Stress in Diagonals. This is determined by taking sections similar to A B, and determining the vertical component of the stress in the diagonal. This vertical component must equal the algebraic sum of the vertical forces on the left, or the shear at the section. The relation of the actual stress in the diagonal to the vertical component, is the same as the relation between the length of the diagonal and the vertical depth. In this manner the stresses are worked out below: Stress in ai = 1.35 X 70,950 = — 96,000 " " bj = 1.35 X 5S,050 = — 78,500 " " ck = 1.35 X 45,150 = — 61,000 " " d1 = 1.35 X 32,250 = — 43,700 " " em = 1.35X 19,350 = — 26,200 " " fn = 1.35 X 6,•50 = — 8,750 The direction of stress in these diagonals will be understood from Fig. 273, which shows the vertical component acting in an opposite direction to the resultant external forces.
Choosing the Sections. The fiber stresses used here are tension, 15,000 lbs.; compression, 12,000 lbs., reduced by Gordon's formula.
Both top and bottom chords are subjected to bending stresses due to the roof and ceiling joists, which come on these chords between the panel points. The bend ing stresses must be added to the direct stresses.
It is necessary at first to assume approximately w 11 a t the direct fiber stress can be without exceeding the able stress reduced for ported length and for the ing stress. Having selected a
section on the basis of this assumed fiber stress, the moment of inertia and the actual stress must be determined. if these vary materially from the allowable, a new section must be chosen and the process repeated. In this ease the process is illustrated below.
Top Chord. Fig. 275 shows the assumed section of top chord. The first step is to determine the position of neutral axis.
Cover plates 5.25 X .19 = 1.00 Side plates 10.5 X 7.3S = 77.50 Angles 1.96 X 1.66 = S.20 S6.70 Radius of gyration r = 4.05 The top chord between panel points may be considered as h beam of span equal to panel length, and fixed at the ends as regards the bending moment caused by the direct load. Therefore, Since the top chord is braced laterally only at the ends and at three points equally distant, the unsupported length is 1S feet 6 inches. From Cambria, the allowable fiber stress in compression for a length of 18 feet 6 inches, and least radius of gyration 4.05, is found to be 11,000 lbs. reduced from 12,000 lbs. The above combined stress is therefore within the limit and close enough not to require redesign.