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Formulating equation of motion

Figure below shows a reinforced concrete framed building subjected to earthquake ground motion. The floor is rigid with the mass of each floor is shown in the figure. Formulate the equation of motion for this building. Prove that the natural frequencies for modes 1, 2 and 3 are 5.977 rad/s, 16.33 rad/s and 22.307 rad/s, respectively, and solve the equation of motion in order to obtain the generalized mass, damping, stiffness and force. Use the stiffness of column, k = 200 kN/m and the damping coefficient, c = 10 kN.s/m. Given:

1946_equation1.jpg

1970_equation2.jpg

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