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 = 40 kN

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

P = 40 kNd = 20 mm
σ = MPa
2.Easy
300 kNØ20110 GPaØ120/50300 mmσr​ = ?

A steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 120 mm, inner diameter 50 mm, E = 110 GPa). Both are 300 mm long and are compressed together between rigid plates by 300 kN. Find the compressive stress σr in the rod.

P = 300 kNrod: Ø20 mm, E = 200 GPatube: Ø120/Ø50 mm, E = 110 GPaL = 300 mm
σr = MPa
3.Medium
P = ?12600 mm500 mmØ25Ø60δ = 0.2 mm

A bar is made of a steel segment (diameter 25 mm, length 600 mm, E = 200 GPa) joined end to end with a segment made of copper (diameter 60 mm, length 500 mm, E = 120 GPa). It is fixed at one end and pulled at the other. Find the axial load P that stretches it by 0.2 mm in total.

segment 1: steel, Ø25 mm, 600 mm, E = 200 GPasegment 2: copper, Ø60 mm, 500 mm, E = 120 GPaδ = 0.2 mm
P = kN
4.Medium
300 kNØ40110 GPaØ100/50800 mmδ = ?

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 100 mm, inner diameter 50 mm, E = 110 GPa). Both are 800 mm long and are compressed together between rigid plates by 300 kN. Find the shortening δ.

P = 300 kNrod: Ø40 mm, E = 200 GPatube: Ø100/Ø50 mm, E = 110 GPaL = 800 mm
δ = mm
5.Hard
Ø 25 mmCopper1.5 mØ 20 mmCopper1 mP = 25 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 = 25 kNsegment 1: Ø25 mm, 1.5 m, copper (E = 117 GPa)segment 2: Ø20 mm, 1 m, copper (E = 117 GPa)
σmax = MPa
6.Hard
Ø 25 mmSteel1.5 mØ 12 mmCopper2 mP = 90 kN

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

P = 90 kNsegment 1: Ø25 mm, 1.5 m, steel (E = 200 GPa)segment 2: Ø12 mm, 2 m, copper (E = 117 GPa)
δ = mm

Answer key

  1. 1. σ = 127.3 MPa
  2. 2. σr = 55 MPa
  3. 3. P = 26.37 kN
  4. 4. δ = 0.2669 mm
  5. 5. σmax = 79.58 MPa
  6. 6. δ = 14.98 mm

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