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 = 45 kN

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

P = 45 kNd = 12 mm
σ = MPa
2.Easy
50 kNØ40120 GPaØ120/70600 mmσr​ = ?

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 120 mm, inner diameter 70 mm, E = 120 GPa). Both are 600 mm long and are compressed together between rigid plates by 50 kN. Find the compressive stress σr in the rod.

P = 50 kNrod: Ø40 mm, E = 200 GPatube: Ø120/Ø70 mm, E = 120 GPaL = 600 mm
σr = MPa
3.Medium
300 kNØ20110 GPaØ100/60600 mmδ = ?

A steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 100 mm, inner diameter 60 mm, E = 110 GPa). Both are 600 mm long and are compressed together between rigid plates by 300 kN. Find the shortening δ.

P = 300 kNrod: Ø20 mm, E = 200 GPatube: Ø100/Ø60 mm, E = 110 GPaL = 600 mm
δ = mm
4.Medium
100 kNØ30120 GPaØ80/50600 mmδ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 80 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: Ø80/Ø50 mm, E = 120 GPaL = 600 mm
δ = mm
5.Hard
Ø 30 mmAluminium1 mØ 12 mmBrass2 mP = 35 kN

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

P = 35 kNsegment 1: Ø30 mm, 1 m, aluminium (E = 70 GPa)segment 2: Ø12 mm, 2 m, brass (E = 100 GPa)
δ = mm
6.Hard
P = ?Ø25100 GPaØ100/50600 mm

A steel rod (diameter 25 mm, E = 200 GPa, allowable stress 120 MPa) sits inside a tube made of brass (outer diameter 100 mm, inner diameter 50 mm, E = 100 GPa, allowable stress 70 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø25 mm, E = 200 GPa, σallow = 120 MPatube: Ø100/Ø50 mm, E = 100 GPa, σallow = 70 MPa
Pmax = kN

Answer key

  1. 1. σ = 397.9 MPa
  2. 2. σr = 8.721 MPa
  3. 3. δ = 0.2923 mm
  4. 4. δ = 0.1179 mm
  5. 5. δ = 6.897 mm
  6. 6. Pmax = 412.3 kN

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