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 16 mm0.5 mP = 90 kN

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

P = 90 kNd = 16 mm
σ = MPa
2.Easy
80 kNØ30110 GPaØ100/50300 mmσr​ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 100 mm, inner diameter 50 mm, E = 110 GPa). Both are 300 mm long and are compressed together between rigid plates by 80 kN. Find the compressive stress σr in the rod.

P = 80 kNrod: Ø30 mm, E = 200 GPatube: Ø100/Ø50 mm, E = 110 GPaL = 300 mm
σr = MPa
3.Medium
Ø 10 mmAluminium0.5 mP = 85 kN

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

P = 85 kNd = 10 mmL = 0.5 mE = 70 GPa
δ = mm
4.Medium
P = ?12500 mm200 mmØ20Ø60δ = 0.25 mm

A bar is made of a steel segment (diameter 20 mm, length 500 mm, E = 200 GPa) joined end to end with a segment made of aluminium (diameter 60 mm, length 200 mm, E = 70 GPa). It is fixed at one end and pulled at the other. Find the axial load P that stretches it by 0.25 mm in total.

segment 1: steel, Ø20 mm, 500 mm, E = 200 GPasegment 2: aluminium, Ø60 mm, 200 mm, E = 70 GPaδ = 0.25 mm
P = kN
5.Hard
P = ?Ø20120 GPaØ100/60400 mm

A steel rod (diameter 20 mm, E = 200 GPa, allowable stress 250 MPa) sits inside a tube made of copper (outer diameter 100 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: Ø20 mm, E = 200 GPa, σallow = 250 MPatube: Ø100/Ø60 mm, E = 120 GPa, σallow = 100 MPa
Pmax = kN
6.Hard
P = ?Ø25100 GPaØ100/50400 mm

A steel rod (diameter 25 mm, E = 200 GPa, allowable stress 200 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 = 200 MPatube: Ø100/Ø50 mm, E = 100 GPa, σallow = 70 MPa
Pmax = kN

Answer key

  1. 1. σ = 447.6 MPa
  2. 2. σr = 20.27 MPa
  3. 3. δ = 7.73 mm
  4. 4. P = 27.88 kN
  5. 5. Pmax = 555 kN
  6. 6. Pmax = 481.1 kN

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