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 σmax occur? What is the magnitude σmax of the maximum bending stress? What is the ratio of the maximum stress to the largest stress σB 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?

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3P P-50b L P 50 lb Mo 800 lb-in. B Mo 800 lb-in. B 2.0 in 3.0 in. b 1.0 in L 20in b1.0 in. L- 20 in