Problem $2(33$ points$)$: Strain field within a loaded continuum

We consider three strain gauges: $G_1,G_2$ and $G_3.$ There is $45$ between $G_1$ and $G_2$ and $45$ 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 $G_3.$

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 ${}_3?$

The measure of $G_1,G_2$ and $G_3$ are indeed ${}_1=-{8\mathrm{.}10}^{-06},{}_2=-{8\mathrm{.}10}^{-06},$ and ${}_3=-{2\mathrm{.}10}^{-06}.$

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