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 worksheetPractise 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
N = 1450 rpmT = ?

A motor delivers 15 kW to a shaft turning at 1450 rpm. Find the torque T in the shaft.

P = 15 kWN = 1450 rpm
T = N·m
2.Easy
T = 1500 N·md = 60 mm

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

T = 1500 N·md = 60 mm
τmax = MPa
3.Medium
d = 12 mmT = 20 N·m250 mmφ = 3.61°

In a torsion test, a solid specimen of diameter 12 mm is twisted by a torque of 20 N·m. The two ends of a gauge length of 250 mm rotate 3.61° relative to each other (the material is still elastic). Find the shear modulus G of the material.

T = 20 N·md = 12 mmL = 250 mmφ = 3.61°
G = GPa
4.Medium
T = 750 N·md = 30 mmL = 1.2 mφ = ?

A solid brass 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 = 750 N·md = 30 mmL = 1.2 mG = 39 GPa
φ = °
5.Hard
d = 40 mmT0​ = 100 N·mACBa = 1.5 mb = 0.5 m

A solid aluminium shaft of diameter 40 mm is fixed to rigid walls at both ends A and B. A torque of 100 N·m is applied at C, 1.5 m from A and 0.5 m from B. Find the angle of rotation φC of section C, in degrees.

d = 40 mmT0 = 100 N·ma = 1.5 mb = 0.5 mG = 26 GPa
φC = °
6.Hard
do​ = ?10 kW, 1500 rpm

A hollow shaft must transmit 10 kW at 1500 rpm. Its inner diameter is to be 0.8 times its outer diameter, and the shear stress must not exceed 75 MPa. Find the smallest outer diameter do.

P = 10 kWN = 1500 rpmdi/do = 0.8τallow = 75 MPa
do = mm

Answer key

  1. 1. T = 98.79 N·m
  2. 2. τmax = 35.37 MPa
  3. 3. G = 38.98 GPa
  4. 4. φ = 16.63 °
  5. 5. φC = 0.3288 °
  6. 6. do = 19.42 mm

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