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 = 50 mmT = ?

A solid circular shaft of diameter 50 mm is made of a material with an allowable shear stress of 40 MPa. Find the largest torque Tmax the shaft can carry.

d = 50 mmτallow = 40 MPa
Tmax = N·m
2.Easy
d = 25 mmT = ?

A solid circular shaft of diameter 25 mm is made of a material with an allowable shear stress of 40 MPa. Find the largest torque Tmax the shaft can carry.

d = 25 mmτallow = 40 MPa
Tmax = N·m
3.Medium
do​ = 60, di​ = 42 mmT = 100 N·mL = 1.5 m

A hollow aluminium shaft (outer diameter 60 mm, inner diameter 42 mm, length 1.5 m) is fixed at one end and twisted by a torque of 100 N·m at the other. Find the angle of twist φ in degrees.

T = 100 N·mdo = 60 mmdi = 42 mmL = 1.5 mG = 26 GPa
φ = °
4.Medium
d = 15 mmT = 75 N·m300 mmφ = 9.98°

In a torsion test, a solid specimen of diameter 15 mm is twisted by a torque of 75 N·m. The two ends of a gauge length of 300 mm rotate 9.98° relative to each other (the material is still elastic). Find the shear modulus G of the material.

T = 75 N·md = 15 mmL = 300 mmφ = 9.98°
G = GPa
5.Hard
do​ = ?50 kW, 500 rpm

A hollow shaft must transmit 50 kW at 500 rpm. Its inner diameter is to be 0.5 times its outer diameter, and the shear stress must not exceed 50 MPa. Find the smallest outer diameter do.

P = 50 kWN = 500 rpmdi/do = 0.5τallow = 50 MPa
do = mm
6.Hard
do​ = ?75 kW, 1800 rpm

A hollow shaft must transmit 75 kW at 1800 rpm. Its inner diameter is to be 0.6 times its outer diameter, and the shear stress must not exceed 80 MPa. Find the smallest outer diameter do.

P = 75 kWN = 1800 rpmdi/do = 0.6τallow = 80 MPa
do = mm

Answer key

  1. 1. Tmax = 981.7 N·m
  2. 2. Tmax = 122.7 N·m
  3. 3. φ = 0.3419 °
  4. 4. G = 25.99 GPa
  5. 5. do = 46.99 mm
  6. 6. do = 30.76 mm

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