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
80 kNØ30120 GPaØ100/50400 mmσr​ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 100 mm, inner diameter 50 mm, E = 120 GPa). Both are 400 mm long and are compressed together between rigid plates by 80 kN. Find the compressive stress σr in the rod.

P = 80 kNrod: Ø30 mm, E = 200 GPatube: Ø100/Ø50 mm, E = 120 GPaL = 400 mm
σr = MPa
2.Easy
Ø 20 mm1 mP = 95 kN

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

P = 95 kNd = 20 mm
σ = MPa
3.Medium
Ø 20 mmCopper1.5 mP = 120 kN

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

P = 120 kNd = 20 mmL = 1.5 mE = 117 GPa
δ = mm
4.Medium
Ø 10 mmBrass0.5 mP = 25 kN

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

P = 25 kNd = 10 mmL = 0.5 mE = 100 GPa
δ = mm
5.Hard
Ø 30 mmAluminium0.5 mØ 20 mmBrass1.5 mP = 70 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 = 70 kNsegment 1: Ø30 mm, 0.5 m, aluminium (E = 70 GPa)segment 2: Ø20 mm, 1.5 m, brass (E = 100 GPa)
σmax = MPa
6.Hard
Ø 30 mmSteel0.5 mØ 16 mmAluminium1 mP = 65 kN

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

P = 65 kNsegment 1: Ø30 mm, 0.5 m, steel (E = 200 GPa)segment 2: Ø16 mm, 1 m, aluminium (E = 70 GPa)
δ = mm

Answer key

  1. 1. σr = 18.86 MPa
  2. 2. σ = 302.4 MPa
  3. 3. δ = 4.897 mm
  4. 4. δ = 1.592 mm
  5. 5. σmax = 222.8 MPa
  6. 6. δ = 4.848 mm

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