# Graphic dynamic prediction of polarized earthquake incidence response for plan-irregular single story buildings

## Abstract

A graphical dynamic model is presented to predict the directional earthquake response of two-ways plan-asymmetric buildings. The theoretical principles inherent to torsional dynamics and vibrations are investigated and the dynamic directional response is rationally explained based on modal rotational kinematics about modal torsional pivots. Seismic forces and response decomposition are handled through geometric modal torsional trends and the earthquake incidence response envelopes are described through directional modal participation radii and graphic spectrum-based ‘8-shaped’ directional influence circles. The graphic approach provides good predictions of the maximum response and of the critical angle computed through directional combination methods. A nonlinear 3D frame model with eccentric infills is analyzed through linear and nonlinear response history analyses (RHA, NLRHA) changing the earthquake incidence angle. Upon confirmation of weak modal coupling, graphic-dynamic modal torsional trends and directional inelastic response envelopes are used to predict the nonlinear response. Directional incremental dynamic analyses and uncoupled modal response history analyses confirm the prediction of polarization.

## Keywords

Plan asymmetry Irregular buildings Torsional behavior Directional earthquake incidence Response spectrum analysis Incremental dynamic analysis## References

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