火灾作用下钢筋混凝土结构非线性分析
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摘要
结构抗火是结构工程领域里的一个重要难题。钢筋混凝土结构的抗火性能虽然优于其它结构,但同样面临抗火问题研究。由于试验设备和火灾试验本身极其昂贵,利用有限元计算软件来模拟钢筋混凝土构件及结构在火灾中的非线性反应变得越来越重要。本文在系统分析和总结目前国内外火灾工程研究概况的基础上,对火灾作用下钢筋混凝土结构进行了非线性有限元分析。其主要内容分为以下几个部分：
1.归纳总结了国内外钢筋和混凝土的高温材料性能的研究成果,包括钢筋、混凝土的热工性能参数及热力学性能参数。二者的热工性能参数和热力学性能参数是研究高温下钢筋混凝土结构力学性能的重要前提。
2.基于有限元-差分混合方法的数学模型,编制了钢筋混凝土结构的内部温度场分析程序,计算结果与现有的国内外试验结果吻合较好。试验和理论分析比较表明本文采用的理论和编制的程序是合理的。
3.考虑到建模需要,简要介绍了本构模型应满足的基本力学原理。然后推导出钢筋混凝土结构材料的高温本构模型的基本公式,给出了建立钢筋和混凝土高温本构模型应遵循的基本步骤。针对钢筋和混凝土高温弹塑性本构模型,基于后退欧拉法建立了弹性预测-塑性修正的数值求解方法,提高了等效塑性应变和塑性变形的计算效率。基于上述本构模型和数值算法,编制了相应的非线性分析程序,并对已有的试验结果进行了数值模拟,验证了本构模型和数值算法的有效性。
4.给出了一种计算高温下钢筋混凝土偏压构件极限承载力的简化计算方法,计算中考虑了高温下结构的材料性能、力学性能和稳定性退化以及侧向挠度的影响。通过此方法能够比较准确地计算出不同温度下钢筋混凝土偏压构件的极限承载力,计算结果与试验结果吻合较好。在此基础上,以四面受火钢筋混凝土方形柱为例,对极限承载力的各个影响因素进行了分析,得出配筋率、钢筋屈服强度对极限承载力影响不大,而混凝土保护层厚度、混凝土受压强度和截面尺寸则是影响极限承载力的主要因素。
5.根据材料在不同温度的本构模型,对考虑薄膜应力效应的钢筋混凝土板的极限承载力进行了分析。通过分析板块中面的平衡方程及位移协调方程,建立了由板位移和Airy应力函数表示的两个微分控制方程。基于能量原理,采用二重Fourier级数解推导了火灾作用下楼板的位移、薄膜应力、应变以及板极限承载力的表达式。所得的计算结果与试验结果吻合较好,同时为考虑薄膜效应时楼板的抗火设计提供了参考。
6.推导出材料在大变形条件下的热弹塑性本构模型,采用梁-柱单元划分和荷载增量法对钢筋混凝土连续梁的抗火性能进行了非线性分析。通过计算火灾作用下钢筋混凝土连续梁的高温极限承载力和力学性能,分析了不同加载位置、荷载大小以及加温跨数等因素作用下变形和内力重分布的变化规律。结果表明,在升温过程中加载位置和加载水平使得连续梁发生剧烈的内力重分布,并产生可变的高温塑性铰,从而改变结构的破坏形态。
Fire resistance of structures is an important and difficult problem in structural engineering. Fire resistance of reinforced concrete structures is better than other ones, but it is also necessary to research the fire resistance properties. Because of the high cost of fire testing facilities and the fire tests itself, it is more and more important to use software of finite element analysis to model the nonlinear response of the reinforced concrete members and structures in fire. Based on the systematic analysis and conclusions of fire resistance research in this thesis, the nonlinear finite element response of reinforced concrete structures is analyzed. The main content is organized as follows:
1. The research results of material performance of the steel and concrete at high temperature are summarized, including the thermal and mechanical performance parameters of steel and concrete in high temperature. These parameters are the important precondition to research the mechanical properties of reinforced concrete structures in high temperature.
2. Based on the hybrid mathematic model of finite element-difference, the analysis program of the internal temperature field are developed, and the computing results show in good agreement with the existing test results. The results of test and theoretical analysis demonstrate that the method and the computer program given in the thesis are reliable.
3. Considering the demand of modeling, the basic mechanical principles that the constitutive model should be satisfied is introduced in brief. Then the basic formulae of constitutive model of reinforced concrete are derived, and the basic steps of establishing the constitutive model of reinforcement and steel in high temperature are given. According to the constitutive model, the numerical solving method of elastic predictor and plastic corrector is established, and the efficiency of computing equivalent plastic strain and plastic deformation is greatly improved. Corresponding, the numerical algorithm of constitutive model of steel and reinforcement in high temperature is established based on the backward Euler method. According to the above constitutive model and numerical algorithm, the program of nonlinear analysis is developed, and the existing tests are simulated, which demonstrates the validity of the constitutive model and numerical algorithm.
4. A simplified calculation approach is provided, which can be used for calculating the ultimate bearing capability of reinforced concrete eccentric compression member. The effects of material property, mechanical performance and stability deterioration of structures under high temperature is considered. By this approach, ultimate bearing capability of the reinforced concrete eccentric compression member under different temperatures can be calculated accurately, and the results are matching well with the test data. Based on this, taking a four-face heated reinforced concrete column for example, each influence parameter on ultimate bearing capability is analyzed. The results indicate that concrete cover, concrete compressed strength and sectional dimension are the main influence parameters on ultimate bearing capacity, while the influences of steel ratio and steel yield strength can be ignored.
5. Considering the constitutive model of materials at different temperatures, ultimate bearing capability of reinforced concrete slabs under membrane effect is analyzed. Based on the force equilibrium and geometric compatibility equation in the middle plane, two governing differential equations expressed by the deflection and Airy stress function are obtained. Based on the principle of energy, the deflection, membrane force, stress, strain and the ultimate bearing capability of slab are deduced by double Fourier series. The calculation results are in good agreement with the test results, therefore, the results can offer the reference for the fire resistance design of slab when the membrane effect is considered.
6. The thermo-elasto-plastic material constitutive model in the condition of large deformation is deduced. The nonlinear analysis of reinforced concrete continuous beam in high temperature is made with beam-columniation element and load increment method. By calculating the ultimate bearing capability and mechanical properties of reinforced concrete continuous beam at high temperature, the change law of internal force redistribution and deformation were analyzed in different load positions, loads levels and different numbers of heating spans. The results show that, in heating process, the internal force redistribution and the forming of plastic hinges at high temperature in continuous beam are caused by the loading position and level, which can change the failure pattern of structure.
1.归纳总结了国内外钢筋和混凝土的高温材料性能的研究成果,包括钢筋、混凝土的热工性能参数及热力学性能参数。二者的热工性能参数和热力学性能参数是研究高温下钢筋混凝土结构力学性能的重要前提。
2.基于有限元-差分混合方法的数学模型,编制了钢筋混凝土结构的内部温度场分析程序,计算结果与现有的国内外试验结果吻合较好。试验和理论分析比较表明本文采用的理论和编制的程序是合理的。
3.考虑到建模需要,简要介绍了本构模型应满足的基本力学原理。然后推导出钢筋混凝土结构材料的高温本构模型的基本公式,给出了建立钢筋和混凝土高温本构模型应遵循的基本步骤。针对钢筋和混凝土高温弹塑性本构模型,基于后退欧拉法建立了弹性预测-塑性修正的数值求解方法,提高了等效塑性应变和塑性变形的计算效率。基于上述本构模型和数值算法,编制了相应的非线性分析程序,并对已有的试验结果进行了数值模拟,验证了本构模型和数值算法的有效性。
4.给出了一种计算高温下钢筋混凝土偏压构件极限承载力的简化计算方法,计算中考虑了高温下结构的材料性能、力学性能和稳定性退化以及侧向挠度的影响。通过此方法能够比较准确地计算出不同温度下钢筋混凝土偏压构件的极限承载力,计算结果与试验结果吻合较好。在此基础上,以四面受火钢筋混凝土方形柱为例,对极限承载力的各个影响因素进行了分析,得出配筋率、钢筋屈服强度对极限承载力影响不大,而混凝土保护层厚度、混凝土受压强度和截面尺寸则是影响极限承载力的主要因素。
5.根据材料在不同温度的本构模型,对考虑薄膜应力效应的钢筋混凝土板的极限承载力进行了分析。通过分析板块中面的平衡方程及位移协调方程,建立了由板位移和Airy应力函数表示的两个微分控制方程。基于能量原理,采用二重Fourier级数解推导了火灾作用下楼板的位移、薄膜应力、应变以及板极限承载力的表达式。所得的计算结果与试验结果吻合较好,同时为考虑薄膜效应时楼板的抗火设计提供了参考。
6.推导出材料在大变形条件下的热弹塑性本构模型,采用梁-柱单元划分和荷载增量法对钢筋混凝土连续梁的抗火性能进行了非线性分析。通过计算火灾作用下钢筋混凝土连续梁的高温极限承载力和力学性能,分析了不同加载位置、荷载大小以及加温跨数等因素作用下变形和内力重分布的变化规律。结果表明,在升温过程中加载位置和加载水平使得连续梁发生剧烈的内力重分布,并产生可变的高温塑性铰,从而改变结构的破坏形态。
Fire resistance of structures is an important and difficult problem in structural engineering. Fire resistance of reinforced concrete structures is better than other ones, but it is also necessary to research the fire resistance properties. Because of the high cost of fire testing facilities and the fire tests itself, it is more and more important to use software of finite element analysis to model the nonlinear response of the reinforced concrete members and structures in fire. Based on the systematic analysis and conclusions of fire resistance research in this thesis, the nonlinear finite element response of reinforced concrete structures is analyzed. The main content is organized as follows:
1. The research results of material performance of the steel and concrete at high temperature are summarized, including the thermal and mechanical performance parameters of steel and concrete in high temperature. These parameters are the important precondition to research the mechanical properties of reinforced concrete structures in high temperature.
2. Based on the hybrid mathematic model of finite element-difference, the analysis program of the internal temperature field are developed, and the computing results show in good agreement with the existing test results. The results of test and theoretical analysis demonstrate that the method and the computer program given in the thesis are reliable.
3. Considering the demand of modeling, the basic mechanical principles that the constitutive model should be satisfied is introduced in brief. Then the basic formulae of constitutive model of reinforced concrete are derived, and the basic steps of establishing the constitutive model of reinforcement and steel in high temperature are given. According to the constitutive model, the numerical solving method of elastic predictor and plastic corrector is established, and the efficiency of computing equivalent plastic strain and plastic deformation is greatly improved. Corresponding, the numerical algorithm of constitutive model of steel and reinforcement in high temperature is established based on the backward Euler method. According to the above constitutive model and numerical algorithm, the program of nonlinear analysis is developed, and the existing tests are simulated, which demonstrates the validity of the constitutive model and numerical algorithm.
4. A simplified calculation approach is provided, which can be used for calculating the ultimate bearing capability of reinforced concrete eccentric compression member. The effects of material property, mechanical performance and stability deterioration of structures under high temperature is considered. By this approach, ultimate bearing capability of the reinforced concrete eccentric compression member under different temperatures can be calculated accurately, and the results are matching well with the test data. Based on this, taking a four-face heated reinforced concrete column for example, each influence parameter on ultimate bearing capability is analyzed. The results indicate that concrete cover, concrete compressed strength and sectional dimension are the main influence parameters on ultimate bearing capacity, while the influences of steel ratio and steel yield strength can be ignored.
5. Considering the constitutive model of materials at different temperatures, ultimate bearing capability of reinforced concrete slabs under membrane effect is analyzed. Based on the force equilibrium and geometric compatibility equation in the middle plane, two governing differential equations expressed by the deflection and Airy stress function are obtained. Based on the principle of energy, the deflection, membrane force, stress, strain and the ultimate bearing capability of slab are deduced by double Fourier series. The calculation results are in good agreement with the test results, therefore, the results can offer the reference for the fire resistance design of slab when the membrane effect is considered.
6. The thermo-elasto-plastic material constitutive model in the condition of large deformation is deduced. The nonlinear analysis of reinforced concrete continuous beam in high temperature is made with beam-columniation element and load increment method. By calculating the ultimate bearing capability and mechanical properties of reinforced concrete continuous beam at high temperature, the change law of internal force redistribution and deformation were analyzed in different load positions, loads levels and different numbers of heating spans. The results show that, in heating process, the internal force redistribution and the forming of plastic hinges at high temperature in continuous beam are caused by the loading position and level, which can change the failure pattern of structure.
引文
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