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 kNØ3070 GPaØ120/50300 mmσr​ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of aluminium (outer diameter 120 mm, inner diameter 50 mm, E = 70 GPa). Both are 300 mm long and are compressed together between rigid plates by 300 kN. Find the compressive stress σr in the rod.

P = 300 kNrod: Ø30 mm, E = 200 GPatube: Ø120/Ø50 mm, E = 70 GPaL = 300 mm
σr = MPa
2.Easy
100 kNØ25110 GPaØ120/60300 mmσr​ = ?

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 120 mm, inner diameter 60 mm, E = 110 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: Ø120/Ø60 mm, E = 110 GPaL = 300 mm
σr = MPa
3.Medium
Ø 12 mmSteel1.5 mP = 75 kN

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

P = 75 kNd = 12 mmL = 1.5 mE = 200 GPa
δ = mm
4.Medium
Ø 10 mmCopper0.5 mP = 30 kN

Find the axial strain ε in the copper bar, in microstrain (µε = 10⁻⁶).

P = 30 kNd = 10 mmL = 0.5 mE = 117 GPa
ε = µε
5.Hard
30 kN12500 mm300 mmØ30Ø60σ2​ = ?

A steel segment (diameter 30 mm, length 500 mm, E = 200 GPa) and a segment made of aluminium (diameter 60 mm, length 300 mm, E = 70 GPa) are joined end to end and fixed between two rigid walls. An axial load of 30 kN acts at the joint, towards segment 2. Find the magnitude of the stress σ2 in segment 2.

segment 1: steel, Ø30 mm, 500 mm, E = 200 GPasegment 2: aluminium, Ø60 mm, 300 mm, E = 70 GPaP = 30 kN
σ2 = MPa
6.Hard
60 kN12600 mm300 mmØ40Ø30σ2​ = ?

A steel segment (diameter 40 mm, length 600 mm, E = 200 GPa) and a segment made of copper (diameter 30 mm, length 300 mm, E = 120 GPa) are joined end to end and fixed between two rigid walls. An axial load of 60 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: copper, Ø30 mm, 300 mm, E = 120 GPaP = 60 kN
σ2 = MPa

Answer key

  1. 1. σr = 75.41 MPa
  2. 2. σr = 19.39 MPa
  3. 3. δ = 4.974 mm
  4. 4. ε = 3265 µε
  5. 5. σ2 = 7.427 MPa
  6. 6. σ2 = 34.21 MPa

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