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)].

Transcribed Image Text:

q=P/L r Sliding support