向量式有限元應用於含功能性支承橋梁數值模擬分析

Numerical Analysis of Bridges with Functional Bearing System Using Vector Form Intrinsic Finite Element

黃文絹(Wen-Chuan Huang)

指導教授 ： 張國鎮

國立臺灣大學/工學院/土木工程學研究所/碩士(2014年)

https://doi.org/10.6342/NTU.2014.01631

摘要

本研究旨在提出功能性支承模型，並將此模擬方法應用向量式有限元素法來探討含功能性支承橋梁在地震下之力學行為。功能性支承具有限制位移、滑動摩擦消能、最適止震塊、足夠的滑動位移及足夠防落長度等特點；在強震下為了避免落橋，防落長度的決定極為重要，然而，在過去分析研究中顯示，採用傳統橡膠支承墊之數值模擬方式，其分析結果中，並無法透過支承之相對位移來判斷其滑動量之大小，甚至會有塑性殘留位移的現象，導致無法判斷分析結果之殘留位移是來自於塑性殘留，亦或是摩擦滑動，故在本研究中提出新的功能性支承模擬方式，為功能性支承模型(Function Bearing Model , FBM)，藉由此數值模擬，能將支承之相對位移分離成橡膠本身之剪變形，以及支承摩擦滑動量，希望藉由提出之功能性支承模型，能有效判斷支承之滑動量，使未來對於防落長度之判斷能更精準。
本研究首先透過SAP2000之靜力分析與動力分析，並與摩擦係數試驗與振動台試驗結果比對，證明功能性支承模型之可行性，而分析結果顯示，此模型能將支承之位移，分離成橡膠自身的彈性位移與支承滑動量，確實達到模型開發時之要求。然而，在分析過程中顯示SAP2000並無法有效考慮速度對於摩擦係數之影響，導致分析所預測之最大反應並無法與試驗結果相符，且SAP2000之非線性分析中並未考慮結構之幾何非線性現象，即無法針對橋梁發生落橋或是碰撞等非線性大變形行為進行分析。故將FBM應用於向量式有限元素法(Vector Form Intrinsic Finite Element, VFIFE)中，首先透過數值算例驗證VFIFE程式中基本元素之準確性、結構幾何大變形功能以及元素斷裂功能，並透過與振動台試驗結果比較，證明VFIFE程式對於單垮含功能性支承橋梁分析之可行性，最後針對支承滑動量過大時，導致橋梁發生落橋現象之案例，進行數值算例驗證，其分析結果顯示VFIFE確實可達到預期之落橋行為。

關鍵字

功能性支承 ； 橡膠支承墊 ； 支承墊滑動 ； 向量式有限元素法

並列摘要

A functional bearing model (FBM) of the bridge is proposed in this research and is applied to Vector Form Intrinsic Finite Element (VFIFE) software to analyze the bridge under seismic loading. Functional bearing system employs displacement limit device to restrict the bridge’s horizontal displacement and dissipate seismic energy through the frictional sliding mechanism. To avoid bridge-falling, the gap between the bridge and bridge-collapse prevention devices is very important. However, in the past research analysis, it’s hard to obtain the bearing’s sliding displacement through the traditional simulation method about rubber bearing. In addition, the displacement obtained by the traditional method includes the residual plastic displacement, which is undesirable in the analysis. Due to the difficulty mentioned above, this research proposes a new simulation method for rubber bearing, called functional bearing model (FBM). It can separate the deformation of bearing into rubber shear deformation and frictional sliding displacement. Therefore, the amount of the gap between the bridge and bridge-collapse prevention devices can be determined clearly.
Structural analysis program SAP2000 is used to build a bridge model. Comparisons between the numerical model and three test results including the frictional coefficient test and shaking table tests are discussed. The comparison results showed that the proposed method is feasible in both static and dynamic analysis. However, neither the influence of the sliding velocity on the friction coefficient nor the geometric nonlinearity can be considered by SAP2000. As a consequence, the prediction of the maximum response doesn’t agree with the experiment result. Also, the non-linear large deformation behavior is not considered, so the bridge-falling or pounding behavior cannot be simulated. In order to obtain the analytical results about bridge-falling mechanism, FBM was applied to VFIFE method. Several examples were built in VFIFE to verify the accuracy of basic element, the non-linear large deformation function and the element fracture function at first. Then manifest the feasibility of VFIFE through comparing the test results and the analytical results of the shaking table test. Finally, the bridge-falling analytical results show that the VFIFE can predict the bridge-falling phenomenon which is due to excessive friction displacement of bearings.

並列關鍵字

Functional bearing systems ； Rubber bearing ； Bearing sliding ； Vector Form Intrinsic Finite Element Method

參考文獻

[6] 陳皇嘉（2005），裝設橡膠支承墊於橋梁縮尺模型之試驗與分析，國立台灣大學土木工程學研究所碩士論文。

[10] 鄭維晉(2011)，裝設橡膠支承墊之斜橋縮尺模型試驗，國立台灣大學土木工程學研究所碩士論文。

[11] 盧智宏（2011），含功能性支承橋梁位移設計法之研究，國立台灣大學工程學研究所博士論文。

[34] 曾子俊(2014)，橋梁含功能性支承與直接基礎之振動台試驗研究，國立台灣大學土木工程學研究所碩士論文。

[4] American Association of State Highway and Transportation Officials. Standard Specifications for Highway Bridges. 17th Edition. Washington, D.C. :2002.