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 = 500 N·md = 40 mm

τ_max = MPa

2.Easy

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

d = 40 mmτ_allow = 40 MPa

T_max = N·m

3.Medium

A hollow shaft must carry a torque of 2000 N·m. Its inner diameter is to be 0.8 times its outer diameter, and the shear stress must not exceed 80 MPa. Find the smallest outer diameter d_o.

T = 2000 N·md_i/d_o = 0.8τ_allow = 80 MPa

d_o = mm

4.Medium

A stepped solid steel shaft is fixed at A. Segment AB has diameter 25 mm and length 1.5 m; segment BC has diameter 20 mm and length 1.5 m. A torque of 200 N·m acts at the free end C. Find the maximum shear stress τ_max in the shaft.

T = 200 N·md₁ = 25 mm, L₁ = 1.5 md₂ = 20 mm, L₂ = 1.5 m

τ_max = MPa

5.Hard

A solid shaft must transmit 100 kW at 1450 rpm without the shear stress exceeding 75 MPa. Find the smallest diameter d that works.

P = 100 kWN = 1450 rpmτ_allow = 75 MPa

d = mm

6.Hard

A solid brass shaft transmits 20 kW at 1450 rpm. The shear stress must not exceed 40 MPa and the twist must not exceed 0.75° per m of length. Find the smallest diameter d that satisfies both limits.

P = 20 kWN = 1450 rpmτ_allow = 40 MPaθ_allow = 0.75°/mG = 39 GPa

d = mm

Answer key

1. τ_max = 39.79 MPa
2. T_max = 502.7 N·m
3. d_o = 59.97 mm
4. τ_max = 127.3 MPa
5. d = 35.5 mm
6. d = 40.26 mm

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