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298_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

# 298_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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292 CHAPTER 3 Torsion Problem 3.5-8 An aluminium tube has inside diameter d 1 50 mm, shear modulus of elasticity G 27 GPa, and torque T 4.0 kN m. The allowable shear stress in the aluminum is 50 MPa and the allowable normal strain is 900 10 6 . Determine the required outside diameter d 2 . Solution 3.5-8 Aluminum tube d 1 50 mm G 27 GPa T 4.0 kN m allow 50 MPa allow 900 10 6 Determine the required diameter d 2 . A LLOWABLE SHEAR STRESS ( allow ) 1 50 MPa A LLOWABLE SHEAR STRESS BASED ON NORMAL STRAIN ( allow ) 2 2 G allow 2(27 GPa)(900 10 6 ) 48.6 MPa â max g 2 t 2 G t 2 G â max N ORMAL STRAIN GOVERNS allow 48.60 MPa R EQUIRED DIAMETER Rearrange and simplify: Solve numerically: d 2 0.07927 m d

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298_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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