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 12 mm1 mP = 20 kN

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

P = 20 kNd = 12 mm
σ = MPa
2.Easy
200 kNØ40110 GPaØ80/60400 mmσr​ = ?

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 80 mm, inner diameter 60 mm, E = 110 GPa). Both are 400 mm long and are compressed together between rigid plates by 200 kN. Find the compressive stress σr in the rod.

P = 200 kNrod: Ø40 mm, E = 200 GPatube: Ø80/Ø60 mm, E = 110 GPaL = 400 mm
σr = MPa
3.Medium
300 kNØ2570 GPaØ80/50400 mmδ = ?

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of aluminium (outer diameter 80 mm, inner diameter 50 mm, E = 70 GPa). Both are 400 mm long and are compressed together between rigid plates by 300 kN. Find the shortening δ.

P = 300 kNrod: Ø25 mm, E = 200 GPatube: Ø80/Ø50 mm, E = 70 GPaL = 400 mm
δ = mm
4.Medium
250 kNØ3070 GPaØ120/50800 mmδ = ?

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 800 mm long and are compressed together between rigid plates by 250 kN. Find the shortening δ.

P = 250 kNrod: Ø30 mm, E = 200 GPatube: Ø120/Ø50 mm, E = 70 GPaL = 800 mm
δ = mm
5.Hard
Ø 30 mmBrass1 mØ 20 mmSteel0.5 mP = 30 kN

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

P = 30 kNsegment 1: Ø30 mm, 1 m, brass (E = 100 GPa)segment 2: Ø20 mm, 0.5 m, steel (E = 200 GPa)
δ = mm
6.Hard
Ø 30 mmAluminium1 mØ 20 mmCopper1 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, 1 m, aluminium (E = 70 GPa)segment 2: Ø20 mm, 1 m, copper (E = 117 GPa)
σmax = MPa

Answer key

  1. 1. σ = 176.8 MPa
  2. 2. σr = 81.1 MPa
  3. 3. δ = 0.3839 mm
  4. 4. δ = 0.2514 mm
  5. 5. δ = 0.6631 mm
  6. 6. σmax = 382 MPa

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