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 20 mm1 mP = 10 kN

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

P = 10 kNd = 20 mm
σ = MPa
2.Easy
150 kNØ30120 GPaØ80/60800 mmσr​ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 80 mm, inner diameter 60 mm, E = 120 GPa). Both are 800 mm long and are compressed together between rigid plates by 150 kN. Find the compressive stress σr in the rod.

P = 150 kNrod: Ø30 mm, E = 200 GPatube: Ø80/Ø60 mm, E = 120 GPaL = 800 mm
σr = MPa
3.Medium
Ø 16 mmSteel0.5 mP = 120 kN

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

P = 120 kNd = 16 mmL = 0.5 mE = 200 GPa
ε = µε
4.Medium
Ø 25 mmAluminium2 mP = 35 kN

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

P = 35 kNd = 25 mmL = 2 mE = 70 GPa
δ = mm
5.Hard
Ø 35 mmCopper1 mØ 20 mmBrass1.5 mP = 90 kN

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

P = 90 kNsegment 1: Ø35 mm, 1 m, copper (E = 117 GPa)segment 2: Ø20 mm, 1.5 m, brass (E = 100 GPa)
δ = mm
6.Hard
Ø 30 mmCopper2 mØ 20 mmBrass0.5 mP = 85 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 = 85 kNsegment 1: Ø30 mm, 2 m, copper (E = 117 GPa)segment 2: Ø20 mm, 0.5 m, brass (E = 100 GPa)
σmax = MPa

Answer key

  1. 1. σ = 31.83 MPa
  2. 2. σr = 74.03 MPa
  3. 3. ε = 2984 µε
  4. 4. δ = 2.037 mm
  5. 5. δ = 5.097 mm
  6. 6. σmax = 270.6 MPa

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