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PROCEEDINGS OF THE ELEVENTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY
Edited by: B.H.V. Topping
Automatic Calculation of Optimum Reinforcement for Flexural and Axial Loading
A. Tomás, G. Sánchez and A. Alarcón
Department of Civil Engineering, Universidad Politécnica de Cartagena (UPCT), Spain
A. Tomás, G. Sánchez, A. Alarcón, "Automatic Calculation of Optimum Reinforcement for Flexural and Axial Loading", in B.H.V. Topping, (Editor), "Proceedings of the Eleventh International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 160, 2012. doi:10.4203/ccp.99.160
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 , 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:
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.
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