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 mm1.5 mP = 50 kN

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

P = 50 kNd = 12 mm
σ = MPa
2.Easy
300 kNØ3070 GPaØ100/50800 mmσr​ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of aluminium (outer diameter 100 mm, inner diameter 50 mm, E = 70 GPa). Both are 800 mm long and are compressed together between rigid plates by 300 kN. Find the compressive stress σr in the rod.

P = 300 kNrod: Ø30 mm, E = 200 GPatube: Ø100/Ø50 mm, E = 70 GPaL = 800 mm
σr = MPa
3.Medium
Ø 12 mmAluminium1.5 mP = 115 kN

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

P = 115 kNd = 12 mmL = 1.5 mE = 70 GPa
δ = mm
4.Medium
50 kNØ30120 GPaØ80/50400 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 400 mm long and are compressed together between rigid plates by 50 kN. Find the shortening δ.

P = 50 kNrod: Ø30 mm, E = 200 GPatube: Ø80/Ø50 mm, E = 120 GPaL = 400 mm
δ = mm
5.Hard
Ø 30 mmBrass1 mØ 20 mmCopper0.5 mP = 40 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 = 40 kNsegment 1: Ø30 mm, 1 m, brass (E = 100 GPa)segment 2: Ø20 mm, 0.5 m, copper (E = 117 GPa)
σmax = MPa
6.Hard
P = ?Ø25100 GPaØ100/60400 mm

A steel rod (diameter 25 mm, E = 200 GPa, allowable stress 250 MPa) sits inside a tube made of brass (outer diameter 100 mm, inner diameter 60 mm, E = 100 GPa, allowable stress 50 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø25 mm, E = 200 GPa, σallow = 250 MPatube: Ø100/Ø60 mm, E = 100 GPa, σallow = 50 MPa
Pmax = kN

Answer key

  1. 1. σ = 442.1 MPa
  2. 2. σr = 108.4 MPa
  3. 3. δ = 21.79 mm
  4. 4. δ = 0.0393 mm
  5. 5. σmax = 127.3 MPa
  6. 6. Pmax = 300.4 kN

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