## Appendix B. Solution of the Stress Cubic Equation

### B.1 Principal Stresses

There are many methods in common usage for solving a cubic equation. A simple approach for dealing with Eq. (1.33) is to find one root, say *σ*_{1}, by plotting it (*σ* as abscissa) or by trial and error. The cubic equation is then factored by dividing by (*σ*_{p} – *σ*_{1}) to arrive at a quadratic equation. The remaining roots can be obtained by applying the familiar general solution of a quadratic equation. This process requires considerable time and algebraic work, however.

What follows is a practical approach for determining the roots-of-stress cubic equation (1.33):

**(a)**

where

**(B.1) ...**