Question $2$

$[30]$

For the plane strain element given in Figure $2,$ determine the following:

a$)$ Element stress ${}_x,{}_y,{}_{xy}$

b$)$ Principal stress ${}_1$

$[20]$

c$)$ Principal stress ${}_2$

$[3]$

d$)$ Principal angle ${}_P$

$[3]$

$[4]$

The nodal displacements are as follows: $u_1=0\mathrm{.}001cm,v_1=0\mathrm{.}005cm,u_2=0\mathrm{.}001cm,v_2=0\mathrm{.}25cm,u_3=0\mathrm{.}0cm,v_3=0\mathrm{.}0cm$

Let $E=210$ GPa

an hour