05-03ChapGere.0007

05-03ChapGere.0007 - h x in terms of the height h B at the...

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Solution 5.7-7 Fully stressed beam with constant height and varying width SECTION 5.7 Fully Stressed Beams 327 h 5 height of beam (constant) b x 5 width at distance x from end b B 5 width at midpoint B ( x 5 L/2 ) A T DISTANCE x s allow 5 M S 5 3 Px b x h 2 Ê b x 5 3 Px s allow h 2 M 5 Px 2 Ê S 5 1 6 b x h 2 A ¢ 0 # x # L 2 A T MIDPOINT B(x 5 L/2) Therefore, N OTE : The equation is valid for and the beam is symmetrical about the midpoint. 0 # x # L 2 b x b b 5 2 x L Ê and Ê b x 5 2 b B x L b B 5 3 PL 2 s allow h 2 Problem 5.7-8 A cantilever beam AB having rectangular cross sections with varying width b x and varying height h x is subjected to a uniform load of intensity q (see figure). If the width varies linearly with x according to the equation b x 5 b B x / L , how should the height h x vary as a function of x in order to have a fully stressed beam? (Express
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Unformatted text preview: h x in terms of the height h B at the fixed end of the beam.) Solution 5.7-8 Fully stressed beam with varying width and varying height x h B h B h x b B b x q h x A B L h x 5 height at distance x h B 5 height at end B b x 5 width at distance x b B 5 width at end B A T DISTANCE x h x 5 B 3 qL x b B s allow s allow 5 M S 5 3 qL x b B h x 2 M 5 qx 2 2 Ê S 5 b x h x 2 6 5 b B x 6 L ( h x ) 2 b x 5 b B ¢ x L ≤ A T THE FIXED END (x 5 L) Therefore, h x h B 5 B x L Ê h x 5 h B B x L h B 5 B 3 qL 2 b B s allow A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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