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ENGR5004 / Week 2
Statics S3 slide 15: Why does uniaxial load give 3D deformation?From lectureCurrent specThird3 marks4 min

ENGR5004 Statics session 03, slide 15 (Summary)

"Even uniaxial load leads to 3D deformation! Why?"

Explain why a bar loaded by an axial force in the xx direction only deforms in all three directions, and write down the strain components.

Formulas you may need
  • ν=−lateral strainaxial strain\nu = -\dfrac{\text{lateral strain}}{\text{axial strain}}; uniaxial: ϵx=σxE\epsilon_x = \dfrac{\sigma_x}{E}, ϵy=ϵz=−νσxE\epsilon_y = \epsilon_z = -\dfrac{\nu\sigma_x}{E} (learn this)
  • Dilatation: e=ϵx+ϵy+ϵz=1−2νE(σx+σy+σz)e = \epsilon_x + \epsilon_y + \epsilon_z = \dfrac{1 - 2\nu}{E}(\sigma_x + \sigma_y + \sigma_z) (learn this)