隧道工程课程设计内容计算书.doc

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=12.30m，Bm=5~15时，i=0.1，此处:=1+0.1×（12.3-5）=1.73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50%折减，即2.2围岩水平均布力：e=0.4×q=0.4×112.104=44.8416kPa三衬砌几何要素3.1衬砌几何尺寸内轮廓半径r1=5.7m，r2=8.2m；内径r1、r2所画圆曲线的终点截面与竖直轴的夹角=90°，=101.6°；截面厚度d=0.45m。此处墙底截面为自内轮廓半径r2的圆心向内轮廓墙底做连线并延长至与外轮廓相交，其交点到内轮廓墙底间的连线。外轮廓线半径：R1=5.7+0.45=6.15mR2=8.2+0.45=8.65m拱轴线半径：=5.7+0.5×0.45=5.925=8.2+0.5×0.45=8.425拱轴线各段圆弧中心角：=90°=11.6°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+S2=9.30696+1.70571=11.01268m将半拱轴线等分为8段，每段轴长为：4 3.3割分块接缝重心几何要素（1）与竖直轴夹角另一方面，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 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1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)0001000.450.00759131.68720.00000.0000131.6872113.311810.23030.97311.36680.16080.450.00759131.687221.17533.4050177.4428226.623630.44810.8942.65320.63320.450.00759131.687283.384452.7990351.2549339.935440.64190.76683.79891.38690.450.00759131.6872182.6370253.2993750.2606453.247260.80120.59844.74362.38190.450.00759131.6872313.6658747.12071506.1396566.559070.91750.39785.43713.56780.450.00759131.6872469.83371676.27282747.6276679.870890.98440.17595.8294.88430.450.00759131.6872643.20003141.58184559.6690792.238280.9992-0.03915.91956.25110.450.00759131.6872823.19015145.84386923.91138101.60.9796-0.20115.74867.61790.450.00759131.68721003.18027642.12689780.1745∑0.068341185.18523540.266718662.449126928.1676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内力计算图示载位移计算表表3截面sinΦcosΦΣ（Q+G)ΣEsina(Q+G）cosaΣE00.00001.00000.00000.00000.00000.00000.000010.23030.9731173.25277.210539.90017.016632.883520.44810.8940337.492328.8421151.230325.7849125.445430.64190.7668485.958863.9934311.936949.0702262.866840.80120.5984609.6391110.4135488.442866.0714422.371450.91750.3978704.0266165.8467645.944465.9738579.970660.98440.1759764.6148227.1362752.686839.9532712.733670.9992-0.0391788.0181290.6812787.3877-11.3656798.753380.9796-0.2011803.5405353.3249787.1483-71.0536858.201918 载位移的计算表表2截面集中力力臂　　△x△y-△x　-△y　QGE0000000000000000-1158.862614.24777.21050.65330.67340.3015-103.7849-9.5944-2.17400.00000.00000.68340.04020.00000.0000-115.55332149.849414.247721.63160.57290.63320.4422-85.8487-9.0216-9.5655173.11027.21051.28640.4724-222.6890-3.4063-446.08443134.076414.247735.15130.45230.55280.5628-60.6427-7.8761-19.7832337.207328.84211.14570.7538-386.3384-21.7412-942.46604109.290214.247746.42000.31160.44220.6533-34.0548-6.3003-30.3262485.531363.99340.94470.9950-458.6815-63.6735-1535.5022579.997414.247755.43320.15080.31160.7035-12.0636-4.4396-38.9972609.0692110.41350.69351.1859-422.3895-130.9393-2144.3315646.198114.247761.28950.02010.16080.7236-0.9286-2.2910-44.3491703.3142165.84670.39201.3166-275.6992-218.3537-2685.953179.013214.247763.5450-0.18090.01010.70351.6305-0.1439-44.7039763.7600227.13620.09041.3668-69.0439-310.4497-3108.664081.132314.247762.6437-0.2211-0.06030.65330.25030.8591-40.9251787.0208290.6812-0.16081.3668126.5529-397.3030-3419.229818 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)00.000131.6870.0001.0000.0000.0000.0001-115.553131.68721.1751.161-15216.891-2446.876-17663.7672-446.084131.68783.3841.633-58743.619-37196.459-95940.0783-942.466131.687182.6372.387-124110.745-172129.192-296239.9364-1535.502131.687313.6663.382-202206.056-481634.605-683840.6615-2144.331131.687469.8344.568-282381.100-1007479.288-1289860.3876-2685.953131.687643.2005.884-353705.752-1727605.005-2081310.7577-3108.664131.687823.1907.251-409371.392-2559021.506-2968392.8978-3419.230131.6871003.1808.618-450268.942-3430103.772-3880372.713Σ-1896004.496-9417616.702-11313621.198主动荷载位移计算表表4计算精度校核：闭合差：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18 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；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18 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R300.00000.00000.000000.00001.00000.00000.000040.41270.20641.42890.300760.22620.86800.49660.26100.149350.77150.59211.42890.862871.95290.95080.30980.82030.267361.00000.88571.42891.290784.85200.99600.08971.28540.115870.74820.87411.35521.208097.43170.9916-0.12931.1979-0.156280.00000.37411.41330.5392108.63130.9476-0.31950.5110-0.1723（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453.24730.80120.59840.14930.11960.26100.1562-0.0365566.55910.91750.39780.41660.38221.08130.4302-0.0479679.87090.98440.17590.53240.52412.36680.41630.1078792.23830.9992-0.03910.37620.37593.5646-0.13940.51528101.60000.9796-0.20110.20390.19974.0756-0.81961.019318 计算表表6截面40.4824-0.1451---------0.145151.8593-0.55910.6533-0.5636-------1.122763.1959-0.96102.0201-1.74290.6935-0.8951-----3.598974.4321-1.33273.3567-2.89612.0603-2.65910.7638-0.9227---7.810685.5376-1.66514.6029-3.97123.4070-4.39722.1407-2.58600.9749-0.5257-13.145318 （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4-0.1451131.6872313.66583.3819-19.1020-45.4990-64.60105-1.1227131.6872469.83374.5678-147.8492-527.4964-675.34566-3.5989131.6872643.20005.8843-473.9342-2314.8367-2788.77087-7.8106131.6872823.19017.2511-1028.5520-6429.5815-7458.13358-13.1453131.68721003.18028.6179-1731.0632-13187.0665-14918.1297Σ-3400.5006-22504.4801-25904.9807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：18 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：18 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00.0000294.20730.0000294.20730-2.47430.0000-2.47431-115.6492294.207366.1080244.66610-2.47430.3287-2.14562-446.4538294.2073260.3209108.07440-2.47431.2943-1.18003-943.2406294.2073570.1817-78.85160-2.47432.83490.36064-1536.7437294.2073979.2457-263.2907-0.1451-2.47434.86882.24945-2146.0126294.20731466.7924-385.0128-1.1227-2.47437.29283.69586-2687.9363294.20732008.0314-385.6977-3.5989-2.47439.98393.91067-3110.7260294.20732569.9496-246.5691-7.8106-2.474312.77772.49288-3421.1228294.20733131.86794.9524-13.1453-2.474315.5715-0.0480主、被动荷载作用下衬砌轴力计算表表10截面00.0000411.1196411.119602.04412.0441132.8835400.0605432.944001.98911.98912125.4454367.5409492.986301.82741.82743262.8668315.2465578.113301.56741.56744422.3714246.0140668.3854-0.03651.22321.18665579.9706163.5434743.5140-0.04790.81310.76526712.733672.3159785.04950.10780.35960.46737798.7533-16.0748782.67860.5152-0.07990.43538858.2019-82.6761775.52581.0193-0.41110.608318 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038743.3464-325.83284.8843189234.1269-1591.4649132219.4048-282.54894.7235152188.3587-1334.6199214232.0210-155.38924.251160501.7445-660.57513-10383.750547.49033.4974-36316.1291166.09254-34672.0249296.22052.5024-86763.2752741.26215-50701.2794486.69151.3165-66748.2343640.72936-50791.4607514.9794000Σ212096.5914-2038.576018 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18 衬砌总内力计算表表12截面MpMσ[M]NpNσ[N]eM/IMy/I0293.7901-2.474353.5897410.92482.0441609.360.08797057.08110.00001244.3136-2.145636.0215432.72171.9891625.81890.05764743.5760762.76702107.9034-1.1800-6.6479492.68451.8274670.0856-0.0099-875.4432-554.33063-78.76420.3606-43.7549577.68951.5674729.8496-0.0600-5761.9597-7991.26194-262.93032.2494-44.5597667.81221.1866783.0077-0.0569-5867.9483-13976.86605-384.44383.6958-25.6600742.78290.7652817.0687-0.0314-3379.0992-12055.95016-385.08283.9106-5.4455784.17370.4673829.5427-0.0066-717.1044-3502.55287-246.14172.4928-4.1415781.68960.4353823.9494-0.0050-545.3887-3409.279384.9446-0.04800.2822774.44840.6083833.49860.000337.1617283.0938Σ-40444.379818 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。图4衬砌结构内力图18