考虑剪力滞效应的薄壁梁静动力特性分析
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摘要
剪力滞问题在很早以前就有学者对其进行研究,但学者们当时仅仅局限于航空领域的金属结构,自从20世纪60年代,由于忽略剪力滞后效应导致多座箱形桥梁破坏才引起各国学者的注意。经过几十年的发展,对剪力滞问题的研究取得了一些成果,可以部分地解决实际桥梁结构中的问题。但许多问题并没有得到完全解决,随着我国交通事业的发展,在一些新建桥梁中有关剪力滞的新问题不断出现。对于这些问题如不认真对待,可能会造成结构局部开裂、局部失稳,或更加严重的破坏。因而对剪力滞后问题的研究具有重要的理论和工程实际意义,本文就以下几个方面进行了研究。
1、直线和曲线矩形截面箱梁的静力学特性分析
以薄壁杆或薄壁曲杆理论为基础,根据实际情况对上下翼板、悬臂翼板设置了一个或两个剪滞纵向位移差函数,由能量变分原理获得了直线和曲线矩形截面箱梁的控制微分方程和边界条件,得到了广义位移的闭合解。系统分析了边界条件、荷载类型、悬臂翼板长度和曲率半径R等因素对直线和曲线矩形截面箱梁剪力滞后效应的影响,明确了上、下翼板的应力变化规律。
2、直线薄壁箱梁自振特性和动力反应的分析
对于直线矩形和梯形截面箱梁,根据其特点分别设置了一个、两个或三个剪滞纵向位移差函数,在考虑剪力滞后效应的前提下,获得了边界条件、跨宽比、箱梁高度和悬臂翼板长度等因素对矩形和梯形截面箱梁自振特性影响的规律。同时,本文以直接法为基础,推导出了矩形截面箱梁的强迫振动方程,明确了剪力滞后效应对矩形截面箱梁动力反应影响的规律,因而本文内容丰富和发展了现行剪滞理论。
3、梯形截面曲箱梁的静力学特性分析
设置了三个不同的纵向剪滞位移差函数以准确反映顶板( u1 ( x ))、底板( u 2( x ))和悬臂板( u3 ( x ))的纵向位移变化,考虑了曲箱梁的弯、扭、翘、剪滞效应和剪切变形的耦合作用,本文内容发展了符拉索夫的曲杆理论,明确了曲线梯形截面箱梁的力学特点。同时制作了曲线梯形截面箱梁的有机玻璃模型桥,设计了测点布置和加载方案,对梯形截面曲箱梁上下翼板剪力滞效应进行了试验研究,理论结果与试验值进行了比较,验证了本文理论分析的正确性。
4、直线和曲线矩形截面箱梁腹板静动力特性分析
将剪力滞后效应引入直线和曲线矩形截面箱梁腹板,根据应变—位移关系获得系统总势能,依据箱梁腹板振动特点求得总动能,利用最小势能原理和哈密顿原理分别获得直线和曲线矩形截面箱梁腹板静、动力特性分析的控制微分方程和自然边界条件,明确了跨宽比、悬臂翼板长度、梁高及腹板厚度对直线和曲线矩形截面箱梁腹板剪滞效应的影响,为矩形截面箱梁腹板的力学特性分析提供理论参考。
5、宽翼薄壁直线工字形梁静、动力特性及曲梁静力特性的分析
为了准确反映工字形梁上、下翼板剪滞效应变化,对直线和曲线工字形梁上、下翼板设置了两个不同的剪滞纵向位移差函数U 1( x )、U 2( x ),推导出了工字形梁的控制微分方程和自然边界条件,通过系统的力学分析,获得了该类结构静、动力特性规律。
6、薄壁箱梁翘曲函数精确度选择的研究
根据箱形结构纵向翘曲位移函数设置的基本原理,选择一系列符合薄壁箱梁基本翘曲模式的翘曲位移函数,依据固有频率方程求出特定边界条件下相应翘曲位移函数箱形结构的自振频率,借助自振频率的大小对所设置翘曲位移函数的精度做出评判,且静力分析结果进一步证明了翘曲位移函数精度选择的必要性。
Shear lag issues were studied by some scholars long before, but they were limited in the aviation structures only. Since 1960s, some scholars started to pay attention to shear lag problem because it resulted in the damage of bridges. Over the past several decades, the research outcomes solved the part of engineering problems relating to shear lag effect. However, the existing research achievements still do not handle the shear lag issues completely and accurately. With the development of communication, new problems about shear lag effect appeared continuously. If these problems are not treated seriously and properly, the local cracking and instability of structures from shear lag effect will appear so that it can cause serious damage of structures. Hence, the analysis of shear lag effect is more and more important and critical in theoretical and practical significances. This dissertation makes some contributions in the shear lag effect on the thin-walled beams which are commonly used in the modern bridges. The main contents of this dissertation are as follows:
(1) The static analysis of straight and curved rectangle box beams
On the basis of the thin-walled bars theory and the thin-walled curved bars theory, the governing differential equations and the natural boundary conditions of straight or curved rectangle box girders are established using an energy variation principle and the closed-form solutions of generalized displacement functions are obtained. The established governing differential equation applies one or two different longitudinal displacement difference functions to accurately reflect the amplitude of change of shear lag in the thin-walled box girder’s wing slabs according to the practical configuration of the beam. The variation in the shear lag effects on straight and curved rectangle box girders, caused by the changes of factors such as natural boundary conditions, types of loading, lengths of cantilever flanges and curvature radius R , is discussed systematically. Meanwhile, an analysis is made for the change of stress in the top and bottom flanges.
(2) The analysis of the natural frequency and dynamic response of straight thin-walled box beams
According to the structural features of straight rectangle and trapezoid box girders, one, two or three warping displacement functions are applied to accurately reflect the amplitude of change of shear lag in the thin-walled box girder’s wing slabs respectively. In consideration of the shear lag effect, the natural frequency relating to the changes of factors such as natural boundary conditions, span-width ratio, height of thin-walled box girders, and length of cantilever flanges, is obtained. Also based on the direct method, the equation of dynamic response about rectangle box girders is deduced. The solution of the equation can rightly reflect the dynamic behaviour of thin-walled structures, which it develops and enriches the shear lag theory.
(3) The static analysis of curved trapezoidal box beams
Three different longitudinal displacement difference functions are employed to accurately reflect the amplitude of change of shear lag in the thin-walled curved box girders with various widths of wing slabs respectively. Then, the governing differential equations and natural boundary conditions are proposed both using the minimum potential principle and taking into account of the curving, torsion, warping torsion (including secondary warping shear effect), shear deformation and shear lag effects. Thus, this dissertation develops Vlasov’s thin-walled curved bars theory and clearly reveals the mechanical performance of curved trapezoid box girders.
A bridge model with continuous curved trapezoid box girder is designed and made in order to verify the proposed analytical techniques. Two loading cases, uniform and concentrated loads, are applied to study the shear lag effect on the top and bottom flanges of curved trapezoid box girder.
(4) The analysis of static and dynamic characteristics of webs of thin-walled straight and curved box beams
In consideration of shear lag effect on thin-walled box girder’s webs, the total potential energy stored in the box girders is obtained according to the relationship of strain-displacement. Also, the total kinetic energy of the box girders can be obtained based on web’s vibrating characteristics. Therefore, the web’s governing differential equations and corresponding natural boundary conditions can be obtained for the static and dynamic analysis of webs about thin-walled straight and curved box girders using the minimum potential principle and Hamilton principle. The web’s shear lag effect on straight and curved rectangle box girders is systematically discussed, involved in the factors such as span-width ratio, length of cantilever flanges, height of thin-walled box girder and thickness of webs. The research results provide a reference for the analysis of web’s mechanical characteristics.
(5) The analysis on static and dynamic characteristics of straight and curved thin-walled I-beams with wide flanges
Two different longitudinal displacement difference functions ( U 1 ( x ), U 2( x )) are proposed in establishing the governing differential equations and corresponding natural boundary conditions, in order to accurately reflect the amplitude of change of shear lag in the thin-walled straight and curved I-beams with various widths of wing slabs. Then the mechanical analysis is conducted for the static and dynamic characteristics about straight and curved thin-walled I-beams.
(6) An approach of accurately selecting longitudinal shear lag warping displacement function of thin-walled box girders
Based on the basic principle of longitudinal warping displacement function setting, this study selects a series of warping displacement functions that conform to basic warping mode of the box girder, in order to obtain the natural frequency equations corresponding to these proposed functions. Then, for the special boundary types, the natural frequency of the beam is determined under these given warping displacement functions. Finally, according to the magnitude of the natural frequency, the precision of warping displacement functions can be judged, and the static calculation examples indicate that the selection of warping displacement functions be necessary.
1、直线和曲线矩形截面箱梁的静力学特性分析
以薄壁杆或薄壁曲杆理论为基础,根据实际情况对上下翼板、悬臂翼板设置了一个或两个剪滞纵向位移差函数,由能量变分原理获得了直线和曲线矩形截面箱梁的控制微分方程和边界条件,得到了广义位移的闭合解。系统分析了边界条件、荷载类型、悬臂翼板长度和曲率半径R等因素对直线和曲线矩形截面箱梁剪力滞后效应的影响,明确了上、下翼板的应力变化规律。
2、直线薄壁箱梁自振特性和动力反应的分析
对于直线矩形和梯形截面箱梁,根据其特点分别设置了一个、两个或三个剪滞纵向位移差函数,在考虑剪力滞后效应的前提下,获得了边界条件、跨宽比、箱梁高度和悬臂翼板长度等因素对矩形和梯形截面箱梁自振特性影响的规律。同时,本文以直接法为基础,推导出了矩形截面箱梁的强迫振动方程,明确了剪力滞后效应对矩形截面箱梁动力反应影响的规律,因而本文内容丰富和发展了现行剪滞理论。
3、梯形截面曲箱梁的静力学特性分析
设置了三个不同的纵向剪滞位移差函数以准确反映顶板( u1 ( x ))、底板( u 2( x ))和悬臂板( u3 ( x ))的纵向位移变化,考虑了曲箱梁的弯、扭、翘、剪滞效应和剪切变形的耦合作用,本文内容发展了符拉索夫的曲杆理论,明确了曲线梯形截面箱梁的力学特点。同时制作了曲线梯形截面箱梁的有机玻璃模型桥,设计了测点布置和加载方案,对梯形截面曲箱梁上下翼板剪力滞效应进行了试验研究,理论结果与试验值进行了比较,验证了本文理论分析的正确性。
4、直线和曲线矩形截面箱梁腹板静动力特性分析
将剪力滞后效应引入直线和曲线矩形截面箱梁腹板,根据应变—位移关系获得系统总势能,依据箱梁腹板振动特点求得总动能,利用最小势能原理和哈密顿原理分别获得直线和曲线矩形截面箱梁腹板静、动力特性分析的控制微分方程和自然边界条件,明确了跨宽比、悬臂翼板长度、梁高及腹板厚度对直线和曲线矩形截面箱梁腹板剪滞效应的影响,为矩形截面箱梁腹板的力学特性分析提供理论参考。
5、宽翼薄壁直线工字形梁静、动力特性及曲梁静力特性的分析
为了准确反映工字形梁上、下翼板剪滞效应变化,对直线和曲线工字形梁上、下翼板设置了两个不同的剪滞纵向位移差函数U 1( x )、U 2( x ),推导出了工字形梁的控制微分方程和自然边界条件,通过系统的力学分析,获得了该类结构静、动力特性规律。
6、薄壁箱梁翘曲函数精确度选择的研究
根据箱形结构纵向翘曲位移函数设置的基本原理,选择一系列符合薄壁箱梁基本翘曲模式的翘曲位移函数,依据固有频率方程求出特定边界条件下相应翘曲位移函数箱形结构的自振频率,借助自振频率的大小对所设置翘曲位移函数的精度做出评判,且静力分析结果进一步证明了翘曲位移函数精度选择的必要性。
Shear lag issues were studied by some scholars long before, but they were limited in the aviation structures only. Since 1960s, some scholars started to pay attention to shear lag problem because it resulted in the damage of bridges. Over the past several decades, the research outcomes solved the part of engineering problems relating to shear lag effect. However, the existing research achievements still do not handle the shear lag issues completely and accurately. With the development of communication, new problems about shear lag effect appeared continuously. If these problems are not treated seriously and properly, the local cracking and instability of structures from shear lag effect will appear so that it can cause serious damage of structures. Hence, the analysis of shear lag effect is more and more important and critical in theoretical and practical significances. This dissertation makes some contributions in the shear lag effect on the thin-walled beams which are commonly used in the modern bridges. The main contents of this dissertation are as follows:
(1) The static analysis of straight and curved rectangle box beams
On the basis of the thin-walled bars theory and the thin-walled curved bars theory, the governing differential equations and the natural boundary conditions of straight or curved rectangle box girders are established using an energy variation principle and the closed-form solutions of generalized displacement functions are obtained. The established governing differential equation applies one or two different longitudinal displacement difference functions to accurately reflect the amplitude of change of shear lag in the thin-walled box girder’s wing slabs according to the practical configuration of the beam. The variation in the shear lag effects on straight and curved rectangle box girders, caused by the changes of factors such as natural boundary conditions, types of loading, lengths of cantilever flanges and curvature radius R , is discussed systematically. Meanwhile, an analysis is made for the change of stress in the top and bottom flanges.
(2) The analysis of the natural frequency and dynamic response of straight thin-walled box beams
According to the structural features of straight rectangle and trapezoid box girders, one, two or three warping displacement functions are applied to accurately reflect the amplitude of change of shear lag in the thin-walled box girder’s wing slabs respectively. In consideration of the shear lag effect, the natural frequency relating to the changes of factors such as natural boundary conditions, span-width ratio, height of thin-walled box girders, and length of cantilever flanges, is obtained. Also based on the direct method, the equation of dynamic response about rectangle box girders is deduced. The solution of the equation can rightly reflect the dynamic behaviour of thin-walled structures, which it develops and enriches the shear lag theory.
(3) The static analysis of curved trapezoidal box beams
Three different longitudinal displacement difference functions are employed to accurately reflect the amplitude of change of shear lag in the thin-walled curved box girders with various widths of wing slabs respectively. Then, the governing differential equations and natural boundary conditions are proposed both using the minimum potential principle and taking into account of the curving, torsion, warping torsion (including secondary warping shear effect), shear deformation and shear lag effects. Thus, this dissertation develops Vlasov’s thin-walled curved bars theory and clearly reveals the mechanical performance of curved trapezoid box girders.
A bridge model with continuous curved trapezoid box girder is designed and made in order to verify the proposed analytical techniques. Two loading cases, uniform and concentrated loads, are applied to study the shear lag effect on the top and bottom flanges of curved trapezoid box girder.
(4) The analysis of static and dynamic characteristics of webs of thin-walled straight and curved box beams
In consideration of shear lag effect on thin-walled box girder’s webs, the total potential energy stored in the box girders is obtained according to the relationship of strain-displacement. Also, the total kinetic energy of the box girders can be obtained based on web’s vibrating characteristics. Therefore, the web’s governing differential equations and corresponding natural boundary conditions can be obtained for the static and dynamic analysis of webs about thin-walled straight and curved box girders using the minimum potential principle and Hamilton principle. The web’s shear lag effect on straight and curved rectangle box girders is systematically discussed, involved in the factors such as span-width ratio, length of cantilever flanges, height of thin-walled box girder and thickness of webs. The research results provide a reference for the analysis of web’s mechanical characteristics.
(5) The analysis on static and dynamic characteristics of straight and curved thin-walled I-beams with wide flanges
Two different longitudinal displacement difference functions ( U 1 ( x ), U 2( x )) are proposed in establishing the governing differential equations and corresponding natural boundary conditions, in order to accurately reflect the amplitude of change of shear lag in the thin-walled straight and curved I-beams with various widths of wing slabs. Then the mechanical analysis is conducted for the static and dynamic characteristics about straight and curved thin-walled I-beams.
(6) An approach of accurately selecting longitudinal shear lag warping displacement function of thin-walled box girders
Based on the basic principle of longitudinal warping displacement function setting, this study selects a series of warping displacement functions that conform to basic warping mode of the box girder, in order to obtain the natural frequency equations corresponding to these proposed functions. Then, for the special boundary types, the natural frequency of the beam is determined under these given warping displacement functions. Finally, according to the magnitude of the natural frequency, the precision of warping displacement functions can be judged, and the static calculation examples indicate that the selection of warping displacement functions be necessary.
引文
1.郭金琼.箱形梁设计理论[M].北京:人民交通出版社,1991.
2.张士铎,邓小华,王文州.箱形薄壁梁剪力滞效应[M].北京:人民交通出版社,1998.
3.倪元增,钱寅泉.弹性薄壁梁桥分析[M].北京:人民交通出版社,1988.
4. AASHTO. AASHTO LRFD bridge design specifications. Washington (DC):American Association of State Highway and Transportation Officials, 1998.
5. BSI. Part5: Code of practice for design of composite bridges. In: Steel, concreteand composite bridges, BS5400. London: British Standards Institution, 1979.
6. BSI. Part 3: Code of practice for design of steel bridges. In: Steel, Concrete and composite bridges, BS5400. London: British Standards Institution, 2000.
7. DIN. Concrete bridges,design and construction, DIN1075. Berlin: Deutsches Institut fur Normung, 1981.
8. JRA. Design specifications for highway bridges, Part II steel bridges. Tokyo: Japan Road Association, 2002.
9.中华人民共和国交通部标准.公路钢筋混凝土及预应力混凝土桥涵设计规范.北京:人民交通出版社,1985, 9-11.
10.中华人民共和国行业标准.公路钢筋混凝土及预应力混凝土桥涵设计规范.北京:人民交通出版社,2004, 16-18.
11.罗旗帜,俞建立.钢筋混凝土连续箱梁桥翼板横向裂缝问题[J].桥梁建设,1997,(1):41-44.
12.周若来,沈成武.某高速公路桥裂缝成因分析[J].武汉理工大学学报,2003, 27(1):84-86.
13.黄培元.普通钢筋混凝土连续箱梁桥开裂等问题的探讨[J].东北公路,2003, 26(1):61-64.
14. Abramento M, Whittle A J. Shear lag analysis of planar soil reinforcement in plance-strain compression. J. Engrg. Mech., ASCE, 1993, 119(2):270-291.
15. Kulek G L, Wu E Y. Shear lag in bolted angle tension members. J. Struct. Engrg., ASCE, 1997, 123(9): 1144-1151.
16.程翔云.梁桥理论与计算.北京:人民交通出版利,1986.
17.项海帆.高等桥梁结构理论.第一版.北京:人民交通出版社,2001, 50-72.
18. Kristek V. Theory of box girder. New York: John Wiley & Sons, 1979, 9-11.
19. Vlasov V Z.Thin-walled elastic beams [M].Washington D C.National Science Foundation,1961.
20. Sedlacek G. A simplified method for the determination of the effective width due to shear lag effects. J. Construct. Steel Research, 1993, (24):155-182.
21. Abdel-Sayed G. Effective width of steel deck plate in bridge. J. Struct. Div, ASCE,1969, 95(7): 1459-1474.
22. Hasebe K, Usuki S, Horie Y. Shear lag analysis and effective width of curved girder bridges. J. Engrg. Mech., ASCE, 1985,111(1):87-92.
23. Ahn I S, Chievanichakorn M, Chen S S, et al. Effective flange width provisions for composite steel bridges. Engineering Structures, 2004, (26): 1843-1851.
24. Reissner E. On the problem of stress distribution in wide flanged box beam. Journal Aero. Sci., 1938, (5):295-299.
25. Lee C K, Wu G J. Shear lag analysis by the adaptive finite element method. 1:Analysis of simple plated structures. Thin-Walled Struct., 2000a, (38):285-309.
26. Lee C K, Wu G J. Shear lag analysis by the adaptive finite element method.
2:Analysis of complex plated structures. Thin-Walled Struct., 2000b, (38):311-336.
27. Song Q G, Scordelis A C. Shear lag analysis of T -, I-, and box beams. J. Struct. Engrg., ASCE, 1990a, 116(5):1290-1305.
28. Van-Dalen K, Narasimham S V. Shear lag in shallow wide-flanged box girder. J. Struct. Div., ASCE, 1976, 102(10):1969-1979.
29. Malcolm D J, Redwood R G. Shear lag in stiffened box girders. J. Struct. Div., ASCE, 1970, 96(7): 1403-1419.
30. Reissner E. Analysis of shear lag in box beam by principle of minimum potential energy. Quarterly of Applied Mathematics, 1946, 5(3): 268-278.
31. Kuzmanvic B O, Graham H J. Shear lag in box girders. J. Struct. Div., ASCE, 1981,107(9): 1701-1712.
32. Foutch D A, Chang P C. A shear Lag anomaly[J]. J Struct Engrg,ASCE,1982,108(7):1653-1658.
33.张士铎,丁芸.变截面悬臂箱梁负剪力滞差分解[J].重庆交通学院学报,1984,11(4): 34-47.
34.张士铎,谢琪.四次抛物线变截面悬臂梁剪力滞效应及差分解[J].结构工程师,1987,(3):35-40.
35. Kristek V, Evans H R, Ahmad M K H. A shear lag analysis for composite box girders. J. Construct. Steel Research, 1990, (16):1-21.
36. Kristek V, Studnicka J. Negative shear lag in flanges of plated structures. J. Struct.Engrg., ASCE, 1991,117(12): 3553-3569.
37.程翔云,罗旗帜,箱梁在压弯荷载共同作用下的剪力滞[J].土木工程学报.1991,24(1):52-64.
38. Moffatt K R, Dowling P J. British shear lag rules for composite girders. J. of the Structureal Division, ASCE, 1978,104(7):1123-1130.
39. Moffatt K R, Dowling P J. Discussion on shear lag in steel box girder bridges. The Structural Engineer, 1976, 54(9):285-298.
40. Moffatt K R, Dowling P J. Shear lag in steel box girder bridges. The Structural Engineer, 1975, 53(10): 439-448.
41. Luo Q Z, Tang J, Li Q S. Calculation of moments on top slab in single-cell box girder. J. Struct. Engrg., ASCE, 2003, 129(1): 130-134.
42. Sung C L, Chai H Y, Dong Y. Analysis of shear lag anomaly in box girders. J. Struct. Engrg., ASCE, 2002,128(11):1379-1386.
43. Shushkewich K W. Negative shear lag explained. J. Struct. Engrg., ASCE, 1991,117(11): 3543-3546.
44. Evans H R, Taherian A R. The prediction of the shear lag effect in box girder. Proc. Instn. Civ. Engrs., Part 2,1997, (63): 69-72.
45.郭金琼,房贞政.箱形梁桥剪滞效应分析[J].土木工程学报,1983,16(1):1-13.
46. Chang S T. Prestress influence on shear lag effect in continuous box girder bridge[J]. J Struct Engrg, ASCE,1992,118(11) :3113-3121.
47.罗许国,戴公连.大悬臂桥面板钢脊骨梁结构模型剪力滞效应有限元分析[J].长沙铁道学院学报,2002,20(1):51-56.
48.郑振.大悬臂变截面箱梁剪力滞效应分析[J].福州大学学报,2001,29(2):62-65.
49.吴幼明,罗旗帜,岳珠峰.薄壁箱梁剪滞效应的能量变分法[J].工程力学,2003,20(4):161-165.
50.韦成龙,曾庆元,刘小燕.薄壁箱梁剪力滞分析的多参数翘曲位移函数及其有限元法[J].铁道学报.2000,22(5):60-64.
51.奥登,里帕格.弹性结构力学.成文山,程翔云,周义武译.第一版.北京:中国建筑工业出版社,1986.
52.龙驭球,包世华.结构力学[M].北京:高等教育出版社,1996.
53.胡海昌.弹性力学的变分原理及其应用[M].北京:科学出版社出,1981.
54.刘世忠,欧阳永金,吴亚平.变截面薄壁箱梁剪力滞剪切变形效应分析[J].中国公路学报,2002,15(3):61-63.
55. Tahan N, Pavlovic M N, Kotsovos M D. Single fourier series solutions for rectangular plates under in-plane forces, with particular reference to the basic problem of colinear compression. Part 2: Stress distribution. Thin-Walled Structures,1993, (17):1-26.
56. Tahan N, Pavlovic M N, Kotsovos M D. Shear lag revisited: the use of singlefourier series for determining the effective breadth in plated structure. Computers and Structures, 1997, 63(4): 759-767.
57.罗旗帜.薄壁箱型梁剪力滞计算的梁段有限元法[J].湖南大学学报,1991,(2):33-55.
58.钱寅泉,倪元增.箱梁剪力滞计算的翘曲函数法[J].铁道学报,1990,12(2):(57-70).
59.谢旭,黄剑源.薄壁箱形梁剪力滞效应分析的刚度法[J].工程力学,1995,(2):95102.
60.黄剑源,杨允表.钱塘江二桥变截面箱形连续梁剪滞效应的有限元分析[J].桥梁建设.1994,(1):7076
61.杨允表,黄剑源.广义有限条分析多室箱梁的剪滞效应[J].桥梁建设,1995,(4):40-45.
62.王修信,黄剑源.变截面多跨梯形箱梁剪滞效应差分解[J].桥梁建设,1993, (2):58-64.
63. Hildbrand P B. The exact solution of shear lag problems in flat panels and box beams assumed rigid in the transverse direction. NACA, 1934, (TN894): 90-95.
64.方同,薛璞.振动理论及应用[M].西安:西北工业大学出版社,2002.2.
65.铁摩辛柯,盖莱.材料力学.胡人礼译.第一版.北京:科学出版社,1978,256-264.
66.宋一凡.公路桥梁动力学[M].北京:人民交通出版社,1999.
67.倪振华.振动力学[M].西安:西安交通大学出版社,1988.
68.刘山洪,何广汉等. PPC箱梁节段模型剪滞效应的试验研究[J].桥梁建设,2000,(3):5-7.
69.吴海林,季文玉.箱梁剪力滞效应影响参数分析[J].工程力学,2000,2(1): 572-577.
70.周坚,涂令康.再论槽型宽梁的剪力滞[J].工程力学,1994,11(2): 65-75.
71.彭大文,颜海.曲线脊骨箱梁的剪力滞效应分析[J].铁道学报,2001,23(4): 10-16.
72. Hoglund, Torsten. Shear Buckling Resistance of Steel and Aluminium P1ate Girders. Thin-Walled Structures.1997,29 (1-4):13-30.
73. Luo, Q.Z.; Wu, Y.M.; Tang, J.; Li, Q.S. Experimental studies on shear lag of box girders. Engineering Structures.2002,24(4): 469-477.
74. Yaping, Wu; Yuanlin, Zhu; Yuanming, Lai; Weideng, Pan. Analysis of shear lag and shear deformation effects in laminated composite box beams under bending loads. Composite Structures.2002,55(2):147-156.
75. Uzoegbo, H.C. Shear Lag in Steel Angles: An Investigation of the South African Standards. Journal of Constructional Steel Research.1998,46(1-3):Volume: 46, Issue:162-162.
76. Tenchev R T. Shear lag in orthotropic beam flanges and plates with stiffeners. Int. J.Solids Structures, 1996, 33(9):1317-1334.
77.陈启流.数学物理方法[M].广州:华南理工大学出版社,1994.
78.黄剑源.薄壁结构的扭转分析(上).北京:中国铁道出版社,1983.
79.黄剑源.薄壁结构的扭转分析(曲线梁与斜支箱形梁).北京:中国铁道出版社,1998.
80.何福宝.薄壁曲杆有限元法[J].固体力学学报,1981,2(2):141-157.
81.吴亚平,赖远明.考虑剪滞效应的薄壁曲梁有限单元法[J].工程力学,2002,19(4):85-89.
82.李琰,辛克贵.薄壁曲梁的横向弯曲稳定分析[J].工程力学,2005,22(1):69-74.
83. Kang Y J, Yoo C H. Thin-walled curved beams. I: Formulation of nonlinear equations[J]. J Engrg. Mech.,ASCE,1994, 120(10) :2072-2101.
84.段海娟,赵人达.曲箱梁考虑剪力滞效应得弯扭耦合分析[J].中国铁道科学,2002,23(1):34-37.
85. Hsu Y T, Fu C C, Schelling D R. EBEF method for distortional analysis of steel box girder bridges. J. Struct Engrg., ASCE,1995,121(3):557-566.
86.李惠生,张罗溪.曲线梁桥结构分析[M].北京:中国铁道出版社,1992
87.彭大文.连续弯箱梁剪滞效应分析和实用计算法研究[J].中国公路学报,1998,11(3):41-49.
88. Yoshimura J, Nirasawa N. On the stress distributions and effective width of curved girder bridges by the folded plate theory. Proc., Japan Soc. of Civ. Engrs., Tokyo,1975, No. 233.
89.肖敏,李新平.连续曲线箱梁剪力滞效应分析[J].中外公路,2004, 24(4):61-65.
90.杨允表.曲线箱梁考虑曲率及剪力滞影响的力学分析[J].土木工程学报,1999,32(1):43-49.
91. Luo Q Z, Tang J, Li Q S. Shear lag of thin-walled curved box girders in box girders bridges. J. Engrg. Mech. , ASCE, 2000, 126(10):1111-1114.
92.罗旗帜.曲线箱梁桥的剪滞效应分析[J].佛山大学学报,1992, 10(2):46-55.
93. Kovanicova, Zuzana;Kristek, Vladimir;Skaloud, Miroslav. Shear lag in the wide flanges ofvertically curved box girders. Acta Technica CSAV (Ceskoslovensk Akademie Ved), 1988,33(4): 414-436.
94.罗旗帜.计算曲线梁桥的传递矩阵法[J].中南公路工程,1990, (3): 32-41.
95. Evans,H.R.&Taherian ,“A.R.A Design Aid for Shear Lag Calculation”,Proc. I. C. E,part2,1980, 69, June P403-424.
96. Evans H R, Taherian A R. The prediction of the shear lag effect in box girder. Proc. Instn. Civ. Engrs., Part 2,1997, (63): 69-72.
97. Shih Toh Chang&Fang Zhen Zheng .“Negative Shear Lag in Cantilever Box Girder With Constant Depth”. J. of Structural Engineering. 1985,(1):20-34.
98.彭大文,王忠.低矮截面箱梁桥剪滞效应分析[J].福州大学学报(自科版),1999,27(4):73-76.
99.经柏林,鲍卫刚.变截面长悬臂宽箱梁桥翼缘有效宽度研究[J].中南公路工程,1998,23 (4):24-26.
100.李运光,宋娃丽.箱梁桥的剪滞效应影响[J].工程力学,1998,(2):415-418.
101. Chang, Shih Toh;Yun, Ding. Shear lag effect in box girder with varying depth. Journal of Structural Engineering ,1988,114(10):2280-2292.
102.王忠,彭大文.预应力对箱梁剪滞效应的影响分析[J].工程力学,1998,(2):449-453.
103.罗旗帜.变截面多跨箱梁桥剪滞效应分析[J].中国公路学报,1998,11(1):63-70.
104.罗旗帜,俞建立.变截面箱梁的负剪力滞[J].重庆交通学院学报,1997,16(3):18-25.
105.钱寅泉,倪元增.梯形截面箱梁桥的剪力滞计算.中国公路学会桥梁工程学会1989年学术会议论文集,1989.
106.张士铎,王文州.荷载横向作用位置对箱梁剪力滞效应的影响[J].湖南大学学报.1995,21(2):109-115.
107. Taherian A R, Evans H R. The bar simulation method for the calculation of shear lag in mufti-cell and continuous box girders. Proc. Instn. Civ. Engrs., Part 2, 1977, (63):881-897.
108.张启伟,张士铎.单索面斜拉桥箱梁恒载剪力滞效应分析[J].中国公路学报,1997,10(1):39-43.
109.罗旗帜.基于能量原理的薄壁箱梁剪力滞理论与试验研究:[湖南大学博士学位论文].长沙:湖南大学土木系,2005.11
110.罗许国.无背索斜拉桥结构模型剪力滞实验研究[J].株洲工学院学报,2004,18(2):110-112.
111. Starink, M.J.; Syngellakis, S. Shear lag models for discontinuous composites: fibre end stresses and weak interface layers. Materials Science and Engineering. 1999,270(2):270-277.
112. Burgan B A, Dowling P J. The treatment of shear lag in design. Thin-Walled Structures, 1990, (9): 121-134.
113. Kristek V. Strudnicka J, Skaloud M. Shear lag in wide flanges of steel bridges. Acta Tech., CSAV,1981(26):464-488.
114. Adekola A O. On shear lag effects in orthotropic composite beams. Int. J. Solids Structures, 1974, 10(4): 735-754.
115. Adekola A O. The dependence of Shear lag on partial interaction in composite beams. Int. J. Solids Structures. 1974, 10 (7): 389-400.
116. Lopez-Anido R, Gangarao H V S. Warping solution for shear lag in thin-walledorthotropic composite beam. J. Engrg. Mech., ASCE, 1996, 122(5):449-457.
117. Pavlovic M N, Tahan N, Kotsovos M D. Shear lag and effective breadth in rectangular plates with material orthotropy. Part 1:Analytical formulation. Thin-Walled Structures,1998a,30(1-4):199-213.
118.蔡松柏,李存权.箱形梁桥剪力滞效应的精确分析[J].中南公路工程,1989, (3):33-41.
119.文国华.横向预应力对悬臂翼板有效分布宽度的影响.中南公路工程,1998,23(4):29-32.
120. Kristek V. Folded plate approach to analysis of shear wall systems and frame structures. Proc. Inst. Civ. Engrs., Part 2, 1979, (67):1065-1075.
121. Fafitis A, Rong A Y. Analysis of thin-walled box girders by paralled processing.Thin-Walled Structures, 1995, (21):233-240.
122.孙广华.德国关于桥梁翼板计算宽度的规定.公路,1997,(3)39-42.
123.项贻强.箱型梁桥翼板的有效宽度及对规范的建议.中国公路学会桥梁工程学会1989年学术会议论文集,1989.10.
124. Kuhn P, Peterson J P. Shear lag in axialy loaded panels. NACA, 1948, TN. 1928.
125. Kuhn P, Chiaritc P T. Shear lag in box beams. Methods of Analysis and Experimental Investigations, NACA, 1942, REP., No. 739.
126. Connor J J, Pouangare C C. Simple model for design of framed-tube Structures. J.Struct. Engrg., ASCE, 1991,117(12):3623-3644.
127. Chang S T. Shear lag effect in simply supported prestressed concrete box girder. J.Bridge Engrg., ASCE, 2004, 9(2):178-184.
128.吴亚平,复合材料薄壁箱梁的剪滞剪切效应分析[J].土木工程学报,1995, 29(4):31-47.
129. Takayanagi, H./Keimnochi, K./Sembokuya, H./Hojo, M./Maki, H. Shear-lag effect in CFRP I-beams under three-point bending. Experimental Mechanics,1994,34(2):100-107.
130. Qi-gen Song&Alexander C. Sordelis.“Shear Lag Analysis of T,I- and Box Beams”. J. ofStructural Engineering,1990,116(5):1306-1318.
131. Ayyub, Bilal M.;Sohn, Young G;Saadatmanesh, Hamid . Prestressed composite I-girders experimental study for negative moment. Journal of Structural Engineering,1992,118(10) :2743-2762.
132. Song Q G, Scordelis A C. Formulas for shear lag effect of T-, I-, and box beams, J.Struct. Engrg., ASCE, 1990b, 116(5): 1306-1318.
133.程翔云,汤康恩. T形梁翼缘的剪力滞及其有效宽度[J].重庆交通学院学报,1984,(4): 28-33.
134.张元海,张清华,李乔.宽翼缘薄壁梁剪滞效应分析的变分解法[J].工程力学,2006,23(1):52-56.
135.刘寒冰,刘文会,张云龙.用变分法分析预应力钢-混凝土组合T梁的剪力滞效应[J].公路交通科技,2004, 21(5):65-66.
136.蔡松柏,程翔云,邵旭东. II型梁剪力滞效应的解析解[J].工程力学,2003, 20(5):82-86.
137.周坚.用余能原理解槽型宽梁的剪力滞问题[J].力学与实践,1985, 7(5): 52-54.
138.邵爱军,吴代华.基于能量法的槽型梁剪滞效应分析[J].武汉理工大学学报,2003,25(3): 52-55.
139.万臻,李乔,毛学明.II型截面主梁斜拉桥剪力滞效应研究[J].西南交通大学学报,2004, 39(5): 623-627.
140.倪元增.槽型宽梁的剪力滞问题[J].土木工程学报,1986, 19(4): 32-41.
141. Lee J A N. Effective width of Tee-beam. The Structural Engineer, 1962, 40(1):21-27.
142.魏丽娜,方放.变截面箱梁桥剪滞效应分析中翼板纵向位移函数的选择[J].桥梁建设,1996(3):28-31.
143. Chang S T, Yun D. Shear lag effect in box girder with varying depth. J. Struct.Engrg., ASCE, 1988, 114(10):2280-2292.
144.杨充表,朱鸿蕾,顾强等.变截面连续箱梁剪力滞效应分析[J].中国市政工程,2000, 90(3): 19-22.
145. Pavlovic M N, Tahan N, Kotsovos M D. Shear lag and effective breadth in rectangular plates with material orthotropy. Part 2: Typical results of parametric studies. Thin-Walled Structures, 1998b, 30(1-4): 215-237.
146. Nakai H, Murayama Y. Researches on negative shear lag of cantilever beams and application to bridge design. Trans. JSCE, 1976, (8):107-109.
147. Chang S T, Zheng F Z. Negative Shear lag in Cantilever box girders with constant depth.J. Struct. Engrg., ASCE, 1987, 113(1):20-35.
148. Luo Q Z, Tang J, Li Q S. Negative Shear lag in box girders with varying depth. J.Struct. Engrg., ASCE, 2001,127(10):1236-1239.
149.吴亚平.多室箱梁剪滞效应的变分法分析[J].兰州铁道学院学报,1992, 1l(2):36-48.
150.魏丽娜,方放,余天庆等.变截面箱形梁桥剪滞效应的近似计算方法[J].土木工程学报,1997, 30(2):64-72.
151.程翔云.悬臂薄壁箱梁的负剪力滞[J].上海力学,1987, (2): 52-62.
152. Luo Q Z, Li Q S,Tang J. Shear lag in box girders bridges. Journal of BridgeEngineering, ASCE, 2002, 7(5):308-313.
153.方志,曹国辉,王济川.钢筋混凝土连续箱梁剪力滞效应试验研究[J].桥梁建设,2000, (4):1-3.
154.牛斌,杨梦蛟,马林.预应力混凝土宽箱梁剪力滞效应试验研究[J].中国铁道科学,2004, 25(2): 25-30.
155.方淑君,戴公连,狄谨.梁板结构在轴力及弯矩作用下截面剪力滞效应的研究[J].长沙铁道学院学报,2001, 19(3): 45-48.
2.张士铎,邓小华,王文州.箱形薄壁梁剪力滞效应[M].北京:人民交通出版社,1998.
3.倪元增,钱寅泉.弹性薄壁梁桥分析[M].北京:人民交通出版社,1988.
4. AASHTO. AASHTO LRFD bridge design specifications. Washington (DC):American Association of State Highway and Transportation Officials, 1998.
5. BSI. Part5: Code of practice for design of composite bridges. In: Steel, concreteand composite bridges, BS5400. London: British Standards Institution, 1979.
6. BSI. Part 3: Code of practice for design of steel bridges. In: Steel, Concrete and composite bridges, BS5400. London: British Standards Institution, 2000.
7. DIN. Concrete bridges,design and construction, DIN1075. Berlin: Deutsches Institut fur Normung, 1981.
8. JRA. Design specifications for highway bridges, Part II steel bridges. Tokyo: Japan Road Association, 2002.
9.中华人民共和国交通部标准.公路钢筋混凝土及预应力混凝土桥涵设计规范.北京:人民交通出版社,1985, 9-11.
10.中华人民共和国行业标准.公路钢筋混凝土及预应力混凝土桥涵设计规范.北京:人民交通出版社,2004, 16-18.
11.罗旗帜,俞建立.钢筋混凝土连续箱梁桥翼板横向裂缝问题[J].桥梁建设,1997,(1):41-44.
12.周若来,沈成武.某高速公路桥裂缝成因分析[J].武汉理工大学学报,2003, 27(1):84-86.
13.黄培元.普通钢筋混凝土连续箱梁桥开裂等问题的探讨[J].东北公路,2003, 26(1):61-64.
14. Abramento M, Whittle A J. Shear lag analysis of planar soil reinforcement in plance-strain compression. J. Engrg. Mech., ASCE, 1993, 119(2):270-291.
15. Kulek G L, Wu E Y. Shear lag in bolted angle tension members. J. Struct. Engrg., ASCE, 1997, 123(9): 1144-1151.
16.程翔云.梁桥理论与计算.北京:人民交通出版利,1986.
17.项海帆.高等桥梁结构理论.第一版.北京:人民交通出版社,2001, 50-72.
18. Kristek V. Theory of box girder. New York: John Wiley & Sons, 1979, 9-11.
19. Vlasov V Z.Thin-walled elastic beams [M].Washington D C.National Science Foundation,1961.
20. Sedlacek G. A simplified method for the determination of the effective width due to shear lag effects. J. Construct. Steel Research, 1993, (24):155-182.
21. Abdel-Sayed G. Effective width of steel deck plate in bridge. J. Struct. Div, ASCE,1969, 95(7): 1459-1474.
22. Hasebe K, Usuki S, Horie Y. Shear lag analysis and effective width of curved girder bridges. J. Engrg. Mech., ASCE, 1985,111(1):87-92.
23. Ahn I S, Chievanichakorn M, Chen S S, et al. Effective flange width provisions for composite steel bridges. Engineering Structures, 2004, (26): 1843-1851.
24. Reissner E. On the problem of stress distribution in wide flanged box beam. Journal Aero. Sci., 1938, (5):295-299.
25. Lee C K, Wu G J. Shear lag analysis by the adaptive finite element method. 1:Analysis of simple plated structures. Thin-Walled Struct., 2000a, (38):285-309.
26. Lee C K, Wu G J. Shear lag analysis by the adaptive finite element method.
2:Analysis of complex plated structures. Thin-Walled Struct., 2000b, (38):311-336.
27. Song Q G, Scordelis A C. Shear lag analysis of T -, I-, and box beams. J. Struct. Engrg., ASCE, 1990a, 116(5):1290-1305.
28. Van-Dalen K, Narasimham S V. Shear lag in shallow wide-flanged box girder. J. Struct. Div., ASCE, 1976, 102(10):1969-1979.
29. Malcolm D J, Redwood R G. Shear lag in stiffened box girders. J. Struct. Div., ASCE, 1970, 96(7): 1403-1419.
30. Reissner E. Analysis of shear lag in box beam by principle of minimum potential energy. Quarterly of Applied Mathematics, 1946, 5(3): 268-278.
31. Kuzmanvic B O, Graham H J. Shear lag in box girders. J. Struct. Div., ASCE, 1981,107(9): 1701-1712.
32. Foutch D A, Chang P C. A shear Lag anomaly[J]. J Struct Engrg,ASCE,1982,108(7):1653-1658.
33.张士铎,丁芸.变截面悬臂箱梁负剪力滞差分解[J].重庆交通学院学报,1984,11(4): 34-47.
34.张士铎,谢琪.四次抛物线变截面悬臂梁剪力滞效应及差分解[J].结构工程师,1987,(3):35-40.
35. Kristek V, Evans H R, Ahmad M K H. A shear lag analysis for composite box girders. J. Construct. Steel Research, 1990, (16):1-21.
36. Kristek V, Studnicka J. Negative shear lag in flanges of plated structures. J. Struct.Engrg., ASCE, 1991,117(12): 3553-3569.
37.程翔云,罗旗帜,箱梁在压弯荷载共同作用下的剪力滞[J].土木工程学报.1991,24(1):52-64.
38. Moffatt K R, Dowling P J. British shear lag rules for composite girders. J. of the Structureal Division, ASCE, 1978,104(7):1123-1130.
39. Moffatt K R, Dowling P J. Discussion on shear lag in steel box girder bridges. The Structural Engineer, 1976, 54(9):285-298.
40. Moffatt K R, Dowling P J. Shear lag in steel box girder bridges. The Structural Engineer, 1975, 53(10): 439-448.
41. Luo Q Z, Tang J, Li Q S. Calculation of moments on top slab in single-cell box girder. J. Struct. Engrg., ASCE, 2003, 129(1): 130-134.
42. Sung C L, Chai H Y, Dong Y. Analysis of shear lag anomaly in box girders. J. Struct. Engrg., ASCE, 2002,128(11):1379-1386.
43. Shushkewich K W. Negative shear lag explained. J. Struct. Engrg., ASCE, 1991,117(11): 3543-3546.
44. Evans H R, Taherian A R. The prediction of the shear lag effect in box girder. Proc. Instn. Civ. Engrs., Part 2,1997, (63): 69-72.
45.郭金琼,房贞政.箱形梁桥剪滞效应分析[J].土木工程学报,1983,16(1):1-13.
46. Chang S T. Prestress influence on shear lag effect in continuous box girder bridge[J]. J Struct Engrg, ASCE,1992,118(11) :3113-3121.
47.罗许国,戴公连.大悬臂桥面板钢脊骨梁结构模型剪力滞效应有限元分析[J].长沙铁道学院学报,2002,20(1):51-56.
48.郑振.大悬臂变截面箱梁剪力滞效应分析[J].福州大学学报,2001,29(2):62-65.
49.吴幼明,罗旗帜,岳珠峰.薄壁箱梁剪滞效应的能量变分法[J].工程力学,2003,20(4):161-165.
50.韦成龙,曾庆元,刘小燕.薄壁箱梁剪力滞分析的多参数翘曲位移函数及其有限元法[J].铁道学报.2000,22(5):60-64.
51.奥登,里帕格.弹性结构力学.成文山,程翔云,周义武译.第一版.北京:中国建筑工业出版社,1986.
52.龙驭球,包世华.结构力学[M].北京:高等教育出版社,1996.
53.胡海昌.弹性力学的变分原理及其应用[M].北京:科学出版社出,1981.
54.刘世忠,欧阳永金,吴亚平.变截面薄壁箱梁剪力滞剪切变形效应分析[J].中国公路学报,2002,15(3):61-63.
55. Tahan N, Pavlovic M N, Kotsovos M D. Single fourier series solutions for rectangular plates under in-plane forces, with particular reference to the basic problem of colinear compression. Part 2: Stress distribution. Thin-Walled Structures,1993, (17):1-26.
56. Tahan N, Pavlovic M N, Kotsovos M D. Shear lag revisited: the use of singlefourier series for determining the effective breadth in plated structure. Computers and Structures, 1997, 63(4): 759-767.
57.罗旗帜.薄壁箱型梁剪力滞计算的梁段有限元法[J].湖南大学学报,1991,(2):33-55.
58.钱寅泉,倪元增.箱梁剪力滞计算的翘曲函数法[J].铁道学报,1990,12(2):(57-70).
59.谢旭,黄剑源.薄壁箱形梁剪力滞效应分析的刚度法[J].工程力学,1995,(2):95102.
60.黄剑源,杨允表.钱塘江二桥变截面箱形连续梁剪滞效应的有限元分析[J].桥梁建设.1994,(1):7076
61.杨允表,黄剑源.广义有限条分析多室箱梁的剪滞效应[J].桥梁建设,1995,(4):40-45.
62.王修信,黄剑源.变截面多跨梯形箱梁剪滞效应差分解[J].桥梁建设,1993, (2):58-64.
63. Hildbrand P B. The exact solution of shear lag problems in flat panels and box beams assumed rigid in the transverse direction. NACA, 1934, (TN894): 90-95.
64.方同,薛璞.振动理论及应用[M].西安:西北工业大学出版社,2002.2.
65.铁摩辛柯,盖莱.材料力学.胡人礼译.第一版.北京:科学出版社,1978,256-264.
66.宋一凡.公路桥梁动力学[M].北京:人民交通出版社,1999.
67.倪振华.振动力学[M].西安:西安交通大学出版社,1988.
68.刘山洪,何广汉等. PPC箱梁节段模型剪滞效应的试验研究[J].桥梁建设,2000,(3):5-7.
69.吴海林,季文玉.箱梁剪力滞效应影响参数分析[J].工程力学,2000,2(1): 572-577.
70.周坚,涂令康.再论槽型宽梁的剪力滞[J].工程力学,1994,11(2): 65-75.
71.彭大文,颜海.曲线脊骨箱梁的剪力滞效应分析[J].铁道学报,2001,23(4): 10-16.
72. Hoglund, Torsten. Shear Buckling Resistance of Steel and Aluminium P1ate Girders. Thin-Walled Structures.1997,29 (1-4):13-30.
73. Luo, Q.Z.; Wu, Y.M.; Tang, J.; Li, Q.S. Experimental studies on shear lag of box girders. Engineering Structures.2002,24(4): 469-477.
74. Yaping, Wu; Yuanlin, Zhu; Yuanming, Lai; Weideng, Pan. Analysis of shear lag and shear deformation effects in laminated composite box beams under bending loads. Composite Structures.2002,55(2):147-156.
75. Uzoegbo, H.C. Shear Lag in Steel Angles: An Investigation of the South African Standards. Journal of Constructional Steel Research.1998,46(1-3):Volume: 46, Issue:162-162.
76. Tenchev R T. Shear lag in orthotropic beam flanges and plates with stiffeners. Int. J.Solids Structures, 1996, 33(9):1317-1334.
77.陈启流.数学物理方法[M].广州:华南理工大学出版社,1994.
78.黄剑源.薄壁结构的扭转分析(上).北京:中国铁道出版社,1983.
79.黄剑源.薄壁结构的扭转分析(曲线梁与斜支箱形梁).北京:中国铁道出版社,1998.
80.何福宝.薄壁曲杆有限元法[J].固体力学学报,1981,2(2):141-157.
81.吴亚平,赖远明.考虑剪滞效应的薄壁曲梁有限单元法[J].工程力学,2002,19(4):85-89.
82.李琰,辛克贵.薄壁曲梁的横向弯曲稳定分析[J].工程力学,2005,22(1):69-74.
83. Kang Y J, Yoo C H. Thin-walled curved beams. I: Formulation of nonlinear equations[J]. J Engrg. Mech.,ASCE,1994, 120(10) :2072-2101.
84.段海娟,赵人达.曲箱梁考虑剪力滞效应得弯扭耦合分析[J].中国铁道科学,2002,23(1):34-37.
85. Hsu Y T, Fu C C, Schelling D R. EBEF method for distortional analysis of steel box girder bridges. J. Struct Engrg., ASCE,1995,121(3):557-566.
86.李惠生,张罗溪.曲线梁桥结构分析[M].北京:中国铁道出版社,1992
87.彭大文.连续弯箱梁剪滞效应分析和实用计算法研究[J].中国公路学报,1998,11(3):41-49.
88. Yoshimura J, Nirasawa N. On the stress distributions and effective width of curved girder bridges by the folded plate theory. Proc., Japan Soc. of Civ. Engrs., Tokyo,1975, No. 233.
89.肖敏,李新平.连续曲线箱梁剪力滞效应分析[J].中外公路,2004, 24(4):61-65.
90.杨允表.曲线箱梁考虑曲率及剪力滞影响的力学分析[J].土木工程学报,1999,32(1):43-49.
91. Luo Q Z, Tang J, Li Q S. Shear lag of thin-walled curved box girders in box girders bridges. J. Engrg. Mech. , ASCE, 2000, 126(10):1111-1114.
92.罗旗帜.曲线箱梁桥的剪滞效应分析[J].佛山大学学报,1992, 10(2):46-55.
93. Kovanicova, Zuzana;Kristek, Vladimir;Skaloud, Miroslav. Shear lag in the wide flanges ofvertically curved box girders. Acta Technica CSAV (Ceskoslovensk Akademie Ved), 1988,33(4): 414-436.
94.罗旗帜.计算曲线梁桥的传递矩阵法[J].中南公路工程,1990, (3): 32-41.
95. Evans,H.R.&Taherian ,“A.R.A Design Aid for Shear Lag Calculation”,Proc. I. C. E,part2,1980, 69, June P403-424.
96. Evans H R, Taherian A R. The prediction of the shear lag effect in box girder. Proc. Instn. Civ. Engrs., Part 2,1997, (63): 69-72.
97. Shih Toh Chang&Fang Zhen Zheng .“Negative Shear Lag in Cantilever Box Girder With Constant Depth”. J. of Structural Engineering. 1985,(1):20-34.
98.彭大文,王忠.低矮截面箱梁桥剪滞效应分析[J].福州大学学报(自科版),1999,27(4):73-76.
99.经柏林,鲍卫刚.变截面长悬臂宽箱梁桥翼缘有效宽度研究[J].中南公路工程,1998,23 (4):24-26.
100.李运光,宋娃丽.箱梁桥的剪滞效应影响[J].工程力学,1998,(2):415-418.
101. Chang, Shih Toh;Yun, Ding. Shear lag effect in box girder with varying depth. Journal of Structural Engineering ,1988,114(10):2280-2292.
102.王忠,彭大文.预应力对箱梁剪滞效应的影响分析[J].工程力学,1998,(2):449-453.
103.罗旗帜.变截面多跨箱梁桥剪滞效应分析[J].中国公路学报,1998,11(1):63-70.
104.罗旗帜,俞建立.变截面箱梁的负剪力滞[J].重庆交通学院学报,1997,16(3):18-25.
105.钱寅泉,倪元增.梯形截面箱梁桥的剪力滞计算.中国公路学会桥梁工程学会1989年学术会议论文集,1989.
106.张士铎,王文州.荷载横向作用位置对箱梁剪力滞效应的影响[J].湖南大学学报.1995,21(2):109-115.
107. Taherian A R, Evans H R. The bar simulation method for the calculation of shear lag in mufti-cell and continuous box girders. Proc. Instn. Civ. Engrs., Part 2, 1977, (63):881-897.
108.张启伟,张士铎.单索面斜拉桥箱梁恒载剪力滞效应分析[J].中国公路学报,1997,10(1):39-43.
109.罗旗帜.基于能量原理的薄壁箱梁剪力滞理论与试验研究:[湖南大学博士学位论文].长沙:湖南大学土木系,2005.11
110.罗许国.无背索斜拉桥结构模型剪力滞实验研究[J].株洲工学院学报,2004,18(2):110-112.
111. Starink, M.J.; Syngellakis, S. Shear lag models for discontinuous composites: fibre end stresses and weak interface layers. Materials Science and Engineering. 1999,270(2):270-277.
112. Burgan B A, Dowling P J. The treatment of shear lag in design. Thin-Walled Structures, 1990, (9): 121-134.
113. Kristek V. Strudnicka J, Skaloud M. Shear lag in wide flanges of steel bridges. Acta Tech., CSAV,1981(26):464-488.
114. Adekola A O. On shear lag effects in orthotropic composite beams. Int. J. Solids Structures, 1974, 10(4): 735-754.
115. Adekola A O. The dependence of Shear lag on partial interaction in composite beams. Int. J. Solids Structures. 1974, 10 (7): 389-400.
116. Lopez-Anido R, Gangarao H V S. Warping solution for shear lag in thin-walledorthotropic composite beam. J. Engrg. Mech., ASCE, 1996, 122(5):449-457.
117. Pavlovic M N, Tahan N, Kotsovos M D. Shear lag and effective breadth in rectangular plates with material orthotropy. Part 1:Analytical formulation. Thin-Walled Structures,1998a,30(1-4):199-213.
118.蔡松柏,李存权.箱形梁桥剪力滞效应的精确分析[J].中南公路工程,1989, (3):33-41.
119.文国华.横向预应力对悬臂翼板有效分布宽度的影响.中南公路工程,1998,23(4):29-32.
120. Kristek V. Folded plate approach to analysis of shear wall systems and frame structures. Proc. Inst. Civ. Engrs., Part 2, 1979, (67):1065-1075.
121. Fafitis A, Rong A Y. Analysis of thin-walled box girders by paralled processing.Thin-Walled Structures, 1995, (21):233-240.
122.孙广华.德国关于桥梁翼板计算宽度的规定.公路,1997,(3)39-42.
123.项贻强.箱型梁桥翼板的有效宽度及对规范的建议.中国公路学会桥梁工程学会1989年学术会议论文集,1989.10.
124. Kuhn P, Peterson J P. Shear lag in axialy loaded panels. NACA, 1948, TN. 1928.
125. Kuhn P, Chiaritc P T. Shear lag in box beams. Methods of Analysis and Experimental Investigations, NACA, 1942, REP., No. 739.
126. Connor J J, Pouangare C C. Simple model for design of framed-tube Structures. J.Struct. Engrg., ASCE, 1991,117(12):3623-3644.
127. Chang S T. Shear lag effect in simply supported prestressed concrete box girder. J.Bridge Engrg., ASCE, 2004, 9(2):178-184.
128.吴亚平,复合材料薄壁箱梁的剪滞剪切效应分析[J].土木工程学报,1995, 29(4):31-47.
129. Takayanagi, H./Keimnochi, K./Sembokuya, H./Hojo, M./Maki, H. Shear-lag effect in CFRP I-beams under three-point bending. Experimental Mechanics,1994,34(2):100-107.
130. Qi-gen Song&Alexander C. Sordelis.“Shear Lag Analysis of T,I- and Box Beams”. J. ofStructural Engineering,1990,116(5):1306-1318.
131. Ayyub, Bilal M.;Sohn, Young G;Saadatmanesh, Hamid . Prestressed composite I-girders experimental study for negative moment. Journal of Structural Engineering,1992,118(10) :2743-2762.
132. Song Q G, Scordelis A C. Formulas for shear lag effect of T-, I-, and box beams, J.Struct. Engrg., ASCE, 1990b, 116(5): 1306-1318.
133.程翔云,汤康恩. T形梁翼缘的剪力滞及其有效宽度[J].重庆交通学院学报,1984,(4): 28-33.
134.张元海,张清华,李乔.宽翼缘薄壁梁剪滞效应分析的变分解法[J].工程力学,2006,23(1):52-56.
135.刘寒冰,刘文会,张云龙.用变分法分析预应力钢-混凝土组合T梁的剪力滞效应[J].公路交通科技,2004, 21(5):65-66.
136.蔡松柏,程翔云,邵旭东. II型梁剪力滞效应的解析解[J].工程力学,2003, 20(5):82-86.
137.周坚.用余能原理解槽型宽梁的剪力滞问题[J].力学与实践,1985, 7(5): 52-54.
138.邵爱军,吴代华.基于能量法的槽型梁剪滞效应分析[J].武汉理工大学学报,2003,25(3): 52-55.
139.万臻,李乔,毛学明.II型截面主梁斜拉桥剪力滞效应研究[J].西南交通大学学报,2004, 39(5): 623-627.
140.倪元增.槽型宽梁的剪力滞问题[J].土木工程学报,1986, 19(4): 32-41.
141. Lee J A N. Effective width of Tee-beam. The Structural Engineer, 1962, 40(1):21-27.
142.魏丽娜,方放.变截面箱梁桥剪滞效应分析中翼板纵向位移函数的选择[J].桥梁建设,1996(3):28-31.
143. Chang S T, Yun D. Shear lag effect in box girder with varying depth. J. Struct.Engrg., ASCE, 1988, 114(10):2280-2292.
144.杨充表,朱鸿蕾,顾强等.变截面连续箱梁剪力滞效应分析[J].中国市政工程,2000, 90(3): 19-22.
145. Pavlovic M N, Tahan N, Kotsovos M D. Shear lag and effective breadth in rectangular plates with material orthotropy. Part 2: Typical results of parametric studies. Thin-Walled Structures, 1998b, 30(1-4): 215-237.
146. Nakai H, Murayama Y. Researches on negative shear lag of cantilever beams and application to bridge design. Trans. JSCE, 1976, (8):107-109.
147. Chang S T, Zheng F Z. Negative Shear lag in Cantilever box girders with constant depth.J. Struct. Engrg., ASCE, 1987, 113(1):20-35.
148. Luo Q Z, Tang J, Li Q S. Negative Shear lag in box girders with varying depth. J.Struct. Engrg., ASCE, 2001,127(10):1236-1239.
149.吴亚平.多室箱梁剪滞效应的变分法分析[J].兰州铁道学院学报,1992, 1l(2):36-48.
150.魏丽娜,方放,余天庆等.变截面箱形梁桥剪滞效应的近似计算方法[J].土木工程学报,1997, 30(2):64-72.
151.程翔云.悬臂薄壁箱梁的负剪力滞[J].上海力学,1987, (2): 52-62.
152. Luo Q Z, Li Q S,Tang J. Shear lag in box girders bridges. Journal of BridgeEngineering, ASCE, 2002, 7(5):308-313.
153.方志,曹国辉,王济川.钢筋混凝土连续箱梁剪力滞效应试验研究[J].桥梁建设,2000, (4):1-3.
154.牛斌,杨梦蛟,马林.预应力混凝土宽箱梁剪力滞效应试验研究[J].中国铁道科学,2004, 25(2): 25-30.
155.方淑君,戴公连,狄谨.梁板结构在轴力及弯矩作用下截面剪力滞效应的研究[J].长沙铁道学院学报,2001, 19(3): 45-48.