Torsion of shafts worksheet with answers

Free printable Torsion of shafts worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

New worksheet Practise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________ Date: ____________

1.Easy

A solid circular shaft carries a torque T. Find the maximum shear stress τ_max in the shaft.

T = 1500 N·md = 60 mm

τ_max = MPa

2.Easy

A solid shaft of diameter 30 mm carries a torque of 200 N·m. Find the shear stress τ_ρ at a radius of 7.5 mm from the centre.

T = 200 N·md = 30 mmρ = 7.5 mm

τ_ρ = MPa

3.Medium

A solid aluminium shaft is fixed at the wall and twisted by a torque T at its free end. Find the angle of twist φ of the free end, in degrees.

T = 100 N·md = 50 mmL = 1 mG = 26 GPa

φ = °

4.Medium

A hollow aluminium shaft (outer diameter 60 mm, inner diameter 45 mm, length 1.5 m) is fixed at one end and twisted by a torque of 500 N·m at the other. Find the angle of twist φ in degrees.

T = 500 N·md_o = 60 mmd_i = 45 mmL = 1.5 mG = 26 GPa

φ = °

5.Hard

A hollow shaft must transmit 15 kW at 1500 rpm. Its inner diameter is to be 0.75 times its outer diameter, and the shear stress must not exceed 80 MPa. Find the smallest outer diameter d_o.

P = 15 kWN = 1500 rpmd_i/d_o = 0.75τ_allow = 80 MPa

d_o = mm

6.Hard

A hollow shaft must transmit 10 kW at 1500 rpm. Its inner diameter is to be 0.75 times its outer diameter, and the shear stress must not exceed 80 MPa. Find the smallest outer diameter d_o.

P = 10 kWN = 1500 rpmd_i/d_o = 0.75τ_allow = 80 MPa

d_o = mm

Answer key

1. τ_max = 35.37 MPa
2. τ_ρ = 18.86 MPa
3. φ = 0.3591 °
4. φ = 1.9 °
5. d_o = 20.72 mm
6. d_o = 18.1 mm

Full step-by-step solutions: practise this topic on examproblems.com.