## 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. (1.28) 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 (1.28):

**(a)**

where