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 mm0.5 mP = 20 kN

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

P = 20 kNd = 20 mm
σ = MPa
2.Easy
80 kNØ40100 GPaØ100/60500 mmσr​ = ?

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of brass (outer diameter 100 mm, inner diameter 60 mm, E = 100 GPa). Both are 500 mm long and are compressed together between rigid plates by 80 kN. Find the compressive stress σr in the rod.

P = 80 kNrod: Ø40 mm, E = 200 GPatube: Ø100/Ø60 mm, E = 100 GPaL = 500 mm
σr = MPa
3.Medium
50 kNØ30100 GPaØ100/60600 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 600 mm long and are compressed together between rigid plates by 50 kN. Find the shortening δ.

P = 50 kNrod: Ø30 mm, E = 200 GPatube: Ø100/Ø60 mm, E = 100 GPaL = 600 mm
δ = mm
4.Medium
Ø 30 mmBrass0.5 mP = 55 kN

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

P = 55 kNd = 30 mmL = 0.5 mE = 100 GPa
δ = mm
5.Hard
20 kN12600 mm300 mmØ40Ø30σ2​ = ?

A steel segment (diameter 40 mm, length 600 mm, E = 200 GPa) and a segment made of aluminium (diameter 30 mm, length 300 mm, E = 70 GPa) are joined end to end and fixed between two rigid walls. An axial load of 20 kN acts at the joint, towards segment 2. Find the magnitude of the stress σ2 in segment 2.

segment 1: steel, Ø40 mm, 600 mm, E = 200 GPasegment 2: aluminium, Ø30 mm, 300 mm, E = 70 GPaP = 20 kN
σ2 = MPa
6.Hard
Ø 25 mmAluminium2 mØ 12 mmCopper1.5 mP = 30 kN

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

P = 30 kNsegment 1: Ø25 mm, 2 m, aluminium (E = 70 GPa)segment 2: Ø12 mm, 1.5 m, copper (E = 117 GPa)
δ = mm

Answer key

  1. 1. σ = 63.66 MPa
  2. 2. σr = 21.22 MPa
  3. 3. δ = 0.04658 mm
  4. 4. δ = 0.389 mm
  5. 5. σ2 = 7.993 MPa
  6. 6. δ = 5.147 mm

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