$2-$ Consider the thin $($steel$)$ plate in Figure. The plate has a uniform

thickness $t=1in.,$ Young's modulus $E=30{10}^6,$ and weight density $$

$=0\mathrm{.}2836l\frac{b}{i}{n}^3.$ In addition to its self$-$weight, the plate is subjected to a

point load $P=100lb$ at its midpoint.

$($a$)$ Model the plate with two finite elements.

$($b$)$ Write down expressions for the element stiffness matrices and element

body force vectors.

$($c$)$ Assemble the structural stiffness matrix $K$ and global load vector $F.$

$($d$)$ Using the elimination approach, solve for the global displacement

vector $Q.$

$($e$)$ Evaluate the stresses in each element.

$($f$)$ Determine the reaction force at the support.