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 kNØ40100 GPaØ120/50600 mmσr​ = ?

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 80 kN. Find the compressive stress σr in the rod.

P = 80 kNrod: Ø40 mm, E = 200 GPatube: Ø120/Ø50 mm, E = 100 GPaL = 600 mm
σr = MPa
2.Easy
Ø 20 mm0.5 mP = 80 kN

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

P = 80 kNd = 20 mm
σ = MPa
3.Medium
Ø 12 mmBrass1 mP = 90 kN

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

P = 90 kNd = 12 mmL = 1 mE = 100 GPa
δ = mm
4.Medium
Ø 12 mmCopper3 mP = 20 kN

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

P = 20 kNd = 12 mmL = 3 mE = 117 GPa
ε = µε
5.Hard
Ø 30 mmSteel1 mØ 20 mmAluminium1 mP = 70 kN

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

P = 70 kNsegment 1: Ø30 mm, 1 m, steel (E = 200 GPa)segment 2: Ø20 mm, 1 m, aluminium (E = 70 GPa)
δ = mm
6.Hard
Ø 30 mmSteel0.5 mØ 20 mmSteel0.5 mP = 10 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 = 10 kNsegment 1: Ø30 mm, 0.5 m, steel (E = 200 GPa)segment 2: Ø20 mm, 0.5 m, steel (E = 200 GPa)
σmax = MPa

Answer key

  1. 1. σr = 13.49 MPa
  2. 2. σ = 254.6 MPa
  3. 3. δ = 7.958 mm
  4. 4. ε = 1511 µε
  5. 5. δ = 3.678 mm
  6. 6. σmax = 31.83 MPa

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