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 = 85 kNd = 25 mm

σ = MPa

2.Easy

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 100 mm, inner diameter 70 mm, E = 120 GPa). Both are 800 mm long and are compressed together between rigid plates by 100 kN. Find the compressive stress σ_r in the rod.

P = 100 kNrod: Ø40 mm, E = 200 GPatube: Ø100/Ø70 mm, E = 120 GPaL = 800 mm

σ_r = MPa

3.Medium

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

P = 90 kNd = 25 mmL = 0.5 mE = 70 GPa

ε = µε

4.Medium

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

P = 60 kNd = 10 mmL = 1 mE = 70 GPa

δ = mm

5.Hard

A steel segment (diameter 20 mm, length 500 mm, E = 200 GPa) and a segment made of brass (diameter 40 mm, length 300 mm, E = 100 GPa) are joined end to end and fixed between two rigid walls. An axial load of 80 kN acts at the joint, towards segment 2. Find the magnitude of the stress σ₂ in segment 2.

segment 1: steel, Ø20 mm, 500 mm, E = 200 GPasegment 2: brass, Ø40 mm, 300 mm, E = 100 GPaP = 80 kN

σ₂ = MPa

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 = 90 kNsegment 1: Ø30 mm, 0.5 m, copper (E = 117 GPa)segment 2: Ø20 mm, 1 m, copper (E = 117 GPa)

σ_max = MPa

Answer key

1. σ = 173.2 MPa
2. σ_r = 27.32 MPa
3. ε = 2619 µε
4. δ = 10.91 mm
5. σ₂ = 48.97 MPa
6. σ_max = 286.5 MPa

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