By George Gamow
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Extra info for A Planet Called Earth
29 the truss is loaded with a concentrated load W at the centre of the span. Let it be required to determine the stresses due to the load W in the various members. The weight W is in the first instance transmitted in its entirety through the vertical strut CD to the point D, whence the weight is taken up in equal moieties by the inclined tierods AD and DB to the abutments or points of support A and B. A weight or force acting in a vertical downward direction at the upper extremity of a vertical strut in the form of a column or pillar exerts in that strut a compressive stress, whose magnitude or intensity is equal to that of the weight or force, hence the stress due to the weight W in the strut CD is a compressive stress = W.
Vertical members are all posts, and capable only of compression. stresses are as under: w = panel dead load. w' = panel live load. W = total weight of truss and load. S = span in feet. W Then stress on centre or half post EI = (w + w')4 = -^. stress on quarter post CG W = (w + w/)2 = stress on eighth post BF = DH = (w + w') W AI The tension on suspending rod AI = — —. tension on suspending rod FG = GH = W AG ——. p CG = W 56 BRIDGE CONSTRUCTION. W FC The tension on suspending rod FC = CH = —. • J J A WFG tension on suspending rod AF = HE.
In these trusses each span A'A = AA = AA", and each span for the purposes of determining the stresses may be regarded as consisting of two sections AB and BA resting on their supports A, B, and A. Let w = W = W = W = the dead and live load carried at each point of support A, B, A, etc. S = maximum stress in any member—then in any vertical post AC or A"C", S = W = W , and in any inclined strut as CB whose lower extremities rest against the verticals in the same horizontal plane as in the middle span of Fig.