317_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

317_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: Sec_3.8.qxd 9/27/08 1:13 PM Page 311 SECTION 3.8 Statically Indeterminate Torsional Members Solution 3.8-11 311 Bar enclosed in a tube TORQUES IN THE BAR (1) AND TUBE (2) FROM EQS. (3-44A AND B) Bar: T1 Ta IPI b IPI + IPI Ta Tube: T2 1187.68 lb-in. IP2 b IP1 + IP2 3812.32 lb-in. (a) MAXIMUM SHEAR STRESSES Bar: t1 T1(d1/2) IP1 T2(d3/2) IP2 Tube: t2 1790 psi 2690 psi ; ; (b) ANGLE OF ROTATION OF END PLATE d1 1.50 in. d2 11.6 6 1.75 in. d3 2.25 in. T1L GIP1 T 2L GIP2 POLAR MOMENTS OF INERTIA 0.354° ; p4 d 32 1 (c) TORSIONAL STIFFNESS G Bar: IP1 Tube: IP2 f 10 psi p4 1d 32 3 0.497010 in.4 4 d2 2 kT 4 1.595340 in. T f 809 k- in. T Problem 3.8-12 The composite shaft shown in the figure is manufactured by shrink-fitting a steel sleeve over a brass core so that the two parts act as a single solid bar in torsion. The outer diameters of the two parts are d1 40 mm for the brass core and d2 50 mm for the steel sleeve. The shear moduli of elasticity are Gb 36 GPa for the brass and Gs 80 GPa for the steel. 0.006180015 rad ; Steel sleeve Brass core T Assuming that the allowable shear stresses in the brass and steel are 48 MPa and s 80 MPa, respectively, determine the maximum permissible torque Tmax that may be applied to the shaft. (Hint: Use Eqs. 3-44a and b to find the torques.) b d1 d2 Probs. 3.8-12 and 3.8-13 Solution 3.8-12 Composite shaft shrink fit d1 d2 GB 40 mm 50 mm 36 GPa GS 80 GPa Allowable stresses: 48 MPa S 80 MPa B ...
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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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