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
300 kNØ30100 GPaØ100/60600 mmσr​ = ?

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 300 kN. Find the compressive stress σr in the rod.

P = 300 kNrod: Ø30 mm, E = 200 GPatube: Ø100/Ø60 mm, E = 100 GPaL = 600 mm
σr = MPa
2.Easy
250 kNØ2070 GPaØ120/60500 mmσr​ = ?

A steel rod (diameter 20 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 250 kN. Find the compressive stress σr in the rod.

P = 250 kNrod: Ø20 mm, E = 200 GPatube: Ø120/Ø60 mm, E = 70 GPaL = 500 mm
σr = MPa
3.Medium
P = ?12300 mm300 mmØ20Ø40δ = 0.5 mm

A bar is made of a steel segment (diameter 20 mm, length 300 mm, E = 200 GPa) joined end to end with a segment made of brass (diameter 40 mm, length 300 mm, E = 100 GPa). It is fixed at one end and pulled at the other. Find the axial load P that stretches it by 0.5 mm in total.

segment 1: steel, Ø20 mm, 300 mm, E = 200 GPasegment 2: brass, Ø40 mm, 300 mm, E = 100 GPaδ = 0.5 mm
P = kN
4.Medium
Ø 25 mmAluminium1 mP = 65 kN

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

P = 65 kNd = 25 mmL = 1 mE = 70 GPa
δ = mm
5.Hard
100 kN12400 mm300 mmØ20Ø30σ2​ = ?

A steel segment (diameter 20 mm, length 400 mm, E = 200 GPa) and a segment made of copper (diameter 30 mm, length 300 mm, E = 120 GPa) are joined end to end and fixed between two rigid walls. An axial load of 100 kN acts at the joint, towards segment 2. Find the magnitude of the stress σ2 in segment 2.

segment 1: steel, Ø20 mm, 400 mm, E = 200 GPasegment 2: copper, Ø30 mm, 300 mm, E = 120 GPaP = 100 kN
σ2 = MPa
6.Hard
Ø 35 mmAluminium1.5 mØ 20 mmAluminium0.5 mP = 10 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 = 10 kNsegment 1: Ø35 mm, 1.5 m, aluminium (E = 70 GPa)segment 2: Ø20 mm, 0.5 m, aluminium (E = 70 GPa)
σmax = MPa

Answer key

  1. 1. σr = 93.16 MPa
  2. 2. σr = 76.15 MPa
  3. 3. P = 69.81 kN
  4. 4. δ = 1.892 mm
  5. 5. σ2 = 90.95 MPa
  6. 6. σmax = 31.83 MPa

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