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 = 105 kN

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

P = 105 kNd = 12 mm
σ = MPa
2.Easy
200 kNØ2570 GPaØ120/70500 mmσr​ = ?

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of aluminium (outer diameter 120 mm, inner diameter 70 mm, E = 70 GPa). Both are 500 mm long and are compressed together between rigid plates by 200 kN. Find the compressive stress σr in the rod.

P = 200 kNrod: Ø25 mm, E = 200 GPatube: Ø120/Ø70 mm, E = 70 GPaL = 500 mm
σr = MPa
3.Medium
Ø 20 mmBrass2 mP = 110 kN

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

P = 110 kNd = 20 mmL = 2 mE = 100 GPa
ε = µε
4.Medium
P = ?12400 mm400 mmØ25Ø60δ = 0.3 mm

A bar is made of a steel segment (diameter 25 mm, length 400 mm, E = 200 GPa) joined end to end with a segment made of aluminium (diameter 60 mm, length 400 mm, E = 70 GPa). It is fixed at one end and pulled at the other. Find the axial load P that stretches it by 0.3 mm in total.

segment 1: steel, Ø25 mm, 400 mm, E = 200 GPasegment 2: aluminium, Ø60 mm, 400 mm, E = 70 GPaδ = 0.3 mm
P = kN
5.Hard
Ø 40 mmCopper1.5 mØ 16 mmSteel0.5 mP = 110 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 = 110 kNsegment 1: Ø40 mm, 1.5 m, copper (E = 117 GPa)segment 2: Ø16 mm, 0.5 m, steel (E = 200 GPa)
σmax = MPa
6.Hard
Ø 30 mmSteel0.5 mØ 16 mmAluminium2 mP = 30 kN

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

P = 30 kNsegment 1: Ø30 mm, 0.5 m, steel (E = 200 GPa)segment 2: Ø16 mm, 2 m, aluminium (E = 70 GPa)
δ = mm

Answer key

  1. 1. σ = 928.4 MPa
  2. 2. σr = 64.47 MPa
  3. 3. ε = 3501 µε
  4. 4. P = 49.22 kN
  5. 5. σmax = 547.1 MPa
  6. 6. δ = 4.369 mm

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