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 30 mm1.5 mP = 45 kN

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

P = 45 kNd = 30 mm
σ = MPa
2.Easy
200 kNØ2570 GPaØ120/50300 mmσr​ = ?

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of aluminium (outer diameter 120 mm, inner diameter 50 mm, E = 70 GPa). Both are 300 mm long and are compressed together between rigid plates by 200 kN. Find the compressive stress σr in the rod.

P = 200 kNrod: Ø25 mm, E = 200 GPatube: Ø120/Ø50 mm, E = 70 GPaL = 300 mm
σr = MPa
3.Medium
300 kNØ25110 GPaØ120/70300 mmδ = ?

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 120 mm, inner diameter 70 mm, E = 110 GPa). Both are 300 mm long and are compressed together between rigid plates by 300 kN. Find the shortening δ.

P = 300 kNrod: Ø25 mm, E = 200 GPatube: Ø120/Ø70 mm, E = 110 GPaL = 300 mm
δ = mm
4.Medium
P = ?12600 mm400 mmØ40Ø40δ = 0.3 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 40 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 0.3 mm in total.

segment 1: steel, Ø40 mm, 600 mm, E = 200 GPasegment 2: copper, Ø40 mm, 400 mm, E = 120 GPaδ = 0.3 mm
P = kN
5.Hard
Ø 40 mmSteel1.5 mØ 20 mmAluminium1 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: Ø40 mm, 1.5 m, steel (E = 200 GPa)segment 2: Ø20 mm, 1 m, aluminium (E = 70 GPa)
δ = mm
6.Hard
Ø 40 mmSteel1 mØ 12 mmAluminium2 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: Ø40 mm, 1 m, steel (E = 200 GPa)segment 2: Ø12 mm, 2 m, aluminium (E = 70 GPa)
σmax = MPa

Answer key

  1. 1. σ = 63.66 MPa
  2. 2. σr = 53.16 MPa
  3. 3. δ = 0.09794 mm
  4. 4. P = 59.52 kN
  5. 5. δ = 4.63 mm
  6. 6. σmax = 176.8 MPa

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