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
Ø 10 mm1.5 mP = 70 kN

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

P = 70 kNd = 10 mm
σ = MPa
2.Easy
100 kNØ40120 GPaØ120/70600 mmσr​ = ?

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 120 mm, inner diameter 70 mm, E = 120 GPa). Both are 600 mm long and are compressed together between rigid plates by 100 kN. Find the compressive stress σr in the rod.

P = 100 kNrod: Ø40 mm, E = 200 GPatube: Ø120/Ø70 mm, E = 120 GPaL = 600 mm
σr = MPa
3.Medium
Ø 12 mmSteel0.5 mP = 10 kN

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

P = 10 kNd = 12 mmL = 0.5 mE = 200 GPa
ε = µε
4.Medium
Ø 10 mmCopper0.5 mP = 20 kN

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

P = 20 kNd = 10 mmL = 0.5 mE = 117 GPa
ε = µε
5.Hard
Ø 30 mmBrass1 mØ 20 mmCopper1.5 mP = 30 kN

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

P = 30 kNsegment 1: Ø30 mm, 1 m, brass (E = 100 GPa)segment 2: Ø20 mm, 1.5 m, copper (E = 117 GPa)
δ = mm
6.Hard
Ø 35 mmAluminium2 mØ 12 mmBrass1 mP = 100 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 = 100 kNsegment 1: Ø35 mm, 2 m, aluminium (E = 70 GPa)segment 2: Ø12 mm, 1 m, brass (E = 100 GPa)
σmax = MPa

Answer key

  1. 1. σ = 891.3 MPa
  2. 2. σr = 17.44 MPa
  3. 3. ε = 442.1 µε
  4. 4. ε = 2176 µε
  5. 5. δ = 1.649 mm
  6. 6. σmax = 884.2 MPa

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