Story Drift Ratio Research Articles

A Quantitative Method for Seismic Robustness of RC Frame Considering Resistance Vulnerability of Column and Storey Drift Ratios

The concept of seismic robustness is proposed by combining the concept of seismic performance and structural robustness. The existing qualitative, quantitative and evaluation methods of seismic robustness are all direct researched on the whole structure, and the influence mechanism of its internal components on the overall seismic robustness is still unclear. It is very important to establish a clear relationship between component design and structural seismic robustness for the structural design, reinforcement design and final evaluation of structural seismic robustness. Based on this, taking the column as the starting point, a quantitative method for the seismic robustness of RC frame by the seismic robustness index is proposed, which takes into account the resistance vulnerability of column and influence of column on the storey drift ratios (SDRs). In which, the resistance vulnerability is represented by the defined control vulnerability coefficient Pimax, and the influence on the SDRs are represented by the storey drift ratio importance coefficients (SDRCs) λ. The method not only reflects the essential mechanical properties of the column, but also reflects the effects brought about by different SALs. The feasibility of the method is demonstrated by numerical examples of two types of failures (assuming single column and two columns failure), and four optimization design proposals are proposed for it. The analysis shows that λ of the target columns to the floor where the target columns located are obviously greater than those on the remaining floors of the target frame. The seismic robustness index R decreases sharply with the increase of the seismic action level (SAL). R is different compare single column failure with two columns failure under 4 SALs. The most effective way to improve the R of the frame under a certain SAL is to retrofit its control column.

Nonmodel rapid seismic assessment of eccentrically braced frames incorporating masonry infills using machine learning techniques

This study investigates the seismic behavior of eccentrically braced frames (EBFs) taking into account the influence of masonry infill walls using a nonmodel scenario-based machine learning framework. Predicting engineering demand parameters (EDPs) by exploiting data-driven approaches and developing the associated fragility curves of infilled EBFs are the main objectives of this research. To this end, a set of 4- and 8-story archetype EBF structures considering 12 distinct infill properties, a total number of 4 bare and 48 infilled EBF models, are created in OpenSees software. A nonlinear pushover analysis is then conducted to assess the overall impact of infills on 4- and 8-story EBFs. Incremental dynamic analysis under 44 far-field ground motions is performed to collect an extensive raw database consisting of 37,164 and 461,480 data points for each variable of bare and infilled EBFs, respectively. It encompasses seismic intensity measure (Saavg), wavelet-based robust damage sensitive feature (rDSF), derived from roof absolute acceleration, frame geometric information, and infill parameter as input features and also EDPs containing peak and residual story drift ratios and peak floor accelerations (PFA) as response variables. After data preprocessing, both regression analysis and machine learning (ML) techniques are utilized to estimate EDPs under two scenarios of Input-Output and Output-Only based on the availability of Saavg. Comparing error measures, particularly in the Extreme Gradient Boosted Tree (ExGBT) algorithm, reveals strong observed-predicted EDP compatibility. Linear equations from bare frame data predict infilled frame EDPs without modification coefficients. Data preprocessing demonstrates that infills decrease drift-based EDPs due to stiffness improvement, while their impact on PFA remains inconclusive. Saavg and rDSF-based fragility curves at three damage states show accurate predictions and effectively reduce vulnerability in infilled 4-story EBFs. However, infills undesirably affect non-ductile behavior in 8-story EBFs, leading to increased global damage as supported by pushover analysis.

Experimental and analytical modelling on a novel self-centering viscous damper

Self-centering (SC) supplemental dampers offer a feasible approach to realize low-damage structures. A novel self-centering viscous damper (SCVD) that incorporates an SC part and a viscous damper (VD) part in parallel, and then series with a length adjustable (LA) part. The working mechanism and hysteretic model were both analyzed for the SCVDs. Dynamic reversed sinusoidal displacement inputs were used in experimental proof-of-concept validation studies. Each component was examined separately to describe and distinguish their distinct contributions to the whole device. Individual results in summing are consistent with hybrid device outcomes for the same input. The SCVDs showed excellent self-centering capability with satisfactory energy dissipation. A maximum equivalent viscous damping ratio (EVDR) of 99.37% was observed. A theoretical model and a numerical model were built and examined for the proposed SCVDs. The inevitable gaps from installation have a noticeable effect on the VD part and the SCVD, especially for small strokes. Except for small strokes, comparisons of test findings and analytical models reveal similar hysteretic reactions, for which the coefficients of determination are greater than 0.9, thereby validating the performance of the theoretical and analytical models to simulate the behavior of the tested SCVDs. In comparison to existing SCVDs, the suggested SCVDs have a more controllable SC ability, length adjustability, and energy dissipation capacity based on the demands of the designers. Furthermore, five distinct lateral resisting components were used in nonlinear response history analysis to compare the seismic and resilient performance amongst the moment resisting frame (MRF), buckling restrained brace (BRB), SC, VD and SCVD systems. Finally, the addition of SCVDs and VD parts can both be effective in controlling the maximum and residual story drift ratios on average. Overall, our findings provide innovative, simple implementable choices for developing low-damage structures.

Shaking table tests of masonry wall reinforced with steel-bar truss units linked by spring dampers

Since unreinforced masonry buildings are vulnerable to earthquakes, various studies have been conducted to improve their seismic performance. In this study, spring dampers were added to steel-bar truss units to improve the performance of the reinforcement method, and shaking table tests were performed to evaluate their seismic performance. Furthermore, a full-scale I-shaped masonry wall was prepared by considering the inner walls of masonry buildings, and steel-bar truss units linked by spring dampers were installed on both sides of the specimen. For the unreinforced specimen, the horizontal spectral acceleration calculated for the flexible components was 0.54 g, the seismic loading level was sequentially increased by 20%, and in-plane excitation was performed. The experimental results showed that the unreinforced masonry specimen resisted up to 220% of the designed seismic acceleration, whereas the reinforced masonry specimen resisted up to 320%. At the end of the experiment with the unreinforced masonry specimen, the response peak acceleration and drift ratio of the reinforced specimen were approximately 36% and 50% lower than those of the unreinforced masonry specimen, respectively. This implies that the diagonal bars constituting the truss units reduced the story drift ratio by suppressing shear deformation, and the vertical bars prevented cracking by introducing an additional axial force on the masonry wall. The experimental results demonstrated that the reinforcement method efficiently improved the seismic performance of the masonry wall in terms of stiffness, ductility, shear force. Because this study was conducted with only one variable, i.e., the presence/absence of the strength method, further research with various variables such as a number of steel-bar truss units, prestressing force level, spring stiffness of spring damper is required to verify the practical applicability of the method.

Seismic and resilient assessment on moment resisting frames with novel self-centering viscous dampers

A new type of self-centering viscous dampers (SCVDs) had been developed by the authors to create low-damage structures [1]. Then, the seismic and resilient performance of steel frames equipped with SCVDs were still mysteries waiting for being discovered. So, performance was analyzed among the five systems which were moment resisting, buckling restrained brace (BRB), self-centering (SC), viscous damper (VD), and SCVD frames. The 3- and 6- story frames with the aforementioned systems were subjected to 20 earthquake records of various ground types using nonlinear response history analysis. In comparison to the MRF system, the SCVD system exhibited a significant improvement. The maximum and residual story drift ratios were reduced by 90.27% and 97.78%, respectively. However, there was an increase in the maximum base shears and overturning moments of the SCVD system by 120.65% and 150.31%, respectively. Overall, MRFs equipped with SCVDs or VD parts possess better seismic and resilient performance with higher certainty than the other systems, in special, the total growth rate of the VD system can be reduced by 22.94% comprehensively. Furthermore, addition of energy dissipation capabilities is more effective in decreasing responses with higher certainty than stiffness or self-centering capabilities of the braces.

Optimal design of semi-rigid connection steel frame with infilled shear walls using dolphin echolocation algorithm

In this paper, the dolphin echolocation algorithm (DEA) was applied for optimization. Two different two-dimensional semi-rigid connection steel frames with infilled shear walls (SFIWs) were optimized to obtain the minimum weight with constraints on the element stresses and storey drift ratio according to the American Institute of Steel Construction (AISC) Load and Resistance Factor Design requirements. With the proposed method, the specific details of the infilled shear walls are not given during the design process, but are characterized by the lateral stiffness. The designer can decide which types of infilled shear walls are used according to the result obtained from the optimization. The infilled shear walls are modeled as braces with equivalent lateral stiffnesses, while the semi-rigid connections are used to obtain the practical behaviors of the SFIWs. The results demonstrate that the proposed method is suitable for optimizing semi-rigid connection steel frames with infilled shear walls.

Seismic performance of the RBS connection with trapezoidal corrugated web (TCW-RBS)

This paper presents an evaluation of the performance of the trapezoidal corrugated web (TCW) reduced beam section (RBS) connection under cyclic loading. A series of experiments were conducted on three TCW-RBS specimens. The tests were carried out up to a 10% story drift ratio, and it was observed that the connection met the code-based limitations for a reduction in strength until reaching an 8% drift, surpassing the existing criterion for qualified connections in special moment frames. Additionally, nonlinear finite element analysis was utilized to investigate the influence of web angles on the behavior of TCW-RBS connections. The findings revealed that increasing the web angle resulted in a decrease in the maximum moment by up to 11%, while simultaneously enhancing the connection's ductility by up to 37%. Furthermore, the axial strain results in the web of the beam indicated that the corrugated web had a negligible impact on the flexural behavior of the connection due to the accordion effect. Notably, the maximum strain values in the flanges near the column face were three times lower than those in the reduced section zone, contributing to a reduced sensitivity of the welds to potential fractures.

Evaluation of performance and storey drift ratio limits of high-rise structural systems with separated gravity and lateral load resisting systems using time history analysis and incremental dynamic analysis

To increase the efficiency of prefabricated construction of high-rise structure, a composite structural system with separated gravity and lateral load resisting systems (referred to as a ‘new separable system’) is proposed. Efficient numerical models of the composite frames, reinforced-concrete (RC) shear walls, RC coupling beams, and braces in the new separable system were developed using the finite-element program MSC.Marc. The fragility curves of these components were developed through parametric analysis and a literature review of previous research and database documents. Through time history analysis, the responses of roof displacement, storey drift, and residual drift were analysed and compared with those of the traditional composite frame–shear wall system. An incremental dynamic analysis (IDA) was performed to obtain the IDA curves of the new separable system and the traditional system, and the seismic fragility curves of the two systems were built. The seismic performance of the new separable system was compared with that of the traditional system in terms of the collapse probability, dynamic safety factor, and risk of seismic damage. The results indicated that for high-rise composite structural systems with separated gravity and lateral resisting systems under frequently occurring earthquakes, the reasonable range of the storey drift ratio limit in design is 1/800 to 1/1000, and a limit value of 1/1000 is recommended conservatively.

Modeling uncertainty of specimens employing spines and force‐limiting connections tested at E‐defense shake table

AbstractIn light of the significant damage observed after earthquakes in Japan and New Zealand, enhanced performing seismic force‐resisting systems and energy dissipation devices are increasingly being utilized in buildings. Numerical models are needed to estimate the seismic response of these systems for seismic design or assessment. While there have been studies on modeling uncertainty, selecting the model features most important to response can remain ambiguous, especially if the structure employs less well‐established lateral force‐resisting systems and components. Herein, a global sensitivity analysis was used to address modeling uncertainty in specimens with elastic spines and force‐limiting connections (FLCs) physically tested at full‐scale at the E‐Defense shake table in Japan. Modeling uncertainty was addressed for both model class and model parameter uncertainty by varying primary models to develop several secondary models according to pre‐established uncertainty groups. Numerical estimates of peak story drift ratio and floor acceleration were compared to the results from the experimental testing program using confidence intervals and root‐mean‐square error. Metrics such as the coefficient of variation, variance, linear Pearson correlation coefficient, and Sobol index were used to gain intuition about each model feature's contribution to the dispersion in estimates of the engineering demands. Peak floor acceleration was found to be more sensitive to modeling uncertainty compared to story drift ratio. Assumptions for the spine‐to‐frame connection significantly impacted estimates of peak floor accelerations, which could influence future design methods for spines and FLC in enhanced lateral‐force resisting systems.

Evaluation and story drift ratio limits of structures with separated gravity- and lateral-load-resisting systems using pushover analysis

In recent years, China has strongly advocated the development of prefabricated buildings. To meet the growing demand for housing construction, it is necessary to develop high-rise prefabricated structures. To increase the construction efficiency of high-rise prefabricated structures, an innovative composite structural system with separated gravity- and lateral-load-resisting systems (referred to as an ‘innovative structural system’) was developed, and its seismic performance was evaluated. At the component level, efficient numerical models of the composite frames, reinforced-concrete (RC) shear walls, RC coupling beams, and braces in the innovative structural system were developed using the general finite-element software MSC.Marc. The fragility curves of these components were developed through parametric analysis and a literature review of previous research and database documents. At the system level, through finite-element analysis, the seismic mechanism of the innovative structural system under lateral loads, including the lateral displacement pattern, plastic development pattern, and failure mode, was compared with that of the traditional composite frame–shear wall system. A static pushover analysis was performed, and the displacement response results of the innovative structural system under the maximum considered earthquake strength were obtained. The damage to the components was evaluated via fragility analysis, and the seismic performance of the innovative structural system was compared with that of the traditional system according to the safety factor. The results indicated that for high-rise composite structural systems with separated gravity- and lateral-load-resisting systems under frequently occurring earthquakes, the reasonable range of the story drift ratio limit in design is 1/800 to 1/1000, and a limit value of 1/1000 is recommended conservatively.

Comprehensive evaluation of target spectra for selecting bidirectional ground motions in nonlinear response history analysis of frame buildings at far‐field sites

AbstractAn ensemble of bidirectional ground motions (GMs) is required as input for nonlinear response history analysis (RHA) of complex 3D structures. In building codes, an ensemble of GMs is often developed from a given design spectrum, or target spectrum. In the research literature, several target spectra have been proposed for such intensity‐based assessments. The present study aims to comprehensively evaluate different options for developing target spectra to select bidirectional GMs as inputs to nonlinear RHAs of 3D structural systems. To achieve this goal, we conducted both intensity‐based and risk‐based assessments of 49 multistory buildings with varying dynamic characteristics, heights, and plan shapes. The results from performing 11,074 bidirectional nonlinear RHAs and deriving the seismic demand hazard suggest that the Conditional Mean Spectrum‐Uniform Hazard Spectrum (CMS‐UHS) Composite Spectrum appears to be the most promising alternative. With less computational effort than use of multiple CMS, the Composite Spectrum tends to accurately estimate story drift ratios (average overestimation of 4%) and floor accelerations (average overestimation of 3%). Moreover, the relative ranking between the various target spectra options remains largely independent of the building type, height, and plan shape. However, the precision in estimates of demand tends to decrease for buildings with increasing complexity (e.g., more realistic, or taller, or more asymmetrical in plan).

Influence of outrigger truss system on the seismic fragility of super high-rise braced mega frame-core tube structure

The braced mega frame-core tube (BMFCT) structure is an efficient seismic structural system for super high-rise buildings of over 500 m high. The outrigger truss (OT) system has become a commonly adopted design option for the super high-rise BMFCT structure, however, its influence on the seismic performance is not clear. In this study, the seismic responses and collapse risks of the 590-m-high BMFCT structures with and without OT system were analyzed. An efficient elasto-plastic modeling method was introduced to establish the accurate FE models. Based on the incremental dynamic analysis-based (IDA) fragility analysis, the deformation responses, energy dissipations, collapse risks and collapse resistance capacities, etc. were researched. The results indicate the average top displacements under earthquakes of ‘one-degree-higher’ rare intensities are reduced by the OT from 1286.51 mm to 1348.31 mm by 4.6%. The OT system can effectively limit the story drift ratios of the BMFCT under earthquakes with the lower intensity. With the increasing seismic intensity, the OT presents an unfavorable effect on the lateral deformations. The OT system increases the proportion of damping energy dissipation from 68.28% to 70.24%, and decreases that of plastic deformation energy dissipation from 20.74% to 20.12%, both by less than 2%. The OT system causes the slope of IDA curves to rise first and then fall, which is the opposite of that without OT. The OT system is detrimental to the structural collapse resistance capacity, reducing the collapse margin ratio from 8.46 to 7.41 by about 14%. The OT's function can effectively reduce the cross-sectional dimensions of main components and ensure the architectural functionality and view-transparency. In the seismic design of BMFCT structures, the OT system should be given more attention, especially in the earthquakes stronger than rare intensity, and recommended to be designed to meet the basic structural stiffness requirement and not to provide excessive lateral stiffness resistance.

Seismic design and hybrid simulation test of existing concrete frames upgraded by metallic damper

Concrete frame makes up a large amount of current building structures. Therefore, there is a high need to upgrade the existing frame owing to material aging, cracking and crushing of concrete which significantly decreased the anti-seismic capacity. In this paper, the metallic damper was employed to upgrade the existing concrete frames. An interactive seismic design process was described to properly determine the yield strength of metallic damper of each floor. Two prototype buildings including one existing concrete frame and one existing concrete frame upgraded by metallic damper were selected as research objects. Hybrid simulation tests were performed to observe the seismic performance of prototype buildings, in which the numerical model was established by OpenSEES software and its accuracy was validated against the test results. The side span in the first story of the prototype building was selected as physical substructure. Based on the test results, it indicated that the metallic damper could significantly decrease the story drift of structure and relatively minor damage was detected on the metallic damper upgraded concrete frame compared with pure concrete frame. Typical failure modes and dynamic responses of two substructures were evaluated and discussed. Afterwards, the global responses of two prototype buildings were analyzed to reveal the influence of metallic damper. It suggested that the strength of metallic damper should be 0.4 to 0.6 times the story shear for better decreasing the story drift ratio and dissipating the input seismic energy. The test and analytical results provided a reasonable upgrade method for existing concrete frame under seismic actions.

Damage-based design of multiple tuned mass dampers to improve the seismic performance of steel frame structures

Tuned mass dampers are robust tools that can control the undesired vibrations induced by wind and earthquakes. Although vibration control systems such as tuned mass dampers have been used many times by researchers to reduce roof displacement, story drift ratio, and roof acceleration, no research has been reported regarding the reduction of damage's value in the structure. Therefore, in this paper, a three-bay ten-story steel frame building is modeled using the OpenSees software. The building is excited by an earthquake. The Park-Ang damage index is utilized here as an objective function to determine the optimum TMD numbers and parameters. The optimal numbers and properties of TMD systems are calculated by a hybrid binary and real-coded particle swarm optimization (PSO) algorithm. The results indicate the ability of multiple tuned mass dampers to reduce the overall damage and damage stories' values. The results show that this objective function also decreases the maximum drift ratio, residual displacements, and roof displacements. It will lead to improving the seismic performance of the structure. Also, the results show that the damage values are distributed uniformly along with the structure's height by selecting the appropriate domain for the value of the story's damage. A comparison between the proposed method and the Den-Hartog method shows that the proposed method's ability to improve the structure's seismic performance is greater than the classical methods. It can also be concluded from the results that by optimally adjusting the parameters of the control system, the residual displacement of the roof and the displacement of the roof have been reduced by 68.91% and 66.01%, respectively.

A New Type of Inerter with Easily Adjustable Inertance and Superior Adaptability: Crank Train Inerter

A new type of inerter, called a crank train inerter (CTI), is investigated for structural vibration isolation. The CTI consists of a crank, a linking rod, a gear-pinion box, and a flywheel that generates inertance. It has advantages of quick adjustment of inertance and strong adaptability to other disturbances. First, the inertial force provided by the CTI is linearized and expressed in a simple format; the minimum length of linking rod and crank are obtained for a CTI operating linearly under various deformed configurations. Then, the motion equation of the coupled structure-CTI system is formulated, and transmissibility is analyzed. Laboratory experiments are next carried out to verify the CTI’s mechanical property and vibration isolation performance. It is shown that the inertance of the CTI obtained in the tests agrees well with the analytical result. CTIs can significantly decrease the amplitude-frequency responses at the fundamental frequency but cannot achieve vibration isolation in a full frequency range. Finally, the seismic control effect of base-isolated buildings with and without CTI is numerically studied. An optimal design method of the CTI is proposed, and the story drift ratio and deformation of the isolation layer can be reduced simultaneously with the optimal inertance. The installation methods of CTIs for buildings are also presented.

Quantification of Equivalent Strut Modeling Uncertainty and Its Effects on the Seismic Performance of Masonry Infilled Reinforced Concrete Frames

ABSTRACT Quantifying aleatory and epistemic uncertainty in nonlinear structural response simulation is key to robust performance-based seismic assessments. This paper focuses on the modeling parameters that are used to describe the nonlinear force-deformation response of the equivalent infill struts used in models of reinforced concrete frames with infills. The variability in several parameters is characterized by developing empirical and theoretical multivariate probability distributions based on the deduced-to-predicted ratios derived using data from 113 physical experiments. The effect of the uncertainty in the infill strut modeling parameters on maximum story drift ratios and associated limit state fragility functions is investigated for a 3-story reinforced concrete frame building with infills. Multiple stripe analysis is performed using hazard-consistent ground motions. Relative to when only record-to-record variability is considered, modeling parameter uncertainty has a non-negligible effect on the dispersion of the maximum story drift ratios, and affects both the median and dispersion of the limit state fragilities.

EESD special issue: AI and data‐driven methods in earthquake engineering – (Part 1)

EESD special issue: AI and data‐driven methods in earthquake engineering – (Part 1)

Optimum design and performance of a base-isolated structure with tuned mass negative stiffness inerter damper

In order to increase the efficiency of the structures to resist seismic excitation, combinations of inerter, negative stiffness, and tuned mass damper are used. In the present work, the optimum tuning frequency ratio and damping of the tuned mass negative stiffness damper-inerter (TMNSDI) for the base-isolated structure were determined by employing the numerical searching technique under filtered white-noise earthquake excitation and stationary white noise. The energy dissipation index, the absolute acceleration, and the relative displacement of the isolated structure were considered as the optimum parameters, obtained by their maximization. Evaluations of base-isolated structures with and without TMNSDI under non-stationary seismic excitations were investigated. The efficiency of the optimally designed TMNSDI for isolated flexible structures in controlling seismic responses (pulse-type, and real earthquakes) were evaluated in terms of acceleration and displacement. A dynamic system was used for deriving the tuning frequency and tuned mass negative stiffness damper inerter (TMNSDI) for white noise excitation by using explicit formulae of the curve fitting method. The proposed empirical expressions, for design of base-isolated structures with supplementary TMNSDI, showed lesser error. Fragility curve results and story drift ratio indicate reduction in seismic response by 40% and 70% in base-isolated structure using TMNSDI.

Seismic performance of rocking‐delayed spine frame system with base initial gaps

AbstractThis study proposes a rocking‐delayed spine frame system that provides initial gaps at the side column bases of the spine frame. This system exhibits a trade‐off behavior between the nonuplifting spine system and uplifting‐allowed rocking frame system. The feasibility of the proposed system was verified on 16 specimens using cyclic loading tests. An evaluation of the force–deformation relationship of the proposed system was proposed and verified by comparing it to the test results. The seismic performance of the proposed system was investigated using nonlinear time‐history analysis. The analysis results clarified the initial gap's influence on seismic responses. A trade‐off between the maximum story drift ratio, peak floor acceleration, and maximum shear force of the spine frame was revealed.

Shaking table tests of a full‐scale 10‐story reinforced‐concrete building (2015). Phase II: Seismic resisting system

AbstractA 10‐story reinforced‐concrete (RC) building was subjected to a shaking table test using E‐Defense, the largest three‐dimensional earthquake simulator in the world, to estimate the effects of a flexible foundation and seismic response of a mid‐rise building. Two structural systems with different base supporting conditions were adopted for two phases of tests for comparative purposes: the first system was free‐standing with base sliding and uplifting, and the second was a conventional RC seismic resisting system with a fixed base. This paper mainly reports the test results for the conventional RC seismic resisting system with a fixed base, which comprises a moment‐resisting frame system in the longitudinal direction and a frame system with multistory shear walls in the transverse direction. The objective of this research was to confirm the seismic capacity of a mid‐rise building designed in accordance with current Japanese building standards and guidelines. Even though the story drift ratio exceeded 3% under extreme motion exceeding the design earthquake, the structure remained stable throughout the tests, satisfying the design concept of collapse prevention performance, whereas relatively severe damage was observed in the beam–column joints. Crack observations indicated massive damage sustained by the beam–column joints. The measured shear deformations at the beam–column joints accounted for more than half of the inter‐story drift at the peak response.