407_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

407_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Problem 5.5-13 Determine the maximum tensile stress s t (due to pure bending about a horizontal axis through C by positive bending moments M ) for beams having cross sections as follows (see figure). (a) A semicircle of diameter d (b) An isosceles trapezoid with bases b 1 ± b and b 2 ± 4 b /3, and altitude h (c) A circular sector with ²± p /3 and r ± d /2 SECTION 5.5 Normal Stresses in Beams 401 Solution 5.5-13 M AX . TENSILE STRESS DUE TO POSITIVE BENDING MOMENT IS ON BOTTOM OF BEAM CROSS - SECTION (a) S EMICIRCLE From Appendix , Case 10: (b) I SOSCELES TRAPEZOID From Appendix , Case 8: (c) C IRCULAR SECTOR WITH From Appendix D, Case 13: A ± r 2 ( a ) a ± p /3, r ± d /2 s t ± Mc I c ± 360 M 73 bh 2 ; c ± h (2 b 1 + b 2 ) 3( b 1 + b 2 ) ± 10 h 21 ± 73 bh 3 756 I C ± h 3 ( b 1 2 + 4 b 1 b 2 + b 2 2 ) 36( b 1 + b 2 ) D s t ± Mc I c ± 768 M (9 p 2 ³ 64) d 3 ± 30.93 M d 3 ; c ± 4 r 3 p ± 2 d 3 p I c ± (9 p 2 ³ 64) r 4 72 p ± (9 p 2 ³ 64) d 4 1152 p D max. tensile stress s t ± Mc I C s t ± 85.24 M d 3 ; I C ± 3.234 * 10 ³ 3 d 4 I C ± c d 4 (4 p ´ 3 1 3 ) 768 ³ d 2 a p 12 b c d 2 a 1 3 p bd 2 d I C ± I x ³ A y bar 2 I x ± 0.02313
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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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