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 = 75 kNd = 20 mm

σ = MPa

2.Easy

A steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of brass (outer diameter 120 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: Ø120/Ø50 mm, E = 100 GPaL = 300 mm

σ_r = MPa

3.Medium

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

P = 20 kNd = 20 mmL = 2.5 mE = 200 GPa

ε = µε

4.Medium

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

P = 50 kNd = 25 mmL = 0.5 mE = 70 GPa

δ = mm

5.Hard

A steel segment (diameter 30 mm, length 400 mm, E = 200 GPa) and a segment made of brass (diameter 30 mm, length 400 mm, E = 100 GPa) are joined end to end and fixed between two rigid walls. An axial load of 40 kN acts at the joint, towards segment 2. Find the magnitude of the stress σ₂ in segment 2.

segment 1: steel, Ø30 mm, 400 mm, E = 200 GPasegment 2: brass, Ø30 mm, 400 mm, E = 100 GPaP = 40 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: Ø16 mm, 2 m, copper (E = 117 GPa)

σ_max = MPa

Answer key

1. σ = 238.7 MPa
2. σ_r = 60.15 MPa
3. ε = 318.3 µε
4. δ = 0.7276 mm
5. σ₂ = 18.86 MPa
6. σ_max = 447.6 MPa

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