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 40 mm is made of a material with an allowable shear stress of 60 MPa. Find the largest torque T_max the shaft can carry.

d = 40 mmτ_allow = 60 MPa

T_max = N·m

2.Easy

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

T = 750 N·md = 50 mm

τ_max = MPa

3.Medium

In a torsion test, a solid specimen of diameter 15 mm is twisted by a torque of 30 N·m. The two ends of a gauge length of 400 mm rotate 3.55° relative to each other (the material is still elastic). Find the shear modulus G of the material.

T = 30 N·md = 15 mmL = 400 mmφ = 3.55°

G = GPa

4.Medium

A solid steel 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 = 50 mmL = 2 mG = 80 GPa

φ = °

5.Hard

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

P = 75 kWN = 1450 rpmτ_allow = 75 MPa

d = mm

6.Hard

A solid brass shaft transmits 5 kW at 500 rpm. The shear stress must not exceed 80 MPa and the twist must not exceed 1° per m of length. Find the smallest diameter d that satisfies both limits.

P = 5 kWN = 500 rpmτ_allow = 80 MPaθ_allow = 1°/mG = 39 GPa

d = mm

Answer key

1. T_max = 754 N·m
2. τ_max = 30.56 MPa
3. G = 38.97 GPa
4. φ = 0.4669 °
5. d = 32.25 mm
6. d = 34.57 mm

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