Abstract

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.

摘要

在本文中，广泛使用的建筑模型由均匀耦合的弯曲梁和剪切梁组成，并通过考虑旋转惯性的影响进行了改进。获得了三角函数和双曲线函数的封闭形式解，允许仅基于位移响应明确制定周期比、模态参与因子 (MPF)、振型和振型导数，而不与弦旋转耦合，这Timoshenko 梁模型就是这种情况。这使得本研究中提出的模型更便于评估建筑物对地面运动的行为，通过明确强调转动惯量在地震响应中的影响，为研究其在减轻建筑物对地面运动的响应方面的有益效果提供了理由。据观察，旋转惯性会导致轻微的基本周期延长，同时显着降低高阶模式与基本模式之间的周期比。这可以增强对地面运动的响应，表现出窄带特性。然而，发现最严重的影响是对 MPF 的影响，该影响显着降低。由于第一模式响应的衰减以及更高模式的影响的严重削弱，这导致整体响应显着降低。结果表明，在评估平面内结构对水平地面运动的响应时，如果不考虑转动惯量，可能会得出保守的结果。而且，