曲墙式衬砌计算Word格式.docx

1、y2/I（1+y） 2/i积分系数1/3面asin a0.0001.0000.45131.687114.4720.2500.9681.5310.19425.5474.956187.7384228.9430.4840.8752.9640.765100.74177.067410.235343.4150.6870.724.2101.676220.708369.906943.00957.8870.8470.5325.1882.869377.8111083.9391971.248571.9160.9510.3105.8324.252559.9342380.8403632.396684.1940.9950

2、.1016.1525.764759.0454375.1376024.915796.4720.994-0.1136.1437.309962.5027034.9289091.6198108.7490.947-0.3215.8068.8171161.08610237.299 -12691.1591053.4983570.348 20157.368 28351.563注：1.I 截面惯性矩，匸bd3/12,b取单位长度2.不考虑轴力的影响。单位位移值计算如下：S 11= S/EhXE 1/1=6.18 X 10-8 X 1053.498=65.1062 X 10-6_ ” 8 6S 12=4S/EhX

3、 y/|=6.18 X 10- X 3570.348=220.6475 X 10S 22=S/ E hXEy2/I=6.18 X 10-8X 20157.368=1245.7253 X 10-6计算精度校核：S 11+2 3 12+ S 22= （65.1062+2*220.6475+1245.7253 ） X 10-6-6=1752.1265X 102 8 -6S S/ EhXE （1+y） /I=6.18 X 10 X 28351.563=1752.1266 X 10闭合差 =0.0001 x 10-6 0342载位移主动荷载在基本结构中引起的位移1）每一块上的作用力（竖向力Q水平力E、自

4、重力G）,分别由下面各式求得,Q =q*b iE =e*h iG =（ d i-i +d）/2* S* r hbi衬砌外缘相邻两截面间的水平投影长度hi 衬砌外缘相邻两截面间的竖直投影长度di接缝i的衬砌截面厚度均由图3直接量得，其值见表3-2。各集中力均通过相应图形的形心。0.87lr/ 4 i14 卜59 1任 tY14匚31厂7 .疋石图3衬砌结构计算图示（单位：表3-2载位移Mp计算表截 投影长度 集中力 SbhQGEaqagae-Qaq-Gag126.461 15.2966.4100.7590.097-96.742-11.6091.4340.571118.448 15.296 18.

5、8660.7170.6990.285-84.928-10.6921.2450.911102.837 15.29630.0990.6230.5940.455-64.067-9.0860.9781.19380.78315.29639.4170.4890.4510.597-39.503-6.8980.6441.38353.19445.6940.3220.2790.692-17.129-4.2670.3111.51225.68949.956-0.1550.1190.7563.982-1.8200.0091.5450.74351.047-0.004-0.0460.7730.0030.7041.50849

6、.824-0.2090.7543.197续表3-2-Gae刀i-1 x y- X 刀 i-1（Q+G- y刀i-1 EM；刀 i-1 E-0.622-108.973-5.377141.7561.433-203.136-3.660-416.766-13.695275.50025.2761.246-343.273-23.026-869.913-23.532393.63355.375-384.973-66.062-1390.881-31.620489.71194.792-315.374-131.097-1890.368-37.767558.201140.486 6.152 5.7640.320-17

7、8.624-212.415-2317.013-39.459599.185190.443 6.143 7.309-0.0095.393-294.234-2644.606-37.568615.224241.489 5.806 8.817-0.337207.330-364.166-2835.8132）外荷载在基本结构中产生的内力块上各集中力对下一接缝的力臂由图直接量得，分别记以 aq、ae、ag内力按下式计算之：弯矩：M ip = M i舟二（Q+G）AyiE-Q*aq Gag - Eaei -1 i -4轴力：N = sin （Q G）-cos： i Ei i式中 Xi、 yi相邻两接缝中心点的坐

8、标增值。 Xi =Xi - X i-1A yi =yi - y i-iMOip和Nfip的计算见表3-2及表3-3。表3-3载位移Nip计算表cos a刀 i （Q+GEiEsin a * E icos a *EiENfp35.4256.20629.219133.32722.119111.2080.726270.53540.224230.311414.78450.391364.393140.486530.62743.609487.018190.443596.11119.266576.844241.489611.304-27.218638.522630.519291.314597.060-93.

9、636690.6963）主动荷载位移计算过程见表3-4表3-4主动荷载位移计算表Mp0（1+y）/IMp01+yMp0/lyMp0/I1.194-14350.405-2783.979-17134.3841.765-54882.723-41985.283-96868.0062.676-114556.441-191996.594-306553.0353.869-183161.260-525489.656-708650.9165.252-248937.362-1058481.662-1307419.0246.764-305121.027-1758717.599-2063838.6268.309-34

10、8260.938-2545439.197-2893700.135131.687 1161.086 9.817-373440.375-3292623.783-3666064.158-1454730.326 -7713271.529 -9168001.855沪厶S/EhX M0/l=6.18 X 10-8 X（ -1454730.326 ） = - 89902.334 X 10-6 2p = S/ E hXEMy/I=6.18 X 10-8X （-7713271.529）= -476680.181 X 10-6 计算精度校核Sp= 1p+A 2psp=A S/ EhXE M0（1+y）/l因此，

11、sp=6.18 X 10-8 X（-9168001.855 ） = -566582.515.515 X 10-6 1p+A2p= - （89902.334+476680.181 ）X 10-6= -566582.515 X 10-6 闭合差 =0.000。3.4.3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按假定拱部弹性抗力的上零点位于与垂直轴接近 45的第3截面,a 3=43.4150 = a b；最大抗力位于第5截面,a 5=71.9159 = a h；拱部各截面抗力强度，按镰刀形分布，最大抗力值以上各截面抗力强度按下式计算:2）各楔块上抗力集中力R，按下式近似计算：

12、九飞1 2外/2式中，外 楔块i外缘长度，由图3量得R的方向垂直于衬砌外缘，并通过楔块上抗力图形的形心。3）抗力集中力与摩擦力之合力 Ri按近似计算：Ri式中 卩 围岩与衬砌间的摩擦系数。取 卩=0.2,则 R 1 八=1.0伯8 r其作用方向与抗力集中力的夹角为 B =arctg卩=11.301 。由于摩擦阻力的方向 与衬砌位移方向相反，其方向朝上。 R的作用点即为R,，与衬砌外缘的交点。将R的方向线延长，使之交于竖直轴。量取夹角书k（自竖直轴反时针方向量度）将Ri分解为水平与竖向两个分力：R= Ri Sin 书 k R v= Ri coS k以上计算例入表3-5中，并参见图3。表3-5弹性

13、抗力及摩擦力计算表截面（T i （ （T h）（T i-1 + Ti）/2 S 外（T h）R（ T h）Ip ksin p k0.00000.56820.2841.59870.463264.4390.9021.00000.7841.278477.1090.9750.89030.9451.540989.2120.55160.7211.1754101.0800.9810.2760.4497111.8880.928续表3-5cos p kRH （ th）RV （ t h）v0.4310.4180.2000.4540.2230.4851.6641.2540.0141.5410.0210.5063.2

14、051.511-0.1921.153-0.2260.2804.358-0.3730.417-0.1680.1134.7760.4414）计算单位抗力图及其相应的摩擦力在基本结构中产生的内力弯矩轴力Nl 二 sin 1 3Rvcos 1 3Rh式中r Ki -力R至接缝中心点K的力臂，由图3量得，计算见表3-6 和表 3-7。表3-6Mr计算表Ri=0.4632 厅 hRs=1.2784 厅 hRs=1.5409 厅 h F7=1.1754 厅 hRb=0.4497 r hMr号r4i-R4r 4ir5i-R5r 5ir6i-R6r6i r 7i -R7r7ir8i-R8r8i（r h）0.54

15、5-0.25-0.2532.071-0.950.720-0.929-1.8803.573-1.652.270-2.900.828-1.27-5.8334.963-2.293.769-4.812.372-3.65 0.879 -1.03-11.806 2 36.175-2.865.158-6.593.872-5.96 2.423 -2.841.05-0.47-18.747 9 9表3-7Nff 0计算表工R/工RH sin a工sinNor （ r h）（c h）（r h） R/（ r h）Rh（ r0.16920.2223-0.053157.8867 0.8467 0.5320 0.1999

16、0.417871.91590.95040.31100.48501.66400.46100.5175-0.056584.19370.99480.10190.50623.20480.50360.32660.177096.47150.9937-0.11190.28044.35830.2786-0.48750.7661108.74930.9472-0.32050.11274.77550.1068-1.53061.63745）单位抗力及相应摩擦力产生的载位移 计算过程见表3-8。表3-8单位抗力及相应摩擦力产生的载位移计算表截面号M,0（.h）（1+y）M. 01/IM. 0y/IML 0（1+y）/I

17、积分系数1/3131.6872-33.271-95.455-128.726-247.564-1052.641-1300.205-768.160-4427.678-5195.838-11.808-1554.912-11364.855-12919.763-18.7451161.086 9.817-2468.447-21764.304-24232.744-3760.404-26826.852-30587.2481. = S/EhX M1/1=6.18 X 10-8 X （-3760.404）= -232.3930 X 10-62. = S/ EhXEM.0y/I=6.18 X 10-8X （-26826.852）= - 1657.8995 X 10-6 校核