The member U,U$ must he designed for a maximum compres sive stress of 16.0 + 0.8 X 14.1 = —27.28. A 6 by 4 by 1-inch angle with an area of 3.61 square inches and a (east radius of gyration of 1.17 will be assumed. The unit-stress P, computed from the formula in the Specifications, is 8 460 pounds per 27 280 square inch; and the required area is 8 460 = 3.23 square inches.
This angle will be used, as the given and required areas are close together, and as the next smaller angle—a 6 by 31 by *-inch angle with an area of 3.42 square inches—gives a required area of 3.58 square inches, tints being too small.
The rivets required in single shear are: 27 280 8 100 X 1.5 = 5.04 (say 5) shop rivets, and 5.04 X 1.5 = 7.6 (say 8) field rivets.
The rivets required in bearing in a I-inch web are: In order to make the joints safe, 6 shop or 9 field rivets should be The member U2 must be designed for a maximum stress of 9.6 + 0.8 X 8.0 = —16.00. A 31 by 3 by --inch with an area of 2.30 square inches and a least rectangular radius gyration of 0.90 will be assumed. The unit-stress P is 7 090 pounds per square inch, and the required area is 16,r 090 = 2.26 square inches. As the required and the actual areas are very close together, this angle will be used.
The rivets required in single shear are: 16 000 X1.5 = 2.96 (say 3) shop rivets, and 2.96 X 11 = 4.44 (say 5) field rivets.
By computation similar to the above, it is found that 4 shop or field rivets are required in bearing. Since the bearing requires most rivets to make the joint safe, 4 shop or 5 field rivets must be used.
If the Specifications would have allowed a 31 by 3. by angle with an area of 2.09 square inches, this angle would have exactly fulfilled the requirements, the required area being 2.09 square inches.
The member must be designed for a maximum compres sive stress of 8.0 + 0.8 X 4.1 = —11.28. A 3 by 3 by -inch angle with an area of 2.11 square inches and a least radius of gyration of 0".91 will be assumed. In this case the unit-stress is 7 160, and the area required is 1.58 square inches. The required area is considerably less than the area of the angle assumed; but it must be used, since it is the smallest allowed by the Specifications, which require that the material shall not be less than and from Table XX1 it is seen that 3 inches is the smallest, size leg in which a inch rivet can be used.
The stresses in all the members of the lower lateral system are less than the stresses in the member just designed, and therefore all members of the lower lateral system will be made of one 3 by 3 by i-inch angle.
For the last member designed in the upper lateral system, and for all members in the lower lateral system, 3 shop or 5 field rivets will be required at the ends. These are more than sufficient to take up the stress, but it has been found that less- than three rivets do not make a good joint.
The stress sheet, Plate II, shows the general arrangement of the lateral system, the number of rivets in the connections and also in the connection plates where they join the flanges.
The intermediate cross-frames do not lend themselves to a theo retical design, since the stresses which come upon them are not easily aseertained. It is good practice to require that all members be of the sizes as given below: The angles in the intermediate eross-frames will therefore be 31 by 3) by y-inch.
The end cross-frames (see Fig. 154) act in a manner somewhat similar to the portal bracing in a bridge, since they transfer all the wind which comes on the top chord and on the train to the abutment. This load, which acts at the level of the ties, is in this case (see Article 24 of the Specifications): It is usually assumed that half of this is transferred to the point a by means of a—b, and from there down a—b' to the masonry. The other half goes directly down b—a' to the masonry. This causes stresses as shown in Fig. 154. Note that the stress in a—b will always he com pression; but the stresses in the diagonal will be either tension or compression according to the direction the wind blows. The mem ber a—b will be a 31 by 3' by ,i-inch angle. To form the connections at its end, 3 shop or 5 field rivets will be used.
The maxi mum compressive stress for which the diagonals are to be designed is 12.70+0.8X12.70 _ —22.86. Here the length is 108 inches if the angle tends to bend one way; but if it bends as shown by the broken lines in Fig. 154, the length will be one-half of this. For this reason, angles with unequal legs should be used, the longer leg extending outward. This allows the greatest rectan gular radius of gyration to be used.