Aligning the Charts $(40$ points $)$

This problem is a slight modification of Segui $4\mathrm{.}7-12$

Follow the steps a$,$ b$,$ and c as outlined in Segui; the only difference is we will look at doing some optimization with sections selection. Oftentimes, the interior columns $($in column lines $2$ and $3)$ are different sizes than the exterior columns $($in column line $3$ and $4).$ The problem asks you to solve for member GF$.$ Please follow the same process for columns CB OR NO $($Again$,$ you should only do one $).$ Assume the loading for Column Line I and $4$ is $\frac{1}{2}$ of that used for Column Line $2$ & $3.$

Something we have not talked about but should be straightforward is Demand Capacity Ratio $($DCR$).$ The DCR is used when discussing what $\%$ of a member is being utilized. This is computed by taking the Pu $($ Ultimate Factored Load$)$ and dividing it by the axial capacity $Pn$ :

$DCR=(P\frac{u}{}Pn)$

Recall, Pn differs based on the supporting conditions for the columns and the surrounding girders.

Determine the following:

$($I$)$ Compute the DCR$\text{'}$s for the interior and exterior columns that you have computed from above. Which column line do you expect to have a higher DCR$?$ Does the calculation support your thought process?

$(2)$ If they do differ, determine another column section for the one that has a lower DCR$,$ such that the DCR$\text{'}$s are within $10\%$ of each other. Said in an example, say column one has a DCR of $0\mathrm{.}34$ and column $2$ has a DCR $0\mathrm{.}60.$ In this case I am asking to change the column I section such that the DCR is within $10\%$ of $0\mathrm{.}60($i$.$e$.0\mathrm{.}54-0\mathrm{.}60$