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
300 kNØ30100 GPaØ120/50800 mmσr​ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of brass (outer diameter 120 mm, inner diameter 50 mm, E = 100 GPa). Both are 800 mm long and are compressed together between rigid plates by 300 kN. Find the compressive stress σr in the rod.

P = 300 kNrod: Ø30 mm, E = 200 GPatube: Ø120/Ø50 mm, E = 100 GPaL = 800 mm
σr = MPa
2.Easy
Ø 12 mm0.5 mP = 20 kN

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

P = 20 kNd = 12 mm
σ = MPa
3.Medium
300 kNØ2070 GPaØ80/60400 mmδ = ?

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 400 mm long and are compressed together between rigid plates by 300 kN. Find the shortening δ.

P = 300 kNrod: Ø20 mm, E = 200 GPatube: Ø80/Ø60 mm, E = 70 GPaL = 400 mm
δ = mm
4.Medium
Ø 25 mmAluminium0.5 mP = 65 kN

Find the axial strain ε in the aluminium bar, in microstrain (µε = 10⁻⁶).

P = 65 kNd = 25 mmL = 0.5 mE = 70 GPa
ε = µε
5.Hard
Ø 25 mmSteel1 mØ 12 mmBrass1 mP = 70 kN

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

P = 70 kNsegment 1: Ø25 mm, 1 m, steel (E = 200 GPa)segment 2: Ø12 mm, 1 m, brass (E = 100 GPa)
δ = mm
6.Hard
20 kN12600 mm300 mmØ40Ø30σ2​ = ?

A steel segment (diameter 40 mm, length 600 mm, E = 200 GPa) and a segment made of bronze (diameter 30 mm, length 300 mm, E = 110 GPa) are joined end to end and fixed between two rigid walls. An axial load of 20 kN acts at the joint, towards segment 2. Find the magnitude of the stress σ2 in segment 2.

segment 1: steel, Ø40 mm, 600 mm, E = 200 GPasegment 2: bronze, Ø30 mm, 300 mm, E = 110 GPaP = 20 kN
σ2 = MPa

Answer key

  1. 1. σr = 55.76 MPa
  2. 2. σ = 176.8 MPa
  3. 3. δ = 0.5536 mm
  4. 4. ε = 1892 µε
  5. 5. δ = 6.902 mm
  6. 6. σ2 = 10.82 MPa

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