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
150 kNØ2070 GPaØ80/60600 mmσr​ = ?

A steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of aluminium (outer diameter 80 mm, inner diameter 60 mm, E = 70 GPa). Both are 600 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/Ø60 mm, E = 70 GPaL = 600 mm
σr = MPa
2.Easy
300 kNØ25120 GPaØ120/60600 mmσr​ = ?

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 120 mm, inner diameter 60 mm, E = 120 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: Ø25 mm, E = 200 GPatube: Ø120/Ø60 mm, E = 120 GPaL = 600 mm
σr = MPa
3.Medium
Ø 20 mmBrass1.5 mP = 90 kN

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

P = 90 kNd = 20 mmL = 1.5 mE = 100 GPa
δ = mm
4.Medium
P = ?12600 mm400 mmØ30Ø30δ = 0.3 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 brass (diameter 30 mm, length 400 mm, E = 100 GPa). It is fixed at one end and pulled at the other. Find the axial load P that stretches it by 0.3 mm in total.

segment 1: steel, Ø30 mm, 600 mm, E = 200 GPasegment 2: brass, Ø30 mm, 400 mm, E = 100 GPaδ = 0.3 mm
P = kN
5.Hard
Ø 25 mmAluminium0.5 mØ 12 mmAluminium1.5 mP = 90 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 = 90 kNsegment 1: Ø25 mm, 0.5 m, aluminium (E = 70 GPa)segment 2: Ø12 mm, 1.5 m, aluminium (E = 70 GPa)
σmax = MPa
6.Hard
Ø 40 mmBrass1.5 mØ 12 mmSteel1.5 mP = 55 kN

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

P = 55 kNsegment 1: Ø40 mm, 1.5 m, brass (E = 100 GPa)segment 2: Ø12 mm, 1.5 m, steel (E = 200 GPa)
δ = mm

Answer key

  1. 1. σr = 138.4 MPa
  2. 2. σr = 53.76 MPa
  3. 3. δ = 4.297 mm
  4. 4. P = 30.29 kN
  5. 5. σmax = 795.8 MPa
  6. 6. δ = 4.304 mm

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