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 kNØ3070 GPaØ120/70800 mmσr​ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of aluminium (outer diameter 120 mm, inner diameter 70 mm, E = 70 GPa). Both are 800 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/Ø70 mm, E = 70 GPaL = 800 mm
σr = MPa
2.Easy
300 kNØ30120 GPaØ80/60800 mmσr​ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 80 mm, inner diameter 60 mm, E = 120 GPa). Both are 800 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: Ø80/Ø60 mm, E = 120 GPaL = 800 mm
σr = MPa
3.Medium
Ø 12 mmAluminium3 mP = 105 kN

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

P = 105 kNd = 12 mmL = 3 mE = 70 GPa
δ = mm
4.Medium
P = ?12400 mm400 mmØ40Ø50δ = 0.4 mm

A bar is made of a steel segment (diameter 40 mm, length 400 mm, E = 200 GPa) joined end to end with a segment made of aluminium (diameter 50 mm, length 400 mm, E = 70 GPa). It is fixed at one end and pulled at the other. Find the axial load P that stretches it by 0.4 mm in total.

segment 1: steel, Ø40 mm, 400 mm, E = 200 GPasegment 2: aluminium, Ø50 mm, 400 mm, E = 70 GPaδ = 0.4 mm
P = kN
5.Hard
Ø 25 mmSteel1 mØ 12 mmCopper1 mP = 105 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 = 105 kNsegment 1: Ø25 mm, 1 m, steel (E = 200 GPa)segment 2: Ø12 mm, 1 m, copper (E = 117 GPa)
σmax = MPa
6.Hard
Ø 35 mmBrass1.5 mØ 16 mmBrass0.5 mP = 45 kN

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

P = 45 kNsegment 1: Ø35 mm, 1.5 m, brass (E = 100 GPa)segment 2: Ø16 mm, 0.5 m, brass (E = 100 GPa)
δ = mm

Answer key

  1. 1. σr = 90.41 MPa
  2. 2. σr = 148.1 MPa
  3. 3. δ = 39.79 mm
  4. 4. P = 88.85 kN
  5. 5. σmax = 928.4 MPa
  6. 6. δ = 1.821 mm

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