Schematic design of distributed mass damping systems for tall buildings

Abstract

As new high-rises grow taller and more slender, the design of tall buildings becomes heavily constrained by the control of lateral displacements and accelerations due to dynamic excitations. This has led to the development of motion control devices, such as the Tuned Mass Damper (TMD) and Tuned Liquid Column Damper (TLCD). Contemporary designs implement devices where the dynamic response is the greatest, often at the top of buildings, occupying entire floors and inhibiting the sale of valuable real estate. Conversely, distributed damping is the concept of dividing the dampers into smaller devices that are placed on several floors throughout the building. Although a greater total mass is required, implementing smaller dampers and using less valuable floor area may be advantageous for buildings with a substantial cost variation between floors. This study presents a methodology where the optimal vertical distribution of TMDs and TLCDs is determined based on the footprint and relative cost of each damping scheme. To perform this analysis, the governing equations for a distributed damping system are developed and its response is derived assuming a periodic excitation. Given the structural properties and performance requirements of the building, a one TMD system is designed using the conventional approach. Ranging through several distribution schemes, the damper mass required for each distribution to meet the same acceleration performance as the one TMD system is determined. This mass is used to calculate the damper footprint for TMD and TLCD systems. From the cost distribution of the building, the relative cost of each scheme may be calculated and compared. Depending on the objective of the designer, the minimum damper footprint or minimum cost scheme may be selected as the optimal distribution. The methodology was demonstrated for 60, 80, 100, and 120-story buildings. It was observed that buildings with approximately half of the floors installed with dampers correspond to the minimum footprint scheme, while the minimum cost scheme was dependent on the building's size constraints and cost distribution. For buildings with significant cost variation in upper floors, distributed damping is not only the least cost solution, but also leads to conveniently small devices.