Analysis and design of concrete structures using strut and tie model by FEM: Application in foundation blocks, short consoles, wall beams and rigid shoes

Neste trabalho tem-se como objetivo realizar análises elástico-lineares a partir de um programa computacional destinado à implementação numérica do Modelo de Bielas e Tirantes, utilizando-se uma formulação baseada no Método dos Elementos Finitos (MEF). Com este modelo é possível analisar o comportamento de elementos estruturais como blocos de fundação, consolos curtos e sapatas rígidas e realizar o dimensionamento das armaduras de aço, representar os valores de tensões, deformações e deslocamentos na região de uma viga representada como o Modelo de Bielas desenvolvido por Montoya et al. [1], além de modelar numericamente via MEF uma viga-parede com uma grande abertura, desenvolvida por Schlaich et al. [2]. Com o fim de validar as implementações numéricas, os resultados foram comparados com modelagens numéricas realizadas com o auxílio do software ANSYS 17 e com expressões normativas.The main objective of this work was to perform elastic-linear analysis through computational program and numerical approach from strut-and-tie model, using a formulation based on Finite Element Method (FEM). In this model, it is possible to analyze the behavior of structural elements such as foundation blocks, wall beams, short consoles; to demosntrate the values of tensions, deformations, and displacements in the region of a beam represented by the Model of cranks developed by Montoya et al. [1]; besides numerically modeling a wall beam via FEM with a large aperture, developed by Schlaich et al. [2]. In order to validate the numerical implementations, the results were compared with numerical modeling performed with the aid of the software ANSYS 17 and normative expressions.Peer Reviewe

Collapse probability and resistance factor calibration of 2D steel frames under gravity loads

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

Nonlinear analysis of structural elements under unilateral contact constraints by a Ritz type approach.

A nonlinear modal solution methodology capable of solving equilibrium and stability problems of uni-dimensional structural elements (beams, columns and arches) with unilateral contact constraints is presented in this work. The contact constraints are imposed by an elastic foundation of the Winkler type, where special attention is given to the case in which the foundation reacts in compression only, characterizing the contact as unilateral. A Ritz type approach with moveable boundaries, where the coordinates defining the limits of the contact regions are considered as additional variables of the problem, is proposed to solve this class of unilateral contact problems. The methodology is illustrated by particular problems involving beams, beam-columns and arches, and the results are compared with available results obtained by finite element and mathematical programming techniques. It is concluded that the Ritz type approach proposed is particularly suited for the analysis of structural problems where the number, but not the length, of the contact regions between the bodies are known a priori. Therefore, it can substitute in these cases finite element applications and be used as a benchmark for more general and complex formulations as well

Thermal analysis of steel-concrete composite cross sections via CS-ASA/FA.

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

Structural reliability of steel portal frames.

O emprego de m?todos para an?lise de confiabilidade estrutural permite a avalia??o da probabilidade de viola??o de estados limites relevantes ao projeto estrutural. Este artigo apresenta procedimento num?rico preciso e eficiente para avalia??o da confiabilidade de p?rticos planos de a?o via an?lise estrutural avan?ada em elementos finitos, considerando os efeitos da n?o linearidade geom?trica e da flexibilidade das liga??es. O m?todo anal?tico FORM (First Order Reliability Method) foi empregado na avalia??o da probabilidade de falha de fun??es de desempenho formuladas para estados limites ?ltimos de resist?ncia e estados limites de servi?o. Os resultados obtidos indicaram que os ?ndices de confiabilidade dos exemplos de p?rticos planos de a?o analisados s?o significativamente afetados pela presen?a das liga??es semirr?gidas e pelos efeitos da n?o linearidade geom?trica.The reliability methods allows the evaluation of the limit states violation probability, which are relevant to the structural design. This paper presents an accurate and efficient numerical procedure for evaluating the reliability of steel frames by advanced finite element structural analysis, considering the effects of geometric nonlinearity and semi?rigid connections. The FORM method was used to estimate the probability of failure of performance functions formulated in terms of the ultimate strength and serviceability limit states. The results indicate that the frame reliability is strongly affected by semi?rigid connections and the effects of geometric nonlinearity

Thermo-structural analysis of reinforced concrete beams.

The objective of this study is to simulate the behavior of reinforced concrete beams in fire situation. In order to achieve this objective, advanced numerical formulations were developed, implemented and evaluated. When exposed to high temperatures, the properties of the material deteriorate, resulting in the loss of strength and stiffness. To achieve the goal, two new modules within the Computational System for Advanced Structural Analysis were created: Fire Analysis and Fire Structural Analysis. The first one aims to determine the temperature field in the cross section of structural elements through thermal analysis by using the Finite Element Method (FEM). The second was designed to perform the second-order inelastic analysis of structures under fire using FEM formulations based on the Refined Plastic Hinge Method coupled with the Strain Compatibility Method. The results obtained of the nonlinear analyses of two reinforced concrete beams under high temperature were compared with the numerical and experimental solutions available in literature and were highly satisfactory. These results also showed that the proposed numerical approach can be used to study the progressive collapse of other reinforced concrete structures in fire situation and extended to the numerical analysis of composite structures under fire condition

Numerical analysis of RC plane structures : a concentrated nonlinear effect approach.

The present work aims to study the nonlinear behavior of reinforced concrete structures via Refined Plastic Hinge Method (RPHM). Pseudo-springs are used at the finite element ends, where the gradual loss of stiffness is determined by the combination of the normal force and bending moment (NM) in the cross section. The limiting of the uncracked, elastic and plastic regimes is done in the NM diagram. The concrete cracking is explicitly simulated with two approaches to calculate the effective moment of inertia of the cross section. The displacement-based formulation is referenced to the co-rotational system and coupled with continuation strategies to allow to overcome the possible critical points in the equilibrium paths. For validation of the numerical simulations, the results found with the proposed formulation are confronted with experimental and numerical data present in literature

Computational procedures for nonlinear analysis of frames with semi-rigid connections.

This work discusses numerical and computational strategies for nonlinear analysis of frames with semi-rigid connections. Initially, the formation of the nonlinear problem is analyzed, followed by the necessary computational approaching for its solution. After that, the matricial formulations and the mathematical modeling of flexible connections, as well as the insertion of the nonlinear process, are presented. Moreover, the necessary procedures for characterization of semi-rigid beam-column elements, the modified stiffness matrix, the internal forces vector and the updating of the connection stiffness along the incremental-iterative process are approached and illustrated through the text. In order to verify the success of the implementations and the considered algorithms, the results for some types of frames considering semi-rigid joints are compared with those supplied by literature. Some considerations and conclusions about the computational implementations and results obtained are presented at the end of this work

Análise da estabilidade elástica de treliças espaciais.

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