Performance-based design of steel building frameworks under seismic loading

Performance-based seismic design involves a set of procedures by which a building structure is designed in a controlled manner such that its behaviour is ensured at predefined performance levels under earthquake loading. The design process is an iterative re-analysis/re-design task, in which an initial design is modified repeatedly to meet code- and designer-specified requirements. As herein, the process when conducted in professional practice is often based on pushover analysis, a nonlinear static procedure that accounts for both geometric and material nonlinearity at multiple performance (loading) levels. The design optimization of building frameworks using pushover analysis to evaluate the seismic demand can be extremely computationally intensive. An algorithm is yet needed to efficiently incorporate pushover analysis together with optimal performance-based design.; The objective of this study is the development of a computer-automated method for the optimum performance-based design of steel building frameworks at the, so-called, operational, immediate occupancy, life safety and collapse prevention performance levels. A new computer-based pushover analysis procedure developed at the University of Waterloo is adopted to predict post-elastic seismic demands under equivalent static earthquake loading. The conventional elastic and geometric stiffness matrices of frame elements are progressively modified to reflect the progressive degradation of structure stiffness due to plastic behavior under incrementally increasing loads.; Two objective criteria are identified for the performance-based seismic design. Minimizing structure cost (interpreted as structure weight) is taken as one objective. The other objective concerns minimizing earthquake damage which, since uniform ductility demand over all stories generally avoids local weak-story collapse, is interpreted as providing a uniform inter-story drift distribution over the height of the building. That is, the overall objective for the design of a building framework is to have minimum weight and uniform ductility demand while, at the same time, meeting all four of the previously noted seismic-related performance levels under specified earthquake ground motions. Displacement and strength constraints corresponding to the various performance levels are both accounted for by the optimization model. Explicit forms of the constraints in terms of member sizing variables are derived using nonlinear pushover sensitivity analysis at the different performance levels.; A modified Dual Method is applied to solve the bi-criteria optimization problem to find the optimal design of steel building frameworks that simultaneously ensure appropriate behavior at all performance levels. A number of numerical experiments and several framework examples are conducted to illustrate the scope, applicability and practicality of the developed design methodology.