Question $2$

At a certain point in a structure the material is subjected to plane stress such that on a vertical plane through

the point, the normal stress is $100$ MPa tension and the shear stress is $80$ MPa counterclockwise $[$see part $($a$)$

of the figure$],$ and on a plane oriented at an angle ${}_1$ the normal stress is $150$ MPa tension and the shear stress

is $35$ MPa counterclockwise $[$part $($b$)$ of the figure$].$ What is the angle ${}_1?$

Ans. $\{$:${}_1=23\mathrm{.}5]$