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 mm1.5 mP = 75 kN

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

P = 75 kNd = 20 mm
σ = MPa
2.Easy
150 kNØ2070 GPaØ80/50800 mmσr​ = ?

A steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of aluminium (outer diameter 80 mm, inner diameter 50 mm, E = 70 GPa). Both are 800 mm long and are compressed together between rigid plates by 150 kN. Find the compressive stress σr in the rod.

P = 150 kNrod: Ø20 mm, E = 200 GPatube: Ø80/Ø50 mm, E = 70 GPaL = 800 mm
σr = MPa
3.Medium
P = ?12600 mm400 mmØ30Ø40δ = 0.25 mm

A bar is made of a steel segment (diameter 30 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 0.25 mm in total.

segment 1: steel, Ø30 mm, 600 mm, E = 200 GPasegment 2: copper, Ø40 mm, 400 mm, E = 120 GPaδ = 0.25 mm
P = kN
4.Medium
Ø 30 mmBrass1.5 mP = 65 kN

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

P = 65 kNd = 30 mmL = 1.5 mE = 100 GPa
δ = mm
5.Hard
Ø 25 mmAluminium1.5 mØ 12 mmSteel1.5 mP = 80 kN

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

P = 80 kNsegment 1: Ø25 mm, 1.5 m, aluminium (E = 70 GPa)segment 2: Ø12 mm, 1.5 m, steel (E = 200 GPa)
δ = mm
6.Hard
Ø 25 mmBrass2 mØ 12 mmSteel2 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: Ø25 mm, 2 m, brass (E = 100 GPa)segment 2: Ø12 mm, 2 m, steel (E = 200 GPa)
σmax = MPa

Answer key

  1. 1. σ = 238.7 MPa
  2. 2. σr = 108.2 MPa
  3. 3. P = 36.25 kN
  4. 4. δ = 1.379 mm
  5. 5. δ = 8.797 mm
  6. 6. σmax = 176.8 MPa

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