A structural member under loading has a uniform state of plane stress which in usual notations is given by σ_x = 3P, σ_y = -2P and τ_xy = √2 P, where P > 0. The yield strength of the material is 350 MPa. If the member is designed using the maximum distortion energy theory, then the value of P at which yielding starts (according to the maximum distortion energy theory) is

The state of stress at a point is $${\sigma _x} = {\sigma _y} = {\sigma _z} = {\tau _{xz}} = {\tau _{zx}} = {\tau _{yz}} = {\tau _{zy}} = 0$$ and $${\tau _{xy}} = {\tau _{yx}} = 50$$MPa. The maximum normal stress (in MPa) at the point is _________.

The state of stress at a point on an element is shown in figure (a). The same state of stress is shownin another coordinate system in figure (b).

The components $$\left( {{\tau _{xx,}}{\tau _{yy,}}{\tau _{xy}}} \right)$$ are given by