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
150 kNØ40120 GPaØ120/50800 mmσr​ = ?

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 120 mm, inner diameter 50 mm, E = 120 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: Ø40 mm, E = 200 GPatube: Ø120/Ø50 mm, E = 120 GPaL = 800 mm
σr = MPa
2.Easy
Ø 30 mm0.5 mP = 115 kN

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

P = 115 kNd = 30 mm
σ = MPa
3.Medium
Ø 25 mmSteel2.5 mP = 50 kN

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

P = 50 kNd = 25 mmL = 2.5 mE = 200 GPa
δ = mm
4.Medium
P = ?12500 mm300 mmØ40Ø30δ = 0.5 mm

A bar is made of a steel segment (diameter 40 mm, length 500 mm, E = 200 GPa) joined end to end with a segment made of aluminium (diameter 30 mm, length 300 mm, E = 70 GPa). It is fixed at one end and pulled at the other. Find the axial load P that stretches it by 0.5 mm in total.

segment 1: steel, Ø40 mm, 500 mm, E = 200 GPasegment 2: aluminium, Ø30 mm, 300 mm, E = 70 GPaδ = 0.5 mm
P = kN
5.Hard
P = ?Ø25120 GPaØ80/60500 mm

A steel rod (diameter 25 mm, E = 200 GPa, allowable stress 120 MPa) sits inside a tube made of copper (outer diameter 80 mm, inner diameter 60 mm, E = 120 GPa, allowable stress 100 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø25 mm, E = 200 GPa, σallow = 120 MPatube: Ø80/Ø60 mm, E = 120 GPa, σallow = 100 MPa
Pmax = kN
6.Hard
P = ?Ø25120 GPaØ120/70600 mm

A steel rod (diameter 25 mm, E = 200 GPa, allowable stress 150 MPa) sits inside a tube made of copper (outer diameter 120 mm, inner diameter 70 mm, E = 120 GPa, allowable stress 80 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø25 mm, E = 200 GPa, σallow = 150 MPatube: Ø120/Ø70 mm, E = 120 GPa, σallow = 80 MPa
Pmax = kN

Answer key

  1. 1. σr = 21.85 MPa
  2. 2. σ = 162.7 MPa
  3. 3. δ = 1.273 mm
  4. 4. P = 62.09 kN
  5. 5. Pmax = 217.2 kN
  6. 6. Pmax = 662.4 kN

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