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 of diameter 25 mm is made of a material with an allowable shear stress of 70 MPa. Find the largest torque T_max the shaft can carry.

d = 25 mmτ_allow = 70 MPa

T_max = N·m

2.Easy

A solid shaft of diameter 50 mm carries a torque of 1500 N·m. Find the shear stress τ_ρ at a radius of 10 mm from the centre.

T = 1500 N·md = 50 mmρ = 10 mm

τ_ρ = MPa

3.Medium

In a torsion test, a solid specimen of diameter 20 mm is twisted by a torque of 30 N·m. The two ends of a gauge length of 400 mm rotate 0.55° relative to each other (the material is still elastic). Find the shear modulus G of the material.

T = 30 N·md = 20 mmL = 400 mmφ = 0.55°

G = GPa

4.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 = 200 N·md = 40 mmL = 2 mG = 39 GPa

φ = °

5.Hard

A hollow shaft transmits 75 kW at 1450 rpm. Find the maximum shear stress τ_max in the shaft.

P = 75 kWN = 1450 rpmd_o = 40 mmd_i = 24 mm

τ_max = MPa

6.Hard

A solid brass shaft transmits 50 kW at 750 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 = 50 kWN = 750 rpmτ_allow = 50 MPaθ_allow = 0.25°/mG = 39 GPa

d = mm

Answer key

1. T_max = 214.8 N·m
2. τ_ρ = 24.45 MPa
3. G = 79.58 GPa
4. φ = 2.338 °
5. τ_max = 45.16 MPa
6. d = 78.57 mm

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