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 kNØ40120 GPaØ120/50300 mmσr​ = ?

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 120 mm, inner diameter 50 mm, E = 120 GPa). Both are 300 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 = 120 GPaL = 300 mm
σr = MPa
2.Easy
Ø 10 mm0.5 mP = 100 kN

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

P = 100 kNd = 10 mm
σ = MPa
3.Medium
P = ?12500 mm500 mmØ40Ø50δ = 0.4 mm

A bar is made of a steel segment (diameter 40 mm, length 500 mm, E = 200 GPa) joined end to end with a segment made of aluminium (diameter 50 mm, length 500 mm, E = 70 GPa). It is fixed at one end and pulled at the other. Find the axial load P that stretches it by 0.4 mm in total.

segment 1: steel, Ø40 mm, 500 mm, E = 200 GPasegment 2: aluminium, Ø50 mm, 500 mm, E = 70 GPaδ = 0.4 mm
P = kN
4.Medium
Ø 20 mmCopper1 mP = 15 kN

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

P = 15 kNd = 20 mmL = 1 mE = 117 GPa
ε = µε
5.Hard
P = ?Ø30100 GPaØ80/50800 mm

A steel rod (diameter 30 mm, E = 200 GPa, allowable stress 160 MPa) sits inside a tube made of brass (outer diameter 80 mm, inner diameter 50 mm, E = 100 GPa, allowable stress 80 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø30 mm, E = 200 GPa, σallow = 160 MPatube: Ø80/Ø50 mm, E = 100 GPa, σallow = 80 MPa
Pmax = kN
6.Hard
Ø 35 mmBrass2 mØ 12 mmBrass2 mP = 80 kN

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

P = 80 kNsegment 1: Ø35 mm, 2 m, brass (E = 100 GPa)segment 2: Ø12 mm, 2 m, brass (E = 100 GPa)
δ = mm

Answer key

  1. 1. σr = 43.7 MPa
  2. 2. σ = 1273 MPa
  3. 3. P = 71.08 kN
  4. 4. ε = 408.1 µε
  5. 5. Pmax = 358.1 kN
  6. 6. δ = 15.81 mm

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