A COMPARITIVE REVIEW OF LINEAR AND NONLINEAR STATIC ANALYSIS METHODS FOR REINFORCED 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.

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

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 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.

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.

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.

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

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.

A general multidisciplinary procedure to approach the study of heritage building is synthesized in this PhD thesis considering the main features necessary to identify the structural behaviour of such type of buildings (historical inquires, geometric survey, material identification, in situ inquires) according to qualitative and quantitative methodologies. An in-depth survey has been carried out on the masonry of the Bell Tower of the “Santa Maria del Carmine” Church in the city of Naples, Italy. The analyses followed a multidisciplinary approach to identify its architectural and structural features, to identify the materials used and the state of damage and interventions made in various periods, to assess the stress state in the masonry under gravity loads, and to define its dynamic behavior. The information gathered represents the starting point for designing a seismic upgrade to meet the standards applied to historic monuments. A detailed historical, architectonical and structural inquires have been developed on the Bell Tower of “Santa Maria del Carmine” sited in Naples. These inquires have been preliminary to the study of the Tower by a finite element model for static and dynamic loads. The Bell Tower of “Santa Maria del Carmine” is an ancient (XVII century) historical masonry building located in city of Naples (Italy). The Tower is 68m high and is made by faced yellow tuff masonry along the initial 41 meters of height and by clay bricks along the upper levels. Internal and external walls are covered by decorative dark stone along the first nine meters. Geometrical and material surveys were performed to evaluate the actual damage state, the sequence of changes in the structures. Detailed experimental in situ investigations have been performed to define the geometry, to find the composing materials, to characterize their mechanical properties, to analyze damage condition and to identify the dynamic behaviour of the structure. The experimental results have been successively used to develop a numerical 3-D FE model. This model has been used to perform a linear static analysis under gravity loads to calibrate the mechanical parameters given by experimental results (i.e. the density of materials) and to check the safety condition for the vertical loads usually acting on the structure. Then, a linear dynamic analysis has been also accomplished to assess the values of Young’s modulus of materials and the constraint conditions offered by the surrounding buildings, based on parametric comparisons with the experimental results (natural frequencies and corresponding modal shapes obtained by dynamic in situ tests). This last study has been useful to understand the behaviour of the Tower under horizontal actions like an earthquake, considering that the structure is located in a medium risk seismic area. Therefore with the assumption of a ‘global behaviour’ of the Tower, a non linear static analysis (Push - over) was carried out based on the results of the previous inquiries, pointing out a low risk condition for the expected seismic actions (peak ground acceleration of 0.168g). Considering that previous numerical analysis evidenced that the Tower satisfied global checks for the expected seismic actions, in this paper attention is focussed on the study of local out-of-plane mechanisms activated by those actions. To prevent the activation of local mechanisms an innovative and low invasive intervention with FRP materials has been designed in the areas where local checks were not satisfying.

Recent research trends have indicated an interest in High-Altitude, Long-Endurance (HALE) aircraft as a low-cost alternative to certain space missions. These missions require a lightweight vehicle operating at low speeds, high lift and minimum drag. These conditions necessitate high-aspect ratio wings. Due to its large span and light weight, the wing structure is very flexible. The wings undergo significant deflections as a result of the fluid loads acting on them, and require the consideration of aeroelastic effects. To reduce the structural deformation and increase the total lift, a sensorcraft model with a joined-wing configuration is employed. The results of the simulation of the complex, three-dimensional flow past the joined wing of a HALE aircraft are used as an input for the structural analysis. In the existing studies to date, only simplified structural models have been examined. In the present work, a semi-monocoque structural model is developed. All stringers, skin panels, ribs and spars are represented by appropriate elements in a finite-element model. Linear and nonlinear static analyses under the aerodynamic load are performed. The stress distribution in the wing is explored. Starting with a structural model with uniform mass distribution, a design optimization is performed. The optimized model has a maximum stress 42% lower and a maximum deflection 26% lower than obtained for the initial model. Linear and nonlinear buckling analyses are performed as well. The nonlinear analysis yields a critical buckling load 18% lower than that predicted by linear analysis. This paper will discuss the details of the structural modeling as well as the results obtained before and after optimizing the model.

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.

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 present work attempts to study the behaviour of building designed for gravity loads only under the effect of lateral seismic load. Such a building is generally deficient against lateral forces and need to be retrofitted against lateral earthquake forces. A retrofitting scheme by providing aluminium shear link with chevron braces is suggested to improve its performance. Past earthquakes have shown a great deal of damages to the deficient RC frame buildings designed without any consideration to the lateral earthquake forces. Chevron braces with the aluminium shear link can be implemented as an effective retrofit measure. A comparison of the performance of building initially designed for gravity load only with the retrofitted building using chevron braces with the aluminium shear link is presented in this paper. The behaviour of building is worked out by performing nonlinear static pushover analysis and nonlinear time history analyses. A parametric study has also been carried out to study the effect of shear link and braces on the retrofitted building. The performance of RC building designed for gravity loads only as evaluated from the nonlinear static pushover analysis lies in life safety and collapse prevention range for DBE and MCE level of earthquakes respectively. The same building when retrofitted by using chevron braces with aluminium shear link show improved performance. This device is very simple, economic, effective and can be placed in a building very easily. The dissipation of damaging energy/damage is localised in shear link which can be replaced after a major earthquake.

Three different buildings built according to the same design have experienced three different near-field strong ground motions over a period of 11 years in three different cities in Turkey. The input motion was known for each because strong-motion sensors were located adjacent or close to the buildings. We examine the performance of the five-story, reinforced concrete-frame buildings. Bidirectional nonlinear time history and nonlinear static analyses on 3-D analytical models are performed. The principal focus is to assess whether the analytical model of the buildings could indicate column-beam damage consistent with that observed at the sites after the earthquakes. Results illustrate that nonlinear time history analyses are capable of indicating the occurrence of shear failure in captive columns; however, they overestimate the global damage. The overestimation is greater where the building sustained a pulse-type motion without significant distress. It appears that difference between visual observations and analytical results persists.