275_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

# 275_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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SECTION 3.4 Nonuniform Torsion 269 Problem 3.4-4 A solid circular bar ABC consists of two segments, as shown in the figure. One segment has diameter d 1 56 mm and length L 1 1.45 m; the other segment has diameter d 2 48 mm and length L 2 1.2 m. What is the allowable torque T allow if the shear stress is not to exceed 30 MPa and the angle of twist between the ends of the bar is not to exceed 1.25°? (Assume G 80 GPa.) L 1 L 2 T A B C d 1 d 2 T Solution 3.4-4 N UMERICAL DATA d 1 56 mm d 2 48 mm L 1 1450 mm L 2 1200 mm G 80 GPa a 30 MPa radians Allowable torque T allow based on shear stress T allow 651.441 N m # T allow t a p d 2 3 16 t max 16 T d 2 3 p f a 1.25 a p 180 b T allow based on angle of twist T allow 459 N m governs ; # T allow G f a L 1 a p 32 d 1 4 b + L 2 a p 32 d 2 4 b f max T G J L 1 a p 32 d 1 4 b + L 2 a p 32 d 2 4 b K Problem 3.4-5
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