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 = 40 kNd = 16 mm

σ = MPa

2.Easy

A steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of aluminium (outer diameter 100 mm, inner diameter 70 mm, E = 70 GPa). Both are 600 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: Ø100/Ø70 mm, E = 70 GPaL = 600 mm

σ_r = MPa

3.Medium

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 100 mm, inner diameter 70 mm, E = 120 GPa). Both are 600 mm long and are compressed together between rigid plates by 50 kN. Find the shortening δ.

P = 50 kNrod: Ø30 mm, E = 200 GPatube: Ø100/Ø70 mm, E = 120 GPaL = 600 mm

δ = mm

4.Medium

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

P = 30 kNd = 25 mmL = 2.5 mE = 200 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 = 100 kNsegment 1: Ø30 mm, 0.5 m, aluminium (E = 70 GPa)segment 2: Ø16 mm, 1 m, steel (E = 200 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 = 25 kNsegment 1: Ø30 mm, 0.5 m, steel (E = 200 GPa)segment 2: Ø20 mm, 0.5 m, aluminium (E = 70 GPa)

δ = mm

Answer key

1. σ = 198.9 MPa
2. σ_r = 58.27 MPa
3. δ = 0.04823 mm
4. ε = 305.6 µε
5. σ_max = 497.4 MPa
6. δ = 0.6568 mm

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