Problem Statement:

An industrial loading dock is being renovated to handle new machinery deliveries. A steel beam needs to be selected to support both a concentrated load and a distributed load from equipment being transported on the dock. A wide$-$flange steel beam will be placed across two supports as shown in the diagram, spanning a total of $18$ feet. On one end of the beam, a $20$ kip piece of equipment will rest, positioned $8$ ft from the left support. In addition, a distributed load from the weight of machinery will act on the beam, starting from the point $\backslash ($ x$=8\backslash$mathrm$\{$ft$\}\backslash )$ to the right end, a distance of $10$ ft $.$

Requirements:

$-$ Select the lightest$-$weight steel beam from Appendix C that can safely support the loads.

$-$ The allowable bending stress for the beam material is $\backslash (\backslash$sigma$\_\{\backslash$text $\{$allow $\}\}=26\backslash$mathrm$\{$ksi$\}\backslash ).$