05-03ChapGere.0003

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Problem 5.7-3 A tapered cantilever beam AB having rectangular cross sections is subjected to a concentrated load P 5 50 lb and a couple M 0 5 800 lb-in. acting at the free end (see figure). The width b of the beam is constant and equal to 1.0 in., but the height varies linearly from h A 5 2.0 in. at the loaded end to h B 5 3.0 in. at the support. At what distance x from the free end does the maximum bending stress s max occur? What is the magnitude s max of the maximum bending stress? What is the ratio of the maximum stress to the largest stress s B at the support? Solution 5.7-3 Tapered cantilever beam SECTION 5.7 Nonprismatic Beams 323 h A = 2.0 in. h B = 3.0 in. B A b = 1.0 in. b = 1.0 in. x P = 50 lb M 0 = 800 lb-in. L = 20 in. P 5 50 lb M 0 5 800 lb-in. L 5 20 in. h A 5 2.0 in. h B 5 3.0 in. b 5 1.0 in. U NITS : pounds and inches A T DISTANCE x: M x 5 Px 1 M 0 5 (50)( x ) 1 800 5 50(16 1 x ) s 1 5 M x S x 5 50(16 1 x )(6) ¢ 2 1 x L 2 5 120,000(16 1 x ) (40 1 x ) 2 S x 5 bh x 2 6 5 b
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