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 =18kN/m3,围岩的弹性抗力系K =0.15 106kN/m2，衬砌材料为C45混凝土，弹性模量为E -3.35 1 07 Kpa 容重亍=25KN/m38ff (R25Kr图1.1结构断面图JX2.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：hq二0.45 2s一1 1 i(B5, i=0.10= 0.45 24 1 0.1 (14.86-5)丄 14.299m浅埋隧道分界深度：H p = 2.5 hq二35.748m因为 hq = 14.299m ： H二34m ： H p = 3

2、5.748m，所以是浅埋隧道2.2竖直和水平荷载垂直力：取 H = 34m, Bt - 14.86m, g = 40广-06 g = 240tan ： = tan g伽+1问 0.839 +tan g - tan(0.704 1) 0.8390.839 - 0.445二 2.744切匹0.283tan 1 tan (ta n g - tanj tan g tan H34q 二 H (1tan =18 34 (10.283 0.445) = 435.567kN / mBt14.86水平力：q = H = 18 34 0.283 二仃3.196kN/m勺二 h =1812.74 340.283 =

3、 238.094kN / m11ee2173.196 238.094 二 205.645kN / m223.半拱轴线长度3.1衬砌的几何尺寸内轮廓线半径：r,二 6.65m， r2 二 2.5m拱顶截面厚度：do二05m ，拱底截面厚度：dn = 0.6m。拱轴线半径：r1 =匚 + 0.5d0 = 6.65 + 0.5汇 0.5 = 6.9m, r2 = r2 + 0.5汇 dn = 2.5+ 0.5汇 0.5 = 2.75m拱轴线各段圆弧中心角：十=109门2 =313.2半拱轴线长度S及分段轴长6109S =汉兀 x a = “ 汉 6.9 = 13.126m18O018O0S2 =丿务

4、汉江汉r2 =卫丄&汉江汉2.75 = 1.487m18002 1800半拱线长度：S = SS2 =13.126 1.487 = 14.613mS 14 613将半拱轴线等分为10段，每段轴长为：S1.4613m10 104.分块图：.-5各分块接缝（截面）中心几何要素5.1与竖直轴夹角J :AS 180、；1 - . : 1 r1兀1.4613 180X 6.9:= 12.1404：2r 片=12.140412.1404 = 24.2808：3= ：2F= 24.280812.1404 =36.4212：43宀1= 36.421212.1404 = 48.5616 ：54宀1=48.561

5、612.1404 = 60.7020：6= ：5T=60.702012.1404 = 72.8424：76= 72.8424 12.1404 =84.9828：8 = ： 7 S = 84.982812.1404 = 97.1232 = 9 S0 = 9 1.4613 13.126 = 0.026m：9 J皿=109 遊邂=109.5417 Q 兀2.75JIJI兰型：二迪逼=30.4459 r2兀 2.75m 空 18匕=109.5417 14613=139.9872r2兀2.75JI另一方面片，乜二109 31 = 140角度闭合差05.2各截面中心点坐标计算x r1 sin 十 6.9

6、0.2103=1.4511r1sin：2=6.90.4112=2.8373x3 二r1sin ：3二6.90.5937二4.0966xr1sin ：4=6.90.7497=5.1727X =r,sin ：5二6.90.8721二6.0174Xg二sinq=6.90.9555 二 6.5929x7=r1sin7=6.90.9962 二 6.8736Xg=Asin- 8=6.90.9923 二 6.8467卷=r2sin ：9a = 2.75 0.9424 3.39 = 6.5216人0 =r2 sin :-10 a =2.75 0.6430 3.93=5.6981% 話 (1-cos： J =6

7、.9 (1 -0.9776) = 0.1543y2=口1- cos：2=6.91 - 0.9115=0.6104y3=r11- cos3= 6.91 - 0.8047=1.3477y4=A1- cos：4= 6.91 - 0.6618二2.3335y5=r11- cos：5=6.91-0.4894二3.5235y6 = r11-cos：6 =6.9 1 -0.2950 =4.8645y7 =1-cos：7iu6.9 1 -0.0875 2 6.2966y8 二 A 1-cos： 8 = 6.91 0.1240 = 7.7566y r1 a2 -r2 cos： 9 二 6.9 1.33 2.75

8、 0.3345 二 9.1499y10 = A a2 - r2 cos： 10 = 6.9 1.33 2.75 0.7659 二 10.33626计算基本结构的单位位移 ik截 面asin acos aXyd1/Iy/IyA2/I(1+yF2/l系 数0001000.596.1540096.1541112.14040.21030.97761.45110.15430.596.15414.83662.2893128.11644224.28080.41120.91152.83730.61040.596.15458.692435.8258249.36462336.42120.59370.80474.0

9、9661.34770.596.154129.5867174.6441529.97154448.56160.74970.66185.17272.33350.596.154224.3754523.57991068.48462560.7020.87210.48946.01743.52350.596.154338.79861193.75691967.50824672.84240.95550.2956.59294.86450.596.154467.74112275.32673306.9632784.98280.99620.08756.87366.29660.596.154605.44333812.234

10、15119.27474897.12320.9923-0.1246.84677.75560.596.154745.7325783.59887371.216729109.54170.9424-0.33456.52169.14990.596.154879.79958050.07739905.8303410139.98720.643-0.76595.698110.33620.596.154993.86710272.807812356.6958E961.543953.602526813.825735682.5707校核35682.570711.46133.35 107961.54= 4.1943 10一

11、5121.4613X3.35 10739536025= 17.246 10、221.46133.35 107 26813.8257 = 116.964 10厘计算得各单位位移如下:计算精度校核为:r 2、12、22 = (4.1194 17.246 2 116.96) 10 = 155.6506 10*:s 1 y 21 461333、 y17 35682.5707 = 155.6506 10EI 3.35 107闭合差 =07.计算主动荷载在基本机构中产生的位移：1p和：2p7.1每一分块上的作用力竖直力：Qi二qb 衬砌外缘相邻两截面之间的水平投影长度 bi，由计算图式得：1.503m,

12、b2 = 1.433m,b = 1.308mb4 =1.116m,b5 =0.88m,b6 =0.592m,b7 =0,291mB校核： b =7.1237.125m2水平压力：Ei二eh衬砌外缘相邻两截面之间的竖直向投影长度 hi，由计算图式得：g = 0.160m, = 0.482m,h3= 0.753m, h4 = 1.023m, h5 = 1.242m馆二 1.381 m, h7 = 1.483m, h8 = 1.518m, h = 1.447m, g0 二 1.289m校核： hi 10.778m H 10.78m自重力：G = d S,钢筋混凝土构件重度丫 = 25kN /m3。G

13、 = 0.5 1.4613 25 = 18.2663KN由上文计算得 q 二 435.567 0.45 二 196.005KN / me 二 205.645 0.45 二 92.54KN / m7.2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)QGEaRs00000001294.595518.266314.80640.69840.72230.32972280.875218.266344.60430.61470.68510.4693256.374518.266369.68260.49910.62050.58944218.74161

14、8.266394.66840.36050.51250.68815172.484418.2663114.93470.20280.3930.74256116.03518.2663127.79770.04150.24780.7685757.037518.2663137.2368-0.11810.10020.76478018.2663140.47570-0.05790.72759018.2663133.90540-0.2010.635910018.2663119.28410-0.45640.4217外荷载在基本结构中产生的内力计算原理如下弯矩：M 0 = M J 冲迟(Q + G)-3 迟 E - Q

15、aQ - Gag - EaE 轴力：NP = sin：(Q G) - cos：E：x：y为相邻两截面中心点的坐标增量，按下式计算：x Xi_iry - -：yi_i7.3 Mip计算表:截面-EaeMiPQqES1二垃9Lr_J-Ary 0000000001-205.7455-13.1937-4.88170000-223.82092-172.654-12.5142-20.9194312.861814.8064-433.689-6.7532-870.35073-127.9565-11.3342-41.0709612.003359.4107-770.6958-43.8035-1865.21164-

16、78.8563-9.3615-65.1413886.6441129.0933-954.1177-127.2602-3099.94865-34.9798-7.1787-85.3391123.652223.7617-949.1488-266.2764-4442.87136-4.8155-4.5264-98.21251314.4027338.6964-756.4388-454.1919-5761.056476.7361-1.8303-104.9451448.704466.4941-406.6512-668.0662-6935.813801.0576-102.19611524.0078603.7309

17、40.9958-880.8434-7876.7991903.6715-85.15041542.2741744.2066501.3933-1037.6473 -8494.5321008.3367-50.30211560.5404878.1121285.105-1041.7043 -8293.096707.4 Np计算表:截面sin %cosW艺(Q+G)送Esin%瓦(Q +OsajE ENiP0010000010.21030.9776312.861814.806465.797314.475351.32220.41120.9115612.003359.4107251.661254.1553197

18、.505930.59370.8047886.6441129.0933526.4154103.878422.537440.74960.66181123.652223.7617842.3656148.0887694.276950.87200.48941314.4027 38.69641146.2726165.7418980.530860.95550.29501448.704466.49411384.2322137.61631246.615970.99620.08751524.0078 603.73091518.168552.79921465.369380.9923-0.12401542.2741

19、744.20661530.3705-92.2841622.654590.9424-0.33451560.5404 8178.1121470.6506-293.7221 1764.3727100.6430-0.76591578.8067 9)97.39611015.1076-763.9065 1779.0141基本结构中，主动荷载产生的弯距校核为：of/7125*M0q=-q x10 - =-196.0057.125江 5.6981 = 2982.4415KN m 4丿y/IMp*(1+y)/I系数0096.154 (I100011-223.8209 )6.154 14.8371.154-215

20、21.24-3320.727-24841.96842-807.3507 )6.154 58.6921.610-77629.875-47385.276-125015.15123-1865.211 )6.154 129.587 2.348-179347.269 -241706.315-421053.58444-3099.948 )6.154 224.375 3.334-298071.981 -695550.967-993622.94825-4442.871 )6.154 338.798 4.524-427199.163 -1505236.252-1932435.41646-5761.056 )6.

21、154 467.740 5.865-553947.731 -2694678.736-3248626.46727-6935.813 )6.154 605.442 7.297-666905.096 -4199234.628-4866139.72548-7876.799 )6.154 745.731 8.756-757384.529 -5873971.452-6631355.98129-8494.532 )6.154 879.798 10.150-816781.923 -7473472.918-8290254.841410-8293.096 7604.7649-2101.1518934273580.

22、92259-326.97054720.6104 4.2541 313020.6028-1390.9654052321029.73372-134.41748821.3477 L5168 731957.36756-472.719422644-31957.76739123.03376022.3335 2*.531-80885.10926311.398447225-81730.84133411.92762283.5235 1.341-109601.0582552.394942246-119055.997619.24739684.8645 ()002909891.8833-4203.68226h 4.3

23、621 10 909891.8833 0.9555 = 3792.408 10位移值为：=4.3621 10 -4203.68226 0.955-17.5208 1013. 计算Xl和X2XX1p X =1149.2708 (-5.0584 208.5仃1) = 94.5126X2 =X2p X2匸 n =693.5149 2.7161 208.5171 = 1259.860114. 计算衬砌截面总的内力M i = M ip M i ；产 h按下式进行计算：Ni 二 NipN 计算过程列入表：表14.1衬砌总内力计算表截面MipMiaM iNipNiaNi01149.2708-5.058377

24、35694.51262504693.51492.7160610511259.86007311032.459249-4.63928913665.08813416729.30216622.6552212831282.9612072765.241595-3.400493695664473142.4756896481345.8683563218.7092307-1.397941878-72.78555511980.608842.1856143281436.34684-332.3607809 1.279551107-65.552495281153.2450611.7974892

25、041528.0522965-850.0007498 4.28404727743.296362951319.9369921.2891402781588.7447846-1238.182369 6.440172927104.70381071451.2027960.729738011603.3656497-1419.756281 6.799810118-1.8795973641526.0518540.3794553421605.1747818-1348.904142 5.322992581-238.96916781536.6586520.347308431609.0783999-999.6692165 2.650645295-446.96434751