet,
whichever be more convenient, draw out the heads full size,
placing one on the other, if this can be done without confusion.
Sometimes as many as six heads can be represented about one:
centre, provided that both pins and heads diminish together.
For hammered heads the method of construction is very sim-
Book,” p =
where d and s may be measured in feet, and c
178 ORD/AVA R Y IRO/W HIGH WA P-B RIDGE.S.
ple. It consists in describing, as in Fig. I of the accompanying
diagrams, a circle of radius CA, equal to that of the pin hole,
and a portion of another circle with a radius CB, equal to that
of the pin hole plus the product of one-
*— half the depth of the bar HK by the
ratio given in the table on p. 20; then
drawing the lines DE and FG parallel to
the sides of the bar, and at a distance
therefrom equal to CB; and with C as a
centre and a radius CD, equal to twice
CB, describing an arc to intersect DE
l/ and FG in the points D and F, finally,
with D and F as centres, and radii equal
to CB, describing the arcs HL and KM,
tangent to the sides of the bar at H and
A , and to the outer circle at L and M.
\ For welded heads the construction is
—N2 - as shown in Fig. 2, where the pin hole
and bar are laid out as before. The dis-
tance AB is equal to one-half of HK multiplied by the ratio given
in the table on p. 20; and the distance SO is equal to HK, or the
diameter of the pin hole, whichever be the greater. The cen-
tres P and R of the arcs OB/, and OTM respectively are found
by trial; then DE and FG are drawn parallel to the sides of the
bar at distances therefrom DH and FK, equal to one and seven-
tenths times PB or R T and with P and R as centres, and
radii equal to two and seven-tenths times PB or RT, or, what
is the same thing, equal to DH plus PB, arcs are described
cutting DE in D, and FG in F; finally, with D and F as cen-
tres, and with radii equal to D.H., arcs are drawn tangent to the
sides of the bar at H and K, and to the arcs OB/, and OTM at
L and M respectively.
These constructions, with slight modifications, are taken from
Trautwine’s “Pocket-Book.”
Next show the posts and the attached sway bracing in two
projections with all their details. There should be allowed a
clearance of about an eighth of an inch for the ends of the posts
inside of the chord. The positions for the stay plates should
O
&
ºs-
Fi
9-
2
T
~

oRD?/ARY IRow HIGHWA K-BRIDGES. I79
be as close to the pin as possible, allowing a little clearance for
the diagonals. The proper positions can be ascertained from
the general elevation. The lattice bars should be close to the
stay plates: it will not be necessary to show more than a few
of them on each strut, the positions of the others being indi-
cated by their centre lines, as shown on Plate VI. This plate
contains a portion of a working-drawing for a model of the
bridge treated in the previous chapter. The small scale of
three-quarters of an inch to the foot was chosen so as not to
make the model too large; and the whole working-drawing is
not given, because of the necessarily limited size of the plate.”
The principal portions are represented; so that one can, by
studying the plate closely, learn all that it is necessary to know
in order to make working-drawings; and students are recom-
mended to give this matter special attention.
Next show in two projections the top chord and batter brace
with all their details, and give several views of each connect-
ing-plate and other detail in the neighborhood of its position on
the elevation. The joints in the channels and plate of the top
chord should be located three or four inches to that side of
each panel point which is farthest from the centre of the bridge,
so that the pin holes shall be bored through a single piece, and
through the thicker of the two abutting pieces. At the hip
joint it is of course unavoidable to bore the pin hole through
the abutting ends of the chord and batter-brace channels.
Next pass to the plan, where the first thing to do is to draw
parallel to the original horizontal line of the elevation traces of
the central vertical planes of the trusses and of the central
plane of the bridge, locating the panel points very carefully, and
as nearly as possible vertically, below their corresponding posi-
tions on the elevation. Then arrange the chord packing on
one side of the plan so as to make the bending-moments on the
pins as small as possible without having any of the chord bars
pull at too great an angle with the plane of the truss.
If any of the panels have trussed bars, the trussing should
be here shown, and the spacing of the rivet holes for same in
* The scale has been further reduced by the engraver.
I8O orDIMARY IRow HIGHWA y—BRIAEES.
the chord bars should be represented close to the plan of the
trussed bars. Near the packing should be drawn separate
views of the lower chord pins; giving their number, diameter,
lengths between shoulders, diameters and lengths of reduced
ends, and the total lengths, also the sizes of the nuts.
At the right-hand end of the plan, show the lower lateral
struts, and complete drawings for the floor system, including
beams, beam hangers, beam-hanger plates, bolts, joists, etc.
Generally the floor beams will be all alike: so it will be suffi-
cient to represent half a beam. It may even do to show only
half of a lateral strut, although there are always several differ-
ent lengths of them in a bridge, provided that there be written
sufficient directions to enable the carpenters to frame all the
struts without possibility of error. In writing dimensions, etc.,
upon a working-drawing, it is immaterial from which direction
the writing be read ; that is, it may be read sidewise, upside
down, or in any direction most convenient to the draughtsman.
In making tracings, this matter can be rectified if it be thought
advisable. Full directions for the manufacturer should be writ-
ten on the drawing. On the rest of the plan, show the upper
lateral struts with their details ; all the lateral rods with their
turn buckles or sleeve nuts, and their eyes in two views; the end
lower lateral strut with its details, and its connection to the
pedestal ; the whole of the portal bracing with its connections;
the ornamental work ; and the name plates. *
Finally, take the list of members, and go carefully over the
drawing with it; seeing not only that each piece is represented,
but that there are sufficient measurements given to have it
manufactured.
The following additional directions and hints may be found
useful. Refer each group of rivets to some local line, which is
itself referred to the end of the piece, or some other prominent
part. Show a section of each member, and write the dimen-
sions of all channels, angles, I-beams, etc., near the section.
Write along each piece its extreme length or lengths, its length
from centre to centre of eyes, and of what it is composed. The
ends of the two pieces of an adjustable rod should be separated
by at least three or four inches in the turn buckle or sleeve nut.
ORDVAWARY IROM HIGH WA V-B RIDGES. I8 I
Mark what rivets are countersunk, and at which end. If the
scale of the drawing be large enough, the countersinking can
be thus represented: draw full parallel lines across the rivet
for countersinking on the upper side, dotted parallel lines for
countersinking on the lower side, and two sets of parallel lines
crossing each other at right angles for countersinking on both
sides. Be careful to always note how many rights and how
many lefts of each piece will be required, when there are both
rights and lefts. f
Do not forget to write conspicuously the scale or scales of
the drawing. Lay out all bevelled edges on an enlarged scale,
say from half to full size, and mark their dimensions along the
edges, referring all measurements to a transverse line through
some well-defined point, as the centre of the pin hole. These
measurements should be checked by calculation. The slight
bevels at the joints of the top chord should be treated with as
much accuracy as the bevels at the hip joints; but, as the bevel
is very slight, it will be legitimate to put it all on one of the
abutting ends, making the other a square cut.
The centre lines for lacing-bars on the under side of a strut
should be dotted. In laying out a long row of rivets—for in-
stance, lattice rivets, or those for the top plate of a chord or
batter brace—calculate the distance of some of the intermediate
rivet holes from one end of the strut. Lay out these holes, then
interpolate the others; because, if the spacing be laid out con-
tinuously from one end with dividers, any error in the span of
the dividers will be multiplied by the number of times the dis-
tance is laid off.
After laying out a complete system of rivets for any member,
check by seeing that the sum of the distances between rivet
holes plus the distance of each end rivet from the end of the
member is equal to the total length of the member. Make
duplicates of as many parts of the bridge as possible, even at
the expense of a small amount of iron, not only to save time in
draughting, but also in the shop, and to facilitate the work
in erection.
Arrange to have as few loose pieces for shipment as possible,
and mark on the drawing of each connecting-piece to what it is
I 82 ORD//VARP WROM A ZGAA WA P-BA’/ DGAE.S.
to be attached, or if it is to be left loose. Thus the hip con-
necting-plates should be attached to either the chords or batter
braces, sometimes to both ; those of the top chord, to that por-
tion through which the pin hole is bored ; those for the upper
lateral struts should be left loose. If there be any reason to
fear rough handling of the iron in transit, it may be necessary
to send some of the connecting-plates separately; but the more
loose pieces, the more field riveting, and the more field riveting,
the greater the erecting expenses, and the longer the time and
the greater the risk in raising the bridge.
Rivet spacing should be as regular as circumstances will per-
mit; and all changes in spacing should be made suddenly, instead
of gradually, so as to facilitate the punching of the holes by
machine.
All measurements should be in feet, inches, and the following
vulgar fractions of inches; viz., halves, quarters, eighths, six-
teenths, thirty-seconds, and sixty-fourths. Workmen do not
seem to understand decimals: so it is better not to use them.
Avoid also the use of the development method, as it is beyond
the comprehension of ordinary workmen.
The length of all main members should be measured on the
drawing, then checked by calculation.
When nuts are placed in a confined position, — for instance,
pin nuts in jaws, – care should be taken that there be ample
room for them to turn in ; as it is very awkward, and sometimes
impossible, to screw up a nut which is stationary, by turning
the pin. Nuts in confined positions may be turned by hammer-
ing them eccentrically.
Be careful to design no connection in such a manner that
there will be rivets that cannot be driven without incon-
venience. This remark is especially applicable to field riveting.
It must be borne in mind, that, no matter how carefully the
bill of iron was prepared, there will be many minor changes
found necessary in making the working-drawings; but, as a
rule, such changes cannot materially affect the total weight of
iron in the bridge.
OA'D/AWARP IRO/V HIGH WA Y-B/C/DGAE.S. I83
CHAPTER XIX.
ORDER BILLS AND SHIPPING BILLS.
WHEN there is necessity for haste in building a bridge, as
there generally is in America, time can be saved by sending a
partial order bill to the manufacturers before starting to make
the working-drawings, or after they are partially pencilled.
Such preliminary order bills should include only those por-
tions which are termed in this treatise “Main Members,” and
those details of the sizes of which the designer is certain ; for
instance, stay plates, pins, brackets, and the plates and angles
for built beams.
The length of the main members in the bill should be three-
quarters of an inch greater than will actually be required, in
order to allow for the dressing of rough ends; and, should there
be any doubt in the designer's mind concerning the exact length
of any piece, he should make the ordered length great enough
to cover any variation which there may be in the design.
Of course, where there are bevelled ends on a piece, the
extreme length plus the allowance for waste must be given.
Where a number of small pieces are to be cut from one large
piece, an extra allowance of length must be made to provide
for the waste in cutting, say from an eighth to a quarter of an
inch for each short length. After finishing the pencilling for
a working-drawing, the remainder of the preliminary order bill
may be made out and sent. It should be divided into the fol-
lowing groups, containing the measurements indicated:—

No. Depth Weight per foot Length Finished length
Channels
I84 OA’DAVARP WA’OAV HIGH WA P-AERYDG E.S.

Angles | No. Thickness | Legs Weight per foot Length Finished length

I-beams No. Depth Weight per foot Length Finished length
Plates No. 1 Thickness Width Length Finished length
e D Length centre to
Eye bars || No. Thickness Depth epths of heads centre of eyes Extreme length
DIAMETER. SHORT PIECE. LoNG PIECE.
Adjustable
rods with ||No. Rod | Upset Diame- Length of Length, Diame- Length of Length,
plain eyes end ter of loop centre of ter of loop centre of
eye eye to end eye eye to end
*
DIAMETER. SHORT PIECE. LoNG PIECE.
Adjustable rods || No. |
with bent eyes Rod Upset | Diameter | Length, centre | Diameter | Length, centre
end of eye of bend to end of eye | of bend to end
DIAMETER.
Pins No. Length between shoulders Extreme length
Body Reduced
ends
Rollers No. Length between shoulders Extreme length






Any details which will not go into one of these groups will
be made of material that the manufacturer keeps in stock; for
instance, fillers, washers, nuts, turn buckles, sleeve nuts, orna-
ORDIMARP IROM HIGHWA P-BRIDGES. 185
mental work, name plates, bolts, and iron hand railing. It
would not be a bad idea for bridge companies to keep blanks
similar to the foregoing, for preliminary order bills.
Pins should be ordered an eighth of an inch greater in diame-
ter than required in the bridge, so that they may be turned
down; and shoe plates and roller plates, one-sixteenth of an
inch thicker, to allow for planing.
Spikes are generally purchased separately, by the keg, from
special dealers.
Lumber is, of course, bought separately: it should be ordered
in the following form:—

No. pieces Thickness Width Length Kind of wood
After the working-drawing is finished, there should be pre-
pared to accompany it a final order bill, in which are to be
grouped all similar pieces, and all their details which are
attached to them in the shop. The following grouping will
cover any case of an ordinary iron highway-bridge designed
according to the method of this treatise:–
TOP CHORD SECTIONS.

Channels. No. Depth Weight per foot Finished length
Top plates No. Width Thickness Finished length
Cover plates . No. Width Thickness Finished length
Stay plates No. | Width Thickness Finished length
Lattice bars No. Width Thickness Length centre to centre of end
- rivet holes
Connecting-plates . No. Width Thickness Finished length
BATTER BRACES.
Channels. No. Depth Weight per foot Finished length
Top plates g No. Width Thickness . Finished length
Cover-plates (hip) . No. Width Thickness Finished length
Stay plates No. Width Thickness Finished length
Lattice bars No. Width Thickness Length centre to centre of end
- rivet holes.
Connecting-plates . No. Width Thickness Finished length
Shoe plates No. Width Thickness Finished length

I86
ORD/AWA R P IRO/W HIGH WA P-BA’/DGE.S.
CHANNEL BOTTOM CHORDS.

Channels. & Cº º No. Depth Weight per foot Finished length
Stay plates . . No. | Width Thickness Finished length
Lacing-bars No. Width Thickness Finished length
Re-enforcing plates No. Width Thickness Finished length
Connecting chord heads. No. Depth Thickness Length centre of eye to end,
and extreme length
POSTS,
Channels. wº º e No. Depth Weight per foot Finished length
Stay plates . . . No. Width Thickness Finished length
Lattice bars . . . No. Width Thickness Finished length
Extension plates No. Width Thickness Finished length
Re-enforcing plates. No. Width Thickness Finished length
UPPER LATERAL STRUTS.
Channels. * & & No. Depth | Weight per foot Finished length
Stay plates No. Width Thickness Finished length
Lacing-bars No. Width Thickness Finished length
Jaw plates . . . No. Width Thickness Finished length
*
END LOWER LATERAL STRUTS.
Channels. No. Depth Weight per foot Finished length
I-beams . e ſº tº No. Depth Weight per foot Finished length
Angle irons . º * No. Legs Weight per foot Finished length
Stay plates . . . No. Width . Thickness Finished length
Lacing-bars No. Width . Thickness Finished length
Jaw plates No. Width . Thickness Finished length
PORTAL STRUTS.
Channels. No. Depth Weight per foot Finished length
Stay plates No. Width Thickness Finished length
Lattice bars No. Width Thickness Finished length
Jaw plates . . . . Îl No. Width Thickness Finished length
Connecting-plate to batter-
brace . . . . . || No. Width Thickness Length of each leg
Connecting-plate for brackets
to channels . . . || No. Width Thickness Finished length
Connecting-plate for name
plates to channels No. Width Thickness Finished length




ORD//VARP WRO/V HIGH WA V-BAC/DGF.S. 187
STIFFENED HIP VERTICALS.

Channels. . . || No. Depth Weight per foot Finished length
Flat bars. . . . No. Width Thickness | Length centre to centre of eyes,
- and extreme length
Stay plates . tº º No. Width Thickness Finished length
Lacing-bars . . . No. Width Thickness Finished length
Re-enforcing plates. . No. | Width Thickness Finished length
Trussing. g No. Width Thickness Finished length
INTERMEDIATE STRUTS.
I-beams . ſº No. Depth Weight per foot Finished length
Connecting-plates . No. Width . Thickness Length of each leg

MAIN DIAGONALS AND PLAIN CHORD BARS.

e Depth of Thickness | Diameter of Length centre to Extreme
No. Depth Thick
O ep ICKINCSS heads of heads eyes centre of eyes length
HIP VERTICALS AND COUNTERS.
No. Section Diameter of en- Lengths of loop | Lengths centre of eyes to ends, or centre

larged end eyes of eye to centre of eye
LATERAL AND WIBRATION RODS.

No. Diam Diameter of Length centre of eye | Length centre of bend or Length centre of bend or
g enlarged end to bend or loop eye to end of short piece eye to end of long piece
STRUTS OF TRUSSED CHORD BARS.
*9 of section Sizes of Section of Length of Length of strut cen- Extreme length
Struts heads trussing trussing tre to centre of eye of strut
SIDE BRACING.
No. Section Size of connecting-plate Extreme length of brace


IRON HAND RAILING.

No. of posts Sizes
of posts No. of panels Size of panel
Total length of railing
I88 ORDIMARY IRON HIGHWA Y-BRIDGES.
BUILT FLOOR BEAMS. ,

Plates . . No. Width Thickness Finished length
Angles . . No. Legs Weight per foot Finished length
TRUSSED FLOOR BEAMS.
I-beams . Q. No. Depth Weight per foot Finished length
Angles . º No. Legs Weight per foot Finished length
Plates . . No. Width Thickness Finished length
ROLLER AND BED PLATES.
Plates . . No. Width Finished Thickness Finished length
Angles . $ No. Legs Weight per foot Finished length
NAME PLATES.
No. Date.
OTHER SEPARATE PLATES.
No. Width Thickness Finished length
PINS AND THEIR NUTS.
No. Diameter Size of nuts Length under head, or extreme length .
BOLTS AND THEIR NUTS.
No. Diameter Size of nuts Length under head, or extreme length ,
BRACKETS.
Angles . º No. Legs Weight per foot Extreme length
Channels. & No. Depth Weight per foot Extreme length
Tee-iron . . No. Legs Weight per foot Extreme length







ORNAMENTAL WORK.

No. of pieces Description
OA’D/AWA R P VRO/W HZGAE/WA P-B/C/DGE.S. 189
BEAM HANGERS AND THEIR NUTS.

Diameter of Diameter | Size of nuts and | No. of nuts and
upset end of eye lock-nuts lock-nuts Length of one leg
No. Section
SETS OF ROLLERS.

Rollers . & tº ſº No. Diameter | Length between shoulders Extreme length
Cross-rods . . .] No. Diameter | Length between shoulders Extreme length
Side-bars . e e & | No. Thickness || Width Extreme length
FILLERS FOR PINS.

No. External diameter Internal diameter Length
TURN BUCKLES AND SLEEVE NUTS.

No. Taps
JAWS.
Plates . . || No. | } Width Thickness Extreme length
Channels. No. Depth' Weight per foot Extreme length
WASHERS.
No. Diameter - Diameter of bolts


SEPARATE RIVETS.

No. Diameter | Length under headſ Kind of head | Position in bridge Parts connected
PIN PILOTS.

No. External diameter Internal diameter
Some companies send also a complete bill of rivets to be used
in the shop; but this is scarcely necessary, as it is more properly
the place of the manufacturer to prepare such a bill.
I90 OAºA)/AVA R P ZAZOAV HIGH WA P-B/C/DGE.S.
The following form will be needed for the purpose: —
RIVETS.

Member
No. Diameter | Length between heads | Kind of heads Parts connected
An allowance of three per cent should be made for waste in
shop rivets, and from ten to twelve per cent in field rivets.
If the hip verticals be flat bars, they are to be transferred to
the group of “Main Diagonals, etc.” The posts, chord bars,
and diagonals of trussed beams, are included under the general
heads of “Posts,” etc. -
The corresponding form of “Shipping Bill” is as follows : —
STRUTS.

Member | No. Length centre to end, or extreme length Mark
BARS.

Member ||No. Section | Diameter of eyes | Sizes of heads | Length centre to centre of eyes | Mark
RODS.

Diameter of | Diameter of . Threads º: of *: Mark
eyes upset ends | R. or L. to end, or centre o 2.I.
eye to centre of eye
Member || No. | Diameter
SIDE BRACING,

No. Section Extreme length Mark
IRON HAND-RAILING.

No. of posts No. of panels Mark, if any
FLOOR-BEAMS.

No. Extreme length Mark
ORD/AWA R P ZA'O/V HIGH WA P-BAE/DGES. I9 I
*
ROLLER AND BED PLATES.

No. Position (fixed or free end) Mark, if any
NAME PLATES.
No. Date
OTHER SEPARATE PLATES.
No. Position Mark


PINS AND THEIR NUTS.

No. 1 Diameter
Length between shoulders | Extreme length
Dimensions of ends | Mark
BOLTS AND THEIR NUTS.

No. Diameter Diameter of upset ends Length under head, or extreme length
BRACKETS.
No. Position Extreme length Mark

ORNAMENTAL WORK.

No. of pieces Description Mark
BEAM HANGERS AND THEIR NUTS.
No. Diameter of eye No. of nuts and lock-nuts Mark
ROLLERS.


No. of sets
I92 ORDVAWARP IROM HIGHWA Pi—BAE/DGES.
FILLERS FOR PINS.

No. External diameter Internal diameter Length Mark
TURN BUCKLES AND SILEEVE NUTS.

No. Taps
JAWS.
No. Position Mark
WASHERS.
No. Diameter Diameter of bolt


SEPARATE RIVETS.

No. Diameter | Length under head || Kind of head Position in bridge | Parts connected
PIN PILOTS.

No. External diameter Internal diameter - Mark
The following is the system of marking iron before shipment
which the author would recommend. It should be thoroughly
comprehended by the manufacturer, the foreman in charge of
erection, and the time-keeper or clerk, if there be either em-
ployed on the work. g
Where the work is very extensive, the time-keeper generally
checks the material as it arrives on the ground.
First, if there be more than one span, each piece of each
span should be marked with a daub of color peculiar to that
span: thus the first span may be white, the second yellow, the
third blue, etc.; care being taken to choose such colors as will
be readily distinguished upon the iron-work.
The colors may be marked in the last column of each division
ORD/AVAA' P /ROM HIGH WA P-PAE/DGE.S. I93
in the “Shipping Bill” and at the end; thus the mark for a main
diagonal may be “3 Bl,” or “2 W.; ” the first representing the
third set of main diagonals in the third span, and the other the
second set in the first span. The letters Bl. are chosen for
blue, so as not to be mistaken for the letter B used elsewhere.
A similar precaution should be taken with the other colors.
In addition to this characteristic color-mark, each piece
should be marked in white paint according to the following
method.
R. and L. denote that the piece, if a main portion, lies to the
right hand or to the left hand when one stands at the nearest
portal, astride the centre plane of the bridge, and looks towards
the centre of the span. If a detail, it denotes that it lies to the
right or left hand when one stands astride the middle vertical
plane of the truss to which the
detail belongs, at the foot of
the nearest batter brace, and
facing the centre of the span.
The numbers can be readily
understood by referring to the
accompanying diagram.
Chord sections are to be numbered, and marked R. or L.
Batter braces are to be marked R. or L.
Channel bottom chords are to be numbered.
Posts to be numbered, and marked R. or L.
Upper lateral struts to be numbered.
End lower lateral struts to be marked Fix, or Fr. (fixed or
free end).
Portal struts to be marked U. or L. (upper or lower).
Intermediate struts to be numbered to correspond to the
posts to which they are to be attached.
Main diagonals and counters to be numbered.
Hip verticals need no mark.
Upper lateral rods to be marked U. I, U. 2, etc.; the numbers
corresponding to those on the diagram. -
Lower lateral rods to be marked L. I, L. 2, etc.; the numbers
corresponding to those on the diagram.
Vibration rods need no marks.
UPPER
LATERAL SYSTEM
TRUS8
W.OWER
SYSTEM)




I94 OA’/D//VA R P /A2O/V HIGH WA P-3A2/ZDGAE.S.
Chord bars to be marked I A, 1 B, I C, 2 A, 2 B, 2 C, etc.;
the numbers corresponding to those on the diagram, and the
letters denoting the position in the panel, A being for those on
the exterior side of the truss, B for those next to the outside, etc.
Side braces to be numbered to correspond to the panel points
to which they belong, and to be marked R. or L.
Iron hand railing requires no marks except E on the end
posts and panels, if these be different in any respect from the
others.
Floor beams to be numbered to correspond to the panel
points.
Roller and bed plates to be marked R. or L., if there be any
difference.
Name plates require no marks.
Separate plates to be numbered so as to correspond to the
panel points to which they belong, and to be marked R. or L.,
if necessary.
Lower chord pins to be marked L. O, L. I, L. 2, etc.; the
numbers corresponding to those of the panel points.
Upper chord pins to be marked U. I, U. 2, U. 3, etc.; the
numbers corresponding to those of the panel points.
Portal diagonal pins to be marked P.
Vibration-rod pins to be marked V.
Pins at middle of posts to be marked M. I., M. 2, M. 3, etc.;
the numbers corresponding to those of the posts.
Lower lateral-rod pins not to be marked, for they should be
shipped attached to the jaws.
Bolts need no mark, but should be boxed before shipment.
Brackets to be marked P. or I. (portal or intermediate), also
R. or L. -
Ornamental work to be marked R. or L. -
Beam hangers to be numbered so as to correspond to the
panel points to which they belong.
Rollers need no marks.
Fillers to be marked the same as the pins to which they
belong.
Turn buckles and sleeve nuts, being attached to the rods
before shipment, require no marks.
wº
ORD/AVA R P ZAPO/W HZGA WA P-BA’/DGAE.S. I95
Jaws to be numbered to correspond to the panel points.
Washers need no marks: they should be boxed, or strung on
bolts, before shipment.
Rivets need no marks, but should be boxed.
Pilot nuts need no marks, as there are so few of them required.
In addition to these marks, there should be others for those
members which are to be riveted together in the field, and
which are assembled in the shop when the rivet holes pre-
viously punched are reamed. These marks should be punched
into the iron with a steel point, and should consist of one, two,
three, or four dots upon each of the pieces so assembled, in
order that no piece during erection will be put into the wrong
place.
I96 OA’D//VAA’ Y / ROAV HIGH WA Y-B RADGE.S.
CHAPTER XX.
ERECTION AND MAINTENANCE.
THE number of men required to erect an iron highway-bridge
will vary from half a dozen to sixty, or even more, according to
the length of span, width of roadway, location, and the time
to be occupied in erection.
For any one bridge, there is a certain number of men which
will be more economical than any other number; and it is only
experience which will enable one to tell beforehand what this
number is.
If there are too few hands, the work will lag, and difficulty
will be experienced in handling heavy pieces: on the other
hand, if there are too many men, the travelling expenses, and,
the time spent in travelling by the extra men, will be wasted,
and the total amount of effective work done by each man per
day will be less.
If, for any reason, there be need for haste, it will be economical
to have a large force of men, notwithstanding the last-mentioned
consideration. For raising ordinary county bridges, the author
would recommend the following numbers of men in a gang: for
pony truss-bridges, six men; for through-spans not exceeding
eighty feet, seven men; from eighty to one hundred feet, eight
men; from one hundred to one hundred and twenty-five feet,
nine or ten men; from one hundred and twenty-five to one
hundred and fifty feet, eleven or twelve men; from one hundred
and fifty to one hundred and seventy-five feet, thirteen or four-
teen men; from one hundred and seventy-five to two hundred
feet, fifteen or sixteen men; from two hundred to two hun-
dred and fifty feet, from sixteen to twenty-four men; and, from
two hundred and fifty to three hundred feet, from twenty-four
ORD/AWA R P /RO/W HIGH WA P-B/C/DGAE.S. I97
to thirty-six men. The long spans require a proportionately
greater number of men, on account of the heavy sections. For
the same reason, the numbers given should be increased, if the
bridge be wider than the ordinary size. For city bridges, which
are proportioned for heavy loads and for smaller intensities of
working-stresses, the numbers should be increased from ten to
twenty per cent. When great haste is necessary, the numbers
should be doubled.
The most economical number of men will depend, too, upon
their skill; for green hands work at a great disadvantage in
bridge-raising. They do not know how to use their strength,
and require the foreman to stand over them to show them how
to do their work; besides, they are often so light-headed as to
be unable to work aloft. Sailors make excellent bridge-men
on account of both their agility and their training, which has
taught them to do in a few minutes many a difficult little piece
of work that ordinary hands would puzzle over for hours.
It is necessary to have a few experienced men in every gang;
the more of them, the better, provided that their travelling
expenses, and wages when travelling, do not render their
employment too expensive.
The cost of raising a bridge depends more upon the foreman
than upon the men. The best men will fail to do their full
quota of work if the foreman be not energetic. Nor does it
suffice to have simply a good worker for a foreman: he must
know how to keep the gang busy, or they will stand by and
look on, while he does all the work. He should also have their
good will, or the progress of the work will be unsatisfactory.
The outfit for a gang to raise ordinary county bridges should
be as follows : —
I forge, 2 pairs of tongs, 2 button setts for each size of rivets,
5 drift-pins of each necessary size, 2 handle cold chisels, I
handle drift pin, I2 cape chisels, 6 plain chisels, 3 wrenches for
§" nuts, 3 wrenches for #" nuts, 2 riveting-hammers, I light
sledge, I heavy sledge, 4 hand lines #" diameter, 4 guy lines
I” diameter by 130' long, 2 fall lines 1" diameter by 130' long,
6 to Io rope slings, 2 sets 8" blocks, 2 snatch blocks, 5 steel
f
I98 ORD/AWARY IROM HIGH WA Y-BRIDGES.
crowbars, 3 cross-cut saws, 2 augers I” diameter, 2 augers
#" diameter, 4 augers #" diameter, 3 axes, 2 adzes, 8 timber
trucks, 4 monkey wrenches, 4 chains, 2 crabs, 2 holding-on bars,
3 jack screws, several large wrenches for pins, and, if neces-
sary, a pile-driver with its appurtenances. The ordinary weight
of a pile-driver hammer varies from sixteen hundred to two
thousand pounds; and the height of the driver is about thirty
feet. The cost for such an apparatus complete is about two
hundred or two hundred and twenty-five dollars.
If the gang be a large one, or if the span exceed one hundred
and fifty feet in length, the numbers of some of the tools on the
list will have to be increased ; for instance, those of the bars,
ropes, and timber trucks.
Bridge carpenters generally carry tools of their own : so, if
there be much timber work in connection with the bridge, it
will be sufficient to employ more carpenters, and not to pur-
chase a larger outfit of carpenters' tools. s”
In getting ready to erect a bridge, the first step is to prepare
the ground in the neighborhood of the site, so that there will
be room to store the material and for the men to work. When
the iron is received at the site, it should be checked, and any
pieces from which the marks have been obliterated should be
re-marked. The iron should be piled systematically, similar
parts being grouped ; and no iron should be allowed to lie upon
the ground. It should be piled so that there will be no trouble
in getting at any piece which may be required; and the parts
to be used first should be placed nearest the bridge site.
The piers and abutments will be supposed to be erected, as
this work does not aim to treat of foundations.
The next step is to put the falsework in place. If the bed of
the stream be dry, or nearly so, the bottom hard, the distance
from the bed to the lower chord less than eighteen feet; and if
there be no danger of a sudden rise of water with a swift cur-
rent, the floor and joists can be used for falsework.
If the distance from the bed of the stream to the bottom
chord be greater than eighteen feet, and the other conditions
be the same, timber bents on mud-sills will be required. The
size of a mud-sill should vary from 6" by 6" to 12" by 12", accord-
OA’Z)/AWA/C P VA’OAV AZGHWA P-B/C/DGAE.S. I99
ing to the hardness of the ground, the weight upon the sill, and
the height of the falsework. It is not necessary that the tim-
bers be square. For ground not especially hard, wide timbers
laid on their flats are preferable, because they distribute the
pressure better.
If there be but one tier per bent, two posts will be enough,
when the width of roadway does not exceed sixteen feet. These
posts should batter about one inch to the foot, and should be
covered by a cap about 6" by 6" or 8" by 8", long enough to pro-
ject two feet beyond each truss. The upper ends of the posts
should lie directly under the trusses, and the caps should be
drift-bolted thereto. If the roadway exceed sixteen feet, there
should be an intermediate vertical post. The bent should be
braced by diagonal flat timbers, say from 2" by 6" to 3" by 8",
according to their length, running in opposite directions, one on
each side of the bent, and bolted or spiked to the posts and cap.
If there be two tiers in a bent, the inclined posts should
batter two inches to the foot (or three inches if there be danger
of high wind), and there should be a vertical post under each
truss. Each tier should be braced with diagonal timbers, as
before. The greater the danger of high wind, the more effec-
tively should each bent be braced. Alternate consecutive bents
should also be braced diagonally on their outer faces, and all
consecutive bents should be connected by longitudinal horizon-
tal planks well spiked to the caps. These planks will be useful,
in fact often necessary, for the workmen in passing from bent
to bent. If there be more than two tiers per bent, the batter
of the inclined posts should be three inches to the foot. A
good height for each tier is sixteen feet.
Where the bottom is soft, or where the water is deep and
rapid, piles will be required to rest the bents upon. There
should be from two to five piles per bent, according to the
width of the latter; a pile being placed below each vertical and
inclined post. These piles should be braced in the direction of
the stream by flat timbers bolted thereto. Any bracing that
may be given them transversely to the stream should be at
such a distance above high-water level as to cause no obstruc-
tion to boats, trees, ice, or other floating objects.
2OO ORD/AVA R P ZAZOAV HIGH WA P-3A&ADGA.S.
If the bottom be bare rock, incapable of holding piles, the
mud-sills must again be resorted to. They should be weighted
so that they may be sunk into place, then drift-bolted to the rock.
This can be done without the aid of a diver. Of course the sills
must be firmly attached to the lower tier before being put down.
The tops of all piles should be cut off to an exact level, so
that, when the bents are erected, the upper surfaces of the
upper caps will lie in the same horizontal plane.
On these caps should be placed timber-beams stretching from
one bent to the next, and lying immediately under the trusses:
joists will answer the purpose. It is generally customary to
place the bents under the panel points; but the author prefers
to put them two feet to one side, so that the floor beams may be
swung into place without taking down the falsework. This
method may, and probably will, require an extra bent at one end
of the span; so, if the bents be expensive, it is better to put one
under each panel point, and remove the upper tiers before swing-
ing the floor-beams. The level of the top of the longitudinal
beams should be at least six inches below the feet of the posts,
so as to permit of the use of camber blocks, like those shown
on Plate VII. The angle which the contiguous faces make with
the horizontal (less, of course, than the angle of friction of the
wood) enables the under block to be easily knocked out when
the spán is to be swung.
The timbers for the caps and posts of the falsework are gen-
erally square, and the sizes for the latter are to be found from
Table XXXIX., after the stresses in them have been ascer-
tained as follows: —
Let
W = weight per foot of the iron-work of the bridge,
W. = average weight per foot in height of one bent of falsework
and the timbers whose weight it supports,
p = wind pressure per square foot,
A = area per lineal foot which the two trusses present to the wind
(it is generally about five or six square feet),
Aſ = the average area subject to wind pressure per foot in height
on one bent, and its share of longitudinal bracing,
2 = panel length,
ORD//VAR}^ A&O/V HIGH WA P-B/P/2>GE.S. 2OI
ci, c, ca, etc. = horizontal distance between centre lines of inclined
posts measured along the caps,
d = depth of truss,
d, d, d, etc. = heights of the different tiers commencing at the top,
A = vertical distance between centre of chord and upper
cap of bent,
and
6 = the angle which the inclined posts make with the ver-
tical ;
then
pAl = pressure on trusses at each panel point,
pA(d. - pressure on upper tier,
pA(d. = pressure on second tier from top,
£A'd, = pressure on third tier from top,
and the stresses F, F, F, etc., in the inclined posts of the
first, second, and third tiers respectively, will be given by
the equations,
A 2.72
A–ºſa (; ; , + 2)+4% | +(ºr **) sec 6,
2
6. 2 2
A-ºſa(######2) lººr,
8
W12 W, ſ , , d.
[º +*(.4 #)] Sec 6,
z-e ‘[a (#4, #2, #2, #2)+******]+
4
C 2
[ºr W. (i. + d. -H #)] sec 6,
2 2
F. = &c. -- &c.
These formulas are obtained under the supposition that the
inclined posts are not aided by the vertical ones, which suppo-
sition is necessary in order to avoid ambiguity: it would be
correct, were the falsework on the verge of overturning. If
the timber be green, the error thus made upon the side of
safety is advantageous; but, if the timber be dry and of good
quality, it is permissible to make a slight reduction in the size
given by Table XXXIX. In applying the table, find the size of
2O2 O/PD/ZVA R P ZZO/V HZGAſ WA P-AEA2//DGAE.S.
square timber required for a stress F and length d, sec 6, that
for a stress F, and length d, sec 6, etc., then take the greatest of
these sizes.
The vertical posts should be strong enough to withstand a
working-stress given by the equation,
s= ****(, ; , Łse. +,-,+%)
where n is the number of the tier considered, and S the stress
in the corresponding vertical post.
One dimension of the vertical posts should be the same as
the side of the square which is the section of the inclined posts;
so that the diagonal braces may be flush with the entire faces
of the bents, and be bolted to the verticals without the inter-
vention of filling-pieces.
These equations seem very long, and no doubt many practical
bridge foremen would look upon them with disdain: neverthe-
less, if the falsework is to be designed by any other method
than that of guessing, this is the way in which it should be
done. The more elevated the bridge, the more important does
it become to properly proportion the falsework. The values of
W, and A’ will have to be assumed, or roughly calculated, before
applying the equations. The other quantities are, or should
be, known. The value of p may be taken from ten to fifteen
pounds per square foot, unless the situation be more than ordi-
narily exposed, when it may be taken at twenty pounds.
Bridge companies can afford to risk the chance of a hurricane
striking the bridge before it is swung.
The sections of the caps are generally made the same as
those of the inclined posts. The caps should be dapped to
receive both upper and lower ends of vertical and inclined
posts. The vertical posts should be drift-bolted through the
caps, the bolt being long enough to project five or six inches
into each post; and the inclined posts should be held in place
by wooden splice pieces, one on each side of the bent, project-
ing above and below the cap, and fastened at each end by a
bolt passing through the two splice pieces and the post. This
attachment may be used for the vertical posts instead of the
OA-AD//WA R P ZA'O/V HIGA WA P-PAPADGZ.S. 2O3
drift bolts, if it be preferred. For additional security against
slipping, a third bolt may be put through the splice pieces and
the cap; or cleats may be nailed to the latter above and below,
at the toe of each inclined post.
All bolt holes in timber should be accurately located and
bored before the falsework is erected. On this account the
bents should be all built after one pattern, so that the parts
may be interchangeable. If the bents be of different heights,
the variation may be effected in the lowest tiers. Bolts are
always preferable to spikes for connecting timbers, especially
when the falsework has to be taken down, and re-erected for
another span. Care should be taken to avoid any unnecessary
injury to the timber, in order that it may not be sold at too
great a loss after the work is finished.
There should be at least two plank walks on top of the lower
falsework, exterior to the trusses, and a runway midway between,
formed of several joists set on edge for the purpose of bringing
out the material thereon upon timber trucks.
The posts of the upper falsework should rest on the caps of
the lower falsework, a few inches inside of the trusses, unless
the bents are placed beneath the panel points, in which case
they should be placed two feet to one side: they should be
attached to the caps by splice timbers and cleats. The height
of the upper falsework should be such that the upper surface of
the cap will be at least six inches below the under sides of the
upper chord sections, so as to permit of the use of camber
blocks between.
The author would suggest that the end bents of upper false-
work be made three or four feet higher than the others, and the
use of four posts instead of two (one on the inside, and one on
the outside, of each truss), in order to aid in raising and holding
in place the heavy batter braces. After the latter are put in
position, a horizontal timber may be firmly bolted to the bent at
the level of the other bent caps, for the temporary flooring to
rest upon. Stout beams stretching from bent to bent will be
required as fulcra for the levers by which the chord sections
are handled. The upper falsework should be braced by diago-
nal timbers, both longitudinally and transversely. The sizes of
2O4 ORD//VARP WRO/W HIGH WA Pi—BA&IDGE.S.
the posts should generally be about 6" by 6": when the trusses
are high and the chord sections heavy, it might be well to
increase the size to 7" by 7”. The caps of the upper falsework
should be deeper than their breadth; because they have to act
as beams, and may be subjected to considerable shock when
the chord sections are being put in place. The method of
bracing shown on Plate VII. is specially advantageous in this
respect.
In both upper and lower falsework, the diagonal bracing in
planes parallel to the axis of the bridge should, for economy's
sake, be placed between alternate pairs of bents; that is, every
other space between bents should be braced. The end spaces
should, however, be braced in any case.
Plate VII, gives an illustration of how the working-drawings
for falsework should be made. For economy of space, the
scale has been taken at an eighth of an inch to the foot; but it
should, if intended for an actual case of framing, be four times
as great. A drawing of this kind should be accompanied by bills
of lumber and iron, prepared in a similar manner to that given
in Chapter XIV. for the span. Measurements of distances
between bolt holes should be both calculated and scaled.
Those on Plate VII. were simply scaled, as the plate is intended
for illustration only.
The foreman of the work should be provided with a blue
print of the working-drawings for the bridge, unless the type of
structure be one with which he is perfectly familiar. He must
also be provided with a “Raising Bill,” which should consist of
a skeleton diagram of one truss, with the following information
written thereon :-
Size of each truss strut, and tie, and mark for same, also number of
pieces of same in a panel of one truss.
Diameters and lengths S. to S. of truss pins, with their marks.
Diameters, lengths, and marks of fillers for same.
Sizes and marks of all separate plates belonging to the trusses, each
in its proper position.
ORD/MA R P IRO/V HIGH WA Pi—B/?/DGE.S. 2O5
A diagram for the lower lateral system, giving the following
information : —
Sizes and marks of rods.
Positions of same, showing which eyes are to go next the trusses.
Sections, lengths, and marks of lateral struts.
Diameters and lengths of lateral pins, if any.
Diameters and lengths of fillers for same.
Sizes and marks of jaws, if there be any difference between them.
A diagram for the upper lateral system and portal bracing,
giving the following information :-
Sizes and marks of rods.
Positions of same, showing which eyes are to go next the trusses.
Sections and marks of lateral and portal struts.
Diameters and lengths of portal pins.
Diameters and lengths of fillers for same.
Diameter and length under head of portal strut attaching bolts.
He should also be provided with a plan of the bottom chord
packing (the transverse dimensions being exaggerated, so that
the size of each piece may be written thereon), a bill of bolts,
giving the number and position of each kind, and a clear state-
ment of the system of marking the iron.
Before starting to erect the bridge, the foreman should study
carefully all the plans, so that he will have a clear picture of
the bridge in his mind's eye, and will not have to be continually
referring to the drawings during the erection. On a work of
any magnitude, there should be kept on hand a few standard
nuts of each size ordinarily used, so that the loss of a nut or
two will cause no delay: for the same reason there should be a
few extra bolts of each size.
The material, as a general rule, is all piled on one side of the
stream : the raising should therefore be commenced at the other
side, so that the passage of the material will not interfere with
the work. If there be no objection, the far end of the bridge
should be the fixed one, so as to start from something perma-
nent; but this is not absolutely necessary.
To illustrate the method of raising, take, for example, the
2O6 ORDVAWARY ZROAV HIGH WA Y-AR/DGE.S.
bridge treated in Chapter XVI., and assume that the founda-
tions, with their anchor bolts and falsework, are in place. The
first thing to be done is to lay out the centre line of the bridge
upon the falsework caps, marking it with a small-headed tack
on each cap, then the centre lines for the trusses in the same
way. This can be done either with a transit, or with a carpen-
ter's chalk-line; care being taken to make the transverse
measurements to the outer lines exactly perpendicular to the
central line. A test of the accurácy of the perpendiculars can
be made by the three, four, and five method, using a tape-line.
Next, mark the exact positions of the panel points upon the
longitudinal beams under the trusses, and place the camber
blocks, levelling over them so as to make the lines joining the
central points of their upper surfaces parallel to the curve of
the chords. It is better to have the blocks a trifle high, say, an
eighth of an inch near the centre, and a sixteenth of an inch
near the ends.
Four small nails will hold each pair of camber blocks from
slipping during the work, and they can be left so as to be
easily extracted before swinging the bridge. Next transfer the
centre lines of the trusses to the tops of the camber blocks, and
mark accurately the first panel points from the fixed end, then,
starting there, pack the chord bars of both chords. It might
be convenient to have a few hard-wood pins to fit the holes
pretty tightly, so as to aid in getting the bars properly placed
longitudinally.
After the chord packing has made some progress, run out the
two batter braces, and hoist them into place by means of pulleys
attached to the cap of the first bent of falsework, which bent
should have been previously guyed and braced so that it cannot
possibly be disturbed by the effect of the pulleys. As soon as
each batter brace is raised, and the anchor bolts pass through
the holes in the shoe plate, the nuts should be tightly screwed
down in order to aid in holding the batter brace in position.
It will not do, however, to rely solely on these, for the
threads of the end bolts might be stripped: consequently a
hard-wood supporting block must be strongly bolted to the two
adjoining posts of the bent of the upper falsework. This block
O/CD//VA R P VRO/V HIGH WA P-B/º/DGAE.S. 2O7
should have a bevelled edge, the angle of bevel being equal to
the slope of the batter brace, so that the iron-work will not rest
on a sharp edge of wood. If the lattice bars interfere with the
bearing, as they are liable to do, rough notches can be cut in a
minute on the bevelled face so as to bring the bearing upon the
channels.
Meanwhile the end lower lateral strut, the portal struts, and
the portal and end lower lateral rods, having been run out, the
three struts are to be put into place; the upper ones being re-
tained there by their connecting bolts, and the lower one by the
end pins, which should also pass through the chord bars, fillers,
and end lateral rods.
Such small portions of the structure as pins, fillers, and beam
hangers, should not be brought out upon the falsework until
required for use, for fear of their being lost overboard. Nothing
more will be said about running out these and other small por-
tions, but it will be assumed that they will be at hand when
wanted. It should be an understood thing between the fore-
man and the men, that any one who drops any portion of the
bridge into the water forfeits a certain amount of his wages.
Such an arrangement will make green hands a little more care-
ful than they are apt to be generally.
As the portal rods are adjusted by turn buckles with single
tap ends, they may be omitted until after the portal struts are
riveted to the batter-braces, because the riveters can then work
to better advantage. They can be left upon the abutment until
required.
Next run out, and hoist upon the falsework, by means of
pulleys attached thereto and timbers used as levers, the end
sections of the top chords, working them into place by the
levers, and attaching them temporarily at the hips by bolts,
putting in at the same time the end diagonals, but omitting the
hip verticals and fillers, so that room may be left for the hold-
ing-on bars. The other ends of the chord sections rest on the
camber blocks.
Next run out, and hoist into place, the first vertical posts,
letting the upper ends lie in the open ends of the chord sec-
tions.
2O8 ORDVAWA R P ZROAV HIGH WA P-AEA’ſ DGAE.S.
Now start the rivet gang at work on the portal, and let them
follow up the work as it progresses, not leaving the portal until
they have made the hip attachment, connected the portal struts,
and put the brackets and ornamental work in place.
Next bring out the second sections of the top chords and the
second set of diagonals. Raise the chord sections into place,
as before, with pulleys and beam levers, holding them there
until temporary bolts are put into a few holes through the con-
necting-plates, filling-plates, and channel webs, and until the
pins are run through the posts, diagonals, and fillers. The latter,
in this case, will not interfere with the riveting.
Next run out and put into place, as before, the second pair of
posts; then bring on the third sections of the chords, the third
set of main diagonals, and the first set of counters, putting all
three into place as before, and so on until the end of the bridge
is reached. Meanwhile the wooden lower lateral struts should
have been framed, and the jaws attached to their ends.
Just before the riveters complete the riveting of the portal,
the first upper lateral and intermediate struts should be run
out, and bolted into place; but the upper lateral and vibration
rods should be omitted, as they would be in the way of the
riveters, and can be readily inserted afterwards. "
About the time that one-half the span is erected, commence
running out the lower lateral struts and rods, putting them into
place, inserting the hip verticals and fillers, and coupling the
lower chords into their final position, leaving the beam hangers
lying horizontally, so that, when the longitudinal supporting.
timbers are removed, they will drop into their proper places.
A little before the riveters reach the end of the span, the
upper lateral and vibration rods should be put into place, and
screwed up about the right amount.
When the end of the bridge is reached by the riveters, and
as soon as they have riveted the hip connection, and attached
the main diagonals and hip verticals, the last couplings of the
bottom chords can be made at the pedestals.
The shoes rest upon the rollers, which should have been put
in exactly transverse to the direction of the bridge, and blocked
so that they cannot move.
ORD/WARP WRO/W HIGH WA Y-B/C/DGE.S. 209
The last connection for each truss can easily be made by
raising the hip either with levers or by jack-screws, and either
pressing against the shoe with jack-screws abutting against
blocks chained to the roller plate, or by attaching a pair of
blocks to the pedestal and first panel-point lower chord pin.
After the final coupling has been made, and the riveting is
finished, knock out the upper chord camber blocks, so as to
bring all the weight of the upper part of the bridge upon the
posts; then take down the upper falsework.
Next knock out the camber blocks of the lower chords, lower-
ing them together gradually so as to bring no shock upon the
bridge.
Next run out the first floor beam to the end of the bridge, and
remove the runway of the second panel, in order that the beam
may be dropped between the lateral struts and lateral rods, and
swung into place, lowering it beneath the ends of the hangers,
then raising it up, inserting the filling-plates, putting on the
hanger plates, and screwing up the nuts. In this way attach
all the floor beams, seeing that the hanger nuts are screwed up
firmly, but not to such an extent as to endanger stripping the
threads. Then bolt all the wooden lateral struts to the beams
through the holes previously bored, which holes should be at
least a quarter of an inch greater than the diameter of the
bolts.
Next screw up every adjustable rod to the proper tension,
which can be ascertained by the sound they make when tapped
with a hammer.
Next wash off any mud or other impurity that there may be
on the iron-work, and give it two good coats of paint wherever
the brush will reach. The best kinds of paint to use are lead
paints, when they can be obtained unadulterated; but they are
at the same time the most expensive of all the paints used for
iron-work. Iron oxide is a good paint, but requires more fre-
quent renewal. The color should be such as to readily show any
sign of rust : various shades of gray are efficient in this respect,
and are at the same time pleasing to the eye.
There remains nothing now to be done except to put on the
joists, floor, hand railing, and felly plank, a matter so simple
2 IO OA&AD/AVA R P /A’O/V HIGH WA P-AEA’ſ DGAE.S.
that it is unnecessary to describe it here; the only point worthy
of attention being, that the joists should be dapped one inch
on to the lateral struts, and that they should go on so hard that
it will be necessary to drive them into place. This can be
accomplished by cutting each dap a sixteenth of an inch short,
and bevelling the end of one dap slightly, in order to give the
joists a start when they are being driven down. When they
come to their bearings, they should be spiked to the lateral
struts by a five-inch spike at each end, driven obliquely.
In regard to the flooring, Mr. James Owen, C.E., in a paper
read before the American Society of Civil Engineers, specifies
as follows: “Lay no plank wider than nine inches. This pre-
vents wide joints in shrinkage. Bore all holes for the spikes to
prevent splitting, and put no spike nearer than four inches
to the end of the planking.”
In long bridges of several spans, it may be economical to dis-
pense with the upper falsework by using a travelling derrick,
running upon wooden stringers, for the purpose of handling the
heavy sections. Under these circumstances, the whole of
the portal might be connected while lying upon the falsework,
then hoisted into place in one piece, and supported there by
shore timbers from the first bent of falsework. The bridge
should be completed as the traveller retreats: otherwise there
will be difficulty in carrying the members past the traveller.
The material should be brought on cars within reach of the
derrick.
The last thing to be done is to take down the falsework, and
draw the piles from the bed of the stream. The latter is easily
accomplished by a crab on the bridge; the rope being attached
to the head of the pile, which is vibrated transversely in all
directions while being lifted by the tension of the rope.
There is no reason why a well-designed iron highway-bridge,
when properly cared for, should not last forever. Under loads
which are light and slowly moving, compared to those of rail-
road-bridges, the iron cannot possibly wear out; and, when
properly protected from the weather, it cannot rust. Of course
the wooden parts of the structure must be replaced from time
to time as they wear out or decay.
OA'D/AVARP IRO/W HIGH WA P-BR/DGE.S. 2II
When knots begin to project above the surface of the floor,
they should be adzed off, both for the comfort of those driving
over the bridge, and to prevent vibration. After half an inch
has been worn off one side of the planks, they should be turned
over; and when another half-inch has been worn off, or before
then if the wood show signs of weakness or decay, they should
be replaced.
It would be well for county commissioners to buy all the
lumber needed for renewal a year before required for use, so
that it may be well seasoned. -
Iron bridges should be thoroughly inspected for rust spots at
least once a year; and, if any be found, the bridge should be
repainted. One or two spots in places where something might
have rubbed off the paint may be touched up with a brush; but,
generally speaking, when rust spots begin to appear, it shows
that two good coats of paint are required immediately.
The adjustable members should be tested occasionally by
tapping with a hammer. This duty should not be intrusted to
an ignorant workman, who will turn away on the nuts until he
shears the thread, or breaks the rod. Whenever, in driving over
a bridge, any of the iron-work rattles, it shows that something is
out of adjustment. Generally speaking, a well-proportioned
iron bridge will not get out of adjustment unless some one
meddles with the nuts or turn buckles. With combination
bridges it is a different matter, for the shrinkage of the wood
may loosen the counters.
APPEN DICES.
APPENDIX I.
A NEGLECTED CONSIDERATION IN HIGHWAY-BRIDGE
- i DESIGNING.
SPECIFICATIONS for highway-bridges generally call for strength
to resist a wind pressure of at least thirty pounds per square
foot of exposed surface; but there are many such structures in
the United States whose trusses would not, unaided, withstand
this pressure. Granting that the lateral rods are large enough,
that the upper lateral and portal struts have sufficient strength
to resist both direct thrust and bending, and even that the lower
lateral rod connection is all that could be desired, still the bridge
may be far from fulfilling the requirements, as the following
investigation will show : —
Let
A = the assumed pressure per square foot,
and
A = the area in square feet per lineal foot of the vertical pro-
jection of that part of the structure lying below a hori-
zontal plane, which passes midway between the chords
of a through Pratt-truss bridge (the windward truss and
h hand-rail are not supposed to shelter the leeward ones);
then
£A = W = wind load per lineal foot for the lower lateral system when
the bridge is empty.
Let
A1 = the total area of bridge per lineal foot exposed to the wind
pressure,
h = the vertical distance of the centre of pressure above the
level of the bed-plate,
= the panel length,
215
2I6 APPENDIX I.
3 = clear width between trusses,
c = width of one truss,
d = depth of trusses,
W = dead load per lineal foot for one truss,
and #
W. = reduced dead load per lineal foot for the windward truss;
then the overturning moment of the wind per lineal foot is p.41%,
and it has the same effect as that of a couple of lever-arm b + c,
and force, -
£4.1%.
3 + 2*
that is, the weight per foot on the leeward truss is increased,
and that on the windward truss is decreased, by this amount,
which gives the equation,
- pAiſh
W. - W. * & + z'
Let
n = number of panels in the bridge,
and
n, - number of any panel, counting from the nearest end of
the span;
then - *
WZ = panel wind load,
and
W.2 = reduced panel dead load.
The compression on the windward bottom chord of the m,”
panel will be
72 /2
º (n *-º-º: n) W 7°
if we consider that the inclination of a lateral rod to a line per.
pendicular to the planes of the trusses is tan T” % The tension
in the same panel, due to the reduced dead load alone, is
|
(ni — o(*=#)n, #.
2
except in the case of the first panel, to find the stress for which
ni must be made equal to two.
APPEAVD/X Z. 217
Now, if this tension be less than the compression just found,
the chord at the panel considered, if not a compression member,
or if it be not externally aided, will buckle; for flat bars cannot
be relied upon, when acting separately, to resist compression.
The following inequality should, therefore, hold true:–
W. W
(n1 – 1) (n − ni + 1)# > n) (n — n).
By inspecting the chord stresses in a few Pratt truss through
bridges, it can be readily seen, that, if this inequality hold true
for the second panel, it will hold true for all the others.
The three following cases are fair samples of bridges with
which the author has met in his practice. The wind pressure
assumed is thirty pounds per square foot.
(1) A 140 span of 12' clear roadway is 23' deep, consists of
seven panels, weighs 460 pounds per lineal foot, presents to the
wind about six square feet of surface below the middle horizontal
plane for every lineal foot, and about eight and a half square
feet above and below. The centre of pressure is about 8 feet
above the shoe plate, and the width of the truss is I foot.
These data give W. = 73, and, for the second panel,
W.
(n, – 1)(n - n + 1) # = 19,
and .
Wy
n1(n — *i); = I5O.
(2) A 150' span of 14 clear roadway is 24' deep, consists of
eight panels, weighs 540 pounds per lineal foot, presents to the
wind about six and a half square feet of surface per lineal foot
for the lower lateral system, and about nine square feet above
and below. The centre of pressure is about 84 feet above the
shoe plate, and the width of the truss is about I foot.
These data give W. = II?, and, for the second panel,
W.
(n1 – 1) (n − n, + 1)* = 34. I,
and
^
n,(n — n)! – I67.I.
218 A PAAAWD/X Z.
(3) A I2O span of 16 clear roadway is 22' deep, consists of
six panels, weighs 530 pounds per lineal foot, and presents the
same surface per lineal foot as in the last case. The centre of
pressure is about 73 feet above the shoe plate, and the width
of the truss is I foot.
These data give W. = I46, and, for the second panel,
W.
(n − 1)(n - n, + 1) # = 33.2,
and
m1(n — n)!} = 97.5.
In all these cases -
(n − 1)(n-n + 1) #3 (n-nº.
How is it, then, that more bridges do not fail by the buckling
of the bottom chord under wind pressure ? For two reasons.
First, the probability of a bridge ever being subjected to a
pressure of thirty pounds per square foot over its whole length
is very small ; and, second, that in a well-built bridge, where the
joists are dapped to the floor beams, the joists would take up
the compression that would tend to buckle any panel of the
chord except the first,
In view of the fact of the small chance that a bridge has of
ever being subjected to the assumed pressure, it would be legiti-
mate to trust somewhat to the stiffness of the joists in cases
where
W. W
(n1 – 1) (n — ni + 1)* < n, (n — n)-;,
and not to make the chords stiffened throughout, except in short
spans.
But, as the joists cannot stiffen the end panels, the chords in
these panels should be proportioned to resist the compression
due to the difference between the longitudinal component of the
greatest stress in the end lateral rod, including the initial ten-
sion, and the reduced dead-load stress, whenever the former is
in excess of the latter. It is often well, for the sake of both
rigidity and appearance, to stiffen the chords in the second
panels when those in the first panels are stiffened.
, APPAEAVD/X /Z. 2I9
APPENDIX II.
DEMONSTRATION OF FORMULA FOR FLOOR BEAMS.
LET the notation be the same as given on p. 19, viz.:-
A = area of bottom flange in Square inches,
A' = area of web in square inches,
A" = area lost by a rivet hole in square inches,
W = the uniformly distributed load in tons,
L = length of beam in feet between centres of supports,
D = depth in feet between centres of gravity of flanges,
and
Z’ = intensity of working tensile stress in tons.
The moment at the centre of the beam is * Let us take
the centre of moments at the middle of the web, which will
correspond with the neutral surface, if we assume, which is
nearly true, that the upper and lower flanges are of the same
area, and are subjected to numerically equal stresses.
The moment of the load is resisted by the sum of the moments
of the flange stresses and those of the web stresses. The sum of
the moments of the flange stresses is
2(4–4).7x #– (4–4)70.
The resisting-moment of the web stresses is found as fol-
lows:– -
The resisting-intensity of stress on the fibre most remote
from the neutral surface may be taken equal to T; then that
for any fibre at the distance a will be, by the common theory
2 Tr º
of flexure, TDſ. The stress on an elementary area at this.
22O AAA’EAVZ)/X YX.
27 ºr
JO/
the width and depth of the web. The moment of this stress is
27:2
*ā-āda, integrating which between the limits
distance will then be -āda, where b and D’ are respectively
gives, for the total resisting-moment of the web,
AD?
25.7" ſt-a- 2ó Z' 3 ſy\8 *ZZ” — 1 a
Equating-moments gives
WZ
* = (4–4")ZD + 47D.
If we put D for D', we will commit a small error on the side of
safety; then will
* = zo(4–4°4-14),
and therefore
A = #. — #A' + A". Q. E. D.
If M be the moment at any section of the beam, and R the
intensity of stress on the fibre most remote from the neutral
surface at the same section when the beam is fully loaded, we
can write the equation
M = ARD + #4'RD,
where A is the area of the top flange, and D' is, as before
assumed, equal to D; from which we have
M
* = 7×4+Hay
and
M
–7–7N,
where S is the stress on the upper flange at the section consid-
ered. This last formula is useful in determining the rivet
spacing in the flanges of built floor beams and plate girders.
S = RA =
AA’FEAWD/X ZYZ. 22 I
APPENDIX III.
METHOD OF FINDING THE LENGTH OF THE LONG DIAGONALS
IN A DOUBLE-INTERSECTION BRIDGE.
Let
2 = panel length of bottom chord = GD or DB in the accom-
panying diagram,
c = half increase of panel length in top chord,
d = depth of truss between centres of chords = AB,
o, - angle between radial line at panel point and perpendicular
to lower chord;
then
0. E sin" Ž’
and
DE: c :: 2; d.
Or
c/
AXE = Z’
2/2 * —
BG= age = Wa-º- V*.*.
When the camber is small, BG can be taken equal to 2GD.
In triangle ABG, AB and BG are known, also angle
ABG = 90° -- 20.

222 APA’EAVD/X III.
AB + BG: AB – BG :: tan # [180° — (90° +20)]:
tan #[BAG – BGA];
AB – BG
tºº = -1 | "…— … ". ° — tº
BAG – BGA = 2 tan ####un(s •)]
Again :
(BAG – BGA) + (BAG + BGA) = 2 BAG =
(BAG – BGA) + (90° – 20), which gives BAG;
also
BGA = 180° – (BAG + 90° +20) = 90° — (BAG + 20):
finally,
AG = AB cos BAG + BG cos BGA = length of diagonal required.
ADDEN DA.
A DD END A.
IN an otherwise very favorable review of this treatise by
“The American Engineer,” there was pointed out a serious
objection to the usual attachment of a floor beam by four
hangers.
In the words of the review, “the inner loop will take nearly
if not quite all the load at the panel point, when the bridge is
first adjusted; and this not only becomes constrained itself,
but also overstrains the inner tension brace.* The number
of inner hangers which are constantly working loose, presum-
ably by stretching, in railroad-bridges in which this detail is
used, demonstrates its unsatisfactory character.”
The author has long recognized the inequality of distribu-
tion of floor-beam load between the inner and outer hangers,
but considered that the low intensity of working-stress on
these members would compensate for the objectionable in-
equality. Such has been also, in all probability, the opinion of
most American engineers; for beams, when not riveted to the
posts, are nearly always suspended by four hangers. The fact
of the inner hangers working loose can have been only lately
discovered. It shows, however, that this detail needs improve-
ment; and as the aim of this treatise is to design structures
not only equal, but in some respects superior, to the best
American bridges, it becomes necessary to correct the newly
discovered fault.
The most simple manner of so doing is to use single beam
* Main diagonal.
225
226 A DDA2/VDA.
hangers; but this method will not always work, owing to the
great bending-movements which they produce upon the pins.
For instance, take the case of a 20' panel of a Class A bridge
having a 24 clear roadway, and two 6' sidewalks. The weight
supported by each single hanger would be about 23 tons, and
the distance between centres of main diagonals would not be
far from ten inches. These data give a vertical bending-
moment upon the pin equal to 57.5 inch-tons, which alone
would call for an iron pin 43" in diameter; but, when combined
with the horizontal moment, it would require a much larger pin
than a practical designer would care to employ.
The double hangers in such a case are a necessity, but the
connection must be such as to distribute the load equally upon
them. Such a distribution can be assured by using the follow-
ing detail : —
On the under side of the beam at each end is attached by
four rivets a plate about five-eighths of an inch thick, six inches
long, and as wide as, or a little wider than, the beam flange.
This plate is placed symmetrically to the plane of the truss;
and the middle of the under side is grooved so as to receive
one-sixth of the surface of a pin about two inches in diameter,
which rests in a similar groove on the top of the beam-hanger
plate. The lateral dimensions of this plate will be slightly
greater than usual, but the thickness need not exceed three-
quarters of an inch. To prevent the plate from rupture by
bending, there are attached to the under side by countersunk
rivets two angle irons, or plates bent into the form of angle
irons, the vertical legs being connected by countersunk rivets,
which in the neighborhood of the pin pass as nearly as may be
through the neutral surface of the T beam, and elsewhere near
the lower edges of the angles.
As the axis of the pin is parallel to the length of the bridge,
the vertical legs must be transverse thereto. This detail will
be readily understood by referring to Plate VIII,
To illustrate how to find the sizes of the stiffening plates,
number of rivets required, etc., let us design a beam-hanger
plate, when the total weight upon the four hangers is forty
tons. The centres of the beam-hanger holes may be assumed
A DDE/VDA. 227
to be situated on the corners of a six-inch square. This would
make the bending-moment on the plate thirty inch-tons, which
would be resisted by the T-shaped section of the two bent
plates combined with the uncut portion of the beam-hanger
plate below the pin. Assuming the latter thickness #", and
the plate stiffeners to be of 6" × 6" × #" angle iron, would
make the T about 12" × 64" X 1", the centre of gravity of
which is about 5" above the bottom. The moment of inertia
is, therefore,
+, × 12 × (1.0)” + 12 × (1.0)” ++, × 1 × (5.5)*
+ 5.5 × (2.25)* = 54+.
The resisting moment is given by the equation
AC/
M =;
so taking R = 4 tons,
M = * * * = 4.3.2.
5
As the bending-moment was thirty inch-tons, the sizes
assumed are ample. f
It will be well to use three-quarter-inch countersunk rivets
(the largest possible), so as to make the different portions of
the T head act together. -
There is a tendency to bend the plate in a direction at right
angles to the one considered, the moment for which is fifteen
inch-tons on each side of the pin. This will be resisted by a
couple whose forces act as compression on the top plate of the
T, and tension on the rivets near the bottom of the angles.
Taking the centre of moments at the middle of the top plate,
and the distance therefrom to the horizontal centre line of the
rivet holes as 4; inches, will make the tension on the rivets
zººs = 3.42 tons. Using an intensity of only two and a half
tons, because of the initial tension on the rivets, will make the
section required 1.37 square inches: consequently two I" rivets
will be sufficient.
228 A DMDAEAWDA.
The difference in the total weight of iron per lineal foot
caused by the use of this detail will be from six to ten pounds,
which weight should be added to those given in Tables I., II.,
and III., under the heading “Floor System,” whenever this
style of beam-hanger plate is to be employed. -
It will be noticed in the diagram on Plate VIII., that the
floor-beam stiffeners at the support are placed close together
so as to take up the vertical reaction of the hangers transferred
by the auxiliary pin. The sectional area of these stiffeners
should be about equal to that of the hangers.
Plate VIII. illustrates a detail by which the foot of a post
may be riveted or bolted to the floor beam, for the purpose of
aiding the distribution of lower lateral rod stresses among the
chord bars. This is accomplished by means of a jaw plate be-
tween the post channels, and by turning up the ends of the
exterior re-enforcing plates, so as to permit the passage of
rivets or bolts. The latter may be considered preferable; as
they need not be screwed up very hard, but should fit with
great accuracy in the holes. Their object is to prevent tor-
sion of the post, but not to aid the beam hangers in resisting
tension. - º
When this detail is employed, the lower chord pin at the first
panel point should pass through holes bored in bent plates, which
are to be well riveted to the floor beam.
It is probable that most bridge designers will consider this
arrangement to possess too much refinement for highway-
bridges, preferring to trust to the rigidity of the joists as sug-
gested on p. 218.
There is no doubt, though, about its being a detail that could
be advantageously employed in railroad-bridges.
When vertical sway bracing is used, the detail for the upper
lateral strut connection, shown on Plate VIII., will be foundt o
be an improvement on the one previously described, in that it
obviates field riveting.
It consists in the use of a double jaw on the end of the
lateral strut, and two nuts of different diameters, the pin being
doubly shouldered. The office of the inner and larger nut is
to press the end of the strut against the chord; and that of
A DDA2/VDA. 229
the outer one, to take up the pull of the bent eyes, the injuri-
ous effect of which is mitigated by the inner jaw plate.
When no vertical sway bracing is used, the detail described
on p. 98 will probably be preferable; because it involves the
spreading apart of the lateral strut channels, and thus furnishes
a greater resistance to bending the strut. The use of the im-
proved detail will not affect the sizes of the lateral strut chan-
nels as given in Table XXV.
Plate VIII. illustrates also an improved connection for the
portal struts, avoiding the necessity for field riveting. The
increased depth of the jaw plate at the pin hole is an impor-
tant feature, its object being to resist the bending effect of that
component of the stress in the portal rods which is parallel to
the length of the batter brace.
Whenever the portal rods exceed 13" in diameter, this im-
proved shape of jaw plate should be employed.
GLOSSARY OF TERMS.
/
GLOSSARY OF TERMS.
Adjustable Member. — A member of a bridge the length of which can be
increased or diminished at will.
Angle Iron. — Iron rolled into the shape shown in section on Plate II.,
Fig. 3.
Apex. — The intersection of a brace with a chord or flange; called also a
panel point.
Axis of Symmetry. — A line dividing an area into two parts equal and
similar to each other, and similarly disposed to the line.
Bar. — A piece of iron flat or square in section.
Batter. — Slope, or inclination, to the vertical; usually measured by the
tangent of the angle, or so many inches to the foot.
Batter Brace. — The inclined end post of a bridge. (Plate I.)
Beam. — A member intended to resist bending.
Beam Hanger. — A rod or square bar supporting a floor beam from a
chord pin. (Plate I. and Plate II., Fig. 13.)
Beam-hanger Nuts. – Nuts on the ends of beam hangers, serving to press
the floor beam against the feet of the posts or against the chord heads.
(Plate II., Fig. 13.)
Beam-hanger Plate. — A plate placed beneath the end of a floor beam for
the beam-hanger nuts to rest against. (Plate II., Fig. 13.)
Beam-trussing Posts. – Posts for trussing beams. (Plate II., Fig. 16.)
Beam-trussing Rods. – Diagonal rods for trussing beams. (Plate II.,
Fig. 16.)
Bearing. — A resting-place, usually for a pin or rivet.
Bearing-Pressure. — The pressure on a bearing.
Bed Plate. — A plate to distribute pressure upon masonry. (Plate III.)
Bending-Moment. — The moment of a force or forces which bend or tend
to bend a piece.
Bending-Stress. – The stress produced in a piece by bending.
Bent. — A frame of timber or iron, usually the former, as a bent of false-
work.
Bent Eye. — An eye on the end of a bar, the plane of which makes an
angle with the direction of the length of the bar.
Bevel. — The slope on the end of a piece.
233
234 GZO.S.S.A R P OF 77A2 RMS.
Bill of Material. — A list of various portions of material giving dimensions
and weights, or other quantitative measurements. f
Block. — A system of one or more pulleys or sheaves, so arranged in a
frame or shell as to multiply the power of the rope passing around them, or
to change its direction.
Board Measure. — The measure of timber, the unit being a piece one foot
square and one inch thick. Timber is sold at so much per thousand feet
board measure, usually written, per M. b. m.
Bolt.—An iron rod with a square head at one end, and a thread and nut at
the other.
Brace. — Generally a strut, but sometimes the term is applied to a tie.
Bracket. — A knee or knee brace to connect a post or batter brace to an
overhead strut. (Plate I. or Plate II., Fig. 12.)
Built-Beam. — A beam made up of plates and angles riveted together.
(Plate II., Fig. 13.)
Burr. — A rough edge or ridge left by a tool in cutting metal. The term
is sometimes used for a nut.
Button Sett. — A tool for forming the heads of rivets.
Camber. — The upward curvature of a truss. It is measured by the height
of the middle point of the centre line of the lower chord above the line
joining the centres of end pins.
Camber Blocks. – Blocks of wood used in erection, so placed as to be
easily removed (Plate VII.)
Cape Chisel. — A tool for cutting iron. It consists of a rounded edge on
the end of a short rod. The edge is very obtuse, so as not to break easily.
Centre of Gravity. — That point of a body about which the weights of all
the different portions balance.
Channel, or Channel Bar. — Iron rolled into the shape shown in section
on Plate II., Fig. 1.
Check Nut, or Lock Nut. — A contrivance to prevent a nut from turning
when subjected to shock.
Chord. — The upper or lower part of a truss, usually horizontal, resisting
compression or tension. (Plate I.)
Chord Bar. — A member of the chord which is subjected to tension.
(Plate I.)
Chord Head. — The enlarged end of a chord bar, through which the pin
passes.
Chord Packing. — The arrangement of the bottom chord of a truss.
Clear Headway. — The vertical distance from the upper surface of the
floor to the lowest part of the overhead bracing. It is a measure of the height
of the highest vehicle that could pass through the bridge.
Clear Roadway. — The horizontal distance, measured perpendicularly to
the planes of the trusses, between the inner edges of the batter braces. It
is a measure of the width of the widest vehicle that could pass through
the bridge.
G/LOSSAA’ V OA' TERM.S. 235
Cleat. — A narrow strip of wood nailed to something for the purpose of
keeping a piece of work in its proper place.
Co-efficient of Friction. — A numerical quantity, which, multiplied into
the normal pressure, gives the frictional resistance. It is equal to the natural
tangent of the angle of repose.
Cold Chisel. — A tool for cutting iron.
Column. — A pillar or strut; a long member which resists compression.
Component. — One of the parts into which a stress may be resolved or
divided.
Compression. — A stress which tends to shorten the member which is
subjected to it.
Concentrated Load. — A load which is, or may be considered, collected at
one or more points.
Connecting Chord Heads. – Chord heads used to connect bottom chord
channels to pins. (Plate II., Fig. Io.)
Connecting-Plate. — A plate used for connecting two pieces.
Continuous Spans. – Consecutive spans connected over the points of
support.
Counter. — An adjustable diagonal which is not subjected to stress by a
uniformly distributed load covering the bridge. (Plate I.)
Countersunk Rivets. – Rivets, the heads of which are let into one or both
of the plates which they connect, so as to leave a flush surface or surfaces.
Couple. — Two equal and parallel forces not acting in the same line.
Cover Plate. — A plate used to cover a joint, or to connect two pieces of
the top chord plate. (Plate II., Figs. I I and 12.)
Crab. — A slow-motion machine, worked by a crank for the purpose of
winding a rope upon a drum, thereby raising a heavy weight.
Dap. — To notch timber onto its bearing.
Dead Load. — The weight of all the parts of the bridge itself, and any
thing that may remain upon it for any length of time.
Deck Bridge.—A bridge in which the passing loads come upon the upper
chords or the upper ends of the posts.
Deflection. — Motion laterally, or at right angles to the length of the piece.
It is also used for the amount of motion, and is generally expressed in inches.
Depth of Truss. – The vertical distance between the centre lines of upper
and lower chords.
Diagonal. — A member running obliquely across a panel. In this work all
the diagonals except the batter braces are tension members.
Diagram of Stresses.—A skeleton drawing of a truss, upon which are
written the stresses in the different members. (Plate V.)
Double Intersection. — The style of truss where the diagonals cross the
posts at the middle of their length, as in the bridge shown on Plate I.
Double-riveted Lacing. — Lacing in which each bar is connected by two
rivets at each end. (Plate II., Fig. 13.)
236 G/LOSSAAC P OF 7A2/2//.S.
Drift Bolt. — A round or square piece of iron, usually from one to three
feet long, without head or nut, used to connect timbers.
Drift Pin. — A slightly tapering rod of hard steel, used for making rivet
holes coincide. Its use is more convenient than advisable.
Effective Area. — The gross area of a section, less that lost by rivet or
pin holes; the net area.
Elastic Limit. — That intensity of stress at which the ratio of stress over
strain commences to show a decided change. For wrought-iron it is from
twelve to fifteen tons.
Erecting-Bill. — A bill of material for a bridge, so arranged as to facilitate
the finding and placing of members during erection.
Expansion Joint. — The connection of pedestal to bed-plate, shown on
Plate III.
Expansion Rollers. — A set of half a dozen or more turned rods of exactly
the same diameter, placed under the shoe plate at one end of a truss to
permit of expansion and contraction. (Plate II., Fig. 9.)
Extension Plate. — A plate riveted to the end of a strut channel, and pro-
jecting beyond it, to permit of the passage of a pin. (Plate 1 I., Fig. 12.)
Eye. — A hole in the end of a member to permit of the passage of a pin.
Eye Bar. — A bar with an eye at each or one end.
Factor, or Factor of Safety. — The ratio of ultimate load to greatest allow-
able working-load. This term is getting out of favor among engineers, as its
use has been somewhat abused. There is no such thing as a factor of safety
for a well-proportioned bridge, for each member should have an intensity of
working-stress proportionate to the character and amount of work which it
has to perform.
Fall Line. — A rope used in erection for raising and lowering weights.
Falsework. —Temporary timber work to support a bridge during erection.
Felly Plank. — A guard rail so placed as to catch the felly of a wheel, and
thus prevent the vehicle from striking the truss. (Plate II., Fig. 13.) In
wide bridges a felly plank is often placed midway between the trusses, to
prevent vehicles passing from one side of the bridge to the other.
Field Riveting. — Riveting done in the field, or during erection. It is the
poorest and most expensive kind of riveting.
Fixed End. — An end of a strut so firmly connected as to prevent all motion
of the strut in the neighborhood of the end.
Filling-Plate. — A plate the function of which is to make flush two surfaces
(Plate II., Fig. 12.)
Filler. — A small ring of iron or piece of pipe placed on a pin in order to
keep in position the members coupled thereon.
Fixed Load. — A load remaining permanently, or for a considerable length
of time, upon a structure or portion of a structure.
Flange. — The upper or lower chord of a beam. It is the principal part
for resisting either compression or tension.
Flexure. — Bending.
4.
*
GZO.S.S.A.A.’ P OF 7A2/0/1/.S. 237
Floor, or Flooring. — That part of the bridge which directly receives the
travel. (Plate II., Fig. 13.) ºr
Floor Beam. — A beam to support a portion of the floor and its load.
(Plate I. and Plate II., Fig. 13.)
Forge. — An apparatus for heating iron.
Framing. — The carpenter work on timber.
Giasticutus Rods. – A term (perhaps unauthorized, but in common use
among bridge builders) to denote a small horizontal rod connecting the middle
points of, two adjacent posts of the same truss, for the professed purpose of
fixing or holding the posts at the middle in order that they may be figured
for half-length. The benefit derived therefrom is more imaginary than real.
Girder. — Any structure to cross a chasm or opening. The term is gener-
ally applied to short structures for places where it is not advisable to use
trusses; for instance, a plate girder, or a rolled girder.
Guard Rail. — See felly plank.
Guys, or Guy Lines. – Lines for bracing the top of a pole, derrick, or any
similar apparatus.
Gyration. — See radius of gyration.
Hammered Head. — A head formed on the end of a bar by hammering.
Hand Lines. – Small ropes used in erection.
Hand Rail, or Hand Railing. — An iron or wooden frame placed on or
near the outside of a bridge in order to prevent persons or animals from
falling therefrom. (Plate IV., or Plate II., Fig. 13.)
Hand-rail Cap. — The upper longitudinal timber or timbers of a wooden
hand-railing. (Plate II., Fig. 13.)
Hand-rail Post. — Post for supporting a hand railing. (Plate II., Fig. 13;
Plate IV.)
Headway. — See clear headway.
Hinged End. — An end of a strut connected only by a pin.
Hip. — The place at which the top chord meets the batter brace.
Hip Joint. — The joint of the top chord and batter brace.
Hip Vertical. — A rod hung from the pin at the hip for the purpose of
suspending the floor beam.
Holding-on Bar. — A lever to hold against one end of a rivet while the
head at the other end is being formed with a button sett.
Hub Plank. — A plank to protect the iron-work of the truss from being
struck by the hubs of passing wheels. (Plate II., Fig. 13.)
I-Beam. — A piece of rolled iron of the section shown on Plate II., Fig. 2.
Initial Tension. — The tension caused in any adjustable member by screw-
ing up the adjusting apparatus.
Intensity. — The intensity of a stress is the amount of stress upon a square
inch of section.
Intermediate Strut.—An overhead strut in high bridges, attached to the
posts of opposite trusses, and lying between the upper lateral strut and
the floor. In deck bridges, if used at all, it would lie between the upper
and lower lateral struts. (Plate I.)
238 G/LOSSAA’ \' OAT TEA?//.S.
Jaw. — A connection on the end of a strut similar to that shown on Plate
II., Fig. I3.
Joint. — A place where two abutting or lapping pieces are connected.
Joist. — A timber beam that supports part of the floor and its load. (Plate I.
and Plate II., Fig. I3.)
Knee, or Knee Brace. — See bracket.
Lacing. — A system of bars, not intersecting each other at the middle, used
to connect the two channels of a strut in order to make them act as one
member. (Plate II., Fig. 12.)
Lacing-Bar. — A bar belonging to a system of lacing.
Lateral Rod. — A tension diagonal of a lateral system. (Plate I.)
Lateral Strut. — A compression member of a lateral system. (Plate I.)
Lateral System. — A system of tension and compression members forming
the web of a horizontal truss connecting the opposite chords of a bridge. Its
purposes are to transmit wind pressure to the piers or abutments, and to
prevent undue vibration from passing loads.
Latticing. — A system of bars crossing each other at the middle of their
lengths, used to connect the two channels of a strut in order to make them
act as one member. (Plate II., Fig. 12.)
Lattice Bar. — A bar belonging to a system of latticing.
Leg. — One of the two portions of an angle iron separated from each other
by the bend.
Lever Arm. — The perpendicular from the centre of moments to the line
of action of a force. The lever arm of a couple is the perpendicular distance
between the lines of action of the two equal and parallel forces.
Live Load. — The moving or passing load upon a structure.
Linville Truss (also called “Double Quadrangular,” “Whipple,” and
“Double System Pratt.” truss). — A truss with vertical posts and diagonal
ties spanning two panels. It is the truss represented on Plate I.
Lock Nut. — See check nut.
Loop Eye. — An eye on the end of a rod or square bar, elongated into the
form of a loop, as shown on Plate II., Fig. 16.
Lower Falsework. — The falsework below the level of the lower chords.
Main Diagonal. — A tension member of a truss, sloping upward towards
the nearer end of the span. Main diagonals in iron bridges are not adjust-
able.
Moment. — The product of a force by its lever arm.
Moment of Inertia. — Represented by the equation, Z = Ap? = XrºdA,
where A is the area of the section considered, p the radius of gyration, and r
the distance of any point from an assumed line lying either in the surface or
outside of it: in other words, the moment of inertia of a surface about any
axis is the product of the area by the square of the radius of gyration; or
it is the summation of the products of each differential of the area by the
square of its distance from the axis. If the axis lie in the surface, the
moment of inertia is called a surface moment of inertia; while, if the axis
G/LOSSAA’ V OA' TEA’A/S. 239
be perpendicular to the surface, the moment of inertia is called a polar
moment of inertia.
Monkey Wrench. — A wrench capable of being adjusted so as to fit nuts
of different sizes.
Moving Load. — See live load.
Mud-Sill. — A timber, usually from 6" by 6" to 12" by 12", at the bottom
of a bent. It is laid horizontally in a trench, and the posts of the bent rest
upon it. *.
Name Plate. — A plate of iron placed in a conspicuous position on a
bridge, containing the name of the maker or designer of the structure.
Negative Rotation. — Rotation in a direction opposite to that of the hands
of a watch.
Net Section. — See effective area.
Neutral Surface. — That part of a member subjected to bending, which is
neither extended nor compressed. In symmetrical wrought-iron beams, with
equal or nearly equal flanges, it is taken to be at the centre line of the web.
Nut. — A small piece of iron with a threaded core to fit on the screw end
of a bolt, rod, or bar. (Plate II., Fig. 6.)
Order Bill – A form of bill used in ordering material from the manufac-
turers.
Ornamental Work. — Fancy work at the portals of a bridge to give it
architectural effect. (Plates I. and VI.) *-
Overhead Bracing. — The upper lateral or vertical sway bracing in
through bridges. The term is usually applied to the vertical sway bracing,
if there be any; if not, to the upper lateral bracing.
Packing. —See chord packing.
Panel. — That portion of a truss between adjacent posts or struts in Pratt
truss bridges; called also a bay.
Panel Length. — The distance between two adjacent panel points of the
same chord.
Panel Point. — See apex.
Pedestal. — The foot of a batter brace or end post. (Plate II., Fig. 9.)
Permanent Set. — The alteration in length of a piece of material which has
been subjected to stress, remaining after the stress has been removed.
Pillar. — See column.
Pilot Nut, or Pin Pilot. — A nut, one end of which is a truncated cone,
used to protect the thread on the end of a pin when the latter is being driven
into place. (Plate II., Fig. 5.)
Pin. — A cylindrical piece of iron used to connect bridge members. (Plate
II., Fig. 5.)
Pitch. — The distance between centres of consecutive rivets of the same
r0W.
Plane of Symmetry. — A plane dividing a body into two equal and sym-
metrical parts similarly disposed in reference to the plane.
Plant. — Tools and apparatus used in construction.
24O GZO.S.S.A.A.’ Y OF TERMS.
Plate. — A piece of flat iron wider than a bar. The common distinction
between the two is that a plate is attached to something else, and acts with it,
while a bar is an independent member.
Plate Girder. — A beam, built of plates and angles, used to span a small
opening, generally less than forty feet.
Pony Truss. – A truss so shallow as not to permit the use of overhead
bracing.
Portal. — The space between the batter braces at one end of a bridge.
Sometimes the term is applied to the portal bracing, though incorrectly.
Portal Bracing. — The combination of struts and ties in the plane of the
batter braces at a portal, which transfers the wind pressure from the upper
lateral system to the abutment or pier.
Portal Strut. — A strut belonging to the portal bracing. (Plate I.)
Positive Rotation. — Rotation in the direction of the hands of a watch.
Post. — A vertical strut. (Plate I.)
Pratt Truss (called also the “Murphy-Whipple,” or “Quadrangular”
truss). — A single-intersection truss with vertical struts and diagonal ties.
Quadrangular Truss. – See Pratt truss.
Radius of Gyration. — The radius of gyration of any surfacé in reference
to an axis is the distance from the axis to that point of the surface in which,
if the whole area were concentrated, the moment of inertia in reference to the
axis would be unchanged. It is therefore equal to the square root of the ratio
of the moment of inertia over the area.
Ream. — To enlarge a rivet hole.
Reamer. — A tool for enlarging rivet holes.
Re-enforcing Plate. — A plate used for the purpose of providing additional
pin bearing, or strength, to compensate for material cut away. (Plate II.,
Figs. II and 13.)
Resolve. — To divide a force into component parts.
Rivet. — A short piece of round iron tightly connecting two or more thick-
nesses of metal, and having, when in place, a head at each end.
Roadway. — The passage-way of a bridge for vehicles; usually means
clear roadway, g. v.
Rod. — A piece of round iron.
Rolled Beam. —An I-beam. (Plate II., Fig. 2.)
Roller. — See expansion roller.
Roller Frame. — A light frame of iron for holding the rollers in position.
(Plate II., Fig. 9.)
Roller Plate. —The plate upon which the rollers rest, and which itself rests
upon the masonry.
Rope Sling. —See sling.
Run. — A line, or string; as, a run of joists.
Set. — The extension or compression of a piece of material under stress.
Shear, or Shearing-Stress. – The resistance which a body offers to the
passage, or to the tendency to passage, of one section along the next consecu-
tive section.
GLOSSA R Y OF TEA’M.S. 24I
Shipping-Bill. — A list of portions of a bridge, arranged in a manner to
facilitate counting and checking when the material is received after shipment.
Shoe. — Another term for pedestal, g. v.
Shoe Plate. — The plate on the under side of the shoe, resting on the
rollers, bed-plate, or masonry.
Side Bracing.—A bracing for pony trusses to attach the panels of the top
chord to the floor beams prolonged, in order to fix the panel points of the
top chord. (Plate III.)
Sidewalks. – Roadways at the sides of a bridge for foot-passengers only.
Single Intersection. — That style of truss in which the diagonals do not
cross the posts. It is represented in skeleton on Plate V.
Skeleton Drawing. — A drawing which shows only the centre lines of
members, such as a diagram of stresses. (Plate V.)
Skew Bridge. — A bridge in which the horizontal lines joining correspond-
ing panel points of the opposite trusses are oblique to the planes of the trusses.
Sledge. — A heavy hammer, or mallet.
Sleeve Nut. — An elongated nut, the core at one end having a right-hand
thread, and that at the other a left-hand thread. Its office is to lengthen or
shorten a tension member. (Plate II., Fig. 16.)
Sling.—A loop of rope, very useful in erection for making a hasty attach-
ment.
Slope. — Inclination to a horizontal plane.
Snatch Block. — A block with one side capable of being opened for the
insertion of the rope. Its office is to change the direction of the rope.
Span. — The length of a bridge from centre to centre of end pins or
bearings.
Spikes. – Large nails for timber work. (Plate II., Fig. 13.)
Splay. — To spread at one end the two main portions of a member.
Splice. — A joint connected by means of plates.
Splice Plate. — A connecting plate at a joint. (Plate II., Fig. I2.)
Spread. — The distance apart laterally.
Staggered Rivets. – Rivets are said to be staggered when each rivet of one
row is opposite to the middle of the space between two rivets of the next row.
Static Load. — Dead load, g. v.
Stay Plate. — A plate always used at the end of a system of lacing or
latticing. (Plate II., Fig. 12.)
Stiffening-Angle. — An angle iron used to stiffen the web of a beam. (Plate
II., Fig. 13.)
Stiffener. — A piece of iron used to stiffen the web of a beam : it may be of
angle or tee section. (Plate II., Fig. 13.)
Strain. — The extension or compression of a piece of material which is or
has been under stress.
Stress. – The internal resisting force of a piece of material which is
strained.
Strut. — A member which resists compression.
242 G/LOSSA R P OF 7TP RMS.
Sub-Punching. — The punching of rivet holes which have to be afterwards
enlarged by reaming.
Sway Bracing. — Bracing transverse to the planes of the trusses. Its
objects are to resist wind pressure, and to prevent undue vibration from
passing loads. (Plate I.)
Table of Data. — A list of the known circumstances that affect the design-
ing of a structure.
Tap. — A screw for cutting a thread in a nut.
Tee or T iron. — A piece of rolled iron of the section shown on Plate II.,
Fig. 4.
Tension. — A stress tending to elongate a body.
Thread. — The spiral part of a screw or nut.
Through Bridge. — A bridge with overhead bracing.
Tie. — A tension member; generally refers to a main truss.
Timber Truck. — A small, strong wooden frame, with an iron roller set
entirely below the upper surface. It is used in bridge erection for moving
large timbers and heavy weights along a runway.
Tongs. – Part of a riveting outfit; used for holding and carrying heated
rivets.
Transverse Component. — A component in a transverse direction; gener-
ally intended for a component perpendicular to the planes of the trusses.
Truss. – An assemblage of tension and compression members so arranged
as to transmit loads from intermediate points to the ends.
Trussing. — A poor substitute for lacing or latticing. (Plate II., Fig. 8,
Plate VI.)
Turn Buckle. — Similar to a sleeve nut, and for the same purpose. The
sides are open, so that a crowbar may be inserted for the purpose of screwing
up. Turn buckles are used for larger bars or rods than are sleeve nuts.
(Plate II., Fig. 16.) *
Ultimate Strength. — The greatest load that a portion of material can
bear.
Uniform Load. — A load so distributed over an entire structure, that equal
lengths everywhere receive equal portions.
U-nut. — A piece of iron, in the shape of the letter U, through which passes
the threaded end of a rod, and which affords a bearing for the nut, with room
to screw up the latter. Its use is not permissible in first-class bridge con-
struction.
Upper Falsework. — The falsework that lies above the level of the lower
chords.
Upset End. — An end of a rod or bar enlarged for the cutting thereon of
a screw-thread.
Vibration Rod. — A tension member for vertical or portal sway bracing.
(Plate I.)
Washer. — A piece of cast or wrought iron to distribute the pressure of a
bolt-head or nut over timber. (Plate II., Fig. 6)
G/LOSSAA’ Y OF 7'EA8/.S. e 243
Web. — The portion of a truss or beam between the flanges. Its office is
principally to resist shear.
Welded Heads. – Heads first worked into shape, then welded on the bars.
Whipple Truss. – See Linville truss.
Wind Shakes. – Cracks in timber caused by the wind while the tree was
living.
Working-Drawings. – Drawings containing all the measurements neces-
sary for construction.
Working-Stress. – The stress, usually the greatest stress, to which a piece
of material is or should be subjected. Sometimes incorrectly employed for
intensity of working-stress.
Wrench. — A tool for screwing up nuts.
IN DEX.
IND EX.
Allowance for waste, 68, 183, 190.
Anchorage, 8, IO4, 148.
Angle irons, 19, 146.
Area opposed to wind pressure, 6, 48.
Bars, best proportions for, 79,80, 89.
Batter braces, limiting slope for, 7.
Batter-brace plates, minimum dimensions
of, I4.
Batter braces, proportioning of, 63, 132.
Batter-brace sections, II, 63.
Beam-hanger plates, 17, IoI, I46.
Beam hangers, 22, 75.
Beams, wooden, 23, 67; Tables xiii., xiv.
Bearings, 21, 77, 93; Tables xxvi-xxviii.,
xxxvi., xxxvii.
Bearing-stress, I 3, 76.
Bed plates, 16, IO4, 146. -
Bending effect of wind on posts and bat-
ter braces, 9, 52.
Bending-stresses, intensities of, 13, 78.
Bents, 199, 200, 203.
Best proportions for bars, 79,80, 89.
Bevels, 181.
Bills of iron, 71, II.3, II4, I51, I52.
of lumber, II 5, I 55.
of rivets, I 51, 190, 192.
of bolts, 188, 191, 205.
Bills, erecting, 2O4, 205.
order, 183, 185.
shipping, 190.
Bolts, 23, 24.
Bond, 168.
Bottom chords, 59, 62, 66, 215.
Braces, side, 7, 164.
batter, 7, 9, 14, 63, I32.
Brackets, 22, 53, Iog, I48.
Bridge lettings, 157.
Bridges, classification of, 5.
styles of, 7, 38.
Built floor beams, 12, 19, 68, Ioy; Tables
xix.-xxi.
Camber, 9, 175, 176.
Camber blocks, 200.
Carpenters’ tools, 198.
Cast-iron, 24.
Cast-iron portals, 58.
Channel bottom chords, II, 66.
Channels, properties of, Table xxviii.
Checking, method of, I 16, 181, 182, 198.
Chord bars, 59, 62, 66, 79.
Chord heads, 20, 177.
Chord packing, 62, 81, I32, 179, 206.
Chord plates, I4, 63.
Chord proportioning, 64, I29, 130.
Chord sections, II, 59, 62, 63, 66.
Classification of bridges, 5.
Clear headway, 7.
Clear roadway, 6.
Closed columns, 56.
Columns, formula for, I2.
Complete design for a bridge, 126.
Compressive stresses, 12.
Connecting-plates, I 5, 94–99, 137–144.
Connection for lateral systems, Io, 98-100.
Continuous spans, 9.
Contract, form of, 167.
Cost, estimates of, II6.
Cost of bidding-expenses, 170.
of blacksmithing, 170.
of erection, I 17.
247
248
IZVD Aº X.
Cost of falsework, 117.
of framing, II?.
of hauling, I 17.
of lumber, 68.
of painting, I 17.
of pile-driver, 198.
Counters, 12, 40, 41, 46, 59, 61, I27, I32.
Countersunk rivets, 91.
Cover plates, I6, 95, I44.
Cutting off flanges of channels, 23, 59, 96.
Data, table or list of, 38, 118.
Dead load, 6, 32, 126, 156.
Deck bridges, 46.
Demonstration of floor-beam formula, 219.
Depths of truss, economic, 38, 124; Ta-
* bles iv., v.
Design for a bridge, 126.
Details, proportioning of, 75, 86, 93, 136.
Diagonals, length of, 177, 22.I.
Diagrams of stresses, 40, 127; Plate v.
Diameters of rivets, I 5, 90; Tables xxix.,
xxxvi., xxxvii.
Dimensions, marking of, 180, 181.
Distribution of material in struts, 59.
Double-intersection bridges, 7, 44.
Draughtsman's equipment, 172.
Draughtsmen, hints to, 180.
Drawings, working, I72.
Economic depths, 38, 124.
Economy, 57, 59, I2O.
Effect of wind pressure on members, 9,
48, 99, 215.
End lower lateral-strut connection, IoA,
I44.
End lower lateral struts, Io, 56, 65, 135.
End panels, stiffened, II, 62, 66, 129, 215.
Equipment, draughtsman's, 172.
for raising gang, 197.
Equivalent length for heads, nuts, etc., II 5.
Erecting-bills, 204, 205.
Erecting-gang, 196.
Erection, 196.
Estimates of cost, I 16.
Expansion, 8.
Expansion joint, Io9, IO4.
Expansion rollers, 21, Io9, 141, 208.
Extension plates, 16, 96, I45.
Eyes, 20, IoS.
Eye-bar heads, 20, 177, 178.
Falsework, 198.
Falsework pillars, sizes of, Table xxxix.
Felly plank, 23, 67. -
Field riveting, 24, 92, 125.
Filling-plates, 145.
Fillers, Ioa.
Final order bill, 185.
Flanges, 19, 68, Io?. t
Floor beams, built, 12, 19, 68, 107; Tables
xix.-xxi.
details for, 19, 30, 7 I, IIo.
limiting depth for, 19.
riveted to posts, IoI.
rolled, I2, 71.
trussed, 30, 72, Io9.
Flooring, 23, 2 Io, 2II.
Floor system, 67.
Foremen, 197, 204.
Form of bond, 168.
of contract, 167.
of proposal, 166.
of specifications, 162.
Formula for built beams, 19, 219
for columns, I2.
for trussed beams, 72.
Framing falsework, II?, 203.
Friction, riveted plates, 90.
shoe, 8, II.
Functions of I-beams, 55, 56.
Gas-pipe struts, 56.
General specifications, 5.
Girders, 18, 19, 71.
Guard rails, 23, 24.
Hammers, pile-driver, 198.
Hand railing, 23, 24, 67.
Hangers, beam, I2, 22, 75.
Heads of eye bars, 20, 177, 178.
Headway, 7.
Hints to draughtsmen, 180.
Hip connection, 83, 95, 137, 138.
Hip verticals, 12, 14, 59, 61; Tables vis-
viii.
Hub plank, 23, 67,115.
I-beams, 13, 55, 56, 71.
AZMZOAX.
249
Inclinations of lattice and lacing bars, 15.
Indirect transferrence of stress by rivets,
92.
Initial tension, Io; Table ix.
Inspection, 2II. -
Intensity of bearing-stress, 13, 76.
of bending-stress, 13, 78. ,
of compressive stress, I2.
of tensile stress, 11, 12.
Intermediate strut connection, 98, 144.
Intermediate struts, 51, 56,65; Table xxv.
Iron, bills of, 7 I, II.3, II4, ISI, I52.
Cast, 24.
hand railing, 23, 24.
weight of, 33, 155, 156.
Jaws, 22, IOO, IO4, IoS, I43, I44, I49.
Joint, sliding expansion, IoS, IoA.
Joints, top chord, 94, 139, 179, 208.
Joists, 23, 67, 209; Tables xv.–xviii.
Knees, or knee braces, 22, 53, Io9, 148.
Labor in erecting, I 17.
in framing, I 17, 198.
Lacing-bars, I 5, Io2, 146, 181; Table xxxi.
Lateral-rod connection, Io, 99, Ioé.
Lateral rods, I4, 48, 61 ; Table xxv.
strut connection, 98, IO4, 144, 145.
struts, 9-II, 49, 56,61, 65, 135; Table
XXV.
systems, 48, 61.
Lattice bars, I 5, IO2, 146; Table xxx.
Lengths, limiting, 6, 7.
of diagonals, 177, 22I.
of lattice and lacing bars, Io2; Table
xxix.
of span, 6, 7.
Letting bridges, I 57.
Limiting depths of pony trusses, 7, 123.
depths of floor beams, 19.
lengths of span, 6, 7.
sizes of sections, 8, 57.
slope of batter braces, 7.
Limit of clear roadway, 6.
List of data, 38, II8.
of members, 28.
Live loads, 5, 32, 37, 126.
Loads, dead, 6, 32, 126, 156.
Loads, live, 5, 32, 37, 126.
Snow, 35, 46.
for wooden beams, 67; Tables xiii.,
xiv.
Lock nuts, 22.
Loop eyes, 20.
Lower end of post re-enforcing, 95, 142.
Lumber, amount per panel, Tables xv.–
xviii.
bill of, II 5, 155.
list of members, 28.
Main diagonals, 59, I77, 22I.
members, 55, 60.
Maintenance of bridges, 211.
Marking iron, system of, 192.
of dimensions, I80, 181.
Material in struts, distribution of, 59, 64.
Materials, bill of, 7 I, II.3, II4, II 5, 151,
I 52, I55.
tests of, 25, 26.
Measurements, method of recording, 180,
181.
Members, list of, 28. -
Method of erecting a bridge, 196.
of finding lengths of diagonals, 176,
22 I.
of recording measurements, 180, 181.
Methods of checking, 116, 181, 182, 198.
Middle of post connection, 96.
Minimum dimensions of chord and batter-
brace plates, I4.
Name plates, 24.
Neglected consideration in highway-
bridge designing, 2I 5.
Number of men required for erecting
bridges, I 17.
Nuts, 22, II 5.
Oak lumber, weight of, 6.
use of tables with, 61, 75.
Order bill, final, 185.
preliminary, 183.
Ornamental work, I49.
Outfit for draughtsman, 172.
for erecting-gang, 197.
Packing, chord, 62, 81, 132, 179, 206.
25O
AWDA.X.
Painting, 25, 117, 209, 2II.
Panel length, most economic, 38, 123, 128.
of top chord, exact, 176.
Pile-driver, 198.
Pilot nuts, 84.
Pin bearing, 21, 77, 93.
Pine lumber, 6, 23, 24.
Pin holes, 21.
Pin pilots, 84.
Pins, proportioning of, 76, 85.
steel, 81, 83.
working bending-moments, etc., for,
Table xii.
Plant, 197.
Plate girders, 7, 19, 71.
Pony trusses, 7, 123.
Portal-strut connection, 99, I43.
Portal struts, 52, 54, 61, 65; Table xxv.
Posts, 9, 40, 41, 43, 45, 46, 59, 64, 133.
Posts, hand rail, 23, 67.
Post sections, II, 58.
Practical method of pin proportioning,85.
Preliminary order bill, 183.
Proportioning of batter braces, 63, 132.
of beam-hanger plates, IoI.
of beam hangers, 75.
of bottom chords, 62, 66, 128.
of brackets, Io9, 148.
of built floor beams, 68.
of chord bars, 62, 66, I28.
of counters, 60, I27, 130.
of details, 75, 86, 93, I36.
of end lower lateral struts, 65, 135.
of expansion rollers, Io9, I4I.
of falsework, 198.
of floor system, 67.
of hip connection, 95, I35.
of intermediate strut connection, 98,
I44.
of intermediate struts; 65.
of joists, 67.
of knee braces or knees, Io9, 148.
of lateral rods, I4, 61.
of lateral-strut connection, 99, Io9,
I43, I45.
of lateral struts, 61, 65.
of lateral systems, 60.
of lower end of posts, 96, I42.
of lower lateral struts, 65, I35.
Proportioning of main truss members, 60.
of middle of post connection, 96.
of pins, 76, 85.
of portal-strut connection, 99, 143.
of portal struts, 61, 65.
of posts, 64, I33.
of re-enforcing plates, 93, 96.
of rivets, 91.
of rolled beams, 71.
of rollers, Io9, 141; Tables xxxiv.,
XXXV.
of shoes, 97, I40.
of side bracing, 7.
of sway bracing, 61.
of top-chord connection, 94, 129.
of top chords, 63, 128.
of trussed beams, Io9.
of upper end of post connection, 95,
I45.
of upper lateral-strut connection, 98,
I43.
of upper lateral struts, 61.
of vibration-rod connection, 98, IoS,
of vibration rods, 61.
Proportions for bars, best, 79,80, 89.
Proposal, form of, 166.
Quality of workmanship, 25, 166.
Ratio of width to depth of bars, 79, 88.
Recording of measurements, 180–182.
Reduction of ends of pins, 84.
Re-enforcing plates, 16, 93, 96, 142.
Rivet heads, 90, 150; Table xxix.
Riveting, field, 24, 92, I25.
rules for, 17, 90.
Rivets, bending-moments, etc., for, Tables
xxxvi., xxxvii.
bill of, I 51, 190, 192.
countersunk, 91.
diameters of, I 5, 90.
in flanges of beams, 20, Io?.
Rivet spacing, 18, 20, Ioy, 181.
Roadway, clear, 6.
Rods, equivalent lengths for upper ends,
etc., II 5.
Roller plates, 16, IO4, 146.
Rollers, 2 I, IO3, 14I.
Rules for riveting, 17, 90.
JAWDAX.
25 I
Scales, 172, 204.
Sections, limiting sizes of, 8.
Sections of members, 8, II.
Shearing-stress, 77, 80, 91.
Shipping-bill, 190.
Shoe connection, 97, I40.
plates, 16, 97, I40, 146.
Side bracing, 7.
Sizes of floor beams, Tables xix.-xxi.
of hip verticals, Tables vi.-viii.
of joists, Tables xv.–xviii.
of lacing-bars, Table xxxi.
of lateral rods, Table xxv.
of lateral struts, Table xxv.
of lattice bars, Table xxx.
of pillars for falsework, Table xxxix.
of pins, 81, 86, 134.
of portal rods, Table xxv.
of portal struts, Table xxv.
of rollers, Tables xxxiv., xxxv.
of sections, limiting, 8, 57.
of stay plates, Tables xxxii., xxxiii.
of vibration rods, Table xxv.
Skeleton diagram, 40, 44.
Skew bridges, 3, 75.
Sleeve nuts, II 5.
Sliding expansion joint, Io9, Io.4,
of pedestal, 8.
Snow load, 35, 46.
Spacing, rivet, 18, 20, IOZ, 181.
Specifications, 5, 162.
general, 5.
on file, 162.
Spikes, 23, 151, 2Io.
Splice plates, I 5, 94, I39.
Star iron, 58.
Stay plates, 137; Tables xxxii., xxxiii.
Steel pins, 81, 83.
Stiffened bottom chords, II, 62, 66, 129,
2I 5.
hip verticals, I4.
Stiffeners, 19, 70.
Stresses on batter braces, 9, 41, 45, 52, 54,
I28.
on beam hangers, 75.
on bottom chords, 41, 43, 45, 128, 215.
on brackets, 53.
on built beams, Ioy.
on chords, 41, 43, 45, 128, 215.
Stresses on counters, 40, 45, 127.
on double-intersection trusses, 44.
on end lower lateral struts, Io, 54, 135.
on falsework, 200.
on floor beams, 73, Ioy.
on hip verticals, 41.
on intermediate struts, 51.
on lateral systems, 48.
on lower lateral rods, 49.
on lower lateral struts, 49.
on main diagonals, 40, 45, I25.
on pins, 76.
on portal rods, 51.
on portal struts, 51, 53.
on single-intersection trusses, 38.
on sway bracing, 61.
on top chords, 41, 43, 44, 128.
on trussed beams, Io9.
on trusses, 38.
on upper lateral rods, 49.
on upper lateral struts, 49.
on upper lateral systems, 48.
on vibration rods, 51.
Structure, test of, 26.
Styles of bridges, 7.
Sway-bracing, 9, 48, 61.
System of marking iron, 192.
Table of data, 38, I 18.
Tee-iron, 19, 58.
Tensile stresses, intensities of, II, 12.
Tension, initial, Io; Table ix.
Test of structure, 26.
Tests of materials, 25.
Thicknesses of webs of channels, Table
xxviii.
Threads, I4.
Timber, 23, 25.
Tools used in erection, 197.
Top-chord connection, 94, 129.
joints in, 94, I39, 179, 208.
panel length of, 176.
Top chords, 41, 43, 44, 63, 128.
Truss, economic depth of, 38, I24.
Trussed beams, 30, 72, Io9.
Trusses, pony, 7, 123.
Trussing, I4, IoS, I48.
Turn buckles, 22, II 5.
Turning-in of channel flanges, 58.
252
ZZWZOAX.
Units, 2.
Upper end of post connection, 16, 95,
I45.
falsework, Ioa.
lateral rods, I4, 49, 61.
lateral-strut connection, 98, 143.
lateral struts, 9, II, 49, 61, 65.
Upset rods, 14, II 5, 165.
Vertical sway bracing, 49, 61.
Vibration rods, 51, 61.
Washers, 22, 152.
Waste, allowance for, 68, 183, 190.
Web stiffening, 19, 70.
thickness of, Table xxviii.
Weights of materials, 6, 68.
of iron, total, in bridges, 35, I55, I56;
Tables i.—iii.
of rivet heads, I 51, 156; Table xxix.
Widths of flanges of channels, Table
xxviii.
Wind pressure, amount of, 6.
area opposed to, 6, 48.
effects of, 9, 48, 99, 215.
Wooden hand railing, 23.
lateral struts, Io, IOO, I49.
Working bearing-stresses, intensities of,
I3, 76.
bending-stresses, intensities of, 13,76.
compressive stresses, intensities of,
I2; Tables x., xi.
drawings, 172.
loads for wooden beams, Tables xiii.,
xiv.
shearing-stresses, intensities of, 76.
tensile stresses, intensities of, II.
Workmanship, 25.
Wrought-iron, weights of, 33, 71, I31, 155,
I56; Tabkes i.-iii.
INDEX TO
Beam-hanger plates, 226.
Floor-beam connection to foot of post,
228.
Floor-beam stiffeners, 228.
Foot of post connection to floor beam, 228.
Improved beam-hanger plates, 226.
ADDENIDA.
Improved portal strut connection, 229.
upper lateral strut connection, 228.
Lateral strut connection, 228.
Portal strut connection, 229.
Proportioning of beam-hanger plates, 226.
Stiffeners for floor beams, 228.
- s TABLE I.
TABLE OF WEIGHTS PER LINEAL FOOT OF IRON PRATT. TRUSS HIGHWAY-BRIDGES.
CLASS A.
y
12' Roadway. 14 Roadway. 16% Roadway. 18' Roadway. As 20 Roadway. 22 Roadway. 24 Roadway.
Span.
LatéRAL | Floor
Lateral. Floor
SYSTEM. SYSTEM.
SYSTEM. System.
LATERAL FLOOR
SYSTEM. SYSTEM.
LATERAL | Floor
LUMBER. tº ºsº º Trusses.
SYSTEM. SYSTEM. U D. L. USSES
D. L. Trusses.
LUMBER. *
LUMBER. D. L. TRUSSEs. LUMBER. tº ºf ºr TRUsses.
ſ {
TRUsses. {{*T* | *toos | Lumeer. D. L. || Trusses. Lateral Floor Luweer. D. L. ||Trusses. º” sº Lumber. D. L.
|
SYSTEM. SYSTEM. System. SYSTEM. System. | SYSTEM.
2O 26 2O 2I 2O 48 2O 266 I61 2O 290 I 2 I _315 I68 2 I 87 6oo
2O 2O 2 I 2O 2O. 2OI 2 I 22 6 22 IO
4. I 3O4 I
I
2 I
22 22 I I I
I472 I O2O

12 Roadway.
Span.
FLOOR
SYSTEM.
LATERAL
TRUSSEs. SYSTEM
2O
2O
LUMBER. D. L. TRUsses.
I
I
I
I
2OO
2 I
TABLE
14 Roadway.
LATERAL
SYSTEM.
2O
2O
Floor
SYSTEM LUMBER.
TABLE II.
y §
WEIGHTS PER LINEAL FOOT OF IRON . PRATT. TRUSS HIGHVVAY - BRIDGES.
CLASS B.
f
OF
16' Roadway. 18' Roadway. 20 Roadway. 22 Roadway. 24' Roadway.
i
FLOor
SYSTEM.
LATERAL
SYSTEM.
FLOOR
SYSTEM.
LATERAL
SYSTEM.
FLOor
SYSTEM.
L. TERAL
S 1stEM.
Floor
SYSTEM.
LATERAL
SYSTEM.
Floor
System.
LaterAL TRUsses.
System.
LUMBER. D. L. Trusses. TRUsses. LUMBER. D. L. TRUSSEs. LUMBER. i D. L.
TRUsses. LUMBER.
Q:
2O 2O 266 2O 290 2I * i
2O- 2O 2I 22
I
I
I I
I IOI
I
I
I
I
3
I
9
! §
LuMBER.
f
Span.
D. L.
567
6

f TABLE III.
er / TABLE OF WEIGHTS PER LINEAL FOOT OF TRON PRATT TRUss HIGHVVAY - BRIDGES.
CLASS C.
12' Roadway. 14 Roadway. 16' Roadway. g 18' Roadway. 20 Roadway. 22 Roadway. 24' Roadway.
LaTERAL | FLOOR
SystEM. SYSTEM.
LATERAL Fuoor
System. SwsTEM.
LATERAL | Floor
SYSTEM. System.
Lateral Floor
SYSTEM. SystEM.
LATERAL | Floor
SYSTEM. SYSTEM.
LaTERAL | FLOOR
LUMBER. D. L. TRusses. j| Sºjº.
| *
TRUsses. g: s: LUMBER. D. L. || TRUSSEs. LUMBER. . L. || Trusses. LUMBER. D. L. Trusses. LUMBER. D. L. Trusses. LUMBER. D. L. || TRUSSEs. Lumber. D.
2O $ 2O * 2O 4O 2O 266 2 I
2O 2O 2O. 2O 2 22
2

TABLE IV.
ECONOMIC DEPTHS AND
PANEL LENGTHS.
Depth.
No. of
Panels.
Span.
SINGLE Double
I6.

TABLE V.
ECONOMIC DEPTHS AND
PANEL LENGTHS.
Depth.
SINGLE Double
I6. 5’
I
2

TABLE VI.
TABLE of SIZES OF HIP VERTICALS FOR BRIDGES
OF CLASS A,
In which the live load is one hundred pounds per square foot of floor, and the
working-stress on the verticals is four tons to the square inch.
The upper figures give the sizes of the hip verticals; the lower ones, the sec-
tions required.
;

Panel 12’ 14' I6' I8’ 20' 22' 24' Panel
..] Length. Roadway. || Roadway. || Roadway. Roadway. || Roadway. Roadway. Roadway. | Length.
y 2 #" D 2 #" D 2 #" D 2 #" [] 2 #"dº 2 ##" D 2 I" [] Aſ
IO o.91 []" I.oé D" I.21 [...]" 1.38 []" 1.51 D" 1.67 []" 1.84 D" IO
II’ 2 #" D 2 #" D 2 ##" D 2 #" D 2 #" D 2 I" D 2 I" […] II’
I.oo []" I.I6 D" I.33 []" 1.52 []” I.66 []" 1.84 []" 2.03 []"
12' 2 #" [] 2 ##" [] 2 #" D 2 ##" [] 2 I" [] 2 I" [1] 2 II's" D 12'
2' 1.09 D" I.26 D" 1.45 D" 1.64 D" I.81 []" 2.oo []” 2.19 D"
I 3’ 2 ##" [] 2 #" [] 2 ##" [] 2 ##" D 2 I" [] 2 II's" D 2 14” [] I 3'
3 I. I8 D." 1.37 D." 1.56 D" 1.77 D" 1.95 D." 2.I6 D" 2.36 E!” 3
14' 2 ##" D 2 #" D 2 #" [] 2 I" [...] 2 II's" D 2 Ił” D 2 14" D 14'
4. 1.27 D" 1.48 D." I.68 D." 1.90 []" 2. Io D’ 2.32 D" 2.53 D." 4
I 5’ 2 #" [] 2 ##" D 2 I" [] 2 II's" D | 2 II's" D 2 I}” D 2 Hºº" D I R'
5 1.36 D" I.59 D" I.81 Dj" 2.04 D" 2.26 []” 2.49 []" 2.72 []” 5
I6' 2 #" D 2 #" D 2 I" [...] 2 I-P's" D 2 I?" D 2 Iºs" D 2 14" D 6'
1.45 D" 1.69 []" 1.93 D" 2.18 []" 2.41 D" 2.66 []" 2.91 D" I
17' 2 #" D 2 I" [] 2 II's" D 2 13" D 2 Iſs" D 2 Iºs" [] 2 Ił" [] Af
7 1.54 []" I.8o []" 2.05 D" 2.32 []" 2.56 []" 2.83 D" 3.09 []" 17
18' 2 ##" [] 2 I" [...] 2 Iºs" [] 2 14” D 2 Iſs" D 2 1+" D 2 Iºs" [] 8’
1.64 []" 1.91 []" 2.17 []" 2.46 D" 2.71 []" 2.99 D" 3.27 D" I
id: 2 #" D 2 I" [] 2 Ił" [] 2 Iºs" [] 2 14" [] 2 Iſs” [] 2 Iºs" [] p
9 1.73 CI" 2.02 D" 2.29 D" 2.61 D" 2.86 D" 3.16 D" 3.46 []" 19
20' 2 I" [] 2 II's" D 2 14" D 2 Iºs" [] 2 Ił" D 2 Hºs" [] 2 Iš" [] 20'
1.84 D". 2.14 D" 2.43 D" 2.76 []" 3.03 D" 3.34 D" 3.66 []" O
2I’ 2 I" [] 2 1+" LI 2 Hºs" [] 2 13" D 2 Iºs" [] 2 1;" D 2 IT's" D 21’
1.95 D." 2.27 D" 2.58 []" 2.92 []" 3.29 D" 3.54 E", 3.87 D" I
22' 2 11s" [] | 2 13" D 2 Iſs" D 2 14" D 2 I-Pº" D 2 13" D 2 Iſs" [] 22'
2.07 DJ" 2.40 DJ" 2.73 D." 3.09 CI" 3.39 D" 3.74 D" 4.09 D"
23' 2 Iºs" D 2 Ił" D 2 1+" D 2 Hºº" [] 2 1;" D 2 Iºs" [] 2 13" D 23'
2.18 []" 2.53 D." 2.87 D" 3.27 D" 3.57 []" 3.95 D" 4.33 D" 3
24' 2 1+" D 2 Iſs" [] 2 Ił" D 2 Iºs" [] 2 1;" D 2 Iºs" [] 2 13" D 24'
2.29 D" 2.65 [1” 3.01 D" 3.45 Cl" 3.74 D" 4.16 []" 4.56 []"
TABLE VII.
TABLE OF SIZES OF HIP VERTICALS FOR BRIDGES
# OF CLASS B,
In which the live load is one hundred pounds per square foot of floor, and the
working-stress on the verticals is five tons to the square inch.
The upper figures give the sizes of the hip verticals; the lower ones, the sec-
tions required.

Panel I2’ 14' I6' I8’ 20' 22' 24' Panel
Length. Roadway. || Roadway. Roadway. Roadway. Roadway. || Roadway. Roadway. | Length.
P 2 #" D 2 #" D 2 #" D 2 #" [] 2 +3* D 2 ” [] 2 g” D f
io o.72 []” o.84 D" o.96 D" 1.09 D" 1.22 D" I.34 D" 1.45 D" IO
! II.” 2 #" [] 2 #" D 2 #" [] 2 +;" D. 2 #" D 2 g” D 2 ##" D II’
o.79 []" o.92 D" I.oé D" I.20 D" 1.33 D" 1.47 []" I.6o DJ."
12’ 2 #" [] 2 #" D 2 #" [] 2 +$" D 2 #" D 2 #" D 2 #" D I2’
o.86 []" I.oo [..]" 1.15 []" 1.31 D" I.44 []” 1.59 D" 1.74 []"
I3” 2 #" [] 2 #" D 2 ##". D 2 #" D 2 +3" D 2 +3" [] 2 I" [] I 3’
3 o.94 []" I.O3 D" 1.24 D" 1.4I D" I.55 D" 1.72 [..]" I.88 D." 3
14' • 2 #"D 2 ##" D 2 #" [] 2 #" D 2 +3* D 2 I" [...] 2 I" D 14'
4. I.OI [...]" 1.17 D" I.34 D" 1.52 D" 1.67 D" 1.85 D" 2.O2 []" 4.
I 5’ 2 #" D 2 ##" D 2 g” [] 2 #" D 2 I " [] 2 I" D 2 II's" D I k”
5 I.O8 []" I.26 D" 1.44 D" I.62 D" I.8o D" 1.98 D" 2.I6 []" 5
I6' 2 ##" [] 2 g” [] 2 #" D 2 ##" D 2 I" [1] 2 II's" . 2 I?" [] I6'
1.15 []" I.35 D" I.54 D" 1.73 D." I.93 D" 2.12 D" 2.31 D"
I 7' 2 ##" [] 2 g” D 2 #" [] 2 I" [...] 2 II's" [] | 2 I ſº" [] 2 I #" [] I 7’
7 1.23 D" 1.43 D" 1.64 D" 1.85 D" 2.05 D" 2.26 []” 2.46 D." 7
is 2 #" G | 2 "El 2 #" | | 2 1" E | 2 iſs" E 2 #" E 2 º' F. is,
1.30 []" 1.52 D" 1.73 CI" 1.96 D" 2.17 D" 2.39 D" 2.61 []"
Io’ 2 g” D 2 ##" D 2 I" [] 2 II's" D 2 13" D 2 I?" [] 2 I s” D Io'
9 1.38 D." I.6I DJ." 1.83 []" 2.07 D" 2.29 D" 2.53 []" 2.76 D" 9
2O’ 2 : " [] 2 ##" [] 2 I" [] 2 II's" D 2 13" D 2 Iºs" [] 2 Ił" [] 20’
1.46 []" 1.71 D" 1.94 []" 2.19 []" 2.42 D" 2.67 D" 2.92 []"
21’ 2 ##" [] 2 I" […] 2 II's" D 2 I?" D 2 Iſs" D 2 14” D 2 14" D 2I’
1.55 D" 1.81 D" | 2.06 []" 2.32 D" 2.57 D" 2.83 D" 3.09 D"
22’ 2 ##" [] 2 I" [] 2 II's" D 2 I?" D 2 Iſs" [] 2 14" D 2 I s” D 22'
1.65 D." 1.91 []" 2.18 D." 2.46 D." 2.72 D" 3.oo []" 3.28 D."
23” 2 ##" [] 2 I* D 2 Ił" D 2 Iſſ,” D 2 Ił" [] 2 Iſs" [] 2 Iſs" [] 22'
3 1.74 D" 2.oi []" 2.29 []" 2.60 D. " 2.86 []" 3.17 D" 3.47 D." 3
24' 2 I" D 2 II's" D 2 13" D 2 I s” [] 2 14" D 2 I s” [] 2 1;" D 24'
1.83 D" 2. I I Dº" 2.41 D" 2.74 D" | | 3:01 D" 3.33 D" 3.65 D"
TABLE VIII.
TABLE OF SIZES OF HIP VERTICALS FOR BRIDGES
OF CLASS C,
In which the live load is eighty pounds per square foot of floor, and the working-
stress on the verticals is five tons to the square inch. &
The upper figures give the sizes of the hip verticals; the lower ones, the sec-
tions required. Q

Panel 12’ 14' I6' .18' 20’ 22’ 24' Panel
Length. Roadway. Roadway. Roadway. Roadway. Roadway. Roadway. || Roadway. | Length.
P 2 #" [] 2 #7 D 2 #" D 2 #" D 2 #" D 2 #" D 2 ##". D A
IO o.60 DJ" o,69 []" o.79 []" o.89 D" I.O.O. D." I. I2 DJ." I.21 []” IO
tº 2 #" E 2 #' E | 2 #" E || 2 "G | 2 #"E | 2 #" H | * * B | 1,
o.65 D" o.75 D" o.87 D" o.98 D." I. Io D" 1.22 D" I.33 D"
12’ 2 #" D 2 #" D 2 #" [] 2 #" D 2 ##" D 2 ##" D 2 #" D 12’
o.71 []" o.82 []" o.95 D." 1.07 D" I.20 []" 1.33 []" 1.45 D"
13' 2 #" D 2 #7 D 2 #" D 2 ##" [] 2 +$" [] 2 #” D 2 ##" [] I 3/
o.77 []" o.89 [I" 1.03 D" I.I6 D" 1.30 CI" 1.43 D" 1.57 D" 3
14' 2 #" D 2 #" [] 2 #" D 2 ##" D 2 #" D 2 #" [] 2 ##" [] 14'
o,83 D" o.97 []" I.I.I []" 1.25 D" I.4o D" I.54 []” 1.69 []" 4.
I5' 2 #" D 2 #" D 2 +$" [I 2 #" [] 2 #" D 2 ##" D 2 I" [...] I R'
o.89 D" 1.04 []" 1.19 D" I.34 D" 1.5o D" 1.65 D." I.81 D" 5
I6' 2 #" D 2 #" D 2 #" [] 2 #" D 2 ##" D 2 ##" [] 2 I" [] I6/
o.95 D" I.I.I D" 1.27 D" 1.42 []" I.6o […]” 1.76 []" 1.92 D"
I-7' 2 #" D 2 ##" [] 2 #" [] 2 #" [] 2 ##" [] 2 I" [] 2 I-P's" [] I '7'
7 I.or []" I.I8 []” I.35 []" 1.51 D" 1.70 []" 1.87 D" 2.04 D" 7
I8’ 2 #" [] 2 #" [] 2 #" [] 2 ##" D 2 I" [] 2 I" […] 2 Iºs" [] I8’
1.07 DT" 1.25 D" I.43 CI" I.6o D" I.8I D" I.99 []" 2.I6 []"
19' 2 #" D 2 ##" D 2 #" C. 2 ##" D 2 I" [] 2 II's" D 2 I}" [] Io'
1.13 D" 1.32 D" 1.51 D" 1.70 []" 1.92 E." 2.II D" 2.30 D" 9
20 | * #" D 2 #" D 2 #" D 2 I" [] 2 II's" D 2 II's" D 2 14" D 20'
I.21 []" 1.41 D" I.61 []" I.8o []” 2.03 D." 2.23 []" 2.43 []"
2I’ 2 #" [] 2 #" D 2 #" [] 2 I" D 2 II's" [] 2 14" [] 2 Iſs" D 2I’
I.28 []" 1.5o []" 1.71 []" 1.91 D" 2. I6 D" 2.36 []" 2.58 D."
22' 2 #" C. 2 ##" [] 2 I" [...] 2 I" D 2 14" D 2 14" [] 2 Iºs" [1 22'
1.36 []" 1.58 D." I.81 D" 2.02 []" 2.28 D." 2.5o D" 2.73 []"
23' 2 #" D 2 ##" [] 2 I" […] 2 II's" D 2 Ił" D 2 Iºs" [] | 2 Ił" [] 23’
I.44 D" 1.67 D" 1.90 CI" 2.13 D" 2.4o D" 2.64 D" 2.88 []" 3
24' 2 #" [] 2 #" D 2 I" [] 2 Iºs" [] 2 14” [] 2 I s” [] 2 14" [] 24'
1.55 CI" 1.75 D" 2.oo []" 2.24 D" 2.52 D" 2.78 D" 3.03 D"
TABLE IX.
TABLE OF GREATEST WORKING STRESSES,
In tons of two thousand (2,000) pounds, on adjustable round and square rods, exclusive of
the initial tensions; also the initial tensions.
Intensity of Working || Intensity of Working || Intensity of Working
Stress = 4 tons. Stress = 5 tons. Stress = 7.5 tons. Initial Tensions.
i
i
(j) ſº
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I

TABLE X.
}
INTENSITIES OF WORKING-STRESS FOR CHANNEL STRUTS.
CLASS A.
Ratio,
ºn | no o O ||Zºº. ºn | n e God
28 2.826
2.
2.
2.
&©***&
ºegeg
7
O.
O.
O.
O.
O.
O.
O.
O.
O.
O.

TABLE XI.
INTENSITIES OF WORKING-STRESS FOR CHANNEL STRUTS.
CT, ASSES B AIND C.
Ratio, Ratio, º " Ratio,
zºº.] an so | O C ||Aº. mm so | @ 9 ||zº.
IO 28 2.7 I2
I
I I
I I
I 2
I
I
I
;
ºº
*tºstº*tºg*º
2
O
I
I.
I.
I
I
I
I
I
I.
I.
I.
I.
I
*
tº†º
:
tº*
2.
3. I27 2.750
I
*

TABLE XII.
TABLE OF WORKING BENDING-MOMENTS FOR I.RON
AND STEEL PINS, AND OF WORKING SHEARING-
STRESSES FOR STEEL PINS.
Resisting Shearing-
Stresses.
Resisting Moments for Bending.
i
i
IRON. STEEL. STEEL.
Classes Lateral Classes Classes
Class A. B and C. System. Class A. B and C. Class A. B and C.
ºr
2. I

TABLE XIII.
FOR FINDING THE SAFE UNIFORMLY DISTRIBUTED LOADS THAT CAN BE
BORNE BY PINE BEAMS.
-
3
The loads being those which will produce a deflection of only 44 of the span, calculated by Trautwine's formula, W= d”. where
W = load in tons, d = depth of beam in inches, and l = length of span in feet.
I6/2”
To find the safe distributed load for any span, look in the upper horizontal line for depth of beam, and in right or left hand vertical
line for length of span. The number found at the intersection of a vertical line through the former, and a horizontal line through the
latter, multiplied by the width of beam in inches, will give the load required.
\
8? Io" II? 12" 14” 15" 17" 187 19"
I.688
I.
I
I
I
2.
2.
I
I
I
I.
I.
I
2
2
2
2
II.
*-ººº&
:
;
2
;
-
I

TABLE XIV.
FOR FINDING THE SAFE UNIFORMLY DISTRIBUTED LOADS THAT CAN BE
BORNE BY OAK BEAMS.
3
The loads being those which will produce a deflection of only 4%g of the span, calculated by Trautwine's formula, W = º where
W = load in tons, d = depth of beam in inches, and l = length of span in feet.
To find the safe distributed load for any span, look in the upper horizontal line for depth of beam, and in right or left hand vertical
line for length of span. The number found at the intersection of a vertical line through the former, and a horizontal line through the
latter, multiplied by the width of beam in inches, will give the load required. -
(l,
9" 15" 17" 187 19"
I
I
I:
2.
2.
I
I.
I.
I
I
I.
I
I
*ſº:.
I
I

# }* * TABLE XV.
TABLE OF PINE LUMBER REQUIRED PER PANEL IN BRIDGES OF CLASSES A AND B
Af (including waste material). -
Flooring 3" thick; hand-rail posts, 4"X6"X4'; hand rail, two pieces, 2"X6"; hub rails, 2"X 12"; and guard rails, 6'X6".

Panel || Roadway, No. of || Roadway, No. of || Roadway, No. of || Roadway, No. of || Roadway, No. of || Roadway, No. of || Roadway, No. of size of |No. Hand- Panel
Length.|| 12’ clear. Joists. || 14’ clear. Joists. || 16’ clear. Joists. || 18' clear. Joists. || 20' clear. Joists. || 22' clear. Joists. || 24’ clear. Joists. || Joists. : . Length.
Io' 691 7 776 8 861 9 946 IO Io31 II III6 - I 2 I2OI I3 3" x 10" 2 Io'
II’ 806 7 902 8 998 9 IO94 IO II90 II I286 I 2 1382 I3 3" x 10" 4 II’
12’ 842 7 944 8 Ioa 6 9 II48 IO || I250 II I352 I 2 I454 I3 3" x 10" 4. 12'
13' 990 7 I I IO 8 I230 9 I350 IO I470 II I 590 I 2 17 Io I3 3" x 12" 4 13'
14' Io26 , 7 II 52 8 1278 9 I4O4 IO I 530 II 1656 I 2 1782 I3 3" x 12" 4 I4'
I5' I 18O 8 I318 9 I456 IO I 594 II I732 I2 1918 I4 2056 I5 3" x 12" 4 I5'
I6' I224 7 I376 8 1528 9 I68o IO 1832 II I984 I 2 2136 I3 3" x 14" 4 I6'
17' I4OO 8 & I565 9 I730 IO I895 II 2060 I 2 2288 I4 || 2453 I 5 3" x 14" 4. 17'
I8’ I436 8 1670 IO 1841 II 2OI2 I 2 2246 I4 24I7 I 5 2588 I6 3" × 14" 4. I8’
19' AZ.43 8 I950 9 2I57 IO sº 5 II 2572 I2 2873 I4 308o I5 4" × 14” 4 I9'
2O’ 1872 9 2085 IO - 2392 I2 2605 I3 2819 I4 3125 I6 3339 I7 4" × 14" 4 20'
21’ I933 7 2177 8 242O 9 2663 IO 3024 I2 3267 I3 35II I4 4” x 16" 6 2I’
22' 2087 8 2336 9 2585 IO 2835 II 32OI I3 345I I4 3817 I6 4” x 16" 6 22'
23' 236, 9 2758 II 3024 I 2 3290 I3 3684 I 5 3950 I6 4344 I8 4” x 16" 6 23'
24' y 2528 IO 2928 I 2 3328 . I4 35OO I5 4OOO 17 4272 I8 4672 2O 4" x 16" 6 24'
TABLE OF PINE LUMBER
# 9.
TABLE XVI.
.*
REQUIRED PER PANEL IN BRIDGES OF CLASS C
(including waste material).
Flooring 3" thick; hand-rail posts, 4"X6"X4' ; hand rail, two pieces, 2"X6"; hub rails, 2"X 12"; and guard rails, 6"X6".

Panel || Roadway, No. of || Roadway, No. of || Roadway, No. of || Roadway, No. of || Roadway, No. of || Roadway, No. of || Roadway, No. of || Size of No. Hand- Panel
Length.|| 12’ clear. Joists, 14’ clear. Joists. || 16’ clear. Joists. || 18' clear. Joists. || 20' clear. Joists. || 22' clear. Joists. || 24’ clear. Joists. || Joists. #: . Length.
Io' 69I 7 776 8 861 9 946 IO Io91 T I III6 I 2 I2OI I3 3" x 10" 2 Io'
II’ 806 7 902 8 998 9 Io94 IO II90 II I286 I 2 1382 I3 3" x 10" 4 II’
12’ 842 7 944 8 IO46 9 II.48 IO I250 II I352 I 2 I454 I3 3" x 10" 4 I2’
13' 94I 7 IOS4 8 1167 9 I28o IO I393 II I 504 I2 1619 I3 3" x 10" 4 13'
14' Io26 7 II 52 8 1278 9 I4O4. IO $ I 530 II 1656 I 2 1782 I3 37 × 12! 4 I4’
15’ 1132 7 1270 8 I408 9 I 546 Io 1684 II 1822 I2 1960 I3 3" x 12" 4 I5'
I6' I216 8 1360 I 504 IO 1648 II T I792 I2 - 1984 I4. 2128 I5 3" x 12" 4 I6’
17' I 337 7 I 502 8 1667 9 1832 IO I997 II 2I62 I 2 2327 I3 3" × 14" 4 17'
18' I373 7 I544 8 1715 9 I886 IO 2I2O I 2 2291 I3 2462 I4 3" x 14" 4 I8’
19' I556 8. I74O 9 I924 IO 2178 I 2 2362 I3 2546 I4 2730 I 5 3" x 14" 4 Ig’
20' 1685 7 1899 8 2 II 2 9 2325 IO 2539 II 2752 I2 2965 I3 4" × 14" 4 2O’
21’ I933 7 2I 17 8 242O 9 2663 IO 29O7 II 3ISO I2 3393 I3 4” x 16" 6 2I’
22' 1969 7 22 IQ 8 2468 9 2717 IO 2967 II 3216 I 2 3465 I3 4" x 16" 6 22'
23' 2236 8 25O2 9 2768 IO 3O34 II 33OO I2 3566 I3 3832 I4 4" x 16" 6 23'
24' 24OO 9 2672 IO 2.944 II 3344 I3 3616 3888 IS 416o I6 4" x 16" 6 24'
I4
TABLE XVII.
TABLE of PINE AND OAK LUMBER REQUIRED PER PANEL IN BRIDGES OF
f f CLASSES A AND B.
Joists and flooring of oak, and other lumber pine. Flooring 24" thick; hand-rail posts, 4"x6"X4'; hand rail, two pieces, 2"X6"; hub rail, 2" × 12";
and guard-rail, 6"X6". - .
The upper figures in each rectangle are for pine, the lower for oak. The quantities include waste material.

Panel || Roadway, No. of || Roadway, No. of || Roadway, No. of || Roadway, No. of || Roadway, No. of || Roadway, No. of || Roadway, No. of || Size of No. Hand- Panel
Length.|| 12' clear. Joists. || 14' clear. Joists. || 16’ clear. Joists. || 18' clear. Joists. || 20' clear. Joists. || 22' clear. Joists. || 24’ clear. Joists. || Joists. #: i. Length.
io || | | 7 || || || 8 || : | 9 || # io || 3 || 1 || }; is || # || 3 || 4'x3' || 2 || 8
II’ : 7 ; 8 § 9 : IO ; ^*. II §: I 2 § I3 24" x 9" 4. II’
12’ : 7 É. 8 ; 9 ; IO §: II : I 2 1: I3 24" × 10" 4 I2’
•º : 7 || || || 8 || : | 9 || : | to || 1: | 1 || 1: | 12 || || || 3 || 4'x4' || 4 || 13
14' à. 7 : 8 ; 9 : IO ſ: II ſ: I 2 #: I3 24" x 12" 4. 14'
I5' ;: 7 §: 8 : 9 ſ: IO #. II ſ: I2 º: I3 24" x 12" 4. I5'
I6' gº § 7 ; 8 * ...; 9 ſ: Io & I I º: I2 1. I 3 3" x 12" 4 I6'
17 || 4 || 7 || 4 || 8 || | | 9 || 1: | to || | | | | || 1: | 1 || || || 3 || 3 × 13' || 4 17'
I8’ ; 7 ;: i. 8 ;: 9 º: IO ſ: II #: I 2 # I 3 3" × 14" 4. I8’
19 || 3. 7 || 3:3 || 8 || 3: 9 || 3: | to || 3: | 1 || 3: | 1 || 3: | 3 || 3"x4" || 4 - || 19.
29' || 3: 7 || 3; 8 || 13. 9 || 18. io || 2: | ti || 3: 12 || 3: | 3 || 4' × 14" || 4 2O’
21’ J .# 7 iš. 8 3: 9 3: IO 3: II .# I 2 .# I3 4" x 15" 6 2I’
22' .# 7 # 8 º: 9 .# IO .# II .# I 2 3: I3 4” x 167 6 22’
23' .# | 7 .# 8 . .# 9 #: IO ; II : I 2 : I3 4' x 16’ 6 23'
24 || 3: | 8 || 3: | 9 || 3 || 1 || 3: | 2 || 3: | 3 || 3: | 4 || 3: is || 4' × 16 || 6 24'
*. TABLE XVIII. .e’
TABLE OF PINE AND OAK LUMBER REQUIRED PER PANEL IN BRIDGEs
A OF CLASS C.
Joists and flooring of oak, and other lumber pine. Flooring 24" thick; hand-rail posts, 4"x6" ×4; hand rail, two pieces, 2"x6"; hub rail, 2" x 12";
and guard rail, 6"X6". *
The upper figures in each rectangle are for pine, the lower for oak. The quantities include waste material.

Panel ||Roadway, No. of |Roadway, No. of Roadway, No. of Rºadway, No. of Roadway, No. of |Roadway, No. of Roadway, No. of Size of *: º: Panel
Length. || 12’ clear. Joists. || 14’ clear. Joists. || 16’ clear. Joists. || 18' clear. Joists. || 20' clear. Joists. || 22' clear. Joists. || 24’ clear. Joists. || Joists. per panel. Length.
io || # | 7 || 3 || 8 || : | 9 || #; to || 3 || 1 || 3: | 12 || # 13 || 23'x3' || 2 | to
* || 3 || 7 || : | 8 || : | 9 || : | to || : | 1 || : | 12 || : | 3 || 23'x3' || 4 || -
13' : -*. 7 : 8 : 9 #. IO ; I I ſ: I 2 ſ: I 3 24" × Io" 4 13'
14 || : | 7 || || || 8 || || || 9 || : io || || || 1 || || || 2 || | | 3 || 4-2 tº || 4 || 4.
15' ; 7 §: 8 ; 9 3. IO i; II º: I 2 º: I3 24" x 12" 4. I5'
I6/ ; 7 § 8 ſ: 9 º: IO # I I & I2 º: 13. 24" x 12" 4. I6'
* | # || 7 || || || 8 || 1:4 || 9 || 1: | to || | | | | | | | 1 || 3: | 3 || 3 × 12" || 4 || 7.
18 || : | 7 || 4 || 8 || 4 || 9 || | | to || | | | || 3: 12 || 1: 13 || 3' x 13' || 4 || s
19 || 3: | 7 || 3: | 8 || 3: | 9 || 3: | to || 3: | 1 || $: | 12 || 3: | 3 || 3 × 14" || 4 || 19.
* || 3: | 7 || 3: | 8 || 1:... 9 || #; to || 3: | 1 || 2: | 12 || 3: | 13 || 3'x14" || 4 || 20
21’ 3; 7 #: 8 .# IO º: I I .# I2 #. dº I3 .# I4 34" × 14" 6 2I’
* | # | * | # | 9 || # | * | *; " || 3: | * | # || 3 || # | * | * * *|| 8 || --
23' .# º 7 * 8 .# 9 .# , IO .# I I : I 2 : I3 4” x 16" 6 23'
24 || 3: 7 || 3: | 8 || 3: | 9 || 3: to || 3 || 1 || 3: | 12 || 3: 13 || 4 x 16"|| 6 || aw
TABLE XIX.
TABLE OF FLOOR BEAMS.
L. fl., 2 2" × 3" 4:# angle
Up, fl., 2 2"x24" 3.5% angle
Up. fl., 2 2" × 23" 3.5% angle
L. fl., 2 2" × 3" 4:# angle
Up. fl., 2 2"x24" 3.5% angle
L. fl., 22" × 3" 4:# angle
I4
12" 42% I, or
Built-beam, 41% per foot
Web, 4' × 19.”
Up. fl., 22" × 2%" 3.5% angle
L. fl., 2 2" × 3" 4:# angle
15" 50% I, or
Built-beam, 41% per foot
Web, 4" × 24”
Up, fl., 2 2" × 2%" 3.5% angle
L. fl., 2 2" × 3" 4% angle
* ~ *-*** * ~.
Up. fl., 2 2" × 3" 4.5% angle
L. fl., 2 24" × 3" 5% angle
Up. fl., 2 2}"X 3" 5.5% angle
L. fl., 2 24" × 23" 6.5% angle
Up. fl., 2 3" x 3” 7.2% angle
L. fl., 2 3"X 3" 7.7% angle
L. fl., 2 3"x 3" 7.2% angle
CLASS A.
º Roadway, 12" Clear. Roadway, 14' Clear. Roadway, 16’ Clear. Roadway, I8’ Clear. Roadway, 2O’ Clear. Roadway, 22' Clear. Roadway, 24' Clear. ºl.
12" 42% I, or 15" 50% I, or 15" 50% I, or Built-beam, 55## per foot Built-beam, 62% per foot Built-beam, 64%+ per foot
Built-beam, 41% per foot Bºbº. 45% per foot º * per foot Web, +" x 28/ Web, +" × 30" Web, +" × 30" A.
Io' Io" 30+ I Web, #"> 19" Web, #" x 22" Web, + *:: // Up. fl., 2 2" × 3" 4.5% angle | Up. fl., 2 24" × 3" 5.5% angle | Up. fl., 2 2" × 3" 6# angle Io
Up. fl., 2 2"x24" 3.5% angle | Up. fl., 2 2"x24" 3.5% angle | Up, fl., 2 2"x24" 3.5% angle | L. fl., 2 24" × 3" 5:# angle L. fl., 2 24" × 23” 6.5% angle | L. fl., 2 3'x3' 7.2% angle
L. fl., 2 2" × 3" 4:# angle L. fl., 2 2" × 3" 4:# angle L. fl., 2 2" × 3" 4:# angle -
-- - - - - - 12" 42% I, or I 5" 50% I, or | Isſ o; I, or & e ſº *
hº * 42}# per foot iº, 47# per foot #: 52% per foot Built-beam, 57% per foot Built-beam, 63% per foot | Built-beam, 67%:# per foot
II’ Ioł" 31# I * Web, +" x 20" Web, 4" × 24” Web, 4" x 26" Web, 3"x 29* Web, +"x 30" Web, #"> 30" II’
Ž Up. à. 2 2" × 24" 3.5% angle | Up. fl., 2 2"x24" 3.5% angle | Up. fl., 2 2" × 3" 4:# angle Up. ft., 2 2" × 24” 4.5% angle | Up. fl., 2 2" × 3" 6% angle Up. fl., 2 3"X 3" 7.2% angle
L. fl. . 2" × 3" 4:# angle L. fl., 2 2" × 3" 4:# angle L. fl., 2 24" × 3" 4.4% angle L. fl., 2 2" × 33" 5.3% angle | L. fl., 2 24" × 3" 6.7% angle | L. fl., 2 3'x3' 7.7% angle
12" 42% I, or 12" 42% I, or - I 5" 50% I, or e * - e g !? 4.
Built-beam, 38%+ per foot | Built-beam, 44% per foot Built-beam, 48## per foot Biºlº # per foot. ºilº, &= per foot Bºbº, &# per foot ºilº º per foot
12' Web, #"x I87 Web, 4" × 2 I " Web, 4" × 25" Web, # × 27 Web, # × 30 Web, # × 30 Web, # × 30 i2’
Upſ. 27.2, 3.34 angle | Up, i. 27%ay 3.5% angle | Upfi, a 27&ay 3.5% angle JP, fl. 4 º' 4.5% angle ||P.” ‘’’’.3's "gº ||P.” ‘’’.3% "gº ||P.” “º 77**
L. fl., 2 2"x24" 3.5% angle | L. fl., 2 2" × 3" 4:# angle L. fl., 2 2" x 3" 4# angle L. fl., 2 2" × 33" Sł angle L. fl., 2 3"X 3" 5.9% angle L. fl., 2 3"X 3" 7.2% angle | L. fl., 2 3'x3' 8.4% angle
12" 42% I, o - I 5" 50% I, o - I 5" 50% I, or • ‘s & *
B º e +. * per foot iº, . 5# per foot É. e |m, 50% per foot Built-beam, 55## per foot | Built-beam, 62% per foot Built-beam, 673; per foot | Built-beam, 75% per foot
13' Web, 4"x 18" Web, #" X 22" Web, 4"x 26" Web, }" X 28'ſ Web, #" X 30" Web, 4" × 30" Web, #" X 34" - 13'
Up, fl., 2 23"x24" 6.5% angle
Built-beam, 52% per foot
Web, "x 26"
Up. fl., 2 2" × 3" 4# angle
L. fl., 2 2%" × 3" 4.4% angle
Built-beam, 57% per foot
Web, 4" × 29"
Up. fl., 2 2" × 24” 4.5% angle
L. fl., 2 2" × 3}" 5.3% angle
Built-beam, 63% per foot .
Web, #" X 30"
Built-beam, 70% per foot
Web, 4" x 30"
• *-*--> ---
Built-beam, 78% per foot
Web, *" x 36"
I6'
12" 42% I, or
Built-beam, 42%% per foot
Web, +"x20"
Up. fl., 2 2" × 24" 3.5% angle
L. fl., 2 2" × 3" 4:# angle "
'15" 50% I, or
Built-beam, 48}# per foot
Web, +"x 25" -
Up. fl., 2 2" × 24" 3.5% angle
L. fl., 2 2" × 3" 4:# angle
Built-beam, 53% per foot
Web, 4" x 27”
Up. fl., 2 2" × 3" 4% angle
L. fl., 2 24" × 3" 4.4% angle
Built-beam, 58% per foot
Web, #"x 30" #
Up. fl., 2 2" × 2%" 4.5% angle
L. fl., 2 2" × 3}" S.3% angle
12" 42% I, or
Built-beam, 44% per foot
Web, +"x21"
Up. fl., 2 2" × 2%" 3.5% angle
L. fl., 2 2" × 3" 4:# angle
I 5" 50% I, or
Built-beam, 50% per foot
Web, 4” x 26" -
Up. fl., 2 2" × 24" 3.5% angle
L. fl., 2 2" × 3" 4:# angle
Built-beam, 55## per foot
Web, +/x 28’ f
Up. fl., 2 2" × 24” 4.5% angle
L. fl., 2 2" × 3" 5:# angle
Built-beam, 60% per foot
Web, +" x 30"
Up. fl., 2 2" × 3" Sºft angle
L. fl., 2 3"X 3" 5.9% angle
I 5" 50% I, or
Built-beam, 45% per foot
Web, +/X 2.2"
Up, fl., 2 2"x24" 3.5% angle
L. fl., 2 2" × 3" 4:# angle
15" 50% I, or
Built-beam, 51# per foot
Web, +" x 25" *
Up. fl., 2 2" × 3" 4# angle
L. fl., 2 24" × 3" 4.4% angle
Built-beam, 56}# per foot
Web, +/x 29"
Up. fl., 2 2" × 24” 4.5% angle
L. fl., 2 2" × 34” S.3% angle
Built-beam, 63% per foot
Web, 4" × 30"
Up. fl., 2 24" × 3" 5.5% angle
L. fl., 2 2;" x 23' 6.5% angle
15" 50% I, or
Built-beam, 46% per foot
Web, +/x 23"
| Up. fl., 2 2" × 24" 3.5% angle
15" 50% I, or
Built-beam, 52% per foot
Web, +7x 26"
Up. fl., 2 2" × 3" 4:# angle
Built-beam, 58% per foot
Web, +"x 30"
Up, fl., 2 2" × 24” 4.5% angle
L. fl., 2 2" × 33" S.3% angle
Built-beam, 65% per foot
Web, 4" x 30" -
Up, fl., 22" × 34" 6.4% angle
L. fl., 2 3" x 3" 7.2% angle
Built-beam, 60% per foot
Web, +" x 30"
Up. fl., 22" × 3" 5:# angle
L. fl., 2 3"X 3" 5.9% angle
Built-beam, 66%; per foot
Web, 4" x 30"
Up, fl., 2 24" × 3" 6.7% angle
L, fl., 2 3" x 34" 7.7% angle
Built-beam, 62% per foot
Web, 4" × 30"
Up, fl., 2 24" × 3" 5.5% angle
L. fl., 2 24" × 23" 6.5% angle
Built-beam, 69% per foot
Web, +" x 30"
Up, fl., 2 3'x3' 7.2% angle
I., fl., 2 3" x 3" 8.4% angle
Built-beam, 63% per foot
Web, +" x 30"
Up. fl., 2 2" × 3" 6% angle
L. fl., 2 24" × 3" 6.7% angle
Built-beam, 70+ per foot
Web, 4" x 30"
Up, fl., 2 3" x 3%" 7.7% angle
I, fl., 2 3"X 3" 8.4% angle
Built-beam, 65% per foot,
Web, +" x 30"
Up. fl., 2 2" × 33" 6.4% angle
I, fl., 2 3"X 3" 7.2% angle
Built-beam, 66%; per foot
Web, +" × 30"
Up. fl., 2 24" × 3' 6.7% angle
L. fl., 2 3" x 34" 7.7% angle
Built-beam, 75% per foot
Web, #"X 34"
Up, fl., 22}"X 24"6.5% angle
I... fl., 2 3"X 3" 7.2% angle
Built-beam, 76%; per foot
Web, ſſ," × 35"
Up. fl., 22%"X 24" 6.5% angle
I... fl., 2 3" × 3" 7.2% angle
Built-beam, 67%:# per foot
Web, +"x 30"
Up, fl., 2 3"X 3"|7.2% angle
L. fl., 2 3"X 3" 7.7% angle
Built-beam, 78% per foot
Web, Ps" × 36"
Up. fl., 2 2" × 33" 6.4% angle
L. fl., 2 3'x3' 7.2% angle
L. fl., 2 27x3" 4% angle L. fl., 2 24" × 3" 4.4% angle
15" 50% I, Ör t • k
Built beam, 48# per foot |*b* 53* Per foot
- 19' Web, 4" × 24" | Web, 4” x 27”
Up. fl., 2 2"X 24" 3.5% angle Up, fl., 2 2" × 3" 4:# angle
L. fl., 2 2" × 3" 4:# angle L. fl., 2 24" × 3" 4.4% angle
15" 50% I, or “. .
Built-beam, 49% per foot Built-beam, 54}# per foot
20' Web, #"x 25" - Web, +" x 27”
Up. fl., 2 2/X 24" 3.5% angle Up. fl., 2 24" × 3" 4.4% angle
L. fl., 2 2" × 3" 4:# angle L. fl., 2 2" × 3" 5:# angle
157 50% I, or ſe
Built-beam; 50% per foot Built-beam, 55%:# per foot
21" | Web, Fºx 26" Web, #"x28"
Up. fl., 2 2" × 2%" 3.5% angle Up, fl., 2 2" × 24” 4.5% angle
I, fl., 2 2" x 3" 4% angle L. fl., 2 2" x 3" 5#. angle
I 5" 50% I, or
Built-beam, 51% per foot Built-beam, 56%+ per foot
22’ Web, +" x 25" Web, +" × 29"
Up fl. 2 2" x 3" 4# angle Up. fl., 2 2"X 2}" 4.5% angle
• * * * > I, fl., 2 2" × 3}" S.3% angle
L. fl., 2 24" × 3" 4.4% angle | ** "" 3#" 5.3 g
I 5" 50% I, or ſº - - -
Built-beam, 52% per foot Built-beam, 58}# per foot
23' Web, 4" x 26" Web, 4" × 30"
Up. fl., 2 2" × 3" 4:# angle Up. fl., 22%"X 24" 4.9% angle
L. fl., 2 24" × 3" 4.4% angle L. fl., 2 24" × 24" 5.4% angle
Built-beam, 53% per foot | Built-beam, 63}# per foot
24' Web, +" x 27” Web, )," x 30"
Up. fl., 2 2" × 3" 4:# angle | Up. fl., 2 2" × 3" 6# angle
ſ2.fl., 2 24" × 3" 4.4% angle | L. fl., 2 24" × 3" 6.7% angle
Panel R A. z
Length. oadway, 12" Clear. Roadway, 14. Clear.
Roadway, 16’ Clear.
Roadway, 18' Clear.
* 14' R |
Up. fl., 2 2" × 3" 6% angle | Up. fl., 2 3'x3%" 7.7% angle | Up. fl., 22" × 33" 6.4% angle || *
L. fl., 2 24" × 3" 6.7% angle | L. fl., 2 3"X 3" 8.8% angle L. fl., 2 3"X 3" 7.2% angle
Built-beam, 65% per foot Built-beam, 75% per foot Built-beam, 81% per foot
Web, 4" × 30" Web, #"X 34" Web, ſ," x 38" i 5''
Up, fl., 2 2" × 3}" 6.4 angle | Up. fl., 2 23" x 23' 6.5% angle | Up. fl., 2 2" × 33" 6.4% angle.
L. fl., 2 3"X 3" 7.2% angle | L. fl., 2 3"X 3" 7.2% angle L. fl., 2 3'x3' 7.2% angle
Built-beam, 67%:# per foot Built-beam, 76## per foot Built-beam, 82}# per foot *
Web, +"x 30" Web, ſº" x 35" Web, ſ," x 38" 16 * *
Up, fl., 2 3'x3' 7.2% angle | Up. fl., 2 23"x24"6.5% angle | Up. fl., 2 24" × 3' 6.7% angle
L. fl., 2 3"X 3" 7.7% angle | L. fl., 2 3" x 3" 7.2% angle | L. fl., 2 3'x3%" 7.7% angle
Built-beam, 70% per foot Built-beam, 78% per foot Built-beam, 86% per foot … . .
Web, #" × 30" Web, #"x 36" Web, #"> 38" - 3.17'
Up, fl., 2 3"x3}" 7.7% angle | Up, fl., 2 2" × 33" 6.4% angle | Up. fl., 2 3'x3}" 7.7% angle -
L. fl., 2 3"X 3" 8.4% angle | L. fl., 2 3"x 3" 7.2% angle | L. fl., 2 3" x 3" 8.4% angle -
Built-beam, 75% per foot ' | Built-beam, 81% per foot Built-beam, 89% per foot N. : " .
Web, is"X34” Web, #"X 38" Web, #"x 38" 18'
Up, fl., 2 23"x24" 6.5% angle Up. fl., 2 2"x 34* 6.4% angle | Up, fl., 2 3'x3' 8.4% angle |
L. fl., 2 3'x3' 7.2% angle | L. fl., 2 3'x3' 7.2% angle | L. fl., 2 3'x33" 9% angle . .
Built-beam, 76}# per foot | Built-beam, 823# per foot | Built-beam, 9: per foot - º
Web, ºs" × 35" Web, Fº" x 38" Web, #"x 38" . . . . . . igº
Up. fl., 2 24" × 23" 6.5% angle. Up. fl., 2 24" × 3" 6.7% angle | Up, fl., 2 3"x3}" 9% angle T’.
L. fl., 2 3"X 3" 7.2% angle | L. fl., 2 3"x 3}" 7.7% angle | L. fl., 2 3"x4" 9.7% angle
Built-beam, 78% per foot Built-beam, 86% per foot Built-beam, 94% per foot
Web, Ps" × 36" Web, ſſ," x 38" Web, #"> 38" 20 |
Up, fl., 2 2" × 33" 6.4% angle | Up, fl., 2 3'x33” 7.7% angle | Up, fl., 2 3"x4" 9.7% angle •
L. fl., 2 3"X3" 7.2% angle | I., fl., 2 3"x 3" 8.4% angle | L. fl., 2 3" x 34" 10.4% angle
Built-beam, 79% per foot | 13uilt-beam, 89% per foot Built-beam, 98% per foot
Web, #" x 37" Web, #"X 38" Web, Ps" x 38" re. ~ *
Up, fl., 2 2" × 33" 6.4% angle | Up. fl., 2 3'x3' 8.4% angle | Up. fl., 2 3'x3}" 10.4% angle 2 I
I, fl., 2 3"X 3" 7.2% angle I, fl., 2 3" x 3%" 9% angle L. fl., 2 3"x 3}." I 1.7% angle
Built-beam, 82}# per foot | Built-beam, 91% per foot Built-beam, lor:# per foot
Web, ſ," x 38" Web, ſº" x 38" Web, ſſ," x 38" 22'
Up, fl., 2 24" × 3" 6.7% angle | Up, fl., 2 3'x3%" 9% angle | Up. fl., 2 3"x4" 11.2% angle
L. fl., 2 3"X3%" 7.7% angle | L. fl., 2 3"x4" 9.7% angle L. fl., 2 3"x4" 12.7% angle
Built-beam, 85% per foot Built-beam, 94% per foot Built-beam, 104% per foot
Web, *," x 38" Web, ſ," x 38" Web, is" x 38" 23’
Up, fl., 2 3"X 3" 7.2% angle | Up, fl., 2 3"x4" 9.7% angle | Up. fl., 2 33"x4" 12# angle 3
L. fl., 2 3"X 3" 8.4% angle | L. fl., 2 3"x 33" io.4% angle | L. fl., 2 33"x4" 13.6% angle
Built-beam, 86% per foot Built-beam, 98% per foot Built-beam, 106% per foot
Web, ſſ," x 38" Web, ſs"X 38" Web, ſſ," x 38" y
Up, fl., 2 3"x 3}" 7.7% angle | Up. fl., 2.3"x3}" io.4% angle | Up, fl., 2 4"x4" 12.9% angle 24
L. fl., 2 3"X3" 8.4% angle | L, fl., 2 3'x3%" | 1.7% angle | L. fl., 2 34"x4" 13.6% angle
Roadway, 20' Clear. Panel
• *****-* * * ~ **-* A *.
Roadway, 22' Clear.
Roadway, 24' Clear.
--- • *- : * ~ *-m-, … º. * - ºrv -º- ºr



TABLE XX.
TABLE OF FLOOR BEAMS.
CI ASS B.
—º-
© Panel
º: Roadway, 12" Clear. Roadway, 14' Clear. Roadway, 16’ Clear. Roadway, 18' Clear. Roadway, 20' Clear. Roadway, 22' Clear. Roadway, 24' Clear. Length.
12" 42% I, or 15" 50% I, or 15" 50% I, or Built-beam, 54% per foot Built-beam, 583% per foot
Built-beam, 41%; per foot Built-beam, 46% per foot Built-beam, 50% per foot Web, 4" x 27” Web, 4" x 30" /
Io' Io" 30% I Iož" 31## I Web, 4" × 19." Web, "x 22" Web, +" x 26" Up. fl., 2 2" × 3" 4.5% angle | Up. fl., 2 2" × 24” 4.5% angle IO
3 // ſ/ // Ye 2 1// fl "X 24" 3.5% angl p 3
Up, fl., 2 2"x24" 3.5% angle | Up, fl., 22"X2%" 3.5% angle.|UP. f. 2 ***'.35% angle | L. fl., 2 24'x3' 5; angle | L.f., 2 2/x34; 8.3% angle
L. fl., 2 2" × 3" 4:# angle L. fl., 2 2" × 3" 4:# angle L. fl., 2 2" × 3" 4:# angle
12" 42% I, or 12" 42% I, or 'I 5" 50% I, or is' sº I, or Built-b # per foot |Built beam, 62# per foot
Built-beam, 384; per foot | Built-beam, 43}# per foot | Built-beam, 48## per foot Built-beam, .53% per foot w. º: #. p O w. º: pe Aſ
// // // // 5 5 II.
II’ Io" 30% I Web, #"x 18" Web, 4" × 20." Web, + º f/ Web, 4" × : // Up, fl., 2 2" × 2%" 4.5% angle | Up. fl., 2 2%"X 3" 5.5% angle *
Up. fl., 2 2/x 24" 3.5% angle | Up. fl., 2 2"x24" 3.5% angle | Up. fl., 2 2"x24" 3.5% angle | Up, fl., 22"X2%"4.5% angle L. fi, 2 24" × 3" 5% angle L. fl., 2 24" × 23" 6.5% angle
L. fl., 2 2"x24" 3.5% angle | L. fl., 22" × 3" 4# angle L. fl., 2 2" × 3" 4# angle L. fl., 2 24" × 3" 5% angle • ***3 •3
12" 42% I, or 15" 50% I, or I 5" 50% I, or ilf- ilt- foot Euilt-b 6 foot
Built-beam, 39% per foot | Built-beam, 45% per foot Built-beam, 50% per foot * º*º per foot *. ºº per too w. rºº per too M
ſ/ // // // 3 Zſ 3. 5 3: I2
12' Io" 30% I Web, 4" × 18" Web, 4" × 3. // Web, 4" × * // Up. fl., 2 2" × 24” 4.5% angle | Up. fl., 22" × 24” 4.5% angle | Up, fl., 22" × 3' 6% angl
| Up. fl., 2 2"x24" 3.5% angle | Up, fl., 2 2"x24" 3.5% angle | Up. fl., 2 2"x24" 3.5% angle L. fl., 2 24" × 3" 5:# angle L. fl., 2 2" × 34" 5.3% angle | L. fl., 2 24" × 3" 6.7% angle
L. fl., 2 2" × 3" 4:# angle L. fl., 22" × 3" 4:# angle L. fl., 2 2" × 3" 4# angle • * * *5 • * * *5 • ****
TV 12" 42% I, or 15" 50% I, or I 5" 50% I, or ilt- $14- Built-b 6 foot
Built-beam, 41; per foot | Built-beam, 46% per foot | Built-beam, 51## per foot * º, * per foot : º,º per foot º pº per roo f
// // // // 3. Aſ y * 3. I
13' Iož" 31# I Web, 3"x 19" Web, + *:: // Web, 4" × º If Up. fl., 2 2" × 24” 4.5% angle | Up. fl., 22" × 3" 5:# angle | Up. fl., 2 3"X3" 6.5% angle 3
Up. fl., 22" x 24" 3.5% angle | Up. fl., 2 2"x24" 3.5% angle | Up. fl., 2 2" × 2%" 4.5% angle L. fl., 22%" × 3" 5% angle L. fl., 2 3"X 3" 5.9% angle | L. fl., 2 3"X3" 7 2# angle
L. fl., 2 2" × 3" 4:# angle L. fl., 2 2" × 3" 4:# angle L. fl., 2 24" × 3" 5:# angle • ***) 3" 5% ang ... fl., 2 3" × 3" 5.9% ang … - \ —f
{ 12" 42% I, or 12" 42% I, or 15" 50% I, or ilf- Raii. t Built-b 62% foot Built-beam, 67.4% per foot
Built-beam, 384; per foot | Built-beam, 42%; per foot | Built-beam, 47% per foot : º, * per foot ; º, g" per foo w. º,: per too w. #" sº p O Aſ
// // 1.// ſy % 9 3. 2 I
14' y . i. * 3.5% angle º yº. 2}" 3.5% angle wº 2%" 3.5% angle Up, fl., 2 2"x24" 4.5% angle | Up. fl., 2 2" × 24” 4.5% angle | Up. fl., 2 24" × 3" 5.5% angle | Up. fl., 2 3"X3" 7.2% angle 4.
p. fl., 2 2 sº • *a*3 º • * * *3 . fl. 2 24" × 3" . f. 2 2" × 33" K. . fl. 2 23"X2%" 6. L. fl., 2 3"X3%" 7. 1
L. fl., 2 2"x24" 3.5% angle | L. fl., 2 2"X3" 4% angle L. fl., 2 2" × 3" 4:# angle L. fl., 2 24" × 3" 5% angle L. fl., 2 2" × 34" 5.3% angle | L. fl., 2 24" × 23" 6.5% angle 2 3"X3%" 7.7% angle
12" 42% I, or I 5" 50% I, or 15" 50% I, or ilt- t ilt- t Built- 63% foot Built-beam, 70% per foot
Built-beam, 38% per foot | Built-beam, 42%:# per foot | Built-beam, 49% per foot . º, * per foo * º,* per foo * º # per too Web, 4" × % P
// // 2 // 3. 2 2 I
15' Web, 4" × 18" Web, 4" × 20 Web, 4" × º: // Up, fl., 22" × 24" 4.5% angle | Up. fl., 2 24" × 24” 4.9% angle Up. fl., 22" × 3' 6# angle Up. fl., 2 3"X3%" 7.7% angle 5
Up. fl., 2 2"x24" 3.5% angle | Up. fl., 2 2"x24" 3.5% angle | Up, fl., 2 2"x24" 3.5% angle L. fl., 2 24" × 3" 5% angle L. fl., 2 2" × 34" 5.3% angle | L. fl., 22%"X 3" 6.7% angle L. fl., 2 3"X 3" 8.4% angle
L. fl., 2 2"x24" 3.5% angle | L. fl., 2 2"X3" 4:# angle L. fl., 2 2" × 3" 4:# angle . fl., 22%" × 3 g • **** 3#" 5.3% ang • * * *3 3" b. g
12" 42% I, or 15" 50% I, or 15" 50% I, or 21151 t- i1+- ilt- Built-
Built-beam, 39% per foot | Built-beam, 44% per foot Built-beam, 51## per foot Built bº. §# per foot | Built bº, &# per foot Built bº 6# per foot Uil bº 7 s: per foot
3. // // // // Web, 4"x28 Web, 4" × 30" Web, 4" × 30 Web, #"X34 y
, 16/ Web, 4" × 18" Web, 4" × 21 Web, #"x26 h Me 2, 1 // // Ye A / // // 16' .
5 If // * // Ye A // Up. fl., 2 2" × 24” 4.5% angle | Up. fl., 2 2" × 3" 5:# angle | Up. fl., 2 3"X 3" 6.5% angle | Up, fl., 2 24" × 23"6.5% angle
, Up. fl., 2 2"x24" 3.5% angle | Up, fl., 2 2" × 24 3.5% anglé | Up. fl., 2 2" × 3" 4# angle L. fl., 22%" × 3" Słł angle L. fl., 2 3"X 3" 5.9% angle | L. fl., 2 3'x3' 7.2% angle | L. fl., 2 3"X 3" 7.2% angle
L; fl., 2 2" × 3" 4:# angle L. fl., 2 2" × 3" 4:# angle L. fl., 2 24" × 3" 4.4% angle • ***5 3 g |~~ 3" × 3" 5. g . fl., 2 3" × 3" 7. g • Alsº tº ºf
12" 42% I, or I 5" 50% I, or 15" 50% I, or . łl H- ilt- Boii. ilt-
3. | Built-beam, 393% per foot | Built-beam, 45% per foot Built-beam, 51## per foot *. º, gº per foot ; º per foot *. º* per foot : º: ſº per foot
... / // // // //X 2 g/ 5 y 2 y ſ
17 Web, 4" x 18 Web, 4' X : // Web, + : I/ Up. fl., 2 24" × 2%" 4.9% angle Up. fl., 2 24" × 3" 5.5% angle | Up. fl., 2 3"X3%" 7.7% angle | Up. fl., 2 23"X2}"6.5% angle 17
f Up.fi, 22"x2" 3.5% angle |Up, fl., 22"x24" 3.5% angle |Up, fl., 22°23'45* angle ||. 24'x 24' 54; angiel L fl., 2 24'x 23' 65: angle |L fl., 2 3'x3'84; angle |L fl., 2 3'x3'72; angle
º L. fl., 2 2" × 3" 4:# angle L. fl., 2 2" × 3" 4:# angle L. fl., 2 2" × 3" 5:# angle • T1-, 2 2+ 5.4% ang • ***3 .5% ang , fl., 2 3" × 3" 8.4% ang . fl., 2 3" × 3" 7. g
12" 42% I, or 15" 50% I, or * * * *1f- e ilf- ilt-
Built-beam, 41% per foot Built-beam, 46% per foot Built-beam, 52%% per foot | Built bº sº per foot Built-beam, 63% per foot | Built-beam, 75% per foot Built-beam, ſº per foot
8’ Web. 4/X ..., Web, 4" × 23" Web, #"X26" Web, 4" x 30" Web, 4" x 30" g Web, #"X34" Web, #"X 36" I8’
I U : #. .. 2}" 3.5% angle | Up ſ 2 .. 24" 3.5% angle Up. fl., 22" × 24” 4.5% angle | Up. fl., 2 24" × 24” 4.9% angle. Up. fl., 2 2" × 3" 6# angle | Up. fl., 2 24" × 23" 6.5% angle | Up. fl., 2 24" × 23" 6.5% angle
: à, % 2" x 3" †: gle g L. fl., % 2" × 3" 4:# angle L. fl., 22" × 34" 5:3# angle | L. fl., 22%"X2}" 5.4% angle | L. fl., 2 24" × 3" 6.7% angle | L. fl., 2 3'x3' 7.2% angle | L. fl., 2 3"X 3" 7.2% angle ,
12" 42% I, or " 15" 50% I, or ſº ilt- ilt- 31) ilf- k D . . . •
Built-beam, 42}# per foot | Built-beam, 49% per foot Built-beam, 534% per foot | Built-beam, &# per foot Built bº, § per foot Built-beam, 76## per foot | Built-beam, 81% per foot J
* r */ Web 7. ſ/ Web, \" x 25" Web, 4" x 27” Web, 4" × 30 Web, 4" × 30 * Web, #"X35" Web, ſ," x 38" . ~, 19’
k-º - **** 29. 2 ;: // Up. fl., 22" × 24” 4.5% angle | Up, fl., 2 2" × 33" 5:3# angle | Up, fl., 2 2" × 33" 6.4% angle | Up, fl., 22#"X2#"6.5% angle | Up. fl., 2 23"x 23' 6.5% angle
- Up. fl., 2 2"x24" 3.5% angle | Up. fl., 2 2"x24" 3.5% angle 'ſ/ // // Nº. 2, ſh h' Me A I/ // Ye ºn ſh h Me Alf
L. fl., 2 2" × 3" 4% angle L. fl., 22" × 3" 4:# angle L. fl., 2 2" × 34" 5.5% angle L. fl., 2 3"X 3" 5.9% angle | L. fl., 2 3"X 3" 7.2% angle |L fl., 2 3'x3'72+ angle |L, fl., 2 3'x3' 72+ angle
15" 50% I, or . 15" 50% I, or º º º *. t th
f Built-beam, 44% per foo Built-beam, 50% per foot Bºltº §# per foot Bºlº, &# per foot Bºbº &# per foot Bºbº * per foot Bºbº 8 sº per foot
20' Web, +" x 21" Web, +"x 26" Web, 4" × 28 Web, 4" × 30 Web, 4" x 30 Web, #"X36 Web, #"X38 20’
Up. à. 2 2" × 24" 3.5% angle | Up. à. 2 2" × 24" 3.5% angle Up. fl., 22" × 24” 4.5% angle | Up, fl., 2 24" x 3" 5.5% angle | Up, fl., 2 24" × 3" 7.2% angle | Up, fl., 2 2" × 33" 6.4% angle | Up. fl., 2 3'x3' 7.2% angle
L. fl., 2 2" × 3" 4:# angle L. f..., * 2" × 3" 4:# angle L. fl., 2 2" × 34" 5:3# angle | L. fl., 2 2" × 34" 6.4% angle | L. fl., 2 3'x3%" 7.7% angle | L. fl., 2 3"x 3" 7.2% angle | L: fl., 2 3'x3' 8.4% angle
I 5" 50% I, or I 5" 50% I, or e º * º te
i. ſº, 45% per foot i. . 52# per foot Built-beam, 57% per foot | Built-beam, &# per foot | Built beam, 70; per foot Built-beam, * per foot | Built-beam, 86% per foot
2I’ Web, +" x 22" Web, 4"x24" Web, 4" × 29" Web, 4" × 30' Web, 4" x 30" Web, #"X37 Web, is" x 38" * 2I’
Up. fl., 2 2" × 2%" 3.5% angle | Up, fl., 2 2" × 24” 4.5% angle Up. fl., 2 24" × #" 4.9% angle. Up, fl., 2 º ×3 6# angle Up. fl., 2 3'x3%" 7.7% angle | Up. fl., 2 : ×3;" 6.4% angle | Up, fl., 2 3"X3%" 7.7% angle
7 & A. & // // Nº. 2, ſ/ / / h Me A hº
L. fl., 2 2" × 3" 4:# angle L. fl., 2 2" × 34" 5.3% angle L. fl., 2 24'x 24" 5.4% angle | L. fl., 2 24'x3' 6.7% angle | L. fl., 2 3'x3' 8.4% angle | L. fl., 2 3'x3' 7.2% angle | L. fl., 2 3'x3' 8.4% angle
If Y
#: * per foot Built-beam, 52}# per foot | Built-beam, 58% per foot Built-beam, 65% per foot Built-beam, 75% per foot Built-beam, 81% per foot Built-beam, 89% per foot
as web, ºxº Web, +/x 25" Web, 4" x 30" Web, +" x 30" Web, #"X 34" Web, ſ," x 38" Web, （," x 38" 22'
Up. à. 2 2" × 2%" 3.5% angle Up. fl., 2 2" × 24” 4.5% angle | Up. fl., 2 24" × 23" 4.9% angle Up, fl., 2 2" × 34" 6.4% angle | Up. fl., 2 24" × 23" 6.5% angle Up. fl., 2 2" × 33" 6.4% angle | Up. fl., 2 3'x3' 8.4% angle
L. fl., 2 2" × 3" 4:# angle L. fl., 2 2" × 34" 5:3# angle | L. fl., 2 24" × 2%" S.4% angle | L, fl., 2 3'x3' 7.2% angle | L. fl., 2 3'x3' 7.2% angle | L. fl., 2 3'x3' 7.2% angle | L. fl., 2 3'x3%" 9% angle
I 5" 50% I, tº * * *
i. ń. º * per foot Built-beam, 53% per foot Built-beam, 60% per foot Built-beam, 66%; per foot | Built-beam, 76## per foot | Built-beam, 82}+ per foot | Built-beam, 91% per foot
23' Web. 4/X * 4" Web, "x 26" Web, +/x30" Web, +/x30" Web, #"X 35" Web, 1s"X 38" Web, ſº"x 38" 23' |
Up. ń. 2" × 24" 3.5% angle Up. fl., 2 2" × 24” 4.5% angle | Up. ſl., 22" × 33" 5:3# angle | Up, fl., 2 24" × 3" 6.7% angle | Up, fl., 2 24" × 24" 6.5% angle Up, fl., 2 24" × 3" 6.7% angle | Up. fl., 2 3'x3}" 9% angle 3
L. fl., 2 2" × 3" 4:# angle L. fl., 2 2" × 3}" S.3% angle | L. fl., 2 3"X 3" 5.9% angle I, fl., 2 3'x3%" 7.7% angle | L. fl., 2 3"X 3" 7.2% angle L. fl., 2 3"X3%" 7.7% angle | L. fl., 2 3"x4" 9.7% angle
// ołł
. º per foot Built-beam, 54% per foot Built-beam, 61%:# per foot | Built-beam, 69% per foot Built-beam, 78% per foot Built-beam, 85% per foot Built-beam, 94% per foot
24' Web, 4/X * Web, +/x 27” Web, +/x30" Web, 3" x 30" Web, ſ," × 36" Web, +,"x 38" Web, ſs" x 38" 2 ,
Up. i. 2" × 24" 3.5% angle Up. fl., 2 2"x24"4.5% angle | Up, fl., 22%"X3" 5.5% angle | Up. fl., 2 3'x3' 7.2% angle | Up. fl., 2 24" × 23" 6.5% angle Up, ſl., 2 3"X3" 7.2% angle | Up, fl., 2 3"x4" 9.7% angle 4
...i...g.” |L n. 22"x3' 53* angle |L fl. 2 2'-3' 64; angle |L fl. 2 3'x3' 84* angle |L fl. 2 3'x3' 7.3; angle |L fl. 2 3'x3' 84; angle |L.A., 2 3'x3' 194; angle
ºi. Roadway, 12" Clear. Roadway, 14. Clear. Roadway, 16’ Clear. Roadway, 18' Clear. Roadway, 20' Clear. Roadway, 22' Clear. Roadway, 24' Clear. º

TABLE XXI.
TABLE OF FLOOR BEAMS.
§ CLASS C. *
# ºi. Roadway, 12" Clear. Roadway, 14' Clear. Roadway, 16' Clear. Roadway, 18' Clear. Roadway, 20' Clear. Roadway, 22' Clear. Roadway, 24' Clear. º
12" 42% I, or 12" 42% I, or I 5" 50% I, or I 5" 50% I, or *
*# Built-beam, 394% per foot | Built-beam, 43%; per foot | Built-beam, 48## per foot | Built-beam, 51# per foot lº, * per foot
Io' , 9" 23## I Io" 30% I Web, 4" × 18" Web, 4" × 20" Web, +" × 24” Web, +" x 26" U i. 2" × 24” 4.5% angl Io'
Up. fl., 2 2"x24" 3.5% angle | Up, fl., 2 2" × 24" 3.5% angle | Up, fl., 2 2" × 2%" 3.5% angle | Up. fl., 2 2" × 23" 3.5% angle Pº # 4.5% angle
L. fl., 2 2" × 3+" 5.3% angle
L. fl., 2 2" × 2%" 3.5% angle | L. fl., 2 2" × 3" 4:# angle L. fl., 2 2" × 3" 4:# angle L. fl., 2 2" × 3" 4:# angle y Žſ b-
12" 42% I, or 12" 42% I, or I 5" 50% I, or I 5" 50% I, or g
Built-beam, 40% per foot | Built-beam, 45% per foot Built-beam, 49%% per foot | Built-beam, 53% per foot º sº per foot
II’ 9" 23## I Io" 30% I Web, +" x 18" Web, +/x 21" Web, 4" x 25" Web, +/x 26" Web, 4 º / II’
Up. fl., 2 2"x24" 3.5% angle | Up. fl., 2 2" × 24" 3.5% angle | Up. fl., 2 2" × 2%" 3.5% angle | Up, fl., 22" × 3" 4:# angle Up, fl., 2 : X #45; angle
L. fl., 2 2" × 3" 4# angle . . L. fl., 2 2" × 3" 4:# angle L. fl., 2 2" × 3" 4:# angle L. fl., 2 2" × 2%" 4.5% angle L. fl., 2 2" × 3%" S.3% angle 4
12" 42% I, or I 5" 50% I, or I 5" 50% I, or g º
Built-beam, 41%; per foot | Built-beam, 46% per foot Built-beam, 50% per foot Built-beam, 53% per foot Built-beam, 58% per foot
º 12' Io" 30% I Iož" 31## I Web, 4" × 19" Web, +" x 22" Web, 3" x 26" Web, 4” x 26" Web, 4" × 30" I2’
º- //
º Up. fl., 2 2" × 24" 3.5% angle | Up. fl., 2 2" × 2%" 3.5% angle | Up. fl., 2 2" × 24" 3.5% angle Up. fl., 2 2" × 3" 4.5% angle | Up. fl., 2 2" × 24” 4.5% angle
ñº. L. fl., 2 2" × 3" 4:# angle L. fl., 2 2" × 3" 4:# angle L. fl., 2 2" × 3" 4:# angle L. fl., 2 24" × 3" 5% angle L. fl., 2 2" × 33" 5.3% angle
ſ 12" 42% I, or 12" 42% I, or 15" 50% I, or I 5" 50% I, or g *
g { Built-beam, 38%+ per foot | Built-beam, 41% per foot | Built-beam, 47# per foot Built-beam, 52% per foot Built-beam, 54%:# per foot | Built-beam, 60% per foot
: 13' Io" 30% I Web, +/x 18" Web, +/x 19" Web, 4" × 23" Web, +/x 26" Web, +7x28" Web, 4" × 30" 1 3'
// *
Up. fl., 2 2" × 24" 3.5% angle | Up. fl., 2 2" × 24" 3.5% angle | Up, fl., 2 2" × 2%" 3.5% angle | Up. fl., 22" × 3" 4:# angle Up. fl., 2 . X * 4.5% angle | Up. fl., **** 5# angle
i. L. fl., 2 2"x24" 3.5% angle | L. fl., 2 2"X3" 4:# angle | L. fl., 2 2" × 3" 4# angle L. fl., 2 2" × 24” 4.5% angle L. fl., 2 24" × 3" 5% angle L. fl., 2 3"X 3" 5.9% angle
f I2" 42% I, or - 12" 42% I, or .15" 50% I, or * * &
; f Built-beam, 384; per foot | Built-beam, 43}# per foot | Built-beam, 48# per foot Built-beam, 533% per foot | Built-beam, 55## per foot | Built-beam, 62% per foot
3. 43% ºf p p // NZ ~ £//
. 14' Io" 30% I Web, 4" × 18" Web, +7x20" Web, 4" × 24". Web, 4" × 26 Web, 4" × 29" Web, 4" × 30" I4'
# Up, fl., 2 2"x24" 3.5% angle | Up. fl., 2 2" × 24" 3.5% angle | Up. fl., 2 2" × 2%" 3.5% angle Up, fl., 2 2"x24" 4.5% angle | Up. fl., 2 2" × 23/4.5% angle | Up. fl., 2 24" × 3" 5.5% angle
- y L. fl., 2 2" × 24" 3.5% angle | L. fl., 2 2"X 3" 4:# angle L. fl., 2 2" × 3" 4:# angle L. fl., 2 2%"X 3" 5% angle L. fl., 2 2%" × 3" 5% angle L. fl., 2 23"X2}" 6.5% angle
#, 12" 42% I, or I 5" 50% I, or 15" 50% I, or e —º- * g
. # Built-beam, 39% per foot | Built-beam, 45% per foot Built-beam, 50% per foot Built-beam, 54% per foot | Built-beam, 57% per foot º º per foot
. 15' 10' 30% I Web, 4” x 18" Web, 4" × 21" Web, 4” x 26" Web, 4" x 27” Web, 4" × 30" Web, 4” x 30 I5'
5 5 5 If /
* # Up, fl., 2 2" × 24" 3.5% angle | Up. fl., 2 2" × 2%" 3.5% angle | Up. fl., 2 2"X 24" 3.5% angle Up, fl., 2 2"x24"4.5% angle | Up. fl., 2 2.7x24" 4.5% angle | U.P. fl. 2 . ×3" 6# angle
3. L. fl., 2 2" × 3" 4:# angle L. fl., 2 2" × 3° 4% angle L. fl., 2 2" × 3" 4:# angle L. fl., 2 24" × 3" 5:# angle L. fl., 2 2" × 33" 5:3# angle |* fl., 2 24" × 3" 6.7% angle
º 12" 42% I, or I 5" 50% I, or I 5" 50% I, or & * ſº & {
t Built-beam, 41% per foot Built-beam, 46% per foot Built-beam, 51## per foot Built-beam, 55## per foot | Built-beam, 60% per foot Built-beam, 65% per foot
I6' Iož" 31## I Web, 4" × 19" Web, +/x 22" Web, 4" × 24" Web, "X28" Web, #"> 30" Web, 4" x 30" I6'
Up, fl. 2 2/x 24' 3.5% angle | Up, fl. 2 2"x24" 3.5% angle | Up, fl. 2 2"x24" 4.5% angle ||PP.” 2" × 24” 4.5% angle | Up. fl., 2 2" × 3" 5:# angle | Up. fl., 2 3"X 3" 6.5% angle
L. fl., 2 2" × 3" 4:# angle L. fl., 2 2"X 3" 4:# angle L. fl., 2 2/x375; angle |* * * 2}"X 3" 5:# angle | L. fl., 2 3'x3' 5.9% angle | L. fl., 2 3"X3" 7.2% angle
12" 42% I, or 12" 42% I, or I 5" 50% I, or I 5" 50% I, or je º $
Built-beam, 384% per foot 'Built-beam, 42%% per foot | Built-beam, 47## per foot | Built-beam, 523% per foot Built-beam, 57% per foot Built-beam, 62% per foot Built-beam, 67%:# per foot
17' Web, +/x 18" Web, 4" × 20" Web, 4" × 23" Web, +/x 25" Web, +"x29" Web, 4" × 30" Web, 4" x 30" . " I’
Up. fl., 2 2" × 24" 3.5% angle | Up. fl., 2 2" × 2%" 3.5% angle | Up. fl., 2 2"X 24" 3.5% angle | Up, fl., 2 2" × 2%" 4.5% angle Up. fl., 2 2" × 24” 4.5% angle | Up. fl., 2 24" × 3" 5.5% angle | Up. fl., 2 3"x 3" 7.2% angle 7
L. fl., 2 2" × 2%" 3.5% angle | L. fl., 2 2" × 3" 4:# angle L. fl., 22" × 3" 4:# angle L. fl. 2 zyk 37 gangle |L, fl. 2 2"X3}" 5:3# angle |L, fl. 2 24'x 24' 6.5% angle |L, fl., 2 3'x34" 7.7% angle
f 12" 42% I, or 15" 50% I, or I 5" 50% I, or e g
Built-beam, 383% per foot | Built-beam, 42}# per foot | Built-beam, 49% per foot Built-beam, 53}# per foot | Built-beam, 59% per foot ' | Built-beam, 63}# per foot | Built-beam, 70% per foot
18' Web, 4” x 18" Web, +"x20" Web, 4” x 25" Web, 4" x 26" Web, 4" × 30" Web, 4" x 30" Web, 4" × 30" I8’
Up. fl., 2 2" × 24" 3.5% angle | Up, fl., 2 2" × 24" 3.5% angle | Up. fl., 2 2" × 24" 3.5% angle Up. fl., 2 3. X * 4.5% angle | Up, fl., 2 :*: 2}" 4.9% angle Up. fl., 22" × 3" 6% angle Up. fl., 2 3"x 3}" 7.7% angle
L. fl., 2 2"X2%" 3.5% angle | L. fl., 2 2" × 3" 4:# angle L. fl., 2 2"X 3" 4:# angle L. fl. 2 24'x3' 5% angle | L. fl., 2 2"x34" 5:3# angle |L, fl., 2 24'x3' 6.7% angle |L, fl., 2 3'x3' 8.4% angle
12" 42% I, or 15" 50% I, or 15" 50% I, or ſº †. \ * t
Built-beam, 39}# per foot | Built-beam, 44% per foot Built-beam, 50%+ per foot Built-beam, 54% # per foot | Built-beam, 60% per foot Built-beam, 65%:# per foot | Built-beam, 75% per foot
Ig' Web, +/x 18" Web, 4"x21" Web, +/x 25" Web, 4” x 27” Web, 4"x30" Web, +" x 30" Web, #"X34" !-
Up, fl., 2 2"x24" 3.5% angle | Up, fl., 2 2"x24" 3.5% angle | Up. fl., 2 2/x3' 4:# angle Up, fl. 2 2"x24" 4.5% angle | Up, fl., 2 2" × 3" 5:# angle | Up. fl., 2 3'x3' 6.5% angle | Up, fl., 2 23"x24" 6.5% angle I9
L. fl., 2 2" × 3” 4% angle L. fl., 2 2" × 3" 4:# angle L. fl., 2 24" × 3" 4.4% angle L. fl., 2 2" × 33" 5:3# angle | L. fl., 2 3'x3' 5.9% angle | L. fl., 2 3'x3' 7.2% angle | L. fl., 2 3"X 3" 7.2% angle
12" 42% I, or I 5" 50% I, or 15" so;I, Or º
Built-beam, 39% per foot | Built-beam, 45% per foot Built-beam, 51## per foot Built-beam, 55## per foot | Built-beam, 62% per foot Built-beam, 67%:# per foot | Built-beam, 76## per foot
20' Web, 4" × 18" Web, +/x 22" Web, 4” x 26" Web, +" x 28/ Web, 4" × 30" Web, 4" × 30" Web, #"X35" *
Up, fl. 2 2"x24" 3.5% angle | Up, fl. 2 2"x24" 3.5% angle|Up, fl. 2 2/x3' 4; angle ||P.” *** * 4.5% angle | Up, fl., 2 24" × 3" 5.5% angle | Up, fl., 2 3"x 3" 7.2% angle | Up. fl., 2 24" x 23' 6.5% angle 2O
L. fl., 2 2" × 3" 4:# angle L. fl., 2 2" × 3" 4:# angle L. fl., 2 24"x 3" 4.4% angle L. fl., 2 2" × 34" 5.3% angle | L. fl., 2 23% 2}" 6.5% angle | L, fl., 2 3"X3}" 7.7% angle . . L. fl., 2 3'x3' 7.2% angle
12" 42% I, or I 5" 50% I, or l
Built-beam, 41% per foot Built-beam, 46% per foot Biºlº sº per foot | Built-beam, 57% per foot Built-beam, 63}} per foot | Built-beam, 70% per foot Built-beam, 78% per foot
2I’ Web, 4" × 197 Web, +/x 23" Web, 4 ×25 // Web, +" x 29" Web, 4" x 30" Web, 4" x 30" Web, #"x 36" y
Up. fl., 2 2" × 24" 3.5% angle | Up. fl., 2 2" × 24" 3.5% angle Up. fl., 2 : x: 4.5% angle | Up, fl., 2 24"x24" 4.9% angle|Up, fl., 2 2" × 3" 6# angle | Up, fl., 2 3'x34" 7.7% angle | Up. fl., 2 2" x 34” 64; angle 2I
L. fl., 2 2" × 3" 4# angle L. fl., 2 2" x 3" 4% angle L. fl., 2 2/X 3 5#. angle L. fl., 2 23"x 23" 5.4% angle L. fl., 2 24" x 3" 6.7% angle L fl., 2 3"x 3" 8.4% angle L. fl., 2 3"x 3" 7.2% angle
12" 42% I, or I 5" 50% I, or w t
Built-beam, 42%# per foot | Built-beam, 47.4% per foot º sº per foot | Built-beam, 58% per foot Built-beam, 65% per foot Built-beam, 75% per foot Built-beam, 81% per foot
22' Web, 4" × 20" Web, 4"x24" Web, + x26 // Web, #"x 30" Web, 4" x 30" Web, ſº "X 34” Web, ſº"x 38" *
Up, fl., 2 2" × 24" 3.5% angle | Up. fl., 2 2"x24" 3.5% angle Up. fl., 2 : X # 4.5% angle | Up, fl., 2 24" × 24" 4.9% angle. Up, fl., 22" × 33" 6.4% angle | Up. fl., 2 2}"X2}" 6.5% angle Up. fl., 2 2" × 33" 6.4% angle 22
L. fl., 2 2" × 3" 4:# angle L. fl., 2 2" × 3" 4:# angle L. fl., 2 2" × 33" 5:3# angle | L. fl., 2 24" × 23" 5.4% angle | L. fl., 2 3'x3' 7.2% angle L. fl., 2 3"X3" 7.2% angle | L. fl., 2 3"x 3" 7.2% angle
15" 50% I, or 15" 50% I, Or ſº e *
Built-beam, 44% per foot Built-beam, 49% per foot Fºllº # per foot | Built-beam, 60% per foot Built-beam, 66%+ per foot ||Built-beam, 76# per foot Built-beam, 823% per foot
23' | Web, 4" × 21" Web, 4" x 25" Web, +/x 7. Web, +"x 3. // Web, 4" × 30" Web, ſº" × 35" | Web, #"x 38" J.
Up. fl., 2 2" × 2%" 3.5% angle | Up. fl., 2 2"x24" 3.5% angle Up. fl., 2 : X * 4.5% angle | Up. fl., 2 2" × 34" 5:3# angle | Up. fl., 2 24" × 3' 6.7% angle | Up. fl., 2 2#"X 24" 6.5% angle Up, fl., 2 24" × 3' 6.7% angle 23
L. fl., 2 2" × 3" 4:# angle L. fl., 2 2" × 3" 4:# angle L. fl., 2 2" × 34" 5:3# angle | L. fl., 2 3'x3' 5.9% angle | L. fl., 2 3'x3}" 7.7% angle | L, fl., 2 3'x3' 7.2% angle L. fl., 2 3"X3}" 7.7% angle
I 5" 50% I, or I 5" 50% I, or * de W
Built-beam, 45% per foot Built-beam, 503% per foot Biºlº # per foot Built-beam, 61%+ per foot | Built-beam, 69% per foot Built-beam, 78% per foot Built-beam, 85% per foot
24' Web, "x 22" Web, +" x 26" Web, 4" × 28 Web, "X 30" Web, 4" x 30" Web, ſº," × 36" Web, ſs" x 38"
t;
Up. fl., 2 2" × 24" 3.5% angle | Up. fl., 22" × 24" 3.5% angle Up. fl., sº * 4.5% angle | Up. fl., 2 *: 3" 5.5% angle | Up, fl., 2 3'x3' 7.2% angle | Up. fl., 2 2" × 34" 64; angle | Up. fl., 2 3"><3" 7.2% angle 24'
L. fl., 2 2" × 3" 4# angle L. fl., 2 2" × 3" 4:# angle L. f. 2 2" × 33" 5:3# angle | L. fl., 2 2" × 34" 64; angle | L. fl., 2 3'x3' 8.4% angle | L. fl., 2 3"X3" 7.2% angle | L. fl., 2 3'x3' 8.4% angle
P el Af º
Cº. th Roadway, 12" Clear. Roadway, 14. Clear. Roadway, 16' Clear. Roadway, 18’ Clear Road p / P
gth. \ y y, tº oadway, 20' Clear. Roadway, 22' Clear. Roadway, 24’ Clear. L i.
ength.



TABLE XXII.
TABLE OF BEAM HANGERS.
CT, ASS A.
&
Four hangers per beam. Up. denotes ends upset; N. up., ends not upset.
A
Panel Roadway, Roadway, Roadway, Roadway, Roadway, Roadway, Roadway, Panel
Length. || 12’ clear. 14’ clear. 16’ clear. 18’ clear. 20' clear. 22' clear. 24’ clear. || Length.
#" G) Up. #" G) Up. #" G) Up. #" G) Up. #" G) Up. #" G) Up. #” G) Up.
Io' #" D Up. #" D Up. #" D Up. #" D Up. #" D-Up. #" D Up. ##" [] Up. 1 o'
1” G) N. up. 1” G) N. up. 1" G) N. up. 14" G) N. up. 14" G) N. up. 14" G) N. up. 14" G) N. up.
#" G) Up. - #" G) Up. ##" G) Up. #" G. Up. #" G) Up. #" G) Up. #" G) Up.
II’ #" D Up. #" [] Up. #" D Up. #" C. Up. #" [] Up. ##" [l, Up. #" [] Up. I I’
1" G) N. up. 1” G) N. up. 14” G) N. up. 1}" G) N. up. 14" G) N. up. 14" G) N. up. 14" G) N. up.
#" G) Up. #" G) Up. ##" G) Up. #" G) Up. #" G) Up. #” G) Up. 1" G) Up.
12" #" D Up. #” D Up. #" D Up. #" D Up. ##" [] Up. #" D Up. #" D Up. I2’
1” G) N. up. 1” G) N. up. 14" G) N. up. 14" G) N. up. 14” G) N. up. 14" G) N. up. 1#" G) N. up.
#" G) Up. ##" G) Up. 4" G) Up. 4" G) Up. #" G) Up. 1" G) Up. Iºs" G) Up.
13' #” D Up. #" D Up. #” [] Up. ##". D Up. +#" [] Up. #" D Up. #” D Up. 13'
1" G) N. up. 14" G) N. up. 14" G) N. up. 14" G) N. up. 14" G) N. up. 1}" G) N. up. 1#" G) N. up.
#" G) Up. ##" G) Up. #" G) Up. #" G) Up. 1" G) Up. 1" G) Up. II's." G) Up. *
14' #" D Up. #" D Up. #" [] Up. #" D Up. #" [] Up. #" D Up. #" D Up. 14'
, 1" O N. up. 14" G) N. up. 14" G) N. up. 14" G) N. up. Ił" G) N. up. 1}" G) N. up, 1#" G) N. up.
#" G) Up. 4" G) Up. #" G) Up. #" G) Up. 1" G) Up. Iºs" G) Up. 14" G) Up.
15' #" D Up. #" D Up. #" [] Up. ##". D Up. #" [] Up. #" D Up. I” D Up. I5'
14" G) N. up. 14" G) N. up. 14" G) N. up. 14” G) N. up. 1}" G) N. up. 1}" G) N. up. 14" G) N. up.
#" G) Up. #" G) Up. #" G) Up. 1" G) Up. Iºs" G) Up. II's" G) Up. 1}" G) Up.
I6' #" D Up. ##". D Up. ##". D Up. #" [] Up. #" D Up. 1" D Up. 1" D Up. I6'
zº 1+" G) N. up. 14" G) N. up. 14" G) N. up. 1}” G) N. up. 1}" G) N. up. 1}" G) N. up. 14" G) N. up.
##" G) Up. #" G) Up. ##" G) Up. 1” G) Up. 11's "G) Up. 14" G) Up. Iºs" G) Up.
17' #" D Up. ##". D Up. #" D Up. ##". D Up. ##". D Up. 1" D Up. II's" [] Up. 17' |
14" G) N. up. 14" G) N. up. 14" G) N. up. 1}" G) N. up. 1;" G. N. up. 14" G) N. up. 14" G) N. up.
4” G) Up. ##" G) Up. 1" G) Up. in G Up. Tº Gup. If," Gup. if," G. Up.
18' #" [] Up. ##". D Up. 4” [] Up. #" D Up. 1” [] Up. 1" D Up. II's" D Up. 18'
14" G) N. up. 14" G) N. up. 14” G) N. up. 1#" G) N. up. 14" G) N. up. 14" G) N. up. 14" G) N. up.
4" G) Up. ##" G) Up. 1" G) up. II's." G) Up. I}" G) up. I lºs" G) Up. 1}" G) Up.
19' #” C. Up. 4” [] Up. 4” D Up. ##" [] Up. 1” [] Up. II's" D Up. I#" C. Up. Ig'
14" G) N. up. 14" G) N. up. 1}" G) N. up. 1}" G) N. up. 13" G) N. up. 13" G) N. up. 1#" G) N. up.
#" G) Up. 1" G) Up. 11's." G) Up. 14" G) Up. 11%;" G) Up. 13." G) Up. 14" G) Up.
20' ##". D Up. 4” D Up. #" [] Up. 17th Up. II's" D Up. II's" D Up. I+" D Up. 2O’
14" G) N. up. 1}" G) N. up. 1#" G) N. up. 13" G) N. up. 14" G) N. up. 1;" G) N. up. 1#" G. N. up.
#" G) Up. 1" G) Up. 11%;" G) Up. 14" G) Up. 11%;" G) Up. 14" G) Up. 11%;" G) Up.
21’ ##". D Up. #" [] Up. ##". D Up. 1" D Up. II's" D Up. 1}" D Up. Iºs" [] Up. 21’
14" G) N. up. 1}" G) N. up. 1}" G) N. up. 14" G) N. up. 14" G) N. up. 1;" G) N. up. 13" G) N. up.
#" G) Up. 11%" G) Up. 14" G) Up. I ſºº" G) Up. 1}" G) Up. Hºs" G) Up. 1}" G) Up.
22' #" D Up. #" D Up. 1” [] Up. Iºs" [] Up. I#" D Up. 14" [] Up. I+," D Up. 22'
14" G) N. up. 1}" G) N. up. 14" G) N. up. 14" G) N. up. 1;" G) N. up. 13" G) N. up. 1#" G) N. up.
1" G) Up. II's "G) Up. 14" G) Up. I#" G) Up. 1}" G) Up. 11%;" G) Up. 1;" G) Up. **-* **, *-
23' #" [] Up. #" [] Up. 1" D Up. I ſº" [] Up. 14" D Up. I#" D Up. I+" [] Up. 23'
1#" G) N. up. 1;" G) N. up. 14" G) N. up. 14" () N. up. 1#" G) N. up. 13" G) N. up. 13" G) N. up.
17 G) Up. I ſº" G) Up. 11%;" G) Up. 1}" G) Up. I tºº" G) Up. 1;" G) Up. 11's." G) Up.
24' #" D Up. 1" D Up. II's" [] Up. 14" D Up. I+" D Up. I lºs" D Up. I+" [] Up. 24'
1}” G) N. up. 1}* @ N. up. 14” G) N. up. 1#" G) N. up. 1#" G) N. up. 13" G) N. up. 14" G) N. up.
Panel Roadway, Roadway, Roadway, Roadway, Roadway, Roadway, Roadway, Panel
Length. 12’ clear. 14’ clear. 16’ clear. 18’ clear. 2O' clear. 22' clear. 24’ clear. || Length.
xxº~~~
sºmsº-

Four hangers per beam.
TABLE XXIII.
TABLE OF BEAM HANGERs.
CLASS B.
Up. denotes ends
upset; N. up., ends not upset.
Roadway,
Roadway,
i
Panel Roadway, Roadway, Roadway, Roadway, Roadway, , || Panel
Length. || 12’ clear. 14’ clear. 16’ clear. 18’ clear. 20’ clear. 22' clear. 24’ clear. Length.
#" G). Up. 3" G) Up. #" G) Up. #" G) Up. #" G) Up. #" G) Up. ##" G. Up.
Io' #" [] Up. #" D Up. #" [] Up. #" [] Up. #" D Up. #" D Up. #" D Up. Io’
1" G) N. up. 17 G) N. up. 1" G) N. up. 1" G) N. up. 1” G) N. up. 1" G) N. up. 1}" G) N. up.
#" G) Up. #" G) Up. #" G) Up. #" G) Up. #" G) Up. #" G) Up. #" G) Up.
II’ #" D Up. #" D Up. #" D Up. #" D Up. #" D Up. #" D Up. #" D Up. II’
1" G) N. up. 1" G) N. up. 1" G) N. up. 1" G) N. up. 1" G) N. up. 1}" G) N. up. 1};" G) N. up.
#" G) Up. #" G) Up. #" G) Up. #" G) Up. ##" G) Up. ##" G) Up. #" G) Up.
12’ #" D Up. #" D Up. #" D Up. '#' D Up. #" D Up. #" [] Up. #" D Up. 12’
1" G) N. up. 1" G) N. up. 1" G) N. up. 1" G) N. up. 14" G) N. up. 14" G) N. up. 1}" G) N. up.
#" G) Up. #" G) Up. #" G) Up. #" G) Up. ##" G) Up. 4" G) Up. 4" G) Up.
13' #" [] Up. #" [] Up. #" D Up. #” [] Up. #" C. Up. #" [] Up. ##" [] Up. 13'
1" G) N. up. 1" G) N. up. 1" G. N. up. 1" G. N. up. 14" G) N. up. 14" G. N. up. 14" G. N. up.
#" G) Up. #" G) Up. #" G) Up. ##" G) Up. #" G) Up. #" G) Up. #"G) Up.
14' #" D Up. #" D Up. #" D Up. #" D Up. #" D Up. #" D Up. ##". D Up. 14'
1" G) N. up. 1" G. N. up. 1" G. N. up. 1}" G. N. up. 14" G) N. up. 14" G. N. up. 14" G. N. up.
#" G) Up. #" G) Up. #" G) Up. ##" G) Up. #" Q Up. ##" G) Up. #" G) Up. -
15' #" D Up. #" [] Up. #" D Up. #" D Up. #" [] Up. +$" [] Up. #" [] Up. 15'
1" G) N. up. 1" G) N. up. 14" G) N. up. 14" G) N. up. 14" G) N. up. 14" G) N. up. 14" G) N. up.
#" G) Up. #" G) Up. #" G. Up. 4" G) Up. #" G) Up. #" G) Up. 1" G) Up.
I6/ #" D Up. #" D Up. #" [] Up. #" [] Up. ##" [] Up. #" [] Up. #" D Up. 16'
1" G) N. up. 1" G) N. up. 14" G) N. up. 1+" G) N. up. 14" G) N, up. 14" G) N. up. 1}" G) N. up.
#" G) Up. ##" G) Up. ##" G) Up. #" G) Up. #" G) Up. 1" G) Up. 1" G) Up.
17' || #" D Up. #" D Up. #" [] Up. ##". D Up. ##". D Up. #" [] Up. #" [] Up. 17'
1" G) N. up. 14" G) N. up. 14" G) N. up. 14" G) N. up. 14" G) N. up. 1}" G) N. up. 1$" G) N. up.
#" G) Up. #" G) Up. #" G) Up. ##" G) Up. ##" G) Up. 1" G) Up. Iſs" G) Up. r
I8/ #" [] Up. #" D Up. #" [] Up. Hi" [] Up. #" [] Up. #" [] Up. #" [] Up. 18'
1" G) N. up. 1}" G) N. up. 14" G) N. up. 14" G) N. up. 14" G) N. up. 1#" G) N. up. 1#" G) N. up. }
#!-Q-Up. ##" G) Up. g" G) Up. +}" G) Up. 1" G) Up. 11%" Q Up. 1 º' G Up.
19' #" [] Up. #" D Up. \}#" [] Up. ##" [] Up. 4" [] Up. ##". D Up. #" D Up. I9'
1" G) N. up. 14" G) N. up. 14" G) N. up. 14" G) N. up. 1}" G) N. up. 1}" G) N. up. 1}" G) N. up.
#" G. Up. 4" G) Up. #" G) Up." | +}" G) Up. 1" G) Up. Iſs" G) Up. 14" G) Up.
20’ #" D Up. #" D Up. ##". D Up. #" D Up. 4” [] Up. #" D Up. 1" E. Up. 2O’
1}" G) N. up. 14" G) N. up. 14" G) N. up. 14" G) N. up. 1;" G) N. up. 1;" G) N. up. 14" G) N. up. -
##" G) Up. 4" G) Up. ##" G) Up. 1" G) Up. II's "G) Up. Iºs" G) Up. 14" G) Up,
21’ #" D Up. #" [] Up. +$" [] Up. #" D Up. ##" [] Up. 1" [] Up. 1" [] Up. 2I’
1}" Q N. up. 14" G) N. up. 14" G) N. up. 1}" G) N. up. 1}" G) N. up. 1;" G) N. up. 14" G) N. up.
4;" G) Up. #" G) Up. ##" G) Up. 1" G) Up. 11's "G) Up. 1}" G) Up. 11%" G) Up.
22' #" [] Up. #" [] Up. #" C. Up. +}” [] Up. #" D Up. 1" [] Up. Iºs" [] Up. 22'
14" Q N. up. 14" Q N. up. 14" G) N. up. 14" G. N. up. 13" G. N. up. 14" G. N. up. 13" G. N. up.
4" G) Up. ##" G) Up. 1" G) Up. Irº" G) Up. 1}" G) Up. 14" G) Up. I#" G) Up.
23' #" [] Up. #" D Up. #" D Up. Hº" D Up. 1" D Up. 1" [] Up. IPs" [] Up. 23'
I}" Q N. up. 1}" G) N. up. 1}" G) N. up. 1}" G) N. up. 14" G) N. up. 14" G) N. up. 14" G) N. up.
#" G) Up. ##" G) Up. 1" G) Up. II's "G) Up. 14" G) Up. Iºs" G) Up. 14" G) Up.
24' ##" [] Up. ##" D Up. #" [] Up. +}" D Up. 1" [] Up. II's" [] Up. 1}" [] Up. 24'
14" G) N. up. 14" G) N. up. 13" G) N. up. 1#" G) N. up. 14" G) N. up. 14" G) N. up. 13" G. N. up.
(..
Panel Roadway, Roadway, Roadway, Roadway, Roadway, Roadway, Roadway, Panel
Length. 12’ clear. 14’ clear. 16’ clear. 18' clear. 20' clear. 22' clear. 24’ clear. Length.

Four hangers per beam.
TABLE
XXLIV.
TABLE OF BEAM HANGERS.
CT, ASS C.
Up. denotes ends
upset; N. up., ends not upset.
Panel Roadway, Roadway, Roadway, Roadway, Roadway, Roadway, Roadway, Panel
Length. || 12’ clear. 14’ clear. 16’ clear. 18’ clear. 20’ clear. 22' clear. 24’ clear. Length.
#" G) Up. #" G) Up. #" G) Up. #" G) Up. #" G) Up. #" G) Up. #" G) Up.
Io' #" [] Up. #" [] Up. #" C. Up. #" D Up. #" [] Up. #" [] Up. #" D Up. Io’
1" G) N. up. 1" G) N. up. 1" G) N. up. 1" G) N. up. 1" G) N. up. 1" G) N. up. 1" G) N. up.
#" G) Up. #" G) Up. #" G) Up. #" G) Up. #" G) Up. #" G) Up. #" G) Up.
II’ #" [] Up. #" [] Up. #" D Up. #" D Up. #" D Up. #" D Up. #" [] Up. II’
1" G) N. up. 1" G) N. up. 1" G) N. up. 1" G) N. up. 1" G) N. up. 1" G) N. up. 1* @ N. up.
#" G) Up. #" G) Up. #" G) Up. #" G) Up. #" G) Up. #" G) Up. º #" G).Up."
12' #" D Up. #" D Up. #" D Up. #" D Up. #" D Up. #" D Up. #" D Up. 12’
1" G) N. up. 1" G) N. up. 1" G) N. up. 1" G) N. up. 1" G) N. up. 1" G) N. up. 14" G) N. up.
#" G) Up. #" G) Up. #" G) Up. #" G) Up. #" G) Up. #" G) Up. #" G). Up.
13' #" D Up. #" D Up. #" [] Up. #" D Up. #” [] Up. #" [] Up. #" D Up. 13'
- 1" G) N. up. 1" G) N. up. 1" G) N. up. 1" G) N. up. 1" G) N. up. 14" G) N. up. 14" G) N. up.
#" G) Up. #" G) Up. #" G) Up. #" G) Up. #" G) Up. ##" G) Up. #"G) Up.
14' #" D Up. #" [] Up. #" [] Up. #" D Up. #" D Up. #" D Up. #" D Up. 14'
1" G) N. up. 1" G) N. up. 1" G) N. up. 1" G) N. up. 1" G) N. up. 14" G) N. up. 14" G) N. up.
#" G) Up. #" G) Up. #" G) Up. #" G) Up. #" G) Up. #" G) Up. #" G) Up.
15' || #" [] Up. #" [] Up. #" [] Up. #" D Up. #" [] Up. #" [] Up. +$" D Up, 15'
1" G) N. up. 1" G) N. up. 1" G) N. up. 1" G) N. up. 14" G) N. up. 14" G) N. up. 1+" G) N. up.
#" G) Up. #" G) Up. #" G) Up. ##" G) Up. #" G) Up. #" G) Up. 4” G) Up.
I6/ #" D Up. #" D Up. #" D Up. #" [] Up. #" [] Up. #" D Up. #" D Up. I6'
1" G) N. up. 1" G) N. up. 1" G) N. up. 1}" G) N. up. 14" G) N. up. 14" G) N. up. 1}" G) N. up. -
#" G) Up. #" G) Up. #" G) Up. ##" G) Up. 4" G) Up. #" G) Up. #" G) Up.
17' #" D Up. #" [] Up. #" [] Up. #" D Up. #" D Up. +}" D Up. +#" D Up. 17'
1" G) N. up. 1" G) N. up. 1" G) N. up. 1}" G) N. up. 14" G) N. up. 14" G) N. up. 14” G) N. up.
#" G) Up. #" G) Up. #" G) Up. ##" G) Up. #" G) Up. #" G) Up. #" G) Up.
18' #" D Up. #" [] Up. #" [] Up. #" D Up. #" D Up. #" D Up. }* D Up. 18”
1" G) N. up. 1" G) N. up. 1}" G) N. up. 1}" G) N. up. 14" G) N. up. 14" G) N. up. 14" G) N. up.
* #" G) Up. #" G) Up. ##" G) Up. 4" G) Up. #" G) Up. #" G) Up, 1" G) Up.
19 || #" D Up. #" D Up. #" D Up. #" D Up. ##" D Up. #" [] Up. #" D Up. 19'
1" G) N. up. 1" G) N. up. 14" G) N. up. 14" G) N. up. 14" G) N. up. 14" G) N. up. 1}” G) N. up.
* @ Up. "G) Up. "G) Up. " G) Up. * G) Up. I” G) Up. 1" G) Up.
I p p
20' #" D Up. #" [] Up. #" D Up. #" D Up. ##" [] Up. #" D Up. #" D Up. 20 |
1" G) N. up. 1 * G) N. up. 14" G) N. up. 14” G) N. up. 14” G) N. up. 1}" G) N. up. 1}” G) N. up.
#" G) Up. #" G) Up. #" G) Up. #" G) Up. ##" G) Up. 1” G) Up. Iſºs" G) Up.
21’ #" D Up. #" D Up. #" D Up. ##" [] Up. #" D Up. #" In Up. ##" In Up. 21”
1" G) N. up. I+" G) N. up. 14" G) N. up. 14" G) N. up. 14" G) N. up. 1}" G) N. up. 1#" G) N. up.
#" G) Up. ##" G) Up. #" G) Up. ##" G) Up. 1" G) Up. 1” G) Up. Iºs" G) Up.
22' #" D Up. #" D Up. ##". D Up. #" D Up. #" [] Up. +}” [] Up. #" D Up. 22’
1" G) N. up. 14" 3) N. up. 14" G) N. up. 14" G) N. up. 1}" G) N. up. 1}" G) N. up. 1}" G) N. up.
##" G) Up. #" G) Up. #" G) Up. #" G) Up. 1" G) Up. 11's "G) Up. 1+" Q Up. ---
23' #" D Up. #" [] Up. ##". D Up. #" [] Up. #" D Up. ##". D Up. 1" D Up. 23'
1}" G) N. up. 14" G) N. up. 1}" G) N. up. 14" G) N. up. 1}" G) N. up. 1#" G) N. up. 13" G) N. up.
##" G) Up. {"G) Up. #" G) Up. 1" Q Up. II's." G) Up. 11'5" G) Up. 14" G) Up.
24' #" [] Up. #" D Up. #" D Up. #" D Up. #" D Up. I+}” C Up. 1” [] Up. 24'
14" G) N. up. 14" G) N. up. 14" G) N. up. 1}" G) N. up. 1;" G) N. up. 1}" G) N. up. 14" G) N. up.
Panel Roadway, Roadway, Roadway, Roadway, Roadway, Roadway, Roadway, Panel
Length. || 12” clear. 14’ clear. 16’ clear. 18’ clear. 20’ clear. 22' clear. 24’ clear. || Length.
TABLE XXV.
TABLE OF LATERAL SYSTEMS AND sway
BRACING.
k
12" Clear Roadway. -
14’ Clear Roadway.
16' Clear Roadway.
#
18' Clear Roadway.
20 Clear Roadway.
22° Clear Roadway.
24 Clear Roadway.
Spart in No. of . * .------ - Span in
3 - a . … -- O 111 . . . - - - - -- . T * •º. - . . - - - -- - - r - - Feet.
Feet. Pan els. Pressure. Panel. 1. PA El. 3. PANEL 4. || PANEL 1. PANEL 2. PANEI, 3. PANEL 4. PANEL 1. PANEL 2. PANEL 3. PANEL 4. PANEL 5. PANEL 6. PANEL 7. PANEL 2. PANEL 3. PANEL 4. | PANEL 5, PANEL 6. PANEL 7. PANEL 8. PANEL 2. PANEL 3. PANEL 4. PANEL 5. PANEL 6. PANEL 7. PANEL 8. || PANEL 1. PANEL 2. PANEL 3. PANEL 4. PANEL 6. PANEL 7. PANEL 8. PANEL I. PANEL 2. PANEL 3. PANEL 4. | PANEL 5. PANEL 6. PANEL 7. PANEL 8. ee
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----------- - - - - - - -

TABLE XXVI.
TABLE FOR FINDING THE NECESSARY width of BEARING-surFACE AT EACH END OF PINS,
Having given the total pressure on said surface, and the diameter of the pin. This table is calculated for a working compressive stress of 6 tons per D" on the projection of the semi-intrados upon a diametral plane. Upper horizontal line shows diameter of pin.
Vertical lines of inches show widths of bearings.
CLASS A. - f
*
3%" | 3?"
Io.88 II.2
I I
* I
I
I
I
I
I
I
I
I
I
I
I
I

Having given the total pressure on said area, and the diameter of the pin.
TABLE XXVII.
TABLE FOR FINDING THE NECESSARY width OF BEARING-SURFACE AT EACH END OF PINS,
{
This table is calculated for a working compressive stress of 73 tons per D" on the projection of the semi-intrados upon a diametral plane.
horizontal line shows diameter of pin. Vertical lines of inches show widths of bearings.
Upper
CT, ASSES B AIND C.
I
I
I
I
I
I
I
I
I
I
I
I
3}”
3}"
3}”
12.66

TABLE XXVIII.
TABLE FOR FINDING THE DIMENSIONS OF UNION IRON MILLS’ CHANNEL EARS.
W represents the weight per foot in pounds, A the area of section in square inches, and F the width of flange in inches.
i.
Thick- tº & ſº tº © 4 º’ tº 7" [..A. * 7" [.. B. 8" [..A. 8" [.. B. & sº º & 9" [.. B. Io" [..A. Thick-
ness of - . ness of
Web i Web
... & jºr A A ... W. A Inches.
O.2
I
I
I
I
I
I
I'7.
I
I
I
I
7*
2

TABLE XXIX.
TABLE OF LENGTHS OF LATTICE OR LACING BARS.
Weight per foot of same, and weight of rivet-heads.
Approximate Lengths, in Feet, between Centres of Rivets. - - Weight per foot, Rivet-Heads.
- in pounds.
II* 11%." I2" 12%." 13." 13;" 14” 144"
DIAME-
OF
# By TER, IN
HEADS
*; § INCHES. 2
POUNDS.
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SPACED AT VARIOUS DISTANCES.
TABLE XXX.
TABLE OF SIZES OF LATTICE BARS FOR
CHANNELS OF VARIOUS DEPTHS, AND
D = depth of channel, and d = distance between inner
faces of channels.
given, the size of lattice bars is to be taken from the column
containing the next largest value of d.
If the value of d lie between the values

Sizes of Lattice-Bars.
JO
d = D d = 1.25 D d = 1.5D d = 1.75/2 d = 2 D
4" || 1" x 14" | 4” x 13” 4" × 14" | }" × 1;" || 4" x 13”
5* 4" × 14" | 4” x 13" | 4" × 1;" || 4" × 13" | }" × 14"
6* +" x 1;" || 3" x 13" | 4" x 14" | 4" × 14" | }" x 2"
7" #" x 13" | }" x 14" | }" × 14" | 4” x 2" | ** x 13”
87 #" × 14" | #" × 14" | #" × 14" | #” x 2" | #” × 23"
9" || #" × 24" | #" × 24" | #" × 23" | #" × 23" | #" × 24”
Io" #" × 24" | #" x 24" | #" × 23" | #" × 23"
I2* ;" x 24" | #" x 24" | #" x 2;"
15" i' x 23' || 1 x 23'
TABLE. XXXI.
TABLE OF SIZES OF LACING-BARS FOR CHAN-
NELS OF VARIOUS DEPTHS, AND SPACED
AT VARIOUS DISTANCES.
D = depth of channel, and d = distance between inner
faces of channels.
given, the size of lacing-bars is to be taken from the column
containing the next largest value of d.
If the value of a lie between the values

Sizes of Lacing-Bars. *
A)
d = D d = 1.25 D d = 1.5/2 d = 1.75D d = 2 D
4" || 4” x 13" | #" x 13" | 4" x 14" | 4" x 2" | }" x 24"
5" 4" × 14" | }" x 2" | 4” x 24" | #" x 2" | #" x 24"
6? #" x 2" 4" x 24" | #" x 2" | #” x 24" | #" × 24”
7" #" x 24" | #" × 2" | #" × 24" | #" × 24" | #" × 2;" |
8* , #" × 23* | *" × 24" | #" × 23" | #" × 2;" | #" × 23"
g” ** X 2}" #" X 2}" ** X 23” †s" X 3" #" X 2#"
Io” ** x 23" | ** x 3" ;" x 23' | }" x 3"
12" #" x 3" | }" × 33" | #" × 33"
15" || }" × 33" | #" x 4"
TABLE XXXII.
TABLE OF STAY PLATES.
To be used in connection with latticing or double-riveted lacing.
D = depth of channel, d = distance between inner faces of channels, t = thickness of stay plate, l = length of
same, and m = number of rivets on each side of stay plate.
If the value of d lie between the values given, the size of stay plates is to be taken from the column.
containing the next largest value of d.
Sizes of Stay Plates.
d = 1.5D.
/

To be used in connection with single-rivet lacing.
D = depth of channel, d = distance between inner faces of channels, t = thickness of stay
TABLE XXXIII.
TABLE OF STAY PLATES.
same, and m = number of rivets on each side of stay plate. -
If the value of d lie between the values given, the size of stay plates is to be taken from the column
containing the next largest value of d.
plate, l = length of
* *
Sizes of Stay Plates.
d = 1.5/).

TABLE XXXIV.
TABLE OF PERMISSIBLE PRESSURES ON ROLLERS FOR BRIDGES OF CLASS A.
Formula, p = o 25Vd, where p is the pressure in tons per lineal inch of roller, and d the diameter of roller in inches. The first and last vertical lines
give the diameters, and the upper and lower lines the length of rollers. The intermediate spaces contain the permissible pressures on the rollers.
II" I 2" 15" I67 17" 2O" 2I ſº 23" 24” 25" 267 277 287 29"
6.61 * .61 8.60

TABLE XXXV. “
TABLE OF PERMISSIBLE PRESSUREs on RolleRS FOR BRIDGES OF CLASSES B AND c.
Formula, p = o 3125Vd, where p is the pressure in tons per lineal inch of roller, and d the diameter of roller in inches. The first and last vertical lines
give the diameters, and the upper and lower lines the length of rollers. The intermediate spaces contain the permissible pressures on the rollers.
e
13." 14" 15" 177 I87 * 19" 23" 24” 25" 27" 287 29" 30"
6. º I O. II.48
IO. g II

TABLE XXXVI.
RIVET TABLE.
CLAss A
{
*.
Bearing-stresses in tons.
BENDING-
MOMENTS |
IN INCH 4" §. Hºs" ##" #" #;" #” ##" | #" ##" - g” #" #” Iº." 1;" Isº,” I-3, ” I gº."
1 ºf
IS
TONS
I+
|
ſ
o.25o" g o.563" | o. 594" | oé25" | o.656” o.688° o.750" o.781" o,875” o.906" o.938" 1.094" | I 1.25" | 1.156" | 1.188" | 1.219" | 1.25o"
I.688
I
2, I IO
2.72 I
2.
2.
Af
O.7
py
I
I.
I
I
I
I
I
I
4.219 || 4,430

TABLE XXXVII.
RIVET TABLE.
CLASSES B AND C.
Bearing-stresses in tons.
BENDING-
MOMENTS
IN INCH E ;" | };" | "s" | #;" || 3" | };" | #" | ##" | #" | ##" | #" | ##" | #" | ##" 4" | ##" | };"
TONS.
o,375" | O.406" o,469" | o.5oo" o.531" | o.563" | o. 594" | o.625" || 0.656” o.688" | o.719" | of 50” o,781"
ſ
Iºs" I+'s" Iºs" Isºs" I fºs"
o,875" o.906” o.938” 1.031" | 1.063" | 1.094" 1.156" | 1.188"
|
I. * 2. IOO 2.222 2.
I
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I. I * ſe ſº 2.
I
2.
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I
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ee&
3.955 4.2 I9
9.757 IO.O2O

TABLE XXXVIII.
LA BOR IN E RECTION.
12' 14' I6' I8’ 20' 22' 24'
Roadway. Roadway. Roadway. Roadway. Roadway. Roadway. Roadway.
I8 2O 2 I, 22
2I 2

TABLE XXXIX. -
TABLE OF WORKING-STRESSES, IN TONS OF 2000 Pounds, FOR SQUARE wooDEN PILLARS.
o,625A K
I + O.OO4
a where P is equal to the working-stress, A the area in G inches, L the length in inches, and D the length of side of square in inches.
Calculated by the formula P=
* 752 !
63" 7" 73" 8m 13%" 14" 144" 15" 15%."
2I Ioz. Io | I I I.81 | 120.8 I 20.18
IOI.O4 I I I I
IO'7. I I I25.74
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TABLE XL.
TABLE OF APPROXIMATE WORKING LOADS FOR I - BEAMS USED AS STRUTS IN LATERAL,
t SYSTEMS OR SWAY BRACING.
Length of Strut h If f/ f'. By ſº If Length of Strut
in feet. 7" 18% I. . 6" 16# I. 6" 13.5% I. 5". 12# I. .5 Iok I. 4” Io:# I. * 4” 8# I. in feet.
SIDE- EDGE- SIDE- EDGE- SIDE- EDGE-
gº () () () º
SIDE- EDGE- SIDE- EDGE-
WAYS. WAYS, WAYS, WAYS. WAYS.
SIDE- EDGE- SIDE- EDGE-
WAYS, WAYS. WAYS,
WAYS, WAYS. WAYS. WAYS. º; #: #} {} {}
2I. 2I, 18.2 I8.2 I6.o I6.o
2I I'7. Iö, I I
2I. I I
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A TABLE XLI.
STRESSES IN SINGLE-INTERSECTION TRUSSES.
* + –2— 3 4.
w = panel live load on one truss, ~ * *
W. = panel dead load on one truss, 1 2 3 \
W" = upper panel dead load on one truss, <!
6 = inclination of diagonal to vertical. ^+. \ \
3. * 4 2 3– 4 5.
4 Panel. 6 Paneſ. 8 Panel.
MEMBER. * Multiply by
W. W.
Top Chord . . . . 5 6
7%
8
3%
3%
6
I
O
Batter Brace.
Diagonal .
To the stress on
each post must
be added W’.

TABLE XLII.
STRESSES IN DOUBLE-INTERSECTION TRUSSES.

* & +–R-2—R-3 4—r—5—R-6—R-7+ —t
w = panel live load on one truss, } 2 3 4 5 6
W = panel dead load on one truss, * * N **.
W’ = upper panel dead load on one truss, *-
& = inclination of short diagonal to vertical, N N N
B = inclination of long diagonal to vertical. &
... 2——3 Lſ 5—S-6 ?—Al–8
*
7 Panel. 8 Panel. 9 Panel. • Io Panel. II Panel. 12 Panel. 13 Panel. 14 Panel. 15 Panel.
MEMBER. Multiply by
78) W. QU) VV, 70 W. 769 W. ZE) PV, - ZU W, Zºy W. 76) W. Zºy W.
Top Chord . 1 || 49 * || 7 * | * 9% 94 || *P* | *P* || 12 I 2 º * || 4 || 4 || * | * ||
{{ {{ 2 || # # 8 # # II; II? * *# I5 I 5 * * 184 18% # 3%
{{ {& s] … Tº s | ST|Tº Tº Tai Tai Tº Tº Tº, Tr. Tº Tº Tai Tad |Tº Tº
{{ {{ • 4 ** % I2% 12% * * I8 I8 * * 23% 23% ** #
{{ {{ • 5 - # * I8 I8 * * 24% 24% * *
{{ { { ... 6 * | * || 24% 24% * | #
4 & 64 7 * # #
Bottom Chord I %). %. 3# 3# - ** §§ 4% 4% # # 5% 5% # # 6% 6% * * || tan a.
{ % {{ 2 || * * 3% 3# §§ # 4% 4} # # 5% 5% ## ## 6% 6% ** lſº
.." € $ 3 || 3.9 39 5 5 * 5.3 6% 6% #} #} • 8 8 * * 9% 9% *** *
&g {{ 4 || 3; 3; 7 7 * # 9% 9% # *** I 2 I 2 *** *** I4% I4% ** **
{{ 46 5 * # # I 13 II} * * I5 I5 * *** 18% 18% 3| **
{{ {{ 6 * | * || 17 | 17 || * | * || 21} | 214 || * | **
{{ {{ . 7 * | * || 23, 23, ſº ſº
<& & & 8 * | * ||
Batter Brace . *T* | *-Tº-Tº-Tº-Tº-Tº-Tº-Tº-Tº-Tº-Tº-Tº-Tº-Tº-Tº. Tº
Diagonal . I § } *. I} *; *# #} 2– # # #% 2% # #} # .3 # # | SęC Q.
& 4 2 || $ # # I * | * +} I} || #} | }} || # 2 #} | {} # 24 || # # ||
{{ • 3 # } # # § $ ## I }} # #} I# #3 ## # 2 # #
$$ • 4 % —# # O § # * # # # # I #} {{ # I} #} #;
&g • 5 # –3 # —# 1% O *r jºr # } {{ +% #} I #; #
6% ... 6 # —% # –4 Hºr —iºr *: O # is # # #} # sec 3.
66 ... 7 * — I *r —fºr # –3 #s —iºs ## O # Hºs
&t ... 8 *; — I #s -}} # –4 # – ſº
& 4 • 9 tº # –4 || + | –I #5 -}}
4& • IO #; —#
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&é {{ 64 2 # —# # "O $ # * # # *r +; I # # # I} #} #$
ſt & 4 {{ 3 # –4 # —% #, O # | . ºr }} # }} }} #} I # }}
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{{ 4& $4. 5 *; –3 His -íºs # O }} #
{{ & 4 {{ 6 |= # —# # —is To the stress on
Fºllºw-E-F-I-I-I-I-H-I-ii-I-Hi-HTH-Hi-Hi-Hi-Hi-HHHHH tº
£6 & 6 Q & 2 || 3 || –% * O * # }} 3 || # *r ## I # }} # I} || # #
$6 &4 (4. • 3 * –4 * —# }} | O #} *F # # * }} }} # I #} }}
44 (6 &é • 4 Aº º ## —# ++ —iºr #} O # #s # } # łł
{{ {{ {{ • 5 }} –3 ## -íºs # O # #
« “ “ . 6 ... r # –% # – ſº ||]

NTERSECTION
GHT IRON HIGHWAY BRIDGE,
DOUBLE |
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DETA|LS FOR A PONY TRU SS
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DETAILS FOR A SINGLE INTERSECTION BRIDGE
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DIAGRAM
& - * * * A4.
Fºs-ſ-ſ-,
**-
– º *...*
of STRESSES AND SECTIONS
**
T'late V.
}
** FC R A |
IGO' SPAN IRON HIGHVVAY BRIDGE. |
ſ CLASS A. \ . \
*. . . . . §§ §§ §§ | lºs
2–/0” 72.5 °/ = 70.50 t,” 2–70%–222?”/T = Z3.34. []" 2–70’–24 Z3ºſ= 4449 D / Sº 3– ~~ ~~
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7%jaz Jec = 74 Z7 ET Zoº Jec = 7, 2.5 L," ſolazºec. = 7& w ET § § * §§ º §§ * f §§ *
46 4%.5/2 = 73 & C. " .5& ſº? J. P. = /2 2.5 []" 6/6% & Z = z*40 E. " Sºk —- ** - 3% sº
%, ’o Zaz.7°od. " 7%"o Lat Rod. Z% "o Zaz Rod.
! 'S |
$
§
s\SP sø }
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© W / RºSP ** "exºs 4-ºx *. Tº NE S.
Nº sº R N º S º *Nº. --> §: G) Int, 7–4 *-**7.
§§§ 3 †Nº S *Nº, & Sº Nº. t *Nº, Jærut
// o' Q -j- tº ſo S S *A ºfº $ [...] § & t #, $
&^' S º SI's *Nº, G|ºs *NN +2.
Q\, N *2NSN S|| N NN *S. S \
(Yºº / N Nº 3|S S-XX* S | || º |
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N, sº º T 'ovº | §§ CŞ: S; *_NSD S.
W. S.Nº. 5 § &\@ 2 Š|S. 2N22 | |\rs &NK» 2 §§ Á |
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s & Y& M =|º s' &\ Sk SS
s © . SRI.); §§s s §ſs *>~
S X. s: §ls, SFS \ sºls, Ts
is N § * § SS ~. to S
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X.5% = 6.5% D – 3% "X .33%" = .9, 5% ri – 3% ºx * = 5. * --. §§
2 XJ24 3.3% ºr 3% Bº .
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$
3. - A),47A
* - &am----------------- /60/? **.
# &earlſoadway. . . ......4 *
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* ~ Jºye Zoad-- ... ... ... //?0%per/7.
Dedd Zoad..... ... ------. 7.4/* , ,
Wind Pressure...----------..JO” a sq.ft.

-º-
S. a connection onowº-ºº-ººrºº º
zºº -
IRON HIGHWAY BRIDGE,
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- ** -- I I
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- Aires ºn toº,” Zºo //e/ºr Wºº, /24 ºz º.º. - -º'--
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a cºlo co-o-o-o-o-o-o-o-o-o-o cle o 'º a 6 s a s º-o º 9 o' o 'º o º o o o o o o o o 'o o o 'o o o o or o ºg o – º º dº º 'º-º-º-º-º-º-º-º-º-º-º º 'º -º-º-º-º-º-º-º-º-º- -º-º-º-º-º:*****
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