斜跨拱桥结构静力性能研究
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摘要
斜跨拱桥是近年来才发展起来的一种桥梁结构形式。该桥型采用单根拱肋斜交横跨主梁的空间布置形式,拱脚分别位于桥梁上下游两侧,拱肋和主梁之间通过吊索连接,吊索空间布置。该类桥型的出现为大跨径曲线梁桥的设计提供了一种新的备选方案。由于这种桥型特殊的空间布置形式,结构的受力也较为复杂。本文根据张家口通泰大桥设计过程中所遇到的问题和难点,主要从以下方面进行了研究：
1.合理拱轴线的求解
合理拱轴线的确定对拱桥的设计具有至关重要的意义。拱桥拱轴线是否合理直接关系到全桥的安全和经济两个方面的问题。偏态拱桥、斜跨拱桥等异型拱桥的出现也使合理拱轴线的求解变得较为复杂。本文基于集中荷载作用下拱桥的合理拱轴线为分段悬链线的假定,推导了拱桥合理拱轴线二阶微分方程,并采用数值解法对方程进行求解以确定对应荷载工况下拱肋的合理拱轴线；根据合理拱轴线的定义,拱肋在对应荷载的合理拱轴状态下,拱肋只承受轴力,不承担弯矩,此时拱肋可以简化为桁架体系,根据这种假设,提出了拱桥合理拱轴线的桁架近似数值解法。结合工程实际,验证了二阶微分方程数值方法和桁架近似数值解法的实用性。对于斜跨拱桥,在拱脚无吊索区段,拱轴线曲率较小,线形较为平直；在跨中吊索集中布置区段,拱轴线曲率较大,可采用多次抛物线进行拟合。
2.斜跨拱桥稳定及其影响因素分析
斜跨拱桥作为一种近年来才发展起来的一种新型桥梁结构形式,由于其典型的空间受力特性,结构受力异常复杂。本文分别采用特征值求解方法和基于弹塑性理论的双重非线性有限元法对张家口通泰大桥的稳定问题进行了分析。与常规拱桥不同,斜跨拱桥的失稳模态不再是单纯的面内失稳或面外失稳,而是表现为面内和面外失稳的复合形式。针对通泰大桥,拱肋的面内抗弯刚度和矢跨比的变化,对结构的整体稳定性有较大影响；与吊索均布的常规拱桥相比,斜跨拱桥由于吊索布置相对集中,其合理矢跨比较常规拱桥更大,一般在0.35左右较为合理。通过研究两座斜跨拱桥稳定性发现,两座斜跨拱桥的第一类稳定系数和第二类稳定系数的比值分别为4.8和6.16,该比值高于常规拱桥。因此在采用第一类稳定分析对斜跨拱桥的整体稳定进行验算时,与常规拱桥相比,斜跨拱桥需要更高的第一类稳定系数。
3.斜跨拱桥合理成桥状态分析
基于能量原理,考虑空间效应的影响,研究了无约束优化方法和有约束优化方法在斜跨拱桥合理成桥状态求解过程中的的应用;讨论了两种优化方法在求解斜跨式拱桥合理成桥索力时的适用性；仅采用以结构应变能最小为目标函数的无约束优化方法不能求解出斜跨拱桥的合理成桥索力,通过构造索力均匀化函数再次优化能够得到较为均匀的索力。基于能量法的有约束优化方法,通过施加合理的约束条件,能够有效地求解斜跨拱桥合理成桥状态对应的索力；通过对关键断面内力的限制,可以方便的考虑活载效应的影响。对比研究结果表明,对于斜跨拱桥除了主梁的弯曲应变能外,主梁的扭转应变能也是影响合理成桥状态的主要因素。合理成桥状态下,斜跨拱桥拱肋和主梁均存在较大的扭矩,拱肋和主梁应采用箱形截面。
4.斜跨拱桥模型实验研究
为了研究斜跨拱桥的整体结构特性,并检验所采用的设计及计算理论的适用性,以张家口通泰大桥为原型,根据相似理论,建立了全桥1：25缩尺试验模型。通过有限元分析和试验结果的对比验证了：现有的空间杆系有限元计算理论能够满足这种新型桥梁结构设计计算的需要,深化了对斜跨拱桥结构受力特性的理解。为实际工程的设计与力学性能研究提供依据,并为同类型桥梁的设计提供参考。
Diagonal-span arch bridge is a new type of bridge developed in recent years. This bridge type using a spatial arrangement with a single arch oblique across the main beam, the two arch springers are respectively located at the upstream and downstream of the bridge, and spatial hangers are used to connect the arch with the mian beam. The emergence of this bridge type provides a new alternative for long-span curved bridge. As the special spatial arrangement, the inner forces of this bridge type are also more complicated than others. Based on the problems and difficulties encountered in the design of Tongtai Bridge in Zhang jia-kou, the following aspects are studyed in this paper:
1. The solving method of the reasonable arch axis
The determination of reasonable arch axis is very important in the design of arch bridge. The arch axis is reasonable or not, is directly related to the aspects of security and economy. The appearance of special-shape arch bridge, such as skewed arch bridge and diagonal-span arch bridge, make solving the reasonable arch axis become more complex. Based on the assumption of the reasonable arch axis is a inverted segmented catenary under concentrated loads, this paper derives the second order differential equations of the reasonable arch axis, and solves the equations with numerical method to obtain the reasonable arch axis under the corresponding load cases; Arch rib can be simplified as a truss system based on the definition of reasonable arch axis when the arch rib is only exposed to axial force under the corresponding load case, according to this assumption, this paper proposed an approximate numerical method to solve the reasonable arch axis of the truss system. Combined with the actual engineering, verify the practicality of the numerical solution method of the second order differential equations and the simplified truss. For the diagonal span arch bridge, in the arch rib near the arch springer without hangers, the curvature of the arch axis is small, the arc axis relatively flat; in the middle of the arch rib, the hangers are centralized arrangement, the curvature of the arch axis is greater, parabola of higher degree can be used to fit the arch rib axis.
2. The analysis of stability of diagonal-span arch bridge and its influence factors
As a new type of bridge structure, curved diagonal-span arch bridge is developed in recent years, as for its typical characteristics of spatail arrangement the structural performance is very complex. This paper uses eigensolvers method and double nonlinear finite element method based on the theory of elastic-plastic to solve the stability of Tongtai Bridge respectively. Compared with conventional arch bridge, under the ultimate load the failure modes of diagonal-span arch bridge performed to be the combination of the in-plan and out-of-plan buckling modal. In the method using eigenvalue analysis, the Tongtai Bridge has large stability factors under different load cases. For Tongtai Bridge, the rib-plane bending stiffness and the rise-to-span ratio changes can greatly affect the overall stability of the structure. Compared with the conventional arch with the hangers are uniform layout, since the hangers of diagonal span arch are relatively arranged concentratly, the rise-to-span ratio of the diagonal-span arch bridge is greater than conventional arch bridge, generally about0.35is more reasonable. By studying stability of the two diagonal-span arch bridge we found that the two diagonal arch stability factors of the first class and second class stability coefficient ratios were4.8and6.16, the ratio is higher than the conventional arch bridge. Therefore, when the first category is adaped to analysis the overall stability on the diagonal-span arch bridge, compared with the conventional arch bridge, the diagonal-span arch bridge require higher first class stability factor.
3. Analysis of reasonable finished state of diagonal-span arch bridge
Based on the energy principle with the consideration of spatial effects, this paper researched the application of unconstrained optimization method and constrained optimization method in solving a reasonable finished state of diagonal-span arch bridge; It discussed the applicability of the two optimization methods in solving hanger forces of reasonable finished state of diagonal-span arch bridge; Cable tension forces of reasonable finished state of diagonal-span arch bridge can not be solved by unconstrained optimization methods which only demand the minimum structural strain energy as the objective function, but relative uniform cable tension forces can be obtained by analysis of unconstrained optimization which objective function reconstructed through adding appropriate weighting factor. The constrained optimization method based on energy method can be effectively used to determine the reasonable finished state of diagonal-span arch bridge. By limiting the force of the key sections, the live load effects can be considered. Comparative study results show that for diagonal-span arch bridge in addition to the main beam bending strain energy, the main beam torsional strain energy can also be a main factor of reasonable finished state of diagonal-span arch bridge. Under the reasonable finished state, there is a big torque in the main beam and the arcrib, for the diagonal-span arch bridge the box-section should be used in main beam and the arcrib.
4. Model experimental research of diagonal-span arch bridge
In order to study the overall structure characteristics of the diagonal span arch bridge characteristics and verify the correctness of the design and calculation methods, based on the similarity theory, a full-bridge1:25reduced scale test model of Zhangjiakou Tongtai Bridge is built. Through the comparison of finite element analysis and experimental results verified that the design theory and calculation method used in this new type bridge structure is adpable. and the understanding of the structure characteristics of the diagonal span arch bridge has deepened. The conclutions provide the basis for the actual engineering design and provide a reference for the same type of bridge.
1.合理拱轴线的求解
合理拱轴线的确定对拱桥的设计具有至关重要的意义。拱桥拱轴线是否合理直接关系到全桥的安全和经济两个方面的问题。偏态拱桥、斜跨拱桥等异型拱桥的出现也使合理拱轴线的求解变得较为复杂。本文基于集中荷载作用下拱桥的合理拱轴线为分段悬链线的假定,推导了拱桥合理拱轴线二阶微分方程,并采用数值解法对方程进行求解以确定对应荷载工况下拱肋的合理拱轴线；根据合理拱轴线的定义,拱肋在对应荷载的合理拱轴状态下,拱肋只承受轴力,不承担弯矩,此时拱肋可以简化为桁架体系,根据这种假设,提出了拱桥合理拱轴线的桁架近似数值解法。结合工程实际,验证了二阶微分方程数值方法和桁架近似数值解法的实用性。对于斜跨拱桥,在拱脚无吊索区段,拱轴线曲率较小,线形较为平直；在跨中吊索集中布置区段,拱轴线曲率较大,可采用多次抛物线进行拟合。
2.斜跨拱桥稳定及其影响因素分析
斜跨拱桥作为一种近年来才发展起来的一种新型桥梁结构形式,由于其典型的空间受力特性,结构受力异常复杂。本文分别采用特征值求解方法和基于弹塑性理论的双重非线性有限元法对张家口通泰大桥的稳定问题进行了分析。与常规拱桥不同,斜跨拱桥的失稳模态不再是单纯的面内失稳或面外失稳,而是表现为面内和面外失稳的复合形式。针对通泰大桥,拱肋的面内抗弯刚度和矢跨比的变化,对结构的整体稳定性有较大影响；与吊索均布的常规拱桥相比,斜跨拱桥由于吊索布置相对集中,其合理矢跨比较常规拱桥更大,一般在0.35左右较为合理。通过研究两座斜跨拱桥稳定性发现,两座斜跨拱桥的第一类稳定系数和第二类稳定系数的比值分别为4.8和6.16,该比值高于常规拱桥。因此在采用第一类稳定分析对斜跨拱桥的整体稳定进行验算时,与常规拱桥相比,斜跨拱桥需要更高的第一类稳定系数。
3.斜跨拱桥合理成桥状态分析
基于能量原理,考虑空间效应的影响,研究了无约束优化方法和有约束优化方法在斜跨拱桥合理成桥状态求解过程中的的应用;讨论了两种优化方法在求解斜跨式拱桥合理成桥索力时的适用性；仅采用以结构应变能最小为目标函数的无约束优化方法不能求解出斜跨拱桥的合理成桥索力,通过构造索力均匀化函数再次优化能够得到较为均匀的索力。基于能量法的有约束优化方法,通过施加合理的约束条件,能够有效地求解斜跨拱桥合理成桥状态对应的索力；通过对关键断面内力的限制,可以方便的考虑活载效应的影响。对比研究结果表明,对于斜跨拱桥除了主梁的弯曲应变能外,主梁的扭转应变能也是影响合理成桥状态的主要因素。合理成桥状态下,斜跨拱桥拱肋和主梁均存在较大的扭矩,拱肋和主梁应采用箱形截面。
4.斜跨拱桥模型实验研究
为了研究斜跨拱桥的整体结构特性,并检验所采用的设计及计算理论的适用性,以张家口通泰大桥为原型,根据相似理论,建立了全桥1：25缩尺试验模型。通过有限元分析和试验结果的对比验证了：现有的空间杆系有限元计算理论能够满足这种新型桥梁结构设计计算的需要,深化了对斜跨拱桥结构受力特性的理解。为实际工程的设计与力学性能研究提供依据,并为同类型桥梁的设计提供参考。
Diagonal-span arch bridge is a new type of bridge developed in recent years. This bridge type using a spatial arrangement with a single arch oblique across the main beam, the two arch springers are respectively located at the upstream and downstream of the bridge, and spatial hangers are used to connect the arch with the mian beam. The emergence of this bridge type provides a new alternative for long-span curved bridge. As the special spatial arrangement, the inner forces of this bridge type are also more complicated than others. Based on the problems and difficulties encountered in the design of Tongtai Bridge in Zhang jia-kou, the following aspects are studyed in this paper:
1. The solving method of the reasonable arch axis
The determination of reasonable arch axis is very important in the design of arch bridge. The arch axis is reasonable or not, is directly related to the aspects of security and economy. The appearance of special-shape arch bridge, such as skewed arch bridge and diagonal-span arch bridge, make solving the reasonable arch axis become more complex. Based on the assumption of the reasonable arch axis is a inverted segmented catenary under concentrated loads, this paper derives the second order differential equations of the reasonable arch axis, and solves the equations with numerical method to obtain the reasonable arch axis under the corresponding load cases; Arch rib can be simplified as a truss system based on the definition of reasonable arch axis when the arch rib is only exposed to axial force under the corresponding load case, according to this assumption, this paper proposed an approximate numerical method to solve the reasonable arch axis of the truss system. Combined with the actual engineering, verify the practicality of the numerical solution method of the second order differential equations and the simplified truss. For the diagonal span arch bridge, in the arch rib near the arch springer without hangers, the curvature of the arch axis is small, the arc axis relatively flat; in the middle of the arch rib, the hangers are centralized arrangement, the curvature of the arch axis is greater, parabola of higher degree can be used to fit the arch rib axis.
2. The analysis of stability of diagonal-span arch bridge and its influence factors
As a new type of bridge structure, curved diagonal-span arch bridge is developed in recent years, as for its typical characteristics of spatail arrangement the structural performance is very complex. This paper uses eigensolvers method and double nonlinear finite element method based on the theory of elastic-plastic to solve the stability of Tongtai Bridge respectively. Compared with conventional arch bridge, under the ultimate load the failure modes of diagonal-span arch bridge performed to be the combination of the in-plan and out-of-plan buckling modal. In the method using eigenvalue analysis, the Tongtai Bridge has large stability factors under different load cases. For Tongtai Bridge, the rib-plane bending stiffness and the rise-to-span ratio changes can greatly affect the overall stability of the structure. Compared with the conventional arch with the hangers are uniform layout, since the hangers of diagonal span arch are relatively arranged concentratly, the rise-to-span ratio of the diagonal-span arch bridge is greater than conventional arch bridge, generally about0.35is more reasonable. By studying stability of the two diagonal-span arch bridge we found that the two diagonal arch stability factors of the first class and second class stability coefficient ratios were4.8and6.16, the ratio is higher than the conventional arch bridge. Therefore, when the first category is adaped to analysis the overall stability on the diagonal-span arch bridge, compared with the conventional arch bridge, the diagonal-span arch bridge require higher first class stability factor.
3. Analysis of reasonable finished state of diagonal-span arch bridge
Based on the energy principle with the consideration of spatial effects, this paper researched the application of unconstrained optimization method and constrained optimization method in solving a reasonable finished state of diagonal-span arch bridge; It discussed the applicability of the two optimization methods in solving hanger forces of reasonable finished state of diagonal-span arch bridge; Cable tension forces of reasonable finished state of diagonal-span arch bridge can not be solved by unconstrained optimization methods which only demand the minimum structural strain energy as the objective function, but relative uniform cable tension forces can be obtained by analysis of unconstrained optimization which objective function reconstructed through adding appropriate weighting factor. The constrained optimization method based on energy method can be effectively used to determine the reasonable finished state of diagonal-span arch bridge. By limiting the force of the key sections, the live load effects can be considered. Comparative study results show that for diagonal-span arch bridge in addition to the main beam bending strain energy, the main beam torsional strain energy can also be a main factor of reasonable finished state of diagonal-span arch bridge. Under the reasonable finished state, there is a big torque in the main beam and the arcrib, for the diagonal-span arch bridge the box-section should be used in main beam and the arcrib.
4. Model experimental research of diagonal-span arch bridge
In order to study the overall structure characteristics of the diagonal span arch bridge characteristics and verify the correctness of the design and calculation methods, based on the similarity theory, a full-bridge1:25reduced scale test model of Zhangjiakou Tongtai Bridge is built. Through the comparison of finite element analysis and experimental results verified that the design theory and calculation method used in this new type bridge structure is adpable. and the understanding of the structure characteristics of the diagonal span arch bridge has deepened. The conclutions provide the basis for the actual engineering design and provide a reference for the same type of bridge.
引文
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