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
do​ = 40, di​ = 24 mmT = 2000 N·m

A hollow circular shaft with outer diameter 40 mm and inner diameter 24 mm carries a torque of 2000 N·m. Find the maximum shear stress τmax.

T = 2000 N·mdo = 40 mmdi = 24 mm
τmax = MPa
3.Medium
T = 250 N·md = 40 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 = 250 N·md = 40 mmL = 1.2 mG = 39 GPa
φ = °
4.Medium
d1​ = 25 mmd2​ = 20 mmT = 250 N·mABC2 m3 m

A stepped solid brass shaft is fixed at A. Segment AB has diameter 25 mm and length 2 m; segment BC has diameter 20 mm and length 3 m. A torque of 250 N·m acts at the free end C. Find the maximum shear stress τmax in the shaft.

T = 250 N·md1 = 25 mm, L1 = 2 md2 = 20 mm, L2 = 3 m
τmax = MPa
5.Hard
Td = ?

A solid shaft must transmit 10 kW at 1500 rpm without the shear stress exceeding 50 MPa. Find the smallest diameter d that works.

P = 10 kWN = 1500 rpmτallow = 50 MPa
d = mm
6.Hard
Tdo​ = 40 mm, di​ = 32 mm

A hollow shaft transmits 5 kW at 1000 rpm. Find the maximum shear stress τmax in the shaft.

P = 5 kWN = 1000 rpmdo = 40 mmdi = 32 mm
τmax = MPa

Answer key

  1. 1. τmax = 18.86 MPa
  2. 2. τmax = 182.9 MPa
  3. 3. φ = 1.754 °
  4. 4. τmax = 159.2 MPa
  5. 5. d = 18.65 mm
  6. 6. τmax = 6.436 MPa

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