空腹式等截面悬链线箱形无铰拱桥设计

1、 桥梁工程课程设计 专 业： 交通工程 学 号： 姓 名： 指 导 教 师： 时 间 ： 2013年6月 南京工业大学交通学院二O一三年六月桥梁工程课程设计任务书一、 设计题目空腹式等截面悬链线箱形无铰拱桥设计二、 设计资料1. 设计标准设计荷载：公路I级，人群荷载3.5桥面净空 净人行道+安全带净跨径；净失高；净跨比 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）；材料容重主拱圈材料容重（包括横隔板、施工超重） 拱上立柱（墙）材料容重 腹空拱圈材料容重 腹孔拱上填料容重钢筋混凝土简支板材料容重主拱圈实腹段填料容重人行道板及栏杆重混凝土材料：强度等级为C40，主要强度指标

2、为：强度标准值 强度设计值 弹性模量 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 抗拉强度设计值 弹性模量 相对界限受压区高度 2)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 抗拉强度设计值 弹性模量 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57m左右，拱脚至拱顶布置46跨左右 (主拱圈的具体几何参照指导书实例修改自定)。3设计计算依据交通部部颁标准公路桥涵设计通用规范(JTG D602004) 交通人民出版社 交通部部颁标准公路钢筋混凝土及

3、预应力混凝土桥涵设计规范(JTG D622004) 交通人民出版社 交通部部颁标准公路圬工桥涵设计规范(JTG D61-2005) 交通人民出版社 公路设计手册-拱桥(上) 人民交通出版社，2000.7三、 主拱圈截面几何要素的计算（一） 主拱圈横截面设计 拱圈截面高度按经验公式估算 拱圈由6个各为1.5m宽的拱箱组成，全宽 （二） 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： 四、 确定拱轴系数（一） 上部结构构造布置1. 主拱圈假定,相应的,查拱桥（上册）表-20（6）得： 主拱圈的计算跨径和计算失高： 拱铰

4、截面的水平投影和竖向投影： 将拱轴沿跨径24等分，每等分长,每等分点拱轴线的纵坐标，相应的拱背面坐标：,拱腹曲面坐标，具体数值见下表：截面号035.443846114.175130.730570.8897160.88971613.2854132515.06484575132.490192170.81792911.594250.775040.8386660.83866610.7555831112.43291589229.536538330.6594589.3479030.816220.7963540.7963548.5515486261058288450.5222847

5、.4034430.853470.7615970.7615976.641846568.165040111423.629230670.4044165.7326490.886390.7333120.7333124.999337656.465960694520.675576830.304144.3112240.91480.7105380.7105383.6006860645.021761709617.7219230.223.1185280.938720.6924320.6924322.4260962423.810960738714.768269170.1507742.1372410.95830.678

6、2840.6782841.4589565132.815525437811.814615330.0954561.3531010.97380.6674880.6674880.6856129712.02058935298.86096150.0532430.7547260.985490.659570.659570.0951560541.414296786105.9073076670.0235210.3334130.993630.6541670.654167-0.320753820.987580265112.9536538330.0058590.0830520.998420.6510290.651029

7、-0.567976540.7340807091200010.650.65-0.650.652.拱上腹孔布置从主拱两端起拱线起向外延伸3m后向跨中对称布置5对圆弧小拱，腹拱圈厚d=0.35m，净跨径l0=4.8m，净矢高f0=0.8m，座落在宽为 0.5m的钢筋混凝土排架式腹拱墩支承的宽为 0.6m的钢筋混凝土盖梁上。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 h=y1+y上(1-1/cos) - (d+f0)，分别计算如表项目1号立柱32.50.916943381.32553311.602180.8155831.29041710

8、.263410072号立柱27.10.764589711.105297.7232510.6268611.1802356.4560981673号立柱21.70.612236040.8850484.7772190.4686691.1043783.5593734994号横墙16.30.459882370.6648062.6206050.3333031.0540831.4354510285号腹拱座11.0950.313030360.4525161.1905360.2182571.0235410.025234161空、实腹段分界线10.990.310067930.4482341.1677340.2160

9、551.0230740.002736639由f0/l0=1/8，查拱桥(上册)表3-2得 sin0=0.6，cos0=0.8，0=36.870腹拱拱脚的水平投影和竖向投影 x=dsin0=0.350.6=0.21m； y=dcos0=0.350.8=0.28m（二）上部恒载计算1、桥面系栏杆：g=52kN/m2、主拱圈恒载3、拱上空腹段恒载腹拱圈外弧跨径 腹拱圈内弧半径腹拱圈重 腹拱侧墙护拱重填料及路面重两腹拱之间起拱线以上部分重力一个腹拱重力： 腹孔下部盖梁重力底梁重力1号立柱重力2号立柱重力3号立柱重力4号横墙重力5号腹拱座重力腹孔集中力拱上实腹段的荷载拱顶填料及桥面系重悬链线曲边三角形腹

10、拱推力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 查拱桥(上册)表(I)-4得 腹拱拱脚推力作用线的纵坐标如图所示，其距x轴的偏心距为： 腹拱推力对各截面重心产生的力矩：验算拱轴系数恒载对l/4截面和拱脚截面的力矩见下表：项目集中力编号重力l/4截面拱脚截面力臂力矩力臂力矩主拱圈P0-125281.0196321411.4988790.26横隔板P1-14P15P0 中接头拱脚段拱上空腹段P131876.91266002.9438465525.342P141781.729

11、86008.34384614866.48P151709.311740013.7438523492.52P161655.268951.4219232353.66519.1438531688.21P17720.5573176.6269234775.07824.3488517544.74实腹段P181625.640812.2269219876.5829.9488548686.07P19827.1439859.4702497833.2627.1921722491.84腹拱推力F799.3023742.7585282204.89813.8151311042.4715147.0515477.5849584

12、54.97264127.9五、拱圈弹性中心及弹性压缩系数1 弹性中心 弹性压缩系数 六、主拱圈截面内力计算(一)结构自重内力计算 (1)假载内力a.求假载 b.假载内力假载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下表项目影响线面积力或力矩表值乘数拱顶截面M0.001985025.0659.949628183.1262H0.12742354.498745.17022831.373l/4M-0.001245025.065-6.23108-114.685H0.12742354.498745.17022831.373拱脚截面M0.00445025.06522.11029

13、406.9472H0.12742354.498745.17022831.373V0.270.8876914.17754260.9423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下表项目拱顶截面l/4拱脚截面 10.938720.73057 00.3446810.682838831.3730275831.373831.373 260.9423 9.7158817469.7158829.715882 821.6571458875.2952778.4593 183.1262302-114.685406.9472 4.80810471.689576-9.36702 229.8412069-98

14、.2694315.9383(2)“拱轴线恒载”内力 a.推力 b.考虑弹性压缩的内力考虑弹性压缩的“拱轴线恒载”内力见下表项目拱顶截面l/4拱脚截面 10.938720.7305717817.6096417018.3117018.3117609.3832716819.4216819.42 17817.6096418129.2723294.56 208.2263708186.6976145.2996 17609.3832717942.5723149.26 4.80810471.689576-9.36702 1001.174192336.0318-1862.96(3)考虑确定m系数偏差影响的恒载内

15、力考虑m系数偏差影响的恒载内力等于“拱轴线m的恒载”内力加上“假载”的内力，计算结果见下表拱顶截面l/4拱脚截面拱轴线恒载假载合计拱轴线恒载假载合计拱轴线恒载假载合计水平力17817.60964831.37302818648.9817018.30727831.373027517849.6817018.31831.37317849.68轴力17609.38327821.65714618431.0417942.57127875.29523818817.8723149.26778.459323927.72弯矩1001.174192229.8412071231.015336.0318449-98.26

16、939119237.7625-1862.96315.9383-1547.032.“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。 (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在这里，对于所要

17、求的每一等分点而言，积分上限为常数，并不计等式前面的负号，则上式为：式中：可根据值从拱桥(例集)附表1-1查得； 可根据值从拱桥(例集)附表1-2查得 主拱圈对各截面的力矩M1的值见下表截面号S1S2*S1-S2M11200000110.0833333330.083870.0037570.003233548.2189100.1666666670.167043330.0142830.0135582299.390.250.251210.031480.0313235312.16980.3333333330.336296670.57574-0.46364-78631.770.4166666670.42

18、2546670.091570.08449114329.3960.50.510310.12890.12625521412.3450.5833333330.60030.1779702740.6666666670.749440.235840.26378744737.1530.750.788460.30330.28804548851.2620.8333333330.888453330.382830.35754860638.6510.9166666670.993206670.4745870.43585373918.86011.103670.580130.5235488790.2

19、6b.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： 对实腹段里每个截面的力矩： 对空腹段里每个截面的力矩： 各截面的力矩见下表区间截面号悬链线曲边三角形矩形块M2kP M实腹段12000000000110.083333330.12046715.908170.750060.73823511.743965820.003472222645.2323656.9763100.166666670.240933127.54270.7502421.4

20、75399188.17636390.0138888892580.9292769.10690.250.3614432.02070.7505432.210427954.95030620.031255807.0916762.041分界点0.310067930.448234827.1440.750835l/2*0空腹段80.33333333827.1440.7508353.5629422947.0656490.05528491610273.4213220.4970.41666667827.1440.7508356.5165955390.1626520.081123911507520465.1760.5

21、827.1440.7508359.4702497833.2596550.10696290519876.5827709.8450.58333333827.1440.75083512.423910276.356660.13280189924678.1734954.5240.66666667827.1440.75083515.3775612719.453660.15864089329479.7542199.230.75827.1440.75083518.3312115162.550660.18447988734281.3349443.8820.83333333827.1440.75083521.28

22、48617605.647670.21031888239082.9156688.5510.91666667827.1440.75083524.2385220048.744670.23615787643884.4963933.2301827.1440.75083527.1921722491.841670.2619968748686.0771177.91 (b)悬链线曲边三角形块从拱顶到任意截面的重力(参见上表) 每一块Pi的重心的横坐标： 在实腹段里，截面重心到任意截面的力臂为，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。每个截面的力矩见上表c.各集中力对各截面的力矩M3拱上空腹段的腹

23、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，产生的力矩；腹拱水平推力Hg作用在第7与第8截面之间，对07截面产生的力矩 。具体计算见下表。截面号竖向力P17P16P15P14P13腹拱推力合力P720.5573171655.2691709.3121781.731876.913F1015.919212lx11.09516.321.727.132.5e0.172603474MMMMMy1MM3120000000110.083333333000000100.16666666700000090.2500000080.333333333518.5240940000

24、518.524170.4166666672646.8009800002.1372409751420.5529314067.35460.54775.077862353.6650003.118528492204.8983719333.64150.5833333336903.354747242.7560004.3112238863158.22263217304.3340.6666666679031.6316212131.853297.657005.7326491724294.37123828755.5130.7511159.908517020.948346.372007.4034433365629.

25、84097942157.0620.83333333313288.185421910.0313395.094341.25309.347902557184.05184560118.6110.91666666715416.462326799.1218443.89603.866011.59424958979.56229379242.820117544.739231688.2123492.5214866.485525.34214.175129511042.46581104159.8d.计算偏离弯矩Mp上部结构恒载对拱圈各截面重心的弯矩：压力线的纵坐标： 式中，Hg为不计弹性压缩的恒载水平推力： 各截面上

26、“恒载压力线”偏离拱轴线的值：i偏离弯矩具体数值见下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M1M2M3Myiy1yMp120000000011548.2188748656.97625501205.1950.064680.0830520.018371989342.3288137102299.3003812769.1055205068.4060.272010.3334070.0613974791144.03107195312.1688186762.0409012074.210.6479950.7547130.1067183311988.5032478-78631.73354

27、13220.4902518.5241-64892.7-3.482641.3530774.83571786490104.86413714329.393720465.16744067.35438861.912.0856282.1372030.05157468961.0009636621412.3353527709.84459333.64158455.823.1371883.118474-0.01871356-348.6932838529205.2687834954.521717304.3381464.124.371994.311148-0.06084152-1133.671713444737.14

28、75942199.198928755.51115691.96.2089125.732548-0.47636392-8876.180808348851.2624249443.876142157.06140452.27.5377427.403313-0.13442889-2504.839449260638.6513256688.553360118.61177445.89.5231039.347738-0.17536483-3267.606796173918.8613863933.230579242.82217094.911.6509811.59405-0.05692724-1060.7362730

29、88790.2582271177.9076104159.8264127.914.1751314.17488-0.0002495-4.648981647(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下表。 截面 12010.504.808020110.0183719890.998421.0015830.0184014.7250530.086946100.0613974790.993631.0064110.0617914.4746980.27649690.1067183310.985491.0147240.108294.0533920.4389484.8357178640.97381.

30、0269054.9658223.45502817.1570570.051574680.95831.0435150.0538192.6709020.1437456-0.0187135550.938721.06528-0.019941.689631-0.033685-0.0608415160.91481.093135-0.066510.496957-0.033054-0.4763639180.886391.128172-0.53742-0.924440.4968153-0.134428890.853471.171687-0.15751-2.595210.4087682-0.1753648340.8

31、16221.22516-0.21485-4.539630.975341-0.0569272410.775041.290256-0.07345-6.785950.4984330-0.00024950.730570.684397-0.00017-9.366780.00159913.251224.1382820.4174由上表1得 (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 拱顶、l/4截面、拱脚三个截面的附加内力见下表。项目拱顶截面l/4拱脚截面 10.938720.73057 00.3446810.682838 4.80810471.6895

32、76-9.367021564.4309821468.5631142.9260539.22911068.2530-348.693-4.64898-5819.037087-5819.04-5819.04 -13340.98504-8810.968830.378 (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 所以，空腹式无铰拱桥恒载压力线的纵坐标空腹式无铰拱恒载压力线的纵坐标值见下表截面 1204.808104700.04508410.9936650.045371572-0.0453

33、71572110.0830524.72505270.0183720.062930.998420.9952580.0632298650.019722074100.3334074.47469770.0613970.1043690.993631.0001160.1043573630.22838061990.7547134.05339170.1067180.1470210.985491.0084810.1457850280.60678148681.3530773.45502774.8357184.872230.97381.0207364.773252643-3.54859956972.1372032.

34、67090170.0515750.083120.95831.0374440.0801196632.05359696563.1184741.6896307-0.018710.0066150.938721.0593340.0062445443.1118218154.3111480.4969567-0.06084-0.043070.91481.08734-0.039609054.3544460445.732548-0.9244433-0.47636-0.46760.886391.122556-0.416545236.20248248537.403313-2.5952083-0.13443-0.136

35、240.853471.166281-0.116819867.54018934829.347738-4.5396333-0.17536-0.18950.816221.219989-0.155328119.538039775111.59405-6.7859453-0.05693-0.085290.775041.285346-0.0663567611.67966721014.17488-9.3667753-0.00025-0.044960.730571.364166-0.0329602314.219995773.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“

36、压力线”及拱轴线偏离的附加内力之和，其结果见下表截面项目拱顶截面l/4拱脚截面拱轴线恒载假载合计拱轴线恒载假载合计拱轴线恒载假载合计水平力Hg18648.982671564.4309820213.4117849.680291564.43098219414.1117849.681564.43119414.11轴力Ng18431.040421564.4309819995.4718817.866511468.56265120286.4323927.721142.92625070.65弯矩Mg1231.015399-13340.985-12110237.7624538-8810.955741-8573

37、.19-1547.038830.3787283.353(二)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 桥梁基频：不计弹性压缩的公路-I级及人群荷载内力见下表截面项目公路I级人群荷载影响线面积车道荷载集中荷载表值乘数面积拱顶截面Mmax10.53605.250.00665025.06487733.16543相应H110.53605.250.06536354.498692723.17003Mmin10.53605.25-0.004965025.064877-24.9243相应H110.53605.250

38、.06167354.498692721.86193L/4截面Mmax10.53605.250.008975025.06487745.07483相应H110.53605.250.04054354.498692714.37138Mmin10.53605.25-0.0015025.064877-5.02506相应H110.53605.250.0865354.498692730.66414拱脚Mmax10.53605.250.018615025.06487793.51646相应H110.53605.250.08977354.498692731.82335相应V汽10.53600.1640170.887

39、69211.6262911.62608人0.1640170.88769211.6262911.62608Mmin10.53605.25-0.014945025.064877-75.0745相应H110.53605.250.03726354.498692713.20862相应V汽10.53600.3359970.88769223.8175623.81713人0.3359970.88769223.8175623.81713接上表：影响线纵坐标汽车力或力矩人群力或力矩表值乘数0.051770.887691750.979174.11850.232435.00085694.817121.6427-0.0

40、12270.88769-601.696-130.8530.12195.00085471.458114.77520.0595870.887692093.429236.64290.136325.00085416.13375.44973-0.0286370.88769-822.558-26.38160.206395.00085728.2155160.98670.0513970.887692408.042490.96140.197315.00085723.8317167.07260.707141448.93860.70714161.03802-0.0613170.88769-2470.53-394.1

41、410.062875.00085264.469569.345260.938261688.18330.938261125.0422计人弹性压缩的公路-I级及人群荷载内力见下表项目拱顶截面人群L/4MmaxMminMmaxMminMmaxMmincos11110.938720.93872sin00000.3446810.344681与M相应的H1694.8169837471.457979121.6427114.7752416.133728.2155与M相应的VN694.8169837471.457979121.6427114.7752390.6324683.5905H8.1200128295.50

42、9716841.4215831.3413254.8631598.510326N8.1200128295.509716841.4215831.3413254.5651457.988813Np686.6969709465.948262120.2211113.4338386.0672675.6016M1750.978655-601.69633174.1185-130.8532093.429-822.558y4.80810474.80810474.8081054.8081051.6895761.689576M39.0418718526.49129546.8351216.4492338.21667814

43、.37884Mp1790.020527-575.20503180.9536-124.4032101.645-808.179接上表人群拱脚截面人群MmaxMminMmaxMmin0.938720.938720.730570.730570.730570.730570.3446806660.3446806660.6828380.6828380.6828380.68283875.44972927160.9867188723.8317264.4695167.072669.34526448.9386688.183361.03802125.042270.82616986151.1214527835.3619

44、663.1311163.7373136.04510.8817469691.8813792028.4590953.0907361.9525020.8104070.8277135151.7660882846.1799612.2579991.4264390.59205969.99845634149.3553644829.182660.8731162.3108135.453236.6428677-26.38159062408.042-2470.53490.9614-394.1411.689576211.68957621-9.36702-9.36702-9.36702-9.367021.48977870

45、33.178733542-79.2365-28.951-18.2891-7.5911238.1326464-23.202857062328.806-2499.48472.6723-401.732(三)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 拱圈材料线胀缩系数 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；当计算混凝土收缩内力时以的系数计入。 因此，计算降低温度时 计算升高温度时 温度变化、混凝土徐变和收缩在弹性中心产生的水平力 温度变化、混凝土徐变和收缩的内力见下表。项目温度上升温度下降拱顶截面L/4拱