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
d = 20 mmT = ?

A solid circular shaft of diameter 20 mm is made of a material with an allowable shear stress of 60 MPa. Find the largest torque Tmax the shaft can carry.

d = 20 mmτallow = 60 MPa
Tmax = N·m
2.Easy
T = 400 N·md = 50 mm

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

T = 400 N·md = 50 mm
τmax = MPa
3.Medium
d1​ = 60 mmd2​ = 30 mmT = 200 N·mABC1 m0.5 m

A stepped solid brass shaft is fixed at A. Segment AB has diameter 60 mm and length 1 m; segment BC has diameter 30 mm and length 0.5 m. A torque of 200 N·m acts at the free end C. Find the angle of twist φC of end C, in degrees.

T = 200 N·md1 = 60 mm, L1 = 1 md2 = 30 mm, L2 = 0.5 mG = 39 GPa
φC = °
4.Medium
do​ = ?T = 250 N·m

A hollow shaft must carry a torque of 250 N·m. Its inner diameter is to be 0.6 times its outer diameter, and the shear stress must not exceed 60 MPa. Find the smallest outer diameter do.

T = 250 N·mdi/do = 0.6τallow = 60 MPa
do = mm
5.Hard
Td = ?

A solid shaft must transmit 10 kW at 1800 rpm without the shear stress exceeding 75 MPa. Find the smallest diameter d that works.

P = 10 kWN = 1800 rpmτallow = 75 MPa
d = mm
6.Hard
d = 50 mmT0​ = 750 N·mACBa = 0.5 mb = 2 m

A solid steel shaft of diameter 50 mm is fixed to rigid walls at both ends A and B. A torque of 750 N·m is applied at C, 0.5 m from A and 2 m from B. Find the maximum shear stress τmax in the shaft.

d = 50 mmT0 = 750 N·ma = 0.5 mb = 2 m
τmax = MPa

Answer key

  1. 1. Tmax = 94.25 N·m
  2. 2. τmax = 16.3 MPa
  3. 3. φC = 2.078 °
  4. 4. do = 29 mm
  5. 5. d = 15.33 mm
  6. 6. τmax = 24.45 MPa

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