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 = 25 mm

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

T = 100 N·md = 25 mm
τmax = MPa
2.Easy
do​ = 30, di​ = 23 mmT = 400 N·m

A hollow circular shaft with outer diameter 30 mm and inner diameter 23 mm carries a torque of 400 N·m. Find the maximum shear stress τmax.

T = 400 N·mdo = 30 mmdi = 23 mm
τmax = MPa
3.Medium
d1​ = 60 mmd2​ = 30 mmT = 750 N·mABC2.5 m1.2 m

A stepped solid brass shaft is fixed at A. Segment AB has diameter 60 mm and length 2.5 m; segment BC has diameter 30 mm and length 1.2 m. A torque of 750 N·m acts at the free end C. Find the angle of twist φC of end C, in degrees.

T = 750 N·md1 = 60 mm, L1 = 2.5 md2 = 30 mm, L2 = 1.2 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 0.8 times its outer diameter, and the shear stress must not exceed 75 MPa. Find the smallest outer diameter do.

T = 250 N·mdi/do = 0.8τallow = 75 MPa
do = mm
5.Hard
do​ = ?10 kW, 500 rpm

A hollow shaft must transmit 10 kW at 500 rpm. Its inner diameter is to be 0.7 times its outer diameter, and the shear stress must not exceed 40 MPa. Find the smallest outer diameter do.

P = 10 kWN = 500 rpmdi/do = 0.7τallow = 40 MPa
do = mm
6.Hard
Td = ?

A solid shaft must transmit 100 kW at 500 rpm without the shear stress exceeding 50 MPa. Find the smallest diameter d that works.

P = 100 kWN = 500 rpmτallow = 50 MPa
d = mm

Answer key

  1. 1. τmax = 32.59 MPa
  2. 2. τmax = 115.3 MPa
  3. 3. φC = 18.79 °
  4. 4. do = 30.64 mm
  5. 5. do = 31.75 mm
  6. 6. d = 57.94 mm

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