Maximum and minimum normal stresses on planes where shear stress is zero.
Principal stresses σ₁,σ₂ are eigenvalues of the stress tensor and act on planes without shear. σ₁,₂=(σx+σy)/2±√(((σx-σy)/2)²+τ²). They determine yielding, cracking and the orientation of strain gauges.
A brittle crack follows the plane perpendicular to σ₁.
Principal stresses are the maximum and minimum normal stresses at a point, and failure criteria are applied to them.
Maximum and minimum normal stresses on planes where shear stress is zero.
Principal stresses are the maximum and minimum normal stresses at a point, and failure criteria are applied to them.
Not necessarily. They are the extremes of normal stress over all planes, so the largest of the three is the maximum and the smallest is the minimum.
It is zero, which is why principal planes are useful for failure calculations.
Typical applications include checking a pressure vessel for the maximum stress that governs yield, interpreting FEA results to find the critical direction in a plate and assessing whether a crack will open in a loaded component.
Study "Mohr's circle" first (topic 61 of 106 in Engineering Mechanics). It covers the groundwork this topic builds on.
Maximum and minimum normal stress. Orthogonal planes. Used in failure theories.
A brittle crack follows the plane perpendicular to σ₁.
The next topic is "Thin-walled pressure vessels", which builds directly on this one.
It is classed as Intermediate in Engineering Mechanics (topic 62 of 106). It is an intermediate topic. Work through the beginner topics in Engineering Mechanics first.
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