Numerical methodology for dynamic analysis of buildings with friction dampers

Abstract

A number of studies on using friction based energy dissipation system for seismic protection of the building have been published in the recent past. The studies show that numerical approximation of the effectiveness of the friction based energy dissipation system depends on the accurate solution of the relevant nonlinear equations of motion. The available numerical models to idealize the behaviour of friction dampers can be categorized into equivalent linearization method, approximation by rigid-perfectly plastic hysteric model and stick-slide condition model. However, it has been observed that the minimum difference in relative velocity or non-identification of exact time of phase transition from stick to slide condition results in a noticeably high fluctuation of relative velocity in the stick-slide model. To identify the exact time for phase transition, this paper presents a numerical methodology for dynamic analysis of buildings with friction damper, leading to improved accuracy of solutions of equations of motion. The mathematical formulation and solution procedure of the proposed methodology has been presented in detail in this paper. The results obtained have been validated with examples from published literature. The response of single degree of freedom (SDOF) system with friction device when subjected to nine different ground motions are presented. The selected ground motion encompasses three ground motions each from soft soil, medium soil and hard soil to evaluate the likely response of the structure under the likely range of expected ground motion characteristics. The spectral variation with reference to pretension force has been investigated and presented. The results indicate that for a particular range of pretension force, beyond a particular stiffness ratio, the reduction in spectral response of the damper added system is independent of frequency of the SDOF system, which shows the robustness of friction devices. INTRODUCTION The use of friction dampers for seismic protection of buildings has attracted the attention of researchers in the recent past. Friction dampers, which dissipate energy through friction force, have been observed to be used efficiently in structures for reduction of earthquake induced vibrations. In these dampers, a large amount of energy is dissipated in the form of heat during earthquake excitation due to frictional resistance developed between moving solid interfaces, at a predefined load. Friction devices can also be designed to decouple structural fundamental frequencies from dominant frequencies of earthquake ground motion. Pall et al. [1] developed limited slip bolts (LSB) for the seismic control of precast and cast-in-place concrete walls. The development of friction dampers [1] began by conducting static and dynamic tests on a variety of simple sliding elements having different surface treatments. The goal was not necessarily to obtain maximum energy dissipation, but rather to identify a system that possesses consistent and predictable response. Experimental results by Pall and Marsh [2] have shown that the hysteretic behaviour of the sliding friction joints is reliable and repeatable, and approaches a rectangular hysteretic loop with insignificant degradation over cycles much greater than that encountered in consecutive earthquakes. They also showed that the friction joints should be tuned in order to optimize seismic performance. However, the study considered only one earthquake record and hence the influence of the seismic excitation characteristics on the efficiency of the proposed structural system was not addressed. Pall and Marsh [3] also proposed a system in which the frictional devices were incorporated with the braces in a moment resisting frame. It was found that the seismic capacity can be improved and the damage control potential of the frame building can be enhanced by incorporating friction dampers in the bracing system of the building. This device can also be used for enhancing the seismic resistance of existing frame buildings. Since such systems use bracings and friction joint, there exists a possibility of slip in friction joint before the buckling of brace occurring at a higher load in tension and a lower load in compression. Generally, structural braces are so designed that they act effectively in tension only, i.e. sliding occurs during tension and no sliding takes place during reversal of load. The friction joints with slotted holes can be used to slide in tension or compression, if the brace is designed to avoid buckling in compression till the designed sliding load is attained. Pall [4] has proposed modified sliding friction devices that can be installed at the intersection of steel bracing. These devices aim to solve the drawbacks encountered in the behavior of steel bracing. The sliding of the device, is designed to be restricted under normal loads and moderate earthquake ground motions. During the severe earthquake, the device slides at a predefined load, prior to the occurrence of yielding of structural elements of the frame. However non-sliding phase occurs in the device in every cycle of motion during an actual earthquake, illustrating the inaccuracy of the assumed hysteretic behaviour. At times, buckling of compression brace occurs, whereas tension brace may not slide. Under such conditions, the validity of hysteresis behaviour assumed by Pall and