Principal stresses

Contribution of forces (3D beam case):

  • Axial force (N) and  bending forces (My, Mz) contribute to normal stress (σx) distribution in the section.
  • Shear force components (Vy, Vz) and twisting (Mx) couple contribute to shearing stress (τy, τz) distribution in the section.

 

Normal and shear stress

 

  • Normal (σx) and shearing (τy, τz) stresses are used to determine principal stresses (σ1, σ2 ), maximum shearing stress (τmax) and operation (θ) of principal planes.

 

Normal, shear stresses and operation

 

  • Analysis is valid only to extent that conditions of applicability of superposition principle of Saint-Venant‘s principle are met.

 

Principal stresses for the beam cross section can be obtained like:

 

Principal stress sigma;1

 

Principal stress sigma;2