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 10 mm1.5 mP = 55 kN

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

P = 55 kNd = 10 mm
σ = MPa
2.Easy
250 kNØ4070 GPaØ80/50600 mmσr​ = ?

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of aluminium (outer diameter 80 mm, inner diameter 50 mm, E = 70 GPa). Both are 600 mm long and are compressed together between rigid plates by 250 kN. Find the compressive stress σr in the rod.

P = 250 kNrod: Ø40 mm, E = 200 GPatube: Ø80/Ø50 mm, E = 70 GPaL = 600 mm
σr = MPa
3.Medium
300 kNØ4070 GPaØ80/60400 mmδ = ?

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of aluminium (outer diameter 80 mm, inner diameter 60 mm, E = 70 GPa). Both are 400 mm long and are compressed together between rigid plates by 300 kN. Find the shortening δ.

P = 300 kNrod: Ø40 mm, E = 200 GPatube: Ø80/Ø60 mm, E = 70 GPaL = 400 mm
δ = mm
4.Medium
80 kNØ20100 GPaØ120/50600 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 600 mm long and are compressed together between rigid plates by 80 kN. Find the shortening δ.

P = 80 kNrod: Ø20 mm, E = 200 GPatube: Ø120/Ø50 mm, E = 100 GPaL = 600 mm
δ = mm
5.Hard
P = ?Ø40120 GPaØ100/60500 mm

A steel rod (diameter 40 mm, E = 200 GPa, allowable stress 200 MPa) sits inside a tube made of copper (outer diameter 100 mm, inner diameter 60 mm, E = 120 GPa, allowable stress 70 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø40 mm, E = 200 GPa, σallow = 200 MPatube: Ø100/Ø60 mm, E = 120 GPa, σallow = 70 MPa
Pmax = kN
6.Hard
P = ?Ø4070 GPaØ80/60800 mm

A steel rod (diameter 40 mm, E = 200 GPa, allowable stress 160 MPa) sits inside a tube made of aluminium (outer diameter 80 mm, inner diameter 60 mm, E = 70 GPa, allowable stress 80 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø40 mm, E = 200 GPa, σallow = 160 MPatube: Ø80/Ø60 mm, E = 70 GPa, σallow = 80 MPa
Pmax = kN

Answer key

  1. 1. σ = 700.3 MPa
  2. 2. σr = 107.4 MPa
  3. 3. δ = 0.2961 mm
  4. 4. δ = 0.04812 mm
  5. 5. Pmax = 498.5 kN
  6. 6. Pmax = 324.2 kN

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