All members are oriented for strong axis bending in the plane of the frame.

Out$-$of$-$plane: Columns are part of a braced frame with bracing provided at the column ends, $\backslash ((\backslash$mathrm$\{$KL$\})\backslash$mathrm$\{$y$\}=16\backslash )\text{'}.$

Steel: A$992$

$($a$)$ Find the lightest W$12$ shape for each column.

$($b$)$ The connection at the right end of the beam $($i$.$e$.,$ the connection to Column $\text{'}$B$\text{'})$ is changed to a pinned connection.

Find the lightest W$12$ shape for each column.