$6\mathrm{.}2-19$ At a point in a structure subjected to plane stress, the stresses are ${}_y=-40$MPa,${}_y=25$MPa, and ${}_{xy}=28$MPa $($the sign convention for these stresses is shown in Fig. $6-1)$ A stress element located at the same point in the structure $($but oriented at a counterclockwise angle ${}_1$ with respect to the $x$ axis $)$ is subjected to the stresses shown in the figure $({}_{b,T_b}$ and $20$ MPa $).$

Assuming that the angle ${}_1$ is between zero and $90,$ calculate the normal stress ${}_b,$ the shear stress ${}_b,$ and the angle ${}_1$

PROB. $6\mathrm{.}2-19$