For the element shown below:

$($a$)$ Obtain the stiffness matrix. The nodal coordinates are given in units of millimeters. Assume plane stress conditions. Let $E=210$GPa,$v=0\mathrm{.}25,$ and $t=10mm.$

$($b$)$ Determine the element stresses ${}_x,{}_y,$ and $T_{xy}$ using the following nodal displacements for the element:

$u_1=2\mathrm{.}0mm,v_1=1\mathrm{.}0mm$

$u_2=0\mathrm{.}5mm,v_2=0\mathrm{.}0mm$

$u_3=3\mathrm{.}0mm,v_3=1\mathrm{.}0mm.$