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
50 kNØ2570 GPaØ100/60800 mmσr​ = ?

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of aluminium (outer diameter 100 mm, inner diameter 60 mm, E = 70 GPa). Both are 800 mm long and are compressed together between rigid plates by 50 kN. Find the compressive stress σr in the rod.

P = 50 kNrod: Ø25 mm, E = 200 GPatube: Ø100/Ø60 mm, E = 70 GPaL = 800 mm
σr = MPa
2.Easy
300 kNØ25110 GPaØ100/70500 mmσr​ = ?

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 100 mm, inner diameter 70 mm, E = 110 GPa). Both are 500 mm long and are compressed together between rigid plates by 300 kN. Find the compressive stress σr in the rod.

P = 300 kNrod: Ø25 mm, E = 200 GPatube: Ø100/Ø70 mm, E = 110 GPaL = 500 mm
σr = MPa
3.Medium
100 kNØ30120 GPaØ120/50600 mmδ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 120 mm, inner diameter 50 mm, E = 120 GPa). Both are 600 mm long and are compressed together between rigid plates by 100 kN. Find the shortening δ.

P = 100 kNrod: Ø30 mm, E = 200 GPatube: Ø120/Ø50 mm, E = 120 GPaL = 600 mm
δ = mm
4.Medium
80 kNØ30100 GPaØ120/70600 mmδ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of brass (outer diameter 120 mm, inner diameter 70 mm, E = 100 GPa). Both are 600 mm long and are compressed together between rigid plates by 80 kN. Find the shortening δ.

P = 80 kNrod: Ø30 mm, E = 200 GPatube: Ø120/Ø70 mm, E = 100 GPaL = 600 mm
δ = mm
5.Hard
Ø 25 mmSteel0.5 mØ 16 mmBrass1 mP = 20 kN

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

P = 20 kNsegment 1: Ø25 mm, 0.5 m, steel (E = 200 GPa)segment 2: Ø16 mm, 1 m, brass (E = 100 GPa)
δ = mm
6.Hard
Ø 40 mmCopper1.5 mØ 12 mmSteel2 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: Ø40 mm, 1.5 m, copper (E = 117 GPa)segment 2: Ø12 mm, 2 m, steel (E = 200 GPa)
σmax = MPa

Answer key

  1. 1. σr = 22.22 MPa
  2. 2. σr = 111.4 MPa
  3. 3. δ = 0.04751 mm
  4. 4. δ = 0.05408 mm
  5. 5. δ = 1.097 mm
  6. 6. σmax = 132.6 MPa

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