考慮升溫與冷卻之鋼結構火害分析

Abstract

鋼材具有重量輕、強度高和韌性強等優點，由於施工快速並具有可回收性，因此鋼材在土木工程的應用日趨普遍。但鋼材存在一致命的缺點，即是高溫會造成鋼材強度的降低，此因素對鋼結構影響非常巨大，當溫度達600℃時，鋼材的極限承載力已衰減至原來的一半，並且會產生大量的變形，因此溫度對鋼結構的影響不可忽視。 本文探討溫度對鋼結構的影響，以力學觀點切入，並以有限元素模擬分析，探討數種二維鋼構架在溫度作用下的行為，包括升溫(Heating)及降溫(Cooling)兩個階段。首先以改良式塑性鉸法模擬結構之材料非線性行為，採用Eurocode 3規範所定義出之材料折減係數，模擬鋼材在高溫下的軟化現象。另外採用更新式拉格蘭治推演法(Updated Lagrangian Formulation)，以能量的角度進行微分方程式的推導，並以變分法推導出梁元素受溫度作用引致的溫度矩陣(thermal stiffness matrix)、溫度力(thermal load)及軟化力(reduced member load)。最後利用本文所建立之數值方法，模擬結構受溫變後的非線性行為，討論不同載重情況、斷面溫度是否為均勻及幾何瑕疵(geometrical imperfection)是否存在等因素，並評估這些因素對結構之臨界溫度(critical temperature)，以及鋼結構受高溫冷卻所造成的永久變形之影響。本文所進行之研究，應有助於工程師對鋼結構受高溫及冷卻後的行為之瞭解。

The objective of this thesis is to investigate the behavior of steel frames under the heating and cooling processes. In the past decades, steel has been wieldy used in civil engineering. Compared with other commonly used materials, the properties of steel, such as strength, drop rapidly with the increase in temperature. For example, when the temperature reaches 600 degrees Celsius, the ultimate strength of steel structures decreases drastically along with large deformation. This thesis focuses on the analysis of the steel structural behavior in the heating and cooling stages using the finite element method. To simulate the softening behavior of steel structures in high temperatures, a nonlinear analysis theory incorporating the refined hinge concept and the reduction coefficients for steel defined by Eurocode 3 is presented. The governing equations for the beam element is derived by the updated Lagrangian formulation, in which the thermal stiffness matrix, thermal loads, and reduced member loads due to the temperature rise are derived by the variational method. Using the numerical method presented in this study, the nonlinear behavior of steel structures under the thermal change is studied considering various factors, such as the loading combination, the uniformity of temperature distribution, and the presence of geometrical imperfections. From the numerical results obtained, the effects of all these factors on the critical temperature and residual deformation of the structure undergoing the heating and cooling processes are evaluated.