A two-story building frame is modeled as shown in Fig. 5.32. The girders are assumed to be rigid, and the columns have flexural rigidities \(E I_{1}\) and \(E I_{2}\), with negligible masses. The stiffness of each column can be computed as

\[\frac{24 E I_{i}}{h_{i}^{3}}, \quad i=1,2\]
For \(m_{1}=2 m, m_{2}=m, h_{1}=h_{2}=h\), and \(E I_{1}=E I_{2}=E I\), determine the natural frequencies and mode shapes of the frame.

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F2(t) El F(t) El m2 x2(1) m El El h FIGURE 5.32 Two-story building frame.