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1.设计荷载计算1.1结构尺寸及地层示意图35062005500138350B1138DB273L1K73L2881280灰色淤泥质粘土kN/mc=12.kPa29253灰色淤泥质粉质粘土kN/mc=12.2kPa164533332q=20kN/m500褐黄色粘土kN/m10003500灰色砂质粉土kN/m人工填土kN/m150043800图1-1结构尺寸及地层示意图如图,按照要求,对灰色淤泥质粉质粘土上层厚度进行调整:mm4380050*849+1350h灰。按照课程设计题目,以下只进行基本使用阶段的荷载计算。1.2隧道外围荷载标准值计算(1)自重2/75.835.025mkNgh(2)竖向土压若按一般公式:21/95.44688.485.37.80.11.90.185.018qmKNhniii由于h=1.5+1.0+3.5+43.8=48.8mD=6.55m,属深埋隧道。应按照太沙基公式或普氏公式计算竖向土压:a太沙基公式:)tan()tan(00100]1[tan)/(pBhBheqeBcB其中:mRBc83.6)4/7.75.22tan(/1.3)4/5.22tan(/0000(加权平均值0007.785.5205.42.7645.19.8)则:2)9.8tan83.68.48()9.8tan83.68.48(11/02.18920]1[9.8tan)83.6/2.128(83.6pmKNeeb普氏公式:20012/73.2699.8tan92.7832tan32pmKNB取竖向土压为太沙基公式计算值,即:21/02.189pmKNe。(3)拱背土压mkNRc/72.286.7925.2)41(2)41(2G22。其中:3/6.728.1645.11.728.10.8645.1mKN。(4)侧向主动土压)245tan(2)245(tan)(q0021chpee其中:21/02.189pmKNe,3/4.785.5205.41.7645.18mKN0007.785.5205.42.7645.19.8kPac1.1285.5205.41.12645.12.12则:2000021/00.121)27.745tan(1.122)27.745(tan02.189qmKNe2000022/06.154)27.745tan(1.122)27.745(tan)85.54.702.189(qmKNe(5)水压力按静水压考虑:a竖向水压:2w1ww1/478.24=48.8×9.8=H=pmKNb侧向水压:2w1ww1/478.24=48.8×9.8=H=qmKN2w2ww2/532.14=5.5)(48.8×9.8=H=qmKN(6)侧向土壤抗力衬砌圆环侧向地层(弹性)压缩量:)R0.0454kEI24()]Rq(q-)q(q-)p[2(p=4c4cw2e2w1e1w1e1其中:衬砌圆环抗弯刚度取2376.123265120.35×0.1103.45EImKN衬砌圆环抗弯刚度折减系数取7.0;则:m34410617.057.366600811.2261)925.2200000.04546.232651.70(24925.2)]14.325(154.06-)24.784(139.19-)24.78402.189([2=2-3r/35.1210617.000002=yk=qmKN(7)拱底反力wcc1RR2π-0.2146R+πg+p=Pe其中:21/02.189pmKNe2/75.8mkNg3/6.728.1645.11.728.10.8645.1mKN,与拱背土压对应则:2R/91.17410955.22π-6.7955.20.2146+75.8π+189.02=PmKN。(8)荷载示意图图1-2圆环外围荷载示意图2.内力计算2.1用荷载-结构法按均质圆环计算衬砌内力取一米长度圆环进行计算,其中荷载采用设计值,即考虑荷载组合系数。计算结果如下表(已考虑荷载组合系数):隧道圆环内力计算结果:表2-1截面/度内力垂直荷载水平荷载水平三角荷载地基抗力自重每米内力pe1+pw1qe1+qw1qe2+qw2-qe1-qw1qk=kδg800.71719.09104.3514.8210.500M/KNm1712.65-1538.06-93.00-15.0930.9797.470N/KN0.002103.3395.3815.33-5.122208.930Q/KN0.000.000.000.000.000.008M/KNm1646.30-1478.48-90.28-14.6529.9592.848N/KN45.362062.5994.4515.18-4.472213.118Q/KN-322.78289.8813.272.134.96-12.5440.5M/KNm267.92-240.61-27.18-4.357.673.4640.5N/KN987.851216.1869.2011.6610.212295.1040.5Q/KN-1156.621038.7259.109.9519.83-29.0273M/KNm-1419.851275.1178.0714.51-25.51-77.6773N/KN2141.88179.8016.722.9435.922377.2573Q/KN-654.84588.0854.689.6116.3413.8790M/KNm-1712.651538.06111.6019.18-35.28-79.0890N/KN2342.080.000.000.0048.242390.3390Q/KN0.000.0019.080.005.1224.20105.5M/KNm-1468.031318.38109.1514.09-33.74-60.16105.5N/KN2174.82150.217.263.6852.482388.45105.5Q/KN603.13-541.65-26.17-13.2719.1141.15138M/KNm179.02-160.77-0.73-3.571.2415.18138N/KN1048.631161.60101.4211.3931.942354.98138Q/KN1164.63-1045.91-91.3210.2634.6772.33159M/KNm1272.75-1143.00-91.38-12.1128.2954.54159N/KN300.791833.21177.3014.3113.142338.74159Q/KN783.58-703.70-68.065.4923.6140.92180M/KNm1712.65-1538.06-130.20-15.0939.5868.88180N/KN0.002103.33209.8515.335.122333.62180Q/KN0.000.000.000.000.000.00内力(红色线条)分布图如下:M15.1854.5468.883.4692.8497.47-77.67-79.08-60.16图2-1弯矩分布图(KNm)2354.982388.452390.332377.252208.932213.112295.102333.622338.74N图2-2轴力分布图(受压KN)Q-29.02-12.540.0013.8724.2041.1572.33图2-3剪力分布图(KN)3.标准管片(B)配筋计算3.1截面及内力确定由上述内力计算,取80截面处内力进行内力计算。根据修正惯用法中的η-ξ法,由于纵缝接头的存在而导致结构整体刚度降低,取圆环整体刚度为:23792.86285120.35×0.1103.457.0EImKN而管片的内力:mKNMs69.12084.92)3.01()1(M;KNNs11.2213N3.2环向钢筋计算假设为大偏心构件。mmNMss5711.221369.120e0取:1.1kmmaa50/;mmahkee7.18750175571.120采用对称配筋:WbxRN;)()2(/0//0ahRAxhbxRNeggW其中:1000mm=b;2W23.1N/mm=R;钢筋选用HRB335钢,则2/g300N/mm=R由此:1.2310001033.23903x)50300(300)2300(1.2310007.1871033.2390/3gAxx得:)16555.0()48.103()1002(0/mmhmmxmma确为大偏心。由此算出:0/gA取:2/6003001000%2.0mmAAgg;选配4B14(A/g=615.75mm2)。3.3环向弯矩平面承载力验算(按偏心受压验算)KNNs33.2390NmmbhbhAIi1011235012238.32101/)292518065(/)18065(/00000iRilc查《混凝土结构基本原理》表4-1,得轴心受压稳定系数:98.02/50.1231615.752mmAg%3350100050.1231/取23500003501000mmANKNRAARggwcu36.8285)30050.12311.23350000(98.0)(N//;满足要求。3.4箍筋计算根据《混凝土结构基本原理》,按照偏心受压构件进行计算。KNV33.72剪跨比:0.31.11300292518065000hl故取0.3。矩形截面钢筋混凝土偏心受压构件斜截面抗剪承载力:csvyvtuNhsAfbhfV07.0175.100其中:ft——混凝土抗拉强度(1.89N/mm2)fyv——钢筋抗剪承载力(HPB235级,210N/mm2)Nc——轴向压力(要求Afc3.0)检验轴压力上限:KNNKNAfcc33.23905.242535010001.233.03.0又由:KNVKNVcu33.7238.4151033.239007.0300100089.11375.13既不需要计算配箍,按构造要求即可。根据《混凝土结构基本原理》中所述构造要求,选配四肢箍A8@200。4.基本使用阶段验算4.1抗浮验算盾构隧道位于含地下水的土层中时受到地下水的浮力作用,故需验算隧道的抗浮稳定性,用抗浮系数:QRPGGKj/其中:G/——隧道自重G——拱背土压力P——垂直荷载Rj——井壁与土壤间摩擦力Q——水浮力则:2.1510925.2925.2226.66772.28925.2275.82)(22211wccwecRRppGRgK(注:上述计算中由于相对于垂直荷载摩擦力非常小,为计算简便,将摩擦力忽略不计)满足要求。4.2管片局部抗压验算由于管片连接时在螺栓上施加预应力,故需验算螺栓与混凝土连接部位的局部抗压强度。在于应力作用下,混凝土所受到的局部压应力:ncAN其中:N——螺栓预应力(同上,取280KN)An——螺帽(或垫片)与混凝土接触净面积,取:22246.125184)31130(mmAn则:22/1.23/4.2246.12518280000mmNRmmNwc即需在螺帽下设置一定厚度的内径为31mm、外径为130mm的钢圆环垫片。4.3管片裂缝验算取最大弯矩处进
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