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 30 mm2 mP = 70 kN

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

P = 70 kNd = 30 mm
σ = MPa
2.Easy
150 kNØ30120 GPaØ80/60300 mmσr​ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 80 mm, inner diameter 60 mm, E = 120 GPa). Both are 300 mm long and are compressed together between rigid plates by 150 kN. Find the compressive stress σr in the rod.

P = 150 kNrod: Ø30 mm, E = 200 GPatube: Ø80/Ø60 mm, E = 120 GPaL = 300 mm
σr = MPa
3.Medium
P = ?12400 mm300 mmØ25Ø30δ = 0.5 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 brass (diameter 30 mm, length 300 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, 400 mm, E = 200 GPasegment 2: brass, Ø30 mm, 300 mm, E = 100 GPaδ = 0.5 mm
P = kN
4.Medium
Ø 16 mmSteel3 mP = 45 kN

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

P = 45 kNd = 16 mmL = 3 mE = 200 GPa
ε = µε
5.Hard
30 kN12400 mm200 mmØ30Ø60σ2​ = ?

A steel segment (diameter 30 mm, length 400 mm, E = 200 GPa) and a segment made of copper (diameter 60 mm, length 200 mm, E = 120 GPa) are joined end to end and fixed between two rigid walls. An axial load of 30 kN acts at the joint, towards segment 2. Find the magnitude of the stress σ2 in segment 2.

segment 1: steel, Ø30 mm, 400 mm, E = 200 GPasegment 2: copper, Ø60 mm, 200 mm, E = 120 GPaP = 30 kN
σ2 = MPa
6.Hard
Ø 30 mmCopper0.5 mØ 16 mmBrass1.5 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: Ø30 mm, 0.5 m, copper (E = 117 GPa)segment 2: Ø16 mm, 1.5 m, brass (E = 100 GPa)
σmax = MPa

Answer key

  1. 1. σ = 99.03 MPa
  2. 2. σr = 74.03 MPa
  3. 3. P = 60.11 kN
  4. 4. ε = 1119 µε
  5. 5. σ2 = 8.781 MPa
  6. 6. σmax = 547.1 MPa

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