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
50 kNØ3070 GPaØ100/60600 mmσr​ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of aluminium (outer diameter 100 mm, inner diameter 60 mm, E = 70 GPa). Both are 600 mm long and are compressed together between rigid plates by 50 kN. Find the compressive stress σr in the rod.

P = 50 kNrod: Ø30 mm, E = 200 GPatube: Ø100/Ø60 mm, E = 70 GPaL = 600 mm
σr = MPa
2.Easy
Ø 10 mm2 mP = 120 kN

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

P = 120 kNd = 10 mm
σ = MPa
3.Medium
300 kNØ30100 GPaØ100/70500 mmδ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of brass (outer diameter 100 mm, inner diameter 70 mm, E = 100 GPa). Both are 500 mm long and are compressed together between rigid plates by 300 kN. Find the shortening δ.

P = 300 kNrod: Ø30 mm, E = 200 GPatube: Ø100/Ø70 mm, E = 100 GPaL = 500 mm
δ = mm
4.Medium
Ø 12 mmAluminium0.5 mP = 85 kN

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

P = 85 kNd = 12 mmL = 0.5 mE = 70 GPa
δ = mm
5.Hard
Ø 30 mmAluminium0.5 mØ 12 mmSteel2 mP = 15 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 = 15 kNsegment 1: Ø30 mm, 0.5 m, aluminium (E = 70 GPa)segment 2: Ø12 mm, 2 m, steel (E = 200 GPa)
σmax = MPa
6.Hard
60 kN12400 mm300 mmØ30Ø40σ2​ = ?

A steel segment (diameter 30 mm, length 400 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 60 kN acts at the joint, towards segment 2. Find the magnitude of the stress σ2 in segment 2.

segment 1: steel, Ø30 mm, 400 mm, E = 200 GPasegment 2: copper, Ø40 mm, 300 mm, E = 120 GPaP = 60 kN
σ2 = MPa

Answer key

  1. 1. σr = 20.27 MPa
  2. 2. σ = 1528 MPa
  3. 3. δ = 0.2768 mm
  4. 4. δ = 5.368 mm
  5. 5. σmax = 132.6 MPa
  6. 6. σ2 = 28.03 MPa

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