Nonlinear Static Analysis Research Articles

Effectiveness of structural walls in improving the serviceability of a seismically-retrofitted RC building

AbstractA moderate earthquake with a magnitude Mw of 6.8 hit the Elazig Province of Turkey on January 24th, 2020, causing fatalities and structural damage/failure. Following the earthquake, a field reconnaissance was conducted at the Administration and Operation Campus of Karakaya Dam, which is 19 km from the earthquake epicenter. The exhibited performances in two side-by-side nominally identical reinforced concrete (RC) buildings with the same material properties and soil conditions differed significantly. The main reason lies in the preventive action taken before the earthquake in one of the buildings. The building retrofitted with additional structural walls had a slight/no damage level. However, the non-retrofitted building suffered severe damage due to large cracks in numerous infill walls, some of which were exposed to partial collapse. That makes the non-retrofitted building unserviceable, requiring evacuation after the earthquake. The field-observed building damage was compared with the seismic performances acquired from their refined numerical models for the recorded ground motions. The photographic documentation exposing the entire performance and damage level in non-retrofitted and retrofitted buildings was quantified by static pushover and nonlinear response history analyses. The post-earthquake performance of nonstructural members in retrofitted and non-retrofitted buildings was simulated with reasonable accuracy.

Investigation of effective parameters on seismic performance of steel frames with CFST columns

The seismic performance of steel frames with composite columns is evaluated by the seismic performance factors. Despite the essentiality of appropriate coefficient values, there are limitations in the building code regarding seismic performance factors of composite structures. These values have been presented in the regulations based on engineering judgment and comparison with similar steel and concrete structures. However, limited research exists on the determination of seismic performance factors for composite structures, where these coefficients are affected by numerous parameters. This article aims to cover the existing gaps and examine the parameters that have received inadequate attention in regulations and articles, despite their significance in the seismic design of composite structures. The present study conducts a nonlinear static pushover analysis of steel structures with concrete-filled tubular steel columns (CFST) to investigate the influential parameters in seismic performance factors. The variables studied in this research encompass the height of the structure, soil type, lateral force-resisting system, and structural irregularity. The findings demonstrate that changes in structural height influence the value of the response modification factor in all examined soil types for IMFs and SMFs. Also, the response modification factors provided in ASCE 7 prove to be conservative for the studied lateral force-resisting systems excluding SMFs in composite structures. In addition, the seismic performance of the studied models has dropped due to the geometric irregularity of the plan and the irregularity of non-parallel systems. Besides, the response modification factor values for composite structures surpass those specified for similar steel structures, while Eurocode 8 and ASCE 7 consider these values to be equal and similar to steel structures, respectively.

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.

Comparative analysis of the sustainability and seismic performance of a social interest house using RC moment frames and bahareque as structural systems

This study compares the seismic performance and environmental impact of a social housing structure designed with reinforced concrete with a structure using Guadua angustifolia “Kunth” cane. The aim is to contrast the implementation of an ecological material such as the Guadua cane, which is an accessible alternative due to its cost and construction time, versus the traditional reinforced concrete (RC) construction method. Both applied to social housing structures. The seismic performance of both methods is analyzed through nonlinear static analysis (pushover) with the objective of establishing the performance; structural and nonstructural damage, performance point, maximum displacements, and structural elements that induce structural failure; and acting forces, against a design earthquake (established by the NEC DS 2015 Standard), with a return period of 475 years. The environmental impact is evaluated through a life cycle assessment of the structure (LCA). Thus, the embodied carbon obtained from each structural element (foundations, beams, columns, floors, and roof support elements) was determined, considering material manufacturing, transportation, and construction. The results obtained demonstrated a higher seismic performance, with 70% less environmental impact on the Guadua cane structure.

An Open-Source Framework for Modeling RC Shear Walls Using Deep Neural Networks

Reinforced concrete (RC) shear walls macroscopic models are simplified strategies able to simulate the complex nonlinear behavior of RC shear walls to some extent, but their efficacy and robustness are limited. In contrast, microscopic models are sophisticated finite element method (FEM) models that are far more accurate and reliable. However, their elevated computational cost turns them unfeasible for most practical applications. In this study, a data-driven surrogate model for analyzing RC shear walls is developed using deep neural networks (DNNs). The surrogate model is trained with thousands of FEM simulations to predict the characteristic curve obtained when a static nonlinear pushover analysis is performed. The surrogate model is extensively tested and found to exhibit a high degree of accuracy in its predictions while being extremely faster than the detailed FEM analysis. The complete framework that made this study possible is provided as an open-source project. The project is developed in Python and includes a parametric FEM model of an RC shear wall in OpenSeesPy, the training and validation of the DNN model in TensorFlow, and an application with an interactive graphical user interface to test the methodology and visualize the results.

Seismic performance of eccentrically braced frames with short-links: IDA approach using chilean earthquakes

In this research the seismic performance of eccentrically braced frames (EBF) with short links using Chilean earthquakes is studied. The study includes nonlinear static and dynamic analyses, calibration of numerical link models with experimental studies, and over 15,000 models analyzed. Results show that higher ductility and deformation are obtained in most archetypes, while models with 8 stories exhibit more stiffness and less ductile behavior. Furthermore, the strength capacity and ductility increase with the increment of the seismic zone and soft type of soil. Moreover, the research provides a table with the seismic design parameters for each archetype group comparing these values with Chilean seismic specifications. Finally, the study concludes that structures designed with more strength and stiffness have a lower collapse probability under extreme events. This research provides valuable information for structural design and includes fragility curves and a discussion of results that can be applied to structural design.

Probability of collapse evaluation for high-rise reinforced concrete buildings in the event of near-fault earthquakes and soil-structure interaction effects

This paper presents a probabilistic evaluation of the seismic performance of 10, 20, and 30-story reinforced concrete buildings with dual systems located in Tehran, Iran, considering the effects of Soil-Structure Interaction (SSI). The buildings are designed according to the Iranian seismic code, and their nonlinear planar models are developed in OpenSEES, accounting for two fixed and flexible-base conditions. The concentrated plasticity approach is employed to simulate the nonlinear response of frame elements, while the displacement-based fiber elements are utilized to model the shear walls. The Winkler springs and dashpot technique was used to capture the uplift of the foundation in flexible-based models. The planar models are then subjected to nonlinear static and dynamic analysis, as well as Incremental Dynamic Analysis (IDA), followed by fragility assessment and collapse risk evaluation using the risk integral method. A suite of pulse-like and non-pulse near-field earthquakes is employed to account for the effects of impulsive characteristics of the ground motions on the performance of buildings with rocking foundation. The probabilistic assessment of building models was conducted based on FEMA P695 methodology. The results indicate that the performance of flexible-base buildings is improved for the strong earthquakes and pulse-like records. However, the advantages of foundation flexibility are diminished in taller buildings due to their larger weight and higher mode effects. The foundation rotation is found to be lower than the performance limits of the seismic code. Finally, the SSI exhibits varying effects on the collapse risk of buildings of different heights, with a positive effect on shorter buildings, whereas its impact on taller buildings depends on the expected seismic hazard level at the site.

IDA-Based Collapse Safety Assessment of Torsional-Irregular Buildings, Considering Ductility and Damage

The complexity in nonlinear behavior of torsional-irregular buildings in combination with uncertainty due to the natural randomness of earthquake records has been always a main challenge for buildings’ seismic design. To find a solution to this challenge, three reinforced concrete (RC) building archetypes were designed and next developed into their nonlinear models. Nonlinear static (pushover) analyses were performed to calculate the capacity of the archetype models in all principal and non-principal directions while incremental dynamic analyses (IDAs) were conducted by applying 30 accelerograms from both near-field and far-field earthquakes. The IDA capacity curves, collapse fragility curves and log-normal cumulative distribution functions (CDFs) were established by including both the aleatory randomness and epistemic uncertainty. Despite previous studies wherein fragility curves were given by evaluating structures’ collapse along structural reference axes or simply on [Formula: see text], [Formula: see text]-axes, in this paper, possible building collapse on a critical non-principal direction (where maximum seismic response was observed) was simulated and its probability was accounted for developing IDA curves and log-normal CDFs. Accordingly, this issue was mirrored in computing available/acceptable collapse margin ratios (CMRs). In addition to the well-known outline used for calculating CMRs in the literature (that is based on estimation of collapse capacity in terms of earthquake intensity measure (IM)), the framework proposed here includes a new method for calculating the CMRs in terms of displacement-based drift, ductility, and damage. The superiority of the proposed method over the former is consistent with the buildings’ design procedure that is governed by storey drift control rather than base-shear strength. Refined statistics of CMRs given by taking into account displacement-based responses illustrate the available CMRs exceed the acceptable CMRs, meaning that a satisfactory safety margin against collapse will be anticipated in the targeted building class if a suitable yielding mechanism with sufficient ductility is provided for seismic force-resisting system by applying seismic design provisions of the current codes.

Seismic Performance of RC Moment Frame Buildings Considering SSI Effects: A Case Study of the New Venezuelan Seismic Code

The Soil–Structure Interaction (SSI) effect has been widely evidenced during several earthquakes around the world. In the Venezuelan context, the seismic event in Caracas in 1967 showed the significant consequences of designing buildings without considering the SSI effect. Nevertheless, limited research on the seismic performance of concrete moment frames (commonly used as structural systems in office and residential buildings in Venezuela and Latin America) considering the SSI effects has been developed, although there have been continuous updates to the Venezuelan Seismic Code. In this research, the influence of the SSI on the seismic performance of RC moment frame buildings designed according to the New Venezuelan Seismic Code was studied. An extensive numerical study of 3D buildings using concrete moment frames supported by mat foundations on sandy and clayey soils was performed. The response spectrum method, non-linear static analysis, and non-linear dynamic analysis were used to assess the seismic response of the archetypes studied. The results show that SSI effects can have a significant impact on the seismic response of RC moment frame buildings, increasing the interstory drift ratio and decreasing the shear forces. As is shown in fragility curves, the probability of collapse increases for cases with flexible bases in comparison to the cases of models with fixed bases. Additionally, in the 24-story archetype, the fixed-base model reached a maximum probability of collapse. Finally, a new proposal for the reduction of the strength-reduction factor (R) must be incorporated into the Venezuelan Seismic Code to improve the safety of the structures. Limitations in the use of RC moment frames must be incorporated for high-rise buildings since, as the present work demonstrates, for high-period structures, the normative provisions are not reached.

Procjena oštećenja i analiza vjerojatnosti oštećenja i oštetljivosti armiranobetonske zgrade

In addition to a concise literature review, this study presents a comparative analysis of reinforced concrete (RC) buildings through damage index (DI) analysis using different methodologies. The seismic response of a five-story RC frame system building, designed in accordance with the EN structural Eurocodes, was analysed through fragility and vulnerability assessments. The Park–Ang methodology was used in the analysis for determining DI and its parameters. Nonlinear static analysis (NSA) and nonlinear dynamic analyses (NDA) were performed, and the fragility and vulnerability curves were constructed using the obtained results and processed through statistical analysis. The results were calculated using four different DI models: the DIPA model using both the NSA and NDA results (M1), modified DIPA model using both the NSA and NDA results (M2), DIPA model using the NSA results (M3), and modified DIPA model using the NSA results (M4).

Evaluating the Seismic Performance of Low-Rise Concrete Buildings Using Nonlinear Static Analysis

Evaluating the Seismic Performance of Low-Rise Concrete Buildings Using Nonlinear Static Analysis

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.

System reduction-based approximate reanalysis method for statically indeterminate structures with high-rank modification

Efficient structural reanalysis for high-rank modification plays an important role in engineering computations which require repeated evaluations of structural responses, such as structural optimization and probabilistic analysis. To improve the efficiency of engineering computations, a novel approximate static reanalysis method based on system reduction and iterative solution is proposed for statically indeterminate structures with high-rank modification. In this approach, a statically indeterminate structure is divided into the basis system and the additional components. Subsequently, the structural equilibrium equations are rewritten as an equation system with the stiffness matrix of the basis system and the pseudo forces derived from the additional elements. With the introduction of the spectral decomposition, a reduced equation system with the element forces of the additional elements as unknowns is established. The approximate solutions of the modified structure can then be obtained by solving the reduced equation system through a pre-conditioned iterative solution algorithm. The computational costs of the proposed method are compared with those of two other reanalysis methods, and numerical examples including static reanalysis and static nonlinear analysis are presented. The results demonstrate that the proposed method has excellent computational performance for both structures with homogeneous material and structures composed of functionally graded beams. Furthermore, the superiority of the proposed method suggests that the combination of system reduction and pre-conditioned iterative solution technology is an effective approach to develop high-performance reanalysis methods.

Geometrically nonlinear bending mesh-free analysis of functionally graded porous sandwich beam

In this work, geometrically nonlinear static bending analysis of sandwich beams with a porous core and two skins made of functionally graded materials using a mesh-free method is presented. The material types of the core and face sheets of the beam are chosen so that the material continuity between the layers is guaranteed. The nonlinear governing equation including geometric nonlinearity is established via the principle of virtual work. This equation is discretized into a system of algebraic equations by the mesh-free approach, which is based on the C1 point interpolation method and polynomial basis functions, and then solved by the direct iterative method. The convergence of the mesh-free method is tested to determine the sufficient mesh level for the analysis. Comparative and comprehensive studies are performed to investigate both the correctness and the influences of several important parameters and boundary conditions on the linear and nonlinear deflections of the beam.

Effects of Multi-Directional Seismic Input on Non-Linear Static Analysis of Existing Reinforced Concrete Structures

Recent studies have shown the importance of including the seismic input directionality in nonlinear analyses for an accurate prediction of the structural demand on frame structures. This paper proposes a new method that includes the multi-directionality of the input seismic forces in Nonlinear Static Analyses (NSAs). Conventionally, the pushover (PO) analyses apply monotonically increasing lateral loads in two directions that typically correspond with the building X and Y directions, that in the case of a rectangular plan are parallel to the building sides. Since in general the direction of the seismic input is a priori unknown, the effects of applying the PO load patterns along varying angles are studied in this paper. Two non-code-conforming reinforced concrete buildings are used as a case study. They have identical structural design but the first one is doubly symmetric while the second one has a significant plan asymmetry due to the translation of the center of mass. PO loads are applied to both structures at angles between 0° and 360° with 15° increments. The results of the NSAs are compared with those of multi-directional NHAs applied at the same angles. The structural demands show that the multi-directional NSAs are more conservative than the conventional NSAs, especially at the corners of the asymmetric- plan building where they can yield significantly higher demands. The base shear capacities in the X and Y directions decrease for intermediate angles due to the interaction between the responses in the X and Y directions that can be captured thanks to the columns’ fiber section discretization. On average the results of the multi-directional NSAs are closer to those of the NHAs, even though they are generally lower.

Seismic design of buckling-restrained knee-braced frames considering cumulative damage

A buckling-restrained knee-braced frame (BRKBF) is an efficient structural system utilizing short buckling-restrained braces (BRBs) as knee bracing elements. Because of the shorter yielding core length compared to those of conventional BRBs, one of the key parameters concerning the performance of this system is the low cycle fatigue cumulative damage of the BRBs. This paper presents a seismic design method considering the cumulative damage, performance evaluation, and collapse assessment of 3-story, 6-story, and 9-story archetype BRKBFs. An energy-based plastic design method was utilized to design the example frames. The frames were then evaluated by nonlinear static analysis and multiple-stripe analysis (MSA). The results indicated that BRKBs were able to accommodate seismic motions with limited damage. The validity of the design methodology considering cumulative damage was also confirmed.

Nonlinear static analysis of the behavior of an existing masonry building under seismic action

Nonlinear static analysis of the behavior of an existing masonry building under seismic action

Nonlinear static behavior analysis of single/double-layer frame tunnels with mortise and tenon joint

Prefabricated tunnels are composed of prefabricated components through joints, and the joints are of weaker stiffness than other parts. The static behavior of a tunnel shows nonlinear characteristics. This study analyzes the nonlinear static behavior of single/double-layer frame tunnels with mortise and tenon joint. The mechanical properties of mortise and tenon joint are studied by large-scale model tests. A finite element model of a prefabricated frame tunnel is established, the nonlinear static behavior of prefabricated frame single/double-layer tunnels is studied, and the mechanical properties of a prefabricated joint tunnel and a wet joint tunnel are compared and discussed. The results show that the deflection and opening values of the mortise and tenon joint show a three-stage nonlinear change during the compression bending process. The single/double-layer tunnels with mortise and tenon joint exhibit a stiffness recovery phenomenon under a static load. The deformation characteristics of the single/double-layer tunnels show obvious differences due to their different structural forms. Overall, the anti-deformationcapability of the prefabricated frame tunnel with mortise and tenon joint is weaker than that with the wet joint. The structural integrity and stability of the prefabricated tunnel are worse than those of the wet joint tunnel, and its stiffness changes greatly.

Nonlinear static analysis of multi-segmented toroidal shells under external pressure

This paper investigates the nonlinear static responses of multi-segmented toroidal shells with egg-shaped cross sections. The discontinuity effect in terms of displacement and the slope at the toroidal shell edge must be constrained by the Lagrange multiplier technique. The structural shape of the multi-segmented toroidal shells can be described by the differential geometry of the shell with the six-center-combined toroidal shells. The energy functional of the multi-segmented toroidal shells can be written in the appropriate form based on the principle of virtual work. The numerical results of the displacement responses and the volume change can be obtained by the nonlinear finite element method via the fifth-order polynomial shape function and a direct iterative method. In this study, the Lagrange multiplier is the internal force at the toroidal shell junction sustaining the smooth curve of the multi-segmented toroidal shells under several loads. Finally, the results of the volume change and the displacement responses for various geometric parameters are presented and discussed.

Behaviour factor and seismic safety of reinforced concrete structures designed according to Eurocodes

Eurocode 8 allows force-based seismic design and safety assessment of buildings as if they were indefinitely linearly elastic. However, to implicitly account for their inelastic deformation capacity, Eurocode 8 allows reduction of the design values of seismic forces through a structure-dependant behaviour factor. Recent studies showed that this design approach yields structures with different probabilities of failure in different sites. However, for optimal design and investment of economic resources, a structural code should ensure similar risk level (lower than an acceptable risk level) for all structures that are designed according to it. To achieve this goal, the use of risk-targeted behaviour factors may be considered; therefore, the behaviour factors adopted for the design of the same structure in zones with different seismicity levels should be different.In this study, reinforced concrete moment-resisting frame buildings designed according to Eurocodes with different design values of seismic acceleration and number of storeys were considered, and their “available” behaviour factors and probabilities of failure were evaluated through nonlinear static analyses. The potential dependency of the available behaviour factor and probability of failure on different design parameters, as well as their dependency on the model adopted to reproduce the nonlinear response of reinforced concrete members, were investigated, and are discussed in this paper. The calculation of the probabilities of failure of the case-study structures showed that their probability of failure in low-seismicity zones was significantly lower than the acceptable risk level, which was not optimal. Conversely, the structures designed for high-seismicity zones had probability of failure similar to or higher than the acceptable risk level, which was optimal or not admissible, respectively. Thus, based on the assessed values of the available behaviour factor and probability of failure, a modification to the current equations for the calculation of the behaviour factor is presented. This modification implies the use of hazard-dependent values for the behaviour factor to have structures with similar and hazard-independent probability of failure. Notably, because the probabilities of failure for structures designed for low-seismicity zones were significantly lower than the acceptable risk level, the proposed hazard-dependent behaviour factor was higher than that currently adopted according to the Eurocode.