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 mm2 mP = 55 kN

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

P = 55 kNd = 20 mm
σ = MPa
2.Easy
50 kNØ25100 GPaØ80/60600 mmσr​ = ?

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of brass (outer diameter 80 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 compressive stress σr in the rod.

P = 50 kNrod: Ø25 mm, E = 200 GPatube: Ø80/Ø60 mm, E = 100 GPaL = 600 mm
σr = MPa
3.Medium
P = ?12600 mm200 mmØ40Ø60δ = 0.4 mm

A bar is made of a steel segment (diameter 40 mm, length 600 mm, E = 200 GPa) joined end to end with a segment made of copper (diameter 60 mm, length 200 mm, E = 120 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, 600 mm, E = 200 GPasegment 2: copper, Ø60 mm, 200 mm, E = 120 GPaδ = 0.4 mm
P = kN
4.Medium
P = ?12500 mm200 mmØ30Ø40δ = 0.5 mm

A bar is made of a steel segment (diameter 30 mm, length 500 mm, E = 200 GPa) joined end to end with a segment made of bronze (diameter 40 mm, length 200 mm, E = 110 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, Ø30 mm, 500 mm, E = 200 GPasegment 2: bronze, Ø40 mm, 200 mm, E = 110 GPaδ = 0.5 mm
P = kN
5.Hard
Ø 35 mmSteel2 mØ 12 mmCopper2 mP = 50 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 = 50 kNsegment 1: Ø35 mm, 2 m, steel (E = 200 GPa)segment 2: Ø12 mm, 2 m, copper (E = 117 GPa)
σmax = MPa
6.Hard
Ø 40 mmCopper0.5 mØ 12 mmAluminium1 mP = 75 kN

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

P = 75 kNsegment 1: Ø40 mm, 0.5 m, copper (E = 117 GPa)segment 2: Ø12 mm, 1 m, aluminium (E = 70 GPa)
δ = mm

Answer key

  1. 1. σ = 175.1 MPa
  2. 2. σr = 31.44 MPa
  3. 3. P = 134.4 kN
  4. 4. P = 100.3 kN
  5. 5. σmax = 442.1 MPa
  6. 6. δ = 9.729 mm

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