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 brass (outer diameter 100 mm, inner diameter 70 mm, E = 100 GPa). Both are 300 mm long and are compressed together between rigid plates by 80 kN. Find the compressive stress σ_r in the rod.

P = 80 kNrod: Ø20 mm, E = 200 GPatube: Ø100/Ø70 mm, E = 100 GPaL = 300 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 = 105 kNd = 25 mm

σ = MPa

3.Medium

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

P = 60 kNd = 20 mmL = 2.5 mE = 70 GPa

ε = µε

4.Medium

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

P = 80 kNd = 12 mmL = 3 mE = 117 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 = 70 kNsegment 1: Ø25 mm, 2 m, aluminium (E = 70 GPa)segment 2: Ø12 mm, 1.5 m, steel (E = 200 GPa)

δ = mm

6.Hard

A steel segment (diameter 20 mm, length 300 mm, E = 200 GPa) and a segment made of brass (diameter 60 mm, length 200 mm, E = 100 GPa) are joined end to end and fixed between two rigid walls. An axial load of 60 kN acts at the joint, towards segment 2. Find the magnitude of the stress σ₂ in segment 2.

segment 1: steel, Ø20 mm, 300 mm, E = 200 GPasegment 2: brass, Ø60 mm, 200 mm, E = 100 GPaP = 60 kN

σ₂ = MPa

Answer key

1. σ_r = 34.53 MPa
2. σ = 213.9 MPa
3. ε = 2728 µε
4. ε = 6046 µε
5. δ = 8.716 mm
6. σ₂ = 18.48 MPa

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