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Computers and Concrete Volume 6, Number 6, December 2009 , pages 505-521 DOI: https://doi.org/10.12989/cac.2009.6.6.505 |
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Closed form ultimate strength of multi-rectangle reinforced concrete sections under axial load and biaxial bending |
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V. Dias da Silva, M. H. F. M. Barros, E. N. B. S. Julio and C. C. Ferreira
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| Abstract | ||
| The analysis of prismatic members made of reinforced concrete under inclined bending, especially the computation of ultimate loads, is a pronounced non-linear problem which is frequently solved by discretizing the stress distribution in the cross-section using interpolation functions. In the approach described in the present contribution the exact analytical stress distribution is used instead. The obtained expressions are integrated by means of a symbolic manipulation package and automatically converted to optimized Fortran code. The direct problem-computation of ultimate internal forces given the position of the neutral axis-is first described. Subsequently, two kinds of inverse problem are treated: the computation of rupture envelops and the dimensioning of reinforcement, given design internal forces. An iterative Newton-Raphson procedure is used. Examples are presented. | ||
| Key Words | ||
| reinforced concrete sections; ultimate limit state; prismatic members; inclined bending; formulation; design. | ||
| Address | ||
| V. Dias da Silva: Department of Civil Engineering, University of Coimbra, Polo II-Pinhal de Marrocos, 3030-290 Coimbra,, Portugal M. H. F. M. Barros: Department of Civil Engineering, University of Coimbra, Polo II-Pinhal de Marrocos, 3030-290 Coimbra,, Portugal E. N. B. S. Julio: Department of Civil Engineering, University of Coimbra, Polo II-Pinhal de Marrocos, 3030-290 Coimbra,, Portugal C. C. Ferreira: Department of Civil Engineering, University of Coimbra, Polo II-Pinhal de Marrocos, 3030-290 Coimbra,, Portugal | ||