Inelastic Displacement Response Research Articles

INELASTIC DISPLACEMENTS MACHINE-LEARNING-BASED ESTIMATIONS FOR THE RC-BUILDINGS SEISMIC DESIGN CONSIDERING SSI EFFECTS

Over the past few decades, scientists have dedicated considerable attention to investigating the impact of soil-structure interaction (SSI) on buildings’ performance. It is now widely recognized that these interaction effects can either positively or negatively influence a building's response to seismic events. Regarding the seismic design of buildings following standard prescriptions and accounting for SSI effects, ASCE 7, for example, guides through the modification process of the design forces obeying the interacting soil-structure system (SSS) behavior in an oversimplified manner. Nevertheless, no recommendations are made for adequately estimating inelastic displacements (IDs) focused on the design process. In an effort to rectify these limitations, this study examines the inelastic displacement response of ductile RC buildings while incorporating the influence of SSI. In that sense, a database of 3D-model structures with varying in-plan and elevation geometries as well as different supporting soil characteristics were generated and later assessed using OpenSeesPy as the modeling and analysis engine. Nonlinear dynamic analyses were executed accounting for flexible-base and fixed-base conditions as per ASCE 41, and their inelastic displacements are used to generate estimation models. The Gradient Boosting Regression Tree (GBRT) technique from machine learning (ML) is used in accomplishing this aim. It was observed that the wave parameter σ, along with the flexible-to-fixed base design shear force ratio, V*, are enough to explain up to 90% of the variation in IDs in the estimation model.

Evaluation of Heating and Buckling Effects on Inelastic Displacement Responses of Lead-Rubber Bearing Subject to Strong Ground Motions

The tendency to use a probabilistic design method rather than a deterministic design method for the design of nuclear power plants (NPPs) will increase because their safety should be considered and strictly controlled in relation to various causes of damage. The distance between a seismically isolated NPP structure and a moat wall is called the clearance to stop. The clearance to stop is obtained from the 90th percentile displacement response of a seismically isolated NPP subject to a beyond design basis earthquake (BDBE) in the probabilistic design method. The purpose of this study is to analyze the effects of heating and buckling effects on the 90th percentile displacement response of a lead-rubber bearing (LRB) subject to a BDBE. The analysis results show that considering the heating and buckling effects to estimate the clearance to stop is conservative in the evaluation of the 90th percentile displacement response. If these two effects are not taken into account in the calculation of the clearance to stop, the underestimation of the clearance to stop causes unexpected damage because of an increase in the collision probability between the moat wall and the seismically isolated NPP.

Seismic assessment of cold-formed steel stud bracing wall panels using direct displacement based design approach

An important advancement in structural engineering in recent years has been the development of performance-based design (PBD). However, its application to cold-formed steel framed buildings remains largely unexplored. This paper presents the assessment of the bracing capacity of cold-formed steel stud bracing wall panels using a direct-displacement based design (DDBD) approach. The fundamentals of DDBD using equivalent damping, and inelastic displacement response spectra approaches are presented. These wall parameters needed for each approach are evaluated from experimental load–deflection response behaviour under quasi-static cyclic loading. Results obtained from the DDBD approach are compared with results from conventional non-linear time history analyses (NLTHA) to confirm the validity of the adopted approach. It is found that results estimated from DDBD method using inelastic displacement response spectra approach correlated much better with NLTHA results than the equivalent damping method.

Equivalent Viscous Damping of Bilinear Hysteretic Oscillators

AbstractAn improved formula to determine the equivalent viscous damping ratio of a single-degree-of-freedom (SDOF) bilinear oscillator is proposed in this paper, which simultaneously considers the influence of the initial period, ductility ratio, and strain hardening ratio. A large number of parameters are considered in order to present comprehensive results. Based on the assumption of secant stiffness, several equivalent linearization approaches are evaluated through parametric analyses. Then, optimization analyses are performed using a genetic algorithm to identify the variation trend of optimal damping ratios. A new formula of an equivalent viscous damping ratio is proposed by nonlinear regression analyses of the optimal damping ratios. Finally, the proposed approach is validated and the results show that the proposed approach leads to better estimates of maximum inelastic displacement response in the entire parameter space considered in this study when compared with other equivalent linearization appr...

지진의 특성주기를 고려한 완만한 곡선형 이력거동시스템의 비탄성 변위비

In order to predict inelastic displacement response without nonlinear dynamic analysis, the equal displacement rule can be used for the structures with longer natural periods than the characteristic period, <TEX>$T_g$</TEX>, of earthquake record. In the period range longer than <TEX>$T_g$</TEX>, peak displacement responses of elastic systems are equal or larger than those of inelastic systems. In the period range shorter than <TEX>$T_g$</TEX>, opposite trend occurs. In the equal displacement rule, it is assumed that peak displacement of inelastic system with longer natural period than <TEX>$T_g$</TEX> equals to that of elastic system with same natural period. The equal displacement rule is very useful for seismic design purpose of structures with longer natural period than <TEX>$T_g$</TEX>. In the period range shorter than <TEX>$T_g$</TEX>, the peak displacement of inelastic system can be simply evaluated from the peak displacement of elastic system by using the inelastic displacement ratio, which is defined as the ratio of the peak inelastic displacement to the peak elastic displacement. Smooth hysteretic behavior is more similar to actual response of real structural system than a piece-wise linear hysteretic behavior such as bilinear or stiffness degrading behaviors. In this paper, the inelastic displacement ratios of the smooth hysteretic behavior system are evaluated for far-fault and near-fault earthquakes. The simple formula of inelastic displacement ratio considering the effect of <TEX>$T_g$</TEX> is proposed.

Inelastic Displacement Response of RC Systems with Cyclic Deterioration—An Energy Approach

Inelastic displacements of reinforced concrete systems are investigated by employing an energy-based approach. A hysteresis model is developed that accounts for stiffness degradation, strength deterioration and pinching. The model is calibrated by using experimental data from literature. Inelastic displacement ratios are calculated under a specific set of ground motion records with long effective durations. The results reveal the importance of deteriorating behavior under long duration excitations, especially for short and medium period structures. The last part of the study is devoted to the introduction of a simple empirical relationship for estimating the inelastic displacement demands of degrading RC structural systems.

Numerical Investigation on the Progressive Collapse Resistance of an RC Building with Brick Infills under Column Loss

Abstract — Interior brick-infill partitions are usually considered as non-structural components and only their weight is accounted for in practical structural design. In this study, their effect on the progressive collapse resistance of an RC building subjected to sudden column loss is investigated. Three notional column loss conditions with four different brick-infill locations are considered. Column-loss response analyses of the RC building with and without brick infills are carried out. Analysis results indicate that the collapse resistance is only slightly influenced by the brick infills due to their brittle failure characteristic. Even so, they may help to reduce the inelastic displacement response under column lo ss. For practical engineering, it is reasonably conservative to only consider the weight of brick-infill partitions in the structural analysis. Keywords — Progressive collapse, column loss, brick-infill partition, compression strut. I. I NTRODUCTION ROGRESSIVE collapse is referred to the phenomenon of widespread propagation of structural failure initiated by local damage. Many practitioners and academic researchers have been engaged in the prevention of progressive collapse since the partial collapse of the Ronan Point apartment building in 1968. Resistance of building structures to progressive collapse has become an important task for the development of structural design codes. It is learned from the history that unexpected abnormal loading is usually the ringleader for a progressive collapse event. Fortunately, the occurrence of a fatal accidental loading is extremely rare as compared to code-specified design loadings. Even so, reliable and simple approaches are undoubtedly required for evaluating the progressive collapse potential of important structures. Detailed step-by-step, linear static analysis procedures have been issued by the US General Service Administration (GSA) [1] and Department of Defense (DoD) [2]. The GSA linear static analysis approach has been applied to evaluate the progressive collapse potential of steel moment frames and RC frames [3-5]. Several analytical studies regarding the progressive collapse

Displacement-Based Design for RC Bridge Columns Based on Chinese Code

A comprehensive study of displacement-based design for reinforced concrete bridge columns is conducted. Section analysis software UC-Fyber is used to analyze the bending moment and curvature performance of columns’ sections, based on this, a new calculation method of target displacement of RC bridge columns is educed. Elastic displacement response spectrum, inelastic displacement response spectrum and inelastic demand spectrum are educed from acceleration spectra of Chinese Code JTG/T B02-01-2008; three simplified methods for displacement demand determination are developed. Example of the displacement-based design of bridge column was studied and checked by dynamic inelastic time-history analysis to clarify the reasonableness of the developed methods. Research shows that target displacement of RC bridge columns is relevant with concrete strength grade, longitudinal reinforcement ratio, height and the section form, etc; equivalent linearization method and inelastic displacement response spectrum method are based on the design response spectrum, could reach the target displacement and consider structure safety requirement; demand spectrum method is a simple and direct way to show design with graphics mode, with deficiency of structure capacity spectrum curve from pushover analysis differing from the reality.

Displacement Reduction Factors for the Design of Medium and Long Period Structures

The estimation of the maximum inelastic displacement response of structures is gaining increasing importance with the development and application of the so-called “Performance-Based Design” (PBD) procedures, in which important performance criteria are directly correlated to the seismic displacement demand. The maximum displacement of a MDOF structure is often estimated using the “equivalent SDOF system” concept, which reduces the problem to the prediction of the maximum inelastic displacement demand of an equivalent SDOF system with characteristics representative of the MDOF structure. This study focuses on the nonlinear response of SDOF systems with medium and long periods (T > 1 s), typical of tall buildings for which PBD is more widely adopted. In particular, the effect of several characteristics on the nonlinear response of the equivalent SDOF is investigated, such as structural period, ground motion spectral shape, sensitivity of spectral shape to damping, and elastic damping ratio. Design equations for the prediction of the max SDOF inelastic displacement accounting for all the identified influencing parameters, and based on the newly introduced Displacement Reduction Factor (DRF) concept, are proposed.

Inelastic displacement demand of bridge columns considering shear-flexure interaction

Reinforced concrete bridge columns exhibit complex hysteretic behavior owing to combined action of shear, bending moment, and axial force under multi-directional seismic shakings. The inelastic displacement of columns can be increased by shear-flexure interaction (SFI). This paper develops a simple yet reliable demand model for estimating the inelastic displacement and ductility based on the nonlinear time history analyses of 24 full-size columns subject to a suite of near-fault ground motions. A coupled hysteretic model is used to simulate the shear-flexure interactive (SFI) behavior of columns and the accumulated material damage during loading reversals, including pinching, strength deterioration, and stiffness softening. Guided by rigorous dimensional analysis, the inelastic displacement responses of bridge columns are presented in dimensionless form showing remarkable order. A dimensionless nonlinearity index is derived taking into account of the column strength, ground motion amplitude, and softening or hardening post-yield behavior. Strong correlation is revealed between the normalized inelastic displacement and the dimensionless structure-to-pulse frequency, the dimensionless nonlinearity index as well as the aspect ratio. Two regressive equations for displacement and ductility demands are proposed and validated against the simulation results. The SFI effects are discussed and included explicitly through the aspect ratio in the proposed model. This study offers a new way to realistically predict the inelastic displacement of columns directly from structural and ground motion characteristics. C.

등가감쇠비를 이용한 역량스펙트럼법에 의한 곡선교의 비탄성지진응답 평가

The capacity spectrum method (CSM), which is known to be an approximate technique for assessing the seismic capacity of an existing structure, was originally proposed for simple building structures that could be modeled as single-degree-of-freedom (SDOF) systems. More recently, however, CSM has increasingly been adopted for assessing most bridge structures, as it has many practical advantages. Some studies on this topic are now being performed, and a few results of these have been presented as ground-breaking research. However, studies have until now been limited to symmetrical straight bridges only. This study evaluates the practical applicability of CSM to the evaluation of irregular curved bridges. For this purpose, the seismic capacities of 3-span prestressed concrete bridges with different subtended angles subjected to some recorded earthquakes are compared with a more refined approach based on nonlinear time history analysis. The results of the study show that when used for curved bridges, CSM induces higher inelastic displacement responses than the actual values, and that the gap between the two becomes larger as the subtended angle increases.

Noniterative Equivalent Linear Method for Evaluation of Existing Structures

The equivalent linear system is one of the approximate methods for estimating the maximum inelastic displacement response of structures in performance-based seismic design and evaluation. Traditionally, the equivalent period and damping of such a system are defined by the ductility ratio (μ=maximum displacement/yield displacement). However, for existing structures, the strength ratio (R=elastic lateral strength/yield lateral strength) is generally known rather than the ductility ratio. If the ductility ratio is used for defining the equivalent period and damping, the maximum inelastic displacement demand of existing structures has to be determined through an iterative procedure until the computed displacement is within an allowable tolerance to the assumed displacement. In addition, it was reported that the existing equivalent linear system may overestimate the maximum inelastic deformation of short-period structures because it is independent of periods of vibration (T). To avoid iteration and improve accuracy, this paper presents results of a comprehensive statistical investigation on the equivalent linearization in which both the equivalent period and damping are defined by strength ratios and periods of vibration. The accuracy of the developed equivalent linear system is also discussed based on a set of 72 recorded earthquake ground motions. In addition to the advantage of noniteration, the recommended equivalent linear system gives good predictions of the mean maximum inelastic displacement of structures for systems with all period ranges.

Effects of hanging wall and forward directivity in the 1999 Chi-Chi earthquake on inelastic displacement response of structures

The characteristics of the inelastic response of structures affected by hanging wall and forward directivity in the 1999 Chi-Chi earthquake are investigated. Inelastic displacement ratios (IDRs) for ground motions impacted by these nearfield effects are evaluated and comprehensively compared to far-field ground motions. In addition, the inelastic displacement responses to hanging wall and footwall ground motions are compared. It is concluded that the inelastic displacement response is significantly affected in the short period range by hanging wall and in the long period range by footwall. Although high peak ground acceleration was observed at hanging wall stations, the IDRs for structures on hanging wall sites are only larger than footwall sites in the very long period range. Forward directivity effects result in larger IDRs for periods longer than about 0.5s. Adopting statistical relationships for IDRs established using far-field ground motions may lead to either overestimation or underestimation in the seismic evaluation of existing structures located in near-field regions, depending on their fundamental vibration periods.

日米の最大級地震動の弾塑性変位応答スペクトルと中低層建物の耐震性について

最大級地震動の弾塑性変位応答スペクトルの特徴を提示して, 建物周期, 復元力特性, 塑性率の各影響度を, 日米の既往の推定式と併せ, 説明するとともに, 建物変形角を抑えるために, 高い降伏強度を与える必要がある中低層建物にっいて, 日米の各耐震設計例を示して, 耐震設計上の留意事項を述べている。

An equivalent linear model of lead-rubber seismic isolation bearings

An equivalent linear model for the seismic analysis of base-isolated bridges with lead-rubber bearings (LRB) is established in this paper using an identification method. Recognizing that the inelastic displacement spectra with constant ductility ratios of an earthquake ground motion can be approximated by the equivalent elastic spectra with appropriate effective period shifts (or effective stiffness) and equivalent damping ratios, the effective stiffness and equivalent damping ratio of lead-rubber isolation bearings are determined based on the identification of the inelastic displacement response spectra of 20 earthquake ground motions. In the identification formulation, a nominal strain hardening ratio of the LRB is used. The proposed equivalent linear model is characterized as a modification of the current equivalent linear model provided by the AASHTO isolation guide specifications so that the proposed model can be readily applied to the practical analysis and design. Numerical comparisons indicate that the proposed model in general can predict comparably accurately with the current practical methods.

Inelastic Response Spectra for Aseismic Building Design

The variability of inelastic response spectra is investigated by time-history analysis using sets of artificial ground motions with different strong-motion durations. It is concluded that the Newmark-Hall inelastic response spectra of elasto-plastic systems are unconservative for 5% damping, and conservative for 2% damping. New inelastic response spectra are proposed for different ductility ratios and damping coefficients. A 10-story steel moment-resisting frame is designed and analyzed to assess the validity of the design procedure based upon modal analysis and inelastic response spectra. The results indicate that at least for this or similar frames, the method is satisfactory. However, the procedure leads to slightly unconservative design for upper-story exterior columns. The study also suggests that the maximum lateral story displacement predicted directly by the SRSS modal analysis using the inelastic displacement response spectrum is too conservative. The conservatism is more pronounced in the upper stories.

Permanent deformations of rigid-plastic structures subject to random dynamic loads

The probabilistic analysis of the inelastic displacement response for simple rigid-plastic structures subject to dynamic loads is considered. The paper presents a method able to approximate the probability density function of the residual displacement at any time t. The procedure is based on the filtered Poisson process theory. This model aims to idealize the input stochastic process (i.e. the loading function) and to describe the output process (i.e. the residual displacement). The extension to elastic-perfectly plastic structures is immediate. Finally a numerical example is developed in order to show the computational aspects of the method.