2) (40 pts) A technician measures strains using a 0-45-90 rosette (angles measured with respect to the x-axis) and gets the following strains: ($\varepsilon_a = 130\times10^{-6}$, $\varepsilon_b = -110\times10^{-6}$, $\varepsilon_c = 140\times10^{-6}$). (a = $0^\circ$, b =$45^\circ$, c = $90^\circ$)
a) Determine $\varepsilon_x$, $\varepsilon_y$, and $\gamma_{xy}$ for this loading condition.
b) After testing, the rosette was inspected and found to be poorly made, with the actual angles being $3^\circ$, $51^\circ$, and $96^\circ$. Determine $\varepsilon_x$, $\varepsilon_y$, and $\gamma_{xy}$ on the element.
c) Compare the answers to a) and b) and comment on the rosette's sensitivity to this kind of error.
