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.

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1.Easy
T = 100 N·md = 30 mm

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

T = 100 N·md = 30 mm
τmax = MPa
2.Easy
N = 3000 rpmT = ?

A motor delivers 45 kW to a shaft turning at 3000 rpm. Find the torque T in the shaft.

P = 45 kWN = 3000 rpm
T = N·m
3.Medium
do​ = ?T = 1500 N·m

A hollow shaft must carry a torque of 1500 N·m. Its inner diameter is to be 0.7 times its outer diameter, and the shear stress must not exceed 75 MPa. Find the smallest outer diameter do.

T = 1500 N·mdi/do = 0.7τallow = 75 MPa
do = mm
4.Medium
do​ = ?T = 2000 N·m

A hollow shaft must carry a torque of 2000 N·m. Its inner diameter is to be 0.7 times its outer diameter, and the shear stress must not exceed 80 MPa. Find the smallest outer diameter do.

T = 2000 N·mdi/do = 0.7τallow = 80 MPa
do = mm
5.Hard
d = 40 mmT0​ = 1500 N·mACBa = 1.5 mb = 1.2 m

A solid brass shaft of diameter 40 mm is fixed to rigid walls at both ends A and B. A torque of 1500 N·m is applied at C, 1.5 m from A and 1.2 m from B. Find the reaction torque TA at wall A.

d = 40 mmT0 = 1500 N·ma = 1.5 mb = 1.2 m
TA = N·m
6.Hard
Td = ?

A solid shaft must transmit 20 kW at 1500 rpm without the shear stress exceeding 50 MPa. Find the smallest diameter d that works.

P = 20 kWN = 1500 rpmτallow = 50 MPa
d = mm

Answer key

  1. 1. τmax = 18.86 MPa
  2. 2. T = 143.2 N·m
  3. 3. do = 51.18 mm
  4. 4. do = 55.13 mm
  5. 5. TA = 666.7 N·m
  6. 6. d = 23.49 mm

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