793_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

793_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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SECTION 9.10 Deflections Produced by Impact 787 Problem 9.10-4 A weight W ± 20 kN falls through a height h ± 1.0 mm onto the midpoint of a simple beam of length L ± 3 m (see figure). The beam is made of wood with square cross section (dimension d on each side) and E ± 12 GPa. If the allowable bending stress in the wood is s allow ± 10 MPa, what is the minimum required dimension d ? A B h W d d L 2 L 2 Solution 9.10-4 Simple beam with falling weight W D ATA : W ± 20 kN h ± 1.0 mm L ± 3.0 m E ± 12 GPa s allow ± 10 MPa C ROSS SECTION OF BEAM ( SQUARE ) d ± dimension of each side M AXIMUM DEFLECTION (E Q . 9-94) d max ± d st ² ( d 2 st ² 2 h d st ) 1/2 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) d st ± WL 3 48 EI ± WL 3 48 E a 12 d 4 b ± WL 3 4 Ed 4 s st ± M S ± a WL 4 ba 6 d 3 b ± 3 WL 2 d 3 s max s st ± d max d st ± 1 + a 1 + 2 h d st b 1/2 I ± d 4 12 S ± d 3 6 S UBSTITUTE (2) AND (3) INTO E Q . (1) S UBSTITUTE NUMERICAL VALUES : S QUARE BOTH SIDES , REARRANGE , AND SIMPLIFY S OLVE NUMERICALLY d ± 0.2804 m ±
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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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