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 mm2 mP = 45 kN

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

P = 45 kNd = 25 mm
σ = MPa
2.Easy
200 kNØ30110 GPaØ120/60400 mmσr​ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 120 mm, inner diameter 60 mm, E = 110 GPa). Both are 400 mm long and are compressed together between rigid plates by 200 kN. Find the compressive stress σr in the rod.

P = 200 kNrod: Ø30 mm, E = 200 GPatube: Ø120/Ø60 mm, E = 110 GPaL = 400 mm
σr = MPa
3.Medium
P = ?12300 mm300 mmØ20Ø40δ = 0.2 mm

A bar is made of a steel segment (diameter 20 mm, length 300 mm, E = 200 GPa) joined end to end with a segment made of aluminium (diameter 40 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 0.2 mm in total.

segment 1: steel, Ø20 mm, 300 mm, E = 200 GPasegment 2: aluminium, Ø40 mm, 300 mm, E = 70 GPaδ = 0.2 mm
P = kN
4.Medium
250 kNØ30100 GPaØ100/60300 mmδ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of brass (outer diameter 100 mm, inner diameter 60 mm, E = 100 GPa). Both are 300 mm long and are compressed together between rigid plates by 250 kN. Find the shortening δ.

P = 250 kNrod: Ø30 mm, E = 200 GPatube: Ø100/Ø60 mm, E = 100 GPaL = 300 mm
δ = mm
5.Hard
Ø 35 mmCopper2 mØ 12 mmCopper1 mP = 20 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 = 20 kNsegment 1: Ø35 mm, 2 m, copper (E = 117 GPa)segment 2: Ø12 mm, 1 m, copper (E = 117 GPa)
σmax = MPa
6.Hard
Ø 30 mmAluminium1.5 mØ 20 mmBrass1 mP = 55 kN

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

P = 55 kNsegment 1: Ø30 mm, 1.5 m, aluminium (E = 70 GPa)segment 2: Ø20 mm, 1 m, brass (E = 100 GPa)
δ = mm

Answer key

  1. 1. σ = 91.67 MPa
  2. 2. σr = 37.23 MPa
  3. 3. P = 24.43 kN
  4. 4. δ = 0.1165 mm
  5. 5. σmax = 176.8 MPa
  6. 6. δ = 3.418 mm

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