大跨PC梁底板受力及影响因素分析.pdf

2023No.352上涵么路桥隧工程SHANGHAI HIGHWAYS大跨PC梁底板受力及影响因素分析张彦【同济大学建筑设计研究院（集团)有限公司，上海2 0 0 0 9 2 摘要：箱型断面大跨PC梁是应用最广、最为常见的中大跨度梁桥方案。在长期的运营过程中，也发现了梁体开裂、跨中下挠等具有代表性的病害。其中,底板开裂是较为常见的病害类型。现针对底板受力进行分析，通过对不同影响因素的定量计算，揭示了恒载、活载对底板受力的影响，并在此基础上，提出了结构优化设计方案。关键词：大跨PC梁；箱型断面；底板开裂；横向框架计算；底板束外崩力0引言大跨PC梁是解决中等跨度需求的经典桥型方案，已有百余年的历史。相比其它类型的桥梁，我国现行规范在经过对服役桥梁的追踪观测后，不断完善，对PC梁受力的研究已较为深入和全面。然而，在实践中，也出现了例如梁体开裂、跨中下挠等病害。这从侧面说明，现今对PC梁，尤其是对大跨、大箱室截面连续梁的研究，还有不全面、不符合实际的地方。在所有病害中,底板开裂是一个广泛的现象，在根据现行规范条文 进行的常规设计中经常被忽视，见下图1。底板开裂主要发生在弧线变高的PC连续梁。可图1 底板开裂见，开裂主要是因底板束的外崩力而产生的。本文主要围绕底板局部受力的影响因素进行分析。1背景工程概况本文背景项目为一座4跨变高度PC连续梁，跨径布置为（8 5+1 5 0+1 5 0+8 5）m=470m，桥宽1 4.2 4m，桥面布置有单向双车道（设计荷载公路-I级）、非机动车道及人行道。中支点梁高9.5 m，跨中梁高4m。梁高以二次抛物线变化，跨中有4m的等高段。底板厚度30 收稿日期：2 0 2 3-0 3-1 4100 cm。跨中标准断面如图2 所示。箱梁采用三向预应力设计。纵、横向钢束采用标准抗拉强度1 8 6 0 MPa的钢绞线，竖向预应力采用抗拉强度9 30 MPa的预应力钢筋。横向桥面板钢束型号3-s15.2,纵桥向间距0.5 m。底板束沿底板底面布置，钢束型号1 5-s15.2。因此，竖向弯曲线型呈二次抛物线型。纵桥向分8 批次张拉，如图3所示。全桥设竖向预应力，型号为D25T930，张拉应力为0.8 fk=744MPa，布置于腹板内及外侧，纵桥向间距2023No.353上语么路桥隧工程SHANGHAIHIGHWAYS28.51.7530.75+23.5+0.75=8.50.75+23.5+0.75=8.531.75人非机动车道机非防撞栏机非防撞栏非机动车道机动车道中分带机动车道人行道人行道桥面设计标高道路中心线图2 跨中标准横断面（单位：m）图3跨中底板束布置0.5m。跨中断面由于剪力减少,减少为每道腹板1 根，按梅花形间隔，布置于腹板内或外侧。通过分析比对，竖向预应力布置在内侧时,对截面受力更为不利。因此，下文的计算模型均按内侧偏置计算。2底板受力分析2.1底板束外崩力的计算模拟根据钢束等效荷载原理 2 ，假设预应力钢束的张拉力N沿管道均匀布置，产生的径向力为q(x)，见下图4。LXNq(x)Np图4底板束径向力计算示意图其中：Npe sin 0=Rg(z)sin 0(1)Npeq()=(2)RR=(1-y)/3(3)假设梁底曲线按二次抛物线变化。(4)2y=ax(1+y2)2/3(1+4a22 y/3R=(5)2a式中,Npe为钢束的张拉力，q(x)为钢束张拉后产生的均布径向力，R为弧线的弯曲半径。x=0时,R=451.84 mo取最长的底板束，x=36.25m，R=45 5.47 m。可知，对二次抛物线来说，从梁高变高点（x=0)至最后一根底板束的张拉点（x=36.25），R 值变化不大，可近似取最小值45 1 m。代人公式（2）可得：Np11718q(x)R45126 kN/m。因此，底板束的外崩力计算模型如图5 所示。54上海么路No.32023桥隧工程SHANGHAI HIGHWAYS-2.2模型介绍采用Midas/Civil2021，建立单梁框架模型。单元及截面尺寸参照中跨跨中位置，计算模型及底板束外崩力加载情况，如图6 所示恒、活载按实际数值及位置加载。计算工况如表1 所示。-261N/Q-26N/gj0-261N/aj9-26k/a9-26N/jQ-26k/j0-26N/4000底板直线及$42.5kN851.5kK147.5kN643.5kN539.5kN435.5EW344.5M240.5kN240.5KN344.5k5435.5kK539.5K643.5kN747.5E5851.5kk942.5k图5 底板束外崩力计算示意图000000000图6 底板束外崩力（单位：kN）表1 模型计算工况工况编号荷载组合工况1：自重+横向预应力工况2：+竖向预应力工况3：+底板束外崩力加载工况4：+二期荷载加载工况5（频遇组合）：+活载（汽车+人群+温度）加载2.3结果整理计算得到的截面上下缘正应力如图7 1 1 所示。HMDA/O0457.32-44.242325.7HiSTAOL图7 工况1 上下缘正应力（单位：MPa）H图8 工况2 上下缘正应力（单位：MPa）HD8M兰ATCANESA11STAUt.ON图9 工况3上下缘正应力（单位：MPa)202355No.3上语么路下转第5 9 页）SHANGHAIHWAYS桥隧工程95358图1 0 工况4上下缘正应力（单位：MPa）图中拉应力为正，压应力为负。由计算结果可知，对于底板而言，底板自重、桥面板横向预应力、竖向预应力以及底板外崩力对底板的作用方向一致，均为跨中正弯矩、近腹板侧负弯矩的受力状态。因此，随着静力荷载的施加，跨中截面上缘受压、下缘受拉的情况进一步累加，见下表2。近腹板侧的情况也类似。表2 恒载分项效应（单位：MPa）效应作用跨中支点上缘下缘上缘下缘自重+横向预应力-0.80.90.7-0.6竖向预应力-0.80.80.2-0.2外崩力-1.01.11.7-1.7二期荷载-0.10.100注：表中的跨中指底板中间，支点指底板近腹板处，下同。恒载作用中，外崩力对底板的效应最大，在1 2MPa间，二期荷载效应最小。叠加活载后，频遇组合底板的最大拉应力4.3MPa，位置出现在底板跨中下缘。背景桥底板底面配筋为D20150，计算后底板对应产生下缘裂缝0.1 3mm，较Haoacs434343HcsH4M4se-CA图1 1 工况5 上下缘正应力（单位：MPa）为接近规范限值。2.4结果分析根据计算结果，恒载对底板下崩开裂的贡献由大到小，依次为：底板束外崩力一横向预应力一竖向预应力一二期荷载。钢束外崩力作为底板受弯的直接作用荷载，占比重最大。但需注意的是，其对支点的作用更大。实际工程中，箱室内底板倒角处也是裂缝多发位置。解决方法是加强底板倒角的配筋；或控制底板竖弯半径，减小外崩力。底板束外崩力与半径成反比。背景工程桥梁底采用二次抛物线，曲线半径变化不大。已建的大跨PC梁桥，高变化曲线多采用多次抛物线，方次n从1.6 3不等,其它参数按背景工程的数值不变,求得R值,如图1 2所示。由于在0 x1的区间内，R值差距过大，不宜显示，故上图截取x1的部分，0,1 区间内趋势一致。由上图的变化可知，n=2时，R值随x的变化不大，近似于常量。以n=2为界，n取大值时,跨中处等效半径趋于无穷大，外崩力近似于0。而随着钢束向支点布置，半径越来越小。x=35时，R=305m。n 取小值时，则趋势相反，以n=1.6为例，x=0.1时，R=68m，x=35 时，R=15000n=1.5-n=1.6n=1.8(u)10.000n=2n=2.6n=35000005101520253035x(m)图1 2 不同n值下的R值变化（单位：m）2023No.359上接第55页）SHANGHA桥隧工程的影响很大，在进行抗倾覆计算时不可忽略。4结语通过某高铁站站前广场基础设施建设工程的钢箱梁抗倾覆计算，可得出以下结论：(1）钢箱梁抗倾覆计算时，不能仅考虑永久荷载和汽车荷载，应包含可能发生的所有失稳效应。(2）梯度温度引起的失稳效应占比较大，在我国规范还未明确前，可参照英国桥梁标准BS5400取值，确保桥梁安全。（3)本文的抗倾覆计算作为规范抗倾覆验算示例715m。因此，n取大值时，外崩力最大出现在近中支点位置；n取小值时，最不利点为跨中弧线起弯点。如果采用高次抛物线，跨中处的外崩力趋近于0。越往中支点靠近，单根钢束的外崩力逐渐增大，但由于底板分批次锚固，外崩力总量并不一定最大，受力薄弱处可能出现在管道局部受压或受剪处。而采用低次抛物线，最不利处位于跨中，同时也是外崩力合力最大的位置，需要加强箍筋、底板底边钢筋的配筋。此外，还可以通过增加跨中隔板、矮隔墙,来改善受力。R值还与a值相关，在确定跨径、梁高后，a值即确定。可通过控制R值的区间来确定n的合理取值。桥面板横向预应力以及腹板竖向预应力的作用，虽然对底板受力是间接作用，但绝对值不可忽视。尤其是桥面板的预应力效应，对箱梁的横向框架受力有很大的影响。背景工程中,竖向预应力布置于腹板外侧，对底板受力的方向与底板束外崩力一致、效用叠加。因此，从底板受力角度出发，偏载布置的竖向预应力设置于腹板内侧，更为有利。活载与温度荷载对底板的效应在1Mpa左右，跨中大于支点，主要通过箱梁的横向框架效应传递。该部分荷载无法消除，存在于所有的箱梁结构。截面抗扭刚度小、变形大的结构更易产生。因此,对于薄壁、大箱室的断面，需要注意底板的尺寸和配筋 3 。3结语本文针对大跨PC梁、大箱室截面的底板受力，进的补充，可供今后的抗倾覆计算参考参考文献1杜军.城市独柱墩桥梁抗倾覆加固改造设计探讨 J.城市道桥与防洪,2 0 2 2(0 3):6 9-7 3+13.2程伟伟.连续钢箱梁桥抗倾覆分析 J.山东交通科技,2 0 2 1(06):88-90.3】日本本州四国连络桥公团.钢床板设计要领同解说M.1989.4英国标准学会.英国标准54 0 0:第1-4 篇：钢桥、混凝土桥及结合桥(上册)M.1978-82版.钱冬生,译.成都：西南交通大学出版社,19 8 7.行分项细化研究，明确了桥面板预应力、竖向预应力、跨中底板束外崩力，以及活载、温度作用对底板受力的影响，并提出了相应的优化思路。通过研究，发现：(1)底板开裂是大跨PC梁的常见病害，主要出现于弧线变化的变高连续梁处(2)底板开裂的最主要因素是底板钢束的外崩力，其值与钢束张拉力（钢束型号及根数）、弧线半径有直接关系。(3)桥面板钢束、竖向预应力、二期荷载均对底板有间接作用，其值主要由箱型截面横向刚度决定。(4)底板跨中、支点均为受力关键截面。通过计算，根据需要，应加强底板底面、底板腹板内倒角及钢束防崩钢筋的配筋。参考文献1中华人民共和国交通运输部.公路钢筋混凝土及预应力混凝土桥涵设计规范：JTG3362-2018S.北京：人民交通出版社股份有限公司,2 0 18.2车俊,武维宏,吴国松.基于水平底板索理念的大跨度PC连续刚构桥徐变下挠控制措施研究及工程应用 J.工程建设与设计,2 0 2 2(11):10 9-112.3于松马.互通立交中曲线梁设计 J.城市道桥与防洪,2 0 19(04):108-110+16.Analysis of the Force and Influencing Factors of Large-span PC Beam FloorAbstract:The large-span PC beam with box section is the most widely used and most common scheme of medium and large span girderbridge.In the long-term operation process,typical representative diseases such as beam cracking and mid-span deflection have also beenfound.Bottom plate cracking is a more common type of disease.In this paper,the influence of constant load and live load on the force of thebase plate is revealed through the quantitative calculation of different influencing factors,and a structural optimization design scheme is pro-posed on this basis.Key words:large span PC beam;box-type section;bottom plate cracking;transverse frame calculation;bottom plate bundle collapse forceDiscussion on the Influence of Gradient Temperature and other Effect on the Anti Overturning Calculation ofSteel BoxGirdersAbstract:Municipal bridges mostly use single-column vase piers,which have a beautiful shape and save road space.However,due to thesmall spacing between its supports,overloading and other factors,multiple beam overturning accidents have also occurred in recent years.This article provides a detailed discussion on the anti overturning calculation of bridges based on current specifications and practical engineer-ing,aiming to provide reference and reference for future bridge design.Key words:steel box girder;anti overturning;specificationDesign Practice and Summary of Low Clearance River-crossing Bridge Slow Passage through ReconstructionAbstract:Taking waterfront space as the starting point,creating a charming quality urban area with temperature,vitality and characteristics,realizing the connection of waterfront and returning the shore to the people will become an important means of urban renewal in the future.Among them,the small bridges of municipal roads across non-navigable rivers often become the breakpoints of riverside slow-moving walk-ways because of the low clearance under the beams.Combined with the practice of similar projects in recent years,this paper sums up the re-construction methods for the slow passage under the low clearance river-crossing bridge,and points out the progressive reconstruction strategywith three types and seven grades,so as to provide some reference for similar projects in the future.Key words:low clearance;under the bridge across the river;slow move channel;through recongstructionComfort Analysis and Vibration Reduction Control of Pedestrian Bridge with Three Span Steel Box Continuous Beam underHuman Induced VibrationAbstract:With the increase of footbridge span and the wide application of lightweight and high-strength materials,the fundamental frequen-cy of the structure is constantly decreasing,which brings a significant problem of comfort of human-induced vibration on bridges.Based on hu-man-induced vibration theory,this paper analyzes the action characteristics of pedestrian load and the similarities and differences between do-mestic and foreign standard evaluation methods for pedestrian comfort.Finite element simulation calculation is used to analyze the human-in-duced vibration response under high-density crowd,and three different beam height schemes are compared,together with their human-in-duced vibration effects and the effects of applying vibration reduction measures.The results show that the vibration control measures based onmultiple TMD have good cost control feasibility under the premise of ensuring the human-induced vibration performance of steel box girderfootbridge structure.Key words:pedestrian bridge;human-induced vibration;damping control;TMDApplication of Jacking and Sliding Technology of Steel Structure Bridge in Chunshentang Bridge Project onJinghong RoadAbstract:With the rapid development of infrastructure construction in China,steel structure bridges have been widely used.Steel structurebridge installation usually uses installation techniques such as large lifting machinery and bridge erecting machines.However,due to limita-tions in the construction site and environmental factors,some projects cannot adopt conventional methods for the installation of steel structurebridges.In recent years,the push sliding technology has gradually been widely applied in the installation of steel structure bridges.Taking thenew construction project of Chunshentang Bridge on Jinghong Road(Jindu Road-Huajing Port)as an example,this article aims to provide ref-erence for similar projects.Key words:steel structure bridge;top push;slippageResearch on the Force of the Transverse Beam of Wide Multicell Concrete Box GirderAbstract:The force of the transverse beam for wide concrete box girder is relatively complex,and the force transmission ratio between the topand bottom plate and the web plate in the simplified calculation of the beam in the conventional design may have a large deviation from the ac-tual force.In order to get the real force mode of the beam,the three-dimensional solid finite element analysis is used to accurately calculatethe force transfer ratio of the top and bottom plates and the web plates.The reasonable prestress layout of the beam is obtained through the cal-culation of Dr.Bridge 4.4.Key words:bridge engineer finite element;beam calculation;wide;force transmission ratio;prestressing forceKey Techniques for Walking Type Jacking Construction of Large-span Steel Box Girders for Bridges AcrossExisting HighwaysAbstract:For the construction of steel box girders crossing existing highways,due to high traffic volume,high safety requirements are re-ZHANGYan(52).CHENNan(56)HUANG Chenghua(60)HEWei,LU Haixiao,ZHU Jianfeng(68)XURen(74).GUAN Ruyi,JIANG Kai,XU Changze,ZHAO Hongjiao（8 1)ZHANG Xiaoxin(85)