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 motor delivers 30 kW to a shaft turning at 300 rpm. Find the torque T in the shaft.

P = 30 kWN = 300 rpm

T = N·m

2.Easy

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

T = 100 N·md = 20 mm

τ_max = MPa

3.Medium

A hollow shaft must carry a torque of 400 N·m. Its inner diameter is to be 0.6 times its outer diameter, and the shear stress must not exceed 50 MPa. Find the smallest outer diameter d_o.

T = 400 N·md_i/d_o = 0.6τ_allow = 50 MPa

d_o = mm

4.Medium

In a torsion test, a solid specimen of diameter 15 mm is twisted by a torque of 40 N·m. The two ends of a gauge length of 200 mm rotate 2.36° relative to each other (the material is still elastic). Find the shear modulus G of the material.

T = 40 N·md = 15 mmL = 200 mmφ = 2.36°

G = GPa

5.Hard

A solid shaft must transmit 5 kW at 1500 rpm without the shear stress exceeding 40 MPa. Find the smallest diameter d that works.

P = 5 kWN = 1500 rpmτ_allow = 40 MPa

d = mm

6.Hard

A solid steel shaft of diameter 60 mm is fixed at A. A torque of 500 N·m acts at B, 2.5 m from A, and a torque of 200 N·m in the opposite direction acts at the free end C, a further 2 m along. Find the maximum shear stress τ_max in the shaft.

d = 60 mmT_B = 500 N·mT_C = 200 N·mAB = 2.5 mBC = 2 m

τ_max = MPa

Answer key

1. T = 954.9 N·m
2. τ_max = 63.66 MPa
3. d_o = 36.04 mm
4. G = 39.08 GPa
5. d = 15.94 mm
6. τ_max = 7.074 MPa

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