Deriving analytical solutions using symbolic matrix structural analysis for continuous beams
Abstract This study investigates the use of symbolic computation in Matrix Structural Analysis (MatSA) for continuous beams, using the MATLAB Symbolic Math Toolbox. By employing symbolic MatSA, analytical expressions for displacements, support reactions, and internal forces are derived, offering dee...
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| Format: | Article |
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Nature Portfolio
2025-05-01
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| Series: | Scientific Reports |
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| Online Access: | https://doi.org/10.1038/s41598-025-98023-x |
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| author | Vagelis Plevris Afaq Ahmad |
| author_facet | Vagelis Plevris Afaq Ahmad |
| author_sort | Vagelis Plevris |
| collection | DOAJ |
| description | Abstract This study investigates the use of symbolic computation in Matrix Structural Analysis (MatSA) for continuous beams, using the MATLAB Symbolic Math Toolbox. By employing symbolic MatSA, analytical expressions for displacements, support reactions, and internal forces are derived, offering deeper insights into structural behavior. This approach facilitates efficient and scalable sensitivity analysis, where partial derivatives of outputs concerning input parameters can be directly computed, enhancing design exploration. The development includes an open-source MATLAB program, hosted on GitHub, enabling symbolic analysis of continuous beams subjected to point and uniform loads. This approach is valuable for both engineering practice and pedagogy, enriching the understanding of structural mechanics and aiding in education by illustrating clear parameter relationships. The program supports deriving influence lines and identifying maximum response values. |
| format | Article |
| id | doaj-art-e30e630d69044b0ba368540d8dbc44d9 |
| institution | OA Journals |
| issn | 2045-2322 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Scientific Reports |
| spelling | doaj-art-e30e630d69044b0ba368540d8dbc44d92025-08-20T02:15:28ZengNature PortfolioScientific Reports2045-23222025-05-0115111610.1038/s41598-025-98023-xDeriving analytical solutions using symbolic matrix structural analysis for continuous beamsVagelis Plevris0Afaq Ahmad1Department of Civil and Environmental Engineering, College of Engineering, Qatar UniversityDepartment of Built Environment, Oslo Metropolitan UniversityAbstract This study investigates the use of symbolic computation in Matrix Structural Analysis (MatSA) for continuous beams, using the MATLAB Symbolic Math Toolbox. By employing symbolic MatSA, analytical expressions for displacements, support reactions, and internal forces are derived, offering deeper insights into structural behavior. This approach facilitates efficient and scalable sensitivity analysis, where partial derivatives of outputs concerning input parameters can be directly computed, enhancing design exploration. The development includes an open-source MATLAB program, hosted on GitHub, enabling symbolic analysis of continuous beams subjected to point and uniform loads. This approach is valuable for both engineering practice and pedagogy, enriching the understanding of structural mechanics and aiding in education by illustrating clear parameter relationships. The program supports deriving influence lines and identifying maximum response values.https://doi.org/10.1038/s41598-025-98023-xMatrix structural analysisSymbolicContinuous beamsStructural analysisSensitivity analysisInfluence lines |
| spellingShingle | Vagelis Plevris Afaq Ahmad Deriving analytical solutions using symbolic matrix structural analysis for continuous beams Scientific Reports Matrix structural analysis Symbolic Continuous beams Structural analysis Sensitivity analysis Influence lines |
| title | Deriving analytical solutions using symbolic matrix structural analysis for continuous beams |
| title_full | Deriving analytical solutions using symbolic matrix structural analysis for continuous beams |
| title_fullStr | Deriving analytical solutions using symbolic matrix structural analysis for continuous beams |
| title_full_unstemmed | Deriving analytical solutions using symbolic matrix structural analysis for continuous beams |
| title_short | Deriving analytical solutions using symbolic matrix structural analysis for continuous beams |
| title_sort | deriving analytical solutions using symbolic matrix structural analysis for continuous beams |
| topic | Matrix structural analysis Symbolic Continuous beams Structural analysis Sensitivity analysis Influence lines |
| url | https://doi.org/10.1038/s41598-025-98023-x |
| work_keys_str_mv | AT vagelisplevris derivinganalyticalsolutionsusingsymbolicmatrixstructuralanalysisforcontinuousbeams AT afaqahmad derivinganalyticalsolutionsusingsymbolicmatrixstructuralanalysisforcontinuousbeams |