Where there is local loading, as in the top flange, the rivets, in addition to the stress caused by the transferring of web stresses, are stressed by the vertical action of the angles being pressed downward by the ties and the consequent upward pressure of the web. Accord ing to Article 15 of the Specifications, the weight of one driver is distributed over three ties (see Fig. 147).
Let ff = w, the load per linear inch caused by one wheel W, which load is assumed to be uniformly distributed over the dis tance I; ws = vi, the vertical load or stress that comes on one rivet in the space s; v = j— , the stress on a rivet due to the distribution of flange stresses when s is a space, and V the shear at that point.
When these two stresses act on the rivet, the maximum stress twill be the ultimate amount that it is allowed to carry, and this will act as shown in Fig. 147: Then, which gives the spacing at any point in the girder flange under localized loading. Note that if w equals zero—that is, if there is no localized loading—there results: which is the same as previously deduced for flanges with out localized load ings. • The rivet spacing for the top flange of the girder which is being designed is given in Table XXIII. Here W =20000;1=(3X 7 4- 3 X 6) = 39 000 inches; w = 513; hl. = 67 inches; and 4 920pounds,which is the bearing of a i-inch rivet in the i-inch web. The top cover-plate is run theentirelength of the span.
The points other than the tenth-points referred to in the first column are for sections taken just to the left and right of the top cover-plate. The values of the reduced shears given in the third column are ob tained as has been previously explained. Although the rivet spacing in the lower flange is considerably greater than that in the upper flange, and accordingly a smaller number of rivets would be required, yet the spacing in the lower flange is made the same as that in the upper. Convenience in the preparing of plans and facility in manu facture make this action economical. Theoretical spacing greater than 6 inches should be dealt with according to Article 54 of the Specifications.
The values of the rivet spacing given in Tables XXII'and XXIII are plotted in Fig. 148. Note that the effect of the localized loading is to decrease the rivet spacing, and also note that the effect increases from the ends toward the center.
The size of the flange angles and the width of the cover-plates for different spans, are a matter of choice. Once the size is deter
mined, the thickness can be computed. The sizes very generally adopted in practice are as follows: For another method of the presentation of this subject, see "Steel Construction," Part IV, pp. 264 to 268.
1. Determine the rivet spacing for the top chord of a plate-girder, loading E 40, and 7 by 9-inch ties being used. The web is f inch thick; distance from back to back of angles, 6 feet 6I inches; flange angles, 6 by 6 by }-inch; and cover-plate, 14 by a-inch, two finch rivets being out of each. First, consider the flange as taking all the bending moment; and second, consider one-eighth the gross area of the web. The total unreduced shear is 80 000 pounds in both cases.
Ass. 3.21 inches; 3.76 inches.
74. Lateral Systems and Cross-Frames, There are two methods in use in common practice in determining where the panels of the lateral bracing shall fall.—namely, (1) To choose the number of panels so that the panel points come opposite the stiffness, and (2) to choose the number of panels so that the placing of the panel points is inde pendent of the stiffener spacing. The lateral systems should be of the Warren type; and in both of the above cases the angles that the diagonals make with the girder should not be greater than 45 degrees. Also,it is best to have all panels the same length and to have an equal number of panels. This latter condition will simplify the drafting very much, since one-half of one girder can be drawn and the other half will be symmetrical, the opposite girder being similar to the one drawn, but being left-handed.
The members of the lateral systems will take tension or com pression according to the direction the wind blows. Cross-frames are placed at intermediate points to stiffen the girders. These are diagonal bracings (see Plate II), and are placed at certain intervals according to the judgment of the engineer. Good practice demands that their number should be about as indicated below : The above is not intended to serve as a hard and fixed rule. Varia tions from the limits given arc to be made as the case demands. • In all cases they are put at the panel points of the bracing, the top and bottom parts acting as sub-verticals in the lateral system. Also, the cross-frames should divide the span into equal parts if possible. In eases where that is not possible, the shortest divisions should come near the ends of the spans.