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
Ø 30 mm2 mP = 95 kN

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

P = 95 kNd = 30 mm
σ = MPa
2.Easy
50 kNØ3070 GPaØ100/70300 mmσr​ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of aluminium (outer diameter 100 mm, inner diameter 70 mm, E = 70 GPa). Both are 300 mm long and are compressed together between rigid plates by 50 kN. Find the compressive stress σr in the rod.

P = 50 kNrod: Ø30 mm, E = 200 GPatube: Ø100/Ø70 mm, E = 70 GPaL = 300 mm
σr = MPa
3.Medium
300 kNØ30120 GPaØ120/60800 mmδ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 120 mm, inner diameter 60 mm, E = 120 GPa). Both are 800 mm long and are compressed together between rigid plates by 300 kN. Find the shortening δ.

P = 300 kNrod: Ø30 mm, E = 200 GPatube: Ø120/Ø60 mm, E = 120 GPaL = 800 mm
δ = mm
4.Medium
Ø 12 mmBrass0.5 mP = 20 kN

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

P = 20 kNd = 12 mmL = 0.5 mE = 100 GPa
δ = mm
5.Hard
Ø 35 mmAluminium2 mØ 16 mmSteel2 mP = 85 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 = 85 kNsegment 1: Ø35 mm, 2 m, aluminium (E = 70 GPa)segment 2: Ø16 mm, 2 m, steel (E = 200 GPa)
σmax = MPa
6.Hard
P = ?Ø20110 GPaØ120/70600 mm

A steel rod (diameter 20 mm, E = 200 GPa, allowable stress 200 MPa) sits inside a tube made of bronze (outer diameter 120 mm, inner diameter 70 mm, E = 110 GPa, allowable stress 80 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø20 mm, E = 200 GPa, σallow = 200 MPatube: Ø120/Ø70 mm, E = 110 GPa, σallow = 80 MPa
Pmax = kN

Answer key

  1. 1. σ = 134.4 MPa
  2. 2. σr = 23.71 MPa
  3. 3. δ = 0.207 mm
  4. 4. δ = 0.8842 mm
  5. 5. σmax = 422.8 MPa
  6. 6. Pmax = 642.6 kN

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