An alternative approach can be used to determine the principal stresses for this type of problem. After reducing the strain gage rosette data, the principal strains can be determined from:

${\epsilon }_{p1},{\epsilon }_{p2}=\frac{{\epsilon }_x-{\epsilon }_y}{2}\pm \sqrt{{\left(\frac{{\epsilon }_x+{\epsilon }_y}{2}\right)}^2+{\left(\frac{{\gamma }_{xy}}{2}\right)}^2}$ $=\frac{770+(-350)}{2}\pm \sqrt{{\left(\frac{770-(-350)}{2}\right)}^2+{\left(\frac{1,940}{2}\right)}^2}$ $= 1,330.04 \mathrm{\mu \epsilon }, -910.04 \mathrm{\mu \epsilon }$

The orientation of the principal strains is determined from:

$\tan 2{\theta }_p=\frac{{\gamma }_{xy}}{{\epsilon }_x-{\epsilon }_y}$ $=\frac{1,940}{770-(-350)}$ $=1.732$