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Nonprismatic Beams
A tapered cantilever beam AB of length L has square cross sections and supports a concentrated load P at the free end [see figure part (a)]. The width and height of the beam vary linearly from hA at the free end to hB at the fixed end
Determine the distance x from the free end A to the cross section of maximum bending stress if hB 3hA.
(a) What is the magnitude σmax of the maximum bending stress? What is the ratio of the maximum stress to the largest stress B at the support?
(b) Repeat (a) if load P is now applied as a uniform load of intensity q= P/L over the entire beam, A is restrained by a roller support and B is a sliding support [see figure, part (b)].
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