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
80 kNØ25120 GPaØ120/50400 mmσr​ = ?

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 120 mm, inner diameter 50 mm, E = 120 GPa). Both are 400 mm long and are compressed together between rigid plates by 80 kN. Find the compressive stress σr in the rod.

P = 80 kNrod: Ø25 mm, E = 200 GPatube: Ø120/Ø50 mm, E = 120 GPaL = 400 mm
σr = MPa
2.Easy
250 kNØ2070 GPaØ100/50500 mmσr​ = ?

A steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of aluminium (outer diameter 100 mm, inner diameter 50 mm, E = 70 GPa). Both are 500 mm long and are compressed together between rigid plates by 250 kN. Find the compressive stress σr in the rod.

P = 250 kNrod: Ø20 mm, E = 200 GPatube: Ø100/Ø50 mm, E = 70 GPaL = 500 mm
σr = MPa
3.Medium
Ø 20 mmSteel2 mP = 55 kN

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

P = 55 kNd = 20 mmL = 2 mE = 200 GPa
ε = µε
4.Medium
P = ?12400 mm400 mmØ20Ø60δ = 0.4 mm

A bar is made of a steel segment (diameter 20 mm, length 400 mm, E = 200 GPa) joined end to end with a segment made of bronze (diameter 60 mm, length 400 mm, E = 110 GPa). It is fixed at one end and pulled at the other. Find the axial load P that stretches it by 0.4 mm in total.

segment 1: steel, Ø20 mm, 400 mm, E = 200 GPasegment 2: bronze, Ø60 mm, 400 mm, E = 110 GPaδ = 0.4 mm
P = kN
5.Hard
Ø 40 mmAluminium1 mØ 20 mmCopper1 mP = 85 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 = 85 kNsegment 1: Ø40 mm, 1 m, aluminium (E = 70 GPa)segment 2: Ø20 mm, 1 m, copper (E = 117 GPa)
σmax = MPa
6.Hard
P = ?Ø25100 GPaØ100/50600 mm

A steel rod (diameter 25 mm, E = 200 GPa, allowable stress 200 MPa) sits inside a tube made of brass (outer diameter 100 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: Ø25 mm, E = 200 GPa, σallow = 200 MPatube: Ø100/Ø50 mm, E = 100 GPa, σallow = 80 MPa
Pmax = kN

Answer key

  1. 1. σr = 13.12 MPa
  2. 2. σr = 105.2 MPa
  3. 3. ε = 875.4 µε
  4. 4. P = 52.27 kN
  5. 5. σmax = 270.6 MPa
  6. 6. Pmax = 549.8 kN

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