$6.$

A $\backslash (120^\{\backslash$circ$\}\backslash )$ strain gauge rosette is attached to a steel bar of width $100$ mm and thickness $10$ mm and the strain readings indicated in Figure Q$4$ were obtained. The bar is subjected to bending moment $\text{'}$ M $\text{'}$ acting in the $\backslash (\backslash$mathrm$\{$x$\}-\backslash$mathrm$\{$y$\}\backslash )$ plane.

Determine:

i$)$ the inclination of gauge A to the $\backslash (\backslash$mathrm$\{$x$\}-\backslash$mathrm$\{$x$\}\backslash )$ axis;

ii$)$ the bending moment M $.$