Inelastic Time-history Analyses Research Articles

5층 철근콘크리트 중간모멘트골조의 비탄성 시간이력해석

In this study, 5-story structures were designed in accordance with KBC2009 for inelastic time history analysis of RC IMRF. Bending moment-curvature relationship for beam and column was identified with fiber model and bending moment-rotation relationship for beam-column joint was calculated with simple and unified joint shear behavior model and moment equilibrium relationship for the joint. The hysteretic behavior was simulated with three-parameter model suggested in IDARC program. The analytical results showed that the inelastic shear behavior of the joint could be neglected in the structural design for seismic design category C but the structure of category D did not satisfy the criteria of FEMA 356 for collapse prevention performance level.

Plastic hinge length of FRP strengthened reinforced concrete columns subjected to both far-fault and near-fault ground motions

In a strong earthquake, an RC column develops plastic deformations in regions often defined as plastic hinge regions. The formation of a plastic hinge in an RC column in these regions depends on the characteristics of the earthquakes as well as on the column details. Recordings from recent earthquakes have demonstrated that ground motions in near field to a rupturing fault can contain a large energy. This energy can cause considerable damage during an earthquake. Therefore, many recently designed and constructed buildings may require strengthening in order to perform well when subjected to near-fault earthquakes. Fiber Reinforced Polymers are considered to be a viable strengthening method due to their relatively easy and quick installation. In this paper, 1350 inelastic time-history analyses have been performed to predict the nonlinear behavior of FRP strengthened RC columns under both far-fault and near-fault earthquakes. The effects of axial load, height-depth ratio and the amount of longitudinal reinforcement, as well as different characteristics of earthquakes, are evaluated and the results are compared with the corresponding experimental data. Based on the results, simple expressions are proposed that can be used to estimate plastic hinge length of FRP strengthened RC columns subjected to both far- and near-fault earthquakes.

Seismic force demand on ductile reinforced concrete shear walls subjected to western North American ground motions: Part 1 — parametric study

A parametric study of regular ductile reinforced concrete (RC) cantilever walls designed with the 2010 National building code of Canada and the 2004 Canadian Standards Association (CSA) standard A23.3 for Vancouver is performed to investigate the influence of the following parameters on the higher mode amplification effects, and hence on the seismic force demand: number of storeys, fundamental lateral period (T), site class, wall aspect ratio, wall cross-section, and wall base flexural overstrength (γw). The study is based on inelastic time-history analyses performed with a multilayer beam model and a smeared membrane model accounting for inelastic shear–flexure–axial interaction. The main conclusions are that (i) T and γware the studied parameters affecting the most dynamic shear amplification and seismic force demand, (ii) the 2004 CSA standard A23.3 capacity design methods are inadequate, and (iii) a single plastic hinge design may be inadequate and unsafe for regular ductile RC walls with γw < 2.0.

Generation of analytical fragility curves for Ghanaian non-ductile reinforced concrete frame buildings

This study is on seismic safety evaluation of non-ductile reinforced concrete (RC) frame buildings in Ghana. Generic 3-, 4- and 6-storey non-ductile RC buildings were characterised for assessment. The generic buildings were designed according to British Standard (BS) 8110. The fragility curve parameters were generated using inelastic time history analyses for seismic demand and inelastic pushover analyses for structural capacity of the buildings. As a result of lack of real time histories in Ghana, 3 suites of 100 synthetic time history records each were generated in order to generate lower and upper bounds for inelastic dynamic response. Parameters of collapse fragility curves with 50% probability of exceedance were established for the generic non-ductile Ghanaian frame buildings using short duration near-fault like records. All the curves represent the probability of exceeding the collapse limit state as a function of the peak ground acceleration (PGA) and spectral acceleration at the fundamental mode period of the generic buildings. Using the data from the nonlinear dynamic analysis of the generic buildings under all 300 synthetic time histories, a pair of three sets of fragility curves was developed. Results obtained showed that the generic non-ductile 3 to 6 storey RC frame buildings subjected to near-fault like ground motions may record high probabilities of collapse, if they are situated in 0.25 to 0.35 g PGA seismic zones.

Assessment of the seismic performance of old riveted steel frame–RC wall buildings

Seismic performance assessment of old dual riveted steel frame–RC wall buildings using the nonlinear dynamic procedure is presented. The study is based on an existing nine-storey building located in Wellington, New Zealand. The building is representative of medium rise steel framed buildings from the first half of the 20th century.A three dimensional numerical model of the building was developed in an inelastic structural analysis program. Nonlinear characterisations necessary for the prediction of the inelastic cyclic behaviours of the structural components were incorporated into the numerical model. Details of the structural configuration and member properties for the analyses were determined from the original engineering drawings, the construction specifications, as-built concrete strength test results and literature on properties of steel sections used around the period the building was constructed. The inelastic time history analyses were conducted using a suite of seven earthquake records relevant to the seismicity of the building's location.Modal properties of the numerical model compare well with results of a physical test conducted on the building. The implemented modelling procedure appeared to have predicted the most probable seismic performance of this type of building, which would not have been captured by other simplified procedures. The assessment also highlighted the adverse effects the characteristics and location of the walls have on the seismic performance of this type of building by introducing significant torsional and vertical irregularities.

Viscous and hysteretic damping

Capacity design, while protecting a structure against undesirable energy dissipations, has major implications on member sizes and overall cost. Furthermore, in some situations where protected elements possess some inelastic deformation capacity, it may be unwarranted. One of these situations is when the forces applied to the protected elements result from viscous dampers. This is because when viscous forces cause yielding in an element, the element deforms, so no deformation in the viscous damper is required. If no deformation is required, the velocity is zero, so there is no force. This implies that very little inelastic yielding is likely to occur in protected elements.
 In order to investigate whether or not this is so, a single storey structure was designed and fitted with braces to reduce its response. Both hysteretic and viscous braces were used to obtain the same peak displacement response. The column strength was decreased by a fixed percentage and inelastic dynamic time history analysis was conducted. The amount of energy dissipated in the columns was then compared to determine whether hysteretic braces or viscous braces caused more column yielding so that appropriate over strength values could be developed for different brace types. It was found that the amount of energy absorbed by the column depends on the period but also on the brace design ductility. However, irrespective of the period or design ductility, the column hysteretic energy dissipated by a viscous brace was lower than that dissipated by a hysteretic brace. It follows that column yielding may be significantly less critical for viscous, rather than for hysteresis, braced structures.

Soil structure interaction effects on strength reduction factors

In this study, strength reduction factors are investigated for SDOF systems with period range of 0.1-3.0 s with elastoplastic behavior considering soil structure interaction for 64 different earthquake motions recorded on different site conditions such as rock, stiff soil, soft soil and very soft soil. Soil structure interacting systems are modeled and analyzed with effective period, effective damping and effective ductility values differing from fixed-base case. For inelastic time history analyses, Newmark method for step by step time integration was adapted in an in-house computer program. Results are compared with those calculated for fixed-base case. A new equation is proposed for strength reduction factor of interacting system as a function of structural period of system (T), ductility ratio (<TEX>${\mu}$</TEX>) and period lengthening ratio (T/T). It is concluded that soil structure interaction reduces the strength reduction factors for soft soils, therefore, using the fixed-base strength reduction factors for interacting systems lead to non-conservative design forces.

Quantifying the seismic response of structures with flexible diaphragms

SUMMARYFloor diaphragm in‐plane stiffness affects building response to horizontal ground accelerations. This paper describes a series of elastic and inelastic time history analyses of symmetric structures with different deformation types, configurations and heights to quantify these effects. It is shown that displacements of single storey elastically responding structures tend to be most significantly affected by diaphragm flexibility. Analyses of these structures were cross‐verified by a closed‐form mechanics‐based formulation developed to describe the response. Simple relationships were proposed to allow designers to conservatively estimate the increase in peak in‐plane displacement resulting from diaphragm flexibility. Copyright © 2012 John Wiley &amp; Sons, Ltd.

Improved procedure for equivalent linearization of bridges supported on hysteretic isolators

Maximum displacement demands can be obtained through non-linear time history analysis, however, many approximate methods have been proposed in recent codes to reduce the required computational time distinctive of non-linear approaches. Some of these methods are based on equivalent linearization of the system by using an effective lateral stiffness (kef) and equivalent damping ratio (ξeq). The dynamic characteristics of earthquake ground motions, ductility capacities, type of hysteretic relationships, and stiffness and strength degradation characteristics of the structure are aspects that strongly affect both, the energy dissipation capacity and the effective stiffness of the system; nevertheless, these conditions have not been adequately accounted for in the analyses. This work presents an improved expression, intended for bridges supported on hysteretic isolators, that takes into account some of these aspects. Since lead rubber bearings (LRB) are the most common isolators used on bridges, the expression is focused on the hysteretic behavior of this type of bearing. A simple and rational expression to evaluate the equivalent damping ratio ξeq, tying the physical behavior of these systems, is proposed. In this way, the prediction capability of the linear equivalent model of bridges supported on LRB isolators is improved. The proposed equation predicts a displacement that is in good agreement with the one obtained through inelastic time history analysis. Furthermore, it can be easily incorporated into the displacement-based design framework, and into the code specifications.

Development of post-tensioned self-centring structures for earthquake resistance

A three-story frame was designed for earthquake resistance by using post-tensioned (PT) columns and beams. Two interior connections, representing the first floor column and beam sizes, were tested under cyclic loading to evaluate the effects of energy dissipation and PT load and on the seismic behaviour. A full-scale one-story two-bay specimen frame, which was a substructure of the three-story PT building, was then built and tested. This paper presents experimental results of the connections and the frame and analytical simulations for the frame subassembly. Time-history analyses of the three-story PT building subjected to the design basis earthquake (DBE) and the maximum considered earthquake (MCE) were conducted to investigate seismic demands of the proposed frame. These tests confirmed the self-centring responses of the connections and the frame. Inelastic time history analyses of the three-story prototype building showed that the proposed frame system can achieve seismic demands under MCE level ground motions.

Inelastic displacement ratios for structures with foundation flexibility

Inelastic displacement ratios have been generally investigated for fixed-base systems without taking into consideration soil structure interaction. In this study, inelastic displacement ratios are investigated for SDOF systems with period range of 0.1–3.0 s with elastoplastic behavior considering soil structure interaction for 64 different earthquake motions recorded on different site conditions such as rock, stiff soil, soft soil and very soft soil. Soil structure interacting systems are modeled with effective period, effective damping and effective ductility values differing from fixed-base case. For inelastic time history analyses, Newmark method for step by step time integration was adapted in an in-house computer program. Results are compared with those calculated for fixed-base case. A new equation is proposed for inelastic displacement ratio of interacting system as a function of structural period of interacting system (T˜), ductility ratio (μ) and period lengthening ratio (T˜/T). The fitness of the regressed function of the inelastic displacement factor is shown in figures. The regressed equation for (C˜μ) should be useful in estimating the inelastic deformation of structure where the global ductility capacity can be estimated.

Seismic Vulnerability Analysis of Reinforced Concrete Frames with Mild Steel Dampers

This study focus on derivation of such fragility curves using conventional old reinforced concrete (RC) frames with Mild Steel Damper (MSD) of flexural energy dissipation braces. A set of stochastic earthquake waves compatible with the response spectrum of China seismic code selected to represent the variability in ground motion. Dynamic inelastic time history analysis was used to analyze the random sample of structures. Weak position was be pointed out, The result reveal that excellent reduction effect for structure of MSD is favorable and obvious under major earthquake.

Research Needs for Use of Capacity Design of RC Frame Structures in China

Standards for seismic design of building structures have been applied in China since 1978 However, the Chinese seismic design philosophy is quite different from the capacity design philosophy incorporated in New Zealand's Standards. In this paper, the disadvantages of Chinese Standards designed RC frame structures (potential structural flexural and shear collapses when subjected to “large earthquakes” at ultimate limit state level) are discussed when compared to New Zealand Standards designed frame structures. To suppress the potential flexural collapse, a cycling research project is presented, comprising of member experimental tests for hysteresis loops (further for hysteresis models), inelastic dynamic time-history analyses for seismic damage assessment purposes (taking overall structural displacement ductility as principle damage measurement), redesign of members if flexural collapse is predicted, experimental tests again of redesigned members etc. Meanwhile, having the potential shear collapse suppressed, the capacity design procedure needs to be applied to seismic design, leading to quantify the structural displacement ductility capacities.

The effect of soil-structure interaction on inelastic displacement ratio of structures

In this study, inelastic displacement ratios and ductility demands are investigated for SDOF systems with period range of 0.1-3.0 s. with elastoplastic behavior considering soil structure interaction. Earthquake motions recorded on different site conditions such as rock, stiff soil, soft soil and very soft soil are used in analyses. Soil structure interacting systems are modeled with effective period, effective damping and effective ductility values differing from fixed-base case. For inelastic time history analyses, Newmark method for step by step time integration was adapted in an in-house computer program. Results are compared with those calculated for fixed-base case. A new equation is proposed for inelastic displacement ratio of interacting system (<TEX>$\tilde{C}_R$</TEX>) as a function of structural period of interacting system (<TEX>$\tilde{T}$</TEX>), strength reduction factor (R) and period lengthening ratio (<TEX>$\tilde{T}/T$</TEX>). The proposed equation for <TEX>$\tilde{C}_R$</TEX> which takes the soil-structure interaction into account should be useful in estimating the inelastic deformation of existing structures with known lateral strength.

Research on Structural Influencing Coefficient of Moment-Resisting Steel Frames

This paper is focused on the evaluation of the structural influencing coefficient in multi-story moment-resisting steel frames involving local bucking effect, with due consideration to both their ductility and overstrength. Ductility and overstrength play an important role in keeping satisfactory performance of structures during strong earthquake. Firstly, moment-resisting steel frames of are designed according to Chinese seismic code. Based on the non-linear shell element method, both inelastic time history and pushover analyses has been performed on these steel frames to get the global capacity envelopes. The results show that number of stores and spans have effect on the behaviour factor values, and that the local buckling affects the ductility capacity of steel frames. Finally, based on the findings presented in the article, tentative influencing coefficient values are proposed for moment-resisting steel frames.

Method for Probabilistic Displacement-Based Design of RC Structures

An approximate method is proposed for seismic design of reinforced concrete (RC) structures to meet multiple structural performance requirements expressed in terms of exceedance probabilities. The method is approximate in nature and rests on two main results: (1) the closed-form solution for the mean annual rate of exceedance of a limit state and (2) the empirical equal-displacement rule. Compliance with design objectives is obtained through a gradient-based search algorithm in the space of the design variables with reference to a linear elastic proxy of the structure. To this purpose, analytical gradients for Cornell’s formula are derived. An application illustrates the method and its validation through inelastic time-history analysis. From the limited investigation carried out, the method appears to offer satisfactory accuracy.

Nonlinear inelastic time-history analysis of truss structures

This paper presents the nonlinear inelastic time-history analysis of truss structures including both geometric and material nonlinearities. The geometric nonlinearity is considered based on an updated Lagrangian formulation, while the material nonlinearity is captured by tracing an empirical stress–strain relationship in the elastoplastic range. The presented truss model is capable of capturing several failure modes of member such as buckling, yielding, inelastic post-buckling, unloading, and reloading. An incremental-iterative solution scheme based on the Newmark method and the Newton–Raphson method is adopted for solving the nonlinear equations of motion. A computer program is developed to predict the nonlinear inelastic responses of truss structures. Numerical examples are presented to demonstrate the capabilities of the proposed program in capturing the nonlinear responses of space truss structures under earthquake loadings.

Study of the Applicability of Modal Pushover Analysis on Irregular Continuous Bridges

The influence of higher modes and their consideration in the pushover analysis of three irregular continuous bridges is discussed. Modal pushover analysis (MPA) is addressed and compared with inelastic time-history analysis (ITHA). In the operation process of MPA, each important mode is used to determine the distribution of forces for the pushover analysis separately, and the displacements of different parts of bridge are monitored to construct pushover curves for each important mode. When the analyses for all important modes of one bridge are completed, the results are combined and compared with the results of ITHA. The investigation shows, for each important mode, adopting different displacement-monitored points obtains different pushover curves. If reasonable pushover curves are selected as capacity spectra, MPA can give the results comparable with ITHA, or else MPA does not work well. Finally, how to choose reasonable displacement-monitored point to construct capacity spectrum of MPA is identified.

Applicability of Modal Pushover Analysis on Bridges

Taking one irregular continuous bridge as an example, modal pushover analysis (MPA) has been conducted to judge whether it would be applicable for seismic analysis of irregular bridge structures. The bridge’s seismic demand in the transverse direction has been determined through two different methods, inelastic time history analysis (ITHA) and MPA respectively. The comparison between those two results indicates that MPA would be suitable only for bridges under elastic or slightly damaged state. Finally, some modifications are used to improve the MPA’s scope of application, and the results illustrate that the adapted MPA will be able to estimate bridges’ seismic demands to some extent.

Seismic design of inelastic structures using equivalent linear system parameters: part 1 – derivation and comparison

This article, which is the first of a two-part article, presents equations for computing equivalent linear system (ELS) parameters using a two-dimensional minimisation technique for estimating inelastic seismic demand of structures from elastic response spectra. Using two hysteretic models, the effects of initial damping, post-yield stiffness and degrading behaviour on the ELS parameters are investigated. The maximum inelastic response of structures modelled as single degree-of-freedom systems computed using the proposed method are compared with five other approximate methods as well as with results obtained using inelastic time-history analysis. It is observed that the proposed approach gives good results for structures that experience ductile behaviour with natural periods in the 0.3- to 3-s range.