三角型承台的验算

1、3、承台设计 构造要求：承台最小宽度不应小于500mm，承台边缘至桩中心的距离不 宜小于桩的直径或边长，边缘挑出部分不应小于150mm，墙下条形承台边缘挑出部分可降 低至75mm。条形和柱下独立承台的最小厚度为500mm，其最小埋深为600mm。本工程中承台混凝土等级C30，取其中的(8)-(A)柱位置的承台为例计算：一、基本资料：承台类型：三桩承台 圆桩直径d = 500mm桩列间距Sa = 900mm 桩行间距Sb = 1560mm桩中心至承台边缘距离Sc = 500mm承台根部高度H = 1100mm 承台端部高度h = 1100mm柱子高度hc = 700mm (X方向)柱子宽度bc

2、= 650mm (Y方向)二、控制内力：Nk = 4666；Fk = 4666； F = 6299.1；三、承台自重和承台上土自重标准值Gk：a = 2(Sc + Sa) = 2*(0.5+0.9) = 2.8mb = 2Sc + Sb = 2*0.5+1.56 = 2.56m承台底部面积 Ab = a * b - 2Sa * Sb / 2 = 2.8*2.56-2*0.9*1.56/2 = 5.76m承台体积 Vct = Ab * H1 = 5.76*1.1 = 6.340m承台自重标准值 Gk = ye * Vct = 25*6.34 = 158.5kN土自重标准值 Gk = ys * (

3、Ab - bc * hc) * ds = 18*(5.76-0.65*0.7)*0.8=76.4kN承台自重及其上土自重标准值Gk = Gk + Gk = 158.5+76.4 = 235.0kN四、承台验算：圆桩换算桩截面边宽bp = 0.866d = 0.866*500 = 433mm1、承台受弯计算：、单桩桩顶竖向力计算：在轴心竖向力作用下Qk = (Fk + Gk) / n (基础规范 8.5.3-1)Qk = (4666+235)/3 = 1633.7kN Ra = 2020kN每根单桩所分配的承台自重和承台上土自重标准值Qgk：Qgk = Gk / n = 235/3 = 78.3

4、kN扣除承台和其上填土自重后的各桩桩顶相应于荷载效应基本组合时的竖向力设计值:Ni = yz * (Qik - Qgk)N = 1.35*(1633.7-78.3) = 2099.7kN、承台形心到承台两腰的距离范围内板带的弯矩设计值：S = (Sa A 2 + Sb A 2) A 0.5 = (0.9A2+1.56A2)A0.5 = 1.801mas = 2Sa = 2*0.9 = 1.800ma = as / S = 1.8/1.801 = 0.999承台形心到承台两腰的距离B1：B1 = Sa / S * 2Sb / 3 + Sc * (Sa + Sb) / S = 1.203m=209

5、9.7*1.801-0.75*0.65/(4-0.999人2)人0.5/3=1063.6kNm号筋 Asy = 3783mm Z = 0.068 p = 0.32%1022110 (As = 3801)、承台形心到承台底边的距离范围内板带的弯矩设计值：承台形心到承台底边的距离B2 = Sb / 3 + Sc = 1.020mM2 = Nmax * as - 0.75 * c2 / (4 - a A 2) A 0.5 / 3(基础规范 8.5.16-5)=2099.7*1.8-0.75*0.7/(4-0.999A2)A0.5/3=1047.7kNm号筋 Asx = 3667mm Z = 0.07

6、6 p = 0.36%1022100 (As = 3801)2、承台受冲切承载力验算：、柱对承台的冲切验算：扣除承台及其上填土自重，作用在冲切破坏锥体上的冲切力设计值：Fl = 6299100N三桩三角形柱下独立承台受柱冲切的承载力按下列公式计算：Fl Pox * (2bc + aoy1 + aoy2) + (0oy1 + 0oy2) * (hc + aox) * 0hp * ft *ho(参照承台规程4.2.1-2)X方向上自柱边到最近桩边的水平距离：aox = 900 - 0.5hc - 0.5bp = 900-700/2-433/2 = 333mm入ox = aox / ho = 333

7、/(1100-110) = 0.337X方向上冲切系数Pox = 0.84 / (Xox + 0.2)(基础规范8.5.17-3)Pox = 0.84/(0.337+0.2)=1.565Y方向(下边)自柱边到最近桩边的水平距离：aoyl = 2 * 1560 / 3 - 0.5bc - 0.5bp = 1040-650/2-433/2 = 498mm入oy1 = aoyl / ho = 498/(1100-110) = 0.504Y方向(下边)冲切系数Poyl = 0.84 / (Xoyl + 0.2)(基础规范8.5.17-4)Poyl = 0.84/(0.504+0.2) = 1.194Y

8、方向(上边)自柱边到最近桩边的水平距离：aoy2 = 1560 / 3 - 0.5bc - 0.5bp = 520-650/2-433/2 = -22mm入oy2 = aoy2 / ho = -22/(1100-110) = -0.022当入oy2 Fl = 6299100N，满足要求。、底部角桩对承台的冲切验算：扣除承台和其上填土自重后的角桩桩顶相应于荷载效应基本组合时的竖向力设计值:Nl = N1 = 2099700N承台受角桩冲切的承载力按下列公式计算：Nl Nl = 2099700N，满足要求。、顶部角桩对承台的冲切验算：(近似计算)扣除承台和其上填土自重后的角桩桩顶相应于荷载效应基本

9、组合时的竖向力设计值:Nl = MaxN2, N3 = 2099700N承台受角桩冲切的承载力按下列公式计算：Nl Nl = 2099700N，满足要求。3、承台斜截面受剪承载力计算：、X方向(上边)斜截面受剪承载力计算：扣除承台及其上填土自重后X方向斜截面的最大剪力设计值：Vx = N2 + N3 = 4199400N柱上边缘计算宽度bxo：Sb / 3 - Sc = 1560/3-500 = 20mm 0.5bc = 325mmbxo = a = 2800mm承台斜截面受剪承载力按下列公式计算：Vx phs * Py * ft * bxo * ho (基础规范 8.5.18-1)X方向上自

10、桩内边缘到最近柱边的水平距离：ay = 520 - 0.5bc - 0.5bp = 520-650/2-433/2 = -22mm入y = ay / ho = -22/(1100-110) = -0.022当 Xy Vx = 4199400N，满足要求。、X方向(下边)斜截面受剪承载力计算：扣除承台及其上填土自重后X方向斜截面的最大剪力设计值：Vx = N1 = 2099700N柱下边缘计算宽度bxo：bxo = 2 * Sc + (2Sb / 3 - 0.5bc + Sc) * Sa / Sb = 2402mm承台斜截面受剪承载力按下列公式计算：Vx phs * Py * ft * bxo

11、* ho (基础规范 8.5.18-1)X方向上自桩内边缘到最近柱边的水平距离：ay =1040 - 0.5bc - 0.5bp = 1040-650/2-433/2 = 498mm入y = ay / ho = 498/(1100-110) = 0.504Py = 1.75 / (Xy + 1.0) = 1.75/(0.504+1.0) = 1.164Phs * Py * ft * bxo * ho = 0.95*1.164*1.43*2402*990 = 3760082NVx = 2099700N，满足要求。、Y方向斜截面受剪承载力计算：扣除承台及其上填土自重后Y方向斜截面的最大剪力设计值：

12、Vy = MaxN2 , N3 = 2099700N承台斜截面受剪承载力按下列公式计算：Vy Phs * Px * ft * byo * ho (基础规范 8.5.18-1)Y方向上自桩内边缘到最近柱边的水平距离：ax = 900 - 0.5hc - 0.5bp = 900-700/2-433/2 = 333mmXx = ax / ho = 333/(1100-110) = 0.337Px = 1.75 / (Xx + 1.0) = 1.75/(0.337+1.0) = 1.309Phs * Px * ft * byo * ho = 0.95*1.309*1.43*2560*990 = 450

13、7164NVy = 2099700N，满足要求。4、柱下局部受压承载力计算：局部荷载设计值F = 6299100N混凝土局部受压面积Al = bc * hc = 455000mm承台在柱下局部受压时的计算底面积按下列公式计算：Ab = (bx + 2 * c) * (by + 2 * c)c = MinCx, Cy, bx, by = Min1050,955,700,650 = 650mmAb = (700+2*650)*(650+2*650) = 3900000mmPl = Sqr(Ab / Al) = Sqr(3900000/455000) = 2.928N F = 6299100N，满足

14、要求。三桩承台的桩基变形验算（扩散法）编号FkGWcsApPb=PoS,1-A1266217.3555.85.97239.129.561-C1574217.3555.85.97290.7111.636-A1208217.3555.85.97229.419.186-C1380217.3555.85.97258.2210.33四桩承台的桩基变形验算（扩散法）编号FkGWcsApPb=PoS,1-B1775283.477015.32129.805.192-A1723283.477015.32126.405.062-C1870283.477015.32136.005.443-A1690283.477015.32124.254.973-C1820283.477015.32132.735.314-A1785283.477015.32130.455.224-B2075283.477015.32149.385.984-C2090283.477015.32150.366.015