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

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

T = 2000 N·md = 50 mm

τ_max = MPa

2.Easy

A solid circular shaft of diameter 60 mm is made of a material with an allowable shear stress of 50 MPa. Find the largest torque T_max the shaft can carry.

d = 60 mmτ_allow = 50 MPa

T_max = N·m

3.Medium

A solid aluminium shaft 3 m long carries a torque of 500 N·m. The angle of twist between its ends must not exceed 0.5°. Find the smallest diameter d that meets this limit.

T = 500 N·mL = 3 mG = 26 GPaφ_allow = 0.5°

d = mm

4.Medium

A stepped solid brass shaft is fixed at A. Segment AB has diameter 30 mm and length 0.8 m; segment BC has diameter 20 mm and length 0.8 m. A torque of 200 N·m acts at the free end C. Find the maximum shear stress τ_max in the shaft.

T = 200 N·md₁ = 30 mm, L₁ = 0.8 md₂ = 20 mm, L₂ = 0.8 m

τ_max = MPa

5.Hard

A solid steel shaft transmits 15 kW at 1450 rpm. The shear stress must not exceed 75 MPa and the twist must not exceed 0.75° per m of length. Find the smallest diameter d that satisfies both limits.

P = 15 kWN = 1450 rpmτ_allow = 75 MPaθ_allow = 0.75°/mG = 80 GPa

d = mm

6.Hard

A solid shaft must transmit 30 kW at 300 rpm without the shear stress exceeding 60 MPa. Find the smallest diameter d that works.

P = 30 kWN = 300 rpmτ_allow = 60 MPa

d = mm

Answer key

1. τ_max = 81.49 MPa
2. T_max = 2121 N·m
3. d = 90.59 mm
4. τ_max = 127.3 MPa
5. d = 31.31 mm
6. d = 43.28 mm

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