345_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

345_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: Sec_3.9-3.11.qxd 9/27/08 1:14 PM Page 339 339 SECTION 3.11 Stress Concentrations in Torsion Problem 3.11-3 A full quarter-circular fillet is used at the shoulder of a stepped shaft having diameter D2 1.0 in. (see figure). A torque T 500 lb-in. acts on the shaft. Determine the shear stress max at the stress concentration for values as follows: D1 5 0.7, 0.8, and 0.9 in. Plot a graph showing max versus D1. Solution 3.11-3 Stepped shaft in torsion D1 (in.) R/D1 K 1.43 1.25 1.11 0.15 0.10 0.05 0.214 0.125 0.056 1.20 1.29 1.41 max(psi) 8900 6400 4900 1.0 in. T R(in.) 0.7 0.8 0.9 D2 D2/D1 500 lb-in. D1 0.7, 0.8, and 0.9 in. Full quarter-circular fillet (D2 R D1 D2 2 D1 2R) D1 2 0.5 in. USE FIG. 3-48 FOR THE STRESS-CONCENTRATION FACTOR tmax Kt nom K Ka 16 T pD3 1 16(500 lb-in.) pD3 1 b 2546 K D3 1 NOTE that max gets smaller as D1 gets larger, even though K is increasing. Problem 3.11-4 The stepped shaft shown in the figure is required to transmit 600 kW of power at 400 rpm. The shaft has a full quarter-circular fillet, and the smaller diameter D1 100 mm. If the allowable shear stress at the stress concentration is 100 MPa, at what diameter D2 will this stress be reached? Is this diameter an upper or a lower limit on the value of D2? ...
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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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