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 = 200 N·md = 50 mm

τ_max = MPa

2.Easy

A motor delivers 55 kW to a shaft turning at 500 rpm. Find the torque T in the shaft.

P = 55 kWN = 500 rpm

T = N·m

3.Medium

A solid steel shaft 0.8 m long carries a torque of 2000 N·m. The angle of twist between its ends must not exceed 3°. Find the smallest diameter d that meets this limit.

T = 2000 N·mL = 0.8 mG = 80 GPaφ_allow = 3°

d = mm

4.Medium

A stepped solid aluminium shaft is fixed at A. Segment AB has diameter 50 mm and length 1.2 m; segment BC has diameter 40 mm and length 2.5 m. A torque of 100 N·m acts at the free end C. Find the angle of twist φ_C of end C, in degrees.

T = 100 N·md₁ = 50 mm, L₁ = 1.2 md₂ = 40 mm, L₂ = 2.5 mG = 26 GPa

φ_C = °

5.Hard

A solid shaft must transmit 75 kW at 1450 rpm without the shear stress exceeding 80 MPa. Find the smallest diameter d that works.

P = 75 kWN = 1450 rpmτ_allow = 80 MPa

d = mm

6.Hard

A solid aluminium shaft transmits 5 kW at 500 rpm. The shear stress must not exceed 50 MPa and the twist must not exceed 0.25° per m of length. Find the smallest diameter d that satisfies both limits.

P = 5 kWN = 500 rpmτ_allow = 50 MPaθ_allow = 0.25°/mG = 26 GPa

d = mm

Answer key

1. τ_max = 8.149 MPa
2. T = 1050 N·m
3. d = 44.41 mm
4. φ_C = 2.623 °
5. d = 31.56 mm
6. d = 54.11 mm

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