Maximum Inter-story Drift Research Articles

Effect of Aftershocks on Seismic Fragilities of Single-Story Masonry Structures

The effect of aftershocks on the fragility of single-story masonry structures is investigated using probabilistic seismic demand analysis Finite element models of an unreinforced masonry (URM) structure and a confined masonry (CM) structure are established and their seismic response characteristics when subjected to mainshock, aftershock, and the mainshock-aftershock sequence are then comparatively investigated. The effects of aftershocks and the use of confining members on the seismic response are studied. Probabilistic seismic demand models of the structures are built, and fragility curves under various conditions are derived to investigate the effect of aftershocks on structural fragility. The maximum roof displacement and maximum inter-story drift ratio are lower in the confined masonry model than in the unreinforced masonry model; additionally, the probability of exceedance (PE) values of each damage limit state reduced, and those of the mainshock-damaged models subjected to aftershock significantly increase compared to those directly subjected to a same-intensity aftershock. The probability of severe damage or collapse compared with the mainshock-damaged CM model is greater than when each is subjected to a same intensity aftershock. The use of confining members benefits aftershock resistance and reduces the failure probability of the mainshock-damaged structure. The PE values significantly increase with the aftershock scaling factor δ. Therefore, the effect of aftershocks should be considered in the seismic design and analysis of masonry structures.

Absolute Displacement-Based Formulation for Peak Inter-Story Drift Identification of Shear Structures Using Only One Accelerometer.

Only one accelerometer is used in this paper for estimating the maximum inter-story drifts and time histories of the relative displacements of all stories of multi-degree-of-freedom (MDOF) shear structures under seismic excitation. The calculation based on the data of one sensor using a conventional method is unstable, and when modal coordinates are used, higher modes should be included, which is different from the estimation based on the responses recorded by many accelerometers. However, the parameters of the higher modes of structures are difficult to obtain from structures under small excitations. To overcome this difficulty, the recorded absolute acceleration is converted into the absolute displacement, and a state-space equation is formulated. Numerical simulations of a nine-story structure were conducted to check the applicability, robustness against environmental noise, and optimal installation location of the accelerometer of the proposed approach. In addition, the effects of the higher modes were analyzed in terms of the number of accelerometers and type of response. Finally, the proposed approach was validated in a simple experiment. The results indicate that it can accurately estimate the time histories of the relative displacements and maximum inter-story drifts of all floors when one accelerometer is used and just the first two modal parameters are incorporated in the model. Furthermore, the approach is robust against environmental noise.

Evaluation of the relative and absolute cumulative input energy time history in the near-fault earthquake with visible pulse in acceleration time history, using the relative and absolute energy reflection spectral approach

Several studies have been carried out to evaluate the impact of near-fault earthquake with fling-step motion effects. The obvious feature of such earthquakes is the existence of a pulse with a significant amplitude in the velocity accelerograms. In this article, in order to investigate the effect of pulse-type near-fault earthquakes on the elastic demands of steel moment frames, a 15stories was simulated. After verifying the modelling process, under the influence of 20 near-field and 2 far-field records were analysed. The relationship between effective cyclic energy, ECE, and the displacement, velocity and hysteretic curve of SDOF systems in near- and far-fault earthquakes was evaluated. Then, studying the energy of relative and absolute cumulative input energy with kinetic energy in one section and maximum inter-story drift for 4 different levels of nonlinear behaviours (R = 1.0, 2.0, 4.0, 6.0) in the other section, the effect of higher modes was evaluated. Studying the inter-story drift profile for two near-fault earthquakes, with and without accelerated pulses, indicates the formation of the maximum drift, IDRmax, in upper stories for low nonlinear degrees (R=1.0 and R=2.0) in Records with visible pulses that verify the participation of higher modes. However, in accelerated pulse-free records, in addition to intensifying the IDRmax in the upper stories, a large-scale demand is imposed in the lower stories. In other words, in the lower stories, the first mode is mainly involved in these records.

Effects of soil–structure interaction on seismic performance of a low-rise R/C moment frame considering material uncertainties

This study investigated the effects of soil–structure interaction (SSI) on the performance of low-rise reinforced concrete (R/C) structures subjected to earthquakes. The uncertainty of material properties, such as steel yield and concrete compressive strengths, was addressed using the Monte Carlo simulation with Latin hypercube sampling. A planar R/C moment frame of three bays and three stories was subjected to 20 selected ground motions for this purpose. In the flexible-base models, the soil was modeled with springs and dashpots, and the mass and moment of inertia of the footing were lumped at the bottom of the column. In contrast, for the fixed-base model, the bottoms of the columns were fixed in all translational and rotational directions. A parametric study was conducted for the shear wave velocity of soil, varying from 1000 to 50 m/s. The responses of the flexible-base and fixed-base models were compared in terms of the ductility, maximum interstory drift, and maximum total drift (ratio of top displacement to building height) for three performance levels in ASCE 41-17: intermediate occupancy (IO), life safety (LS), and collapse prevention (CP). The pushover analysis results indicate that a higher shear wave velocity leads to a higher ductility capacity. The uncertainty of the material properties produces an extensive range of ductility factors. The seismic drift responses of the flexible-base models are larger than those of the fixed-base model, particularly in the range of shear wave velocities less than 180 m/s (i.e., soft soil). From the failure probability analyses, the threshold shear wave velocity below which the effects of SSI should be considered is approximately 180 m/s for IO and 100 m/s for both LS and CP.

Seismic loss risk assessment of RC frame structures designed according to Chinese code

According to the PEER probabilistic seismic loss assessment methodology, a structure-level seismic risk assessment method was proposed and implemented for a set of RC frames designed according to Chinese seismic code. These frames were designed for fortification intensities of 6,7 and 8 and classified into 4,6 and 8 stories. Through incremental dynamic time history analysis (IDA), the statistical relationships of the maximum inter-story drift ratio with the seismic spectral acceleration were obtained and used to determine fragility curve for each damage states. The site seismic hazard model was established based on Chinese seismic code, and the probability distribution of each discrete intensity levels was derived. Using loss index from the Chinese standard and Hazus, the structure means annual frequency of collapse, the Expected Annual Financial Loss (EAL) and the Expected Annual Fatalities (EAF) were calculated. The variation trends of these performance metrics with seismic fortification intensities and structure heights were evaluated, and the weaknesses of the current seismic code of China were pointed out. It was concluded that the method proposed in this paper is simple and reliable for practical applications.

Correlation between pulse-like ground motion intensity measures and seismic demands of buildings with three structural systems (moment-resisting frames, structural walls and combination of moment-resisting frames and shear walls)

In this study, the distribution of correlation coefficients between maximum interstory drift ratio (MIDR) of multistorey building structures and ground motion characteristics intensity measures (IMs) is evaluated and compared. For this purpose, a continuum building model is used to estimate the MIDR of multistory building structure including higher mode effects. The MIDRs are computed for building structures with three different lateral resisting systems (structural walls, moment-resisting frames, and their combination) and fundamental periods that ranges from 0.05 to 10s. Nine different ground motion parameters of pulse-like ground motions including PGD, PGA, PGV, Ic, CAV, Ia, SMV, ESD, SMA are selected as ground motion characteristics IMs. The effects of the type of lateral resisting system and the acceleration pulse on the distribution of correlation coefficients are also considered in the study. Based on the assessment results, MIDRs in mid and long-period buildings show a high correlation to PGV, SED and SMV, while a low correlation occurs with respect to PGA and SMA. Also, type of lateral resisting system causes changes in the correlation coefficients and results showed that long-period shear wall structure gives lower coefficients with respect to other structural systems.

Seismic performance of self-centering steel-timber hybrid shear wall structures

This paper presents the seismic performance assessment of self-centering steel-timber hybrid shear wall (SC-STHSW) structures. The hybrid structure introduces extra re-centering action to itself through the combination of the post-tensioned steel frame (PTSF) with the light-framed wood shear wall. Slip friction dampers (SFDs) are used as connectors between the frame and the wood wall. An OpenSees model for the SC-STHSW was established and validated versus experimental results. Then, a 9-story SC-STHSW structure was designed with the direct displacement-based design procedure, and the design was checked through nonlinear time history analysis. Based on the designed 9-story SC-STHSW structure, the influence of a key parameter (i.e., self-centering ratio α E ) on the structure's dynamic performance was investigated by considering different hazard levels. The dynamic response of three 9-story SC-STHSW structures with different α E values was compared in terms of maximum inter-story drift (MaxISD) and maximum residual inter-story drift (MaxRISD). Meanwhile, the fragility curve of a 9-story conventional steel-timber hybrid shear wall (STHSW) structure without self-centering capability was calculated based on the cloud analysis, and the fragility curves were compared with those of the 9-story SC-STHSW. It was found that the increase of α E was not only beneficial to decrease the system's MaxRISD but also positive in enhancing system's control over its MaxISD. The lower limit of α E was suggested to be 0.6 when the system was used in high seismic regions. The 9-story SC-STHSW ( α E = 0.6) was comparable to the 9-story STHSW system in regards to the control of MaxISD, which illustrated the advancement of the new system since, at the same time, it had better re-centering ability to decrease post-earthquake repair costs. • A self-centering steel-timber hybrid shear wall structure was designed through the direct displacement-based design. • The influences of α E on the new structure’s seismic performance were explored. • Based on cloud analysis, the seismic fragility of the new structure was compared with the other structure.

Fast optimization of outriggers for super-tall buildings using a sensitivity vector algorithm

This study proposes a simple engineering method to fast determine the quantity and placement of outriggers for super-tall buildings. At first, a sensitivity vector algorithm (SVA) is proposed by applying the vector dot-product algorithm to optimize outriggers in super-tall buildings towards the constraints of the maximum interstory drift . The proposed SVA is then demonstrated by a super-tall building under the wind load control and verified by the exhaustive search algorithm (ESA). Finally, the SVA is applied to optimize the outriggers for a super-tall building in the high-intensity seismic area . The results show that the optimal outrigger scheme relates to both the quantity and placement, rather than simply proportional to the quantity. Increasing the quantity of outriggers can reduce the interstory drift in the adjacent area of the added outrigger but may increase the interstory drift in other zones. The sensitivity vector algorithm can be used for the optimization of outriggers not only for the single-mode-driven wind load, but also for the multi-mode-driven seismic load, which is very helpful for the preliminary design of super-tall buildings. • Sensitivity vector algorithm is proposed to optimize quantity and placement of outriggers using vector dot-product algorithm. • Optimal outrigger scheme relates to both the quantity and placement, rather than simply proportional to the quantity. • Sensitivity vector algorithm can be used for both the single-mode-driven wind load and the multi-mode-driven seismic load.

Seismic collapse assessment of steel plate shear walls considering the mainshock–aftershock effects

This study evaluates the effect of mainshock–aftershock sequences on the collapse of steel plate shear wall (SPSW) systems. For this purpose, three 9-, 14- and 20-story SPSWs are selected considering the practical range of heights used in this system. After numerical modeling of the structures, they are initially subjected to static-pushover analyses to evaluate their plastic behavior in large inelasticity regions. The incremental dynamic analysis is subsequently performed to capture the collapse capacity of the structures under aftershock excitations preceded by mainshocks that pose various levels of damage expressed in terms of maximum inter-story drift (MID). Evaluation of the median collapse capacities under aftershock excitations exhibit the same reduction ratios at similar mainshock MIDs for the different structures. This reduction is predicted via a quadratic polynomial for given mainshock MID values. Investigation of the mainshock-aftershock effects on distribution of the MIDs and maximum ductility demands at the collapse state shows that the prior mainshock damage mainly affects the collapse capacity by consuming the energy-absorption capacity of the infill plates, thus causing strength deterioration. Irrespective of the mainshock damage level, the structures were found to collapse when their first-story columns reach a threshold softening level.

Multiple failure function based fragility curves for structures equipped with TMD

This paper presents a procedure to develop fragility curves of structures equipped with TMD considering multiple failure functions. The failure criteria considered are maximum inter-story drift ratio as a safety criterion, maximum absolute acceleration as a convenience criterion and TMD stroke length. The relationship between intensity measure and responses of the structure was assumed to follow the power-law model, and a regression analysis was used to estimate its properties. A nonlinear eight-story shear building subjected to near-fault earthquakes was used for the numerical studies. Fragility curves using multiple and single failure functions for an uncontrolled structure and a structure equipped with optimal TMDs were developed. Numerical analysis showed that using multiple failure functions led to increasing the fragility when compared with using the single failure function for both the uncontrolled and controlled structures. However, TMDs slightly reduced the seismic fragility and have the capability to improve the reliability of the structure. Also, it was found that the fragility was significantly influenced by the values of the capacity thresholds of both the acceleration of the structure and TMD stroke length, which should be selected by considering the target performance and application of the structure and control device.

Probabilistic damage evaluation of base-isolated reinforced concrete structures under near-fault pulse-like bidirectional seismic excitations

In this article, seismic fragility of a base-isolated special Reinforced Concrete (RC) moment frame is investigated under near-fault pulse-type ground motion records. The vulnerability of the displacement-dominated performance of isolator devices to a likely vibration resonance caused by such records is the focus of the study. For this purpose, Lead-Rubber Bearings (LRBs) and Triple Friction Pendulum Bearings (TFPBs) are utilized to represent various isolator behaviorisms in different period ranges. The structures are modelled in three dimensions to account for the axial-bending-bending interaction in the isolator devices. The models are then subjected to IDAs under three sets of near-fault pulse-type ground motion records with different pulse periods. Four different damage states are considered and the IDA results are used for deriving fragilities that express probabilities of exceeding these states at various intensity levels. The study revealed that despite the amplifying effects of the employed records, using isolators is still feasible. That is, even for pulse periods near to the effective period of isolators, resonance has not led to higher failure probabilities in the isolated buildings compared to their fixed-base counterparts. Furthermore, at longer pulse periods, the gradual yielding behavior of TFPBs made them more effective than the LRBs. Results also disclosed that at lower intensities, damage of base-isolated structures is mainly caused due to excessive floor acceleration while at higher intensities the maximum inter-story drift plays the dominant role. This suggest these two response parameters to be alternatively used as the Engineering Demand Parameter (EDP) when defining damage states at the medium and high intensity levels.

Analytical approach for the design and optimal allocation of shape memory alloy dampers in three-dimensional nonlinear structures

The purpose of this paper is to present a simplified nonlinear equations-model that is intended to design shape memory alloy (SMA) dampers in three-dimensional structures of unsymmetrical-plan and in yielding shear-frames. The equations-model is based on a schematic idealization of the SMA damper's hysteretic behavior and the structure's transient tangent stiffness matrix, which corresponds to yielding shear-frames, and is commensurate with structural design methodologies. As of today, there are very few seismic design methodologies that use SMA dampers. In this paper, the analytical equations-model is implemented in a seismic retrofit search algorithm modified for SMA dampers. The algorithm sequentially places the SMA dampers at the story with the maximum interstory drift gain magnitude, calculated using the transfer function matrix between the ground acceleration components and the frames' interstory drifts. The transfer function matrix stems from a linear state-space formulation, but the tangent stiffness matrix is nonlinear. In order to cater to this issue, a new iterative approach suggests updating the tangent stiffness matrix in accordance with the transfer function matrix's peak interstory drift magnitudes – until the tangent stiffness matrix converges. A numerical example shows that the iterative process takes no more than two iterations.

Optimal Seismic Design of Stiffness and Gap of Hysteretic-Viscous Hybrid Damper System in Nonlinear Building Frames for Simultaneous Reduction of Interstory Drift and Acceleration

The viscous-hysteretic hybrid (HVH) damper system recently introduced by one of the authors has a clear property that, when the hysteretic dampers with gap mechanism become active (stiffness element starts working), the acceleration of building frames with this damper system as a stopper attains large values in spite of the advantageous feature to prevent excessive deformation. It is therefore desired that both the maximum interstory drift and the maximum acceleration exhibit an acceptable value with appropriate compromise. The double impulse as a simplified version of one-cycle sine wave as a representative of the main part of near-fault ground motions can simulate the maximum interstory drifts properly. However, it cannot simulate the maximum accelerations due to its impulsive nature. In this case, the sine wave corresponding to the double impulse can play an important role in the reliable simulation of the maximum accelerations. Even in such circumstance, the analysis using the double impulse is important because it enables to obtain the critical timing of the input, i.e. the nonlinear resonant frequency of the sine wave without repetition. The investigations on the criticality of the sine wave corresponding to the critical double impulse show that the critical timing of the double impulse leads to the nonlinear resonant frequency of the sine wave in view of the maximum interstory drift, the maximum top acceleration and the maximum relative acceleration for the constant input acceleration and the constant input velocity except for some cases. It is demonstrated finally that the index in terms of the maximum interstory drift and the maximum acceleration can be introduced as an appropriate parameter for deriving the optimally compromised gap quantity of hysteretic dampers with gap mechanism for various input velocity levels and various hysteretic damper stiffness ratios.

Hybrid simulation tests of high-strength steel composite K-eccentrically braced frames with spatial substructure

Based on the spatial substructure hybrid simulation test (SHST) method, the seismic performance of a high-strength steel composite K-eccentrically braced frame (K-HSS-EBF) structure system is studied. First, on the basis of the existing pseudostatic experiments, a numerical model corresponding to the experimental model was established using OpenSees, which mainly simulated the shear effect of the shear links. A three-story and five-span spatial K-HSS-EBF was taken as the prototype, and SHST was performed with a half-scale SHST model. According to the test results, the validity of the SHST model was verified, and the main seismic performance indexes of the experimental substructure under different seismic waves were studied. The results show that the hybrid simulation results are basically consistent with the numerical simulation results of the global structure. The deformation of each story is mainly concentrated in the web of the shear link owing to shear deformation. The maximum interstory drifts of the model structure during Strength Level Earthquake (SLE) and Maximum Considered Earthquake (MCE) meet the demands of interstory limitations in the Chinese seismic design code of buildings. In conclusion, the seismic response characteristics of the K-HSS-EBFs are successfully simulated using the spatial SHST, which shows that the K-HSS-EBFs have good seismic performance.

Numerical Investigation of Energy Dissipation Device to Improve Seismic Response of Existing Steel Buildings with Soft-First-Story

Retrofitting buildings in densely populated areas with a soft story configuration on the first floor can pose a daunting challenge to the community. Against this backdrop, this study set out to evaluate the seismic retrofit strategy's adequacy in enhancing the seismic performance of buildings with a soft story. The proposed strategy utilizes an earthquake energy dissipation device consisting of a combination of a diagonal brace and a metallic-yielding damper at the ground story level. Two prototype buildings, one with five and the other with ten floors, were chosen to assess the proposed retrofit strategy's seismic response through nonlinear static and dynamic analyses. The seismic capacity, lateral displacement response, maximum inter-story drift ratio, energy dissipation, and collapse fragility are the major response parameters used to compare original and retrofitted buildings. The nonlinear static analysis results revealed that the seismic capacity for buildings equipped with a yielding damper was higher than that of the original buildings. It was also found that retrofitted frame buildings had a desirable structural behavior with a higher value of dissipated energy and a lower value of residual displacements and inter-story drift ratio, in turn reducing the likelihood of soft-story failure.

Collapse Capacity of Ordinary RC Moment Frames Considering Mainshock-Aftershock Effects

ABSTRACT The effect of mainshock-aftershock (MS-AS) sequences on seismic performance of ordinary reinforced concrete (RC) moment frames (ORCFs) is studied by considering various levels of mainshock damage represented by maximum inter-story drift (MID) parameter. Incremental dynamic analysis (IDA) is performed to extract collapse capacity of structures under aftershock records after imposing the intended mainshock damage. The study results indicate that a smooth reduction in aftershock collapse capacity occurs due to increase in mainshock damage level. Regression equations are also provided to aid in predicting the aftershock collapse capacity in presence of various mainshock damage levels.

Machine Learning for Extracting Features of Approximate Optimal Brace Locations for Steel Frames

A method is presented for extracting features of approximate optimal brace types and locations for large-scale steel building frames. The frame is subjected to static seismic loads, and the maximum stress in the frame members is minimized under constraints on the number of braces in each story and the maximum interstory drift angle. A new formulation is presented for extracting important features of brace types and locations from the machine learning results using a support vector machine with radial basis function kernel. A nonlinear programming problem is to be solved for finding the optimal values of the components of the matrix for condensing the features of a large-scale frame to those of a small-scale frame so that the important features of the large-scale frame can be extracted from the machine learning results of the small-scale frame. It is shown in the numerical examples that the important features of a 24-story frame are successfully extracted using the machine learning results of a 12-story frame.

Shaking-table tests of a full-scale ten-story reinforced-concrete building (FY2015). Phase I: Free-standing system with base sliding and uplifting

In this paper, results are presented from shaking-table tests of a full-scale 10-story reinforced-concrete structure to confirm the behavior of a free-standing system with a base that permits both sliding and uplifting. The purpose of this system is to use the seismic resistance of the structure during a small or medium earthquake and a sliding and uplifting behavior of the free-standing system during a large earthquake. Cast-iron plates were installed on the grade beams of the lower part of the specimen building to generate a low friction coefficient. Thus, the specimen building should be able to move sideways during large earthquakes, although the specimen building should not move sideways during small earthquakes. In the tests, the specimen building was moved sideways during tests with JMA-Kobe 25%, 50%, and 100% amplitude excitations but not during that with JMA-Kobe 10% amplitude excitation, and the specimen building was uplifted at one of its corners for all amplitude excitations. The base sliding displacement was 84–189 mm, and the corner uplift was 5–40 mm. The sliding and uplift behavior led to small maximum inter-story drift ratios, and these behaviors did not increase the base overturning moments. Thus, allowing sliding and uplifting behavior can reduce building damage in an extremely large earthquake.

Reliability Based Design Optimization of Reinforced Concrete Frames Using Genetic Algorithm

This paper introduces a new framework for reliability based design optimization (RBDO) of the reinforced concrete (RC) frames. This framework is constructed based on the genetic algorithm (GA) and finite element reliability analysis (FERA) to optimize the frame weight by selecting appropriate sections for structural elements under deterministic and probabilistic constraints. Modulus of elasticity of the concrete and steel bar, dead load, live load, and earthquake equivalent load are considered as random variables. Deterministic constraints include the code design requirements that must be satisfied for all the frame elements according to the nominal values of the aforementioned random variables. On the other hand, this framework provides the minimum required reliability index as the probabilistic constraint. The first-order reliability method (FORM) using the Newton-type recursive relationship will be used to compute the reliability index. The maximum inter-story drift is considered as an engineering demand parameter to define the limit-state function in FORM analysis. To implement the proposed framework, a mid-rise five-story RC frame is selected as an example. Based on the analysis results, increasing the minimum reliability index from 6 to 7 causes an 11 % increase in the weight of the selected RC frame as an objective function. So, we can obtain a trade-off between the optimized frame weight and the required reliability index utilizing the developed framework. Furthermore, the high values of the reliability index for the frame demonstrate the conservative nature of code requirements for interstory drift limitations based on the linear static analysis method.

Deformation-dependent peak floor acceleration for the performance-based design of nonstructural elements attached to R/C structures

This study introduces a simple and efficient method to determine the peak floor acceleration (PFA) at different performance levels for three types of plane reinforced concrete (RC) structures: moment-resisting frames (MRFs), infilled–moment-resisting frames (I-MRFs), and wall-frame dual systems (WFDSs). By associating the structural maximum PFA response with the deformation response, the acceleration-sensitive nonstructural components, and the building contents, can be designed to adhere to the performance-based seismic design of the supporting structure. Thus, the proposed method can accompany displacement-based seismic design methods to design acceleration-sensitive nonstructural elements to comply with the deformation target of the supporting structure. The PFA response shape is represented by line segments defined by key points corresponding to certain floor levels. These key points are defined by explicit empirical expressions developed herein. The maximum PFA response is correlated with the maximum interstory drift ratio (IDR) and other vital characteristics of the supporting structure such as the fundamental period. The proposed expressions are established based on extensive nonlinear dynamic analyses of 19 MRFs, 19 WFDSs, and 19 I-MRFs under 100 far-fault ground motions scaled to capture different deformation targets. Realistic examples demonstrate the efficiency of the proposed method to assess the PFA response at a given IDR, making the method suitable in the framework of performance-based design.