大跨度钢拱桥极限承载力综合三因素检算方法研究
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摘要
随着我国桥梁建设的发展,出现了一些造型新颖、构造复杂的大跨度钢拱桥。其极限承载力是设计建造中的关键问题。在实际工程中,通过复杂非线性分析确定钢拱桥极限承载力的方法实用性不强。为此,本文尝试建立一种简化检算的框架,实现采用线性方法检算钢拱桥极限承载力这个复杂的非线性问题。以国内在建的重庆菜园坝大桥、广州新光大桥等工程为背景,本文开展了以下几方面的研究工作。
1 总结钢拱桥极限承载力分析中常用的非线性梁单元理论。通过理论分析与试验结果的对比,指出可以采用商用有限元软件的非线性梁单元分析钢拱桥极限承载力,同时也可以模拟残余应力、组合截面等问题。提出采用双重非线性超参数板壳单元建立钢拱桥模型,结合实体单元和杆单元建立高精度全桥模型,同时将准Newton-Raphson法和线性搜索法结合,提高非线性计算收敛效率。为了较好地满足求解精度和速度问题,还对3种不同网格密度的钢拱板壳单元模型的计算时间和精度进行了对比,确定恰当的模型规模。通过该模型进一步说明钢拱桥极限承载力的本质。与非线性梁单元的结果进行比较后,提出考虑节点板、加劲肋和横隔板后的非线性梁单元模型的改进方案。最后指出非线性有限元计算对于设计而言相对复杂,在其基础上建立简化检算方法更具实际意义。
2 通过实际钢拱桥和两个模型结构的非线性分析计算和对比,得到钢拱桥达到极限承载力过程中的应力和内力变化情况。参数变化对钢拱桥极限承载力的影响,都可以从拱肋各项内力的变化体现出来。进而提出横向初始缺陷与横向位移因素检算指标R_(11),并推导其表达式,以便在极限承载力简化检算方法体现这两方面因素的影响。
3 采用Ritz法推导非均匀横撑布置时的拱结构侧倾临界荷载。提出采用非线性规划方法,优化横撑布置。将弹性侧倾临界荷载的表达式代入非线性规划软件Lingo,运用序列线性规划方法求解横撑间距优化问题。为了提高求解效率,采用启发式方法生成初始解;采用逐次线性规划方法寻找搜索方向;采用最陡边策略,找到使目标值下降最多的变量进行迭代。提出拱圈整体横向刚
More than ever before in China, the application of steel arch bridges have become popular. Some novel and complex steel arch bridges have appeared. The problem of ultimate load carrying capacity is a key point in the design and construction of long-span steel arch bridges. In spite of many scholars have researched this problem and some regulations have been introduced in codes, theoretical studies in our country are still not comprehensive and cannot guide real design works precisely. Non-linear numerical analysis method for the ultimate load carrying capacity has been used in some design works of long-span steel arch bridges. But this method is inefficient and cannot incarnate the essence of collapse of an entire steel arch bridge. Based on Caiyuanba Bridge in Chongqing and Xinguang Bridge in Guangzhou, the main contents of this dissertation are summarized as follows:Nonlinear beam element theories used to analyze ultimate load carrying capacity of steel arch bridges are inducted. After comparing with the results of theoretical analysis and model tests, it is point out that commercial FEA software can be used in calculating ultimate load carrying capacity of steel arch bridges. Residual stress by welding and composite profile could be simulated simply using beam element in commercial FEA software, such as ANSYS. High precision entire steel arch bridge models are established by dual nonlinear supper-parametric shell elements, brick elements and truss elements. In order to get higher accuracy, BFGS(Broyden-Fletcher-Goldfarb-Shanno) method of quasi-Newton method and line search method are combined. To prove the accuracy and convergence of the results, three FE meshes are tested. On this basis, suitable model dimension is determined and this method can further reveal the essence of ultimate load carrying capacity. After comparing the results of this higher accuracy model with those of nonlinear beam element, schemes of modifying nonlinear beam element model are presented considering the influences of integral gusset plates, stiffener and internal diaphragms. Finally, it is pointed that nonlinear analysis is too complicated to guild design work and simplify
check method is more practical.On the grounds of nonlinear calculation for a real steel arch bridge and two test models, variations of stresses and internal forces have been obtained. Then main emphasis is put on the essence of ultimate load carrying capacity. The reasons for this instability phenomenon might be explained as follows: Due to the yielding of profiles and the diffusion of plastic zones at arch ribs, the stiffness of profiles is reduced. As the result, the nonlinear displacement will become relatively considerable. The effects of design parameters can be reflected by the variations of the internal forces at key profiles. So the effects of many factors can be reflected by the variations of the internal forces at key profiles. Formula of effect index R/; is firstly put forwarded. So the influences of lateral initial crookedness and lateral loads can be embodied in simple check method for ultimate load carrying capacity of long-span steel arch bridges.The calculation formula of the critical load of the circle ribs with non-uniform distributed bracings has deduced with the method of Ritz. Non-linear programming is adopted to optimize of the bracing location for the first time. Formula of the critical load of the circle ribs is imported into software Lingo to solve the problem of bracing location optimization. In order to decrease numbers of total iterations, three strategies, heuristic method for generating a good starting point, successive linear programming to compute new search directions, and the steepest-edge strategy when selecting variables to iterate on, are used. In order to reflect the effects of total lateral stiffness of ribs, formula of effect index R21 is put forwarded. So the effects of stiffness, numbers and locations of bracings on ultimate load carrying capacity of long-span steel arch bridges can be embodied in simple check method.Two preconditions, lateral stiffness of main girder and loads transferred through hangers, resulting in non-directional loads effects are specifically pointed out and certificated. Very few researches, however, have been reported so far on the second condition. Using Ritz method, a formula of lateral critical buckling load of steel arch bridges under non-directional and directional loads is proposed, in accordance with mechanical characteristics of long-span steel arch bridges. For the first time, it is illustrated theoretically that only the loads transferred through
hangers can result in non-directional loads effect of steel arch bridges. Distribution factor for loads is introduced to present the ratio of non-directional loads to directional loads. According to the results calculated, relationship of ultimate load carrying capacity and this factor is founded. In order to reflect the effects of non-directional loads, formula of effect index R3/ is put forwarded. So this factor can be embodied in simple check method for ultimate load carrying capacity of long-span steel arch bridges.Based on the factor index of lateral initial crookedness and lateral loads /?//, the factor index of total lateral stiffness of ribs R21 ,and the factor index of non-directional loads R31, a synthetical index is finally put forwarded to establish Rf=RnR2iR.3i, for checking ultimate load carrying capacity of steel arch bridges. And a safety index K= RtfR is also proposed. Through comparison with the results of model tests, specifications of different countries and four steel arch bridges, accuracy and efficiency of the synthetical three factors method is finally verified. If./? corresponding to the linear internal forces at key profiles under dead loads and full span loads is less than Ri, the entire steel arch bridge is still not reach its ultimate load carrying capacity state.According to a systematical summary of achievements obtained by dozens of domestic and foreign scholars, effects of sixteen factors, such as lateral stiffness of ribs and non-directional loads effects, on ultimate load carrying capacity have been reflected. Differences of Eurocode3, DIN 18800, JHSB, JSSC, AASHTO, JTJ 025-86 and TB 10002.2-99 have been compared through a steel arch bridge model. The synthetical three factors check method proposed in this dissertation has reflected main factors which affect the ultimate load carrying capacity of long-span steel arch bridges.
1 总结钢拱桥极限承载力分析中常用的非线性梁单元理论。通过理论分析与试验结果的对比,指出可以采用商用有限元软件的非线性梁单元分析钢拱桥极限承载力,同时也可以模拟残余应力、组合截面等问题。提出采用双重非线性超参数板壳单元建立钢拱桥模型,结合实体单元和杆单元建立高精度全桥模型,同时将准Newton-Raphson法和线性搜索法结合,提高非线性计算收敛效率。为了较好地满足求解精度和速度问题,还对3种不同网格密度的钢拱板壳单元模型的计算时间和精度进行了对比,确定恰当的模型规模。通过该模型进一步说明钢拱桥极限承载力的本质。与非线性梁单元的结果进行比较后,提出考虑节点板、加劲肋和横隔板后的非线性梁单元模型的改进方案。最后指出非线性有限元计算对于设计而言相对复杂,在其基础上建立简化检算方法更具实际意义。
2 通过实际钢拱桥和两个模型结构的非线性分析计算和对比,得到钢拱桥达到极限承载力过程中的应力和内力变化情况。参数变化对钢拱桥极限承载力的影响,都可以从拱肋各项内力的变化体现出来。进而提出横向初始缺陷与横向位移因素检算指标R_(11),并推导其表达式,以便在极限承载力简化检算方法体现这两方面因素的影响。
3 采用Ritz法推导非均匀横撑布置时的拱结构侧倾临界荷载。提出采用非线性规划方法,优化横撑布置。将弹性侧倾临界荷载的表达式代入非线性规划软件Lingo,运用序列线性规划方法求解横撑间距优化问题。为了提高求解效率,采用启发式方法生成初始解;采用逐次线性规划方法寻找搜索方向;采用最陡边策略,找到使目标值下降最多的变量进行迭代。提出拱圈整体横向刚
More than ever before in China, the application of steel arch bridges have become popular. Some novel and complex steel arch bridges have appeared. The problem of ultimate load carrying capacity is a key point in the design and construction of long-span steel arch bridges. In spite of many scholars have researched this problem and some regulations have been introduced in codes, theoretical studies in our country are still not comprehensive and cannot guide real design works precisely. Non-linear numerical analysis method for the ultimate load carrying capacity has been used in some design works of long-span steel arch bridges. But this method is inefficient and cannot incarnate the essence of collapse of an entire steel arch bridge. Based on Caiyuanba Bridge in Chongqing and Xinguang Bridge in Guangzhou, the main contents of this dissertation are summarized as follows:Nonlinear beam element theories used to analyze ultimate load carrying capacity of steel arch bridges are inducted. After comparing with the results of theoretical analysis and model tests, it is point out that commercial FEA software can be used in calculating ultimate load carrying capacity of steel arch bridges. Residual stress by welding and composite profile could be simulated simply using beam element in commercial FEA software, such as ANSYS. High precision entire steel arch bridge models are established by dual nonlinear supper-parametric shell elements, brick elements and truss elements. In order to get higher accuracy, BFGS(Broyden-Fletcher-Goldfarb-Shanno) method of quasi-Newton method and line search method are combined. To prove the accuracy and convergence of the results, three FE meshes are tested. On this basis, suitable model dimension is determined and this method can further reveal the essence of ultimate load carrying capacity. After comparing the results of this higher accuracy model with those of nonlinear beam element, schemes of modifying nonlinear beam element model are presented considering the influences of integral gusset plates, stiffener and internal diaphragms. Finally, it is pointed that nonlinear analysis is too complicated to guild design work and simplify
check method is more practical.On the grounds of nonlinear calculation for a real steel arch bridge and two test models, variations of stresses and internal forces have been obtained. Then main emphasis is put on the essence of ultimate load carrying capacity. The reasons for this instability phenomenon might be explained as follows: Due to the yielding of profiles and the diffusion of plastic zones at arch ribs, the stiffness of profiles is reduced. As the result, the nonlinear displacement will become relatively considerable. The effects of design parameters can be reflected by the variations of the internal forces at key profiles. So the effects of many factors can be reflected by the variations of the internal forces at key profiles. Formula of effect index R/; is firstly put forwarded. So the influences of lateral initial crookedness and lateral loads can be embodied in simple check method for ultimate load carrying capacity of long-span steel arch bridges.The calculation formula of the critical load of the circle ribs with non-uniform distributed bracings has deduced with the method of Ritz. Non-linear programming is adopted to optimize of the bracing location for the first time. Formula of the critical load of the circle ribs is imported into software Lingo to solve the problem of bracing location optimization. In order to decrease numbers of total iterations, three strategies, heuristic method for generating a good starting point, successive linear programming to compute new search directions, and the steepest-edge strategy when selecting variables to iterate on, are used. In order to reflect the effects of total lateral stiffness of ribs, formula of effect index R21 is put forwarded. So the effects of stiffness, numbers and locations of bracings on ultimate load carrying capacity of long-span steel arch bridges can be embodied in simple check method.Two preconditions, lateral stiffness of main girder and loads transferred through hangers, resulting in non-directional loads effects are specifically pointed out and certificated. Very few researches, however, have been reported so far on the second condition. Using Ritz method, a formula of lateral critical buckling load of steel arch bridges under non-directional and directional loads is proposed, in accordance with mechanical characteristics of long-span steel arch bridges. For the first time, it is illustrated theoretically that only the loads transferred through
hangers can result in non-directional loads effect of steel arch bridges. Distribution factor for loads is introduced to present the ratio of non-directional loads to directional loads. According to the results calculated, relationship of ultimate load carrying capacity and this factor is founded. In order to reflect the effects of non-directional loads, formula of effect index R3/ is put forwarded. So this factor can be embodied in simple check method for ultimate load carrying capacity of long-span steel arch bridges.Based on the factor index of lateral initial crookedness and lateral loads /?//, the factor index of total lateral stiffness of ribs R21 ,and the factor index of non-directional loads R31, a synthetical index is finally put forwarded to establish Rf=RnR2iR.3i, for checking ultimate load carrying capacity of steel arch bridges. And a safety index K= RtfR is also proposed. Through comparison with the results of model tests, specifications of different countries and four steel arch bridges, accuracy and efficiency of the synthetical three factors method is finally verified. If./? corresponding to the linear internal forces at key profiles under dead loads and full span loads is less than Ri, the entire steel arch bridge is still not reach its ultimate load carrying capacity state.According to a systematical summary of achievements obtained by dozens of domestic and foreign scholars, effects of sixteen factors, such as lateral stiffness of ribs and non-directional loads effects, on ultimate load carrying capacity have been reflected. Differences of Eurocode3, DIN 18800, JHSB, JSSC, AASHTO, JTJ 025-86 and TB 10002.2-99 have been compared through a steel arch bridge model. The synthetical three factors check method proposed in this dissertation has reflected main factors which affect the ultimate load carrying capacity of long-span steel arch bridges.
引文
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