Nonlinear Static Analysis Research Articles

Effects of near-fault and far-fault ground motions on nonlinear dynamic response and seismic damage of masonry structures

This study explores the seismic behavior of masonry buildings in close proximity to a fault rupture as compared to those located farther away. It takes into account the distinctive features of near-fault ground motions, such as forward directivity and the fling effect, which have the potential to cause significant earthquake-related damage. The study employs a dataset comprising 100 earthquake records, which represent both near-fault and far-fault ground motions and conducts an analysis of nineteen masonry buildings with varying typologies. Analytical models for each of these buildings are constructed using experimental data concerning the quality of masonry materials. Nonlinear static and dynamic analyses are carried out to evaluate the buildings' capacity to withstand seismic deformations and the extent of damage incurred. The findings indicate that near-fault ground motions exert a more significant influence on the dynamic response and result in greater damage to masonry structures when compared to far-fault ground motions.

Choice of the shape imperfections model in dynamics problems of a long flexible cylindrical shell subjected to force couples

The issue of modeling geometrical imperfections in the dynamics problems of thin-walled shells was little researched. In cases when the natural modes of shell coincided with its buckling modes, the issue of choosing a dangerous imperfection model did not arise. When these shell modes did not coincide, it was important to investigate and compare the effect of different imperfections models on the static and dynamic characteristics of such shells. The choosing the shape imperfections model of a long flexible cylindrical shell subjected to force couples, the natural and buckling modes of which did not coincide, was studied using procedures of the finite element analysis software NASTRAN. The shell wall as a set of plat rectangular elements with six degrees of freedom at the node in the cylindrical coordinate system was modeled. The action of force couples as the concentrated forces were distributed at the nodes of the shell edges in accordance to the presentation of A.S. Volmir. The linear buckling problem and the geometrical nonlinear static analysis of the perfect shell by the Lanzosh method and the Newton-Raphson one were performed, respectively. The long half-waves buckling mode was taken as the first shell imperfections model. The modeling of the second shape imperfections as the first natural mode of the perfect shell using the natural vibration analysis by the Lanzosh method was performed. The different amplitudes of geometrical imperfections in proportion to the shell thickness using a program adapted to this software were set. The results of the geometrical nonlinear static analysis of the imperfect shell by the Newton-Raphson method showed that the shape imperfection model in the form of long half-waves more reduced the values of critical buckling loads. Investigations of natural shell vibrations by the Lanzosh method revealed the same influence of different imperfections models on the natural frequencies and natural forms. We think that the shape imperfections model in the form of long half-waves in studies of forced vibrations and dynamic stability of a long flexible cylindrical shell subjected to force couples will be more effective.

Identification of the most suitable probability distributions for ultimate strength of FRP-strengthened X-shaped tubular joints under axial loads

This paper focuses on identifying the most appropriate probability distributions for characterizing the ultimate strength of FRP-strengthened X-shaped tubular joints under axial loads. The study begins by verifying the accuracy of finite element (FE) models through a comparison with experimental results. Subsequently, 218 FE nonlinear static analyses are conducted to generate two reliable datasets for strength ratios. To determine the most suitable probability distribution models, 16 different distributions are fitted to the data, and their accuracy is evaluated using Kolmogorov-Smirnov and Chi-squared goodness-of-fit tests. The findings reveal that the Generalized Extreme Value distribution provides the best fit for describing the ultimate strength under compressive axial load, while the Burr distribution is identified as the most suitable model for tensile axial load. The analysis of probability differences revealed that the proposed probability distribution models for compressive and tensile loads exhibit minimal disparities, with a slight difference of 5.24% and 4.80%, respectively. The identified probability distribution models enhance the reliability and confidence in predicting the behavior and performance of these joints, contributing valuable insights to the field of structural engineering.

An improved FSDT with an efficient mesh-free approach for nonlinear static analysis of FG-GOPRC beams

The aim of this paper is to enhance the First Shear Deformation Theory (FSDT) beam and apply it to investigate the linear and nonlinear static bending behavior of beams containing functionally graded graphene oxide powder-reinforced composite (FG-GOPRC). In this study, we propose an improvement to the FSDT by utilizing a high-order mesh-free approach. Unlike some existing FSDT methods, our proposed study uses a nonlinear shear deformation term coupling, which is crucial to illustrate the effect of nonlinear cases of various boundary conditions under a strong formulation, even without selective or reduced integration, resulting in lower computation costs. Using the principle of minimum potential energy, the governing equations are rewritten in a matrix–vector strong form and discretized using the Radial Point Interpolation Method with variable shape parameter (VS-RPIM) and linearized using a High Order Path Following Techniques (HOPFT). To account for the behavior of GOPRC, we utilized the modified Halpin–Tsai model to estimate the effective Young’s modulus, while the rule of mixture was employed to determine the effective Poisson’s ratio. Furthermore, the weight fractions of the graphene oxide powder (GOP) vary continuously through the thickness direction of the composite beams. To validate the proposed numerical model, we provide various comparison studies to demonstrate its robustness and accuracy. Additionally, we conduct parametric studies to examine the effects of different parameters, such as length-to-thickness ratio, GOP distribution patterns, weight fraction, and size of GOP, types of loads, and boundary conditions on the nonlinear bending behavior of FG-GOPRC beams. We also investigate the neglected term in some literature, which is of interest in our study. In summary, this paper proposes an enhanced FSDT to investigate the nonlinear static behavior of FG-GOPRC beams. The proposed model is validated through various comparison studies and parametric analyses, demonstrating its robustness and accuracy. Our study provides useful insights into the nonlinear bending behavior of FG-GOPRC beams and highlights the importance of nonlinear shear deformation term coupling.

Nonlinear Static Analysis of Building with Different Aspect Ratio


 
 
 
 The earthquake resistant design of structures requires that systems ought to maintain, adequately, any ground motions of an depth that would arise for the duration of their construction or in their regular use. However floor motions are unique inside the consequences they have got on structural responses. The most accurate evaluation method for structures subjected to strong ground motions is the time history analysis . This evaluation entails the integration of the equations of motion of a multi-degree-of-freedom system, MDOF, within the time domain the usage of a stepwise answer which will constitute the real reaction of a structure. This technique is time-eating even though for application in all sensible functions. The necessity for faster techniques that could make certain a dependable structural assessment or design of structures subjected to seismic loading brought about the pushover analysis.
 Pushover analysis is based totally on the belief that systems oscillate predominantly inside the first mode or inside the decrease modes of vibration at some stage in a seismic occasion. This ends in a reduction of the multi-degree-of-freedom, MDOF machine, to an equivalent single-degree- of-freedom, ESDOF gadget, with properties expected by a nonlinear static evaluation of the MDOF system. The ESDOF device is then eventually subjected to a nonlinear time- history analysis or to a response spectrum analysis with consistent- ductility spectra, or damped spectra. The seismic demands calculated for the ESDOF device are converted through modal relationships to the seismic demands of the MDOF machine.
 The objective of this thesis record is to emphasise the use of non-linear static procedure i.e pushover analysis a seismic overall performance assessment of R.C frames .
 
 
 

Novel nodal relaxation algorithm with its application on nonlinear analysis of tensegrity-based structures

This study proposes a robust technique for static and dynamic nonlinear analysis of tensegrity-based structures using a novel method, entitled the Node Relaxation algorithm (NR). Regular numerical algorithms are usually invalid in dealing with flexible tensegrities due to singularities arising from large displacements and/or rotations following any alteration of the internal actuated components or externally applied loads. Especially in tackling dynamic problems, it becomes even more challenging to predict structural deformation when its member forces are varied constantly. In this paper, a novel iterative algorithm, consisting of consecutive releasing and restraining of each node, is raised to oblige the structural form to gradually evolve to its final equilibrium configuration. The tangential unbalance force on each node, selected as the sensitivity index, is employed to accelerate the structure searching for its stable state. The Newmark-β method is also adopted to update the position of free nodes in each iterative step, which assists the NR algorithm in finding updated equilibrium structural configuration during the nonlinear dynamic analysis. Two kinds of tensegrity-based structures, namely the spring-rod tensegrity and the cable-rod tensegrity, are given as the illustrative examples to confirm the effectiveness and robustness of the presented method.

Computational modelling of historic masonry railroad arch bridges

The problems encountered during the analyzes of structural response of historic masonry railroad arch bridges are described in this paper. The attention is mainly focused on the stiffness of the masonry arches, their strengths and appropriate estimation of railroad load intensity. Issues related to computational modelling of two, existing, almost 130 years old masonry arch railroad bridges are presented in this context. The main properties and results of detailed inspection of the structures are shown. Computational models that were created in the finite element method environment in order to efficiently describe the responses of the bridges under typical loading conditions and estimate their load carrying abilities are presented. The outcomes of several nonlinear static analyses that were conducted for this purpose are discussed. What is more the results of finite element analyses are reviewed against the inspected bridge condition and final conclusions are formulated on that basis. All the analyses allowed to find the possible causes of the deterioration of the bridges condition.

A Review on Seismic Analysis of RCC and Steel Structures using Linear and Non-linear Static Analysis

Abstract: An earthquake can cause significant harm to various aspects, including buildings, general life, and particularly multistory structures. In India, structures constructed in earthquake-prone regions, as defined by IS 1893: 2002, must be designed to withstand the loads, stresses, and consequences of earthquakes. Several techniques are available for assessing multi-story structures in this context, such as the Response Spectrum Method, Equivalent Lateral Force Method, Time History Method, and adhering to specific code provisions. Numerous researchers have undertaken studies to analyze multi-story buildings using one or more of these methods. However, there exists still a confusion about an effective and efficient method preferred for seismic design of multi-story buildings. Among the various approaches, the seismic coefficient method and response spectrum method are the most widely used. This comparative investigation aims to review research reports that have employed the Equivalent Lateral Force Method and Response Spectrum Method to analyze multi-story buildings in earthquake-prone areas. The design response spectrum serves as the initial reference point for most established seismic design and assessment procedures. It primarily dictates the inertia forces that buildings and structures must withstand during an earthquake. This paper aims to introduce and discuss contemporary concepts regarding the creation and utilization of earthquake design response spectra. Additionally, the paper highlights the various methods of seismic analysis being investigated in the past literature. It also gives an overview of various investigations being carried out using linear and non-linear static analysis of RCC structures. Many of the ideas presented are specifically aimed at aiding engineers who work in regions with low to moderate seismic activity. The main objective is to inform engineers about modern approaches to developing response spectra. This knowledge can then be applied effectively in both analytical and design contexts when dealing with earthquake-related challenges

PERILAKU STRUKTUR BETON BERTULANG DENGAN DAN TANPA PENGARUH LUBANG PINTU DAN JENDELA PADA DINDING

Infill walls are structural components in buildings that have a room-dividing function. For structural design, infill walls are generally modeled as an open frame. However, if infill walls are combined with structural frames in modeling, these infill walls will contribute better to structural rigidity. In this research, three models have been made. Model M1 is an open frame model, model M2 is a Fully Infilled Wall Frame model and model M3 is a Fully Infilled Wall Frame model with door openings. The purpose of this study was to determine the behavior of reinforced concrete frame structures with and without taking into account the effect of the presence of door and window holes in the walls due to earthquake loads. The research method used is a quantitative method with Pushover nonlinear static analysis. The results of the analysis show that the Fully Infilled Wall Frame model is 23.97% and 8.1% stiffer than the open frame model and the Fully Infilled Wall Frame with 24.8% door openings and 41.6% window openings due to the X and Y direction earthquake loads.

Nonlinear inelastic analysis of space semi-rigid steel frames subjected to static load using plastic-zone method

A new hybrid element based on plastic-zone method is proposed for static nonlinear analysis of space semi-rigid steel frames. Four zero-length nonlinear rotational springs are added to the beam ends to model both in- and out-of-plane connection rotational behavior with appropriate semi-rigid connection models. The von Mises yield criteria are applied to govern material plasticity along the member length and throughout the cross-section using Newton–Cotes integration points. The modified generalized displacement control method is used to solve the system of nonlinear equilibrium equations. Some numerical examples are investigated to show the reliability and visual illustration of the proposed hybrid element.

Analysis of transversely isotropic compressible and nearly-incompressible soft material structures by high order unified finite elements

This work proposes high-order beam (1D) and plate (2D) finite element models for the large strain analysis of compressible and incompressible transversely isotropic hyperelastic media, defined within the Carrera Unified Formulation (CUF) framework. The strain energy density function adopted in fiber-reinforced hyperelastic materials modeling is presented and expressed in terms of invariants and pseudo-invariants of the right Cauchy-Green strain tensor. The explicit expression of the tangent elasticity tensor is derived through the assumption of coupled formulation of strain energy functions. Refined fully nonlinear beam and plate models are defined in a total Lagrangian formulation, deriving the governing equations of the nonlinear static analysis through the Principle of Virtual Displacements in terms of fundamental nuclei, in resulting expressions of internal and external forces vectors, and tangent stiffness matrix independent of kinematic models and approximation theories adopted. The iterative Newton-Raphson linearization scheme coupled with the arc-length constraint is adopted to obtain actual numerical solutions. Different benchmark analyses in hyperelasticity are performed to assess the capabilities of our proposed model, analyzing the three-dimensional stress field for moderate to large strain states and comparing actual numerical results with exact closed-form solutions or results available in the literature, demonstrating the capabilities and reliability of CUF models in the analysis of fiber-reinforced soft materials and structures.

Nonlinear Static Analysis for Seismic Evaluation of Existing RC Hospital Building

Nonlinear Static Analysis otherwise known as pushover analysis will be used in this study to evaluate the seismic performance of an existing reinforced concrete (RC) hospital structure. This method aids in determining the structure’s ability to withstand lateral loads and calculating its local and global deformation requirements. The study begins with a thorough analysis of the geometry, materials, and structural elements of the structure, followed by a review of pertinent building regulations and codes. A finite element model in three dimensions of the hospital building is created, encapsulating the main features of the structure’s behavior under seismic loading. The lateral force method of analysis and static pushover analysis is then carried out and compared, and the findings are used to pinpoint crucial weak places, potential failure mechanisms, and regions needing additional research or fortification. Recommendations are given to improve the seismic performance of the current RC hospital building based on the pushover analysis’s findings. These adjustments can be made to the structural system via retrofitting techniques or to non-structural elements. For engineers, architects, and legislators concerned with the seismic assessment and renovation of hospital buildings and other crucial infrastructure, the findings from this study are valuable.

Seismic collapse safety assessment of suspended zipper-braced frames

Seismic evaluation of suspended zipper-braced frames, which are an alternative to inverted-V-braced frames to improve their seismic behavior, is of greatest significance to determine the level of confidence in this type of seismic system during severe earthquakes. The arrangement and design parameters of these frames are mentioned in some references, but there is no probabilistic assessment of collapse risk based on various collapse uncertainties. To evaluate the probability of collapse and margin of safety, eighteen suspended zipper-braced frames with different geometry parameters in the most severe seismic design category (D max) have been designed. The designed frames were modeled in OpenSees software by considering the effect of gusset plate connections and evaluated by performing more than 15,800 dynamic and nonlinear static pushover analyses using FEMA P695 methodology. Total collapse uncertainty is considered in the evaluation of the probabilistic behavior of frames. The results show that the adjusted collapse margin ratio (ACMR) of designed frames by considering the total collapse uncertainty of 0.726 and 0.529 is 27% and 64% higher than the acceptance criteria, respectively. The results also indicate that a response modification coefficient of much more than 6 can be used for the economic design of long-period suspended zipper-braced frames.

A meshfree orthotropic laminated shell model for geometrically nonlinear static and dynamic analysis

A meshfree orthotropic laminated shell model for geometrically nonlinear static and dynamic analysis

A simplified micro-model based on discrete elements and elastic bodies for non-linear static analysis of in-plane loaded masonry panels

In this paper, a simplified micro-model based on a combination of continuum (2D) and discrete elements was developed to estimate non-linear behavior and failure prediction of masonry panels subjected to in-plane loads. Bricks were substituted by 2D elastic elements which connected via eight bi-component non-linear springs to each other. Each spring has axial and shear behavior which is represented by mortar axial stress–strain curve, including softening and brick–mortar cohesion-friction law, respectively. Substantial simplifications are accomplished due to employing elastic panels and concentration non-linearity at the discrete elements in terms of the possibility of implementation in commercial software. The validation process was conducted at two levels; first: a masonry cell under possible in-plane loading conditions and second: ten experimental panels having different geometrical and mechanical properties subjected to vertical and horizontal actions simultaneously. The obtained results including global behavior and crack pattern were compared with experimental ones as well as available numerical predictions from the literature. High accuracy was observed despite convergence ease and reduction in both pre-processing and analysis time.

Seismic Behavior and Modeling of Ductile Composite Steel-Trussed Concrete Beam to Column Joints

This paper presents an experimental and numerical study on a ductile beam-column connection between a composite reinforced concrete truss (CRCT) beam and a reinforced concrete (RC) or concrete-filled tube (CFT) column subjected to bending and shear loads. Two experimental models with different beam-column joint testing schemes, extracted from the same prototype three-dimensional structure designed according to the rules of the capacity design provided by seismic code, were subjected to quasi-static cyclic tests by applying gravitational loads and the horizontal seismic force. The main objective of this paper is to verify the ductile behavior of both specimens experimentally and to simulate the experimental global and local responses by nonlinear static analysis, considering different modeling approaches. The comparison between the experimental and numerical results highlights, for both models considered, the ductile and dissipative capacity of the connection system, designed following the criteria of the hierarchy of resistances proposed by the current Italian code. The results of different experimental setups demonstrate that the tests can be repeated and the results can be reproduced by means of simple nonlinear models.

Comparative evaluation of seismic performance and environmental impact of traditional and dissipation-based retrofitting solutions for precast structures

Seismic rehabilitation is crucial to extend the nominal service life and help reduce the seismic losses of reinforced concrete precast industrial buildings. Along with traditional retrofitting techniques, the latest decades are witnessing a growing use of innovative solutions, the latter including devices that can dissipate the ingoing seismic energy and are characterised by the replaceability after a seismic event. The goal of this work is to compare two retrofitting solutions, respectively of traditional and innovative type, in terms of structural performance enhancement and their own life cycle environmental impact. A case study single-storey precast industrial building was retrofitted firstly adopting a traditional solution with concrete jacketing of columns, and then using two innovative energy dissipation devices, namely a friction rotation damper for beam-to-column connections and a bracing system with dissipative sacrificial elements. A comparative analysis of the seismic response of the structure in its as-built and post-retrofit configurations was undertaken, subjecting three 3D numerical models created in OpenSees to nonlinear static and dynamic analyses in both the main directions. Subsequently, two environmental impact metrics were adopted to compare the life cycle environmental impact of both the traditional and innovative retrofitting solutions, confirming that the one encompassing the dissipation-based devices is expected to be more environment-friendly, under a life cycle perspective, than the traditional concrete jacketing.

Determining the seismic performance factors of quasi-X bracing systems

This paper proposes two novel quasi-X bracing systems to resolve the drawbacks of concentrically braced frames (CBFs) and enhance their ductility. The seismic performance factors (SPFs) for moment-resisting frames equipped with these braces are determined according to the FEMA P695 approach. In pursuit of this aim, a three-dimensional set of 2-, 4-, 6-, and 8-story archetypes in two separate seismic design categories (SDC Cmax and Cmin) were designed considering presumed SPFs. Initially, non-linear static (pushover) analysis was carried out on each of the archetypes, and their period-based ductility and over-strength factors were extracted. Afterward, the archetypes' seismic performance was evaluated by performing incremental dynamic analysis (IDA) under far-field ground motion (FFGM) records, and the accuracy of the presumed response modification factor was examined as per FEMA P695. Based on the obtained results, a response modification factor of 5 is deemed acceptable for the design of both quasi-X bracing systems. Furthermore, the values of the deflection amplification factor and the over-strength factor are acquired as 5 and 3, respectively.

Methodology for Evaluating Seismic Analysis and Performance of Reinforced Concrete Buildings in Seismic Zones III and V

Reinforced concrete buildings are widely used in contemporary construction practices, particularly in India, where design standards such as IS 875 and IS 1983:2016 are adhered to. This research delves into the seismic performance of reinforced concrete (RC) frames, employing both linear and nonlinear analyses. A seven-story building, designed in accordance with Indian standards, is modeled using Finite Element Software ETABS v21.0.0. The study evaluates the response of these buildings, focusing on parameters like base shear and story displacement, for structures located in seismic Zones III and V. The capacity of the building is assessed through displacement-controlled nonlinear static analysis, known as pushover analysis. Time history loading is applied to the structure to ascertain the seismic demand at varying Peak Ground Acceleration (PGA) levels. Fragility curves are developed to quantify hazard levels and determine the probability of exceeding different PGA levels for both Zone III and Zone V, employing the First Order Second Order Method (FOSM). The study reveals that buildings in Zone V are more vulnerable to seismic events compared to their counterparts in Zone III. Keywords: Reinforced concrete, Response spectrum, Pushover analysis, Story displacement, Base shear, ETABS.

EVALUATION OF THE SEISMIC ANALYSIS AND PERFORMANCE OF BUILDING IN ZONE III AND ZONE V

Reinforced Concrete buildings are very popular practice in today’s context. The Reinforced concrete buildings in India are designed considering the IS 875 and IS 1983:2016 code guidelines. In this research, the seismic performance of reinforced concrete RC frame has been studied using linear and nonlinear analysis. The seven-story building has been modelled according to Indian standard code with the help of Finite Element Software ETABS v21.0.0. The response of the buildings in terms of Base shear, story displacement was studied for both building in zone III and V. The capacity of building is evaluated using displacement controlled nonlinear static analysis (Pushover). The time history load is applied to the structure to determine the seismic demand of the building at different PGA levels. The hazard levels have been quantified by plotting fragility curve for both Zone III and Zone V. For different damage state, the capacity and demand value are used to obtain the probability of exceeding at different PGA levels. The fragility curve is developed using First Order Second Order Method (FOSM). From the study, it is found, the buildings of Zone V are more vulnerable than compared to buildings of Zone III. Keywords: Reinforced concrete, Response spectrum, Pushover analysis, Story displacement, Base shear, ETABS.