Principal Stress Formula

Principle stress determines the maximum normal stress induced at every point in a stressed body, which has at least three planes. There will be numerous planes passing through a point, each one has normal stress point which is different from the other. Among all, normal stress would be maximum on any one plane and on the particular plane called as principal stress. Below given the principal stress formula to find the principal stress equation of a stressed body.

Principal Stress Equation


σ1,2 = (σx + σy)/2 ± √ ((σx - σy)/2)2 + τxy2 

Where,
τxy = Shear Stress
σx = Stress at x axis
σy = Stress at y axis

In the Principal stress formula, shear stress will always be zero and it is calculated based on the stress at x and y-axis. The maximum shear stress will occur when both the principal stresses σ1 and σ are equal. Use the above principal stress equation to know the maximum shear stress.


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