(Solved): Problem 3.3-16 A hollow aluminum tube used in a roof structure has an outside diameter d. - 104 mm ...

Problem 3.3-16 A hollow aluminum tube used in a roof structure has an outside diameter d. - 104 mm and an inside diameter d, - 82 mm (see figure). The tube is 2.75 m long, and the aluminum has shear modulus G-28 GPa (a) If the tube is twisted in pure torsion by torques acting at the ends, what is the angle of twist (in degrees) when the maximum shear stress is 48 MPa? (b) What diameter d is required for a solid shaft (see figure) to resist the same torque with the same maximum stress? (c) What is the ratio of the weight of the hollow tube to the weight of the solid shaft? Solution 3.3-16 NUMERICAL DATA d? - 104 mm d?-82 mm L-2.75 x 10¹ mm G=28 GPa 1,- (m/32)(d?-4;¹) 1?-7.046 x 10 mm (a) FIND ANGLE OF TWIST 48 MPa 21 6= *-(1) 6= 21 6 = (max) Gdy -0.091 rad -5.19? (b) REPLACE HOLLOW SHAFT WITH SOLID SHAFT-FIND DIAMETER 16T That Set as expression equal to Ta 327d? 4?- Then solve for d dong88.4 mm (c) RATIO OF WEIGHTS OF HOLLOW AND SOLID SHAFTS WEIGHT IS PROPORTIONAL TO CROSS-SECTIONAL AREA A?-(d2²-4²) 0.524 So the weight of the tube is 52% of the solid shaft, but they resist the same torque. Problem 3.3-16 A hollow aluminum tube used in a roof structure has an outside diameter d? - 104 mm and an inside diameter d, - 82 mm (see figure). The tube is 2.75 m long, and the aluminum has shear modulus G-28 GP. (a) If the tube is twisted in pure torsion by torques acting at the ends, what is the angle of twist (in degrees) when the maximum shear stress is 48 MPa? (b) What diameter d is required for a solid shaft (see figure) to resist the same torque with the same maximum stress? (c) What is the ratio of the weight of the hollow tube to the weight of the solid shaft?