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 12 mm2 mP = 110 kN

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

P = 110 kNd = 12 mm
σ = MPa
2.Easy
50 kNØ30100 GPaØ80/60600 mmσr​ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of brass (outer diameter 80 mm, inner diameter 60 mm, E = 100 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: Ø30 mm, E = 200 GPatube: Ø80/Ø60 mm, E = 100 GPaL = 600 mm
σr = MPa
3.Medium
P = ?12600 mm400 mmØ25Ø40δ = 0.2 mm

A bar is made of a steel segment (diameter 25 mm, length 600 mm, E = 200 GPa) joined end to end with a segment made of copper (diameter 40 mm, length 400 mm, E = 120 GPa). It is fixed at one end and pulled at the other. Find the axial load P that stretches it by 0.2 mm in total.

segment 1: steel, Ø25 mm, 600 mm, E = 200 GPasegment 2: copper, Ø40 mm, 400 mm, E = 120 GPaδ = 0.2 mm
P = kN
4.Medium
50 kNØ20110 GPaØ120/60300 mmδ = ?

A steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 120 mm, inner diameter 60 mm, E = 110 GPa). Both are 300 mm long and are compressed together between rigid plates by 50 kN. Find the shortening δ.

P = 50 kNrod: Ø20 mm, E = 200 GPatube: Ø120/Ø60 mm, E = 110 GPaL = 300 mm
δ = mm
5.Hard
Ø 40 mmSteel1.5 mØ 16 mmCopper0.5 mP = 120 kN

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

P = 120 kNsegment 1: Ø40 mm, 1.5 m, steel (E = 200 GPa)segment 2: Ø16 mm, 0.5 m, copper (E = 117 GPa)
δ = mm
6.Hard
Ø 30 mmBrass0.5 mØ 16 mmCopper1 mP = 55 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 = 55 kNsegment 1: Ø30 mm, 0.5 m, brass (E = 100 GPa)segment 2: Ø16 mm, 1 m, copper (E = 117 GPa)
σmax = MPa

Answer key

  1. 1. σ = 972.6 MPa
  2. 2. σr = 27.68 MPa
  3. 3. P = 22.82 kN
  4. 4. δ = 0.01506 mm
  5. 5. δ = 3.267 mm
  6. 6. σmax = 273.5 MPa

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