Peak Interstory Drift Ratio Research Articles

Numerical Modelling of CFS Three-Story Strap-Braced Building under Shaking-Table Excitations.

In recent research activities, shake-table tests were revealed to be useful to investigate the seismic behavior of cold-formed steel (CFS) buildings. However, testing full-scale buildings or reduced-scale prototypes is not always possible; indeed, predicting tools and numerical models could help designers to evaluate earthquake response. For this reason, numerical modelling of two strap-braced prototype buildings, recently tested on shake-table at University of Naples Federico II in cooperation with Lamieredil S.p.A. company, was developed. The models were validated trough the comparison between experimental and numerical results, in term of dynamic properties (fundamental period of vibration and modal shapes), peak roof drift ratios and peak inter-story drift ratios. Although dynamic properties of mock-ups were captured with accuracy by the developed models, the comparison highlighted the need to consider accumulation of damage and rocking phenomenon in the modelling to capture with good accuracy the seismic behavior of CFS strap-braced building, subjected to high intensity records.

Peak Velocity of Viscous Dampers for Direct Displacement Based Design of RC Moment Resisting Frames

ABSTRACT Previous researchers have extended the direct displacement-based design (DDBD) procedure, to design reinforced concrete moment-resisting frame (RC-MRF) buildings with linear viscous dampers (LVDs). In those studies, the viscous damper forces are found to be larger than the design viscous damper forces because the actual relative structural velocity is different from the pseudo-velocity and also due to higher-mode effects. In the present study, a damper velocity correction factor is introduced along the height of the RC-MRF with LVDs, to calculate the corrected velocity of the LVD from the design velocity of the LVD, when the DDBD procedure is used. The damper velocity correction factor is proposed using the results of nonlinear response history analysis (NLRHA) for a set of RC-MRFs with LVDs, which are designed using the DDBD procedure. The DDBD procedure is then used to design RC-MRFs with nonlinear viscous dampers (NLVDs) making use of the proposed damper velocity correction factor, by calculating the NLVD characteristics using the equal energy (EE) dissipation approach or the equal power (EP) consumption approach. The accuracy of the proposed damper velocity correction factor is evaluated by carrying out NLRHA of two sets of RC-MRFs with NLVDs, one set where the damper velocity correction factor is not used, and the other set where it is used. When the damper velocity correction factor is used; the design LVD forces either agree with NLRHA results or are slightly more conservative, the design NLVD forces are close to the NLRHA results, and the maximum value of peak inter-story drift ratio (IDR) along the height of the RC-MRF from NLRHA is close to the design IDR limit. There is no significant difference in the peak story shear forces whether the damper velocity correction factor is used or not.

Seismic response of SMA-based self-centering buckling-restrained braced frames under near-fault ground motions

Self-centering buckling-restrained braces (SC-BRBs) consisting of BRBs as the primary load-resisting elements and shape-memory alloy (SMA) bars as the supplemental re-centering elements have shown the higher axial resistance in tension and compression along with negligible residual deformation under cyclic loading. Superplastic characteristics of Nickle and Titanium (NiTi) SMA bars provide the self-centering mechanism, which minimizes the residual drift response of buckling-restrained braced frames (BRBFs) under earthquake loadings. The present study is focused on the seismic performance of low to high-rise BRBFs equipped with SC-BRBs, conventional BRBs, and Hybrid braces (i.e., a combination of BRBs and SC-BRBs) under near-field ground motions. 3-story, 9-story, and 20-story frames with both moment-resisting and non-moment-resisting beam-to-column connections have been considered in this study. Nonlinear dynamic analyses have been carried out on eighteen nos. of numerical models developed using a computer software OpenSees for a set of forty near-field ground motions. Though SC-BRBFs exhibited negligible residual drift response, they showed a higher peak interstory drift ratios as compared to BRBFs. Low-rise BRBFs with pinned beam-to-column connections are found to be more vulnerable to failure under near-fault ground motions. The use of Hybrid frames resulted in the improved seismic performance of 9-story and 20-story building frames.

Comparative seismic fragility assessment of buckling restrained and self-centering (friction spring and SMA) braced frames

In seismic regions, steel braced frames are one of the most commonly used seismic lateral force resisting systems for their reliable performance. This study presents a comparative seismic performance of different braced steel frames at their system levels. Three types of bracings for steel frames are investigated: Buckling Restrained Bracing (BRB), Superelastic Shape Memory Alloy (SMA) bar reinforced Piston Based Self Centering (named as PBSC) bracing, and Friction Spring Based Piston Bracing (named as SBPB). A methodology to evaluate the structural response of the building in a probabilistic framework is used. The procedure to estimate the probability of exceeding certain limit states conditioned on the ground motion intensity is applied to the structures. Emphasis is given to the estimation of the probability of exceedance of peak Interstory Drift Ratios (IDR). The peak interstory drift ratio provides a way to estimate the damage to structural components. For this purpose, four, six, eight, and twelve-story structures, designed with the three bracing types are used. A large number of Incremental Dynamic Analyses are performed to derive three-dimensional (3D) vulnerability functions that involve building heights and bracing types. This versatile 3D format enables the interpolation of results to arrive at the seismic fragilities of structures with different stories. The results show that the SBPB and PBSC frames outperformed the BRB frames in terms of damage probability.

Risk-based mainshock-aftershock performance assessment of SMA braced steel frames

This study presents a methodology to generate probabilistic seismic demand models and hazard curves for steel frames with or without shape memory alloy (SMA) bracing systems under mainshock – aftershock sequences. First, three post-mainshock damage states were defined based on both peak inter-story drift and residual drift ratios. Incremental dynamic analyses (IDA) were performed considering only mainshock events to determine spectral acceleration demands corresponding to each mainshock damage level. Then, aftershock IDA were conducted on the post-mainshock SMRF and SMA frames at three damage states. To estimate the peak and residual drift response of SMRF and SMA braced frames subjected to a mainshock – aftershock sequence, empirical seismic demand models were developed. Next, a risk-based seismic performance evaluation study was conducted to generate seismic demand hazard curves for maximum and residual interstory displacement response. Results reveal the advantages of SMA braces in enhancing post-event functionality of steel frame buildings. In addition, defining damage states based on residual drifts is recommended while comparing the aftershock performance of conventional steel moment resisting frames with self-centering steel buildings.

Comparison of Scaling Ground Motions Using Arithmetic with Logarithm Values for Spectral Matching Procedure

In recent studies, spectral matching is the most commonly proposed method for selecting earthquake records for time-history analysis of structures. However, until now, there have been no serious investigations of the effects of coordinate values on the scaling of ground motions. This paper investigated the influence of using arithmetic and logarithmic values of response spectra in spectral matching procedures (i.e., ASM and LSM methods) on the results of nonlinear structural time-history analysis. Steel moment resisting frame structures of the 3-, 9-, and 20-stories, which represent low-, medium-, and high-rise buildings, respectively, were used as examples. Structural benchmark responses were determined by calculating the arithmetic mean and median of peak interstory drift ratio (PIDR) demands based on the three record sets developed by the American SAC Steel Project. The three record sets represent seismic hazard levels with 50%, 10%, and 2% probabilities exceeded in 50 years, and their average acceleration spectra were also taken as the target spectrum. Moreover, another 40 record components for selection were scaled both by ASM and LSM methods. The seven components whose spectra were best compatible with the target spectra were selected for the structural time-history analysis. The scale factors obtained by the LSM method are nearly larger than that of the ASM method, and their ranking and selection of records are different. The estimation accuracies of structural mean (median) responses by both methods can be controlled within an engineering acceptable range (±20%), but the LSM method may cause larger structural responses than the ASM method. The LSM method has a better capacity for reducing the variability of structural responses than the ASM method, and this advantage is more significant for longer-period structures (e.g., 20-story structure) with more severe nonlinear responses.

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.

Seismic fragility analyses of steel building frames installed with superelastic shape memory alloy dampers: Comparison with yielding dampers

Smart materials such as shape memory alloys have unique material properties that can potentially mitigate earthquake hazards on the built environment. Implementation of shape memory alloy-based devices on building structures should incorporate two key factors: (1) distinct mechanical features of the devices and (2) inherent large uncertainty stemming from material properties, building geometry, and ground motions. This study conducts seismic fragility analyses of steel building frames installed with superelastic shape memory alloy dampers, which enable both factors to be appropriately considered. First, a thermomechanical constitutive model is utilized to capture all essential characteristics of the shape memory alloy damper. Next, a probabilistic seismic analysis framework is developed to obtain the seismic demands of three critical engineering demand parameters (i.e. peak interstory drift ratio, residual drift ratio, and top floor acceleration) of the building when subjected to modeling uncertainty and a large set of realistic ground motion inputs. Nonlinear time history responses and the associated short-time Fourier transform demonstrate the superior control efficiency of the shape memory alloy damper in limiting the building’s residual drift and top floor acceleration. Furthermore, seismic fragilities of the buildings when installed with shape memory alloy dampers are compared with those when equipped with yielding dampers. The study indicates that under different levels of ground motions and various ranges of modeling uncertainty in structural parameters, shape memory alloy damper consistently outperforms the yielding damper in reducing the seismic fragility of the building at both component and system levels.

Optimization Approach to Uniformly Distributed Peak Interstory Drifts along Building Heights

AbstractThis study developed a seismic design approach, which has no need of additional structural members, to uniformly distribute the peak interstory drift ratios along building heights. The gene...

Seismic performance and damage analysis of RC frame–core tube building with self-centering braces

This paper examines the seismic responses of a reinforced concrete (RC) frame–core tube building with pre-pressed spring self-centering energy dissipation braces (PS-SCEDBs). The PS-SCEDB is a passive energy dissipation device with disc springs and friction pads. Parameters of PS-SCEDBs installed on the structure are designed according to the principle of equivalent stiffness, based on the parameters of a buckling-restrained brace (BRB) equipped on the original RC frame–core tube structure. The constitutive models of self-centering flag-shaped and bilinear elastoplastic hysteresis for PS-SCEDBs and BRBs, respectively, are developed and experimentally verified. The seismic performance of RC frame–core tube structures with PS-SCEDBs and BRBs, respectively, are studied and compared using non-linear time history analysis. Results show that the PS-SCEDB can substantially reduce residual drift ratios of a concentrically braced building while still capable of effectively controlling the peak inter-story drift ratio and damage of components adjacent to braces under rare earthquakes. The structure with PS-SCEDBs can effectively dissipate seismic energy without increasing damage to beams, columns, and shear walls.

Seismic fragility analysis of steel reinforced concrete frame structures based on different engineering demand parameters

Nowadays, performance-based seismic design is the focus of earthquake engineering research, in which the seismic performance of a structure is mainly evaluated based on seismic fragility. However, the role of Engineering Demand Parameters (EDPs) on the seismic fragility analysis of Steel Reinforced Concrete (SRC) frame structures remains unclear. This paper presents results on the effects of EDPs on the seismic behavior of a plan-asymmetric SRC building. For this purpose, a nonlinear finite element model of the SRC frame structure was numerically developed using the OpenSees software. This finite element model was then validated using experimental results. The peak interstory drift ratios, as well as the component-based and material-based damage indices, were accordingly employed as EDPs. This study additionally shows seismic fragility curves for an SRC frame structure. The achieved results for the mentioned EDPs were both compared and analyzed. The findings indicated that the EDPs play a role in the seismic fragility analysis for the SRC frame structures. The fragility curves based on a damage index could display the probability of exceeding the ultimate limit states subjected to different seismic intensities, and also showed a similar manner with those based on peak interstory drift ratios. It can be concluded that for an SRC frame structure, the results of seismic fragility analysis using the component-based damage index proved to be more cost-effective and reliable.

Performance-based plastic design approach for multi-story self-centering concentrically braced frames using SMA braces

Self-centering concentrically braced frames (SCCBFs) are emerging as one of the high performance seismically resistant framing systems, known for the capability of controlling peak seismic demands and eliminating residual deformation. In the process of developing SCCBFs, shape memory alloys (SMAs) are deemed as the potential candidate for the key component of SCCBFs, due to the excellent superelastic capacity and desirable flag-shape hysteresis. For the SCCBFs using SMA braces (SMABs), an economical and effective design approach based on the performance-based plastic design was recently derived. This study aims to extend the ad hoc design approach to low-to-high rise multi-story SCCBFs using SMABs, and to examine its generality. As such, the seismic performance of four SCCBFs with various story numbers was intensively analyzed by subjecting them to ground motion records corresponding to design-basis earthquake. The analysis results show that all the resulting frames were capable of coinciding well with the prescribed targets of peak interstory drift ratios and ductility demands. In addition, the structures returned to at-rest positions without producing residual deformation after earthquake events. Therefore, this study successfully validates the applicability of the ad hoc design approach to SCCBFs with various story numbers.

Influence of ground motion duration on damage index-based fragility assessment of a plan-asymmetric non-ductile reinforced concrete building

The role of ground motion duration on the seismic performance of building structures remains unclear. This paper presents results on the effects of ground motion duration on the seismic behaviour of a 3-D plan-asymmetric reinforced concrete building. A three-story reinforced concrete building tested in Europe is used asa case study. A nonlinear model of the building with fibre-section distributed inelasticity displacement-based beam-column elements is subjected to two ground motion sets: (1) long-duration bi-directional earthquake ground motions, and (2) short-duration bi-directional earthquake ground motions. A new ground motion selection procedure is proposed to isolate the effect of duration on the structural response and on damage assessment. For comparative studies, long- and short-duration ground motions are selected so that they have similar response spectra. The damage assessment is performed analysing global and local responses. Global responses of the structure are evaluated in terms of peak roof drift ratios, peak interstory drift ratios (IDRs), IDR envelopes, normalized roof displacements relative to motion of the centre of gravity of the roof, and dissipated energy. Local responses assessed include moment-curvature or moment-rotation response in beams and columns as well as the hysteretic energy dissipated at selected sections of the structure. Two damage indices available in the literature are used to characterize the level of damage that the structure experiences, through damage index-based fragility curves that are developed as part of the work. For the short-duration motions, fragility curves developed independently from interstory responses and from the damage indices are similar, thus providing confidence into the use of the damages indices for fragility curve development. In addition, results indicate that for the vintage plan-asymmetric building analysed, the ground motion duration plays a role in the damage predicted using the two damage indices.

Energy Dissipation and Vibration Control: Modeling, Algorithm, and Devices

The topic of vibration control and energy dissipation is among the oldest and most relevant in the field of engineering [...]

Evaluation of a Simplified Method to Estimate the Peak Inter-Story Drift Ratio of Steel Frames with Hysteretic Dampers

In this paper, a simplified method is proposed to estimate the peak inter-story drift ratios of steel frames with hysteretic dampers. The simplified method involved the following: (1) the inelastic spectral displacement is estimated using a single-degree-of-freedom (SDOF) system with multi-springs, which is equivalent to a steel frame with dampers and in which multi-springs represent the hysteretic behavior of dampers; (2) the first inelastic mode vector is estimated using a pattern of story drifts obtained from nonlinear static pushover analysis; and (3) the effects of modes higher than the first mode are estimated by using the jth modal period, jth mode vector, and jth modal damping ratio obtained from eigenvalue analysis. The accuracy of the simplified method is estimated using the results of nonlinear time history analysis (NTHA) on a series of three-story, six-story, and twelve-story steel moment resisting frames with steel hysteretic dampers. Based on the results of a comparison of the peak inter-story drift ratios estimated by the simplified method and that computed via NTHA using an elaborate analytical model, the accuracy of the simplified method is sufficient for evaluating seismic demands.

Simplified estimation method of inelastic seismic demands of buildings with seesaw system using fluid viscous dampers

In this paper, the simplified estimation method, which is useful for structural reliability assessment and design, is proposed to estimate the inelastic seismic demands of buildings with a seesaw energy dissipation system (SEDS) using fluid viscous dampers (FVDs). The proposed method considers the inelastic spectral displacement and the inelastic first mode vector. In this method, the inelastic spectral displacement is estimated using a single-degree-of-freedom (SDOF) system equivalent to a multi-story frame with an SEDS using FVDs, and the inelastic first mode vector is estimated using a pattern of floor displacements obtained from nonlinear static pushover analysis (NSPA) of a multi-story frame, which considers the behavior of velocity-dependent dampers. Nonlinear time history analysis (NTHA) was performed on series of three- and six-story steel moment-resisting frames with an SEDS using FVDs and a corresponding equivalent SDOF system model. Also, NSPA was performed on an inelastic multi-story frame with an additional spring, which considers the viscous behavior of velocity-dependent dampers. Comparing the results of the peak inter-story drift ratio estimated by the proposed method with those computed via NTHA, the proposed method has sufficient accuracy for the evaluation of seismic demands.

Spatial seismic modeling of base‐isolated buildings pounding against moat walls: effects of ground motion directionality and mass eccentricity

SummaryStructural impact between adjacent buildings may induce local and, in some extreme cases, severe damage, especially in the case of seismically isolated buildings. This study parametrically investigates in the three‐dimensional domain the effect of pounding on the peak response of base‐isolated buildings, which are simulated as nonlinear three‐dimensional multi‐degree‐of‐freedom systems. Firstly, it is shown that considering unidirectional, instead of bidirectional, excitations may lead to underestimation of the base drift demands. Subsequently, the peak responses of seismically isolated buildings utilizing lead rubber bearings are studied while varying important parameters, such as the incidence angle of seismic excitations, the available seismic clearance, and mass eccentricities, under the action of bidirectional horizontal excitations. A large number of numerical simulations are performed using a specially developed software that implements an efficient approach to model impacts, taking into account arbitrary locations of contact points. It is found that the peak interstory drift ratio is significantly influenced by the directionality of the ground motion. Therefore, the seismic performance of structures should ideally be assessed examining the peak structural response while bidirectional ground motions are imposed at various incident angles. Furthermore, it is also observed that the interstory drift ratios increase while decreasing the available gap size, up to a certain value. Finally, the parametric analyses indicate that the effects of impact are more severe for structures with mass eccentricities, and in which case, the estimation of the critical incidence angle becomes more laborious. Copyright © 2016 John Wiley & Sons, Ltd.

Shake table test and numerical study of self‐centering steel frame with SMA braces

SummaryGiven their excellent self‐centering and energy‐dissipating capabilities, superelastic shape memory alloys (SMAs) become an emerging structural material in the field of earthquake engineering. This paper presents experimental and numerical studies on a scaled self‐centering steel frame with novel SMA braces (SMAB), which utilize superelastic Ni–Ti wires. The braces were fabricated and cyclically characterized before their installation in a two‐story one‐bay steel frame. The equivalent viscous damping ratio and ‘post‐yield’ stiffness ratio of the tested braces are around 5% and 0.15, respectively. In particular, the frame was seismically designed with nearly all pin connections, including the pinned column bases. To assess the seismic performance of the SMA braced frame (SMABF), a series of shake table tests were conducted, in which the SMABF was subjected to ground motions with incremental seismic intensity levels. No repair or replacement of structural members was performed during the entire series of tests. Experimental results showed that the SMAB could withstand several strong earthquakes with very limited capacity degradation. Thanks to the self‐centering capacity and pin‐connection design, the steel frame was subjected to limited damage and zero residual deformation even if the peak interstory drift ratio exceeded 2%. Good agreement was found between the experimental results and numerical simulations. The current study validates the prospect of using SMAB as a standalone seismic‐resisting component in critical building structures when high seismic performance or earthquake resilience is desirable under moderate and strong earthquakes. Copyright © 2016 John Wiley & Sons, Ltd.

Influence of earthquake ground‐motion duration on damage estimation: application to steel moment resisting frames

SummaryThis paper presents an analytical study evaluating the influence of ground motion duration on structural damage of 3‐story, 9‐story, and 20‐story SAC steel moment resisting frame buildings designed for downtown Seattle, WA, USA, using pre‐Northridge codes. Two‐dimensional nonlinear finite element models of the buildings are used to estimate the damage induced by the ground motions. A set of 44 ground motions is used to study the combined effect of spectral acceleration and ground motion significant duration on drift and damage measures. In addition, 10 spectrally equivalent short‐duration shallow crustal ground motions and long‐duration subduction zone records are selected to isolate duration effect and assess its effect on the response. For each ground motion pair, incremental dynamic analyses are performed at at least 20 intensity levels and response measures such as peak interstory drift ratio and energy dissipated are tracked. These response measures are combined into two damage metrics that account for the ductility and energy dissipation. Results indicate that the duration of the ground motion influences, above all, the combined damage measures, although some effect on drift‐based response measures is also observed for larger levels of drift. These results indicate that because the current assessment methodologies do not capture the effects of ground motion duration, both performance‐based and code‐based assessment methodologies should be revised to consider damage measures that are sensitive to duration. Copyright © 2016 John Wiley & Sons, Ltd

Optimal semi-active control of seismically excited MR-equipped nonlinear buildings using FLC and multi-objective NSGAII algorithms considering ground excitations

Among the variety of control algorithms, fuzzy logic control (FLC) strategies have the advantage of not depending on the system model behavior, of being simple, and intrinsically robust, and therefore they have recently been used to control the dynamic response of multi-story buildings equipped with semi-active supplemental damping devices. However, their tuning has shown to be a difficult task, especially when they use a multi-objective strategy. Introducing several FLC-based control strategies, an optimal semi-active control strategy using an advanced multi-objective optimization procedure called Non-dominated Sorting Genetic Algorithm II (NSGAII) has been proposed in this paper to mitigate the nonlinear structural response of a new generation of benchmark buildings. Besides peak inter-story drift ratio and peak floor acceleration, the base shear force as an extra objective has been used as the three-objective function for the multi-objective optimal design problem. The robustness of the optimized semi-active algorithms which were produced using binary tournament-based parents has been assessed for 3-story and 20-story nonlinear benchmark buildings experiencing nonlinear behavior during a wide range of earthquake records. The results showed that the performance of optimized semi-active control systems is acceptable and in some cases work much better than the non-optimized controllers taken in previous studies.