PD = 5 X 20X 15 + 2 X 20X 8 + 16X 20X 10 = 5 020 pounds.
Therefore, In the case of a single-track railroad bridge, there are only two stringers upon which the weight of the track, the engine, and the train is supported. These join the floor-beam at points equally distant from the center of same. The weight of the ties, rails, and fastenings is usually taken at 400 pounds per linear foot of one track. As regards the live load, the proposition reduces itself to placing the wheel loads so that the sum of the reactions of stringers in the adjacent panels will be a maximum on the floor beam under consideration. This is discussed in Article 47, page 87 (see Fig. 94).
In determining the values of the maximum moment and shear in the floor-beam, the case is that of a beam symmetrically loaded with two equal concentrated loads. Each load is equal to the dead weight of one stringer, one-half the track weight in one panel, and the maxi mum sum total of the reactions due to the wheel loads on the stringers in adjacent panels which meet at that point. This latter quantity is called the floor-beam reaction. For a general arrangement of the loads, see Fig. 105. The distance a has become standard for single-track spans, and is 6 feet 6 inches.
Let it be required to determine the maximum shears and moments in the floor-beam of the truss of Article 47.
The weight of the stringer may be obtained by the formula of Table II, and is: Stringer = 20 (123.5 + 10 X 20) - 2 = 3 200 pounds.
The weight of one-half of the ties, rails, etc., in one panel is: } Track = (400 X 20) _ 2 = 4 000 pounds.
The weight that comes from the engine wheels is given in Article 47, page 87 (see Fig. 94), and is 65.55. Each load is therefore the sum of all the above weights, as follows: 3 200 + 4 000 + 65 550 = 73 750.
The maximum shear (see Fig. 105) is seen to be 73 750 pounds; and the maximum moment occurs at C and D, and is: M = 73 750 X 27 — X 12 = 4 646 250 pound-inches.
For any particular engine the floor-beam reactions for different length panels are easily tabulated for future reference: Table XI gives the floor-beam reactions for panel lengths from 10 to 24 feet inclusive.
In many cases it is desirable to keep the dead-load shears and moments separate from those of the live load; and this can easily be done.
In neither of the above cases has the weight of the beam itself been taken into account. This should be clone in the final design. The method of procedure is to compute the moment and shears as above; then make a provisional design of the beam. Next, com pute the weight of the beam thus designed, and add the moments and shears caused by this weight to the other dead-load moments and shears ; then.re-design the beam and compute its weight. If this last weight varies 10 per cent from the previous weight, another re design should be made. The above proceeding belongs to Bridge Design, Part II, and will there be treated.
57. Moments in Plate-Girders. Plate girders are of two classes —namely (1) those which have the ties or floor laid directly upon the upper flanges of the girders; these are called deck plate-girder bridges; and (2) those in which the webs of the girders are connected with each other at intervals by floor-beams which in turn carry stringers or joists in exactly the same manner as in the floor system of a railroad or highway truss-bridge; this latter type is called a through plate-girder bridge. Figs. 106 and 107 show cross-sections of deck and through girder bridges spectively, for way service. Fig.
108 is a side view of a deck girder bridge. Fig.
109 is a longitudinal section of a through plate-girder rail road bridge. The section is taken down the middle of the track. The bridge shown has 5 panels. An odd number of panels should be chosen, as this does not bring a floor-beam at the center of the span, and hence the great moment which would then be caused is avoided.
The analysis of the shears and moments of a through plate girder is precisely the same as that for a truss bridge. The shear is constant between any two panel points as 0-1 or 1-2, etc., and the moments are computed for the points 1, 2, 3, and 4.