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 = 60 kNd = 20 mm

σ = MPa

2.Easy

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 80 mm, inner diameter 60 mm, E = 120 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: Ø30 mm, E = 200 GPatube: Ø80/Ø60 mm, E = 120 GPaL = 800 mm

σ_r = MPa

3.Medium

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

P = 65 kNd = 10 mmL = 2 mE = 200 GPa

δ = mm

4.Medium

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

P = 105 kNd = 20 mmL = 2 mE = 70 GPa

ε = µε

5.Hard

A steel rod (diameter 25 mm, E = 200 GPa, allowable stress 150 MPa) sits inside a tube made of copper (outer diameter 100 mm, inner diameter 50 mm, E = 120 GPa, allowable stress 50 MPa). They are compressed together between rigid plates. Find the largest load P_max.

rod: Ø25 mm, E = 200 GPa, σ_allow = 150 MPatube: Ø100/Ø50 mm, E = 120 GPa, σ_allow = 50 MPa

P_max = kN

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 = 25 kNsegment 1: Ø35 mm, 1 m, aluminium (E = 70 GPa)segment 2: Ø16 mm, 2 m, copper (E = 117 GPa)

σ_max = MPa

Answer key

1. σ = 191 MPa
2. σ_r = 39.48 MPa
3. δ = 8.276 mm
4. ε = 4775 µε
5. P_max = 335.4 kN
6. σ_max = 124.3 MPa

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