Mechanics

Principal directions 2D

Finds the two perpendicular principal directions of a plane stress state.

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Calculates the maximum in-plane shear stress of a plane stress state.

Transforms sigma_x, sigma_y, and tau_xy for a specified axis angle theta.

Calculates the two principal stresses, maximum in-plane shear, and principal-axis direction for a plane stress state.

Calculates Tresca equivalent stress for plane stress with the third principal stress set to zero.

Calculates von Mises equivalent stress for plane stress.

Calculates allowable stress as yield strength divided by safety factor.

{theta}_{1} = \frac{1}{2} \cdot atan2 (2 \cdot {tau}_{xy}, {sigma}_{x} - {sigma}_{y})

{theta}_{2} = {theta}_{1} + \frac{π}{2}