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 = 400 N·md = 40 mm

τ_max = MPa

2.Easy

A solid circular shaft of diameter 25 mm is made of a material with an allowable shear stress of 80 MPa. Find the largest torque T_max the shaft can carry.

d = 25 mmτ_allow = 80 MPa

T_max = N·m

3.Medium

A solid brass 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 = 400 N·md = 50 mmL = 1.5 mG = 39 GPa

φ = °

4.Medium

A stepped solid steel shaft is fixed at A. Segment AB has diameter 50 mm and length 0.8 m; segment BC has diameter 40 mm and length 2.5 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 = 50 mm, L₁ = 0.8 md₂ = 40 mm, L₂ = 2.5 mG = 80 GPa

φ_C = °

5.Hard

A solid shaft must transmit 100 kW at 1800 rpm without the shear stress exceeding 40 MPa. Find the smallest diameter d that works.

P = 100 kWN = 1800 rpmτ_allow = 40 MPa

d = mm

6.Hard

A solid brass shaft transmits 30 kW at 300 rpm. The shear stress must not exceed 40 MPa and the twist must not exceed 1° per m of length. Find the smallest diameter d that satisfies both limits.

P = 30 kWN = 300 rpmτ_allow = 40 MPaθ_allow = 1°/mG = 39 GPa

d = mm

Answer key

1. τ_max = 31.83 MPa
2. T_max = 245.4 N·m
3. φ = 1.437 °
4. φ_C = 2.014 °
5. d = 40.73 mm
6. d = 61.48 mm

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