For $()/(\_(()/()))$ Equations $(5-36)$ show that the principal stresses are given by

$\backslash$sigma $\_(1)=($K$\_($I$))/(\backslash$sqrt$(2\backslash$pi r$))$cos$((\backslash$theta $)/(2))(1+$sin$((\backslash$theta $)/(2)))$

$\backslash$sigma $\_(2)=($K$\_($I$))/(\backslash$sqrt$(2\backslash$pi r$))$cos$((\backslash$theta $)/(2))(1-$sin$((\backslash$theta $)/(2)))$

$\backslash$sigma $\_(3)=\{(0($plane stress$))$:$\}$

$\backslash$sqrt$((2)/(\backslash$pi r$))$vK$\_($I$)$cos$((\backslash$theta $)/(2))($plane strain$)$