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
Ø 12 mm0.5 mP = 100 kN

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

P = 100 kNd = 12 mm
σ = MPa
2.Easy
50 kNØ25120 GPaØ120/60600 mmσr​ = ?

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 120 mm, inner diameter 60 mm, E = 120 GPa). Both are 600 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: Ø120/Ø60 mm, E = 120 GPaL = 600 mm
σr = MPa
3.Medium
Ø 10 mmCopper1 mP = 20 kN

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

P = 20 kNd = 10 mmL = 1 mE = 117 GPa
ε = µε
4.Medium
Ø 30 mmAluminium0.5 mP = 75 kN

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

P = 75 kNd = 30 mmL = 0.5 mE = 70 GPa
ε = µε
5.Hard
P = ?Ø40120 GPaØ120/60300 mm

A steel rod (diameter 40 mm, E = 200 GPa, allowable stress 200 MPa) sits inside a tube made of copper (outer diameter 120 mm, inner diameter 60 mm, E = 120 GPa, allowable stress 80 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø40 mm, E = 200 GPa, σallow = 200 MPatube: Ø120/Ø60 mm, E = 120 GPa, σallow = 80 MPa
Pmax = kN
6.Hard
30 kN12600 mm300 mmØ25Ø60σ2​ = ?

A steel segment (diameter 25 mm, length 600 mm, E = 200 GPa) and a segment made of copper (diameter 60 mm, length 300 mm, E = 120 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, Ø25 mm, 600 mm, E = 200 GPasegment 2: copper, Ø60 mm, 300 mm, E = 120 GPaP = 30 kN
σ2 = MPa

Answer key

  1. 1. σ = 884.2 MPa
  2. 2. σr = 8.96 MPa
  3. 3. ε = 2176 µε
  4. 4. ε = 1516 µε
  5. 5. Pmax = 846.1 kN
  6. 6. σ2 = 9.269 MPa

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