彈性支點(diǎn)法算例

1、設(shè)計(jì)條件1、土層參數(shù)物理量代號(hào)數(shù)值重度r20.6內(nèi)聚力c19.4內(nèi)摩擦角13.9主動(dòng)土壓力系數(shù)Ka0.610.60地基比例系數(shù)m25002、基坑設(shè)計(jì)深度73、圍護(hù)樁墻樁墻長(zhǎng)13樁距750樁直徑600地連墻墻計(jì)算寬度b1墻身剛度EI1.2900E+05墻身的變形系數(shù)0.4544330.4544334、內(nèi)支撐支撐道數(shù)2第一道支撐深度1.01.0第二道支撐深度4.54.5支支撐撐剛剛度度K4.8000E+055、其它條件距基坑3m處有老建筑，木樁基礎(chǔ)，埋深7m，基底附加壓力50kPa（一）第一階段計(jì)算1、主動(dòng)土壓力強(qiáng)度計(jì)算深度(m)主動(dòng)土壓力強(qiáng)度0.00P101.00P212.3613.00P316

2、0.68開挖面以下Pl12.36Pl148.32l12.0Pl/l12.42、荷載函數(shù)計(jì)算開挖面以上樁段長(zhǎng)度h11q10q212.36z1=h1時(shí)X1(h1)0.10301(h1)0.5150M1(h1)2.0600Q1(h1)6.18003、無(wú)量綱系數(shù)查表開挖面以下樁段長(zhǎng)度l12計(jì)算樁長(zhǎng)l5.5根據(jù)l查表無(wú)量綱系數(shù)z2=0時(shí)Bx0Ax01.62042.4307B0A0-1.7475-1.62044、解總方程(1)生成總方程矩陣0.4544EI129000.00EI58621.882EI26639.733EI12105.9830.0938440.042651/EI7.75194E-06(2)總

3、矩陣及行列式計(jì)算(3)待定系數(shù)計(jì)算結(jié)果本表結(jié)果a111.2218E-02a12-1.3034E-03M02.0600Q06.185、初始變位101.0915E-026、內(nèi)力及變位計(jì)算開挖面以上樁段樁深局部坐標(biāo)z z1 1a1100.001.22177E-0211.001.22177E-02開挖面以下樁段樁深z2z2/l10.000.002.21.200.103.42.400.204.63.600.305.84.800.4076.000.508.27.200.609.48.400.7010.69.600.8011.810.800.901312.001.00第一階段實(shí)際樁深0.001.001.00

4、2.203.404.605.807.008.209.4010.6011.8013.00（二）第二階段計(jì)算1、主動(dòng)土壓力強(qiáng)度計(jì)算深度(m)主動(dòng)土壓力強(qiáng)度0.0P10.01.0P212.364.5P355.6213.0P4160.68開挖面(4.5m深)以下Pl55.62Pl105.06l8.5Pl/l12.42、荷載函數(shù)計(jì)算h11q10q212.36z1=h1時(shí)X1(h1)0.10301(h1)0.5150M1(h1)2.0600Q1(h1)6.1800第一道開挖面間樁段長(zhǎng)度h23.5q112.36q255.62z2=h2時(shí)X2(h2)131.37972(h2)165.6047M2(h2)164

5、.0275Q2(h2)118.96503、無(wú)量綱系數(shù)查表開挖面以下樁段長(zhǎng)度l8.5計(jì)算樁長(zhǎng)l3.8633根據(jù)l查表無(wú)量綱系數(shù)z3=0時(shí)Bx0Ax01.62302.4475B0A0-1.7509-1.62304 4、解解總總方方程程(1)生成總方程矩陣X1(h1)1(h1)M1(h1)Q1(h1)0.4544EI1.2900E+051/EI7.7519E-06K/EI3.7209K105.24E+03(2)總矩陣及行列式計(jì)算(3)待定系數(shù)計(jì)算結(jié)果未知量本表結(jié)果a118.550362E-03a122.572354E-03a211.112351E-02a222.576346E-03a237.9844

6、96E-06a24-1.213098E-04M0-162.54Q025.075、初始變位及支撐力201.6056E-02第一道支撐力R1=K(a21-10)R1100.07100.076、內(nèi)力及變位計(jì)算第一道支撐以上樁段樁深局部坐標(biāo)z z1 1a1100.008.55036E-0311.008.55036E-03第一道開挖面間樁段樁深z2a2110.001.1124E-021.50.501.1124E-0221.001.1124E-022.51.501.1124E-0232.001.1124E-023.52.501.1124E-0243.001.1124E-024.53.501.1124E-0

7、2開挖面以下樁段樁深z3z3/l4.50.000.005.350.850.106.21.700.207.052.550.307.93.400.408.754.250.509.65.100.6010.455.950.7011.36.800.8012.157.650.90138.501.00第二階段實(shí)際樁深0.001.001.001.502.002.503.003.504.004.504.505.356.207.057.908.759.6010.4511.3012.1513.00（三）第三階段計(jì)算1、主動(dòng)土壓力強(qiáng)度計(jì)算深度(m)主動(dòng)土壓力強(qiáng)度0.0P10.01.0P212.364.5P355.62

8、7.0P486.5213.0P5160.68開挖面(深7m)以下Pl86.5286.52l6.06.0Pl/l74.1674.162、荷載函數(shù)計(jì)算第一道支撐以上樁段長(zhǎng)度h11q10q212.36z1=h1時(shí)X1(h1)0.10301(h1)0.5150M1(h1)2.0600Q1(h1)6.1800第一道第二道間樁段長(zhǎng)度h23.5q112.36q255.62z2=h2時(shí)X2(h2)131.37972(h2)165.6047M2(h2)164.0275Q2(h2)118.9650第二道開挖面間樁段長(zhǎng)度h32.5q155.62q286.52z3=h3時(shí)X3(h3)100.58593(h3)164.

9、9609M3(h3)206.0000Q3(h3)177.67503、無(wú)量綱系數(shù)查表開挖面以下樁段長(zhǎng)度l6l2.7270根據(jù)l查表無(wú)量綱系數(shù)z4=0時(shí)Bx0Ax0B0A0單位備注KN/m3kPa度取用kN/mmm從地面起算mmmmmKN/m2按1m計(jì)m從地面起算m從地面起算兩道相同備注kN/m2kN/m2kN/m2kN/m2均布荷載kN/m2三角形荷載m0.0m處土壓1.0m處土壓kNm3距基坑3m處有老建筑，木樁基礎(chǔ)，埋深7m，基底附加壓力50kPakNm2kNmkNm備注Ex0Fx02.04961.0000E0F0-0.84440.0000Bx0Ax0X1(h1)1.62042.43070.

10、1030B0A01(h1)-1.7475-1.62040.5150M1(h1)2.0600Q1(h1)6.18002EI3EIEI26639.7312105.98129000.0EI2EIEI58621.8826639.73129000.0EIEI129000.00129000.0EIEI129000129000.0系數(shù)項(xiàng)矩陣未知項(xiàng)11-6.0826E-05-2.0079E-04a1112.9810E-056.0826E-05a12-7.7519E-060M0-7.7519E-06Q0a11a12M0Q0書中結(jié)果差值單位備注4.7442E-037.4735E-03-9.0622E-04-3.9

11、721E-040.28131.7787E+00kNm2.36253.8175E+00kN4.5200E-036.3950E-03ma12a13a14h1q1q2-1.30343E-030.000.001.00012.36-1.30343E-030.000.001.00012.36Bx(z2)Ax(z2)Ex(z2)Fx(z2)B(z2)A(z2)1.620402.430662.049631.0000-1.74749-1.620400.809971.566281.588221.0000-1.20232-1.477070.288850.845211.158391.0000-0.70677-1.12

12、1650.011550.343820.802801.0000-0.32424-0.70322-0.093940.059960.544321.0000-0.08263-0.34623-0.10246-0.059330.378851.00000.03378-0.10873-0.07228-0.081250.284641.00000.065670.01199-0.03771-0.061000.235281.00000.056310.05184-0.01195-0.031320.208861.00000.037610.052650.00505-0.004450.191381.00000.025990.

13、045390.018430.019690.176021.00000.023730.04334KN/m2KN/m2KN/m2KN/m2按均布荷載kN/m2三角形荷載mkN/m3m0.0m處土壓1.0m處土壓kNm3kNm2kNmkNm1m處土壓4.5m處土壓kNm3kNm2kNmkNm備注Ex0Fx02.06621.0000E0F0-0.84220.0000系數(shù)項(xiàng)矩陣11-1010-10000-20-3.7209-3.72090013.512.25172a11a12a21a22a23書中結(jié)果差值相對(duì)誤差單位備注3.8912E-034.6592E-03119.736%3.2451E-03-6.72

14、75E-04-20.731%4.7024E-036.4211E-03136.550%3.2452E-03-6.6885E-04-20.611%1.0920E-066.8925E-06631.181%-1.1160E-04-9.7098E-068.701%kNmkN1.2200E-023.8558E-0331.605%m87.551.2524E+0114.305%kNa12a13a14h1q1q22.57235E-030.000.001.00012.362.57235E-030.000.001.00012.36a22a23a24h2q1q22.5763E-037.9845E-06-1.2131E

15、-043.512.3655.622.5763E-037.9845E-06-1.2131E-043.512.3655.622.5763E-037.9845E-06-1.2131E-043.512.3655.622.5763E-037.9845E-06-1.2131E-043.512.3655.622.5763E-037.9845E-06-1.2131E-043.512.3655.622.5763E-037.9845E-06-1.2131E-043.512.3655.622.5763E-037.9845E-06-1.2131E-043.512.3655.622.5763E-037.9845E-06

16、-1.2131E-043.512.3655.62Bx(z3)Ax(z3)Ex(z3)B(z3)A(z3)E(z3)1.622002.446262.06532-1.75076-1.62200-0.841821.015151.823401.73782-1.36207-1.54806-0.833800.557691.255311.41967-0.98829-1.34786-0.790550.239120.781991.12668-0.65404-1.07152-0.705700.039600.422070.87303-0.38051-0.77525-0.59187-0.066940.173750.6

17、6616-0.17783-0.50568-0.46925-0.108090.020240.50559-0.04395-0.29238-0.35742-0.10871-0.063180.384080.03252-0.14681-0.27069-0.08807-0.102630.290260.06788-0.06523-0.21591-0.05889-0.120510.211650.07909-0.03303-0.19173-0.02765-0.131980.138050.08042-0.02817-0.18771深度KN/m20KN/m20KN/m20.75KN/m21KN/m2相鄰基礎(chǔ)(木樁)

18、，樁尖-7m，附加壓力略去4.5770.0m處土壓71.0m處土壓13kNm3kNm2kNmkN1m處土壓4.5m處土壓kNm3kNm2kNmkNmkNm3kNm2kNmkNm備注Ex0Fx0E0F0線位移(mm)05101520253014121086420第二階段第一階段角位移(1000弧度)3210-1-2-314121086420第二階段第一階段線位移(mm)05101520253014121086420第二階段第一階段角位移(1000弧度)3210-1-2-314121086420第二階段第一階段Ex0PlFx0PPl ll2.049612.361.0000148.3212.0E0P

19、lF0Pll-0.844412.360.0000148.3212.0450.042650.01938340.093840.04265常數(shù)項(xiàng)矩陣9.5481E-0311-6.0826E-05-2.0079E-04-8.6611E-04012.9810E-056.0826E-05-1.5969E-0500-7.7519E-060-4.7907E-05000-7.7519E-06系數(shù)矩陣行列式的值6.0093E-11X1(z1)1(z1)M1(z1)Q1(z1)1/EIx00007.7519E-061.2218E-020.1030000.5150002.066.187.7519E-061.0915E

20、-02E(z2)F(z2)Bm(z2)Am(z2)Em(z2)Fm(z2)-0.844420.00001.000000.000000.000000.0000-0.823800.00000.967140.494810.100840.0000-0.725150.00000.813860.749290.251990.0000-0.560840.00000.568570.733370.329090.0000-0.380670.00000.315450.547470.312430.0000-0.228050.00000.120910.317920.236650.0000-0.122830.00000.0

21、08580.132800.146790.0000-0.063410.0000-0.032830.025280.073510.0000-0.036880.0000-0.03026-0.012760.027530.0000-0.028670.0000-0.01136-0.009540.005690.0000-0.027680.00000.000000.000000.000000.0000實(shí)際樁深x(mm)0.012.2181.010.9151.010.9152.29.3743.48.0004.66.9245.86.1907.05.7578.25.5369.45.43910.65.39611.85.

22、37213.05.351X1(h1)0.1030001(h1)0.515000M1(h1)2.060000Q1(h1)6.180000書中所列無(wú)量綱系數(shù)Bx0Ax0X2(h2)Ex0Pl1.62302.4475131.37972.066255.62B0A02(h2)E0Pl-1.7509-1.6230165.6047-0.842255.62M2(h2)164.0275Q2(h2)118.96502EI3EIEI426639.7312105.981.2900E+050.04265EI2EIEI358621.8826639.731.2900E+050.09384EIEI1.2900E+051.29

23、00E+05EIEI1.2900E+051.2900E+05未知項(xiàng)常數(shù)項(xiàng)矩陣a11-7.9845E-07a12-3.9922E-06a21-1.5969E-05-6a22-4.0662E-0242.875-6.0924E-05-2.0217E-04a231.9871E-0236.752.9868E-056.0924E-05a24-5.1532E-0321-7.7519E-060M0-1.2715E-0360-7.7519E-06Q0-9.2221E-04a24M0Q0X1(z1)1(z1)M1(z1)Q1(z1)1/EIx00007.7519E-068.5504E-030.1030000.51

24、50002.066.187.7519E-061.1124E-02X2(z2)2(z2)M2(z2)Q2(z2)1/EIx00007.7519E-061.1124E-020.035410.289691.802507.725007.7519E-061.2399E-020.618002.575008.2400018.540007.7519E-061.3591E-023.389349.5596920.8575032.445007.7519E-061.4623E-0211.5360024.7200041.2000049.440007.7519E-061.5427E-0230.1757852.304697

25、0.8125069.525007.7519E-061.5953E-0266.7440097.33500111.2400092.700007.7519E-061.6166E-02131.37972165.60469164.02750118.965007.7519E-061.6056E-02Bm(z3)Am(z3)Em(z3)BQ(z3)AQ(z3)EQ(z3)1.000000.000000.000000.000001.000000.000000.987110.368920.05725-0.091620.845740.249560.918530.635340.16668-0.262480.5032

26、30.283720.786220.757070.26257-0.405800.125320.194360.612120.742060.31218-0.47273-0.185470.057280.428270.627680.30809-0.45752-0.38022-0.074110.263370.461380.25918-0.38016-0.45361-0.169140.135930.286940.18264-0.27054-0.42666-0.214600.052790.137800.09882-0.15726-0.32857-0.206010.010870.036800.02959-0.0

27、6218-0.18277-0.138460.000000.000000.000000.000000.000000.00000 x(mm)8.5511.1211.1212.4013.5914.6215.4315.9516.1716.0616.0515.1513.5511.559.467.505.814.423.262.251.29基坑形態(tài)深度主動(dòng)土壓力100.750000112.3604.555.620786.52-4786.5201386.520130彎矩kNm150100500-50-100-150-200-25014121086420第二階段第一階段彎矩kNm150100500-50-10

28、0-150-200-25014121086420第二階段第一階段a119.5481E-031-6.0826E-05-2.0079E-04-8.6611E-0412.9810E-056.0826E-05-1.5969E-050-7.7519E-060-4.7907E-0500-7.7519E-067.3419E-13MQ-1.3034E-030.000.00-1.2994E-032.066.18BQ(z2)AQ(z2)EQ(z2)FQ(z2)M0Q00.000001.000000.000000.00002.06006.1800-0.159590.720590.286670.00002.06006

29、.1800-0.385430.199140.226440.00002.06006.1800-0.47879-0.223240.049570.00002.06006.1800-0.42084-0.41249-0.098270.00002.06006.1800-0.27976-0.39513-0.162890.00002.06006.1800-0.13280-0.26850-0.154450.00002.06006.1800-0.02643-0.12565-0.109020.00002.06006.18000.02728-0.02166-0.059440.00002.06006.18000.034

30、350.02277-0.022600.00002.06006.18000.000000.000000.000000.00002.06006.1800(103弧弧度度)M(kNm)Q(kN)-1.3030.000.00-1.2992.066.18-1.2992.066.18-1.22614.7612.10-1.02526.957.03-0.7473 30 0. .8 84 4-0.48-0.47226.79-5.62-0.25718.74-7.13-0.12010.61-5.98-0.0514.68-3.77-0.0241.41-1.72-0.0180.19-0.44-0.0170.000.00

31、Bx0Ax0Ex01.62202.44632.0653B0A0E0-1.7508-1.6220-0.841811-1000010-1000000-2000-3.720900-60013.512.2542.8750001736.750000221000006系數(shù)矩陣行列式的值MQ2.5724E-030.0000E+000.0000E+002.5763E-032.0600E+006.1800E+00MQ2.5763E-032.0600E+00-9.3894E+012.4956E-03-4.3084E+01-8.6169E+012.2483E-03-8.3594E+01-7.5354E+011.85

32、56E-03-1.1792E+02-6.1449E+011.3442E-03-1.4453E+02-4.4454E+017.4717E-04-1.6186E+02-2.4369E+011.0342E-04-1.6838E+02-1.1938E+00-5.4214E-04-1.6254E+022.5071E+01M0Q0Pl23-162.5425.0755.620.4544330.2065100.093845-162.5425.0755.620.4544330.2065100.093845-162.5425.0755.620.4544330.2065100.093845-162.5425.075

33、5.620.4544330.2065100.093845-162.5425.0755.620.4544330.2065100.093845-162.5425.0755.620.4544330.2065100.093845-162.5425.0755.620.4544330.2065100.093845-162.5425.0755.620.4544330.2065100.093845-162.5425.0755.620.4544330.2065100.093845-162.5425.0755.620.4544330.2065100.093845-162.5425.0755.620.4544330

34、.2065100.093845(103弧弧度度)M(kNm)Q(kN)2.570.000.002.582 2. .0 06 66.182.582.06-93.892.50-43.08-86.172.25-83.59-75.351.86-117.92-61.451.34-144.53-44.450.75-161.86-24.370.10- -1 16 68 8. .3 38 8-1.19-0.54-162.5425.07-0.54-162.5425.07-1.51-124.6758.52-2.16-69.3566.73-2.44-15.3156.91-2.3925.5337.28-2.1448.

35、0015.19-1.805 52 2. .4 45 5-3.99-1.4742.93-16.98-1.2425.64-21.84-1.138.23-16.94-1.110.000.00剪力kN2001000-100-200-30014121086420第二階段第一階段彎矩kNm150100500-50-100-150-200-25014121086420第二階段第一階段彎矩kNm150100500-50-100-150-200-25014121086420第二階段第一階段剪力kN2001000-100-200-30014121086420第二階段第一階段a12M019.5481E-03-6.0

36、826E-05-2.0079E-0410-8.6611E-042.9810E-056.0826E-0500-1.5969E-05-7.7519E-06000-4.7907E-050-7.7519E-060-7.8326E-14PlPl/l23412.3612.40.4544330.2065100.0938450.04264612.3612.40.4544330.2065100.0938450.04264612.3612.40.4544330.2065100.0938450.04264612.3612.40.4544330.2065100.0938450.04264612.3612.40.454

37、4330.2065100.0938450.04264612.3612.40.4544330.2065100.0938450.04264612.3612.40.4544330.2065100.0938450.04264612.3612.40.4544330.2065100.0938450.04264612.3612.40.4544330.2065100.0938450.04264612.3612.40.4544330.2065100.0938450.04264612.3612.40.4544330.2065100.0938450.042646書中所列無(wú)量綱系數(shù)Bx0Ax0Ex01.62302.4

38、4752.0662B0A0E0-1.7509-1.6230-0.8422a1100-7.9845E-071-100-3.9922E-061000-1.5969E-050000-4.0662E-020-3.7209-6.0924E-05-2.0217E-041.9871E-02012.9868E-056.0924E-05-5.1532E-0300-7.7519E-060-1.2715E-03000-7.7519E-06-9.2221E-04003 3. .8 83 33 30 0E E- -0 07 741/EIxMQ0.0426467.7519E-061.6050E-02-5.3986E-04

39、-162.5425.070.0426467.7519E-061.5152E-02-1.5111E-03-124.6758.520.0426467.7519E-061.3550E-02-2.1604E-03-69.3566.730.0426467.7519E-061.1552E-02-2.4373E-03-15.3156.910.0426467.7519E-069.4590E-03-2.3939E-0325.5337.280.0426467.7519E-067.5033E-03-2.1387E-0348.0015.190.0426467.7519E-065.8131E-03-1.7955E-03

40、52.45-3.990.0426467.7519E-064.4156E-03-1.4720E-0342.93-16.980.0426467.7519E-063.2594E-03-1.2416E-0325.64-21.840.0426467.7519E-062.2496E-03-1.1313E-038.23-16.940.0426467.7519E-061.2910E-03-1.1119E-030.000.00Q019.5481E-03-2.0079E-04111-8.6611E-046.0826E-05010-1.5969E-050000-4.7907E-05-7.7519E-06001.23

41、791E-1051/EIxMQ0.0193807.7519E-061.0915E-02-1.2995E-032.066.180.0193807.7519E-069.3745E-03-1.2260E-0314.7612.100.0193807.7519E-068.0004E-03-1.0254E-0326.957.030.0193807.7519E-066.9241E-03-7.4713E-0430.84-0.480.0193807.7519E-066.1903E-03-4.7188E-0426.79-5.620.0193807.7519E-065.7570E-03-2.5687E-0418.7

42、4-7.130.0193807.7519E-065.5364E-03-1.2032E-0410.61-5.980.0193807.7519E-065.4385E-03-5.0732E-054.68-3.770.0193807.7519E-065.3963E-03-2.4117E-051.41-1.720.0193807.7519E-065.3721E-03-1.7831E-050.19-0.440.0193807.7519E-065.3509E-03-1.7369E-050.000.0000000-100000-200000-6003.512.2542.875-6.0924E-05-2.021

43、7E-041736.752.9868E-056.0924E-050221-7.7519E-0600060-7.7519E-063 3. .2 27 77 74 4E E- -0 09 9-6.0826E-059.5481E-032.9810E-05-8.6611E-04-7.7519E-06-1.5969E-050-4.7907E-053.7137E-10a121-7.9845E-07-100000-3.9922E-060-10000-1.5969E-0500-2000-4.0662E-02-3.720900-6001.9871E-0213.512.2542.875-6.0924E-050-5.1532E-0301736.752.9868E-050-1.2715E-0300221-7.7519E-060-9.2221E-0400060a21011-7.9845E-0700001-3.9922E-06-10000-1.5969E-050-2000-4.0662E-0200-2.0217E-04001.9871E-023.512.256