Near-optimal bilinear fit of capacity curves for equivalent sdof analysis

T he bilinear approximation of force - deformation capacity curves is investigated for structural systems with non - neg ative - stiffness. This piecewise linear approximation process factually links capacity and demand; it lies at the core of the nonlinear static assessment pr o- cedure s, and it has become part of seismic guidelines and codes, such as ASCE - 41 and Eur o- code 8. D es pite codification, the various fitting rules , used to derive the bilinear representation , can pr o duce highly heterogeneous results for the same capacity curve. This is especially valid for highly - curved backbones resulting from structural models with accur ate representation of the initial, uncracked , stiffness or buildings characterized by a global co l- lapse mechanism that lead s to a gradual plasticization of the elements. The error introduced by the bilinearization of the force - deformation relationship is q ua n- tified by studying it at the single - degree - of - freedom (SDOF) level, away from any inte r ference from multi - degree - of - freedom (MDOF) effects, thus avoiding the issue related to MDOF - SDOF approximation. Incremental Dynamic Analysis (IDA) is employed to e nable a direct comparison of the actual backbones versus their bilinear approximations in terms of the spe c- tral acceleration capacity for a continuum of limit - states, allow ing a direct compar i son of the results in terms of seismic perfo r mance. Code - based p rocedures 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 c a pac ity curve shape .