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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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310 CHAPTER 3 Torsion Solution 3.8-10 Bar enclosed in a tube d 1 25.0 mm d 2 30.0 mm d 3 37.5 mm G 80 GPa P OLAR MOMENTS OF INERTIA Tube: I P 2 p 32 1 d 3 4 d 2 4 2 114.6229 * 10 9 m 4 Bar: I P 1 p 32 d 1 4 38.3495 * 10 9 m 4 T ORQUES IN THE BAR (1) AND TUBE (2) FROM E QS . (3-44 A AND B ) (a) M AXIMUM SHEAR STRESSES (b) A NGLE OF ROTATION OF END PLATE 1.03° (c) T ORSIONAL STIFFNESS ; k T T f 22.3 kN # m ; f T 1 L GI P 1 T 2 L GI P 2 0.017977 rad ; Tube: t 2 T 2 ( d 3 /2) I P 2 49.0 MPa ; Bar: t 1 T 1 ( d 1 /2) I P 1 32.7 MPa Tube: T 2 T a I P 2 I P 1 + I P 2 b 299.7217 N # m Bar: T 1 T a I P 1 I P 1 + I P 2 b 100.2783 N # m Problem 3.8-11 A solid steel bar of diameter d 1 1.50 in. is enclosed by a steel tube of outer diameter d 3 2.25 in. and inner diameter d 2 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
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