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研究生:邱東茳
研究生(外文):Dung-Jiang Chiou
論文名稱:應用HHT頻譜於鋼結構房屋建築地震損傷之研究
論文名稱(外文):Structural damage detection for benchmark buildings using the Hilbert-Huang transform
指導教授:許文科許文科引用關係蔣偉寧蔣偉寧引用關係唐治平唐治平引用關係
指導教授(外文):Wen-Ko HsuWei-Ling ChiangJhy-Pyng Tang
學位類別:博士
校院名稱:國立中央大學
系所名稱:土木工程研究所
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:2011
畢業學年度:99
語文別:中文
論文頁數:242
中文關鍵詞:希爾伯特-黃轉換損傷指標層間變位角半功率帶寬法
外文關鍵詞:HHTinter-story drifthalf-power bandwidthDamage detection index
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有別於傳統上使用快速傅立葉轉換(Fast Fourier Transform, FFT)進行頻率域分析,本文藉由希爾伯特-黃轉換(Hilbert-Huang Transform, HHT)之輔助,探討房屋結構模型受不同強度地震作用下,系統加速度頻率反應曲線之變化,並提出新的結構損傷指標,相當阻尼比之比值(RED),作為偵測結構安全與提供預警之參考。
本文區分二大主軸,第一部份應用SAP2000有限元素軟體建立房屋結構模型,進行數值模擬分析,藉以瞭解RED對於偵測結損傷之敏感度。第二部分再以國家地震中心提供之鋼結構標竿模型試驗數據(NCREE-99-002與NCREE-06-020)進行分析,探討RED對於真實結構損傷診斷之可行性。上述研究同時採用HHT與FFT作為分析工具,並比較結果之差異性。最後提出一快速損傷評估流程,作為鋼結構房屋建築健康診斷之參考。
研究成果顯示:
1、當桿件斷面勁度折減為原來之90%時,觀察HHT加速度頻譜反應曲線即能發現頻寬有增大現象,表示結構已經產生損傷,但相同結果卻無法由FFT頻譜得知。
2、由四跨門型構架之HHT頻譜分析結果得知,僅斷面勁度產生折減之桿件的阻尼比有所提高,其餘完整桿件之RED值則維持不變,顯示HHT頻譜對於偵測桿件損傷與否的敏感度甚高。
3、依具遲滯型勁度折減之構架分析結果顯示,當結構系統維持線彈性反應時,無論以FFT或HHT分析,顯著頻率位置皆無變化,阻尼比亦僅有極微小之改變,即RED近似於1。
4、而當結構系統進入反應非線性階段,觀察HHT頻譜可發現RED有隨PGA值提高呈現正向遞增之趨勢。但由FFT頻譜得知,須在地震規模相當大,即結構受損嚴重時,相當阻尼比才有明顯改變。
5、透過HHT頻譜得知,房屋結構模型最先發生桿件降伏處的樓層,其相當阻尼比增加幅度亦較其他樓層明顯,表示觀察RED之變化量能判斷結構產生降伏的樓層位置。
6、隨地震力持續提高,結構非線性反應愈趨顯著,由HHT頻譜可看出頂樓處之RED增大幅度遠大於其他樓層。因此,量取頂樓之加速度反應進行HHT分析便能瞭解結構物發生損害之時機。
7、由鋼結構數值模型及標竿模型之相當阻尼比與最大層間變位角關係曲線分析結果顯示,當系統之相當阻尼比<3%,即RED<1.5時,結構物屬於輕微損壞階段。而在1.5 RED 2.5之間,系統達到中度破壞。若結構之相當阻尼比超過5%,也就是RED>2.5,則建築物可能已經進入嚴重破壞階段。
8、本研究提出以HHT頻譜為計算基礎之鋼結構房屋建築損傷評估流程,具備簡單且有效的診斷模式,其頂樓加速度頻譜能即時反應結構體之損傷程度,若能進一步量取其他樓層與可能優先破壞位置之地震訊號,則更利於偵測出建築物構件局部損傷之位置與時機。
This study investigates the feasibility of detecting structural damage using the HHT method. A damage detection index, the ratio of equivalent damping ratio (RED) is proposed. The nonlinear SDOF and MDOF with various predominant frequency models are then constructed by using the SAP2000 program, while the adjusted PGA El Centro and Chi-Chi (TCU068) earthquakes are used as excitations. Next, the damage index using the Hilbert-Huang Transform (HHT) and the Fast Fourier Transform (FFT) methods are evaluated separately based on the acceleration responses to earthquakes. Based on an analysis of shaking table test data from benchmark models subjected to adjusted Kobe and El Centro earthquakes are also used to demonstrate the efficiency of damage index in the HHT spectra in detecting structural damage.
Results indicate that, when the response of the structure is in the elastic region, the RED value only slightly changes in both the HHT and the FFT spectra. Additionally, RED values estimated from the HHT spectra vs. the PGA values change incrementally when the structure response is nonlinear i.e., member yielding occurs, but not in the RED curve from the FFT spectra. Moreover, the RED value of the top floor changes more than those from the other floors. Furthermore, structural damage is detected only when using the acceleration response data from the top floor.
Therefore, the ratio of equivalent damping ratio, RED, estimated from the smoothed HHT spectra is an effective and sensitive damage index for detecting structural damage. Finally, an effective structural monitoring procedure is proposed to detect the structural damage when during earthquakes. Results of this study also demonstrate that the HHT is a powerful method in analyzing the nonlinear responses of steel structures to strong ground motions.
摘 要 I
Abstract III
目 錄 V
表 目 錄 VIII
圖 目 錄 X

第1章 緒論 1
1.1 研究動機與目的 1
1.2 文獻回顧 3
1.3 論文內容 20
第2章 希爾伯特-黃轉換(HHT)理論介紹 21
2.1 瞬時頻率(Instantaneous Frequency) 22
2.2 內建模態函數(Intrinsic Mode Functions) 24
2.3 經驗模態分解法(Empirical Mode Decomposition) 26
2.4 IMF分量的完整性與正交性 29
2.5 整體經驗模態分解法(Ensemble Empirical Mode Decomposition) 31
2.6 希爾伯特頻譜(Hilbert Spectrum) 33
第3章 房屋結構損傷指標敏感度分析 44
3.1 損傷指標之建立 44
3.2 SAP2000非線性動力歷時分析 50
3.3 桿件初始勁度損傷敏感度分析 53
3.3.1 桿件勁度折減量損傷分析 54
3.3.2 小結一 57
3.4 桿件遲滯型勁度損傷敏感度分析 58
3.4.1 頂樓加速度頻率反應曲線分析比較 59
3.4.2 小結二 74
3.4.3 一樓與頂樓加速度頻率反應曲線分析比較 76
3.4.4 小結三 80
第4章 房屋結構損傷指標可行性分析 168
4.1 鋼結構標竿模型介紹 168
4.2 感應器設置與地震力輸入 169
4.3 SAP2000非線性靜力推覆分析 169
4.4 標竿模型數值模擬分析 170
4.5 相當阻尼比之比值分析 171
4.5.1 標竿模型A之RED分析 171
4.5.2 標竿模型B之RED分析 173
第5章 鋼結構建築損傷程度評估 210
5.1 最大樓層相對位移角損傷程度評估 210
5.1.1 標竿模型A之層間變位角分析 212
5.1.2 標竿模型B之層間變位角分析 213
5.2 相當阻尼比損傷程度評估 213
5.2.1 數值模型之損傷程度分析 214
5.2.2 標竿模型之損傷程度分析 215
5.3 鋼結構房屋建築損傷評估流程 216
第6章 結論與建議 225
6.1 結論 225
6.2 建議 229

參考文獻 231





表 目 錄
表 3 1 樑斷面不同勁度折減率之頻譜分析結果 81
表 3 2 門型構架斷面不同勁度折減率之頻譜分析結果 82
表 3 3 門型構架A與B桿件頻譜分析結果 83
表 3 4 四跨門型構架A至E桿件頻譜分析結果(IA=100%,IB=100%,IC=100%,ID=100%,IE=90%) 84
表 3 5 四跨門型構架A至E桿件頻譜分析結果(IA=100%,IB=100%,IC=90%,ID=100%,IE=100%) 85
表 3 6 四跨門型構架A至E桿件頻譜分析結果(IA=100%,IB=100%,IC=90%,ID=100%,IE=90%) 86
表 3 7 不同結構系統之顯著模態頻率 87
表 4 1 標竿模型尺寸規格表 176
表 4 2 標竿模型之地震力輸入規模 176
表 4 3 標竿模型A受不同PGA作用下,各樓層RED之變化(FFT) 177
表 4 4 標竿模型A受不同PGA作用下,各樓層RED之變化(HHT) 178
表 4 5 標竿模型B受不同PGA作用下,各樓層RED之變化(FFT) 179
表 4 6 標竿模型B受不同PGA作用下,各樓層RED之變化(HHT) 179
表 5 1 層間變位角與結構物損傷程度之關係 (ATC-40) 219
表 5 2 層間變位角與結構物損傷程度之關係 (FEMA-273) 219



圖 目 錄
圖 2 1原始訊號 35
圖 2 2局部極大值包絡線與局部極小值包絡線之均值包絡線 35
圖 2 3原始訊號與局部均值之差值 36
圖 2 4 El Centro 地震歷時記錄 36
圖 2 5應用EMD分解El Centro 地震波所得之IMF分量: (a)原始歷時c1及IMF分量:c2~c6 (b) IMF分量: c7~c11及餘數c12 37
圖 2 6原始歷時與C12分量疊加結果 38
圖 2 7原始歷時與C11~C12分量疊加結果 38
圖 2 8原始歷時與C10~C12分量疊加結果 39
圖 2 9原始歷時與C9~C12分量疊加結果 39
圖 2 10原始歷時與C8~C12分量疊加結果 40
圖 2 11原始歷時與C7~C12分量疊加結果 40
圖 2 12原始歷時與C6~C12分量疊加結果 41
圖 2 13原始歷時與C5~C12分量疊加結果 41
圖 2 14原始歷時與C4~C12分量疊加結果 42
圖 2 15原始歷時與C3~C12分量疊加結果 42
圖 2 16原始歷時與C2~C12分量疊加結果 43
圖 3 1 (a)RR與PGA關係曲線 (b)半帶寬法之定義【117】 (c)受簡諧外力作用下具阻尼系統之加速度反應因子【117】 (d)主頻偏移量(SV)與頻寬比(RB)之定義 89
圖 3 2 桿件局部坐標系統示意圖 90
圖 3 3非線性動力直接積分歷時分析流程圖 91
圖 3 4 (a)懸臂樑(b)門型構架示意圖(SAP2000) 92
圖 3 5 El Centro與TCU068 (a)地震歷時紀錄(b)反應譜(ξ=2%) 92
圖 3 6 樑桿件斷面不同勁度折減程度之FFT原始頻譜圖(El Centro) 93
圖 3 7 樑桿件斷面不同勁度折減程度之FFT平滑頻譜圖(El Centro) 93
圖 3 8 樑桿件斷面不同勁度折減程度之HHT原始頻譜圖(El Centro) 94
圖 3 9 樑桿件斷面不同勁度折減程度之HHT平滑頻譜圖(El Centro) 94
圖 3 10 樑桿件斷面不同勁度折減程度之FFT原始頻譜圖(TCU068) 95
圖 3 11 樑桿件斷面不同勁度折減程度之FFT平滑頻譜圖(TCU068) 95
圖 3 12 樑桿件斷面不同勁度折減程度之HHT原始頻譜圖(TCU068) 96
圖 3 13 樑桿件斷面不同勁度折減程度之HHT平滑頻譜圖(TCU068) 96
圖 3 14 門型構架桿件斷面不同勁度折減程度之FFT原始頻譜圖 (El Centro) 97
圖 3 15 門型構架桿件斷面不同勁度折減程度之FFT平滑頻譜圖 (El Centro) 97
圖 3 16 門型構架桿件斷面不同勁度折減程度之HHT原始頻譜圖 (El Centro) 98
圖 3 17 門型構架桿件斷面不同勁度折減程度之HHT平滑頻譜圖 (El Centro) 98
圖 3 18 門型構架桿件斷面不同勁度折減程度之FFT原始頻譜圖(TCU068) 99
圖 3 19 門型構架桿件斷面不同勁度折減程度之FFT平滑頻譜圖(TCU068) 99
圖 3 20 門型構架桿件斷面不同勁度折減程度之HHT原始頻譜圖(TCU068) 100
圖 3 21 門型構架桿件斷面不同勁度折減程度之HHT平滑頻譜圖(TCU068) 100
圖 3 22 門型構架A與B桿件之HHT原始頻譜圖(El Centro; IA=90%,IB=100%) 101
圖 3 23 門型構架A與B桿件之HHT平滑頻譜圖(El Centro; IA=90%,IB=100%) 101
圖 3 24 門型構架A與B桿件之HHT原始頻譜圖(TCU068; IA=90%,IB=100%) 102
圖 3 25 門型構架A與B桿件之HHT平滑頻譜圖(TCU068; IA=90%,IB=100%) 102
圖 3 26 四跨門型構架A至E桿件示意圖 103
圖 3 27 四跨門型構架A至E桿件之HHT原始頻譜圖(El Centro; IA=100%,IB=100%,IC=100%,ID=100%,IE=90%) 103
圖 3 28 四跨門型構架A至E桿件之HHT平滑頻譜圖(El Centro; IA=100%,IB=100%,IC=100%,ID=100%,IE=90%) 104
圖 3 29 四跨門型構架A至E桿件之HHT原始頻譜圖(TCU068; IA=100%,IB=100%,IC=100%,ID=100%,IE=90%) 104
圖 3 30 四跨門型構架A至E桿件之HHT平滑頻譜圖(TCU068; IA=100%,IB=100%,IC=100%,ID=100%,IE=90%) 105
圖 3 31 四跨門型構架A至E桿件之HHT原始頻譜圖(El Centro; IA=100%,IB=100%,IC=90%,ID=100%,IE=100%) 105
圖 3 32 四跨門型構架A至E桿件之HHT平滑頻譜圖(El Centro; IA=100%,IB=100%,IC=90%,ID=100%,IE=100%) 106
圖 3 33 四跨門型構架A至E桿件之HHT原始頻譜圖(TCU068; IA=100%,IB=100%,IC=90%,ID=100%,IE=100%) 106
圖 3 34 四跨門型構架A至E桿件之HHT平滑頻譜圖(TCU068; IA=100%,IB=100%,IC=90%,ID=100%,IE=100%) 107
圖 3 35 四跨門型構架A至E桿件之HHT原始頻譜圖(El Centro; IA=100%,IB=100%,IC=90%,ID=100%,IE=90%) 107
圖 3 36 四跨門型構架A至E桿件之HHT平滑頻譜圖(El Centro; IA=100%,IB=100%,IC=90%,ID=100%,IE=90%) 108
圖 3 37 四跨門型構架A至E桿件之HHT原始頻譜圖(TCU068; IA=100%,IB=100%,IC=90%,ID=100%,IE=90%) 108
圖 3 38 四跨門型構架A至E桿件之HHT平滑頻譜圖(TCU068; IA=100%,IB=100%,IC=90%,ID=100%,IE=90%) 109
圖 3 39 單自由度系統,不同PGA作用下,系統之轉角與彎矩關係曲線 (El Centro,f1=2.71Hz) 109
圖 3 40 單自由度系統,不同PGA作用下,系統反應之(a)FFT原始頻譜(b)FFT平滑頻譜(c)FFT能量分佈頻譜(El Centro,f1=2.71Hz) 111
圖 3 41 單自由度系統,不同PGA作用下,系統反應之(a)HHT原始頻譜(b)HHT平滑頻譜(c)HHT能量分佈頻譜(El Centro,f1=2.71Hz) 112
圖 3 42 多自由度系統,不同PGA作用下,一樓柱底之轉角與彎矩關係曲線(El Centro,f1 =2.78Hz) 113
圖 3 44 多自由度系統,不同PGA作用下,系統反應之(a)HHT原始頻譜(b)HHT平滑頻譜(c)HHT能量分佈頻譜(El Centro,f1=2.78Hz) 116
圖 3 45 單自由度系統,不同PGA作用下,系統之轉角與彎矩關係曲線(TCU068,f1=2.71Hz) 116
圖 3 46 單自由度系統,不同PGA作用下,系統反應之(a)FFT原始頻譜(b)FFT平滑頻譜(c)FFT能量分佈頻譜(TCU068,f1=2.71Hz) 118
圖 3 47 單自由度系統,不同PGA作用下,系統反應之(a)HHT原始頻譜(b)HHT平滑頻譜(c)HHT能量分佈頻譜(TCU068,f1=2.71Hz) 119
圖 3 48 多自由度系統,不同PGA作用下,一樓柱底之轉角與彎矩關係曲線(TCU068,f1=2.78Hz) 120
圖 3 49 多自由度系統,不同PGA作用下,頂樓反應之(a)FFT原始頻譜(b)FFT平滑頻譜(c)FFT能量分佈頻譜(TCU068,f1=2.78Hz) 121
圖 3 50 多自由度系統,不同PGA作用下,頂樓反應之(a)HHT原始頻譜(b)HHT平滑頻譜(c)HHT能量分佈頻譜(TCU068,f1=2.78Hz) 123
圖 3 51 SV與RR關係曲線(SDOF,f1=2.71Hz;MDOF,f1=2.78Hz;El Centro,TCU068) 123
圖 3 52 RED與RR關係曲線(SDOF,f1=2.71Hz;MDOF,f1=2.78Hz;El Centro,TCU068) 124
圖 3 53 單自由度系統,不同PGA作用下,系統之轉角與彎矩關係曲線(El Centro,f1 =0.97Hz) 124
圖 3 54 單自由度系統,不同PGA作用下,系統反應之(a)FFT原始頻譜(b)FFT平滑頻譜(c)FFT能量分佈頻譜(El Centro,f1=0.97Hz) 126
圖 3 55 單自由度系統,不同PGA作用下,系統反應之(a)HHT原始頻譜(b)HHT平滑頻譜(c)HHT能量分佈頻譜(El Centro,f1=0.97Hz) 127
圖 3 56 多自由度系統,不同PGA作用下,一樓柱底之轉角與彎矩關係曲線(El Centro,f1 =0.95Hz) 128
圖 3 57 多自由度系統,不同PGA作用下,頂樓反應之(a)FFT原始頻譜(b)FFT平滑頻譜(c)FFT能量分佈頻譜(El Centro,f1=0.95Hz) 129
圖 3 58 多自由度系統,不同PGA作用下,頂樓反應之(a)HHT原始頻譜(b)HHT平滑後頻譜(c)HHT能量分佈頻譜(El Centro,f1=0.95Hz) 131
圖 3 59 單自由度系統,不同PGA作用下,系統之轉角與彎矩關係曲線(TCU068,f 1=0.97Hz) 131
圖 3 60 單自由度系統,不同PGA作用下,系統反應之(a)FFT原始頻譜(b)FFT平滑頻譜(c)FFT能量分佈頻譜(TCU068,f1=0.97Hz) 133
圖 3 61 單自由度系統,不同PGA作用下,系統反應之(a)HHT原始頻譜(b)HHT平滑頻譜(c)HHT能量分佈頻譜(TCU068,f1=0.97Hz) 134
圖 3 62 多自由度系統,不同PGA作用下,一樓柱底之轉角與彎矩關係曲線(TCU068,f1=0.95Hz) 135
圖 3 63 多自由度系統,不同PGA作用下,頂樓反應之(a)FFT原始頻譜(b)FFT平滑頻譜(c)FFT能量分佈頻譜(TCU068,f1=0.95Hz) 136
圖 3 64 多自由度系統,不同PGA作用下,頂樓反應之(a)HHT原始頻譜(b)HHT平滑頻譜(c)HHT能量分佈頻譜(TCU068,f1=0.95Hz) 138
圖 3 65 SV與RR關係曲線(SDOF,f1=0.97Hz;MDOF,f1=0.95Hz;El Centro,TCU068) 138
圖 3 66 RED與RR關係曲線(SDOF,f1=0.97Hz;MDOF,f1=0.95Hz;El Centro,TCU068) 139
圖 3 67 單自由度系統,不同PGA作用下,系統之轉角與彎矩關係曲線(El Centro,f1 =0.49Hz) 139
圖 3 68 單自由度系統,不同PGA作用下,系統反應之(a)FFT原始頻譜(b)FFT平滑頻譜(c)FFT能量分佈頻譜(El Centro,f1=0.49Hz) 141
圖 3 69 單自由度系統,不同PGA作用下,系統反應之(a)HHT原始頻譜(b)HHT平滑頻譜(c)HHT能量分佈頻譜(El Centro,f1=0.49Hz) 142
圖 3 70 多自由度系統,不同PGA作用下,一樓柱底之轉角與彎矩關係曲線(El Centro,f2 =1.45Hz) 143
圖 3 71 多自由度系統,不同PGA作用下,頂樓反應之(a)FFT原始頻譜(b)FFT平滑頻譜(c)FFT能量分佈頻譜(El Centro,f 2=1.45Hz) 144
圖 3 72 多自由度系統,不同PGA作用下,頂樓反應之(a)HHT原始頻譜(b)HHT平滑頻譜(c)HHT能量分佈頻譜(El Centro,f 2=1.45Hz) 146
圖 3 73 單自由度系統,不同PGA作用下,系統之轉角與彎矩關係曲線(TCU068,f1 =0.49Hz) 146
圖 3 74 單自由度系統,不同PGA作用下,系統反應之(a)FFT原始頻譜(b)FFT平滑頻譜(c)FFT能量分佈頻譜(TCU068,f1=0.49Hz) 148
圖 3 75 單自由度系統,不同PGA作用下,系統反應之(a)HHT原始頻譜(b)HHT平滑頻譜(c)HHT能量分佈頻譜(TCU068,f1=0.49Hz) 149
圖 3 76 多自由度系統,不同PGA作用下,一樓柱底之轉角與彎矩關係曲線(TCU068,f1 =0.48Hz) 150
圖 3 77 多自由度系統,不同PGA作用下,頂樓反應之(a)FFT原始頻譜(b)FFT平滑頻譜(c)FFT能量分佈頻譜(TCU068,f1=0.48Hz) 151
圖 3 78 多自由度系統,不同PGA作用下,頂樓反應之(a)HHT原始頻譜(b)HHT平滑頻譜(c)HHT能量分佈頻譜(TCU068,f1=0.48Hz) 153
圖 3 79 SV與RR關係曲線(SDOF,f1=0.49Hz;MDOF,f1=0.48Hz(f2=1.45Hz);El Centro,TCU068) 153
圖 3 80 RED與RR關係曲線(SDOF,f1=0.49Hz;MDOF,f1=0.48Hz(f2=1.45Hz);El Centro,TCU068) 154
圖 3 81 多自由度系統,不同PGA作用下,1F反應之(a)HHT原始頻譜(b)HHT平滑頻譜(c)HHT能量分佈頻譜(El Centro,f1=2.78Hz) 155
圖 3 82 多自由度系統,不同PGA作用下,1F反應之(a)HHT原始頻譜(b)HHT平滑頻譜(c)HHT能量分佈頻譜(TCU068,f1=2.78Hz) 157
圖 3 83 RED與RR關係曲線(MDOF,f1=2.78Hz;El Centro,TCU068;1F vs 3F) 157
圖 3 84 (a)RED與PGA關係曲線(b)局部放大示意圖(MDOF,f1=2.78Hz;El Centro,TCU068;1F vs 3F) 158
圖 3 85 多自由度系統,不同PGA作用下,1F反應之(a)HHT原始頻譜(b)HHT平滑頻譜(c)HHT能量分佈頻譜(El Centro,f1=0.95Hz) 160
圖 3 86 多自由度系統,不同PGA作用下,1F反應之(a)HHT原始頻譜(b)HHT平滑頻譜(c)HHT能量分佈頻譜(TCU068,f1=0.95Hz) 161
圖 3 87 RED與RR關係曲線(MDOF,f1=0.95Hz;El Centro,TCU068;1F vs 10F) 162
圖 3 88 (a)RED與PGA關係曲線(b)局部放大示意圖(MDOF,f1=0.95Hz;El Centro,TCU068;1F vs 10F) 163
圖 3 89 多自由度系統,不同PGA作用下,1F反應之(a)HHT原始頻譜(b)HHT平滑頻譜(c)HHT能量分佈頻譜(El Centro,f2=1.45Hz) 164
圖 3 90 多自由度系統,不同PGA作用下,1F反應之(a)HHT原始頻譜(b)HHT平滑頻譜(c)HHT能量分佈頻譜(TCU068,f1=0.48Hz) 166
圖 3 91 RED與RR關係曲線(MDOF,f1=0.48Hz;El Centro,TCU068;1F vs 20F) 166
圖 3 92 (a)RED與PGA關係曲線(b)局部放大示意圖(MDOF,f1=0.48Hz;El Centro,TCU068;1F vs 20F) 167
圖 4 1 標竿模型A (NCREE-99-002) 結構示意圖 180
圖 4 2 標竿模型B (NCREE-06-020) 結構示意圖 180
圖 4 3 標竿模型A加速度計配置圖 181
圖 4 4 標竿模型A位移計配置圖 181
圖 4 5 標竿模型B位移計、加速度計、荷重計配置圖(紅色箭頭為位移計與加速度計,藍色箭頭為荷重計) 182
圖 4 6 標竿模型B震動台試驗照片(NCREE-06-020) 182
圖 4 7 (a)Kobe (b)El Centro地震歷時紀錄 183
圖 4 8 標竿模型A之(a)3D示意圖(b)X-Y平面示意圖(SAP2000) 183
圖 4 9 標竿模型B之(a)3D示意圖(b)X-Y平面示意圖(SAP2000) 184
圖 4 10 標竿模型A之(a)Drain-2D (b)SAP2000桿件起始降伏位置分析結果 184
圖 4 11 標竿模型B之(a)ABAQUS (b)SAP2000桿件起始降伏位置分析結果 185
圖 4 12 運用FFT及HHT頻譜計算損傷指標,RED之流程圖 186
圖 4 13 運用HHT頻譜建立損傷指標,RED之細部流程圖 187
圖 4 14 標竿模型A受不同PGA作用下,一樓反應之FFT原始頻譜 188
圖 4 15 標竿模型A受不同PGA作用下,一樓反應之FFT平滑頻譜 188
圖 4 16 標竿模型A受不同PGA作用下,二樓反應之FFT原始頻譜 189
圖 4 17 標竿模型A受不同PGA作用下,二樓反應之FFT平滑頻譜 189
圖 4 18 標竿模型A受不同PGA作用下,三樓反應之FFT原始頻譜 190
圖 4 19 標竿模型A受不同PGA作用下,三樓反應之FFT平滑頻譜 190
圖 4 20 標竿模型A受不同PGA作用下,四樓反應之FFT原始頻譜 191
圖 4 21 標竿模型A受不同PGA作用下,四樓反應之FFT平滑頻譜 191
圖 4 22 標竿模型A受不同PGA作用下,五樓反應之FFT原始頻譜 192
圖 4 23 標竿模型A受不同PGA作用下,五樓反應之FFT平滑頻譜 192
圖 4 24 標竿模型A受不同PGA作用下,一樓反應之HHT原始頻譜 193
圖 4 25 標竿模型A受不同PGA作用下,一樓反應之HHT平滑頻譜 193
圖 4 26 標竿模型A受不同PGA作用下,二樓反應之HHT原始頻譜 194
圖 4 27 標竿模型A受不同PGA作用下,二樓反應之HHT平滑頻譜 194
圖 4 28 標竿模型A受不同PGA作用下,三樓反應之HHT原始頻譜 195
圖 4 29 標竿模型A受不同PGA作用下,三樓反應之HHT平滑頻譜 195
圖 4 30 標竿模型A受不同PGA作用下,四樓反應之HHT原始頻譜 196
圖 4 31 標竿模型A受不同PGA作用下,四樓反應之HHT平滑頻譜 196
圖 4 32 標竿模型A受不同PGA作用下,五樓反應之HHT原始頻譜 197
圖 4 33 標竿模型A受不同PGA作用下,五樓反應之HHT平滑頻譜 197
圖 4 34 標竿模型A受不同PGA作用下,一樓反應之HHT能量頻譜 198
圖 4 35 標竿模型A受不同PGA作用下,五樓反應之HHT能量頻譜 198
圖 4 36 標竿模型A各樓層FFT平滑頻譜比較 199
圖 4 37 標竿模型A各樓層HHT平滑頻譜比較 199
圖 4 38 標竿模型A之(a) RED與PGA值關係曲線(b)局部放大示意圖 200
圖 4 39 標竿模型B受不同PGA作用下,一樓反應之FFT原始頻譜 201
圖 4 40 標竿模型B受不同PGA作用下,一樓反應之FFT平滑頻譜 201
圖 4 41 標竿模型B受不同PGA作用下,二樓反應之FFT原始頻譜 202
圖 4 42 標竿模型B受不同PGA作用下,二樓反應之FFT平滑頻譜 202
圖 4 43 標竿模型B受不同PGA作用下,三樓反應之FFT原始頻譜 203
圖 4 44 標竿模型B受不同PGA作用下,三樓反應之FFT平滑頻譜 203
圖 4 45 標竿模型B受不同PGA作用下,一樓反應之HHT原始頻譜 204
圖 4 46 標竿模型B受不同PGA作用下,一樓反應之HHT平滑頻譜 204
圖 4 47 標竿模型B受不同PGA作用下,二樓反應之HHT原始頻譜 205
圖 4 48 標竿模型B受不同PGA作用下,二樓反應之HHT平滑頻譜 205
圖 4 49 標竿模型B受不同PGA作用下,三樓反應之HHT原始頻譜 206
圖 4 50 標竿模型B受不同PGA作用下,三樓反應之HHT平滑頻譜 206
圖 4 51 標竿模型B受不同PGA作用下,一樓反應之HHT能量頻譜 207
圖 4 52 標竿模型B受不同PGA作用下,三樓反應之HHT能量頻譜 207
圖 4 53 標竿模型B各樓層FFT平滑頻譜比較 208
圖 4 54 標竿模型B各樓層HHT平滑頻譜比較 208
圖 4 55 標竿模型B之(a) RED與PGA值關係曲線(b)局部放大示意圖 209
圖 5 1 (a)層間變位角示意圖 (b)最大層間變位角示意圖 220
圖 5 2 標竿模型層間變位角計算分析流程圖 221
圖 5 3 標竿模型A層間變位角與PGA關係曲線 222
圖 5 4 標竿模型B層間變位角與PGA關係曲線 222
圖 5 5 標竿模型A及B之相當阻尼比與最大樓層相對位移角關係曲線 223
圖 5 6 鋼結構房屋數值模型之相當阻尼比與最大樓層相對位移角關係曲線 223
圖 5 7鋼結構房屋建築損傷評估流程圖 224
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