QUESTION $2$

$[25$ MARKS$]$

For the plane strain element shown in Figure Q$2$ below, the nodal displacements are given as: $u_1(0\mathrm{.}001mm),v_1(0\mathrm{.}005mm),u_2(0\mathrm{.}001mm),v_2(0\mathrm{.}00025mm),u_3(0mm)$ and $v_3(0mm).$ The coordinates are given in units of millimeters.

Determine the element stresses ${}_x,{}_y,{}_{xy}$ and ${}_1,{}_2$ and the principal angle ${}_p.$

Let $E=210$GPa and $v=0\mathrm{.}25$ and use unit thickness for plane strain.

TOTAL $=55$ MARKS