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
100 kNØ20110 GPaØ80/50800 mmσr​ = ?

A steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 80 mm, inner diameter 50 mm, E = 110 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: Ø80/Ø50 mm, E = 110 GPaL = 800 mm
σr = MPa
2.Easy
150 kNØ30100 GPaØ100/70800 mmσr​ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of brass (outer diameter 100 mm, inner diameter 70 mm, E = 100 GPa). Both are 800 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: Ø100/Ø70 mm, E = 100 GPaL = 800 mm
σr = MPa
3.Medium
Ø 30 mmAluminium2.5 mP = 45 kN

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

P = 45 kNd = 30 mmL = 2.5 mE = 70 GPa
δ = mm
4.Medium
80 kNØ25110 GPaØ80/60500 mmδ = ?

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 80 mm, inner diameter 60 mm, E = 110 GPa). Both are 500 mm long and are compressed together between rigid plates by 80 kN. Find the shortening δ.

P = 80 kNrod: Ø25 mm, E = 200 GPatube: Ø80/Ø60 mm, E = 110 GPaL = 500 mm
δ = mm
5.Hard
Ø 35 mmAluminium2 mØ 16 mmAluminium1.5 mP = 25 kN

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

P = 25 kNsegment 1: Ø35 mm, 2 m, aluminium (E = 70 GPa)segment 2: Ø16 mm, 1.5 m, aluminium (E = 70 GPa)
δ = mm
6.Hard
Ø 35 mmAluminium1 mØ 12 mmSteel1 mP = 30 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 = 30 kNsegment 1: Ø35 mm, 1 m, aluminium (E = 70 GPa)segment 2: Ø12 mm, 1 m, steel (E = 200 GPa)
σmax = MPa

Answer key

  1. 1. σr = 50.03 MPa
  2. 2. σr = 55.36 MPa
  3. 3. δ = 2.274 mm
  4. 4. δ = 0.1176 mm
  5. 5. δ = 3.407 mm
  6. 6. σmax = 265.3 MPa

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