Solved Problems

Problem: A solid steel shaft with a diameter of 50 mm is subjected to a torque of 2 kN$\cdot$m. Determine the maximum shear stress in the shaft.

Problem: A hollow aluminum shaft ($G = 26$ GPa) has an outer diameter of 80 mm and an inner diameter of 60 mm. If the shaft is 2 m long and subjected to a torque of 1.5 kN$\cdot$m, determine the angle of twist in degrees.

Problem: A solid steel shaft transmits 50 kW of power at 4 Hz (240 rpm). If the allowable shear stress is 60 MPa, determine the minimum required diameter of the shaft.

Problem: A composite shaft consists of a steel segment (length 1 m, diameter 50 mm, $G_{st} = 80$ GPa) and an aluminum segment (length 1.5 m, diameter 40 mm, $G_{al} = 26$ GPa) connected end-to-end. The shaft is fixed at one end and subjected to a torque of 800 N$\cdot$m at the free end. Determine the total angle of twist.

Problem: A thin-walled rectangular steel tube has outer dimensions of $100 \text{ mm} \times 150 \text{ mm}$ and a uniform wall thickness of $5 \text{ mm}$. It is subjected to a torque of $5 \text{ kN}\cdot\text{m}$. Determine the average shear stress in the wall.

Problem: A solid steel shaft ($G = 80 \text{ GPa}$) is $1 \text{ m}$ long and has a diameter of $40 \text{ mm}$. It is fixed at both ends (A and B). A torque of $500 \text{ N}\cdot\text{m}$ is applied at point C, which is $0.4 \text{ m}$ from A. Determine the reaction torques at A and B.

Problem: A flanged bolt coupling consists of six 10-mm diameter steel bolts on a bolt circle 300 mm in diameter. The bolts connect two solid steel shafts that transmit 60 kW of power at 150 rev/min. Calculate the maximum shear stress developed in the bolts.

Problem: A closely coiled helical spring is subjected to an axial load of 300 N. The spring wire has a diameter of 10 mm and the mean coil diameter is 100 mm. Assuming the spring has 15 active coils and a shear modulus $G = 83 \text{ GPa}$, determine the maximum shear stress and the elongation of the spring. Use the Wahl correction factor.