钢筋混凝土结构可靠性若干问题研究
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摘要
钢筋混凝土结构由于其本身的众多优点,目前仍然是我国土木工程界应用最为广泛的一种建筑结构。但是这并不等于钢筋混凝土结构就是完美的建筑结构,从钢筋混凝土结构开始应用于建筑结构至今的100多年间,许多钢筋混凝土结构由于种种原因会发生提前失效,从而不能完成预定的使用功能。因此近些年来,钢筋混凝土结构的可靠性问题已逐渐成为各国专家们关注的一个热点问题。钢筋混凝土结构的可靠性方面研究主要包括安全性、适用性和耐久性三个方面。目前,在安全性方面国内外专家已经做了大量的研究,而且取得了一些成绩。但是对于适用性和耐久性方面研究开展的还较少,还需要进一步的研究。
在工程结构分析中通常采用定值的方法,就是将实际工程结构承受的荷载和结构所用的材料性能一律当作定值来处理。但是实际上结构的几何尺寸、承受荷载、材料参数、计算模式等等都受到各种因素的影响。为了更准确的反映钢筋混凝土结构的可靠性问题,本文将以上因素视为随机变量,结合可靠度设计基本理论,通过概率分析,对钢筋混凝土结构正常使用极限状态的可靠性,框架结构节点强柱弱梁可靠性,CFRP加固钢筋混凝土结构的可靠性等进行了一些研究,本文的创造性研究成果主要包括：
1、本文针对蒙特卡洛方法存在的计算量大,计算时间长的缺点,借助曲线拟合的思想,提出改进蒙特卡洛可靠度分析方法。文中方法通过对蒙特卡洛方法计算得到的数据进行曲线拟合,借助Levenberg-Marquardt优化方法计算结构的失效概率,最后通过对一个平面桁架结构进行可靠度分析来验证了本文方法的可行性。结果表明,本文方法精度较高、计算量小、计算时间短,为大型复杂结构的可靠度分析提供了一种有效手段。
2、本文考虑计算模式、材料强度、几何尺寸的随机性,对建筑抗震设计规范所提出的抗震概念设计进行了讨论,分析了钢筋混凝土结构的节点强柱弱梁可靠性。得出了不同抗震等级下节点强柱弱梁设计的可靠度,最后确定了2010版建筑抗震设计规范中框架柱端弯矩增大系数的调整对强柱弱梁的失效概率的影响,新规范调整后的柱端弯矩增大系数使强柱弱梁设计可靠性大大增加,达到了规范调整的目的。在此基础上结合实际设计实例,应用实际设计软件广厦CAD分析了现行规范中该系数调整对建筑结构造价的影响,结果表明造价提高很小。
3、针对现行国家标准尚未给出钢筋混凝土结构构件正常使用极限状态下目标可靠度指标的情况,本文提出基于模糊失效准则的混凝土结构构件正常使用状态下可靠度分析方法,首先构造钢筋混凝土结构模糊隶属函数,然后通过建立等效功能函数方法使混凝土结构模糊可靠度问题转化为传统可靠度计算问题,通过JC法求解,最后计算出正常使用状态下钢筋混凝土结构构件横向裂缝的模糊可靠度指标。
4、针对长期以来建筑结构的加固研究主要集中在设计和施工的理论方面,而对于加固结构的可靠性方面缺少系统的研究。本文根据可靠度基本理论,建立CFRP加固钢筋混凝土梁的模糊可靠性分析模型。考虑材料、几何尺寸、计算模式的不确定性,确定了极限状态方程中各个随机变量的平均值和标准差,然后根据模糊数学和模糊可靠度的基本理论,分析CFRP加固混凝土结构模糊可靠性。通过和常规可靠度分析方法相比较,说明常规可靠度算法偏于不安全。
The reinforced concrete structure is widespread in the field of civil engineering, because it has so many advantages. But it is not to say that the reinforced concrete structure is perfect structure. It has been one century from beginning of application for reinforced concrete. Many structures failed for various reasons, so that the function can not be completed. In recent years, the reliability of reinforced concrete structre has becomed a hot issue. The reinforced concrete structure reliability consists of three parts:durability, safety and serviceability. Formerly, the safety of the RC structure has been paid more attention. But the study on the serviceability and durability of RC structure have lagged behind the requirements of engieering practice. It needs much attention.
Most of the models treat structure analysis from a deterministic point of view. In these models, the load and material parameters are deterministic. However, the geometric size, the working load, the material property and model of calculation are effected by several factors. In order to have a more accurate prediction of the reliability of the reinforced concrete structure, the geometric size, the working load, the material property and model of calculation should be treated as random variables.The reliability of serviceability limit states of RC structre and the strong beam weak column relaibility of RC structre and reliability of CFRP strengthened reinforced concrete beams were discussed in this paper by methodology of reliability and analysis of probability. The main creative contents includes as following:
1. To overcome shortcomings of large amount of computational efforts and long computation time existing in Monte Carlo simulaiton for system reliability analysis, an improved method was proposed in the light of curve fitting. Reliability problem was reformed by depending on a optimal parameter, the failure probability was treated as a function of this paramter by exploiting the regularity of it and fitting the relaibility function by Levenberg-Marquardt method. A ten-bar truss structure numerical example was given to proved the feasibility of the proposed method. Result indicates that the proposed method has high computational accuracy with less computational efforts and computation time, providing an effective way to analyze reliability of large complex structures.
2. Uncertainty of calculation, geometric size and concrete strength were considered as random variables, seismic concept design issued by the national Code for Seismic Design of Buildings (GB50011—2010) were discussed. The strong beam weak column relaibility of RC structre was analysed by enhanced Monte Carlo simulation in the light of curve fitting. Influence of moment augment factor of column issued by the national Code for Seismic Design of Buildings on strong beam weak column relaibility were discussed. Result indicates that new moment augment factor of column improve the strong beam weak column relaibility of reinforced concrete structure. Influence of moment augment factor column on building cost were discussed by computer design software Guang Sha CAD. Result indicates that the increase of cost is very small.
3. According to the national standard "Code for Design of Concrete Structure", the reliability index for the structural members of reinforced concrete have not been given, which are controlled by serviceability limit states. A methodological framework was proposed, which made use of fuzzy invalidation rule for reliability analysis of reinforced concrete members. Firstly, A membership function was chosen. Secondly, A equivalent function was established to deal with the fuzzy reliability of concrete structure by traditional JC method. Finally, the fuzzy reliability index of transverse crack of reinforced concrete structure was obtained.
4. In recent years, study on the reliability analysis of strengthened structure have lagged behind the design and construction of structures. The fuzzy reliability analysis model was derived based on structural reliability theory. Geometric size, material property and uncertainty of calculation were considered as random variables, mean value and normal deviation of each random variable in performance function were determined. The reliability of CFRP strengthened RC beams were discussed by fuzzy mathematics and fuzzy reliability thorey. Result indicates that the fuzzy reliability index of CFRP strengthened RC beams were obtained, which decreases compare with the traditional reliability analysis method. Numerical results show that the fuzzy reliability analysis of CFRP strengthened RC beams provide more safety than traditional analysis does.
在工程结构分析中通常采用定值的方法,就是将实际工程结构承受的荷载和结构所用的材料性能一律当作定值来处理。但是实际上结构的几何尺寸、承受荷载、材料参数、计算模式等等都受到各种因素的影响。为了更准确的反映钢筋混凝土结构的可靠性问题,本文将以上因素视为随机变量,结合可靠度设计基本理论,通过概率分析,对钢筋混凝土结构正常使用极限状态的可靠性,框架结构节点强柱弱梁可靠性,CFRP加固钢筋混凝土结构的可靠性等进行了一些研究,本文的创造性研究成果主要包括：
1、本文针对蒙特卡洛方法存在的计算量大,计算时间长的缺点,借助曲线拟合的思想,提出改进蒙特卡洛可靠度分析方法。文中方法通过对蒙特卡洛方法计算得到的数据进行曲线拟合,借助Levenberg-Marquardt优化方法计算结构的失效概率,最后通过对一个平面桁架结构进行可靠度分析来验证了本文方法的可行性。结果表明,本文方法精度较高、计算量小、计算时间短,为大型复杂结构的可靠度分析提供了一种有效手段。
2、本文考虑计算模式、材料强度、几何尺寸的随机性,对建筑抗震设计规范所提出的抗震概念设计进行了讨论,分析了钢筋混凝土结构的节点强柱弱梁可靠性。得出了不同抗震等级下节点强柱弱梁设计的可靠度,最后确定了2010版建筑抗震设计规范中框架柱端弯矩增大系数的调整对强柱弱梁的失效概率的影响,新规范调整后的柱端弯矩增大系数使强柱弱梁设计可靠性大大增加,达到了规范调整的目的。在此基础上结合实际设计实例,应用实际设计软件广厦CAD分析了现行规范中该系数调整对建筑结构造价的影响,结果表明造价提高很小。
3、针对现行国家标准尚未给出钢筋混凝土结构构件正常使用极限状态下目标可靠度指标的情况,本文提出基于模糊失效准则的混凝土结构构件正常使用状态下可靠度分析方法,首先构造钢筋混凝土结构模糊隶属函数,然后通过建立等效功能函数方法使混凝土结构模糊可靠度问题转化为传统可靠度计算问题,通过JC法求解,最后计算出正常使用状态下钢筋混凝土结构构件横向裂缝的模糊可靠度指标。
4、针对长期以来建筑结构的加固研究主要集中在设计和施工的理论方面,而对于加固结构的可靠性方面缺少系统的研究。本文根据可靠度基本理论,建立CFRP加固钢筋混凝土梁的模糊可靠性分析模型。考虑材料、几何尺寸、计算模式的不确定性,确定了极限状态方程中各个随机变量的平均值和标准差,然后根据模糊数学和模糊可靠度的基本理论,分析CFRP加固混凝土结构模糊可靠性。通过和常规可靠度分析方法相比较,说明常规可靠度算法偏于不安全。
The reinforced concrete structure is widespread in the field of civil engineering, because it has so many advantages. But it is not to say that the reinforced concrete structure is perfect structure. It has been one century from beginning of application for reinforced concrete. Many structures failed for various reasons, so that the function can not be completed. In recent years, the reliability of reinforced concrete structre has becomed a hot issue. The reinforced concrete structure reliability consists of three parts:durability, safety and serviceability. Formerly, the safety of the RC structure has been paid more attention. But the study on the serviceability and durability of RC structure have lagged behind the requirements of engieering practice. It needs much attention.
Most of the models treat structure analysis from a deterministic point of view. In these models, the load and material parameters are deterministic. However, the geometric size, the working load, the material property and model of calculation are effected by several factors. In order to have a more accurate prediction of the reliability of the reinforced concrete structure, the geometric size, the working load, the material property and model of calculation should be treated as random variables.The reliability of serviceability limit states of RC structre and the strong beam weak column relaibility of RC structre and reliability of CFRP strengthened reinforced concrete beams were discussed in this paper by methodology of reliability and analysis of probability. The main creative contents includes as following:
1. To overcome shortcomings of large amount of computational efforts and long computation time existing in Monte Carlo simulaiton for system reliability analysis, an improved method was proposed in the light of curve fitting. Reliability problem was reformed by depending on a optimal parameter, the failure probability was treated as a function of this paramter by exploiting the regularity of it and fitting the relaibility function by Levenberg-Marquardt method. A ten-bar truss structure numerical example was given to proved the feasibility of the proposed method. Result indicates that the proposed method has high computational accuracy with less computational efforts and computation time, providing an effective way to analyze reliability of large complex structures.
2. Uncertainty of calculation, geometric size and concrete strength were considered as random variables, seismic concept design issued by the national Code for Seismic Design of Buildings (GB50011—2010) were discussed. The strong beam weak column relaibility of RC structre was analysed by enhanced Monte Carlo simulation in the light of curve fitting. Influence of moment augment factor of column issued by the national Code for Seismic Design of Buildings on strong beam weak column relaibility were discussed. Result indicates that new moment augment factor of column improve the strong beam weak column relaibility of reinforced concrete structure. Influence of moment augment factor column on building cost were discussed by computer design software Guang Sha CAD. Result indicates that the increase of cost is very small.
3. According to the national standard "Code for Design of Concrete Structure", the reliability index for the structural members of reinforced concrete have not been given, which are controlled by serviceability limit states. A methodological framework was proposed, which made use of fuzzy invalidation rule for reliability analysis of reinforced concrete members. Firstly, A membership function was chosen. Secondly, A equivalent function was established to deal with the fuzzy reliability of concrete structure by traditional JC method. Finally, the fuzzy reliability index of transverse crack of reinforced concrete structure was obtained.
4. In recent years, study on the reliability analysis of strengthened structure have lagged behind the design and construction of structures. The fuzzy reliability analysis model was derived based on structural reliability theory. Geometric size, material property and uncertainty of calculation were considered as random variables, mean value and normal deviation of each random variable in performance function were determined. The reliability of CFRP strengthened RC beams were discussed by fuzzy mathematics and fuzzy reliability thorey. Result indicates that the fuzzy reliability index of CFRP strengthened RC beams were obtained, which decreases compare with the traditional reliability analysis method. Numerical results show that the fuzzy reliability analysis of CFRP strengthened RC beams provide more safety than traditional analysis does.
引文
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