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 steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 80 mm, inner diameter 60 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: Ø80/Ø60 mm, E = 120 GPaL = 300 mm

σ_r = MPa

2.Easy

A solid round bar carries an axial tensile load P. Find the normal stress σ in the bar.

P = 40 kNd = 12 mm

σ = MPa

3.Medium

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

P = 110 kNd = 12 mmL = 2 mE = 200 GPa

ε = µε

4.Medium

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

P = 35 kNd = 12 mmL = 1.5 mE = 117 GPa

δ = mm

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 = 15 kNsegment 1: Ø40 mm, 1 m, steel (E = 200 GPa)segment 2: Ø20 mm, 1 m, steel (E = 200 GPa)

σ_max = MPa

6.Hard

A steel segment (diameter 25 mm, length 600 mm, E = 200 GPa) and a segment made of brass (diameter 60 mm, length 400 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, Ø25 mm, 600 mm, E = 200 GPasegment 2: brass, Ø60 mm, 400 mm, E = 100 GPaP = 80 kN

σ₂ = MPa

Answer key

1. σ_r = 48.97 MPa
2. σ = 353.7 MPa
3. ε = 4863 µε
4. δ = 3.968 mm
5. σ_max = 47.75 MPa
6. σ₂ = 22.98 MPa

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