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

P = 20 kNd = 12 mm

σ = MPa

2.Easy

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 120 mm, inner diameter 70 mm, E = 110 GPa). Both are 800 mm long and are compressed together between rigid plates by 100 kN. Find the compressive stress σ_r in the rod.

P = 100 kNrod: Ø40 mm, E = 200 GPatube: Ø120/Ø70 mm, E = 110 GPaL = 800 mm

σ_r = MPa

3.Medium

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of brass (outer diameter 100 mm, inner diameter 70 mm, E = 100 GPa). Both are 300 mm long and are compressed together between rigid plates by 200 kN. Find the shortening δ.

P = 200 kNrod: Ø30 mm, E = 200 GPatube: Ø100/Ø70 mm, E = 100 GPaL = 300 mm

δ = mm

4.Medium

Find the axial strain ε in the aluminium bar, in microstrain (µε = 10⁻⁶).

P = 75 kNd = 10 mmL = 3 mE = 70 GPa

ε = µε

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, aluminium (E = 70 GPa)segment 2: Ø12 mm, 1.5 m, brass (E = 100 GPa)

σ_max = MPa

6.Hard

The stepped bar is fixed at the wall and loaded at its free end. Find the total elongation δ.

P = 105 kNsegment 1: Ø40 mm, 1.5 m, copper (E = 117 GPa)segment 2: Ø20 mm, 1 m, aluminium (E = 70 GPa)

δ = mm

Answer key

1. σ = 176.8 MPa
2. σ_r = 18.66 MPa
3. δ = 0.1107 mm
4. ε = 13642 µε
5. σ_max = 486.3 MPa
6. δ = 5.846 mm

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