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 25 mm, E = 200 GPa) sits inside a tube made of aluminium (outer diameter 120 mm, inner diameter 50 mm, E = 70 GPa). Both are 600 mm long and are compressed together between rigid plates by 250 kN. Find the compressive stress σ_r in the rod.

P = 250 kNrod: Ø25 mm, E = 200 GPatube: Ø120/Ø50 mm, E = 70 GPaL = 600 mm

σ_r = MPa

2.Easy

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of brass (outer diameter 100 mm, inner diameter 50 mm, E = 100 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: Ø40 mm, E = 200 GPatube: Ø100/Ø50 mm, E = 100 GPaL = 500 mm

σ_r = MPa

3.Medium

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

P = 120 kNd = 16 mmL = 2 mE = 70 GPa

ε = µε

4.Medium

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

P = 15 kNd = 12 mmL = 2 mE = 200 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 = 25 kNsegment 1: Ø40 mm, 1.5 m, brass (E = 100 GPa)segment 2: Ø12 mm, 0.5 m, aluminium (E = 70 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 = 45 kNsegment 1: Ø40 mm, 1.5 m, steel (E = 200 GPa)segment 2: Ø20 mm, 2 m, copper (E = 117 GPa)

δ = mm

Answer key

1. σ_r = 66.45 MPa
2. σ_r = 23.8 MPa
3. ε = 8526 µε
4. δ = 1.326 mm
5. σ_max = 221 MPa
6. δ = 2.717 mm

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