立面不規則建築結構物之簡化分析方法

Simplified Analysis of Vertically Irregular Building Structures

曹智嘉(Chih-Chia Tsaur)

指導教授 ： 蔡克銓

國立臺灣大學/工學院/土木工程學研究所/碩士(2014年)

https://doi.org/10.6342/NTU.2014.02294

摘要

耐震規範中對立面不規則之建築結構有其定義與限制，另要求須以動力分析方法進行結構設計。採用習見之簡化分析方法，如模態側推分析法(Modal Pushover Analysis)或解耦合模態歷時分析法(Uncoupled Modal Response History Analysis)，除少數情形如底層較強或下半結構較強者外，對立面不規則結構進行地震反應分析之結果尚屬準確可應用。前人的研究建議，若立面不規則結構物之立面不規則特性來自底層較強或下半結構較強者，仍應使用嚴謹之整體結構有限元素模型非線性動力歷時分析法進行分析，而不應使用簡化分析方法。習見之簡化分析方法如上述二者，可歸類為單自由度簡化分析方法，原因為其結構在特定模態下之反應計算單純由該模態分布φn與求解相對應之單自由度系統運動方程式之反應Dn相乘而得。
本研究中將一立面規則之結構進行立面不規則特性之分配，使其分為上下二部分，稱為上結構與下結構，分配時僅將兩部分中其中一部分進行各樓層之質量、勁度及強度之改變，使原立面規則之結構形成立面不規則。此一經立面不規則特性分配之結構，在特定模態下之上下部結構非線性反應不以模態分布等比例產生反應，亦即其上下結構非線性反應不以單獨之單自由度反應Dn決定。
本研究提出雙自由度之簡化分析方法，以描述前述上下部結構反應在特定模態下不以模態成等比例之立面不規則結構物行為。建立雙自由度模態桿以模擬該模態雙自由度系統運動方程式之反應Dpn與Dbn。
驗證例中以規範FEMA355c建議之九層樓鋼結構模型取單向構架，基本週期2.78秒，進行立面不規則特性之分配為1.下半結構較強2.底層較強之3. 下半結構較強且勁度較大2.底層較強且勁度較大之立面不規則結構四種模型，並以三種回歸週期(小地震72年、設計地震475年及最大考量地震2475年)之地震歷時各20個輸入進行分析。視整體結構有線元素非線性歷時分析反應為真值，並與簡化分析方法(單自由度與雙自由度方法)所得進行比較。
對於前人研究中不建議使用簡化分析方法之立面不規則結構物(底層較強或下半結構較強)，本研究証實在最大考量地震及設計地震作用下，採雙自由度方法計算層間位移角之準確性，普遍高於單自由度方法；能將單自由度簡化分析方法對下部有較小層間位移角之樓層的高估誤差由最高為80-140%降至最高為30%，對上部有較大層間位移角之樓層的低估誤差由最高為70%降至40%。另在小地震作用下，結構多保持在彈性範圍內，雙自由度方法與單自由度方法等效。本研究所提之雙自由度方法能有效提高習見簡化分析方法之準確性與適用性，可用於底層或下半結構強度較大之立面不規則結構的耐震分析。

關鍵字

立面不規則 ； 簡化分析 ； 振態分析 ； 動力歷時分析 ； 非線性結構分析

並列摘要

Most seismic building design codes describe the features in the vertically irregular structures and prescribe that the dynamic analysis procedures be adopted in the design of these irregular structures. In recent researches, it has been shown that seismic responses for vertically irregular structures can be estimated reasonably well by simplified analysis procedures such as modal pushover analysis (MPA) or uncoupled modal response history analysis (UMRHA), as long as the building does not have a strong lower-half or a strong first-story feature. For either one of these two vertical irregularities, it is suggested that a rigorous finite element model (FEM) response history analysis procedures be considered in order to avoid the unsatisfactory results computed from the simplified procedures. These simplified methods consider each mode as one single-degree-of-freedom. Thus, it is identified as the single DOF method (SDM) in this research.
In this study, a vertically regular reference structure is modified into a vertically irregular two-part structure, consisting of a super-structure and a sub-structure. During the modifications, one of the two parts is adjusted by tuning its story masses, strengths or stiffness, making the modified structure vertically irregular. Responses of the two parts in a given mode are no longer considered as mode-shape-proportional at the inelastic state. That is, the top and bottom part’s responses are not determined by using only one degree of freedom Dn. In this study, a two-degree-of-freedom method (2DM) is developed to describe the non-proportional responses of the super-structure and the sub-structure in a specific mode. A two-degree-of-freedom (2DOF) modal stick model is constructed accordingly in order to incorporate the two response variables Dpn and Dbn into the 2DOF equation of motion.
The LA-9, 9-story steel 2D frame model with a fundamental period T1=2.78 sec. from SAC project is modified into four irregular building structure models: each having 1. a strong first story 2. a strong-and-stiff first story 3. strong lower half 4. strong-and-stiff lower half. Using 60 (20 each for OBE, DBE and MCE) ground motion records, results computed from 2DM, SDM and the FEM (considered as the exact responses) are compared. Analytical results show that the 2DM has an overall more accurate evaluation for inter story drift ratios under DBEs and MCEs, reducing the overestimation of SDM for lower stories from 80-140% to at most 30%, and the underestimation of SDM at upper stories from 70% to at most 40%. The 2DM also have consistent results with SDM in OBEs. It appears that the 2DM improves the precision of modal superposition and reliability of the MPA or UMRHA. It expands the applications of the simplified analysis procedures.

並列關鍵字

vertical building irregularity ； simplified analysis ； modal analysis ； response history analysis ； nonlinear dynamic analysis

參考文獻

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