This is true for any truss with horizontal chords and a simple system of webbing with diagonals and verticals.
38. Maximum and Minimum Stresses. Some specifications require the member to be designed for the maximum stress, while others take into account the range of stress. In this latter case it is necessary to determine the minimum as well as the maximum stress. Except where a reversal of stress occurs—and this does not happen in trusses with horizontal chords—few specifications require any but the maximum stresses to be com puted. For that reason, little space will here be devoted to the minimum stresses, their computation in succeed ing articles being thought to illustrate them sufficiently.
(a) The maximum stress in a member is equal to the sum of the dead-toad stress and the live-load stress of the same sign.
(b) The minimum stress is equal to the sum of the dead-load stress and the live load stress of the opposite sign, or to the dead load stress alone, according to which gives the smallest value algebraically. By this latter statement it should be seen that if the maximum stress is —58.60, then 0 or } 18.00 would be smaller than —3.00.
(c) It is evident that the minimum in all counters and in all main members in panels where counters are employed will be zero, for when the counter is acting the main member is not, and therefore its stress is zero. The reverse is also true.
(d) An exception to a is seen in the case of the counters. Here it is evident that the maximum stress is equal to the algebraic sum of the dead-load shear and the live-load shear of opposite sign times the secant of the angle which the counter makes with the vertical.
While it is true that in trusses with horizontal chords the loading for maxi mum shears will give the maximum live-load stress to be added to the (lead load for the maximum stress, it is not always true that the loading for minimum live-load shears will give the stress to add to the dead-load stress to get the minimum stress. However, the loading for the minimum live-load shears will give the live-load stress to be added to the dead-load stress for the minimum stress, except in the case of verticals placed between panels each of which contains counters, and in that case it may or may not do so. In such cases a loading
must be assumed—preferably the one for minimum shears—and the shears in the panels on each side of the vertical must be com puted for the loading assumed.
If the resultant shear is the same sign as the live load, then the main diagonal acts; if it is of different sign, then the counter acts.
As an example, let it be re quired to find the minimum stress in the vertical of the truss of Figs. 39 and 40. It is assumed that the loading for minimum shears will give the result. The section a — a is then passed, and the live load placed on and all points to the left. The shears will then be as shown in Fig. 41. To obtain the shear in the panel under this loading, it must be re membered that a load is at and so the shear is the shear in the panel with the panel load at added, or, —67.5 + 5S.5 = —9.0. The diagonals now act as indicated by Fig. 41, and the total stress in is determined by passing a circular section around and it is : As there is no load at the stress in is = 0. The same result will occur if points L, or and to the left are loaded; but if points L, and to the left are loaded, the members and will act, and the stress in will then be equal to the shear on the section a — a. The stresses are: Dead-load, — 22.0; and live-load, a 13.5, which gives a total of — 8.5; but as the maximum stress is —22.0 — 126.0 = — 148.0, it is evident that 0 and not —8.5 is the minimum.
The computation of the maximum stress is as follows: Load points L. and to the right. The shear on a — a is, for dead load, +22.0; and for + live load, +126.0; and the equations of the stresses are: + 22.0 + = 0 = — 22.0 + 126.0 + U,L, = 0 = — 126.0