$1.)(25$ points$)$ The diagram below shows the framing plan of the $\backslash (2^\{\backslash$text $\{$nd $\}\}\backslash )$ floor framing above a small library in a two$-$story building. The library measures $\backslash (30^\{\backslash$prime$\}\backslash$mathrm$\{$x$\}45^\{\backslash$prime$\}\backslash )$ in plan. There is a large opening as shown to allow daylight to penetrate down to the library from a skylight above. Self$-$weights $($in lbs$.$ per linear foot$)$ and area loads $($in lbs$.$ per square foot$)$ area given to the right. To move forward with design, we need to start by determining the loads on all the primary structural members shown in the sketch below. Draw FBDs $($at relative scale$)$ for G$1,$ G$2,$ B$1,$ B$2,$ B$3,$ B$4,$ B$5$ and B$6.$ For each, please determine the load patterns and reactions and show them on the FBDs you have drawn. Also indicate in a small table the loads you expect from the girders G$1$ and G$2$ on the top of the corner columns, C$1,$ C$2,$ C$3,$ and C$4.$ The direction of joists is shown by the double half arrows. Joists are close enough together that beam loads from the joists can be considered as distributed loads.

Area Loads

$-$ Dead load $=18$ psf

$-$ Live load $\backslash (=40\backslash$mathrm$\{$psf$\}\backslash )$

Beam Weights

$-$ G$1-$ G$2=60$ plf

$-$ B$1-$ B$2=30$ plf

$-$ B$3-$ B$6=45$ plf