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 10 mm0.5 mP = 110 kN

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

P = 110 kNd = 10 mm
σ = MPa
2.Easy
300 kNØ3070 GPaØ120/60500 mmσr​ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of aluminium (outer diameter 120 mm, inner diameter 60 mm, E = 70 GPa). Both are 500 mm long and are compressed together between rigid plates by 300 kN. Find the compressive stress σr in the rod.

P = 300 kNrod: Ø30 mm, E = 200 GPatube: Ø120/Ø60 mm, E = 70 GPaL = 500 mm
σr = MPa
3.Medium
250 kNØ40110 GPaØ120/60500 mmδ = ?

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 120 mm, inner diameter 60 mm, E = 110 GPa). Both are 500 mm long and are compressed together between rigid plates by 250 kN. Find the shortening δ.

P = 250 kNrod: Ø40 mm, E = 200 GPatube: Ø120/Ø60 mm, E = 110 GPaL = 500 mm
δ = mm
4.Medium
Ø 16 mmSteel3 mP = 40 kN

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

P = 40 kNd = 16 mmL = 3 mE = 200 GPa
δ = mm
5.Hard
30 kN12300 mm300 mmØ20Ø40σ2​ = ?

A steel segment (diameter 20 mm, length 300 mm, E = 200 GPa) and a segment made of copper (diameter 40 mm, length 300 mm, E = 120 GPa) are joined end to end and fixed between two rigid walls. An axial load of 30 kN acts at the joint, towards segment 2. Find the magnitude of the stress σ2 in segment 2.

segment 1: steel, Ø20 mm, 300 mm, E = 200 GPasegment 2: copper, Ø40 mm, 300 mm, E = 120 GPaP = 30 kN
σ2 = MPa
6.Hard
Ø 25 mmBrass0.5 mØ 20 mmCopper0.5 mP = 120 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 = 120 kNsegment 1: Ø25 mm, 0.5 m, brass (E = 100 GPa)segment 2: Ø20 mm, 0.5 m, copper (E = 117 GPa)
σmax = MPa

Answer key

  1. 1. σ = 1401 MPa
  2. 2. σr = 81.62 MPa
  3. 3. δ = 0.1055 mm
  4. 4. δ = 2.984 mm
  5. 5. σ2 = 16.85 MPa
  6. 6. σmax = 382 MPa

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