792_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

792_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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786 CHAPTER 9 Deflections of Beams Problem 9.10-3 A cantilever beam AB of length L 6 ft is constructed of a W 8 21 wide-flange section (see figure). A weight W 1500 lb falls through a height h 0.25 in. onto the end of the beam. Calculate the maximum deflection d max of the end of the beam and the maximum bending stress s max due to the falling weight. (Assume E 30 10 6 psi.) Solution 9.10-2 Weight W dropping onto a simple beam Height h is very large. M AXIMUM DEFLECTION (E Q . 9-95) M AXIMUM BENDING STRESS For a linearly elastic beam, the bending stress s is proportional to the deflection d . s max A 2 h s 2 st d st (1) s max s st d max d st A 2 h d st d max 1 2 h d st For a RECTANGULAR BEAM (with b , depth d ): Substitute (2) and (3) into (1): s max A 18 WhE AL ; I bd 3 12 S bd 2 6 I S 2 3 bd 3 A (3) d st WL 3 48 EI s 2 st d st 3 WEI S 2 L (2) s st M S WL 4 S s 2 st W 2 L 2 16 S 2 W = 1500 lb h = 0.25 in. A B W 8 21 L = 6 ft Solution 9.10-3 Cantilever beam D ATA : L 6 ft 72 in. W 1500 lb h 0.25 in. E 30 10 6 psi W 8 21 I 75.3 in. 4 S 18.2 in.
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