794_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

794_Mechanics - 09Ch09.qxd 788 1:37 PM Page 788 CHAPTER 9 Deflections of Beams Solution 9.10-5 Simple beam of wide-flange shape DATA W L 4000 lb 10

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788 CHAPTER 9 Deflections of Beams Problem 9.10-6 An overhanging beam ABC of rectangular cross section has the dimensions shown in the figure. A weight W ± 750 N drops onto end C of the beam. If the allowable normal stress in bending is 45 MPa, what is the maximum height h from which the weight may be dropped? (Assume E ± 12 GPa.) Solution 9.10-5 Simple beam of wide-flange shape D ATA : W ± 4000 lb h ± 0.5 in. L ± 10 ft ± 120 in. s allow ± 18,000 psi E ± 30 ² 10 6 psi M AXIMUM DEFLECTION (E Q . 9-94) M AXIMUM BENDING STRESS For a linearly elastic beam, the bending stress s is proportional to the deflection d . (1) S TATIC TERMS s st AND d st (2) (3) S UBSTITUTE (2) AND (3) INTO E Q . (1): 4 s allow S WL ± 1 + a 1 + 96 hEI WL 3 b 1/2 2 h d st ± 2 h a 48 EI WL 3 b ± 96 hEI WL 3 s max s st ± s allow a 4 S WL b ± 4 s allow S WL s st ± M S ± WL 4 S d st ± WL 3 48 EI s max s st ± d max d st ± 1 + a 1 + 2 h d st b 1/2 or d max d st ± 1 + a 1 + 2 h d st b 1/2 d max ± d st + ( d 2 st + 2 h d st ) 1/2 R EQUIRED SECTION MODULUS
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This note was uploaded on 12/22/2011 for the course MEEG 310 taught by Professor Staff during the Fall '11 term at University of Delaware.

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