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 10 mm0.5 mP = 75 kN

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

P = 75 kNd = 10 mm
σ = MPa
2.Easy
300 kNØ20110 GPaØ80/60400 mmσr​ = ?

A steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 80 mm, inner diameter 60 mm, E = 110 GPa). Both are 400 mm long and are compressed together between rigid plates by 300 kN. Find the compressive stress σr in the rod.

P = 300 kNrod: Ø20 mm, E = 200 GPatube: Ø80/Ø60 mm, E = 110 GPaL = 400 mm
σr = MPa
3.Medium
80 kNØ30110 GPaØ100/60500 mmδ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 100 mm, inner diameter 60 mm, E = 110 GPa). Both are 500 mm long and are compressed together between rigid plates by 80 kN. Find the shortening δ.

P = 80 kNrod: Ø30 mm, E = 200 GPatube: Ø100/Ø60 mm, E = 110 GPaL = 500 mm
δ = mm
4.Medium
200 kNØ25120 GPaØ100/70500 mmδ = ?

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 100 mm, inner diameter 70 mm, E = 120 GPa). Both are 500 mm long and are compressed together between rigid plates by 200 kN. Find the shortening δ.

P = 200 kNrod: Ø25 mm, E = 200 GPatube: Ø100/Ø70 mm, E = 120 GPaL = 500 mm
δ = mm
5.Hard
P = ?Ø20100 GPaØ100/60800 mm

A steel rod (diameter 20 mm, E = 200 GPa, allowable stress 150 MPa) sits inside a tube made of brass (outer diameter 100 mm, inner diameter 60 mm, E = 100 GPa, allowable stress 60 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø20 mm, E = 200 GPa, σallow = 150 MPatube: Ø100/Ø60 mm, E = 100 GPa, σallow = 60 MPa
Pmax = kN
6.Hard
Ø 30 mmSteel1 mØ 16 mmSteel2 mP = 50 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 = 50 kNsegment 1: Ø30 mm, 1 m, steel (E = 200 GPa)segment 2: Ø16 mm, 2 m, steel (E = 200 GPa)
σmax = MPa

Answer key

  1. 1. σ = 954.9 MPa
  2. 2. σr = 196.9 MPa
  3. 3. δ = 0.05761 mm
  4. 4. δ = 0.1728 mm
  5. 5. Pmax = 339.3 kN
  6. 6. σmax = 248.7 MPa

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