NEAR-OPTIMAL BILINEAR FIT OF CAPACITY CURVES FOR EQUIVALENT SDOF ANALYSIS

The bilinear approximation of force-deformation capacity curves is investigated for structural systems with non-negative-stiffness. This piecewise linear approximation process factually links capacity and demand; it lies at the core of the nonlinear static assessment pro- cedures, and it has become part of seismic guidelines and codes, such as ASCE-41 and Euro- code 8. Despite codification, the various fitting rules, used to derive the bilinear representation, can produce highly heterogeneous results for the same capacity curve. This is especially valid for highly-curved backbones resulting from structural models with accurate representation of the initial, uncracked, stiffness or buildings characterized by a global col- lapse mechanism that leads to a gradual plasticization of the elements. The error introduced by the bilinearization of the force-deformation relationship is quan- tified by studying it at the single-degree-of-freedom (SDOF) level, away from any interference from multi-degree-of-freedom (MDOF) effects, thus avoiding the issue related to MDOF - SDOF approximation. Incremental Dynamic Analysis (IDA) is employed to enable a direct comparison of the actual backbones versus their bilinear approximations in terms of the spec- tral acceleration capacity for a continuum of limit-states, allowing a direct comparison of the results in terms of seismic performance. Code-based procedures are found to be less than ideal wherever there are significant stiffness changes, while in general remaining relatively conservative. The practical fitting rules determined allow, instead, a near-optimal fit regardless of the details of the capacity curve shape.