Concept explainers
A magnesium-alloy wire of diameter d = 4mm and length L rotates inside a flexible tube in order to open or close a switch from a remote location (see figure). A torque Tis applied manually (either clockwise or counterclockwise) at end 5, 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 T0 = 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 = 0.04N − m/m (torque per unit distance) acting along the entire length of the wire.
(a)
If the allowable shear stress in the wire is T allow = 30 MPa, what is the longest permissible length Lmaxof the wire?
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Mechanics of Materials (MindTap Course List)
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- Mechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage Learning