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 = 65 kNd = 25 mm

σ = MPa

2.Easy

A steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of aluminium (outer diameter 120 mm, inner diameter 60 mm, E = 70 GPa). Both are 400 mm long and are compressed together between rigid plates by 200 kN. Find the compressive stress σ_r in the rod.

P = 200 kNrod: Ø20 mm, E = 200 GPatube: Ø120/Ø60 mm, E = 70 GPaL = 400 mm

σ_r = MPa

3.Medium

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

P = 115 kNd = 30 mmL = 0.5 mE = 70 GPa

ε = µε

4.Medium

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

P = 40 kNd = 20 mmL = 1 mE = 100 GPa

ε = µε

5.Hard

A steel segment (diameter 20 mm, length 400 mm, E = 200 GPa) and a segment made of aluminium (diameter 50 mm, length 400 mm, E = 70 GPa) are joined end to end and fixed between two rigid walls. An axial load of 100 kN acts at the joint, towards segment 2. Find the magnitude of the stress σ₂ in segment 2.

segment 1: steel, Ø20 mm, 400 mm, E = 200 GPasegment 2: aluminium, Ø50 mm, 400 mm, E = 70 GPaP = 100 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 = 40 kNsegment 1: Ø35 mm, 0.5 m, steel (E = 200 GPa)segment 2: Ø16 mm, 1 m, copper (E = 117 GPa)

δ = mm

Answer key

1. σ = 132.4 MPa
2. σ_r = 60.92 MPa
3. ε = 2324 µε
4. ε = 1273 µε
5. σ₂ = 34.95 MPa
6. δ = 1.804 mm

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