台灣是由歐亞大陸板塊與菲律賓海板塊相互碰撞擠壓而成，每年會有15000至18000個大大小小的地震，因此在台灣設計建築結構時地震力是最重要的考量因素之一。現今社會越來越多造型獨特的建築，這些外觀特殊的建築往往會有平面不對稱的情形，受震時平移及旋轉的變形往往同時發生，角落位移有可能比質心位移還大甚多，且以傳統的靜力分析方法無法準確地預測其受震反應，因此常須採動力分析方得以檢核其耐震性能。隨著都市人口密度增加，高樓層建築也越來越多，許多高層建築加裝液態黏滯性阻尼器來增強其制震能力。本研究探討簡化的動力分析方法以計算加裝液態黏滯性阻尼器的平面不對稱建築之受震反應。以便用於初步設計、大量分析以及參數研究。
本研究主要分為兩個部分：一為具線性液態黏滯性阻尼器之非彈性平面不對稱建築的簡化分析，另一為具非線性液態黏滯性阻尼器之彈性平面不對稱建築的簡化分析。兩個部分均採用模態疊加法來計算結構之受震反應。第一部分，本研究利用動力分析軟體建立振態桿狀模型並設置雙線性參數以探討結構受震進入非彈性之反應。再比較本研究提出之簡化方法與傳統單自由度模態運動方程式運算結果之準確度。而第二部分使用數學軟體藉Newmark-β法計算具有外加非線性阻尼器的多自由度模態運動方程式。針對非線性外加阻尼項的計算，本文提出預測修正法以及等效阻尼係數法兩種簡化方法。預測修正法在分析過程中，預估了非線性項次的速度，並且修正上一步計算產生的不平衡力。等效阻尼係數法於Newmark-β法每一個計算步距計算每支非線性阻尼器對應於線性阻尼器之等效阻尼係數，再以此係數建置新的阻尼矩陣，進而求得下一步的結構反應。
上述兩個部份的研究均以PISA3D動力分析軟體建置有限元素模型之受震反應作為精確解比較其準確度。本研究第一部份中提出的簡化方法，在多數案例中誤差值均較傳統單自由度方法小，縱使有些分析案例峰值準確度沒有明顯優於或甚至劣於傳統簡化方法，但本研究提出之簡化方法預估之結構動態反應趨勢與有限元素模型分析得到的結果較相近。第二個部份之分析案例中，在阻尼指數 的情況，兩種簡化方法均有良好的表現，隨著 值增大，兩種簡化方法準確度均劇烈下滑。另外預測修正法於 的分析案例中受震反應隨著時間衰減的趨勢比較緩慢，等效阻尼係數法預測之受震反應隨著時間衰減的情形有比較精確的表現。兩種簡化方法均能有效地節省分析所需時間，等效阻尼係數法耗時約為有限元素法之16%，預測修正法耗時只為有限元素法之8%。

Seismic loading is one of the most important load cases while designing buildings in Taiwan. There are more and more high-rise buildings with grotesque appearance assembled with fluid viscous dampers in order to enhance the ability of energy dissipation. The response of these special-shaped buildings, which usually are asymmetric-plan structures, excited by bi-directional ground motions can’t be evaluated accurately using traditional static analysis procedures. This research proposes simplified seismic analysis methods for non-proportionally damped asymmetric-plan buildings. Simplified methods could be effectively applied to preliminary design, parametric study, and extensive analyses to save computation time.
This study includes two parts: 1) simplified seismic analyses of inelastic asymmetric-plan buildings with linear viscous dampers, and 2) simplified seismic analyses of elastic asymmetric-plan buildings with nonlinear viscous dampers. In the first part, the multi-degree-of-freedom (MDOF) modal stick with supplemental damping is constructed using a general purpose nonlinear dynamic response analysis program PISA3D. The stated MDOF modal sticks, instead of the conventional single-degree-of-freedom (SDOF) modal sticks, are used in the uncoupled modal response history analysis procedures. In the second part, two simplified methods, including the predictor-corrector method (PC) and the effective-damping-coefficient method (EDC), are proposed to solve the MDOF modal equations of motion. The PC method first predicts the velocity of the nonlinear term, then corrects the unbalanced force at the next time step. The EDC method computes the damping coefficient of the equivalent linear viscous damper corresponding to each nonlinear viscous damper at each time step. The MDOF modal equations of motion resulting from the equivalent linear viscous dampers instead of the nonlinear viscous dampers are solved by using step-by-step integration method. The Newmark-βmethod are implemented by using the MATLAB program.
In this study, the seismic responses computed from the complete finite element models of buildings are considered as the exact solution. Most of the seismic responses obtained from the proposed simplified method in the first part of this study are more accurate than those obtained from the other conventional simplified method. In addition, the proposed simplified method captures the trend of dynamic responses much better than the other simplified method. In the second part of this study, both the PC and EDC methods perform satisfactorily when the damping exponent η is less than or equal to one. When η is more than one, the accuracies of the estimated responses resulting from both methods decrease significantly. The EDC method is better than the PC method in capturing the decayed responses occurred after the main excitation of earthquakes. These two simplified methods significantly improve the computation efficiency. The computation times by using the EDC and PC methods are about 16% and 8%, respectively, of that cost by analyzing the complete finite element models of buildings.

目錄
論文口試委員審定書........................................................................................................i
致謝...................................................................................................................................ii
摘要..................................................................................................................................iii
Abstract...........................................................................................................................iv
目錄..................................................................................................................................vi
表目錄............................................................................................................................viii
圖目錄..............................................................................................................................xi
第一章 緒論 1
1.1 研究動機 1
1.2 文獻回顧 2
1.3 論文架構 5
第二章 具線性阻尼器之非彈性平面不對稱建築的簡化分析 6
2.1 簡介 6
2.2 分析方法 6
2.3 單向平面不對稱建築之分析驗證 22
2.3.1 建築模型及地震歷時之介紹 22
2.3.2 分析結果比較 26
2.4 雙向平面不對稱建築之分析驗證 27
2.4.1 建築模型及地震歷時之介紹 27
2.4.2分析結果比較 28
2.5 誤差來源分析 30
第三章 具非線性阻尼器之彈性平面不對稱建築的簡化分析 32
3.1 簡介 32
3.2 分析方法 32
3.2.1 預測修正法(Predictor-Corrector Method) 32
3.2.2 等效阻尼係數法(Effective Damping Coefficient Method) 41
3.3 單向平面不對稱建築之分析驗證 42
3.3.1建築模型及地震歷時之介紹 42
3.3.2分析結果比較 42
3.4 雙向平面不對稱建築之分析驗證 44
3.4.1建築模型及地震歷時之介紹 44
3.4.2分析結果比較 45
3.5 誤差來源探討 46
第四章 結論與建議 50
4.1 結論 50
4.2 建議 51
參考文獻 53

[1]內政部營建署，「建築物耐震設計規範與解說」，營建雜誌社，2011。
[2]李鴻晶，王通，廖旭 (2011)，「關於Newmark-γ,β法機裡的一種解釋」，地震工程與工程震動，第31卷 第2期。
[3]周錫元，俞瑞芳 (2006)，「非比例阻尼線性體系基於規範反應譜的CCQC法」，工程力學，第23卷 第2期。
[4]俞瑞芳，周錫元 (2006)，「具有過阻尼特性的非比例阻尼線性系統的複振型分解法」，建築結構學報，第27卷 第1期。
[5]郭哲英，李青寧 (2007)，「Newmark精細積分格式及其在地震反應分析中的應用」，地震工程與工程震動，第27卷 第4期。
[6]游宜哲 (2006)，「物件導向非線性靜動態三維結構分析程式之擴充」，國立台灣大學土木工程研究所碩士論文，蔡克銓教授指導。
[7]蔣通，賀磊 (2007)，「非線性黏滯阻尼器消能結構設計方法探討」，世界地震工程，第23卷 第1期。
[8]Chopra, A. K., and Goel, R. K., (1999), “Capacity-Demand-Diagram Methods Based on Inelastic Design Spectrum”, Earthquake Spectra, vol. 15, No. 4, 637-656.
[9]Chopra, A. K., and Goel, R. K., (2002), “A Modal Pushover Analysis Procedure for Estimating Seismic Demands for Buildings”, Earthquake Engineering and Structural Dynamics, vol. 31, 561-582.
[10]Chopra, A. K., and Goel, R. K., (2004), “A Modal Pushover Analysis Procedure to Estimate Seismic Demands for Unsymmetric-Plan Buildings”, Earthquake Engineering and Structural Dynamics, vol. 33, 903-927.
[11]Chopra, A. K. (2007), “Dynamic of Structures: Theory and Applications to Earthquake Engineering”, Prentice Hall, 3rd ed., Englewood, Cliffs, N J.
[12]Federal Emergency Management Agency (FEMA) (1995), NEHRP Recommendation Provisions for the Development of Seismic Regulations for New Building, Volumn1 and 2, Washington, D.C.
[13]Goel, R. K. (2001), “Simplified Analysis of Asymmetric Structures with Supplemental Damping”, Earthquake Engineering and Structural Dynamics, vol. 30, 1399-1416.
[14]Gupta, A. and Krawinkler, H. (1999), “Seismic demands for performance evaluation of steel moment resisting frame structures.” (SAC task 5.4.3), Report No. 132, John A. Blume Earthquake Engineering Center, Department of Civil and Environmental Engineering, Stanford University, Stanford, CA, U.S.A.
[15]Lin, B. Z., Yu, Y. J., Chuang, M. C., and Tsai, K. C., (2011), “PISA3D Standard Edition R3.2 User’s Manual”, National Center for Research on Earthquake Engineering, Taiwan Department of Civil Engineering, National Taiwan University.
[16]Lin, J. L., and Tsai, K. C., (2007a), “Simplified Seismic Analysis of Asymmetric Building Systems”, Earthquake Engineering and Structural Dynamics, vol. 36, 459-479.
[17]Lin, J. L., and Tsai, K. C., (2007b), “Simplified Seismic Analysis of One-Way Asymmetric Elastic Systems with Supplemental Damping”, Earthquake Engineering and Structural Dynamics, vol. 36, 783-800.
[18]Lin, J. L., and Tsai, K. C., (2008), “Seismic Analysis of Two-Way Asymmetric Building Systems under Bi-Directional Seismic Ground Motions”, Earthquake Engineering and Structural Dynamics, vol. 37, 305-328.
[19]Lin, J. L., Tsai, K. C., and Miranda, E., (2009a), “Seismic History Analysis of Asymmetric Buildings with Soil–Structure Interaction”, ASCE journal, vol. 135, No. 2, 101-112.
[20]Lin, J. L., Tsai, K. C., and Yang, W. C., (2012a), “Inelastic Responses of Two-Way Asymmetric-Plan Structures under Bidirectional Ground Excitations—Part I: Modal Parameters”, Earthquake Spectra, vol. 28, No. 1, 105-139.
[21]Lin, J. L., Yang, W. C., and Tsai, K. C., (2012b), “Inelastic Responses of Two-Way Asymmetric-Plan Structures under Bidirectional Ground Excitations—Part II: Response Spectra”, Earthquake Spectra, vol. 28, No. 1, 141-157.
[22]Lin, J. L., and Tsai, K. C., (2013) “Application of Supplemental Damping Characteristics to Response Spectrum Analyses of Non-Proportionally Damped Multi-Story Asymmetric-Plan Buildings”, Earthquake Spectra, vol. 29, No. 1, 207-232.
[23]Lin, J. L., Tsai, K. C., Chuang, M. C., (2013) “Effective Oscillators for the Seismic Analysis of Inelastic One-Way Asymmetric-Plan Buildings”, Engineering Structures, vol. 52, 38-52.
[24]Martinez-Rodrigo, M., and Romero, M. L., (2003), “An Optimum Retrofit Strategy for Moment Resisting Frames with Nonlinear Viscous Dampers for Seismic Applications”, Engineering Structures, vol. 25, 913-925.
[25]McGuire, W., Gallagher, R. H., and Ziemian, R. D., (1999), “Matrix Structural Analysis”, John Wiley & Sons, Inc., 2nd ed..
[26]Pekcan, G., Mander, J. B., and Chen, S. S., (1999), “Fundamental Considerations for the Design of Non-linear Viscous Dampers”, Earthquake Engineering and Structural Dynamics, vol. 28, 1405-1425.
[27]Song, J., Chu, Y. L., Liang, Z., and Lee, G. C., (2008), “Modal Analysis of Generally Damped Linear Structures Subjected to Seismic Excitations”, Technical Report MCEER-08-0005.
[28]Tsai, K. C., and Li, J. W. (1994), “DRAIN2D, A General Purpose Computer Program for Static and Dynamic Analyses of Inelastic 2D Structures, Supplemented with a Graphic Processor, VIEW2D, User’s Guide”, CEER/R83-03, Center for Earthquake Engineering Research, National Taiwan University.
[29]UBC (1997). “Uniform Building Code”, International Conference of Building Officials, Volumn2, Whittier, CA.
[30]Warburton, G. B., and Soni, S. R., (1977), “Errors in Response Calculations for Non-Classically Damped Structures”, Earthquake Engineering and Structural Dynamics, vol. 5, 365-376.
[31]Yang, W. C., Lin, J. L., and Tsai, K. C. (2011a), “Inelastic Response Spectra for Two-Way Asymmetric-Plan Structures under Bi-Directional Ground Excitations”, NCREE-11-009, National Center for Research on Earthquake Engineering.
[32]Yang, W. C., Lin, J. L., and Tsai, K. C. (2011b), “Inelastic Response Spectra for Asymmetrical Structures (SAS) – Program User’s Manual”, NCREE-11-010, National Center for Research on Earthquake Engineering.
[33]Zhou, X. Y., Yu, R. F., and Dong, D., (2004), “Complex Mode Superposition Algorithm for Seismic Response of Non-Classically Damped Linear MDOF System”, Beijing University of Technology, Pingleyuan No. 100, Beijing, 100022, P. R. China.