南京工业大学桥梁工程课程设计

2014 桥梁工程课程设计 .页脚11级桥梁工程课程设计专业：交通工程专业：交通工程班级：交通学号：02姓名：指导教师：罗韧南京工业大学交通学院二0一四年六月目录HYPERLINK1．课程设计任务书 3HYPERLINK1.1设计题目 3HYPERLINK1.2设计资料 3HYPERLINK1.2.1设计标准 3HYPERLINK1.2.2材料数据与结构布置要求 3HYPERLINK1.2.3设计计算依据 4HYPERLINK1.3设计内容 4HYPERLINK1.4设计成果 5HYPERLINK2．空腹式等截面悬链线箱形无铰拱桥设计计算书 5HYPERLINK2.1主拱圈截面几何要素的计算 5HYPERLINK2.1.1主拱圈横截面设计 5HYPERLINK2.1.2箱形拱圈截面几何性质 6HYPERLINK2.2确定拱轴系数 6HYPERLINK2.2.1上部结构构造布置 7HYPERLINK2.2.2主拱圈 7HYPERLINK2.2.3拱上腹孔布置 9HYPERLINK2.3结构恒载计算 9HYPERLINK2.3.1主拱圈 9HYPERLINK2.3.2横隔板 10HYPERLINK2.3.3拱上空腹段恒载 12HYPERLINK2.3.4拱上实腹段 14HYPERLINK2.3.5腹拱推力 14HYPERLINK2.3.6验算拱轴系数 15HYPERLINK2.3.7拱圈弹性中心及弹性压缩系数 16HYPERLINK2.4主拱圈截面内力验算 16HYPERLINK2.4.1结构自重内力计算 16HYPERLINK2.4.2活载内力计算 26HYPERLINK2.5温度变化、混凝土收缩、徐变的内力计算 28HYPERLINK2.6主拱圈正截面强度验算 29HYPERLINK2.7拱上结构强度与稳定性验算 32HYPERLINK2.7.1立柱强度与稳定性验算 32HYPERLINK2.7.2横墙强度验算 33HYPERLINK3.课程设计小结 33HYPERLINK参考文献 331．课程设计任务书1.1设计题目空腹式等截面悬链线箱形无铰拱桥设计1.2设计资料1.2.1设计标准设计荷载：公路—I级，人群荷载3.5kN/m2桥面净空净－8+2×(0.75m+0.25m)人行道+安全带净跨径L0＝80m净高f0＝16m净跨比f0/L0＝1/51.2.2材料数据与结构布置要求拱顶填料平均厚度(包括路面，以下称路面)hd＝0.5m，材料容重γ1＝22.0kN/m3主拱圈材料容重(包括横隔板、施工超重)γ2＝25.0kN/m3拱上立柱（墙）材料容重γ2＝25kN/m3腹孔拱圈材料容重γ3＝23kＮ/m3

腹孔拱上填料容重γ4＝22kN/m3

主拱圈实腹段填料容重γ1＝22kN/m3人行道板及栏杆重52.0kN/m(双侧)；混凝土材料：强度等级为C30(C40)，主要强度指标为：强度标准值fck=20.1(26.8)MPa，ftk=2.01(2.65)MPa强度设计值fcd=13.8(18.4)MPa，ftd=1.39(1.65)MPa弹性模量Ec=3.0(3.25)×104MPa普通钢筋1)纵向抗拉普通钢筋采用HRB400钢筋，其强度指标为抗拉强度标准值fsk=400MPa抗拉强度设计值fsd=330MPa弹性模量Es=2.0×l05MPa相对界限受压区高度xb=0.53，xpu=0.19852)箍筋及构造钢筋采用HRB335钢筋，其强度指标为抗拉强度标准值fsk=335MPa抗拉强度设计值fsd=280MPa弹性模量Es=2.0×105MPa本桥采用支架现浇施工方法。主拱圈为单箱六室截面的钢筋混凝土拱圈，由C30(C40)混凝土现场浇筑而成。拱上建筑可采用简支板形式或圆弧拱形式，净跨为5～7m左右，拱脚至拱顶布置4～6跨左右(主拱圈的具体几何参照指导书实例修改自定)。1.2.3设计计算依据交通部部颁标准《公路桥涵设计通用规范》(JTGD60－2004)交通人民出版社交通部部颁标准《公路钢筋混凝土及预应力混凝土桥涵设计规范》(JTGD62－2004)交通人民出版社交通部部颁标准《公路圬工桥涵设计规范》(JTGD61-2005)交通人民出版社《公路设计手册-拱桥(上)》人民交通出版社，2000.71.3设计内容确定主拱圈截面构造尺寸，计算拱圈截面的几何、物理力学特征值；确定主拱圈拱轴系数m及拱上建筑的构造布置和几何构造尺寸；结构恒载计算；主拱结构内力计算(恒载、活载)；温度变化、混凝土收缩徐变引起的内力；主拱结构的强度和稳定验算；拱上立柱(墙)的内力、强度及稳定性验算；手工绘制2张相关施工图。1.4设计成果空腹式等截面悬链线无铰拱设计计算书空腹式等截面悬链线无铰拱设计纵断面施工图空腹式等截面悬链线无铰拱设计横断面施工图悬链线箱形无铰拱桥纵断面参考图1-4-1悬链线箱形无铰拱桥横断面参考图1-4-22．空腹式等截面悬链线箱形无铰拱桥设计计算书2.1主拱圈截面几何要素的计算2.1.1主拱圈横截面设计拱圈截面高度按经验公式估算D=l0/100+Δ=80/100+0.6=1.4m拱圈由六个各为1.5m宽的拱箱组成，全宽B0=9.0m构造图如图2-1-1所示：图2-1-1拱圈横断面构造图2.1.2箱形拱圈截面几何性质截面积：绕箱底边缘的静面矩：主拱圈截面重心轴：主拱圈截面绕重心轴的惯性矩：拱圈截面绕重心轴的回转半径：2.2确定拱轴系数2.2.1上部结构构造布置上部结构构造布置如图2-2-1所示：图2-2-1上部结构构造布置（尺寸单位：mm）2.2.2主拱圈假定m=2.514，相应的，，查《拱桥》(上册)表(III)-20(7)得：sinφj=0.69198，cosφj=0.72191，φj=43.7876˚主拱圈的计算跨径和计算矢高：脚拱截面水平投影脚拱截面竖向投影计算跨径半跨径计算矢高将拱轴沿跨径24等分，每等分长Δl=，每等分点拱轴线的纵坐标y1=[表(III)-1值]×f，相应的拱背曲面坐标:，拱腹曲面坐标:。具体位置见图2-3-1图2-3-1拱轴坐标具体位置表2-2-1主拱圈截面坐标表截面号xy1/fy1cosφy上/cosφy下/cosφy1-y上/cosφy1+y下/cosφ040.485116.1930.721910.9793464560.95995345715.21365354177981250.90364914.632788260.746230.9474290770.92866810513.6853591815.56145636237.111250.81401813.181393470.769690.9185516250.90036248412.2628418514.08175596335.4243750.73072411.832613730.792180.8924739330.87480118210.940139812.70741491433.73750.65340810.580635740.81360.8689773840.8517699129.7116583611.43240566532.0506250.5817389.4200834340.833870.8478539820.8310647948.57222945210.25114823630.363750.5154058.3459531650.852910.828926850.8125124577.5170263159.158465622728.6768750.4541257.3536461250.870680.8120090040.7959296186.5416371218.149575743826.990.3976356.4389035550.887180.7969070540.7811267165.6419965017.220030271925.3031250.3456915.5977743630.902380.7834836760.7679691484.8142906876.3657435111023.616250.2980714.8266637030.91630.771581360.7563025214.0550823435.5829662241121.9293750.254574.122252010.928970.7610579460.7459874923.3611940644.8682395021220.24250.2153.4814950.940420.7517917530.7369047872.7297032474.2183997871318.5556250.1791922.9016560560.95070.7436625640.7289365732.1579934923.6305926291416.868750.1469922.3802414560.959850.7365734230.7219878111.6436680333.1022292671515.1818750.1182621.9150165660.967920.7304322670.7159682621.1845842992.6309848281613.4950.0928771.5039572610.974980.725143080.7107838110.7788141812.2147410721711.8081250.070731.145330890.981070.7206417480.7063716150.4246891421.8517025051810.121250.0517240.8375667320.986240.7168640490.7026687220.1207026831.540235454198.4343750.0357790.5793693470.990530.7137593010.699625453-0.134389951.2789948206.74750.0228250.3696052250.993680.7114966590.697407616-0.341891431.067012841215.0606250.0128070.2073837510.996640.7093835290.69533633-0.501999780.902720081223.373750.0056820.0920086260.998510.7080550020.694034111-0.616046380.786042737231.6868750.0014190.0229778670.999630.7072616870.693256505-0.684283820.7162343722400010.7070.693-0.7070.6932.2.3拱上腹孔布置由，查《拱桥》(上册)表3-2，得sinφ0=0.43219，cosφ0=0.90178，腹拱拱脚的水平投影和竖向投影x'=d'×sinφ0=0.5×0.43219=0.216095m；y'=d'×cosφ0=0.5×0.90178=0.45089m从主拱两端起拱线起向外延伸后向跨中对称布置3对圆弧小拱，腹拱圈厚d'=0.5m，净跨径l'0=8m，净矢高f'0=0.8m。腹拱拱顶的拱背和主拱拱顶的拱背在同一标高。腹拱墩墩中线的横坐标lx，以及各墩中线自主拱拱背到腹拱起拱线的高度，分别计算如表2-2-2：表2-2-2腹拱墩高计算表项目lxξkξy1tanφcosφh1号立墙31.1160.7691.2098.8160.6341.1847.3862号立墙22.6160.5590.8794.4020.4141.0823.0443号腹拱座14.1160.3490.5481.6490.241.0280.329空、实腹段分界线13.6660.3380.5311.5440.2311.0260.225注:,,,,2.3结构恒载计算恒载计算，按主拱圈、横隔板、拱上空腹段、拱上实腹段以及腹拱推力共五个部分进行。2.3.1主拱圈P0~12=[表（Ⅲ）—19（7）值]Ar2l=0.51408×6.12×25×80.97=6368.6338kN·mM1/4=[表（Ⅲ）—19（7）值]Ar22/4=0.12530×6.12×25×80.972/4=31421.7804kN·mMj=[表（Ⅲ）—19（7）值]Ar2l2/4=0.50610×6.12×25×80.972/4=126915.9063kN·m2.3.2横隔板横隔板的设置受箱肋接头位置的控制，必须先确定接头位置后再按箱肋轴线等弧长布置横隔板。①箱肋有关几何要素a.箱肋截面积A'=2×0.2×1.4+1.1×0.1+2×0.1×0.1/2=0.79m2b.箱肋截面静矩J'=2×0.2×1.4×1.4/2+1.1×0.2×0.2/2+2×0.1×0.1×(0.1/3+0.2)/2=0.4163m3c.截面重心距箱底的距离y'下=J'/A'=0.527md.箱肋计算跨径l'=l0+2y'下sinφj=80+2×0.527×0.69198=80.7293me.箱肋轴线弧长S'=2×0.52764l'=85.1920m②确定箱肋接头、设置横隔板确定接头位置箱肋分三段吊装合拢，接头宜选在箱肋自重作用下弯矩值最小的反弯点附近，即ξ=0.35~0.37之间，此处相应的弧长为图：图2-3-2箱肋分段计算示图式中值，根据ξ值从《拱桥(例集)》的附表1-1内插算得。b.布置横隔板横隔板沿箱肋中轴线均匀设置，取板间间距Δl'=2.56m，中段箱肋设11道横隔板，端横隔板到接头中线的距离为0.3m，座落在宽为0.6m的钢筋混凝土排架式腹拱墩支承的宽为0.7m的钢筋混凝土盖梁上。则中段箱肋弧长之半为：SII/2=(2.56×10+2×0.3)/2=13.1m，则接头位置刚好在ξ=0.37处。端段箱肋弧长SI=(S'-SII)/2=(85.1920-26.2)/2=29.496m端段箱肋设12道横隔板，则端横隔板距起拱面的长度为：ΔS=SI-2.56×11-0.3=1.036m③横隔板与接头加强部分的重力横隔板厚均为0.06m。靠拱脚的一块为实心板，其余均为空心板。接头处两相邻横隔板之间以及拱脚截面至第一块横隔板之间的箱底板和两侧板均加厚0.10m。加强后的断面尺寸图2-3-3图2-3-3横隔板a.横隔板重力空心板P=[(1.1×1.02-0.68×0.62+4×0.12/2)×0.06+4×0.12×1.02/2]×25×7=11.1342kN实心板P=(1.1×1.02×0.06+4×0.12×1.02/2)×7×25=15.351kNb.中接头加强部分P=[2×0.1×0.54×1.02+0.1×0.54×(1.1-2×0.1)-4×0.12×1.02/2]×7×25=24.213kNc.拱脚加强段P=[0.1×2×1.02×0.6775+0.1×0.6775×(1.1-2×0.1)-2×0.12×1.1/2]×7×25=32.9324kNd.各集中力作用线的横坐标各集中力作用线的横坐标lx，可以根据值从《拱桥(例集)》书后附表1查得ξ值，再由l=l'×ξ/2求得。lx的值和各集中力分别对l/4和拱脚截面的力臂见表2-3-1.表2-3-SEQ表\*ARABIC1横隔板的横坐标与力臂计算表集中力编号Sx2Sx/l肋ξlx=l肋ξ/2力臂l/4-lxl/2-lx1号2.560.06340.07272.934817.247637.42992号5.120.12680.14535.86614.316334.49863号7.680.19030.21788.789611.392731.5754号10.240.25370.289911.70278.479628.66195号12.80.31710.361714.59915.583225.76566号15.360.38050.378415.27594.906425.08887号17.920.4440.449618.14712.035322.217663.96118号20.480.50740.520120.99219.37269号23.040.57080.589823.806216.558410号25.60.63420.658626.582413.782211号28.160.69760.726229.313811.050912号30.720.76110.792731.99898.365813号33.280.82450.857734.62255.742214号35.840.88790.921337.18883.1759283.285415号38.40.95130.983139.68310.68160号000020.182340.3647中接头14.080.34880.370114.93785.244525.4269拱脚加强段41.7024791.03310.991640.02390.34082.3.3拱上空腹段恒载①腹孔上部(见图2-3-4)腹拱圈外弧跨径l外=l'+2d'sinφ0=8+2×0.5×0.43219=8.43219m腹拱圈内弧半径R0=l'/(2sinφ0)=8/(2×0.43219)=9.2552m腹拱圈重力Pa=2φ0Rd'γ3B0=2×25˚36'24"×π/180×(9.2552+0.5/2)×0.5×23×9=879.3505kN腹拱上面的护拱重Pb=(2sinφ0-sinφ0cosφ0-φ0)R2γ2B0=(2×0.43219-0.43219×0.90178-25˚36'24"×π/180˚)×(9.2552+0.5/2)2×22×9=495.8681kN填料及桥面系重力Pc=l外hdγ1B0=8.43219×0.5×22×9=834.7868kN图2-3-4腹孔上部构造Pd={(0.6-x')y'γ4+[(f'0+d'-y')γ2+hdγ1](0.6-2x')}B0={(0.6-0.216095)×0.45089×23+[(0.8+0.5-0.45089)×22+0.5×22]×(0.6-2×0.216095)}×9=80.6576kN一个腹拱总重力：P=ΣPi=879.3505+495.8681+834.7868+80.6576=2290.663kN②腹孔下部1号腹拱墩:P=[7.3861-(0.5×1+3.14×0.5²/2）/9]×0.6×25=109.304kN2号腹拱墩:P=[3.0438-(0.5×1+3.14×0.5²/2）/9]×0.6×25=44.1695kN3号腹拱墩:P=(0.3294+0.45089/2)×(14.1162-13.6662)×2×25=12.4840125kN图2-3-5腹孔墩以上部分③腹孔集中力P13=2290.663+109.304=2399.967kNP14=2290.663+44.1695=2334.8325kNP15=（2290.663-80.6576）/2+12.4840125=1117.4867kN2.3.4拱上实腹段图2-3-6曲边三角形块拱顶填料及桥面系重P16=l×hdγ1B0=13.6662×0.5×22×9=1352.9538kN悬链线曲边三角形，见图2-3-6P17=lf1(shkξ-kξ)γ2B0/[2(m-1)k]=80.97×15.92065/[2×(2.514-1)×1.572999]×(sh0.53098512-0.53098512)×22×9=1356.0686kN式中f1=f+y上(1-1/cosφj)=16.193+0.707×(1-1/0.72191)=15.92065m其重心距原点(拱顶)的水平距离ηlx=[(shkξ-kξ/2)-(chkξ-1)/kξ]lx/(shkξ-kξ)=0.7509lx=10.2625m2.3.5腹拱推力图2-3-7腹拱拱脚受力图靠近主拱拱顶一侧的腹拱，一般多做成两平铰拱，在较大的恒载作用下和考虑到周围的填料等构造的作用，可以折中地按无铰圆弧拱计算其推力，而不计弯矩的影响。腹拱拱脚的水平推力F=(C1g1+C2g2+C3g3)RB0式中g1=γ1hd=22×0.5=11kN/m2g2=γ2{(R+d'/2)-[(R+d'/2)2-l2/4]½}=22×{(9.2552+0.5/2)-[(9.25525+0.5/2)2-8.5972/4]½}=22.6046kN/m2g3=γ3d'=23×0.5=11.5kN/m2由f0/l'0=1/10和b=I/AR2=0.0003查《拱桥》(上册)表(I)-4得C1=0.6103，C2=0.08473，C3=0.6170F=(0.6103×11+0.08473×22.6046+0.6170×11.5)×9.2552×9=1309.7662kN腹拱拱脚推力作用线的纵坐标见图2-3-8所示，其距x轴的偏心距为：e=d'+f0-y'/2-y上=0.895345m腹拱推力对各截面重心产生的力矩Mi=Fx(yi-e)2.3.6验算拱轴系数恒载对l/4截面和拱脚截面的力矩见表2-3-2表2-3-2半拱恒载对拱脚和1/4截面产生的弯矩表集中力编号恒重l/4拱脚截面力臂力矩kN·m力臂力矩kN·mp1195.410118.37253590.172062p2171.443124.68254231.644316p3200.82688.47961702.93093328.66255756.198155p0-126368.63389976.186331745.53761p132399.96718.372544093.39371p142334.832524.682557629.50318p151117.48678.47969475.84022128.662532029.96254p161352.953813.792618660.7505833.876445833.20411p171356.068611.1340215098.4949131.7054642994.77875F1309.76627.637610003.4703324.882732590.51942合计16807.388664917.67328300494.9139假定的拱轴系数m=2.514，y1/4/f=0.215由表2-3-2可知：，小于半级。因此,可选定m=2.514为设计的拱轴系数。2.3.7拱圈弹性中心及弹性压缩系数弹性中心ys=[表(III)-3值]×f=0.316474×16.193=5.12466m2弹性压缩系数γ2w=I/A=1.551/6.12=0.25343γ2w/f2==0.25343/16.1932=0.000966511=[表(III)-9值]×γ2w/f2=11.6060×0.00096651=0.0112173=[表(III)-11值]×γ2w/f2=10.9881×0.00096651=0.01062011/(1+)=0.0110992.4主拱圈截面内力验算2.4.1结构自重内力计算在确定m系数时，其实计算值很难与选定的拱轴系数在“五点”重合，对于大跨径拱桥必须用“假载法”计入“五点”存在的偏离的影响。当用“假载法”计入“五点的偏离之后，相应三铰拱的恒载压力线在“五点”以外与选定的拱轴线有偏离。对于大跨径无铰拱桥，这种偏离的影响很大，不可忽视。下面分别计算这两种偏离的影响:1.用假载法计算确定m系数时在“五点”存在的偏差确定拱轴系数时，恒载压力线在l/4截面与拱脚截面的纵坐标之比值是0.21603，并不等于为使用手册数表进行计算所选用的m'=2.514的拱轴线上相应两点的比值0.215，两者之间相差0.00103。这个偏差的影响可比拟为虚设的均布荷载作用在选定的拱轴线上，先单独求出，然后算出所选定的“拱轴线”恒载产生的内力，将两者相加后为“五点”的恒载压力线内力。(1)假载内力a.求假载由式得：b.假载内力假载qx产生的内力可以将其直接布置在内力影响线上求得。不考虑弹性压缩的假载内力见表2-4-1表2-4-1不考虑弹性压缩的假载内力表项目影响线面积ω乘数ω力或力矩(qxω)[表(III)-14(51)值]拱顶截面M10.00675-0.004540.00221l26556.140914.48907139157.2339538H10.067770.060390.12816l2/f404.87551.88878563.0918517l/4截面M10.00858-0.01006-0.00148l26556.1409-9.703088532-105.2969464H10.039490.088660.12815l2/f404.87551.88473125563.0479151拱脚截面M10.02046-0.015090.00537l26556.140935.20647663382.0571638H10.091910.036240.12815l2/f404.87551.88473125563.0479151V10.166670.333380.50005l80.9740.4890485439.3831054c.计入弹性压缩的假载内力计入弹性压缩的假载内力计算见表2-4-2表2-4-2项目拱顶截面l/4截面拱脚截面cosφ10.940420.72191sinφ00.340010.69198H1563.0918517563.0479151563.0479151V100439.3831054m1H1/(1+m)6.2497564626.249268816.24926881N=[1-m1/(1+m)]×H1cosφ+V1sinφ556.841857523.624359706.0026601M1157.2339538-105.2969464382.0571638y=ys-y15.124661.07641-11.06834M=M1+m1H1y/(1+m)189.2630514-98.56991458312.8854956(2)“拱轴线恒载”内力a.推力Hg=(ΣMj+qxl2/8)/f=(300494.9139+10.8519×80.972/8)/16.193=19106.29513kNb.考虑弹性压缩的内力表2-4-2考虑弹性压缩的内力表项目拱顶截面l/4截面拱脚截面cosφ10.940420.72191H'g=Hg-F19106.2951317796.5289317796.52893[1-μ1/(1+μ)]H'g18693.447817411.9829317411.98293N'=H'g/cosφ18693.447818515.1133824119.32641ΔN=μ1H'gcosφ/(1+μ)207.4864848205.5070756267.7106067N=N'-ΔN18485.9613218309.6063123851.6158y=ys-y15.124661.07641-11.06834ΔV=μ1H'gy/(1+μ)1086.780763212.624562-2186.342514(3)考虑确定m系数偏差影响的恒载内力考虑m系数偏差影响的恒载内力等于“拱轴线m的恒载”内力减去“假载”的内力，计算结果见表2-4-3表SEQ表格\*ARABIC1-4-3空腹无铰拱的实际恒载内力计算表截面拱顶截面l/4截面拱脚截面项目恒载内力附加内力合计恒载内力附加内力合计恒载内力附加内力合计水平力Hg18549.45-228.0318321.4217239.69-228.0317011.6517241.27-228.0317013.24轴力Ng17929.12-228.0317701.0917785.98-214.4517571.5323145.61-164.6222980.99弯矩Mg897.52-931.3-33.78311.195551.995863.19-2499.23-10838.54-13337.772.“恒载压力线”偏离拱轴线的影响“恒载压力线”(指空腹式无铰拱桥不考虑拱轴线的偏离和恒载弹性压缩影响的恒载压力线，也就是人们所说的“三铰拱恒载压力线”)与拱轴线在“五点”以外的偏离影响可以用一般力学原理进行计算，参见图13。图2-4-1拱轴压力线示意图(1)“恒载压力线”偏离拱轴线的偏离弯矩Mp计算恒载偏离弯矩Mp，首先要计算出桥跨结构沿跨径各等分段的分块恒载对各截面的力矩，再算各截面压力线的纵坐标，然后才能求得Mp。下面按主拱圈、拱上实腹段和各集中力三部分计算各分块恒载对各截面的力矩。a.主拱圈自重对各截面产生的力矩Ml(图2-4-1)图2-4-2主拱圈自重计算图在这里，对于所要求的每一等分点而言，积分上限ξ为常数，并不计等式前面的负号，则上式为：式中：可根据ξ值从《拱桥(例集)》附表1-1查得；可根据ξ值从《拱桥(例集)》附表1-2查得=0.759953k=1.573主拱圈对各截面的力矩M1的值见表2-4-4。表SEQ表\*ARABIC2-4-4主拱圈自重对各截面产生的弯矩值表截面号ξS1S2ξ×S1-S2M1(kN•m)0123452400000230.04170.04170.001700220.08330.08360.00520.0018442.3324210.1250.12570.01050.00521307.1511200.16670.16820.01760.01042617.7979190.20830.21120.02650.01754386.7514180.250.25480.03740.02636595.3138170.29170.29910.05030.03699265.4053160.33330.34420.06540.049312368.5607150.3750.39040.08270.063715974.2012140.41670.43760.10240.079920048.7309130.45830.48610.12460.098224620.7404120.50.53610.14960.118529703.9895110.54170.58760.17750.140835309.4847100.58330.6410.20860.165341451.497390.6250.69630.24320.19248145.164180.66670.75380.28160.22155410.28170.70830.81370.3240.252363280.835160.750.87630.37090.286371802.404450.79170.94170.42270.322880960.333740.83331.01030.47980.362190800.416630.8751.08230.54280.4042101365.334520.91671.1580.61220.4493112681.714410.95831.23770.68860.4975124756.2319011.32180.77270.5491137699.119b.拱上实腹段恒载对各截面产生的弯矩M2计算拱上实腹段的恒载时，必须将拱顶填料及面层的矩形板块和其下面的悬链线曲边三角形块分开才能准确计算，否则只能是近似的。(a)矩形板块从拱顶到每个截面的矩形板块的重力：P1=γ1B0h’dl·ξ1/2对实腹段里每个截面的力矩：Mi=Pi(l·ξ/2)/2=(l2/4)γ1B0h’dξ2i/2对空腹段里每个截面的力矩：Mi=Pk[l·ξi/2-(l/2)ξk/2]=(l2/4)γ1B0h’dξk(ξi-ξk/2)(i<k)式中k表示空、实腹段的分界点，取为：γ1l2B0h’d/4=80.972×9×0.5/4=7376.6585kN·m(b)悬链线曲边三角形块从拱顶到任意截面的重力Pi=l·f1γ2B0(shkξi-kξi)/[2(m-1)k]=5087.1402×(shkξi-kξi)每一块Pi的重心的横坐标：ηi=[(shkξi-kξi/2)-(chkξi-1)/kξi]/(shkξi-kξi)在实腹段里，截面重心到任意截面的力臂为l·(1-ηi)·ξi/2，在空腹段里，整块曲边三角形面积的重心到每个截面的力臂为l·(ξi-ηkξk)/2。每个截面的力矩见表2-4-5。表2-4-5拱上实腹段恒载对各截面产生的力矩计算表区间截面号ξ悬链线曲边三角形矩形块M2=MΔ+M恒kξpηlξ(1-η)/2MΔξ2/2M恒012345678910实腹段24000000000230.04170.06560.23930.750.4220.1010.0009141.08141.1811220.08330.1311.9090.75010.84291.60910.0035562.9677564.5768210.1250.19666.45770.75021.26438.16470.00781267.69131275.8561200.16670.262215.33940.75031.685325.85120.01392254.5752280.4262190.20830.327729.98520.75042.104563.10360.02173520.2383583.3416180.250.393351.9620.75062.5238131.1420.03135070.76525201.9073170.29170.458882.7730.75092.942243.52140.04256903.45267146.9739分界点0.2910.457782.17440.7509l(ξ-0.2536)/2(ξ1-0.1455)×0.1455空腹段160.333382.17440.75093.3617276.24290.05554579.78174856.0245150.37582.17440.75093.7823310.80430.07035152.76965463.5739140.416782.17440.75094.2028345.36570.08685725.75766071.1234130.458382.17440.75094.6224379.84430.1056297.37156677.2158120.582.17440.75095.043414.40570.1256870.35957284.7652110.541782.17440.75095.4636448.96720.14677443.34757892.3147100.583382.17440.75095.8832483.44570.17018014.96148498.407190.62582.17440.75096.3038518.00710.19538587.94949105.956680.666782.17440.75096.7243552.56860.22229160.93749713.50670.708382.17440.75097.1439587.04710.25089732.551310319.59860.7582.17440.75097.5645621.60860.281310305.53910927.14850.791782.17440.75097.9851656.170.313410878.52711534.69740.833382.17440.75098.4047690.64860.347211450.14112140.7930.87582.17440.75098.8253725.210.382812023.12912748.33920.916782.17440.75099.2458759.77140.420212596.11713355.88910.958382.17440.75099.6654794.250.459213167.73113961.9810182.17440.750910.086828.81140.513740.71914569.531(c.)各集中力对各截面的力矩M3拱上空腹段的腹孔和横隔板等各集中力及其相应的横坐标lx。在前面已经求出，各竖向集中力到截面的力臂a=l·ξi/2-lx(取a>0)，产生的力矩M'3=Pa；腹拱水平推力H'g作用在第7与第8截面之间，对0~7截面产生的力矩M"3=H'g(y1-e)。具体计算见下表。表2-4-6各集中力对各截面的力矩计算表截面竖向力p1p2p3腹拱水平力合计M3P=11.134211.134211.13421309.7662lx=10.215.821.40.2483ξMMM240.04170230.08330220.1250210.16670200.20830190.250180.2917128.7244128.7244170.291128.4089128.4089160.3333147.4764147.4764150.375166.2734166.273140.416774.2662185.0704259.3367130.458393.0182203.8224296.8406120.5111.8152222.6194334.4346110.5417130.6122241.4165372.0287100.5833149.3642260.1684409.532690.625168.1612278.9654447.126680.6667186.9582124.6067297.7625609.327470.7083205.7102143.3587316.5144665.583360.75224.5072162.1557335.3114721.974450.7917243.3043180.9527354.1085778.365540.8333262.0562199.7047372.8604834.621330.875280.8532218.5017391.6575891.012420.9167299.6503237.2987174.9472410.45451122.350710.9583318.4022256.0507193.6992429.20641197.358501337.1992274.8477212.4962448.00351272.5466(d.)计算偏离弯矩Mp上部结构恒载对拱圈各截面重心的弯矩：Mi=M1+M2+M3压力线的纵坐标：yi=Mi/Hg式中，Hg为不计弹性压缩的恒载水平推力：Hg=∑Mj/f=300494.9139/16.193=18557.0876kN各截面上“恒载压力线”偏离拱轴线的值：Δy=y1-yi偏离弯矩具体数值见表2-4-7。表2-4-7偏离弯矩计算表截面号主拱圈拱上实腹段集中力合计“恒载压力线”拱轴线偏心偏离弯矩M1M2M3Mi=M1+M2+M3y2=M2/Hgy1Δy=yl-y2Mp=HgΔy1234567892400000000230141.18110141.18110.00540.0230.0176327.043622442.3324564.576801006.90920.07270.0920.0193358.251211307.15111275.856102583.00720.15740.20740.05927.8566202617.79792280.426204898.22410.35950.36960.0101187.6686194386.75143583.341607970.0930.49530.57940.0841559.6035186595.31385201.9073128.724411925.94560.72620.83760.11142066.3641179265.40537146.9739128.408916540.78810.91971.14530.22564186.25171612368.56074856.0245147.476417372.06161.39151.5040.11252087.51971515974.20125463.5739166.273421604.04851.79211.9150.12292280.09331420048.73096071.1234259.336726379.1912.16932.38020.21093913.98051324620.74046677.2158296.840631594.79682.57242.90170.32926109.34941229703.98957284.7652334.434637323.18933.15923.48150.32235980.58871135309.48477892.3147372.028743573.82813.72314.12230.39917406.43341041451.49738498.4071409.532650359.4374.39924.82670.42747931.6137948145.16419105.9566447.126657698.24745.26475.59780.33316181.0838855410.2819713.506609.327465733.11446.10566.43890.33336184.5414763280.835110319.5984665.583374266.01687.03537.35360.31845908.278671802.404410927.1479721.974483451.52678.09858.3460.24744591.3254580960.333711534.6973778.365593273.39659.29579.42010.12432307.5732490800.416612140.7898834.6213103775.827710.513410.58060.06731248.29543101365.334512748.3392891.0124115004.686111.917411.8326-0.0848-1573.19182112681.714413355.88861122.3507127159.953713.326513.1814-0.1452-2693.64331124756.231913961.98111197.3585139915.571514.863614.6328-0.2308-4282.81920137699.11914569.53051272.5466153541.196116.527916.193-0.3349-6214.6835(2)偏离弯矩Mp在弹性中心产生的赘余力赘余力各项的计算见表2-4-8。表2-4-8偏离弯矩Mp在弹性中心产生的赘余力计算表截面Δycosφ1/cosφΔy/cosφys-y1(ys-y1)Δy/cosφ12345672401105.12470230.01760.99961.00040.01765.10170.0898220.01930.99851.00150.01935.03270.0973210.050.99661.00340.05024.91730.2467200.01010.9941.00610.01024.75510.0483190.0840.99051.00960.08484.54530.3855180.11140.98621.0140.1134.28710.4842170.22560.98111.01930.233.97940.9151160.11250.9751.02560.11543.62070.4178150.12290.96791.03310.1273.20970.4075140.21090.95991.04180.21972.74450.603130.32920.95071.05190.34632.2230.7697120.32230.94041.06340.34271.64320.5631110.39910.9291.07650.42961.00240.4306100.42740.91631.09130.46640.2980.13990.33310.90241.10820.3691-0.4731-0.174780.33330.88721.12720.3757-1.3142-0.493770.31840.87071.14850.3657-2.2289-0.815160.24740.85291.17250.2901-3.2213-0.934450.12430.83391.19920.1491-4.2954-0.640340.06730.81361.22910.0827-5.4559-0.45133-0.08480.79221.2623-0.107-6.70790.71812-0.14520.76971.2992-0.1886-8.05671.51991-0.23080.74621.3401-0.3093-9.50812.94090-0.33490.72191.3852-0.4639-11.06835.1347Σ27.70933.135612.4017由以上数据可得ΔX1=-(3.135553602×18557.0876)/27.7093=-2099.898682kN·mΔX2=-（2×12.4017×1.059×18557.0876）/((0.0106201+1)×16.1932×80.97×0.099621)=-228.0338898kN(3)“恒载压力线”偏离拱轴线的附加内力“恒载压力线”偏离拱轴线在拱圈任意截面中产生的附加内力为:ΔM=ΔX1-ΔX2(ys-y1)+Mp；ΔN=ΔX2cosφ；ΔQ=ΔX2sinφ拱顶、l/4截面、拱脚三个截面的附加内力见下表:表2-4-9压力线”偏离拱轴线的附加内力计算表项目拱顶截面l/4截面拱脚截面cosφ10.940420.72191sinφ00.340010.69198y=ys-y15.124661.07641-11.06834ΔN=ΔX2cosφ-228.03389-214.447631-164.619945ΔQ=ΔX2sinφ0-77.5338029-157.794891Mp07406.4334-6214.6835ΔX1-2099.89868-2099.89868-2099.89868ΔM=ΔX1-ΔX2y+Mp-931.3025285551.992677-10838.5388(4)空腹式无铰拱的恒载压力线空腹式无铰拱桥在恒载作用下考虑压力线与拱轴线的偏离以及恒载弹性压缩的影响之后，拱中任意截面存在三个内力这三个力的合力作用点的偏心距为ei=Mg/Ng，则空腹式无铰拱桥恒载压力线的纵坐标y=y1-ei/cosφ空腹式无铰拱恒载压力线的纵坐标值见表2-4-10。表2-4-10空腹式无铰拱的恒载压力线计算表截面y1ys-yΔyMg/HgcosφNg/Hge1=Mg/Ngy=y1-e1/cosφ0123456782405.124700.006710.97660.0069-0.0069230.0235.10170.01760.00620.99960.9770.00630.0167220.0925.03270.01930.00450.99850.97810.00460.0873210.20744.91730.050.00180.99660.98010.00190.2055200.36964.75510.0101-0.00190.9940.9828-0.0020.3716190.57944.54530.084-0.00690.99050.9864-0.0070.5864180.83764.28710.1114-0.01290.98620.9909-0.0130.8508171.14533.97940.2256-0.02010.98110.9964-0.02021.1659161.5043.62070.11250.37060.9751.00280.36961.1249151.9153.20970.1229-0.03810.96791.0105-0.03771.9539142.38022.74450.2109-0.0490.95991.0194-0.0482.4303132.90172.2230.3292-0.06120.95071.0296-0.05942.9642123.48151.64320.3223-0.07470.94041.0414-0.07183.5578114.12231.00240.3991-0.08970.9291.0547-0.08514.2139104.82670.2980.4274-0.10620.91631.0699-0.09934.93595.5978-0.47310.3331-0.12420.90241.0871-0.11435.724486.4389-1.31420.3333-0.14390.88721.1064-0.13016.585577.3536-2.22890.3184-0.16530.87071.1281-0.14657.521968.346-3.22130.2474-0.18850.85291.1525-0.16368.537859.4201-4.29540.1243-0.21360.83391.1797-0.18119.6373410.5806-5.45590.0673-0.24080.81361.2101-0.19910.8251311.8326-6.7079-0.0848-0.270.79221.2438-0.217112.1067213.1814-8.0567-0.1452-0.30160.76971.2812-0.235413.4872114.6328-9.5081-0.2308-0.33550.74621.3227-0.253714.9728016.193-11.0683-0.3349-0.3720.72191.3683-0.271916.56963.空腹无铰拱的实际恒载内力空腹式无铰拱的实际恒载内力等于计人拱轴系数m的偏差影响的内力与“压力线”及拱轴线偏离的附加内力之和，其结果见表2-4-11。表格SEQ表格\*ARABIC2-4-11空腹无铰拱的实际恒载内力计算表截面拱顶截面l/4截面拱脚截面项目恒载内力附加内力合计恒载内力附加内力合计恒载内力附加内力合计水平力Hg18549-2281832117240-2281701217241-22817013轴力Ng17929-2281770117786-2141757223146-16522981弯矩Mg898-931-3431155525863-2499-10839-133382.4.2活载内力计算1.公路-I级和人群荷载内力车道荷载的均布荷载标准值采用10.5KN/m，计算剪力时，所加集中力荷载P采用360KN人群荷载K2=2·b·g人=2×0.75×3.5=5.25kN不计弹性压缩的公路-I级及人群荷载内力见表2-4-11。表2-4-12不计弹性压缩的公路-I级及人群荷载内力计算表截面项目公路-I级人群荷载合计影响线面积力或力矩车道荷载集中荷载（Ⅲ）-14（51）值乘数面积拱顶截面Mmax36.753605.254020.0069l26556.140945.368518238.135相应H136.753605.254020.0678l2/f404.87527.466711041.622Mmin36.753605.25402-0.0046l26556.1409-30.4205-12229.04相应H136.753605.254020.0601l2/f404.87524.32499778.6058l/4截面Mmax36.753605.254020.0088l26556.140957.497423113.937相应H136.753605.254020.0401l2/f404.87516.22336521.7832Mmin36.753605.25402-0.0102l26556.1409-67.0693-26961.87相应H136.753605.254020.0879l2/f404.87535.572314300.072拱脚截面Mmax36.753605.254020.0198l26556.1409130.008352263.326相应H136.753605.254020.0917l2/f404.87537.114914920.186相应V汽车36.75360396.750.5l80.9740.48516062.424人群3605.25365.250.331616.1935.36961961.246Mmin36.753605.25402-0.0146l26556.1409-95.8508-38532.01相应H136.753605.254020.0363l2/f404.87514.67675900.041相应V汽车36.75360396.750.5l80.9740.48516062.424人群5.255.250.331616.1935.369628.1904计弹性压缩的公路-I级及人群荷载内力见表2-4-13:。表2-4-13考虑弹性压缩的汽车和人群荷载内力计算表项目拱顶截面l/4截面拱脚截面MmaxMminMmaxMminMmaxMmincosφ10.94040.7219sinφ00.340.692与M相应的H111041.62159778.60586521.783214300.071714920.18635900.041与M相应的V18023.669816090.6142N=H1cosφ+Vsinφ11041.62159778.605868.7981150.851112592.840911182.161ΔH=μ1H1/(1+μ)122.5556108.536972.388158.7225165.605565.4871ΔN=ΔHcosφ122.5556108.536968.0752149.2659119.552247.2758Np=N-ΔN10919.06599670.06890.7231.585212473.288711134.8853M18238.135-12229.038523113.937-26961.867252263.3262-38532.0135y=ys-y15.12471.0764-11.0683ΔM=ΔHy628.0559556.214677.9192170.8505-1832.9775-724.8329Mp=M+ΔM18866.1909-11672.823923191.8562-26791.016750430.3487-39256.84642.5温度变化、混凝土收缩、徐变的内力计算温度变化为其它可变荷载，混凝土收缩、徐变为永久荷载，似乎要分项计算，但考虑到习惯和可能，还是将三者一起计算。拱圈合拢温度7℃月平均最低气温2℃月平均最高气温30℃拱圈材料弹性模量E=3.25×104MPa拱圈材料线胀缩系数a=0.000010=1×10-5混凝土收缩作用按下降10℃温度的影响计入。混凝土徐变作用的影响：当计算温度内力时以β=0.7；当计算混凝土收缩内力时以β=0.45的系数计入。因此，计算降低温度时Δt=0.7×(2-7)+0.45×(-10)=-8℃计算升高温度时Δt=0.7×(30-7)+0.45×(-10)=11.6℃温度变化、混凝土徐变和收缩在弹性中心产生的水平力Ht=α·EI·Δt/{[(表(III)-5值]×(1+µ)f2}=1×10-5×3×107×1.551Δt/(0.088588×1.0106201×16.1932)=19.8205Δt温度变化、混凝土徐变和收缩的内力见表2-5-1。表2-5-1温度变化、混凝土收缩、徐变内力计算表项目温度上升温度下降拱顶截面l/4截面拱脚截面拱顶截面l/4截面拱脚截面Δt11.6-8Ht229.9178-158.564cosφ10.94040.721910.94040.7219y=ys-y15.12471.0764-11.06835.12471.0764-11.0683Nt=Htcosφ229.9178216.2147165.9777-158.564-149.1136-114.4674M=-Hty-1178.2597-247.48352544.7992812.5929170.6783-1755.03392.6主拱圈正截面强度验算根据桥规(JTJD60-2004)的规定，构件按极限状态设计的原则是：荷载效应不利组合的设计值小于或等于结构抗力效应的设计值。即或式中：承载能力极限状态下作用几本基本组合的效应组合设计值；结构重要性系数，对于公路-Ⅰ级标准采用1.1的安全系数；第i个永久作用效应的分项系数，按照JTGD60-2004的表4.1.6采用；第i个永久作用效应的标准值和设计值；汽车荷载效应分项系数，取用1.4；汽车荷载效应的标准值和设计值；在作用效应组合中除去汽车荷载效应和风荷载以外的其他第i个可变作用效应的分项系数，取用1.4在作用效应组合中除去汽车荷载效应外的其他第j个可变作用效应的标准值和设计值；在作用效应组合中，除汽车荷载效应外的其他可变作用效应的组合系数，当永久作用与汽车荷载和人群荷载组合时，人群荷载的组合系