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Structural and Multidisciplinary Optimization
Published in: Structural and Multidisciplinary Optimization 6/2012

01-06-2012 | Industrial Application

Optimal design of rectangular RC sections for ultimate bending strength

Authors: A. F. M. Barros, M. H. F. M. Barros, C. C. Ferreira

Published in: Structural and Multidisciplinary Optimization | Issue 6/2012

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Abstract

A minimum cost problem for ultimate strength in bending of rectangular reinforced concrete sections is investigated. The design variables are section depth and steel reinforcement areas. State equations are those of equilibrium with compression depth as state variable. The Kuhn-Tucker optimality conditions are solved analytically and formulas for nondimensional design and state variables are obtained in four cases: Two singly-reinforced solutions with either maximum allowable depth or smaller; Two doubly-reinforced with maximum allowable depth and either maximum compression depth or smaller. Each of the solutions is optimal in a region of the plane ‘nondimensional bending moment’–‘cost-effectiveness ratio of concrete to steel’. The formulas are for an arbitrary concrete constitutive law with tension cut-off and are specialized for the parabola-rectangle law of Eurocode 2.
previous article Minimum cost design of a cellular plate loaded by uniaxial compression
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Literature
Adamu A, Karihaloo BL, Rozvany GIN (1994) Minimum cost design of reinforced concrete beams using continuum-type optimality criteria. Struct Optim 7:91–102CrossRef
Adamu A, Karihaloo BL (1995) Minimum cost design of RC frames using the DCOC method part I: columns under uniaxial bending actions. Struct Optim 10:16–32CrossRef
Al-Salloum YA, Siddiqi GH (1994) Cost-Optimum Design of Reinforced Concrete Beams. ACI Struct J 91(6):647–655
Barros AM, Barros MHM, Ferreira CC (2011) Analytical solutions of the optimality conditions for the sizing of rectangular reinforced concrete sections (in Portuguese), vol 27(1), pp 29–42. Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería
Barros MHFM, Martins RAF, Barros AFM (2005) Cost optimization of singly and doubly reinforced concrete beams with EC2-2001. Struct Multidisc Optim 30:236–242CrossRef
Bazaraa MS, Sherali HD, Shetty CM (1993) Nonlinear programming: theory and algorithms. John Wiley & Sons
Ceranic B, Frier C (2000) Sensitivity analysis and optimum design curves for the minimum cost design of singly and doubly reinforced concrete beams. Struct Multidisc Optim 20:260–268CrossRef
Eurocode 2 (1991) Design of concrete structures—Part 1-1: General rules and rules for buildings. CEN European Committee for Standardization. ENV 1992-1-1:1991
Eurocode 2 (2001): Design of concrete structures—Part 1-1: General rules and rules for buildings. CEN European Committee for Standardization. EN 1992-1-1
Haug EJ, Arora JS (1979) Applied optimal design: mechanical and structural systems. Wiley
Kanagasundaram S, Karihaloo BL (1990) Minimum cost design of reinforced concrete structures. Struct Optim 2:173–184CrossRef
Lepš M, Šejnoha M (2003) New approach to optimization of reinforced concrete beams. Comput Struct 81:1957–1966CrossRef
Samman MM, Erbatur HF (1995) Steel ratios for cost optimum reinforced concrete beams. Build Environ 30(4):545–551CrossRef
Metadata
Title
Optimal design of rectangular RC sections for ultimate bending strength
Authors
A. F. M. Barros
M. H. F. M. Barros
C. C. Ferreira
Publication date
01-06-2012
Publisher
Springer-Verlag
Published in
Structural and Multidisciplinary Optimization / Issue 6/2012
Print ISSN: 1615-147X
Electronic ISSN: 1615-1488
DOI
https://doi.org/10.1007/s00158-011-0717-9

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