The section must now be examined for tension, and in order that both legs of the angle may be considered as effective section, both legs must be connected at the end. The area required will be ig 760 = 2.04 square inches. Considering one rivet-hole is taken out of the angle, the net area is — 1 X (f + b ) X = 4.25 square inches, which is amply sufficient.
If the 4-inch leg only were as sumed to be connected, the grcss area would be 4 X = 2.00 square inches, and the net area would then be 2.00 — 1 X (h + -) X 1-inch = 1.50 square inches, which is not sufficient. If the 6-inch leg were connected, the area would be sufficient. See Fig. 152 for method of connection and 'rivets.
The number of rivets required (see Specifications, Article 38 and 40) is computed as follows: If the member were not subjected to both tension and compression, the number of rivets required in single shear would be: But according to Article 38 of the Specifications, this number must be increased 50 per cent, and accordingly 4.86 X 12 = 7.29 (say 8) shop rivets are to be used. In the above formula, 0.6013 is the area of the cross-section in square inches of a -inch rivet. In order that both legs should be connected, a clip angle as shown in Fig. 152 is used; and the same number of rivets must go through both legs of the clip angle, since the stress in the vertical leg of the main angle is transferred to the clip angle and from there into the connecting plate.
The above number of rivets makes the joint safe so that it will not shear off in the plane between the connection plate and the hori zontal leg of the angle. The joint must also be designed so that there will be sufficient rivets in bearing to prevent them from tearing out of the connecting plate. The number required is: This 5.34 must be increased 50 per cent, making a total of 5.34 X 1.5 = 8.01 = say, 8 shop rivets as before.
The above rivets are shop rivets, since it is assumed that the span, being a small one, will be riveted complete in the shop and shipped to the bridge site ready to place in position without any further riveting. In case the girders are shipped separately, then the lateral bracing must be riveted up in the field; and according to last part of Article
.40 of the Specifications, the rivets, being field rivets, must have the allowed unit-stresses reduced one-third, which is equivalent to having the number of shop rivets increased 50 per cent. This will make the required number of field rivets 8 X 1.5 = 12.
As a rule, the connection plates are b inch thick, seldom more. Also, the members of the upper lateral system are connected on the lower side of the connection plate in order not to interfere with the ties. Note that the use of the clip angles requires a smaller connec tion plate than would be necessary if these angles were not used, since in the latter case all the rivets must then be placed in one mw in the horizontal leg of the angle.
The number of rivets required in the connection plate and the flange of the girder must be sufficient to take up the component of that member parallel to the girder. For the case in hand, the num ber (see Fig. 153) is: from which, x = 5.5 (say 6) rivets.
Additional rivets should also be put in, in order to take up the compo nent of the other lateral diagonal which meets at this point.
The member Ui U, is to be designed for a maximum compressive stress of 20.6 + 0.8 X 16.0 = —33.4. A 6 by 4 by angle with an area of 4.18 square inches will be assumed. The least rectangular radius of gyra tion is 1.1G. The unit allowable load is : P = 13 000 —00X = 8 420 pounds per square inch.
The required area is 33 400 8 420 3.97 square inches. As this is very near the area assumed, and as trials with other angles do not give required areas which cone any closer, this angle will be used.
The rivets required in single shear are: 33 400 8 100X 1.5 = 6.21 (say 7) shop rivets, and 6.21 X 1.5 = 9.3 (say 10) field rivets.
The rivets required in bearing in the *-inch connection plate are: 334O0 380 X 1.5 = 6.78 (say 7) shop rivets, and7 • 6.78 X 1.5 = 10.17 (say 11) field rivets.
The above computations show the joint to be weakest in bearing, and therefore 7 shop or 11 field rivets must be used. It is not neces sary to investigate this member for tension, as the computations for the first diagonal indicate that the area will be sufficient, both legs being connected.