$(12$ points$)$ Difficulty $(4/5)$

Dimensions and Loads:

Problem Statement:

A W$8$x$40$ beam is loaded and supported as shown. Find the following, assuming the beam is composed of Structural Steel, and neglecting the effect of self$-$weight.

$($a$)$ The deflection of the beam midway between the supports.

$($b$)$ The slope of the beam at point C$.$

$($c$)$ The deflection of the beam at point $D.$

$($d$)$ The deflection of the beam at point $B.$

$($e$)$ The location on the beam $($relative to point A $)$ of maximum downward deflection.

$($f$)$ The maximum downward deflection of the beam.

Answers:

$($Denote upward deflections with positive values, and downward deflections with negative values. Denote positive slopes with positive values and negative slopes with negative values.$)$

$($a$)y_{AC-\text{m}\text{i}\text{d}\text{p}\text{o}\text{i}\text{n}\text{t}}=-{2\mathrm{.}861}^{*}{10}^{-3}ft$

$($b$){}_C=$

$($c$)y_D=$

$($d$)y_B=$

$($e$)x_{\text{m}\text{a}\text{x}-\text{d}\text{o}\text{w}\text{n}\text{w}\text{a}\text{r}\text{d}-\text{d}\text{e}\text{f}\text{l}\text{e}\text{c}\text{t}\text{i}\text{o}\text{n}}=$

$($f$)y_{\text{m}\text{a}\text{x}-\text{d}\text{o}\text{w}\text{n}\text{w}\text{a}\text{r}\text{d}}=$

be sure to include units with your answers