عنوان مقاله [English]
Structural optimization is currently one of the most important topics in structural engineering and has a wide range of applicability. The objective of structural optimization is to find design variables for a structure that minimize cost and satisfy various design requirements. A large number of optimization techniques have been developed and used in structural optimization. Among optimization methods, the mathematical programming method is attractive due to its generality and rigorous theoretical basis. The main difficulty with the use of mathematical programming for structural optimization problems to which the structural form is specific is the formulation of constraints, such as displacement and stress limitations, as explicit functions of the design variables.
The material costs of reinforced concrete frames are dependent on dimensions, reinforcement ratios and formworks of structural elements, and the unit costs of concrete, steel reinforcement and formwork. Whilst trying to optimize the cost of a structure, certain conditions have to be met so that the equilibriums of the sections are maintained and the requirements of relevant standards are satisfied. Although various structural optimization methods are developed, the minimum cost of reinforced concrete frames is difficult to achieve using existing design methods. There are an infinite number of alternative dimensions and reinforcement ratios for structural elements that can yield a similar force or moment of resistance. These elements are often the major components in reinforced concrete skeletal structures, and hence their economical design requires consideration as it is an important factor in achieving the overall cost reduction of a structure.In this study, the application of the consistent approximation (CONAP) method is presented for optimum design of reinforced concrete moment resisting frames (RCMRFs). For this purpose, design of the RCMRFs is formulated as an optimization problem. Design variables are the dimensions of concrete sections and reinforcement areas. The objective function is the total cost of the frame which includes the cost of concrete, formwork and reinforcing steel for individual members of the frame. Design constraints are defined based on the requirements of design code requirements for concrete constructions. In the optimum design model, the objective function and design constraints are explicitly formulated using the CONAP concept and the primary optimization problem is replaced with a sequence of explicit problems. Each sub-problem is first generated based on the analysis and sensitivity analysis results Also, and then is efficiently solved by using sequential quadratic programming (SQP) method. The proposed method is demonstrated through a design example and the optimum results are compared with those in the available literature. It is shown that the proposed method can be easily applied to obtain rational, reliable, economical and practical designs for RCMRFs. Also, it is shown that the proposed algorithm is converged in just a few iterations.