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 = 25 mmT = ?

A solid circular shaft of diameter 25 mm is made of a material with an allowable shear stress of 50 MPa. Find the largest torque Tmax the shaft can carry.

d = 25 mmτallow = 50 MPa
Tmax = N·m
2.Easy
T = 400 N·md = 40 mm

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

T = 400 N·md = 40 mm
τmax = MPa
3.Medium
do​ = ?T = 2000 N·m

A hollow shaft must carry a torque of 2000 N·m. Its inner diameter is to be 0.5 times its outer diameter, and the shear stress must not exceed 80 MPa. Find the smallest outer diameter do.

T = 2000 N·mdi/do = 0.5τallow = 80 MPa
do = mm
4.Medium
d1​ = 60 mmd2​ = 30 mmT = 200 N·mABC1.5 m0.8 m

A stepped solid steel shaft is fixed at A. Segment AB has diameter 60 mm and length 1.5 m; segment BC has diameter 30 mm and length 0.8 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 = 1.5 md2 = 30 mm, L2 = 0.8 mG = 80 GPa
φC = °
5.Hard
Td = ?

A solid shaft must transmit 100 kW at 3000 rpm without the shear stress exceeding 60 MPa. Find the smallest diameter d that works.

P = 100 kWN = 3000 rpmτallow = 60 MPa
d = mm
6.Hard
d = 60 mmTB​ = 100 N·mTC​ = 500 N·mABC0.8 m2.5 m

A solid steel shaft of diameter 60 mm is fixed at A. A torque of 100 N·m acts at B, 0.8 m from A, and a torque of 500 N·m in the opposite direction acts at the free end C, a further 2.5 m along. Find the magnitude of the angle of twist φC of end C, in degrees.

d = 60 mmTB = 100 N·mTC = 500 N·mAB = 0.8 mBC = 2.5 mG = 80 GPa
φC = °

Answer key

  1. 1. Tmax = 153.4 N·m
  2. 2. τmax = 31.83 MPa
  3. 3. do = 51.4 mm
  4. 4. φC = 1.61 °
  5. 5. d = 30.01 mm
  6. 6. φC = 0.8837 °

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