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03-02ChapGere.0011

03-02ChapGere.0011 - Aluminum tube d 1 5 50 mm G 5 27 GPa T...

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Problem 3.5-9 A solid steel bar ( G 5 11.8 3 10 6 psi) of diameter d 5 2.0 in. is subjected to torques T 5 8.0 k-in. acting in the directions shown in the figure. (a) Determine the maximum shear, tensile, and compressive stresses in the bar and show these stresses on sketches of properly oriented stress elements. (b) Determine the corresponding maximum strains (shear, tensile, and compressive) in the bar and show these strains on sketches of the deformed elements. 214 CHAPTER 3 Torsion Problem 3.5-8 An aluminum tube has inside diameter d 1 5 50 mm, shear modulus of elasticity G 5 27 GPa, and torque T 5 4.0 kN ? m. The allowable shear stress in the aluminum is 50 MPa and the allowable normal strain is 900 3 10 2 6 . Determine the required outside diameter d 2 . Solution 3.5-8
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Unformatted text preview: Aluminum tube d 1 5 50 mm G 5 27 GPa T 5 4.0 kN ? m t allow 5 50 MPa e allow 5 900 3 10 2 6 Determine the required diameter d 2 . A LLOWABLE SHEAR STRESS ( t allow ) 1 5 50 MPa A LLOWABLE SHEAR STRESS BASED ON NORMAL STRAIN ( t allow ) 2 5 2 G e allow 5 2(27 GPa)(900 3 10 2 6 ) 5 48.6 MPa e max 5 g 2 5 t 2 G Ê t 5 2 G e max N ORMAL STRAIN GOVERNS t allow 5 48.60 MPa R EQUIRED DIAMETER Rearrange and simplify: Solve numerically: d 2 5 79.3 mm d 2 5 0.07927 m d 2 4 2 (419.174 3 10 2 6 ) d 2 2 6.25 3 10 2 6 5 t 5 Tr I P Ê 48.6 MPa 5 (4000 N # m)( d 2 / 2) p 32 [ d 2 4 2 (0.050 m) 4 ] T T d 2 d 1 T T = 8.0 k-in. d = 2.0 in. A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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