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 20 mm0.5 mP = 50 kN

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

P = 50 kNd = 20 mm
σ = MPa
2.Easy
200 kNØ3070 GPaØ100/50300 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 300 mm long and are compressed together between rigid plates by 200 kN. Find the compressive stress σr in the rod.

P = 200 kNrod: Ø30 mm, E = 200 GPatube: Ø100/Ø50 mm, E = 70 GPaL = 300 mm
σr = MPa
3.Medium
150 kNØ3070 GPaØ100/60400 mmδ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of aluminium (outer diameter 100 mm, inner diameter 60 mm, E = 70 GPa). Both are 400 mm long and are compressed together between rigid plates by 150 kN. Find the shortening δ.

P = 150 kNrod: Ø30 mm, E = 200 GPatube: Ø100/Ø60 mm, E = 70 GPaL = 400 mm
δ = mm
4.Medium
50 kNØ20100 GPaØ120/50400 mmδ = ?

A steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of brass (outer diameter 120 mm, inner diameter 50 mm, E = 100 GPa). Both are 400 mm long and are compressed together between rigid plates by 50 kN. Find the shortening δ.

P = 50 kNrod: Ø20 mm, E = 200 GPatube: Ø120/Ø50 mm, E = 100 GPaL = 400 mm
δ = mm
5.Hard
P = ?Ø25100 GPaØ80/60800 mm

A steel rod (diameter 25 mm, E = 200 GPa, allowable stress 250 MPa) sits inside a tube made of brass (outer diameter 80 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: Ø80/Ø60 mm, E = 100 GPa, σallow = 50 MPa
Pmax = kN
6.Hard
Ø 40 mmAluminium1 mØ 20 mmCopper1.5 mP = 35 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 = 35 kNsegment 1: Ø40 mm, 1 m, aluminium (E = 70 GPa)segment 2: Ø20 mm, 1.5 m, copper (E = 117 GPa)
σmax = MPa

Answer key

  1. 1. σ = 159.2 MPa
  2. 2. σr = 72.24 MPa
  3. 3. δ = 0.1216 mm
  4. 4. δ = 0.02005 mm
  5. 5. Pmax = 159 kN
  6. 6. σmax = 111.4 MPa

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