(* ::Package:: *)

(*         PRINCIPAL STRESSES-2 D          *)

(* This file calculates the two in-plane principal stresses
from equation (1.11).
To use this file in cylindrical polar coordinates,uncomment the two lines below and comment the present expressions for \[Sigma]1,\[Sigma]2. *)





(* \[Sigma]1=(\[Sigma]rr+\[Sigma]\[Theta]\[Theta])/2+Sqrt[((\[Sigma]rr-\[Sigma]\[Theta]\[Theta])/2)^2+\[Sigma]r\[Theta]^2];
\[Sigma]2=(\[Sigma]rr+\[Sigma]\[Theta]\[Theta])/2-Sqrt[((\[Sigma]rr-\[Sigma]\[Theta]\[Theta])/2)^2+\[Sigma]r\[Theta]^2]; *)



\[Sigma]1:=(\[Sigma]xx+\[Sigma]yy)/2+Sqrt[((\[Sigma]xx-\[Sigma]yy)/2)^2+\[Sigma]xy^2]
\[Sigma]2:=(\[Sigma]xx+\[Sigma]yy)/2+Sqrt[((\[Sigma]xx-\[Sigma]yy)/2)^2+\[Sigma]xy^2]

