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Article(id=1228046476337672212, tenantId=1146029695717560320, journalId=1225147924628267009, issueId=1228046469559681568, articleNumber=null, orderNo=null, doi=10.16385/j.cnki.issn.1004-4523.2024.02.011, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1654358400000, receivedDateStr=2022-06-05, revisedDate=1662048000000, revisedDateStr=2022-09-02, acceptedDate=null, acceptedDateStr=null, onlineDate=1770718695959, onlineDateStr=2026-02-10, pubDate=1709049600000, pubDateStr=2024-02-28, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1770718695959, onlineIssueDateStr=2026-02-10, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1770718695959, creator=13701087609, updateTime=1770718695959, updator=13701087609, issue=Issue{id=1228046469559681568, tenantId=1146029695717560320, journalId=1225147924628267009, year='2024', volume='37', issue='2', pageStart='191', pageEnd='364', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1770718694343, creator=13701087609, updateTime=1770795432451, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1228368332575928712, tenantId=1146029695717560320, journalId=1225147924628267009, issueId=1228046469559681568, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1228368332575928713, tenantId=1146029695717560320, journalId=1225147924628267009, issueId=1228046469559681568, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=286, endPage=296, ext={EN=ArticleExt(id=1228046477428191281, articleId=1228046476337672212, tenantId=1146029695717560320, journalId=1225147924628267009, language=EN, title=Study on the influence of expansion joints and bearing diseases on the vehicle-induced dynamic response of simply supported beam bridges, columnId=null, journalTitle=Journal of Vibration Engineering, columnName=null, runingTitle=null, highlight=null, articleAbstract=

Medium and small span bridges make up a large proportion of highway bridges in China. Due to harsh service conditions，the expansion joints are prone to diseases，which can exacerbate vehicle vibrations，and subsequently lead to the damage of the end bearings and other components. In order to study the influence of expansion joint and bearing parameters on the vehicle-induced dynamic response of simply supported beam bridge，this paper establishes a numerical analysis method of vehicle-expansion joint-bridge coupling dynamic response （VBCV-J）. The effectiveness of VBCV-J analysis method is verified using measured data，followed by an investigation the influence of expansion joint and support parameters. The results show that： The speed is closely related to vehicle vibration. When the vehicle speed is high and the Road Surface Condition （RSC） is “normal”，the impact effect of vehicles on expansion joints and the ends of beams can exceed the specified values.. If the girder in the expansion joint is higher than the pavement，the impact on the expansion joint will significantly increase，conversely，it will decrease. When the girder in the expansion joint is higher or lower than the road surface，the impact at the end of the main beam will increase. A reduction in the support stiffness of the expansion joint or a void in the side support of the main beam will significantly increase the impact effect on both the expansion joint and the end of the main beam. A decrease in the stiffness of the main beam support primarily results in an increased impact on the entire main beam. Damage to the expansion joints not only affects their own impact，but also greatly increases the impact on the end members of the simply supported beams. During design and maintenance，sufficient attention should be given to the end members of the beams.

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中小跨径桥梁在中国公路桥梁中占比大，其伸缩缝服役环境恶劣，易发生损伤造成过往车辆剧烈振动、桥梁支座损伤等病害。为探明伸缩缝、支座参数对简支梁桥车致动力响应的影响，建立了车-伸缩缝-桥梁耦合动力响应（VBCV-J）数值分析方法，并通过实测数据验证了该方法，进而开展了伸缩缝、支座参数影响规律的研究。研究结果表明：车速与车辆的振动密切相关，在车速较高、路面状况“一般”时，伸缩缝、梁端的冲击效应会超出规范值。伸缩缝中梁高于路面会导致该部件的冲击效应增大明显，反之则有所减小；而伸缩缝中梁高于或低于路面，均会造成该桥梁端冲击效应增大。伸缩缝弹性支撑刚度的降低、主梁边支座脱空均会引起伸缩缝、主梁梁端的冲击效应增大。支座刚度降低则主要导致主梁整体的冲击效应增大。伸缩缝的破损不仅影响自身冲击效应，还会大幅增大简支梁桥梁端构件的冲击作用，在设计和养护中，应对伸缩缝及梁端构件给予足够的重视。

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吴喜德（1976―），男，硕士，高级工程师。 E-mail： 。
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侯剑岭（1990—），男，博士，工程师。 E-mail： 。

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侯剑岭（1990—），男，博士，工程师。 E-mail： 。

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侯剑岭（1990—），男，博士，工程师。 E-mail： 。

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Beijing： China Communications Press， 2015., articleTitle=null, refAbstract=null), Reference(id=1228046515470528539, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228046476337672212, doi=null, pmid=null, pmcid=null, year=2016, volume=21, issue=2, pageStart=6015006, pageEnd=null, url=null, language=null, rfNumber=［14］, rfOrder=18, authorNames=Deng L, Yan W C, Zhu Q J, journalName=Journal of Bridge Engineering, refType=null, unstructuredReference=Deng L， Yan W C， Zhu Q J. Vehicle impact on the deck slab of concrete box-girder bridges due to damaged expansion joints［J］. Journal of Bridge Engineering， 2016， 21（2）： 6015006., articleTitle=Vehicle impact on the deck slab of concrete box-girder bridges due to damaged expansion joints, refAbstract=null), Reference(id=1228046515550220318, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228046476337672212, doi=null, pmid=null, pmcid=null, year=2022, volume=52, issue=2, pageStart=212, pageEnd=221, url=null, language=null, rfNumber=［15］, rfOrder=19, authorNames=许维炳, 侯剑岭, journalName=东南大学学报, refType=null, unstructuredReference=许维炳，侯剑岭. 考虑车辆过缝的车桥耦合振动分析方法［J］. 东南大学学报， 2022， 52（2）： 212-221., articleTitle=考虑车辆过缝的车桥耦合振动分析方法, refAbstract=null), Reference(id=1228046515646689313, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228046476337672212, doi=null, pmid=null, pmcid=null, year=2022, volume=52, issue=2, pageStart=212, pageEnd=221, url=null, language=null, rfNumber=［15］, rfOrder=20, authorNames=Xu Weibing, Hou Jianling, journalName=Journal of Southeast University, refType=null, unstructuredReference=Xu Weibing， Hou Jianling. 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Relation between β and driving position

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工况行驶距离
100
0
010
0
001
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β值与行驶位置关系

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工况行驶距离
100
0
010
0
001
), ArticleFig(id=1228046513138496430, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228046476337672212, language=EN, label=Tab.2, caption=

Results of dynamic characteristics

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构件单元主要参数
主梁Solid65Ec=3.45×1010 Pa, ρ=2.6×103 kg/m3, μ=0.3
伸缩缝Beam188Es=2.05×1011 Pa, ρ=7.87×103 kg/m3, μ=0.2
橡胶支撑Combin14k0=8×104 kN/m, c0=5×103 N·s/m
桥梁支座Combin14k1=2.4×106 kN/m, c1=5×103 N·s/m
), ArticleFig(id=1228046513209799602, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228046476337672212, language=CN, label=表2, caption=

桥梁模态分析

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构件单元主要参数
主梁Solid65Ec=3.45×1010 Pa, ρ=2.6×103 kg/m3, μ=0.3
伸缩缝Beam188Es=2.05×1011 Pa, ρ=7.87×103 kg/m3, μ=0.2
橡胶支撑Combin14k0=8×104 kN/m, c0=5×103 N·s/m
桥梁支座Combin14k1=2.4×106 kN/m, c1=5×103 N·s/m
), ArticleFig(id=1228046513306268601, tenantId=1146029695717560320, journalId=1225147924628267009, articleId=1228046476337672212, language=EN, label=Tab.3, caption=

Results of dynamic characteristics

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类别阶次自振频率/Hz误差
计算值实测值
主梁15.024.833.78%
27.747.473.49%
伸缩缝1118.9117.31.34%
2124.4123.50.72%
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桥梁模态分析

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类别阶次自振频率/Hz误差
计算值实测值
主梁15.024.833.78%
27.747.473.49%
伸缩缝1118.9117.31.34%
2124.4123.50.72%
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伸缩缝及支座病害对简支梁桥车致动力响应的影响研究
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侯剑岭 1, 2 , 刘灵灵 1 , 吴喜德 1 , 许维炳 2 , 陈彦江 2 , 王瑾 2 , 刘钧岩 2 , 王博 2 , 李岩 3 , 张轩 4
振动工程学报 | 2024,37(2): 286-296
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振动工程学报 | 2024, 37(2): 286-296
伸缩缝及支座病害对简支梁桥车致动力响应的影响研究
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侯剑岭1, 2 , 刘灵灵1, 吴喜德1 , 许维炳2, 陈彦江2, 王瑾2, 刘钧岩2, 王博2, 李岩3, 张轩4
作者信息
  • 1交通运输部水运科学研究所, 北京　100088
  • 2北京工业大学城市建设学部, 北京　100124
  • 3哈尔滨工业大学交通科学与工程学院, 黑龙江　哈尔滨　150090
  • 4中建二局第一建筑工程有限公司, 北京　100176

    • 侯剑岭（1990—），男，博士，工程师。 E-mail： 。

通讯作者:

吴喜德（1976―），男，硕士，高级工程师。 E-mail： 。
Study on the influence of expansion joints and bearing diseases on the vehicle-induced dynamic response of simply supported beam bridges
Jian-ling HOU1, 2 , Ling-ling LIU1, Xi-de WU1 , Wei-bing XU2, Yan-jiang CHEN2, Jin WANG2, Jun-yan LIU2, Bo WANG2, Yan LI3, Xuan ZHANG4
Affiliations
  • 1China Waterborne Transport Research Institute, Beijing 100088,China
  • 2Faculty of Architecture, Civil and Transportation Engineering, Beijing University of Technology, Beijing 100124,China
  • 3School of Transportation Science and Engineering, Harbin Institute of Technology, Harbin 150090, China
  • 4The First Construction Engineering Co., Ltd. of China Construction Second Engineering Bureau, Beijing 100176,China
出版时间: 2024-02-28 doi: 10.16385/j.cnki.issn.1004-4523.2024.02.011
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摘要
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中小跨径桥梁在中国公路桥梁中占比大，其伸缩缝服役环境恶劣，易发生损伤造成过往车辆剧烈振动、桥梁支座损伤等病害。为探明伸缩缝、支座参数对简支梁桥车致动力响应的影响，建立了车-伸缩缝-桥梁耦合动力响应（VBCV-J）数值分析方法，并通过实测数据验证了该方法，进而开展了伸缩缝、支座参数影响规律的研究。研究结果表明：车速与车辆的振动密切相关，在车速较高、路面状况“一般”时，伸缩缝、梁端的冲击效应会超出规范值。伸缩缝中梁高于路面会导致该部件的冲击效应增大明显，反之则有所减小；而伸缩缝中梁高于或低于路面，均会造成该桥梁端冲击效应增大。伸缩缝弹性支撑刚度的降低、主梁边支座脱空均会引起伸缩缝、主梁梁端的冲击效应增大。支座刚度降低则主要导致主梁整体的冲击效应增大。伸缩缝的破损不仅影响自身冲击效应，还会大幅增大简支梁桥梁端构件的冲击作用，在设计和养护中，应对伸缩缝及梁端构件给予足够的重视。

简支梁桥  /  伸缩缝  /  支座  /  参数分析

Medium and small span bridges make up a large proportion of highway bridges in China. Due to harsh service conditions，the expansion joints are prone to diseases，which can exacerbate vehicle vibrations，and subsequently lead to the damage of the end bearings and other components. In order to study the influence of expansion joint and bearing parameters on the vehicle-induced dynamic response of simply supported beam bridge，this paper establishes a numerical analysis method of vehicle-expansion joint-bridge coupling dynamic response （VBCV-J）. The effectiveness of VBCV-J analysis method is verified using measured data，followed by an investigation the influence of expansion joint and support parameters. The results show that： The speed is closely related to vehicle vibration. When the vehicle speed is high and the Road Surface Condition （RSC） is “normal”，the impact effect of vehicles on expansion joints and the ends of beams can exceed the specified values.. If the girder in the expansion joint is higher than the pavement，the impact on the expansion joint will significantly increase，conversely，it will decrease. When the girder in the expansion joint is higher or lower than the road surface，the impact at the end of the main beam will increase. A reduction in the support stiffness of the expansion joint or a void in the side support of the main beam will significantly increase the impact effect on both the expansion joint and the end of the main beam. A decrease in the stiffness of the main beam support primarily results in an increased impact on the entire main beam. Damage to the expansion joints not only affects their own impact，but also greatly increases the impact on the end members of the simply supported beams. During design and maintenance，sufficient attention should be given to the end members of the beams.

simple supported bridge  /  expansion joint  /  bearing  /  parameter analysis
侯剑岭, 刘灵灵, 吴喜德, 许维炳, 陈彦江, 王瑾, 刘钧岩, 王博, 李岩, 张轩. 伸缩缝及支座病害对简支梁桥车致动力响应的影响研究. 振动工程学报, 2024 , 37 (2) : 286 -296 . DOI: 10.16385/j.cnki.issn.1004-4523.2024.02.011
Jian-ling HOU, Ling-ling LIU, Xi-de WU, Wei-bing XU, Yan-jiang CHEN, Jin WANG, Jun-yan LIU, Bo WANG, Yan LI, Xuan ZHANG. Study on the influence of expansion joints and bearing diseases on the vehicle-induced dynamic response of simply supported beam bridges[J]. Journal of Vibration Engineering, 2024 , 37 (2) : 286 -296 . DOI: 10.16385/j.cnki.issn.1004-4523.2024.02.011
正文
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引言
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截至2020年末，中国公路桥梁共87.83万座，其中中小跨径桥梁为78.64万座，占总数量的86.15%。中小跨径桥梁随服役年限增长，易会出现耐久性降低、局部构件疲劳破损等问题。特别是桥梁伸缩缝服役环境恶劣，受重载直接作用，极易发生疲劳损伤，国内外伸缩缝病害引起的交通事故屡见不鲜［1］。伸缩缝损伤会造成过往车辆振动加剧，也会造成梁端构件（支座、桥面板等）的损伤。而支座等构件的损伤又会增大伸缩缝-桥梁的车致动力响应，形成恶性循环。
国内外众多学者通过现场实验及数值分析开展了伸缩缝、支座等参数变化对桥梁车致动力响应影响的研究。在伸缩缝研究方面，Hou等［2］对大跨度CFST拱桥的常见病害进行了调查及实测，研究结果表明伸缩缝病害会引发车致振动显著增大，并引发支座等构件的损伤。Deng等［3-4］利用Road Surface Condition（RSC）来仿真伸缩缝处路面形式，采用车-桥耦合振动分析方法探究了伸缩缝损伤对预应力混凝土箱梁桥桥面板的影响，结果表明伸缩缝损伤会导致桥面板和伸缩缝的车辆冲击作用显著增大。Ding等［5-6］采用弹簧-阻尼单元模型对伸缩缝的受到的车辆冲击作用进行研究，包括不同形式模数式伸缩缝以及间隙宽度对车辆荷载的影响。在支座病害研究方面，Roeder等［7］、Wang等［8］和陈树礼等［9］对桥梁支座的车致疲劳损伤进行了研究，结果表明车辆荷载作用下，梁端部件受冲击效应显著，易发生疲劳破坏，从而改变桥梁的约束条件和受力特性，使桥梁的动静力响应发生显著增大。综上，在伸缩缝、支座等部件发生损伤时，桥梁车致动力响应规律会发生显著变化。兼顾考虑伸缩缝、支座病害影响的车致动力响应分析方法亟待建立。
鉴于此，本文以典型的中等跨径简支梁桥为原型桥，结合车轮缝等效力、位移模型和模态综合法建立了车-伸缩缝-桥耦合振动（Vehicle-Bridge Coupling Vibration Considering Expansion Joint Parameters 以下简称VBCV-J）数值分析方法；进而对车速、路面、伸缩缝、支座等参数对VBCV-J系统响应的影响规律进行了研究。研究成果可为VBCV-J响应分析所借鉴，也可为中小跨径桥梁的伸缩缝病害机理及预防措施提供理论支撑。
1　VBCV-J分析方法
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VBCV-J车辆驶入桥梁过程包括两个阶段：第一阶段为车辆前、后轴通过伸缩缝阶段，第二阶段为车辆完全行驶至桥面阶段。其中，车-桥耦合振动方法（VBCV）在第二阶段车-桥耦合动力响应计算中取得了较好的效果，鉴于此，在车辆完全行驶至主梁时采用VBCV分析方法进行计算。车辆模型采用多自由度的车辆模型［10］。通过假定车轮与桥面之间接触点的位移、作用力协调关系，从而得到车-桥耦合振动方程：
式中　 M，C和K分别为质量、阻尼和刚度矩阵；“V”（vehicle）和“B”（bridge）分别表示车辆和桥梁；“r”和“G”分别为不平整度和自重引起的耦合作用力；CVB，CBV，C，KVB，KBV，K为矩阵耦合项，其中，CVB=C，KVB=K。
在计算车辆过缝时，由于伸缩缝处的桥面不连续，车辆与桥面之间为点接触关系，会导致车辆过缝的计算结果失真。鉴于此，本文基于车辆过缝过程参数化，提出了车轴等效力、等效位移模型，并对车辆过缝时的车-桥耦合振动方程进行了推导。
1.1　VBCV-J等效力模型
以中国自主研发广泛应用于各型桥梁的双缝式、直梁连杆链条式伸缩缝为例。该型伸缩缝构造形式及过缝示意如图1所示。图1中，L1为车辆起点与桥头的距离，s0为间隙宽，s为接触长度，lc为中梁宽，l0为边梁宽。
车胎作用于伸缩缝横梁的竖向力，与其和车胎的接触长度相关［11-12］。受车胎接触长度影响，车辆过缝可分为两种工况：
Case 1：间隙较大，伸缩缝中梁会发生单独承受车轴重量的情况，即；
Case 2：间隙较小，伸缩缝中梁不会发生单独承受车轴重量的情况，即。
对比分析两种工况，Case 1为更不利工况。鉴于此，本文主要对Case 1进行研究。假定车胎总作用力为F，FSTG和FMTG分别表示作用于边梁、中梁的竖向力，各作用力可由下式表示：
式中　等效力系数表示梁节点受到分力与总作用力比值，系数β与行驶位置的关系如表1所示。
《公路工程技术标准》规定，在计算构件和连接构件的承载能力极限状态时，车辆荷载按《公路桥涵设计通用规范》（JTG D60—2015）［13］中的规定进行取值。基于上述规定，车胎的接触面长度s取0.2 m。对双缝式伸缩缝单间隙宽80 mm时，系数β变化规律如图2所示。
由图2可知，在车辆通过伸缩缝时，系数β可有效反映各横梁所承受车辆荷载的分配比例。系数β为VBCV-J动力平衡方程的建立提供了将面荷载转化为点荷载的计算方法。
1.2　VBCV-J等效位移模型
分布式弹簧阻尼单元（Distributed Spring-Damper Element）的有效性在模拟车辆与伸缩缝动力耦合响应中得到了验证［5］。考虑到实际大型桥梁的复杂程度和计算分析效率，本文借鉴分布式弹簧阻尼单元的思想，引入等效位移分配系数α来考虑车轮过缝过程中车轮与伸缩缝边梁和中梁的位移协调关系［14］，如图3所示。
如图3所示，车辆与伸缩缝的相互作用力是由节点A与B之间的位移差产生，为将面接触转换为点接触，设置轮胎节点B，其位移等效于接触面的平均位移。车胎和伸缩缝各梁的接触长度与节点B的位移值相关，等效位移如下式所示：
式中　 UB为等效位移值；LSTG，LMTG分别为与边梁、中梁的接触长度；L为LSTG与LMTG之和；USTG，UMTG分别为边梁、中梁对应节点的位移。等效位移系数α为不同车辆过缝参数化分析提供了理论基础，后续可对不同车型、车载车胎的接触进行深层次研究，得出更为精确的虚拟节点位移变化规律。本研究对α进行了合理的简化，将系数α设定为线性函数。结合车辆过缝的等效力分析可假定α=β。
1.3　车-缝-桥耦合振动方程
以三轴车前轴行驶至伸缩缝状态为例［10］，对VBCV-J的主要公式项进行介绍。前轴左轮与桥梁接触面的等效竖向位移如下式所示：
则：
式中　 xi，，分别表示车轮节点、伸缩缝边梁、中梁的纵向坐标；表示模态坐标值；表示第n阶模态的竖向分量，下标“v”表示竖向。
车施加于桥梁的等效竖向力如下式所示：
文中给出了VBCV-J方程主要项的表达式，其他常规项表达式可见参考文献［10，15］。在车辆完全行驶至桥梁时，运行VBCV振动程序，其矩阵形式与VBCV-J矩阵一致，使计算得以实现。VBCV-J数值计算方法采用Newmark-β法，程序运行稳定、收敛性好，桥梁动力响应计算结果可靠。
2　实测与数值分析
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对典型公路简支梁桥进行实测，主梁由四片小箱梁组成，跨径布置为30×3 m，桥面宽度为12.75 m。采用双缝式伸缩缝，支座采用板式橡胶支座。
2.1　现场测试
2.1.1　自振频率测试
对伸缩缝、主梁自振频率进行测试，加速度测点A-SSF和A-ZL分别布置于伸缩缝中梁中部和主梁跨中位置，采用FDD方法对伸缩缝、主梁环境激励下的动力信号进行频谱分析，如图4所示。
由图4可知，伸缩缝、桥梁中梁的竖向一阶自振频率分别为117.3 Hz，4.83 Hz，伸缩缝的基频要远大于主梁的竖向基频。
2.1.2　行车试验
由于伸缩缝可利用空间的限制，故将位移测点（D-SSF）布置于临近伸缩缝边梁的主梁位置处，主梁位移测点（D-ZL）布置于跨中截面。车速为60 km/h，RSC为“较好”，测点横向布置于距离防撞护栏50 cm位置处，车道布置如图5（a）所示。
试验车采用12自由度二轴车模型，前轴总重约9.14 t，后轴总重25.1 t，由于篇幅限制，详细参数见文献［10，15］。测点D-SSF，D-ZL的位移时程曲线分别如图5（b），（c）所示。
2.2　数值分析
利用ANSYS建立多尺度、精细化的伸缩缝-桥梁耦合分析模型，如图6所示；模型主要参数如表2所示。
采用质量归一化对伸缩缝-桥梁结构模态进行分析，表3给出了主梁、伸缩缝前两阶竖向振动频率计算值与实测值的对比。
由表3可知，桥梁部件前两阶竖向自振频率误差范围为0.72%~3.78%，ANSYS分析模型与实桥在动力特性方面偏差满足工程需求，桥梁-伸缩缝模态信息（振动频率、模态位移、模态内力等）可进一步用于VBCV-J分析。
二轴车的计算方法与前文三轴车相似，可根据前文公式进行推导。需要指出的是，在采用VBCV-J分析方法对行车实验进行模拟时，为使得参与计算的振型数量达到精度要求，本文选取主梁的主要振型（前50阶振型）以及包含伸缩缝局部振动的振型（前50阶振型）进行计算。各测点竖向位移实测与数值分析结果的对比如图7所示。
如图7所示，梁端测点竖向位移最大值误差为4.76%，跨中测点位移最大值误差为2.32%，需要说明的是，由于实际车道的RSC与数值模拟之间的误差，导致两者之间存在误差。上述计算结果表明理论值与实测值吻合较好，本文提出的VBCV-J分析方法及基于MATLAB平台编制的数值求解方法行之有效。
3　VBCV-J参数影响分析
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车辆采用与2.2节一致的二轴车，VBCV-J分析测点包括伸缩缝各横梁（STG1，MTG，STG2）、主梁梁端 （S）、1/4跨 （Q）、1/2跨 （M），测点横向布置位置与2.2节一致。需要说明的是，边梁节点耦合于主梁梁端对应节点，梁端边支座距离梁端较近，边梁STG-2测点、梁端边支座的动力响应规律与主梁梁端 （S） 测点一致。鉴于此，本文主要考察该型桥梁梁端 （S） 的车致动力响应规律。
3.1　车速、路面参数影响规律
3.1.1　车　速
为获得车辆行驶速度对桥梁动力响应的影响规律，对车速在10~100 km/h范围内，路面考虑为光滑路面，对原型桥进行VBCV-J分析，其他参数均为设计值。图8给出了车速60 km/h时各测点竖向位移时程曲线。
采用动力放大系数DAF来表示车辆的冲击作用（动力放大系数值，DAF=最大动力响应/最大静力响应），简支梁桥各测点的DAF值随车速的变化规律如图9所示。
如图9（a）所示，随着车速增大，中梁DAF值先减小后增大，当车速达50~100 km/h阶段，前、后轴过缝DAF值增大，最大值分别为1.40，1.22。由于前轴轴重较轻，虽然前轴过缝时DAF值较大，但伸缩缝结构的受力处于相对较低状态。如图9（b）所示，由于车辆过缝产生振荡，简支梁桥主梁梁端测点的DAF值较其他测点大。随着行驶速度增加，梁端测点DAF值增大，梁端至跨中测点的DAF最大值依次减小（从1.17减小至1.02），1/4跨、跨中测点DAF值较梁端DAF值分别减小12.0%，12.8%。车速与车辆的振动密切相关，当车辆振动频率与各部件的振动频率接近时，该测点的冲击效应也会更为明显，车速的研究结果可为桥梁-伸缩缝健康防护提供理论支撑。
3.1.2　RSC-路面等级
鉴于桥梁各测点在车速较高时DAF值较大，对车速为60~100 km/h时的路面平整度-RSC（Road Surface Condition）进行参数影响分析，RSC为四个等级：理想-0、好-1、较好-2、一般-3。各测点DAF值与车速、RSC的关系如图10所示。
由图10可见，伸缩缝中梁测点DAF随RSC、车速的增大而增大。当车速达100 km/h，RSC为“一般”，前、后轴过缝时，伸缩缝中梁的DAF分别达1.70和1.50，均大于设计值1.45。与“RSC-理想”相比，前、后轴过缝，中梁DAF值分别增大21.73%和27.40%。RSC级别对主梁测点DAF值的影响较大。行驶速度达100 km/h，RSC为“一般”时，各测点DAF值达最大值，梁端至跨中各测点DAF值从1.47减小至1.18，其中梁端DAF值大于设计值1.27。与“理想”路面相比，梁端至跨中各测点DAF值增幅范围从24.79%减小至15.18%。
综上，可预见的是，简支梁桥服役达到一定年限，路面恶化情况，在长期重载车辆反复作用下，伸缩缝、简支梁梁端部件会发生较为严重的疲劳损伤。
3.2　伸缩缝参数影响规律
3.2.1　高　差
仅考虑伸缩缝处的RSC来模拟高差（与路面高差为-2 ~+2 cm），车速为60 km/h，进行参数影响分析。高差+2 cm时，各测点的竖向位移时程曲线如图11所示。
桥梁各测点DAF值随高差的变化规律如图12所示。由图12可知，伸缩缝中梁高差导致车辆与桥梁之间相互作用发生变化，伸缩缝中梁测点DAF值与高差近似成正比关系，在高于路面时2 cm时，伸缩缝中梁DAF最大值为2.20和2.11，远大于设计值1.45。伸缩缝中梁高于或低于路面均会引起梁端冲击效应的增大，高差为-2 cm时，梁端DAF值为1.53，大于设计值1.27。需要指出的是，伸缩缝中梁低于路面时，伸缩缝的冲击效应有所减小，但梁端的冲击效应显著增大。主梁其他部位测点受到的影响较小，增幅为1.20%~1.53%。
3.2.2　伸缩缝支撑刚度
随伸缩缝服役年限的增加，弹性支撑刚度k0会有所减小，车速为60 km/h，RSC为“理想”，对弹性支撑刚度分别为k0，k0，k0，k0四种工况进行分析，各工况下简支梁桥各测点DAF值变化规律如图13所示。
如图13所示，弹性支撑刚度k0的降低导致伸缩缝整体的结构承载力和抗震性能变差，车辆的震荡更为明显，中梁的冲击效应增大，支撑刚度为k0时，中梁DAF最大值为1.82和1.51，分别增大54.60%和35.50%。随伸缩缝弹性支撑刚度k0降低，梁端冲击效应变大，DAF最大值达1.25，增幅达9.27%，而伸缩缝支撑刚度的变化对主梁其他部位DAF值的影响相对较小。
3.3　支座参数影响规律
由前文分析可知，伸缩缝病害对主梁梁端的冲击效应影响显著，会导致梁端支座在长期服役过程中损伤或破坏。在实际的简支梁桥检测中，支座的损伤与脱空也是屡见不鲜。鉴于此，本节开展了考虑支座损伤的VBCV-J分析。
3.3.1　支座支撑刚度
本节共设计了四种支座的损伤工况，支撑刚度k1折减为80%（0.8k1），60%（0.6k1），40%（0.4k1），20%（0.2k1）。考虑车速10~100 km/h、RSC-理想，各工况桥梁各测点DAF值变化规律如图14所示。
由图14可知，伸缩缝中梁DAF随简支梁桥支座刚度降低变化较小，前、后轴过缝DAF值分别达1.41和1.23，增幅分别为0.60%和1.04%。主梁各测点DAF值随支座损伤程度加深而增大，DAF达1.40，1.15和1.08，增幅为24.20%，13.30%和6.30%，梁端的冲击效应受影响最为显著。简支梁桥支座刚度的降低对伸缩缝冲击效应的影响很小，但对简支梁桥主梁影响较大。这是由于主梁的支撑体系发生变化，导致桥梁整体振动特性发生改变，而伸缩缝边界锚固于两跨桥梁之间，一跨桥梁支座发生轻度损伤对其动力特性影响相对较小。
3.3.2　支座脱空
根据实际桥梁检测，梁端边支座脱空现象屡见不鲜，基于此开展梁端边支座脱空对VBCV-J动力响应的影响研究。图15给出了车速为60 km/h、RSC-理想时，桥梁各测点的竖向位移时程曲线。
各车速下简支梁桥各测点的DAF值随车速的变化规律如图16所示。由图16可知，由于主梁梁端边支座脱空，对于该支座影响范围内伸缩缝、主梁不能提供有效支撑，对后轴过缝的影响较大，伸缩缝中梁DAF达1.40和1.30，较支座无损伤时分别增大3.76%，6.73%。支座脱空对简支梁桥主梁各测点冲击效应影响较大，简支梁桥主梁梁端至跨中测点的DAF最大值分别达1.50，1.24和1.16，较支座无损伤时分别增大38.40%，8.81%和14.08%。梁端测点DAF值远超设计值1.27。
4　结论
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本文提出了VBCV-J数值分析方法，并通过实测进行了验证。进而以简支梁桥为原型，探究了车速、路面不平整度（RSC）、伸缩缝、支座等参数对该型桥梁的车致动力响应的影响规律，主要结论如下：
（1）主梁测点的冲击效应随距离梁端位置的增加而减小。在车速较高、路面状况“一般”时，伸缩缝、主梁梁端会产生显著的车辆冲击效应，超出规范值。
（2）伸缩缝中梁测点DAF值与高差近似成正比关系，在高于路面2 cm时，DAF达2.20，远超规范值1.45。伸缩缝中梁高于或低于路面均会引起梁端冲击效应的增大，而主梁其他测点受高差影响较小（DAF增幅为1.20%~1.53%）；伸缩缝支撑刚度降低会导致伸缩缝中梁、简支梁梁端冲击效应增大。
（3）支座发生损伤，刚度下降时，简支梁桥主梁的冲击效应会显著增大，伸缩缝受到影响较小。当支座支撑刚度降低为1/3原刚度时，梁端DAF值增幅最大，DAF值达1.40。梁端边支座脱空时，简支梁桥主梁DAF值会显著增大，梁端及伸缩缝DAF均会有所增大。
（4）伸缩缝、支座病害的服役环境恶劣，文中对单车作用下的桥梁动力响应进行了研究，可预见的是在多重病害耦合作用及车队重载反复作用，极易发生疲劳破坏。伸缩缝及梁端构件亟需提高自身的抗震性能和安全储备，对多车的参数影响规律的研究将是下一步研究重点。
基金
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  • 国家自然科学基金资助项目(51908015)
  • 国家自然科学基金资助项目(51978021)
  • 国家自然科学基金资助项目(52108428)
  • 国家自然科学基金资助项目(52178446)
  • 交通运输部水运科学研究所面上项目(172201)
文献
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2024年第37卷第2期
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doi: 10.16385/j.cnki.issn.1004-4523.2024.02.011
  • 接收时间：2022-06-05
  • 首发时间：2026-02-10
  • 出版时间：2024-02-28
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  • 收稿日期：2022-06-05
  • 修回日期：2022-09-02
基金
国家自然科学基金资助项目(51908015)
国家自然科学基金资助项目(51978021)
国家自然科学基金资助项目(52108428)
国家自然科学基金资助项目(52178446)
交通运输部水运科学研究所面上项目(172201)
作者信息
    1交通运输部水运科学研究所, 北京　100088
    2北京工业大学城市建设学部, 北京　100124
    3哈尔滨工业大学交通科学与工程学院, 黑龙江　哈尔滨　150090
    4中建二局第一建筑工程有限公司, 北京　100176

通讯作者:

吴喜德（1976―），男，硕士，高级工程师。 E-mail： 。
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https://castjournals.cast.org.cn/joweb/zdgcxb/CN/10.16385/j.cnki.issn.1004-4523.2024.02.011
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2种不同金属材料的力学参数
科
Family		 属数
Number of
genus		 种数
Number of
species		 占总种数比例
Percentage of
total species (%)		 属
Genus		 种数
Number of
species		 占总种数比例
Percentage of total
species (%)
鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
栓菌属 Trametes 5 2.39
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