An electric motor of mass \(500 \mathrm{~kg}\) operates on the first floor of a building frame that can be modeled by a steel girder supported by two reinforced concrete columns, as shown in Fig. 12.41. If the operating speed of the motor is \(1500 \mathrm{rpm}\), design the girder and the columns such that the fundamental frequency of vibration of the building frame is greater than the operating speed of the motor. Use two beam and two bar elements for the idealization. Assume the following data:

\[\begin{aligned}& \text { Girder: } E=200 \mathrm{GPa}, \quad ho=250 \mathrm{~kg} / \mathrm{m}^{3}, \quad h / b=2 \\& \text { Columns: } E=30 \mathrm{GPa}, \quad ho=75 \mathrm{~kg} / \mathrm{m}^{3}\end{aligned}\]

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Motor Girder 3 m -Columns 3 m 6 m FIGURE 12.41 Electric motor on building frame. b th Cross section of girder Id Cross section of columns