03-03ChapGere.0019

# 03-03ChapGere.0019 - T 5 1100 N m(see figure If the...

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Stress Concentrations in Torsion The problems for Section 3.11 are to be solved by considering the stress-concentration factors. Problem 3.11-1 A stepped shaft consisting of solid circular segments having diameters D 1 5 2.0 in. and D 2 5 2.4 in. (see figure) is subjected to torques T . The radius of the fillet is R 5 0.1 in. If the allowable shear stress at the stress concentration is 6000 psi, what is the maximum permissible torque T max ? Solution 3.11-1 Stepped shaft in torsion 254 CHAPTER 3 Torsion T T R D 2 D 1 T T R D 2 D 1 D 1 5 2.0 in. D 2 5 2.4 in. R 5 0.1 in. t allow 5 6000 psi U SE FIG . 3-48 FOR THE STRESS - CONCENTRATION FACTOR T max < 6200 lb-in. 5 p (2.0 in.) 3 (6000 psi) 16(1.52) 5 6200 lb-in. T max 5 p D 1 3 t max 16 K K < 1.52 t max 5 K t nom 5 K ¢ 16 T max p D 1 3 R D 1 5 0.1 in. 2.0 in. 5 0.05 D 2 D 1 5 2.4 in. 2.0 in. 5 1.2 Problem 3.11-2 A stepped shaft with diameters D 1 5 40 mm and D 2 5 60 mm is loaded by torques
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Unformatted text preview: T 5 1100 N ? m (see figure). If the allowable shear stress at the stress concentration is 120 MPa, what is the smallest radius R min that may be used for the fillet? Solution 3.11-2 Stepped shaft in torsion T T R D 2 D 1 D 1 5 40 mm D 2 5 60 mm T 5 1100 N ? m t allow 5 120 MPa U SE F IG . 3-48 FOR THE STRESS-CONCENTRATION FACTOR From Fig. (3-48) with , we get ∴ R min < 0.10(40 mm) 5 4.0 mm R D 1 < 0.10 D 2 D 1 5 1.5 and K 5 1.37 D 2 D 1 5 60 mm 40 mm 5 1.5 K 5 p D 1 3 t max 16 T 5 p (40 mm) 3 (120 MPa) 16(1100 N # m) 5 1.37 t max 5 K t nom 5 K ¢ 16 T p D 1 3 ≤ Probs. 3.11-1 through 3.11-5 A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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