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 = 65 kN

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

P = 65 kNd = 20 mm
σ = MPa
2.Easy
50 kNØ20110 GPaØ120/70500 mmσr​ = ?

A steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 120 mm, inner diameter 70 mm, E = 110 GPa). Both are 500 mm long and are compressed together between rigid plates by 50 kN. Find the compressive stress σr in the rod.

P = 50 kNrod: Ø20 mm, E = 200 GPatube: Ø120/Ø70 mm, E = 110 GPaL = 500 mm
σr = MPa
3.Medium
P = ?12400 mm300 mmØ20Ø30δ = 0.4 mm

A bar is made of a steel segment (diameter 20 mm, length 400 mm, E = 200 GPa) joined end to end with a segment made of copper (diameter 30 mm, length 300 mm, E = 120 GPa). It is fixed at one end and pulled at the other. Find the axial load P that stretches it by 0.4 mm in total.

segment 1: steel, Ø20 mm, 400 mm, E = 200 GPasegment 2: copper, Ø30 mm, 300 mm, E = 120 GPaδ = 0.4 mm
P = kN
4.Medium
Ø 25 mmBrass0.5 mP = 45 kN

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

P = 45 kNd = 25 mmL = 0.5 mE = 100 GPa
δ = mm
5.Hard
P = ?Ø40110 GPaØ80/60300 mm

A steel rod (diameter 40 mm, E = 200 GPa, allowable stress 120 MPa) sits inside a tube made of bronze (outer diameter 80 mm, inner diameter 60 mm, E = 110 GPa, allowable stress 60 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø40 mm, E = 200 GPa, σallow = 120 MPatube: Ø80/Ø60 mm, E = 110 GPa, σallow = 60 MPa
Pmax = kN
6.Hard
Ø 30 mmAluminium2 mØ 16 mmCopper0.5 mP = 30 kN

The stepped bar is fixed at the wall and loaded at its free end. Find the total elongation δ.

P = 30 kNsegment 1: Ø30 mm, 2 m, aluminium (E = 70 GPa)segment 2: Ø16 mm, 0.5 m, copper (E = 117 GPa)
δ = mm

Answer key

  1. 1. σ = 206.9 MPa
  2. 2. σr = 11.32 MPa
  3. 3. P = 40.39 kN
  4. 4. δ = 0.4584 mm
  5. 5. Pmax = 269 kN
  6. 6. δ = 1.85 mm

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