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 = 45 kNd = 16 mm

σ = MPa

2.Easy

A steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 80 mm, inner diameter 50 mm, E = 120 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: Ø80/Ø50 mm, E = 120 GPaL = 400 mm

σ_r = MPa

3.Medium

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

P = 20 kNd = 12 mmL = 3 mE = 70 GPa

δ = mm

4.Medium

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

P = 85 kNd = 10 mmL = 1 mE = 100 GPa

ε = µε

5.Hard

A steel rod (diameter 20 mm, E = 200 GPa, allowable stress 200 MPa) sits inside a tube made of brass (outer diameter 120 mm, inner diameter 60 mm, E = 100 GPa, allowable stress 70 MPa). They are compressed together between rigid plates. Find the largest load P_max.

rod: Ø20 mm, E = 200 GPa, σ_allow = 200 MPatube: Ø120/Ø60 mm, E = 100 GPa, σ_allow = 70 MPa

P_max = kN

6.Hard

The stepped bar is fixed at the wall and loaded at its free end. Find the total elongation δ.

P = 20 kNsegment 1: Ø30 mm, 1 m, aluminium (E = 70 GPa)segment 2: Ø20 mm, 2 m, copper (E = 117 GPa)

δ = mm

Answer key

1. σ = 223.8 MPa
2. σ_r = 92.94 MPa
3. δ = 7.579 mm
4. ε = 10823 µε
5. P_max = 637.7 kN
6. δ = 1.492 mm

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