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 10 mm1.5 mP = 40 kN

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

P = 40 kNd = 10 mm
σ = MPa
2.Easy
50 kNØ30100 GPaØ80/50300 mmσr​ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of brass (outer diameter 80 mm, inner diameter 50 mm, E = 100 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: Ø80/Ø50 mm, E = 100 GPaL = 300 mm
σr = MPa
3.Medium
P = ?12300 mm200 mmØ25Ø60δ = 0.2 mm

A bar is made of a steel segment (diameter 25 mm, length 300 mm, E = 200 GPa) joined end to end with a segment made of aluminium (diameter 60 mm, length 200 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, Ø25 mm, 300 mm, E = 200 GPasegment 2: aluminium, Ø60 mm, 200 mm, E = 70 GPaδ = 0.2 mm
P = kN
4.Medium
200 kNØ40120 GPaØ100/70600 mmδ = ?

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 100 mm, inner diameter 70 mm, E = 120 GPa). Both are 600 mm long and are compressed together between rigid plates by 200 kN. Find the shortening δ.

P = 200 kNrod: Ø40 mm, E = 200 GPatube: Ø100/Ø70 mm, E = 120 GPaL = 600 mm
δ = mm
5.Hard
Ø 40 mmSteel2 mØ 20 mmBrass1.5 mP = 60 kN

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

P = 60 kNsegment 1: Ø40 mm, 2 m, steel (E = 200 GPa)segment 2: Ø20 mm, 1.5 m, brass (E = 100 GPa)
δ = mm
6.Hard
Ø 30 mmSteel2 mØ 20 mmSteel1 mP = 120 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 = 120 kNsegment 1: Ø30 mm, 2 m, steel (E = 200 GPa)segment 2: Ø20 mm, 1 m, steel (E = 200 GPa)
σmax = MPa

Answer key

  1. 1. σ = 509.3 MPa
  2. 2. σr = 22.34 MPa
  3. 3. P = 49.18 kN
  4. 4. δ = 0.1639 mm
  5. 5. δ = 3.342 mm
  6. 6. σmax = 382 MPa

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