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 20 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 80 mm, inner diameter 50 mm, E = 110 GPa). Both are 800 mm long and are compressed together between rigid plates by 250 kN. Find the compressive stress σ_r in the rod.

P = 250 kNrod: Ø20 mm, E = 200 GPatube: Ø80/Ø50 mm, E = 110 GPaL = 800 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 = 20 kNd = 12 mm

σ = MPa

3.Medium

A steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 80 mm, inner diameter 60 mm, E = 110 GPa). Both are 500 mm long and are compressed together between rigid plates by 150 kN. Find the shortening δ.

P = 150 kNrod: Ø20 mm, E = 200 GPatube: Ø80/Ø60 mm, E = 110 GPaL = 500 mm

δ = mm

4.Medium

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

P = 80 kNd = 25 mmL = 2 mE = 200 GPa

ε = µε

5.Hard

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

P = 35 kNsegment 1: Ø25 mm, 0.5 m, steel (E = 200 GPa)segment 2: Ø20 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 = 10 kNsegment 1: Ø40 mm, 2 m, steel (E = 200 GPa)segment 2: Ø16 mm, 0.5 m, brass (E = 100 GPa)

σ_max = MPa

Answer key

1. σ_r = 125.1 MPa
2. σ = 176.8 MPa
3. δ = 0.2461 mm
4. ε = 814.9 µε
5. δ = 1.014 mm
6. σ_max = 49.74 MPa

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