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
300 kNØ20120 GPaØ80/50600 mmσr​ = ?

A steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 80 mm, inner diameter 50 mm, E = 120 GPa). Both are 600 mm long and are compressed together between rigid plates by 300 kN. Find the compressive stress σr in the rod.

P = 300 kNrod: Ø20 mm, E = 200 GPatube: Ø80/Ø50 mm, E = 120 GPaL = 600 mm
σr = MPa
2.Easy
300 kNØ40110 GPaØ100/70500 mmσr​ = ?

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 100 mm, inner diameter 70 mm, E = 110 GPa). Both are 500 mm long and are compressed together between rigid plates by 300 kN. Find the compressive stress σr in the rod.

P = 300 kNrod: Ø40 mm, E = 200 GPatube: Ø100/Ø70 mm, E = 110 GPaL = 500 mm
σr = MPa
3.Medium
Ø 30 mmAluminium0.5 mP = 10 kN

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

P = 10 kNd = 30 mmL = 0.5 mE = 70 GPa
δ = mm
4.Medium
Ø 25 mmCopper2 mP = 85 kN

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

P = 85 kNd = 25 mmL = 2 mE = 117 GPa
δ = mm
5.Hard
Ø 40 mmCopper0.5 mØ 16 mmAluminium1.5 mP = 20 kN

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

P = 20 kNsegment 1: Ø40 mm, 0.5 m, copper (E = 117 GPa)segment 2: Ø16 mm, 1.5 m, aluminium (E = 70 GPa)
δ = mm
6.Hard
100 kN12600 mm300 mmØ40Ø30σ2​ = ?

A steel segment (diameter 40 mm, length 600 mm, E = 200 GPa) and a segment made of aluminium (diameter 30 mm, length 300 mm, E = 70 GPa) are joined end to end and fixed between two rigid walls. An axial load of 100 kN acts at the joint, towards segment 2. Find the magnitude of the stress σ2 in segment 2.

segment 1: steel, Ø40 mm, 600 mm, E = 200 GPasegment 2: aluminium, Ø30 mm, 300 mm, E = 70 GPaP = 100 kN
σ2 = MPa

Answer key

  1. 1. σr = 139.4 MPa
  2. 2. σr = 86.71 MPa
  3. 3. δ = 0.1011 mm
  4. 4. δ = 2.96 mm
  5. 5. δ = 2.2 mm
  6. 6. σ2 = 39.97 MPa

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