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 kNØ20100 GPaØ80/50400 mmσr​ = ?

A steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of brass (outer diameter 80 mm, inner diameter 50 mm, E = 100 GPa). Both are 400 mm long and are compressed together between rigid plates by 100 kN. Find the compressive stress σr in the rod.

P = 100 kNrod: Ø20 mm, E = 200 GPatube: Ø80/Ø50 mm, E = 100 GPaL = 400 mm
σr = MPa
2.Easy
Ø 12 mm0.5 mP = 45 kN

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

P = 45 kNd = 12 mm
σ = MPa
3.Medium
Ø 10 mmSteel1.5 mP = 105 kN

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

P = 105 kNd = 10 mmL = 1.5 mE = 200 GPa
ε = µε
4.Medium
P = ?12600 mm200 mmØ40Ø30δ = 0.2 mm

A bar is made of a steel segment (diameter 40 mm, length 600 mm, E = 200 GPa) joined end to end with a segment made of copper (diameter 30 mm, length 200 mm, E = 120 GPa). It is fixed at one end and pulled at the other. Find the axial load P that stretches it by 0.2 mm in total.

segment 1: steel, Ø40 mm, 600 mm, E = 200 GPasegment 2: copper, Ø30 mm, 200 mm, E = 120 GPaδ = 0.2 mm
P = kN
5.Hard
P = ?Ø2570 GPaØ120/70800 mm

A steel rod (diameter 25 mm, E = 200 GPa, allowable stress 150 MPa) sits inside a tube made of aluminium (outer diameter 120 mm, inner diameter 70 mm, E = 70 GPa, allowable stress 100 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø25 mm, E = 200 GPa, σallow = 150 MPatube: Ø120/Ø70 mm, E = 70 GPa, σallow = 100 MPa
Pmax = kN
6.Hard
Ø 35 mmCopper0.5 mØ 12 mmBrass0.5 mP = 15 kN

The stepped bar is fixed at the wall and loaded at its free end. Find the largest normal stress σmax in the bar.

P = 15 kNsegment 1: Ø35 mm, 0.5 m, copper (E = 117 GPa)segment 2: Ø12 mm, 0.5 m, brass (E = 100 GPa)
σmax = MPa

Answer key

  1. 1. σr = 54.18 MPa
  2. 2. σ = 397.9 MPa
  3. 3. ε = 6685 µε
  4. 4. P = 42.15 kN
  5. 5. Pmax = 465.3 kN
  6. 6. σmax = 132.6 MPa

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