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.

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1.Easy
Ø 12 mm0.5 mP = 55 kN

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

P = 55 kNd = 12 mm
σ = MPa
2.Easy
300 kNØ30120 GPaØ120/50400 mmσr​ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 120 mm, inner diameter 50 mm, E = 120 GPa). Both are 400 mm long and are compressed together between rigid plates by 300 kN. Find the compressive stress σr in the rod.

P = 300 kNrod: Ø30 mm, E = 200 GPatube: Ø120/Ø50 mm, E = 120 GPaL = 400 mm
σr = MPa
3.Medium
Ø 25 mmAluminium0.5 mP = 80 kN

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

P = 80 kNd = 25 mmL = 0.5 mE = 70 GPa
δ = mm
4.Medium
Ø 16 mmAluminium1.5 mP = 20 kN

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

P = 20 kNd = 16 mmL = 1.5 mE = 70 GPa
ε = µε
5.Hard
Ø 40 mmBrass1 mØ 20 mmCopper1.5 mP = 45 kN

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

P = 45 kNsegment 1: Ø40 mm, 1 m, brass (E = 100 GPa)segment 2: Ø20 mm, 1.5 m, copper (E = 117 GPa)
δ = mm
6.Hard
Ø 30 mmSteel1.5 mØ 20 mmBrass1.5 mP = 90 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 = 90 kNsegment 1: Ø30 mm, 1.5 m, steel (E = 200 GPa)segment 2: Ø20 mm, 1.5 m, brass (E = 100 GPa)
σmax = MPa

Answer key

  1. 1. σ = 486.3 MPa
  2. 2. σr = 47.51 MPa
  3. 3. δ = 1.164 mm
  4. 4. ε = 1421 µε
  5. 5. δ = 2.195 mm
  6. 6. σmax = 286.5 MPa

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