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
100 kNØ25120 GPaØ120/60400 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 400 mm long and are compressed together between rigid plates by 100 kN. Find the compressive stress σr in the rod.

P = 100 kNrod: Ø25 mm, E = 200 GPatube: Ø120/Ø60 mm, E = 120 GPaL = 400 mm
σr = MPa
2.Easy
Ø 30 mm1 mP = 50 kN

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

P = 50 kNd = 30 mm
σ = MPa
3.Medium
P = ?12300 mm500 mmØ25Ø50δ = 0.5 mm

A bar is made of a steel segment (diameter 25 mm, length 300 mm, E = 200 GPa) joined end to end with a segment made of brass (diameter 50 mm, length 500 mm, E = 100 GPa). It is fixed at one end and pulled at the other. Find the axial load P that stretches it by 0.5 mm in total.

segment 1: steel, Ø25 mm, 300 mm, E = 200 GPasegment 2: brass, Ø50 mm, 500 mm, E = 100 GPaδ = 0.5 mm
P = kN
4.Medium
P = ?12500 mm200 mmØ20Ø30δ = 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 brass (diameter 30 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 0.5 mm in total.

segment 1: steel, Ø20 mm, 500 mm, E = 200 GPasegment 2: brass, Ø30 mm, 200 mm, E = 100 GPaδ = 0.5 mm
P = kN
5.Hard
Ø 40 mmAluminium1.5 mØ 20 mmBrass0.5 mP = 30 kN

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

P = 30 kNsegment 1: Ø40 mm, 1.5 m, aluminium (E = 70 GPa)segment 2: Ø20 mm, 0.5 m, brass (E = 100 GPa)
δ = mm
6.Hard
Ø 35 mmCopper2 mØ 16 mmBrass1.5 mP = 65 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 = 65 kNsegment 1: Ø35 mm, 2 m, copper (E = 117 GPa)segment 2: Ø16 mm, 1.5 m, brass (E = 100 GPa)
σmax = MPa

Answer key

  1. 1. σr = 17.92 MPa
  2. 2. σ = 70.74 MPa
  3. 3. P = 89.25 kN
  4. 4. P = 46.35 kN
  5. 5. δ = 0.989 mm
  6. 6. σmax = 323.3 MPa

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