Stiffness-Matrix Formulation of Beams with Shear Effect on Elastic Foundation

Aydoğan, Metin

doi:10.1061/(asce)0733-9445(1995)121:9(1265)

Cited by 52 publications

(13 citation statements)

References 5 publications

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“…A deflexão de vigas prismáticas de concreto armado é um assunto que, apesar da fundamentação antiga e largamente difundida entre engenheiros, arquitetos e calculistas, ainda oferece alguns atrativos, sobretudo quando se abrem discussões quanto às distintas abordagens possíveis. Muitos autores empregam diferentes modelos de representação do comportamento das vigas, dentre estes, além do modelo clássico baseado em princípios e resultados diretos da teoria da elasticidade [1,12], a teoria das deformações (por cisalhamento) de primeira ordem [3,9], e o modelo dos carregamentos por funções de singularidade a ser discutido aqui [2], porém, com o adendo da representação de cargas distribuídas em rampa por séries de integrações por partes (devida ao próprio autor deste tratado). Seja como for, as premissas clássicas são preservadas no presente trabalho:…”

Section: Introductionunclassified

Tratado Prático Sobre Funções de Singularidade: Modelamento de Cargas em Vigas de Concreto Armado

Serpa

2020

CALIBRE

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Present treatise deals with applications of singularity functions from a broad perspective in civil engineering, extending its use to hyperstatics, and deepening mathematical questions little explored before. The content is presented through examples discussed in detail, giving to the reader a clear and objective reading. Original mathematical formulations are developed, such as the Macaulay-Serpa series. The treatise is extended to the calculation of hyperstatic porticoes and to the modeling of triangular loads. In this context, the theory appears as an important instrument for the analysis of ruptures in reinforced concrete beams. For the accomplishment of this treatise, an exhaustive search of bibliographical references was made, showing that the existent literature on the subject, mostly of foreign origin, is quite limited.Key words: Singularity functions, reinforced concrete, hyperstatics, discontinuous loading, elastic curve.==================================================================================== O presente tratado versa sobre aplicações das funções de singularidade numa ampla perspectiva da engenharia civil, estendendo seu uso à hiperestática e aprofundando questões matemáticas pouco exploradas anteriormente. O conteúdo é apresentado através de exemplos discutidos em detalhes, proporcionando ao leitor uma leitura clara e objetiva. Formulações matemáticas originais são desenvolvidas, como a série Macaulay-Serpa. O tratado é estendido ao cálculo de pórticos hiperestáticos e à modelagem de cargas triangulares. Nesse contexto, a teoria aparece como um instrumento importante para a análise de rupturas em vigas de concreto armado. Para a realização deste tratado, foi feita uma busca exaustiva das referências bibliográficas, mostrando que a literatura existente sobre o assunto, principalmente de origem estrangeira, é bastante limitada.Palavras-Chave: Funções de singularidade, concreto armado, hiperestática, carga descontínua, curva elástica.

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Section: Introductionunclassified

Tratado Prático Sobre Funções de Singularidade: Modelamento de Cargas em Vigas de Concreto Armado

Serpa

2020

CALIBRE

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“…Other types of foundation models have also been covered extensively such as a beam resting on a visco-elastic foundation, which has been studied by Sonoda et al [9] and a beam on nonlinear foundation has also been studied [10]. On the other hand, and in addition to the classical beam theory, some researchers went further to study the analysis of Timoshenko's beam on an elastic foundation considering the effect of shear deformation as it was studied in [11][12][13]. Moreover, the computer coding, as a power of solving many engineering problems, has also been utilized in the analysis of the beam on an elastic foundation as it has been presented by Teodorue [14], who developed a new computer code based on FEM for a beam on an elastic foundation using Matlab software, making it easy to perform different kinds of problems with slight changes in the input data.…”

Section: Introductionmentioning

confidence: 99%

Galerkin method for bending analysis of beams on non-homogeneous foundation

Musa¹

2017

J. Appl. Math. Comput. Mech.

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Abstract. In this study, a mathematical formulation for static bending analysis of a beam on a non-homogenous foundation is presented. The proposed method offers an accurate procedure for analysis and design of a beam resting on a varying soil bed. The Winkler foundation model is used and presented using discontinuous functions to account for the sudden change in the soil stiffness coefficient. The solution of the governing differential equation is then obtained using the Galerkin method with the help of approximation functions that satisfy the boundary conditions. A systematic approach for setting the approximation functions for different support and soil conditions is suggested. The accuracy of the proposed method is verified through two numerical examples, and they showed an excellent agreement with the finite element method (FEM) and available literature results. MSC: 65L60, 74S05

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“…For a beam on two-parameter foundation, Giger and Shirima [4] presented the complete force-displacement relationship for a Timoshenko beam element based on the exact solution of two differential equations governing the ACCEPTED MANUSCRIPT A C C E P T E D M A N U S C R I P T 4 problem concerned. Aydogan [5] developed a stiffness matrix method for a beam element with shear effect on a foundation of Winkler assumption, where a second-order term of the derivative of the beam's deflection was taken as the shear effect. Yin [6] proposed an analytical solution for an infinite Timoshenko beam on Winkler foundation subjected a point load, and developed a finite element model for the same problem, proving that the shear deformation can not be ignored.…”

Section: Introductionmentioning

confidence: 99%

Static interaction analysis between a Timoshenko beam and layered soils by analytical layer element/boundary element method coupling

Cai

2016

Applied Mathematical Modelling

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Stiffness-Matrix Formulation of Beams with Shear Effect on Elastic Foundation

Cited by 52 publications

References 5 publications

Tratado Prático Sobre Funções de Singularidade: Modelamento de Cargas em Vigas de Concreto Armado

Tratado Prático Sobre Funções de Singularidade: Modelamento de Cargas em Vigas de Concreto Armado

Galerkin method for bending analysis of beams on non-homogeneous foundation

Static interaction analysis between a Timoshenko beam and layered soils by analytical layer element/boundary element method coupling

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