Nonlinear Static Method Research Articles

Comparison of seismic assessment guidelines using a case study reinforced concrete wall building

There are several seismic assessment standards and guidelines available around the world that can be used to identify vulnerable buildings. The assessment procedures and criteria in these documents are different, and thus, the assessment outcomes for a particular building, if assessed using different standards, can also be different. In this study, provisions of the linear static and non-linear static analysis procedures of three prominent seismic assessment documents, the American Society of Civil Engineers /Structural Engineers Institute standard ASCE 41 (2017) [1], the New Zealand Seismic Assessment Guidelines (2017) [2], and the European Standard EN 1998-3 (2005) [3] (also known as Eurocode 8 Part-3 or EC8-3) are discussed and compared, highlighting some of their similarities and differences. A reinforced concrete (RC) wall building used in FEMA P-2006 (2018) [4] for demonstration of ASCE 41 provisions is taken as the case study building for comparison of the assessment provisions. The linear and non-linear static analysis procedures specified in the three documents are applied to the case study building and the assessment outcomes are compared. The assessment results are found to vary across the analysis methods and guidelines. However, the critical governing vulnerability for the building is found to be the same. It is observed that with the simplifying modelling assumptions, coupled with the inherent conservatism in the assessment using linear static analysis, a more conservative outcome is obtained using the linear static methods as compared to the non-linear static methods. Overall, EC8-3 provisions are found to be the most conservative of all three guidelines considered for the assessment of the example building.

Experimental Investigation of High-performance Fiber-reinforced Cementitious Composite and its Effect on RC Beams by Numerical Method

In the present study, experimental investigations were initially conducted on high-performance fiber-reinforced cementitious composite (HPFRCC). A total of 9 samples were examined and subjected to a 4-point bending test. The sample lengths were standardized at 500 and 1700 mm. The variables under scrutiny included the impact of Micro Steel, Macro Steel, and polyvinyl alcohol fibers. Furthermore, the models were scrutinized under two conditions: with and without glass fiber reinforced polymer (GFRP) bars. The number of samples was 9. In the second part of the article, subsequent to verifying the experimental samples from the current study alongside a concrete beam, numerical analyses were carried out to assess the influence of HPFRCC on the behavior of RC beams. Similarly, the impact of GFRP diameter, as well as the height of HPFRCCs, on the seismic performance of RC beams, was investigated by conducting 36 numerical analyses. The analyses were carried out using nonlinear static methods, with monotonic loading. The model outputs encompass elastic stiffness, ultimate strength, relative stiffness, and energy dissipation. The experimental results showed that the use of macro steel fibers in models without GFRP rebars has better results on the flexural behavior of HPFRCC. Moreover, by reinforcing RC beams with HPFRCC, a 70% increase in energy dissipation was observed. The elastic stiffness and ultimate strength of the strengthened beam are directly proportional to the ratio of the HPFRCC's elastic flexural stiffness to that of the original beam. These results increase proportionally as this ratio rises.

The Impact of Buckling Restrained Braces in Strengthening Deficient Reinforced Concrete Structures

Seismic strengthening for existing structures is a sustainable solution that is utilized to enhance building safety, reduce damages, and prevent failure in a future earthquake event. The choice of seismic strengthening techniques has to be accurate, efficient, and adjusted to make RC structures stronger in the building sector. Buckling-restrained brace (BRB) system is one of the successful strengthening strategies, that it is possible to utilize in both RC and steel structures. Therefore, this paper explores the possibility of employing buckling restrained braces in existing RC buildings and assesses the impact of different BRB bracing distributions and positions on seismic force resistance. In this work, a five-story RC building was considered, and to upgrade their performance seismic was modeled using four types of BRB systems, consisting of two types of bracing configurations with two arrangements: diagonal in the central bay, diagonal in the corner bays, chevron in the central bay, and chevron in the corner bays. To assess the efficiency of the four proposed BRB systems, firstly, the nonlinear static pushover method was conducted to investigate the lateral strength of structures. Secondly, a parametric study was undertaken using dynamic time history analysis to study various factors such as roof displacement, shear force, and roof acceleration of the original and strengthened models. The numerical study was executed using the Seismostruct software. The results and different performance levels were examined and compared. The obtained results indicate that the BRB and concrete structures can successfully work together to resist the reliability of strengthening RC structures. It was observed that the four prediction systems of the BRB models were excessively effective at upgrading the seismic resistance of the existing structure and provided significantly less damage, especially when using the chevron BRBs with the corner arrangement compared to the other models.

Effects of infill wall thickness and arrangement on the seismic performance of the reinforced concrete frames

In this study, it is aimed to investigate the seismic behavior of the reinforced concrete (RC) frames with and without infill walls having different thickness and arrangement. To this, 3, 4, 5, 6, and 7 story RC frames consisting of 4 and 5 bays were studied. Infill walls were introduced into the frame models by considering four different arrangements over the height of the structure such as full infill frame (FIF), full infill frame with soft story (FI-SSF), exterior bay infill frame (EBIF), and exterior bay infill frame with soft story (EBI-SSF). For each case, four different infill wall thicknesses of 10 to 25 cm were taken into account. Thus, a total of 170 different frame models with and without infill walls were investigated thorough nonlinear static analysis method by means of SAP 2000 program. The infill panels were modeled by utilizing equivalent diagonal compression strut. As a result of the analyses, the capacity curves of the structures, maximum base shear force, initial stiffness, and mechanism of the plastic hinge formation in the structures were determined and comparatively discussed. It was observed that both wall thickness and arrangement have significant impact on the lateral load carrying capacity and hinge formation of the case studied structures, on the other hand, with their compatible choice the greatest seismic performance could be achieved.

The choice of the control displacement in pushover analysis of bridges: a case study

Seismic assessment of existing bridges requires consideration of the structural inelastic behaviour. Non-linear static methods (i.e., pushover) have become a standard tool in civil engineering practice for the analysis of various structural typologies, including bridges, due to simplicity compared to non-linear dynamic analysis. Nevertheless, the extensions of the applicability of pushover methods to bridges seem to show peculiar relevant questions. This work presents a case study of non-linear static analyses of an existing reinforced concrete (RC) highway beam bridge. Among the numerous proposals available, traditional pushover analysis has been chosen as the analysis method. The simply supported beams bridge has a total length of around 706 m, with 16 spans of 43 m each; the simple deck is made of reinforced concrete beams pinned over the multiple stem piers, whose height varies regularly from 11 m to 5.5 m. Non-linear behaviour of bearing devices, soil-abutment interaction system and expansion joints (closure) have been accounted for. The analysis has been performed in both longitudinal and transverse directions, subjecting the structure to the following load distributions: (i) constant along the deck and (ii) one that considers the contribution of the modes according to the response spectrum analysis. The case study seems to confirm the importance of the reference point selection in the bridge seismic assessment via pushover method. The pushover has been compared with the results of dynamic non-linear analysis.

The effect of floor slabs in a structure with frame shear walls modeling in pushover analysis

Pushover is a nonlinear static analysis method that provides information on nonlinear structures’ behavior due to earthquakes. Subsequently, it has been recommended as a reliable tool to help know the capacity of structures. Another consideration is its easiness of interpretation than the nonlinear dynamic analysis. Numerical modeling of the structure plays an important role in this analysis since every detail of modeling could give different results. The objective of this study is to analyze the effect of the existence of floor slabs in a structure with frame shear walls modeling, which considers the frequent attempt to simplify structural modeling. The effect of the position of components assignation is going to be analyzed too, especially floor slabs and beams, whether it was assigned with centroid or top center insertion point in pushover analysis. In this study, an existing hospital building with vertical irregularity has been modeled into four various models using SAP2000. As the result of pushover analysis, every model gives its pushover curves which reflect its behavior. Those results show that the models with floor slabs have higher capacities. In addition, the combination of the assignation of floor slabs and the top center insertion point gives the highest capacity compared to the other models.

Effects of the extended N2 method on non-linear static procedures of reinforced concrete frame structures

This paper intends to contribute to the validation of the extended N2 nonlinear static method of seismic analysis through the study of two existing reinforced concrete frames. The scope is to further investigate the limitations of the original N2 method in predicting the seismic response of plan asymmetric buildings and to assess the higher accuracy of the extended N2 method. The two case study buildings are representative of the Italian construction between the ’70s and ’90s. One is designed for gravity loads only, the other is designed according to an old seismic code. Two modelling strategies are used, one with distributed and the other with lumped plastic hinges. Three eccentricities eCM between centre of mass and plan geometric centre are considered (eCM = 0%, 5% and 15%). The pushover analyses are carried out following the N2 method, the N2 method plus the 100:30 directional combination rule and the extended N2 method. The results are compared with those obtained from nonlinear history analyses. For each building the seismic demand is assessed for three hazard levels. The results indicate that the application of the extended N2 method significantly enhances the shape of the demand prediction, particularly for buildings with higher plan eccentricities. On the other hand, the directional combination does not significantly change the results and should be neglected.

Effect of alternative load path design method on preventing progressive collapse and reducing the rehabilitation cost using FEMA-P58

The alternative load path (ALP) method is an important modern design approach to prevent progressive collapse of buildings by redesigning adjacent structural elements to provide an alternative load path in case of partial collapse. This may lead to tangible changes in the mass and stiffness of the building, which means a change in the seismic behavior of the building. This shows the fact that choosing and designing an alternative load path is not an easy task. Studying the improvement in the seismic behavior of the building, whether direct or indirect, as a result of using the ALP, is the main objective of this paper. To achieve this goal, this study examined approximately 96 models, including the study of the possibility of progressive collapse occurring, whether there is or isn't an alternative path for the loads using non-linear static and dynamic analysis, as well as evaluating the study models using various seismic evaluation methods, where both the nonlinear static pushover analysis method and the FEMA-P58 method were used and compared. The study models are divided into two sections, with and without (ALP). The study models are also categorized by building height using heights of 6, 9, 12 and 15 floors. The models were also divided based on the locations of weak points in the original design that may be susceptible to damage and lead to progressive collapse, whether they are internal, side, or corner weak columns. The findings from the examined models indicate that the efficiency of (ALP) systems is more prominent in low and mid-height buildings compared to tall buildings. Additionally, the results demonstrate that the FEMA-P58 method yields similar predictions regarding building behavior as traditional seismic assessment methods like pushover analysis, but in a simplified manner that benefits non-engineers by providing clear insights into the financial and temporal aspects of different structural system solutions.

Nonlinear seismic analysis of irregular base isolated structures using a new modified lateral load pattern

Nowadays, seismic isolation systems are increasingly used by engineers for retrofitting existing structures and designing new ones. Nevertheless, limited studies have been conducted on the performance evaluation of the nonlinear static analysis methods for estimating the seismic demands of the base isolated structures. The current study proposes a new modified lateral load pattern for seismic analysis of base isolated structures using modified capacity spectrum method (MCSM). Moreover, this study investigates the applicability of the modal pushover analysis (MPA) and modified capacity spectrum methods for assessing the base isolated structures with setback irregularity. To this end, two types of steel moment resisting structures including 3-story (low-rise) and 9-story (medium-rise) with different irregularities in elevation are considered. All the structures are isolated by three types of lead rubber bearing (LRB) isolators with various stiffnesses. In order to consider the effect of ground motion, two types of near-fault and far-fault ground motions are selected. To evaluate the performance of the MCSM and MPA methods, the structural seismic demands estimated by these methods are compared with their benchmark values obtained by the nonlinear time history analysis method. The obtained results show the superiority of the modified capacity spectrum method and the effectiveness of the new modified lateral load pattern presented for this method.

Evaluation of the Seismic Behavior of RC Buildings through the Direct Modeling of Masonry Infill Walls

The direct modeling of masonry infill walls on many buildings, based on damage recorded by various past earthquakes, has become increasingly necessary in order to identify the seismic behavior of these elements, which constitute an important part of reinforced concrete buildings. In this paper, several 3D models were analyzed by the nonlinear static (pushover) method, when ignoring, and when considering, masonry infill walls. The finite element software SAP analyzed the proposed models. These models represent low and mid-rise reinforced concrete buildings infilled with double-leaf hollow bricks. The properties of materials used in Algeria, either in the frame elements or the infill elements, were used. The results obtained were compared according to two parameters, the natural time period of the building and the pushover curve, by varying the values of the dead load and the concrete compressive strength. The results were discussed according to the suggested parameters. The results showed that indirect modeling of such walls, either by taking assumptions embedded in the seismic behavior factor or by means of the macro-modal, can lead to a poor appreciation of the seismic behavior of such buildings. Consequently, direct modeling of walls by the infill of the real void showed acceptable results to some extent. This contributes greatly towards understanding the seismic behavior of this type of building.

Resistance of Gable Structure of Nuclear Island to Progressive Collapse in Conventional Island Shield Building of Nuclear Power Plants

The gable wall of the conventional island of a nuclear power plant carries various pipeline loads connecting the nuclear island and the conventional island. If the gable wall collapses and is damaged due to the progressive collapse of the main plant structure of the conventional island, it will directly threaten the safety of the nuclear island. Therefore, it is of great significance to systematically study the resistance of the gable structure of the nuclear island to progressive collapse for the safe operation of nuclear power plants. Based on the SAP2000 finite element analysis platform, this paper established a model of the reinforced concrete frame structure of the first span of the shield building on the conventional island of a nuclear power plant, including the gable. According to the alternate path method, the node displacement and bearing capacity responses were used to determine the critical components in the gable, and single column failures of the top four in importance were selected as different analysis conditions. Nonlinear static and dynamic methods were used to analyze the displacement, internal force change, hinge sequence of the gable structure on the side of the nuclear island, and the ability of the gable to resist progressive collapse. The analysis results showed that the gable structure of the nuclear island had good resistance to progressive collapse under four single column failure conditions, whether by nonlinear static or dynamic analysis, and the overall vertical displacement obtained by the nonlinear static analysis was larger than that obtained by the dynamic analysis.

The Seismic Resistance Analysis of Frame Structures and Wall Structures Using Ferrocement and Expanded Metal

This article presents a study of the use of ferrocement and expanded metal in the columns, beams, and walls of a reinforced concrete building structure to increase its seismic resistance. This study focused on a concrete building with three stories, located in Thailand. In the design of the reinforcement structure, a calculation and analysis of seismic resistance were conducted in a comparison of the original concrete building structure with the reinforced concrete building structure using the nonlinear static force method (pushover analysis method). The results showed that the seismic resistance of the reinforced concrete building structure was higher than the design value (DPT), with different seismic resistance values for the reinforced frames, columns, and walls of approximately 14%, 81%, and 19%. In particular, it had increased stiffness values for the frames, columns, and walls and increased ductility values for the walls. Moreover, the seismic resistance values originating from the reinforcement were significantly higher than those of the concrete building structure. Therefore, reinforcement should be applied to all concrete building structures with the implementation of the damage index, ensuring that it is reduced to the allowable level.

A Methodology for Assessing the Component-Level Fragility Curves and Its Application to a Class of Integral Abutment Bridges

Seismic vulnerability assessment of structures is a major research area and the output, i.e., fragility curves (FCs), within a probabilistic framework, devises effective seismic disaster mitigation. The present study proposes a novel methodology for obtaining the structural component-level FC through two new approaches with respect to the assessment of seismic demand and the computation of fragility. The present study evolves an existing nonlinear static method by a few steps to be able to assess the probabilistic demands and develops a numerical computation technique that exploits the actual profiles of the evaluated distributions of the structural capacity and demand data in a study to obtain the fragility magnitudes. The substitute methodology is implemented to derive the FCs of a class of integral abutment bridges while assessing the demands in a simple manner and avoiding the complexities of dynamic analysis and yet with reliable precision as well as averting the misjudgment of fragilities stemming from the lognormal or normal fit on the data, which are practically very rough fit or misfit to it, as imposed in the traditional fragility formulation.

Fast Nonlinear Static Aeroelasticity Method for High-Aspect-Ratio Wings at Different Mach Regimes

A low-computational-cost method is proposed in this paper to predict steady-state nonlinear aeroelastic response for high-aspect-ratio wings. This fast nonlinear static aeroelasticity method relies on a simple but robust mathematical approach. The work presented in this paper evaluates the accuracy of a nonlinear aerodynamic method on a large range of Mach numbers for a geometry representative of a typical industrial high-aspect-ratio-wing aircraft. The robustness of the method relies on the accurate estimation of the local pressure field based on an aerodynamic database using a local incidence estimated with a vortex lattice method. The database can be filled with flight test, wind tunnel test, or high-fidelity numerical simulation. The structural deformation is provided by a coupled aeroelastic high-fidelity numerical simulation, and so this paper focuses mainly on the development and validation of the aerodynamic model. Then, the flexible coefficients of the wing are compared to the high-fidelity aeroelastic numerical simulations for a set of Mach numbers ranging from subsonic to transonic conditions. The results presented in this paper show that the present method is very accurate for low-Mach-number regimes (error is lower than 1% on lift), and it is also adapted to transonic flow regimes because the error on lift is lower than 5%. For high Mach numbers, the current solution commits larger errors on drag and pitching moment coefficients.

On the seismic response of rack structures affected by pinching

The nonlinear static and dynamic behavior of rack structures affected by joint pinching are studied using a simplified single-degree-of-freedom system. Since the joints of steel rack structures play a crucial role in the capacity design methodology, as they are the main source of energy dissipation, their behavior is widely studied in the literature, highlighting their reduced hysteresis loop. However, no systematic study investigates and associates these characteristics with a possible increase in displacement demand. Using a single-degree-of-freedom system focuses attention on the type of cyclic behavior and allows a comparison of linear and nonlinear responses, the latter evaluated using both elastic-plastic and pinching laws. At prescribed ductility, the elastic-plastic and pinching responses can be compared with the prescriptions of Italian and European building codes. This simplified method was also applied to case studies of experimental pushover tests on racks found in the literature. Results showed that neglecting the joint pinching behavior for a rack structure can lead to an underestimation of the displacement demand in the case of the application of the nonlinear static seismic analysis method and hence to the overestimation of the q-factor for the application of linear seismic analysis methods.

Nonlinear Seismic Analysis of Perforated cold-formed steel shear wall with Upright Section

During the last few decades, cold-formed steel (CFS) is extensively used in mid- and low-rise housing due to the increasing demand of rapid constructions along with its various advantages in comparison with other structural material. Cold-formed steel framed shear walls (CFSFSW) are most common and primary lateral load resisting system. However, adopting it in the seismic zone is difficult, especially because many design components remain open. In this research an effort has been made to design the shear wall system with both unperforated and perforated upright sections using nonlinear static analysis method. In ABAQUS, a general-purpose finite element analysis software, three-dimensional models using shell elements are used to simulate a shear wall system. A comparative study regarding the lateral load capacities with respect to maximum allowable lateral deflection including different parameters like column sections, thickness and perforation arrangements are presented here. It was found that increasing thickness and including Chanel stiffeners improves the lateral strength of original upright section. The developed modelling protocol helps to estimate its lateral performance under earthquake with reasonable accuracy.

SEISMIC PERFORMANCE OF REINFORCED CONCRETE FRAME WITH CONCRETE JACKETED COLUMNS

The study presents the effectiveness of Reinforced Concrete (RC) jacketed columns in enhancing the seismic performance of a five-story RC frame. The performance of the structure is examined using a non-linear static method also known as pushover analysis. The retrofitting approach used in this study is a local level approach and its effect on the global behavior of the frame. SAP 2000 has been used to perform the analysis for the frames before and after jacketing the columns. The sequence of hinges formation has been studied for both frames. The change in ductility capacity and elastic stiffness before and after jacketing of the columns is obtained using bilinear curves. Both the structural parameters calculated for existing and jacketed structures showed a substantial increase in their respective values after jacketing. Variation of base shear for both the frames is obtained using capacity curves or pushover curves. The pushover curve obtained as a result of static nonlinear analysis indicated a considerable increase in the strength of the jacketed frame which is almost double the capacity of the existing frame.

Fragility-based framework for optimal damper placement in low-rise moment-frame buildings using machine learning and genetic algorithm

Commonly, seismic fragility is used as an assessment tool rather than a design constraint for existing building structures. In addition, the degree of seismic fragility safety margin after retrofitting existing structures is usually unknown during the early retrofit design stage. The current study proposes a framework that allows the designer to assign the preferred seismic fragility margin as a design variable before retrofit of a structure using soft computing techniques. In addition, it provides the design damping ratio to achieve the optimal damper capacity distribution required for retrofit. To this end, a machine learning model (MLM) is used to construct safety margin curve (SMC) graphs for the structural system considering different limit states to obtain the design damping ratio. This MLM is trained with a wide range of structural systems subjected to various levels of ground motion intensities for predicting seismic responses of the system. The main role of the MLM and SMC is to provide a reasonable approximate range for damper capacity in each story to reduce the computational time required for the optimization process. After that, a genetic algorithm (GA) optimization process is implemented to obtain the optimum capacities of the energy dissipation devices (EDDs) required for retrofitting the structure using the design damping ratio obtained from the SMC. Displacement-dependent EDDs are used in the current study because of their effectiveness in dissipating seismic energy. The EDDs are arranged such that the seismic demands are controlled to achieve the required basic seismic safety objective maintaining the optimal EDD capacity for each story. The reliability and robustness of the framework are investigated using various case-study examples and validated by comparing the results with those obtained from nonlinear time history (NLTH) and nonlinear static methods. The proposed framework is validated for low-rise moment-resisting frame buildings that can be represented using a single degree of freedom (SDOF) system. The framework is expected to enable researchers and engineers to effectively implement the required level of seismic safety in retrofitted structures with less computational cost and allows the designer to select the most suitable retrofit scheme considering multiple limit state criteria checks.

Modal Pushover Analysis for Seismic Performance Assessment of Underground Structures

ABSTRACT Pushover analysis as an efficient nonlinear static analysis method has been widely applied to the seismic inelastic performance evaluation of above-ground structures. Although it has the main advantage of high computational efficiency compared to nonlinear dynamic time-history analysis (THA), the assumption that the fundamental mode dominates structural response limits its application to long-period structures. Improved pushover analysis has been developed to consider the higher mode effect, named modal pushover analysis (MPA), but all research mainly focused on buildings and bridges. Since the mechanical behaviors of the underground structures and above-ground structures under seismic exaction are not exactly the same, so far, MPA suitable for seismic performance assessment of underground structures still has not been developed. Therefore, the aim of this investigation is to develop MPA for the seismic performance assessment of underground structures. A prototype subway station structure and a soft site are used to study the applicability of the developed MPA and compare it with the traditional pushover analysis procedure and nonlinear THA. Numerical analysis results of the subway station illustrate the applicability and potential of the developed MPA for underground structures.

Seismic Retrofitting of RC Frame Structure Using Energy Dissipation Device

Abstract: This study examines the performance-based design of structure that is increasing commonly in earthquake resistance design. to ensure any structure possess earthquake resistant design, certain minimum performance objective is desired at different level of seismic excitation. With the help of some devices, Lowto medium rise buildings are performing well forthe seismic actions. In the present work, originally deficient RC frame is analyzed with static analysis and after this static non- linear analysis is performed in which suitable energy dissipation devices are installed sequentially. first analyzed with Viscous fluid Damper then Lead- rubber isolator is used has designed as per performance-based design criteria of G+6 RC frame building. These models are analyzed for important residential use and located at seismic zone IV. Linear static and nonlinear static methods are used to analyze the structure with help of CSI ETABSv18 software. Results which are discussed is minimum performance level, story drift,performance point and performance objective. After analysis of results, structure which is installed with Led-rubber bearing isolator is performed well during an earthquake and satisfy with desired minimum performance level. In case of viscous fluid damper, it is not satisfactory to achieve desired minimum performance up to this extent it helps to reduce floor acceleration.