Ductility Design Via Optimum Design of Nonlinear Elastic Frames

A new overall structural flexibility, referred to as “system flexibility,” is defined in this paper for building frames composed of material with an arbitrary, stable, nonlinear, elastic stressstrain relation which are to be designed to support a set of prescribed lateral loads. The necessary and sufficient conditions for global optimality, and the closedform optimum design formula, are derived for the problem of optimum design of a building frame composed of nonlinear elastic beams and linear elastic columns for specified system flexibility. It is shown that, if the cost factors in the optimality conditions are reinterpreted as control parameters for maximum memberend strains, then the closedform optimal design formula derived here can be utilized as a set of practically useful design formulas for ductility design of a building frame consisting of yielding beams weak beams and linear elastic columns. It is demonstrated further through a series of time history analyses that this static ductility design method is potentially useful also as a dynamic ductility design method for earthquake loadings.