不對稱建築結構耐震性能分析

Abstract

平面不對稱結構在受地震力作用時會同時產生平移與旋轉的變形，所以相較於對稱結構更容易因受震而產生破壞。除了繁雜與耗時的非線性動力歷時分析外，目前仍缺少一個有系統且簡化的分析方法來進行平面不對稱結構的受震反應分析。 在本研究中，針對單向不對稱與雙向不對稱結構的運動方程式分別推導出兩個及三個自由度的振態運動方程式，並依此建立兩個及三個自由度的振態桿狀模型。 經由數學證明可知此種多自由度的振態桿狀模型在彈性狀態只有一個子振態對振態反應有貢獻，且等於單自由度振態桿狀模型的反應;其餘的子振態則對振態反應毫無貢獻。故在彈性狀態下，多自由度的振態桿狀模型是完全相當於單自由度的振態桿狀模型，所不同的是前者提供了平移與旋轉在彈性的振態反應中所各自貢獻的比例。在非彈性狀態，振態平移與旋轉不再成比例變化，振態遲滯迴圈呈現分叉的特性，故在非彈性動力反應中平移與旋轉反應彼此會交互影響。多自由度的振態桿狀模型具有模擬此一特性的能力。藉由多自由度的振態桿狀模型可同時得到結構質量中心的平移與旋轉反應，故可求得結構角隅處的位移、速度與加速度反應。 在本研究中，利用兩個自由度的振態桿狀模型建立平移與旋轉的非彈性反應譜。比較兩個自由度與單自由度的振態桿狀模型所建立的非彈性反應譜，可確認後者僅是前者的一個特例。藉由改變多自由度的振態桿狀模型的參數，可觀察到非彈性反應譜變化的趨勢與範圍，有助於不對稱結構的設計並可應用於將來相關規範的修訂。 本研究提供了一個簡化但具有普遍性與系統化的不對稱結構分析方法，並對目前地震工程發展的主流性能設計法作出貢獻。作者希望將來能將此研究成果進一步擴展至以機率為核心的地震工程領域。

Plane-asymmetric structures that suffered from torsional and translational deformations are most vulnerable to seismic excitations. Instead of lengthy and complicated nonlinear response time history analysis, there is still void of a more systematic and simpler assessment method to deal with this type of structures. Thus, this research is conducted. In this study, a more rational and informative multi-degree-of-freedom modal stick is derived for asymmetric structures from investigating the modal equation of motion representing the dynamic behavior of a single-degree-of-freedom (SDOF) modal stick. At elastic state, the proposed modal sticks are equivalent eventually to the conventional SDOF modal stick. In addition, they can provide the information about the quantities of translational and rotational displacements at the center of mass observed in each mode. Meanwhile, at inelastic state, they can simulate the bifurcation of hysteretic loops due to the non-proportionality of the translational and rotational deformations. Hence, the interaction of translational and rotational motion is captured. Moreover, in utilizing the proposed modal sticks, the rotational displacement, velocity and acceleration at center of mass are available and are required to acquire the corner responses of asymmetric structures. Several translational and rotational inelastic response spectra are constructed based from the proposed modal stick. It illustrated further that the SDOF modal stick is just a special case of the proposed modal stick. By investigating the constructed spectra, the trends on the responses resulted from varying the parameters in the proposed sticks are more understood as compared with the responses in SDOF modal stick. And, this will be helpful to the design of asymmetric structures and can be considered for the revision of code in the future. It is believed that this study will provide a systematic, generalized and simpler assessment method to deal with asymmetric structures. Alongside, the contributions on the art of performance-based earthquake engineering are achieved. It is hoped also to extend these researches to probabilistic-based earthquake engineering.