- 期刊
立面不規則建築受震反應簡化分析方法
A Simplified Seismic Analysis Procedure for Vertically Irregular Buildings
摘要
耐震規範中對立面不規則建築有其定義與限制，並且要求須以動力分析方法進行結構設計。除了以有限元素分析法（finite element method, FEM）進行全結構的非彈性動力分析外，振態側推分析法(modal pushover analysis method)是常用的簡化分析方法之一。進行振態側推分析可以得到各振態的非彈性受力與變形關係，由此受力與變形關係可以建立代表該振態的單自由度振態系統。再進行各單自由度振態系統的非線性反應歷時分析，並將各振態造成的反應歷時相加，即可求得結構的總反應，在本研究中稱此簡化分析方法為單自由度振態分析方法（single-degree-of-freedom modal analysis method, SDM）。相關文獻顯示SDM會高估底層或下半結構較強或較強且較硬之立面不規則建築之下部樓層的受震反應，建議對此類結構仍應採用較為複雜與耗時的FEM來分析其受震反應。然而此類型之立面不規則結構物常見於實際工程中，若能發展適合的簡化分析方法，則將有助於工程的應用。有鑒於單自由度振態系統無法反映上述類型結構上下兩部分顯著不同的受震反應，本研究提出二自由度振態分析方法（two-degree-of-freedom modal analysis method, 2DM），將每個振態系統以兩個自由度分別代表上部及下部結構的振態反應，經由疊加各振態所造成的反應歷時以估算結構的總反應歷時。本研究以一棟9層樓及一棟20層樓規則平面抗彎矩構架做為原型建築，修改每一個原型建築成為四個立面不規則構架(底層較強、底層較強且較硬、下半結構較強、下半結構較強且較硬)做為研究之標的建築。以FEM、SDM及2DM分析上述八個立面不規則構架分別受到60筆地震記錄作用下的反應。本研究顯示當結構保持彈性，2DM與SDM分析結果完全相同；當結構進入非彈性，一般而言2DM估算的各樓層反應較SDM準確，能夠有效降低被SDM高估的下部結構的最大層間位移比。
並列摘要
Most seismic building design codes describe the features of vertically irregular buildings. In addition, these building design codes prescribe that dynamic analysis should be adopted in the seismic analysis and design of these irregular structures. Besides the finite element method (FEM), which performs inelastic dynamic analysis to complete finite element models, the modal pushover analysis (MPA) method is one of common simplified seismic analysis procedures. The force-deformation relationship of each vibration mode obtained from the MPA method is employed to construct the corresponding single-degree-of-freedom (SDOF) modal system. The modal response histories are obtained from performing nonlinear response history analysis to each SDOF modal system. The total seismic responses of the building are estimated by adding up the seismic response histories resulting from all vibration modes. This study designates the aforementioned simplified method as the single-degree-of-freedom modal analysis method (SDM). Some research literatures showed that using SDM leads to overestimated seismic responses of the lower parts of the vertically irregular buildings, which have stronger or stronger-and-stiffer bottom story or lower half. Instead of the SDM, the complicated and time-consuming FEM was thus suggested for the seismic analysis of this type of buildings. Nevertheless, this type of vertically irregular buildings is common. It would benefit engineering practice if there are simplified seismic analysis methods available to this type of irregular buildings. In light of the incompetence of using the SDOF modal systems to simultaneously reflect the seismic responses of the super- and sub-structures of the buildings, this study proposes the two-degree-of-freedom modal analysis method (2DM). 2DM is basically the same as SDM, except that 2DM represents each vibration mode as a two-degree-of-freedom modal system. One 9-story and one 20-story regular moment resisting frames are selected as the prototype building in this study. Each of the two prototype buildings are further varied into four vertically irregular buildings as the target buildings. The four variations include buildings with stronger, stronger-and-stiffer first story; stronger, stronger-and-stiffer lower half. FEM, SDM, and 2DM are applied to the eight target buildings subjected to the selected 60 ground motions. This study shows that the analysis results obtained from 2DM are the same as those obtained from SDM as long as the structures remain elastic. While the structures become inelastic, 2DM generally results in more accurate estimations of inter-story drifts, compared with those obtained from SDM. The overestimated peak inter-story drifts of the substructures by using SDM are effectively reduced by using 2DM.