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 GPaØ120/70400 mmσr​ = ?

A steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 120 mm, inner diameter 70 mm, E = 120 GPa). Both are 400 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: Ø120/Ø70 mm, E = 120 GPaL = 400 mm
σr = MPa
2.Easy
Ø 20 mm0.5 mP = 35 kN

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

P = 35 kNd = 20 mm
σ = MPa
3.Medium
Ø 20 mmAluminium2 mP = 10 kN

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

P = 10 kNd = 20 mmL = 2 mE = 70 GPa
δ = mm
4.Medium
Ø 20 mmAluminium3 mP = 80 kN

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

P = 80 kNd = 20 mmL = 3 mE = 70 GPa
ε = µε
5.Hard
100 kN12300 mm500 mmØ25Ø50σ2​ = ?

A steel segment (diameter 25 mm, length 300 mm, E = 200 GPa) and a segment made of bronze (diameter 50 mm, length 500 mm, E = 110 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, Ø25 mm, 300 mm, E = 200 GPasegment 2: bronze, Ø50 mm, 500 mm, E = 110 GPaP = 100 kN
σ2 = MPa
6.Hard
30 kN12600 mm300 mmØ30Ø40σ2​ = ?

A steel segment (diameter 30 mm, length 600 mm, E = 200 GPa) and a segment made of bronze (diameter 40 mm, length 300 mm, E = 110 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, 600 mm, E = 200 GPasegment 2: bronze, Ø40 mm, 300 mm, E = 110 GPaP = 30 kN
σ2 = MPa

Answer key

  1. 1. σr = 62.62 MPa
  2. 2. σ = 111.4 MPa
  3. 3. δ = 0.9095 mm
  4. 4. ε = 3638 µε
  5. 5. σ2 = 28.98 MPa
  6. 6. σ2 = 15.8 MPa

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