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 mm2 mP = 15 kN

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

P = 15 kNd = 12 mm
σ = MPa
2.Easy
200 kNØ25100 GPaØ80/50400 mmσr​ = ?

A steel rod (diameter 25 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 200 kN. Find the compressive stress σr in the rod.

P = 200 kNrod: Ø25 mm, E = 200 GPatube: Ø80/Ø50 mm, E = 100 GPaL = 400 mm
σr = MPa
3.Medium
Ø 30 mmSteel1 mP = 15 kN

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

P = 15 kNd = 30 mmL = 1 mE = 200 GPa
δ = mm
4.Medium
Ø 16 mmCopper3 mP = 20 kN

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

P = 20 kNd = 16 mmL = 3 mE = 117 GPa
ε = µε
5.Hard
Ø 30 mmAluminium1 mØ 16 mmSteel0.5 mP = 35 kN

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

P = 35 kNsegment 1: Ø30 mm, 1 m, aluminium (E = 70 GPa)segment 2: Ø16 mm, 0.5 m, steel (E = 200 GPa)
δ = mm
6.Hard
Ø 25 mmAluminium0.5 mØ 16 mmCopper1.5 mP = 55 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 = 55 kNsegment 1: Ø25 mm, 0.5 m, aluminium (E = 70 GPa)segment 2: Ø16 mm, 1.5 m, copper (E = 117 GPa)
σmax = MPa

Answer key

  1. 1. σ = 132.6 MPa
  2. 2. σr = 98.89 MPa
  3. 3. δ = 0.1061 mm
  4. 4. ε = 850.2 µε
  5. 5. δ = 1.143 mm
  6. 6. σmax = 273.5 MPa

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