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 25 mm1 mP = 20 kN

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

P = 20 kNd = 25 mm
σ = MPa
2.Easy
80 kNØ20110 GPaØ100/50800 mmσr​ = ?

A steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 100 mm, inner diameter 50 mm, E = 110 GPa). Both are 800 mm long and are compressed together between rigid plates by 80 kN. Find the compressive stress σr in the rod.

P = 80 kNrod: Ø20 mm, E = 200 GPatube: Ø100/Ø50 mm, E = 110 GPaL = 800 mm
σr = MPa
3.Medium
P = ?12300 mm200 mmØ30Ø60δ = 0.25 mm

A bar is made of a steel segment (diameter 30 mm, length 300 mm, E = 200 GPa) joined end to end with a segment made of brass (diameter 60 mm, length 200 mm, E = 100 GPa). It is fixed at one end and pulled at the other. Find the axial load P that stretches it by 0.25 mm in total.

segment 1: steel, Ø30 mm, 300 mm, E = 200 GPasegment 2: brass, Ø60 mm, 200 mm, E = 100 GPaδ = 0.25 mm
P = kN
4.Medium
150 kNØ2070 GPaØ100/50600 mmδ = ?

A steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of aluminium (outer diameter 100 mm, inner diameter 50 mm, E = 70 GPa). Both are 600 mm long and are compressed together between rigid plates by 150 kN. Find the shortening δ.

P = 150 kNrod: Ø20 mm, E = 200 GPatube: Ø100/Ø50 mm, E = 70 GPaL = 600 mm
δ = mm
5.Hard
Ø 40 mmSteel1 mØ 20 mmSteel1 mP = 110 kN

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

P = 110 kNsegment 1: Ø40 mm, 1 m, steel (E = 200 GPa)segment 2: Ø20 mm, 1 m, steel (E = 200 GPa)
δ = mm
6.Hard
Ø 30 mmCopper1 mØ 16 mmBrass1 mP = 85 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 = 85 kNsegment 1: Ø30 mm, 1 m, copper (E = 117 GPa)segment 2: Ø16 mm, 1 m, brass (E = 100 GPa)
σmax = MPa

Answer key

  1. 1. σ = 40.74 MPa
  2. 2. σr = 22.51 MPa
  3. 3. P = 88.36 kN
  4. 4. δ = 0.1894 mm
  5. 5. δ = 2.188 mm
  6. 6. σmax = 422.8 MPa

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