Read $($PW$-$Ch $4$ ; KH$-$Ch$.6,$ App C$)$

Problem $1$:

The following displacement field has been determined for the $10$ inch by $10$ inch, thin square plate shown below.

The plate is made of steel with a Young's modulus $=30{10}^6$ psi and Poisson's ratio $=0\mathrm{.}30.$

$u(x,y)=0\mathrm{.}10+0\mathrm{.}001x+0\mathrm{.}0005y+0\mathrm{.}00004xy$

$v(x,y)=0\mathrm{.}05+0\mathrm{.}002x+0\mathrm{.}0006y+0\mathrm{.}00003xy$

The displacements are given in inches and $x$ and $y$ are also given in inches.

$($a$)$ Compute the displacement of the upper right hand comer of the plate $(x=10\mathrm{.}0,y=10\mathrm{.}0)(10$pts$)$

$($b$)$ Compute the strains ${}_{x0}$ and ${}_{yz}$ at the center of the plate. $(10$ pts$)$

$($c$)$ Compute the stress ${}_{zx}$ at the center of the plate $(10$ pts $).$