Numerical analysis of progressive collapse for reinforced concrete frames

Current codes and guidelines provide different methods to perform nonlinear static analysis of structures that require some non-intuitive assumptions in their application. In the present paper an energy-based method for nonlinear static analysis that allows to overcome these assumptions is proposed. In the method the capacity and the demand are both expressed in terms of energy. An energy capacity curve is computed considering that at each step the work of the lateral forces is equal to the structure internal work. The demand is represented in terms of an energy quantity, defined pseudo-energy, that is computed from both the maximum response displacement and the maximum response force. Constant ductility pseudo-energy spectra are introduced as energy demand design spectra, alternative to the input energy demand spectra. The definition of the performance point does not require iterative procedures for equating the internal dissipated energy to the demand energy. For the direct evaluation of the performance point two different operative procedures are proposed. The proposed method is evaluated comparing the earthquake-induced deformations of single degree-of-freedom systems resulting from the application of the presented nonlinear static analysis procedures with those obtained from the time-history analysis and from the application of the EC8 nonlinear static analysis procedure. The method is also applied in the case of a RC plane frame representing the inner frame of a six story building. The results obtained with the proposed method are in good agreement with those computed using nonlinear dynamic analyses, moreover they are characterized by a better accuracy with respect to the results obtained with the method provided by EC8.

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

Design of safe structures with resistance to progressive collapse is of paramount importance in structural engineering. In this paper, an efficient optimization technique is used for optimal design of steel moment frames subjected to progressive collapse. Seismic design specifications of AISC-LRFD code together with progressive collapse provisions of UFC are considered as the optimization constraints. Linear static, nonlinear static and nonlinear dynamic analysis procedures of alternate path method of UFC are considered in design process. Three design examples are solved and the results are discussed. Results show that frames, which are designed solely considering the AISC-LRFD limitations, cannot resist progressive collapse, in terms of UFC requirements. Moreover, although the linear static analysis procedure needs the least computational cost with compared to the other two procedures, is the most conservative one and results in heaviest frame designs against progressive collapse. By comparing the results of this work with those reported in literature, it is also shown that the optimization technique used in this paper significantly reduces the required computational effort for design. In addition, the effect of the use of connections with high plastic rotational capacity is investigated, whose results show that lighter designs with resistance to progressive collapse can be obtained by using Side Plate connections in steel frames.

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.

This paper presents a comparative review of three major seismic analysis methods used for reinforced concrete (RC) structures: linear static analysis, nonlinear static (pushover) analysis, and nonlinear time-history analysis. The study evaluates their underlying theory, modelling requirements, assumptions, accuracy, and level of computational effort. Published global and regional research was reviewed to assess when each method is appropriate for performance evaluation and design. The findings show that linear static analysis is simple and code-friendly but often unreliable for irregular, taller, or higher–mode-sensitive buildings. Nonlinear static analysis better represents inelastic behaviour, stiffness degradation, and hinge formation but may overlook torsional and higher-mode effects. Nonlinear time-history analysis offers the most realistic predictions of seismic response; however, it requires significant modelling detail, computational resources, and careful selection of earthquake records. This review highlights conditions where simplified methods are acceptable and where nonlinear approaches are necessary for accurate and safe seismic assessment and retrofit decisions.

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

In this paper, a simplified analysis procedure to calculate the column removed point displacement at progressive collapse analysis of reinforced concrete structures is proposed. The energy absorption capacity under the column missing event is used for formulations. The approximate method is simple to utilize, user friendly, yet accurate. For progressive collapse analysis of structures, linear static analysis, nonlinear static analysis, linear dynamic analysis and nonlinear dynamic analysis can be performed. In this paper, the nonlinear static analysis from alternate load path method is used and the reason of initial local collapse has not been considered. In fact, an energy-based method by using load-displacement curve of RC frame and considering the effect of floor slab for the progressive collapse analysis is considered. The accuracy of the proposed method is demonstrated by comparing the results to three experimental and analytical results. Finally, the effects of the spans length, sections dimensions, material properties and the beams reinforcements of column removed spans on substructure behavior is studied, as well.

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.

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.

Two-dimensional reinforced concrete frames with the storey of different heights are simulated to the column removal scenario to understand the progressive collapse behaviour by using General Services Administration (GSA 2003) guidelines. Numerical modelling of 4-, 8- and 12-storey structures with different analyses procedures were evaluated such as Linear Static Analysis (LSA), Linear Dynamic Analysis (LDA) and Nonlinear Static Analysis (NLSA) using ETABS 2015. The liner results demonstrate the corner column removal and thus make the structure more vulnerable to progressive collapse when compared to the middle column removal and nonlinear results indicate that the progressive collapse of the structures decreases with increasing the height of the storey.

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.

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.

A linear analysis is inadequate in assessing the seismic demand of a structure under the severe earthquake condition; therefore, a nonlinear static pushover analysis is needed. A pushover analysis helps to identify critical members which are likely to reach their critical state during an earthquake. Therefore, it is necessary to pay proper attention during the design and detailing of the structure. Due to the presence of the infill wall, stiffness of the RC frame increases and it changes the frame action of the moment resisting frame to a truss action thereby affecting the seismic response of the structure. In the present study, G+7 Story commercial cum residential reinforced concrete building is considered for push over analysis. The building has a basement, tower room for a staircase and a machine room for an elevator at the roof top. The shops are located on the ground, first and second story, auditorium rooms on third and fourth story and residential apartment on the remaining floors. As an auditorium room needs column free space for functional requirements, therefore, these are provided with floating columns. Four types of building models are analyzed using push over analysis. Model 1 has no infill walls (conventional model) while models 2, 3 and 4 are created with red clay brick infill wall, hollow concrete block infill wall and AAC block infill wall respectively. An equivalent strut approach is used for the modeling of infill walls. The nonlinear static analysis is performed for the seismic evaluation assessment using ETABS v18 software.  A comparison is made between various models in terms of story displacement, story drift, base shear, performance point and plastic hinge state. The results reveal that the inclusion of infill walls causes a significant increase in the stiffness of the structure and, in turn, reduces story displacement and story drift significantly. The AAC block infill being lighter in weight shows better performance. The formation of plastic hinges developed in the models shows a few deficiencies in the structure which need to be retrofitted for enhancing strength.

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.

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.