Draw free-body diagrams and derive the equations of motion

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Reference no: EM131465206

Question: The framed structure shown in Figure P5.83 has three square floors. The bottom floor has mass m1 = 2000 kg and is supported to the foundation by four solid columns with square cross sections. These columns are cantilevered from the foundation and

350_5.83.png

they are welded to the bottom floor. The second floor has mass m2 = 2000 kg and is supported to the first floor by four solid columns with square cross sections. These columns are cantilevered from the first floor and they are welded to the second floor. The top floor has mass m3 = 1000 kg and is supported from the second floor by four solid columns with square cross sections. The top columns are welded to the second floor but pinned to the top floor. All of the columns have length l1 = l2 = 4 m and cross-sectional dimensions b1 = b2 = 75 mm. They are made from steel with a modulus of elasticity E = 2.1 × 1011 Pa. A model is required to account for motion of the foundation due to earthquake excitation defined by x(t).

Tasks: (a) Draw free-body diagrams and derive the equations of motion using x1, x2, x3 as coordinates and x(t) as the input variable.

(b) State your equations of motion in conventional matrix format for vibration analysis.

Reference no: EM131465206

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