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 = 40 kNd = 16 mm

σ = MPa

2.Easy

A steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 100 mm, inner diameter 70 mm, E = 120 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 = 120 GPaL = 300 mm

σ_r = MPa

3.Medium

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

P = 100 kNd = 25 mmL = 1.5 mE = 117 GPa

ε = µε

4.Medium

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

P = 120 kNd = 20 mmL = 1.5 mE = 100 GPa

ε = µε

5.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 = 70 kNsegment 1: Ø25 mm, 1 m, steel (E = 200 GPa)segment 2: Ø16 mm, 1 m, aluminium (E = 70 GPa)

σ_max = MPa

6.Hard

A steel segment (diameter 30 mm, length 400 mm, E = 200 GPa) and a segment made of bronze (diameter 50 mm, length 300 mm, E = 110 GPa) are joined end to end and fixed between two rigid walls. An axial load of 50 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: bronze, Ø50 mm, 300 mm, E = 110 GPaP = 50 kN

σ₂ = MPa

Answer key

1. σ = 198.9 MPa
2. σ_r = 29.44 MPa
3. ε = 1741 µε
4. ε = 3820 µε
5. σ_max = 348.2 MPa
6. σ₂ = 17.08 MPa

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