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= 4.2 tons per square inch

The intensity of shearing stress per square inch is

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In Mr. Theodore Cooper's standard specifications for iron and steel railroad bridges and viaducts, the webs of plate web girders are referred to as follows: "The webs of plate web girders must be stiffened at intervals of about the depth of the girder wherever the shearing strain per square inch exceeds the strain allowed by the following formula :

where H

Allowed shearing stress in pounds =

12000

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ratio of depth of web to its thickness; but no

web plate shall be less than inch thick.

Applying this formula to the foregoing example—

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So that the shearing stress in the web plate is less than this amount, and it is therefore safe.

A common rule in America is to put in stiffeners when the intensity of shearing stress exceeds 4000 lbs. per square inch.

The function of the stiffener is to stiffen the web by supporting the elementary columns and preventing them from buckling. They should be spaced at intervals not exceeding the depth as the girder, and usually consist of double angles riveted to the web plate.

There will be no necessity for stiffeners in the longitudinal stringer.

The weight may now be calculated thus:

88 feet of angles 5 × 3 × at 16-7 lbs. per lineal foot 20 feet of web plate 28" x 3" at 35

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2257

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1470 lbs.
700

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slightly above the assumed weight of 110 lbs. per lineal foot, so that no recalculation is necessary. This longitudinal is illustrated on Plate II.

Cross-Girders or Floor Beams.-The dead load upon the crossgirders is the weight of the rails, guard rails, sleepers, and longitudinal stringers, also the weight of the cross-girder. It will be most convenient to consider both the live and dead load as concentrated at the points of attachment of the stringers; hence we have the load discharged by each stringer

(200+113)20 = 6260 lbs.

Assume that the cross-girder weighs 150 lbs. per foot, therefore the load concentrated at the points of attachment of the stringers will be, since the cross-girders are 15 feet span— 5 x 150 825 lbs.

=

Therefore the total concentrated dead load is

6260 + 825 = 7085 lbs. = 3.16 tons

To find the maximum live load upon the cross-girders, we must find the maximum reaction produced by the engine wheels

R

on the two longitudinal stringers on each side of the crossgirder. It can easily be proved that the maximum reaction will occur when the sum of the loads on the left of the cross-girder is as nearly as possible equal to the sum of the loads on the right. Hence with the consolidation engine, Fig. 326, the fourth wheel will rest immediately over the cross-girder, Fig. 321. The reaction on the middle cross-girder from the loads on the left is

R1 = 2%{4(1·67) + 6(975) + 6(15.5)} = 7 tons

The reaction from the loads on the right is

R2 = 2{4(3·59) + 4(8·42) + 6(15·5)} = 7·9 tons

The total reaction which gives the maximum live load on the cross-girder is

24 tons

R = R1 + R2 + 6 = 7 + 7·9 + 6 = 20·9 tons

Hence the girder is loaded as shown in Fig. 321.
The maximum bending moment is-

24 × 4 = 96 foot-tons

The working stress may be taken the same as in the longi

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The total depth should be arranged so as to reduce the flange section, and leave room for the attachment of the stringers to the web plate direct without packing pieces; 3 feet effective depth will be convenient.

The moment of resistance is

fad = 4.5 × 3 × a = 13.5a

.. 13.5a96

96 13.5

= 7·1 square inches

Hence the flanges may be made in a similar manner to those of the longitudinal stringer, but with angles 5 × 3 × 1, thusTwo angles 2(8) 7·125 square inches.

=

Rivets. Assume that the rivets are of an inch in diameter and 4 inches pitch as before, then

1.8f=24

.f45 tons per square inch

which is safe, since the rivets are in double shear. The pressure on the bearing area is

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Thickness of Web.-It now remains to be seen whether the web is thick enough to resist buckling.

The maximum intensity of shearing stress is

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which is safe, according to Mr. Cooper's rule, without stiffeners; the attachment of the stringers will, however, considerably stiffen the web over the 5-feet panels, while the middle panel is hardly stressed at all.

If we apply Rankine's formula, the factor of safety against buckling is about 1.7. This factor is very small, but when the assumptions are considered upon which the buckling stress is calculated it is clear that the factor of safety is understated, and therefore the 3-inch web may be adopted.

The weight of the cross-girders may now be calculated

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or 125 lbs. per foot run, which is considerably below the assumed weight of 150 lbs. per foot, so that no recalculation is necessary.

The weight of the stringers and cross-girders per lineal foot of truss is 314 lbs.

The web plate between the stringers may be replaced with two angles 3 × 3 × 3, as the shearing stress is practically

nothing. If this is done, the weight per foot run of truss is 301 lbs.

In the cross-girder shown on Plate II., for which the above calculation was used, the thickness of the web is increased, as the cross-girders act as compression members in the lower lateral system of wind bracing. For the same reason the plate is retained throughout the web, the central 7 feet not being replaced with angles.

The open deck which we have investigated would not be suitable for a bridge over a street in a town, and some form of continuous deck would have to be adopted; this would, however, add considerably to the dead load to be carried.

In the case of a floor of plates riveted to the top flanges of the cross-girders and longitudinals, if these are used, we should have for the plate floor, ballast, sleepers, and rails about 1400 lbs. per lineal foot of bridge instead of 400 with the American deck.

Sir B. Baker estimates1 the weight of the deck and wind bracing for a double-line railway bridge as follows:

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The weight of the deck in a road bridge is easily estimated when the design and live load to be carried is decided upon.

1 "Long Span Bridges," by Sir B. Baker.

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