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 25 mm0.5 mP = 30 kN

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

P = 30 kNd = 25 mm
σ = MPa
2.Easy
100 kNØ20120 GPaØ100/50300 mmσr​ = ?

A steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 100 mm, inner diameter 50 mm, E = 120 GPa). Both are 300 mm long and are compressed together between rigid plates by 100 kN. Find the compressive stress σr in the rod.

P = 100 kNrod: Ø20 mm, E = 200 GPatube: Ø100/Ø50 mm, E = 120 GPaL = 300 mm
σr = MPa
3.Medium
P = ?12300 mm400 mmØ25Ø40δ = 0.5 mm

A bar is made of a steel segment (diameter 25 mm, length 300 mm, E = 200 GPa) joined end to end with a segment made of brass (diameter 40 mm, length 400 mm, E = 100 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, Ø25 mm, 300 mm, E = 200 GPasegment 2: brass, Ø40 mm, 400 mm, E = 100 GPaδ = 0.5 mm
P = kN
4.Medium
P = ?12600 mm400 mmØ40Ø60δ = 0.4 mm

A bar is made of a steel segment (diameter 40 mm, length 600 mm, E = 200 GPa) joined end to end with a segment made of copper (diameter 60 mm, length 400 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, Ø40 mm, 600 mm, E = 200 GPasegment 2: copper, Ø60 mm, 400 mm, E = 120 GPaδ = 0.4 mm
P = kN
5.Hard
Ø 30 mmBrass1.5 mØ 20 mmCopper2 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: Ø30 mm, 1.5 m, brass (E = 100 GPa)segment 2: Ø20 mm, 2 m, copper (E = 117 GPa)
σmax = MPa
6.Hard
Ø 30 mmCopper0.5 mØ 20 mmSteel2 mP = 115 kN

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

P = 115 kNsegment 1: Ø30 mm, 0.5 m, copper (E = 117 GPa)segment 2: Ø20 mm, 2 m, steel (E = 200 GPa)
δ = mm

Answer key

  1. 1. σ = 61.12 MPa
  2. 2. σr = 25.98 MPa
  3. 3. P = 80.14 kN
  4. 4. P = 112.2 kN
  5. 5. σmax = 79.58 MPa
  6. 6. δ = 4.356 mm

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