Nonlinear Static Analysis Research Articles

Numerical and analytical investigation of U-shape dampers and its effect on steel frames

Yielding dampers are one of the structural systems which dissipate a portion of the seismic force via premature yielding. The numerical and analytical methods were used in this study to investigate the behavior of the U-Shape Damper (USD) and its effect on steel frames. For this purpose at first, extensive parametric studies were performed using calibrated USD model. The parametric studies involved investigating the effect of USD dimensions on its elastic stiffness, strength, effective stiffness, and equivalent viscous damping ratio. Finite element models were analyzed under cyclic loading using nonlinear static analysis. An analytical equation was then presented to estimate seismic parameters of the USD. In the second part, the effect of this damper on the steel frame was investigated using push over analysis. The seismic parameters of the frame, including elastic stiffness, strength, ductility, and energy dissipation, were investigated through 56 numerical models to determine the effects of the number of USDs and the axial force of the column. The results indicated that reducing the radius and increasing the thickness of the damper led to an increase in effective stiffness, energy dissipation, and strength, while reducing the equivalent viscous damping ratio. Furthermore, the results obtained from the steel frame equipped with a USDs revealed that the addition of the damper mitigates the adverse effects of axial force on the frame.

Evaluation of rapid visual screening assessment of existing buildings using nonlinear numerical analysis

Different methodologies are available in the literature to perform seismic assessment of existing buildings. Amongst the simplified ones, Rapid Visual Screening (RVS) methodologies have been recently developed and proposed. RVS methods are simplified procedures that can be implemented rather quickly for preliminary assessment of building vulnerability without the need to perform a detailed model and numerical analysis. Their application is particularly useful in regions characterised by high seismicity or where an important share of the buildings was not designed according to seismic provisions. The outcome of RVS methods is a safety index, based on the data from simplified forms that are filled during visual inspection of the buildings. For this reason, the accuracy of the results could be significantly affected by building features that cannot be considered by such forms. To address this issue and to evaluate the effectiveness of RVS methods, this paper focuses on the comparison between the results of a specific RVS method and those from advanced numerical modelling and nonlinear analyses of masonry-infilled reinforced concrete buildings. Several case-study buildings were selected from a database developed in the framework of a recently concluded European project, which focused on the seismic risk assessment of residential buildings in Northern Algeria, a seismic prone region. The buildings are analysed using detailed structural finite element models, through both nonlinear static and dynamic analysis, considering also the influence of mechanical and geometrical properties of the masonry infills. The comparison results show that, despite the significant variability observed in the RVS vulnerability assessment outcomes, there is a fair overall match with the nonlinear analysis results, confirming the utility of RVS methods at an initial assessment stage, as well as the need for further extended validation research efforts.

Modelling non-linear dynamic behaviour of rocking bridge piers with shape memory alloys

In recent years, accelerated bridge construction has led to the substantial application of precast post-tensioned segmental (PPS) bridge piers. However, PPS piers are not widely used in high-seismicity regions due to their low energy-dissipation capacity (EDC). To address this deficiency, a series of shape memory alloy (SMA)–concrete composite PPS piers were examined in this work. Non-linear static and dynamic analyses were performed on experimentally validated finite-element models of the SMA–concrete composite piers and the results were compared with those of piers without SMA bars. It was found that the length, area and post-tensioning ratio of the SMA bars affected the EDC of the piers, and an optimal design of the bars is required to reach the highest EDC possible. The effects of SMA bars on the frequency response functions of piers were investigated for the first time in this study and it was found that, unlike the piers without SMA bars, sub-harmonics and super-harmonics were not seen in the responses of the SMA–concrete composite piers, mainly the drift responses. Furthermore, the SMA–concrete composite piers experienced a significant reduction in drift responses compared with piers without SMA bars.

Numerical formulation for advanced non-linear static analysis of semi-rigid planar steel frames

Numerical formulation for advanced non-linear static analysis of semi-rigid planar steel frames

Influence of the modelling approach on the seismic assessment of RC structures by nonlinear static analyses

Different modelling approaches are available for the evaluation of the nonlinear response of structures. The goals of this paper are to determine the implications of two frame modelling strategies, one based on lumped plasticity and the other on distributed plasticity combined with a fibre section modelling, to assess the differences in predicting the structural response of existing RC framed buildings, and to provide guidelines on the range of applicability of the two different modelling approaches. The study is carried out using two RC framed buildings as studies. Both buildings are characterized by seismic deficiencies typical of existing buildings belonging to the Mediterranean building stocks, but with different ductility capacities and collapse mechanisms. For each case study, two 3D numerical models are built in OpenSees, considering the above mentioned models. For each plan direction, two pushover analyses are run on each numerical model with two distributions of forces. The seismic response is assessed at the Damage Limitation (DL), Significant Damage (SD) and Near Collapse (NC) limit states. The seismic responses assessed by the two numerical models showed that the lumped phenomenological plastic hinge model tends to provide more conservative results than the distributed plasticity, fibre-section model, leading to relevant differences especially in case of structures with a low ductile behaviour.

Numerical modelling for the seismic assessment of complex masonry heritage buildings: the case study of the Giralda tower

Existing heritage buildings can be especially vulnerable to earthquakes. They were designed only considering gravity loads and some of them are located in earthquake prone areas, such as the southwestern Iberian Peninsula. Besides, there is a high uncertainty in the definition of their constructive parameters and complex geometry. Due to that, it is paramount to develop accurate numerical models to obtain a reliable assessment of their seismic behaviour. Given this, the main objective of this manuscript is to analyse the seismic behaviour of the Giralda tower, located in Seville (Spain). It was declared as a Word Heritage Site of Outstanding Universal Value by the UNESCO in 1987. Seville has a moderate seismic hazard, but it has been shown that the soft alluvial strata amplify the seismic action. The tower has a brick and stone masonry structure, which was constructed in several construction phases. A 3D Finite Element Model of the tower has been developed using OpenSees software, employing a 3D CAD model. Modal analyses and nonlinear static analyses have been applied to calibrate and to assess the tower’s seismic behaviour. The results showed significant differences in function of the load pattern. It should be remarked that the boundary conditions have a notable effect upon getting a good calibration of the model. Regarding the damage, it has been found to match the historic records: the ramps would be ruined and, in the outer wall, it would be concentrated near the openings, especially close to the belfry.

Analysis of Adaptive Pushover in Confined Masonry Dwellings with Height Irregularity in the Lima Metropolitan Area

Non-engineered confined masonry dwellings are characterized by having different masonry units. One of the most common cases in the Lima Metropolitan Area is that this type of dwelling has its first floors with handmade solid units and upper floors are composed of industrial horizontal hollowed (tubular) bricks. Nonlinear static analysis by the incrementally increasing loading pattern is inadequate to estimating earthquake response of structures with height irregularity, such as non-engineered confined masonry dwellings, because the loading pattern changes during the history of reversal loads due to damaging earthquakes. This paper presents the effect of nonlinear static analysis using adaptive loading patterns in confined masonry dwellings when the type of masonry units changes drastically. Nonlinear static analyses are applied using non-adaptive and adaptive displacement-based pushover procedures. A series of nonlinear time history analyses are also conducted to measure the error in the estimation of the seismic response. The adaptive loading pattern is based on displacement approximation by the modal analysis at each step of incremental-increasing loads. The load pattern is updated considering the modal analysis of an equivalent linear model using the equivalent stiffness of the structure at the secant of the maximum previous response. The application of the adaptive loading pattern in nonlinear static analysis significantly approximates the earthquake response of confined masonry dwellings with height irregularity provided by the change of masonry bricks.

Investigating the effect of the structural interactions due to floors and lintels on the lateral response of multi-storey Cross-Laminated Timber shear walls

The lateral behaviour of multi-storey Cross-Laminated Timber (CLT) structures is significantly influenced by the effects of the structural interactions between primary and secondary structural elements and their connections. In case of platform-type structures, in addition to the connections placed at the base of the walls, other structural components including the floor diaphragms and the lintels above the openings influence the lateral performances of the CLT shear walls. However, it is common practice in structural design to model multi-storey CLT shear walls by considering the wall base connections, while neglecting the effects of these structural interactions. This study investigates in detail the lateral behaviour of multi-storey CLT shear walls, comparing the results of simplified modelling strategy, typically adopted in practical design, and more advanced modelling strategies that take into account the effects of these structural interactions. Different shear wall configurations, including different geometries, number of storeys, and connection properties were analysed by means of linear elastic and nonlinear static analyses. The results of the numerical analyses highlighted significant differences between the lateral behaviour of multi-storey CLT shear walls modelled with these different modelling strategies and suggest that simplified modelling strategies may not always be reliable to describe the behaviour of multi-storey CLT shear walls.

“Progressive collapse analysis of flat slab building in hilly terrain using Non-Linear Analysis: A study on bracing system as a structural Remedy”

Progressive collapse is a term used to describe the failure of a structure, such as a building or bridge, due to the structure’s inability to reallocate the loads after the failure of a key component or portion of the structure. It is a cataclysmic structural failure that may occur when a primary structural member or a portion of a structure is damaged or fails, resulting in a string of structural failures that leads to the partial or complete breakdown of the structure. This research paper investigates the progressive collapse behaviour of an earthquake-resistant flat slab building lying in hilly terrain upon removal of the column at three different locations, using non-linear static analysis. The study involves the use of a finite element method-based software tool to simulate the collapse behaviour of the building. The results of the analysis indicate that the building lying in hilly terrain, designed to resist earthquake forces can be vulnerable to progressive collapse due to the abrupt removal of a crucial structural component and this can be significantly mitigated through the implementation of strategies, such as the provision of an alternate load path through the use of steel bracing systems. Evaluation of the outcomes is done in terms of vertical joint displacements at the top of the deleted column and the formation of plastic hinges in the adjacent structural members. The findings of this research paper provide valuable insights into the progressive collapse potential of a flat slab building designed for earthquake loads, in hilly terrain under extreme loading conditions. The results can be used to inform the design and construction of buildings that are more resilient and robust to extreme events, thereby lowering the possibility of progressive collapse and ensuring the safety of the occupants.

A practical framework for performance-based reliability analysis of subway stations based on a fault–structure combined system

It is necessary to pay particular attention to the uncertainties that exist in an engineering problem to reduce the risk of seismic damage of infrastructures against natural hazards. Moreover, certain structural performance levels should be satisfied during strong earthquakes. However, these performance levels have been only well described for aboveground structures. This study investigates the main uncertainties involved in the performance-based seismic analysis of a multi-story subway station. More than 100 pulse-like and no pulse-like ground motions have been selected. In this regard, an effective framework is presented, based on a set of nonlinear static and dynamic analyses performed by OpenSees code. The probabilistic seismic demand models for computing the free-field shear strain of soil and racking ratio of structure are proposed. These models result in less variability compared with existing relations, and make it possible to evaluate a wider range of uncertainties through reliability analysis in Rtx software using the Monte Carlo sampling method. This work is performed for three different structural performance levels (denoted as PL1–PL3). It is demonstrated that the error terms related to the magnitude and location of earthquake excitations and also the corresponding attenuation relationships have been the most important parameters. Therefore, using a fault–structure model would be inevitable for the reliability analysis of subway stations. It is found that the higher performance level (i.e. PL3) has more sensitivity to random variables than the others. In this condition, the pulse-like ground motions have a major contribution to the vulnerability of subway stations.

An energy-based methodology to estimate the ultimate condition of complex continuous masonry structures

Performance-based assessment procedures for existing structures based on pushover-like nonlinear static analyses require the definition of progressive damage states on the pushover curve, which may be associated with proper limit states for safety verification purposes. In Codes, the “ultimate condition” of the structure, i.e. a damaged state in which the structure is conventionally supposed to be no longer able to carry vertical and horizontal loads, is typically identified when the base shear shows a decay higher than a given threshold (usually 15–20%). In the case of masonry structures, this issue is not always straightforward depending on the complexity of the structure and the failure mode activated. The challenge especially arises in case of monumental buildings, such as complex continuous structures (e.g. towers) and buildings composed of many macro-elements (e.g. churches), dominated by flexural failure modes (e.g. overturning mechanisms). Indeed, in these cases, pushover curves may not show a significant softening for large horizontal displacements (e.g. masonry crushing is not activated). Accordingly, the application of the aforementioned approach results impossible. In this paper, an energy-based methodology to estimate the ultimate condition of masonry structures is introduced. Although the procedure is potentially applicable to any typology of masonry structure, it is tentatively applied here to continuous tower-like structures. A preliminary calibration phase to set the energy ratio thresholds is addressed by considering various simplified benchmarks subjected to several load scenarios. To this aim, the model is subdivided into several portions, and the ratio between the dissipated energy and the total energy is tracked in each portion of the structure along with the pushover analysis. The ultimate condition of the structure is then found as soon as such ratio reaches a pre-defined threshold in a portion, calibrated in such a way to highlight where in the structure the damage is mainly localized. The methodology is then tested on a real case study application, i.e., the bell tower of the San Francesco da Paola church in Rome, modelled through a suitable nonlinear continuum modelling approach. Results prove that the methodology is general, effective, and easy to use.

Nonlinear static analysis of functionally graded porous sandwich plates resting on Kerr foundation

The main purpose of this work is to explore the nonlinear static bending analysis of functionally graded porous sandwich plates with a ceramic core (FSCC) subjected to a transverse uniform load resting on Kerr foundation (KF) using the mixed interpolation of tensorial components for the four-node rectangular element (called MITC4). Porosity appearing in two skin layers is assumed according to the uneven porosity distribution with a porosity factor Ω . The advantage of this element is fast convergence, high accuracy and cancels the shear-locking phenomenon. The present study considers the geometrical nonlinearity resulting from mid-plane stretching based on the von Kármán geometrical nonlinearity. The first-order shear deformation theory (FSDT) is employed to approximate the displacement field of the plate due to its simplicity and efficiency. The current formulation’s authenticity is evaluated by comparing it with previously published works. For the first time, the nonlinear bending of FSCC subjected to a transverse uniform load resting on the Kerr foundation is investigated. Furthermore, the influence of input parameters on the nonlinear bending behavior of FSCC is fully provided.

Seismic performance and SSI effects of a two-storey RC school building during the 2014 Cephalonia, Greece, earthquake sequence

The response of a two-storey RC school building in the town of Argostoli, Cephalonia Island, Greece, during the seismic sequence of January and February 2014, is examined. The structure was built following an older generation of seismic codes dating from the 1950s, which provide limited strength and ductility against lateral loads. Despite the severity of ground shaking and the two successive events, the building suffered relatively minor damage, like most of the RC buildings in the town. Following a short presentation of some basic seismological, structural and geotechnical aspects of the seismic sequence, the paper focuses on the seismic performance of the structure at hand. To this end, a series of detailed non-linear static and time-history dynamic analyses are reported, which highlight the interplay of soil, foundation and superstructure in modifying the seismic demand. It is demonstrated that SSI had an unexpectedly important (detrimental) role in the behaviour of the structure, increasing its natural period by about 25% and aggravating ductility demand in almost all columns, despite the moderately soft soil conditions (average VS = 180 m/s). The results shed light on the seismic performance of the building and help drawing conclusions on the engineering effects of the 2014 Cephalonia earthquake sequence.

Failure mechanisms and behaviour of adobe masonry buildings: A case study

Non-linear static analyses are amongst engineering community one of the most common analysis approaches for the seismic assessment of existing buildings, due to a good trade-off between information needed and results produced to assess structural safety. Pushover analyses, in fact, can provide hindsight onto structural behaviour well into the non-linear range, up unto conditions of collapse initiation and structural failure.Reliable information concerning the material’s mechanical behaviour – especially in the non-linear range - is, however, required – something which is challenging for earth-based materials, such as adobe masonry, due to the acknowledged variation of their mechanical properties.In this paper, a non-linear constitutive law for adobe masonry, numerically calibrated using experimental results and defined within the widely used computer program SAP2000®, a Finite Element software package commonly used by practicing engineers for building design and structural verification, is proposed. A total strain crack-based macro-modelling approach was pursued, and mechanical properties were validated through numerical modelling and comparison with values available in literature.The proposed constitutive model, whose reliability was proven by good agreement with experimental data, is then used to evaluate the expected seismic performance of a real case study given by an adobe building in central Portugal, representative of the city of Aveiro’s earthen heritage. Therefore, starting from this application, more hindsight over the structural behaviour of Portuguese adobe masonry buildings under failure conditions was provided, also showing the implemented model suitability for large scale structural analysis in the SAP2000® software. Sensitivity analyses are run in Finite Element environment and the structural behaviour considering different boundary conditions of the building, namely isolated and aggregate conditions, is assessed through a multi-criteria approach accounting for displacement and acceleration capacity, drift levels and safety against in-plane and out-of-plane failures.

Progressive collapse resistance and uncertainty analysis of post-tensioned steel frames

Post-tensioned (PT) steel frames with prestressed strands and replaceable energy dissipation angles demonstrate enhanced resilience during earthquakes compared to traditional steel frames. This study aimed to investigate the collapse resistance of PT steel frames in the different column removal scenarios. A macro model of a typical PT connection was developed using OpenSeesPy, a python library for the OpenSees finite element software framework. The model was validated by experimental results and applied to a six-story, four-bay office building. The collapse resistance mechanism of the building was analyzed in detail through a static pushdown nonlinear analysis, considering the edge column and middle column removal scenarios on the ground floor. A probabilistic analysis was conducted, incorporating uncertainty modeling and sensitivity analysis, to determine the effect of parameters on the collapse resistance of the structure. The collapse fragility functions corresponding to different structural performance levels were developed by the Latin hypercube sampling method with random pushdown analysis under the edge column removal and middle column removal scenarios, respectively. The uncertainty analysis results indicated that the PT steel frame investigated in this work has good collapse resistance.

Nonlinear static analysis of bi-directional functionally graded sandwich plates in thermal environments by a higher-order finite element model

This study addresses nonlinear static behaviours of bi-directional functionally graded (2D-FGM) sandwich plates lying on an elastic foundation in thermal environments for the first time. The plates comprise two 2D-FGM face sheets and a homogeneous core layer. The material properties of the face sheets change according to the power law in both the longitudinal and thickness directions. Furthermore, the material properties also possess temperature-dependent characteristics in the thermal environment. For the analysis purpose, a higher-order finite element model (FEM) based on Shi’s plate theory that takes into account the geometrically nonlinear von Kármán without regard to material nonlinearity is established. The minimum potential energy principle is used to establish the weak form of governing equations. The four-node rectangular element with the Lagrange and Hermitian interpolation functions is used to discretize the domain of the plate. The nonlinear equilibrium equations are solved by employing Newton–Raphson iterative procedure. The numerical examples comparing the obtained results with the published results in open literature have confirmed the accuracy and convergence of the proposed model. Finally, a few novel parametric studies are conducted to show the effects of the material properties, geometric parameters, temperature, elastic foundation stiffness, and boundary conditions on the nonlinear static behaviours of the 2D-FGM sandwich plates.

Analysis and Design of Earthquake Resisting Building with Shear Walls by Using ETAB Software

The present study shows the seismic behaviour of buildings under the action of earthquake load by performing Non-linear Static analysis. Nowadays buildings with shear walls are more popular than buildings without shear walls in earthquake-prone areas due to their resistance during earthquakes. So, this study aims to find the prime location of the shear wall and then investigate the effectiveness of the best shear wall for the RCC structure. In this study, G+13 & G+5 RCC building is considered for the analysis under zone I to zone IV with suitable load combination. The structure is analyzed for earthquakes in the type of structural system using ETABS software. The shear wall starts from the foundation level and should continue throughout the building.

Nonlocal Strain Gradient Model for the Nonlinear Static Analysis of a Circular/Annular Nanoplate.

A nonlinear static analysis of a circular/annular nanoplate on the Winkler-Pasternak elastic foundation based on the nonlocal strain gradient theory is presented in the paper. The governing equations of the graphene plate are derived using first-order shear deformation theory (FSDT) and higher-order shear deformation theory (HSDT) with nonlinear von Karman strains. The article analyses a bilayer circular/annular nanoplate on the Winkler-Pasternak elastic foundation. HSDT while providing a suitable distribution of shear stress along the thickness of the FSDT plate, eliminating the defects of the FSDT and providing good accuracy without using a shear correction factor. To solve the governing equations of the present study, the differential quadratic method (DQM) has been used. Moreover, to validate numerical solutions, the results were compared with the results from other papers. Finally, the effect of the nonlocal coefficient, strain gradient parameter, geometric dimensions, boundary conditions, and foundation elasticity on maximum non-dimensional deflection are investigated. In addition, the deflection results obtained by HSDT have been compared with the results of FSDT, and the importance of using higher-order models has been investigated. From the results, it can be observed that both strain gradient and nonlocal parameters have significant effects on reducing or increasing the dimensionless maximum deflection of the nanoplate. In addition, it is observed that by increasing load values, the importance of considering both strain gradient and nonlocal coefficients in the bending analysis of nanoplates is highlighted. Furthermore, replacing a bilayer nanoplate (considering van der Waals forces between layers) with a single-layer nanoplate (which has the same equivalent thickness as the bilayer nanoplate) is not possible when attempting to obtain exact deflection results, especially when reducing the stiffness of elastic foundations (or in higher bending loads). In addition, the single-layer nanoplate underestimates the deflection results compared to the bilayer nanoplate. Because performing the experiment at the nanoscale is difficult and molecular dynamics simulation is also time-consuming, the potential application of the present study can be expected for the analysis, design, and development of nanoscale devices, such as circular gate transistors, etc.

Assessment of seismic retrofitting interventions in reinforced concrete structures

Destruction of reinforced concrete (RC) structures, particularly non-ductile RC structures, in recent earthquakes demonstrate their vulnerability under lateral forces generated in an earthquake. Despite the extensive literature on the subject and the wide variety of strengthening techniques available, there is no consensus on the efficiency of these techniques in improving the seismic performance of RC structures. In this study, a five-storeyed RC-framed building is considered to evaluate its seismic performance through static non-linear pushover analysis. To examine the effect of various cases encountered in practice, the pushover analysis is carried out on the RC frame for various cases, i.e. a bare RC frame, an RC frame with masonry infills but with an open ground storey, and RC frames with shear walls with a variety of thicknesses and steel reinforcement ratios. Further, to investigate the effect of retrofitting, the RC frame is strengthened using local jacketing and bracings. From the results, it is observed that the initial stiffness and base shear of masonry infilled RC frame with an open ground storey exhibit an increase of 2.6%, and 19%, respectively, as compared to the bare frame. The use of shear walls increases the initial stiffness and base shears, and they increase by 6–14% and 8–20%, respectively, with an increase in the reinforcement ratio in the shear wall. Retrofitting with the use of both diagonal bracings causes the base shear to increase by a factor of 7.7 as compared to that of the open ground storey. Finally, the probability of damage to the RC frame in all cases was compared using seismic fragility curves.

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

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