The Mechanical
Engineering Handbook




General 2D Stress Transformation Equations Calculator
























How This Is Calculated



$$\sigma_{N} = \frac{\sigma_x + \sigma_y}{2} + \left(\frac{\sigma_x - \sigma_y}{2}\right)\cos\left(\theta \right) + \tau_{xy}\sin \left(2\theta \right) $$ $$\tau_s = \left(\frac{\sigma_x - \sigma_y}{2}\right)\sin(2\theta) - \tau_{xy}\cos(2\theta) $$ where:

σN   =   Normal Stress   (Pa, N/m², kPa, MPa)

τs   =   Shear Stress   (Pa, N/m², kPa, MPa)

σx   =   Normal Stress in x direction   (Pa, N/m², kPa, MPa)

σy   =   Normal Stress in y direction   (Pa, N/m², kPa, MPa)

τxy   =   Shear Stress in xy direction   (Pa, N/m², kPa, MPa)

θ   =   Angle   (° or rad)

Assumptions



  • The material is homogeneous and continuous.
  • The material follows Hookes Law, i.e. the stress-strain relationship is linear.
  • The stress in the thickness direction (out-of-plane stress) is assumed to be zero.
  • Deformations are insufficient such that the original geometry is not altered.


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