DANE: σ_x σ_y τ_xy

$\mathbf{\sigma}_{\mathbf{1}} = \ \frac{\sigma_{x} + \sigma_{y}}{2} + \ \frac{1}{2}\sqrt{{(\sigma_{x} - \sigma_{y})}^{2} + 4\tau_{\text{xy}}^{2}}$ $\mathbf{\sigma}_{\mathbf{2}} = \ \frac{\sigma_{x} + \sigma_{y}}{2} - \ \frac{1}{2}\sqrt{{(\sigma_{x} - \sigma_{y})}^{2} + 4\tau_{\text{xy}}^{2}}$ $\tan{2\alpha = \frac{2\tau_{\text{xy}}}{\sigma_{x} - \sigma_{y}}}$ → $\mathbf{\alpha} = \frac{1}{2}\ arctan(\frac{2\tau_{\text{xy}}}{\sigma_{x} - \sigma_{y}})$

n	n*45	$$\sigma_{xn} = \frac{\sigma_{1} + \sigma_{2}}{2} + \frac{\sigma_{1} - \sigma_{2}}{2}\cos\left( 2n \right)$$	$$\sigma_{yn} = \frac{\sigma_{1} + \sigma_{2}}{2} - \frac{\sigma_{1} - \sigma_{2}}{2}\cos\left( 2n \right)$$	$$\tau_{\text{xyn}} = \frac{\sigma_{1} - \sigma_{2}}{2}sin(2n)$$
0	0	$$\sigma_{x0} = \frac{\sigma_{1} + \sigma_{2}}{2} + \frac{\sigma_{1} - \sigma_{2}}{2}\cos\left( 0 \right)$$	$$\sigma_{y0} = \frac{\sigma_{1} + \sigma_{2}}{2} - \frac{\sigma_{1} - \sigma_{2}}{2}\cos\left( 0 \right)$$	$$\tau_{xy0} = \frac{\sigma_{1} - \sigma_{2}}{2}sin(0)$$
1	45	$$\sigma_{x45} = \frac{\sigma_{1} + \sigma_{2}}{2} + \frac{\sigma_{1} - \sigma_{2}}{2}\cos\left( 90 \right)$$	$$\sigma_{y45} = \frac{\sigma_{1} + \sigma_{2}}{2} - \frac{\sigma_{1} - \sigma_{2}}{2}\cos\left( 90 \right)$$	$$\tau_{xy45} = \frac{\sigma_{1} - \sigma_{2}}{2}sin(90)$$
2	90	$$\sigma_{x90} = \frac{\sigma_{1} + \sigma_{2}}{2} + \frac{\sigma_{1} - \sigma_{2}}{2}\cos\left( 180 \right)$$	$$\sigma_{y90} = \frac{\sigma_{1} + \sigma_{2}}{2} - \frac{\sigma_{1} - \sigma_{2}}{2}\cos\left( 180 \right)$$	$$\tau_{xy90} = \frac{\sigma_{1} - \sigma_{2}}{2}sin(180)$$
3	135	$$\sigma_{x135} = \frac{\sigma_{1} + \sigma_{2}}{2} + \frac{\sigma_{1} - \sigma_{2}}{2}\cos\left( 270 \right)$$	$$\sigma_{y135} = \frac{\sigma_{1} + \sigma_{2}}{2} - \frac{\sigma_{1} - \sigma_{2}}{2}\cos\left( 270 \right)$$	$$\tau_{xy135} = \frac{\sigma_{1} - \sigma_{2}}{2}sin(270)$$
4	180	$$\sigma_{x180} = \frac{\sigma_{1} + \sigma_{2}}{2} + \frac{\sigma_{1} - \sigma_{2}}{2}\cos\left( 360 \right)$$	$$\sigma_{y180} = \frac{\sigma_{1} + \sigma_{2}}{2} - \frac{\sigma_{1} - \sigma_{2}}{2}\cos\left( 360 \right)$$	$$\tau_{xy180} = \frac{\sigma_{1} - \sigma_{2}}{2}sin(360)$$
5	225	$$\sigma_{x225} = \frac{\sigma_{1} + \sigma_{2}}{2} + \frac{\sigma_{1} - \sigma_{2}}{2}\cos\left( 450 \right)$$	$$\sigma_{y225} = \frac{\sigma_{1} + \sigma_{2}}{2} - \frac{\sigma_{1} - \sigma_{2}}{2}\cos\left( 450 \right)$$	$$\tau_{xy225} = \frac{\sigma_{1} - \sigma_{2}}{2}sin(450)$$
6	270	$$\sigma_{x270} = \frac{\sigma_{1} + \sigma_{2}}{2} + \frac{\sigma_{1} - \sigma_{2}}{2}\cos\left( 540 \right)$$	$$\sigma_{y270} = \frac{\sigma_{1} + \sigma_{2}}{2} - \frac{\sigma_{1} - \sigma_{2}}{2}\cos\left( 540 \right)$$	$$\tau_{xy270} = \frac{\sigma_{1} - \sigma_{2}}{2}sin540)$$
7	315	$$\sigma_{x315} = \frac{\sigma_{1} + \sigma_{2}}{2} + \frac{\sigma_{1} - \sigma_{2}}{2}\cos\left( 630 \right)$$	$$\sigma_{y315} = \frac{\sigma_{1} + \sigma_{2}}{2} - \frac{\sigma_{1} - \sigma_{2}}{2}\cos\left( 630 \right)$$	$$\tau_{xy315} = \frac{\sigma_{1} - \sigma_{2}}{2}sin(630)$$
8	360	$$\sigma_{x360} = \frac{\sigma_{1} + \sigma_{2}}{2} + \frac{\sigma_{1} - \sigma_{2}}{2}\cos\left( 720 \right)$$	$$\sigma_{y360} = \frac{\sigma_{1} + \sigma_{2}}{2} - \frac{\sigma_{1} - \sigma_{2}}{2}\cos\left( 720 \right)$$	$$\tau_{xy360} = \frac{\sigma_{1} - \sigma_{2}}{2}sin(720)$$