+78.0 - U,L, X 0.7685 = 0 .'. U,L, = + 101.6 For the maximum stresses in the verticals, sections 1-1, 2-2, and 3-3 are passed, and in each case the panel points to the left of these loaded. The shears are V, , 628.4 (1 + 2 + 3 + 4 + 5) _ +117.0 It is seen that the section 3-3 cuts the member and therefore the stress in this must be determined before the stress equation can be written, as its ver tical component will enter into it. However, by comparing the dead load shear in that panel, which is 15.0, and the live-load shear V3_3, . which is +46.8, it is seen that the resultant shear is - I -; and, as this is of opposite sign from the dead load shear, a counter is required and is acting. The stress in U,L, is zero, and the diagonals act as in Fig. 44, the section 3 3 then cutting three members. The stress equation is + 46.8 + = 0, from which E. = 46.8.
Care should be taken not to add to this 46.8 the 10.0 derived as dead-load stress on page 44, in order to get the maximum stress, as the 10.0 previously derived was the dead-load stress in U,L, when and were acting. The dead-load stress which goes with the live-load stress of 46.8 acts simultaneously with it, and is the dead-load stress in U,L, when the members U,L, and are acting as in Fig. 44. The dead-load shear on the section 3 3 would then be the left reaction minus the loads at points U L L,; or, Remember that this +5.0 can act only when the live load tends to
produce a stress of 46.8; and thus the total stress in U,L, with live load in that position is 46.8 + 5.0 = 43.8, while with dead load only in the truss the stress is 10.0.
The dead-load shears and the maximum .-1- and live-load shears should now be written for inspection, in order to investigate for counters and then for the minimum stresses. Those whose derivation has not been given should be easily computed by the stu dent at this time. The shears are From a study of these it is seen that a counter is required in the 4th panel according to rule a, Article 37; and according to rule b of the same article, the maximum stress is (-46.8 + 15.0) X 1.302 = +41.4, the minimum stress for it and also U,L, being zero according to the same article. A counter is also required in panel 5, as the truss is symmetrical.
The minimum live-load stress in U,L, is zero, and occurs when no live load is at the point L,.
The minimum live-load stresses in the diagonals and U,L, occur when the truss is loaded successively to the left of the sections a a and b b, in which case the shears are 7.8 and 23.4 respectively. The stress equations are section 1 1 and loading the panel points to the left. The shear is the same at this section as it is at the section bb namely, 23.4. The stress equation is