316_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

316_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: Sec_3.8.qxd 9/27/08 310 1:13 PM Page 310 CHAPTER 3 Torsion Solution 3.8-10 Bar enclosed in a tube TORQUES IN THE BAR (1) AND TUBE (2) FROM EQS. (3-44A AND B) Bar: T1 Ta IP1 b IP1 + IP2 Ta Tube: T2 100.2783 N # m IP2 b IP1 + IP2 299.7217 N # m (a) MAXIMUM SHEAR STRESSES Bar: t1 Tube: t2 d1 25.0 mm G d2 30.0 mm d3 37.5 mm POLAR MOMENTS OF INERTIA Bar: IP1 Tube: IP2 p 1d 4 32 3 38.3495 * 10 4 d22 T2(d3/2) IP2 4 m 114.6229 * 10 T1L GIP1 T 2L GIP2 1.03° f 9 32.7 MPa 49.0 MPa ; ; (b) ANGLE OF ROTATION OF END PLATE 80 GPa p4 d 32 1 T1(d1/2) IP1 ; 0.017977 rad (c) TORSIONAL STIFFNESS 9 m4 kT T f Problem 3.8-11 A solid steel bar of diameter d1 1.50 in. is enclosed by a steel tube of outer diameter d3 2.25 in. and inner diameter d2 1.75 in. (see figure). Both bar and tube are held rigidly by a support at end A and joined securely to a rigid plate at end B. The composite bar, which has length L 30.0 in., is twisted by a torque T 5000 lb-in. acting on the end plate. (a) Determine the maximum shear stresses 1 and 2 in the bar and tube, respectively. (b) Determine the angle of rotation (in degrees) of the end plate, assuming that the shear modulus of the steel is G 11.6 106 psi. (c) Determine the torsional stiffness kT of the composite bar. (Hint: Use Eqs. 3-44a and b to find the torques in the bar and tube.) 22.3 kN # m ; Tube A B T Bar End plate L d1 d2 d3 ...
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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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