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
50 kNØ40100 GPaØ100/70500 mmσr​ = ?

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of brass (outer diameter 100 mm, inner diameter 70 mm, E = 100 GPa). Both are 500 mm long and are compressed together between rigid plates by 50 kN. Find the compressive stress σr in the rod.

P = 50 kNrod: Ø40 mm, E = 200 GPatube: Ø100/Ø70 mm, E = 100 GPaL = 500 mm
σr = MPa
2.Easy
Ø 30 mm1.5 mP = 100 kN

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

P = 100 kNd = 30 mm
σ = MPa
3.Medium
Ø 25 mmSteel2 mP = 95 kN

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

P = 95 kNd = 25 mmL = 2 mE = 200 GPa
δ = mm
4.Medium
Ø 10 mmCopper1 mP = 35 kN

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

P = 35 kNd = 10 mmL = 1 mE = 117 GPa
ε = µε
5.Hard
Ø 35 mmCopper1.5 mØ 12 mmBrass2 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: Ø35 mm, 1.5 m, copper (E = 117 GPa)segment 2: Ø12 mm, 2 m, brass (E = 100 GPa)
σmax = MPa
6.Hard
Ø 30 mmBrass0.5 mØ 20 mmSteel0.5 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: Ø30 mm, 0.5 m, brass (E = 100 GPa)segment 2: Ø20 mm, 0.5 m, steel (E = 200 GPa)
δ = mm

Answer key

  1. 1. σr = 15.34 MPa
  2. 2. σ = 141.5 MPa
  3. 3. δ = 1.935 mm
  4. 4. ε = 3809 µε
  5. 5. σmax = 486.3 MPa
  6. 6. δ = 1.353 mm

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