Analysing Flexural Response in RC Beams: A Closed-Form Solution Designer Perspective from Detailed to Simplified Modelling
This paper presents a detailed analytical approach for the bending analysis of reinforced concrete beams, integrating both structural mechanics principles and Eurocode 2 provisions. The general analytical expressions derived for the curvature were applied for the transverse displacement analysis of...
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MDPI AG
2024-10-01
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| author | Denis Imamović Matjaž Skrinar |
| author_facet | Denis Imamović Matjaž Skrinar |
| author_sort | Denis Imamović |
| collection | DOAJ |
| description | This paper presents a detailed analytical approach for the bending analysis of reinforced concrete beams, integrating both structural mechanics principles and Eurocode 2 provisions. The general analytical expressions derived for the curvature were applied for the transverse displacement analysis of a simply supported reinforced concrete beam under four-point loading, focusing on key limit states: the initiation of cracking, the yielding of tensile reinforcement and the compressive failure of concrete. The displacement’s results were validated through experimental testing, showing a high degree of accuracy in the elastic and crack propagation phases. Deviations in the yielding phase were attributed to the conservative material assumptions within the Eurocode 2 framework, though the analytical model remained reliable overall. To streamline the computational process for more complex structures, a simplified model utilising a non-linear rotational spring was further developed. This model effectively captures the influence of cracking with significantly reduced computational effort, making it suitable for serviceability limit state analyses in complex loading scenarios, such as seismic impacts. The results demonstrate that combining detailed analytical methods with this simplified model provides an efficient and practical solution for the analysis of reinforced concrete beams, balancing precision with computational efficiency. |
| format | Article |
| id | doaj-art-fdcf7c20ceea4a4293e9beb5cb4d58a3 |
| institution | DOAJ |
| issn | 2227-7390 |
| language | English |
| publishDate | 2024-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-fdcf7c20ceea4a4293e9beb5cb4d58a32025-08-20T02:49:49ZengMDPI AGMathematics2227-73902024-10-011221332710.3390/math12213327Analysing Flexural Response in RC Beams: A Closed-Form Solution Designer Perspective from Detailed to Simplified ModellingDenis Imamović0Matjaž Skrinar1Faculty of Civil Engineering, Transportation Engineering and Architecture, Chair of Mechanics of Structures, University of Maribor, Smetanova 17, SI-2000 Maribor, SloveniaFaculty of Civil Engineering, Transportation Engineering and Architecture, Chair of Mechanics of Structures, University of Maribor, Smetanova 17, SI-2000 Maribor, SloveniaThis paper presents a detailed analytical approach for the bending analysis of reinforced concrete beams, integrating both structural mechanics principles and Eurocode 2 provisions. The general analytical expressions derived for the curvature were applied for the transverse displacement analysis of a simply supported reinforced concrete beam under four-point loading, focusing on key limit states: the initiation of cracking, the yielding of tensile reinforcement and the compressive failure of concrete. The displacement’s results were validated through experimental testing, showing a high degree of accuracy in the elastic and crack propagation phases. Deviations in the yielding phase were attributed to the conservative material assumptions within the Eurocode 2 framework, though the analytical model remained reliable overall. To streamline the computational process for more complex structures, a simplified model utilising a non-linear rotational spring was further developed. This model effectively captures the influence of cracking with significantly reduced computational effort, making it suitable for serviceability limit state analyses in complex loading scenarios, such as seismic impacts. The results demonstrate that combining detailed analytical methods with this simplified model provides an efficient and practical solution for the analysis of reinforced concrete beams, balancing precision with computational efficiency.https://www.mdpi.com/2227-7390/12/21/3327reinforced concrete structuresnon-linear behaviourtransverse displacementmoment–curvature diagramrotational spring model |
| spellingShingle | Denis Imamović Matjaž Skrinar Analysing Flexural Response in RC Beams: A Closed-Form Solution Designer Perspective from Detailed to Simplified Modelling Mathematics reinforced concrete structures non-linear behaviour transverse displacement moment–curvature diagram rotational spring model |
| title | Analysing Flexural Response in RC Beams: A Closed-Form Solution Designer Perspective from Detailed to Simplified Modelling |
| title_full | Analysing Flexural Response in RC Beams: A Closed-Form Solution Designer Perspective from Detailed to Simplified Modelling |
| title_fullStr | Analysing Flexural Response in RC Beams: A Closed-Form Solution Designer Perspective from Detailed to Simplified Modelling |
| title_full_unstemmed | Analysing Flexural Response in RC Beams: A Closed-Form Solution Designer Perspective from Detailed to Simplified Modelling |
| title_short | Analysing Flexural Response in RC Beams: A Closed-Form Solution Designer Perspective from Detailed to Simplified Modelling |
| title_sort | analysing flexural response in rc beams a closed form solution designer perspective from detailed to simplified modelling |
| topic | reinforced concrete structures non-linear behaviour transverse displacement moment–curvature diagram rotational spring model |
| url | https://www.mdpi.com/2227-7390/12/21/3327 |
| work_keys_str_mv | AT denisimamovic analysingflexuralresponseinrcbeamsaclosedformsolutiondesignerperspectivefromdetailedtosimplifiedmodelling AT matjazskrinar analysingflexuralresponseinrcbeamsaclosedformsolutiondesignerperspectivefromdetailedtosimplifiedmodelling |