The girders are assumed to be rigid, and the columns have flexural rigidities El, and El with damping C and C, but negligible masses. The stiffness of each column can be computed as 24EI hi Kolumn for i = 1,2 Hint: the columns need to be modeled as springs in parallel. The building is being excited by wind gusts F, (t) and F(t). Considering For m = 2m, m = m, c = c=c, h = 2h, h= h, and El, = El = El. The building is being excited by wind gusts F (t) and F (t). Considering For m = 2m, m = m c = C = c, h = 2h, h = h, and El = El = El. a) Find the governing equations of the 2 DOF model of the building using Newton's 2nd Law. b) Rewrite the governing equations if this system was under undamped free vibration (no damping and no forces acting on the structure as shown in the model below). FAD El El My m Building Frame EL EL Which can also be modeled as 1 F(t). F(t) m kolumns 2 F(t) k Kolum Alternative Model x (1) m M m Model F (1) *(e) k m X (t) k x (t) m2 Undamped Free Vibration Model all the steps below, continue with the assumption of undamped free vibration. Write the governing equations in the matrix form. Find the total kinetic energy in the system. Find the total potential energy in the system. The girders are assumed to be rigid, and the columns have flexural rigidities El, and El with damping C and C, but negligible masses. The stiffness of each column can be computed as 24EI hi Kolumn for i = 1,2 Hint: the columns need to be modeled as springs in parallel. The building is being excited by wind gusts F, (t) and F(t). Considering For m = 2m, m = m, c = c=c, h = 2h, h= h, and El, = El = El. The building is being excited by wind gusts F (t) and F (t). Considering For m = 2m, m = m c = C = c, h = 2h, h = h, and El = El = El. a) Find the governing equations of the 2 DOF model of the building using Newton's 2nd Law. b) Rewrite the governing equations if this system was under undamped free vibration (no damping and no forces acting on the structure as shown in the model below). FAD El El My m Building Frame EL EL Which can also be modeled as 1 F(t). F(t) m kolumns 2 F(t) k Kolum Alternative Model x (1) m M m Model F (1) *(e) k m X (t) k x (t) m2 Undamped Free Vibration Model all the steps below, continue with the assumption of undamped free vibration. Write the governing equations in the matrix form. Find the total kinetic energy in the system. Find the total potential energy in the system. The girders are assumed to be rigid, and the columns have flexural rigidities El, and El with damping C and C, but negligible masses. The stiffness of each column can be computed as 24EI hi Kolumn for i = 1,2 Hint: the columns need to be modeled as springs in parallel. The building is being excited by wind gusts F, (t) and F(t). Considering For m = 2m, m = m, c = c=c, h = 2h, h= h, and El, = El = El. The building is being excited by wind gusts F (t) and F (t). Considering For m = 2m, m = m c = C = c, h = 2h, h = h, and El = El = El. a) Find the governing equations of the 2 DOF model of the building using Newton's 2nd Law. b) Rewrite the governing equations if this system was under undamped free vibration (no damping and no forces acting on the structure as shown in the model below). FAD El El My m Building Frame EL EL Which can also be modeled as 1 F(t). F(t) m kolumns 2 F(t) k Kolum Alternative Model x (1) m M m Model F (1) *(e) k m X (t) k x (t) m2 Undamped Free Vibration Model all the steps below, continue with the assumption of undamped free vibration. Write the governing equations in the matrix form. Find the total kinetic energy in the system. Find the total potential energy in the system.