降低沿建築物高度上各層最大層間位移角差異之耐震設計法

為了使建築物的各樓層層間位移角分布較為均勻，前人提出許多方法如Strongback型式之結構系統。而本研究則希望在不增加額外結構之構件的情況降低結構各層最大層間位移角之分布差異，研究中提出的設計方法採用林瑞良博士提出的廣義建築模型 (Generalized Building Model, GBM)作為分析工具。廣義建築模型可顯示出結構模型的撓曲及剪力變形之趨勢，將此趨勢利用彎剪變形因子α表示，並利用廣義建築模型找出該結構模型各層最大層間位移角分布最均勻時所對應之彎剪變形因子，以α_opt表示，之後將原結構模型之桿件重新設計直到彎剪變形因子α與α_opt相同後，比較調整後之結構模型與原始結構模型的層間位移角分布情形，希望能夠利用此最佳化方法降低結構模型之最大層間位移角分布的差異。　　研究中採用振態疊加法中的SRSS法則進行最大層間位移角計算，利用所得之各層最大層間位移角的變異係數來評估其分佈均勻性。考量結構愈靠近底層重要性通常愈高，因此在計算變異係數時，採用各層之樓層剪力與基底剪力的比值作為計算標準差時各樓層之權重。　　重新設計後，將最佳化之結構模型及原始結構模型利用PISA3D結構分析程式進行475年回歸期之設計地震的非線性反應歷時分析，比較最佳化結構模型及原始結構模型的最大層間位移角分布結果。　　研究中所採用的驗證例為SAC鋼研究計畫 (FEMA355c, 2000)中的九層及二十層鋼構造抗彎矩構架，進行歷時分析時，地震歷時只施加於此3D結構模型之z向。利用此方法對九層結構模型進行最佳化分析後，最佳化之九層結構模型利用振態分析法所得最大層間位移角分布之變異係數比原結構模型小。進行20個歷時分析後，其中的14個歷時分析中所得到的最佳化之LA-9模型的最大層間位移角分布之變異係數比原始LA-9模型低，顯示此方法確實能夠有效地降低九層樓模型的各樓層最大層間位移角分布之差異性；但在進行二十層模型最佳化設計時，利用廣義建築模型所估算的動力參數，如振態參與因子及模態形狀與實際有限元素模型所得之結果皆存在明顯誤差，故利用振態分析法所得之最大層間位移角變異係數反而比原始LA-20模型高。但在進行20個歷時分析時，其中的12個歷時分析所得最佳化之LA-20模型的最大層間位移角分布之變異係數又比原始LA-20模型低，顯示此設計方法應用在LA-20模型之效果並不一致。

關鍵字

層間位移角分布；廣義建築模型；振態疊加法；變異係數；非線性反應歷時分析； PISA3D

並列摘要

Some recent studies proposed seismic design methods in order to result in uniform inter-story drift ratios of a building. For instance, strong-back systems, which need additional structural members, were incorporated into the original building system. The aim of this study is to develop an approach, which has no need of additional structural members, to make the peak inter-story drift ratio of every story uniformly distributed along the building height. The generalized building model (GBM) (Lin 2016) was employed as the vehicle of the proposed approach. The GBM is capable of simulating the flexural-shear combined deformation of a building in terms of a flexural-shear deformation factor, denoted as α. At first, the value of α of the GBM representing the original building model is computed. The optimal value of α (denoted as αopt), which minimizes the variation the peak inter-story drift ratio of every story along the building height of the GBM, is then figured out. The properties of the structural members, e.g., the moment inertia of beams and columns, of the original building model are accordingly adjusted until the corresponding value of α is almost equal to α_opt. In the aforementioned process, the peak inter-story drift ratio of every story is estimated by using the spectrum analysis method, in which the peak modal responses are combined according to the square-root-of-the-sum-of-the-squares (SRSS) method. The proposed approach adopts the coefficient of variation (COV) of the peak inter-story drift ratio of every story distributed along the building height as the optimization objective. Moreover, it is clear that the seismic risk resulting from a collapsed lower story is usually much larger than that resulting from a collapsed higher story. Therefore, the ratio of story shear to base shear, which is available in the building seismic design code, is used as the weighting factor while computing the value of the aforementioned COV. In order to verify the effectiveness of the proposed approach, this study compared the distribution of the peak inter-story drift ratios of the optimized building model with that of the original building model. These peak inter-story drift ratios were obtained from performing nonlinear response history analyses (NRHA) to the two building models. An ensemble of 20 ground motion records with a 475-year return period was used in the NRHA. The structural analysis program PISA3D was used in these analyses. The 9-story and 20-story steel moment resisting frames, which were the prototype buildings located in Los Angeles in SAC steel research project (FEMA355c 2000), were used as the example buildings in this study. For the 9-story example building, the peak elastic inter-story drift ratio of every story, which was estimated by means of spectrum analysis method, was less varied among stories after applying the proposed approach to redesign this building. In addition, 14 of the 20 NRHA results for the 9-story example building show that the variations of the peak inter-story drift ratios of the optimized building model were indeed reduced. This confirmed the effectiveness of the proposed approach applied to the 9-story example building. Nevertheless, after applying the proposed approach to the 20-story example building, the variation of the peak elastic inter-story drift ratios, which was evaluated by using the spectrum analysis method, was conversely increased. This unexpected outcome maybe results from the errors in the estimated modal parameters of the 20-story building by using the GBM. Among the 20 NRHA results for the 20-story example building, 12 results still indicate that the peak inter-story drift ratios were more uniformly distributed along the building height in the optimized model in comparison with the original model. This indicates that the assessments of the effectiveness of the proposed approach are not consistent in terms of the results obtained from applying the spectrum analysis and the NRHA to the 20-story example building.

並列關鍵字

generalized building model ； modal superposition method ； coefficient of variation ； nonlinear response history analysis ； PISA3D

參考文獻

1. ASCE (2010) Minimum Design Loads for Buildings and other Structures. ASCE/SEI 7–10.American Society of Civil Engineers (ASCE): Reston, VA.

2. ATC40 (1996) Seismic evaluation and retrofit of concrete buildings. Report ATC-40, Applied Technology Council, Redwood City, California

4. Chopra, A.K. and Chintanapakdee, C. (2004) “Inelastic Deformation Ratios for Design and Evaluation of Structures: Single-Degree-of-Freedom Bilinear Systems.” J. Struct. Eng., 130(9), 1309-1319.

5. Chopra, A. K.and Cruz, E. F. (1986) ‘‘Evaluation of building code formulas for earthquake forces.’’ J. Struct. Engrg., ASCE, 112, 1881–1899.

6. Chopra, A. K.and Goel R.K. (2002) “A modal pushover analysis procedure for estimating seismic demands for buildings.” Earthquake Engineering and Structural Dynamics 31: 561-582.

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降低沿建築物高度上各層最大層間位移角差異之耐震設計法

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