Residual Inter-story Drift Ratios Research Articles

Mainshock-aftershock effect on the seismic performance of multi-story CBFs equipped with SMA-friction damping braces

This paper aims to understand the effect of mainshock-aftershock earthquake sequences on the seismic performance of multi-story concentrically braced frames (CBFs) equipped with shape memory alloy (SMA) friction damping braces (SMAFDBs), based on a comparison with those equipped with buckling-restrained braces (BRBs). The SMAFDB is a serial connection of SMA damper and friction damper. The friction damper starts to slip and serves as the “fuse” element to protect the SMA damper under destructive earthquake events. Ten ground motion records corresponding to the maximum considered earthquake (MCE) hazard level are defined as the mainshock input, and the aftershock input is generated by appropriately scaling the mainshock input to four seismic hazard levels. To achieve a fair comparison, the considered CBFs are first designed to exhibit identical mean height-wise peak interstory drift ratios under the design-basis earthquake (DBE) ground motions. Then, these two frames are subjected to four suites of mainshock-aftershock earthquake sequences and their seismic responses are compared against each other. It indicates that both the peak and residual interstory drift ratios of the SMAFDB frame (SMAFDBF) are smaller than that of the BRB frame (BRBF) on average during the aftershock earthquakes, which is found primarily attributed to the fact that the former suffers from smaller post-mainshock residual deformation. The higher seismic capacity of the SMAFDBF over the BRBF is also confirmed by conducting fragility analysis. Finally, the recentering capacity under aftershock earthquakes are analyzed for both frames, based on the maximum residual interstory drift ratios.

Seismic performance analysis of multi-story steel frames equipped with FeSMA BRBs

Buckling-restrained braces (BRBs) have been widely used in seismic prone areas around the world. However, one major problem associated with the steel BRB frames is the excessive residual deformation under strong earthquakes, mainly due to the low post-yield stiffness ratio of the steel BRBs. Recently, the community has fabricated the iron-based shape memory alloy (FeSMA) BRBs, which exhibited full hysteresis with high post-yield stiffness ratios, but the seismic behavior of the FeSMA BRB frames still remains unknown. As such, this paper conducts seismic performance analysis of multi-story steel frames equipped with the FeSMA BRBs, through a comparison with those equipped with conventional steel BRBs. Incremental dynamic analysis (IDA) is further conducted to establish the probability seismic demand models. Based on the IDA data, bivariate fragility analysis is conducted to quantify the probability of exceedance, conditioned on various limitations of the maximum and residual interstory drift ratios. According to current analysis, it indicates that both the maximum interstory drift ratios and the maximum floor accelerations are comparable between these two types of BRB frames. The major advantage of the FeSMA BRBs over the steel BRBs is that the former can better control residual interstory drift ratios.

Seismic retrofitting of SMRFs using varied yielding cross-section damper: A companion paper

This paper is a companion paper to our recent research titled “Seismic Performance of a New S-shaped Mild Steel Damper with Varied Yielding Cross-sections”. In this study, the newly developed varied yielding cross-section damper is employed for seismic retrofitting of steel moment-resisting frames (SMRFs) and a retrofitting design method without performing nonlinear time-history analysis is proposed. The damper has the feature of preventing energy dissipation plate from plasticity concentration-induced failure and of being conveniently replaced post-earthquake. Its hysteretic behavior has been verified through a series of cyclic loading tests. Three prototypes respectively with 3, 9 and 20 stories are adopted as typical low-, mid- and high-rise SMRFs to be damper-retrofitted. And the dampers are designed using the proposed retrofitting procedure in which performance objective of different seismic hazard level and story drift concentration are incorporated. Subsequently, experimentally validated numerical modelling approach for the damper is provided, and detailed numerical models for the bare frames (BFs) and damper-retrofitted frames (DFs) are established. In order to analyze the effectiveness of the developed dampers and the retrofitting design method, seismic performance of the BFs and DFs is assessed by conducting pushover and nonlinear dynamic analyses. The results indicate that the retrofitting strategy can significantly enhance the bearing capacity against strong earthquakes and mitigate the structural damages by reducing inter-story drift ratio and residual inter-story drift ratio; the proposed retrofitting design procedure has ability to achieve the expected seismic performance level and mitigate the story drift concentration.

Blast Performance of Steel Frames Equipped with NiTi SMA Bolts: Design Procedure and Numerical Evaluation

This study evaluated the performance of smart steel moment-resisting frame structures (MRFs) equipped with nickle titanium shape-memory alloy (NiTi SMA) connection systems subjected to blast overpressure. A total of five NiTi SMA–based connections were designed conforming to current European standards, and their numerical models were developed. To study the effect of number of parameters, e.g., section profiles, bolt diameter, and bolt preload, a parametric study has been conducted on NiTi SMA–based connections. The numerical models were validated against experimental data, and key design procedures have been proposed. A simplified Kingery blast calculation framework was adapted to determine the blast reflected overpressure profile. The strength of the NiTi SMA bolts and steel components were adjusted due to a high strain rate of blast loading. Four MRFs equipped with a NiTi SMA–based connection were designed with different heights. Global-level transient analyses were performed on the MRFs subjected to blast overpressure. The results showed that in addition to relatively large maximum interstory drift ratio, the NiTi SMA–based connections significantly reduced the residual interstory drift ratio compared with the steel bolted connection system counterpart. The results also revealed that the proposed key design procedures are essential to emphasize the role of NiTi SMA bolts.

Incremental Dynamic Analysis Considering Main Aftershock of Structures Based on the Correlation of Maximum and Residual Inter-Story Drift Ratios

Aftershocks often occur after strong earthquakes and aggravate structural damage. Commonly, the incremental dynamic analysis (IDA) considering the main aftershocks only used a single index such as the maximum or the residual inter-story drift ratio. However, results of IDA using different indices may suggest that a structure has collapsed but is still repairable, which is not realistic. Given these shortcomings, this paper proposes selecting two indices in the IDA method based on the correlation between the maximum and the residual inter-story drift ratio, considering the main aftershocks. The influence of the double-indices model on the structural vulnerability analysis was discussed by establishing a commercial building in SAP2000 software, and single-index and double-index IDA were carried out, respectively. The joint distribution probability of the two indices under fixed seismic intensity was also calculated. The difference between the single-index and double-index IDA results was compared considering both the main shock and the main aftershock. The results showed that the effect of aftershocks would improve the correlation coefficient between the maximum and the residual inter-story drift ratio, and the building model has a higher probability of overrun after considering the correlation of the two indices. This paper provides a new method for IDA and vulnerability analysis using multiple indices.

Dual-Objective Control of Maximum and Residual Drift Ratios of Super-Tall Buildings Based on Self-Centering Energy Dissipation Outriggers

It is critical to ensure the seismic resilience of super-tall buildings using high performance materials. The seismic resilience of these buildings can be enhanced by simultaneously controlling the maximum and residual inter-story drift ratios. To realize such dual-objective control, a prevailing trend is to adopt self-centering energy dissipation outriggers. In this study, taking a real engineering practice as the prototype building, super-tall building study cases with energy dissipation outriggers, and with self-centering energy dissipation outriggers are designed. Based on nonlinear time-history analysis, the seismic performances of these study cases are evaluated and compared with emphasis on the maximum, and residual inter-story drift ratios. The dual-objective control effect of self-centering energy dissipation outriggers and energy dissipation outriggers are analyzed and compared. The results indicate that self-centering energy dissipation outriggers are more effective than energy dissipation outriggers for achieving the dual-objective control of the maximum and residual drift ratios of super-tall buildings.

Investigating Approximate Methods to Predict Residual Interstory Drift Ratio Demands in Steel Eccentrically Braced Frames

Investigating Approximate Methods to Predict Residual Interstory Drift Ratio Demands in Steel Eccentrically Braced Frames

Seismic performance evaluation of glulam structures with either braced frames or knee-braced frames as the main lateral load resisting system

The glulam knee-braced frames and braced frames are both conventional structural systems that are generally adopted in engineering practice. However, it remains a question what are the advantages and challenges of the knee-braced frames compared with the braced frames and how to choose the appropriate lateral-resisting structures for the projects under a given design requirements. This paper provides numerical models of 3- story, 5- story, 6- story and 9- story glulam braced frames and glulam knee-braced frames with the same architectural plan view. Increment dynamic analysis (IDA) is performed to determine the limit state of MaxISDR (maximum inter-story drift ratio) for the glulam braced frames and the glulam knee-braced frames under different seismic hazard levels, i.e., IO (Immediate Occupancy), LS (Life Safety), CP (Collapse Prevention) and CD (Complete Destroy). Fifty earthquake records are adopted for the subsequent probabilistic seismic demand analysis based on the MaxISDR and ResISDR (residual inter-story drift ratio) damage indices. The fragility curves of these two types of structures are highlighted. The results show that, the limit state of MaxISDR for the glulam braced frames under the IO, LS, CP and CD hazard level are recommended to be 0.6%, 1.2%, 2.0% and 3.5% respectively. The limit state of MaxISDR for the glulam knee-braced frames under the IO, LS, CP and CD hazard levels are recommended to be 1.0%, 2.0%, 3.2% and 5.5% respectively. In addition, for the structural height that below 6 stories, the knee-braced frames have lower probability of MaxISDR exceedance than the braced frames under the earthquake with high PGA and lower probability of ResISDR exceedance than the braced frames. However, for the structural height of 9-stories, the recoverability of the knee-braced frames decreases rapidly. Adding some braces to the knee-braced frames can be a good solution to increase the lateral stiffness of the structures. The comparison results may provide technical reference for the structural design of glulam structures.

Seismic Behavior of a Class of Mixed Reinforced Concrete-Steel Buildings Subjected to Near-Fault Motions

This paper investigates the seismic behavior of a class of mixed reinforced concrete-steel buildings. In particular, mixed buildings constructed by r/c (reinforced concrete) at their lower story(ies) and structural steel at their upper story(ies) are studied from the viewpoint of their wide application in engineering praxis. The need to investigate the seismic behavior for this type of mixed buildings arises from the fact that the existent literature is small and that modern seismic codes do not offer specific seismic design recommendations for them. To study the seismic behavior of mixed r/c-steel buildings, a 3-D numerical model is employed and five realistic r/c-steel mixed buildings are simulated. Two cases of the support condition, i.e., fixed or pinned, of the lowest steel story to the upper r/c one are examined. The r/c and steel parts of the mixed buildings are initially designed as separate structures by making use of the relevant seismic design guidelines of Eurocode 8, and then the seismic response of these buildings is computed through non-linear time-history analyses. The special category of near-fault seismic motions is selected in these time-history analyses to force the mixed r/c-steel buildings under study to exhibit a strong non-linear response. Seismic response indices in terms of inter-story drift ratio, residual inter-story drift ratio and peak floor absolute accelerations are computed. The maximum values of these indices are discussed by comparing the two aforementioned kinds of support conditions and checking the satisfaction of specific seismic performance limits. Conclusions regarding the expected seismic behavior of mixed r/c-steel buildings under near-fault seismic motions are drawn. Finally, the need to introduce specific design recommendations for mixed r/c-steel buildings in modern seismic codes is stressed.

Post-Earthquake Damage Assessment of Buildings: Comprehensive Experimentally-based Maximum Drift Ratio Predictive Model Based on Residual Drift Ratio

ABSTRACT In this paper, a post-earthquake damage assessment method for 11 different structural systems is proposed. The method is mainly based on residual inter-story drift ratios of all structural elements in the building, an important response parameter due to its simplicity of measure after the earthquake. nearly 2000 test specimens representing structural elements characterized by different structural systems (walls, frames, etc.) and materials (masonry, reinforced concrete, and steel) which were tested under quasi-static cyclic loading provided more than 100,000 data points that were used to correlate the residual drift ratio and damage states in structural elements. The damage severity of each structural element was then determined based on the weighted average of each damage state’s exceedance probabilities given a residual drift ratio. The method also considers the damage propagation among different structural elements by considering the weighted average overall damage scores in structural elements concerning their load-bearing contribution. The pre-earthquake condition of the building and the level of experienced earthquake intensity is the other input parameters for the proposed method, which finally leads to the building’s overall damage score. To verify the accuracy of the proposed method’s results, an example building hit by the Ezgeleh earthquake is evaluated, and the results are compared with those of other post-earthquake damage assessment methods.

Effects of cyclic strain hardening on performance of eccentrically braced frames

Performance based seismic design (PBSD) procedures have been developed in recent years. Studies conducted in the past revealed that strain hardening ratio (SHR) used in numerical modeling can be influential on the performance of steel structural systems. In this paper, the effects of SHR on the performance assessment of eccentrically braced frame (EBF) buildings were studied by using FEMA P-58 methodology. The numerical model was validated using the pseudo-dynamic test results of the DUAREM structure. Seismic performance of six archetype EBFs with different number of stories and link length to bay width (e/L) ratios were evaluated under design basis earthquake (DBE), maximum considered earthquake (MCE), and collapse level earthquake (CLE). Irreparable residual drift, repair cost and unsafe placards were calculated for SHR ranging between 0 and 0.01. The results showed that the residual interstory drift ratio is more influenced by the SHR when compared with the interstory drift ratio, link rotation angle and story acceleration. The replacement decision was found to depend on the SHR, the number of stories, the e/L ratio, and the seismic hazard. Under MCE and CLE level events, almost all of the archetypes with SHR ≤ 0.003 required replacement while replacement can be avoided for some of the archetypes with SHR > 0.003. Under DBE level events, 3-story archetypes and 6-story archetypes with SHR ≥ 0.002 did not require replacement. Nine-story archetype with e/L = 0.08 required replacement for SHR = 0 only, while archetypes with e/L = 0.12 required replacement for SHR ≤ 0.003. The study demonstrated the strong influence and sensitivity of the repair cost to the SHR.

A Physical-organizational Method for the Functionality Assessment of A Hospital Subjected to Earthquakes

ABSTRACT Hospitals play vital roles in mitigation and recovery in earthquake-hit communities. This paper aims to clarify the effect of physical damage on hospital organizations and represent a holistic method for the functionality assessment of a hospital. The efficiency of the method is demonstrated based on the case study of a general hospital. The results indicate that the functionality of hospitals would be significantly affected after the maximum considered earthquake. A considerable gap exists between the hospital treatment capacity and the patient demand for medical services. The method will assist hospital stakeholders and managers in design and upgrade criteria selection. Abbreviation: CT: Imaging Procedure; DBE: Design Basis Earthquake; DES: Discrete Event Simulation; DR: Digital Radiography; EDPs: Engineering Demand Parameters; HVAC: Heating Ventilation and Air Conditions; MCE: Maximum Considered Earthquake; OR: Operation Room; PFA: Peak Floor Acceleration; PFV: Peak Floor Velocity; PIDR: Peak Inter-story Drift ratio; RC: Reinforced Concrete; RIDR: Residual Inter-story Drift Ratio; RR: Resuscitation Room; SLE: Service Level Earthquake; UPS: Uninterruptible Power Supply; US: Ultrasound Room; WT: Waiting Time

Component deformation-based collapse evaluation of RC frameunder different collapse criteria

Developments in performance-based earthquake engineering have emphasized the importance of evaluation of structural collapse resistance. Several collapse criteria were proposed to define structural collapse in various perspective. In this paper, collapse resistant capacity of ductile reinforced concrete (RC) frame was evaluated using different collapse criteria. Since most of the criteria focus on overall structural response, a component deformation-based method was adopted to describe the damage in component level. Incremental dynamic analysis (IDA) of a 6-story ductile RC frame conforms to current codes was conducted in OpenSEES. The collapse resistant capacity under different collapse criteria was compared. Moreover, relationship between overall structural response and the distribution of damaged components were discussed through the component deformation-based method. It was indicated that the story of maximum inter-story drift ratio is neither consistent with the one which is most seriously damaged nor with the story of maximum residual inter-story drift ratio. Furthermore, the component deformation-based method can depict structural damaged state and formation of collapse mechanism more reasonably. The analysis result evidences that structure conforms to current code have the good ductility and hardly reaches physical collapse under rare earthquake, however, the structure is more likely to be demolished due to unacceptable residual deformation.

Seismic performance assessment of steel frame structures equipped with buckling-restrained slotted steel plate shear walls

The near-fault ground motion records may impose high seismic energy input to the building structures. The steel plate shear walls (SPSW) are one of the robust and efficient lateral-force resisting and energy-dissipating components and SPSWs are increasingly equipped in steel moment frame to form a dual structural system. A modified type of buckling-restrained SPSW with inclined slots has been proposed and applied in the steel frame. This paper presents the seismic performance of steel frame-SPSW system subjected to near-fault ground motions. Four multi-story (5-, 10-, 15- and 20-story) steel frame-SPSW structures were selected and designed. The accuracy of the SPSW models' predictions was assessed using previous experimental results. Nonlinear time-history analysis assuming two groups of 15 near-fault ground motions and 15 far-fault ground motions was used to predict the structures' interstory drift ratios, floor accelerations, residual interstory drift ratios and drift concentration factor. Incremental dynamic analysis was used to predict collapse probabilities using the same groups of ground motions. The analytical results can provide significant insights to the seismic behavior of steel frame-SPSW structures when subjected to near-fault ground motions.

An advanced intensity measure for residual drift assessment of steel BRB frames

To assess the safety of structures after the occurrence of an earthquake or decide about demolition or repair of structures, maximum residual interstory drift ratio (MRD) is one of the most important engineering demand parameters. For evaluating the probability of exceedance of MRD in structure from a specified limit, nonlinear dynamic analyses are performed by employing an intensity measure (IM). IMs link the structural seismic response analyses with the seismic hazard analysis. Employing an optimal IM in seismic evaluation of structures makes the results more realistic and reliable. The power of an IM to predict the seismic response of structures with low dispersion is called efficiency. Moreover, the ability of an IM for rendering the seismic response of structures independent from the other features of the ground motion is named sufficiency. In this study, the efficiency and sufficiency of some traditional and advanced IMs (including scalar and vector ones) for predicting MRD capacity of steel buckling restrained braced frames are evaluated. It is shown that all of the IMs considered do not have sufficiency with regard to scale factor (SF). Then, (Sa(T1),SaRatioOp‒D) as an optimal vector IM (optimized by multi-objective particle swarm optimization algorithm) having improved sufficiency with regard to SF is proposed.

Performance comparison of BRBFs designed using different response modification factors

This paper presents details of the numerical examination and performance comparison of steel buckling restrained braced frames (BRBFs) designed with different response modification factors, using the next-generation performance assessment approach. Archetypal BRBF designs were conducted following the US provisions and considering response factors equal to or less than the codified limit. The archetypical buildings were subjected to ground-motions acquired from the FEMA P695 Far-Field record-set and scaled to MCE and DBE intensity levels. The FEMA P-58 performance assessment procedure was used to evaluate the results. The interstory drift ratio, residual interstory drift ratio, and peak story acceleration demands were determined and converted to performance quantities by using the Performance Assessment Calculation Tool (PACT). The repair time, probabilistic distribution of repair cost, unsafe placard probabilities, and irreparable residual drift probabilities were obtained, and a comparative study of response modification factors in terms of these results was conducted. The results show that designs with higher response factors result in higher repair costs, due to the damage of drift sensitive components and high residual drifts. On the other hand, BRBFs designed with lower response factors were found to experience higher accelerations, which result in an increase in the repair cost for acceleration sensitive components. An ideal response factor is proposed herein based on the consequence measures. The study was complemented by investigating the behavior of self-centering BRBFs and comparing their performance with those of conventional BRBFs.

Seismic upgrading of multistory steel moment‐resisting frames by installing shape memory alloy braces: Design method and performance evaluation

The installation of a damping bracing system is regarded as an effective means to upgrade the seismic capacity of steel moment-resisting frames (MRFs), a common structural form for buildings. However, conventional damping braces are incapable of eliminating residual deformation demand. Shape memory alloy (SMA) braces present an emerging seismic upgrading solution to this problem. However, the corresponding design method is yet to be developed. Therefore, this study proposes a simple and straightforward design method for seismic upgrading of MRFs through the installation of SMA braces. The maximum and residual interstory drift ratios are selected as performance target. Two benchmark frames with three or six stories are adopted to validate the proposed design method. A group of seismic ground motions corresponding to the design basis earthquake level are input to the frames with or without SMA braces. Seismic analysis results indicate that the frames equipped with properly designed SMA braces exhibit responses that satisfy the design target satisfactory. To quantify the seismic upgrading effect, peak and residual interstory drift ratios and peak floor acceleration demands are selected as critical factors to build single- or multiple-parameter indices. Based on the relevant performance indices, comparisons between the original and upgraded frames show that the overall seismic performance of MRFs can be improved by 10%–30% when SMA braces are installed. In addition, the reduction of residual deformation has a significant impact on the evaluation result because of the evident benefit to seismic performance.

Seismic Performance of Steel Structure-Foundation Systems Designed According to Eurocode 8 Provisions: The Case of Near-Fault Seismic Motions

The seismic performance of steel structure-foundation systems subjected to near-fault earthquakes was assessed on the basis of response results from nonlinear time-history seismic analyses. The structural results included the maximum values for residual interstory drift ratios, base shears, and overturning moments of the steel structures, as well as the maximum values for residual settlement and tilting of the foundations. In order to reveal the influence of soil-building-interaction on the aforementioned response results, the steel building-foundation systems were designed according to Eurocode 8 provisions, assuming initially fixed and then compliant base conditions. It was concluded that for the case of near-fault seismic motions, good seismic performance of steel building-foundation hybrid systems designed according to European Codes was not guaranteed. A particular thing to note for these systems under near-fault seismic motions was that the seismic performance of the steel structure was most likely unacceptable, while one of the foundations was always acceptable.

Behavior and application of self-centering dampers equipped with buckling-restrained SMA bars

This study proposes a new type of self-centering damper equipped with novel buckling-restrained superelastic shape memory alloy (SMA) bars. The new solution aims to address some critical issues related to degradation and loss of superelasticity observed in existing tension-only SMA-based self-centering devices, and in addition, to encourage enhanced material utilization efficiency. The cyclic tension-compression behavior of individual SMA bars is experimentally studied first, and subsequently, two proof-of-concept self-centering dampers are manufactured and tested. A simple yet effective numerical model capturing the flag-shaped response of the dampers is then established, and a preliminary system-level analysis is finally conducted to demonstrate the effectiveness of the proposed damper in structural seismic control. The individual SMA bar specimens show asymmetrical flag-shaped hysteretic responses with satisfactory self-centering capability and moderate energy dissipation. Through a specially designed configuration, the proposed damper shows desirable symmetrical and stable hysteretic behavior, and maintains excellent self-centering capability at 6% bar strain. The system-level dynamic analysis indicates that the dampers, as a means of retrofitting, could effectively reduce both the peak and residual inter-story drift ratios of a six-story steel frame. In particular, the mean residual inter-story drift ratio is reduced from over 0.5% to below 0.2% under the maximum considered earthquake, implying elimination of necessary structural realignment even after strong earthquakes.

Assessment of a 12-story Reinforced Concrete Special Moment Frame Building Using Performance-Based Seismic Engineering Standards and Guidelines: ASCE 41, TBI, and LATBSDC.

A 160-foot (≈ 49 m) tall 12-story reinforced concrete special moment frame building is designed following ASCE 7-16 and ACI 318-14, and assessed using three Performance-Based Seismic Engineering (PBSE) standards and guidelines including ASCE/SEI 41, the Tall Buildings Initiative (TBI) guidelines for performance-based design of tall buildings, and the Los Angeles Tall Buildings Structural Design Council (LATBSDC) procedures. The assessments are performed at the combination of two performance and hazard levels including Collapse Prevention (CP) at the risk-targeted maximum considered earthquake (MCER) hazard level and Immediate Occupancy (IO) at a frequent ground motion level with 50 percent probability of exceedance in 30 years, i.e. serviceability performance level. Based on the recommendations of each of the three PBSE documents, nonlinear finite element models are implemented in OpenSees. Through nonlinear time-history response analyses, the finite element models are subjected to eleven ground motions that are selected following the ground motion selection recommendations in ASCE 7-16. Assessment results indicate that for the serviceability performance level, the code-compliant building meets the design requirements of the three PBSE documents for the interstory drift ratio and inelastic deformation of the structural components. At the MCER hazard level, although the building essentially satisfies the design requirements for the peak interstory drift ratios and inelastic deformation, the mean of the residual interstory drift ratios as well as the envelope of the residual drift ratios do not meet the limits of the TBI and LATBSDC guidelines. The results indicate that the newly designed building meets the ASCE 41 acceptance criteria but does not meet the design requirements set in TBI and LATBSDC guidelines.