A Statistical Approach to Equivalent Linearization with Applications to Performance-Based Engineering

A new methodology for calculating optimal effective linear parameters for use in predicting the earthquake response of structures is developed. The methodology is applied to several single-degree-of-freedom inelastic structural models subjected to a suite of earthquake acceleration time histories. Separately, far-field and near-field earthquakes are analyzed. Error distributions over a two-dimensional parameter space of period and damping are analyzed through a statistical approach with optimization criterion most applicable to structural design. Four hysteretic models are analyzed: bilinear, stiffess degrading, strength degrading and pinching. Initial structural periods are analyzed in groups for several second slope ratios (alpha) at different levels of ductility. It was discovered that as ductility increases, the accuracy of the effective parameters decrease but the consequences of bad parameter selection become less severe. The new effective parameters are intended for use in displacement-based structural analysis procedures as used in Performance-Based Engineering. Of the several procedures available, Nonlinear Static Procedures, such as the Capacity Spectrum Method, are widely used by structural engineers because the nonlinear characteristics of both structural components and the global structure are utilized without running a nonlinear time history analysis. Effective linear parameters are used in the Capacity Spectrum Method to calculate the expected displacement demand, or Performance Point, for a structure. Because several sources of error exist within the Capacity Spectrum Method, an analysis that isolates the error from the effective linear parameters is performed. The new effective linear parameters show considerable improvement over the existing effective linear equations. The existing linear parameters are extremely unconservative at the lower ductilities and conservative at the higher ductilities. The new parameters lead to a significant improvement in both cases. A modification to the Capacity Spectrum Method is introduced to account for the new effective linear period. Currently, the Capacity Spectrum Method uses the secant period as the effective linear period. The modification preserves the basic Performance Point calculation. Finally, a new, entirely graphical solution procedure using a Locus of Performance Points provides crucial insight into the effects of strengthening, stiffening and increasing building ductility not available in the current procedure.

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