Structural Cross Sections

The orientation of maximum shear stress is:

${\theta }_{s1}={\theta }_1-{45}^{°}={157.5}^{°}-{45}^{°}={112.5}^{°}$

And the normal stresses acting on the planes of maximum shear stresses are:

${\sigma }_{\mathit{av}}=\frac{{\sigma }_x-{\sigma }_y}{2}=\frac{80+30}{2}=55\mathrm{N}/{\mathrm{mm}}^2$

Result

Principal stresses and maximum shear of the stress element are:

${\sigma }_{x1}=19.65\mathrm{N}/{\mathrm{mm}}^2$ at $\theta =67.5°$

${\sigma }_{x1}=90.35\mathrm{N}/{\mathrm{mm}}^2$ at $\theta =157.5°$

${\sigma }_1=90.35\mathrm{N}/{\mathrm{mm}}^2$

${\sigma }_2=19.65\mathrm{N}/{\mathrm{mm}}^2$

${\tau }_{\mathit{max}}=35.35\mathrm{N}/{\mathrm{mm}}^2$

${\theta }_{s1}=\mathrm{112.5\; ...}$