Inelastic Seismic Response Research Articles

Numerical artifacts associated with Rayleigh and modal damping models of inelastic structures with massless coordinates

SummaryThe paper presents a detailed reexamination of the effects of three damping models on the inelastic seismic response of structures with massless degrees of freedom. The models considered correspond to (a) Rayleigh damping based on current properties (tangent stiffness), (b) Rayleigh damping based on initial properties, and (c) modal damping. The results suggest that some nonzero damping forces/moments at massless DOFs obtained in multistory frames for the case of Rayleigh damping with tangent stiffness may be numerical artifacts rather than a deficiency of the damping model. The results also indicate that significant artificial numerical oscillations in the velocities of the secondary components of MDOF structures are introduced when modal damping or mass‐proportional damping is used.

Effect of site amplification on inelastic seismic response

The available models for effective periods of site and structure are reviewed in context of frequency tuning in the inelastic seismic response of soil-structure system. The effect of seismic intensity and ductility demand, on the effective periods, is investigated, and inelastic site amplification is shown to be strongly correlated to the normalized effective period. Two non-dimensional parameters, analogous to the conventional site amplification factors in codes, are defined to quantify the inelastic site amplification. It is shown that the inelastic site amplification factor (i.e. ratio of constant ductility spectral ordinates at soil site to those at rock outcrop) is able to represent the site effects more clearly, as compared to the inelastic site amplification ratio (i.e. ratio of inelastic spectral ordinates at soil site to the corresponding elastic spectral ordinates at rock outcrop). Further, the peak in the amplification factor corresponding to the effective site period diminishes rapidly with increasing ductility demand.

Optimal design of multiple damped-outrigger system incorporating buckling-restrained braces

The outrigger system is an effective solution in mitigating seismic responses of core-tube-type tall buildings by mobilizing the axial stiffness of the perimeter columns. The concept of damped-outrigger has been proposed which introduces dampers in the outrigger system to dissipate seismic energy. This study investigates the seismic behavior of a damped-outrigger system incorporating buckling-restrained brace (BRB-outrigger). The outrigger effect combined with the energy dissipation mechanism of the buckling-restrained brace (BRB) effectively reduce the seismic response of the building. This study proposes the methods to evaluate the inelastic seismic response of structures with multiple damped-outriggers based on a spectral analysis (SA) procedure. For the structure with BRB-outriggers, the optimal outrigger elevations, and the relationships between the axial stiffness of the BRB, the axial stiffness of the perimeter column, and the flexural rigidity of the core structure in order to minimize the seismic response are the primary research objectives of this study. Analytical models with building heights of 64 m, 128 m, 256 m, and 384 m are used to perform the SA and the nonlinear response history analysis. This study concludes with a design recommendation for preliminary design purposes.

Responses and capacity curves of mid- and high-rise wood buildings subjected to seismic excitations

The design and modelling of 10-, 15-, and 20-storey wood buildings with cross-laminated timber and glulam structural members are presented in the present study. The system is platform-type construction with a cross-laminated timber core, perimeter walls as lateral load resisting system, and glulam columns as the gravity system. The designed buildings satisfy requirements stipulated in applicable design codes in Canada. The hysteretic models and the associated parameters used to model the fasteners for wood members are developed. Assessments of the nonlinear inelastic seismic responses and capacity curves of the designed buildings are carried out using the incremental dynamic analysis (IDA) and nonlinear static pushover analysis (NSPA) methods. The results indicate that the NSPA curve closely approximates the mean capacity curve estimated using the IDA curves for wood buildings. The post-yield stiffness ratio to initial stiffness for the wood buildings ranges from approximately 0.35 to 0.55. The results also show that the effect of the record-to-record variability on the IDA curves is substantial.

Estimating inelastic seismic response of reinforced concrete frame structures using a wavelet support vector machine and an artificial neural network

Modern building codes increasingly enforce evaluating the inelastic response of structures to ensure their safety in major seismic events. Although an inelastic dynamic analysis provides the most realistic and accurate measure for the seismic response, its application for large-scale structures is hampered by the excessive computational burden involved. This is particularly the case for the optimization of inelastic structures subjected to dynamic loads using metaheuristic algorithms where numerous analyses are required before the design converges to the optimum. In this regard, developing predictive models with sufficient accuracy will significantly help to reduce the computational demand, thus making the seismic analysis and optimization of large structures more feasible and common practice. Motivated by this need, this paper reports a study on the capabilities of a wavelet weighted least squares support vector machine (WWLSSVM) and a feedforward, backpropagation artificial neural network (ANN) to accurately predict the inelastic seismic responses of structures. The force- and displacement-based seismic responses of an 18-story reinforced concrete frame subjected to different earthquake ground motion records scaled to the design basis earthquake and maximum considered earthquake levels are used to train the models and examine their accuracies. The first three natural periods of the frame and combinations thereof are considered as the inputs for the model. The results indicate that both models exhibit satisfactory prediction performances, with the ANN model having a slight edge on accuracy in most of the cases studied, especially when a smaller number of samples are used for training. A parametric sensitivity analysis shows that the seismic responses predicted by the ANN model generally exhibit less sensitivity to the inputs than do those predicted by the WWLSSVM model. The results also indicate that force- and displacement-based responses exhibit the highest sensitivity to the first and second natural periods, respectively.

Seismic performance assessment of different fibers reinforced concrete columns using incremental dynamic analysis

Different fiber-reinforced concrete (FRC) has been widely used in the recent decades, which can improve the mechanical behavior and dynamic performance of reinforced concrete (RC) columns remarkably. This paper aims to compare the seismic behavior of columns constructed with different FRC material, namely steel fibers reinforced concrete (SFRC), polypropylene fibers reinforced concrete (PFRC) and steel-polypropylene hybrid fiber reinforced concrete (HySPFRC). 3-D nonlinear finite element models have been built to represent the seismic behavior of different FRC columns, which are calibrated with the available experimental results of quasi-static tests. The seismic capacity of bridge columns with different FRC material are assessed based on four flexural damage states through the nonlinear static pushover analysis, such as a) yielding of longitudinal steels; b) core concrete crushing; c) buckling and d) fracture of longitudinal of steels. Incremental dynamic analyses (IDA) are conducted using the selected suite of 20 near-fault as-recorded ground motions to evaluate the inelastic seismic responses of different bridge columns. IDA curves are generated based on the intensity measure, namely peak ground acceleration (PGA) in this paper and seismic demands (i.e. maximum drift, residual drift, displacement ductility and curvature ductility) through nonlinear dynamic time-history analysis. It can be concluded from the IDA results that the SFRC, PFRC and HySPFRC are all effective to enhance the seismic performance, thus reducing the anticipated damage of the bridge columns. Moreover, SFRC and HySPFRC are more effective to improve the seismic capacity of bridge columns for the slight and moderate damage states, while PFRC and HySPFRC are more effective at the extensive and complete damage states.

A Simple Analysis Method for Estimation of Required Damping Ratio for Seismic Response Reduction

This paper proposes a simple analysis method to estimate the additional damping ratio required to achieve a target seismic performance level. The proposed method employs the Newmark and Hall′s design response spectrum and the simple version of the N2 method. With the help of combining the characteristic of the two methods, it is possible to approximately estimate additional damping ratios required to achieve target elastic or inelastic seismic responses of a building structure without iteration. To examine the validity and effective range of the proposed method, time history response analysis is conducted, and the results are compared with those of a numerical analysis in which the post-yield stiffness ratio is considered. The analytical results show that the post-yield stiffness ratio and the yield displacement are important factors that affect the validity of the proposed analysis method; it is also found that the proposed simple analysis procedure may be quite efficient in evaluating the performance point and the damping requirements for seismic response reduction of building structures.

An accurate algorithm of numerical integration for computing seismic responses of inelastic structures

The paper proposes an algorithm that makes numerical integrations with conditions for stability to be usable for computing inelastic seismic responses of structures. The numerical integrations with conditions cannot be applied to solving directly the equation of the motion, but the numerical integrations utilized for linear problems generally give exacter responses than that without any conditions. The method of modal analysis can clear the condition by applying the eigenvalue analysis to the equation of the motion expressed by the tangent stiffness in the inelasticity. The paper shows considerable difference between the result by the numerical integration with conditions and that without any condition, and the former result will be exacter than the latter from several proofs in the discussion

Inelastic seismic response of torsionally unbalanced structures with soft first story

The objective of this paper is to investigate the influence of the coupling of torsional and soft-first-story effects to the seismic behavior of reinforced concrete frame buildings. For this purpose, several structural models, considering the variation of structural stiffness in the plane of each story and over the height of the structure, were generated. The effect of masonry infills non-uniformly distributed in plan was also examined. Each model was subjected to six strong ground motions acting, simultaneously, in two orthogonal directions. Inelastic dynamic analysis was performed. Results from 708 cases were exanimated, and useful conclusions concerning the inelastic response are derived.

Damage Index Distributions in RC Dual Lateral Load-Resistant Multi-Story Buildings Considering SSI Effects Under Bidirectional Earthquakes

Inelastic seismic responses of flexibly supported reinforced concrete (RC) moment-resisting frames representing short-to-tall structures stiffened with ductile RC structural walls were evaluated considering both far-field and near-field ground motions. A dual shear wall-frame resisting system with symmetric reference plan was created by adding shear walls into excitation direction of the three-dimensional frames developed by generic structure algorithm. The current study also aims to take into account soil–structure interaction effects in to damage assessment of multi-story RC buildings in terms of ductility demand, damage index, story shear force and overturning moment, as well as kinetic energy profile over the structure height. In doing so, the developed set of generic frames was considered accounting for different values of story strength, stiffness distribution and number of stories. A realistic modeling of nonlinear ductile behavior of RC elements was developed in combination with the sub-structuring method to consider the foundation flexibility in nonlinear seismic responses. Conducting a parametric study through nonlinear static analyses (pushover) as well as nonlinear response history analyses, the results indicated that the near-field ground motion presents much more damage than the far-field one. Inelastic dynamic responses to near-field records demonstrated that structures with a fundamental period greater than the pulse period respond differently from those that have shorter periods. The results were also presented as charts and tables that provide helpful information for engineering design purposes such as damage assessment of multi-story RC buildings with specific fundamental natural period and base shear strength.

Seismic response analysis of reinforced concrete frames using inelasticity‐separated fiber beam‐column model

SummaryEvaluating the inelastic seismic response of structures accurately is of great importance in earthquake engineering and generally requires refined simulation, which is a time‐consuming process. Because the material nonlinearity generally occurs in a small part of the whole structure, many researches focus on taking advantage of this characteristic to improve the computational efficiency and the inelasticity‐separated finite element method (IS‐FEM) proposed recently provide a generic finite element formulation for solving this kind of problems efficiently. Although the fiber beam‐column element is widely used for the simulation of reinforced concrete (RC) framed structures, the inelastic deformation is often detected in a large part of the numerical model under earthquake excitation so that it is hard to achieve high efficient computation when applying the IS‐FEM to the inelastic response analysis of RC fiber models directly. In this paper, a new numerical scheme for seismic response analysis of RC framed structures model by fiber beam‐column element is proposed based on the IS‐FEM. To implement the RC fiber model for use in IS‐FEM and improve the computational performance of proposed scheme, a method of identifying the local domains with severe section inelasticity level is proposed and a modified Kent‐Park concrete material model is developed. Because the Woodbury formula is adopted as the solver, the global stiffness matrix can keep unchanged throughout the analysis and the main computational effort is only invested on a small matrix representing local inelastic behavior. The numerical examples demonstrate the validity and efficiency of the proposed scheme.

Inelastic Parametric Analysis of Seismic Responses of Multistorey Bidirectional Eccentric Structure

This paper conducts a parametric study on the seismic response of multistorey bidirectional eccentric structures from elastic stage to inelastic stage. Based on a simplified multistorey bidirectional eccentric model composed of bidirectional lateral load‐resisting members, a general law is proposed for three‐stage natural frequency variation behaviour from elastic stage to inelastic stage of eccentric frame structures with different layers. Different simplification treatments are conducted on each stage and the three stable parameter analysis stages are defined. The corresponding dynamic stiffness matrices and motion equations in different loading stages are derived. On this basis, a parametric analysis of seismic response of a three‐storey bidirectional regular eccentric structure from elastic stage to inelastic stage is conducted. Effects of the uncoupled torsion to lateral frequency ratios (Ω) and bidirectional eccentricities on the seismic responses are investigated. The results reveal that as Ω increases, translational displacement in the load direction first decreases and then increases; meanwhile, the displacement perpendicular to load direction and torsion displacement first rise and then decrease sharply. When Ω = 1.1, the coupling effect between the translation in the load direction and the torsion is at its strongest condition. Increasing the eccentricities leads to a decrease in the displacement in the load direction as well as an increase in the displacement perpendicular to load direction and torsion displacement. Variation regularity of inelastic seismic response is remarkably different from that in elastic stage. The lateral‐torsional coupling effect of the bidirectional eccentric structure is closely related to both the period ratio and the bidirectional eccentricities.

Functional Model to Estimate the Inelastic Displacement Ratio

Abstract In this paper a functional model to estimate the inelastic displacement ratio as a function of the ductility factor is presented. The coefficients of the functional model are approximated using nonlinear regression. The used data is in the form of computed displacement for an inelastic single degree of freedom system with a fixed ductility factor. The inelastic seismic response spectra of constant ductility factors are used for generating data. A method for selecting ground-motions that have similar frequency content to that of the ones picked for the comparison is presented. The variability of the seismic response of nonlinear single degree of freedom systems with different hysteretic behavior is presented.

Damage-Based Inelastic Seismic Spectra

Current inelastic seismic spectra suffer from a conceptual limitation: they are significant only on the maximum demand of ductility and they do not include any influence of the number of response cycles, yield excursions, stiffness and strength degradation and damage potential to structures. This paper presents a stochastic approach for obtaining damage-based inelastic seismic spectra. In order to consider the cumulative damage phenomenon in structural systems under strong ground motions, the authors adopt the Park and Ang damage model that includes the displacement ductility and the hysteretic energy. The novelty is that the peak theory of random processes is adopted to achieve damage-based seismic spectra. This approach has some advantages compared with the standard statistical approaches based on a large number of recorded accelerograms. First, it drastically reduces the computational effort, while allowing us to typify the seismic motion by some parameters such as the frequency content, peak acceleration, energy content and strong motion duration, i.e. all the parameters that affect the structural response under seismic actions. Besides, it allows to obtain the following stochastic inelastic seismic response spectra: damage-based (i) displacement and acceleration inelastic spectra, (ii) response modification factor spectra, (iii) yield strength demand spectra, and (iv) damage-based inelastic displacement ratio spectra.

Shake-table testing and numerical modelling of inelastic seismic response of semi-rigid cold-formed rack moment frames

An experimental program consisting of quasi-static cyclic, pull-back and seismic shake table tests was conducted to examine the inelastic seismic response of cold-formed selective rack structures. Hysteretic response of the connectors and base plates are presented. In the seismic tests, racks could sustain up to 10% drifts without collapse. Pallet sliding was observed in the tests. A numerical model is proposed in OpenSees to predict the rack seismic response, including pallet sliding. It is used to study the response of 6-bay racks having 3–6 levels. Displacements are sensitive to assumed viscous damping, base plate properties and pallet sliding.

Influence of Post-Yield Stiffness on Inelastic Seismic Response: A Stochastic Analysis

The main objective of this study is to evaluate inelastic response spectra conditioned on constant displacement ductility demand for a single degree of freedom system, which has positive post-yield stiffness. To develop this analysis, the nonlinear Bouc–Wen model is used and it is subject to a seismic action modeled by a nonstationary stochastic process. The study utilises stochastic linearisation technique and peak theory to obtain inelastic response spectra. More in detail, inelastic acceleration spectra, response modification factor spectra, strength reduction factor spectra, yield strength spectra, and inelastic displacement ratio spectra are obtained for constant displacement ductility demand. The novelty of the present study with respect to the previous ones in this field is to obtain inelastic response spectra in stochastic terms, starting from a stochastic model of the seismic motion. Results suggest that the effect of post-yield stiffness must be considered when determining inelastic response.

Refined Analysis of Fatigue Crack Initiation Life of Beam-to-Column Welded Connections of Steel Frame under Strong Earthquake

This paper presents a refined analysis for evaluating low-cycle fatigue crack initiation life of welded beam-to-column connections of steel frame structures under strong earthquake excitation. To consider different length scales between typical beam and column components as well as a few crucial beam-to-column welded connections, a multiscale finite element (FE) model having three different length scales is formulated. The model can accurately analyze the inelastic seismic response of a steel frame and then obtain in detail elastoplastic stress and strain field near the welded zone of the connections. It is found that the welded zone is subjected to multiaxial nonproportional loading during strong ground motion and the elastoplastic stress-strain field of the welded zone is three-dimensional. Then, using the correlation of the Fatemi-Socie (FS) parameter versus fatigue life obtained by the experimental crack initiation fatigue data of the structural steel weldment subjected to multiaxial loading, the refined evaluation approach of fatigue crack initiation life is developed based on the equivalent plastic strain at fatigue critical position of beam end seams of crucial welded connections when the steel frame is subjected to the strong earthquake excitation.

Investigating effects of various base restraints on the nonlinear inelastic static and seismic responses of steel frames

This paper deals with effects of various base restraints on the nonlinear inelastic static and seismic response of plane and space steel frames. The inelastic behavior is captured by a plastic fiber beam-column method, in which the beam-column member is monitored by integration points along the member length, and the cross-section is meshed into several sub-sections. The second-order effects are considered through the use of stability functions and the geometric stiffness matrix. The effect of shear deformation is also taken into account. The column-base restraint is simulated by using a multi-spring connection element developed by authors. The independent hardening model is employed for performing hysteretic loops of rotational springs under seismic loadings, whereas mathematical models are adopted for representing moment-rotation curves of those springs under static loadings. The accuracy and efficiency of the proposed program are compared with an experimental test, numerical examples of previous studies or SAP2000 commercial software. The results show significant differences of steel frames with various base restraints. Nonlinear semi-rigid base restraints perform strongly damping ability due to energy dissipation through moment-rotation hysteretic loops.

Nonlinear seismic analysis of a super 13-element reinforced concrete beam-column joint model

Several two-dimensional analytical beam column joint models with varying complexities have been proposed in quantifying joint flexibility during seismic vulnerability assessment of non-ductile reinforced concrete (RC) frames. Notable models are the single component rotational spring element and the super element joint model that can effectively capture the governing inelastic mechanisms under severe ground motions. Even though both models have been extensively calibrated and verified using quasi-static test of joint sub-assemblages, a comparative study of the inelastic seismic responses under nonlinear time history analysis (NTHA) of RC frames has not been thoroughly evaluated. This study employs three hypothetical case study RC frames subjected to increasing ground motion intensities to study their inherent variations. Results indicate that the super element joint model overestimates the transient drift ratio at the first story and becomes highly un-conservative by under-predicting the drift ratios at the roof level when compared to the single-component model and the conventional rigid joint assumption. In addition, between these story levels, a decline in the drift ratios is observed as the story level increased. However, from this limited study, there is no consistent evidence to suggest that care should be taken in selecting either a single or multi component joint model for seismic risk assessment of buildings when a global demand measure such as maximum inter-storey drift is employed in the seismic assessment framework.

Inelastic Seismic Response of Building with Friction Damper

Dampers are used to control response of structure in recent years. Seismic response is reduced by adding energy dissipation capacity to the building. Dampers are provided to dissipate energy to reduce the damages on buildings. Relative displacement of two floors are opposed by damper elements. Dampers dissipate energy with no or little degradation in strength and stiffness. This work presents the response of structure with energy dissipation device i.e. friction damper built on soft soil when the structure is subjected to a ground motion. Parameters that influence strength and stiffness of structure and energy dissipating device are studied. Response of structure with energy dissipating device is analyzed and it is shown that building with damper shows better performance during earthquake. Building structures are designed using results from elastic analysis, though inelastic behavior well observed during the earthquake. Actual response of the structure can be estimated in the inelastic range by using nonlinear structural analysis programs. Inelastic Damage indices of structural component, overall building are computed by formulating Modified Park and Ang model. Nonlinear analysis program IDARC 2D is used for modeling and analysis. Modeling of friction damper is done using a Wen–Bouc model without stiffness and strength or strength degradation. These devices are modeled with an axial diagonal element. Pseudo force approach is introduced to consider the forces in damper elements, that is, forces in damper elements are subtracted from external load vector. Smooth hysteretic model is used to model response of friction dampers. Nonlinear dynamic analysis is carried out using Newmark-Beta integration method and the pseudo-force method. Damaged state of structure is obtained to observe whether elements are cracked, yielded or failed during analysis. Response parameters such as lateral floor displacement, storey drift, base shear are also computed.