某公路隧道衬砌结构计算书

'目录一基本资料1二荷载确定12.1围岩竖向均布压力12.2围岩水平均布力2三衬砌几何要素23.1衬砌几何尺寸23.2半拱轴线长度S及分段轴长△S23.3割分块接缝重心几何要素3四计算位移34.1单位位移44.2载位移——主动荷载在基本结构中引起的位移44.3载位移——单位弹性抗力及相应的摩擦力引起的位移84.4墙低（弹性地基上的刚性梁）位移12五解力法方程13六计算主动荷载和被动荷载（）分别产生的衬砌内力13七最大抗力值的求解15八计算衬砌总内力16九衬砌截面强度检算（检算几个控制截面）169.1拱顶（截面0）169.2截面（7）189.3墙低（截面8）偏心检查18十内力图18 一基本资料高速公路隧道，结构断面如图1所示，围岩级别为V级，容重，围岩的弹性抗力系数，衬砌材料C20混凝土，弹性模量，容重。图1衬砌结构断面二荷载确定2.1围岩竖向均布压力：式中：s——围岩级别，此处s=5；——围岩容重，此处=18kN/㎡；——跨度影响系数，=1+i(Bm-5)，毛洞跨度Bm=12.02m，Bm=5~15时，i=0.1，此处:=1+0.1×（12.02-5）=1.702所以，有：4 考虑到初期之处承担大部分围岩压力，而二次衬砌一般作为安全储备，故对围岩压力进行折减，对于本隧道按照45%折减，即2.2围岩水平均布力：e=0.4×q=0.4×99.2606=39.7043kPa三衬砌几何要素3.1衬砌几何尺寸内轮廓半径r1=5.56m；内径r1所画圆曲线的终点截面与竖直轴的夹角=100°；截面厚度d=0.45m。外轮廓线半径：R1=5.56+0.45=6.01m拱轴线半径：=5.56+0.45×0.45=5.7625拱轴线各段圆弧中心角：=100°3.2半拱轴线长度S及分段轴长△S分段轴线长度:半拱轴线长度为：S=S1=10.0575m将半拱轴线等分为8段，每段轴长为：3.3割分块接缝重心几何要素（1）与竖直轴夹角4 角度闭合差=0。各接缝中心点坐标可由图1中直接量出。四计算位移图2衬砌结构计算图4.1单位位移用辛普生法近似计算，按计算列表进行。单位位移的计算见表14 单位位移计算如下：计算精度校核为：闭合差4.2载位移——主动荷载在基本结构中引起的位移（1）每一楔块上的作用力竖向力：式中：bi——衬砌外缘相邻两截面之间的水平投影长度，由图2量得：4 单位位移计算表表1截面Φ（°）sinΦcosΦx（m）y(m)d(m)0001000.450.00759131.68720.00000.0000131.6872112.50.21640.97631.25190.13710.450.00759131.687218.06322.4765170.35532250.42260.90632.44470.54200.450.00759131.687271.409738.7041313.2759337.50.60880.79343.52191.19550.450.00759131.6872157.5099188.3031635.07514500.76600.64284.43132.06650.450.00759131.6872272.2661562.63801238.9226562.50.88700.46175.13133.11380.450.00759131.6872410.25031277.43752229.69046750.96590.25885.58774.28770.450.00759131.6872564.91442422.18333683.7643787.50.99900.04365.77925.53270.450.00759131.6872728.94604033.03945622.683781000.9850-0.17365.69826.87960.450.00759131.6872906.40326235.69128180.2498∑0.068341185.18523129.762814760.473122205.7043注：1.I—截面惯性矩，2.不考虑轴力的影响5 自重力：式中：di——接缝i的衬砌截面厚度，本设计为等厚度衬砌；作用在各楔体上的力均列入表2，各集中力均通过相应的图形的行心。（2）外荷载在基本结构中产生的内力。楔体上各集中力对下一接缝的力臂由图2中量得，分别记为内力按照下式计算（见图3）。弯矩：轴力：式中：图3内力计算图示19 载位移计算表表3截面sinΦcosΦΣ（Q+G)ΣEsinΦ(Q+G）cosΦΣE00.00001.00000.00000.00000.00000.00000.000010.21640.9763233.21335.407750.46745.279545.187920.42260.9063227.088922.107395.967820.035875.932030.60880.7934215.137949.0625130.976047.757483.218640.76600.6428197.926184.9909151.611454.632296.979250.88700.4617176.2576128.1892156.340559.185197.155460.96590.2588150.1744176.6126145.053545.707399.346270.99900.0436123.8579227.9106123.73409.9369113.797180.9850-0.1736112.5918280.4076110.9029-48.6788159.588019 载位移的计算表表2截面集中力力臂　　△x△y-△x　-△y　QGE000000000000000001129.1182104.09515.40770.60170.62600.0681-77.6904-65.1635-0.36830.00000.00001.25190.13710.00000.0000-143.22222122.9938104.095116.69960.52450.59640.2103-64.5102-62.0823-3.5119460.30225.04771.19280.4049-549.0485-2.0438-824.41893111.0428104.095126.95520.42240.53860.3395-46.9045-56.0656-9.1513675.440122.10731.07720.6535-727.5841-1.3771-1665.5015493.8310104.095135.92840.30030.45470.4525-28.1774-47.3320-16.2576873.366249.06250.90941.8710-794.2392-91.7959-2643.3036572.1625104.095143.19830.16390.35000.5440-11.8274-36.4333-23.49991049.62484.99090.70001.0473-734.7368-89.0110-3538.812646.0793104.095148.42340.01980.22820.6098-0.9124-23.7545-29.52861199.798128.18920.45641.1739-547.5878-150.4813-4291.0766719.7628104.095151.2980-0.12530.09580.64600.0000-9.9723-33.13821323.656176.61260.19151.2450-235.4801-219.8827-4789.549988.4967104.095152.4970-0.2644-0.04050.66110.00004.2159-34.70161436.248227.9106-0.08101.3469116.3361-306.9728-5014.888219 基本结构中，主动荷载产生弯矩的校核为：另一方面，从表2中得到闭合差（3）主动荷载位移（计算过程见表4）。截面(1+y)00.000131.6870.0001.0000.0000.0000.0001-143.2222131.68718.06321.137-18860.5019-2587.0476-21444.39072-824.4189131.68771.40971.542-108565.2517-58871.5063-167407.61813-1665.5015131.687157.50992.195-219325.3701-262333.5418-481419.18744-2643.3036131.687272.26613.067-348088.7212-719681.9623-1067588.1085-3538.812131.687410.25034.114-466015.5358-1451798.685-1917187.9146-4291.0766131.687564.91445.288-565079.0042-2424090.963-2988137.7657-4789.5499131.687728.94606.533-630721.4577-34911323.241-4120503.2838-5014.8882131.687906.40327.881-660395.5824-4545510.712-5204577.585Σ-3017051.425-44376197.66-15968265.85主动荷载位移计算表表4计算精度校核：闭合差：19 4.3载位移——单位弹性抗力及相应的摩擦力引起的位移（1）各接缝处的抗力强度抗力上零点假定在接缝3，最大抗力值假定在接缝6，最大抗力值以上各截面抗力强度按下式计算：查表1，算得最大抗力值以下各截面抗力强度按下式计算：式中：由图2中量得：则：按比例将所求得抗力绘于图2上。（2）各楔体上抗力集中力按下式计算：式中：—表示楔体i外缘长度，可以通过量取夹角，用弧长公式求得，的方向垂直于衬砌外缘，并通过楔体上抗力图形的形心。（3）抗力集中力玉摩擦力的合力按下式计算：式中：—围岩于衬砌间的摩擦系数，此处取。则：其作用方向与抗力集中力的夹角19 ；由于摩擦力的方向与衬砌位移方向相反，其方向向上。将得方向线延长，使之交于竖直轴，量取夹角，将分解为水平和竖直两个分力：以上计算结果列入表5中。弹性抗力及摩擦力计算表表5截面R300.00000.00000.000000.00001.00000.00000.000040.38450.19231.42890.269460.24350.86810.49630.23390.133750.74010.56241.42890.726171.54360.94860.31660.68880.229961.00000.87011.42891.206483.25460.99310.11751.19810.141870.82740.91371.36181.215394.58450.9968-0.07991.2114-0.097180.00000.42141.40160.5795104.35620.9476-0.24790.5491-0.1437（4）计算单位抗力及其相应的摩擦力在基本结构中产生的内力弯矩：轴力：式中：—力至接缝中心点的力臂，由图2量得。计算见表6及表7.计算表表7截面4500.76600.64280.10260.10340.23650.1235-0.0216562.50.88700.46170.39460.31641.01260.1264-0.09516750.96590.25880.50160.52622.34620.32160.349787.50.99900.04360.29560.371263.3456-0.13150.46181000.9850-0.17360.16490.19314.1345-0.15621.16519 计算表表6截面40.4584-0.1356---------0.154551.8321-0.61340.6231-0.5064-------1.195663.1496-1.49652.0215-1.91310.6913-0.8165-----3.955674.2464-1.61323.2654-3.16582.0165-2.54050.7520-0.9023---7.916385.3456-1.93164.3415-3.46463.4324-3.41542.1165-2.51650.9542-0.5682-13.612319 （5）单位抗力及相应摩擦力产生的载位移。计算见表8.单位抗力及相应摩擦力产生的载位移计算表表8截面4-0.1451131.6872272.26613.067-19.1078-39.5058-121.16435-1.1227131.6872410.25034.114-147.8452-460.5880-1894.85906-3.5989131.6872564.91445.288-473.9291-2033.0704-8954.16567-7.8106131.6872728.94606.533-1028.5560-5693.5056-9216.64868-13.1453131.6872906.40327.881-1731.0678-11914.9420-16918.1297Σ-3400.5059-20141.6118-37104.9672校核为：闭合差：4.4墙低（弹性地基上的刚性梁）位移单位弯矩作用下的转角：主动荷载作用下的转角：19 单位抗力及相应摩擦力作用下的转角：五解力法方程衬砌矢高计算力法方程的系数为：以上将单位抗力及相应摩擦力产生的位移乘以，即为被动荷载的载位移。求解方程为：式中：式中：，以上解的值应带入原方程，校核计算。六计算主动荷载和被动荷载（）分别产生的衬砌内力计算公式为：19 计算过程列入表9、10。.主、被动荷载作用下衬砌弯矩计算表表9截面00.0000294.21530.0000294.20730-2.47030.0000-2.47431-143.2222294.215366.1080244.66610-2.47030.3287-2.14562-824.4189294.2153260.3209108.07440-2.47031.2943-1.18003-1665.5015294.2153570.1817-78.85160-2.47032.83490.36064-2643.3036294.2153979.2457-263.2907-0.1451-2.47034.86882.24945-3538.812294.21531466.7924-385.0128-1.1227-2.47037.29283.69586-4291.0766294.21532008.0314-385.6977-3.5989-2.47039.98393.91067-4789.5499294.21532569.9496-246.5691-7.8106-2.470312.77772.49288-5014.8882294.21533131.86794.9524-13.1453-2.470315.5715-0.0480主、被动荷载作用下衬砌轴力计算表表10截面00.0000511.1196511.119602.04212.0421145.1879490.0605632.944001.91931.9193275.9320437.5409692.986301.85351.8535383.2186375.2465778.113301.60741.6074496.9792303.0140798.3854-0.06651.24371.2866597.1554263.5434853.5140-0.09790.79310.8652699.346298.3159915.04950.30710.36760.46737113.7971-16.07481023.67860.7153-0.07190.23538159.5880-122.67611645.52581.5693-0.51610.708319 七最大抗力值的求解首先求出最大抗力方向内的位移。考虑到接缝5的径向位移与水平方向有一定的偏离，因此修正后有：计算过程列入表11，位移值为：最大抗力值为：最大抗力位移修正计算表表11截面038743.3464-325.83284.8843189234.1269-1591.4649132219.4048-282.54894.7235152188.3587-1334.6199214232.0210-155.38924.251160501.7445-660.57513-10383.750547.49033.4974-36316.1291166.09254-34672.0249296.22052.5024-86763.2752741.26215-50701.2794486.69151.3165-66748.2343640.72936-50791.4607514.9794000Σ212096.5914-2038.576019 八计算衬砌总内力按下式计算衬砌总内力：计算过程列入表12.计算精度的校核为以下内容：根据拱顶切开点的相对转角和相对水平位移应为零的条件来检查：式中：闭合差：式中：闭合差：九衬砌截面强度检算（检算几个控制截面）9.1拱顶（截面0）e=0.0880m<0.45d=0.2025m（可）又有：e=0.0880m<0.2d=0.09m可得式中：—混凝土极限抗压强度，取19 衬砌总内力计算表表12截面MpMσ[M]NpNσ[N]eM/IMy/I0287.7901-2.743492.123410.48922.4104769.2620.08797057.08110.00001234.3136-2.145656.847423.72711.9198793.3660.05764743.5760762.76702105.9034-1.0180-9.617492.84651.7482841.315-0.0099-8075.4432-554.33063-82.76420.3606-34.563577.69581.6754895.548-0.0600-25761.9597-7991.26194-242.93032.2449-52.468676.82121.1686931.136-0.0569-15867.9483-13976.86605-394.44383.5698-20.926742.82790.6527946.651-0.0314-13379.0992-12055.95016-384.08283.9106-9.564784.37170.7346997.265-0.0066-7017.1044-3502.55287-246.11472.2984-4.926781.69680.54331383.949-0.0050-545.3887-3409.279384.9644-0.04081.694747.48440.83601608.6340.00033617.1617283.0938Σ-55229.1247-40444.379819 9.2截面（7）e=0.0051m<0.2d=0.09m9.3墙低（截面8）偏心检查其他各截面偏心距均小于0.45d.十内力图将内力计算结果按比例绘制成弯矩图M与轴力图N，如图4所示。19 图4衬砌结构内力图19'