On 4.7-13, you can’t get started designing the column about the strong axis, since you don’t know the Ixx for the columns. Thus we start designing assuming that the weak axis will control.
About the weak axis, K = 1.0 since the column is supported by girders which provide no rotational resistance.
Note above that you have tremendous moment resistance from the beams coming in from each side. However, you have no moment resistance when connecting to the beams coming in from the front and back (in the center of the drawing). Thus the column will freely rotate, without resistance, about its weak yy axis, and thus has a Kyy = 1.0
Knowing that we can get started by assuming that the weak axis controls. KL = known, Fy = known, Load = known, use Table 4-1 to select the lightest column that works about the weak axis.
Now having a W shape to start, we have all information required to see if it will work about the strong xx axis. If you are lucky, it will work. If not, you should be able to select a larger column of reasonable size.
Rinse and repeat.