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 shaft of diameter 50 mm carries a torque of 2000 N·m. Find the shear stress τ_ρ at a radius of 10 mm from the centre.

T = 2000 N·md = 50 mmρ = 10 mm

τ_ρ = MPa

2.Easy

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

T = 750 N·md = 30 mm

τ_max = 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 = 200 N·md = 30 mmL = 1.5 mG = 26 GPa

φ = °

4.Medium

In a torsion test, a solid specimen of diameter 12 mm is twisted by a torque of 40 N·m. The two ends of a gauge length of 400 mm rotate 5.63° relative to each other (the material is still elastic). Find the shear modulus G of the material.

T = 40 N·md = 12 mmL = 400 mmφ = 5.63°

G = GPa

5.Hard

A solid shaft must transmit 75 kW at 3000 rpm without the shear stress exceeding 50 MPa. Find the smallest diameter d that works.

P = 75 kWN = 3000 rpmτ_allow = 50 MPa

d = mm

6.Hard

A solid steel shaft transmits 75 kW at 500 rpm. The shear stress must not exceed 40 MPa and the twist must not exceed 0.5° per m of length. Find the smallest diameter d that satisfies both limits.

P = 75 kWN = 500 rpmτ_allow = 40 MPaθ_allow = 0.5°/mG = 80 GPa

d = mm

Answer key

1. τ_ρ = 32.59 MPa
2. τ_max = 141.5 MPa
3. φ = 8.314 °
4. G = 79.99 GPa
5. d = 28.97 mm
6. d = 67.61 mm

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