角型或L型等幾何不對稱結構於強震作用下，常因質量中心與勁度中心不重合致產生頗大之扭力變形，並進而造成結構之毀損，由於結構之偏心方向與大小，不但受其內部剪力牆配置之影響，亦且與其外部之幾何形狀有關，因此本文將針對L型高層含牆結構，於不同地震力作用方向、不同下部結構埋設深度及不同土壤性質下之受震力行為，從事系統性之縝密分析，期能充分了解此類結構之扭力變形特性；於其間，有效之3-D土壤-結構互制模式將予採用，而結構之版、牆元件則將以退化殼元素（degenerated shell element）模擬之，俾能求得更真實之受震反應。研究結果顯示，結構之扭矩效應將隨其地下埋設深度與土壤鬆軟程度之增加，而愈形舒緩。

Highly asymmetric structures would usually exhibit significant torsional effects arising from the non-coincidence of mass and shear centers, when subjected to a strong ground excitation. Since the significance of structural asymmetry not only depends upon the inner layout of shear walls but also affects by the outer geometric shape, a multistory walled building with a plane view of the L letter will be investigated in detail so as to detect its seismic behaviors under various parameters containing the acting direction of seismic force, the embedded depth of the structure and the property of the soil. Furthermore, to fully comprehend the characteristics of torsional deformations, a family of degenerated shell elements will be used for modeling the wall as well as the slab, and an elaborated soil-structure model is utilized in analyses. It is shown in the results that the torsional effects would be relieved following the increase of either embedded depth or the soft extent of the soil.

中文摘要	I
英文摘要	II
本文目錄	III
表目錄	V
圖目錄	VI
符號說明	VIII
第一章 前言	1
第二章 不對稱結構之有限元素模擬	6
第2-1節  退化殼元素	6
§2-1-1  幾何形式與位移函數之關係	7
§2-1-2  應變場之定義	10
§2-1-3  彈性矩陣	14
§2-1-4  勁度矩陣與質量矩陣之合成	15
第2-2節  空間樑柱元素	16
§2-2-1  勁度矩陣	17
§2-2-2  質量矩陣	18
§2-2-3  轉置矩陣	19
第三章 不對稱結構之扭矩極值推導	22
第3-1節  運動方程式之建立	22
第3-2節  扭矩極值之理論推導	27
第四章 不對稱結構震力分析與討論	29
第4-1節  剪力牆厚度之影響	30
第4-2節  下部結構樓層數之影響	31
第4-3節  土壤性質之影響	32
第五章 結論與展望	34
第5-1節  結論	34
第5-2節  展望	35
參考文獻	36
附表	41
附圖	42
附錄	57



表目錄 表4 - 1 樑、柱、牆與樓版之材料與斷面性質..............................................41 表4 - 2 土壤之材料性質.................................................................................41

圖目錄 圖2-1 四點shell元素 (a)整體座標系統 (b)、(c)、(d)局部座標 系統................................................................................................42 圖2-2 假設於自然應變場下之插補函數(interpolation functions) 與插補點.........................................................................................43 圖2-3 插補點對應於應變分量之修正.....................................................43 圖2-4 空間樑柱元素對應元素座標之位移..............................................44 圖2-5 空間樑柱元素對應元素座標之節點力..........................................44 圖2-6 空間樑柱元素局部座標x-y-z與大域座標X-Y-Z之關係............44 圖3-1 不對稱結構示意圖.........................................................................45 圖4-1 平面配置圖（a）上部結構（b）下部結構..................................45 圖4-2 含近域土壤之3-D結構模式.........................................................46 圖4-3 近域土壤有限元素模式.................................................................46 圖4-4 集集地震﹙TCU084﹚E-W向地表加速度歷時圖........................47 圖4-5 集集地震﹙TCU084﹚傅氏頻譜圖................................................47 圖4-6 集集地震﹙TCU084﹚擬加速度反應譜………….………………48 圖4-7 L型結構與地震輸入角λ之關係..................................................48 圖4-8 剪力牆厚度為20cm時，頂層柱A、B、C之層間扭轉角..........49 圖4-9 剪力牆厚度為30cm時，頂層柱A、B、C之層間扭轉角..........49 圖4-10 剪力牆厚度為40cm時，頂層柱A、B、C之層間扭轉角..........50 圖4-11 頂層柱A於不同剪力牆厚度下之層間扭轉角……......................50 圖4-12 頂層柱B於不同剪力牆厚度下之層間扭轉角.............................51 圖4-13 頂層柱C於不同剪力牆厚度下之層間扭轉角.............................51 圖4-14 不同土壤性質時，考慮不同剪力牆厚度下各樓層柱A 之層間扭轉角.................................................................................52 圖4-15 不同土壤性質時，考慮不同剪力牆厚度下各樓層柱A延 X向之層間位移.............................................................................52 圖4-16 考慮或未考慮下部結構時產生於頂層柱A延X向之位移 歷時圖............................................................................................53 圖4-17 考慮或未考慮下部結構時產生於頂層柱A之層間扭轉角 歷時圖............................................................................................53 圖4-18 不同埋設深度時，考慮不同土壤性質下頂層柱A之層間 扭轉角............................................................................................54 圖4-19 不同埋設深度時，考慮不同土壤性質下各樓層柱A之層 間扭轉角.........................................................................................54 圖4-20 不同埋設深度時，考慮不同土壤性質下各樓層柱A延X 向之層間位移.................................................................................55
圖4-21 考慮埋設深度一層時，頂層柱A於不同土壤性質下之 層間扭轉角.....................................................................................55 圖4-22 考慮埋設深度二層時，頂層柱A於不同土壤性質下之 層間扭轉角.....................................................................................56 圖4-23 考慮埋設深度三層時，頂層柱A於不同土壤性質下之 層間扭轉角.....................................................................................56

1.	Hejal, Reem and Chopra, Anil K., “Lateral-Torsional Coupling in Earthquake Response of Frame Buildings,” Journal of Structural Engineering, Vol.115, No. 4, Apr. 1989, pp.852-867.
2.	Reem Hejel and Anil K. Chopra “Earthquake Analysis of A Class of Torsionally-Coupled Buildings” Earthquake Engineering and Structure Dynamic, July, 1989, Vol.18, pp.305-323。
3.	Michel Bruneac and Stephen A. Mahin “Normalizing Inelastic Seismic Response of Structure Having Eccentricities in Plan” Journal of Structural Engineering, May, 1991, Vol.116, pp.3358-3378.
4.	Tsuneyoshi Nakamura and Yutaka Nakamura “Stiffness Design of 3-D Shear Building for Specified Seismic Drifts” Journal of Structural Engineering,  January, 1993, Vol.119, pp.49-61.
5.	David Johnson and Ali Nadjai “Elastoplastic Analysis of Spatial Shear Wall Systems by A Discrete Force Method” Structure Engineering Review, 1996, Vol.8, No.4, pp.345-356.
6.	S. C. Ng and J. S. Kuang “Triply Coupled Vibration of Asymmetric Wall-Frame Structures” Journal of Structural Engineering, August, 2000, Vol.126, No.8, pp.982-987.
7.	S. C. Ng and J. S. Kuang “Dynamic Coupling of Asymmetric Shear Wall Structures: An Analytical Solution” International Journal of Solids and Structures, Vol.38, No, 48-49, Nov 16, 2001, pp.8723-8733.
8.	李紀州, “RC剪力牆對受損L型結構物補強之耐震行為” 國立中興大學土研所碩論, 2002年6月。
9.	黃裕智, “質量偏心與強度偏心之互制效應” 國立台灣科技大學營建所碩論, 2003年7月。
10.	Quanfeng Wang, Lingyun Wang and Qiangsheng Liu, “Effect of Shear Wall Height on Earthquake Response” Engineering Structures, Vol.23, Issue.4, April, 2001, pp. 376-384.
11.	H. S. Kim and D. G. Lee, “Analysis of Shear Wall with Opening Using Super Elements” Engineering Structures, Vol.25, Issue.8, July, 2003, pp. 981-991.
12.	Ahman, S.、Irons, B. M. and Zienkiewics, O. C., “Analysis of thick and thin shell structures by curved finite elements”, International Journal for Numerical Methods in Engineering, Vol. 2, No 3, pp 419-451, 1970.
13.	Zienkiewics, O. C.、Taylor, R. L. and Too, J. M., “Reduced integration technique in general analysis of plates and shells”, International Journal for Numerical Methods in Engineering, Vol. 3, No 2, pp 275-290, 1971.
14.	Dvorkin, E. N. and Bathe, K. J., “A coutinuum mechanics based four-node shell element for general non-linear analysis”, Engineering Computations, Vol. 1, No 1, pp 77-88, 1984.
15.	Park, N. C. and Stanley, G. M., “A curved C°shell element based on assumed natural-coordinate strains”, Journal of Applied Mechanics, Vol. 53, No 2, pp 278-290, 1986.
16.	Choi, C. K. and Paik, J. G., “An Effective four node degenerated shell element for geometrically nonlinear analysis”, Thin-Walled Structures, Vol. 24, No 3, pp 261-283, 1996.
17.	Prasad, N. S. and Sridhar, S., “Elasto-plastic analysis using shell element considering geometric and material nonlinearities”, Structural Engineering and Mechanics, Vol. 6, No 2, pp 217-227, 1998.
18.	Yang, H. T., “A survey of recent shell finite elements”, International Journal for Numerical Methods in Engineering, Vol. 47, No 1, pp 101-127, 2000.
19.	邱乾艷, “三維殼元素於有限元素法之架構” 國立成功大學土研所碩論, 2002年6月。
20.	Tsicnias T. G. and Hutchinson G. L., “Soil-Structure Interaction Effects on the Steady-State Response of Torsionally Coupled Buildings” Earthquake Engineering and Structural Dynamics, Vol.12, No.2, Mar-Apr, 1984, pp.237-262.
21.	Gupta V. K. and Trifunac M. D., “Seismic Response of Multistoried Buildings Including the Effects of Soil-Structure Interaction” Soil Dynamics and Earthquake Engineering, Vol.10, No.8, Nov., 1991, pp.414-422.
22.	Wolf J. P. and Song C., “Dynamic-Stiffness Matrix In Time Domain of Unbounded Medium by Infinitesimal Finite Element Cell Method,” Earthquake Engineering and Structural Dynamics, Vol.23, No.11, Nov.,  1994, pp.1181-1198.
23.	Song C. and Wolf J. P., “Consistent Infinitesimal Finite-Element-Cell Method: Out of Plane Motion,” Journal of Engineering Mechanics, Vol.121, May, 1995, pp. 613-619.
24.	Wolf John P. and Song C., “Consistent Infinitesimal Finite-Element Cell Method: In-Plane Motion,” Computer Methods in Applied Mechanics and Engineering, Vol.123, Jun., 1995, pp.355-370.
25.	Wolf, J. P. and Song, C, “Consistent infinitesimal finite-element-cell method：three-dimensional vector wave equation”, International Iournal for Numerical Methods in Engineering, Vol. 39, No. 13, pp. 2189-2208, 1996.
26.	H. Shakib and A. Fuladgar, “Dynamic Soil-Structure Interaction on the Seismic Response of Asymmetric Buildings” Soil Dynamics and Earthquake Engineering, Vol.24, Issue.5, 2004, pp. 379-388.