Softening in Reinforced Concrete Beams and Frames

Bažant, Zdeněk P.; Pan, Jiaying; Pijaudier‐Cabot, Gilles

doi:10.1061/(asce)0733-9445(1987)113:12(2333)

Cited by 85 publications

(49 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Junges [2] analyzed a continuous beam of two spans under uniformly distributed loading, obtaining convergence of the solution upon mesh refinement for meshes with at least 10 elements in each span. The authors also follow the recommendation given by Bazant et al [16] of not utilizing elements with length smaller than the height of their cross section. Stramandinoli [9] also investigated the effect of number of layers on the section discretization and concluded that beyond 10 layers there is no change in the numerical solution.…”

Section: Comparison Between Simplified and Fe Models For Short-term Dmentioning

confidence: 72%

Comparison between simplified and FE models for short-term deflection in continuous RC beams

Junges

Rovere

2017

Rev. IBRACON Estrut. Mater.

View full text Add to dashboard Cite

ResumoIn this work, a comparative study of different simplified methods and nonlinear finite element (FE) models used for calculating short-term deflections (vertical displacements of the longitudinal axis) in continuous reinforced concrete (RC) beams, under service loads, is performed. The simplified methods employed are the one proposed by Branson and the bilinear method recommended by the European Code CEB -Design Manual on Cracking and Deformations. Two finite element models are utilized: the first one with frame elements in which material nonlinearities are considered along the element and its cross section divided into layers, by using of constitutive relationships for steel and concrete, while the second one utilizes beam elements, with physical nonlinearity considered by means of moment-curvature diagrams, obtained from Branson equation. Several examples of continuous RC beams under service loads are analysed and the results obtained by the different models are compared taking as reference the nonlinear frame element model. A few conclusions and recommendations regarding the use of the different methods are drawn at the end of the work.Keywords: deflections, beams, reinforced concrete, nonlinear analysis.Neste trabalho é realizado um estudo comparativo dos resultados de flecha (deslocamento vertical do eixo longitudinal) imediata de vigas contínuas de concreto armado sob cargas de serviço, obtidos por diferentes métodos simplificados e por modelos não lineares de elementos finitos (EF). Os métodos simplificados abordados são o proposto por Branson e o método Bilinear recomendado pelo CEB -Manual de projeto sobre Fissuração e Deformações. São utilizados dois modelos de EF: o primeiro com EF de pórtico plano, sendo a não linearidade dos materiais considerada ao longo do elemento e da seção discretizada em camadas, a partir de relações constitutivas do aço e do concreto, enquanto que o segundo utiliza EF de viga, sendo a não linearidade física considerada por meio de diagramas momento-curvatura, obtidos a partir da fórmula de Branson. Os resultados dos diferentes modelos são comparados entre si para diversas vigas de projeto, adotando como referência os resultados do modelo não linear de elementos de pórtico plano. A partir da análise dos resultados, extraem-se algumas conclusões e recomendações quanto ao uso dos métodos simplificados e modelos de EF estudados.Palavras-chave: flecha, vigas, concreto armado, análise não linear.

show abstract

Section: Comparison Between Simplified and Fe Models For Short-term Dmentioning

confidence: 72%

Comparison between simplified and FE models for short-term deflection in continuous RC beams

Junges

Rovere

2017

Rev. IBRACON Estrut. Mater.

View full text Add to dashboard Cite

show abstract

“…The present study extends the preceding paper in this issue (10) and uses the same, layered finite element model as well as the same notations.…”

Section: Introductionmentioning

confidence: 76%

“…It is assumed that there is no bond slip between steel and concrete. All the computations are based on the layered finite element model defined in Appendix I of the preceding paper (10), and the numerical step-by-step algorithm, in which very small increments of load-point displacements ware prescribed, consists of the direct iteration method (iterative secant stiffness algorithm) as described in the preceding paper. This algorithm has been converging well in the softening regime, although it does not permit calculation of possible snapback instabilities.…”

Section: Model Structure and Solution Methodsmentioning

confidence: 99%

Ductility, Snapback, Size Effect, and Redistribution in Softening Beams or Frames

1987

Self Cite

View full text Add to dashboard Cite

A layered finite element model with strain-softening material properties, whose applicability to reinforced concrete was corroborated by comparisons with experimental data in the preceding paper, is used in a parametric study aimed at the effect of several factors: structure size, finite element size, downward sl9pe of strain-softening stress-strain relation, length of the plastic yield plateau before the onset of strain softening (if any), and end-restraint stiffness. T() quantify t~e response, several new response characteristics are introduced: the ductile stren~h ening factor, characterizing how strain softening reduces the maximum load compared to the plastic limit load; the redistribution ratio, characterizing the degree of bending moment redistribution in comparison to that in plastic limit analysis; the energy safety factor, describing the energy to deform the structure to the peak load; and the ductility factor, characterizing the deflection increase at maximum load relative to the deflection from elastic analysis. The condition of snapback instability, which determines the ductility factor, is derived analytically for an elastically restrained beam. Finally, it is shown that strain-softening segments in beams cannot be modeled as softening hinges except for sufficiently slender beams.

show abstract

“…Such descending branch of the stress-strain relation leads to mathematical difficulties as the boundary value problem becomes ill-posed and the response is no longer unique. Initially, localization has been studied for classic finite elements that build on the use of displacement interpolation func- tions, both for uni-dimensional beam formulations [100] and multi-dimensional SEMs, such as membranes, shells, solids, etc [101]. Following the more recent development of forcebased beam elements, the specific features of localization afflicting this type of approach have also been studied [49].…”

Section: Localization and Other Numerical Issuesmentioning

confidence: 99%

Modelling Approaches for Inelastic Behaviour of RC Walls: Multi-level Assessment and Dependability of Results

Almeida

Tarquini

Beyer

2014

Arch Computat Methods Eng

View full text Add to dashboard Cite

The severe damage and collapse of many reinforced concrete (RC) wall buildings in the recent earthquakes of Chile (2010) and New Zealand (2011) have shown that RC walls did not perform as well as required by the modern codes of both countries. It seems therefore appropriate to intensify research efforts towards more accurate simulations of damage indicators, in particular local engineering demand parameters such as material strains, which are central to the application of performance-based earthquake engineering. Potential modelling improvements will necessarily build on a thorough assessment of the limitations of current state-ofthe-practice simulation approaches for RC wall buildings. This work compares different response parameters obtained from monotonic analyses of RC walls using numerical tools that are commonly employed by researchers and specialized practitioners, namely: plastic hinge analyses, distributed plasticity models, and shell element models. It is shown that a multi-level assessment-wherein both the global and local levels of the response are jointly addressed during pre-and post-peak response-is fundamental to define the dependability of the results. The displacement demand up to which the wall response can be predicted is defined as the first occurrence between the attainment of material strain limits and numerical issues such as localization. The present work also presents evidence to discourage the application of performance-based assessment of RC walls relying on nonregularized strain EDPs.

show abstract

Softening in Reinforced Concrete Beams and Frames

Cited by 85 publications

References 15 publications

Comparison between simplified and FE models for short-term deflection in continuous RC beams

Comparison between simplified and FE models for short-term deflection in continuous RC beams

Ductility, Snapback, Size Effect, and Redistribution in Softening Beams or Frames

Modelling Approaches for Inelastic Behaviour of RC Walls: Multi-level Assessment and Dependability of Results

Contact Info

Product

Resources

About