A Matrix Formulation for the Moment Distribution Method Applied to Continuous Beams
The Moment Distribution Method is a quite powerful hand method of structural analysis, in which the solution is obtained iteratively without even formulating the equations for the unknowns. It was formulated by Professor Cross in an era where computer facilities were not available to solve frame pro...
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | Advances in Civil Engineering |
| Online Access: | http://dx.doi.org/10.1155/2011/725395 |
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| author | Arlindo Pires Lopes Adriana Alencar Santos Rogério Coelho Lopes |
| author_facet | Arlindo Pires Lopes Adriana Alencar Santos Rogério Coelho Lopes |
| author_sort | Arlindo Pires Lopes |
| collection | DOAJ |
| description | The Moment Distribution Method is a quite powerful hand method of structural analysis, in which the solution is obtained iteratively without even formulating the equations for the unknowns. It was formulated by Professor Cross in an era where computer facilities were not available to solve frame problems that normally require the solution of simultaneous algebraic equations. Its relevance today, in the era of personal computers, is in its insight on how a structure reacts to applied loads by rotating its nodes and thus distributing the loads in the form of member-end moments. Such an insight is the foundation of the modern displacement method. This work has a main objective to present an exact solution for the Moment Distribution Method through a matrix formulation using only one equation. The initial moments at the ends of the members and the distribution and carry-over factors are calculated from the elementary procedures of structural analysis. Four continuous beams are investigated to illustrate the applicability and accuracy of the proposed formulation. The use of a matrix formulation yields excellent results when compared with those in the literature or with a commercial structural program. |
| format | Article |
| id | doaj-art-a99210b122db457981fc667a0f0ed480 |
| institution | Kabale University |
| issn | 1687-8086 1687-8094 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Civil Engineering |
| spelling | doaj-art-a99210b122db457981fc667a0f0ed4802025-02-03T05:47:41ZengWileyAdvances in Civil Engineering1687-80861687-80942011-01-01201110.1155/2011/725395725395A Matrix Formulation for the Moment Distribution Method Applied to Continuous BeamsArlindo Pires Lopes0Adriana Alencar Santos1Rogério Coelho Lopes2Department of Civil Engineering, Portland State University, Portland, OR 97201-3252, USACoordenação de Engenharia Mecânica, Escola Superior de Tecnologia, Universidade do Estado do Amazonas, Avenida Darcy Vargas 1200, 69065-020, Manaus, AM, BrazilCoordenação de Engenharia Mecânica, Escola Superior de Tecnologia, Universidade do Estado do Amazonas, Avenida Darcy Vargas 1200, 69065-020, Manaus, AM, BrazilThe Moment Distribution Method is a quite powerful hand method of structural analysis, in which the solution is obtained iteratively without even formulating the equations for the unknowns. It was formulated by Professor Cross in an era where computer facilities were not available to solve frame problems that normally require the solution of simultaneous algebraic equations. Its relevance today, in the era of personal computers, is in its insight on how a structure reacts to applied loads by rotating its nodes and thus distributing the loads in the form of member-end moments. Such an insight is the foundation of the modern displacement method. This work has a main objective to present an exact solution for the Moment Distribution Method through a matrix formulation using only one equation. The initial moments at the ends of the members and the distribution and carry-over factors are calculated from the elementary procedures of structural analysis. Four continuous beams are investigated to illustrate the applicability and accuracy of the proposed formulation. The use of a matrix formulation yields excellent results when compared with those in the literature or with a commercial structural program.http://dx.doi.org/10.1155/2011/725395 |
| spellingShingle | Arlindo Pires Lopes Adriana Alencar Santos Rogério Coelho Lopes A Matrix Formulation for the Moment Distribution Method Applied to Continuous Beams Advances in Civil Engineering |
| title | A Matrix Formulation for the Moment Distribution Method
Applied to Continuous Beams |
| title_full | A Matrix Formulation for the Moment Distribution Method
Applied to Continuous Beams |
| title_fullStr | A Matrix Formulation for the Moment Distribution Method
Applied to Continuous Beams |
| title_full_unstemmed | A Matrix Formulation for the Moment Distribution Method
Applied to Continuous Beams |
| title_short | A Matrix Formulation for the Moment Distribution Method
Applied to Continuous Beams |
| title_sort | matrix formulation for the moment distribution method applied to continuous beams |
| url | http://dx.doi.org/10.1155/2011/725395 |
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