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 20 mm2 mP = 65 kN

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

P = 65 kNd = 20 mm
σ = MPa
2.Easy
80 kNØ25120 GPaØ100/50300 mmσr​ = ?

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 100 mm, inner diameter 50 mm, E = 120 GPa). Both are 300 mm long and are compressed together between rigid plates by 80 kN. Find the compressive stress σr in the rod.

P = 80 kNrod: Ø25 mm, E = 200 GPatube: Ø100/Ø50 mm, E = 120 GPaL = 300 mm
σr = MPa
3.Medium
Ø 12 mmCopper0.5 mP = 100 kN

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

P = 100 kNd = 12 mmL = 0.5 mE = 117 GPa
ε = µε
4.Medium
P = ?12500 mm500 mmØ20Ø60δ = 0.2 mm

A bar is made of a steel segment (diameter 20 mm, length 500 mm, E = 200 GPa) joined end to end with a segment made of copper (diameter 60 mm, length 500 mm, E = 120 GPa). It is fixed at one end and pulled at the other. Find the axial load P that stretches it by 0.2 mm in total.

segment 1: steel, Ø20 mm, 500 mm, E = 200 GPasegment 2: copper, Ø60 mm, 500 mm, E = 120 GPaδ = 0.2 mm
P = kN
5.Hard
20 kN12600 mm500 mmØ40Ø60σ2​ = ?

A steel segment (diameter 40 mm, length 600 mm, E = 200 GPa) and a segment made of aluminium (diameter 60 mm, length 500 mm, E = 70 GPa) are joined end to end and fixed between two rigid walls. An axial load of 20 kN acts at the joint, towards segment 2. Find the magnitude of the stress σ2 in segment 2.

segment 1: steel, Ø40 mm, 600 mm, E = 200 GPasegment 2: aluminium, Ø60 mm, 500 mm, E = 70 GPaP = 20 kN
σ2 = MPa
6.Hard
Ø 35 mmCopper1 mØ 16 mmCopper2 mP = 105 kN

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

P = 105 kNsegment 1: Ø35 mm, 1 m, copper (E = 117 GPa)segment 2: Ø16 mm, 2 m, copper (E = 117 GPa)
δ = mm

Answer key

  1. 1. σ = 206.9 MPa
  2. 2. σr = 19.87 MPa
  3. 3. ε = 7557 µε
  4. 4. P = 21.21 kN
  5. 5. σ2 = 3.437 MPa
  6. 6. δ = 9.86 mm

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