高速公路隧道工程课程设计计算书

PAGE高速公路隧道工程课程设计计算书目录HYPERLINK\l"_Toc282798273"一基本资料1HYPERLINK\l"_Toc282798274"二荷载确定1HYPERLINK\l"_Toc282798275"2.1围岩竖向均布压力1HYPERLINK\l"_Toc282798276"2.2围岩水平均布力2HYPERLINK\l"_Toc282798277"三衬砌几何要素2HYPERLINK\l"_Toc282798278"3.1衬砌几何尺寸2HYPERLINK\l"_Toc282798279"3.2半拱轴线长度S及分段轴长△S2HYPERLINK\l"_Toc282798280"3.3割分块接缝重心几何要素3HYPERLINK\l"_Toc282798281"四计算位移3HYPERLINK\l"_Toc282798282"4.1单位位移4HYPERLINK\l"_Toc282798283"4.2载位移——主动荷载在基本结构中引起的位移4HYPERLINK\l"_Toc282798284"4.3载位移——单位弹性抗力及相应的摩擦力引起的位移8HYPERLINK\l"_Toc282798285"4.4墙低（弹性地基上的刚性梁）位移12HYPERLINK\l"_Toc282798286"五解力法方程13HYPERLINK\l"_Toc282798287"六计算主动荷载和被动荷载（）分别产生的衬砌内力13HYPERLINK\l"_Toc282798288"七最大抗力值的求解15HYPERLINK\l"_Toc282798289"八计算衬砌总内力16HYPERLINK\l"_Toc282798290"九衬砌截面强度检算（检算几个控制截面）16HYPERLINK\l"_Toc282798291"9.1拱顶（截面0）16HYPERLINK\l"_Toc282798292"9.2截面（7）18HYPERLINK\l"_Toc282798293"9.3墙低（截面8）偏心检查18HYPERLINK\l"_Toc282798294"十内力图18PAGE5一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：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：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4.1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：PAGE6单位位移计算表表1截面Φ（°）sinΦcosΦx（m）y(m)d(m)0001000.450.00759131.687220.00000.0000131.68722113.3118110.23030.97311.36680.16080.450.00759131.6872221.17533.4050177.44288226.6236330.44810.8942.65320.63320.450.00759131.6872283.384452.7990351.25499339.9354440.64190.76683.79891.38690.450.00759131.68722182.63700253.29933750.26066453.2472660.80120.59844.74362.38190.450.00759131.68722313.66588747.120771506.13996566.5590770.91750.39785.43713.56780.450.00759131.68722469.833771676.272282747.62776679.8708990.98440.17595.8294.88430.450.00759131.68722643.200003141.581184559.66990792.2382880.9992-0.03915.91956.25110.450.00759131.68722823.190115145.843386923.911138101.60.9796-0.20115.74867.61790.450.00759131.687221003.180027642.126689780.17445∑0.068341185.185523540.2666718662.4449126928.16676注：1.I—截面惯性矩，2.不考虑轴力的影响PAGE19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+GG）cosaΣE00.00001.00000.00000.00000.00000.00000.000010.23030.9731173.252777.210539.90017.016632.883520.44810.8940337.4923328.8421151.2303325.7849125.4454430.64190.7668485.9588863.9934311.9369949.0702262.8668840.80120.5984609.63911110.41355488.4428866.0714422.3714450.91750.3978704.02666165.84677645.9444465.9738579.9706660.98440.1759764.61488227.13622752.6868839.9532712.7336670.9992-0.0391788.01811290.68122787.38777-11.36566798.7533380.9796-0.2011803.54055353.32499787.14833-71.05366858.20199载位移的计算表表2截面集中力力臂△x△y-△x-△yQGE0000000000000000--1158.8626614.24777.21050.65330.67340.3015-103.78449-9.5944-2.17400.00000.00000.68340.04020.00000.0000-115.553332149.8494414.247721.63160.57290.63320.4422-85.84877-9.0216-9.5655173.110227.21051.28640.4724-222.68990-3.4063-446.084443134.0764414.247735.15130.45230.55280.5628-60.64277-7.8761-19.78322337.2073328.84211.14570.7538-386.33884-21.74122-942.466604109.2902214.247746.42000.31160.44220.6533-34.05488-6.3003-30.32622485.5313363.99340.94470.9950-458.68115-63.67355-1535.50022579.997414.247755.43320.15080.31160.7035-12.06366-4.4396-38.99722609.06922110.413550.69351.1859-422.38995-130.93993-2144.33315646.198114.247761.28950.02010.16080.7236-0.9286-2.2910-44.34911703.31422165.846770.39201.3166-275.69992-218.35337-2685.9553179.013214.247763.5450-0.18090.01010.70351.6305-0.1439-44.70399763.76000227.136220.09041.3668-69.04399-310.44997-3108.6664081.132314.247762.6437-0.2211-0.06030.65330.25030.8591-40.92511787.02088290.68122-0.16081.3668126.55299-397.30330-3419.22298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)00.000131.6870.0001.0000.0000.0000.0001-115.5533131.68721.1751.161-15216.8891-2446.8776-17663.77672-446.0844131.68783.3841.633-58743.6619-37196.4459-95940.00783-942.4666131.687182.6372.387-124110..745-172129..192-296239..9364-1535.5002131.687313.6663.382-202206..056-481634..605-683840..6615-2144.3331131.687469.8344.568-282381..100-10074799.288-12898600.3876-2685.9553131.687643.2005.884-353705..752-172760557577-3108.6664131.687823.1907.251-409371..392-25590211.506-29683922.8978-3419.2330131.6871003.18008.618-450268..942-34301033.772-38803722.713Σ-18960044.496-94176166.702-113136221.1988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R300.00000.00000.000000.00001.00000.00000.000040.41270.20641.42890.300760.22620.86800.49660.26100.149350.77150.59211.42890.862871.95290.95080.30980.82030.267361.00000.88571.42891.290784.85200.99600.08971.28540.115870.74820.87411.35521.208097.43170.9916-0.12931.1979-0.156280.00000.37411.41330.5392108.631330.9476-0.31950.5110-0.1723（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453.24730.80120.59840.14930.11960.26100.1562-0.0365566.55910.91750.39780.41660.38221.08130.4302-0.0479679.87090.98440.17590.53240.52412.36680.41630.1078792.23830.9992-0.03910.37620.37593.5646-0.13940.51528101.600000.9796-0.20110.20390.19974.0756-0.81961.0193计算表表6截面40.4824-0.14510.145151.8593-0.55910.6533-0.56361.122763.1959-0.96102.0201-1.74290.6935-0.89513.598974.4321-1.33273.3567-2.89612.0603-2.65910.7638-0.92277.810685.5376-1.66514.6029-3.97123.4070-4.39722.1407-2.58600.9749-0.5257-13.14533（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4-0.1451131.68722313.665883.3819-19.10200-45.49900-64.601005-1.1227131.68722469.833774.5678-147.84992-527.49664-675.345566-3.5989131.68722643.200005.8843-473.93442-2314.83367-2788.777087-7.8106131.68722823.190117.2511-1028.55520-6429.58815-7458.133358-13.14533131.687221003.180028.6179-1731.06632-13187.00665-14918.11297Σ-3400.50006-22504.44801-25904.99807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：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：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00.0000294.207330.0000294.207330-2.47430.0000-2.47431-115.64992294.2073366.1080244.666110-2.47430.3287-2.14562-446.45338294.20733260.32099108.074440-2.47431.2943-1.18003-943.24006294.20733570.18177-78.851660-2.47432.83490.36064-1536.74437294.20733979.24577-263.29007-0.1451-2.47434.86882.24945-2146.01126294.207331466.79224-385.01228-1.1227-2.47437.29283.69586-2687.93363294.207332008.03114-385.69777-3.5989-2.47439.98393.91067-3110.72260294.207332569.94996-246.56991-7.8106-2.474312.77772.49288-3421.12228294.207333131.867794.9524-13.14533-2.474315.5715-0.0480主、被动荷载作用下衬砌轴力计算表表10截面00.0000411.11966411.1196602.04412.0441132.8835400.06055432.9440001.98911.98912125.44544367.54099492.9863301.82741.82743262.86688315.24655578.1133301.56741.56744422.37144246.01400668.38544-0.03651.22321.18665579.97066163.54344743.51400-0.04790.81310.76526712.7336672.3159785.049550.10780.35960.46737798.75333-16.07488782.678660.5152-0.07990.43538858.20199-82.67611775.525881.0193-0.41110.6083七最大抗力值的求解首先求出最大抗力方向内的位移。考虑虑到接缝5的径向位移移与水平方向向有一定的偏偏离，因此修修正后有：计算过程列入表111，位移值为为：最大抗力值为：最大抗力位移修正正计算表表11截面038743.34464-325.832284.8843189234.11269-1591.46649132219.40048-282.548894.7235152188.33587-1334.61199214232.02210-155.389924.251160501.74445-660.575513-10383.7750547.49033.4974-36316.11291166.092554-34672.00249296.220552.5024-86763.22752741.262115-50701.22794486.691551.3165-66748.22343640.729336-50791.44607514.97944000Σ212096.55914-2038.57760八计算衬砌总内力按下式计算衬砌总总内力：计算算过程列入表表12.计算精度的校核为为以下内容：：根据拱顶切开点的