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 kNØ20100 GPaØ80/60500 mmσr​ = ?

A steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of brass (outer diameter 80 mm, inner diameter 60 mm, E = 100 GPa). Both are 500 mm long and are compressed together between rigid plates by 250 kN. Find the compressive stress σr in the rod.

P = 250 kNrod: Ø20 mm, E = 200 GPatube: Ø80/Ø60 mm, E = 100 GPaL = 500 mm
σr = MPa
2.Easy
Ø 25 mm0.5 mP = 95 kN

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

P = 95 kNd = 25 mm
σ = MPa
3.Medium
Ø 10 mmSteel2.5 mP = 70 kN

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

P = 70 kNd = 10 mmL = 2.5 mE = 200 GPa
δ = mm
4.Medium
P = ?12500 mm500 mmØ25Ø30δ = 0.5 mm

A bar is made of a steel segment (diameter 25 mm, length 500 mm, E = 200 GPa) joined end to end with a segment made of brass (diameter 30 mm, length 500 mm, E = 100 GPa). It is fixed at one end and pulled at the other. Find the axial load P that stretches it by 0.5 mm in total.

segment 1: steel, Ø25 mm, 500 mm, E = 200 GPasegment 2: brass, Ø30 mm, 500 mm, E = 100 GPaδ = 0.5 mm
P = kN
5.Hard
Ø 40 mmCopper2 mØ 16 mmSteel2 mP = 40 kN

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

P = 40 kNsegment 1: Ø40 mm, 2 m, copper (E = 117 GPa)segment 2: Ø16 mm, 2 m, steel (E = 200 GPa)
δ = mm
6.Hard
Ø 40 mmAluminium0.5 mØ 16 mmBrass1 mP = 90 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 = 90 kNsegment 1: Ø40 mm, 0.5 m, aluminium (E = 70 GPa)segment 2: Ø16 mm, 1 m, brass (E = 100 GPa)
σmax = MPa

Answer key

  1. 1. σr = 176.8 MPa
  2. 2. σ = 193.5 MPa
  3. 3. δ = 11.14 mm
  4. 4. P = 41.1 kN
  5. 5. δ = 2.534 mm
  6. 6. σmax = 447.6 MPa

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