大跨度钢桁架拱桥预拱度设置及拼装误差理论研究
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摘要
随着我国高速铁路建设的发展，客运专线对大桥的安全性和舒适性提出了更高要求，桥梁结构需要具有足够的竖向刚度、一定的横向刚度和匀顺的成桥线形。除制造误差（包括材料的物理参数和杆件的几何尺寸误差）之外，预拱度设置和螺栓对孔拼装精度是决定大跨度钢桁架拱桥成桥线形的主要因素。为了使成桥状态与设计要求更加吻合，本文从当前钢桁架拱桥的设计计算方法和施工工艺出发，研究了若干影响落梁线形的关键技术。主要完成了以下研究工作：
（1）理论预拱度计算有限元模型特殊区域等效处理
针对大跨度钢桁架拱桥理论预拱度计算的常用梁单元计算模型不方便直接考虑整体节点构造和横隔板加强等缺陷问题，选取具有普遍性特点的桁架杆件，通过建立实体模型和梁单元模型，对整体节点翼板、采用高强螺栓附加拼接板的弦杆连接特性、弦杆横隔板的影响和竖杆、斜腹杆与弦杆节点的连接分别作数值对比分析，探索出特殊区域的相应等效处理方法。经东莞东江大桥荷载试验验证，对钢桁梁特殊区域等效处理后的空间有限元计算模型，具有较高的计算精度。
（2）大跨度钢桁梁桥厂制预拱度设置
针对常用的斜杆形下承式钢桁架拱桥结构，采用有限单元法，以相对预拱度作为荷载参数，将通常由求解杆件伸缩引起拱度的逆问题转化为由相对预拱度求解杆件伸缩量的正问题，推导了杆件的伸缩公式。然后将该方法编译成计算程序和做成“杆件伸缩-预拱值”对照表格，方便设置预拱度时兼顾杆件伸缩的统一性，避免反复试算。使用该方法设置预拱度，容易使成桥节点的预拱值落在理论预拱线上，从而得到更加匀顺的预拱度线形。在此基础上，根据预拱度设置引起错孔的允许范围，推导了相对预拱度允许值的计算公式，对于错孔较厉害的杆件连接，提出了螺栓孔布置的处理方法。
（3）杆件连接拼装误差计算
根据杆件拼装定位施工工艺，分析了弦杆定位、竖杆和拱肋拼装定位的状态，重点研究了大跨度钢桁梁常用悬臂拼装架设方法的拼装误差，通过引入定位拼装误差概念，推导了梅花形定位安装杆件的定位拼装误差计算公式。
在此基础上，将定位拼装误差计算公式应用于厦深铁路榕江特大桥弦杆拼装误差计算，计算分析结果揭示了定位拼装误差的变化规律：定位拼装的线误差对杆端的偏位影响较小，杆端偏位主要来自定位拼装的角误差；在拼接接头的对角位置打入定位冲钉，能减小定位拼装误差。
（4）累积拼装误差对桥梁状态的影响
运用工艺尺寸链理论和定位拼装误差计算方法，推导悬臂拼装的误差线形和合龙口的极值拼装误差，揭示了拼装误差累积规律。在此基础上，分析了拼装误差对大跨度拱桥线形和内力的影响。通过采用极值法求解了榕江特大桥施工过程的拼装误差，得出：拼装累积误差对高精度合龙和成桥线形以及内力均有较大影响。
（5）拼装误差控制技术研究
首先根据拼装误差的控制要求，采用极值法推导了螺栓孔直径和定位冲钉直径之差的关系式；然后将工艺尺寸链理论应用于拼装误差控制，采用增环和减环错开技术将拼装误差分散，能减小拼装累积误差对成桥线形和内力的影响。根据施工工艺，对杆件连接的拼装误差提出控制措施，以及较系统地阐述了合龙误差调整技术。
With the developing of rapid transit railway construction, higher requirements of safetyand comfort of the bridges are needed for Passenger Dedicated Lines. That is to say, thebridges should have enough vertical stiffness, some lateral stiffness and smooth curve.Besides forming errors, camber setting and installation accuracy are also two key elements tothe shape of long-span steel trussed arch bridges. To make the shape and stress distribution ofthe completed bridges agree well with the corresponding design value, the paper researchedthe camber computation, the camber setting, the installation error compute and the installationerror control techniques according to the design procedures and construction technology ofthe long-span steel trussed arch bridge. The main research work covers the following aspects:
(1) Equivalent process method in some special areas about finite element model ofcomputational camber.
To solve the problem of the common beam elements, which can not directly consider thespecial structure of integral joint and diaphragm reinforced effect of chord member of steeltrussed arch bridge, a solide element model and several beam element models were erectedfor the common component parts. Then, frange plate of integral joint, high strength boltaddition with buttcover plate connection, diaphragm reinforced effect of chord member anddiagonal members and integral joint connection were computed with these models. Throughcomparing the calculation results, equivalent process method was obtained for solving thesespecial areas of steel trussed arch bridge. The result of the acceptance loading test ofDongjiang Bridge presents that the equivalent process method can get higher precision. So, amore reasonable camber will be obtained by the proposed method.
(2) Study on fabrication camber setting of long-span steel truss bridge
Based on the finite element method, taken the relative camber between two adjacentnodes as displacement load, some computational formulas of member bar extension orcontraction were deduced for the frequently-used N type steel truss girder. The proposedmethod can be compiled conveniently and made a comparison table between the relativecamber and the length of member bars. So, the proposed method could avoid compute andadjust repeatedly, and a close to the theoretical camber curve could be designed easily by theproposed method. On that basis, a computational formula of the allowable value of relativecamber according to the fixed position boundary of driftpin, and some processing methods ofbolt hole were proposed for severe deviation closure members.
(3) Installation error compute of member bars
The fixed position of the chord member, vertical member and diagonal member werediscussed according to the construction technology. Then, the installation error was studiedunder cantilever construction of long-span stell trussed bridges. Through introducing fixedposition error concept, the computational equations were deduced by quincuncial fixedposition.
On that basis, the installation error of chord member connection of Rongjiang Bridgewas obtained by the proposed equations. The calculated results present that: the line error offixed position has small influence on the cantilever end, and most of deviation of thecantilever end comes from angle error of fixed position; when two across corners bolt holesplay fixed position of the chord member role, the deviation is smallest.
(4) The influence of cumulative installation error on finished bridge
Based on dimension chain theory and calculation method of fixed position error, theinstallation error line of cantilever construction and the extremum installation error of closurewere deduced. Then, the paper analysed the influence on the shape and stress of the stelltrussed bridge by the installation error. The installation error of construction of RongjiangBridge was researched by extremum method, which presents that: the cumulative installationerror has great influence on high precision closured, the shape and the stress of the bridge.
(5) Research on installation error control technology
Based on dimension chain theory, the relationship between the diameter of bolt hole and thediameter of driftpin was deduced according the allowable installtion error value. The positiveinstallation error internodes by the negative installation error internodes distribution canminimize the influence on the shape and the stress of the bridge. According to constructiontechnology, the paper proposed some installation error control measures for the member barconnection, and researched a systematic adjust technology about closure error.
（1）理论预拱度计算有限元模型特殊区域等效处理
针对大跨度钢桁架拱桥理论预拱度计算的常用梁单元计算模型不方便直接考虑整体节点构造和横隔板加强等缺陷问题，选取具有普遍性特点的桁架杆件，通过建立实体模型和梁单元模型，对整体节点翼板、采用高强螺栓附加拼接板的弦杆连接特性、弦杆横隔板的影响和竖杆、斜腹杆与弦杆节点的连接分别作数值对比分析，探索出特殊区域的相应等效处理方法。经东莞东江大桥荷载试验验证，对钢桁梁特殊区域等效处理后的空间有限元计算模型，具有较高的计算精度。
（2）大跨度钢桁梁桥厂制预拱度设置
针对常用的斜杆形下承式钢桁架拱桥结构，采用有限单元法，以相对预拱度作为荷载参数，将通常由求解杆件伸缩引起拱度的逆问题转化为由相对预拱度求解杆件伸缩量的正问题，推导了杆件的伸缩公式。然后将该方法编译成计算程序和做成“杆件伸缩-预拱值”对照表格，方便设置预拱度时兼顾杆件伸缩的统一性，避免反复试算。使用该方法设置预拱度，容易使成桥节点的预拱值落在理论预拱线上，从而得到更加匀顺的预拱度线形。在此基础上，根据预拱度设置引起错孔的允许范围，推导了相对预拱度允许值的计算公式，对于错孔较厉害的杆件连接，提出了螺栓孔布置的处理方法。
（3）杆件连接拼装误差计算
根据杆件拼装定位施工工艺，分析了弦杆定位、竖杆和拱肋拼装定位的状态，重点研究了大跨度钢桁梁常用悬臂拼装架设方法的拼装误差，通过引入定位拼装误差概念，推导了梅花形定位安装杆件的定位拼装误差计算公式。
在此基础上，将定位拼装误差计算公式应用于厦深铁路榕江特大桥弦杆拼装误差计算，计算分析结果揭示了定位拼装误差的变化规律：定位拼装的线误差对杆端的偏位影响较小，杆端偏位主要来自定位拼装的角误差；在拼接接头的对角位置打入定位冲钉，能减小定位拼装误差。
（4）累积拼装误差对桥梁状态的影响
运用工艺尺寸链理论和定位拼装误差计算方法，推导悬臂拼装的误差线形和合龙口的极值拼装误差，揭示了拼装误差累积规律。在此基础上，分析了拼装误差对大跨度拱桥线形和内力的影响。通过采用极值法求解了榕江特大桥施工过程的拼装误差，得出：拼装累积误差对高精度合龙和成桥线形以及内力均有较大影响。
（5）拼装误差控制技术研究
首先根据拼装误差的控制要求，采用极值法推导了螺栓孔直径和定位冲钉直径之差的关系式；然后将工艺尺寸链理论应用于拼装误差控制，采用增环和减环错开技术将拼装误差分散，能减小拼装累积误差对成桥线形和内力的影响。根据施工工艺，对杆件连接的拼装误差提出控制措施，以及较系统地阐述了合龙误差调整技术。
With the developing of rapid transit railway construction, higher requirements of safetyand comfort of the bridges are needed for Passenger Dedicated Lines. That is to say, thebridges should have enough vertical stiffness, some lateral stiffness and smooth curve.Besides forming errors, camber setting and installation accuracy are also two key elements tothe shape of long-span steel trussed arch bridges. To make the shape and stress distribution ofthe completed bridges agree well with the corresponding design value, the paper researchedthe camber computation, the camber setting, the installation error compute and the installationerror control techniques according to the design procedures and construction technology ofthe long-span steel trussed arch bridge. The main research work covers the following aspects:
(1) Equivalent process method in some special areas about finite element model ofcomputational camber.
To solve the problem of the common beam elements, which can not directly consider thespecial structure of integral joint and diaphragm reinforced effect of chord member of steeltrussed arch bridge, a solide element model and several beam element models were erectedfor the common component parts. Then, frange plate of integral joint, high strength boltaddition with buttcover plate connection, diaphragm reinforced effect of chord member anddiagonal members and integral joint connection were computed with these models. Throughcomparing the calculation results, equivalent process method was obtained for solving thesespecial areas of steel trussed arch bridge. The result of the acceptance loading test ofDongjiang Bridge presents that the equivalent process method can get higher precision. So, amore reasonable camber will be obtained by the proposed method.
(2) Study on fabrication camber setting of long-span steel truss bridge
Based on the finite element method, taken the relative camber between two adjacentnodes as displacement load, some computational formulas of member bar extension orcontraction were deduced for the frequently-used N type steel truss girder. The proposedmethod can be compiled conveniently and made a comparison table between the relativecamber and the length of member bars. So, the proposed method could avoid compute andadjust repeatedly, and a close to the theoretical camber curve could be designed easily by theproposed method. On that basis, a computational formula of the allowable value of relativecamber according to the fixed position boundary of driftpin, and some processing methods ofbolt hole were proposed for severe deviation closure members.
(3) Installation error compute of member bars
The fixed position of the chord member, vertical member and diagonal member werediscussed according to the construction technology. Then, the installation error was studiedunder cantilever construction of long-span stell trussed bridges. Through introducing fixedposition error concept, the computational equations were deduced by quincuncial fixedposition.
On that basis, the installation error of chord member connection of Rongjiang Bridgewas obtained by the proposed equations. The calculated results present that: the line error offixed position has small influence on the cantilever end, and most of deviation of thecantilever end comes from angle error of fixed position; when two across corners bolt holesplay fixed position of the chord member role, the deviation is smallest.
(4) The influence of cumulative installation error on finished bridge
Based on dimension chain theory and calculation method of fixed position error, theinstallation error line of cantilever construction and the extremum installation error of closurewere deduced. Then, the paper analysed the influence on the shape and stress of the stelltrussed bridge by the installation error. The installation error of construction of RongjiangBridge was researched by extremum method, which presents that: the cumulative installationerror has great influence on high precision closured, the shape and the stress of the bridge.
(5) Research on installation error control technology
Based on dimension chain theory, the relationship between the diameter of bolt hole and thediameter of driftpin was deduced according the allowable installtion error value. The positiveinstallation error internodes by the negative installation error internodes distribution canminimize the influence on the shape and the stress of the bridge. According to constructiontechnology, the paper proposed some installation error control measures for the member barconnection, and researched a systematic adjust technology about closure error.
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