Inter-story Drift Ratio Research Articles

Effective range of base isolation design parameters to improve structural performance under far and near-fault earthquakes

Triple Friction Pendulum Isolators (TFPIs) have been widely used to enhance the seismic capacity of structures in the recent decade. This study intends to measure the effect of different Ground Motion (GM) sets, including Far-Fault (FF) and Near-Fault (NF) records, on the seismic response of the Triple Friction Pendulum (TFP) isolated structures. For this aim, different Engineering Demand Parameters (EDP), including Inter-story Drift Ratio (IDR), absolute floor acceleration, base shear, residual displacement, and damage energy are measured using numerous Nonlinear Time History (NTH) analyses. A three-dimensional mid-rise special moment resisting frames (SMFs) steel building isolated with TFPIs has been designed as per ASCE 7-16. In addition, the separate and simultaneous effect of raising the damping ([Formula: see text]) and the period ([Formula: see text]) of the base isolation system on the seismic responses of the superstructure are measured to assess the structural performance and estimate the damage energy. The [Formula: see text] and the [Formula: see text] are amplified up to 30% and 4.5 times of the superstructure period in incremental steps, respectively. The results show that the damage energy of the superstructure in the Initial Design Parameters' Values (IDPVs) of the isolator under NF records with Forward-Directivity pulses (NF-FD-GMs) is more significant than damping energy, while an inverse trend has occurred for other GM sets. Increasing the IDPVs up to a certain level reduces most EDPs and consequently causes an improvement in the seismic performance of the superstructure. The novel developed empirical relationships can be utilized as useful tools to predict IDRs and the damage states of the superstructure. The variations of the EDPs with respect to simultaneous or separate increasing the IDPVs are also reported for different GM sets.

Seismic vulnerability analysis for shallow-buried underground frame structure considering 18 existing subway stations

The variability of structural engineering parameters is not accounted for in available literature on seismic vulnerability of underground frame structures. This study investigates the seismic vulnerability of 18 existing subway stations with different site condition, structural stiffness, reinforcement ratio and buried depth employing two-dimensional (2D) finite element analysis considering soil-structure interaction. The peaks of structure inter-story drift ratio under different earthquake intensity of different ground motion records are obtained from non-linear dynamic time-history analysis. Taking the inter-story drift ratio as the damage measure (DM) and the peak ground acceleration (PGA) as the ground motion intensity measure (IM), the seismic vulnerability curves of 18 subway stations are constructed. The comparison of seismic fragility curves of different subway stations demonstrates that site conditions are critical to the post-earthquake structure probability of failure. Furthermore, representative seismic fragility curves are established based on the data collected form the computed results of 18 subway stations, which can aid in evaluating the seismic performance of existing urban underground frame structures in China. The results of this study can provide reference for the performance-based seismic design of urban underground frame structures.

A generalized hybrid model considering earthquake-induced internal force distribution rules for super high-rise frame-core tube structures

To efficiently control of the stiffnesses of the two sub-systems, i.e., the frame part and core tube part, of the frame core-tube structure commonly-used in super high-rise buildings, via the distributions of story shear force ratio and overturning moment ratio, as well as elastic inter-story drift ratio, a generalized hybrid model (GHM) is developed in which the feature of the flexure-shear coupled model (FSM) and the modified rocking model (SSM) has been integrated. It can be transformed into the FSM and SSM in some specific cases. The dynamic properties of the GHM are obtained in a semi-analytical way with the assistance of the analytical solution for the free vibration of the FSM and the analytically generated rotational stiffness matrix using the force method. To calibrate the four parameters, η, μ, α and (EIT)0, associated with the GHM, the corresponding stiffness-based calibration indexes of T1, T2/T1, RV-1 and RM-1 are selected. The trust-regional-dogleg algorithm is adopted to solve the nonlinear equations consisting of the model parameters and targeted indexes. The effectiveness and applicability of the GHM are demonstrated from the case study on a series of finite element models with different parameters, from the aspects of the distributions of the inter-story drift ratios, the story shear force ratios and overturning moment ratios, as well as the vibration periods and modal mass participation coefficients. The two distribution ratios are observed to be controlled efficiently by adjusting the ratios of the shear stiffness of the frame and the axial stiffness of the frame column to the flexural stiffness of the core tube, respectively.

Seismic Performance Target and Fragility of Masonry Infilled RC Frames under In-Plane Loading

Masonry infilled RC frames are one of the most common structural forms, the damage of which, in earthquake events, usually cause serious losses. The determination of the seismic performance target is the key foundation of performance-based seismic evaluation and design for masonry infilled RC frames. In this paper, an extensive database of experimental tests on infilled RC frames loaded in an in-plane direction is collated. According to the crack propagation and elastic-plastic characteristics of infilled RC frames, the damage process is divided into four stages, and then the criteria of the damage states (DS) are proposed. In addition, the seismic performance targets expressed as inter-story drift ratio (IDR) for the four stages are suggested, which would support the performance-based in-plane seismic analysis of infilled RC frames. Finally, the proposed in-plane seismic performance target is utilized to analyze the fragility of two masonry infilled RC frame structures.

Reliability Analysis of Response-Controlled Buildings Using Fragility Curves

The number of buildings with passive control systems is steadily growing worldwide. For this reason, this study focuses on the reliability analysis of these systems employing fragility curves. The structural performance evaluation is obtained for a 10-story steel building with two different sections (trimmed and conventional). The trimmed section of the building was evaluated with hysteresis and oil dampers, while the conventional section of the building was evaluated without damper. The fragility curves were obtained from the incremental dynamic analysis using 20 ground motion records. Spectral acceleration response at the fundamental period of the building was considered and used as the intensity measure for the ground motion records. The maximum inter-story drift ratio of the building was employed as the damage measure. In addition, the seismic energy absorption rate was compared between hysteresis and oil dampers. As a result, hysteresis dampers were found to be more effective for high ground motion intensities. On the other hand, the oil damper dissipates energy immediately, even for low ground motion intensities. Furthermore, the combination of different types of dampers improved the seismic performance of the trimmed section of the building to almost the same level as the conventional section of the building. Eventually, a combination of hysteresis and oil dampers in a building is suggested to improve structural performance.

Effects of gaps on the seismic performance of traditional timber frames with straight mortise-tenon joint: Experimental tests, energy dissipation mechanism and hysteretic model

The gaps are very common in the mortise-tenon (M-T) joints of the column-frame layer for the existing ancient timber buildings, which severely threaten the whole stability and safety of the structures. To study the effects of gaps on the seismic performance of traditional timber frames with straight M-T joint. Three 1/3.2-scaled straight M-T jointed timber frames, including one intact timber frame as a contrast and two timber frames with different gaps, were fabricated using Pinus sylvestris logs, and subjected them to reversed cyclic loading tests in strict accordance with the international test standard ISO-16670. The failure modes, load-displacement hysteretic response, strength, initial elastic stiffness, ductility, and stiffness degradation of the specimens were analyzed. The energy dissipation mechanisms of the timber frames with different gaps were evaluated, based on the law of energy conservation. Results indicated that the strength, initial elastic stiffness, and hysteretic energy dissipation capacity of the timber frames with gaps decreased significantly with increasing damaged degree. The gap can weaken the ductility of the timber frame, however, the inter-story drift ratio of the timber frame with gap can reached 0.16, indicating good deformation capacity. The gap had little effect on the degradation degree of the residual stiffness of the timber frame under large displacement amplitude. When the damage degree was 10%, under large displacement amplitude, the hysteretic energy consumption, elastic strain energy, and gravitational potential energy of the timber frame approximately accounted for 54%, 16%, and 30% of the total input energy, respectively. Based on the experimental results, the empirical formulas related to key cyclic performance parameters, considering the gap effects, were established. Based on the empirical relationships of the key hysteretic parameters of the timber frame with gaps, an improved hysteretic model for a timber frame with a gap was proposed and also validated. Good agreement between the model predictions and experimental results was observed.

Seismic performance quantification of buckling-restrained steel plate shear wall-RC frame structures

The beam-connected buckling-restrained steel plate shear wall (SPSW) has the advantages of high bearing capacity, strong energy dissipation and good ductility, and flexible arrangement in the structure, which can reduce the force acting on the frame columns and avoid premature failure of the frame columns. To determine the SPSW configuration in structures to fully exploit the seismic performance, a plastic design method of the steel plate shear wall-RC frame structure (SPSW-RCF) was proposed based on energy balance in this paper. The expected global failure mechanism was constructed and the double lateral resistance SPSW-RCF system was decomposed into SPSW system and RC frame system by using shear force ratio. The design base shear was calculated based on the energy balance principle to determine the design lateral story shear forces of the SPSW and RC frame systems, and then the design of SPSWs could be completed. Considering the post-yield behavior of SPSWs and the plastic internal force distribution mechanism, internal forces of beams and columns were calculated, and then the design of the RCF could be completed. 56 SPSW-RCF structures with different story numbers and story shear ratios were designed, SPSW thickness and reinforcements of the SPSW-RCF were compared. By performing the nonlinear dynamic analysis under 22 ground motions, the maximum interstory drift ratios, SPSW maximum displacement ductility, yield mechanism, residual drift ratio and story shear ratio of structures with different story numbers and story shear ratios were comparatively investigated. Furthermore, the actual SPSW-resisted story shear ratio was quantified and the recommended design SPSW-resisted story shear ratio was suggested.

Seismic behavior of linked column system as a steel lateral force resisting system

In previous research, the seismic behavior of linked column frame (LCF) system as a dual structural steel frame system that Consists of the primary linked column (LC) and the secondary moment frame (MF) systems has been evaluated. In this research, based on the high capacity of the linked column system in lateral load resisting, this system has been used as the only lateral load resisting system in the building frame. Studies have shown that this approach not only eliminates the main disadvantages of the LCF system, but also preserves the ability to repair structures after an earthquake. Therefore, the designed models of the linked column system have been evaluated using nonlinear static pushover analysis, nonlinear dynamic time history analysis, incremental dynamic analysis and endurance time method analysis. In the evaluation of the seismic behavior of the linked column system, design approach, structural stability and collapse mechanism, ductility, the seismic performance factors of response modification coefficient (R), overstrength factor (Ω0) and deflection amplification factor (Cd), the values of interstory drift ratio at the DBE and MCE seismic hazard levels, maximum seismic capacity and fragility curves, permanent displacement after the earthquake and the weight of steel used in the structure have been investigated. Each of the analysis results shows that the linked column system has a suitable seismic behavior against earthquakes. Therefore, in a preliminary evaluation, the linked column system is introduced as a steel lateral load resisting system that provides the ability to repair structures after an earthquake.

A steel hysteretic damper for seismic design and retrofit of precast portal frames

In this paper a steel hysteretic damper is proposed which can be installed at the beam-column joint of precast concrete structures and can greatly improve the seismic performance of these structures. The damper is made of a few steel plates with reduced sections placed in parallel, which yield under in-plane bending caused by joint rotation and dissipate energy induced by seismic activity. As less attention has been paid to seismic performance evaluation and design of precast portal frames, a procedure for design and performance estimation is established based on the available theoretical formulation and is verified by comparing their results with those obtained by analysis. The efficiency of the proposed damper is investigated by retrofitting a portal frame and evaluating its seismic performance before and after retrofit. The results show that the developed damper can significantly reduce the maximum interstory drift ratio and prevent the global collapse of the structure, which is of particular interest in practice. The hysteretic behavior and the energy dissipation capability of the frame are compared before and after the retrofit. It is observed that most of the seismic energy is dissipated by the dampers installed in the retrofitted frame, which protects the frame against seismic damage.

Seismic Performance Evaluation of Damaged Ancient Timber Structures with Looseness Mortise-Tenon Joints

ABSTRACT In order to investigate the seismic performance of damaged ancient timber structures with looseness mortise-tenon joints, the shaking table test of an intact ancient timber structure was carried out. The experimental model’s failure modes, main modal parameters, and dynamic response curves were investigated. In addition, the finite element models (FEMs) with looseness mortise-tennon joints were built by OpenSees, and the natural periods, acceleration, and displacement time history curves of intact FEM and experimental model are compared. Moreover, incremental dynamic analysis (IDA) of damaged models was performed, where the ground peak acceleration (PGA) and maximum inter-story drift ratio θ max are taken as intensity measure (IM) and damage measure (DM) of the motions of the ground, respectively. The seismic fragility of damaged models was studied by probabilistic seismic demand analysis to evaluate the seismic performance of the damaged structures from the perspective of probabilistic.

Experimental investigation of a new self-centering shear wall with resilient hinge devices

In order to reduce the residual displacement of building structures caused by the damage on the reinforced concrete shear wall, this study develops a novel self-centering shear wall with resilient hinge devices. One device and three wall specimens are designed, and their hysteretic performance is investigated under low cyclic loading tests. The resilient hinge device which uses disc springs as the spring system is essentially a self-centering axial loaded device with an asymmetric flag-shaped hysteretic response. The experimental results demonstrate that the novel wall exhibits symmetrical flag-shaped hysteretic behavior and has a high self-centering performance. Its residual inter-story drift ratio is only 0.58% at a loading inter-story drift ratio reaching 3%. Compared with the conventional wall, the proposed self-centering shear wall has less wallboard damage, 10% degradation in peak bearing capacity, at least 50% improvement in deformation capacity, 26% degradation in equivalent viscous damping ratio, and 70% increase in total energy dissipation.

Engineering demand parameters for the definition of the collapse limit state for code-conforming reinforced concrete buildings

This article discusses the main Engineering Demand Parameters (EDPs) found in the literature to define collapse of newly constructed reinforced concrete buildings. Currently, the definition of building collapse is still under debate, as different building codes and authors define them with different EDPs and even different values of the same EDPs.The EDPs can be defined locally (chord rotation, Local Damage Index, etc.) or globally (Inter-Story Drift Ratio, Roof Drift Ratio, Global Damage Index, etc.). A modified Global Damage Index that considers damage in both structural and non-structural elements is proposed in this paper The study compares the outcomes of some of these EDPs when applied to two case study moment-resisting reinforced concrete frames designed and analyzed in the framework of the RINTC — Reluis Project funded by the Italian Civil Protection Department (Ricci et al., 2018). One is a 6-story buildings (in Naples) the other a 9-story building (in L’Aquila). Nonlinear static and multiple-stripe dynamic analyses were carried out on 3D models with concentrated hinges. In addition to the above mentioned EDPs this study proposes and tests a new economic EDP that assumes that collapse is reached when the repair costs become larger than the reconstruction costs. Complete validation of the proposed economic EDP requires additional testing on code-conforming and, most importantly, on non-conforming older buildings, where brittle failures become an important issue.

Numerical simulation of irregular section underground structure shaking table test model

Based on the the large shaking table test results on irregular section subway station structure in soft soil, an overall time-history numerical simulation is conducted to study the nonlinear dynamic interaction of the soil-irregular underground structure. Typical test results, including the acceleration of the soil, acceleration, and deformation of the structure, were analyzed. Satisfactory consistency between the simulation and test results is verified, and the difference between these results was discussed in detail. The maximum inter-story drift ratio was approximately 1/472 under input PGA ​= ​0.54 g. The strain responses of columns were significantly larger than those of the side walls and slabs. The components in the lower layers of the irregular subway station structure, particularly in the central columns, underwent cumulative damage. The research results could provide a simplified analysis method to quantitatively evaluate the damage of irregular underground structures in soft soil.

A simplified ductility-based design procedure for seismic retrofit of structures using hysteretic devices

The main aim of this study is to derive a simple ductility-based seismic retrofit procedure for buildings using hysteretic devices. In the procedure it is tried to minimize the assumptions while taking more details into consideration compared to previous approaches. With an available seismic retrofit device, the proposed procedure distributes the devices along the height of the structure to satisfy a given performance limit state through a numerical iterative method. The pushover curve and the modal characteristics of the structure are the only required input parameters, and the estimation of the pushover curve after retrofit, its modal characteristics, and maximum interstory drift ratios are byproducts of this procedure. The derived method was applied to seismic retrofit of a case study structure using buckling-restrained braces. The structure was designed to meet the enhanced performance objective of the 1% maximum drift ratio under the Maximum Considered Earthquake level. The nonlinear time history analysis of the structure subjected to 22 pairs of earthquake records showed that the median of the drift ratio demand is 0.8%, satisfying the given limit state. The results show that the proposed procedure can be implemented efficiently in estimating the required amount of seismic retrofit devices and the structural behavior after retrofit.

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

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

Amplitude scaling of ground motions as a potential source of bias: Large‐scale investigations on structural drifts

AbstractThe question of whether amplitude scaling of ground motion (GM) records introduces bias is controversial in earthquake engineering. In this study, this research question is formally defined with a focus on evaluating bias in determining an engineering demand parameter (EDP) as a result of nonlinear response history analyses (NLRHA) when using scaled rather than unscaled GM that have the same level of intensity. The analysed structures are 10 planar steel frame buildings ranging from low‐ to high‐rise, where the EDP of interest is the maximum interstory drift ratio, while the structural responses range from linear to collapse. A unique contribution is the depth of the research, which employs an unprecedented number of more than 17,000 recorded GM, resulting in approximately 3.4 million NLRHA. For a thorough investigation, the most relevant intensity measures are discussed and considered, as well as novel spectral information describing the sustained vibration amplitude. The introduction of bias is examined from different points of view, using first simple and intuitive statistical methods, then machine learning techniques, and finally a novel GM selection approach. In the numerous investigations, no bias could be detected under the inherent uncertainty of the calculations. The results indicate that scaled records can be safely used in NLRHA to assess the seismic structural behaviour if spectral and scenario compatibility are ensured and it is verified that the sustained amplitude is also consistent.

Intelligent design method for beam and slab of shear wall structure based on deep learning

Beam and slab design is a critical component of shear wall structure design. Currently, conventional manual design is time-consuming, and defining objective functions and design variables of an optimization design is challenging. In contrast, deep learning methods can learn high-dimensional image features and generate new designs, providing new solutions for efficient and intelligent structural design. Therefore, based on deep neural networks, this study proposes an intelligent layout design method for beams of reinforced concrete shear-wall structures using the input of fused building space and element attributes. This method learned the implicit laws of existing designs and realized the inferential generation of new layout schemes. Subsequently, based on mathematical statistics, methods to determine the type and size of coupling and frame beams are proposed. A typical case study shows that the structural performance of the beam and slab designed by this method was comparable to that of competent engineers. The maximum inter-story drift ratio of the result designed by the proposed method differs from that designed by engineers by no more than 5 × 10−5. The differences in the maximum vertical typical-floor-slab displacement, the concrete consumption, and the steel consumption between the design result of the proposed method and the engineer's design result are 0.8%, 2.88%, and 6.20%, respectively. Moreover, the design efficiency was significantly improved by more than 30 times.

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

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

Genetic Algorithm for Optimal Placement of Steel Plate Shear Walls for Steel Frames

Frame structures equipped with steel plate shear walls (SPSWs) have been widely used in high-rise buildings due to their good seismic performance. In this study, the strip model and combined strip model were used to analyze the performance of SPSWs. Furthermore, an improved genetic algorithm (IGA) was established to optimize the steel frame for 5, 10, and 20 stories. For each layer, layout optimization was conducted to determine the best configurations of the SPSWs, and two cases of size optimizations of conventional SPSW configurations in the frame were conducted. Results indicate the following: (i) the total weight of the five-story steel frame of layout optimization to determine the best SPSW configuration was approximately 10% lighter than those of the size optimization of conventional SPSW configurations, and this proportion gap expanded to approximately 15–25% for the 10-story and 20-story steel frames; (ii) the steel frame weight could be significantly reduced if the average percentages of story shear resisted by web plates are increased; and (iii) in the steel frame of layout optimization, the structural elements, especially the plate elements, were better utilized than those of size optimization when their inter-story drift ratios met the specification requirements. These results highlight the prominent performances of some important indicators of the design of an SPSW system with the layout optimized using IGA.

Large scale loss assessment using stick-it model: A comparison with actual cost data

The estimation of expected seismic losses at regional scale represents a critical issue for the assessment of the seismic risk and for the evaluation of the seismic resilience of large communities. In a performance-based approach, the assessment of economic losses requires the computation of the building performances in terms of engineering demand parameters such as interstory drift ratios and peak floor accelerations in order to assess the distribution and the extent of the damage experienced by various building components. The Stick-IT model (Stick for Infilled frames Typologies) was recently proposed to predict the response, in terms of engineering demand parameters, for infilled RC building typologies. The Stick-IT is a MDOF system consisting of a series of lumped masses connected by nonlinear shear link elements. The model parameters can be defined for building typologies starting from low-level information that can be easily retrieved at the large scale via image-based processing techniques integrated with information about typical construction features, such as in plan dimensions, the number of stories or the percentage of infills openings and considering the infills consistency.This paper adopts the Stick-IT model within a probabilistic framework to predict damage and expected losses for a set of residential buildings located in L'Aquila town that suffered damage during the 2009 L'Aquila earthquake. By comparing the predicted losses with the actual repair costs, the application shows the advantages and the potentiality of the proposed model when adopted for large scale loss assessments.