地下建筑结构课程设计

1、1 二次衬砌内力计算1.1基本资料 结构断面图如图1所示。围岩级别为V级，容重,围岩的弹性抗力系，衬砌材料为C45混凝土，弹性模量为容重图1.1 结构断面图2.计算作用在衬砌结构上的主动荷载2.1隧道深浅埋的确定坍落拱高度按下式计算：级围岩，s=5；B5，i=0.1浅埋隧道分界深度：因为，所以是浅埋隧道2.2竖直和水平荷载垂直力：取水平力：3.半拱轴线长度3.1衬砌的几何尺寸内轮廓线半径：内径所画圆曲线端点截面与竖直轴线的夹角：拱顶截面厚度：， 拱底截面厚度：。拱轴线半径：拱轴线各段圆弧中心角：3.2半拱轴线长度S及分段轴长半拱线长度：将半拱轴线等分为10段，每段轴长为：分块图：5各分块接缝（

2、截面）中心几何要素5.1与竖直轴夹角:另一方面 角度闭合差5.2各截面中心点坐标计算6计算基本结构的单位位移截面sincosxyd1/Iy/Iy2/I(1+y)2/I系数0001000.596.1540096.1541112.14040.21030.97761.45110.15430.596.15414.83662.2893128.11644224.28080.41120.91152.83730.61040.596.15458.692435.8258249.36462336.42120.59370.80474.09661.34770.596.154129.5867174.6441529.971

3、54448.56160.74970.66185.17272.33350.596.154224.3754523.57991068.48462560.7020.87210.48946.01743.52350.596.154338.79861193.75691967.50824672.84240.95550.2956.59294.86450.596.154467.74112275.32673306.9632784.98280.99620.08756.87366.29660.596.154605.44333812.23415119.27474897.12320.9923-0.1246.84677.75

4、560.596.154745.7325783.59887371.216729109.54170.9424-0.33456.52169.14990.596.154879.79958050.07739905.8303410139.98720.643-0.76595.698110.33620.596.154993.86710272.807812356.6958961.543953.602526813.825735682.5707校核35682.5707计算得各单位位移如下：计算精度校核为：闭合差 = 07.计算主动荷载在基本机构中产生的位移和7.1每一分块上的作用力竖直力：衬砌外缘相邻两截面之间的水

5、平投影长度，由计算图式得：校核：m水平压力：衬砌外缘相邻两截面之间的竖直向投影长度，由计算图式得：校核：自重力： ，钢筋混凝土构件重度 = 25kN /m3。由上文计算得 7.2各分块外力及力臂表各外力对各分分块截面的力臂可由分块图量出计算得各分块外力如下表：截面集中力(KN)力臂(m)QGE00000001294.595518.266314.80640.69840.72230.32972280.875218.266344.60430.61470.68510.4693256.374518.266369.68260.49910.62050.58944218.741618.266394.66840

6、.36050.51250.68815172.484418.2663114.93470.20280.3930.74256116.03518.2663127.79770.04150.24780.7685757.037518.2663137.2368-0.11810.10020.76478018.2663140.47570-0.05790.72759018.2663133.90540-0.2010.635910018.2663119.28410-0.45640.4217外荷载在基本结构中产生的内力计算原理如下弯矩：轴力：为相邻两截面中心点的坐标增量，按下式计算：7.3计算表：截面-Eae000000

7、0001-205.7455-13.1937-4.88170000-223.82092-172.654-12.5142-20.9194312.861814.8064-433.689-6.7532-870.35073-127.9565-11.3342-41.0709612.003359.4107-770.6958-43.8035-1865.21164-78.8563-9.3615-65.1413886.6441129.0933-954.1177-127.2602-3099.94865-34.9798-7.1787-85.3391123.652223.7617-949.1488-266.2764-4

8、442.87136-4.8155-4.5264-98.21251314.4027338.6964-756.4388-454.1919-5761.056476.7361-1.8303-104.9451448.704466.4941-406.6512-668.0662-6935.813801.0576-102.19611524.0078603.730940.9958-880.8434-7876.7991903.6715-85.15041542.2741744.2066501.3933-1037.6473-8494.5321008.3367-50.30211560.5404878.1121285.1

9、05-1041.7043-8293.09677.4计算表：截面（Q+G)0010000010.21030.9776312.861814.806465.797314.475351.32220.41120.9115612.003359.4107251.661254.1553197.505930.59370.8047886.6441129.0933526.4154103.878422.537440.74960.66181123.652223.7617842.3656148.0887694.276950.87200.48941314.4027338.69641146.2726165.7418980.5

10、30860.95550.29501448.704466.49411384.2322137.61631246.615970.99620.08751524.0078603.73091518.168552.79921465.369380.9923-0.12401542.2741744.20661530.3705-92.2841622.654590.9424-0.33451560.5404878.1121470.6506-293.72211764.3727100.6430-0.76591578.8067997.39611015.1076-763.90651779.0141基本结构中，主动荷载产生的弯距

11、校核为：从计算表中得出：闭合差(可以）7.5主动荷载计算表截面1/Iy/I1+yMpy/IMp*(1+y)/I系数0096.1540100011-223.820996.15414.8371.154-21521.24-3320.727-24841.96842-807.350796.15458.6921.610-77629.875-47385.276-125015.15123-1865.21196.154129.5872.348-179347.269-241706.315-421053.58444-3099.94896.154224.3753.334-298071.981-695550.967-9

12、93622.94825-4442.87196.154338.7984.524-427199.163-1505236.252-1932435.41646-5761.05696.154467.7405.865-553947.731-2694678.736-3248626.46727-6935.81396.154605.4427.297-666905628-4866139.72548-7876.79996.154745.7318.756-757384.529-5873971.452-6631355.98129-8494.53296.154879.79810.150-8167

13、81.923-7473472.918-8290254.841410-8293.09696.154993.86511.336-797413.144-8242221.741-9039634.8861-4206166.71-26852426-31058592.71校核-31058592.71主动位移计算如下：计算精度校核：闭合差为08.解主动荷载的力法方程8.1墙底位移计算单位弯距作用下的转角：主动荷载作用下的转角：8.2解力法方程衬砌矢高力法方程系数如下：将各系数代入力法方程，得出立法方程式如下：解方程得： 9.主动荷载下的各截面的内力 计算公式为： 计算过程列入下表： 表9.1 主动荷载产生的衬

14、砌内力计算表截面001149.270801149.27081-223.82091149.2708107.00934911032.4592492-807.35071149.2708423.321495765.2415953-1865.21161149.2708934.6500307218.70923074-3099.94861149.27081618.317019-332.36078095-4442.87131149.27082443.59975-850.00074986-5761.05641149.27083373.603231-1238.1823697-6935.8131149.270843

15、66.785919-1419.7562818-7876.79911149.27085378.624158-1348.9041429-8494.5321149.27086345.591984-999.669216510-8293.09671149.27087168.30870924.48280938 表9.2 主动荷载产生的衬砌内力计算表截面x2p*cos00693.5149693.5149693.5149151.322693.5149677.9801662729.30216622197.5059693.5149632.1388314829.64473143422.5374693.5149558

16、.07144980.608844694.2769693.5149458.96816081153.2450615980.5308693.5149339.40619211319.93699261246.6159693.5149204.58689551451.20279671465.3693693.514960.682553751526.05185481622.6545693.5149-85.99584761536.65865291764.3727693.5149-231.98073411532.391966101779.0141693.5149-531.16306191247.851038单位弹性

17、反力及相应摩擦力作用下基本结构产生的位移和抗力上零点假定在接缝4，最大抗力值假定在接缝6，；BH弧最大抗力值以上各截面抗力强度按下式计算：所以计算可得：AH弧最大抗力值以下各截面抗力强度按下式计算：式中：-所考察截面外缘点到h点的垂直距离； -墙角外缘点到h点的垂直距离。由图测量可得：则：按比例将所求得的抗力绘于图1上。10.1各楔块上的力 各楔块上抗力集中力按下式近似计算： 式中：-楔快i外缘长度，可通过量取夹角，用弧长公式求得，的方向垂直于衬砌外缘，并通过楔块上抗力图形的形心。抗力集中力与摩擦力的合力： 式中：-围岩与衬砌间的摩擦系数，此处取=0.2。则： 其作用方向与抗力集中力的夹角。由

18、于摩擦阻力的方向与衬砌位移的方向相反，其方向向上。画图时，也可取切向：径向=1：5的比例求出合力的方向。的作用即为与衬砌外缘的交点。将的方向线延长，使之交于竖直轴，量取夹角,将分解为水平与竖直两分力：10.2分解得到的水平力跟竖直力截面4001.51500010050.56550.28281.5150.436865.9650.91330.40730.3989717990.177925808610.78281.5151.209378.7160.98070.19571.1859689310.23663561670.90360.95181.5151.470590.151-0.00261.470523

19、105-0.0038497980.64910.77641.5151.1995102.0170.9781-0.20821.17317334-0.24972949190.29460.47191.5150.7290113.6980.9157-0.40190.667534527-0.2929993531000.14731.5150.22761350.7121-0.70210.162049878-03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，由分块图量得。表10.1结构内力图1截面R5=0.4368R6=1.2093R7=1.4

20、705R8=1.1995R9=0.7290R10=0.2276r5i -R5r5ir6i -R6r6ir7i -R7r7ir8i -R8r8ir9i -R9r9ir10i -R10r10i50.5211-0.22760000000000-0.227761.9793-0.86460.7022-0.849200000000-1.713773.3913-1.48132.155-2.60600.7864-1.1564000000-5.243884.71-2.05733.5895-4.34082.2436-3.29920.822-0.98600000-10.683395.8431-2.55234.901

21、6-5.92753.6374-5.34882.2488-2.69740.8459-0.616600-17.1427106.5592-2.86515.8894-7.12214.7842-7.03523.5416-4.24812.2221-1.61990.9805-0.2232-23.1135表10.2 结构内力图2截面560.7020.87210.48940.1779258080.3989717990.15520.1953-0.0401672.84240.95550.2950.4145614251.5849407290.39610.4676-0.0715784.98280.99620.08750

22、.4107116353.0554638350.40920.26740.1418897.12320.9923-0.1240.1609821444.2286371740.1597-0.52440.68419109.54170.9424-0.3345-0.1320172094.896171701-0.1244-1.63781.513410139.98720.643-0.7659-0.2918033465.058221579-0.1876-3.87413.686510.4单位抗力及相应摩擦力产生的载位移截面1/Iy/I(1+y)系数5-0.227696.1538338.79794.5235-21.88

23、460488-77.11040529-98.9950101746-1.713796.1538467.74025.8645-164.7787671-801.5663124-966.345079427-5.243896.1538605.44207.2966-504.2112964-3174.816849-3679.02814648-10.68396.1538745.73048.7556-1027.211045-7966.637984-8993.84902929-17.14396.1538879.797710.1499-1648.364593-15082.37119-16730.73579410-2

24、3.11396.1538993.864911.3362-2222.402779-22971.19961-25193.602391-4434.741461-37948.26733-42383.00879校核-42383.00879校核为：闭合差10.5墙底位移单位抗力及相应摩擦力作用下的转角：解单位弹性反力及摩擦力作用下的力法方程力法方程：衬砌矢高求解方程为：11.2单位弹性反力及摩擦力作用下各截面的内力 表11.1 单位弹性反力及摩擦力作用产生的衬砌内力计算表截面x1x2yi00-5.0583773560-5.05837735610-5.0583773560.41908822-4.639289

25、13620-5.0583773561.657883666-3.4004936930-5.0583773563.660435478-1.39794187840-5.0583773566.3379284631.2795511075-0.22761648-5.0583773569.5700411134.2840472776-1.7137287-5.05837735613.212278986.4401729277-5.24376254-5.05837735617.101950016.7998101188-10.68331315-5.05837735621.064683095.3229925819-17

26、.14266436-5.05837735624.851687012.65064529510-23.11349798-5.05837735628.07375024-0.098125101 表11.2 单位弹性反力及摩擦力作用产生的衬砌内力计算表截面x2x2cosi002.7160610512.7160610512.716061051102.7160610512.6552212832.655221283202.7160610512.4756896482.475689648302.7160610512.1856143282.185614328402.7160610511.7974892041.797

27、4892045-0.04012.7160610511.3292402781.2891402786-0.07152.7160610510.801238010.7297380170.14182.7160610510.2376553420.37945534280.68412.716061051-0.336791570.3473084391.51342.716061051-0.9085224220.604877578103.68652.716061051-2.0802311591.60626884112最大抗力值的求解首先求出最大抗力方向内的位移。由式：12.1最大抗力位移修正计算表截面积分系数011

28、0506.8077-486.382438104.8645537560.366-2366.007371199274.9278-446.08549380.15434.7102467604.7649-2101.1518934273580.92259-326.97054720.61044.2541313020.6028-1390.9654052321029.73372-134.41748821.34773.516873957.36756-472.719422644-31957.76739123.03376022.33352.531-80885.10926311.398447225-81730.8413

29、3411.92762283.52351.341-109601.0582552.394942246-119055.997619.24739684.86450002909891.8833-4203.68226位移值为：则可得最大抗力:13.计算和计算衬砌截面总的内力按下式进行计算：计算过程列入表：表14.1 衬砌总内力计算表截面Nip01149.2708-5.05837735694.51262504693.51492.7160610511259.86007311032.459249-4.63928913665.08813416729.30216622.6552212831282.9612072765.241595-3.400493695664473142.4756896481345.8683563218.7092307-1.397941878-72.78555511980.608842.