高速公路隧道工程課程設(shè)計計算書

PAGE高速公路隧道工程課程設(shè)計計算書目錄HYPERLINK\l"_Toc282798273"一基本資料1HYPERLINK\l"_Toc282798274"二荷載確定1HYPERLINK\l"_Toc282798275"2.1圍巖豎向均布壓力1HYPERLINK\l"_Toc282798276"2.2圍巖水平均布力2HYPERLINK\l"_Toc282798277"三襯砌幾何要素2HYPERLINK\l"_Toc282798278"3.1襯砌幾何尺寸2HYPERLINK\l"_Toc282798279"3.2半拱軸線長度S及分段軸長△S2HYPERLINK\l"_Toc282798280"3.3割分塊接縫重心幾何要素3HYPERLINK\l"_Toc282798281"四計算位移3HYPERLINK\l"_Toc282798282"4.1單位位移4HYPERLINK\l"_Toc282798283"4.2載位移——主動荷載在基本結(jié)構(gòu)中引起的位移4HYPERLINK\l"_Toc282798284"4.3載位移——單位彈性抗力及相應(yīng)的摩擦力引起的位移8HYPERLINK\l"_Toc282798285"4.4墻低（彈性地基上的剛性梁）位移12HYPERLINK\l"_Toc282798286"五解力法方程13HYPERLINK\l"_Toc282798287"六計算主動荷載和被動荷載（）分別產(chǎn)生的襯砌內(nèi)力13HYPERLINK\l"_Toc282798288"七最大抗力值的求解15HYPERLINK\l"_Toc282798289"八計算襯砌總內(nèi)力16HYPERLINK\l"_Toc282798290"九襯砌截面強(qiáng)度檢算（檢算幾個控制截面）16HYPERLINK\l"_Toc282798291"9.1拱頂（截面0）16HYPERLINK\l"_Toc282798292"9.2截面（7）18HYPERLINK\l"_Toc282798293"9.3墻低（截面8）偏心檢查18HYPERLINK\l"_Toc282798294"十內(nèi)力圖18PAGE5一基本資料高速公路隧道，結(jié)構(gòu)斷面如圖1所示，圍巖級別為V級，容重，圍巖的彈性抗力系數(shù)，襯砌材料C20混凝土，彈性模量，容重。圖1襯砌結(jié)構(gòu)斷面二荷載確定2.1圍巖豎向均布壓力：式中：s——圍巖級別，此處s=5;——圍巖容重，此處=18kN/㎡；——跨度影響系數(shù)，=1+i(Bm-5)，毛洞跨度Bm=12.30m，Bm=5~15時，i=0.1，此處:=1+0.1×（12.3-5）=1.73所以，有：考慮到初期之處承擔(dān)大部分圍巖壓力，而二次襯砌一般作為安全儲備，故對圍巖壓力進(jìn)行折減，對于本隧道按照50%折減，即2.2圍巖水平均布力：e=0.4×q=0.4×112.104=44.8416kPa三襯砌幾何要素3.1襯砌幾何尺寸內(nèi)輪廓半徑r1=5.7m，r2=8.2m；內(nèi)徑r1、r2所畫圓曲線的終點(diǎn)截面與豎直軸的夾角=90°，=101.6°；截面厚度d=0.45m。此處墻底截面為自內(nèi)輪廓半徑r2的圓心向內(nèi)輪廓墻底做連線并延長至與外輪廓相交，其交點(diǎn)到內(nèi)輪廓墻底間的連線。外輪廓線半徑：R1=5.7+0.45=6.15mR2=8.2+0.45=8.65m拱軸線半徑：=5.7+0.5×0.45=5.925=8.2+0.5×0.45=8.425拱軸線各段圓弧中心角：=90°=11.6°3.2半拱軸線長度S及分段軸長△S分段軸線長度:半拱軸線長度為：S=S1+S2=9.30696+1.70571=11.01268m將半拱軸線等分為8段，每段軸長為：3.3割分塊接縫重心幾何要素（1）與豎直軸夾角另一方面，角度閉合差=0。各接縫中心點(diǎn)坐標(biāo)可由圖1中直接量出。四計算位移圖2襯砌結(jié)構(gòu)計算圖4.1單位位移用辛普生法近似計算，按計算列表進(jìn)行。單位位移的計算見表1單位位移計算如下：計算精度校核為：閉合差4.2載位移——主動荷載在基本結(jié)構(gòu)中引起的位移（1）每一楔塊上的作用力豎向力：式中：bi——襯砌外緣相鄰兩截面之間的水平投影長度，由圖2量得：PAGE6單位位移計算表表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—截面慣性矩，2.不考慮軸力的影響PAGE19自重力：式中：di——接縫i的襯砌截面厚度，本設(shè)計為等厚度襯砌；作用在各楔體上的力均列入表2，各集中力均通過相應(yīng)的圖形的行心。（2）外荷載在基本結(jié)構(gòu)中產(chǎn)生的內(nèi)力。楔體上各集中力對下一接縫的力臂由圖2中量得，分別記為內(nèi)力按照下式計算（見圖3）。彎矩：軸力：式中：圖3內(nèi)力計算圖示載位移計算表表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載位移的計算表表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基本結(jié)構(gòu)中，主動荷載產(chǎn)生彎矩的校核為：另一方面，從表2中得到閉合差（3）主動荷載位移（計算過程見表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主動荷載位移計算表表4計算精度校核：閉合差：4.3載位移——單位彈性抗力及相應(yīng)的摩擦力引起的位移（1）各接縫處的抗力強(qiáng)度抗力上零點(diǎn)假定在接縫3，最大抗力值假定在接縫6，最大抗力值以上各截面抗力強(qiáng)度按下式計算：查表1，算得最大抗力值以下各截面抗力強(qiáng)度按下式計算：式中：由圖2中量得：則：按比例將所求得抗力繪于圖2上。（2）各楔體上抗力集中力按下式計算：式中：—表示楔體i外緣長度，可以通過量取夾角，用弧長公式求得，的方向垂直于襯砌外緣，并通過楔體上抗力圖形的形心。（3）抗力集中力玉摩擦力的合力按下式計算：式中：—圍巖于襯砌間的摩擦系數(shù)，此處取。則：其作用方向與抗力集中力的夾角；由于摩擦力的方向與襯砌位移方向相反，其方向向上。將得方向線延長，使之交于豎直軸，量取夾角，將分解為水平和豎直兩個分力：以上計算結(jié)果列入表5中。彈性抗力及摩擦力計算表表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）計算單位抗力及其相應(yīng)的摩擦力在基本結(jié)構(gòu)中產(chǎn)生的內(nèi)力彎矩：軸力：式中：—力至接縫中心點(diǎn)的力臂，由圖2量得。計算見表6及表7.計算表表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計算表表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）單位抗力及相應(yīng)摩擦力產(chǎn)生的載位移。計算見表8.單位抗力及相應(yīng)摩擦力產(chǎn)生的載位移計算表表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校核為：閉合差：4.4墻低（彈性地基上的剛性梁）位移單位彎矩作用下的轉(zhuǎn)角：主動荷載作用下的轉(zhuǎn)角：單位抗力及相應(yīng)摩擦力作用下的轉(zhuǎn)角：五解力法方程襯砌矢高計算力法方程的系數(shù)為：以上將單位抗力及相應(yīng)摩擦力產(chǎn)生的位移乘以，即為被動荷載的載位移。求解方程為：式中：式中：，以上解的值應(yīng)帶入原方程，校核計算。六計算主動荷載和被動荷載（）分別產(chǎn)生的襯砌內(nèi)力計算公式為：計算過程列入表9、10。.主、被動荷載作用下襯砌彎矩計算表表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、被動荷載作用下襯砌軸力計算表表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內(nèi)的位移?？紤]慮到接縫5的徑向位移移與水平方向向有一定的偏偏離，因此修修正后有：計算過程列入表111，位移值為為：最大抗力值為：最大抗力位移修正正計算表表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計算襯砌總內(nèi)力按下式計算襯砌總總內(nèi)力：計算算過程列入表表12.計算精度的校核為為以下內(nèi)容：：根據(jù)拱頂切開點(diǎn)的