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研究生： 連寬宏
Lien, Kuan-Hung
論文名稱： 高溫環境下鋼結構之向量式有限元分析
Vector Form Intrinsic Finite Element Analysis of Steel Structures Exposed to Fire
指導教授： 邱耀正
Chiou, Yaw-Jeng
學位類別： 博士
Doctor
系所名稱： 工學院 - 土木工程學系
Department of Civil Engineering
論文出版年： 2009
畢業學年度： 97
語文別： 中文
論文頁數： 191
中文關鍵詞： 半剛性接頭 、向量式有限元素法 、斷裂 、冷卻 、火害 、鋼結構
外文關鍵詞： cooling effect, semi-rigid joint, fire, Vector Form Intrinsic Finite Element (VFIFE), fracture, steel structures
相關次數： 點閱：93  下載：5 
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    • 本文以向量式有限元素法之理論為基礎，加入熱應變效應，建立平面鋼結構在高溫環境下的數值分析模式。該法有別於傳統的結構分析方法，其計算程序屬向量力學，不需建立結構勁度矩陣亦不需任何的迭代計算。文中同時考慮材料與幾何非線性行為，依鋼材之溫度－應力－應變曲線，以及分別考量升溫與降溫階段之應力變化模式，追蹤平面剛架元素在溫度作用過程中內力的變化結果，以探討鋼結構受火害之行為。另外，本研究進一步將結構接頭以二結點、多自由度彈簧系統、無質量僅具勁度性質之零長度虛擬元素模擬。建立一個可同時考慮軸力、剪力與彎矩具半剛性效應之廣義接頭分析模式，可適用於各種不同類型之接頭，進而擴展向量式有限元素法的應用範圍。
    本文所建立的分析模式，皆先與文獻中相關之數值算例，以及試驗研究結果比較，再進行數值範例研討，以確保分析模式與計算機程式之正確性。經大量且廣泛的驗證結果，顯示本文所建立的鋼結構火害分析與廣義接頭模式結果良好，可有效模擬鋼結構各種不同接頭形式，以及鋼結構受火害過程，分別在升溫與冷卻降溫階段的結構行為。最後，根據本文建立之數值分析模式，分別討論了不同邊界條件對結構在升溫與冷卻階段行為的影響、伴隨地震引發火災與桿件斷裂之結構行為、拱狀結構承載能力隨溫度上升而增加的特殊現象，與結構在火場中桿件逐漸失效之破壞歷程等目前文獻中較少觸及之議題。

    This study adopted the Vector Form Intrinsic Finite Element (VFIFE) method to investigate the nonlinear behavior of steel structures during the heating as well as the cooling phases of fire, and trace the changes in internal element force. The temperature dependent constitutive relations of steel which include strain reversal effects are adopted, and the two-dimensional frame element is employed. In addition, the steel frames with semi-rigid joints are investigated by the method. The structural connections are modeled by the two-node multi-degree of freedom spring system and dummy element with stiffness but without actual mass and length. The proposed model can simulate various joints, and the application of VFIFE was widely extended.
    The numerical model is first verified by comparing the results with the published experimental and analytical results for steel structures. The fire responses of structures, such as the axial restraining effect, buckling of shallow arch, catenary action, fracture of elements in fire caused by an earthquake, cooling effect, and failure behaviors of different members in a fire, are then fully studied. The proposed numerical model can effectively predict the nonlinear behavior of the steel structure in both heating and cooling phases.
    The numerical results also show that the elastic bearing capacity of shallow arch rises with the increase in temperature. The shallow arch deflects upward before buckling with increasing temperature, and its deflection is much smaller than that of the beam structure with the same span. The structure deflects downward after buckling and shows catenary action when it is re-balanced. In the case of fire induced by an earthquake, the deformation of the structure is significantly affected by the aftershock, fire, and fracture of structural elements. In addition, the steel beam without axial constraint will seriously distort due to large displacement when the temperature reaches the critical value. In contrast, the steel beam with axial constraint will suppress the displacement effectively due to the catenary action. However, structures with constraints in fires will induce thermal stresses, and the members of those structures will reach the plastic stage at lower temperatures when they are cooled to room temperature. This phenomenon indicates that these structures will probably reach the plastic phase in the early stage of a fire, and induce a considerable permanent deformation that causes great damage even the fire is put out.

    摘要 I Abstract II 誌謝 IV 目錄 V 表目錄 VIII 圖目錄 IX 第一章 緒論 1 1.1 研究動機 1 1.2 研究方法與目的 3 1.3 論文內容與架構 8 第二章 高溫環境下鋼材性能資料 10 2.1 前言 10 2.2 國外高溫環境下鋼材性能資料 10 2.2.1 降伏強度與彈性模數 11 2.2.2 熱膨脹係數 14 2.2.3 單位質量 15 2.3 國內高溫環境下鋼材性能資料 15 第三章 含溫度效應之向量式有限元分析 27 3.1 前言 27 3.2 向量式有限元素法 31 3.2.1 基本假設 31 3.2.2 移動基礎架構 32 3.2.3 基本方程式 33 3.2.4 常溫下平面剛架元素節點內力 35 3.2.5 具溫度效應平面剛架元素節點內力 38 3.2.6 桿件斷裂分析 42 3.3 高溫環境下鋼材之材料性質 44 3.4 數值分析模式與耐火試驗之驗證 45 3.4.1 簡支梁不同載重之耐火試驗 45 3.4.2 受壓鋼柱具軸向溫差之耐火試驗 46 3.4.3 鋼結構耐火試驗 47 3.5 不同軸向束制鋼梁之耐火行為 48 3.5.1 斷面溫度分佈之影響 48 3.5.2 懸鍊線效應 49 3.5.3 熱挫屈效應 50 3.6 單層雙跨鋼結構在不同火災情境下之行為 53 3.6.1 鋼結構局部受火行為 53 3.6.2 鋼結構全面受火行為 54 3.7 地震與火害聯合作用下之斷裂分析 54 3.7.1 單跨雙層鋼結構全面受火之地震與斷裂分析 55 3.7.2 五層三跨鋼結構局部受火之地震與斷裂分析 56 3.8 拱狀結構受火害行為分析 59 3.8.1 高溫環境下兩桿平面靜定桁架之彈性挫屈分析 60 3.8.2 Williams toggle frame高溫環境下之穩定性分析 61 3.8.2.1 定溫加載之彈性挫屈分析 61 3.8.2.2 桿件角度之影響 62 3.8.2.3 不同邊界條件之影響 63 3.8.2.4 定載升溫之非線性穩定性分析 64 3.8.3 淺拱之非線性穩定性分析 65 第四章 鋼結構火害後冷卻階段之行為 110 4.1 前言 110 4.2 冷卻階段材料組成率與溫度變化之關係 111 4.3 高溫環境下鋼材之材料性質 112 4.4 數值分析模式之驗證 112 4.4.1 斷面非均溫簡支梁火害後之數值分析 113 4.4.2 簡支梁含冷卻之耐火試驗 114 4.4.3 簡支柱含冷卻之耐火試驗 116 4.5 不同軸向束制鋼梁火害後之冷卻行為 118 4.6 鋼柱火害後之冷卻行為 120 4.7 五層三跨鋼結構火害後之冷卻行為 122 4.7.1 受局部火害鋼結構之定溫冷卻分析 123 4.7.2 鋼結構火害中桿件逐漸失效之歷時分析 124 第五章 結論與建議 144 參考文獻 149 附錄A：半剛性接頭之向量式有限元分析 161 A.1 前言 161 A.2 廣義接頭之運動方程式 163 A.3 結果與討論 166 A.3.1 含彈性支承柱之幾何非線性反應分析 166 A.3.2 含半剛性支承梁之靜力與動力幾何非線性反應分析 167 A.3.3 含半剛性接頭之單層門型剛架彈性挫屈分析 168 A.3.4 含半剛性接頭之雙層剛架彈性穩定性分析 169 A.3.5 Williams toggle frame之穩定性分析 169 A.3.6 含非線性柔性接頭與支承之鋼結構的分析 171 A.3.6.1 單層門型剛架之非線性分析 171 A.3.6.2 單跨三層剛架之非線性分析 172 A.3.7 含半剛性接頭非彈性平面剛架之斷裂分析 172

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