$(10$ pts$)$

$5.$ Using the Moment$-$Area Method, determine the location, $x_m,$ of the maximum deflection, $y_{\text{m}\text{a}\text{x}},$ for the beam with loading shown. The deflected shape sketch is provided below. Note that $y_{\text{m}\text{a}\text{x}}$ does not occur under the load; it occurs somewhere between Point A and the load at Point B$.$

The M$/$EI diagram is provided and the slope at point A has already been calculated for you:

${}_A=\frac{-2667(k-f{t}^2)}{EI}.$

EI is constant for this beam.

Deflectec