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 kNØ40110 GPaØ120/60300 mmσr​ = ?

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 120 mm, inner diameter 60 mm, E = 110 GPa). Both are 300 mm long and are compressed together between rigid plates by 80 kN. Find the compressive stress σr in the rod.

P = 80 kNrod: Ø40 mm, E = 200 GPatube: Ø120/Ø60 mm, E = 110 GPaL = 300 mm
σr = MPa
2.Easy
Ø 30 mm1 mP = 120 kN

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

P = 120 kNd = 30 mm
σ = MPa
3.Medium
250 kNØ30100 GPaØ120/50600 mmδ = ?

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 600 mm long and are compressed together between rigid plates by 250 kN. Find the shortening δ.

P = 250 kNrod: Ø30 mm, E = 200 GPatube: Ø120/Ø50 mm, E = 100 GPaL = 600 mm
δ = mm
4.Medium
50 kNØ20100 GPaØ120/60800 mmδ = ?

A steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of brass (outer diameter 120 mm, inner diameter 60 mm, E = 100 GPa). Both are 800 mm long and are compressed together between rigid plates by 50 kN. Find the shortening δ.

P = 50 kNrod: Ø20 mm, E = 200 GPatube: Ø120/Ø60 mm, E = 100 GPaL = 800 mm
δ = mm
5.Hard
P = ?Ø2070 GPaØ120/50800 mm

A steel rod (diameter 20 mm, E = 200 GPa, allowable stress 120 MPa) sits inside a tube made of aluminium (outer diameter 120 mm, inner diameter 50 mm, E = 70 GPa, allowable stress 80 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø20 mm, E = 200 GPa, σallow = 120 MPatube: Ø120/Ø50 mm, E = 70 GPa, σallow = 80 MPa
Pmax = kN
6.Hard
50 kN12500 mm300 mmØ25Ø50σ2​ = ?

A steel segment (diameter 25 mm, length 500 mm, E = 200 GPa) and a segment made of aluminium (diameter 50 mm, length 300 mm, E = 70 GPa) are joined end to end and fixed between two rigid walls. An axial load of 50 kN acts at the joint, towards segment 2. Find the magnitude of the stress σ2 in segment 2.

segment 1: steel, Ø25 mm, 500 mm, E = 200 GPasegment 2: aluminium, Ø50 mm, 300 mm, E = 70 GPaP = 50 kN
σ2 = MPa

Answer key

  1. 1. σr = 13.51 MPa
  2. 2. σ = 169.8 MPa
  3. 3. δ = 0.1394 mm
  4. 4. δ = 0.0439 mm
  5. 5. Pmax = 430.2 kN
  6. 6. σ2 = 17.83 MPa

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