Nonlinear Static Procedures Research Articles

Assessment the Behavior of Seismic Designed Steel Moment Frames Subjected to Progressive Collapse

Recent investigations reveal that progressive collapse phenomenon is dominant behavior in the majority of steel structures. Although the design of buildings is based on the fact that they need to withstand all the loads exerted on the structure, failure occurs as a result of inadequate design and modeling techniques, particularly for abnormal and extreme loading conditions. Once one or more load bearing member is eliminated from the structure, progressive collapse, mainly in columns, will commence. By the time a column is eliminated from the structure as a result of a sudden motor vehicle strike or earthquake or fire or any other internal or external factor that could take one column out of the system, the weight of the building (gravity load) will be distributed among other columns within the structure. Failure commences in the part of the structure that has lost a column unless other columns are designed appropriately against gravity loads and are capable of redistribution of additional loads imposed on them. Failure of vertical load bearing elements will continue until the stabilization of extra loading. Hence, this could lead to serious damage and collapse of the building which will lead to higher damage to the building than the primary damage. This research is based on the regulations conforming to the specifications of UFC guidelines and the structures have been modeled using SAP2000 (2012). In order to study the effects of the progressive collapse on the seismic design of special steel moment frames, SMRF, two 5-story and 15-storystructures are modeled in SAP2000 (2012). In order to have a better understanding of progressive collapse and obtain reliable results, Linear Static (LS), Nonlinear Static (NLS) and Nonlinear Dynamic analyses (NLD) procedure for single and 2 adjacent columns removal have been implemented in this study. Having a good perception of the possibility of progressive collapse involves incorporation of demand capacity ratio, plastic hinges formation and vertical displacements of removed column’s location plus axial force in columns adjacent to the removed column. Other factors such as number of stories and the amount of local damage resulted from the removal of 2 adjacent columns could also lead to a better understanding of the structural behavior.

Seismic assessment and retrofitting of existing structure based on nonlinear static analysis

Seismic assessment and retrofitting of existing structure is a complicated work that typically requires more sophisticated analyses than performing a new design. Before the implementation of a Code for seismic design of buildings (GBJ 11-89), not enough attention has been paid on seismic performance of structures and a great part of the existing reinforced concrete structures built in China have been poorly designed according to the new version of the same code (GB 50011-2010). This paper presents a case study of seismic assessment of a non-seismically designed reinforced concrete building in China. The structural responses are evaluated using the nonlinear static procedure (the so-called pushover analysis), which requires its introduction within a process that allows the estimation of the demand, against which the capacity is then compared with. The capacity of all structural members can be determined following the design code. Based on the structural performance, suitable retrofitting strategies are selected and implemented to the existing system. The retrofitted structure is analyzed again to check the effectiveness of the rehabilitation. Different types of retrofitting strategy are discussed and classified according to their complexity and benefits. Finally, a proper intervention methodology is utilized to upgrade this typical low-rise non-ductile building.

Effectiveness of nonlinear static procedures for slender masonry towers

This paper investigates the accuracy of pushover-based methods in predicting the seismic response of slender masonry towers, through comparison with the results from a large number of nonlinear time-history dynamic analyses. In particular, conventional pushover analyses, in both their force- and displacement-based variants, are considered, and seismic assessment through the well-established N2 method is also addressed. The study is conducted by applying a simple non-linear elastic model recently developed and implemented in the computational code MADY to represent slender masonry structures. The model enables both pushover analyses and non-linear dynamic analyses to be performed with a minimum of effort. A multi-record incremental dynamic analysis carried out for a quite large number of structural cases, each of which is subjected to a comprehensive set of dynamic nonlinear analyses, is used to evaluate the accuracy of pushover methods in predicting the global structural response, as represented by the usual capacity curve together with a damage curve, both of which are compared with dynamic envelopes. Local responses, in terms of lateral displacements and the distribution of damage along the tower height are also compared. The results reveal that the key issue in the accuracy of pushover methods is the nature of the lateral load applied, that is, whether it is a force or a displacement. Different ranges of expected deformation are suggested for adopting each type of lateral load to better represent the actual behaviour of masonry towers and their damage under seismic events through pushover methods.

The influence of infilled panels in retrofitting interventions of existing reinforced concrete buildings: a case study

During the seismic events occurred in the last decades, the existing reinforced concrete (RC) building stock has often exhibited a significant brittle collapse of joints and secondary elements such as infill walls. A quite common strategy, in the attempt of mitigating this vulnerability, is the generalised implementation of strengthening interventions on the structural elements, even in the absence of a complete seismic assessment procedure. This paper presents some considerations about the effects induced by strengthening interventions involving the tying of the infill panels to the RC frame. Within this context, an appraisal of the actual displacement capacity and the possible alteration induced on the global collapse mechanism is provided. The analyses and discussion of results are presented with reference to an actual case study concerning a school building, which was part of a wide vulnerability assessment investigation performed in the Province of Foggia, Italy. In particular, seismic analyses performed using nonlinear static analysis procedures on the strengthened configuration and on the original structure are critically compared and discussed.

Pushover Analysis of G+3 Reinforced Concrete Building with soft storey

Many urban multistorey buildings in India today have open first storey as an unavoidable feature. This is primarily being adopted to accommodate parking or reception lobbies in the first storey. This paper highlights the importance of explicitly recognizing the presence of the open first storey in the analysis of the building and also for immediate measures to prevent the indiscriminate use of soft first storeys in buildings. Alternate measures, involving stiffness balance of the open first storey and the storey above, are proposed to reduce the irregularity introduced by the open first storey. The structural engineering profession has been using the nonlinear static procedure (NSP) or pushover analysis. Modeling for such analysis requires the determination of the nonlinear properties of each component in the structure, quantified by strength and deformation capacities, which depend on the modeling assumptions. Pushover analysis is carried out for either user-defined nonlinear hinge properties or default-hinge properties, available in some programs based on the FEMA-356 and ATC-40 guidelines. This paper aims to evaluate the zone -II selected reinforced concrete building to conduct the non-linear static analysis (Pushover Analysis). The pushover analysis shows the pushover curves, capacity spectrum, plastic hinges and performance level of the building. This non-linear static analysis gives better understanding and more accurate seismic performance of buildings of the damage or failure element.

Evaluation of displacement coefficient method for seismically retrofitted buildings with various ductility capacities

SUMMARYThis research study is aimed at evaluating the accuracy of the displacement coefficient method (DCM) of FEMA 440 and associated nonlinear static procedure (NLSP) for actual buildings with soft story mechanism and various ductility capacities. The DCM and associated NLSP are evaluated using two existing seismically vulnerable buildings with soft story mechanism. The buildings are first retrofitted using a ductile steel‐brace‐link system to represent those with good ductility capacity and then retrofitted with RC squat infill shear panels (SISPs) to represent those with relatively poor ductility capacity. The evaluation of the DCM of FEMA 440 and associated NLSP is then performed by comparing the roof displacements (target displacements), maximum interstory drifts, and maximum plastic hinge rotations of the original and retrofitted buildings obtained from NLSP (at the target displacement level of DCM) with those obtained from nonlinear response history (NRH) analyses for three different seismic performance levels. It is observed that the DCM, and hence, the NLSP fail to accurately predict the NRH analyses results mainly due to uncertainties in the coefficient C1 of the DCM in the short period range, the inability of the DCM to capture the failure of structural members beyond a certain lateral displacement or plastic rotation limit and associated soft story mechanism. Copyright © 2013 John Wiley & Sons, Ltd.

EFFECT OF VARIATION OF PLASTIC HINGE LENGTH ON THE RESULTS OF NON-LINEAR ANALYSIS

The nonlinear Static procedure also well known as pushover analysis is method where in monotonically increasing loads are applied to the structure till the structure is unable to resist any further load. It is a popular tool for seismic performance evaluation of existing and new structures. In literature lot of research has been carried out on conventional pushover analysis and after knowing deficiency efforts have been made to improve it. But actual test results to verify the analytically obtained pushover results are rarely available. It has been found that some amount of variation is always expected to exist in seismic demand prediction of pushover analysis. Initial study is carried out by considering user defined hinge properties and default hinge length. Attempt is being made to assess the variation of pushover analysis results by considering user defined hinge properties and various hinge length formulations available in literature and results compared with experimentally obtained results based on test carried out on a G+2 storied RCC framed structure. For the present study two geometric models viz bare frame and rigid frame model is considered and it is found that the results of pushover analysis are very sensitive to geometric model and hinge length adopted.

A new pushover procedure for two‐way asymmetric‐plan tall buildings under bidirectional earthquakes

SUMMARYConventional pushover analyses despite of extensive applications are unable to estimate the general responses of asymmetric‐plan tall buildings because of ignoring the effects of higher modes and torsion. A consecutive modal pushover procedure is one of the recent nonlinear static pushover procedures that used to analyse the seismic response of one‐way asymmetric‐plan tall buildings under one‐directional seismic ground motions. In this paper, a modified consecutive modal pushover procedure (MCMP) has been proposed to estimate the seismic demands of two‐way asymmetric‐plan tall buildings under two horizontal components of earthquakes simultaneously. The accuracy of the MCMP procedure is evaluated using different buildings and comparing with the results of FEMA (Federal Emergency Management Agency) procedures, the practical modal pushover procedure and nonlinear time history analyses as an exact solution. The results show the proposed MCMP procedure is able to estimate the displacements and storey drifts accurately and introduces a great improvement in predicting the plastic hinge rotations. Copyright © 2013 John Wiley & Sons, Ltd.

Evaluation of Nonlinear Static Procedures in the Assessment of Building Frames

In recent years a number of nonlinear static procedures (NSPs) have been developed and proposed. Such pushover-based seismic assessment procedures are relatively straightforward to employ and are generally chosen over nonlinear dynamic analysis, especially within the realm of design office application. Parametric comparisons between the different NSPs available, however, are still somewhat sparse. In this work, five commonly employed NSPs (the N2 method, capacity spectrum method, modal pushover analysis, adaptive modal combination procedure, and the adaptive capacity spectrum method) are applied in the assessment of 16 frames subjected to a large number of input motions with a view to assess the accuracy level of such approaches through comparison with nonlinear dynamic analysis results. The evaluation shows that all the NSPs are able to accurately predict displacements and to produce reasonable estimates for other response parameters, with limited dispersion. Even though no single NSP tested led to consistently superior results, modal pushover analysis and the adaptive capacity spectrum method seemed to perform slightly better.

Performance of Existing Modernist Buildings in Barcelona

AbstractSeismic vulnerability of a set of unreinforced masonry aggregated buildings of more than 70 years old located in Barcelona (Spain) is investigated. Four different model buildings are studied: they consist of three isolated buildings and one aggregated system, which are representative of most typical structural configurations used in the city. The aggregated building blocks are built individually without any gaps between them, thus interacting under lateral loads. The seismic hazard is described by the elastic response spectrum defined in Eurocode-8. Capacity curves are obtained using a nonlinear static analysis procedure; they are used to obtain the displacement-based fragility functions, the performance point, the probability damage matrices, and the mean damage factor, corresponding to the specified seismic action. In spite of the low-to-moderate seismic hazard in the region, the results show a high percentage of buildings having moderate and severe damage, depending on the soil type. Their brit...

Optimization of modal load pattern for pushover analysis of building structures

Nonlinear Static Procedures (NSPs) have been developed as a practical tool to estimate the seismic demand of structures. Several researches have accomplished to minimize errors of NSPs, namely pushover procedures, in the Nonlinear Time History Analysis (NTHA), as the most exact method. The most important issue in a typical pushover procedure is the pattern and technique of loading which are extracted based on structural dynamic fundamentals. In this paper, the coefficients of modal force combination is focused involving a meta-heuristic optimization algorithm to find the optimum load pattern which results in a response with minimum amount of errors in comparison to the NTHA counterpart. Other parameters of the problem are based on the FEMA recommendations for pushover analysis of building structures. The proposed approach is implemented on a high-rise 20 storey concrete moment resisting frame under three earthquake records. In order to demonstrate the effectiveness and robustness of the studied procedure the results are presented beside other well-known pushover methods such as MPA and the FEMA procedures, and the results show the efficiency of the proposed load patterns.

Capacity, fragility and damage in reinforced concrete buildings: a probabilistic approach

The main goals of this article are to analyze the use of simplified deterministic nonlinear static procedures for assessing the seismic response of buildings and to evaluate the influence that the uncertainties in the mechanical properties of the materials and in the features of the seismic actions have in the uncertainties of the structural response. A reinforced concrete building is used as a guiding case study. In the calculation of the expected spectral displacement, deterministic nonlinear static methods are simple and straightforward. For not severe earthquakes these approaches lead to somewhat conservative but adequate results when compared to more sophisticated procedures involving nonlinear dynamic analyses. Concerning the probabilistic assessment, the strength properties of the materials, concrete and steel, and the seismic action are considered as random variables. The Monte Carlo method is then used to analyze the structural response of the building. The obtained results show that significant uncertainties are expected; uncertainties in the structural response increase with the severity of the seismic actions. The major influence in the randomness of the structural response comes from the randomness of the seismic action. A useful example for selected earthquake scenarios is used to illustrate the applicability of the probabilistic approach for assessing expected damage and risk. An important conclusion of this work is the need of broaching the fragility of the buildings and expected damage assessment issues from a probabilistic perspective.

Towards Displacement-Based Seismic Assessment of Concrete Dams Using Non-linear Static and Dynamic Procedures

The current paper demonstrates the application of a displacement-based procedure in the seismic safety assessment of large concrete dams. Two dam structures, double arch and gravity, are used as case studies and analyzed through conventional force-based approaches for various seismic levels. Non-linear static analyses are used for the assessment of structural capacity and non-linear dynamic analyses—to obtain the maximum response for each seismic level. The safety of the dams is assessed through displacement-based damage indicators in the form of damage indexes (DIs) and safety factors (SFs). The DI accounts for the accumulated inelastic deformations in the structure and is related to pre-defined damage levels (DLs), while SF evaluates the structural safety margins in terms of seismic load intensity. In addition, the paper provides an assessment of the applicability of non-linear static procedures (NSP) for seismic assessment of large concrete dams. The results obtained from NSP for seismic level maximum credible earthquake (MCE) are compared with a set of ten dynamic non-linear analyses for the same seismic intensity. NSP results tend to give a more conservative prediction, but are still consistent with the results calculated via non-linear dynamic analyses.

A new dynamic increase factor for nonlinear static alternate path analysis of building frames against progressive collapse

This paper presents a new empirical method for calculating the dynamic increase factor (DIF) that is used to amplify the gravity loads on the affected bays of a building frame, when the nonlinear static alternate path analysis is carried out to predict the peak dynamic responses to sudden column removal. The new method defines the DIF as a function of max(Mu/Mp), where the maximum operator is applied to all beams within the affected bays immediately adjacent to and above the removed column, and Mu and Mp are the factored moment demand under original unamplified static gravity loads and the factored plastic moment capacity, respectively, of an affected beam. Therefore, 1–max(Mu/Mp) directly, albeit approximately, measures the percentage level of the overall residual capacity of a building frame to remain essentially elastic while withstanding the dynamic effect of gravity loads upon sudden column removal, after the static effect of gravity loads has been resisted by the damaged frame. A step-by-step nonlinear static analysis procedure using the new DIF is described. As an illustration, empirical DIF formulas are derived from curve fitting data points generated by the nonlinear static alternate path analysis of three model steel moment frames originally designed to resist different levels of earthquake. It is found from the numerical examples that the new DIF is well correlated with max(Mu/Mp) for different column removal scenarios. Hence, the new DIF can be used with nonlinear static analysis in lieu of nonlinear dynamic analysis to assess the potential of building frames for progressive collapse.

Considering dynamic parameters of damaged structure in MPA and YPS nonlinear static procedures for asymmetric buildings

SUMMARYThe yield point spectra and modal pushover procedures have already been used in seismic design of new buildings and vulnerability evaluation of existing structures. This paper initially identifies the similarities and differences of the two procedures. Then, the modal characteristics of damaged structure are used to modify their methodologies. The applications of the procedures in estimating displacement, interstory drift index and plastic hinge rotation responses of asymmetric buildings are investigated for three 5‐story reinforced concrete moment‐resisting frame‐building models. The results show considerable improvement in estimating the responses of those asymmetric buildings. Copyright © 2013 John Wiley & Sons, Ltd.

Evaluation of Flexible Performance of Reinforced Concrete Structures Using a Nonlinear Static Procedure Provided by Fuzzy Logic

The performance assessment is usually carried out by using plastic hinge rotations at the ends of beam and column sections in the nonlinear structural analysis. The guidelines and requirements are given in some recommended documents (FEMA356, ATC40) and in Turkish Earthquake Resistant Design Code 2007 (TERDC 2007). The rules and the boundaries in various recommended documents and codes are defined within strict intervals, i.e. crisply. Approximations in structural system modeling and numerical analysis make the accuracy of those limitations questionable. This paper deals with an efficient approach for the performance evaluation of existing structural systems. It is shown that the performance levels can be flexible by using certain weighted values depending on the number and deformation levels of the elements (flexible performance). Herein, fuzzy set theory is used with fuzzy inputs, a set of corresponding rules (rule base) and a defuzzification of the outputs for the performance level of structural systems. In the numerical treatment of the method, the damages and the corresponding performance levels in FEMA356 are considered and MATLAB Fuzzy Toolbox and Simulink software options are used. The methodology can be tested by use of real data (obtained from non-linear analysis of structural systems) or generated data. The method is tested with a frame system building and a bridge pier data and the necessary performance levels are determined and finally the results are discussed comparatively in tables and graphs.

Shaking table tests of structures with hysteretic dampers: experimental results versus prediction using non-linear static methods

The use of seismic hysteretic dampers for passive control is increasing exponentially in recent years for both new and existing buildings. In order to utilize hysteretic dampers within a structural system, it is of paramount importance to have simplified design procedures based upon knowledge gained from theoretical studies and validated with experimental results. Non-linear Static Procedures (NSPs) are presented as an alternative to the force-based methods more common nowadays. The application of NSPs to conventional structures has been well established; yet there is a lack of experimental information on how NSPs apply to systems with hysteretic dampers. In this research, several shaking table tests were conducted on two single bay and single story 1:2 scale structures with and without hysteretic dampers. The maximum response of the structure with dampers in terms of lateral displacement and base shear obtained from the tests was compared with the prediction provided by three well-known NSPs: (1) the improved version of the Capacity Spectrum Method (CSM) from FEMA 440; (2) the improved version of the Displacement Coefficient Method (DCM) from FEMA 440; and (3) the N2 Method implemented in Eurocode 8. In general, the improved version of the DCM and N2 methods are found to provide acceptable accuracy in prediction, but the CSM tends to underestimate the response.

Assessment of Nonlinear Static Procedures for Determination of Target Displacement in Asymmetric Buildings

The conventional procedure for pushover or non-linear static analysis (NSA) has some drawbacks in predicting the inelastic seismic demands of buildings which are asymmetric in plan. In this research, fifteen asymmetric buildings comprising of steel moment frames have been designed and their seismic responses have been studied by pushover analysis. Using methods proposed in FEMA-356, ATC-40, and FEMA-440, the target displacements for these structures have been obtained. Subsequently pushover analyses have been repeated using lateral forces corresponding to 100% of target displacement in principal direction and 30% of target displacement in perpendicular direction. Results of this study indicate that target displacements results from FEMA-440 methods for the roof center of mass ( CM) are closest to the NTHA results but displacements obtained for the stiff side of structure in all NSA methods are underestimated. Therefore a correction factor has been derived using the Least Squares Method to modify the demand displacements obtained from pushover analysis for the stiff side of asymmetric buildings.

현장타설 끼움 전단벽 및 철골가새를 활용한 기존 학교 건물의 내진보강

This study proposes a procedure for evaluating the seismic performance and retrofit of a typical reinforced building (R/C) school buildings contructed in the 1980s. The procedure is derived from the Japanese Standard for Evaluation of Seismic Capacity of Existing Reinforced Concrete Buildings and Nonlinear Static Procedure (NSP) specified in Federal Emergency Management Agency (FEMA 356). In this study, the Japanese Standard was applied for evaluating the additionally required seismic performance in the existing school building. Cast-in-place (CIP) reinforced concrete infill walls and steel braces were used to seismically retrofit the existing school building located in the region of Hongsung in Chungnam. In the pushover analysis, i.e NSP, the hinge properties of columns, beams, infill walls and steel braces were carefully calibrated based on the existing experiment results in the available literatures. The predicted seismic performance for the retrofitted building was compared to that for the virgin building. Based on the seismic evaluation with the Japanese Standard and the FEMA 356 criteria, the addition of CIP reinforced concrete infill walls and steel braces have superior constructablility and can improve effectively the seismic performance of the existing school buildings constructed in 1980s.

Nonlinear analysis of out‐of‐plane masonry façades: full dynamic versus pushover methods by rigid body and spring model

SUMMARYThe paper proposes a systematic comparison between two methods of analysis that are well established in the field of earthquake engineering: nonlinear dynamic analysis and nonlinear static procedure (NSP), applied to the out‐of‐plane seismic response of two masonry façades representative of many ancient Italian churches. The comparison is based on extensive numerical analyses, which focus on the flexural and torsional mechanisms, while the in‐plane damage mechanisms and the possible detachment between the façade and the lateral walls because of a poor connection have been presently disregarded. The computations, both in the static and in the dynamic field, are based on a rigid body and spring model specifically implemented for this issue, computationally efficient and equipped with a realistic model of damage and hysteresis at the mesoscale. An innovative aspect of this study is the heuristic modelling of three‐wythe masonry, to include some typical texture effects on the macroscale nonlinear response. For each façade, two different masonry textures were considered, performing extensive dynamic analyses that offered a detailed overview about the performance under earthquakes of different intensities. In parallel, NSP and the classical N2‐based seismic assessment were applied. A critical discussion and comparison of the results of the two methods is presented to rationally appraise limits and opportunities. In particular, flexural and twisting out‐of‐plane mechanisms were clearly appraised in the dynamic field, whereas NSPs were not always able to describe the collapse, because they missed the partial failures determined by higher vibration modes, as could be expected. Copyright © 2012 John Wiley & Sons, Ltd.