Trade-off Pareto optimum design of an innovative curved damper truss moment frame considering structural and non-structural objectives

Abstract

This research aims to develop a novel and cost-effective seismic force-resisting system called “curved damper truss moment frame” (CDTMF) by coupling the recently developed curved dampers (CDs) with conventional steel trusses. In this proposed system, the CDs are adopted as primary fuses, while semi-rigid connections are used as secondary fuses to dissipate the input seismic energy through a two-phased energy dissipation mechanism called the equivalent energy design procedure (EEDP). To validate the adequacy and feasibility of incorporating the CDTMF system in multi-story framed structures, the multi-objective NSGA II optimization technique was applied to the optimum seismic design of selected CDTMF prototypes. Their seismic performance was then compared with the recently proposed buckling restrained knee braced truss moment frame (BRKBTMF) systems, which were designed based on the same procedure to make a consistent comparison. This comparison was based on the results of nonlinear static analysis (pushover), nonlinear time history analysis (NTHA) and incremental dynamic analysis (IDA) on three-, six- and nine-story steel framed structures (low- to mid-rise systems). Since damage to non-structural acceleration-sensitive elements would depend on the floor acceleration, and because the main cause of damage in non-structural displacement-sensitive elements and structural members is generally due to the story drift, the objective functions of the optimization process were the median maximum story drift and the peak floor acceleration. In order to achieve the two-phased energy dissipation mechanism, the primary constraints (PCs) and secondary constraints (SCs) corresponding to the primary and secondary fuses are applied. The outcomes of the pushover analysis showed that the optimal CDTMF structures exhibited higher ductility and energy dissipation capacity compared to the BRKBTMFs. The results of the nonlinear dynamic analysis also indicated that the newly proposed CDTMF system can control the roof displacement, story drift, and roof acceleration during an earthquake excitation more efficiently than the BRKBTMF system. Finally, the outputs of the IDA show that the CDTMFs can fulfilled the FEMA P695 code requirements. Hence, it can be considered as a reliable seismic force resisting system.

Introduction

In recent years, there are many novel structural systems that have been proposed as alternatives seismic load resisting systems. In contrast to conventional seismic force-resisting systems, in which the energy dissipation mechanism is based on the yielding of the primary structural members, in these newly proposed seismic force-resisting systems, the energy dissipation is mainly concentrated in designated energy dissipation devices called structural fuses [1], [2], [3]. As an example, the seismic design and performance of knee-braced frames were investigated by Leelataviwat et al. (2011) [4]. In their study, the frames were designed to dissipate energy via knee braces and formation of plastic hinges in beams. Similarly, Junda (2011) presented the seismic performance of the knee braced frames with partially restrained (PR) connections [5]. Shin et al. (2012) also employed steel channel sections to develop new knee braces in buckling restrained knee bracing (BRKB) systems [6].

Leelataviwat et al. (2013) investigated the seismic behavior of ductile knee-braced moment frames, where the feasibility and effectiveness of this system were demonstrated through half-scale specimens [4]. Yang et al. (2013) and Yang and Li (2014) have introduced an innovative seismic force-resisting system, which is a combination of steel trusses and buckling-restrained braces (BRBs) called buckling restrained knee braced truss moment frame (BRKBTMF) [7], [8]. In a follow-up study, Yang et al. (2015) investigated the effect of using BRKBTMF system on seismic behavior of long-span structures, comparing the results with conventional steel moment frame systems for a 4-story office building case study [9]. Doung (2015) developed a performance-based plastic design methodology for buckling restrained knee braced frames with single plate shear connections [2]. In a more recent study, Li et al. (2018) proposed a new seismic structural system called diagrid structure fused with shear link (DSSL) and demonstrated its efficiency through nonlinear dynamic analyses [10], [11]. Yang et al. (2018) introduced an innovative damped H-frame, which consists of H-frames and BRBs. Their proposed system was designed based on an equivalent energy design procedure, and nonlinear dynamic analysis was employed to assess its performance [12]. In another relevant study, Junda et al. (2018) demonstrated the applicability of buckling-restrained knee braces (BRKBs) as a new reliable seismic force-resisting system [13].

Along with the above-mentioned structural fuse systems, yielding dampers can also be considered as cost-effective passive control devices with desirable seismic behavior. Murakami et al. (2013) improve the seismic performance of structures by applying oil, hysteretic, and mass-dampers simultaneously [14]. Shiomi et al. (2018) proposed a dual hysteretic damper (DHD) to improve the seismic performance of structures against a wider range of ground motions [15]. Bazzaz et al. (2015) investigated the behavior of steel replaceable circular dissipaters to improve structural ductility under monotonic loading [16]. Hsu and Halim (2017) also proposed an innovative steel curved dampers (CDs) to improve the seismic performance of steel frames. The feasibility and applicability of their proposed systems were evaluated with experimental cyclic tests [17]. In a follow-up study, Hsu and Halim (2018) investigated the seismic performance of a new A-brace system that could utilize the ductility capacity of the main structure, stiffness of traditional braces, and energy dissipation capacity of steel CDs to improve the seismic response of the whole structural system [18]. Jamkhaneh et al. (2019) proposed a new U-shape metallic damper as a cost-effective energy dissipation system. Experimental and numerical analyses indicated that their proposed system could considerably improve the ductility and energy absorption capacity of structures [19]. In a more recent study, Kazemi et al. (2019) introduced an off-center bracing system using steel ring plastic and composite material to improve the energy dissipation capacity of structures under cyclic loading conditions [20]. Dehghani et al (2020) introduced an innovative force resisting system called toggle-brace-curved damper (TBCD) in order to concentrate the damage in designated passive curved damper elements [21].

A wide range of optimization techniques have been recently developed to solve complex optimization problems in structural engineering [22], [23]. Kaveh et al. (2011) presented a method for performance-based multi-objective optimization of large steel structures, relying on the non-dominated sorting genetic algorithm (NSGA II) including differential evaluation operators [24]. Liang et al. (2015) proposed a multi-objective Particle Swarm Optimization (PSO) to solve structural optimization problems. The effectiveness of their proposed algorithm was demonstrated through the performance-based optimization design of truss and frame structures [25]. In another relevant study, Mokarram and Banan (2018) proposed a new optimization technique, called Surrogate Fast Converting Multi-Objective Particle Swarm Optimization (FC-MOPSO), to reduce the computational time of solving performance-based design optimization problems [26]. Dehghani et al. (2019) studied the performance-based design optimization of steel X-braced frames considering soil-structure using a cluster-based NSGA II algorithm [22]. In a more recent study, Fathizadeh et al. (2020) proposed an engineered cluster-based genetic algorithm (ECGA) to optimize the moment-resisting steel frames considering soil-structure interaction based on performance objectives [27].

The purpose of the present study is to enhance the performance of steel frames against seismic actions by proposing an innovative and cost-effective seismic structural system called curved damper truss moment frame (CDTMF). The proposed system on the one hand focuses on the advantages of steel trusses with semi-rigid connections to columns and their ability to cover long-span distances, and on the other hand, utilizes cost-effective curved dampers which are simply made of steel plates. The curved dampers and semi-rigid connections account for primary and secondary structural fuses dissipating the earthquake imposed energy via a two-phased energy dissipation mechanism according to the equivalent energy design procedure (EEDP) concept [12], while other structural members tend to remain elastic. It is worth mentioning that the CDs are to take most of the structural damages, yet they are designed to be decoupled from the gravity system, hence they can be replaceable easily if and when needed. In this study, the Multi-objective Non-dominated Sorting Genetic Algorithm (NSGA II) is employed for the optimum seismic design of the proposed CDTMF system by considering the median maximum floor acceleration (related to damage to acceleration-sensitive non-structural elements) and story drift (related to damage to displacement-sensitive non-structural elements and structural elements) as objective functions. The design variables are the characteristics of the primary structural fuses (CDs and BRBs) and the primary and secondary constraints (PCs and SCs) are considered to ensure the CDTMF system achieves the two-phased energy dissipation system. The optimization process is performed under seven ground motion records adopted from the PEER NGA West2 database [28] at two different seismic hazard levels, namely the Basic Safety Earthquake 1 (BSE-1) and the Basic Safety Earthquake 2 (BSE-2) with 10% and 2% probability of exceedance in 50 years, respectively. Having been introduced by Yang et al. (2014) [9], the BRKBTMF system is optimally designed based on the same procedure to make the comparisons consistent. Then, the seismic performance of the obtained optimal structures is evaluated via nonlinear pushover, nonlinear time history analysis (NTHA), and incremental dynamic analysis (IDA) [29]. The IDA is performed using twenty-two far-field ground motion records adopted from FEMA P695 [30] to assess the structural collapse capacity. Three prototype structures of three-, six- and nine-story are considered and the non-linear finite element models are constructed in OpenSees [31].