269_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

269_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: Sec_3.3.qxd 9/27/08 1:27 PM Page 263 263 SECTION 3.3 Circular Bars and Tubes Solution 3.3-15 d2 1.25 in. d1 0.625 in. a 12 ksi p 1 d24 d142 32 d2 2 d24 d12 1 tp 16 a d2 ta (a) MAX. PERMISSIBILE VALUE OF TORQUE T1max T1max T1max T1max ta taIp T1max d 2 1 tapd3 16 1 (12)p (1.25)3 16 ; 4.60 in.-k T1 – SOLID BAR p4 d 32 d 2 (b) MAX. PERMISSIBILE VALUE OF TORQUE T2 – HOLLOW BAR T2max T2max 4.31 in.-k T2max (c) PERCENT ; DECREASE IN TORQUE IN WEIGHT DUE TO HOLE IN & PERCENT DECREASE (b) percent decrease in torque T2max T1max (100) 6.25% T1max ; percent decrease in weight (weight is proportional to x-sec area) A1 d1 d2 p2 d 42 A2 A1 A1 (100) A2 p2 1d 42 d122 ; 25 % Problem 3.3-16 A hollow aluminum tube used in a roof structure has an outside diameter d2 104 mm and an inside diameter d1 82 mm (see figure). The tube is 2.75 m long, and the aluminum has shear modulus G 28 GPa. (a) If the tube is twisted in pure torsion by torques acting at the ends, what is the angle of twist (in degrees) when the maximum shear stress is 48 MPa? (b) What diameter d is required for a solid shaft (see figure) to resist the same torque with the same maximum stress? (c) What is the ratio of the weight of the hollow tube to the weight of the solid shaft? d1 d2 d ...
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