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 = 95 kNd = 25 mm

σ = MPa

2.Easy

A steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 120 mm, inner diameter 60 mm, E = 110 GPa). Both are 800 mm long and are compressed together between rigid plates by 150 kN. Find the compressive stress σ_r in the rod.

P = 150 kNrod: Ø20 mm, E = 200 GPatube: Ø120/Ø60 mm, E = 110 GPaL = 800 mm

σ_r = MPa

3.Medium

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

P = 120 kNd = 16 mmL = 3 mE = 200 GPa

ε = µε

4.Medium

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

P = 120 kNd = 16 mmL = 2.5 mE = 70 GPa

ε = µε

5.Hard

A steel segment (diameter 20 mm, length 600 mm, E = 200 GPa) and a segment made of bronze (diameter 40 mm, length 500 mm, E = 110 GPa) are joined end to end and fixed between two rigid walls. An axial load of 30 kN acts at the joint, towards segment 2. Find the magnitude of the stress σ₂ in segment 2.

segment 1: steel, Ø20 mm, 600 mm, E = 200 GPasegment 2: bronze, Ø40 mm, 500 mm, E = 110 GPaP = 30 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 = 80 kNsegment 1: Ø30 mm, 1.5 m, brass (E = 100 GPa)segment 2: Ø12 mm, 1 m, steel (E = 200 GPa)

δ = mm

Answer key

1. σ = 193.5 MPa
2. σ_r = 30.12 MPa
3. ε = 2984 µε
4. ε = 8526 µε
5. σ₂ = 17.31 MPa
6. δ = 5.234 mm

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