PC梁現有預力之有限元素反算法

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姓名

紀秉良(Ping-Liang Chi) 查詢紙本館藏

畢業系所

土木工程學系

論文名稱

PC梁現有預力之有限元素反算法
(Backward Finite Element Analysis of the Existing Prestress of PC Beam)

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摘要(中)

本論文使用有限元素法，模擬單股後拉預力混凝土梁受預力或外力作用的撓度變化，並利用撓度反算現有預力，計算使用自行撰寫的物件導向 C++程式，其名為 PCBAP (預力混凝土梁分析程式，Prestressed Concrete Beam Analysis Program)。撓度分析分成兩個階段：預力加載階段、服務階段。預力加載階段是模擬預力施加後結構上拱行為，計算流程可拆解成三個部分：第一部分計算鋼腱的摩擦損失與夾片滑動損失，決定鋼腱任意斷面處的內力狀態。第二部分將梁元素節點位置的鋼腱內力轉化為等值節點力，加載至結構上。第三部分進行有限元計算，求解元素節點的位移。服務階段則是模擬預力結構物於承載外部作用力的撓度反應，計算流程可化為兩個部分：第一部分藉由 Kim 的等效撓曲剛度公式，模擬預力加勁後的梁體。第二部分施加外荷載進行有限元計算，求解元素節點的位移。全文緊扣著兩階段的分析概念，而反算現有預力則是不斷的重複正算步驟，當迭代出最接近實驗撓度的結果，其計算收斂結束並輸出現有預力的數值。

本研究致力於物件導向程式的設計，PCBAP 程式是直指著高擴充性此目標，孕育而生的預力梁結構分析軟體，在第三章會針對程式的架構及物件(object)的抽象化作詳細的說明。PCBAP 程式所具備的功能有：摩擦損失和夾片滑動損失後的起始預力分布計算、桿系結構的撓度分析、預力混凝土梁的撓度分析、預力混凝土梁的現有預力反算，這些功能會在各章節的算例作驗證，與 SAP2000 的模擬結果、簡支預力梁的靜載實驗作比對。在模擬實驗的過程中發現，正算撓度能很好的符合實驗量測的結果，但是反算預力卻不盡理想，這歸咎於結構撓度隨預力大小變化的升降幅度非常小，也就是撓度對預力此物理量的敏感度很低，這也是反算預力算不準的主要原因。

摘要(英)

This thesis aims at studying the deflection behavior of post-tensioning prestressed concrete beam with single tendon and using the structural deflection to calculate the existing pre-forced.The finite element program which coded by the object-oriented language C++ and named it
PCBAP (Prestressed Concrete Beam Analysis Program).Structural deflection analysis is divided into two phases: the preload phase and the service phase. The preload phase simulates the arching behavior of the structure after the prestressing force is applied. The calculation process can be divided into three parts : the first part, the friction loss and the anchor slip loss
are calculated and then initial prestressing force value of any section is obtained. In the second part, the internal force of the tendon at the position of the beam element’s node is converted into the equivalent nodal force and loaded onto the structure. The third part performs finite element calculations to solve the displacement of element nodes. The service phase is to
simulate the bearing performance of the PC structure. The calculation process can be divided into two parts: the first part considers the PC beam strengthened by the equivalent bending rigidity formula of Kim. The second part applies an external load to the finite element model to solve the displacement of the element nodes. The full text is closely linked to the two-stage analysis concept, and the calculation of the existing pre-forced is completed by repeating the positive calculation steps. The simulation result of the existing pre-forced is closest to the result of the experimental deflection.
This research is devoted to the design of the object-oriented program.
The PCBAP program focus on the high-expansion of the goal and then the PC beam structure analysis software is born. In the chapter 3, the frame of the program and the abstraction of the object are discussed in detail. The functions of the PCBAP program include: the initial pre-force distribution calculation after friction loss and the anchor slip loss, deflection analysis of the rod
structure, deflection analysis of the PC beam, and existing pre-force calculation of the PC beam. These functions will be verified in each chapter and the simulation is compared with the results of SAP2000 and the static load test of the simple supported PC beam. During the simulation of experiment, it is found that the calculation deflection can be in good accordance with the
experimental measurement results, but the inverse-calculation existing pre-forced is not ideal. This is attributed to the fact that the scale of the deflection is smaller than the scale of the pre-forced. That is, the sensitivity of the deflection to the pre-forced physical quantity is very low, which is also the main reason for the inaccuracy of the inverse-calculation.

關鍵字(中)

★ 後拉預力梁
★ 現有預力
★ 反算

關鍵字(英)

★ post-tensioning prestressed concrete beam
★ existing pre-forced
★ inverse problem

論文目次

第一章緒論 1
1-1 研究動機 1
1-2 研究目的 2
1-3 文獻回顧 3
1-4 內容大綱 7
第二章預力混凝土梁之預力損失 9
2-1 先拉式與後拉式預力混凝土梁 9
2-1-1 先拉式預力 10
2-1-2 後拉式預力 10
2-2 鋼腱預拉應力損失 12
2-2-1 摩擦損失 14
2-2-2 夾片滑動損失 19
2-2-3 彈性縮短及長期損失 24
2-3 計算例題 25
2-4 小結 30
第三章有限元素分析法 34
3-1 引言 34
3-2 平面桁架元素 35
3-2-1 局部坐標系中的元素勁度矩陣 35
3-2-2 整體坐標系中的元素勁度矩陣 37
3-3 平面梁元素 39
3-3-1 局部坐標系下的元素勁度矩陣 39
3-3-2 整體坐標系中的元素勁度矩陣 41
3-3-3 處理鉸接點 43
3-3-4 引入支承約束條件 46
3-3-5 轉化非節點荷載 48
3-4 物件導向有限元程式設計方法 49
3-4-1 鋼腱線型類 51
3-4-2 鋼腱類 54
3-5 算例與小結 62
第四章預力混凝土梁有限元素分析 66
4-1 等效荷載法 66
4-2 等效剛度 76
4-3 預力混凝土結構撓度分析 79
4-3-1 預拱計算 81
4-3-2 外力加載撓度計算 83
4-4 靜力反算法 84
4-4-1 以預拱反算 85
4-4-2 以外力造成的撓度反算 87
4-5 其他算例探討 89
4-6 小結 97
第五章結論與建議 100
5-1 結論 100
5-2 建議 102
參考文獻 103
附錄一非線性有限元素分析 106
附 1-1 引言 106
附 1-2 基本假定 107
附 1-3 材料應力-應變關係 107
附 1-4 梁元素勁度矩陣推導 109
附 1-4-1 元素位移模式 110
附 1-4-2 元素截面分析 112
附 1-4-3 元素切線勁度方程式 116

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指導教授

王仲宇(Chung-Yue Wang)

審核日期

2018-7-12

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