下承式拱桥设计计算书(总30页)

下承式拱桥设计计算书一、 设计资料1设计标准设计荷载：汽车-20级，挂车-100，人群荷载3.0kN/M2。桥面净宽：净-9m+和附21.0m人行道拱肋为等截面悬链线矩形拱,矩形截面高为2.2m,宽为1.0m 。净跨径：=110m净矢高：=22m净矢跨比: = 1/52主要构件材料及其数据桥面铺装：10cm厚C50混凝土，1 =25kN/m3; 2cm沥青砼桥面铺装,材料容重2=23kN/m3;桥面板：0.5m厚空心简支板，C30级钢筋砼3 =25kN/m3;主拱圈、拱座：C40级钢筋砼矩形截面， =25 kN/m3;拉杆：HDPE护套高强度钢丝束，上端为冷铸锚头，下端为穿销铰。=18kN/m3 3 计算依据1）中华人民共和国交通部标准公路桥涵设计通用规范人民交通出版社，1985年。2）中华人民共和国交通部标准公路桥涵设计手册拱桥上、下册，人民交通出版社，1978年。3)中华人民共和国交通部标准，公路桥涵地基与基础设计规范，人民交通出版社，JTJ024-85二、 主拱圈截面几何要素的计算（一）主拱圈横截面尺寸如图1所示 图1 拱圈横断面构造（尺寸单位：cm） （二）主拱圈截面几何性质截面积： 绕肋底边缘的静面矩：主拱圈截面重心轴 y下=1.0m y上= y下=1.0m主拱圈截面绕重心轴的惯性矩 主拱圈截面绕重心轴的回转半径 （三）计算跨径和计算矢高计算跨径: =45.039、=2.2m、=1.8m =计算矢高: 三、 主拱圈的计算（一）拱轴系数的确定 吊杆及拱圈构造如图2 图2 吊杆及拱圈构造图假定拱轴系数m=1.988，相应的=0.601,f0/ l0=,查拱桥（上册）表（）-20（5）得 sinj=0.67354, cosj=0.73915拱脚截面的水平投影和竖向投影 x=Hsinj=2.00.67354=1.346m y=Hcosj=2.00.73915=1.478m将拱脚沿跨径24等分，每等分长=4.583m,每等分点拱轴线的纵坐标y1=表（）-1值f,相应的拱背曲面坐标,拱腹曲面坐标。具体数值见表1，具体位置见图3。 图3 拱轴坐标示意图截面号 cos123456789054.9961.00000022.22400.73915150.4130.90803120.18000.76006245.8300.82178318.26300.78036341.2470.74100116.46800.79997436.6640.66544214.78900.81884532.0810.59488213.22100.83689627.4980.52911011.75900.85406722.9150.46793210.33900.87032818.3320.4111649.13800.88563913.7490.3586377.97000.89997109.1660.3101956.89400.91332114.5830.2656935.90500.925561200.2250005.00000.93701 表1 主拱圈几何性质表 (二)、桥面结构恒载计算1.桥面系(1) 桥面铺装: 2cm厚沥青砼铺装，=22/m3 0.0898.522=126.738cm厚现浇C50砼，=25/m30.0898.524=138.241cm防水层，=0.2/m2 0.289=14.4 (2) 空心板：0.5m厚空心板，空心板折减率为0.70.5980.725=630（3） 普通横梁：宽0.6m,厚0.4m砼矩形截面梁。=25/m3 (4) 人行道：a.人行道铺装 =24/m3 1.00.02242=0.96/mb.人行道板、缘石=25/m3 （0.081.30.10.220.10.30）252=8.7/mc.人行道下填砂层=18/m3 1.00.02182=0.72/md.人行道块件内水管铸铁容重为78.5/m3，水的容重为10 /m3，水管内径为36cm,外径为38cm。 20.0178.5(0.362/4)102=3.6752KN/me.人行道块件里填砂砾石或装电缆，=18/m3 1.00.6(0.362/4)182=0.6575/m以上5项共为：0.968.70.723.67520.65755.0=19.7127/m(5) 栏杆：6/m(6) 吊杆：DPE护套高强度钢丝束，=18kN/m3 以上所有荷载相加得： 吊杆纵向间距为5米，所以，每根吊杆所承受的压力为（7）、主拱圈 0.523813.625=47.079 图4 盖梁、立柱构造图(尺寸单位：cm) 2 计算活荷载 横向分布系数： 1.32 1.130 0.716 纵向荷载： 汽20： 挂100： 汽20+人群： 挂100： 汽20+人群控制设计 吊杆内力总和： 吊杆采用高强钢丝索组成，抗拉标准强度R=1600kP。考虑吊杆构件在可变荷载反复作用下的疲劳强度问题，采用0.4R控制设计，则需钢丝为： 吊杆采用高强钢丝索组成吊杆，吊杆用热聚乙烯防腐。（三）、验算拱轴系数恒载对跨及拱脚截面的力矩见表二。 部位项目吊吊竿11吊竿10吊竿9吊竿8吊竿7吊竿6吊竿5吊竿4吊竿3吊竿2吊竿145.7145.7145.7145.7145.7145.7145.7145.7145.7145.7145.71对l/4点力臂27.50 22.5017.5012.507.502.507.5012.5017.5022.5027.50对l/4力矩1257.021028.48799.92571.38342.83114.27342.83571.38799.921028.481257.02对拱脚力臂5.0010.0015.0020.0025.003.0035.0040.0045.0050.0055.00对拱脚力矩228.55457.10685.65914.201142.751371.301599.851828.402056.952285.502514.05 表2 恒载对跨及拱脚截面的力矩由表二知可知，该值与0.601之差为0.0006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m=1.988 （四）、主拱圈截面内力计算 大跨径拱桥应验算拱顶、3/8拱跨、1/4拱跨和拱脚4个截面，必要时应验算1/8拱跨截面。1、 弹性中心 表（）3值 =0.34206822.2240=7.6022、 弹性压缩系数 =表（）9值 =11.01050.0014=0.01567 =表（）11值 =9.126440.0014=0.01422 =0.015401 （五）、主拱圈截面内力的验算 大跨径拱桥应验算拱顶、拱脚、拱跨1/8、1/4、3/8、等截面的内力。1、结构自重内力计算 在确定m系数时，其实算得的数值很难与选定的拱轴系数“五点”重合，对于大跨径拱桥必须用“假载法”计入“五点”存在的偏离影响。1.用假载法计算确定m系数时在“五点”存在的偏差(1) 假载内力a. 求假载由式 得 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表3. 不计弹性压缩的假载内力 表3项目影响线面积力或力矩（）表（）-14（35）值乘数 拱顶截面0.00660-0.00496=0.0016420.33301027.17430.06536+0.06167=0.1270370.75063574.1505截面0.00335-0.00480=-0.00145-17.9773-908.17000.02211+0.10492=0.1270370.75063574.1505截面0.00897-0.00100=0.0079798.81344991.81580.04054+0.08650=0.1270470.75063574.1505截面0.00847-0.00768=0.000799.7946494.79960.06392+0.06312=0.1270470.75063574.1505拱脚截面0.001861-0.01494=-0.013079-162.1557-8191.71680.08977+0.03726=0.1270370.75063574.15050.555.67352812.4916c.计入弹性压缩的假载内力计入弹性压缩的假载内力见表4项目拱顶截面截面L/4截面截面拱脚截面10.938720.7305700.344690.682843253.97503253.97503253.97502553.386829.132829.132829.13283224.84223752.08404100.49501022.1529-640.13382275.44816.85682.4099-13.35621221.9107-569.93171886.3446计入弹性压缩的假载内力 见表4注：L/4截面的轴力以作近似计算。(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”内力见表5。表5项目拱顶截面截面L/4截面截面拱脚截面10.938720.7305739601.384738429.8563 38429.856339246.833538085.793838085.793839601.384740938.572052602.5655354.5512322.9784251.361739246.833540615.593652351.20386.85682.4099-13.35622431.0866829.1562-4595.3676注：从拱顶到第8截面，第七截面到拱脚。(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，计算结果见表6。考虑“五点”偏差的恒载内力 表6 截面项目拱顶截面L/4截面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39601.38473224.842236376.542538429.85633224.842235205.014138429.85633224.842235205.0141轴 力39246.83353224.842236021.991340615.59363752.084036863.509652351.20384100.495048250.7088 弯 矩2431.08661221.91071209.1759829.1562-569.93171399.0937-4595.36761886.3446-6481.71222.“恒载压力线”偏离拱轴线的影响（图13）(1)“恒载压力线”偏离拱轴线的偏离弯矩计算恒载偏离弯矩，首先要计算出桥跨结构沿跨径等分段的分块恒载对各截面的力矩，再计算各截面压力线的纵坐标，然后才能求得，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（图14） 式中，可根据值查附表1-1得。主拱圈对各截面的力矩见表7。 主拱圈自重对各截面产生的弯矩 表7截面号（kN.m）0123451200000110.083330.0833870.0037560.0031931308.2687100.167770.1681540.0144110.0138005654.277390.250000.2512100.0314800.03132312833.980380.333330.3362930.0565860.05551122744.535470.416670.4225500.0886920.08737235941.536760.500000.5103100.1289000.12615551689.518550.583330.6002960.1779680.17220370556.776640.666670.6928340.2358390.22605392620.750130.750000.7884600.3033000.288045118020.736820.833330.8884490.3828270.357544146496.589110.916670.9932240.4745910.435868178588.300501.000001.1036700.5801300.523540214510.1701b.拱上实腹段恒载对各截面产生的弯矩计算拱上实腹段的恒载时，必须将拱顶填料及面层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，否则只能近似的计算。(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 式中k表示空，实腹段的分解点取 。各截面力矩见表8。拱上实腹段恒载对各截面产生的力矩 表8区间截面号 悬链线曲边三角形 矩形块 012345678 910实腹段12 000000000110.083330.120545.87240.75001.052648.28530.00351422.24701470.5323100.167770.2409367.31350.75022.1044772.97450.01395648.35246421.326990.250000.36141244.70100.75053.15273924.16880.031312718.951916643.120780.333330.48192966.03630.75104.194812441.92910.055622593.409735035.3388分界点0.33495 0.48423009.04190.7510空腹段70.416673009.04190.75107.767223371.83030.084634377.742157749.572460.500003009.04190.751011.979036045.31290.113846243.345782288.658650.583333009.04190.751016.190948719.09650.143058108.9493106828.045840.666673009.04190.751020.403361394.38460.172169933.9173131328.301930.750003009.04190.751024.615274068.16820.201381799.5210155867.689220.833333009.04190.751028.820786722.69390.230593665.1246180387.818510.916673009.04190.751033.039499416.93900.2597105530.7283204947.667301.000003009.04190.751037.2513112090.72250.28885117376.0141229466.7366(b) 悬链线曲边三角形块从拱顶到任意截面的重力（见表9）。 每一块P的重心的横坐标拱上各集中力对各截面产生的力矩 表9截面竖向力6.701613.403213.403213.403213.40321069.170613.403202.24964.49796.73988.976817.430011.2056120000110.083334.211928.226526.301100000100.166678.424356.456382.760752.626322.577700090.2500012.636184.6821139.2123109.076679.029349.0463019.172880.3333316.8480112.9086195.6653165.5309135.4822105.4993075.626270.4166721.0604141.1384252.1249221.9905191.9419161.95893885.3660132.085960.5000025.2723169.3648308.5779278.4434248.3948218.41188384.7566188.538850.5833329.4841197.5906365.0295334.8950304.8464274.863412887.8893244.990440.6666733.6965225.8205421.4891391.3547361.3060331.323017391.6636301.450030.7500037.9084254.0469477.9420447.8076417.7590387.776021894.9032357.903020.8333342.1202282.2727534.3936504.2592474.2106444.227626398.0360414.354610.9166746.3326310.5026590.8533560.7189530.6702500.663130901.1687470.814201.0000050.5445338.7290647.3062617.1718587.1232557.140235405.0498527.2671截面中接头39.064010.3903P613.403213.5000P713.403215.6300P813.403217.8218P16(柱)2957.848024.2800P913.403219.9966P1013.403222.1496P15(柱)3432.865031.0800P1113.403224.2816120000000001100000000010000000000987.7299000000008252.263644.873916.32510000007416.8169101.333672.784743.4076014.25830006581.3504157.7865129.237799.86052935.072670.711341.8542013.27865745.8802214.2381185.6893156.312315392.9368127.162998.3058069.73054910.4334270.6977242.1489212.771827852.5757183.6225154.76548982.0520126.189831074.9671327.1507298.6019269.224740310.7357240.0754211.218323440.9754182.642721239.4968383.6023355.0534325.676352768.5999296.5270267.669937899.5162239.094311404.0500440.0619411.5131382.136065228.2388352.9867324.129652360.1167295.554001568.5837496.5148467.9660438.588977686.3988409.4396380.582566819.0008352.0069上表截面P12P13P14(柱)P14P15P16P13(柱)P17P1813.403213.40324057.271613.403213.403213.40324855.275013.403213.403226.390328.474137.880030.531432.567434.548444.680036.506138.43131200000000011000000000100000000009000000000800000000070000000006000000000541.466813.53720000000497.926569.9969042.422515.133600003154.3794126.4498115.226598.875471.586545.0348018.795302210.8310182.901417203.6430155.3270128.0381101.4863075.246949.44311267.2906239.361034294.4939211.7866184.4977157.94608023.8275131.7065105.90270323.7436295.814051383.3162268.2396240.9507214.398928473.7602188.1595162.3556续上表截面P19P20P21P22P23拱脚加强段腹拱水平推力合计13.403213.403213.403213.403220.291239.06401171.528440.326442.169343.977045.751447.485247.89631200000001100000058.8210000000223.0129000000580.84800000001121.3670000003.04762811.78538468.4760000004.44694451.105018302.5250000006.14766443.523438128.9640000008.17458818.094367437.60300000010.556911609.143578595.08224.04270000013.329614857.4403155858.30180.502355.801531.57267.78990016.532818610.0801217514.000136.9552112.254588.025564.242962.0769103.449320.213022921.5389269468.16在实腹段里，截面重心到任意截面的力臂为，在实腹段里，整块曲边三角形面积的重心到每个截面的力臂为。每个截面的力矩见表10。c.各集中力对各截面的力矩拱上实腹段的腹空和横隔板等各集中力及相应的横坐标在前面的过程中已经求出，各竖向集中力到截面的力臂，产生的力矩；腹拱水平推力作用在第7与第8截面之间，对0-7截面产生的力矩。具体见表11。d.计算偏离弯矩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，为不计弹性压缩的恒载水平推力=36409.2090kN.各截面上“恒载压力线”偏离拱轴线的值偏离弯矩偏离弯矩 表12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1234567891200000000111308.26871470.532358.822837.62100.077940.11840.04051474.5730105654.27736421.3269223.01212298.61620.337790.47540.13765009.9072912833.980316643.1207580.8430057.94000.825561.07620.25069124.1478822744.535435035.33881121.3658901.23001.617761.92950.311711348.7505735941.536757749.57248468.47102159.60002.805873.04760.24178800.1058651689.518582288.658618302.52152280.70004.182484.44690.26449626.5949570556.7766106828.045838128.96215513.80005.919216.14760.22848315.8633492620.7501131328.301967437.60291386.70008.003108.17450.17146240.53843118020.7368155867.689278595.08352483.50009.6811610.55690.875731872.62162146496.5891180387.8185155858.30482742.700013.2588113.32960.07082577.77201178588.3005204947.6673217514.00601050.000016.5081916.53280.0246895.66650214510.1701229466.7366269468.16713445.100019.5951820.21300.617822493.6093(3) 偏离弯矩在弹性中心产生的赘余力赘余力见表13计算表 表13截面1234 5671201.000000.50000.00006.85680.0000110.04050.998421.00160.04066.73840.2736100.13760.993631.00640.13856.38140.883890.25060.983491.01680.25485.78061.472980.31170.973801.02690.32014.92731.577370.24170.958301.04350.25223.80920.960760.26440.938721.06530.28182.40990.679150.22840.914801.09310.24970.70920.177140.17140.886391.12820.1934-1.3177-0.254830.87570.853471.17171.0260-3.7001-3.796320.07080.816221.22520.0867-6.4728-0.561210.02460.775041.29030.0317-9.6760-0.306700.61780.730570.68440.8456-13.3562-11.294013.25343.7211-10.1885由表13可得751.8502kN.m(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表14。(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“压力线”偏离拱轴线的附加内力 表14项目拱顶截面L/4截面拱脚截面10.938720.7305700.344690.682846.85682.4099-13.3562751.8502705.7768549.27920259.1552513.393409626.594922493.609310222.456710222.456710222.45675067.170218037.167842757.9276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将有关数据代入内力公式中，得所以，空腹式无铰拱恒载压力线的纵坐标见表15，其形状见图13。3.空腹式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入拱轴系数m的偏差影响的内力与“压力线”及拱线偏离的附加内力之和，其结果见表16。空腹式无铰拱恒载压力线 表15截面0123456781206.856800.05811.000000.49370.1177-0.1177110.11846.73840.04050.09780.998420.99530.09830.0199100.47546.38140.13760.19270.993631.00010.19250.281791.07625.78060.25060.30180.983491.01060.29860.772681.92954.92730.31170.35750.973801.02070.35021.569973.04763.80920.24170.28050.958301.03740.27042.765464.44692.40990.26440.29430.938721.05840.28094.147556.14760.70920.22840.24750.914801.08730.22765.898848.1745-1.31770.17140.17770.886391.12260.15837.9959310.5569-3.70010.87570.86680.853471.16630.74329.6863213.3296-6.47280.07080.04440.816221.22000.036413.2830116.5328-9.67600.0246-0.02210.775041.2854-0.017216.5550020.2130-13.35620.61780.54780.730571.36420.535519.4800恒载内力表 表16截面项目拱顶截面L/4截面拱脚截面表8表14合计表8表14合计表8表14合计水平力36376.5425751.850237128.3935205.0141751.850235956.864335205.0141751.850235956.86轴力36021.9913751.850236773.8436863.5096705.776837569.2948250.7088 549.279248799.99弯矩1209.17595067.17026276.3461399.093718037.167819436.26-6481.712242757.927636276.22 2、活载内力计算（1） 汽车20和人群荷载的内力 双车道的汽车等代荷载 人群荷载 213.0=6.0 kN 汽车和人群荷载的数值见表三。 不记弹性压缩的汽车20级及人群荷载内力见表4。 记入弹性压缩的汽车20级及人群荷载内力见表5。 截面项 目汽车20级等代荷载人群荷载 合计拱顶截面 相应 相应 截面 相应 相应 拱脚截面 相应 相应 相应相应 表3 汽车20级和人群荷载表 截面项目计算荷载 影响线面积力或力矩表（）14（35）值乘数面积拱顶截面相应相应截面相应相应拱脚截面相应相应汽人相应相应汽人 表4 不记弹性压缩的汽车20级及人群荷载内力 项目拱顶截面截面拱脚截面 与M相应的与M相应的 表5 考虑弹性压缩的汽车20级及人群荷载内力（2）挂车100的内力挂车100的等代荷载为80的1.25倍。不记弹性压缩的挂车100的荷载内力见表6。记入弹性压缩的挂车100荷载内力见表7 截面项 目挂车100级等代荷载影响线面积 力或力矩拱顶截面 相应 相应 截面 相应 相应 拱脚截面 相应 相应 相应相应 表6 不记弹性压缩的挂车100的荷载内力项目拱顶截面截面拱脚截面轴力与M相应的与M相应的弯矩 表7 记入弹性压缩的挂车100荷载内力3 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 拱圈材料弹性摸量=3.00拱圈材料线膨胀系数=0.000010=1混凝土收缩作用按下降10温度的影响记入。混凝土徐变作用的影响，当计算温度内力时以=0.7；当计算混凝土收缩内力时以=0.45的系数记入。于是 降低温度时=0.7（2-7）+0.45（-10）=-8 升高温度时=0.7（30-7）+0.45（-10）=11.6 它们在弹性中心产生的水平力 29.1 温度变化、混凝土徐变和收缩的内力见表8。项目 温度上升 温度下降拱顶截面截面拱脚截面拱顶截面截面拱脚截面 表8 温度变化、混凝土徐变和收缩的内力（六）、主拱圈正截面强度验算 根据桥规（JTJ02185）的规定，构件按极限状态设计的原则是：荷载效应不利组合的设计值小于或等于结构抗力效应的设计值。即 1、 正截面受压强度验算（1） 荷载组合 根据桥规（JTJ02189、JTJ02285）