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Computers and Concrete
  Volume 18, Number 5, November 2016, pages 983-998

Development of optimum design curves for reinforced concrete beams based on the INBR9
Alireza Habibi, Fouad Ghawami and Mohammad S. Shahidzadeh

    Structural optimization is one of the most important topics in structural engineering and has a wide range of applicability. Therefore, the main objective of the present study is to apply the Lagrange Multiplier Method (LMM) method for minimum cost design of singly and doubly reinforced rectangular concrete beams. Concrete and steel material costs are used as objective cost function to be minimized in this study, and ultimate flexural strength of the beam is considered to be as the main constraint. The ultimate limit state method with partial material strength factors and equivalent concrete stress block is used to derive general relations for flexural strength of RC beam and empirical coefficients are taken from topic 9 of the Iranian National Building Regulation (INBR9). Optimum designs are obtained by using the LMM and are presented in closed form solutions. Graphical representation of solutions are presented and it is shown that proposed design curves can be used for minimum cost design of the beams without prior knowledge of optimization and without the need for iterative trials. The applicability of the proposed relations and curves are demonstrated through two real life examples of SRB and DRB design situations and it is shown that the minimum cost design is actually reached using proposed method.
Key Words
    Reinforced Concrete Beam, Structural Optimization, Lagrange Multiplier Method, Design Curves, INBR9
Alireza Habibi, Fouad Ghawami and Mohammad S. Shahidzadeh: DepartmentofCivilEngineering,UniversityofKurdistan,Sanandaj,Iran

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