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
100 kNØ40110 GPaØ120/50800 mmσr​ = ?

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 120 mm, inner diameter 50 mm, E = 110 GPa). Both are 800 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/Ø50 mm, E = 110 GPaL = 800 mm
σr = MPa
2.Easy
100 kNØ20120 GPaØ100/50300 mmσr​ = ?

A steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 100 mm, inner diameter 50 mm, E = 120 GPa). Both are 300 mm long and are compressed together between rigid plates by 100 kN. Find the compressive stress σr in the rod.

P = 100 kNrod: Ø20 mm, E = 200 GPatube: Ø100/Ø50 mm, E = 120 GPaL = 300 mm
σr = MPa
3.Medium
Ø 30 mmAluminium1 mP = 15 kN

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

P = 15 kNd = 30 mmL = 1 mE = 70 GPa
δ = mm
4.Medium
80 kNØ20120 GPaØ100/70400 mmδ = ?

A steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 100 mm, inner diameter 70 mm, E = 120 GPa). Both are 400 mm long and are compressed together between rigid plates by 80 kN. Find the shortening δ.

P = 80 kNrod: Ø20 mm, E = 200 GPatube: Ø100/Ø70 mm, E = 120 GPaL = 400 mm
δ = mm
5.Hard
Ø 35 mmCopper1.5 mØ 20 mmCopper0.5 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: Ø35 mm, 1.5 m, copper (E = 117 GPa)segment 2: Ø20 mm, 0.5 m, copper (E = 117 GPa)
δ = mm
6.Hard
Ø 40 mmCopper0.5 mØ 20 mmBrass1 mP = 115 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 = 115 kNsegment 1: Ø40 mm, 0.5 m, copper (E = 117 GPa)segment 2: Ø20 mm, 1 m, brass (E = 100 GPa)
σmax = MPa

Answer key

  1. 1. σr = 15.63 MPa
  2. 2. σr = 25.98 MPa
  3. 3. δ = 0.3032 mm
  4. 4. δ = 0.05888 mm
  5. 5. δ = 0.9425 mm
  6. 6. σmax = 366.1 MPa

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