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 bronze (outer diameter 120 mm, inner diameter 50 mm, E = 110 GPa). Both are 500 mm long and are compressed together between rigid plates by 80 kN. Find the compressive stress σ_r in the rod.

P = 80 kNrod: Ø25 mm, E = 200 GPatube: Ø120/Ø50 mm, E = 110 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 = 80 kNd = 30 mm

σ = MPa

3.Medium

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

P = 95 kNd = 12 mmL = 2.5 mE = 117 GPa

ε = µε

4.Medium

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 300 kN. Find the shortening δ.

P = 300 kNrod: Ø25 mm, E = 200 GPatube: Ø120/Ø50 mm, E = 70 GPaL = 600 mm

δ = mm

5.Hard

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

P = 55 kNsegment 1: Ø35 mm, 1 m, aluminium (E = 70 GPa)segment 2: Ø12 mm, 1.5 m, steel (E = 200 GPa)

δ = mm

6.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: Ø40 mm, 2 m, copper (E = 117 GPa)segment 2: Ø12 mm, 1.5 m, copper (E = 117 GPa)

σ_max = MPa

Answer key

1. σ_r = 14.21 MPa
2. σ = 113.2 MPa
3. ε = 7179 µε
4. δ = 0.2392 mm
5. δ = 4.464 mm
6. σ_max = 486.3 MPa

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