- Dampad Connection Perimeter Columns Beam And Floor Slab Omitted For Clarity Outrigger Doors Central Core Figure 3 Outr 1 (317.81 KiB) Viewed 16 times
Dampad connection Perimeter columns (beam and floor slab omitted for clarity Outrigger Doors Central core Figure 3. Outrigger layout with a beight of 212.88 metres from the ground to its architectural spire. The layout of the outrigger in this building is illustrated in Figure 3. Figure 4 presents a simple model of the core-to-perimeter-column outrigger system in which the building core is modeled as a uniform cantilever beam, and the outrigger, located at, is assumed to be massless and infinitely rigid. The intrinsic damping of the structure is assumed 1.5% of the critical damping in each mode. This homework uses the assumed modes method to study the effectiveness of such a supplemental damping system. ca Ha - och EI, PA Figure 4. Idealized model of the core-to-perimeter-column outrigger system. a. Show that the following assumed modes are admissible functions for the idealized model in Figure 4: W.00-¹¹.7-1.2....N where h is the height of the building. b. Derive the equations of motion for the building's response using 2 assumed modes. Mi+Cq+Kq G₂(t) where the matrix C can he written as C=C₁+C Here, C, is the damping associated with the intrinsic damping of the systern (assumed to be 1.5% in each mode), and C, is the damping matrix associated with the darmped outrigger system. (Optional) Formulate the state space representation of the system. Calculate the frequency, damping, and mode shapes associated with the first three natural vibration modes of the building. Use the following parameters for the system: p4 85000 kg/m, EI= 2.1×10 N·m², 140 m, 0.6, and c₁ - 5x10' N-m/s. e 15 m, Hint: determine the mass, damping, and stiffness matrices symbolically in Matlab