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
200 kNØ2070 GPaØ80/60600 mmσr​ = ?

A steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of aluminium (outer diameter 80 mm, inner diameter 60 mm, E = 70 GPa). Both are 600 mm long and are compressed together between rigid plates by 200 kN. Find the compressive stress σr in the rod.

P = 200 kNrod: Ø20 mm, E = 200 GPatube: Ø80/Ø60 mm, E = 70 GPaL = 600 mm
σr = MPa
2.Easy
Ø 20 mm1.5 mP = 75 kN

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

P = 75 kNd = 20 mm
σ = MPa
3.Medium
300 kNØ40110 GPaØ80/50300 mmδ = ?

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 80 mm, inner diameter 50 mm, E = 110 GPa). Both are 300 mm long and are compressed together between rigid plates by 300 kN. Find the shortening δ.

P = 300 kNrod: Ø40 mm, E = 200 GPatube: Ø80/Ø50 mm, E = 110 GPaL = 300 mm
δ = mm
4.Medium
Ø 10 mmCopper0.5 mP = 60 kN

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

P = 60 kNd = 10 mmL = 0.5 mE = 117 GPa
δ = mm
5.Hard
Ø 30 mmCopper1 mØ 16 mmAluminium2 mP = 115 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 = 115 kNsegment 1: Ø30 mm, 1 m, copper (E = 117 GPa)segment 2: Ø16 mm, 2 m, aluminium (E = 70 GPa)
σmax = MPa
6.Hard
P = ?Ø30100 GPaØ80/50600 mm

A steel rod (diameter 30 mm, E = 200 GPa, allowable stress 250 MPa) sits inside a tube made of brass (outer diameter 80 mm, inner diameter 50 mm, E = 100 GPa, allowable stress 80 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø30 mm, E = 200 GPa, σallow = 250 MPatube: Ø80/Ø50 mm, E = 100 GPa, σallow = 80 MPa
Pmax = kN

Answer key

  1. 1. σr = 184.5 MPa
  2. 2. σ = 238.7 MPa
  3. 3. δ = 0.153 mm
  4. 4. δ = 3.265 mm
  5. 5. σmax = 572 MPa
  6. 6. Pmax = 358.1 kN

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