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.

New worksheetPractise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________   Date: ____________

1.Easy
80 kNØ30110 GPaØ80/50800 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 800 mm long and are compressed together between rigid plates by 80 kN. Find the compressive stress σr in the rod.

P = 80 kNrod: Ø30 mm, E = 200 GPatube: Ø80/Ø50 mm, E = 110 GPaL = 800 mm
σr = MPa
2.Easy
150 kNØ25120 GPaØ80/60600 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 600 mm long and are compressed together between rigid plates by 150 kN. Find the compressive stress σr in the rod.

P = 150 kNrod: Ø25 mm, E = 200 GPatube: Ø80/Ø60 mm, E = 120 GPaL = 600 mm
σr = MPa
3.Medium
Ø 10 mmCopper3 mP = 60 kN

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

P = 60 kNd = 10 mmL = 3 mE = 117 GPa
ε = µε
4.Medium
Ø 16 mmCopper1 mP = 25 kN

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

P = 25 kNd = 16 mmL = 1 mE = 117 GPa
δ = mm
5.Hard
80 kN12300 mm500 mmØ20Ø60σ2​ = ?

A steel segment (diameter 20 mm, length 300 mm, E = 200 GPa) and a segment made of brass (diameter 60 mm, length 500 mm, E = 100 GPa) are joined end to end and fixed between two rigid walls. An axial load of 80 kN acts at the joint, towards segment 2. Find the magnitude of the stress σ2 in segment 2.

segment 1: steel, Ø20 mm, 300 mm, E = 200 GPasegment 2: brass, Ø60 mm, 500 mm, E = 100 GPaP = 80 kN
σ2 = MPa
6.Hard
Ø 25 mmBrass0.5 mØ 16 mmAluminium2 mP = 80 kN

The stepped bar is fixed at the wall and loaded at its free end. Find the largest normal stress σmax in the bar.

P = 80 kNsegment 1: Ø25 mm, 0.5 m, brass (E = 100 GPa)segment 2: Ø16 mm, 2 m, aluminium (E = 70 GPa)
σmax = MPa

Answer key

  1. 1. σr = 33.45 MPa
  2. 2. σr = 82.86 MPa
  3. 3. ε = 6529 µε
  4. 4. δ = 1.063 mm
  5. 5. σ2 = 20.65 MPa
  6. 6. σmax = 397.9 MPa

Full step-by-step solutions: practise this topic on examproblems.com.