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
100 kNØ30110 GPaØ100/60800 mmσr​ = ?

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 800 mm long and are compressed together between rigid plates by 100 kN. Find the compressive stress σr in the rod.

P = 100 kNrod: Ø30 mm, E = 200 GPatube: Ø100/Ø60 mm, E = 110 GPaL = 800 mm
σr = MPa
2.Easy
Ø 10 mm2 mP = 80 kN

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

P = 80 kNd = 10 mm
σ = MPa
3.Medium
100 kNØ3070 GPaØ120/60300 mmδ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of aluminium (outer diameter 120 mm, inner diameter 60 mm, E = 70 GPa). Both are 300 mm long and are compressed together between rigid plates by 100 kN. Find the shortening δ.

P = 100 kNrod: Ø30 mm, E = 200 GPatube: Ø120/Ø60 mm, E = 70 GPaL = 300 mm
δ = mm
4.Medium
Ø 10 mmSteel1.5 mP = 85 kN

Find the elongation δ of the steel bar under the axial load.

P = 85 kNd = 10 mmL = 1.5 mE = 200 GPa
δ = mm
5.Hard
20 kN12400 mm500 mmØ30Ø50σ2​ = ?

A steel segment (diameter 30 mm, length 400 mm, E = 200 GPa) and a segment made of brass (diameter 50 mm, length 500 mm, E = 100 GPa) are joined end to end and fixed between two rigid walls. An axial load of 20 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: brass, Ø50 mm, 500 mm, E = 100 GPaP = 20 kN
σ2 = MPa
6.Hard
P = ?Ø30100 GPaØ100/60800 mm

A steel rod (diameter 30 mm, E = 200 GPa, allowable stress 200 MPa) sits inside a tube made of brass (outer diameter 100 mm, inner diameter 60 mm, E = 100 GPa, allowable stress 100 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø30 mm, E = 200 GPa, σallow = 200 MPatube: Ø100/Ø60 mm, E = 100 GPa, σallow = 100 MPa
Pmax = kN

Answer key

  1. 1. σr = 28.81 MPa
  2. 2. σ = 1019 MPa
  3. 3. δ = 0.04081 mm
  4. 4. δ = 8.117 mm
  5. 5. σ2 = 5.361 MPa
  6. 6. Pmax = 644 kN

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