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Steel and Composite Structures Volume 29, Number 2, October25 2018 , pages 243-256 DOI: https://doi.org/10.12989/scs.2018.29.2.243 |
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Computational Lagrangian Multiplier Method using optimization and sensitivity analysis of rectangular reinforced concrete beams |
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Mehran Shariat, Mahdi Shariati, Amirhossein Madadi and Karzan Wakil
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| Abstract | ||
| This study conducts an optimization and sensitivity analysis on rectangular reinforced concrete (RC) beam using Lagrangian Multiplier Method (LMM) as programming optimization computer soft ware. The analysis is conducted to obtain the minimum design cost for both singly and doubly RC beams according to the specifications of three regulations of American concrete institute (ACI), British regulation (BS), and Iranian concrete regulation (ICS). Moreover, a sensitivity analysis on cost is performed with respect to the effective parameters such as length, width, and depth of beam, and area of reinforcement. Accordingly, various curves are developed to be feasibly utilized in design of RC beams. Numerical examples are also represented to better illustrate the design steps. The results indicate that instead of complex optimization relationships, the LMM can be used to minimize the cost of singly and doubly reinforced beams with different boundary conditions. The results of the sensitivity analysis on LMM indicate that each regulation can provide the most optimal values at specific situations. Therefore, using the graphs proposed for different design conditions can effectively help the designer (without necessity of primary optimization knowledge) choose the best regulation and values of design parameters. | ||
| Key Words | ||
| optimum design; Lagrangian Multiplier Method; sensitivity analysis; reinforced concrete beam | ||
| Address | ||
| (1) Mehran Shariat, Amirhossein Madadi: Department of Civil Engineering, Hakim Sabzevari University, Sabzevar, Iran; (2) Mahdi Shariati: Faculty of Civil Engineering, University of Tabriz, Tabriz, Iran; (3) Karzan Wakil: Information Technology Department, Technical College of Informatics, Sulaimani Polytechnic University, Iraq; (4) Karzan Wakil: University of Human Development, Iraq. | ||