圬工拱桥设计计算表(新规范)

1、截面号y1/fy1coswd/(2*cosw) y1-d/(2*cosw)y1+d/(2*cosw)x016.121800.695540.575095.546716.6968915.2874010.801921 4.909200.753450.530894.378315.4400914.01345截面高度d（m）20.634833 3.886320.805830.496383.389944.3827012.739500.830.494427 3.026780.851440.469792.556993.4965811.46555惯性矩i40.377084 2.308430.889770.4495

2、51.858882.7579910.191600.06666666750.279778 1.712740.920930.434341.278402.147098.91765m60.21.224360.945520.423050.801311.647417.643703.570.135693 0.830690.964370.414780.415911.245466.36975计算跨径80.085198 0.521570.978370.408840.112720.930415.0958030.574890.047214 0.289030.988350.40471-0.115680.693753.8

3、2185100.020761 0.127090.994990.40201-0.274920.529112.54790计算矢跨比110.005157 0.031570.998770.40049-0.368920.432061.273950.2002237141200.0000010.40000-0.400000.400000.00000第二栏由手册附录（iii）表（iii）1查得p575第四栏由手册附录（iii）表（iii）20（8）查得 p1014注:该种颜色格子为数据自动输出栏红色字体为人为输入栏0,01.6921,0.05193.3843,0.2085.0764,0.46936.7685,

4、0.83778.4606,1.315810.1528,1.906811.8449,2.614813.537,3.444715.2291,4.402716.9213,5.494918.6134,6.729120.3055,8.1139数据输入栏系数k（m2-1）0.5l01/3cm算d的系数m1.23.3541019663.1072325065抵抗矩w回转半径r矢高f00.106666667 0.2309401086相应的y1/4/fsinwjcoswj00.20.71850.695530计算矢高f拱脚截面投影x拱脚截面投影y计算跨径一半6.121800.57480.556415.2874xyx

5、,y000,01.27395-0.031571.27395,-0.031572.5479-0.127092.5479,-0.127093.82485-0.289033.82485,-0.289035.0958-0.521575.0958,-0.521576.36975-0.830696.36975,-0.830697.6437-1.224367.6437,-1.224368.91865-1.712748.91865,-1.7127410.1916-2.3084310.1916,-2.3084311.46555-3.0267811.46555,-3.0267812.7395-3.8863212.

6、7395,-3.8863214.01345-4.909214.01345,-4.909215.2874-6.121815.2874,-6.1218腹拱圈计算数据输入栏截面高d净跨径净矢高f净矢跨比sinw0cosw0水平投影x0.3210.5100.3项目xjk*jfy1ktgw1#横墙15.57481.01881.9610340376.12186.4246881.92484731.07387242#横墙13.17480.861808 1.6588483466.12184.2162251.92484730.78049673#拱座10.37480.67865 1.3062983756.12182

7、.4037871.92484730.5274831空实分界7.67480.502034 0.9663394736.12181.2351091.92484730.3465259注:该种颜色格子为数据自动输出栏红色字体为人为输入栏该种颜色要注意主拱计算跨径的一半k（m2-1）0.5m水平投影y横墙厚15.28741.92484733.3541023.500.8coswhy1dcosw1df0.6814871 4.937736 6.4246880.80.6814870.310.7883124 2.808812 4.2162250.80.7883120.310.8844923 1.05155 2.40

8、37870.80.8844920.310.9448773 -0.08823 1.2351090.80.9448770.31该种颜色格子为数据自动输出栏红色字体为人为输入栏该种颜色要注意2、恒载计算(1)主拱圈恒载（半拱和1/4点拱脚）腹拱圈参数截面高度dp012=表()-19对应m的值*a*0.3表值ap112水平投影x0.554580.82430.5748325.55850.3m1/4=表()-19对应m的值*a*2(与第二版不一样,二版/4)主拱圈参数表值am1/4a0.0315140.82430.5748565.62940.8mj=表()-19对应m的值*a*2(与第二版不一样，二版/4

9、)表值amj0.130690.82430.57482345.6912(2)拱上空腹段的恒载腹孔上部腹拱圈外弧跨径外=+2*d*sinw02.6腹拱内弧半径r0=0.725001*=1腹拱圈重pa=1.522024*(r0+d/2)*d*2426.01239004腹拱侧墙护拱重p b=0.11889*(r0+d)2*23=19.7填料及路面重pc=外*hd*2026两拱之间起拱线以上部分的重量pd=7.98一个腹拱重p=79.69239004腹孔下部1#横墙p=h1#-(0.5+3.1415926*0.52/2)/9*0.9*2452.024766022#横墙 p18.285339883#拱座

10、p=(h3#+0.5*y)*x*24-0.635231739集中力p13=p+p1#=131.7171561p14=p+p2#=97.97772992p15= (p-pd)/2+p3# =35.22096328(3)拱上实腹段的恒载拱顶填料及桥面重p16=x*hd*76.748悬链线曲边三角形部分p17=(1*f1)/(m-1)*k)*(shkjo-kjo)*59.53794728式子中的 f1=f-y1(1/cosj-1) =5.946674191k=ln（m +（m2-1）0.5）=1.9248473 0=x/l=0.502034355（m2-1）0.5=3.354101966k0=0.9

11、66339473shko=1.12391631chko=1.504389535重心位置x=5.7855665（4）各块恒载对拱脚及拱跨1/4截面的力矩计算见下表分块号恒重kn1/4截面拱脚截面力臂 m力矩kn*m力臂m力矩kn*mp0-12325.55851565.629442345.691188p13131.71716/2-x12.1126 278.2656639p1497.97773/2-x24.9126481.325396p1535.2209630/2-x37.6126 268.1231051p1676.748/4-x分界/23.8063 292.12591 /2-x分界/211.458

12、78.7646p1759.537947 /4-x1.8581335 110.62945 /2-x9.5018335 565.7196619合计726.76031968.384814817.889615m1/4/mj理论比值差值差值允许值注:该种颜色格子为数据自动输出栏0.20099770.2-0.00099770.0025红色字体为人为输入栏净跨径净矢高f净矢跨比sinw0cosw0210.510竖向投影y0计算跨径一半计算跨径sinwjcoswj计算矢高h净跨径 截面高dm2415.287430.57480.71850.695510.1218300.83.5对应m=3.5，表()-19（8）

13、，截面号0；f/l=1/5的系数对应pk0.55458对应mk0.13069对应m=3.5，表()-19（8），截面号12；f/l=1/5的系数对应mk0.031514f/l1/5 圆弧腹拱上部恒载计算r0、pa、pb的系数r0所对应pa所对应pb所对应由p235表32查得0.53.141593矢跨比1/5不用改填料及路面重hd=0.5m填料及路面重度=20kn/m3例题l1f1mj0kkj0 shkjo9.8239701腹拱圈参数主拱圈参数该种颜色格子为数据自动输出栏红色字体为人为输入栏p17#div/0!弹性中心离拱顶距离ys，拱桥上附表（）-3弹性中心ys=附表（）-3值*f02.005

14、807771=附表（）-9值*(r/f0)*(r/f0),r=i/a0.01594132（1代表每米宽）=附表（）-11值*(r/f0)*(r/f0),r=i/a0.013122431/（1+）0.01573484hg787.005393计入弹性压缩的恒载内力(表1-4)项目拱顶1/4截面拱脚y=y2-y12.005807770.78144777 -4.11599cosw10.945520.69554hg=(1-1/（1+）)hg774.6219854774.621985 774.621985ng774.6219854820.643166 1122.88955mg24.838735279.67

15、698629 -50.97001规范5.1.4条1款拱的强度验算用的公路-级汽车荷载效应每米拱宽承载均布荷载2.471（拱圈填料为.5m通规4.3.2不计汽车冲击）每米拱宽承载集中荷载66.424拱顶截面弯矩及其相应的轴向力影响线面积和坐标影响线正弯矩均布荷载考虑弹性压缩弯矩影响线面积m1*l*l7.21679801相应轴向力影响线面积=n1*l10.93996919集中荷载不考虑弹性压缩（24号截面）弯矩影响线面积=m2*l1.70148762相应水平力影响线坐标=h1*l/f1.165246592拱脚截面弯矩及其相应的轴向力影响线面积和坐标影响线正弯矩均布荷载考虑弹性压缩弯矩影响线面积m1

16、*l*l19.48161535相应轴向力影响线面积=n1*l13.85313613集中荷载不考虑弹性压缩（24号截面）弯矩影响线面积=m2*l1.703627856相应水平力影响线坐标=h1*l/f0.994587486相应左拱脚反力影响线坐标0.29396（截面号17）拱顶拱脚正弯矩mmax负弯矩mmin 正弯矩mmax 负弯矩mmin均布荷载m均17.83270788-9.9327259 48.1390715 -31.276537n均27.0326638621.6519693 34.2310994 26.7720152集中力m集113.0196137-22.339906 113.16177

17、7 -117.0408h中77.4003396436.5520956 66.0644792 21.7527764h-1.217882325-0.5751415 -1.0395143 -0.3422766m=h*(y1-ys)2.442837831.15362339 -4.2786329 -1.4088077h=h中+h76.1824573135.976954 65.0249649 21.4104999m=m集+m115.4624515-21.186282 108.883144 -118.4496与mmax相应左拱脚反力v=1.2*h中*坐标值23.3043772与mmin相应左拱脚反力r=1.

18、2*h中*坐标值74.2900353轴向力h中cosw+rsinwn61.969058轴向力h中cosw+rsinwn68.2683931汽车荷载效应汇总表 荷载效应单位拱顶拱脚正弯矩mmax负弯矩mmin 正弯矩mmax 负弯矩mmin轴向力kn104.433003558.2040649 96.2001574 95.0404083弯矩kn.m91.59662509-32.272632 145.170763 148.317334注：规范5.1.1条，汽车荷载产生的拱各截面正弯矩，拱顶至拱脚1/4点，乘以0.7折减系数；拱脚乘以0.9折减系数，拱跨1/4点至拱脚，用直线插入法确定。规范5.1.4

19、条1款拱的强度验算用的温度作用效应0.000363877均布荷载考虑弹性压缩相应轴向力影响线面积=n1*l13.85313613温度变化1度每米拱宽的弹性中心赘余力ht0.464354994kn/度温度上升23.4ht10.86590687温度下降15.1ht-7.011760414温度效应汇总表项目拱顶拱脚温升温降温升温降轴向力nht*cosw10.86590687-7.0117604 7.55767286 -4.8769598弯矩mht(y1-ys)-21.7949204214.0642435 44.7239882 -28.860351剪力vht*sinw007.8070169 -5.03

20、78613规范5.1.4条2款拱的整体“强度稳定”验算用的荷载效应a半拱全部自重-主腹拱顶上填料后均布荷载37.53982431kn/m拱桥上附表（）-14（75）取1/4拱跨处与mmax相应的h影响线面积与mmin相应的h影响面积之和a*b=738.79828knwm=0.38089203 弧度 = 21.8235058规范5.1.4拱的轴向力=h/coswm=-795.83293kn规范5.1.4条2款，轴向力偏心距可取水平推力计算时同一荷载布置的拱跨1/4处弯矩设计值d除以轴向力设计值d。均布荷载作用下拱跨1/4处正负弯矩影响线总面积，按拱桥上附表（）-14（75）为：（）*l*l=弯矩

21、为：按第8款，由于在合龙之前，裸拱受力时间不长，温度变化不大，所以温度作用效应乘以0.7。温度作用轴向力按下式计算：0.0003638778.193322419kn5.287143954kn温度作用的偏心距计算，可先计算温度作用下1/4跨弯矩，然后除以相应轴向力。温度作用下1/4跨弯矩为：温度上升0.7t(y1-ys)=-4.481857473kn/m温度下降0.7t(y1-ys)=-2.892138797kn/m拱脚截面直接抗剪强度验算的荷载效应1）自重剪力自重产生的左拱脚反力为j 726.76031kn/m自重产生的左拱脚考虑弹性压缩的水平推力：774.6219854kn自重产生的剪力为：

22、1062.027692kn2）汽车荷载剪力附表（）-30.32765附表（）-911.2017附表（）-119.22091拱桥上附表（）-14（75）负弯矩正弯矩负弯矩-4.019719099m10.00772-0.00438.762431932n10.357810.28659拱桥上附表（）-13（46）-0.3363228拱桥上附表（）-12（10）m20.05565-0.0110.550284469h20.233310.11018拱桥上附表（）-14（75）负弯矩正弯矩负弯矩-12.65744107m10.02084-0.0135410.83448613n10.453090.35436弹性

23、中心离拱顶距离ys，拱桥上附表（）-3（1代表每米宽）规范5.1.4条1款拱的强度验算用的公路-级汽车荷载效应（拱圈填料为.5m通规4.3.2不计汽车冲击）拱顶截面弯矩及其相应的轴向力影响线面积和坐标拱脚截面弯矩及其相应的轴向力影响线面积和坐标拱桥上附表（）-13（46）-1.762025724拱桥上附表（）-12（10）m20.05572-0.057630.327483687h20.199140.065570.93709（截面号7）拱桥上附表（）-13（50）（）-12（10）m,n乘以面积图乘法人群荷载效应（利用汽车荷载中均布荷载效应乘以x）人群荷载（kn/m2）3人行道总宽（m）1.5桥

24、宽（m）8.5每米桥宽人群荷载（kn/m）为汽车均布荷载的x倍0.5294117650.214250006 人群荷载效应汇总表 荷载效应单位拱顶拱脚正弯矩mmax 负弯矩mmin 正弯矩mmax 负弯矩mmin轴向力kn5.79174839 4.63893455 7.33401325 5.73590442弯矩kn.m3.82065777 -2.1280866 10.3137964 -6.7009982温度引起的弹性中心赘余力结构升温23.4度规范5.1.4条1款拱的强度验算用的温度作用效应10.83448613结构降温-15.1度表值0.098911拱桥上附表（）-5u见第4款u0.01332

25、a0.0000080.040280.0886b19.68038726度0.008730.01079-1.925725894-72.29141172kn/m规范5.1.4条2款拱的整体“强度稳定”验算用的荷载效应拱桥上附表（）-14（75）取1/4拱跨处与mmax相应的h影响线面积与mmin相应的h影响面积之和（）-7（10）为汽车均布荷载的x倍0.214250006单位拱宽的计算荷载（表15）截面项目汽车20级等代荷载人群荷载合计k202/9*k20拱顶mmax42.841349.5202978 0.52941176 10.04971相应h26.3103165.8467369 0.529411

26、76 6.376149mmin30.598826.7997378 0.52941176 7.32915相应h24.027565.3394578 0.52941176 5.868871/4跨径mmax39.2758288.7279618 0.52941176 9.257374相应h23.8792925.3065093 0.52941176 5.835921mmin20.7770084.6171129 0.52941176 5.146525相应h23.1792925.1509538 0.52941176 5.680366拱脚mmax22.1195284.9154507 0.52941176 5.4

27、44862相应h22.9677965.1039547 0.52941176 5.633366相应v7.942521.7650044 0.52941176mmin31.1873246.9305164 0.52941176 7.459928相应h14.4907883.2201751 0.52941176 3.749587相应v14.6965363.2658969 0.52941176不计弹性压缩的汽车和人群内力（表16）截面项目计算荷载影响线面积表(iii)值乘数面积拱顶mmax10.049710.007252934.8184 6.7774334相应h6.37614870.069132/f152.

28、7032 10.556372mmin7.3291495-0.004562934.8184 -4.262772相应h5.86886950.059032/f152.7032 9.01406941/4截面mmax9.25737350.008822934.8184 8.2450982相应h5.83592110.040352/f152.7032 6.1615738mmin5.1465247-0.010472934.8184 -9.787549相应h5.68036550.087812/f152.7032 13.408867拱脚mmax5.44486240.019942934.8184 18.640279相

29、应h5.63336640.092422/f152.7032 14.112829相应v汽车1.76500440.1706730.57485.2182011人群0.5294118 0.5294117616.186659mmin7.4599282-0.014092934.8184 -13.17159相应h3.74958690.035752/f152.7032 5.4591391相应v汽车3.26589690.3293330.574810.069199人群0.5294118 0.5294117616.186659计入弹性压缩的汽车和人群内力（表17）项目拱顶1/4截面拱脚mmaxmminmmaxmmi

30、nmmaxmmin轴向力cosw10.945520.6955sinw00.3255640180.7185与m相应的h67.30899455 52.902397 35.9584583 76.16727 79.50274 20.469516与m相应的v17.77956 41.454373n67.30899455 52.902397 38.0303519 80.55596 68.06876 44.021515dh1.059011147 0.8323439 0.56575512 1.198383 1.250862 0.3220587dn1.059011147 0.8323439 0.53493278

31、1.133096 0.869975 0.2239918np66.24998341 52.070053 37.4954191 79.42286 67.19879 43.797524弯矩m68.11123675 -31.24249 76.3279543 -50.3719 101.4938 -98.25912yys-y12.0060.78164-4.1158dmdn*y2.124376361 1.6696818 0.41812486 0.885673 -3.58064 -0.921905mpm+dm70.23561311 -29.57281 76.7460792 -49.4862 97.91311

32、-99.18103不计入弹性压缩的挂车内力（表18）截面项目挂车100等代荷载影响线面积力或力矩k801.25/9*k80拱顶mmax82.73787611.491372 6.77743336 77.88201相应h67.440169.3666889 10.5563716 98.87825mmin43.5470886.0482067 -4.2627719 -25.7821相应h40.0011045.5557089 9.01406937 50.079551/4截面mmax82.89189211.512763 8.24509824 94.92386相应h54.5666167.5786967 6.1

33、6157376 46.6967mmin55.9206327.7667544 -9.7875486 -76.0175相应h48.6608686.7584539 13.4088672 90.62321拱脚mmax54.426387.5592194 18.6402788 140.906相应h44.583866.1922028 14.1128289 87.3895相应v12.6080321.7511156 5.21820112 9.137673mmin77.90567210.820232 -13.171591 -142.52相应h45.5918926.3322072 5.45913908 34.568

34、4相应v38.7298445.379145 10.0691989 54.16368计入弹性压缩的挂车内力(表1-9)项目拱顶1/4截面拱脚mmaxmminmmaxmminmmaxmmin轴力cosw10.945520.6955sinw00.3255640180.7185与m相应的h198.87824855 50.079545 46.6966985 90.62321 87.389534.5684与m相应的v9.137673 54.163681n98.87824855 50.079545 49.3873197 95.84484 67.34481 62.958927dh1.555708388 0.7

35、879303 0.73470603 1.425827 1.374949 0.5438845dn1.555708388 0.7879303 0.69467925 1.348148 0.956277 0.3782717np97.32254017 49.291615 48.6926404 94.49669 66.38854 62.580655弯矩m77.88200573 -25.78213 94.9238602 -76.0175 140.906 -142.5197yys-y12.0060.78164-4.1158dmdn*y3.120751026 1.5805882 0.54298909 1.053

36、766 -3.93585 -1.556891mpm+dm81.00275676 -24.20154 95.4668493 -74.9637 136.9701 -144.0766轴向力温度内力(表1-10)合拢温度拱圈线膨胀系数项目温度上升150c0.000008拱顶1/4截面拱脚温度变化在弹性中心产生的水平力htcosw10.945520.695511.54885yys-y12.0060.78164-4.1158nt=ht*cos11.5488510.91966865 8.0322252mt=-ht*y-23.166993 -9.027043114 47.532757主拱圈荷载效应不利组合的设

37、计值(1-11)编号荷载效应系数拱顶1/4截面mnmn1恒载1.2或0.924.839112774.623 9.678586 820.644112汽车-20级mmax1.4 70.2356131 66.24998 76.74608 37.4954193汽车-20级mmin1.4 -29.572811 52.07005 -49.4862 79.422864挂车-100mmax1.4 81.0027568 97.32254 95.46685 48.692645挂车-101mmin1.4 -24.201537 49.29162 -74.9637 94.4966896温度上升1.4 -23.16699

38、3 11.54885 -9.02704 10.9196697温度下降1.4 23.1669931 -11.5489 9.027043 -10.91967荷载组合mjnjmjnj8组合i恒+汽mmax1128.136793 1022.298 119.0588 1037.26659恒+汽mmin-19.046734 1002.446 -60.5699 1095.964910组合恒+汽mmax+温升0.876.5624019 830.7728 85.13676 842.0432411恒+汽mmin+温升-41.18442 814.8912 -58.5662 889.0019812恒+汽mmax+温降

39、128.456466 804.9033 105.3573 817.5831913恒+汽mmin+温降10.7096448 789.0218 -38.3457 864.5419214组合恒+挂mmax0.8114.568635 852.6393 116.2143 842.354115恒+挂mmin-9.2215609 798.8447 -76.9908 893.65464主拱圈抗力效应设计值(表1-12)截面编号与上表对应e0mj/nj查表值rajm截面面积a拱顶80.125342 0.7724429123001.9219-0.0190.9932766123001.921100.092158 0

40、.8626287123001.92111-0.05054 0.9542963123001.921120.159592 0.6767197123001.921130.013573 0.9965575123001.921140.134369 0.7470658123001.92115-0.01154 0.9975077123001.9211/4截面80.114781 0.8019014123001.9219-0.05527 0.9458328123001.921100.101107 0.8391522123001.92111-0.06588 0.9247486123001.921120.12886

41、4 0.7625505123001.92113-0.04435 0.9644262123001.921140.137964 0.7369561123001.92115-0.08615 0.877833123001.921拱脚80.063273 0.9301759123001.9219-0.14197 0.7256944123001.921100.108589 0.8189354123001.92111-0.09399 0.8579054123001.921120.017245 0.994455123001.92113-0.19073 0.5942283123001.921140.101284

42、0.8386799123001.92115-0.18317 0.6136428123001.921注:该种颜色格子为数据自动输出栏红色字体为人为输入栏拱脚查表数据输入栏目汽20级拱顶1/4截面拱脚计算跨径跨径50mmmax34.131.719.430.5748相应h19.919.818.530.5748相应v630.5748mmin23.8202430.5748相应h18.219.110.830.5748相应v11.230.5748跨径60mmmax29.627.81830.5748相应h16.617.716.230.5748相应v530.5748mmin20.319.620.330.5748相应h15.2178.930.5748相应v9.430.5748人行道宽度b0.75计算矢高6