Effect of Rotational Inertia on Building Response to Earthquakes via a Closed-Form Solution

In this article, a widely used building model, comprised of uniform coupled flexural and shear beams, herein improved by allowing for the effects of rotational inertia. Closed-form solutions in terms of trigonometric and hyperbolic functions are obtained, allowing for the explicit formulation of period ratios, modal participation factors (MPFs), mode shapes, and mode shape derivatives based solely on displacement response, without coupling with chord rotations, which is the case for the Timoshenko beam model. This makes the model proposed in this study more convenient for assessing building behavior to ground motion, by explicitly highlighting the effect of rotational inertia in their response to earthquakes, making the case for studying its beneficial effects in mitigating response of buildings to ground motion. It is observed that rotational inertia induces mild fundamental period lengthening, while notably reducing period ratios between higher modes and the fundamental one. This can lead to an enhanced response to ground motion showcasing narrow-band characteristics. However, the most severe effect is found to be on the MPF, which is significantly diminished. This leads to important reductions on the overall response, as a consequence of attenuation of the first-mode response, along with severe undercutting of the effects of higher modes. The results demonstrate that without considering the rotational inertia in the assessment of in-plane structural response to horizontal ground motion can lead to conservative results. Moreover, the results showcase the advantages of providing supplemental rotational inertia as a way to improve the seismic behavior of buildings.