APPLICATION OF CONSTRAIN CONTROL METHOD OF OPTIMIZATION IN SEISMIC DESIGN OF STEEL FRAMES

In performance-based seismic design of structures, the main objective is to design the structure such that its performance is predictable under certain risk levels. In PBD, in addition to strength, other seismic performance parameters, such as ductility, stiffness and drift have a profound effect on the performance of the structure. In order to predict the performance of a structure (or structural component) subjected to a certain demand earthquake, its capacity curve should first be established. There are different methods of determining the capacity curve of a system, including: nonlinear static (pushover), cyclic or time-history dynamic loading analyses. The pushover analysis method is a practical method, which while being relatively simple, reasonably accurately estimates the seismic performance parameters of the structure and its components, such asductility, behavior factor and toughness and can easily be utilized in optimization algorithms. Optimization problems are generally solved subject to certain constraints. The optimum answer to a system takes place when these constraints are used to the maximum and the variables which maximize the value of all constraints are the optimized answer. An optimization method is developed, based on conventional engineering design philosophy, whereby optimum design is achieved gradually by controlling the problem constraints (Mansouri & Maheri, 2019). In the developed method, termed ‘Constraint Control Method’ (CCM), by considering the ratio of any constraint value to its limit value, the constraints are transformed into coefficients ranging from 0 to 1. They are, therefore, dimensionless so that they could be compared with each other and the constraint value is significant; that is, when the value of the constraint is zero, the answer is far from the optimum answer and the constraint value of one is the maximum value which a constraint could reach. In this study, two sets of constraints are defined for the CCM. The first set, (CRs) includes the stress constraints for members undergoing axial force and bending moments due to gravity loads, based on the AISC-LRFD specifications (AISC, 2001) and specified according to Equation 1.