In the design of reinforced concrete (RC) columns, ductility is provided by allowing yielding of steel in the part of section under tensile stresses. This situation cannot be provided for RC columns since sections of columns are generally under compressive stresses resulting from axial loading including weight of all upper stories, flexural moments, and shear forces. To practically provide ductility, axial force is limited, and stirrups are densely designed. These rules are given in design regulations and must be checked during optimization. In this chapter, an optimum design methodology for biaxial loaded column is presented. Uniaxial loaded column methodology is given with the computer code. Finally, the slenderness effects are presented via ACI 318: Building code requirements for structural concrete and optimum results are given for several numerical cases using various metaheuristic algorithms.
TopIntroduction
Columns of structures are the most important part and design of columns must be provided in the safest rules in design. In structures, all vertical loads are supported by columns. The major parts of vertical loads are self-weight of RC members and all loads on stories above columns are directed via slabs to beams, and beams to columns as axial forces. Since axial forces are big, flexural moments are not generally effective at changing stresses as tensile stresses in sections. For that reason, reinforced concrete (RC) columns are compressive controlled members and the rules for these members are considered in design since the yielding of rebar cannot be provided before concrete and crushing of concrete is not acceptable for columns. In order to ensure ductility, the general rules in design codes are as follows:
Also, second order effects are needed to be considered for columns since axial forces are big and horizontal deflection under dynamic forces appears.
In this chapter, an optimum design of biaxial loaded column with flexural moments around two directions is presented by using a modified harmony search (HS) approach. Then, a method using JA and uniaxial loaded columns is given with the optimum design code. Finally, the design formulations to consider slenderness effects are given and the optimum results are presented for different algorithms.
TopOptimum Design Of Rc Biaxial Load Columns
In this section, the design methodology using a modified harmony search (HS) algorithm developed by Nigdeli, Bekdaş, Kim and Geem (2015) is presented. In this methodology, classical HS (Geem, Kim, & Loganathan, 2001) is combined with several random search stages. These random search stages are used for the two following reasons:
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If a set of design variables do not provide a design constraint, are directly neglected after a violation and a new set is generated. This process continues until all constraints are provided.
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In the optimum design, there are several design variables that are related to each other. Also, the required safety criteria are respected to various types of loads such as flexural moment, axial force and shear force. The optimum design must be suitable for multiple types of loadings.
To conduct a full iterative stage, the number of variable evaluations may increase. In that case, computational time is saved by neglecting violated solutions via additional random stages.