PBL剪力连接键群的简化有限元计算方法及其应用
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摘要
自PBL剪力连接键(Perfobond-Leiste Strip)问世后,因其在钢-混凝土复合结构中具有良好的力学性能,桥梁结构中对其应用日益广泛,尤其是大跨度桥梁结构。
目前,各国学者通过试验对PBL剪力连接键的力学行为进行研究,所得到的成果对实际应用具有极大的意义,同时基于三维实体的有限元计算方法也得到-定的推广。但是,现有计算方法在实际应用中有一定局限,故提出简化有限元计算方法对于工程计算至关重要。就有关文献看,对于简化有限元计算方法的研究仍较少。
本文立足于现有的钢-混凝土结合段分析理论,针对PBL剪力连接键的简化计算方法和PBL剪力连接键群的工作效应进行了以下几个方面的研究：
(1)根据PBL剪力连接键单向荷载作用下的荷载-滑移曲线公式,推导PBL剪力连接键在单向荷载作用下的非线性刚度矩阵；
(2)根据弹塑性理论,将一维问题拓展至多维情况,推导PBL剪力连接键在双向荷载作用下的非线性刚度矩阵,得到弹塑性刚度矩阵的显式表达；
(3)通过矩阵位移法和有限元法阐述适用于有限元计算的PBL剪力连接键刚度矩阵计算过程；
(4)以南京长江第四大桥作为工程实例,研究分布式锚固系统的力学行为,应用有限元软件对结构进行模拟计算并探讨PBL剪力连接键群的工作性能。
(5)以鄂东长江公路大桥作为工程实例,研究钢-混凝土结合段的力学行为,应用有限元软件对结构进行模拟计算并探讨PBL剪力连接键群的工作性能；
Since the perfobond-leiste strip (PBL shear connector) had been designed, because of the excellent mechanical properties in steel-concrete composite structure, it was widely used in bridge structure, especially in the long span bridges.
Now, domestic and foreign scholars have researched the mechanical behaviors of PBL shear connector through test methods. The results were meaningful to practical application, and the finite element method based on3-D was widely promoted. However, existing calculation methods for PBL shear connector also had limitations in practical applications. It was important to propose a simplified finite element method for engineering calculation. According to the existing references, there was still little research in simplified finite element method.
This thesis was based on the existing analysis theories of steel-concrete composite structure, in connection with the simplified calculation methods of PBL shear connector and its mechanical behaviors. In summary, the thesis studied following aspects:
(1) Based on the load-slip curve equation of PBL shear connection, its nonlinear stiffness matrix was derived in unidirectional force case.
(2) Based on the elastic-plastic theory, the thesis extended the1-D to2-D case, derived the nonlinear stiffness matrix of PBL shear connection under bi-directional force case and gained an explicit expression of the elastic-plastic stiffness matrix at last.
(3) Taking the matrix displacement method and finite element method, the stiffness matrix calculation process which was suitable for finite element calculation was researched.
(4) Taking Fourth Nanjing Yangtze River Bridge as an engineering example, the thesis researched the mechanical behavior of the anchoring system. The structure was simulated and the effectiveness of PBL shear connectors was analyzed by using Ansys software.
(5) Taking Edong Yangtze River Highway Bridge as an engineering example, the thesis researched the mechanical behavior of the steel-concrete composite section. The structure was simulated and the effectiveness of PBL shear connectors was analyzed by using Ansys software.
目前,各国学者通过试验对PBL剪力连接键的力学行为进行研究,所得到的成果对实际应用具有极大的意义,同时基于三维实体的有限元计算方法也得到-定的推广。但是,现有计算方法在实际应用中有一定局限,故提出简化有限元计算方法对于工程计算至关重要。就有关文献看,对于简化有限元计算方法的研究仍较少。
本文立足于现有的钢-混凝土结合段分析理论,针对PBL剪力连接键的简化计算方法和PBL剪力连接键群的工作效应进行了以下几个方面的研究：
(1)根据PBL剪力连接键单向荷载作用下的荷载-滑移曲线公式,推导PBL剪力连接键在单向荷载作用下的非线性刚度矩阵；
(2)根据弹塑性理论,将一维问题拓展至多维情况,推导PBL剪力连接键在双向荷载作用下的非线性刚度矩阵,得到弹塑性刚度矩阵的显式表达；
(3)通过矩阵位移法和有限元法阐述适用于有限元计算的PBL剪力连接键刚度矩阵计算过程；
(4)以南京长江第四大桥作为工程实例,研究分布式锚固系统的力学行为,应用有限元软件对结构进行模拟计算并探讨PBL剪力连接键群的工作性能。
(5)以鄂东长江公路大桥作为工程实例,研究钢-混凝土结合段的力学行为,应用有限元软件对结构进行模拟计算并探讨PBL剪力连接键群的工作性能；
Since the perfobond-leiste strip (PBL shear connector) had been designed, because of the excellent mechanical properties in steel-concrete composite structure, it was widely used in bridge structure, especially in the long span bridges.
Now, domestic and foreign scholars have researched the mechanical behaviors of PBL shear connector through test methods. The results were meaningful to practical application, and the finite element method based on3-D was widely promoted. However, existing calculation methods for PBL shear connector also had limitations in practical applications. It was important to propose a simplified finite element method for engineering calculation. According to the existing references, there was still little research in simplified finite element method.
This thesis was based on the existing analysis theories of steel-concrete composite structure, in connection with the simplified calculation methods of PBL shear connector and its mechanical behaviors. In summary, the thesis studied following aspects:
(1) Based on the load-slip curve equation of PBL shear connection, its nonlinear stiffness matrix was derived in unidirectional force case.
(2) Based on the elastic-plastic theory, the thesis extended the1-D to2-D case, derived the nonlinear stiffness matrix of PBL shear connection under bi-directional force case and gained an explicit expression of the elastic-plastic stiffness matrix at last.
(3) Taking the matrix displacement method and finite element method, the stiffness matrix calculation process which was suitable for finite element calculation was researched.
(4) Taking Fourth Nanjing Yangtze River Bridge as an engineering example, the thesis researched the mechanical behavior of the anchoring system. The structure was simulated and the effectiveness of PBL shear connectors was analyzed by using Ansys software.
(5) Taking Edong Yangtze River Highway Bridge as an engineering example, the thesis researched the mechanical behavior of the steel-concrete composite section. The structure was simulated and the effectiveness of PBL shear connectors was analyzed by using Ansys software.
引文
[1]白玲,史永吉.复合结构桥梁的特性[J].中国铁道科学,2003,24(1)：80-87
[2]M.R. Veldanda and M.U. Hosain. Behaviour of perfobond rib shear connectors push-out tests. Can. J. Civ. Eng.1992.19:1-10
[3]E.C. Oguejiofor, M.U. Hosain. A parametric study of perfobond rib shear connectors [J]. Can. J. Civil Engng,1994,21:614-625
[4]Roberts WS, Heywood RJ. Development and testing of a new shear connector for steel concrete composite brdiges[J]. Fourth international bridge engineering conference,1995: 137-145
[5]宗周红,车惠民.剪力连接件静载和疲劳试验研究[J].福州大学学报,1999,27(6)：61-66
[6]Isabel Valente, Paulo J.S. Cruz. Experimental analysis of Perfobond shear connection between steel and lightweight concrete [J] Journal of Construction Steel Research, 2004,60:465-479
[7]胡建华,叶梅新,黄琼.PBL剪力连接件承载力试验[J].中国公路学报,2006,19(6)：65-72
[8]Hyeong-Yeol Kim, Youn-Ju Jeong. Experimental investigation on behaviour of steel-concrete composite bridge decks with perfobond ribs. Journal of Constructional Steel Research 62 (2006) 463-471
[9]刘玉擎,周伟翔,蒋劲松.开孔板连接件抗剪性能试验研究[J].桥梁建设,2006,06：1-4
[10]胡建华,侯文崎.PBL剪力键承载力影响因素和计算公式研究[J].铁道科学与工程学报,2007,4(6)：12-18
[11]J.da.C Vianna, L.F. Costa-Neves, P.C.G da S. Vellasco, S.A.L. de Andrade. Experimental assessment of Perfobond and T-Perfobond shear connectors'structural response[J]. Journal of Constructional Steel Reasearch,2009,65:408-421
[12]J.P.S Canadido-Martins, L.F. Costa-Neves, P.C.G da S. Vellasco. Experimental evaluation of the structural response of Perfobond shear connectors [J]. Engineering Structures,2010,32:1976-1985
[13]Jin-Hee Ahn, Chan-Goo Lee, Jeong-Hun Won, Sang-Hyo Kim. Shear resistance of the perfobond-rib shear connector depending on concrete strength and rib arrangement [J]. Journal of Constructional Steel Research,2010,66:1295-1307
[14]Joao Paulo C. Rodrigues. Behaviour of Perfobond shear connectors at high temperatures. Engineering Structures,33 (2011) 2744-2753. doi:10.1016/j.engstruct.2011.05.004
[15]李乔,武焕陵,唐亮,崔冰.南京长江三桥桥塔钢混结合段内力分布规律研究[J].中国 公路学会桥梁和结构工程分会2005年全国桥梁学术会议论文集,2005
[16]张清华,李乔,唐亮.桥塔钢-混凝土结合段剪力键破坏机理及极限承载力[J].中国公路学报,2007,20(1)：85-90
[17]娄学全,武焕陵,崔冰,赵灿晖.悬索桥主缆分布传力锚固系统设计与施工[M].人民交通出版社,2012.4
[18]李小珍,肖林,张迅,刘德军.斜拉桥钢-混凝土结合段PBL剪力键承载力试验研究[J].钢结构,2009,24(5)：22-27
[19]夏嵩,赵灿晖,张育智,李乔.PBL传剪器极限承载力的试验研究[J].西南交通大学学报,2009,44(2)：166-170
[20]王振海,李乔,赵灿晖.PBL剪力键破坏形态及极限承载力试验研究[J].防灾减灾工程学报,2011,31(5)：517-522
[21]E.C. Oguejiofor, M.U. Hosain. Behavior of perfobond rib shear connectors in composite beams:full-size tests[J].Can. J. Civil Engng,1992,19(2):224-235
[22]E.C. Oguejiofor, M.U. Hosain. Tests of full-size composite beams with perfobond rib connectors[J]. Can. J. Civil Engng,1995,22(1):80-92
[23]叶梅新,蒋彪.混合型自锚式悬索桥连接部位传力研究[J].铁道科学与工程学报,2006,3(3)：1-6
[24]胡建华,蒲怀仁.PBL剪力键钢混结合段设计与试验研究[J].钢结构,2007,2(22)：62-67
[25]Sang-Hyo Kim. Experimental study on joint of spliced steel–PSC hybrid girder, Part I:Proposed parallel-perfobond-rib-type joint[J]. Engineering Structures,33 (2011) 2382-2397. doi:10.1016/j.engstruct.2011.04.012
[26]Sang-Hyo Kim. Experimental study on joint of spliced steel–PSC hybrid girder, part Ⅱ:Full-scale test of spliced hybrid Ⅰ-girder[J]. Engineering Structures,33 (2011) 2668-2682. doi:10.1016/j.engstruct.2011.05.016
[27]E.C. Oguejiofor, M.U. Hosain. Numerical analysis of push-out specimens with perfobond rib connectors [J]. Computers & Structures,1997,62(4):617-624
[28]张清华,李乔,唐亮.剪力连接件的三维非线性仿真分析方法[J].西南交通大学学报,2005,40(5)：595-599
[29]刘荣,余俊林,刘玉擎,吴定俊.鄂东长江大桥混合梁结合段受力分析[J].桥梁建设,2010,3：33-35
[30]C. Kalfas, P. Pavlidis, E. Galoussis. Inelastic behavior of shear connection by a method based on FEM[J]. J. Construc. Steel Res.,1997,44:107-114
[31]张清华,李乔,卜一之.PBL剪力连接件群传力机理研究Ⅰ——理论模型[J].土木工程学报,2011,4(44)：71-77
[32]张清华,李乔,卜一之.PBL剪力连接件群传力机理研究Ⅱ——极限承载力[J].土木工程学报,2011,5(44)：101-108
[33]王振海,赵灿晖,李乔.PBL剪力键荷载-滑移关系试验研究[J].西南交通大学学报,2011.8(46)：547-552
[34]黄阳林,朱文军,谢东,李哲.南京长江第四大桥北锚碇锚固系统安装测量定位[J].公路,2010.6(6)：25-29
[35]Youn-Ju Jeong, Hyeong-Yeol Kim, Hyun-Bon Koo. Longitudinal shear resistance of steel-concrete composite slabs with perfobond shear connectors [J]. Journal of Constructional Steel Research,2009,65:81-88
[36]Kazimierz Furtak. Direct shear strength of concrete in strip connectors [J]. Archives of civil and mechanical engineering,2005,2:49-60
[37]刘玉擎,周伟翔.开孔钢板连接件的受力性能及其应用[J].哈尔滨工业大学学报,2005,37：381-384
[38]王建新,胡旭辉,钟豪.组合箱梁剪力键设计分析[J].山西建筑,2005,31(20)：73-74
[39]白玲,史志强,史永吉.剪力键布置方式对连续组合梁桥受力特性的影响[J].中国铁道科学,2003,24(2)：67-70
[40]聂建国,卫军.剪力连接件在钢-混凝土组合梁中的实际工作性能[J].郑州工学院学报,1991,12(4)：43-47
[41]聂建国,沈聚敏,袁彦声,林伟,王文辉.钢-混凝土组合梁中剪力连接件实际承载力的研究[J].建筑结构学报,1996,17(2)：21-28
[42]聂建国,谭英,王洪全.钢-高强混凝土组合梁栓钉剪力连接件的设计计算[J].清华大学学报,1999,39(12)：94-97
[43]王洪全,石中柱,聂建国.推出试件中栓钉剪力连接件的极限抗剪强度分析[J].哈尔滨建筑大学学报,1997,30(5)：199-202
[44]苏庆田,刘玉擎,曾明根.苏通大桥索塔栓钉剪力连接件的力学性能试验[J].同济大学学报,2008,36(7)：916-920
[45]林传金,宗周红,唐朝阳.中22栓钉剪力连接件荷载-滑移关系试验研究[J].哈尔滨工业大学学报,2005,37：376-380
[46]叶梅新,吏林山.混凝土受拉状态下钢-混凝土组合结构中栓钉的承载力的研究[J].长沙铁道学院学报,2003,21(1)：8-12
[47]叶梅新,罗如登.群钉钢-混凝土组合件栓钉受力状态研究[J].钢结构,1999,3(14)：39-42
[48]叶梅新,张晔芝.桁梁结合梁及其剪力连接件试验研究[J].铁道学报,1999,21(1)：67-71
[49]Huu Thanh Nguyen, Seung Eock Kim. Finite element modeling of push-out tests for large stud shear connectors[J]. Journal of Constructional Steel Research,2009,65: 1909-1920
[50]Seung Eock Kim, Huu Thanh Nguyen. Finite element modeling and analysis of a hybrid steel-PSC beam connection[J]. Engineering Structures,2010
[5l]唐进,叶梅新.钢-混凝土组合结构中密集型剪力钉群的受力状态[J].长沙铁道学院学报,1999,17(4)：68-73
[52]刘玉擎.有限弹簧元在桥梁结构分析中的应用研究[J].桥梁建设,2005,06：19-22
[53]周伟翔,刘玉擎,曾明根,邵长宇.连续组合梁桥钢与混凝土连接技术的研究[J].第十七届全国桥梁学术会议,2006
[54]周浩.南京长江三桥桥塔钢-混结合段剪力键选型试验研究[D].西南交通大学研究生学位论文,2005
[55]赵洁,聂建国.钢板-混凝土组合梁的非线性有限元分析[J].工程力学,2009,26(4)：105-112
[56]白玲.超静定组合结构桥梁受力特性的3D-FEM模拟分析[D].铁道科学研究院,2003
[57]陈开利,余天庆,习刚.混合梁斜拉桥的发展与展望[J].桥梁建设,2005(2)：1-4
[58]赵灿晖.基于Prager硬化的钢管混凝土非线性梁单元[J].地震工程与工程振动,2006,12(26)：128-132
[59]刘明虎,徐国平,刘峰.鄂东大桥混合梁钢-混凝土结合部研究与设计[J].公路交通科技,2010,12(27)：78-85
[2]M.R. Veldanda and M.U. Hosain. Behaviour of perfobond rib shear connectors push-out tests. Can. J. Civ. Eng.1992.19:1-10
[3]E.C. Oguejiofor, M.U. Hosain. A parametric study of perfobond rib shear connectors [J]. Can. J. Civil Engng,1994,21:614-625
[4]Roberts WS, Heywood RJ. Development and testing of a new shear connector for steel concrete composite brdiges[J]. Fourth international bridge engineering conference,1995: 137-145
[5]宗周红,车惠民.剪力连接件静载和疲劳试验研究[J].福州大学学报,1999,27(6)：61-66
[6]Isabel Valente, Paulo J.S. Cruz. Experimental analysis of Perfobond shear connection between steel and lightweight concrete [J] Journal of Construction Steel Research, 2004,60:465-479
[7]胡建华,叶梅新,黄琼.PBL剪力连接件承载力试验[J].中国公路学报,2006,19(6)：65-72
[8]Hyeong-Yeol Kim, Youn-Ju Jeong. Experimental investigation on behaviour of steel-concrete composite bridge decks with perfobond ribs. Journal of Constructional Steel Research 62 (2006) 463-471
[9]刘玉擎,周伟翔,蒋劲松.开孔板连接件抗剪性能试验研究[J].桥梁建设,2006,06：1-4
[10]胡建华,侯文崎.PBL剪力键承载力影响因素和计算公式研究[J].铁道科学与工程学报,2007,4(6)：12-18
[11]J.da.C Vianna, L.F. Costa-Neves, P.C.G da S. Vellasco, S.A.L. de Andrade. Experimental assessment of Perfobond and T-Perfobond shear connectors'structural response[J]. Journal of Constructional Steel Reasearch,2009,65:408-421
[12]J.P.S Canadido-Martins, L.F. Costa-Neves, P.C.G da S. Vellasco. Experimental evaluation of the structural response of Perfobond shear connectors [J]. Engineering Structures,2010,32:1976-1985
[13]Jin-Hee Ahn, Chan-Goo Lee, Jeong-Hun Won, Sang-Hyo Kim. Shear resistance of the perfobond-rib shear connector depending on concrete strength and rib arrangement [J]. Journal of Constructional Steel Research,2010,66:1295-1307
[14]Joao Paulo C. Rodrigues. Behaviour of Perfobond shear connectors at high temperatures. Engineering Structures,33 (2011) 2744-2753. doi:10.1016/j.engstruct.2011.05.004
[15]李乔,武焕陵,唐亮,崔冰.南京长江三桥桥塔钢混结合段内力分布规律研究[J].中国 公路学会桥梁和结构工程分会2005年全国桥梁学术会议论文集,2005
[16]张清华,李乔,唐亮.桥塔钢-混凝土结合段剪力键破坏机理及极限承载力[J].中国公路学报,2007,20(1)：85-90
[17]娄学全,武焕陵,崔冰,赵灿晖.悬索桥主缆分布传力锚固系统设计与施工[M].人民交通出版社,2012.4
[18]李小珍,肖林,张迅,刘德军.斜拉桥钢-混凝土结合段PBL剪力键承载力试验研究[J].钢结构,2009,24(5)：22-27
[19]夏嵩,赵灿晖,张育智,李乔.PBL传剪器极限承载力的试验研究[J].西南交通大学学报,2009,44(2)：166-170
[20]王振海,李乔,赵灿晖.PBL剪力键破坏形态及极限承载力试验研究[J].防灾减灾工程学报,2011,31(5)：517-522
[21]E.C. Oguejiofor, M.U. Hosain. Behavior of perfobond rib shear connectors in composite beams:full-size tests[J].Can. J. Civil Engng,1992,19(2):224-235
[22]E.C. Oguejiofor, M.U. Hosain. Tests of full-size composite beams with perfobond rib connectors[J]. Can. J. Civil Engng,1995,22(1):80-92
[23]叶梅新,蒋彪.混合型自锚式悬索桥连接部位传力研究[J].铁道科学与工程学报,2006,3(3)：1-6
[24]胡建华,蒲怀仁.PBL剪力键钢混结合段设计与试验研究[J].钢结构,2007,2(22)：62-67
[25]Sang-Hyo Kim. Experimental study on joint of spliced steel–PSC hybrid girder, Part I:Proposed parallel-perfobond-rib-type joint[J]. Engineering Structures,33 (2011) 2382-2397. doi:10.1016/j.engstruct.2011.04.012
[26]Sang-Hyo Kim. Experimental study on joint of spliced steel–PSC hybrid girder, part Ⅱ:Full-scale test of spliced hybrid Ⅰ-girder[J]. Engineering Structures,33 (2011) 2668-2682. doi:10.1016/j.engstruct.2011.05.016
[27]E.C. Oguejiofor, M.U. Hosain. Numerical analysis of push-out specimens with perfobond rib connectors [J]. Computers & Structures,1997,62(4):617-624
[28]张清华,李乔,唐亮.剪力连接件的三维非线性仿真分析方法[J].西南交通大学学报,2005,40(5)：595-599
[29]刘荣,余俊林,刘玉擎,吴定俊.鄂东长江大桥混合梁结合段受力分析[J].桥梁建设,2010,3：33-35
[30]C. Kalfas, P. Pavlidis, E. Galoussis. Inelastic behavior of shear connection by a method based on FEM[J]. J. Construc. Steel Res.,1997,44:107-114
[31]张清华,李乔,卜一之.PBL剪力连接件群传力机理研究Ⅰ——理论模型[J].土木工程学报,2011,4(44)：71-77
[32]张清华,李乔,卜一之.PBL剪力连接件群传力机理研究Ⅱ——极限承载力[J].土木工程学报,2011,5(44)：101-108
[33]王振海,赵灿晖,李乔.PBL剪力键荷载-滑移关系试验研究[J].西南交通大学学报,2011.8(46)：547-552
[34]黄阳林,朱文军,谢东,李哲.南京长江第四大桥北锚碇锚固系统安装测量定位[J].公路,2010.6(6)：25-29
[35]Youn-Ju Jeong, Hyeong-Yeol Kim, Hyun-Bon Koo. Longitudinal shear resistance of steel-concrete composite slabs with perfobond shear connectors [J]. Journal of Constructional Steel Research,2009,65:81-88
[36]Kazimierz Furtak. Direct shear strength of concrete in strip connectors [J]. Archives of civil and mechanical engineering,2005,2:49-60
[37]刘玉擎,周伟翔.开孔钢板连接件的受力性能及其应用[J].哈尔滨工业大学学报,2005,37：381-384
[38]王建新,胡旭辉,钟豪.组合箱梁剪力键设计分析[J].山西建筑,2005,31(20)：73-74
[39]白玲,史志强,史永吉.剪力键布置方式对连续组合梁桥受力特性的影响[J].中国铁道科学,2003,24(2)：67-70
[40]聂建国,卫军.剪力连接件在钢-混凝土组合梁中的实际工作性能[J].郑州工学院学报,1991,12(4)：43-47
[41]聂建国,沈聚敏,袁彦声,林伟,王文辉.钢-混凝土组合梁中剪力连接件实际承载力的研究[J].建筑结构学报,1996,17(2)：21-28
[42]聂建国,谭英,王洪全.钢-高强混凝土组合梁栓钉剪力连接件的设计计算[J].清华大学学报,1999,39(12)：94-97
[43]王洪全,石中柱,聂建国.推出试件中栓钉剪力连接件的极限抗剪强度分析[J].哈尔滨建筑大学学报,1997,30(5)：199-202
[44]苏庆田,刘玉擎,曾明根.苏通大桥索塔栓钉剪力连接件的力学性能试验[J].同济大学学报,2008,36(7)：916-920
[45]林传金,宗周红,唐朝阳.中22栓钉剪力连接件荷载-滑移关系试验研究[J].哈尔滨工业大学学报,2005,37：376-380
[46]叶梅新,吏林山.混凝土受拉状态下钢-混凝土组合结构中栓钉的承载力的研究[J].长沙铁道学院学报,2003,21(1)：8-12
[47]叶梅新,罗如登.群钉钢-混凝土组合件栓钉受力状态研究[J].钢结构,1999,3(14)：39-42
[48]叶梅新,张晔芝.桁梁结合梁及其剪力连接件试验研究[J].铁道学报,1999,21(1)：67-71
[49]Huu Thanh Nguyen, Seung Eock Kim. Finite element modeling of push-out tests for large stud shear connectors[J]. Journal of Constructional Steel Research,2009,65: 1909-1920
[50]Seung Eock Kim, Huu Thanh Nguyen. Finite element modeling and analysis of a hybrid steel-PSC beam connection[J]. Engineering Structures,2010
[5l]唐进,叶梅新.钢-混凝土组合结构中密集型剪力钉群的受力状态[J].长沙铁道学院学报,1999,17(4)：68-73
[52]刘玉擎.有限弹簧元在桥梁结构分析中的应用研究[J].桥梁建设,2005,06：19-22
[53]周伟翔,刘玉擎,曾明根,邵长宇.连续组合梁桥钢与混凝土连接技术的研究[J].第十七届全国桥梁学术会议,2006
[54]周浩.南京长江三桥桥塔钢-混结合段剪力键选型试验研究[D].西南交通大学研究生学位论文,2005
[55]赵洁,聂建国.钢板-混凝土组合梁的非线性有限元分析[J].工程力学,2009,26(4)：105-112
[56]白玲.超静定组合结构桥梁受力特性的3D-FEM模拟分析[D].铁道科学研究院,2003
[57]陈开利,余天庆,习刚.混合梁斜拉桥的发展与展望[J].桥梁建设,2005(2)：1-4
[58]赵灿晖.基于Prager硬化的钢管混凝土非线性梁单元[J].地震工程与工程振动,2006,12(26)：128-132
[59]刘明虎,徐国平,刘峰.鄂东大桥混合梁钢-混凝土结合部研究与设计[J].公路交通科技,2010,12(27)：78-85