空腹式等截面悬链线箱形无铰拱桥课程设计说明书

1、桥梁工程课程设计桥梁工程课程设计任务书设计题目空腹式等截面悬链线箱形无铰拱桥设计1.设计资料设计标准设计荷载：公路I 级，人群荷载3.5 kN / m2桥面净空 净 8+2 （ 0.75m+0.25m） 人行道+安全带f0/L0:1/ 5净跨径L0 : 70m ；净失高 f0 :14m ；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）hd 0.5m ； 材料容重3 1=22.0kN /m33主拱圈材料容重（包括横隔板、施工超重）2 =25.0 kN /m3拱上立柱（墙）材料容重2 =25.0 kN / m3腹空拱圈材料容重3=23kN / m3腹孔拱上填料容重4=

2、22kN / m33钢筋混凝土简支板材料容重2 =25 kN / m33主拱圈实腹段填料容重1=22kN / m3人行道板及栏杆重52.0kN / m3混凝土材料：强度等级为 C40 ，主要强度指标为：强度标准值fck26.8MPa , ftk 2.65MPa强度设计值fcd 18.4 MPa, ftd 1.65 MPa4弹性模量 Ec 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fsk400MPa抗拉强度设计值fsd330MPa弹性模量Es52.0 105相对界限受压区高度0.53,pu0.19852) 箍筋及构造钢筋采用 HR

3、B335钢筋，其强度指标为抗拉强度标准值fsk335MPa抗拉强度设计值fsd280MPa5 弹性模量Es2.0 105 MPa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 D60 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 (JTG D62 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 (JTG D

4、61-2005) 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H 也 a）K （0.6 及）1.3mb100拱圈由6个各为1.5m宽的拱箱组成，全宽B0 9.0m12A (1300 200 2 1100 150 2 250 100 4) 6/10002 5.4m2绕箱底边缘的静面矩C13001300S 1300 1500(1300 150 2) (1500 200 2)2 210010093100 250 (1300 150 )100 250 (150 )6/103.51m3 3主拱圈截面重

5、心轴：S 3.51 一 一一 一 y下 0.65m, y上=1.3 0.65 0.65mA 5.4主拱圈截面绕重心轴的惯性矩：113 913Ix 9 1.33 9 1.3 (0.65-)21.1 (1.3 2 0.15)6122121.3 2136 1.1 (1.3 2 0.15) (0.65)12 (0.10.25 0.5 0.1 0.25)2 36.159m4_221_3_12(0.65 0.15 0.1)0.25 0.10.5 0.25 0.1 (0.65 0.15 0.1)13 363拱圈截面绕重心轴的回转半径：r 或 0.463m四、确定拱轴系数（一） 上部结构构造布置假定 m 2.

6、24,相应的 2 0.22, f0 1,查拱桥（上册）表-20 （6）flo 5得： sin j 0.68284,cos j 0.73057, j 43.070主拱圈的计算跨径和计算失高：l 10 2 y下 sin j 70 2 0.65 0.68284 70.888mff0 y下（1 cos j） 14 0.65 （1 0.731） 14.175m拱较截面的水平投影和竖向投影：x Hsin j 1.3 0.663 0.888my H cos j 1.3 0.731 0.9497m将拱轴7目跨径24等分，每等分长= 2.92m,每等分点拱轴线的纵坐标24yy 表（）1值f ,相应的拱背面坐标：

7、y y，拱腹曲面坐标cosy1yy1，cos具体数值见下表:截面号xy1 / fy1cosy上 / cosy下 / cosy y上 / cosy1 y 下 /cos035.443846114.175130.730570.8897160.88971613.2854132515.06484575132.490192170.81792911.594250.775040.8386660.83866610.7555831112.43291589229.536538330.6594589.3479030.816220.7963540.7963548.551548626105828

8、8450.5222847.4034430.853470.7615970.7615976.641846568.165040111423.629230670.4044165.7326490.886390.7333120.7333124.999337656.465960694520.675576830.304144.3112240.91480.7105380.7105383.6006860645.021761709617.7219230.223.1185280.938720.6924320.6924322.4260962423.810960738714.768269170.1507742.13724

9、10.95830.6782840.6782841.4589565132.815525437811.814615330.0954561.3531010.97380.6674880.6674880.6856129712.02058935298.86096150.0532430.7547260.985490.659570.659570.0951560541.414296786105.9073076670.0235210.3334130.993630.6541670.654167-0.320753820.987580265112.9536538330.0058590.0830520.998420.65

10、10290.651029-0.567976540.7340807091200010.650.65-0.650.652.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l'0=4.8m ,净矢高f'0=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 艮 以及各墩中线自主拱拱背到腹拱起拱线的高度h=yi+y上X(1-1/cosh-(d'+ f0),分别计算如表k ln(m , m2 1) 1.144

11、56项目lx2lx/lky1tan1/ cosh1号立柱32.50.916943381.32553311.602180.8155831.29041710.263410072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11.0950.313030360.4525161.19

12、05360.2182571.0235410.025234161空、实腹段分界线10.990.310067930.4482341.1677340.2160551.0230740.002736639由f'o/l'0=1/8 ,查拱桥（上册）表3-2得sin M=0.6 , cos M=0.8 ,如=36.87 0腹拱拱脚的水平投影和竖向投影x'=d' x sin（j）0=0.35 X0.6=0.21m; y'=d' x cos 40=0.3 5X 0.8=0.28m（二）上部恒载计算1、桥面系栏杆：g=52kN/m拱顶填料及沥青表处面层重力=22k

13、N / m3l外 10 2d sin 0 4.8 2 0.35 0.6 5.22m腹拱圈内弧半径102sin 04.82 0.64m腹拱圈重Pa2 0Rd 3B0 2 36.87/180 5.22 0.35/ 2 0.35 23 9 389.28kN腹拱侧墙护拱重2Pb2sin 0 sin 0cos 00 R 4B02 0.6 0.6 0.8 36.87/18025.22 0.35/222 9 264.077kN填料及路面重PC l外hd 1B05.22 0.747 22 9 772.1424kN两腹拱之间起拱线以上部分重力 ''.'''Pd0.6 x

14、y 2f0 d y 4 hd 1 0.6 2x B00.6 0.210.28 250.6 0.35 0.28 22 0.747 220.6 2 0.219 82.2kN一个腹拱重力：PCpi 1507.702kN腹孔下部盖梁重力P 0.6 0.5 9 4 1.5 0.5 /2 0.5 0.325 82.5kN底梁重力-一 一 2一一P 0.5 0.5 9 4/2 0.7 1.3 0.5 0.3 2/2 0.3 0.525 70.125kN1号立柱重力P 4 10.263 0.8 2 0.5 0.5 25 216.585kN2号立柱重力P46.4560.820.50.5 25121.4025kN

15、3号立柱重力P43.5590.820.50.5 2548.984kN4号横墙重力0.52P 0.6 9 1.435 0.5 8.2 2/2 0.3 0.4 2 0.3 10.5 25 147.567kN25号腹拱座重力P 0.025 0.5 0.28 0.21 25 9 7.807kN腹孔集中力P131507.70282.570.125216.5851876.913kNP141507.70282.570.125121.40251781.73kNP151507.70282.570.12548.98 1709.31kNP161507.702147.5665 1655.269kNP171507.70

16、2 82.2024 /2 7.81 720.56kN拱上实腹段的荷载拱顶填料及桥面系重P18 lxhd 1B0 10.99 0.747 22 9 1625.64kN悬链线曲边三角形P19 shk2 m 1 ksh0.448 0.448 22 9 827.144kN-70.888 13.9351B02 2.24 1 1.4456式中f1f y上 1 1/ cos j 14.175 0.65 1 1/0.73113.935m其重心距原点的水平距离shkk /2chk 18.252mshk k靠近主拱拱顶一侧的腹拱， 一般多做成两平较拱, 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

17、地按无较圆弧拱计算其推力，而不计弯 矩的影响。腹拱拱脚的水平推力F (Cigi C2g2 C3g3)RB0 式中 2 g11hd 22 0.747 16.44kN/m22212、g22 R d'/2 R d '/212/4 2_2_2?_2 22 6.125 0.35/2 6.125 0.35/25.7647 /4? 17.461kN/mg33d' 25 0.35 8.05kN/m2_， ,fc 1 -1由-和b 7 0.000586查拱桥(上册)表(I)-4得l08AR2Ci 0.7855, C2 0.1062 C3 0.8084F 0.7855 16.44 0.10

18、62 17.461 0.8084 8.056.125 9 799.3 kN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：.1e d' f0 y' y上 0.35 0.8 0.28/2 0.65 0.36m 2腹拱推力对各截面重心产生的力矩：Mi Fx yi e验算拱轴系数恒载对1/4截面和拱脚截面的力矩见下表:项目集中力编力重力1/4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P131876.91266002.9438465525.342P141781.729860

19、08.34384614866.48P151709.311740013.7438523492.52P161655.268951.4219232353.66519.1438531688.21P17720.5573176.6269234775.07824.3488517544.74实腹段P181625.640812.2269219876.5829.9488548686.07P19827.1439859.4702497833.2627.1921722491.84腹拱推力F799.3023742.7585282204.89813.8151311042.47215147.0515477.584958454

20、.97264127.9由表可知,M1/4Mj58454.97264127.90.2213,m 2.24。该值与0.225之差小于半级即0.0025,所以可以确定上面拟定的桥跨结构形式的设计拱轴系数五、拱圈弹性中心及弹性压缩系数1 弹性中心 Vs 表 III3值f 0.3392 1 4.175 4.808m2弹性压缩系数2_2_22w/f 0.4632 /14.170.001068u1表 III 9值2w/f211.0501 0.0010680.011801u表 III11 值2w/f29.14719 0.0010680.00976884u1/(1 u) 0.011687六、主拱圈截面内力计算(

21、一)结构自重内力计算(1)假载内力a.求假载由式(M/ qxl2 /32)/( M j qxl2/ 8) 0.22得： 2_qxM? 0.22 M j / 0.22/8 1/ 32 l 18.405kN/mb.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 下表项目影响线面积3-H 口 L 4日表值乘数3与为i拱顶截卸M0.001985025.0659.949628183.1262H0.12742354.498745.17022831.3731/4M-0.001245025.065-6.23108-114.685H0.12742354.498745.1

22、7022831.373拱脚截面M0.00445025.06522.11029406.9472H0.12742354.498745.17022831.373V0.270.8876914.17754260.9423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卸l/4拱脚截面cos10.938720.73057sin00.3446810.682838Hi831.3730275831.373831.373Vi260.94233H1/(1 u)9.7158817469.7158829.715882N821.6571458875.2952778.4593Mi183.1262302-11

23、4.685406.9472y4.80810471.689576-9.36702M229.8412069-98.2694315.9383(2) “拱轴线恒载”内力a.推力22HgMj qxl /8 264127.9 18.40533 70.8882/8 1781761kNf14.175b.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卸l/4拱脚截面cos10.938720.73057， _Hg Hg f17817.6096417018.3117018.31(1 U1/(1 u)Hg17609.3832716819.4216819.42, N Ha /cos g17817.6

24、096418129.2723294.564'，、N u1H gcos /(1 u)208.2263708186.6976145.2996,N N N17609.3832717942.5723149.26y4.80810471.689576-9.36702M1001.174192336.0318-1862.96（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”内力加上“假载”的内力，计算结果见下表拱顶截面I/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 载假载合计平力17817.60964831.37302818648.9817018.30

25、727831.373027517849.6817018.31831.37317849.轴力17609.38327821.65714618431.0417942.57127875.29523818817.8723149.26778.459323927.弯矩1001.174192229.8412071231.015336.0318449-98.26939119237.7625-1862.96315.9383-1547.2.“恒载压力线”偏离拱轴线的影响“恒载压力线”（指空腹式无钱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“三校拱恒载压力线”）与拱轴线在“五点”以外的偏

26、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Mp。下面按主拱圈、拱上实腹段和各集力矩，再算各截面压力线的纵坐标，然后才能求得 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M iMiA50(i) ,12 * 4sh2k id i02sh2k i di .12sh2k id i在这里，对于所要求的每一等分点而言, 则上式为：I212 M1 A 5 丁 01 2sh2k 1d 1 0 积分上限E为常数，并不计等式前面的负号,式中：S o 

27、1;12sh2k 1d ,可根据E值从拱桥（例集）附表1-1查得;S22sh2k 1d可根据E值从拱桥（例集）附表1-2查得l2A 55.4 25 70.888 /4 169595.9kN m5 4主拱圈对各截面的力矩 M1的值见下表截面号S1S2子S1-S2M11200000110.0833333330.083870.0037570.003233548.2189100.1666666670.167043330.0142830.0135582299.390.250.251210.031480.0313235312.16980.3333333330.336296670.57574-0.46364

28、-78631.770.4166666670.422546670.091570.08449114329.3960.50.510310.12890.12625521412.3450.5833333330.60030.1779702740.6666666670.749440.235840.26378744737.1530.750.788460.30330.28804548851.2620.8333333330.888453330.382830.35754860638.6510.9166666670.993206670.4745870.43585373918.86011.10

29、3670.580130.5235488790.26b.拱上实腹段恒载对各截面产生的弯矩M 2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：PiB°hdlf/2对实腹段里每个截面的力矩：_2_2_Mi P(l /2)/2 l /4 1B0hd i /2Mi Pki/2 l /2 k/22_-l /4 iBohd k( i k/2) I k对空腹段里每个截面的力矩：式中k表示空、实腹段的分界点，取为：185826.9kN?m1l2B0hd/4 22 70.8882

30、9 0.747/4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M2kEPn(1)/2M 2/2M.实腹段12000000000110.083333330.12046715.908170.750060.73823511.743965820.003472222645.2323656.9763100.166666670.240933127.54270.7502421.475399188.17636390.0138888892580.9292769.10690.250.3614432.02070.7505432.210427954.95030620.031255807.0916762.041分界

31、点0.310067930.448234827.1440.750835l/2*0空腹段80.33333333827.1440.7508353.5629422947.0656490.05528491610273.4213220.4970.41666667827.1440.7508356.5165955390.1626520.081123911507520465.1760.5827.1440.7508359.4702497833.2596550.10696290519876.5827709.8450.58333333827.1440.75083512.423910276.356660.1328018

32、9924678.1734954.5240.66666667827.1440.75083515.3775612719.453660.15864089329479.7542199.230.75827.1440.75083518.3312115162.550660.18447988734281.3349443.8820.83333333827.1440.75083521.2848617605.647670.21031888239082.9156688.5510.91666667827.1440.75083524.2385220048.744670.23615787643884.4963933.230

33、1827,1440.75083527,1921722491.841670.2619968748686.0771177.91(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)P l f1 2B0(shk i k。/ 2 m 1 k每一块Pi的重心的横坐标：i (shk i k i / 2) (chk i 1)/k/(shk i k i)在实腹段里，截面重心到任意截面的力臂为l(1 i)?i/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 ( i k k)/2o每个截面的力矩见上表c.各集中力对各截面的力矩M3拱上空腹段的腹孔和横隔板等各集中力及其相应的横坐标lx。在前面已

34、经求出，各竖向集中力到截面的力臂 a li/2晨(取a 0),产生的力矩 M 3R ；腹拱水平推力H'g .一 一 、 、 ' 作用在第7与第8截面之间，对07截面产生的力矩 M 3 H'g y1 e 。具体计算见下表。面号竖向力P17P16P15P14P13腹拱推力合力P720.5573171655.2691709.3121781.731876.913F1015.919212lx11.09516.321.727.132.5e0.172603474工MMMMMy1MM312000000110.08333333300000100.1666666670000090.2500

35、00080.333333333518.5240940000518.5270.4166666672646.8009800002.1372409751420.5529314067.360.54775.077862353.6650003.118528492204.8983719333.650.5833333336903.354747242.7560004.3112238863158.22263217304.40.6666666679031.6316212131.853297.657005.7326491724294.37123828755.30.7511159.908517020.948346.37

36、2007.4034433365629.84097942157.20.83333333313288.185421910.0313395.094341.25309.347902557184.05184560118.10.91666666715416.462326799.1218443.89603.866011.59424958979.56229379242.0117544.739231688.2123492.5214866.485525.34214.175129511042.46581104159d.计算偏离弯矩M p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：y M

37、i/Hg式中，Hg为不计弹性压缩的恒载水平推力：Hg Mj/f 264127.9/14.175 18633.19kN g各截面上“恒载压力线”偏离拱轴线的值：y y1 yii偏离弯矩Mp Hg y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M1M2M3Myiy1国Mp120000000011548.2188748656.97625501205.1950.064680.0830520.018371989342.3288137102299.3003812769.1055205068.4060.272010.3334070.0613974791144.031071953

38、12.1688186762.0409012074.210.6479950.7547130.1067183311988.5032478-78631.7335413220.4902518.5241-64892.7-3.482641.3530774.83571786490104.86413714329.393720465.16744067.35438861.912.0856282.1372030.05157468961.0009636621412.3353527709.84459333.64158455.823.1371883.118474-0.01871356-348.6932838529205.

39、2687834954.521717304.3381464.124.371994.311148-0.06084152-1133.671713444737.1475942199.198928755.51115691.96.2089125.732548-0.47636392-8876.180808348851.2624249443.876142157.06140452.27.5377427.403313-0.13442889-2504.839449260638.6513256688.553360118.61177445.89.5231039.347738-0.17536483-3267.606796

40、173918.8613863933.230579242.82217094.911.6509811.59405-0.05692724-1060.736273088790.2582271177.9076104159.8264127.914.1751314.17488-0.0002495-4.648981647(2)偏离弯矩Mp在弹性中心产生的赘余力XiM 1M p pdss EIy1p12cosH g112M 1ds01s EI12cosM 2M pds0O I一y(y s - y 1)2ps_EJ2 l12cosu222M 2ds2N 2ds(1)表(III)5值f21Hgs EI s EA赘余

41、力各项的计算见下表。截回ycos1/ cosy / cosys y1ys y / cos12010.504.808020110.0183719890.998421.0015830.0184014.7250530.086946100.0613974790.993631.0064110.0617914.4746980.27649690.1067183310.985491.0147240.108294.0533920.4389484.8357178640.97381.0269054.9658223.45502817.1570570.051574680.95831.0435150.0538192.67

42、09020.1437456-0.0187135550.938721.06528-0.019941.689631-0.033685-0.0608415160.91481.093135-0.066510.496957-0.033054-0.4763639180.886391.128172-0.53742-0.924440.4968153-0.134428890.853471.171687-0.15751-2.595210.4087682-0.1753648340.816221.22516-0.21485-4.539630.975341-0.0569272410.775041.290256-0.07

43、345-6.785950.4984330-0.00024950.730570.684397-0.00017-9.366780.001599213.251224.1382820.4174由上表1得X14.4.13928 18633.19 /13.255819.04kNgmX218633.19 1564.431kN2 2.9536 20.41741 0.009769 0.099879 70.888 14.175“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MX1X2 ys yMpNX 2cosQ 6 X2sin拱顶、l/4截面、拱脚三个截面的附加内力见下

44、表。项目拱顶截卸l/4拱脚截面cos10.938720.73057sin00.3446810.682838y ysy14.80810471.689576-9.36702NX2 cos1564.4309821468.5631142.926Q X2 sin0539.22911068.253Mp0-348.693-4.64898X1-5819.037087-5819.04-5819.04Mx1x2 y M p-13340.98504-8810.968830.378(4)空腹式无较拱的恒载压力线空腹式无钱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Mg

45、iHg/(1) X2(ys yi) Xi MpNgHg /cos iHg/(1) XzcosQg iHg/(1)X2sin这三个力的合力作用点的偏心距为e Mg/Ng所以，空腹式无较拱桥恒载压力线的纵坐标yy1s / cos i空腹式无钱拱恒载压力线的纵坐标值见下表截回y1ys yyMg/HgcosNg /Hg ggSy11204.808104700.04508410.9936650.045371572-0.0453715110.0830524.72505270.0183720.062930.998420.9952580.0632298650.0197220100.3334074.474697

46、70.0613970.1043690.993631.0001160.1043573630.228380690.7547134.05339170.1067180.1470210.985491.0084810.1457850280.606781481.3530773.45502774.8357184.872230.97381.0207364.773252643-3.548599572.1372032.67090170.0515750.083120.95831.0374440.0801196632.053596963.1184741.6896307-0.018710.0066150.938721.0

47、593340.0062445443.11182154.3111480.4969567-0.06084-0.043070.91481.08734-0.039609054.35444645.732548-0.9244433-0.47636-0.46760.886391.122556-0.416545236.202482437.403313-2.5952083-0.13443-0.136240.853471.166281-0.116819867.540189329.347738-4.5396333-0.17536-0.18950.816221.219989-0.155328119.5380397111.59405-6.7859453-0.05693-0