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 100 mm, inner diameter 70 mm, E = 70 GPa). Both are 400 mm long and are compressed together between rigid plates by 200 kN. Find the compressive stress σ_r in the rod.

P = 200 kNrod: Ø25 mm, E = 200 GPatube: Ø100/Ø70 mm, E = 70 GPaL = 400 mm

σ_r = MPa

2.Easy

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of aluminium (outer diameter 100 mm, inner diameter 60 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: Ø25 mm, E = 200 GPatube: Ø100/Ø60 mm, E = 70 GPaL = 600 mm

σ_r = MPa

3.Medium

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

P = 15 kNd = 16 mmL = 2.5 mE = 200 GPa

δ = mm

4.Medium

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

P = 45 kNd = 10 mmL = 2 mE = 70 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 = 30 kNsegment 1: Ø40 mm, 0.5 m, brass (E = 100 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 = 15 kNsegment 1: Ø40 mm, 2 m, copper (E = 117 GPa)segment 2: Ø16 mm, 1.5 m, steel (E = 200 GPa)

δ = mm

Answer key

1. σ_r = 105.7 MPa
2. σ_r = 44.44 MPa
3. δ = 0.9325 mm
4. δ = 16.37 mm
5. σ_max = 149.2 MPa
6. δ = 0.7636 mm

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