The dynamic behavior of floors in high-rise buildings and their contribution to damping - an analytical model

Abstract

The resistance of buildings to static loads is very well defined and regulated in codes compared with the resistance to dynamic loads. However in particular for high-rise buildings the resistance to dynamic loading is of great importance for the design and much less defined. The magnitude of vibrations depends on mass, stiffness and damping properties of the building and on the loading frequency. Damping is the most important factor to reduce the amplitude of vibration at resonance. Whereas stiffness and mass can be determined quite accurately during the design phase of a building for damping it is not yet possible to give an accurate prediction in the design phase. The empirical fomula's developed by Jeary (1986), Tamura (2003, 2012), Lagomarisono (1993) and Davenport and Hill-Carol (1986) based on full-scale measurements in Japan, United States, Italy and Great Brittain show large deviations in the predicted damping values. Damping in buildings can be assigned to structural damping, aerodynamic damping, intrinsic material damping, radiation damping, damping in non-structural elements and to additional dampers. Damping in floors both comprises intrinsic material damping and structural damping. The Eurocode prescribes damping ratio's of 1% to 2% for buildings categorized in steel buildings, concrete buildings or a combination of both. Full scale measurements in the Netherlands showed a scatter in damping ratio's between 1% and 3.5% and no clear distinction between material types could be made. Damping is not only dependent on structural properties of all individual components, but also on loading and on response characteristics. Understanding the influence of individual components to damping is key to predict damping in a building accurately. In this research project the focus will be on the contribution of damping in floors to the damping ratio of sender dutch high-rise buildings under wind loading. Here both damping in structural parts, in the connections between the floor and the main structure, and damping in floor-materials are studied. The goal of this thesis is to describe the damping mechanisms present in floors when buildings are excited by wind load using an simple analytical model. A one-dimensional model is designed, representing the expected behavior of floors in buildings based on the structural lay-out of dutch high-rise buildings. This model consists of an Euler-Bernoulli beam element including material damping following Kelvin-Voight's model and at both boundaries a rational spring, viscous damper and coulomb friction damper representing the structural damping. A solution for the model response is calculated using the Galerkin Approximation Method, where the product of linear modes shapes based on linear boundary conditions and generalized time dependent coordinates approximate the solution, combined with numerical integration following Runge-Kutta. These methods provided accurate solutions. The model was validated with an experiment. The set-up enclosed two steel columns, hinged connected to the floor, and a concrete bar, clamped between the two steel profiles. Some adjustments on the joint lay-out were made during the experiments. Measured accelerations showed a highly damped system and the decrease of amplitude of vibration was accompanied by a decrease in damping ratio's. Odd modes of the beam coincided with the natural frequencies of the system, with a clear first natural frequency. Strong coupling of higher modes was present at high amplitudes of vibration at the small beginning of the response, but these faded out quickly. Small changes in the natural frequencies of the system with time were detected, but for a founded conclusion further studies are recommended on this subject. A comparison of the experimental outcome with the analytical one-dimensional model was made and a good fit for the computed response was found. In further studies extension of the model to include a second lateral dimension and torsional modes can be made, or a calibration algorithm can be developed to determine an optimal fit for the damping parameters. Also experiments to study the non-linear material properties of concrete during high amplitude vibrations can be performed in future research to obtain more understanding the damping mechanisms in floors.