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 16 mm0.5 mP = 35 kN

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

P = 35 kNd = 16 mm
σ = MPa
2.Easy
100 kNØ20120 GPaØ120/70800 mmσr​ = ?

A steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 120 mm, inner diameter 70 mm, E = 120 GPa). Both are 800 mm long and are compressed together between rigid plates by 100 kN. Find the compressive stress σr in the rod.

P = 100 kNrod: Ø20 mm, E = 200 GPatube: Ø120/Ø70 mm, E = 120 GPaL = 800 mm
σr = MPa
3.Medium
Ø 30 mmBrass3 mP = 85 kN

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

P = 85 kNd = 30 mmL = 3 mE = 100 GPa
δ = mm
4.Medium
P = ?12600 mm400 mmØ25Ø60δ = 0.5 mm

A bar is made of a steel segment (diameter 25 mm, length 600 mm, E = 200 GPa) joined end to end with a segment made of brass (diameter 60 mm, length 400 mm, E = 100 GPa). It is fixed at one end and pulled at the other. Find the axial load P that stretches it by 0.5 mm in total.

segment 1: steel, Ø25 mm, 600 mm, E = 200 GPasegment 2: brass, Ø60 mm, 400 mm, E = 100 GPaδ = 0.5 mm
P = kN
5.Hard
Ø 30 mmAluminium2 mØ 16 mmSteel1 mP = 65 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 = 65 kNsegment 1: Ø30 mm, 2 m, aluminium (E = 70 GPa)segment 2: Ø16 mm, 1 m, steel (E = 200 GPa)
σmax = MPa
6.Hard
Ø 40 mmAluminium2 mØ 20 mmAluminium2 mP = 40 kN

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

P = 40 kNsegment 1: Ø40 mm, 2 m, aluminium (E = 70 GPa)segment 2: Ø20 mm, 2 m, aluminium (E = 70 GPa)
δ = mm

Answer key

  1. 1. σ = 174.1 MPa
  2. 2. σr = 20.87 MPa
  3. 3. δ = 3.608 mm
  4. 4. P = 66.43 kN
  5. 5. σmax = 323.3 MPa
  6. 6. δ = 4.547 mm

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