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
300 kNØ40100 GPaØ120/50500 mmσr​ = ?

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of brass (outer diameter 120 mm, inner diameter 50 mm, E = 100 GPa). Both are 500 mm long and are compressed together between rigid plates by 300 kN. Find the compressive stress σr in the rod.

P = 300 kNrod: Ø40 mm, E = 200 GPatube: Ø120/Ø50 mm, E = 100 GPaL = 500 mm
σr = MPa
2.Easy
250 kNØ40100 GPaØ120/70800 mmσr​ = ?

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of brass (outer diameter 120 mm, inner diameter 70 mm, E = 100 GPa). Both are 800 mm long and are compressed together between rigid plates by 250 kN. Find the compressive stress σr in the rod.

P = 250 kNrod: Ø40 mm, E = 200 GPatube: Ø120/Ø70 mm, E = 100 GPaL = 800 mm
σr = MPa
3.Medium
Ø 20 mmAluminium2.5 mP = 90 kN

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

P = 90 kNd = 20 mmL = 2.5 mE = 70 GPa
δ = mm
4.Medium
Ø 30 mmSteel0.5 mP = 115 kN

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

P = 115 kNd = 30 mmL = 0.5 mE = 200 GPa
ε = µε
5.Hard
P = ?Ø40120 GPaØ100/60300 mm

A steel rod (diameter 40 mm, E = 200 GPa, allowable stress 160 MPa) sits inside a tube made of copper (outer diameter 100 mm, inner diameter 60 mm, E = 120 GPa, allowable stress 70 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø40 mm, E = 200 GPa, σallow = 160 MPatube: Ø100/Ø60 mm, E = 120 GPa, σallow = 70 MPa
Pmax = kN
6.Hard
40 kN12500 mm300 mmØ25Ø60σ2​ = ?

A steel segment (diameter 25 mm, length 500 mm, E = 200 GPa) and a segment made of bronze (diameter 60 mm, length 300 mm, E = 110 GPa) are joined end to end and fixed between two rigid walls. An axial load of 40 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: bronze, Ø60 mm, 300 mm, E = 110 GPaP = 40 kN
σ2 = MPa

Answer key

  1. 1. σr = 50.59 MPa
  2. 2. σr = 50.13 MPa
  3. 3. δ = 10.23 mm
  4. 4. ε = 813.5 µε
  5. 5. Pmax = 498.5 kN
  6. 6. σ2 = 11.89 MPa

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