Keywords: cross section, flexural-axial loading, automated design, optimum reinforcement.

The design of reinforced concrete members for combined flexure and axial loading is a common case in structural engineering. In this type of design, the reinforcement of a cross section is obtained in order to resist some certain flexural moment and axial force. The section is usually rectangular. It is known that the solution to this kind of problems is indeterminate, since there are three unknown variables (the top and bottom reinforcement, and the neutral axis depth) and only two equilibrium equations. In conventional calculation procedures [1], a further condition is required in order to solve the problem, so it is advisable to manage these procedures by programming them in computer codes.

As a result of the infinite number of solutions, an optimization problem to obtain the optimum reinforcement in the section can be proposed as an ideal method of solving the equation system [2,3,4]. Optimization procedures involve, in most cases, complex calculations that require adequate computer methods. However, a easy-to-implement optimization problem is proposed in this paper, entailing a negligible computational cost (tenths of a second) in any currently available personal computer.

The proposed method allows:

1. considering high-strength concrete and the minimum area of reinforcement,
2. constraining the neutral axis depth in order to guarantee certain curvatures to comply with ductility criterion,
3. and choosing between the standards ACI 318 or Eurocode 2.

Four numerical examples are presented. In three of them, the results obtained by ACI 318 are compared with those obtained using Eurocode 2 and using the conventional method, whilst in the fourth example, high-strength concrete is used.

This study aims not so much as to obtain the reinforcement, which has already been solved [4,5], but to have an automated design procedure for calculating the optimum reinforcement by means of the implementation of a simple optimization method. Thus, the interest of the proposed procedure focuses on automating the calculation of reinforcement, in which the structural engineer may include certain design conditions, such as the minimum reinforcement, the high-strength concrete and, or a certain ductility criterion.

1

A.H. Nilson, D. Darwin, C.W. Dolan, "Design of Concrete Structures", 14th Ed., McGraw-Hill, New York, 2010.

2

E. Raue, S. Hahn, "Optimum reinforcement design of concrete cross-sections considering deformation constraints", J. Civ. Eng. Manag., 11(1), 65-71, 2005.

3

A. Tomás, P. Martí, "Design of reinforcement for concrete co-planar shell structures using optimization techniques", Meccanica, 45(5), 657-669, 2010. doi:10.1007/s11012-009-9263-6

4

L.M. Gil-Martín, M. Aschheim, E. Hernández-Montes, M. Pasadas-Fernández, "Recent developments in optimal reinforcement of RC beam and column sections", Eng. Struct., 33(4), 1170-1180, 2011. doi:10.1016/j.engstruct.2010.12.038

5

E. Hernández-Montes, L.M. Gil-Martín, M. Aschheim, "Design of concrete members subjected to uniaxial bending and compression using reinforcement sizing diagrams", ACI Struct. J., 102(1), 150-158, 2005.

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