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 = 10 kN

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

P = 10 kNd = 12 mm
σ = MPa
2.Easy
100 kNØ25100 GPaØ100/70400 mmσr​ = ?

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of brass (outer diameter 100 mm, inner diameter 70 mm, E = 100 GPa). Both are 400 mm long and are compressed together between rigid plates by 100 kN. Find the compressive stress σr in the rod.

P = 100 kNrod: Ø25 mm, E = 200 GPatube: Ø100/Ø70 mm, E = 100 GPaL = 400 mm
σr = MPa
3.Medium
300 kNØ40100 GPaØ100/50600 mmδ = ?

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of brass (outer diameter 100 mm, inner diameter 50 mm, E = 100 GPa). Both are 600 mm long and are compressed together between rigid plates by 300 kN. Find the shortening δ.

P = 300 kNrod: Ø40 mm, E = 200 GPatube: Ø100/Ø50 mm, E = 100 GPaL = 600 mm
δ = mm
4.Medium
Ø 12 mmCopper1 mP = 40 kN

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

P = 40 kNd = 12 mmL = 1 mE = 117 GPa
δ = mm
5.Hard
60 kN12600 mm200 mmØ25Ø60σ2​ = ?

A steel segment (diameter 25 mm, length 600 mm, E = 200 GPa) and a segment made of brass (diameter 60 mm, length 200 mm, E = 100 GPa) are joined end to end and fixed between two rigid walls. An axial load of 60 kN acts at the joint, towards segment 2. Find the magnitude of the stress σ2 in segment 2.

segment 1: steel, Ø25 mm, 600 mm, E = 200 GPasegment 2: brass, Ø60 mm, 200 mm, E = 100 GPaP = 60 kN
σ2 = MPa
6.Hard
Ø 40 mmCopper1.5 mØ 12 mmBrass1 mP = 30 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 = 30 kNsegment 1: Ø40 mm, 1.5 m, copper (E = 117 GPa)segment 2: Ø12 mm, 1 m, brass (E = 100 GPa)
σmax = MPa

Answer key

  1. 1. σ = 88.42 MPa
  2. 2. σr = 40.1 MPa
  3. 3. δ = 0.2142 mm
  4. 4. δ = 3.023 mm
  5. 5. σ2 = 19.02 MPa
  6. 6. σmax = 265.3 MPa

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