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研究生:戴均穎
研究生(外文):Jyun-Ying Dai
論文名稱: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
論文名稱(外文):A study of seismic design method for reducing the variation of peak inter-story drifts along the building height
指導教授:蔡克銓蔡克銓引用關係
口試委員:林瑞良田堯彰陳誠直
口試日期:2017-06-20
學位類別:碩士
校院名稱:國立臺灣大學
系所名稱:土木工程學研究所
學門:工程學門
學類:土木工程學類
論文種類:學術論文
論文出版年:2017
畢業學年度:105
語文別:中文
論文頁數:110
中文關鍵詞: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
外文關鍵詞:generalized building modelmodal superposition methodcoefficient of variationnonlinear response history analysisPISA3D
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  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。
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.
口試委員審定書 i
致謝 ii
摘要 iii
Abstract v
目錄 viii
表目錄 xi
圖目錄 xiv
第一章 緒論 1
1.1. 研究動機 1
1.2. 文獻回顧 1
1.2.1. Strongback系統 1
1.2.2. 估計側向位移之簡化分析模型 2
1.3. 論文架構 2
第二章 降低各層最大層間位移角差異之最佳化設計法 4
2.1. 第一種廣義建築模型 4
2.2. 第二種廣義建築模型 5
2.3. α參數對廣義建築模型的模態形狀影響 6
2.4. 最佳化設計法流程 7
2.5. 非線性反應歷時分析 13
第三章 九層建築結構模型之案例分析 14
3.1. 結構模型介紹 14
3.1.1. 結構系統 14
3.1.2. 結構分析模型 14
3.2. 構件斷面尺寸參數分析 15
3.2.1. 參數分析方法 15
3.2.2. 參數分析結果 15
3.3. 彈性反應分析 16
3.3.1. 設計流程 16
3.3.2. 彈性最佳化設計結果探討 19
3.4. 非彈性反應分析 20
3.4.1. 容量譜法分析結果 20
3.4.2. 非彈性最佳化設計結果 21
3.5. PISA3D非線性反應歷時分析 22
3.5.1. 地震加速度歷時介紹 22
3.5.2. 地震歷時調整方法 22
3.5.3. 非線性反應歷時分析結果 22
3.6. 比較第一種及第二種廣義建築模型之模擬效果 23
3.6.1. 振態參數之模擬結果比較 23
第四章 二十層建築結構模型之案例分析 24
4.1. 結構模型介紹 24
4.1.1. 結構系統 24
4.1.2. 結構分析模型 24
4.2. 構件斷面尺寸參數分析 25
4.2.1. 參數分析方法 25
4.2.2. 參數分析結果 25
4.3. 彈性反應分析結果 25
4.3.1. 設計流程 25
4.3.2. 彈性最佳化設計結果探討 27
4.3.3. 誤差探討 28
4.4. 非彈性反應分析結果 29
4.4.1. 容量譜法分析結果 29
4.4.2. 非彈性重新設計結果 29
4.5. PISA3D非線性反應歷時分析 30
4.5.1. 地震加速度歷時介紹 30
4.5.2. 地震歷時調整方法 30
4.5.3. 非線性反應歷時分析結果 30
第五章 結論與建議 31
5.1. 研究結論 31
5.2. 建議 32
參考文獻 33

表目錄
表3- 1 LA-9 z向抗彎構架尺寸 35
表3- 2 LA-9構架樓高及質量 35
表3- 3 α,A_C/A_C0= 0.2 36
表3- 4 α,A_C/A_C0= 0.4 37
表3- 5 α,A_C/A_C0= 0.6 38
表3- 6 α,A_C/A_C0= 0.8 39
表3- 7 α,A_C/A_C0= 1.0 40
表3- 8 α,A_C/A_C0= 1.2 41
表3- 9 α,A_C/A_C0= 1.4 42
表3- 10 α,A_C/A_C0= 1.6 43
表3- 11 α,A_C/A_C0= 1.8 44
表3- 12 α,A_C/A_C0= 2.0 45
表3- 13 T_1,A_C/A_C0=0.2 46
表3- 14 T_1,A_C/A_C0=0.4 47
表3- 15 T_1,A_C/A_C0=0.6 48
表3- 16 T_1,A_C/A_C0=0.8 49
表3- 17 T_1,A_C/A_C0=1.0 50
表3- 18 T_1,A_C/A_C0=1.2 51
表3- 19 T_1,A_C/A_C0=1.4 52
表3- 20 T_1,A_C/A_C0=1.6 53
表3- 21 T_1,A_C/A_C0=1.8 54
表3- 22 T_1,A_C/A_C0=2.0 55
表3- 23 LA-9模型側向勁度及側向勁度比 56
表3- 24 當α=0.24時之GBM與LA-9模型前三振態比較 56
表3- 25 LA-9模型週期、振態參與因子與彈性譜位移誤差 56
表3- 26 計算LA-9模型最大層間位移角分布的變異係數時所採用之各層權重 56
表3- 27 LA-9彈性設計結果 57
表3- 28 LA-9之容量譜法分析結果 57
表3- 29 la1-la20地震特性 58
表3- 30 採用S_a (T_1)法調整10/50地震記錄之調整倍率 58
表3- 31 LA-9模型及最佳化LA-9模型動力反應之變異係數結果 59
表3- 32 LA-9模型及最佳化LA-9模型動力反應平均結果 59
表3- 33 利用第二種GBM模擬LA-9之動力參數誤差 59
表4- 1 LA-20 z方向抗彎構架尺寸 60
表4- 2 LA-20樓高及質量 61
表4- 3 α,A_C/A_C0= 0.4 62
表4- 4 α,A_C/A_C0= 0.6 63
表4- 5 α,A_C/A_C0= 0.8 64
表4- 6 α,A_C/A_C0= 1.0 65
表4- 7 α,A_C/A_C0= 1.2 66
表4- 8 α,A_C/A_C0= 1.4 67
表4- 9 α,A_C/A_C0= 1.6 68
表4- 10 α,A_C/A_C0=1.8 69
表4- 11 α,A_C/A_C0=2.0 70
表4- 12 T_1,A_C/A_C0= 0.4 71
表4- 13 T_1,A_C/A_C0= 0.6 72
表4- 14 T_1,A_C/A_C0= 0.8 73
表4- 15 T_1,A_C/A_C0= 1.0 74
表4- 16 T_1,A_C/A_C0= 1.2 75
表4- 17 T_1,A_C/A_C0= 1.4 76
表4- 18 T_1,A_C/A_C0= 1.6 77
表4- 19 T_1,A_C/A_C0= 1.8 78
表4- 20 T_1,A_C/A_C0= 2.0 79
表4- 21 LA-20模型之側向勁度及側向勁度比 80
表4- 22 當α=0.45時之GBM與LA-20模型前三振型比較 80
表4- 23 LA-20模型週期、振態參與因子與彈性譜位移誤差 81
表4- 24 計算LA20模型最大層間位移角分布的變異係數時採用之權重 81
表4- 25 當α=0.41時之GBM與最佳化設計之LA-20模型前三振型比較 81
表4- 26 最佳化之LA-20模型週期、振態參與因子與彈性譜位移誤差 82
表4- 27 LA-20彈性設計結果 82
表4- 28 LA-20之容量譜法分析結果 82
表4- 29 採用S_a (T_1)法調整10/50地震記錄之調整倍率 82
表4- 30 初始LA-20模型及最佳化之LA-20模型動力反應之變異係數結果 83
表4- 31 初始LA-20模型及最佳化之LA-20模型動力反應平均結果 83

圖目錄
圖1- 1 (a)傳統CBF (b)加裝Strongback之CBF示意圖 84
圖1- 2 採用Rocking Core為Strongback之CBF示意圖 84
圖1- 3 連續梁簡化模型示意圖 85
圖2- 1 (a)廣義建築模型示意圖 (b)純剪力桿變形 (c)純撓曲桿變形 85
圖2- 2 α從0至1增量0.1之GBM振態形狀 85
圖2- 3 容量譜及需求譜ADRS格式示意圖 86
圖2- 4 容量譜雙線性簡化示意圖 86
圖3- 1 LA-9平面圖 87
圖3- 2 LA-9 z向立面圖 87
圖3- 3 LA9模型之α隨梁柱斷面尺寸改變之變化情形 89
圖3- 4 LA-9基本週期隨梁柱斷面尺寸改變之情形 91
圖3- 5 LA-9模型對應α從0至1增量0.01之GBM振態形狀 92
圖3- 6 LA-9模型與GBM各樓層模態形狀差值之均方根 92
圖3- 7 當α=0.24時之GBM與LA-9模型前三振態比較 92
圖3- 8 折減後之洛杉磯工址設計反應譜 93
圖3- 9 LA-9模型對應GBM之最大層間位移角分布之變異係數 93
圖3- 10 最佳化之LA-9模型對應GBM之最大層間位移角分布之變異係數 94
圖3- 11 α^((0)) 之GBM及α_opt之GBM最大層間位移角分布圖 94
圖3- 12 LA-9模型及α^((0))之GBM最大層間位移角分布圖 95
圖3- 13 α^((1)) 之GBM及α_opt 之GBM最大層間位移角分布圖 95
圖3- 14 最佳化LA-9模型及α^((1))之GBM最大層間位移角分布圖 96
圖3- 15 LA-9前三振態之側向力分布 96
圖3- 16 LA-9前三模態之容量曲線 97
圖3- 17 LA-9前三模態之ADRS格式容量曲線 97
圖3- 18 LA設計反應譜 97
圖3- 19 ADRS格式需求譜 98
圖3- 20 LA-9第一模態容量譜法分析結果 98
圖3- 21 LA-9第二模態容量譜法分析結果 99
圖3- 22 LA-9第三模態容量譜法分析結果 99
圖3- 23 洛杉磯地震加速度反應譜 (ζ=5%) 100
圖3- 24 經S_a (T_1)法修正至LA-9基本週期之加速度反應譜 100
圖3- 25 LA-9及最佳化設計LA-9之動力反應分析結果 101
圖3- 26 兩種型式的GBM模擬LA-9最大層間位移角分布比較圖 101
圖4- 1 LA-20 平面圖 102
圖4- 2 LA-20 z向立面圖 102
圖4- 3 LA-20模型對應α從0至1增量0.01之GBM振態形狀 103
圖4- 4 LA-20模型與GBM各樓層模態形狀差值之均方根 103
圖4- 5 當α=0.45時之GBM與LA-20模型的前三振態比較 103
圖4- 6 LA-20初始模型對應GBM最大層間位移角之變異係數 104
圖4- 7 α^((0))之GBM及α_opt之GBM最大層間位移角分布圖 104
圖4- 8 LA-20模型及之α^((0))之GBM最大層間位移角分布圖 105
圖4- 9 α^((2))之GBM及α_opt之GBM最大層間位移角分布圖 105
圖4- 10 最佳化LA-20模型及α^((2)) 之GBM最大層間位移角分布圖 106
圖4- 11 當α=0.41時之GBM與最佳化LA-20模型的前三振態比較 106
圖4- 12 LA-20前三振態之側向力分布 107
圖4- 13 LA-20前三模態之容量曲線 107
圖4- 14 LA-20前三模態之ADRS格式容量曲線 107
圖4- 15 LA-20第一模態容量譜法分析結果 108
圖4- 16 LA-20第二模態容量譜法分析結果 108
圖4- 17 LA-20第三模態容量譜法分析結果 109
圖4- 18 經S_a (T_1)法修正至LA-20基本週期之加速度反應譜 109
圖4- 19 初始LA-20及最佳化LA-20動力反應分析結果 110
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17.Shome, N.,Cornell, C.,Bazzurro,P. and Carballo, J.(1998) “Earthquakes, records, and nonlinear responses.” Earthquake Spectra 1998;14:469-500
18.Shome, N.,Cornell, C.,Bazzurro,P. and Carballo, J.(1998) “Normalization and Scaling accelerograms for nonlinear structural analysis.” Sixth U.S National Conference on Earthquake Engineering, Seattle, WA
19.Uang, C.M, and Maarouf, A. (1993) ‘‘Safety and economy considerations of UBC seismic force reduction factors.’’ Proc., 1993 Nat. Conf., Central United States Earthquake Consortium, Memphis, 121–130.
20.Uniform Building code (1994), Volumn 2, Structural Engineering Design provisions. International Conference of Building Officals, Whittier, Calif.
21.內政部營建署 (2011)「建築物耐震設計規範」。
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