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 kNØ4070 GPaØ100/70300 mmσr​ = ?

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of aluminium (outer diameter 100 mm, inner diameter 70 mm, E = 70 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: Ø40 mm, E = 200 GPatube: Ø100/Ø70 mm, E = 70 GPaL = 300 mm
σr = MPa
2.Easy
Ø 30 mm2 mP = 60 kN

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

P = 60 kNd = 30 mm
σ = MPa
3.Medium
Ø 30 mmAluminium2.5 mP = 105 kN

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

P = 105 kNd = 30 mmL = 2.5 mE = 70 GPa
δ = mm
4.Medium
Ø 20 mmBrass2 mP = 55 kN

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

P = 55 kNd = 20 mmL = 2 mE = 100 GPa
δ = mm
5.Hard
Ø 25 mmBrass0.5 mØ 20 mmBrass1.5 mP = 120 kN

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

P = 120 kNsegment 1: Ø25 mm, 0.5 m, brass (E = 100 GPa)segment 2: Ø20 mm, 1.5 m, brass (E = 100 GPa)
δ = mm
6.Hard
Ø 35 mmSteel0.5 mØ 12 mmAluminium0.5 mP = 70 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 = 70 kNsegment 1: Ø35 mm, 0.5 m, steel (E = 200 GPa)segment 2: Ø12 mm, 0.5 m, aluminium (E = 70 GPa)
σmax = MPa

Answer key

  1. 1. σr = 37.61 MPa
  2. 2. σ = 84.88 MPa
  3. 3. δ = 5.305 mm
  4. 4. δ = 3.501 mm
  5. 5. δ = 6.952 mm
  6. 6. σmax = 618.9 MPa

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