05-01ChapGere.0012

05-01ChapGere.0012 - 296 A-PDF Stresses in Beams (Basic...

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Problem 5.5-13 Determine the maximum tensile stress s t (due to pure bending by positive bending moments M ) for beams having cross sections as follows (see figure): (a) a semicircle of diameter d , and (b) an isosceles trapezoid with bases b 1 5 b and b 2 5 4 b /3, and altitude h . Solution 5.5-13 Maximum tensile stress 296 CHAPTER 5 Stresses in Beams (Basic Topics) CC h (a) (b) d b 2 b 1 (a) S EMICIRCLE From Appendix D, Case 10: s t 5 Mc I C 5 768 M (9 p 2 2 64) d 3 5 30.93 M d 3 c 5 4 r 3 p 5 2 d 3 p I C 5 p 2 2 64) r 4 72 p 5 p 2 2 64) d 4 1152 p (b) T RAPEZOID From Appendix D, Case 8: s t 5 Mc I C 5 360 M 73 bh 2 c 5 h (2 b 1 1 b 2 ) 3( b 1 1 b 2 ) 5 10 h 21 5 73 bh 3 756 I C 5 h 3 ( b 1 2 1 4 b 1 b 2 1 b 2 2 )
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