A plane-stress element has σxx=200 MPa, σyy=100 MPa and shear stress of magnitude 100 MPa with directions shown. Find the normal stress on the indicated 45° plane in MPa (nearest integer).
The indicated plane has its normal at 45° to x, with positive τxy for the shown arrows. Use $\sigma_n=(\sigma_x+\sigma_y)/2+(\sigma_x-\sigma_y)\cos(2\theta)/2+\tau_{xy}\sin(2\theta)$. At θ=45°, this is 150+0+100=250 MPa.
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