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313_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

# 313_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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SECTION 3.8 Statically Indeterminate Torsional Members 307 Problem 3.8-7 A stepped shaft ACB is held against rotation at ends A and B and subjected to a torque T 0 acting at section C (see figure). The two segments of the shaft ( AC and CB ) have diameters d A and d B , respectively, and polar moments of inertia I PA and I PB , respectively. The shaft has length L and segment AC has length a . (a) For what ratio a/L will the maximum shear stresses be the same in both segments of the shaft? (b) For what ratio a/L will the internal torques be the same in both segments of the shaft? ( Hint : Use Eqs. 3-45a and b of Example 3-9 to obtain the reactive torques.) Combine Eqs. (2) and (5) and solve for T 0 : (6) Substitute numerical values: ( T 0 ) CB 240.0 N m 1 16 p d B 3 t allow a 1 + L B d A 4 L A d B 4 b ( T 0 ) CB 1 16 p d B 3 t allow a 1 + L B I PA L A I PB b S EGMENT AC GOVERNS ( T 0 ) max 150 N m NOTE: From Eqs. (4) and (6) we find that which can be used as a partial check on the results.

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