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 kNØ30110 GPaØ100/50300 mmσr​ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 100 mm, inner diameter 50 mm, E = 110 GPa). Both are 300 mm long and are compressed together between rigid plates by 50 kN. Find the compressive stress σr in the rod.

P = 50 kNrod: Ø30 mm, E = 200 GPatube: Ø100/Ø50 mm, E = 110 GPaL = 300 mm
σr = MPa
2.Easy
150 kNØ40110 GPaØ120/70400 mmσr​ = ?

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 120 mm, inner diameter 70 mm, E = 110 GPa). Both are 400 mm long and are compressed together between rigid plates by 150 kN. Find the compressive stress σr in the rod.

P = 150 kNrod: Ø40 mm, E = 200 GPatube: Ø120/Ø70 mm, E = 110 GPaL = 400 mm
σr = MPa
3.Medium
Ø 30 mmCopper0.5 mP = 65 kN

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

P = 65 kNd = 30 mmL = 0.5 mE = 117 GPa
ε = µε
4.Medium
Ø 30 mmCopper1.5 mP = 20 kN

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

P = 20 kNd = 30 mmL = 1.5 mE = 117 GPa
δ = mm
5.Hard
40 kN12600 mm300 mmØ20Ø30σ2​ = ?

A steel segment (diameter 20 mm, length 600 mm, E = 200 GPa) and a segment made of bronze (diameter 30 mm, length 300 mm, E = 110 GPa) are joined end to end and fixed between two rigid walls. An axial load of 40 kN acts at the joint, towards segment 2. Find the magnitude of the stress σ2 in segment 2.

segment 1: steel, Ø20 mm, 600 mm, E = 200 GPasegment 2: bronze, Ø30 mm, 300 mm, E = 110 GPaP = 40 kN
σ2 = MPa
6.Hard
Ø 40 mmCopper1.5 mØ 16 mmCopper0.5 mP = 85 kN

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

P = 85 kNsegment 1: Ø40 mm, 1.5 m, copper (E = 117 GPa)segment 2: Ø16 mm, 0.5 m, copper (E = 117 GPa)
δ = mm

Answer key

  1. 1. σr = 12.67 MPa
  2. 2. σr = 27.98 MPa
  3. 3. ε = 786 µε
  4. 4. δ = 0.3627 mm
  5. 5. σ2 = 40.3 MPa
  6. 6. δ = 2.674 mm

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