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The dead weight was specified to be the weight of the structure and
floor, without any allowance for snow.
The wind load was specified to be 2,000 lbs. p. 1 . f. bridge, of which
1,000 lbs. was assumed to be a moving load and 1,000 lbs. a fixed load.
The specifications state that some of the eye bars and pins will be of
nickel steel of the following chemical requirements:
Per Cent., Max.
Phosphorus (Basic) ...04
Phosphorus (Acid) .06
Sulphur .05
Per Cent., Min.
Nickel.^. 3.25
The annealed specimens of this material were required to have the fol¬
lowing physical values:
Elastic limit. 48,000 lbs. minimum per sq. in.
Ultimate strength. 85,000 lbs. minimum per sq. in.
1,600,000
Elongation in 8 inches
ultimate.
The full sized annealed bars of this material (up to a maximum size of
16 inches bv 2^ inches) were required to show the following results:
Elastic limit. 48,000 lbs. minimum per sq. in. .
Ultimate strength. . . .'. 85,000 lbs. minimum per sq. in.
Elongation in 18 ft. 9 per cent.
47
All other material in the structure was to be of open hearth steel, speci¬
mens (except rivets and steel casting’s) to show the following chemical
results:
Per Cent., Max.
Phosphorus (Basic).04
Phosphorus (Acid).08
Sulphur .05
And to have the following physical values:
Elastic limit, plates and shapes. . . . 30,000 lbs. per sq. in. minimum.
Elastic limit, eye bars. y 2 of ultimate.
Ultimate strength, plates and shapes 60,000 lbs. desired.
Ultimate strength, eye bars. 66,000 lbs. desired.
Elongation, per cent, in 8 inches. . . —r-r— I - ^ Q ° - QQC) -—
ultimate strength.
And annealed full-size eye 1 }ars to show results as follows:
Elastic limit . 28,000 lbs. per sq. in. minimum.
Ultimate strength. 56,000 lbs. per sq. in. minimum.
Elongation in body of bar. 10 per cent.
We have examined the detailed reports of the mill inspectors on this
material, and find that they show the metal fulfilled the above specifications.
48
With the above loads and quality of material, the following unit
stresses were specified:
For Dead
Load and
Regular Live
Load or for Dead
Load and Wind.
For Dead
Load and
Congested
Live Load.
r
For Nickel Steel in Eye Bars and Pins:
Tension .
%
Shear on pins.
Bearing on diameter of pins.
Bending on outer fibre of pins.
Pounds Per Square Inch.
30,000
39,000
20,000
24,000
40,000
48,000
40,000
48,000
For Structural Steel in Main Members
of Trusses, Towers and Bracing:
Tension .
Compression .
Shear on shop rivets, bolts and pins.
Bearing on diameter of shop rivets,
bolts and pins...-.
Bending on outer fibre of pins.
20,000
20,000-90 1 /r*
13,000
25,000
25,000
24,000
24,000-100 1 /r
16,000
30,000
30,000
For Structural Steel in Secondary
Members of Trusses:
Tension in sub-verticals (hangers) . .
Compression in sub-diagonals.
Shear on shop rivets and bolts.
Bearing on diameter of shop rivets
and bolts .
Pounds Per Square Inch.
18,000
18,000-80 i/r*
12,000
24,000
For Structural Steel in Floor System
of Roadway and Footways and in
all Floor Beams:
Tension chords . 15,000
Shear on shop rivets, bolts and web-
plates, net section. 10,000
Bearing on shop rivets and bolts. .. . 20,000
* Where i=length and r=radius of gyration both in inches.
49
For Dead
Load and
Congested
Live Load.
f --->
Pounds Per Square Inch.
For Structural Steel in Floor System
(Including Brackets) for Railroad
and Trolley Tracks:
Tension chords . 10,000
Shear on shop rivets, bolts and web-
plates, net section. .. 7,000
Bearing on shop rivets and bolts. . . . 14,000
Allowable Pressure on Masonry:
For dead load and regular live load. . 550
For dead load and congested live load 650
These specifications and original contract drawings, which show
the general dimensions of the bridge as built, form the basis of our
investigation, and in addition thereto we used the detailed shipping
invoices showing the exact scale weight of each and every piece in the
structure, and the detailed shop drawings showing the areas of the
sections.
We also computed, from the various contract drawings, the weight
of the flooring material, including paving blocks, roadway concrete, side¬
walk concrete, rails, ties and other materials for the various tracks, rail¬
ings, pipes, wires and all other material required on the structure.
For Dead
Load and
Regular Live
Load or for Dead
Load and Wind.
50
We also figured the amount of steel which will be required at some
future time to complete the two sidewalks in their final position (as
shown on Diagram 3) and all of these weights were found to be as
follows:
lbs. p. 1. f. lbs. p. h f
bridge. bridge.
2 outside footwalk stringers. 176^
Overhanging footwalk brackets. iooJAdd'l steel....
Footw^alk gratings. 127J
2 upper outside railings. 142]
2 upper inside railings. 90C.
Reinforced concrete slabs for footwalk.
Rails and contact rails for four upper tracks
Guard timbers and ties for four upper tracks
403
232
=:oo
330
640
2 lower railings. 174
Rails and conductor rails, 4 lower tracks. ... 375
Wood paving blocks of roadway.1,041
Concrete under roadway paving blocks.3,200
Pipes, mail chutes, telephone, telegraph and feeder wires. 405 -
7,300
This total load of 7,300 lbs. p. 1 . f. bridge is referred to in this report
and on the drawings as “ additional material ” being all the dead load
except the shipped weight of structural steel.
From the above data we have carefully computed the live and dead
stresses and unit stresses in each and every fnember of the structure,
making our calculations on the following basis:
Dead Load. —We have taken for the dead load the scale weights
of each piece as shipped and given on the various invoices, and we have
apportioned these shipping weights to their proper panel points, arriv¬
ing at the panel point dead loads as shown in detail on sheets 1 to 3,
inclusive. To these scale weights of structural material, we have added
the weight of “ additional material " as heretofore given ; this material
being taken as uniform along the entire length of bridge, and apportioned
to the panel points in proportion to the panel lengths. These two items
constitute the entire dead load of the completed structure, and the result-
/
5i
ing panel loads aie shown in detail on sheets i to 3 and are summarized
on sheets 4 to 6, which latter sheets show the points of application as
used for the dead load calculations.
d he actual shipping weight of steel now in the structure, as at
present finished (as shown on Diagram 4) is 105,152,010 lbs., made up
as follows:
Nickel steel eye bars. 9,179,133 lbs.
Nickel steel pins . 1,460,563 lbs.
Nickel steel links and pin plates. 1,010,034 lbs.
Nickel steel castings . 119,900 lbs.
Total nickel steel.
Structural steel eye bars . 5,654,400 lbs.
Structural steel pins. 38,566 lbs.
Structural steel other than eye bars
and pins . 84,795,779 lbs.
Steel castings . 2,253,094 lbs.
Small iron castings . 47,786 lbs.
Cast-iron curb. 592,755 lbs.
11,769,630 lbs.
Total structural steel
93,382,380 lbs.
Total weight. 105,152,010 lbs.
This weight is distributed as follows:
Towers . 12,633,200 lbs.
Anchorages . 995.500 lbs.
Trusses, Bracing and Floor. 91,493,310 lbs.
Total . 105,152,010 lbs.
The dead load® stresses have been figured on the assumption that
both rocker arms will be adjusted when the entire dead load is in place,
so that no dead load will pass through them, thus making the dead load
stresses entirely independent of these rocker arms and making their
values computable by the ordinary static methods.
Live Load.— In accordance with the terms of the specifications, we
have assumed the live load to be “ placed so as to give the greatest strain
52
in each part of the structure,” and this condition requires that some sec¬
tions of the bridge may be loaded and at same time other sections un¬
loaded ; for instance, the maximum compression in the rocker arms
occurs with the two Island lever arms, and the two shore anchor arms
loaded, and the other portions unloaded, and the maximum tension in
these rocker arms occurs with the two shore lever arms and the Island
span loaded and the other portions unloaded.
For the secondary members, except in a few cases where the bottom
chord is not straight between adjacent main panel points, the live load
stresses were figured with the local loads specified.
As the two rocker members connecting the ends of the lever arms
cause the adjacent ends of the lever arms to move up and down together,
the structure is continuous from end to end for live load stresses, and
these stresses cannot be computed by the usual static method and must
be found by means of the elastic properties of the materials.
%
While this method is well known and has been in use for some time,
we give in an appendix an adaptation of it to this structure, which takes
into account the simultaneous action of both the rocker arms and gives
a simple and precise method of computing their stresses for any given
loading.
This adaptation has been worked out by Mr. Clarence W. Hudson,
who has had charge of these calculations for us.
With the stresses in the rocker arms known, the stresses in all
the other members of the structure may be readily computed.
In computing the deflections of this structure, we have used the
gross area of all riveted tension members. We have allowed nothing
for play of pin holes, and we have not considered the tie plates, battens,
or lattice on riveted members, nor the influence of the lateral system or
the buckle plate floor. All of these matters have some slight influence
on the actual deflections, but as it is only the ratio of certain deflections
that is used to determine the stresses, to a certain extent, one influence
ofifsets the other, and the stresses thus determined are not subject to
serious error. We have computed deflections, using a modulus of elas¬
ticity of 28,000,000 lbs. for both carbon and nickel steel.
Wind Loads. —We have computed the wind stresses on the assump¬
tion that all wind pressure is transmitted by 'the transverse bracing
\
53
directly to the lower chord, the upper horizontal bracing being for
vibration only.
We have computed the stresses for a fixed load of 1,000 lbs. p.l.f. over
the entire structure and for an additional live load of 1,000 lbs. p.l.f. placed
so as to give the greatest stress in each member.
The wind stresses have been computed by the same general method
that was used for the live load stresses in the main trusses.
The formulae for these wind stresses are similar in terms to those for
the live load stresses, but differ in some of their signs due to the fact that
a horizontal force at one end of either of the Island lever arms produces
motion at the end of the other lever arm opposite in direction to the force.
We only show the chord stresses on our stress sheet as the web stresses
cannot be given with accuracy since there is a solid buckle plate floor which
carries a large portion of the wind shear.
Erection Stresses —We have computed the erection stresses using a
traveller weighing 647 tons distributed as shown on sheet 10. This weight
and spacing we have taken from the contractor’s drawings (as this traveller
had been removed before we started this investigation).
For the stresses in the Island span we have assumed a traveller on
the East and West lever arm simultaneously, and we have taken traveller
weights in such positions as to give maximum strains in every member,
with the outer limiting position of the forward wheels 4 panels from the
ends of the lever arms.
I11 addition to the stresses caused by the travellers, we have computed
the simultaneous dead load stresses, assuming that all the weight of steel
was in place, but not including the weight of “ additional material ”
(amounting to 7,300 lbs. p.l.f. bridge), none of which was placed on the
structure until after the removal of the travellers.
All erection stresses have been computed by simple static methods as
the rocker arms were not rigidly connected till after the removal of the
travellers.
Snow Load —The specifications do not call for any snow load on this
structure, so that we have not figured any stresses for such a load, but in
our opinion, a bridge of this character, with a practically solid lower floor
87 feet wide and an upper deck with two sidewalks and four lines of rail¬
road track, should have been calculated for a considerable snow load.
54
We made a stress sheet for the loads called for in the specifications,
but it was evident that the structure could not safely carry these loads,
so we had to find the maximum safe carrying capacity of the structure.
The final stresses under the conditions of safety hereinafter recommended
are shown on our general stress sheet (Sheet No. 7) submitted herewith.
This stress sheet also shows the effective area of each member, the final
unit stresses, and the wind stresses in the chords.
The areas marked T for the main posts, U17-L17, U57-L57, U75-L75,
and U107-L107, are the areas at their points of maximum width, and these
posts decrease in area towards their ends, as the side plates keep the same
thickness but decrease in width, giving the areas marked B at the bottom.
The areas marked T for the other vertical posts are exclusive of the area
of the transverse diaphragms in these posts, and the areas marked B are
inclusive of these diaphragms.
We have made no additions, for reverse stresses, as the specifications
state that the sections are to be computed for the stress requiring the great¬
est area, so that the unit stresses here shown are the direct stresses from
dead and live loads without any additions for reverse stresses, snow, wind,
impact, or secondary stresses.
We have also computed the stresses in many of the floor beams and
stringers for the upper and lower floors, using the local live loads speci¬
fied, and for the cases computed we find the maximum flange stresses to be
as follows:
Lower floor trolley stringers with
cover plates . from 4,600 lbs. to 7,000 lbs. per sq. in.
Lower floor trolley stringers with¬
out cover plates. from 7,200 lbs. to 11,000 lbs. per sq. in.
Lower floor roadway stringers. . . from 7,900 lbs. to 14,600 lbs. per sq. in.
Upper floor elevated railway
stringers . from 6,500 lbs. to 9,100 lbs. per sq. in.
Upper floor sidewalk stringers. . . from 4,100 lbs. to 10,800 lbs. per sq. in.
Upper floor floorbeams. from 13,000 lbs. to 14,400 lbs. per sq. in.
Lower floor floorbeams. from 15,000 lbs. to 16,000 lbs. per sq. in.
All of these stresses are for the static loads without impact.
The two pairs of outside trolley stringers on the lower floor are built of
certain sections on the Island span and its lever arms, and of the same sec-
55
tions (for similar panel lengths), with additional cover plates on all other
*
portions of the structure, thus making some portions of these tracks much
stronger than others, as shown by the above stresses.
We are informed that the Island span and lever arm outside stringers
had been completed for the specified trolley loads, when it was decided that
subway trains might be run on these tracks and the remaining outside
stringers were cover-plated. This, however, leaves these tracks without
uniformity as to carrying capacity, unless cover plates are added to the out¬
side stringers on the Island span and its lever arms.
The upper floor beams all have the same thickness of web, and the first
cover runs the full length top and bottom, regardless of whether they carry
a 20^-ft. panel or a 40-ft. panel, and this was undoubtedly done to carry the
traveller during erection.
In a few of the lower floor beams and trolley stringers, the unit stresses
exceed those specified; and this excess has been caused by their having been
computed for a dead load less than the actual weight as finally called for
by the flooring contracts, but this excess is so slight that, in our opinion, it
will not affect their safety.
While the erection stresses are passed and can never recur again, we
considered it advisable to compute these stresses to find if they had been
greater than the stresses to which the structure may be subjected under
traffic; and on sheet 10 we give the erection stresses for the chords and for
such web members as will have the maximum erection stresses, though we
did not consider it of sufficient value to compute all the minor web stresses
from erection.
From this stress sheet we find that the maximum erection stresses in
the chords do not equal the completed dead load stresses, and only in a few
diagonals near the main piers do they equal the specified live and dead load
stresses; so they furnish no data in the way of a full size test to determine
the carrying capacity of the members, as the structure under tiaffic will be
subjected to greater stresses than it was during erection.
We have examined the general design and details of the anchorages
at the Manhattan and Queens ends and find the sections and the weight of
masonry sufficient to carry the uplifts. We also find the pressure on the
masonry of the main piers to be within safe limits.
5 &
We have not made a complete investigation of the secondary stresses
in this structure, but we have made a limited investigation to approximately
determine what the secondary stresses caused by temperature, distortion
due to deflection, and bending due to own weight of members, amount to.
We find that the secondary stresses due to temperature are generally
small, except in the post U75-L75, where in our opinion, the maximum stress
from this source will occur, as this is the free end of the Island span, and
a variation of ±60° F. will move the top of this post and bend it around
its fixed lower end, producing a fibre stress of 3,200 lbs. per sq. in.
The secondary stresses, due to distortion of the true figure of the trusses
by the live load, are quite considerable, as the vertical deflection of the point
L37 is 18 5/10 inches, and of the point L91, 14 2/10 inches for a live load
of 3,000 lbs. p. 1. f. truss.
We have made a careful analytical computation of the horizontal move¬
ment of the point U17 (and ether similar points over the main piers) caused
by this distortion, and for a live load of 3,000 lbs. p. 1. f. truss in the position
giving the maximum direct stress in the post U17-L17 we find this move¬
ment causes a fibre stress in the lower fixed end of U17-L17 of 2,600 lbs.
per sq. inch, which is the maximum stress from this source, which occurs
simultaneously with a maximum direct stress. The fibre stresses in the
other similar posts are about the same, except that for U75-L75 it is reduced
to 1,400 lbs. per sq. inch owing to the fact that this is the free end of the
Island span; but this should be added to the temperature fibre stress in this
post as above given. This distortion also causes some horizontal movement
of the top ends of the rocker arms relative to their bottom ends and this
relative movement causes additional secondary stresses, but the stresses
found from this cause were so small as to be safely negligible.
The fibre stresses due to bending of members from their own weight
depends to some extent on the total live load and dead load direct stresses
on the members, but for a live load of 3,000 lbs. p. 1. f. truss we find this
fibre stress to be about 1,200 lbs. per sq. in. for many of the members, with
extreme values running as high as 3,500 lbs. per sq. in.
There are also secondary stresses due to impact, and to bending in the
vertical posts and hangers, caused by accelerating or retarding the moving
loads on the upper floor, but we have not computed any values for these,
57
3 .s \\ e arc of the opinion that they are negligible in this structure where the
relative value of live load as compared with the dead load is so small.
The above maximum values of all these secondary stresses will prob¬
ably not occur in the same members at the same time, but it will be seen that
they may cause considerable increases in the direct unit stresses heretofore
shown.
In addition to figuring the stresses on all members we have had a large
number of the actual bridge members measured and calipered in the field,
and we find that they agree with the sections we took from the shop draw¬
ings and used in these calculations, which sections we show in detail on
sheets 8 and 9.
We have also computed the weight of a number of members from the
shop drawings and find such weights agree with the shipping weights on
the invoices, showing that the scale weights used for the dead load are
correct.
We have figured the net sections of the riveted tension members from
the shop detail drawings.
We have not carefully examined all the details of this structure, but we
have checked the end connections of such members as are most heavily
stressed and find them equal in strength to those members.
>
We have carefully considered the form and details of the lower chord
as this feature has been criticised in the public journals, and the impression
has been given that the lower chords in this structure are weaker than those
of the Quebec Bridge, which, in our opinion, is not the case.
There is no full-size experimental data for the carrying capacity of
such large compression members as are used in this structure, though the
recent tests on models of compression members for the Quebec Bridge
showed that such members when properly latticed carried 32,000 lbs. per sq.
in. before failure, with a ratio of length to radius of gyration of 25. The
only safety is to keep within the limits gained from experience on a smaller
scale, as the means do not exist for learning the absolute carrying capacity
of such sections, and a practical method of testing could not be provided
in any reasonable time.
In our opinion, however, it is safe to follow the established practice for
compression values, provided the limits set are not too high and the details
are sufficient to make the member act as a unit and not fail in detail.
58
The heavier sections of the lower chord of this bridge are built up of four
vertical webs, each 48 inches deep and varying in thickness with the sections
required. Each web has an 8-inch by 6-inch angle, top and bottom, forming
a “ built-up channel.” Each outside pair of these “ built-up " channels is
latticed together, top and bottom, with 5-inch by 5^-inch double lacing bars,
having two rivets in each end and one rivet at each intersection, the length
of these lattice bars being about 45 inches, c. to c. of end rivets. This gives
two separate built-up channel chords 48 inches deep and 25 inches b. to b.
of angles. These two separate sections are then connected together
with top and bottom tie plates 15 inches long and ^2 inch thick, spaced
about 5 feet, c. to c. The entire chord is thus about 70 inches wide, b. to
b. of outside angles. While this chord is not as stiff transversely as it would
be if properly latticed from outside rib to outside rib, and while in our
opinion the lattice on the centre line, where the longitudinal shear due to
bending is at its maximum, should not have been omitted, yet we believe
that the chord is as strong horizontally as vertically for the following
reasons:
The radius of gyration of the chord about its horizontal axis averages
14 inches and the radius of gyration of each outside latticed pair of chan¬
nels around a vertical axis averages 12 inches, without any allowance for
the connecting of these two pairs by the tie plates, which certainly add ap¬
preciably to the transverse stiffness, though the exact amount cannot be
computed. However, the radius of gyration of the whole chord as a unit
around a vertical axis is about 27, and while it would not be safe or proper
to use this radius (owing to the omission of