羅俊雄臺灣大學:土木工程學研究所趙書賢Chao, Shu-HsienShu-HsienChao2010-07-012018-07-092010-07-012018-07-092009U0001-0502200915452800http://ntur.lib.ntu.edu.tw//handle/246246/187863本研究的主要目的在於研究一套新的理論，以用來模擬不同形式之結構物在受到外力載重下之非線彈性行為。首先本研究提出了全新的雙向非線彈性組成率遲滯模型，其可用來模擬不同的結構系統、材料或桿件在受到雙向載重時的非線彈性行為。常見的遲滯行為例如強度衰減、勁度衰減以及擠壓效應等等，以及受到雙向載重的雙向互制行為，皆可由本研究所提出的雙向非線彈性組成率遲滯模型來模擬。著本研究利用新的雙向組成率遲滯模型，配合梁柱構架系統以及傳統的虛擬力法概念，提出了一套分析結構物非線彈性行為的理論梁柱構架模型，我們稱此分析方法為修正之虛擬力法。在虛擬力法中，藉由不同型式的塑性機制以及遲滯模型之行為，我們可以模擬由不同材料所組成之結構桿件其非線彈性行為及其破壞模式，例如撓曲破壞、剪力破壞以及撓剪破壞等等。結構系統簡單的P-Δ效應亦可利用本文所提出的理論模型來加以模擬。 而本研究採用了反覆載重實驗以及動力實驗的實驗資料來驗證本文所提出的分析理論模型。比較後的結果可以證明本文所提出之理論模型可以準確的模擬不同的結構物之非線彈性行為，包括不同程度的強度衰減、勁度衰減、擠壓效應以及雙向互制之行為等等。 最後本研究採用了三種不同結構系統（鋼構架、鋼筋混凝土構架以及承重牆系統），以及三種不同樓層的高度（3樓、12樓以及24樓）等九個基元構架系統，透過漸增動力分析之方法，來瞭解各結構之耐震容量以及需求，並探討不同結構系統之間之差異，以及其易損性曲線。The objective of this study is to develop a new algorithm to simulate nonlinear inelastic behavior of structures subjected to biaxial static or dynamic loading. First, the new biaxial constitutive hysteretic model is developed to simulate nonlinear inelastic behavior of system subjected to uniaxial or biaxial loading. The strength and stiffness deterioration, pinching phenomenon and biaxial effect can also be considered by the proposed biaxial hysteretic model. It can be used to simulate not only global but also local inelastic behavior of structures. Next, a new algorithm, which is called the modified force analogy method, is developed based on the proposed biaxial hysteretic model and theory of force analogy method. The damage condition, failure type of structural element and collapse time of structure can also be simulated by the modified force analogy method. The cyclic loading test data and dynamic collapse test data are used to verify the proposed algorithm. It is found that the proposed algorithm can simulate nonlinear inelastic behavior of structures subjected to uniaxial or biaxial loading approximately. Finally, the drift demand of different structural systems, such as steel frame (SF), reinforced concrete frame (RCF) and reinforced concrete wall building (RCWB), are studied by using incremental dynamic analysis (IDA). A total of nine generic structures with different heights, structural systems and inelastic behavior are designed according to current seismic code to realize the difference of their drift demand. The relationships between maximum inter-story drift ratio (IDRmax) and reduction factor (R) for different structural systems are constructed, and uncertainty due to ground motion is investigated. Probability of damage condition of different structural systems under different excitation levels is also discussed. The information of this study is useful to preliminary design and seismic performance assessment.誌謝…………………………………………………………………………………….一文摘要……………………………………………………………………………….二文摘要……………………………………………………………………………….三hapter 1 Introduction…………………………………………………...1-1 Introduction and Background……………………………… …….1-2 Objectives and Report Organization……………………………...4hapter 2 Uniaxial and Biaxial Hysteretic Model………………………8-1 Uniaxial Hysteretic Model………………………………………...8-2 Biaxial Hysteretic Model………………………………………...24-3 Verification of the Proposed Biaxial Hysteretic Model………….43-4 Summary…………………………………………………………47hapter 3 Modified Force Analogy Method…………………………...77-1 Element Type of Modified Force Analogy Method……………..77-2 Governing Equation of Modified Force Analogy Method………80-3 Implementation of the Proposed Hysteretic Model……………...91-4 Considering the P-Δ Effect………………………………………99-5 Dynamic Analysis Method of MFAM………………………….101-6 Energy Evaluation of MFAM…………………………………..104-7 Verification of MFAM………………………………………….105hapter 4 Drift Demand of Different Structural Systems……...……127-1 Generic Structural Models……………………………………...128-2 Ground Motions Used in This Study……………………………130-3 Incremental Dynamic Analysis Results………………………...131-4 Fragility analysis of IDA curves………………………………..133-5 Fragility Analysis Results of Nine Structural Models…………..135-6 Performance Assessment of Different Structural System………137-7 Summary and Conclusions……………………………………...140hapter 5 Summary and Conclusion…………………………………150eference………………………………………………………………..154ppendix A……………………………………………………………...158ppendix B……………………………………………………………...160ist of Figures-1(a) Illustration of the simulated results of the tangent stiffness hysteretic model subjected to loading with different rate………………………………… ……..7-1(b) Illustration of the simulated results of the constitutive hysteretic model………7-1(a) Back-bone curve of the proposed non-deteriorating hysteretic model………..49-1(b) Back-bone curve of the proposed deteriorating hysteretic model…………….49-2(a) Tri-linear inelastic system with k3 = 0………………………………………...50-2(b) Elastic system with stiffness ku………………………………………………..50-3(a) Spring 1: Hysteretic spring……………………………………………………51-3(b) Spring 2: Post-yielding spring………………………………………………...51-3(c) Spring 3: Ultimate spring…………………….………………………………..51-4 Force versus displacement diagrams of the proposed uniaxial hysteretic model with different type of deteriorating parameters…………………….………....52-5 Illustration of inelastic displacement……………………………………….....53-6 Illustration of secant stiffness method…………………………………………53-7 Illustration of tangent stiffness method with correction of unbalance force…..54-8 Ground motion acceleration time histories collected in 921 Chi-Chi Earthquake at CHY028 station and TCU052 station………………………………………54-9(a) Ductility spectrum with reduction factor equal to 3 evaluated by secant stiffness method (SSM), tangent stiffness method (TSM) and inelastic displacement method (IDM) for data collected in 921 Chi-Chi earthquake at station CHY028 for east-west direction……………………………………..55-9(b) Ductility spectrum with reduction factor equal to 3 evaluated by secant stiffness method (SSM), tangent stiffness method (TSM) and inelastic displacement method (IDM) for data collected in 921 Chi-Chi earthquake at station TCU028 for east-west direction……………………………………..55-10(a) Notations of the proposed biaxial hysteretic model for displacement field which shows the zero force point O’………………………………………...56-10(b) Notations of the proposed biaxial hysteretic model for the force acts at point A……………………………………………………………………………..56-11 Illustration of loading state, unloading state or neutral loading state of the biaxial spring………………………………………………………………...57-12 Illustration of updating zero force point……………………………………...57-13 Illustration of the proposed biaxial hysteretic model subjected to different displacement patterns (k=1, fc=0.1, fn=1). (a) displacement pattern diagram; (b) force versus displacement diagram for x-direction; (c) force versus displacement diagram for y-direction………………………………………..58-14 Illustration of the proposed biaxial hysteretic model subjected to different displacement rate and its corresponding force pattern (k=1, fc=0.1, fn=1); (a1), (b1): displacement diagrams in two-direction for two different deformation rates; (a2), (b2): force diagrams in two-direction which corresponding to the deformation rate shown in (a1) and (b1)…………………………………….59-15 Ductility spectrum with reduction factor equal to 3 for (a) records collected at station TCU052 and for (b) records collected at station CHY028 in Chi-Chi earthquake (EW and NS: results of uniaxial hysteretic model for two directions respectively; BD: results of biaxial hysteretic model; SRSS: square root of sum squares for results of uniaxial hysteretic model)………………..60-16(a) Illustration of flexural failure reinforced concrete column for biaxial cyclic loading test………………………………………………………………….....61-16(b) Illustration of shear failure reinforced concrete column for biaxial cyclic loading test……………………………………………………………..……...62-17 Three different cyclic loading displacement control test procedures in two directions for three flexural failure columns (F1C, F2Cand F3C) and three shear failure columns (S1C, S2C and S3C)…………………………………...63-18(a) Illustration of procedure to determine the modal parameters (such as k, Fc, Fn, αp, αs) by using the 0.5% drift ratio test results of experiment for F1C….…...64-18(b) Illustration of procedure to determine the modal parameters (such as k, Fc, Fn, αp, αs) by using the 0.5% drift ratio test results of experiment for S1C…..…..65-19 Procedure to determine the modal parameters (such as , , , and ) by using the relationship between system stiffness (or strength) and hysteretic energy for F1C and S1C……………………………………………66-20 Comparison of force versus displacement diagrams between experiment and simulation for flexural failure column F1C…………………………………...67-21 Comparison of force versus displacement diagrams between experiment and simulation for flexural failure column F2C. ……………………………….....68-22 Comparison of force versus displacement diagrams between experiment and simulation for flexural failure column F3C…………………………………...69-23 Comparison of force versus displacement diagrams between experiment and simulation for shear failure column S1C……………………………………...70-24 Comparison of force versus displacement diagrams between experiment and simulation for shear failure column S2C. ………………………………….....71-25 Comparison of force versus displacement diagrams between experiment and simulation for shear failure column S3C……………………………………...72-26(a) Absorbed hysteretic energy of simulation and experiment results for different maximum drift ratio for flexural failure columns……………………………..73-26 (b) Absorbed hysteretic energy of simulation and experiment results for different maximum drift ratio for shear failure columns………………………………..74-1 3-DBeam-column elements with three types of plastic mechanisms……….110-2 Internal force versus plastic deformation and force versus displacement relationships for ATE, BTE and CTE………………………………………111-3 Planar frame structure constructed by ATE, BTE and CTE; (a) Illustration of GDOFs; (b) Illustration of LDOFs…………………………………………112-4 The illustrated analyzed structure and three kinds of virtual structure developed from the analyzed structure to derive system matrices K, KP and KR………112-5 Illustration of the development of the governing equation of MFAM……….113-6 Illustration of the analysis procedure of the nonlinear governing equation of MFAM……………………………………………………………………….114-7 Shear capacity model for CTE……………………………………………….115-8 P-Δ effect of column fixed at two ends………………………………………115-9(a) Analytical model for cyclic loading test of RC bridge column……………...116-9(b) Comparison between simulation and experiment results for cyclic loading test of RC bridge column………………………………………………………...116-9(c1) Moment versus plastic rotation diagram for cyclic loading test of RC bridge column……………………………………………………………………….117-9(c2) Shear force versus plastic sliding length diagram for cyclic loading test of RC bridge column………………………………………………………………..117-10(a) Analytical model for cyclic loading test of a two-stories RC frame……….118-10(b1) Story shear force versus story drift diagram for 1st story for cyclic loading test of a two-stories RC frame……………………………………………………118-10(b2) Story shear force versus story drift diagram for 2nd story for cyclic loading test of a two-stories RC frame……………………………………………………119-10(c1) Moment versus plastic rotation diagram for the bottom of 1st story column for cyclic loading test of two-stories RC frame…………………………………119-10(c2) Moment versus plastic rotation diagram for 1st story beam for cyclic loading test of two-stories RC frame………………………………………………....120-10(c3) Moment versus plastic rotation diagram for 2nd story beam for cyclic loading test of two-stories RC frame…………………………………………………120-11 Damage conditions after cyclic loading test of two-stories RC frame for (a) 1st story column; (b) 1st story beam; (c) 2nd story beam………………………...121-12(a) Design details of the non-ductile RC portal frame for dynamic collapse test..................................................................................................................122-12(b) Analytical model of the non-ductile RC portal frame for dynamic collapse test…………………………………………………………………………..122-12(c) Achieved acceleration time history of the non-ductile RC portal frame for dynamic collapse test………………………………………………………...123-12(d) Comparison between experimental and analytical result of the non-ductile RC portal frame for dynamic collapse test………………………………………123-1 Illustration of 3-stories generic model for (a) SF and RCF; (b) RCWB……..141-2 Capacity curves of 3-stories generic model for (a) SF; (b)RCF; (c)RCWB…142-3 Spectral acceleration of 66 individual records and mean spectral acceleration…………………………………………………………………..143-4 Results of IDA for 3-stories RCF subjected to 66 near-fault ground motions………………………………………………………………………143-5 Exceeding probability of IDRmaxi equal to 1%, 5%, and 10% for 3-stories RCF…………………………………………………………………………..144-6 IDA curves with exceeding probability equal to 16%, 50% and 84% for 3-stories RCF………………………………………………………………...144-7 Coefficient of variation for 3-stories RCF subjected to 66 near-fault ground motions………………………………………………………………………145-8(a) IDA curves with exceeding probability equal to 16%.....................................145-8(b) IDA curves with exceeding probability equal to 50%.....................................146-8(c) IDA curves with exceeding probability equal to 84%.....................................146-9 Coefficient of variation for 3, 12 and 24-stories models……………………..147-10(a) Fragility curves of nine generic models for moderate damage performance level.………………………………………………………………………..147-10(b) Fragility curves of nine generic models for severe damage performance level…..………………………………………………….……………..…148-10(c) Fragility curves of nine generic models for near collapse performance level……………………………………………………………………….1481 (a) Illustration of zero force point O’ of the uniaxial hysteretic model; (b) Displacement field which shows the zero force point O’ of the biaxial hysteretic model; (b) The force distribution of the biaxial hysteretic model acts at point A………………………………………………………………163ist of Tables-1 Parameters used to simulate a non-ductile RC bridge column………………...75-2 Parameters used to simulate the two-stories RC frame………………………..76-1 Parameters used to simulate the non-ductile RC portal frame……………….124-2 Non-dimensional parameters for the simulated model………………………125-3 Characteristics of nine structural models…………………………………….126-1 Characteristics of nine structural models………………………..…………...149-2 Performance levels and damage conditions corresponding to IDRmax……….1491499310 bytesapplication/pdfen-US遲滯模型構架模型雙向載重虛擬力法Hysteretic modelFrame modelBiaxial loadforce analogy methodthesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/187863/1/ntu-98-D92521005-1.pdf