293_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

293_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: Sec_3.5-3.7.qxd 9/27/08 1:10 PM Page 287 287 SECTION 3.5 Pure Shear Pure Shear Problem 3.5-1 A hollow aluminum shaft (see figure) has outside diameter d2 4.0 in. and inside diameter d1 2.0 in. When twisted by torques T, the shaft has an angle of twist per unit distance equal to 0.54°/ft. The shear modulus of elasticity of the aluminum is G 4.0 106 psi. d2 T T L (a) Determine the maximum tensile stress max in the shaft. (b) Determine the magnitude of the applied torques T. d1 d2 Probs. 3.5-1, 3.5-2, and 3.5-3 Solution 3.5-1 Hollow aluminum shaft d2 4.0 in. G 4.0 d1 2.0 in. (a) MAXIMUM TENSILE STRESS 0.54°/ft 106 psi max max MAXIMUM SHEAR STRESS max Gr (from Eq. 3-7a) r d2 /2 u max (4.0 max 6280 psi ; 2.0 in. 10 6 6283.2 psi Use the torsion formula tmax T rad/in. 106 psi)(2.0 in.)(785.40 max. (b) APPLIED TORQUE 1 ft prad (0.54°/ft) a ba b 12 in. 180 degree 785.40 occurs on a 45° plane and is equal to 10 6 tmaxIP r IP p [(4.0 in.)4 32 23.562 in.4 rad/in.) T (6283.2 psi) (23.562 in.4) 2.0 in. 74,000 lb-in. Tr IP ; (2.0 in.)4] ...
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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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