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 一般結構物，並非僅由梁柱系統來承受荷重及水平力，事實上，建築物通 常皆有樓板，且為加強抵抗水平力，而常使用剪力牆，以減少構架的側向 位移。但工程界分析時常只取梁柱來分析，將樓版視為剛性，但此作法並 不是很合理。為了進一步了解樓版及剪力牆之結構行為，本文以有限元素 法完成房屋結構之靜力與動力分析，其中梁與柱以古典梁及 Mindlin梁理 論模擬之，樓版以 Mindlin板分析，剪力牆則有兩種作法，其一以 Mindlin摺板分析之，另一法則為將其模擬成等效斜撐桿件來計算其效應 。本文首先驗證所發展元素的正確性：古典梁與 Mindlin梁元素、 Mindlin平板元素、摺板元素及平板附加加勁梁。在某些題目中，完成了 靜力分析、自由振動分析與動力分析（含阻尼與不含阻尼），並與以往文 獻或與教科書比較數值答案。最後將房屋結構模擬成梁柱結構，樓版則以 平板元素分析，剪力牆則以摺板或等效斜撐桿件分析之，以探討結構物之 靜力、自由振動及動力分析。本文有限元素法推導中，首先以最小勢能原 理推導得靜力分析的有限元素法控制方程式，繼而引入慣性力所產生的動 能，並以變分原理推導得自由振動分析與動力分析。阻尼矩陣則以雷利法 分析，由大域勁度矩陣及大域質量矩陣疊加而成。靜力分析乃以 skyline 法求解，自由振動分析則以subspace法解得特徵值為自然振動頻率，而動 力分析則分別以振態疊加法與 Newmark-.beta.法完成梁柱結構位移歷時 分析結果之驗證。在房屋結構模擬成梁柱結構加版、牆的題目中，為了減 少電腦時間，則僅以Newmark-.beta.法分析。
 The building structures consist of beams, columns, and floors. And, the shear wall is frequently used to resist the lateral seismic loadings. However, the buildings are usually modeled as beam-column systems and the floors are assumed to be rigid diaphrams in the structural design. The viewpoint is of course due to that a large amount of computing efforts can be reduced. To further study the behaviors of floors and shear walls, the finite element method is adopted in the static and dynamic analyses of structures in the thesis. The beams and columns are modeled by the classical beam theory and the Mindlin beam theory,respectively. The floors are modeled by the Mindlin plate theory. There are two models for the shear walls:the folded plate theory and the equivalent brace element. Several finite elements are developed:the classical beam element,the Mindlin beam element, the Mindlin plate element, the folded plate element and the plate reinforced by beam element. compared with the theoretical and the other finite element solutions, every element is validated through the static, the free vibration, and the dynamic analyses. Accurate results and fast convergence are found in the developed elements. In the present study, the static analysis is solved by the active column solver. the natural frequency is solved by the the subspace method, and the dynamic analysis is solved by the modal superposition method and the Newmark-.beta. method. After all the elements are validated, the damped dynamic responses of the building structures due to the Taipei earthquake(1986) are studied by several models: the space frame, the space frame with the floor, the space frame with the shear wall, the space frame with the floor and the shear wall. The effects of different models are studied for single span building, multilpe span building, one story building, and four story building, The effects of shear wall modeled by the plate element or the equivalent brace element are also compared.
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