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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Unformatted text preview: Sec_3.4.qxd 284 9/27/08 1:09 PM Page 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 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 0.04 N m/m (torque per unit distance) acting along the entire length of the wire. T0 = torque Flexible tube B d A t (a) If the allowable shear stress in the wire is allow 30 MPa, what is the longest permissible length Lmax of the wire? (b) If the wire has length L 4.0 m and the shear modulus of elasticity for the wire is G 15 GPa, what is the angle of twist (in degrees) between the ends of the wire? Solution 3.4-19 Wire inside a flexible tube d 4 mm T0 0.2 N m t 0.04 N m/m (b) ANGLE OF TWIST L 1 (a) MAXIMUM LENGTH Lmax 30 MPa allow Equilibrium: T tL T0 16T From Eq. (3-12): tmax pd3 tL + T0 L Lmax 4 m G 15 GPa angle of twist due to distributed torque t 16tL2 pGd4 T pd3tmax 16 2 angle of twist due to torque T0 T0 L GIP pd 3tmax 16 (from problem 3.4-16) 32 T0 L pGd4 (from Eq. 3 -15) total angle of twist 1 1 (pd3tmax 16t 16T0) 1 (pd3tallow 16t 16T0) Substitute numerical values: Lmax f ; 4.42 m ; 16L pGd 4 2 (tL + 2T0) ; Substitute numerical values: 2.971 rad 170° ; T ...
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This note was uploaded on 12/22/2011 for the course MEEG 310 taught by Professor Staff during the Fall '11 term at University of Delaware.

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