Applicability of Damped Outrigger Systems Using Timoshenko Beam Theory

Abstract

Recently, applying damped outriggers in high-rise buildings to reduce vibration due to earthquake and wind has attracted a lot of attention. By placing energy dissipated devices vertically between the end of outriggers and perimeter columns, the damped outrigger systems emphasize the supplementary damping rather than stiffness. This paper investigates the applicability of viscously damped outrigger systems using Timoshenko beam theory. First, the building is modeled as a cantilevered Timoshenko beam, and the damped outriggers are simplified as equivalent complex rotational spring. With the assembly of dynamic stiffness of the damped outrigger system, the Wittrick–Williams algorithm and Newtonian iteration are then combined to calculate the dynamic characteristic of the system. The proposed approach has been verified by finite element method through a case study. The shear deformation and rotatory inertia of the core, later blended as slenderness ratio of the height-radius following Timoshenko beam theory, stiffness ratios of core-column and core-outrigger, and the number of damped outriggers are subsequently evaluated associated with supplementary damping as applicability analysis. This study shows the following: (1) adding damping amplifies twice to triple as the slenderness ratio increases from 5 to 25 for the first mode; (2) configurating more damped outriggers could provide stable damping contribution across modes with diminishing benefit; (3) Timoshenko beam analysis is better suited while Euler–Bernoulli beam analysis is an acceptable approximation only when the slenderness ratio of one-damped outrigger system is bigger than 25 and the first mode is predominant; and finally (4) the stiffness ratios of core-column, core-outrigger and stiffness of dampers have substantial influence on structural damping, particularly within the range smaller than 1, 10 and 4, respectively, but the presence of properly designed negative stiffness of dampers could bring substantial improvement. This study could serve as guidelines to apply damped outrigger systems in high-rise buildings.