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 kNØ25120 GPaØ100/60500 mmσr​ = ?

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 100 mm, inner diameter 60 mm, E = 120 GPa). Both are 500 mm long and are compressed together between rigid plates by 150 kN. Find the compressive stress σr in the rod.

P = 150 kNrod: Ø25 mm, E = 200 GPatube: Ø100/Ø60 mm, E = 120 GPaL = 500 mm
σr = MPa
2.Easy
Ø 16 mm0.5 mP = 80 kN

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

P = 80 kNd = 16 mm
σ = MPa
3.Medium
Ø 12 mmCopper1 mP = 110 kN

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

P = 110 kNd = 12 mmL = 1 mE = 117 GPa
ε = µε
4.Medium
Ø 12 mmBrass0.5 mP = 85 kN

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

P = 85 kNd = 12 mmL = 0.5 mE = 100 GPa
ε = µε
5.Hard
Ø 25 mmCopper0.5 mØ 12 mmBrass0.5 mP = 35 kN

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

P = 35 kNsegment 1: Ø25 mm, 0.5 m, copper (E = 117 GPa)segment 2: Ø12 mm, 0.5 m, brass (E = 100 GPa)
δ = mm
6.Hard
Ø 30 mmAluminium2 mØ 12 mmAluminium0.5 mP = 65 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 = 65 kNsegment 1: Ø30 mm, 2 m, aluminium (E = 70 GPa)segment 2: Ø12 mm, 0.5 m, aluminium (E = 70 GPa)
σmax = MPa

Answer key

  1. 1. σr = 42.77 MPa
  2. 2. σ = 397.9 MPa
  3. 3. ε = 8313 µε
  4. 4. ε = 7516 µε
  5. 5. δ = 1.852 mm
  6. 6. σmax = 574.7 MPa

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