三角型承台的验算
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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 =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'' =γc * Vct =25*6.34 =158.5kN土自重标准值Gk' =γs * (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:(1)、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 =78.3kN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 =γz * (Qik - Qgk)N =1.35*(1633.7-78.3) =2099.7kN(2)、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 ^ 2 + Sb ^ 2) ^ 0.5 =(0.9^2+1.56^2)^0.5 =1.801mαs =2Sa =2*0.9 =1.800mα =αs / 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 =1.203mM1 =Nmax * [S - 0.75 * c1 / (4 - α ^ 2) ^ 0.5] / 3(基础规范8.5.16-4)=2099.7*[1.801-0.75*0.65/(4-0.999^2)^0.5]/3=1063.6kN·m②号筋Asy =3783mmζ =0.068 ρ =0.32%10Φ22@110(As =3801)(3)、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 * [αs - 0.75 * c2 / (4 - α ^ 2) ^ 0.5] / 3(基础规范8.5.16-5)=2099.7*[1.8-0.75*0.7/(4-0.999^2)^0.5]/3=1047.7kN·m①号筋Asx =3667mmζ =0.076 ρ =0.36%10Φ22@100(As =3801)2、承台受冲切承载力验算:(1)、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 ≤ [βox * (2bc + aoy1 + aoy2) + (βoy1 + βoy2) * (hc + aox)] * βhp * 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 =333mmλox =aox / ho =333/(1100-110) =0.337X 方向上冲切系数βox =0.84 / (λox + 0.2)(基础规范8.5.17-3)βox =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:aoy1 =2 * 1560 / 3 - 0.5bc - 0.5bp =1040-650/2-433/2 =498mmλoy1 =aoy1 / ho =498/(1100-110) =0.504Y 方向(下边)冲切系数βoy1 =0.84 / (λoy1 + 0.2)(基础规范8.5.17-4)βoy1 =0.84/(0.504+0.2) =1.194Y 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 =-22mmλoy2 =aoy2 / ho =-22/(1100-110) =-0.022当λoy2 < 0.2 时,取λoy2 =0.2,aoy2 =0.2ho =0.2*990 =198mmY 方向(上边)冲切系数βoy2 =0.84 / (λoy2 + 0.2)(基础规范8.5.17-4)βoy2=0.84/(0.2+0.2) =2.1[βox * (2bc + aoy1 + aoy2) + (βoy1 + βoy2) * (hc + aox)] * βhp * ft * ho=[1.565*(2*650+498+198)+(1.194+2.1)*(700+333)]*0.975*1.43*990=9029023N ≥ Fl=6299100N,满足要求。
(2)、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 ≤ β12 * (2c2 + a12) * tg(θ2 / 2) * βhp * ft * ho(基础规范8.5.17-10)θ2 =2 * arctg(Sa / Sb) =2*arctg(900/1560) =60°c2 =[Sc * ctg(θ2 / 2) + Sc + 0.5bp] * Cos(θ2 / 2)=[500*ctg30°+500+433/2]*Cos30°=1371mma12 =(2Sb / 3 - 0.5bp - 0.5bc) * Cos(θ2 / 2)=(2*1560/3-433/2-650/2)*Cos30°=432mmλ12 =a12 / ho =432/(1100-110) =0.436底部角桩冲切系数β12 =0.56 / (λ12 + 0.2)(基础规范8.5.17-11)β12 =0.56/(0.436+0.2) =0.88β12 * (2c2 + a12) * tg(θ2 / 2) * βhp * ft * ho=0.88*(2*1371+432)*tg30°*0.975*1.43*990=2229798N ≥ Nl =2099700N,满足要求。
(3)、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组合时的竖向力设计值:Nl =Max{N2, N3} =2099700N承台受角桩冲切的承载力按下列公式计算:Nl ≤ β11 * (2c1 + a11) * tg(θ1 / 2) * βhp * ft * ho(基础规范8.5.17-8)θ1 =arctg(Sb / Sa) =arctg(1560/900) =60°c1 =ctgθ1 * 2Sc + Sc + 0.5bp =ctg60°*2*500+500+433/2 =1293mma11 =Sa - 0.5bp - 0.5bc =900-433/2-650/2 =333mmλ11 =a11 / ho =333/(1100-110) =0.337底部角桩冲切系数β11 =0.56 / (λ11 + 0.2)(基础规范8.5.17-9)β11 =0.56/(0.337+0.2) =1.043β11 * (2c1 + a11) * tg(θ1 / 2) * βhp * ft * ho=1.043*(2*1293+333)*tg30°*0.975*1.43*990=2433399N ≥ Nl =2099700N,满足要求。
3、承台斜截面受剪承载力计算:(1)、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 ≤ βhs * βy * ft * bxo * 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 =520 - 0.5bc - 0.5bp =520-650/2-433/2 =-22mmλy =ay / ho =-22/(1100-110) =-0.022当λy < 0.3 时,取λy =0.3βy =1.75 / (λy + 1.0) =1.75/(0.3+1.0) =1.346βhs * βy * ft * bxo * ho =0.95*1.346*1.43*2800*990 =5069495N ≥ Vx =4199400N,满足要求。
(2)、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 ≤ βhs * βy * ft * bxo * 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 =498mmλy =ay / ho =498/(1100-110) =0.504βy =1.75 / (λy + 1.0) =1.75/(0.504+1.0) =1.164βhs * βy * ft * bxo * ho =0.95*1.164*1.43*2402*990 =3760082N ≥ Vx =2099700N,满足要求。