344_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

344_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: Sec_3.9-3.11.qxd 338 9/27/08 1:14 PM Page 338 CHAPTER 3 Torsion Stress Concentrations in Torsion D2 The problems for Section 3.11 are to be solved by considering the stress-concentration factors. R D1 T Problem 3.11-1 A stepped shaft consisting of solid circular T segments having diameters D1 2.0 in. and D2 2.4 in. (see figure) is subjected to torques T. The radius of the fillet is R 0.1 in. If the allowable shear stress at the stress concentration is 6000 psi, what is the maximum permissible torque Tmax? Probs. 3.11-1 through 3.11-5 Solution 3.11-1 Stepped shaft in torsion USE FIG. 3-48 FOR THE STRESS-CONCENTRATION FACTOR R D1 K D1 2.0 in. D2 1.52 0.1 in. allow 6000 psi D2 D1 0.05 Tmax Tmax 2.4 in. 2.0 in. Ka Kt nom tmax pD3tmax 1 16K p(2.0 in.)3(6000 psi) 16(1.52) 2.4 in. R 0.1 in. 2.0 in. 1.2 16 Tmax pD3 1 b 6200 lb-in. ; 6200 lb-in. Problem 3.11-2 A stepped shaft with diameters D1 40 mm and D2 60 mm is loaded by torques T 1100 N m (see figure). If the allowable shear stress at the stress concentration is 120 MPa, what is the smallest radius Rmin that may be used for the fillet? Solution 3.11-2 Stepped shaft in torsion USE FIG. 3-48 FOR THE STRESS-CONCENTRATION FACTOR tmax Kt nom K D1 40 mm D2 60 mm T allow 1100 N m D2 D1 Ka 16T pD3 1 pD3tmax 1 16 T 60 mm 40 mm From Fig. (3-48) with 120 MPa we get Rmin b p(40 mm)3(120 MPa) 16(1100 N # m) 1.5 D2 D1 1.5 and K R L 0.10 D1 0.10(40 mm) 4.0 mm ; 1.37, 1.37 ...
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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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