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
150 kNØ20120 GPaØ120/50300 mmσr​ = ?

A steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 120 mm, inner diameter 50 mm, E = 120 GPa). Both are 300 mm long and are compressed together between rigid plates by 150 kN. Find the compressive stress σr in the rod.

P = 150 kNrod: Ø20 mm, E = 200 GPatube: Ø120/Ø50 mm, E = 120 GPaL = 300 mm
σr = MPa
2.Easy
Ø 12 mm1 mP = 55 kN

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

P = 55 kNd = 12 mm
σ = MPa
3.Medium
Ø 20 mmCopper2 mP = 35 kN

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

P = 35 kNd = 20 mmL = 2 mE = 117 GPa
ε = µε
4.Medium
Ø 10 mmAluminium2.5 mP = 70 kN

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

P = 70 kNd = 10 mmL = 2.5 mE = 70 GPa
ε = µε
5.Hard
Ø 35 mmSteel2 mØ 16 mmAluminium0.5 mP = 95 kN

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

P = 95 kNsegment 1: Ø35 mm, 2 m, steel (E = 200 GPa)segment 2: Ø16 mm, 0.5 m, aluminium (E = 70 GPa)
δ = mm
6.Hard
Ø 35 mmBrass0.5 mØ 12 mmCopper0.5 mP = 85 kN

The stepped bar is fixed at the wall and loaded at its free end. Find the largest normal stress σmax in the bar.

P = 85 kNsegment 1: Ø35 mm, 0.5 m, brass (E = 100 GPa)segment 2: Ø12 mm, 0.5 m, copper (E = 117 GPa)
σmax = MPa

Answer key

  1. 1. σr = 25.33 MPa
  2. 2. σ = 486.3 MPa
  3. 3. ε = 952.2 µε
  4. 4. ε = 12732 µε
  5. 5. δ = 4.362 mm
  6. 6. σmax = 751.6 MPa

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