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 = 30 kNd = 20 mm

σ = MPa

2.Easy

A steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of brass (outer diameter 120 mm, inner diameter 60 mm, E = 100 GPa). Both are 800 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: Ø120/Ø60 mm, E = 100 GPaL = 800 mm

σ_r = MPa

3.Medium

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

P = 10 kNd = 10 mmL = 1.5 mE = 100 GPa

ε = µε

4.Medium

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

P = 110 kNd = 10 mmL = 3 mE = 100 GPa

δ = mm

5.Hard

A steel segment (diameter 25 mm, length 400 mm, E = 200 GPa) and a segment made of aluminium (diameter 50 mm, length 300 mm, E = 70 GPa) are joined end to end and fixed between two rigid walls. An axial load of 20 kN acts at the joint, towards segment 2. Find the magnitude of the stress σ₂ in segment 2.

segment 1: steel, Ø25 mm, 400 mm, E = 200 GPasegment 2: aluminium, Ø50 mm, 300 mm, E = 70 GPaP = 20 kN

σ₂ = MPa

6.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 = 105 kNsegment 1: Ø40 mm, 1.5 m, copper (E = 117 GPa)segment 2: Ø20 mm, 2 m, aluminium (E = 70 GPa)

σ_max = MPa

Answer key

1. σ = 95.49 MPa
2. σ_r = 17.56 MPa
3. ε = 1273 µε
4. δ = 42.02 mm
5. σ₂ = 6.633 MPa
6. σ_max = 334.2 MPa

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