RC結構等效線性系統之研究與應用

Abstract

現今之耐震設計已逐漸朝向性能設計法為主，而為掌握結構物於地震後之使用功能及損害程度，如何準確預測非線性多自由度結構之位移反應成為性能設計成功與否之關鍵。而等效線性化法即為於此目的下所發展出之方法，其原理為將原本之非線性系統轉換為一等效線性系統，使此等效線性系統配合彈性位移反應譜所查得之位移反應值近似於非線性系統於非線性歷時分析中所得之最大位移。然而既有之等效線性系統大多經由實證分析所得，缺乏明確之物理意義，故本文之目的在於提出一以力學原理推導且適用於RC結構之等效線性系統，其中採用一新式線性勁度－阻尼系統以及等平均能量原理推導等效線性系統，並利用Takeda勁度遞減遲滯模型及考慮遲滯迴圈於真實地震下之不對稱性模擬RC結構受震時之非線性行為。所提出之等效線性系統將採用400個非線性單自由度系統配合十筆地震歷時進行驗證，並與既有之等效線性系統比較與討論。由驗證及比較之結果可發現所提出之等效線性系統不僅有明確之物理意義，更擁有良好之準確性。最後將介紹所提出之等效線性系統應用於RC結構之位移設計法及耐震能力評估之原理及流程，並提供示範例。

In order to readily estimate the maximum displacement of nonlinear multiple-degree-of-freedom structures under earthquake excitation, a method called equivalent linearization is developed and utilized in performance-based seismic design and evaluation. In equivalent linearization, the maximum displacement of the nonlinear structure derived from nonlinear time-history analysis is approximated by the response displacement of an equivalent linear system obtained by elastic spectrum. Many studies have been done for determining the equivalent linear system; however, most of these equivalent linear systems are derived by experimental analysis and consequently lack of explicit physical meaning. The purpose of this thesis is to propose a theory-based equivalent linear system which is applicable to RC structures. A modified linear stiffness-damping system and equal-average energy principle are used to derive the equivalent linear system, and Takeda hysteretic model is combined with the asymmetry of hysteretic loops to represent the nonlinear hysteretic behavior of RC structures during an earthquake. The proposed equivalent linear system is evaluated by 400 nonlinear single-degree-of- freedom systems with ten earthquake ground motions and compared with existing equivalent linear systems. Results show that the proposed equivalent linear system not only has explicit physical meaning, but has great accuracy of estimation for maximum inelastic displacement. Finally, applications of the proposed equivalent linear system are introduced, and the relative examples are presented.