We consider three strain gauges: G$1$ G$2$ and G$3.$ There is $45\backslash$deg between G$1$ and G$2$ and $45\backslash$deg between G$2$ and G$3.$ The three strain gauge are installed on a structure supposed to be subject to a biaxial load. If there is no defect $($damage or cracks$)$ in the structure, the biaxial loads should be orientated along the direction of G$1$ and G$3.$

$1.$ If there is no cracks in the structure, what should be the relationship between the longitudinal strain in the direction of G$2.2,$ and the longitudinal strains in the direction of G$1$ and G$3,1$ and $3?$

$2.$ The measure of G$1,$ G$2$ and G$3$ are indeed

$1=2\mathrm{.}10^-06,$

$2-1\mathrm{.}10^-06,$

$3=-1\mathrm{.}10^-06$

A$.$ Is $2$ satisfying the relationship determined in the previous question? What can you conclude?

B$.$ Determine the orientations of the biaxial load

C$.$ Determine the magnitude of the strain along the two direction of loads