A building frame is modeled by four identical steel columns, each of weight \(w\), and a rigid floor of weight \(W\), as shown in Fig. 2.79. The columns are fixed at the ground and have a bending rigidity of \(E I\) each. Determine the natural frequency of horizontal vibration of the building frame by assuming the connection between the floor and the columns to be (a) pivoted as shown in Fig. 2.79 (a) and (b) fixed against rotation as shown in Fig. 2.79(b). Include the effect of self weights of the columns.

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W W f f f f -El - FIGURE 2.79 Building frame. (b)