An energy-based approach for nonlinear static analysis of structures

This research investigates numerically the potential failure of different framed structures after removal of a corner column. This study is directed towards the role of the joint above the removed column in terms of framed structures stability and internal forces redistribution utilizing linear static, nonlinear static and nonlinear dynamic analysis procedures. First, the preliminary linear static analysis as a part of more detailed nonlinear static and dynamic analysis to model reinforced concrete frames is performed. For nonlinear numerical models, three different moment-rotation capacity curves are considered for the joint above the removed column. These curves are taken according to FEMA 356 regulation according to the reinforcement condition at the joint location to represent normal joint, anchorage deficient joint and shear deficient joint. In linear static models, the results confirmed that, the more moment the joint can resist at the removed column location, the less moment is generated at the beam’s other end. In nonlinear static analysis, the model with normal plastic hinge properties recorded a higher carrying capacity than the model with both shear and anchorage plastic hinges. Nonlinear dynamic analysis with less assumptions offer the more representative modeling for the considered case study which is obvious from its closer perdition of internal forces and deflection compared to the reference findings.

In this study, a new empirical method is presented to obtain Dynamic Increase Factor (DIF) in nonlinear static analysis of structures against sudden removal of a gravity load-bearing element. In this method, DIF is defined as a function of minimum ratio of difference between maximum moment capacity (Mu) and moment demand (Md) to plastic moment capacity (Mp) under unamplified gravity loads of elements. This function determines the residual strength of a damaged building before amplified gravity loads. For each column removal location, a nonlinear dynamic analysis and a step-by-step nonlinear static analysis are carried out and the modified empirical DIF formulas are derived, which correspond to the ratio min of beams in the bays immediately adjacent to the removed column, and at all floors above it. Therefore, the new DIF can be used with nonlinear static analysis instead of nonlinear dynamic analysis to assess the progressive collapse potential of a moment frame structure. The proposed DIF formulas can estimate the real residual strength of a structure based on critical member.

This paper presents a multi-dimensional variable-kinematics finite element model for nonlinear static analyses of structures with complex geometries. The approach incorporates higher-order beam models and classical solid finite elements in a unified framework, enabling refined modeling of complex geometries. The finite element procedure proposed follows the Carrera Unified Formulation (CUF) and uses a pure displacement-based methodology. The governing equations are derived within the classical continuum mechanics framework, and weak-form equilibrium equations are established using the Principle of Virtual Displacements (PVD). Within the CUF framework, higher-order beam and hexahedral solid models are defined in a unified manner, and the governing equations are written in terms of invariants of mathematical models used and the theory of structures approximation. A coupling technique is used between the beam and solid elements at the nodal level using superposition. The capabilities of fully nonlinear variable-kinematics models are investigated for the static analysis of various rectangular and curved structures. The numerical results are compared with solutions obtained using commercial software. Finally, the proposed methodology is applied to analyze more complex geometries in engineering applications. The results show the capabilities of variable-kinematics models in terms of both accuracy and computational efficiency for the computation of highly nonlinear deformed states and localized phenomena, such as stress concentrations and buckling.

This study is the compared seismic performance that are difference between the performance of structures on various site classes and beam-column connection. this analysis model was designed the previous earthquake load. To compare the performance levels of the structure was subjected to nonlinear static and nonlinear dynamic analysis. Nonlinear analysis was used to The Perform 3D program. Nonlinear static analysis was compared with the performance point and Nonlinear dynamic analysis was compared the drift ratio(%). Analysis results, the soft site class of the displacement was more increase than rock site classes of the displacement. Also The smaller the displacement was increased beam-column connection stiffness.

The main objective of this paper is to evaluate the load-displacement capacity of steel moment-resisting frame structures using the conventional non-linear static analysis method and incremental dynamic analysis approach. Emphasis was put on the influence of different lateral load patterns on the plastic hinge of structural components and also on the seismic behavior of the structures which is influenced by the behavior of their components [(EEsof, electronic engineering software)]. Firstly, to get an idea, two simple frames were selected and analytically tested using the conventional push-over and then the results were compared with dynamic analysis approach using a simple harmonic time-history. The results show that the axial forces in columns obtained from dynamic approach are smaller than those of the other non-linear static methods and this influences the plastic hinge lengths. Then three sets of steel moment-resisting frames were loaded under different load patterns frequently used in conventional push-over analysis methods. The outputs of the structural analysis, in the forms of story shear versus story drift ratios of upper, middle and lower portions show that in general, nonlinear static analysis results in smaller axial forces in columns which cause smaller component deformations, thus weaker structural load-deformation capacities. Key words: Performance- based engineering,nonlinear static analysis, lateral load pattern, plastic hinge.

Nonlinear structural analysis, which can account for geometrical or material nonlinearities beyond the scope of linear methods, typically incurs high computational costs. Recent advances have shown that quantum computers can accelerate various numerical simulations. Although quantum acceleration of linear structural analysis via the Quantum Linear System Algorithm (QLSA) has been studied, its application to nonlinear structural analysis remains unexplored. Here, we introduce our proposed quantum algorithm for accelerating nonlinear structural analysis, summarizing its key features and performance results from our recent study.

A novel approach for seismic nonlinear analysis of inelastic framed structures is presented in this paper. The nonlinear analysis refers to the evaluation of structural response considering P -delta effect, which is in the form of geometric nonlinearity, and inelastic behavior refers to material nonlinearity. This novel approach uses finite element formulation to derive the elemental stiffness matrices, particularly to derive the geometric stiffness matrix in a general form. At the same time, this approach separates the inelastic displacement from total deflection of the structure by applying two additional constant matrices, namely, the force–recovery matrix and the moment-restoring matrix in the force analogy method. The benefit behind this treatment is explicitly locating and calculating the inelastic response, together with strategically separating the coupling effect between the material nonlinearity and geometric nonlinearity, during the time history analysis. Comparison with the traditional increme...

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.

Investigation of progressive collapse resistance and inelastic response for an earthquake-resistant RC building subjected to column failure

Importance of ‘DAF’ in evaluating structural adequacy of gravity-load designed RC buildings

SummaryThis study is carried out to evaluate the response modification, overstrength, and deflection amplification factors for steel diagrid system. To quantify these factors, the rational procedure introduced in Federal Emergency Management Agency (FEMA) P695, which is based on low probability of structural collapse and encompasses nonlinear static and dynamic analyses, is used. To this end, a series of diagrid structures with various slopes of external braces are designed. Nonlinear static analyses are performed to obtain system overstrength and period‐based ductility. Incremental dynamic analyses are then performed to assess collapse margin ratio (CMR) of the archetypes. The effects of spectral shape of different ground motions are considered in CMR values to obtain an adjusted CMR (ACMR), for each archetype. The values of calculated ACMRs are compared with the acceptable values of FEMA P695 to assess reliability of presumed seismic performance factors of diagrid systems. The results show that values of calculated ACMRs for steel diagrid systems designed using the response modification factor equal to 4.50 are acceptable. It is also observed that as the slope of the peripheral diagonal elements increases, the overstrength and the collapse margin ratios decrease, and the ductility of system increases.

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 structural analysis involves the definition of the model and selection of the analysis type. The model should represent the stiffness, the mass, and the loads of the structure. The structures can be represented using simplified models, such as the lumped mass models, and advanced models resorting the finite element method (FEM) and discrete element method (DEM). Depending on the characteristics of the structure, different types of analysis can be used such as limit analysis, linear and nonlinear static analysis, and linear and nonlinear dynamic analysis. Unreinforced masonry structures present low tensile strength, and the linear analyses seem to not be adequate for assessing their structural behavior. On the other hand, the static and dynamic nonlinear analyses are complex, since they involve large time computational requirements and advanced knowledge of the practitioner. The nonlinear analysis requires advanced knowledge on the material properties, analysis tools, and interpretation of results. The limit analysis with macro-blocks can be assumed as a more practical method in the estimation of maximum load capacity of structure. Furthermore, the limit analysis requires a reduced number of parameters, which is an advantage for the assessment of ancient and historical masonry structures, due to the difficulty in obtaining reliable data. The observation of the damage in masonry buildings caused by earthquakes in the past has been shown that the masonry structures can be discretized into several macro-blocks and interfaces. The macro-blocks are portions of a structure with similar material properties and structural behavior, to which the mechanical properties of the material can be assigned or, by simplification, they can be assumed to be infinitely rigid. The interfaces in a macro-modelling represent, in general, the cracks associated to the failure mechanisms. However, in a micro-modelling strategy applied to masonry, in which the units and the joints are individually considered, the interfaces simulate the behavior of the joints. Furthermore, different criteria for the strength parameters of macro-blocks and interfaces can be considered. The limit analysis (Fig. 1) with macro-blocks is a simplified and powerful structural analysis tool to evaluate the ultimate capacity of masonry structures by static models, involving the equilibrium of the macro-blocks through the limit analysis basic concepts.

Pushover analysis as known as non-linear static analysis is one of the structural analysis procedures that is widely used in seismic assessment and performance evaluation of existing structures . In the nonlinear analysis procedure, the behavior of the structure due to external loads acting can be seen from the status of the joints formed. One of the joint models that is less commonly used in non-linear static analysis is the fiber hinge joint modeling. Fiber hinge is a nonlinear joint model that can consider distributed plasticity along with its structural elements. Study this learn possibility difference in results analysis use fiber hinge because properties component specified nonlinear _ researcher . In order to study the impact of the use of joint modeling variations in nonlinear analysis, a regular reinforced concrete structure model with 4 height variations namely 3, 4, 5, and 6 floors which were analyzed with two different types of joint modeling. Fiber hinges and conventional lumped hinges will be defined in the cross section. Research results show that the use of fiber hinge in each model produces score relative moment _ small however given rotation _ relatively more big than lumped hinge as well relative base shear value small than lumped hinges. Considering the fiber hinge is method that gives state of natural response so that deformation globally generated _ more big than lumped hinges. This thing take effect to determination structure performance value.

Given the vast advancements in computing power in the last several decades, nonlinear dynamic analysis has gained wide acceptance by practicing engineers as a useful way of assessing and improving the seismic performance of structures. Nonlinear structural analysis software packages give engineers the ability to directly model nonlinear component behavior in detail, resulting in improved understanding of how a building will respond under strong earthquake shaking. One key component, in particular, for understanding the behavior of moment-resisting frames is the plastic rotation of the flexural hinges. Performance-based standards typically use plastic rotation as the primary parameter for defining the acceptance criteria in moment-resisting frames. Since plastic rotation is a key parameter in the seismic damage assessment, the concept as well as the method to calculate this quantity must be understood completely. Though engineers rely on the plastic rotation output from seismic structural analysis software packages to determine acceptable performance, the actual calculation methods used in achieving such plastic rotation quantities usually lay within a so-called “black box”. Based on the outputs obtained from most structural analysis software packages, it can be shown that running an algorithm considering material nonlinearity by itself will produce reasonably accurate results. Moreover, separately running an algorithm considering geometric nonlinearity also can produce accurate results. However, when material nonlinearity is combined with geometric nonlinearity in an analysis, obtaining accurate results or even stable solutions is more difficult. The coupling effect between the two nonlinearities can significantly affect the global response and the local plastic rotation obtained from the analysis and therefore needs to be verified through some analytical means. Yet, the verification process is difficult because a robust analytical framework for calculating plastic rotation is currently unavailable and urgently needed. In view of this gap, an improved analytical approach based on small displacement theory is derived to calculate the plastic rotations of plastic hinges at various locations of moment-resisting frames. Both static and dynamic analysis with nonlinear geometric effects will be incorporated in the derivation. Here the element stiffness matrices are first rigorously derived using a member with plastic hinges in compression, and therefore the coupling of geometric and material nonlinearity effects is included from the beginning of the derivation. Additionally, plastic rotation is handled explicitly by considering this rotation as an additional nonlinear degree-of-freedom. Numerical simulation is performed to calculate the nonlinear static and dynamic responses of simple benchmark models subjected to seismic excitations. Results are compared with various software packages to demonstrate the feasibility of the proposed method in light of the output results among software packages in calculating plastic rotations.