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
250 kNØ40100 GPaØ100/60800 mmσr​ = ?

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of brass (outer diameter 100 mm, inner diameter 60 mm, E = 100 GPa). Both are 800 mm long and are compressed together between rigid plates by 250 kN. Find the compressive stress σr in the rod.

P = 250 kNrod: Ø40 mm, E = 200 GPatube: Ø100/Ø60 mm, E = 100 GPaL = 800 mm
σr = MPa
2.Easy
150 kNØ25100 GPaØ120/50800 mmσr​ = ?

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of brass (outer diameter 120 mm, inner diameter 50 mm, E = 100 GPa). Both are 800 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: Ø120/Ø50 mm, E = 100 GPaL = 800 mm
σr = MPa
3.Medium
Ø 10 mmAluminium1.5 mP = 85 kN

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

P = 85 kNd = 10 mmL = 1.5 mE = 70 GPa
ε = µε
4.Medium
Ø 25 mmCopper2 mP = 60 kN

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

P = 60 kNd = 25 mmL = 2 mE = 117 GPa
δ = mm
5.Hard
P = ?Ø20120 GPaØ120/70300 mm

A steel rod (diameter 20 mm, E = 200 GPa, allowable stress 250 MPa) sits inside a tube made of copper (outer diameter 120 mm, inner diameter 70 mm, E = 120 GPa, allowable stress 80 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø20 mm, E = 200 GPa, σallow = 250 MPatube: Ø120/Ø70 mm, E = 120 GPa, σallow = 80 MPa
Pmax = kN
6.Hard
Ø 25 mmCopper1.5 mØ 20 mmCopper2 mP = 100 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 = 100 kNsegment 1: Ø25 mm, 1.5 m, copper (E = 117 GPa)segment 2: Ø20 mm, 2 m, copper (E = 117 GPa)
σmax = MPa

Answer key

  1. 1. σr = 66.31 MPa
  2. 2. σr = 29.05 MPa
  3. 3. ε = 15461 µε
  4. 4. δ = 2.089 mm
  5. 5. Pmax = 638.8 kN
  6. 6. σmax = 318.3 MPa

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