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 50 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 = 50 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 = 100 N·md = 40 mm

τ_max = MPa

3.Medium

A stepped solid aluminium shaft is fixed at A. Segment AB has diameter 75 mm and length 0.8 m; segment BC has diameter 25 mm and length 0.5 m. A torque of 750 N·m acts at the free end C. Find the angle of twist φ_C of end C, in degrees.

T = 750 N·md₁ = 75 mm, L₁ = 0.8 md₂ = 25 mm, L₂ = 0.5 mG = 26 GPa

φ_C = °

4.Medium

In a torsion test, a solid specimen of diameter 15 mm is twisted by a torque of 75 N·m. The two ends of a gauge length of 250 mm rotate 8.31° relative to each other (the material is still elastic). Find the shear modulus G of the material.

T = 75 N·md = 15 mmL = 250 mmφ = 8.31°

G = GPa

5.Hard

A solid shaft must transmit 100 kW at 1800 rpm without the shear stress exceeding 75 MPa. Find the smallest diameter d that works.

P = 100 kWN = 1800 rpmτ_allow = 75 MPa

d = mm

6.Hard

A solid shaft must transmit 5 kW at 1500 rpm without the shear stress exceeding 80 MPa. Find the smallest diameter d that works.

P = 5 kWN = 1500 rpmτ_allow = 80 MPa

d = mm

Answer key

1. T_max = 1473 N·m
2. τ_max = 7.958 MPa
3. φ_C = 21.97 °
4. G = 26.01 GPa
5. d = 33.03 mm
6. d = 12.65 mm

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