Abstract The current advanced analysis techniques for steel frames generally use structural analyses with geometric and material nonlinearities to capture the collapse strength of the steel frame. Unfortunately, the true strength of a steel frame cannot be predicted with accuracy because of the uncertainties of the most significant design variables. Building codes of steel structures apply a resistance factor to account for the uncertainties present in the design variables and thus ensure a target level of structural reliability. This article examines the reliability of planar steel frames subject to gravitational loads by advanced structural analysis (second-order inelastic analysis). To calculate the collapse probability of planar steel frames, we utilized the first-order reliability method (FORM). The advanced analyses were performed using the program MASTAN2 and considered the geometric nonlinearities and inelasticity of the steel. The collapse probabilities of planar steel frames were evaluated and the adequacy of the resistance factor applied was discussed. The current inelastic design procedure of ANSI 360 reduces the yield strength and stiffness of all members by a factor of 0.90. Thus, the present study suggests that the adopted resistance factor must be equal to 0.85 for the target reliability index equal to 3.0, or it must be equal to 0.69 for the target reliability index equal to 3.8.

Abstract Population growth in urban centers, together with the lack of physical space, has led to the construction of increasingly tall and slender buildings. Multiple-story structures present substantial challenges to civil engineering because they have specific requirements for their design, construction, and use. The increased number of foors leads to more lateral displacements resulting from horizontal actions. Under these conditions, to ensure system stability, structural bracing components are commonly adopted. In addition, along with the use of more resistant materials and new construction techniques, it is necessary to improve the methodologies adopted in the structural analysis to offer professionals in the area the conditions to undertake safer and more economical projects with better speed and efficiency. Thus, in this study, numerical analyses were applied to steel planar reticulated structures to evaluate their stability and strength when inserting bracing systems. The study compared the arrangement of the bars and analyzed the influence of the parameters of the bracing systems, such as the properties of the cross-section and the position of the inverted-V-braced system. The MASTAN2 program was used to perform nonlinear static assessments using reticulated finite elements that considered both geometrical and physical nonlinearities. It was observed that the inverted-V-braced system had a substantial impact on all of the structures that were analyzed, providing increased stiffiness and, as a result, significantly reducing the frame’s lateral displacement. centers space buildings Multiplestory Multiple story design actions addition techniques efficiency Thus systems crosssection cross section invertedVbraced inverted V braced MASTAN nonlinearities result frames frame s displacement

Abstract The present paper aims to test recent (Truly self-starting two sub-step method and three-parameter single-step implicit method) and classical (Generalized-α, HHT-α, and WBZ-α methods) time integration methods using the geometrically nonlinear Positional Finite Element Method (PFEM). The numerical formulation is based on the total Lagrangian approach and uses the Hessian matrix to obtain the response. The mixed hardening inelastic model applied to PFEM is also presented. Two examples validate the time integration algorithms and the inelastic model. In the first example, the mixed hardening inelastic model is compared with the the bilinear stress-strain model and the elastic-perfectly plastic hinge model, and aspects such as amplitude decay and period elongation are discussed. In the second example, the implemented algorithms are verified in a severe geometrically nonlinear example, considering the influence of numerical dissipation, time interval, and the number of elements in the response. Results show the relevance of numerical damping for numerical stabilization and the good performance of the Generalized-α algorithm.

Abstract The inelastic second-order behavior of steel structural columns under minor-axis bending is presented in this article. To study this behavior, a nonlinear frame element formulation is adopted in which the steel's plasticity process is accompanied at the nodal points of each finite element through the refined plastic-hinge method (RPHM). A tangent modulus approach is employed in order to consider the stiffness degradation in function of the internal forces' variation, and the second-order effects, residual stresses and geometric imperfections are considered in the modeling of column behavior. As a criterium for defining the ultimate limit state of the column cross-section, strength surfaces are adopted. These surfaces describe the interaction between the axial force and bending moment (N-M interaction diagrams). To solve the nonlinear equilibrium equation for the structural system, the Newton-Raphson method is used, coupled with continuation strategies. Columns with different slenderness, boundary and loading conditions are analyzed, and the results obtained are comparable to those found by other researchers. The results lead to the conclusion that the numerical approach adopted in this study can be used for a better behavioral understanding of the steel column under weak-axis bending.

Abstract Recent scientific and computational advances have facilitated the analysis of slender structural systems subject to instability. With the employment of more sophisticated numerical tools and algorithms, it is possible to accurately determine the critical points (limit and bifurcation loads) as well as the post-critical behavior of the structural system. In the computational context, efficient data structures are needed to enable code and graphic interface expansion for the generation of models and visualization of the results obtained. Thus, an interactive object-orientated graphic computational system is presented herein. It has been developed using MATLAB/GUI, with pre-processing, analysis and post-processing capacities for planar structural frames. The nonlinear finite element developed and implemented for the structure modeling is formulated considering second order effects. Therefore, with the computational tool presented, the geometric nonlinear effects and stability of the structural system can be directly addressed, and the visualization of the numerical results are accessed through interactive controls that permit data inclusion and analysis verification. The engineer-designer can see the structural model discretization, the equilibrium path, its deformation configuration, the force and bending moment diagrams at the moment that he runs the program and in each load step. It is also possible to export the images, videos or tables of the obtained numerical results. The example presented demonstrates the capacity of the developed graphic computational system.

Abstract The design codes for structural design traditionally establish the adoption of partial safety factors to deal with uncertainties. These standards do not allow one to know the real probabilities of failure of a structure. What is needed, from a practical and scientific point of view, is a more consistent approach, based on reliability theory. This article addresses an initial attempt at determining the safety levels of structures based on advanced analysis and design with structural reliability theory. In this context, the authors consider the effects of the geometric nonlinearity and flexibility of connections in the reliability analysis, which aims at setting a certain displacement as the service limit state. For this purpose, a computer program was written called Structural Reliability Module. This program uses a First Order Reliability Method to analyse reliability. To carry out the structural analysis of steel structures, this study uses the program Computational System for Advanced Structural Analysis. Validating the Structural Reliability Module involved comparing the results from other authors with those generated by the program. Results for the structures under study indicate the efficiency of the implemented measures. Results suggest that, when a certain displacement is set as a service limit state, the reliability of the structures under analysis are only slightly influenced by geometric nonlinearity but considerably so by semi-rigid connections.

Abstract When exposed to high temperatures, such as in a fire situation, the physical and resistance characteristics of the materials employed in the structure deteriorate as the temperature increases. This fact promotes a considerable loss in the bearing capacity and stiffness of the structural system. The verification of a structure exposed to fire depends primarily and principally on the thermal analysis of the cross section of the structural element. This analysis permits determination of the temperature variation or temperature range in the element from the boundary conditions provided by the fire model adopted. As such, this study had the objective of performing a thermal analysis in a transient regime by means of a finite element method on steel-concrete composite cross sections that are employed in civil construction through use of the Computational System for Advanced Structural Analysis/Fire Analysis (CS-ASA/FA). Two cross sections are analyzed and the results obtained were satisfactory. In addition, different iterative solution processes were adopted in the analysis. Parametric studies were also performed related to the mesh variation of the finite elements and time increase. From the results, it was possible to conclude that CS-ASA/FA can supply the necessary information when a thermo-structural analysis is performed for the evaluation of strength and stiffness losses of the structural material when exposed to fire.

Grande parte dos procedimentos numéricos para obtenção de caminhos de equilíbrio dos problemas estruturais com comportamento estático não linear baseia-se no método de Newton-Raphson, ao qual são acoplados métodos de continuação. Nesse contexto, esse trabalho usa uma técnica, referida como fluxo normal, no processo de obtenção da resposta aproximada não linear estática de sistemas estruturais. Tal técnica trata-se, basicamente, de uma modificação estabelecida no esquema iterativo de Newton-Raphson, na tentativa de acelerar o processo de solução e/ou contornar problemas de convergência. Para ultrapassar os pontos limites e traçar a trajetória de equilíbrio completa das estruturas, adotam-se três diferentes estratégias de iteração: comprimento de arco, norma mínima dos deslocamentos residuais e deslocamento generalizado. Com esse procedimento, é avaliado o desempenho dessas estratégias, quando associadas à técnica do fluxo normal. Dois arcos com caminhos de equilíbrio não lineares são usados no estudo. Os resultados encontrados permitem concluir que a associação da estratégia do deslocamento generalizado com a técnica do fluxo normal contribui para a eficiência da metodologia de solução não linear.

A large part of the numerical procedures for obtaining the equilibrium path or load-displacement curve of structural problems with static nonlinear behavior is based on the Newton-Raphson iterative scheme to which are coupled the path-following methods. In this context, this study uses one technique, referred to as normal flow, in the process of obtaining the approximate nonlinear static response of structural systems. Basically, this technique is an adaptation made with in the Newton-Raphson iterative scheme in an attempt to speed up the nonlinear solution process and/or remove convergence problems. To overcome the critical points and to trace the whole nonlinear equilibrium path, three different strategies are used in association with the normal flow technique: the cylindrical arc-length, the minimum residual displacement norm and the generalized displacement. With this procedure, the performance of these strategies when associated with the normal flow technique is valued. Two arches with highly nonlinear load-displacement curves are used in the study. The results obtained demonstrated that the association of the generalized displacement strategy with the normal flow technique contributes to the improvement of the nonlinear solution methodology.

Esse trabalho apresenta um estudo referente à análise da estabilidade e vibração não linear de pórticos de aço planos do tipo galpão. Especial atenção é voltada à influência do pré-carregamento estático nas frequências naturais e nos modos de vibração dessas estruturas. Nesse sentido, foi utilizada uma formulação não linear de elementos finitos de viga-coluna que permite considerar as ligações entre os membros estruturais como semirrígidas. Para resolver o problema de equilíbrio estático não linear, um processo incremental e iterativo do tipo Newton acoplado ao método do comprimento de arco é adotado. Uma vez obtida convergência em cada passo de carga, emprega-se o método de Jacobi, para se determinarem as frequências naturais e os modos de vibração da estrutura pré-carregada. Todo o processo de solução não linear adotado é detalhado em um algoritmo. A influência de um parâmetro geométrico (altura da tesoura) e outro físico (rigidez dos apoios) no comportamento do pórtico tipo galpão é destacada nas análises. Objetiva-se, assim, obter uma melhor compreensão de alguns fenômenos de instabilidade e sensibilidade estrutural e mostrar a importância desses parâmetros e do pré-carregamento estático na flambagem e na vibração dessa estrutura de grande aplicação prática.

This paper presents a study on the stability and nonlinear vibration analysis of planar pitched-roof frames. Special attention is dedicated to the influence of static preloading in natural frequencies and vibration modes of these structures. For this, used was a nonlinear beam-column element formulation that considers connection flexibility between the structural members. The global nonlinear static equilibrium problem is solved using an incremental-iterative procedure, where in each load increment, the Newton-type iteration scheme is coupled to an arc-length strategy. At convergence in each load step, the Jacobi method determines the natural frequencies and vibration modes of the preloaded structure. The complete nonlinear solution strategy adopted is detailed in an algorithm. The influence of a geometric parameter (scissors' height) and other physical (support's stiffness) in the pitched-roof frame behavior is highlighted in the analysis. The goal is thus to have a better understanding of some instability phenomena and structural sensitivity, and to show the importance of these parameters and static preloading on the buckling and vibration of these frames, which have great practical application.

Esse trabalho apresenta uma nova ferramenta computacional, para análise avançada estática e dinâmica de estruturas de aço reticuladas planas, desenvolvida com base no Método dos Elementos Finitos. Duas fontes de não linearidades são consideradas nas análises: a geométrica, que considera os efeitos da deslocabilidade da estrutura; e a física, causada, principalmente, pelas características mecânicas dos materiais utilizados na construção civil. Imperfeições relacionadas com o carregamento, geometria do sistema e tensões residuais podem, também, serem consideradas. Para se ilustrarem alguns dos recursos e análises que diferenciam essa ferramenta dos programas comerciais existentes, a estabilidade estática e dinâmica de alguns sistemas estruturais, com ligações rígidas e semirrígidas, é avaliada. As respostas obtidas por outros pesquisadores são usadas, para validar as formulações e as metodologias de solução não linear, implementadas nessa ferramenta, e para atestar a eficiência desse programa caseiro de análise estrutural.

A new computational tool for advanced static and dynamic analyses of steel framed structures based on the Finite Element Method has been developed and is presented herein. Two sources of nonlinearity can be considered in these analyses, i.e.: the geometric, which considers the nonlinear effects of structure displacements; and the physical, which considers the nonlinear effects of the mechanical characteristics of the material used in civil construction. Loading, geometric and residual stress imperfections can also be considered. To illustrate some of the features and capabilities that differentiate this tool from existing commercial programs, static and dynamic stability analyses of some structural systems with rigid and semi-rigid connections are evaluated. The results obtained by other researchers are used to validate the nonlinear formulations and numerical solution methodologies implemented in CS-ASA, and to attest the efficiency of the structural analysis program presented herein.

Nesse trabalho, um elemento finito híbrido, que incorpora em sua formulação os efeitos não lineares de segunda ordem, da inelasticidade do aço e da semirrigidez da ligação, é utilizado para modelar e analisar sistemas estruturais reticulados planos em aço. Trata-se do elemento finito clássico de pórtico plano que apresenta, em suas extremidades, pares de molas dispostas em série. Uma das molas é representada pelo parâmetro Sc, que define o grau de rigidez da ligação entre as barras; a outra mola é representada pelo parâmetro Ss, que avalia a plastificação da seção. A matriz de rigidez desse elemento incorpora todos os efeitos não lineares supracitados. O presente trabalho faz uma averiguação da eficiência computacional do elemento híbrido na simulação isolada e combinada desses efeitos não lineares. Problemas clássicos de equilíbrio e estabilidade são inicialmente modelados e, em seguida, a atenção é voltada para a análise de sistemas estruturais com ligações flexíveis. Por fim, o referido elemento é utilizado em análises inelásticas de pórticos planos baseadas no método da rótula plástica refinado. Através dessas análises, é possível verificar e validar o emprego do elemento híbrido na modelagem numérica de diversos problemas estruturais não lineares na engenharia civil.

In this work, a hybrid finite element that incorporates in its formulation the second-order effect, material yielding and connection flexibility effects are presented to study the behavior of plane steel frames. In fact, it is the classic beam-column finite element that presents, at its ends, pairs of springs arranged in sequence. One of the springs is represented in the mathematical formulation of this element by the parameter Sc, which defines the joint stiffness of the members; the other spring, whose rigidity is simulated by the parameter Ss, evaluates the plastification of the cross section. The element stiffness matrix incorporates these three mentioned nonlinear effects. Therefore, the aim of this work is to investigate the computer efficiency of this hybrid finite element in the isolated and combined simulation of these nonlinear effects. Initially, equilibrium and stability of classic structural problems with high nonlinear behavior and critical points in the equilibrium paths are studied. Semi-rigid structural systems with initial geometric imperfections are also evaluated. Later, the hybrid element is tested in the inelastic analysis of plane steel frames based on refined plastic-hinge method. Through these examples, it was possible to validate and verify the use of the proposed hybrid finite element in the numerical modeling of various nonlinear structural problems in civil engineering.

Esse artigo aborda a influência da configuração geométrica inicial na carga-limite de portais planos de aço, determinada empregando-se uma análise inelástica de segunda ordem baseada na aplicação do método da zona plástica. Essa configuração geométrica inicial inclui imperfeições como a curvatura inicial e o fora de prumo, que fazem parte dos requerimentos mínimos para se qualificar essa análise inelástica como avançada. Os passos necessários para desenvolver essa análise serão mostrados, incluindo a formulação, as exigências de cálculo e os exemplos utilizados nesse estudo. Finalmente, são apresentados as conclusões e um roteiro de análise, que podem auxiliar o engenheiro a estabelecer a configuração inicial mais crítica, a partir da qual pode-se determinar a carga-limite de um problema estrutural mais complexo.

This paper studies the contribution of initial geometric configuration to the limit load defined by a second-order plastic-zone inelastic analysis applied to steel plane frames. This initial configuration must include geometric imperfections (out-of-straightness and out-of-plumb) that are required for qualifying the inelastic analysis as advanced one. The necessary steps to apply this analysis are shown, including formulation, requirements and the studied examples. Lastly, a step-by-step procedure and a conclusion are given, providing the critical initial configuration by which the engineer will define the limit load for more complex structural problems.

Esse trabalho fornece um estudo sobre o comportamento inelástico de segunda ordem de estruturas metálicas, tendo como base o emprego do método dos elementos finitos e do método da rótula plástica. Atenção especial é dada à formulação de um elemento finito híbrido, em especial da sua matriz de rigidez, que é modificada durante o processo de carregamento da estrutura, para incorporar os efeitos inelásticos da estrutura. O conceito da seção montada é introduzido juntamente com os fundamentos da abordagem plástica-refinada empregada. Ao final desse artigo, através da análise de vários problemas encontrados na literatura, verifica-se a eficácia, tanto da formulação inelástica desenvolvida, quanto das implementações computacionais realizadas.

This work supplies a study of the second-order inelastic behavior of steel frames based on the finite element method and plastic-hinge method. Special attention is given to hybrid finite element formulation, specifically to its tensile strength matrix, which is modified to accommodate inelastic effects during the loading process of the structure. The section assemblage concept is introduced together with refined plastic-hinge procedures. At the end of this paper, using structural steel examples found in literature, the computational implementation effectiveness and developed formulation are verified.

O presente trabalho fornece um estudo da estabilidade de treliças espaciais através da utilização de uma formulação elástica não-linear, baseada no método dos elementos finitos, que leva em consideração os efeitos de segunda ordem e a mudança de geometria da estrutura. Especial atenção é dada ao cálculo da matriz de rigidez, onde tais efeitos são levados em consideração, e à obtenção do vetor de forças internas do elemento. A partir daí, foi realizada uma implementação computacional para que a análise do comportamento de treliças espaciais fosse possível. Ao final desse artigo, através da análise de problemas estruturais encontrados na literatura, pretende-se verificar a eficácia tanto da formulação empregada quanto da implementação computacional realizada.

The present work supplies a stability study of the spatial trusses using a nonlinear elastic formulation, based in the finite elements method, where the second-order effects and the structural geometry changing are considered. Special attention is given to the stiffness matrix and the internal force vector calculations. From thus, it was made a computational implementation for the analysis of the spatial trusses behaviour. At the end of this paper, using structural examples found in the literature, the computational implementation efficacy and the formulation proposed are verified.

Esse trabalho fornece algumas formulações de elementos finitos circulares para análise de arcos e anéis. Atenção especial é dada ao cálculo da matriz de rigidez dos elementos finitos desenvolvidos, onde os efeitos das deformações de flexão, cisalhantes e de membrana são levados em consideração. O acoplamento desses efeitos permite a análise do comportamento de arcos esbeltos e espessos. No final do artigo, através da análise de problemas estruturais encontrados na literatura, pretende-se verificar a eficiência das formulações implementadas. O objetivo é conhecer a melhor modelagem numérica para obtenção dos deslocamentos e forças resultantes de sistemas estruturais curvos.

A study of curved beam element formulations for arch and ring models is presented in this paper. Flexural, axial and shear deformation effect is all taken into account as derivations of the beam element stiffness matrices. They contain the coupled influences of shear and membrane locking effects. At the end of this paper, using numerical and analytical responses to the structural problems found in literature, the formulation efficiency verifies. So, the best numerical models are found and the displacements and resultant forces are obtained for the thin and thick curved structural systems.