The number of rivets required will be governed by the shear, since the angle is connected by one leg only; and it is: 91. The Lateral Systems. The stresses in these systems must be computed according to (10) and Article 54, Part I. They are given on the stress sheet, Plate III (p. 251). Since according to (68) these members must be constructed of rigid shapes, it is customary, in com puting the stresses, to assume that one-half the shear is taken by each of the diagonals in any given panel; that is, one diagonal is in tension, and the other diagonal is in compression. The stresses given on the stress sheet are computed by making this assumption. Also, since both diagonals in each panel are considered as acting at the same time, the stresses in all the verticals are zero.
The section of the upper lateral members will be made up of two angles placed apart a distance equal to the depth of the top chord. Fig. 193 shows the section. The radius of gyration about the axis parallel to the long leg will be consider ably larger than that about an axis parallel to the shorter leg. In fact, it is so much greater that the strut will not need to be examined with respect to this axis. The diagram of the first panel is given in Fig. 194. The radius of gyration is to be taken about the horizontal axis if the entire length is to be taken; and the radius of gyration is to be taken about the vertical axis if one-half the length is taken, in which case it will bend as shown by the broken line in Fig. 194. The members are designed for the latter conditions only, since they are amply safe in regard to the first condition if they satisfy the latter. The length in this latter con dition is 13.5 feet, which requires a radius of gyration not less than l3.5 X 12 = 1.35.
120 Two angles 5 by 3 by -inch, with a total area of 5.72 square inches and a radius of gyration equal to 1.61, will be assumed and investigated to determine if they are sufficient.
The unit-stress is computed to be P = (16 000-70 X X 1 = 11 000 pounds per square inch, and the required area is 0.61 square inch. The required area is very much less than the given area; but the angle chosen must be used, since this is the smallest one which conforms to the requirements of the Specifications.
The width of the lattices (46) must be 21 inches; and according to Table XXV, the thickness must be -- inch, the distance c being 23 inches.
Single shear governs the number of rivets required. In accord ance with (20) and (23), their number is 2X6 6 013X 1 700 = 2 rivets. Field rivets 3 in number are used in all places, since the lateral system is riveted up after the trusses are swung into place.
Since this is the minimum sized angle which will give a radius of gyration greater than 1.35, it must be used in the remainder of the panels of the top chord. Four angles of the minimum size might have been used, and would have been satisfactory, except that the area would have been excessive.
The stresses in the lower lateral system are computed according to (10), a similar assumption to that for the upper lateral system being made—namely, that both diagonals in each panel are stressed at the same time, one taking tension and the other taking compression. Fig. 195 shows the first panel of the lower lateral system. These diagonals are connected to the stringers wherever they cross them, and also to each other where they cross in the center. This reduces the length which must be used in computing the cross-section of the member. In this case it is the distance C—A, and is equal to 90 inches.
Since the angle is free to move about either axis, angles with even legs should preferably be employed, since this will give greater economy. The radius of 'gyration must be greater than = 0.75.
One angle 31 by 31 by a --inch, with an area of 2.48 square inches and a radius of gyration of 1.07, will be assumed and investigated. The allowable unit-stress is P = (16 000 — 70 X 90 11 = 12 650 r pounds per square inch, and the required area is120650 = 2.38 square inches. This is nearly equal to the given area, and therefore the angle chosen will be taken for the section.
This angle must now be investigated for tension, one rivet-hole being taken out of the section. The net area is 2.48 — a 4- 1) 30 5 2.10 square inches. The required net area is 16 000X 14 = 1.53 square inches, which shows the angle to be sufficiently strong.
Single shear determines the number of rivets to be required. These are: 2 X 30 5008 field rivets.
6013X 11 All rivets in the lower lateral system are field rivets, since this system also must be riveted up in the field after the trusses are swung into place.
The total stress in the second panel is 21 500 pounds, and a 31 by 3 by i-inch angle, with an area of 2.30 square inches and a least radius of gyration of 0.90, will be assumed and examined. The allowable unit-stress in compression is 11 (16 000 — 70 X = 11 250 pounds per square inch, and the required area is =1.91 square inches. Since this is less than the given area, and since the size of the angle (72) is the smallest allowable, this angle must be used.