装配式连续弯桥横向分布计算的广义梁格法
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摘要
云南地处云贵高原，绝大部分为山地，山高谷深、河流密集、地形险峻、植被茂盛。由于地形受限，导致了山区高速公路的工程造价远远高于平原区高速公路。对于还处在经济欠发达的云南广大山岭地区，所选桥型的造价是否合理是一个非常现实的问题，所以山区桥梁的设计不仅要考虑其技术的可行性，更重要的是要考虑所选桥型的经济性指标是否达到了最佳范围。对于山区高速公路桥梁来说，根据工程所处的地理环境和施工条件进行多方案的技术经济指标论证，又考虑了工程费用的节约、良好经济指标的取用后，装配式连续弯桥不愧为最佳方案之一。
一般地说，曲线桥梁作为一种空间结构，可以应用结构分析的通用程序来求解。然而，对于荷载在桥上沿纵、横向移动的公路桥梁，采用象有限单元法这样的计算机方法于实际设计时，仍感不便。因此，研究曲线梁桥的荷载横向分布规律，来确定桥梁大部分的设计内力，仍然是一种有效而使于实用的方法。
但是，关于装配式连续弯桥横向分布的理论大多有两个特点：一、“忽略”横梁作用的简支窄桥理论；二、考虑弯扭耦合作用的简支宽桥理论。现有的计算理论与山区高速公路中常用的中小跨径连续弯桥的实际受力情形不符。因此，有必要在考虑装配式简支弯桥弯扭耦合作用的前提下，再进一步继续研究装配式连续弯桥的横向分布规律。
本文基于广义梁格法，在仔细考虑曲线架桥弯扭耦合作用的基础上，根据各梁的弹簧系数所建立的线性方程，导出装配式连续弯桥中各主梁荷载横向分布影响线的规律。只要在此影响线上横向加载，就可求得主梁的荷载横向分布系数，从而可按熟知的直梁桥计算步骤，方便地算出主梁和横梁的各项内力。
Yunan Province is located in YUNGUI highland. Most of the areas are characterized with having high mountains and deep valleys, highly dense mountain streams and lush vegetation. Due to the restrain of the steep terrain, the construction expenditure of highway in mountainous areas is far more costly than that in the flatland.
It is becoming a very realistic and significant issue with regard to the construction cost of proposed bridge type, especially for Yunan mountainous areas with relatively low Gross Domestic Product (GDP). Therefore, the technical design for rural bridge not only needs to take the feasibility of technology into account, but, more importantly, the optimal cost-effectiveness of chosen bridge type.
As for rural highway bridge, Assembly and Continuous Curvilinear (ACC) Bridge stands out to be an optimal option. After the validation of technical and economical index of a variety of schemes based on geographic environments and construction conditions, ACC Bridge has been proved to cut construction expenditure and bring about favourable economical effects.
Generally speaking, as a spatial structure, the feasible solution to the curvilinear bridge can be obtained by means of general equation developed in the field of applied structure analysis. However, for the case of moving loading applied along the lateral and longitudinal directions of highway bridges, it is inconvenient to utilize the finite element analysis in the practical design. So, it is cost-effective to research the lateral loading distribution of curvilinear bridge for the purpose of determining the internal force distributions in the
bridges.
There are two main properties in the theory of lateral distribution for ACC Bridges: 1) ignoring crossbeam's function in the theory of simple-narrow bridges; 2) considering the function of torsion coupling in simple-narrow bridges. Given the fact that current computation theory does not accord with the commonly used methodology for small-span curvilinear bridge in the rural highway, it is recommended to investigate the lateral distribution of the ACC Bridge on the premise of the function of torsion coupling of ACC
Bridge.
This article is developed based on a generalized method of Leonhardt-Homberg. After the careful examinations of the torsion coupling function of curvilinear bridges, the lateral distribution of ACC bridges can be derived on the basis of linear equations constructed with each beam's elasticity coefficients. Once the loading is implied on the ACC Bridge along the lateral direction, it is relatively easy to calculate the lateral distribution coefficients for girder beams. And then with the computational procedure developed for linear beams, the internal force can be calculated for girder and lateral beams, respectively.
一般地说，曲线桥梁作为一种空间结构，可以应用结构分析的通用程序来求解。然而，对于荷载在桥上沿纵、横向移动的公路桥梁，采用象有限单元法这样的计算机方法于实际设计时，仍感不便。因此，研究曲线梁桥的荷载横向分布规律，来确定桥梁大部分的设计内力，仍然是一种有效而使于实用的方法。
但是，关于装配式连续弯桥横向分布的理论大多有两个特点：一、“忽略”横梁作用的简支窄桥理论；二、考虑弯扭耦合作用的简支宽桥理论。现有的计算理论与山区高速公路中常用的中小跨径连续弯桥的实际受力情形不符。因此，有必要在考虑装配式简支弯桥弯扭耦合作用的前提下，再进一步继续研究装配式连续弯桥的横向分布规律。
本文基于广义梁格法，在仔细考虑曲线架桥弯扭耦合作用的基础上，根据各梁的弹簧系数所建立的线性方程，导出装配式连续弯桥中各主梁荷载横向分布影响线的规律。只要在此影响线上横向加载，就可求得主梁的荷载横向分布系数，从而可按熟知的直梁桥计算步骤，方便地算出主梁和横梁的各项内力。
Yunan Province is located in YUNGUI highland. Most of the areas are characterized with having high mountains and deep valleys, highly dense mountain streams and lush vegetation. Due to the restrain of the steep terrain, the construction expenditure of highway in mountainous areas is far more costly than that in the flatland.
It is becoming a very realistic and significant issue with regard to the construction cost of proposed bridge type, especially for Yunan mountainous areas with relatively low Gross Domestic Product (GDP). Therefore, the technical design for rural bridge not only needs to take the feasibility of technology into account, but, more importantly, the optimal cost-effectiveness of chosen bridge type.
As for rural highway bridge, Assembly and Continuous Curvilinear (ACC) Bridge stands out to be an optimal option. After the validation of technical and economical index of a variety of schemes based on geographic environments and construction conditions, ACC Bridge has been proved to cut construction expenditure and bring about favourable economical effects.
Generally speaking, as a spatial structure, the feasible solution to the curvilinear bridge can be obtained by means of general equation developed in the field of applied structure analysis. However, for the case of moving loading applied along the lateral and longitudinal directions of highway bridges, it is inconvenient to utilize the finite element analysis in the practical design. So, it is cost-effective to research the lateral loading distribution of curvilinear bridge for the purpose of determining the internal force distributions in the
bridges.
There are two main properties in the theory of lateral distribution for ACC Bridges: 1) ignoring crossbeam's function in the theory of simple-narrow bridges; 2) considering the function of torsion coupling in simple-narrow bridges. Given the fact that current computation theory does not accord with the commonly used methodology for small-span curvilinear bridge in the rural highway, it is recommended to investigate the lateral distribution of the ACC Bridge on the premise of the function of torsion coupling of ACC
Bridge.
This article is developed based on a generalized method of Leonhardt-Homberg. After the careful examinations of the torsion coupling function of curvilinear bridges, the lateral distribution of ACC bridges can be derived on the basis of linear equations constructed with each beam's elasticity coefficients. Once the loading is implied on the ACC Bridge along the lateral direction, it is relatively easy to calculate the lateral distribution coefficients for girder beams. And then with the computational procedure developed for linear beams, the internal force can be calculated for girder and lateral beams, respectively.
引文
1．(日)岛田静雄等，吴在辉译，《曲线梁的计算公式》，人民交通出版社，1981．
2．(日)高岛春生，谷岳峰译，《公路桥横向分布实用计算法》，人民交通出版社，1984．
3．张大伦等，《材料力学》(上下册)，同济大学出版社，1987。
4．姚玲森：《曲线梁》，人民交通出版社，1992。
5．李惠生等，《曲线梁桥结构分析》，中国铁道出版社，1992。
6．朱伯钦，《结构力学》(上下册)，同济大学出版社，1993。
7．同济大学数学教研室，《线性代数》，高等教育出版社，1993。
8．杜国华等，《桥梁结构分析》，同济大学出版社，1994。
9．刑志成，《弯斜桥计算理论与实用计算》，人民交通出版社，1994。
10．孙广华，《曲线梁桥计算》，人民交通出版社，1995。
11．Autotools工作群，(AutoCAD ADS-C程序设计实务》，清华大学出版社，1995。
12．姚玲森：《桥梁工程》，人民交通出版社，1995。
13．贺拴海，《公路桥梁荷载横向分布实用计算方法》，人民交通出版社，1996。
14．徐光辉，《梁桥》(上下册)，人民交通出版社，1996。
15．范立础，《桥梁工程》(第二版)(上下册)，人民交通出版社，1996。
16．邵容光，《混凝土弯梁桥》，人民交通出版社，1996。
17．方铁，《AutoCADC语言高级编程》，清华大学出版社，1997。
18．郑振飞，《斜、弯桥跨分析的广义梁格法》，人民交通出版社，1998。
19．陈建春，《MiCrosoft Visual C++图形系统开发技术基础》，电子工业出版社，1998。
20．郭朝勇等，《AutoCAD R14二次开发技术》，清华大学出版社，1999。
21．徐岳等，《预应力混凝土连续梁桥设计》，人民交通出版社，2000。
22．邓建中等，《计算方法》，西安交通大学出版社，2000．
23．项海帆，《高等桥梁结构理论》，人民交通出版社，2001。
24. Anthony H.DePiero; Robert K.Paasch; and Steven C.Lovejoy: Finite-Element Modeling of Bridge Deck Connection Details, SEI, 2002
25. Ali R.Khaloo and H.Mirzabozorg: Load Distribution Factors in Simply Supported Skew Bridges, SEI, 2002
26. Rajan Sen, P.E., EASCE; Antoine N. Gergess, P.E., M.ASCE; and Camille Issa, F.ASCE.. Finite-Element Modeling of Heat-Curved I-girders, SEI, 2002
27. Mitsuru Ito; Eiki Karatani; and Yoshihide Komuro: Moment-Inelastic Rotation Behavior of Longitudinally Stiffened Beams, SEI, 2002
28. Khaled Sennah, M.ASCE; John B.Kennedy, EASCE; and SaidNour: Design for Shear in Curved Composite Multiple Steel Box Girder Bridges, SEI, 2002
29．贺拴海，《桥梁结构理论与计算方法》，人民交通出版社，2003。
2．(日)高岛春生，谷岳峰译，《公路桥横向分布实用计算法》，人民交通出版社，1984．
3．张大伦等，《材料力学》(上下册)，同济大学出版社，1987。
4．姚玲森：《曲线梁》，人民交通出版社，1992。
5．李惠生等，《曲线梁桥结构分析》，中国铁道出版社，1992。
6．朱伯钦，《结构力学》(上下册)，同济大学出版社，1993。
7．同济大学数学教研室，《线性代数》，高等教育出版社，1993。
8．杜国华等，《桥梁结构分析》，同济大学出版社，1994。
9．刑志成，《弯斜桥计算理论与实用计算》，人民交通出版社，1994。
10．孙广华，《曲线梁桥计算》，人民交通出版社，1995。
11．Autotools工作群，(AutoCAD ADS-C程序设计实务》，清华大学出版社，1995。
12．姚玲森：《桥梁工程》，人民交通出版社，1995。
13．贺拴海，《公路桥梁荷载横向分布实用计算方法》，人民交通出版社，1996。
14．徐光辉，《梁桥》(上下册)，人民交通出版社，1996。
15．范立础，《桥梁工程》(第二版)(上下册)，人民交通出版社，1996。
16．邵容光，《混凝土弯梁桥》，人民交通出版社，1996。
17．方铁，《AutoCADC语言高级编程》，清华大学出版社，1997。
18．郑振飞，《斜、弯桥跨分析的广义梁格法》，人民交通出版社，1998。
19．陈建春，《MiCrosoft Visual C++图形系统开发技术基础》，电子工业出版社，1998。
20．郭朝勇等，《AutoCAD R14二次开发技术》，清华大学出版社，1999。
21．徐岳等，《预应力混凝土连续梁桥设计》，人民交通出版社，2000。
22．邓建中等，《计算方法》，西安交通大学出版社，2000．
23．项海帆，《高等桥梁结构理论》，人民交通出版社，2001。
24. Anthony H.DePiero; Robert K.Paasch; and Steven C.Lovejoy: Finite-Element Modeling of Bridge Deck Connection Details, SEI, 2002
25. Ali R.Khaloo and H.Mirzabozorg: Load Distribution Factors in Simply Supported Skew Bridges, SEI, 2002
26. Rajan Sen, P.E., EASCE; Antoine N. Gergess, P.E., M.ASCE; and Camille Issa, F.ASCE.. Finite-Element Modeling of Heat-Curved I-girders, SEI, 2002
27. Mitsuru Ito; Eiki Karatani; and Yoshihide Komuro: Moment-Inelastic Rotation Behavior of Longitudinally Stiffened Beams, SEI, 2002
28. Khaled Sennah, M.ASCE; John B.Kennedy, EASCE; and SaidNour: Design for Shear in Curved Composite Multiple Steel Box Girder Bridges, SEI, 2002
29．贺拴海，《桥梁结构理论与计算方法》，人民交通出版社，2003。