## 70%-damped spectral acceleration as a ground motion intensity measure for predicting highly nonlinear response of structures

Kenny Buyco, & Thomas HeatonPublished August 14, 2017, SCEC Contribution #7590, 2017 SCEC Annual Meeting Poster #238

In engineering practice, the most common ground motion intensity measure for predicting structural response is spectral acceleration (Sa) with a period of T1 (the structure’s fundamental period) and a damping ratio of 5%, denoted here Sa(T1,5%). Sa(T1,5%) can accurately predict linear response of structures and small levels of damage, but it does not perform as well when used to predict nonlinear response, during which severe damage will cause period-lengthening of the structure and energy dissipation through hysteretic cycles.

In this study, we investigate Sa with high damping, much larger than 5%, as a ground motion intensity measure for predicting highly nonlinear response of buildings. We perform incremental dynamic analysis with 50 ground motions on 22 steel moment frame building models with heights of three, nine, and twenty stories. We find that Sa with a damping ratio in the range of 50%-100% works best for predicting highly nonlinear response. From this range, we choose a damping ratio of 70% because Sa with 70% damping and period T, Sa(T,70%), computed for a ground motion is equivalent to the ground motion’s peak acceleration after being low-pass filtered by a 2nd-order Butterworth filter with a cutoff period of T. The equivalence of Sa(T,70%) to a low-pass filter indicates that ground motions with significant long period components are most damaging to structures.

When T is chosen properly (between T1 and 2T1), Sa(T,70%) provides an estimate of the maximum base shear (in units of g) experienced by the building while it undergoes severe damage. So while the traditional Sa(T1,5%) predicts the base shear for a linear elastic building, Sa(T,70%) can approximate the base shear experienced by a building as it undergoes highly nonlinear response leading to collapse. The destructive power of a ground motion can thus be easily estimated for a building given T1 and its base shear capacity.

We find that Sa(1.5T1,70%) compares favorably to other common intensity measures at predicting many levels of highly nonlinear response, including collapse. Sa(T1,70%) is particularly effective for predicting a maximum interstory drift ratio of 0.03, a common collapse-prevention limit in building design. Furthermore, a ground motion’s 70%-damped spectrum is considerably “smoother” with respect to period than its 5%-damped spectrum, so nonlinear response predictions are not as sensitive to T1 when Sa(T1,70%) is used as the intensity measure.

**Citation**

Buyco, K., & Heaton, T. (2017, 08). 70%-damped spectral acceleration as a ground motion intensity measure for predicting highly nonlinear response of structures. Poster Presentation at 2017 SCEC Annual Meeting.

**Related Projects & Working Groups**

Earthquake Engineering Implementation Interface (EEII)