拱桥计算程序

等截面悬链线圬工拱桥计算程序

一、设计资料

（一）设计标准

荷载汽车20挂车100人群（KN/m)3净跨径lo(m)50孔径数据净矢高fo(m)10车道布置净矢跨比(fo/lo) 1/5车行道(m)7人行道(m)1桥面总宽度(m)13车道数C2（二）材料及其数据1、拱上建筑拱顶填料厚桥面系换算厚度（m)度（m)0.50.24换算容重护拱容重腹拱容重拱腔填料容r1(KN/m3)r2(KN/m3)r3(KN/m3)重r4(KN/m3)202324192、主拱圈砂浆标号10料石标号40容重极限抗压强r5(KN/m3)度(KN/m2)246500极限抗剪强度(KN/m2)330弹性模量拱圈设计温(KN/m2)差(0C)520000020二、主拱圈计算

（一）确定拱轴系数

1、拟定上部结构尺寸（1）、主拱圈几何尺寸截面高度d'(m)0.9849采用截面横截面面积高度d(m)A（m2)1.01.0000惯性矩I(m4)0.0833截面抵抗截面回转假定拱轴系数m矩W(m3)半径γw(m)0.16670.28872.8140y1/4/f0.21sinφj0.70097计算跨径计算矢高jl(m)f(m)0.7131950.7010.14cosφ拱脚水平投影X(m)0.70拱脚竖向投影Y(m)0.71主拱圈截面坐标表

截面号101234567101112y1/f21.0000000.8100480.720.5084710.3908200.2919880.2100000.1432180.0903080.0502130.0221330.0055060.000000y1310.14348.21666.56575.15763.922.96182.13011.45270.91600.50930.22450.05580.0000cosφ40.713190.7310.811000.852380.888000.917820.942120.961370.976140.986960.994330.998601.00000d/(2*cos拱圈顶面y上拱圈底面yφ)(m)下(m)50.70110.620.61650.58660.56310.480.53070.52010.51220.50660.50290.50070.500069.44237.56255.94924.57103.40122.41701.59940.93260.40380.0027-0.2783-0.4449-0.5000710.84458.87087.18225.74424.52733.50652.66081.97281.42831.01590.72740.55660.5000x825.35023.23821.12519.01316.90014.78812.67510.5638.4506.3384.2252.1130.000（2）、拱上构造几何尺寸(a)腹拱圈砂浆标号10料石标号40截面高度d'(m)0.3净跨径l'（m)3净矢高f'(m)0.6净矢跨比f'/l' 1/5sinφ0cosφ0拱脚水平投影X'(m)0.66550.7241380.21拱脚竖向投影Y'(m)0.22(b)腹拱墩砂浆标号10块石标号40横墙厚度（m)0.8腹拱墩高度计算表项目1#横墙2#横墙3#拱座空、实腹段分界线X(m)ξ=X/Lκξy1=f/(m-h=y1+d/2*(1-tgφcosφ=Ln(m+SQRT(1)*(chκξ-=2*f*k/(m-=1/SQRT(tgφ1/cosφi)-1)/l*shκξ*tgφ+1)m2-1)*ξ1)(d'+f')22.301018.501014.997514.410.87970.72980.59160.58751.49071.23671.00250.99567.452.84973.05343.00800.78780.0.44070.43670.78550.86150.91510.916.423.872.112.062、恒载计算(1)主拱圈恒载PkP0~12=Pk*A*0.55288r5*l672.76M1/4kM1/4=Mk*A*r0.126145*l/41945.52MjkMj=Mj*A*r50.52303*l/48066.97(1)拱上空腹段恒载(a)腹孔上部腹拱圈外弧腹拱圈内腹拱圈重Pa侧墙护拱重R跨径l'外弧半径R0（KN)Pb(KN)3.412.1825.4816.750.725001Aa1.52202Ab0.118填料及路面两腹拱间一个腹拱重Pc（KN）以上重Pd重P(KN)50.5214.87107.63(b)腹孔下部1#横墙P1(KN)121.282#横墙P2(KN)72.393#拱座P3(KN)11.00集中力P13(KN)228.91集中力P14(KN)180.01集中力P15(KN)57.38

F1ξ=X/Lκξ=Ln(m+SQRT(m2-1)*ξ(C)拱上实腹段的恒载拱顶填料及桥面重P16曲边三角形部分重P17shκξ1.1684chκξ1.5379重心位置(m)11.23220.43269.249.94230.58750.9956第 1 页

上部结构计算

(E)半拱恒载对拱脚和1/4拱跨截面的弯距分块号P0-12P13P14P15P16P17合计恒重（KN）672.76228.91180.0157.38220.43269.241628.73(2.32)5.231.44(133.25)1152.47388.793353.53l/4截面力臂(m)力矩(KN.m)1945.52拱脚截面力臂(m)力矩(KN.m)8066.97698.061233.00594.033946.503801.4818340.043.056.8510.3517.9014.123、验算拱轴系数ΣM1/4/ΣMj0.18判断修改拱轴系数(二）拱圈弹性中心及弹性压缩系数ys/f0.3334弹性中心ys3.3821rw20.0833rw2/f20.00081系数11.1272系数9.18594μ1μ0.007440.00901μ1/（1+μ）0.005(三）主拱圈截面内力计算1、恒载内力计算

(1）不计弹性压缩的恒载推力

Hg'=ΣMj/f=

1808.08(KN)

(2）计入弹性压缩的恒载内力计算表项目y=ys-y1cosφHg=(1-μ1/（1+μ）)*Hg'Ng=Hg'*μ1/（1+μ）*cosφMg=μ1/（1+μ）*Hg'*y拱顶3.381.000001791.901808.08.703*l/8截面2.870.986961791.901831.96.47l/4截面1.250.942121791.901919.1620.25l/8截面-1.780.852381791.902121.21-28.72拱脚-6.760.713191791.902535.19-109.361、活载内力计算

（1）、汽车、挂车和人群荷载的内力车道折减系单位拱宽汽车等代荷载单位拱宽人群等代荷载单位拱宽挂车等代荷载K1系数K2（KN）K2系数数ξ0.153850.346150.096151.00单位拱宽的计算荷载表截面项目Mmax拱顶相应的H1Mmin相应的H1Mmaxl/4截面相应的H1Mmin相应的H1Mmax相应的H1相应的VMmin相应的H1相应的V汽车-20级等代荷载K2039.796224.359328.084622.022437.183624.271921.4820.424320.511718.23885.600928.934113.491813.8107K16.12253.747.32073.38815.72063.73413.30563.14223.15562.80600.86174.45142.07572.1247人群荷载K20.350.350.350.350.350.350.350.350.350.350.350.350.350.35合计6.468.09374.66693.73426.06674.08033.65183.48843.50183.15214.79762.4218拱脚l/4截面拱顶截面不计弹性压缩的汽车和人群内力计算表项目Mmax相应的H1Mmin相应的H1Mmax相应的H1Mmin相应的H1Mmax相应的H1相应的VMmin相应的H1相应的V汽车人群汽车人群计算荷载系数6.468.09374.66693.73426.06674.08033.65183.48843.50183.15210.86170.3.79762.42182.12470.350.00730.0691-0.00460.05900.00880.0404-0.01050.08780.01990.09240.50000.1707-0.01410.03580.50.32933影响线面积乘数2570.59253.422570.59253.422570.59253.422570.59253.422570.59253.4250.702570.59253.4250.70面积18.636817.5192-11.721914.959722.672610.2257-26.914122.253251.257523.421525.35058.6531-36.21969.059925.350516.6974120.5671.7192-.704455.8626137.8041.7238-98.283577.6271179.493673.827521.84392.9953-173.7621.941553.86285.7799力或弯矩拱脚不计弹性压缩的挂车内力计算表计入弹性压缩的汽车和人群内力计算表项目cosφsinφ与M相应的Hi与M相应的V拱顶Mmax1.00000.000071.719271.71920.160.1671.0776120.562.1699122.724655.862655.86260.49970.499755.3628-.70441.6902-53.0142MminMmaxl/4截面Mmin0.94210.335341.723844.28710.37330.3513.9355137.800.4673138.015377.627182.39620.69440.6281.7419-98.28350.8694-97.4141Mmax拱脚Mmin0.71320.701073.827524.839270.060.66040.471069.5936179.4936-4.46175.028221.941559.2657.45620.19630.140057.3162-173.76-1.3271-175.0926截面项目Mmax汽车-20级等代荷载K8077.158462.792539.422434.57277.120550.007951.8565.494450.281841.244811.63671.393442.616836.12051.25/9*K80影响线面积18.636817.5192-11.721914.959722.672610.2257-26.914122.253251.257523.421525.3505-36.21969.059925.3505力或弯矩138.2676105.7766-44.433149.7293168.127149.1697-134.1997.3458247.819392.886128.3633-248.638437.125588.047.41916.03773.79063.32427.414.808.98624.374.83483.96581.11886.884.09783.4731拱顶相应的H1Mmin相应的H1Mmax相应的H1轴向力N=H1*cosφ+V*sinφ△H=μ1/（1+μ）*H1l/4截面Mmin相应的H1Mmax相应的H1相应的VMmin相应的H1相应的V△N=△H*cosφNP=N-△NM弯矩y=ys-y1△M=△H*y3.38211.2520-6.7613拱脚MP=M+△M第 2 页

上部结构计算

计入弹性压缩的挂车内力计算表项目cosφsinφ与M相应的Hi与M相应的V拱顶MmaxMminMmax1.00000.0000105.7769.7293105.77660.946349.72930.4449l/4截面MminMmax0.94210.335349.169797.345852.19050.4399103.320.8708拱脚Mmin0.71320.701092.886137.125528.363388.0486.12730.830988.19480.3321轴向力N=H1*cosφ+V*sinφ△H=μ1/（1+μ）*H1△N=△H*cosφ弯矩NP=N-△NMy=ys-y1△M=△H*yMP=M+△M0.94630.4449104.830449.2845138.2676-44.43313.38213.20031.5046141.4679-42.92860.41440.820451.7761102.5059168.1271-134.191.25200.55071.0903168.6778-133.10860.59260.236985.534687.9579247.8193-248.6384-6.7613-5.6182-2.2455242.2011-250.8840温度内力计算表项目cosφy=ys-y1Nt=Ht*cosφMt=-Ht*y拱顶1.000003.386.7812-22.9348温度上升l/4截面0.942121.256.3887-8.4901拱脚0.71319-6.7.836345.8495拱顶1.000003.38-6.781222.9348温度下降l/4截面0.942121.25-6.38878.4901拱脚0.71319-6.76-4.8363-45.8495温度产生拱圈砌体的水平力线膨胀系系数Ht（KN）数8.00E-060.0993736.7812(四）主拱圈正截面强度验算

（1）主拱圈荷载效应不利组合的设计值编号1234567101112131415组合III组合II荷载效应恒载汽车-20级Mmax汽车-20级Mmin挂车-100Mmax挂车-100Mmin温度上升温度下降荷载组合组合I恒+汽Mmax恒+汽Mmin恒+汽Mmax+温升恒+汽Mmin+温升恒+汽Mmax+温降恒+汽Mmin+温降恒+挂Mmax恒+挂Mmin0.80.811.4系数1.2或0.9拱顶M(KN.m)N(KN).701808.08122.72-53.01141.47-42.93-22.9322.93Mj(KN.m)237.46-24.991.28-45.68215.655.70210.96-8.6971.0855.36104.8349.286.78-6.78Nj(KN)2269.201704.781822.951371.421807.761356.231853.161357.01l/4截面M(KN.m)N(KN)20.251919.16138.02-97.41168.68-133.11-8.498.49Mj(KN.m)217.52-118.151.51-104.03183.53-85.01208.36-134.5043.9481.7451.78102.516.39-6.39Nj(KN)23.501841.6818.751480.501884.441466.191900.381496.60拱脚M(KN.m)N(KN)-109.362535.19175.03-175.09242.20-250.8845.85-45.85Mj(KN.m)146.61-376.36168.-249.7465.94-352.44192.53-385.9869.5957.3285.5387.9.84-4.84Nj(KN)2379.113122.481908.702503.4017.872492.561921.142532.30（2）主拱圈截面抗力材料安全系截面形状数rm系数m1.928主拱圈抗力效应的设计值计算表

截面编号101112131415101112131415101112131415e0=Mj/Nj0.1046-0.01470.0901-0.03330.11930.00420.1138-0.000.0920-0.020.0866-0.07030.0974-0.05800.1096-0.090.0616-0.12050.0884-0.09980.0347-0.14140.1002-0.1524α=（1-(e0/y))m/(1+e0/yw)2RN=α*A*Raj/rm2992.223376.713084.793340.9521.613384.702929.803383.753073.303226.083105.663196.053039.4732.132958.623086.293237.862882.823095.443024.253337.082730.353021.3127.36[e0]0.25应力值判断偏心距判断满足要求满足要求满足要求满足要求满足要求满足要求满足要求满足要求满足要求满足要求满足要求满足要求满足要求满足要求满足要求满足要求满足要求修改截面满足要求满足要求满足要求满足要求满足要求满足要求满足要求满足要求满足要求满足要求满足要求满足要求满足要求满足要求满足要求满足要求满足要求满足要求满足要求满足要求满足要求满足要求满足要求满足要求满足要求满足要求满足要求满足要求满足要求满足要求拱圈l/4截面拱脚0.88390.99740.91120.98690.810.99980.860.99950.90780.95290.91740.94410.780.96120.87390.91160.950.85150.91430.330.98570.80650.240.78200.30.250.30.250.3第 3 页

上部结构计算

（2）主拱圈正截面受剪强度验算（a）内力计算恒载Qg94.48Ng2535.19KH17.56Hp98.11汽车-20级+人群荷载KV12.71Vp58.34Qp27.16Np110.87KG34.83Hp107.82挂车-100荷载KG19.72Vp48.07Qp41.29Np110.59（b）荷载组合组合IQj151.402Nj3197.453组合IIIQj136.944Nj2557.651强度验算组合I组合III2381.0741933.213判断组合I组合III满足要求满足要求(五）主拱圈稳定性验算悬链线弧长系数 l/rS56.063lo20.183β20.183α0.002α*β(β-3)1.105750.694主拱圈稳定性验算计算表截面拱顶l/4截面拱脚Nj=0.77*1.2*Nge0=Mg/Ng0.0300.0110.043[e0]0.3500.3500.350α=(1-(e0/y)8)/((1+e0/rw)2)φ0.5870.5900.583RN=φ*α*A*Raj/rm1965.4971994.8581931.820判断应力满足要求满足要求修改截面判断偏心距满足要求满足要求满足要求1670.6611773.3002342.5190.90.9990.978(五）主拱圈裸拱强度和稳定性验算(1）弹性中心的弯距和推力弯矩系数0.18636弹性中心水平力系数弯矩MS2874.3290.53288推力HS804.285(2）截面内力拱顶截面M1.134N804.285系数0.12614l/4截面M-78.169系数0.273N861.656系数0.52303拱脚截面M系数245.3590.55288N########(3）裸拱强度和稳定性验算表截面拱顶l/4截面拱脚Nj=0.77*1.2*Nge0=Mg/Ng0.1920.0910.235[e0]0.3500.3500.350α=(1-(e0/y)8)/((1+e0/rw)2)φ0.4760.5600.434RN=φ*α*A*Raj/rm1118.71726.433884.630判断应力满足要求满足要求修改截面判断偏心距满足要求满足要求满足要求743.160796.170965.7570.6940.9100.602第 4 页