结构缺陷和损伤对桁架拱桥极限承载力的影响研究
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摘要
我国已建公路钢筋混凝土桁架拱桥大多存在如下病害：下弦杆拱脚处横向开裂；弦杆端部节点裂缝；桁架拱片歪扭；横系梁、横拉杆、横隔板竖向开裂；桥面板裂缝、破碎；伸缩缝破损或者缺少；人行道变形下垂,位于两跨接缝处人行道和拉杆横向裂缝。有必要研究在役钢筋混凝土桁架拱桥存在多种缺陷和损伤情况下的极限承载力,为确定其实际承载能力和进行安全性评估提供依据。
本文综述了国内外拱桥承载力研究状况,缺陷和损伤对拱结构影响的研究进展,分析比较了拱桥极限承载力不同分析方法,以某桁架拱桥为工程背景,对该类有缺陷和损伤钢筋混凝土桁架拱桥的极限承载力进行了分析研究。
论文根据钢筋混凝土桁架拱桥的各杆件均以承受轴力为主、节点处弯矩较小的受力特点,基于钢筋与混凝土共同工作、协调变形原理,推导出适合于钢筋混凝土桁架单元分析的理想弹塑性复合材料拉压不对称本构关系；按比拟杆—附加弹簧模型简化等效桩土相互作用；对钢筋混凝土桁架拱桥建立考虑非线性效应的有限元分析数值模型。分别采用线弹性、几何非线性及双重非线性等分析方法对三种不同结构形式桁架拱桥进行了极限承载力对比分析,研究了非线性效应对于钢筋混凝土桁架拱桥承载力分析结果的影响程度。结果表明,钢筋混凝土桁架拱桥极限承载力分析,更宜采用考虑几何非线性和材料非线性的双重非线性分析方法。荷载作用工况对拱桥极限承载力有很大影响,给出了不同荷载工况下结构的破坏过程及破坏模式,并归纳出两种最不利的荷载工况。
通过数学方法,从条件随机变量出发,推导出缺陷随机分布方式；论文基于双重非线性分析方法,研究了具有不同的面内、面外缺陷分布形式桁架拱桥的极限承载力。对于三种结构形式的桁架拱桥,将一阶特征值屈曲模态作为结构的面内、外缺陷分布形式,随着缺陷幅值的增大,结构极限承载力不断下降；在缺陷幅值控制在跨径的1/1500以内时,缺陷对结构的极限承载力影响很小；当缺陷幅值超过跨径的1/1500后,随着缺陷幅值的增大,极限承载力会有很大下降。与面内缺陷相比,当缺陷幅值在跨径的1/500以内时,同样的缺陷幅值,面外缺陷对于极限承载力的影响要小于面内缺陷；但是,当缺陷幅值超过跨径的1/500以后,同样的缺陷幅值,面外缺陷对于极限承载力的影响要大于面内缺陷。无论面内缺陷分布方式还是面外缺陷分布方式,特征值屈曲形式的缺陷分布不一定是最不利的缺陷分布方式,如六阶随机缺陷分布方式对极限承载力的影响就大于特征值屈曲形式的缺陷分布方式。但是,一者高阶的缺陷分布方式出现的概率较小,再者特征值屈曲形式的缺陷分布方式对极限承载力的影响要大于绝大多数随机缺陷分布方式,所以,大多数情况下,可以近似地认为特征值屈曲形式的缺陷分布方式接近于最不利的缺陷分布方式。
损伤程度的增大,引起结构刚度的下降,导致结构变形的增大;而且随着损伤程度越大,结构变形的增大速率越大,呈非线性变化。随着损伤程度的增大,结构的极限活荷载系数成线性下降。通过规律性分析,得出有损伤结构极限活荷载系数λ=λ0(1-1.1×η)。实桥非线性分析与简化分析结果对比表明,含缺陷、损伤桁架拱桥结构简化分析方法与非线性分析所得极限活荷载系数相差较小,本文推导的简化分析方法可以作为在一定缺陷和损伤情况下,桁架拱桥结构极限承载力近似计算方法。综合目前国内外常见的几种结构稳定安全系数定义,给出了适合于在役旧钢筋混凝土桁架拱桥的结构稳定安全系数定义方法及最低容许值为5的建议。我国现行《公路桥涵施工技术规范》(JTJ041-2000)所给拱肋施工允许偏差略显保守,轴线横向偏位的允许范围可略大于竖向偏位的允许范围。
本文的研究有助于了解桁架拱桥的破坏形式、破坏过程,和影响该类桁架拱桥极限承载力的主要因素,并为在役拱桥运营多年后有缺陷和损伤桁架拱桥极限承载能力评估、超载能力和安全性评价等提供了有益的经验和建议。
Most of the as-built reinforced concrete trussed arch bridges on highways in our contry have following defects:transverse crack in lower chord near arch spring; crack at the end nodes of chords; distortion of the truss pieces; vertical crack in straining beams, tie rods, and transverse diaphragms; crack even crush of deck slabs; breakage or lack of expansion and contraction joints; deflection of sidewalks; transverse crack in sidewalks and tie rods near the joint seams between two span. It is necessary to study the ultimate load bearing capacity of reinforced concrete trussed arch bridge in service which contains multiple defects and damage, and provide basis in order to determine the actual bearing capacity and conduct safety evaluation.
This paper reviews research conditions of bearing capacity of arch bridge, and research outcome about the infection of defects and damage to the arch structure. Analysing and comparing the different analytical methods of ultimate load bearing capacity of trussed arch bridge. Under the background of one trussed arch bridge, the ultimate load bearing capacity of reinforced concrete trussed arch bridge with defects and damage has been studied.
Because all staffs of RC trussed arch bridge mainly bear axial forces, and only bear very small bending moment near the nodes, so spatial beam cells can be adopted to simulate the structure in the paper; moreover based on the theory that the steel and concrete can work together and distort in phase, the steel and concrete of RC trussed structure can be equal to one ideal elastic-plastic combined material with dissymmetrical constitutive relation of stress-press, the constitutive relation deduced by the paper can benefit to the same kind of RC trussed structure. Furthermore, the reciprocity of peg and soil is equaled to pole-spring model. Three kinds of trussed arch bridges with different structural forms are contrasted and analyzed, considered linearity, geometric nonlinearity, and dual nonlinearity respectively(both geometric nonlinearity and material nonlinearity), and the nonlinear influence on the analysis effects of RC trussed multi-arch bridges is studied. The analysis effects indicate:In order to get accurate results, the influence of geometric and material nonlinearity must be considered when the ultimate load bearing capacity of RC trussed arch bridges is studied. Loading form of the arch bridge has great influence on ultimate load bearing capacity, given the structure failure process and damage model under different load operating forms, and sumed up the most two adverse load forms.
By mathematical methods, from the conditional random variables, the randomly distributed modes of defects are deduced. Based on dual nonlinear analysis method, the ultimate load bearing capacity of trussed arch bridge with different distributive defects in plane and out plane is studied. For the three structural forms of the trussed arch bridge, the first buckling mode as the mode of defect distribution in plane and out plane, with the defect amplitude increase, the ultimate load bearing capacity of structure falls; when defect amplitude less than 1/1500 of the span, the defects have little effect on the ultimate load bearing capacity; when the defect amplitude more than 1/1500 of the span, along with the defect amplitude increases, the ultimate bearing capacity will be greatly decreased. Compared with the in-plane defects, when the defect amplitude less than the 1/500 of the span, to the same defect amplitude, the ultimate bearing capacity of the trussed bridge with out-plane defects is less than that with in-plane defects; However, when the defect amplitude more than the 1/500 of the span, to the same defect amplitude, the ultimate bearing capacity of the trussed bridge with out-plane defects is more than that with in-plane defects. Regardless of the distribution mode of in-plane defects or out-plane defects, eigenvalue buckling mode as the distribution mode of defects is not necessarily the most unfavorable distribution mode, such as the 6th-order distribution mode of random defects impacts more on the ultimate bearing capacity than that eigenvalue buckling distribution mode does. However, a high-level distribution mode of random defects happens almost impossible, on the other hand, eigenvalue buckling mode as the distribution impacts more on the ultimate bearing capacity than that the vast majority distribution modes of random defects, so in most cases, eigenvalue buckling mode as the distribution mode of defects is close to the most unfavorable distribution mode.
Increament of damage degree leads to structural stiffness degrading, results in structural deformation increasing; and the larger the damage degree is, the bigger the increase rate of the structural deformation is. As the damage degree increasing, the ultimate bearing capacity declines linearly. Through the regularity analysis, damage ultimate live load factor of the structureλ=λ0(1-1.1×η)can be deduced. The comparison between simplify analysis and dual nonlinear analysis of the real trussed arch bridge with defects and damage shows that, the difference of calculation result by simplify analysis method and by dual nonlinear method is very small. The simplify analysis method dedued in this paper is exact, and can be adopted in the same kind of bridges'structure analysis. Three different definitions of stability assurance coefficient are discussed and the second definitions of stability assurance coefficient is suggested to measure the overall stability level of old RC trussed multi-arch bridges, its lowest allowance value of stability assurance coefficient is suggested to be 5 in the paper. the bias allowance of the arch rib construction is more conservative in " Technical Specifications for Construction of Highway Bridges and Culvers" (JTJ041-2000), and may be appropriate to relax, the horizontal axis deviation of the allowable range may be slightly larger than the vertical deviation of the allowable range.
The research work benefits to learning about the process until the whole trussed arch bridge structure finally failures and many influence factor on the ultimate load bearing capacity of this kind of old trussed arch bridges; provides many useful experiences and advices on evaluation of ultimate load bearing capacity, overrunning capacity, security evaluation, and so on of trussed arch bridges with defects and damage in service for many years.
本文综述了国内外拱桥承载力研究状况,缺陷和损伤对拱结构影响的研究进展,分析比较了拱桥极限承载力不同分析方法,以某桁架拱桥为工程背景,对该类有缺陷和损伤钢筋混凝土桁架拱桥的极限承载力进行了分析研究。
论文根据钢筋混凝土桁架拱桥的各杆件均以承受轴力为主、节点处弯矩较小的受力特点,基于钢筋与混凝土共同工作、协调变形原理,推导出适合于钢筋混凝土桁架单元分析的理想弹塑性复合材料拉压不对称本构关系；按比拟杆—附加弹簧模型简化等效桩土相互作用；对钢筋混凝土桁架拱桥建立考虑非线性效应的有限元分析数值模型。分别采用线弹性、几何非线性及双重非线性等分析方法对三种不同结构形式桁架拱桥进行了极限承载力对比分析,研究了非线性效应对于钢筋混凝土桁架拱桥承载力分析结果的影响程度。结果表明,钢筋混凝土桁架拱桥极限承载力分析,更宜采用考虑几何非线性和材料非线性的双重非线性分析方法。荷载作用工况对拱桥极限承载力有很大影响,给出了不同荷载工况下结构的破坏过程及破坏模式,并归纳出两种最不利的荷载工况。
通过数学方法,从条件随机变量出发,推导出缺陷随机分布方式；论文基于双重非线性分析方法,研究了具有不同的面内、面外缺陷分布形式桁架拱桥的极限承载力。对于三种结构形式的桁架拱桥,将一阶特征值屈曲模态作为结构的面内、外缺陷分布形式,随着缺陷幅值的增大,结构极限承载力不断下降；在缺陷幅值控制在跨径的1/1500以内时,缺陷对结构的极限承载力影响很小；当缺陷幅值超过跨径的1/1500后,随着缺陷幅值的增大,极限承载力会有很大下降。与面内缺陷相比,当缺陷幅值在跨径的1/500以内时,同样的缺陷幅值,面外缺陷对于极限承载力的影响要小于面内缺陷；但是,当缺陷幅值超过跨径的1/500以后,同样的缺陷幅值,面外缺陷对于极限承载力的影响要大于面内缺陷。无论面内缺陷分布方式还是面外缺陷分布方式,特征值屈曲形式的缺陷分布不一定是最不利的缺陷分布方式,如六阶随机缺陷分布方式对极限承载力的影响就大于特征值屈曲形式的缺陷分布方式。但是,一者高阶的缺陷分布方式出现的概率较小,再者特征值屈曲形式的缺陷分布方式对极限承载力的影响要大于绝大多数随机缺陷分布方式,所以,大多数情况下,可以近似地认为特征值屈曲形式的缺陷分布方式接近于最不利的缺陷分布方式。
损伤程度的增大,引起结构刚度的下降,导致结构变形的增大;而且随着损伤程度越大,结构变形的增大速率越大,呈非线性变化。随着损伤程度的增大,结构的极限活荷载系数成线性下降。通过规律性分析,得出有损伤结构极限活荷载系数λ=λ0(1-1.1×η)。实桥非线性分析与简化分析结果对比表明,含缺陷、损伤桁架拱桥结构简化分析方法与非线性分析所得极限活荷载系数相差较小,本文推导的简化分析方法可以作为在一定缺陷和损伤情况下,桁架拱桥结构极限承载力近似计算方法。综合目前国内外常见的几种结构稳定安全系数定义,给出了适合于在役旧钢筋混凝土桁架拱桥的结构稳定安全系数定义方法及最低容许值为5的建议。我国现行《公路桥涵施工技术规范》(JTJ041-2000)所给拱肋施工允许偏差略显保守,轴线横向偏位的允许范围可略大于竖向偏位的允许范围。
本文的研究有助于了解桁架拱桥的破坏形式、破坏过程,和影响该类桁架拱桥极限承载力的主要因素,并为在役拱桥运营多年后有缺陷和损伤桁架拱桥极限承载能力评估、超载能力和安全性评价等提供了有益的经验和建议。
Most of the as-built reinforced concrete trussed arch bridges on highways in our contry have following defects:transverse crack in lower chord near arch spring; crack at the end nodes of chords; distortion of the truss pieces; vertical crack in straining beams, tie rods, and transverse diaphragms; crack even crush of deck slabs; breakage or lack of expansion and contraction joints; deflection of sidewalks; transverse crack in sidewalks and tie rods near the joint seams between two span. It is necessary to study the ultimate load bearing capacity of reinforced concrete trussed arch bridge in service which contains multiple defects and damage, and provide basis in order to determine the actual bearing capacity and conduct safety evaluation.
This paper reviews research conditions of bearing capacity of arch bridge, and research outcome about the infection of defects and damage to the arch structure. Analysing and comparing the different analytical methods of ultimate load bearing capacity of trussed arch bridge. Under the background of one trussed arch bridge, the ultimate load bearing capacity of reinforced concrete trussed arch bridge with defects and damage has been studied.
Because all staffs of RC trussed arch bridge mainly bear axial forces, and only bear very small bending moment near the nodes, so spatial beam cells can be adopted to simulate the structure in the paper; moreover based on the theory that the steel and concrete can work together and distort in phase, the steel and concrete of RC trussed structure can be equal to one ideal elastic-plastic combined material with dissymmetrical constitutive relation of stress-press, the constitutive relation deduced by the paper can benefit to the same kind of RC trussed structure. Furthermore, the reciprocity of peg and soil is equaled to pole-spring model. Three kinds of trussed arch bridges with different structural forms are contrasted and analyzed, considered linearity, geometric nonlinearity, and dual nonlinearity respectively(both geometric nonlinearity and material nonlinearity), and the nonlinear influence on the analysis effects of RC trussed multi-arch bridges is studied. The analysis effects indicate:In order to get accurate results, the influence of geometric and material nonlinearity must be considered when the ultimate load bearing capacity of RC trussed arch bridges is studied. Loading form of the arch bridge has great influence on ultimate load bearing capacity, given the structure failure process and damage model under different load operating forms, and sumed up the most two adverse load forms.
By mathematical methods, from the conditional random variables, the randomly distributed modes of defects are deduced. Based on dual nonlinear analysis method, the ultimate load bearing capacity of trussed arch bridge with different distributive defects in plane and out plane is studied. For the three structural forms of the trussed arch bridge, the first buckling mode as the mode of defect distribution in plane and out plane, with the defect amplitude increase, the ultimate load bearing capacity of structure falls; when defect amplitude less than 1/1500 of the span, the defects have little effect on the ultimate load bearing capacity; when the defect amplitude more than 1/1500 of the span, along with the defect amplitude increases, the ultimate bearing capacity will be greatly decreased. Compared with the in-plane defects, when the defect amplitude less than the 1/500 of the span, to the same defect amplitude, the ultimate bearing capacity of the trussed bridge with out-plane defects is less than that with in-plane defects; However, when the defect amplitude more than the 1/500 of the span, to the same defect amplitude, the ultimate bearing capacity of the trussed bridge with out-plane defects is more than that with in-plane defects. Regardless of the distribution mode of in-plane defects or out-plane defects, eigenvalue buckling mode as the distribution mode of defects is not necessarily the most unfavorable distribution mode, such as the 6th-order distribution mode of random defects impacts more on the ultimate bearing capacity than that eigenvalue buckling distribution mode does. However, a high-level distribution mode of random defects happens almost impossible, on the other hand, eigenvalue buckling mode as the distribution impacts more on the ultimate bearing capacity than that the vast majority distribution modes of random defects, so in most cases, eigenvalue buckling mode as the distribution mode of defects is close to the most unfavorable distribution mode.
Increament of damage degree leads to structural stiffness degrading, results in structural deformation increasing; and the larger the damage degree is, the bigger the increase rate of the structural deformation is. As the damage degree increasing, the ultimate bearing capacity declines linearly. Through the regularity analysis, damage ultimate live load factor of the structureλ=λ0(1-1.1×η)can be deduced. The comparison between simplify analysis and dual nonlinear analysis of the real trussed arch bridge with defects and damage shows that, the difference of calculation result by simplify analysis method and by dual nonlinear method is very small. The simplify analysis method dedued in this paper is exact, and can be adopted in the same kind of bridges'structure analysis. Three different definitions of stability assurance coefficient are discussed and the second definitions of stability assurance coefficient is suggested to measure the overall stability level of old RC trussed multi-arch bridges, its lowest allowance value of stability assurance coefficient is suggested to be 5 in the paper. the bias allowance of the arch rib construction is more conservative in " Technical Specifications for Construction of Highway Bridges and Culvers" (JTJ041-2000), and may be appropriate to relax, the horizontal axis deviation of the allowable range may be slightly larger than the vertical deviation of the allowable range.
The research work benefits to learning about the process until the whole trussed arch bridge structure finally failures and many influence factor on the ultimate load bearing capacity of this kind of old trussed arch bridges; provides many useful experiences and advices on evaluation of ultimate load bearing capacity, overrunning capacity, security evaluation, and so on of trussed arch bridges with defects and damage in service for many years.
引文
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