05-03ChapGere.0001 - h x 5 height and width at distance x S...

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Nonprismatic Beams Problem 5.7-1 A tapered cantilever beam AB of length L has square cross sections and supports a concentrated load P at the free end (see figure on the next page). The width and height of the beam vary linearly from h A at the free end to h B at the fixed end. Determine the distance x from the free end A to the cross section of maximum bending stress if h B 5 3 h A . 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 5.7-1 Tapered cantilever beam SECTION 5.7 Nonprismatic Beams 321 A h A h B B x P L S QUARE CROSS SECTIONS h A 5 height and width at smaller end h B 5 height and width at larger end
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Unformatted text preview: h x 5 height and width at distance x S TRESS AT DISTANCE x A T END A : x 5 s A 5 A T SUPPORT B : x 5 L s B 5 2 PL 9( h A ) 3 s 1 5 M x S x 5 6 Px ( h A ) 3 1 1 2 x L 3 S x 5 1 6 ( h x ) 3 5 h A 3 6 1 1 2 x L 3 h x 5 h A 1 ( h B 2 h A ) x L 5 h A 1 1 2 x L h B h A 5 3 C ROSS SECTION OF MAXIMUM STRESS Set Evaluate the derivative, set it equal to zero, and solve for x . M AXIMUM BENDING STRESS Ratio of s max to s B s max s B 5 2 s max 5 ( s 1 ) x 5 L / 4 5 4 PL 9( h A ) 3 x 5 L 4 d s 1 dx 5 A B x P L A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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