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
150 kNØ3070 GPaØ120/50300 mmσr​ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of aluminium (outer diameter 120 mm, inner diameter 50 mm, E = 70 GPa). Both are 300 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/Ø50 mm, E = 70 GPaL = 300 mm
σr = MPa
2.Easy
Ø 12 mm1.5 mP = 115 kN

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

P = 115 kNd = 12 mm
σ = MPa
3.Medium
P = ?12600 mm400 mmØ40Ø30δ = 0.2 mm

A bar is made of a steel segment (diameter 40 mm, length 600 mm, E = 200 GPa) joined end to end with a segment made of aluminium (diameter 30 mm, length 400 mm, E = 70 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, Ø40 mm, 600 mm, E = 200 GPasegment 2: aluminium, Ø30 mm, 400 mm, E = 70 GPaδ = 0.2 mm
P = kN
4.Medium
Ø 30 mmCopper3 mP = 115 kN

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

P = 115 kNd = 30 mmL = 3 mE = 117 GPa
δ = mm
5.Hard
Ø 25 mmBrass0.5 mØ 20 mmSteel0.5 mP = 15 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 = 15 kNsegment 1: Ø25 mm, 0.5 m, brass (E = 100 GPa)segment 2: Ø20 mm, 0.5 m, steel (E = 200 GPa)
σmax = MPa
6.Hard
Ø 30 mmSteel1.5 mØ 12 mmSteel1.5 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, 1.5 m, steel (E = 200 GPa)segment 2: Ø12 mm, 1.5 m, steel (E = 200 GPa)
δ = mm

Answer key

  1. 1. σr = 37.71 MPa
  2. 2. σ = 1017 MPa
  3. 3. P = 19.1 kN
  4. 4. δ = 4.172 mm
  5. 5. σmax = 47.75 MPa
  6. 6. δ = 6.923 mm

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