A tapered cantilever beam AB having rectangular cross sections is subjected to a concentrated load P= 50 lb and a couple M0= 800 lb-in. acting at the free end [see figure part (a)]. The width b of the beam is constant and equal to 1.0 in., but the height varies linearly from hA= 2.0 in. at the loaded end to hB= 3.0 in. at the support.
(a) At what distance x from the free end does the maximum bending stress #max occur? 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, in addition to P and M0, a triangular distributed load with peak intensity q0= 3P/L acts upward over the entire beam as shown. What is the ratio of the maximum stress to the stress at the location of maximum moment?
