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 kNØ40100 GPaØ100/60500 mmσr​ = ?

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of brass (outer diameter 100 mm, inner diameter 60 mm, E = 100 GPa). Both are 500 mm long and are compressed together between rigid plates by 100 kN. Find the compressive stress σr in the rod.

P = 100 kNrod: Ø40 mm, E = 200 GPatube: Ø100/Ø60 mm, E = 100 GPaL = 500 mm
σr = MPa
2.Easy
80 kNØ40110 GPaØ100/50800 mmσr​ = ?

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 100 mm, inner diameter 50 mm, E = 110 GPa). Both are 800 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: Ø100/Ø50 mm, E = 110 GPaL = 800 mm
σr = MPa
3.Medium
Ø 30 mmBrass2 mP = 55 kN

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

P = 55 kNd = 30 mmL = 2 mE = 100 GPa
ε = µε
4.Medium
Ø 30 mmAluminium1 mP = 45 kN

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

P = 45 kNd = 30 mmL = 1 mE = 70 GPa
δ = mm
5.Hard
P = ?Ø40110 GPaØ100/50300 mm

A steel rod (diameter 40 mm, E = 200 GPa, allowable stress 250 MPa) sits inside a tube made of bronze (outer diameter 100 mm, inner diameter 50 mm, E = 110 GPa, allowable stress 100 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø40 mm, E = 200 GPa, σallow = 250 MPatube: Ø100/Ø50 mm, E = 110 GPa, σallow = 100 MPa
Pmax = kN
6.Hard
Ø 35 mmBrass1.5 mØ 16 mmBrass1.5 mP = 30 kN

The stepped bar is fixed at the wall and loaded at its free end. Find the total elongation δ.

P = 30 kNsegment 1: Ø35 mm, 1.5 m, brass (E = 100 GPa)segment 2: Ø16 mm, 1.5 m, brass (E = 100 GPa)
δ = mm

Answer key

  1. 1. σr = 26.53 MPa
  2. 2. σr = 17.79 MPa
  3. 3. ε = 778.1 µε
  4. 4. δ = 0.9095 mm
  5. 5. Pmax = 817.5 kN
  6. 6. δ = 2.706 mm

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