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
50 kNØ25120 GPaØ80/60400 mmσr​ = ?

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 80 mm, inner diameter 60 mm, E = 120 GPa). Both are 400 mm long and are compressed together between rigid plates by 50 kN. Find the compressive stress σr in the rod.

P = 50 kNrod: Ø25 mm, E = 200 GPatube: Ø80/Ø60 mm, E = 120 GPaL = 400 mm
σr = MPa
2.Easy
100 kNØ40100 GPaØ80/50400 mmσr​ = ?

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of brass (outer diameter 80 mm, inner diameter 50 mm, E = 100 GPa). Both are 400 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: Ø80/Ø50 mm, E = 100 GPaL = 400 mm
σr = MPa
3.Medium
Ø 20 mmCopper2 mP = 80 kN

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

P = 80 kNd = 20 mmL = 2 mE = 117 GPa
δ = mm
4.Medium
Ø 12 mmBrass2.5 mP = 85 kN

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

P = 85 kNd = 12 mmL = 2.5 mE = 100 GPa
δ = mm
5.Hard
Ø 35 mmBrass1 mØ 20 mmAluminium1 mP = 25 kN

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

P = 25 kNsegment 1: Ø35 mm, 1 m, brass (E = 100 GPa)segment 2: Ø20 mm, 1 m, aluminium (E = 70 GPa)
δ = mm
6.Hard
20 kN12600 mm500 mmØ20Ø40σ2​ = ?

A steel segment (diameter 20 mm, length 600 mm, E = 200 GPa) and a segment made of brass (diameter 40 mm, length 500 mm, E = 100 GPa) are joined end to end and fixed between two rigid walls. An axial load of 20 kN acts at the joint, towards segment 2. Find the magnitude of the stress σ2 in segment 2.

segment 1: steel, Ø20 mm, 600 mm, E = 200 GPasegment 2: brass, Ø40 mm, 500 mm, E = 100 GPaP = 20 kN
σ2 = MPa

Answer key

  1. 1. σr = 27.62 MPa
  2. 2. σr = 35.87 MPa
  3. 3. δ = 4.353 mm
  4. 4. δ = 18.79 mm
  5. 5. δ = 1.397 mm
  6. 6. σ2 = 11.23 MPa

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