The live-load shears at the left end and at the tenth-points, wheel 2 being at the section in all cases, are computed from the gen eral formula, which is: — ZP, in which, R = Left reaction; r P = All loads to left of section, and is equal to 10 000 pounds for all sections except the end of the girder.
The computations and results can be conveniently placed in tabular form, and are given in Table XVIII.
In order to illustrate the use of the relation W> 1 4 1, let point 3 in the above span be taken. Place wheel 2 at point 3; then, as wheels 1 to 13 are on the girder, the total weight W is 212. As 1 = 100, 141 = 125. Therefore, as 212 is greater than 125, wheel 2 is the correct wheel.
The curves of maximum live-load moments and shears are shown in Fig. 112. They should always be drawn. From them the shear or moment at any desired section can be determined. For exam ple, let it be desired to determine the maximum live-load shear and moment at a point 24 feet from the left end of the girder. By drawing the ordinate, shown by a broken line in Fig. 112, and scaling, the following values are found: i"_, = 88 000 pounds; = 2 440 000 pound-feet.
A similar set of curves for the dead-load shears and moments should be made. The set for the deck plate-girder in hand is shown in Fig. 113. These are easily constructed by laying off the max imum values of the shear at the end, and the maximum value of the moment at the center. The shear curve is a straight line from the end to the center, while the moment curve is a parabola from the center to the end.
The stresses in the lateral systems of plate-girders are computed in a manner the same as that employed for the lateral systems of trusses, the unit-load being taken according to the specifications used.
59. Stresses in Plate-Girders. The stresses in plate-girders are treated in the Instruction Paper on Steel Construction, Part IV, pages 251 to 263, and the student is referred to this treatise for infor mation regarding this subject.
The stress in the flange is seen to depend upon the distance from center of gravity to center of gravity. This distance, in turn, depends upon the depth of the girder. Certain approximate rules have been proposed in order to determine this, but the following formula will give the width of the web plate in accordance with best modern practice: _ d + 0.543 in which d = Width of the web plate, in the even inch; 1 = Span, in feet.
For example, let it be required to determine the width of the web plate of a plate-girder of 80-foot span center to center of end bearings.
80 80 d 0.005 X 80 + 0.543 0.94 85.2 (say 86) inches.
If the resultant value had been 85 inches, the width would have been taken as either 84 or 86. The reason for this is that the wide plates kept in stock at the mills are usually the even inch in width and can therefore be procured more quickly than if odd-inch widths were ordered, in which case the purchaser would be forced to wait until they were rolled—often a period of several months. The distance back to back of flange angles, the so-called depth of girder, is one-half inch more than the width of the web. This is due to the fact that each pair of flange angles extend one-fourth inch beyond the edge of the web plate, so as to keep any small irregularities caused on the edge of the web plate by the rolling, from extending beyond the backs of the angles.