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 = 50 kNd = 25 mm

σ = MPa

2.Easy

A steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of brass (outer diameter 80 mm, inner diameter 50 mm, E = 100 GPa). Both are 300 mm long and are compressed together between rigid plates by 300 kN. Find the compressive stress σ_r in the rod.

P = 300 kNrod: Ø20 mm, E = 200 GPatube: Ø80/Ø50 mm, E = 100 GPaL = 300 mm

σ_r = MPa

3.Medium

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

P = 15 kNd = 20 mmL = 1 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 60 mm, E = 70 GPa). Both are 400 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/Ø60 mm, E = 70 GPaL = 400 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 = 15 kNsegment 1: Ø40 mm, 1 m, brass (E = 100 GPa)segment 2: Ø16 mm, 1.5 m, copper (E = 117 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 = 110 kNsegment 1: Ø40 mm, 1.5 m, copper (E = 117 GPa)segment 2: Ø12 mm, 1.5 m, steel (E = 200 GPa)

σ_max = MPa

Answer key

1. σ = 101.9 MPa
2. σ_r = 162.5 MPa
3. ε = 408.1 µε
4. δ = 0.1734 mm
5. δ = 1.076 mm
6. σ_max = 972.6 MPa

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