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 = 20 kNd = 10 mm

σ = MPa

2.Easy

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 100 mm, inner diameter 50 mm, E = 110 GPa). Both are 300 mm long and are compressed together between rigid plates by 200 kN. Find the compressive stress σ_r in the rod.

P = 200 kNrod: Ø30 mm, E = 200 GPatube: Ø100/Ø50 mm, E = 110 GPaL = 300 mm

σ_r = MPa

3.Medium

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

P = 120 kNd = 30 mmL = 0.5 mE = 100 GPa

ε = µε

4.Medium

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

P = 45 kNd = 12 mmL = 2.5 mE = 117 GPa

δ = mm

5.Hard

A steel segment (diameter 20 mm, length 300 mm, E = 200 GPa) and a segment made of copper (diameter 30 mm, length 300 mm, E = 120 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, Ø20 mm, 300 mm, E = 200 GPasegment 2: copper, Ø30 mm, 300 mm, E = 120 GPaP = 40 kN

σ₂ = MPa

6.Hard

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

P = 65 kNsegment 1: Ø35 mm, 1 m, brass (E = 100 GPa)segment 2: Ø16 mm, 1.5 m, aluminium (E = 70 GPa)

δ = mm

Answer key

1. σ = 254.6 MPa
2. σ_r = 50.68 MPa
3. ε = 1698 µε
4. δ = 8.502 mm
5. σ₂ = 32.51 MPa
6. δ = 7.603 mm

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