Elsevier

Journal of Building Engineering

Optimal design of rotational friction dampers for improving seismic performance of inelastic structures

Abstract

Rotational friction dampers (RFDs) have been proposed as one of the passive control devices in order to enhance the seismic performance of inelastic structures and dissipate the input energy of earthquakes through friction in their rotating plates. The efficiency, performance and design of an RFD strongly depend on its frictional moment and the length of its vertical rigid beam. Hence, the main contribution of this study is to propose an optimal design of the RFD for the seismic vibration control of an inelastic single–story steel moment–resisting frame (SMRF). For achieving this purpose, the parameters of the RFD subjected to an artificial earthquake were first optimized through minimizing the ratio of seismic input energy to dissipated the energy in the RFD. Modeling results show that the optimized RFD is able to give an average reduction of 54%, 75% and 97% versus the structure without an RFD in terms of the maximum and residual roof displacements and the cumulative hysteresis energy of the SMRF, respectively. Then, the seismic performance of the SMRF equipped with the optimized RFD was assessed subjected to four historic earthquake records. The results indicate that the optimal RFD–equipped structure subjected to the historic earthquakes exhibits a better seismic performance in all measures compared with the uncontrolled structure.

Introduction

The intrinsic capability of structures designed based on the traditional seismic codes is not sufficient for the dissipation of the seismic input energy. Hence, various passive control devices have been proposed and developed for the seismic retrofit of existing structures. These devices have also been used in the design of new structures to mitigate the seismic hazards and enhancing their safety and serviceability. Frictional dampers as a type of passive control devices have successfully been utilized to improve the seismic performance of structures through the high potential of seismic energy dissipation. A number of experimental studies on friction devices were conducted by Pall and Marsh [1]; Constantinou et al. [44], Aiken and Kelly [2]; Fitzgerald et al. [45], Grigorian and Popov [3].

A new friction damper so–called the rotational friction damper (RFD) was introduced by Mualla and Belev [4]. They implemented experimental and numerical studies on a single story frame equipped with RFD. Liao et al. [5] evaluated the seismic performance of the RFD with a set of full–scale testing on a shaking table. Lee et al. [47] proposed a bracing–friction damper system which was modified using the optimal slip load distribution for the seismic retrofitting of a damaged building. Kim et al. [6] introduced a combined system of RFDs connected to high strength tendons to improve the seismic and progressive collapse–resisting capacity of existing structures. Kaur et al. [7] investigated the seismic responses of a moment resisting frame equipped with friction dampers. The results demonstrated that the substantial reduction of the earthquake responses was achieved in the mid–rise and high–rise buildings equipped with friction dampers. Beheshti–Aval et al. [8] introduced the design of a new combination of friction/hysteretic damper which was installed in the middle of cross bracing. Choi and Kim [9] proposed frictional hysteretic energy dissipating devices as an alternative to coupling beams in a reinforced concrete (RC) shear wall system. The analysis results showed that the maximum allowable ductility demand of the retrofitted RC shear wall system was increased. Sanati et al. [10] introduced a novel rotational damper called a Rotational Friction Viscoelastic Damper (RFVD). In the RFVD, a number of viscoelastic pads were added to the RFD for dissipation the energy in low excitation frequencies. Bonchev et al. [11] proposed a new design of columns linked with friction dampers for the seismic retrofit of steel moment resisting frames. In order to eliminate the damage expected in the conventional link elements, RFDs as seismic links were used instead of short steel beams.

For the mitigation of structural seismic responses and damages, it is highly important that passive control devices are efficiently used in the design of new structures or the seismic retrofit of existing structures. For this purpose, the optimal design of dampers has been considered as an important challenge for engineering designers. Moreschi and singh [12] proposed the optimal simultaneous design of the yielding metallic and friction dampers for the seismic-excited buildings. Fallah and Honarparast [13] optimized the slip loads of Pall friction dampers for building frame in two cases. In the first case, it was assumed that the dampers of all stories have same slip load. In the second case, each damper had its own slip load. Miguel et al. [14] implemented the simultaneous optimization of the friction forces and the distribution of friction dampers in structures subjected to seismic loading in order to obtain a desired level of reduction in the response. Nabid et al. [15] presented a practical methodology for the optimum design of friction wall dampers in RC frames subjected to seven spectrum–compatible design earthquakes. They found that the high energy dissipation capacity was considerably provided by a uniform cumulative distribution. Kim and An [16] implemented the optimal distribution of friction dampers in order to effectively reduce the seismic responses of an existing RC structures designed without considering seismic load. Recently, Nabid et al. [17] have proposed a practical performance–based optimization methodology for the seismic design of RC frames with friction wall dampers. They concluded that a uniform distribution of damage along the height of the building was achieved by distributing the slip loads of the friction wall dampers.

The main focus of this study is to propose an optimum design process of the RFD based on the energy concept in a nonlinear structure subjected to earthquake excitations. For this purpose, a modified particle swarm optimization based on the passive congregation, called PSOPC, as a powerful metaheuristic optimization algorithm is utilized for finding the optimal parameters of an RFD in an inelastic single–story steel moment-resisting frame (SMRF). The ratio of the seismic input energy to the dissipated energy in the RFD is considered as objective function in the optimum design process, while the frictional moment and the length of the vertical rigid beam of the RFD are selected as the design variables. Considering four well-known earthquakes, the seismic performance of the structure equipped with the optimal RFD is also compared with those given for the corresponding structure without the RFD.

Section snippets

Components of an RFD and mechanism of its action

An RFD shown in Fig. 1 includes a central (vertical) plate, two side plates, and two friction pad disks.

The central plate connects the damper device to the beam center of frame. Furthermore, the ends of the two horizontal plates are connected to the inverted V–braces which can be pretensioned for avoiding their buckling. During an earthquake, the bracing system and the forces of friction at the interface of the steel plates and friction pads can resist the horizontal motion of the frame. The

Optimization problem

A structure can withstand a strong earthquake, if the input energy of the earthquake is less than the capacity of energy absorption in the structure [[19], [20], [21], [22], [23]]. During the ground motion, the input energy of an earthquake transmitted to a structure can be dissipated through the movements and deformations of structural members consisting of the kinetic energy, damping energy, elastic strain energy and inelastic hysteretic energy. When a structure is equipped by an RFD, the RFD

Seismic energy equation

The equation of motion of a multi–degree–of–freedom system is expressed as: M u ¨ t + C u ˙ t + F r t = − M r x ¨ g t where M is the mass matrix; C is the viscous damping matrix; F r (t) is the global nonlinear restoring force vector at time t; u ¨ t , u ˙ t and u t are the response vectors of acceleration, velocity and displacement respectively; r is the support influence vector; and x ¨ g t is the ground acceleration at time t. Eq. (9) can be transformed into an energy balance equation as follows: E k ( t ) + E d ( t ) + E a ( t ) = E i ( t ) where

Modeling of a SMRF

In this study, the single–story SMRF system introduced by Xue [35]; shown in Fig. 3(a), was considered for the numerical studies. The height and width of the structure are equal to 13 and 30 ft, respectively.

The open–source finite element software OpenSees [36] was utilized for the nonlinear dynamic analysis of the SMRF. The lumped plasticity model was employed in the structural elements, which was modeled by zero–length plastic hinges (rotational springs) at the ends of the elastic beam–column

Optimum design of the RFD under an artificial earthquake record

For the optimum design of the RFD, the upper and lower bounds for the frictional moment and the length of vertical rigid beams of the RFD are shown in Table 1.

In the PSOPC algorithm, the population size (N) and the maximum number of iterations (l max ) are set to 30 and 150, respectively. The upper and lower bounds for the inertia weight (i.e. ω max and ω min ) and r p 1 are also set to 0.4, 0.1 and 25, respectively. These parameters were selected based on general recommendations in the literature [29

Conclusions

This study presented the optimal design of an RFD to enhance seismic performance of an inelastic SMRF. Based on the energy concept, a ratio of seismic input energy to dissipated energy in the RFD was considered as the objective function to reduce the cumulative hysteresis energy of the structure and mitigate major structural damages. The influential parameters of the RFD including its frictional moment and the length of its vertical rigid beam were selected as design variables of the

Conflicts of interest

The authors declare that they have no conflict of interest.

Replication of results

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

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