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 = 1000 N·md = 30 mm

τ_max = MPa

2.Easy

A shaft turning at 750 rpm carries a steady torque of 200 N·m. Find the power P it transmits.

T = 200 N·mN = 750 rpm

P = kW

3.Medium

A solid aluminium 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 = 200 N·md = 30 mmL = 1 mG = 26 GPa

φ = °

4.Medium

A stepped solid aluminium shaft is fixed at A. Segment AB has diameter 40 mm and length 1.2 m; segment BC has diameter 30 mm and length 1.5 m. A torque of 250 N·m acts at the free end C. Find the angle of twist φ_C of end C, in degrees.

T = 250 N·md₁ = 40 mm, L₁ = 1.2 md₂ = 30 mm, L₂ = 1.5 mG = 26 GPa

φ_C = °

5.Hard

A solid steel shaft transmits 10 kW at 1450 rpm. The shear stress must not exceed 50 MPa and the twist must not exceed 0.75° per m of length. Find the smallest diameter d that satisfies both limits.

P = 10 kWN = 1450 rpmτ_allow = 50 MPaθ_allow = 0.75°/mG = 80 GPa

d = mm

6.Hard

A solid shaft must transmit 100 kW at 1000 rpm without the shear stress exceeding 80 MPa. Find the smallest diameter d that works.

P = 100 kWN = 1000 rpmτ_allow = 80 MPa

d = mm

Answer key

1. τ_max = 188.6 MPa
2. P = 15.71 kW
3. φ = 5.542 °
4. φ_C = 13.02 °
5. d = 28.29 mm
6. d = 39.32 mm

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