When the concentrated load is at the middle of a span, adjacent unloaded spans will be under negative moment throughout their lengths. Maximum negative moment is approximately the same as positive moment, and ;-inch square bars 5 inches apart will therefore he put through the top as well as the bottom of the slab.
With concrete extending 1 inch below the steel, the total depth of slab is S inches and the weight of slab = S X150/12=100 pounds per square foot as assumed.
Girders.—The maximum stresses in the girder occur when a pair of wheels are directly over the girder. A portion of this load is dis tributed by the slab to adjacent girders. This rolling load consists of one wheel carrying 14,000 pounds and one carrying 6000 pounds, 12 feet apart.. Assuming this distributed over a width of 6 feet (see Section 150), the load carried by one girder covers 4 feet of width and the loads are 14000X4/6=9333 and 6000X4/6=4000 pounds.
Assuming the stem of girder to weigh 250 pounds per foot, the dead load is 1SOX4+250=970 pounds per linear foot of girder.
The position of moving load for maximum moment is that in which the heavier wheel is as far to one side of the middle of the beam as the center of gravity of the two loads is to the other, and the moment (taking length of beam as 25 feet) is: Maximum shear occurs when the heavier load is adjacent to the support, and the center of gravity of the loads (considering the loads distributed over 2 feet of length) is 5.1 feet from the center of support.
The girder is a T-beam with flange 48 inches wide and 8 inches thick, and stem 12 inches wide and 20 inches deep.
From Table VII (p. 163), we see that for and R=95, L=600 and Then A = .0068 X48 X20 = 6.53 inches. From Table X (p. 166), it is found that four 1k-and two 11-inch round bars will answer. These are placed in two rows, two 1- and one 14 inch bars in each row, making the total depth of the beam 24 inches. The weight of stem is then= 16 X 12X 150 "144 = 200 pounds per foot, which is less than the assumed weight.
Diagonal Tension.—The maximum shear at the middle of the girder occurs when the moving load is at one side of the middle of the beam, or V (middle) = 9333X 11.5 X25 =4293 pounds; with
impact this becomes 5366 pounds and v (middle) = 5376 12X.S75X20 =25.5 pounds. The ina. mum unit shear varies from 25.5 at the middle to 120 at the supports. Stirrups are necessary from the support to the point where the shear is 40 Using Formula 13 of Section 108, if U-shaped stirrups of 1-inch round steel be used. the spacing at the ends should be Use this spacing for eight stirrups, then change to 12 inches spacing and continue to middle of girder. Two of the horizontal rods may also be turned up near the abutment.
154. Through Girder Bridges.—For spans of considerable length, or where the head room under the roadway is too contracted to permit the use of T-beam construction, through girders may be used at the sides of the roachvay, the slab floor being hung from the bottoms of the side girders. The floors in such bridges may be simple slabs, extending from one girder to the other, or the floor slab may be carried by T-beams across the bridge from girder to girder.
Fig. S2 shows a bridge of this type. The method of design is the same as for the other types. If the loading of Example 2 be used, the T-beam cross-girder would carry the two loads of 14,000 pounds each, 6 feet apart, or if the width of the bridge and importance of traffic are sufficient, two passing trucks might give a loading of four such wheels spaced 6, 2, and 6 feet apart. In a bridge for heavy traffic, where passing loads might come upon it, each girder should be able to carry the whole weight of a truck as a rolling load in addition to the dead weight of one-half the bridge. On a country highway, design ing for the passing of a single truck is usually sufficient, as the meeting of two unusually heavy loads on the bridge is a very remote contin gency.
When sidewalks are to be carried at the side of the roadway, the through girder may be placed between the roadway and sidewalk, and the sidewalk carried by cantilever beams attached to the girders. These cantilevers should be continuations of the eross-girders, the tension steel extending through the main girder and being anchored into the cross-girders.