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430_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

# 430_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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424 CHAPTER 5 Stresses in Beams (Basic Topics) Solution 5.6-17 Ratio of weights of three beams Beam 1: Rectangle Beam 2: Square ( ) Beam 3: Circle are the same in all three beams. Since and are the same, the section moduli must be the same. (1) R ECTANGLE : A 1 2 b 2 2 a 3 S 2 b 2/3 2.6207 S 2/3 S bh 2 6 2 b 3 3 b a 3 S 2 b 1/3 s M S section modulus S M s L , g , M max , and s max ( d diameter) a side dimension ( h 2 b ) (2) S QUARE : (3) C IRCLE : Weights are proportional to the cross-sectional areas (since and are the same in all 3 cases). W 1 : W 2 : W 3 1 : 1.260 : 1.408 ; A 1 : A 2 : A 3 2.6207 : 3.3019 : 3.6905 W 1 : W 2 : W 3 A 1 : A 2 : A 3 g L A 3 p d 2 4 p 4 a 32 S p b 2/3 3.6905 S 2/3 S p d 3 32 d a 32 S p b 1/3 A 2 a 2 (6 S ) 2/3 3.3019 S 2/3 S a 3 6 a (6 S ) 1/3 Solution 5.6-16 N UMERICAL DATA take 1st moments to find distances 1st moments about base c 1 1 2 11385 186 t + t 2 131 + t c 1 55 t 2 (152 2 t ) ( t ) + 2.55 t a 55 2 b 2.55 t + t (152 2 t ) c 2 t 2 (152 2 t ) ( t ) + 2.55 t a 55 2 b 2.55 t + t (152 2 t ) c 1 b c 2 c 2 t 2 ( h 2 t ) ( t ) + 2 bt a b 2 b 2 bt + t ( h 2 t ) c 1 & c 2 h 152 mm b 55 mm ratio of top to bottom stresses
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