265_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

# 265_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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SECTION 3.3 Circular Bars and Tubes 259 Problem 3.3-10 The steel axle of a large winch on an ocean liner is subjected to a torque of 1.65 kN ± m (see figure). What is the minimum required diameter d min if the allowable shear stress is 48 MPa and the allowable rate of twist is 0.75°/m? (Assume that the shear modulus of elasticity is 80 GPa.) T T d Solution 3.3-10 N UMERICAL DATA T ² 1.65 kN m ³ a ² 48 MPa G ² 80 GPa MIN . REQUIRED DIAMETER OF SHAFT BASED ON ALLOWABLE RATE OF TWIST d min ² a 32 T p G u a b 1 4 d 4 ² 32 T p G u a p 32 d 4 ² T G u I p ² T G u u ² T GI p u a ² 0.75 a p 180 b rad m # d min ² 0.063 m d min ² 63.3 mm ^ governs M IN . REQUIRED DIAMETER OF SHAFT BASED ON ALLOWABLE SHEAR STRESS d min ² 0.056 m d min ² 55.9 mm d min ² c 16 T pt a d 1 3 t ² Td 2 a p 32 d 4 b t ² Td 2 I p ; Problem 3.3-11 A hollow steel shaft used in a construction auger has
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Unformatted text preview: outer diameter d 2 ² 6.0 in. and inner diameter d 1 ² 4.5 in. (see figure). The steel has shear modulus of elasticity G ² 11.0 ´ 10 6 psi. For an applied torque of 150 k-in., determine the following quantities: (a) shear stress 2 at the outer surface of the shaft, (b) shear stress 1 at the inner surface, and (c) rate of twist µ (degrees per unit of length). Also, draw a diagram showing how the shear stresses vary in magnitude along a radial line in the cross section. d 2 d 1 d 2 Sec_3.3.qxd 9/27/08 1:27 PM Page 259...
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