Uniform Inter-story Drift Research Articles

Theoretical and experimental research on the rocking truss system with post-tensioned rocking connection

The weak story failure often occurs in steel frame structures and the collapse risk of the frames will increase because of concentrated plastic deformation in the soft story. The work presented in this paper aims to avoid the soft story mechanisms and the improve self-centering capacity of steel frames by employing the innovative rocking truss. Compared with the previous rocking system, it is more flexible in application and suitable for retrofit of existing buildings. The theoretical approach to quantifying the stiffness demand of the rocking truss was proposed and presented two critical parameters (equivalent bending stiffness ratio η and the rotation stiffness ratio λ) for the design of the rocking truss. The 1/3 scaled steel frame with rocking truss (SFRT) was tested and theoretical analysis results were validated by test results. The finite element model of SFRT was built following the boundary conditions of the test specimen. The numerical results are consistent with the experimental observations. The nonlinear static and dynamic analysis results of the SFRT were compared with those of the same steel frame (SF) with a bracing system. It was found that the rocking truss can reduce the maximum and residual drifts of the main frame as expected, and the plastic development of the RBS at the beam end in SFRT is less than that in SF with a bracing system. The parametric analysis of the rocking connections with different values of prestressing force was carried out. The results confirm that the rotational stiffness and load-bearing capacity of the rocking connection can be accurately evaluated by the theoretical force-displacement curve. The effect of the equivalent bending stiffness ratio η and the rotation stiffness ratio λ on the lateral deformation pattern of structures was discussed by theoretical analysis, and the design procedure of the rocking truss is recommended to satisfy the demand of uniform inter-story drift and self-centering capacity.

Seismic and collapse performance of a hybrid structure comprising steel frame with precast concrete shear walls and cladding panels

AbstractA hybrid structure constructed by replacing external steel beams and columns in the steel frame (SF) to precast concrete shear walls with insulation (PCSWs) and precast concrete cladding panels (PCCPs, SFPCSW) is proposed in this paper to avoid the problem of columns protruding from walls and PCCPs directly connected with SF. Numerical models of the SF and SFPCSW structures are established in ETABS software based on an 18‐story assembled steel residential building to investigate the seismic performance and collapse resistance capacity of SFPCSW. Time history analysis results show that the SFPCSW exhibits bending‐shearing lateral deformation and has more uniform interstory drift ratios than the SF. Under major earthquakes (i.e., probability of exceedance of 2% in 50 years), the damage of SF is concentrated in stories 1–6; for SFPCSW, the plastic hinges mainly appear in the concrete beams between PCSWs at each story, and the damage in PCSWs and the internal frame is small. Using pinned connections between the steel beam and PCSW reduces the structural lateral stiffness and increases the earthquake load carried by the internal frame. The incremental dynamic analysis results show that the SF and SFPCSW have similar collapse resistance capacities.

Hybrid self-centering companion spines for structural and nonstructural damage control

This paper intends to develop a new lateral force-resisting system – the hybrid self-centering companion spines system (denoted as the HSCS system) – for obtaining better seismic resilience by controlling both structural and nonstructural damage. The HSCS system consists of two rigid spines pinned to the ground and several hybrid dampers. The two rigid spines can facilitate the structure to avoid soft-story mechanisms and control higher mode responses by promoting uniform inter-story drift distribution under strong earthquakes. The hybrid damper is made of a friction spring damper and a viscous damper in parallel and provides the self-centering feature, energy-absorbing capacity, and acceleration- and velocity-control capacity for reducing structural and nonstructural damage. A performance-based design (PBD) procedure was developed for the HSCS system based on the concept of the direct displacement-based design method. The three-story and six-story demonstration buildings were considered in this study to investigate the seismic performance of steel buildings equipped with the proposed HSCS systems. Four designs with different design parameters were performed for the demonstration buildings based on the proposed PBD procedure. The three- and six-story self-centering companion spines systems (denoted as SCS systems) were considered for highlighting the benefits of adopting HSCS systems. Nonlinear dynamic analyses were conducted to evaluate the structural and nonstructural damage of the designed buildings under earthquakes. The analysis results indicate that the designed HSCS systems can achieve the desired performance objective and nonlinear behavior under dynamic excitations. The HSCS systems can show excellent structural damage control performance and post-earthquake recoverability by controlling the residual inter-story drift much smaller than 0.2% even under MCE excitations. The excellent nonstructural damage control capacity can be also observed in the designed HSCS systems, while most of the nonstructural components are only slightly damaged even under MCE excitations. Moreover, the HSCS systems can achieve smaller absolute floor acceleration and floor velocity responses than SCS systems under both DBE and MCE although they are designed to achieve similar maximum inter-story drift responses under DBE.

Hybrid self-centering rocking core system with fiction spring and viscous dampers for seismic resilience

This research presents a novel aseismic system, the hybrid self-centering rocking core (HSRC) system, for obtaining better seismic resilience in steel buildings. Two hybrid self-centering dampers are introduced in the HSRC system to control structural and nonstructural damage. A rocking core, i.e., a steel braced frame with pinned base is included in the HSRC system to facilitate uniform inter-story drift responses under earthquakes. The steel braces in the rocking core can also work as a reserve energy-absorbing mechanism against structural collapse subjected to extreme seismic events whose intensities are more significant than those of the maximum considered earthquakes in design codes. The desired nonlinear responses of the HSRC system were analyzed. Direct displacement-based design steps were developed for the HSRC system. Three-story and six-story HSRC systems were designed following the proposed design method. Nonlinear dynamic analysis results indicate that the designed HSRC systems can show desired nonlinear responses and achieve the expected performance objective under earthquakes. Moreover, seismic fragility analyses were also conducted based on the incremental dynamic analysis results to assess the performance in controlling structural and nonstructural damages of the HSRC system under earthquakes of different intensities. The results confirm that the proposed HSRC system has excellent capacity in resisting structural collapse, achieving reliable post-earthquake recoverability, and controlling structural and nonstructural damage under rare seismic events.

Performance-based seismic design method for retrofitting steel moment-resisting frames with self-centering energy-absorbing dual rocking core system

This research intends to propose an upgraded strategy for steel moment-resisting frames (SMRFs) by implementing Self-Centering Energy-absorbing Dual Rocking Core (SEDRC) systems to achieve enhanced seismic performance, improved seismic resilience, and avoid inter-story drift concentration. A performance-based method is developed to design the SEDRC system for upgrading the existing SMRF. The maximum inter-story drift and drift concentration factor are adopted as the design performance objectives. Two prototype SMRFs with three and nine stories are introduced to validate the proposed performance-based design procedure. Nonlinear static analyses were first performed for the original SMRFs and the updated ones (denoted as SEDRC-MRFs) to investigate the efficiency of the proposed retrofit strategy. The pushover curves of the analytical structures confirm that the SEDRC systems can increase the stiffness and strength of SMRFs, and SEDRC-MRFs upgraded through the proposed design procedure show no strength deterioration before the fracture of the brace in the SEDRC system. A set of 18 ground motions were chosen to study the seismic performance of the designed SEDRC-MRFs. The analysis results indicate that SEDRC-MRFs can obtain the desired performance objectives. The SEDRC system could reduce the maximum and residual inter-story drifts of SMRFs and promote uniform inter-story drift distribution. Moreover, the designed SEDRC-MRFs can be used immediately without the need for repairing structural members after the design basis earthquakes and can be repaired economically after the maximum considered earthquakes.

STIFFNESS DETERMINATION METHOD UNIFORMIZING ENVELOPED INTER-STORY DRIFT ANGLE IN MULTIPLE SEISMIC RESPONSES

Uniform inter-story drift angle in seismic response of buildings is effective in improving structural performance. Because it is expected to prevent pancake collapse due to concentration of deformation, and to decrease the maximum inter-story drift angle by efficient absorption of damping energy in each story.

Self-centering companion spines with friction spring dampers: Validation test and direct displacement-based design

This paper aims to propose self-centering companion spines with friction spring dampers (denoted as SCS) for obtaining better post-earthquake resilience in steel building structures. Two typical configurations of SCSs in buildings were first introduced. The SCS mainly consists of two rigid spines (RSs) and many friction spring dampers (FSDs). The two RSs have adequate strength and stiffness to create uniform inter-story drift distribution in SCS. The FSDs are the lateral force-resistant and energy-absorbing components and provide self-centering capacity for SCS. Some validation tests were further performed to investigate the hysteretic behavior of the developed SCS. Two different loading protocols were adopted in the experiments to test the stability of SCS subjected to different loading histories. 6% was set as the maximum loading roof drift to indicate the superior deformability of SCS. Moreover, three repeated loadings were performed for each loading protocol to study the behavior of SCS under aftershocks or multiple earthquakes. The experimental results show that the developed SCS can obtain stable and convincing self-centering hysteretic responses under repeated loading with different loading protocols, and no strength or stiffness deterioration can be found. These observations confirm that SCS is fully recoverable after earthquakes and has the potential to be used as a resilient seismic-resistant system in the building located in seismic regions. Lastly, the direct displacement-based design (DDBD) method was developed for SCS. A three-story SCS was designed on the basis of the proposed DDBD method. Nonlinear static and dynamic analyses were performed to validate the efficiency of the proposed DDBD procedure. The numerical results show that the designed SCS can show the anticipated nonlinear behavior and obtain the expected performance target.

Performance-based design of self-centering energy-absorbing dual rocking core system

The Self-centering Energy-absorbing Dual Rocking Core system (denoted as the SEDRC system) is a newly developed high-performance steel lateral force-resisting system that can achieve negligible residual inter-story drifts and avoid structural damage during rare earthquakes. Compared to many existing re-centering systems, the SEDRC system also has larger deformability and can obtain a more uniform inter-story drift responses when subjected to ground motions. This research focuses on developing a performance-based design procedure for the SEDRC systems. The seismic force reduction factor model and constant-ductility demand model have been derived via parametric nonlinear dynamic analyses of single-degree-of-freedom systems with the hysteretic behavior of the SEDRC system for developing the Displacement-Based Design (DBD) procedure. Following the developed DBD method, three six-story SEDRC systems with different parameters have been designed to achieve the desired performance objectives. Systematic numerical studies, including nonlinear static analyses, nonlinear dynamic analyses, and incremental dynamic analyses, have been conducted to validate whether the designed SEDRC system can obtain the prescribed performance target and investigate the effect of some design parameters on the seismic responses of the SEDRC systems. According to the results from the numerical studies, it can be observed that the three SEDRC systems designed through the proposed DBD method can successfully obtain the desired performance target. Moreover, higher inter-story drift at the bearing of the shear friction spring damper, as well as the higher enhanced yield-strength ratio of BRBs, can enhance the collapse-resistant capacity of the SEDRC system. Higher bearing inter-story drift can further reduce the residual inter-story drift leading to a lower collapse probability of the SEDRC system subjected to rare seismic events.

Seismic design and performance evaluation of low-rise steel buildings with self-centering energy-absorbing dual rocking core systems under far-field and near-fault ground motions

This research focuses on seismic design and performance evaluation of low-rise steel buildings with self-centering energy-absorbing dual rocking core systems (denoted as SEDRC systems) under far-field and near-fault ground motions. The SEDRC system consists of two rocking cores (RCs) and several shear friction spring dampers (SFSDs). These SFSDs are located between the two RCs and arranged over the height of the SEDRC system to absorb energy and provide a self-centering feature. The two RCs are considered as two buckling restrained braced frames in this paper, which are utilized to obtain uniform inter-story drift distribution in buildings. The two RCs can also act as a backup lateral force-resisting and energy-dissipation system if necessary. A direct displacement-based design (DDBD) procedure is introduced for the SEDRC system. A physical test was conducted to investigate the stability of the SEDRC system under repeated loading with near-fault loading protocol. The test results show that the SEDRC specimen can get stable self-centering behavior under repeated rounds of tests, indicating that the SEDRC system can be fully recoverable against multiple earthquakes before the development of the bearing action in SFSDs. The computational model of the SEDRC system was created and verified with the test results. A three-story representative building was designed through the proposed DDBD method, and the numerical models of the building were generated using the verified modeling method. Forty far-field ground motions and twenty near-fault ground motions were selected to perform Nonlinear Dynamic Analyses (NDA) on the designed building. The NDA results show that the designed three-story SEDRC system can satisfy the drift limit under DBE far-field excitations. And the designed SEDRC system can also survive and achieve small residual drifts subjected to the fault-normal components of the selected near-fault excitations and MCE far-field excitations.

Drift-based seismic design procedure for Buckling Restrained Braced Frames

In this paper, a drift-based seismic design (Dr.BSD) procedure is proposed by which a multi-story frame can be proportioned for a predetermined maximum inter-story drift uniformly distributed along all stories. While conceptually the proposed step-by-step design procedure is applicable for any lateral load resisting system, this study mainly focuses on Buckling-Restrained Braced Frames (BRBFs). Dr.BSD has a coupled theoretical-empirical basis developed for medium to high-rise multistory frames. It accounts for higher mode effects, flexural-shear behavior of the frame, and material and geometrical nonlinearities. From nonlinear dynamic analyses, it is shown that regular or moderately irregular BRBFs designed according to Dr.BSD would experience a rather uniform inter-story drift distribution close to the predefined target inter-story drift. In addition to the maximum inter-story drift, residual inter-story drift would be rather uniform in all stories. Sensitivity studies show that Dr.BSD is applicable for different target ductility demands, different target inter-story drifts, frames with different aspect ratios, and different design spectra with different soil types.

Comparative seismic fragility assessment of mid-rise steel buildings with non-buckling (BRB and SMA) braced frames and self-centering energy-absorbing dual rocking core system

During the past two decades, many emerging smart lateral force-resisting systems have been proposed for achieving better post-earthquake recoverability than the conventional ones in steel buildings. The Self-centering Energy-absorbing Dual Rocking Core (SEDRC) system has been developed recently by the authors for achieving excellent self-centering behavior with large deformability in steel buildings. This paper intends to investigate the benefit of steel buildings using the SEDRC system compared to that using other emerging smart lateral force-resisting system (e.g., shape memory alloy braced frame (SMABF)) and conventional one (e.g., buckling restrained braced frame (BRBF)). For this purpose, first, three six-story steel buildings with BRBFs, SMABFs, and SEDRC systems, were designed to obtain similar inter-story drifts subjected to the design basis earthquakes. Second, nonlinear static and dynamic analyses were conducted to preliminarily study the seismic performance of the designed buildings. Then, incremental dynamic analyses (IDAs) with far-field and near-fault ground motion inputs were conducted to study the seismic responses of the designed buildings under different seismic hazard levels. Finally, the results from the IDAs were analyzed in a probability framework. The inter-story drifts, residual inter-story drifts, and floor acceleration responses of the considered systems were analyzed to investigate the seismic fragility of the structural and nonstructural components in the designed buildings. The analysis results indicate that the SEDRC system can achieve the best structural collapse-resistant capacity under both far-field and near-fault ground motions because of the excellent deformability. The SMABF and SEDRC system show better seismic resilience performance by controlling the residual inter-story drift responses than BRBF. Moreover, the SEDRC system can obtain a smaller exceedance probability of damage states associated with nonstructural components depending on floor acceleration responses than SMABF because of uniform inter-story drift responses.

Seismic design of structures with yielding dampers based on drift demands

Application of passive structural control using metallic yielding dampers (MYDs) in the design of buildings is considered more often in recent years. Design of a building structure equipped with dampers is more complicated compared to an ordinary structure; but recent design codes provide guidelines in this regard, which normally involve a trial and error process. In this paper, a fairly simple procedure for the design of structures incorporating MYDs is proposed. The aim of this procedure is to design a structure, which undergoes a uniform inter-story drift, when subjected to seismic excitation. The procedure is applied to design several low- and mid-rise structures and their behaviors are studied using nonlinear time history analysis. The results indicate that the proposed method is successful in designing the structures, in which ductility demands for various stories and subsequently the yielding dampers are fairly uniform allowing optimum utilization of dampers.

An energy based method for seismic design of frame structures equipped with metallic yielding dampers considering uniform inter-story drift concept

Application of passive control systems in earthquake-resistant structures has attracted much attention in recent decades. One of the most important obstacles to the widespread use of these systems is the lack of simple methods for analysis and design of these systems. Energy based approach is one of design methods that has been considered extensively in recent years. In this paper, an energy-based method is proposed for seismic design of the building structures equipped with metallic yielding dampers. Considering the concepts of energy balance in the structure, the required equations to determine the number of dampers in each story are developed so that uniform drift and ductility demands are achieved in different stories. A step-by-step design flowchart is presented, and then several building structures are designed using a computer code written based on it. To check efficiency of the method, seismic responses of designed structures are evaluated under two sets of artificial and real records using dynamic analysis of the FE models. The responses are compared with the assumptions and objectives of the proposed design method. The results indicate a good agreement and it is concluded that the proposed method can be successfully used to design building structures equipped with metallic yielding dampers.

Mitigating Inter-Story Drift Concentration of Concentrically Braced Steel Frames Using Energy-Dissipative Columns

ABSTRACT Concentrically braced steel frames (CBSF) always suffer from weak-story failure with a large inter-story drift concentrated on the weakest story. A novel system of Energy-Dissipative Column (EDC) is proposed in this paper to improve the seismic behavior of low and mid-rise CBSFs. The EDC system consists of dual hinge supported steel boundary branches and replaceable steel strip dampers between them. Nonlinear dynamic analyses are conducted on 3-story and 6-story benchmark CBSF buildings with and without EDCs. The effectiveness of EDCs with different stiffness ratios on mitigating the seismic responses of CBSFs under design based and maximum considered earthquakes are investigated. The results show that the presence of EDCs in an existing multi-story CBSF can not only dissipate seismic energy to reduce the maximum inter-story drift, but facilitate more uniform inter-story drift distribution by redistributing the seismic forces along the structural height. It is found that the maximum inter-story drift and drift concentration can be reduced by half when the lateral stiffness ratio of EDC to CBSF reaches 0.2.

Comprehensive nonlinear seismic performance assessment of MR damper controlled systems using virtual real‐time hybrid simulation

SummaryMagnetorheological (MR) dampers have gained significant attention in seismic mitigation of structural systems due to their distinguished characteristics such as inherent stability and minimum power requirements. Their performance in control of nonlinear structural response, however, has not been widely investigated. This paper provides comprehensive nonlinear seismic performance assessment of a three‐story benchmark structure equipped with a large‐scale MR damper using virtual real‐time hybrid simulation to efficiently capture the nonlinear behavior of the damper. The framework is first verified by means of available experimental results of an actual RTHS on the same structural system. A set of 12 earthquake ground motions, each one scaled to have 12 different intensities are then utilized to perform nonlinear dynamic analyses. An energy‐based adaptive passive‐on control strategy is proposed, and its performance is compared with passive‐on, passive‐off, and uncontrolled response of the structure in terms of interstory drifts shown by fragility curves, residual drifts, MR damper control force, and the ability to maintain a uniform interstory drift along the height of the structure.

Seismic-resistant self-centering rocking core system with buckling restrained columns

Conventional concentrically braced frame (CBF) systems have limited drift capacity prior to brace buckling, and related damage leads to deterioration in strength and stiffness. CBFs are also susceptible to soft-story failure. A pin-supported self-centering rocking core system with buckling-restrained columns (SCRC-BRC) is being developed to provide significant drift capacity while limiting damage due to residual drift and soft-story mechanisms.The SCRC-BRC system consists of beams, columns, and braces branching off a central column, with buckling restrained columns (BRCs) incorporated into the system at the first story external column positions. The BRCs and friction generated at lateral-load bearings at each floor level are used to dissipate energy to reduce the overall seismic response of the SCRC-BRC system. Vertically-aligned post-tensioning bars provide additional overturning moment resistance and aid in self-centering the system to eliminate residual drift. The pin support condition at the base of the central column and the lateral stiffness of the system enable it to exhibit a nearly uniform inter-story drift distribution.In this study, the suite of 44 DBE-level ground motions used in FEMA P695 is numerically applied to several SCRC- BRCs to demonstrate the seismic performance of the system. The results show that the SCRC-BRC system has a nearly uniform inter-story drift response, high ductility, and a high energy dissipation capacity, and is an effective seismic-resistant system.

EVALUATION METHOD OF CONTRIBUTION FACTOR OF STRUCTURAL COMPONENTS FOR SEISMIC CAPACITY ASSUMING INVARIABLE INTER-STORY DRIFT BEFORE AND AFTER DAMAGED AND INVESTIGATION OF APPLICABILITY TO RC FRAMES WITH BEAM YIELDING MECHANISM

Main purpose of this study is to investigate residual seismic capacity of damaged buildings. An evaluation method of residual seismic capacity (R) using contribution factors of structural components (Er) was proposed. Er is evaluated by assuming invariable inter-story drift distribution for a building even after damage to focus on the investigation of effect of location of components. Then, modeling methods of damaged buildings were discussed using SDOF models. Finally, it was shown that the proposed method can estimate Rappropriately for buildings with uniform inter-story drift distribution but cannot for buildings with non-uniform distribution through dynamic analyses of prototype frames.

Seismic Design and Response of Framed Structures with Stiffening Bracing Systems

ABSTRACTStiffening Bracing System (SBS) is proposed as an alternative to conventional braced frames. SBS is intended to reduce the floor accelerations while maintaining uniform inter-story drift along the building height. The system ensures that additional damping devices distributed over the building’s height work efficiently. An iterative design procedure is developed to maintain a desired target performance. The procedure accounts for higher mode effects and supplemental damping. A series of nonlinear response history analyses on braced frames with various heights demonstrated the adequacy of the proposed procedure in achieving target structural performance and seismic demand prediction.

Improving inter-story drift distribution of steel moment resisting frames through stiff rocking cores

This investigation assesses adequacy of the Stiff Rocking Core (SRC) technology for rehabilitating steel Moment Resisting Frames (MRFs) vulnerable to drift concentrations and soft-story failures. The technology installs a single or multiple SRCs pinned to the foundation and connected to a deficient multi-story steel MRF to re-distribute seismic forces along its height and create more uniform inter-story drift and ductility demand distributions. This research team implemented the SRC technology in two archetype steel MRFs including one three-story and one nine-story. Results from nonlinear static analyses show that the SRC technology can reduce inter-story drift concentration in both steel MRFs regardless of the seismic force distributions and drift limits considered in design. Additionally, the SRC extending along the entire height of a steel MRF is more preferable than the one extending over the bottom portion of the system, although these two SRC options can be both valid in many cases.

Seismic design of multistory tension-only concentrically braced beam-through frames aimed at uniform inter-story drift

In this paper, a seismic design procedure aimed at achieving uniform inter-story drift in multistory tension-only concentrically braced beam-through frames (TOCBBTFs) is presented. The TOCBBTF is designed so that the columns and beams would remain elastic for their negligible lateral stiffness while tension-only concentric braces resist all lateral loads as a reliable way of absorbing seismic energy under seismic loading. The hysteretic energy dissipation of the tension braces can be treated as supplemental damping ratio of the structure, and lateral stiffness ratio between braces and main structure exerts a significant impact on seismic behavior of the structure. Three performance objectives of seismic design procedure aiming for uniform inter-story drift along the building height are established first. From the perspective of supplemental viscous damping and proper lateral stiffness of the structure, the seismic design method is proposed and applied to 4- and 6- story model structures to demonstrate the design procedure. Time-history analyses are carried out to verify whether the pre-specified performance objectives are achieved or not. The analysis results show that the seismic performance of the 4- and 6-story model structure designed with the proposed design procedure agrees very well with the pre-specified design objectives.