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1、个人资料整理仅限学习使用空腹式等截面悬链线箱型无铰拱桥设计计算书一、 设计资料 自拟）设计荷载：公路 -级，人群荷载 3.5KN/m2净跨径： L0=50+学号 =50+24=74m ，矢跨比： f0/L0=1/5 ，所以f0=14.8m，桥宽2.5+10+2.5拱顶填土包括桥面的平均高度hd=0.6m，材料容重1=22.5KN/m3护拱及拱腔为 1 号石灰砂浆砌筑片石，122.5 KN/m3主拱圈 40 号钢筋混凝土，材料容重：2=25 .5KN/m3腹拱圈 30 号混凝土，材料容重：3= 24.5 KN/m3拱上立柱 墙）材料容重：425 KN/m3桥面铺装为 8cm 钢筋混凝土 425
2、KN/m3）+6cm沥青混凝土 523 KN/m3）人行道板及栏杆重52.0 KN/m双侧）合拢温度： 15oc最高月平均温度 35oc最低月平均温度 0oc二、 设计内容1、确定主拱圈截面构造尺寸，计算拱圈截面几何特性、物理力学特征值；2、确定主拱圈拱轴系数m，拱轴线悬链线方程及拱上建筑的构造布置和几何构造尺寸；3、拱圈弹性中心及弹性压缩系数；4、主拱圈结构内力计算 恒载、活载）；5、温度变化、混凝土收缩徐变引起的内力；6、主拱结构的强度和稳定计算。三、 流程图四、 详细计算（一） 主拱圈截面构造及截面几何要素计算精选学习资料 - - - - - - - - - 名师归纳总结 - - - -
3、 - - -第 1 页，共 22 页个人资料整理仅限学习使用1、主拱横截面设计拱圈截面高度按经验公式估算D=L0/100+=74/100+0.8=1.54m 为方便计算，取 D=1.6m 拱圈由 9 个 1.5m 宽的拱箱组成，全宽B0=13.5m 构造图如附图所示：2、箱型拱圈截面几何性质截面积： A=1.6*1.5-1.2*1.2+0.1*0.1*2）*9=8.82m2绕箱底边缘的净矩：S=1.6*1.5*0.8-1*1.2*0.8-2=3.1108m4拱圈截面绕重心轴的回转半径r= 1/2=0.594m (二确定拱轴系数精选学习资料 - - - - - - - - - 名师归纳总结 -
4、- - - - - -第 2 页，共 22 页个人资料整理仅限学习使用拱轴系数 m的确定，一般采用“五点重合法”，先假定一个m值，定出拱轴线，拟定上部结构各种几何尺寸，计算出半拱恒载对拱桥截面形心的弯矩Mj和自拱顶跨截面形心的弯矩。其比值=。求得值后，可由m =表(III-20(8得：sin j=0.70097，cosj= 0.71319 ，j=44.50490主拱圈的计算跨径和计算矢高：l =l0+2下ysin j=74+2*0.8*0.70097=75.12m jyffcos1下014.8+0.8*-1值 f ，相应的拱背曲面坐标y1=y1上y/cos ，拱腹曲面坐标 y1=y1+y下/c
5、os 。截面号xy1/f （查表 -1）y1cos( 查表 -20（8）y上/cos y下/cos y1-(y 上/cos )y1+（y下/cos)037.56115.0290.713191.12172072 1.1217207213.9072792816.15072072134.430.81004812.174211390.76431 1.046695712 1.04669571211.1275156813.2209071231.30.6472899.7281063810.8110.986436498 0.9864364988.74166988310.71454288328.170.5084
6、717.6418106590.85238 0.938548535 0.9385485356.7032621248.580359194425.040.39082 5.873633780.8880.900900901 0.9009009014.9727328796.774534681521.910.2919884.3882876520.91782 0.871630603 0.8716306033.5166570495.259918255618.780.213.156090.94212 0.849148728 0.8491487282.3069412724.005238728715.650.1432
7、182.1524233220.96137 0.832145792 0.8321457921.320277532.984569114812.520.0903081.3572389320.97614 0.819554572 0.8195545720.537684362.17679350499.390.0502130.7546511770.98696 0.810569831 0.810569831-0.0559186541.565221008106.260.0221330.3326368570.99433 0.804561866 0.804561866-0.4719250091.1371987231
8、13.130.0055060.0827496740.99860.80112157 0.80112157-0.7183718960.8838712441200010.80.8-0.80.8主拱圈几何性质表 (m=2.814) (d+ f0，分别计算如下表由 D0=f0/l0=1/8，则 R0=5.95, sin 0=0.470588，cos0=0.882353, 0=28.072472腹拱拱脚的水平投影和竖向投影x=d sin 0=0.4*0.470588=0.1882m ；y=d cos0=0.4*0.882353=0.3529m k=lnm+m2-1）1/2）=1.694573307 项目
9、lx =2lx/lk y1=(f/(m-1)*(chk -1)tan =(2fk*shk )/(l*(m-1) 1/cos =(tan )2+1 h1号立柱 32.50.8652822151.46628414510.620902520.7667033991.2600928949.2628282092号立柱 25.80.6869009581.1640040296.2757464730.5402194971.1365901225.0164743753号立柱 19.10.5085197020.8617239133.2712155620.3634742241.0640082292.0700089794
10、号立柱 12.40.3301384450.5594437971.3306791840.2201944391.0239558540.1615145空实腹段分界线12.05 0.3208200210.5436530441.2548067770.2133711781.0225102740.086798558多加的 可删14.85 0.3953674120.6699790631.9300570580.2695916991.0357025070.751495052腹孔墩高度计算表2、上部结构恒载计算精选学习资料 - - - - - - - - - 名师归纳总结 - - - - - - -第 4 页，共
11、22 页个人资料整理仅限学习使用1）人行道板及栏杆重52.0 KN/m双侧）2）拱顶填料及沥青表层处重0.5*6*10/2*2*22.5+0.08*10/2*2*25+0.06*10/2*2*23=168.8KN/m以上两部分恒载有拱圈平均分担，则换算成容重为122.5 KN/m3的计算平均填料厚度为hd=52+168.8）/13.5/22.5=0.72691358KN/m （2） 主拱圈P0-12=表-198）值）A2l Ml/4=表-198）值） A2l2/4 Mj=表-19 表-19 表-19 8.82 0.55288 9341.0398 0.12614 40023.28758 表-19
12、 0.52303 165953.54 3、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：箱肋构造图：精选学习资料 - - - - - - - - - 名师归纳总结 - - - - - - -第 5 页，共 22 页个人资料整理仅限学习使用a、箱肋截面积 A=2*0.15*1.6+1.2*0.2+0.5*2*0.1*0.1=0.73m2b、截面静矩J=2*0.15*1.6*1.6/2+1.2*0.2*0.2/2+2*0.5*0.1*0.1*确定箱肋接头、设置横隔板a、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
13、的反弯点附近，即=0.350.37 之间，此处相应的弧长为Sx=13.1m则接头位置接近 =0.35 处。b、端段箱肋弧长SI=1/2(S - S=1/2*(82.69679462-2626.2=28.24839731mc、端肋设置 11 道横隔板，则端横隔板距离起拱面的长度为S=SI-2.56*10-0.3=2.34839731m 3横隔板与接头加固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0.1m，断面尺寸如图：精选学习资料 - - - - - - - - - 名师归纳总结 - - - -
14、 - - -第 6 页，共 22 页个人资料整理仅限学习使用a横隔板重力空心板P=(1.2*1.2-0.4*0.1*0.1/2-0.8*0.68+4*0.08*0.08/2*0.06*25.5*11=15.261444KN实心板P=(1.2*1.2-4*0.1*0.1/2*0.06*25.5*11=23.8986KN b中间接头加强部分P=(1*0.1+2*1*0.1+0.1*0.1*(0.3*2-0.06*25.5*11=46.9557KNc. 拱脚加强段P=(1*0.1+2*1*0.1+0.1*0.1*2.34839731*25.5*11=40.2057KNd. 各集中力的作用横坐标各集中
15、力作用线的横坐标lx可以根据 k=Sx/(l /2值从书后附表1 查得值，再由 lx=l /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下表。精选学习资料 - - - - - - - - - 名师归纳总结 - - - - - - -第 7 页，共 22 页个人资料整理仅限学习使用l/4-lxl/2-lx1号2.56 0.06846021 0.0684280972.5587991416.221235.001200862号5.12 0.13692042 0.136732877 5.112986938 13.6670132.447013063号7.68 0.20538063 0.2
16、04779965 7.657538645 11.1224629.902461364号10.240.27384084 0.272397996 10.18604618 8.59395427.373953825号12.8 0.34230105 0.339494776 12.69506206 6.08493824.864937946号13.4 0.35834642 0.355133181 13.27984434 5.50015624.280155667号15.960.42680663 0.421273155 15.75308142 3.02691921.80691858（l/4-lx)64.21664
17、1288号18.520.49526684 0.486532181 18.1933763819.366623629号21.080.56372705 0.550733661 20.5941254516.9658745510号23.640.63218726 0.613495898 22.9410555214.6189444811号26.2 0.70064747 0.674816443 25.2340749812.3259250212号28.760.76910768 0.734531677 27.4670654410.0929345613号31.320.83756789 0.792484361 29.
18、634147167.92585284314号33.880.90602810.84852283 31.729648765.83035124515号36.440.97448831 0.902428485 33.745395913.814604086（l/2-lx)282.80314760号000018.7837.56中接头13.1 0.35032374 0.347335551 12.988259875.7917424.57174013拱脚加强段 40.171.07434926 0.927116501 34.668579192.891420813集中力编号Sx2Sx/llx=l*/2力臂各集中力的横
19、坐标与力臂计算表4、拱上空腹段（1） 腹孔上部腹孔上部构造：精选学习资料 - - - - - - - - - 名师归纳总结 - - - - - - -第 8 页，共 22 页个人资料整理仅限学习使用腹拱圈外弧跨径l外=l0+2dsin 0=6+2*0.4*0.470588=6.37647m腹拱圈内弧半径 R0=l 0/2sin 0）=6.0/*0.4*24.5*13.5=852.400341KN腹拱上的护拱重力Pb=(2sin 0-sin 0cos0- 0R22 B0=(2*0.470588-0.470588*0.882353-28.072472*3.1415926/180*(6.375+0.
20、4/2*(6.375+0.4/2*22.5*13.5=472.6508439KN填料及桥面系重力Pc=l外hd1B0=6.37647*0.72691358*22.5*13.5=1407.924664KN腹拱墩起拱线以上部分重力Pd=(0.6-0.1882*0.3529*25+(1.15-0.3529*22.5+0.72691358*22.5* (0.6-2*0.1882*13.5=152.5556KN一个腹拱总重力P=Pi=852.400341+472.6508439+1407.924664+152.5556=2885.531489KN(2腹孔下部 /2*0.7*13.5*25=94.5KN
21、1 号立柱重力 P=6*(9.26282821-0.4*0.6*0.5*25 =398.827269KN2 号立柱重力 P=6*(5.01647438-0.4*0.6*0.5*25=207.7413469KN3 号立柱重力 P=6*(2.07000898-0.4*0.6*0.5*25=75.15040405KN 4 号立柱重力 P=6*(0.1615145-0.1*0.6*0.5*25=2.768153KN(3腹孔集中力P13=2885.531489+118.125+94.5+398.827269=3496.98376KNP14=2885.531489+118.125+94.5+207.741
22、3469=3305.897836KN P15=2885.531489+118.125+94.5+75.15040405=3173.306893KN P16=2885.531489+118.125+94.5+2.768153=3100.925KN 5. 拱上实腹段拱上实腹段构造：精选学习资料 - - - - - - - - - 名师归纳总结 - - - - - - -第 9 页，共 22 页个人资料整理仅限学习使用(1拱顶填料及桥面系重P17=lxhdB01=12.4*0.72691358*22.5*13.5=2737.92KN2）悬链线曲边三角形P18=lf1/2m-1 ） k ） shk -
23、k ） 2B0=75.12*14.7072793/2*2.814-1）*1.69457331 ）*sh0.543653044-0.543653044）*25*13.5=1648KN式中： f1=f+y上1-1/cos j）=15.029+0.8*1-1/0.0.71319）=14.7072793m其重心距原点的距离为lx=shk-k /2 ）-chk-1）/k ）/RB0式中： g1=1hd=22.5*0.72691358=16.35556KN/m2 g2=2(R+d/2-(R+d /22-l2/41/2=16.53815155 KN/m2 g3=3d=24.5*0.4=9.8KN/m2由 D
24、0=f 0/ l 0=1/8 ，b=I/AR2=0.000272 查表可得C1=0.7769488 ， C2=0.1072884 ， C3=0.7900976 F=0.7769488x16.35556+0.1072884x16.53815155+0.7900976x9.8 ）精选学习资料 - - - - - - - - - 名师归纳总结 - - - - - - -第 10 页，共 22 页个人资料整理仅限学习使用X13.5x6.575=1972.723268KN腹拱拱脚推力的纵坐标e=d+f0-y /2-y上=0.4+0.75-0.3529/2-0.8=0.17355m 腹拱推力对各截面重心产
25、生的力矩 Mi=FXyi-e）7、验算拱轴系数项目集中力编号重力（ KN ）力臂力矩（ KN m ）力臂力矩（ KN m ）主拱圈P0-129341.0398540023.28758165953.5445P1-14213.660216（l/4-lx)=I5913720.54145（l/2-lx)=I6760423.7816P1523.89863.81460408691.1636972P07.63072218.78 143.304959237.56 286.6099183中接头46.9557 5.791740132271.955212124.57174013 1153.783258拱脚段204.
26、2048882.891420813 590.4422635P133496.983765.06 17694.73782P143305.8978411.76 38877.35855P153173.3068918.46 58579.24525P163100.924646.73 20869.2228425.16 78019.26399P172737.926.3817467.929625.1668886.0672P181648.405229.46479378815601.8154628.24479379 46558.86543腹拱推力F1972.723272.98254 5883.72605514.85
27、545 29305.6918729273.5516113981.7831548725.81750.20772083 0.21 0.002279横隔板及加强段拱上空腹段实腹段l/4 截面拱脚截面半拱恒载对拱脚和 l/4 截面产生的弯矩由表可知：=113981.7831/548725.8175=0.20772083 该值与 m=2.814，y?/ f =0.210 之差小于半级0.0025，所以可以确定上面拟定的设计拱轴系数 m=2.814。三）拱圈弹性中心及弹性压缩系数1、弹性中心ys=表）-3 值）f=0.333431*15.029=5.0111m 2、弹性压缩系数rw2/f2=0.594/1
28、5.029 ）2=0.001562 1=表）-9 值）*rw2/f2=11.1272*0.001562=0.017381 =表）-11 值）*rw2/f2=9.18594*0.001562=0.014348 1/1+）=0.017135 *作近似计算。2）“拱轴线恒载”内力精选学习资料 - - - - - - - - - 名师归纳总结 - - - - - - -第 12 页，共 22 页个人资料整理仅限学习使用a、推力b、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 截面拱脚截面cos 10.942120.71319Hg=Hg-F38591.5084736618.78523661
29、8.7852（1- 1/(1+)）*Hg37930.2429735991.3223235991.32232Ng=Hg/cos38591.5084738868.4936151345.06261N= 1/(1+)*Hg*cos661.2654977591.1453327447.5002546N=Ng- N37930.2429738277.3482850897.56236Y=ys-y15.01111.85501-10.0179M= 1/(1+)*Hg*y3313.6675351163.949925-6285.86043考虑弹性压缩的拱轴线恒载内力注：从拱顶到第 8 截面 F=0，第七截面到拱脚F=1
30、972.723268KN 。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，计算结果见下表：截面项目拱轴线恒载假载qx合计（减去假载）拱轴线恒载 假载qx合计拱轴线恒载 假载qx合计水平力 38591.5085 2096.4189936495.08948 36618.7852 2096.4189934522.36621 36618.78522096.58256934522.2轴力37930.2432096.4189935833.8239838277.348281975.07825936302.2700250897.5623626
31、62.27462448235.2弯矩3313.66754 855.99119832457.6763371163.949925-344.91307521508.863001-6285.860431097.080336-7382.9考虑“五点”偏差的恒载内力拱顶截面l/4 截面拱脚截面2、“恒载压力线”偏离拱轴线的影响“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。悬链线曲边三角形块从拱顶到任意截面的重力见下表每一块pi 的重心横坐标精选学习资料 - - - - - - - - - 名师归纳总结 - - - - - - -第 14 页，共 22 页个人资料整理仅限学习使用
32、c、拱上空腹段的腹孔和横隔板等各集中力及相应的横坐标lx在前面已经求出，各竖向集中力到截面的力臂0），产生的力矩 =Pa；腹拱水平推力作用在第 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竖向力P=lxaMaMaMaMaM12000011 0.08333333 3.12999998723.88415976 0.571200847 8.71734974310 0.16666667 6.26000001347.76831982 3.701200872 56.485669851.147013075 17.5050758190.259.39 71.652479586.831200
33、86 104.25398944.277013062 65.27339534 1.732461355 26.439861968 0.3333333312.52 95.53663943 9.961200859 152.02230917.407013061113.041715 4.862461354 74.20818166 2.333953816 35.619505467 0.4166666715.65 119.4207993 13.09120086 199.790628810.53701306 160.8100348 7.992461357 121.9765014 5.463953818 83.3
34、878252260.518.78 143.3049592 16.22120086 247.558948513.66701306 208.5783545 11.12246136 169.7448211 8.593953817 131.15614495 0.58333333 21.90999999167.1891189 19.35120085 295.327268116.79701305256.346674 14.25246134 217.513140611.7239538 178.92446444 0.66666667 25.04000001 191.073279 22.48120087 343
35、.095588219.92701307 304.1149941 17.38246137 265.2814607 14.85395383 226.692784530.7528.17 214.9574387 25.61120086 390.863907723.05701306 351.8833137 20.51246136 313.0497803 17.98395382 274.46110412 0.83333333 31.29999999238.8415985 28.74120085 438.632227226.18701305 399.6516332 23.64246134 360.81809
36、9821.1139538 322.22942361 0.91666667 34.43000001262.7257586 31.87120087 486.400547329.31701307 447.4199533 26.77246137 408.5864199 24.24395383 369.99774370137.56 286.6099183 35.00120086 534.168866932.44701306 495.1882728 29.90246136 456.3547394 27.37395382 417.76606327.6307220P0#P1#15.2614442.558799
37、1415.2614445.11298693815.2614447.65753864515.26144410.18604618拱上各集中力对各截面产生的力矩P2#P3#P4#中接头P6#P7#aMaMaMaMaM3.25000000110078.005092.95493794445.096619962.66174013124.98387122.37015566436.171997946.3819783.899216.08493794392.864939665.79174013271.95521215.50015566383.940317643.0269185846.19514849.509999
38、98729489.79339.214937931140.63325928.92174012418.92655258.63015565131.70863726.15691856793.9634679312.6400000139195.6875112.34493796188.401579312.0517401565.897894711.76015568179.47695739.286918592141.73178815.7748901.581615.47493794236.169898815.1817401712.869235114.89015566227.245276812.4169185818
39、9.500107618.8999999958607.4756918.60493793283.938218418.3117401859.840575518.02015565275.013596315.54691857237.268427122.0300000168313.369921.73493796331.706538521.44174011006.81191821.15015568322.781916418.67691859285.036747225.1678019.2639924.86493794379.47485824.57174011153.78325824.28015566370.5
40、5023621.80691858332.80506673100.92464212.446.955712.9882598715.26144413.27984434P16P5#15.26144415.7530814215.26144412.69506206P8#P15P9#P10#P14P11#P12#aMaMaMaMaMaMaM3.71662361156.721043112.8099999878916.9923316.846623636104.48936325.94000001318849.442994.44587456167.850465642.09894449232.032923839.97
41、6623623152.25768279.0728781.893527.575874548115.61878525.2289444879.801243362.377834.9778722.93592501844.8064552413.10662361200.026002312.1999999938714.3440610.70587454163.38710478.358944467127.56956295.49999998718182.438066.06592500592.574774773.83293454758.4961216.23662364247.794322415.33000001486
42、46.7947213.83587456211.155424811.48894449175.3378838.63000001328529.898379.19592503140.34309496.962934572106.264419.36662362295.5626419 18.4658579.2452516.96587455258.923744314.61894448223.1062025 11.7638877.3585512.32592502188.111414410.09293456154.032815.26144425.2340749815.26144427.4670654415.261
43、44420.5941254515.26144422.9410555225.83305.89783615.26144418.193376383173.30689319.1精选学习资料 - - - - - - - - - 名师归纳总结 - - - - - - -第 15 页，共 22 页个人资料整理仅限学习使用P13#P13P14#P15#拱脚加强段腹拱推力FaMaMaMaMaMaMM3032.6015095121.759065267.619726470.4283512.152423322 3903.76944614873.41283.156095883.72605527062.92414.388
44、287652 8314.51103448678.55035.8736337811244.687971899.95757.641810659 14732.81157103554.7499.728106381 18848.49569138352.5454.79585285673.19163979 1.930000013 6749.17869812.17421139 23673.98396 180788.787.925852843120.95995935.0617694.73782 5.83035124 88.979579033.814604086 91.163697 2.891420813 590
45、.44226315.02929305.69187228914.281合计3496.98375932.515.26144431.7296487623.898633.7453959115.26144429.63414716204.204888134.668579191972.7232680.17355d、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“恒载压力线”偏离拱轴线的值偏离弯矩具体数值见下表：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+M3yi=Mi/Hgy1y=y1-yiMp=H
46、g y0 165953.5445 127009.3669 228914.281 548725.81815.02915.029001 138107.9466 113938.2928180788.78 432835.01911.8548777912.17421139 0.319333603 11659.231642113272.574 100867.2186 138352.545 352492.3379.6543796 9.728106381 0.073726781 2691.8483143 91261.28182 87796.14454 103554.749 282612.1757.740438
47、3857.641810659 -0.09862773 -3601.010014 71624.21957 74725.07049 71899.9575 218249.2485.977608191 5.87363378 -0.10397441 -3796.223535 44663.25105 61653.99627 48678.5503 154995.7984.2451653784.388287652 0.143122274 5225.5563826 40021.70111 48582.92222 27062.9241 115667.5473.1680076193.15609 -0.0119176
48、2 -435.1257697 27621.20152 35511.84811 14873.4128 78006.46242.1365116912.152423322 0.015911631 580.95168788 17604.09811 22440.77399 470.428351 40515.30051.1096697681.357238932 0.247569164 9039.0306769 9937.603987 11367.74342 267.619726 21572.96710.5908599750.754651177 0.163791202 5980.20233910 2033.
49、741825 4647.915348 121.759065 6803.41624 0.186338130.332636857 0.1462987275341.5322811 1012.780327 1101.637971 32.6015095 2147.019810.0588045240.0827496740.02394515 874.26454361200000000截面号偏离弯矩 Mp2）偏离弯矩 Mp在弹性中心产生的赘余力赘余力各项计算见下表：精选学习资料 - - - - - - - - - 名师归纳总结 - - - - - - -第 16 页，共 22 页个人资料整理仅限学习使用截面y
50、cos1/cos y/cos ys-y1(ys-y1)* y/cos M= X1-X2(ys-y1)+Mp000.713191.4021508990-10.01790-3198.38585610.3193336030.764311.3083696410.417806391-7.163111392-2.992793728634.6782720.0737267810.8111.2330456230.090908485-4.717006381-0.428815903-183.75793523-0.0986277260.852381.173185668-0.115708634-2.6307106590