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，此处通过考虑旋转惯性的影响进行了改进。获得了基于三角函数和双曲函数的闭式解，从而可以仅基于位移响应而无需与弦旋转耦合地明确表示周期比，模态参与因子（MPF），众数形状和众数形状导数。季莫申科梁模型就是这种情况。通过明确强调旋转惯性在地震响应中的作用，这使得本研究中提出的模型更易于评估建筑物对地震动的行为，从而为研究其在减轻建筑物对地震动的响应中的有益作用提供了理由。可以看出，旋转惯性引起了适度的基本周期延长，同时显着减小了高模和基本模之间的周期比。这会导致对显示窄带特性的地面运动的响应增强。但是，发现最严重的影响是对MPF的影响，该影响已大大降低。由于第一模式响应的衰减，这会导致总体响应的显着降低，同时严重削弱了更高模式的影响。结果表明，在评估平面结构对水平地面运动的响应时，如果不考虑旋转惯性，则可能导致保守的结果。此外，