• Computers and Concrete
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• v.18 no.5
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• pp.983-998
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• 2016

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) 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.

• Computers and Concrete
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• v.24 no.2
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• pp.117-123
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• 2019

Optimization is an important subject which is widely used in engineering problems. In this paper, an analytical method is developed for optimum design of reinforced concrete beams considering both flexural and shear effects. A closed-form formulation is derived for optimal height and rebar of beams. The total material cost of steel and concrete is considered as the objective function which is minimized during the optimization process. The ultimate flexural and shear capacities of the beam are considered as the main constraints. The ultimate limit state is considered for deriving the relations for flexural capacity of the beam. The design requirements are considered according to the item 9 of the Iranian National Building. Analytical formulas and some curves are proposed to be used for optimum design of RC beams. The proposed method can be used to perform the optimization of RC beams without the need of any prior knowledge in optimization. Also, the results of the studied numerical example show that the proposed method results in a better design comparing with the other methods.