A torque of 30 lb·in. is applied to one end of a 5-in.-long composite shaft that consists of two polymer tubes. The outer tube has a polar moment of inertia of 0.0306 in.4 and a shear modulus of 175 ksi. The inner tube has a polar moment of inertia of 0.00365 in.4 and a shear modulus of 160 ksi. Determine the magnitude of the torque produced in the outer tube.

A dump truck axle with a diameter of 1.787 in. and a length of 37.5 in. failed when the shear stress reached 85 ksi on the outer surface. The shear modulus of the steel is G = 11,900 ksi. Assuming the shaft did not yield prior to failure, determine the angle of twist of the axle when it failed.

A load of P = 10 N is applied to a hex wrench that has lengths a = 35 mm and b = 121 mm. Determine the torque applied to the set screw.

A dump truck axle with a diameter of 1.76 in. and a length of 36 in. failed while transmitting a power of 540 hp and a torque of 6,960 lb-ft. At what speed was the axle spinning when it broke?

A steel socket extension (2) has a diameter of 0.48 in. and a length of L = 1.8 in. It connects socket (3) to ratchet handle (1) which is 6.8 in. long. If a perpendicular force of 19 lb is applied to the end of the ratchet handle, determine the socket extension’s angle of twist.

A steel socket extension (2) has a diameter of 0.32 in. and a length of L = 2.0 in. It connects socket (3) to ratchet handle (1) which is 5.3 in. long. If a perpendicular force of 5.0 lb is applied to the end of the ratchet handle, determine the socket extension’s angle of twist.

A dump truck axle with a diameter of 1.621 in. and a length of 38.0 in. failed when the shear stress reached 80 ksi on the outer surface. The shear modulus of the steel is G = 11,300 ksi. Assuming the shaft did not yield prior to failure, determine the angle of twist of the axle when it failed.

A torque of 22 lb·in. is applied to one end of a 6-in.-long composite shaft that consists of two polymer tubes. The outer tube has a polar moment of inertia of 0.0355 in.4 and a shear modulus of 180 ksi. The inner tube has a polar moment of inertia of 0.00701 in.4 and a shear modulus of 165 ksi. Determine the magnitude of the torque produced in the inner tube.

A steel socket extension (2) has a diameter of 0.62 in. and a length of L = 1.3 in. It connects socket (3) to ratchet handle (1) which is 8.6 in. long. If a perpendicular force of 24.0 lb is applied to the end of the ratchet handle, determine the maximum shear stress in the socket extension.

A steel socket extension (2) has a diameter of 0.62 in. and a length of L = 1.3 in. It connects socket (3) to ratchet handle (1) which is 8.9 in. long. If a perpendicular force of 23.0 lb is applied to the end of the ratchet handle, determine the socket extension’s angle of twist.