What are principal stresses and how are they calculated?

Principal stresses are the maximum and minimum normal stresses acting on planes where shear stress is zero. They are calculated using σ₁,₂ = (σx + σy)/2 ± √[(σx - σy)/2]² + τxy². Principal planes are oriented at angle θp = (1/2)tan⁻¹(2τxy/(σx - σy)). They are critical for failure analysis using theories like von Mises and Tresca.