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 16 mm1.5 mP = 35 kN

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

P = 35 kNd = 16 mm
σ = MPa
2.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
3.Medium
P = ?12500 mm500 mmØ20Ø60δ = 0.5 mm

A bar is made of a steel segment (diameter 20 mm, length 500 mm, E = 200 GPa) joined end to end with a segment made of aluminium (diameter 60 mm, length 500 mm, E = 70 GPa). It is fixed at one end and pulled at the other. Find the axial load P that stretches it by 0.5 mm in total.

segment 1: steel, Ø20 mm, 500 mm, E = 200 GPasegment 2: aluminium, Ø60 mm, 500 mm, E = 70 GPaδ = 0.5 mm
P = kN
4.Medium
Ø 30 mmSteel2.5 mP = 70 kN

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

P = 70 kNd = 30 mmL = 2.5 mE = 200 GPa
δ = mm
5.Hard
Ø 30 mmSteel0.5 mØ 16 mmCopper1 mP = 95 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 = 95 kNsegment 1: Ø30 mm, 0.5 m, steel (E = 200 GPa)segment 2: Ø16 mm, 1 m, copper (E = 117 GPa)
σmax = MPa
6.Hard
Ø 40 mmSteel1 mØ 16 mmBrass1 mP = 85 kN

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

P = 85 kNsegment 1: Ø40 mm, 1 m, steel (E = 200 GPa)segment 2: Ø16 mm, 1 m, brass (E = 100 GPa)
δ = mm

Answer key

  1. 1. σ = 174.1 MPa
  2. 2. σr = 93.16 MPa
  3. 3. P = 47.69 kN
  4. 4. δ = 1.238 mm
  5. 5. σmax = 472.5 MPa
  6. 6. δ = 4.566 mm

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