E=200GPa, v=0.3, t=10mm
Now $x_1,y_1=10,20$
$x_2,y_2=70,20$
$x_3,y_3=40,60$

$\beta_1=y_2-y_3=20-60=-40$
$\beta_2=y_3-y_1=60-20=40$
$\beta_3=y_1-y_2=20-00=0$

$\gamma_1=-(x_2-x_3)=-(70-40)=-30$
$\gamma_2=-(x_3-x_1)=-(40-10)=-30$
$\gamma_3=-(x_1-x_2)=-(10-70)=60$

$2A=\begin{vmatrix}1&x_1&y_1\\1&x_2&y_2\\1&x_3&y_3 \end{vmatrix}=\begin{vmatrix}1&10&20\\1&70&20\\1&40&60 \end{vmatrix}$

$\hspace{1cm}=1(70*60*-40*20)-10(60-20)+20(40-70)$
$\hspace{1cm}=3400-400+(-600)$
$\therefore 2A=2400\,mm^2$

$\begin{bmatrix}B\end{bmatrix}=\frac{1}{2A}\begin{bmatrix}\beta_1&0&\beta_2&0&\beta_3&0 \\ 0&\gamma_1&0&\gamma_2&0&\gamma_3 \\ \gamma_1&\beta_1&\gamma_2&\beta_2&\gamma_3&\beta_3\end{bmatrix}$

$\begin{bmatrix}B\end{bmatrix}=\frac{1}{2400}\begin{bmatrix}-40&0&40&0&0&0 \\ 0&-30&0&-30&0&60 \\ -30&-40&-30&40&60&0 \end{bmatrix}$

$\begin{bmatrix}B\end{bmatrix}=\begin{bmatrix}-0.0167&0&0.0167&0&0&0 \\ 0&-0.0125&0&-0.0125&0&0.025 \\ -0.0125&-0.0167&-0.0125&0.0167&0.025&0 \end{bmatrix}$

$\begin{bmatrix}B\end{bmatrix}^T=\begin{bmatrix}-0.0167&0&-0.0125 \\ 0&-0.0125&0.0167 \\ 0.0167&0&-0.0125 \\ 0&-0.0125&0.0167 \\ 0&0&0.025 \\ 0&0.025&0 \end{bmatrix}$

Plane-Stress …