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