508_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

508_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: 06Ch06.qxd 502 9/24/08 5:32 AM Page 502 CHAPTER 6 Stresses in Beams (Advanced Topics) (c) MAXIMUM APPLIED MOMENT MAXIMUM UNIFORM DISTRIBUTED LOAD From Mallow qmax L 3L qmax a b a b + M0 2 4 ; 665lb/ft L 3L q a b a b + Mo_max 2 4 From Mallow M0_max ; 486 lb-ft y Problem 6.2-6 A plastic-lined steel pipe has the cross-sectional shape shown in the figure. The steel pipe has outer diameter d3 100 mm and inner diameter d2 94 mm. The plastic liner has inner diameter d1 82 mm. The modulus of elasticity of the steel is 75 times the modulus of the plastic. Determine the allowable bending moment Mallow if the allowable stress in the steel is 35 MPa and in the plastic is 600 kPa. z d1 C Solution 6.2-6 Steel pipe with plastic liner MAXIMUM MOMENT BASED UPON THE STEEL (1) From Eq. (6-6a): Mmax (s1)allow c (s1)allow E1I1 + E2I2 d (d3/2)E1 (E1/E2)I1 + I2 (d3/2)(E1/E2) 768 N # m MAXIMUM MOMENT BASED UPON THE PLASTIC (2) (1) Pipe: ds Es (s1)allow (2) Liner: d2 Ep 100 mm E1 d2 94 mm From Eq. (6-6b): modulus of elasticity Mmax 35 MPa 94 mm E2 (s2)allow d1 (s2)allow c 32 mm modulus of elasticity STEEL GOVERNS. 600 kPa E1 75E2 E1/E2 I1 p4 (d 64 3 d 4) 2 1.076 * 10 I2 p4 (d 64 2 d 4) 1 1.613 * 10 (s2)allow c 75 6 6 m4 m4 E1I1 + E2I2 d (d2/2)E2 (E1/E2)I1 + I2 d (d2/2) Mallow 1051 N # m 768 N # m ; d2 d3 ...
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