经济型贝雷桁架双导梁架桥机拼装设计及应用研究
摘要
贝雷桁架拼装式架桥机结构形式变化很多,随着架梁的数量,梁的跨径、重量和现有的贝雷桁架器材的数量等条件而定。本文是基于汝郴高速水口高架桥预制梁的架设工作,对经济型贝雷桁架架桥机拼装设计及应用展开研究。汝郴高速水口高架桥工程特点是：20m空心板梁比40mT梁重量小很多,而20m空心板梁数量较多,40mT梁数量不到总梁数的十分之一。
工地现有架设20mT梁贝雷桁架架桥机,如果另外购置拼装40mT梁架桥机,费用较高,周期较长。如何利用现有20mT梁架桥机,经合理改造后,能安全、经济地实现40mT梁的架设任务,是本文研究的重点。主要取得以下研究成果：
(1)改装后的贝雷桁架架桥机,单边主导梁采用3排加强贝雷桁架,40m跨中设临时支墩,架梁过程中T梁沿架桥机中心线运行。通过初步计算得到,抗弯能力及刚度完全满足要求；但抗剪能力相当不足,究其原因是中支腿上方竖杆应力相对加大,发现贝雷桁架拼装的连续结构很难像简支结构那样充分的发挥贝雷桁架片的性能,为此必须采取补强措施。本文提出了在中支腿处用4排贝雷桁架片加强、增设加强竖杆等加强措施。然后利用有限元软件建立贝雷桁架架桥机主导梁模型,经计算分析得出,通过上述加强方案,静力计算满足要求。特别是在中支腿前后增设加强竖杆,贝雷桁架架桥机的整体抗剪能力明显提高,能完全满足架设40mT梁的抗剪要求,并且所需材料较少,能充分发挥贝雷桁架架桥机的整体作用。
(2)改装后的贝雷桁架架桥机能够满足稳定性要求。分析比较了风荷载对贝雷桁架架桥机稳定性的影响,得出风荷载对贝雷桁架架桥机稳定性影响较小。
(3)本文通过模型对比计算,发现支撑架角钢类型对贝雷桁架架桥机的影响较大。增设加强竖杆后,对运梁天车位于支腿附近的架梁工况稳定性有较大的提高,对其他架梁荷载工况也有一定的提高,所以应该增设加强竖杆。释放贝雷桁架架桥机临时支墩上部的横向约束,架桥机整体稳定性会降低,应控制临时支墩墩顶的位移。
The structure of Bailey truss bridging machine changes a lot depending on the conditions of the number of the beams, beam span, weight, and the existing quantity of Bailey truss.This article is based on the erection of precast beams of the Ru Chen high-speed outlet viaduct and the assembly design and application of the the economical Bailey truss bridge machine.The project Features of Ru Chen high-speed outlet viaduct is: 20m hollow beams weight less than 40m T-beams, and 20m hollow beams have a large number,40m T-beam accounts one-tenth of the total beams.
The site has already got 20m T-beam truss girder bridge machine,if the site purchase the 40m T-beam truss girder bridge machine,it will cost a lot in money and time.The focus of this paper is how to achieve 40m T-beam task with the existing 20m T-beam bridge machine safely and economically.The following results have been achieved.
(1)The modified Bailey truss bridge machine, with 3 rows of strengthening Bailey truss in the side beam, setting temporary buttress in 40m span,the bridge machine runs along the T-beam center line.The Initial calculate shows the flexural capacity and stiffness fully meet the requirements; but short of shear strength, the reason is that the leg above the vertical bar has a relative increase stress and found that Bailey truss structure is difficult to work fully as simple structure, this must be taken to reinforce measures.In this paper,4 rows Bailey truss strengthen in the leg, additional strengthening measures such as strengthening the vertical bar. Then use the finite element software to establish the leading beam model of the Bailey Truss bridge machine, the calculation shows that it meets the demand through the strengthening program, Especially strengthening the vertical bar before and after the legs,the shear strength of Bailey truss bridge machine Increase obviously to fully meet the shear requirements of 40m T-beam, and the small amount of material required, to give full play to Bailey truss bridge machine.
(2)The modified Bailey truss bridge machine meets the stability requirements. The paper analysis and compare the stability effects of the wind load on the Bailey truss bridge machine, draw the conclusion that the wind load on the Bailey truss bridge machine stability is less affected.
(3) By comparing the calculation model it was found that the type of angle steel support frame affect a lot in Bailey truss bridge machine. After the addition of strengthening the vertical bar, the stability of the girder crane in the leg near the girder condition has greatly improved,and the stability of other girder loading conditions have improved to some extent, the strengthening vertical bar should be established.The release of the upper part of the lateral buttress constraints will reduce the overall stability of bridge machine,so we should control the displacement of top of the temporary support Buttress.
工地现有架设20mT梁贝雷桁架架桥机,如果另外购置拼装40mT梁架桥机,费用较高,周期较长。如何利用现有20mT梁架桥机,经合理改造后,能安全、经济地实现40mT梁的架设任务,是本文研究的重点。主要取得以下研究成果：
(1)改装后的贝雷桁架架桥机,单边主导梁采用3排加强贝雷桁架,40m跨中设临时支墩,架梁过程中T梁沿架桥机中心线运行。通过初步计算得到,抗弯能力及刚度完全满足要求；但抗剪能力相当不足,究其原因是中支腿上方竖杆应力相对加大,发现贝雷桁架拼装的连续结构很难像简支结构那样充分的发挥贝雷桁架片的性能,为此必须采取补强措施。本文提出了在中支腿处用4排贝雷桁架片加强、增设加强竖杆等加强措施。然后利用有限元软件建立贝雷桁架架桥机主导梁模型,经计算分析得出,通过上述加强方案,静力计算满足要求。特别是在中支腿前后增设加强竖杆,贝雷桁架架桥机的整体抗剪能力明显提高,能完全满足架设40mT梁的抗剪要求,并且所需材料较少,能充分发挥贝雷桁架架桥机的整体作用。
(2)改装后的贝雷桁架架桥机能够满足稳定性要求。分析比较了风荷载对贝雷桁架架桥机稳定性的影响,得出风荷载对贝雷桁架架桥机稳定性影响较小。
(3)本文通过模型对比计算,发现支撑架角钢类型对贝雷桁架架桥机的影响较大。增设加强竖杆后,对运梁天车位于支腿附近的架梁工况稳定性有较大的提高,对其他架梁荷载工况也有一定的提高,所以应该增设加强竖杆。释放贝雷桁架架桥机临时支墩上部的横向约束,架桥机整体稳定性会降低,应控制临时支墩墩顶的位移。
The structure of Bailey truss bridging machine changes a lot depending on the conditions of the number of the beams, beam span, weight, and the existing quantity of Bailey truss.This article is based on the erection of precast beams of the Ru Chen high-speed outlet viaduct and the assembly design and application of the the economical Bailey truss bridge machine.The project Features of Ru Chen high-speed outlet viaduct is: 20m hollow beams weight less than 40m T-beams, and 20m hollow beams have a large number,40m T-beam accounts one-tenth of the total beams.
The site has already got 20m T-beam truss girder bridge machine,if the site purchase the 40m T-beam truss girder bridge machine,it will cost a lot in money and time.The focus of this paper is how to achieve 40m T-beam task with the existing 20m T-beam bridge machine safely and economically.The following results have been achieved.
(1)The modified Bailey truss bridge machine, with 3 rows of strengthening Bailey truss in the side beam, setting temporary buttress in 40m span,the bridge machine runs along the T-beam center line.The Initial calculate shows the flexural capacity and stiffness fully meet the requirements; but short of shear strength, the reason is that the leg above the vertical bar has a relative increase stress and found that Bailey truss structure is difficult to work fully as simple structure, this must be taken to reinforce measures.In this paper,4 rows Bailey truss strengthen in the leg, additional strengthening measures such as strengthening the vertical bar. Then use the finite element software to establish the leading beam model of the Bailey Truss bridge machine, the calculation shows that it meets the demand through the strengthening program, Especially strengthening the vertical bar before and after the legs,the shear strength of Bailey truss bridge machine Increase obviously to fully meet the shear requirements of 40m T-beam, and the small amount of material required, to give full play to Bailey truss bridge machine.
(2)The modified Bailey truss bridge machine meets the stability requirements. The paper analysis and compare the stability effects of the wind load on the Bailey truss bridge machine, draw the conclusion that the wind load on the Bailey truss bridge machine stability is less affected.
(3) By comparing the calculation model it was found that the type of angle steel support frame affect a lot in Bailey truss bridge machine. After the addition of strengthening the vertical bar, the stability of the girder crane in the leg near the girder condition has greatly improved,and the stability of other girder loading conditions have improved to some extent, the strengthening vertical bar should be established.The release of the upper part of the lateral buttress constraints will reduce the overall stability of bridge machine,so we should control the displacement of top of the temporary support Buttress.
引文
[1]杜业昆 邱式中.桥梁施工专项技术手册[M].北京：人民交通出版社,2004
[2]饶阳.架桥机在大跨径组合段及匝道T梁施工中的研究及运用—卢浦大桥浦西引桥龙华东路段T梁吊装施工[J].建筑施工.2003,25(6)：442-444
[3]金仁兴 陈刚 李旭东 张年杰 邓文武.沪闵高架二期节段箱梁拼装施工技术[J].上海建设科技.2004,(1)：21-22
[4]秘志辉.逐跨拼装预制节段预应力混凝土桥梁若干施工关键技术研[D].上海：同济大学,2005
[5]孟钢 刘晓霞.宁德特大桥32m预应力混凝土简支箱梁制、运、架综合技术.江苏科技信息[J].2009,(10)：42-45
[6]陈晓剑.高速铁路900 t箱梁架设关键技术[J].山西建筑.2010,36(11)：299-300
[7]陈龙剑.铁路客运专线砼箱梁制梁、运粱、架梁施工设备[M].北京：中国铁道出版社,2007
[8]邢双喜.客运专线组合箱梁架设施工技术[J].桥梁建设,2007(z1)：62-65
[9]陈龙剑 何建豫 胡国庆.铁路客运专线混凝土箱梁制梁运梁架梁施工设备[M].北京：中国铁道出版社,2007
[10]刘中天.意大利NICOLA YJ-550型运架梁一体机一种新型的架架设备[J].铁道工程学报[J].2001(z1)：98-102
[11]刘中天 蒋建设 刘亚滨 刘利国.YJ-550t运架梁一体机适应穿越隧道及隧道口架梁的改造方案[J].铁道工程学报,2004(z1)：133-136
[12]熊伟 蒋建设 廖宇峰.城市轨道交通高架桥整孔箱梁架设施工技术[J].铁道科学与工程学报,2007,4(3)：73-78
[13]郭献珍.轮胎式运架一体机架设铁路梁技[J].施工技术,2001,30(11)：46-47
[14]刘海鹰 牛红涛.运架梁一体机架梁施工技术[J].2008,34(12)：301-302
[15]交通部第一公路工程总公司.公路施工手册一桥涵[M].北京：人民交通出版社,1999
[16]黄绍金 刘陌生.装配式公路钢桥多用途使用手册[M].北京：人民交通出版社,2001
[17]交通部公路规划设计院主编.装配式公路钢桥使用说明[M].北京：人民交通出版社,1969
[19]"Sir Donald Bailey's Bridge." (http://www.150th.com/rivers/bailey.htm). June 11,2001
[20]英国ACROW公司编.贝雷(BAILEY)使用手册.1974
[21]张克武 唐宏宾 吴康雄.贝雷片拼装架桥机的设计与使用[J].建筑机械化.2006,27(3)：26-28
[22]吴时明 侯四海.贝雷片拼装80t×40m架桥机[J].筑路机械与施工机械[J].2002,19(2)：13-14
[23]赖玉春.贝雷式(321)桁架梁组装架桥机在架设铁路标准桥梁中的应用[J].职业圈.2007,(10)：188-189
[24]G. H. Paulino,1. F. M. Menezes, J. B. Cavalcante Neto. A methodology for adaptive finite element analysis:Towards an integrated computational environment. Computational Mechanics,1999, (23):361-388
[25]王海林 熊学军.六四军用梁拼组架轿机的若干技术问题[J].桥梁建设,2003,(4)：47-50
[26]段东明 刘嘉武.六四式军用梁用于架桥关键技术研究[J].国防交通工程与技术,2003,1(3)：24-26
[27]董忠红 张培森 吕彭民.拼装式架桥机事故分析及补强方案研究[J].筑路机械与施工机械化,2006,(8)：1-4
[28]王章荣.采用贝雷片拼装架桥机架设T梁的设计与施工[J].福建建设科技,2004,(4)：42-66
[29]张立华 潘存军 夏学文.衡阳湘江三桥40m T梁架设新工艺[J].中外公路.2002,22(5)：54-57
[30]黄雄.30m双导梁式架桥机在广惠高速公路西支江文布桥工程中的应用[J].中国科技信息.2006,(9)：104-105
[31]黄建民.大吨位架桥机在大源渡闸坝上部结构施工中的应用[J].湖南水利水电.2003,(1)：6-7
[32]Aoki, T. and Fukumoto, Y. On scatter in Bucking Strength of steel Colums, JSCE, No.201, May,1972
[33]沈祖炎 陈杨骥 陈以一.钢结构基本原理[M].中国建筑出版设.2004
[34]刘庆谭.材料力学教程[M].北京：机械工业出版设.2005
[35]P. A. Djondiorov, Invariant properties of Timoshenko beam equations, Int.J. Eng. Sci,1995,33(14):2103-2109
[36]麻永铭 陈华.贝雷式架桥机施工及其结构安全验算实例[J].湖南城建高等专科学校学报.2001,10(4)：31-33
[37]尤晋闽 和丽梅 吕彭民.六四军用梁拼装式架桥机结构强度研究[J].建设机械技术与管理,2005,(12)：80-82
[38]Babuska I. Finite element methods for domain with corners. Computing.1980
[39]辛明林.JSB3080贝雷桁架双导梁架桥机[J].山西建筑,2000,(2)：186-187
[40]郭祥君.军用器材拼装双导梁架桥机施工技术[J].科技信息,2007,(16)：81-82
[41]John Robinson. Towards automated stress analysis(Finite element mode-amplitude technique). Finite Element in Analysis and Design,1996, (22):195-210
[42]樊又洪 邹建华.TJl65架桥机机臂强度有限元计算[J].中国水运,2007,(4)：29-31
[43]K. Kiss, L. Dunai. Stress history generation for truss bridges using multi-level midels. Computers and Structress,2000, (78):329-339
[44]Li Showing, Duan Shujin, Li Yunfeng. Bearing Capacity of Pin-connected Steel Structure. Proceeding of the 8th international conference of enhancement and promotion of computing methods for engineering and science,2001
[45]王锡朝 马怀祥 高成雷.架桥机倾覆原因分析及预防措施[J].中国铁路,2000,8：18-19
[46]颜全胜 曾庆元.大跨度架桥机刚桁架的稳定与极限载荷分析[J].华南理工 大学学报,2000,28(5)：48-53
[47]孙训方 方孝淑 关来泰.材料力学[M].高等教育出版社,1994
[48]中华人民共和国国家质量监督检验检疫总局中国国家标准化管理委员会.起重机设计规范[M].北京：中国标准出版设.2008
[49]胡伟雄.九洲大桥30/80型架桥机的加工与使用[J].公路与汽运.2004,(5)：101-102
[50]R. Sedaghati, B. Tabarrok. Optimum design of truss structures undergoing large defleetions subjeet to a system stability constraint. International Journal of Numerical Methods in Engineering,2000,48:421-434
[51]田朝霞.跨墩多支点拼装式双导梁架桥机设计及应用[J].国防交通工程与技术.2004,2(2)：20-22
[52]陈骥.钢结构稳定理论与技术[M].北京：科学出版社.2008
[53]李国豪.桥梁结构稳定与振动[M].北京：中国铁道出社.1992
[54]周尚猛 李亚东 高翔.贝雷桁架门式起重机设计及其稳定性分析[J].建筑机械.2007,27(8)：58-61
[55]刘良谋 徐关尧.21m“321”装配式公路钢桥整体稳定性研究[J].国防交通工程与技术.2007,5(1)：34-36
[56]Borri C-, Hufendick H.W., Geometrically nonlinear behavior of space beam structures J.Struct.Mech,1985,13(1):1-25
[57]Galambos, T. V. ed. Guide to Stability Design Criteria for Metal Structures, 5th. Ed. John Wiley&Sons.1998
[58]TONG Gen. Shu. Seismic force modification factor for ductile structures. Journal of Zhejiang University SCIENCE.2005
[59]Zheng Chang-liang. On the Stability Analysis of Plates and Shells Using a Quadrilateral,16-Degrees of Freedom Plat Shell Element DKQ 16. Applied Mathematics and Mechanics.2004
[60]Department of the Army (DOA). Bailey bridge, FM5-277, Washington D.C. 1986
[61]Foss, C. F. JANE'S military vehicles and ground support equipment,4th Ed., JANE'S Information Group, Alexandria, Va.1983
[62]Gastebled O J, May I M. Bifurcation in the numerical simulation of softening mechanisms [J]. Computers and Structures,2000,78(6):745-755
[63]Thompson J M T, Hunt G W. Static and Dynamic Instability Phenomena[M]. London; Wiley,1983
[64]Crisfeld M A. A new arc-length method for handling sharp snap-backs[J]. Computers and Structures,1998,66(5):705-709
[65]Crandall M G, Rabinowitz P H. Bifurcations from simple eigenvalues [J]. Functional Anal,1997,8(3):321-340
[66]李元齐 沈祖炎.稳定分析中极值点与分支点失稳的跟踪策略及程序实现[J].土木工程学报,1998,31(3)：65-71
[2]饶阳.架桥机在大跨径组合段及匝道T梁施工中的研究及运用—卢浦大桥浦西引桥龙华东路段T梁吊装施工[J].建筑施工.2003,25(6)：442-444
[3]金仁兴 陈刚 李旭东 张年杰 邓文武.沪闵高架二期节段箱梁拼装施工技术[J].上海建设科技.2004,(1)：21-22
[4]秘志辉.逐跨拼装预制节段预应力混凝土桥梁若干施工关键技术研[D].上海：同济大学,2005
[5]孟钢 刘晓霞.宁德特大桥32m预应力混凝土简支箱梁制、运、架综合技术.江苏科技信息[J].2009,(10)：42-45
[6]陈晓剑.高速铁路900 t箱梁架设关键技术[J].山西建筑.2010,36(11)：299-300
[7]陈龙剑.铁路客运专线砼箱梁制梁、运粱、架梁施工设备[M].北京：中国铁道出版社,2007
[8]邢双喜.客运专线组合箱梁架设施工技术[J].桥梁建设,2007(z1)：62-65
[9]陈龙剑 何建豫 胡国庆.铁路客运专线混凝土箱梁制梁运梁架梁施工设备[M].北京：中国铁道出版社,2007
[10]刘中天.意大利NICOLA YJ-550型运架梁一体机一种新型的架架设备[J].铁道工程学报[J].2001(z1)：98-102
[11]刘中天 蒋建设 刘亚滨 刘利国.YJ-550t运架梁一体机适应穿越隧道及隧道口架梁的改造方案[J].铁道工程学报,2004(z1)：133-136
[12]熊伟 蒋建设 廖宇峰.城市轨道交通高架桥整孔箱梁架设施工技术[J].铁道科学与工程学报,2007,4(3)：73-78
[13]郭献珍.轮胎式运架一体机架设铁路梁技[J].施工技术,2001,30(11)：46-47
[14]刘海鹰 牛红涛.运架梁一体机架梁施工技术[J].2008,34(12)：301-302
[15]交通部第一公路工程总公司.公路施工手册一桥涵[M].北京：人民交通出版社,1999
[16]黄绍金 刘陌生.装配式公路钢桥多用途使用手册[M].北京：人民交通出版社,2001
[17]交通部公路规划设计院主编.装配式公路钢桥使用说明[M].北京：人民交通出版社,1969
[19]"Sir Donald Bailey's Bridge." (http://www.150th.com/rivers/bailey.htm). June 11,2001
[20]英国ACROW公司编.贝雷(BAILEY)使用手册.1974
[21]张克武 唐宏宾 吴康雄.贝雷片拼装架桥机的设计与使用[J].建筑机械化.2006,27(3)：26-28
[22]吴时明 侯四海.贝雷片拼装80t×40m架桥机[J].筑路机械与施工机械[J].2002,19(2)：13-14
[23]赖玉春.贝雷式(321)桁架梁组装架桥机在架设铁路标准桥梁中的应用[J].职业圈.2007,(10)：188-189
[24]G. H. Paulino,1. F. M. Menezes, J. B. Cavalcante Neto. A methodology for adaptive finite element analysis:Towards an integrated computational environment. Computational Mechanics,1999, (23):361-388
[25]王海林 熊学军.六四军用梁拼组架轿机的若干技术问题[J].桥梁建设,2003,(4)：47-50
[26]段东明 刘嘉武.六四式军用梁用于架桥关键技术研究[J].国防交通工程与技术,2003,1(3)：24-26
[27]董忠红 张培森 吕彭民.拼装式架桥机事故分析及补强方案研究[J].筑路机械与施工机械化,2006,(8)：1-4
[28]王章荣.采用贝雷片拼装架桥机架设T梁的设计与施工[J].福建建设科技,2004,(4)：42-66
[29]张立华 潘存军 夏学文.衡阳湘江三桥40m T梁架设新工艺[J].中外公路.2002,22(5)：54-57
[30]黄雄.30m双导梁式架桥机在广惠高速公路西支江文布桥工程中的应用[J].中国科技信息.2006,(9)：104-105
[31]黄建民.大吨位架桥机在大源渡闸坝上部结构施工中的应用[J].湖南水利水电.2003,(1)：6-7
[32]Aoki, T. and Fukumoto, Y. On scatter in Bucking Strength of steel Colums, JSCE, No.201, May,1972
[33]沈祖炎 陈杨骥 陈以一.钢结构基本原理[M].中国建筑出版设.2004
[34]刘庆谭.材料力学教程[M].北京：机械工业出版设.2005
[35]P. A. Djondiorov, Invariant properties of Timoshenko beam equations, Int.J. Eng. Sci,1995,33(14):2103-2109
[36]麻永铭 陈华.贝雷式架桥机施工及其结构安全验算实例[J].湖南城建高等专科学校学报.2001,10(4)：31-33
[37]尤晋闽 和丽梅 吕彭民.六四军用梁拼装式架桥机结构强度研究[J].建设机械技术与管理,2005,(12)：80-82
[38]Babuska I. Finite element methods for domain with corners. Computing.1980
[39]辛明林.JSB3080贝雷桁架双导梁架桥机[J].山西建筑,2000,(2)：186-187
[40]郭祥君.军用器材拼装双导梁架桥机施工技术[J].科技信息,2007,(16)：81-82
[41]John Robinson. Towards automated stress analysis(Finite element mode-amplitude technique). Finite Element in Analysis and Design,1996, (22):195-210
[42]樊又洪 邹建华.TJl65架桥机机臂强度有限元计算[J].中国水运,2007,(4)：29-31
[43]K. Kiss, L. Dunai. Stress history generation for truss bridges using multi-level midels. Computers and Structress,2000, (78):329-339
[44]Li Showing, Duan Shujin, Li Yunfeng. Bearing Capacity of Pin-connected Steel Structure. Proceeding of the 8th international conference of enhancement and promotion of computing methods for engineering and science,2001
[45]王锡朝 马怀祥 高成雷.架桥机倾覆原因分析及预防措施[J].中国铁路,2000,8：18-19
[46]颜全胜 曾庆元.大跨度架桥机刚桁架的稳定与极限载荷分析[J].华南理工 大学学报,2000,28(5)：48-53
[47]孙训方 方孝淑 关来泰.材料力学[M].高等教育出版社,1994
[48]中华人民共和国国家质量监督检验检疫总局中国国家标准化管理委员会.起重机设计规范[M].北京：中国标准出版设.2008
[49]胡伟雄.九洲大桥30/80型架桥机的加工与使用[J].公路与汽运.2004,(5)：101-102
[50]R. Sedaghati, B. Tabarrok. Optimum design of truss structures undergoing large defleetions subjeet to a system stability constraint. International Journal of Numerical Methods in Engineering,2000,48:421-434
[51]田朝霞.跨墩多支点拼装式双导梁架桥机设计及应用[J].国防交通工程与技术.2004,2(2)：20-22
[52]陈骥.钢结构稳定理论与技术[M].北京：科学出版社.2008
[53]李国豪.桥梁结构稳定与振动[M].北京：中国铁道出社.1992
[54]周尚猛 李亚东 高翔.贝雷桁架门式起重机设计及其稳定性分析[J].建筑机械.2007,27(8)：58-61
[55]刘良谋 徐关尧.21m“321”装配式公路钢桥整体稳定性研究[J].国防交通工程与技术.2007,5(1)：34-36
[56]Borri C-, Hufendick H.W., Geometrically nonlinear behavior of space beam structures J.Struct.Mech,1985,13(1):1-25
[57]Galambos, T. V. ed. Guide to Stability Design Criteria for Metal Structures, 5th. Ed. John Wiley&Sons.1998
[58]TONG Gen. Shu. Seismic force modification factor for ductile structures. Journal of Zhejiang University SCIENCE.2005
[59]Zheng Chang-liang. On the Stability Analysis of Plates and Shells Using a Quadrilateral,16-Degrees of Freedom Plat Shell Element DKQ 16. Applied Mathematics and Mechanics.2004
[60]Department of the Army (DOA). Bailey bridge, FM5-277, Washington D.C. 1986
[61]Foss, C. F. JANE'S military vehicles and ground support equipment,4th Ed., JANE'S Information Group, Alexandria, Va.1983
[62]Gastebled O J, May I M. Bifurcation in the numerical simulation of softening mechanisms [J]. Computers and Structures,2000,78(6):745-755
[63]Thompson J M T, Hunt G W. Static and Dynamic Instability Phenomena[M]. London; Wiley,1983
[64]Crisfeld M A. A new arc-length method for handling sharp snap-backs[J]. Computers and Structures,1998,66(5):705-709
[65]Crandall M G, Rabinowitz P H. Bifurcations from simple eigenvalues [J]. Functional Anal,1997,8(3):321-340
[66]李元齐 沈祖炎.稳定分析中极值点与分支点失稳的跟踪策略及程序实现[J].土木工程学报,1998,31(3)：65-71