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 10 mm1.5 mP = 80 kN

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

P = 80 kNd = 10 mm
σ = MPa
2.Easy
150 kNØ30100 GPaØ120/60600 mmσr​ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of brass (outer diameter 120 mm, inner diameter 60 mm, E = 100 GPa). Both are 600 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: Ø120/Ø60 mm, E = 100 GPaL = 600 mm
σr = MPa
3.Medium
Ø 20 mmCopper1.5 mP = 110 kN

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

P = 110 kNd = 20 mmL = 1.5 mE = 117 GPa
δ = mm
4.Medium
Ø 10 mmBrass2.5 mP = 80 kN

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

P = 80 kNd = 10 mmL = 2.5 mE = 100 GPa
δ = mm
5.Hard
Ø 35 mmCopper0.5 mØ 12 mmCopper1.5 mP = 95 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 = 95 kNsegment 1: Ø35 mm, 0.5 m, copper (E = 117 GPa)segment 2: Ø12 mm, 1.5 m, copper (E = 117 GPa)
σmax = MPa
6.Hard
Ø 40 mmSteel1.5 mØ 20 mmCopper0.5 mP = 25 kN

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

P = 25 kNsegment 1: Ø40 mm, 1.5 m, steel (E = 200 GPa)segment 2: Ø20 mm, 0.5 m, copper (E = 117 GPa)
δ = mm

Answer key

  1. 1. σ = 1019 MPa
  2. 2. σr = 30.32 MPa
  3. 3. δ = 4.489 mm
  4. 4. δ = 25.46 mm
  5. 5. σmax = 840 MPa
  6. 6. δ = 0.4893 mm

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