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 kNØ25120 GPaØ100/70300 mmσr​ = ?

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 100 mm, inner diameter 70 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: Ø25 mm, E = 200 GPatube: Ø100/Ø70 mm, E = 120 GPaL = 300 mm
σr = MPa
2.Easy
250 kNØ30110 GPaØ80/50600 mmσr​ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 80 mm, inner diameter 50 mm, E = 110 GPa). Both are 600 mm long and are compressed together between rigid plates by 250 kN. Find the compressive stress σr in the rod.

P = 250 kNrod: Ø30 mm, E = 200 GPatube: Ø80/Ø50 mm, E = 110 GPaL = 600 mm
σr = MPa
3.Medium
250 kNØ40100 GPaØ120/50600 mmδ = ?

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of brass (outer diameter 120 mm, inner diameter 50 mm, E = 100 GPa). Both are 600 mm long and are compressed together between rigid plates by 250 kN. Find the shortening δ.

P = 250 kNrod: Ø40 mm, E = 200 GPatube: Ø120/Ø50 mm, E = 100 GPaL = 600 mm
δ = mm
4.Medium
Ø 12 mmBrass1.5 mP = 55 kN

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

P = 55 kNd = 12 mmL = 1.5 mE = 100 GPa
δ = mm
5.Hard
40 kN12500 mm500 mmØ20Ø30σ2​ = ?

A steel segment (diameter 20 mm, length 500 mm, E = 200 GPa) and a segment made of aluminium (diameter 30 mm, length 500 mm, E = 70 GPa) are joined end to end and fixed between two rigid walls. An axial load of 40 kN acts at the joint, towards segment 2. Find the magnitude of the stress σ2 in segment 2.

segment 1: steel, Ø20 mm, 500 mm, E = 200 GPasegment 2: aluminium, Ø30 mm, 500 mm, E = 70 GPaP = 40 kN
σ2 = MPa
6.Hard
Ø 40 mmAluminium0.5 mØ 12 mmBrass2 mP = 45 kN

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

P = 45 kNsegment 1: Ø40 mm, 0.5 m, aluminium (E = 70 GPa)segment 2: Ø12 mm, 2 m, brass (E = 100 GPa)
δ = mm

Answer key

  1. 1. σr = 34.55 MPa
  2. 2. σr = 104.5 MPa
  3. 3. δ = 0.1265 mm
  4. 4. δ = 7.295 mm
  5. 5. σ2 = 24.93 MPa
  6. 6. δ = 8.214 mm

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