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290_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

# 290_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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284 CHAPTER 3 Torsion Problem 3.4-19 A magnesium-alloy wire of diameter d 4 mm and length L rotates inside a flexible tube in order to open or close a switch from a remote location (see figure). A torque T is applied manually (either clockwise or counterclockwise) at end B , thus twisting the wire inside the tube. At the other end A , the rotation of the wire operates a handle that opens or closes the switch. A torque T 0 0.2 N m is required to operate the switch. The torsional stiffness of the tube, combined with friction between the tube and the wire, induces a distributed torque of constant intensity t 0.04 N m/m (torque per unit distance) acting along the entire length of the wire. (a) If the allowable shear stress in the wire is allow 30 MPa, what is the longest permissible length L max of the wire? (b) If the wire has length L 4.0 m and the shear modulus of

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290_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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