320_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

320_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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314 CHAPTER 3 Torsion (a) Determine the allowable torque T 1 that may be applied to the ends of the shaft if the angle of twist between the ends is limited to 8.0°. (b) Determine the allowable torque T 2 if the shear stress in the brass is limited to ± b ² 70 MPa. (c) Determine the allowable torque T 3 if the shear stress in the steel is limited to s ² 110 MPa. (d) What is the maximum allowable torque T max if all three of the preceding conditions must be satisfied? Solution 3.8-14 d 2 d 1 T A BC T = 2.0 m Steel shaft Steel shaft Brass sleeve Brass sleeve 1.0 m = 2.0 m d 2 = 90 mm d 1 = 70 mm L 2 L 2 d 2 d 1 d 1 statics T b ² T 1 ³ T s now find twist of 3 segments: ´ ² T 1 L 4 G b I Pb + T s L 4 G s I Ps + T 1 L 2 G s I Ps T b ² T 1 a G b I Pb G s I Ps + G b I Pb b (a) A LLOWABLE TORQUE T 1 BASED ON TWIST AT ENDS OF 8 DEGREES First find torques in steel ( T s ) & brass ( T b ) in segment in which they are joined - 1 degree stat-indet; use
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