Axial stress & strain worksheet with answers

Free printable Axial stress & strain 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 steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of aluminium (outer diameter 120 mm, inner diameter 70 mm, E = 70 GPa). Both are 500 mm long and are compressed together between rigid plates by 100 kN. Find the compressive stress σ_r in the rod.

P = 100 kNrod: Ø20 mm, E = 200 GPatube: Ø120/Ø70 mm, E = 70 GPaL = 500 mm

σ_r = MPa

2.Easy

A solid round bar carries an axial tensile load P. Find the normal stress σ in the bar.

P = 25 kNd = 10 mm

σ = MPa

3.Medium

Find the elongation δ of the aluminium bar under the axial load.

P = 120 kNd = 10 mmL = 2 mE = 70 GPa

δ = mm

4.Medium

Find the elongation δ of the copper bar under the axial load.

P = 120 kNd = 16 mmL = 2 mE = 117 GPa

δ = mm

5.Hard

The stepped bar is fixed at the wall and loaded at its free end. Find the largest normal stress σ_max in the bar.

P = 55 kNsegment 1: Ø25 mm, 0.5 m, copper (E = 117 GPa)segment 2: Ø12 mm, 1 m, aluminium (E = 70 GPa)

σ_max = MPa

6.Hard

A steel segment (diameter 20 mm, length 400 mm, E = 200 GPa) and a segment made of copper (diameter 30 mm, length 400 mm, E = 120 GPa) are joined end to end and fixed between two rigid walls. An axial load of 40 kN acts at the joint, towards segment 2. Find the magnitude of the stress σ₂ in segment 2.

segment 1: steel, Ø20 mm, 400 mm, E = 200 GPasegment 2: copper, Ø30 mm, 400 mm, E = 120 GPaP = 40 kN

σ₂ = MPa

Answer key

1. σ_r = 34.18 MPa
2. σ = 318.3 MPa
3. δ = 43.65 mm
4. δ = 10.2 mm
5. σ_max = 486.3 MPa
6. σ₂ = 32.51 MPa

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