Strength Reduction Factors: A Unified Analytic Expression for Narrowband and Broadband Ground Motion Records

Abstract

Strength reduction factors are an important component of the force modification factors used in the calculation of seismic code forces, as they account for the effect of the nonlinear hysteretic behavior of the structure. They are expressed as the ratio between the elastic strength demand and the inelastic strength demand induced in a structure by the earthquake. The evaluation of strength reduction factors has applications in the substantiation of seismic force modification factors in building design codes and in the direct application of the capacity spectrum method. The paper presents a study performed on two sets of accelerograms having different spectral content types, i.e. narrow frequency band records and broad frequency band records. Based on constantductility spectra of strength reduction factors, computed with 50% and 10% probability of exceedance, a unified analytic formula is developed, to describe the variation with ductility and vibration period of these factors. By modifying the values of the coefficients of the variables, the formula can be adapted for each type of spectral content. The formula is further refined, by determining a new set of coefficients, to also account for the influence of the predominant period of the ground motion in the case of narrow frequency band records.