三桩桩基承台计算项目名称_____________日期_____________设计者_____________校对者_____________一、设计依据《建筑地基基础设计规范》 (GB50007-2011)①《混凝土结构设计规范》 (GB50010-2010)②《建筑桩基技术规范》 (JGJ 94－2008)③二、示意图三、计算信息承台类型: 三桩承台计算类型: 验算截面尺寸构件编号: CT21. 几何参数矩形柱宽bc=500mm 矩形柱高hc=550mm圆桩直径d=600mm承台根部高度H=1250mmx方向桩中心距A=1800mmy方向桩中心距B=1800mm承台边缘至边桩中心距 C=600mm2. 材料信息柱混凝土强度等级: C35 ft_c=1.57N/mm2, fc_c=16.7N/mm2承台混凝土强度等级: C30 ft_b=1.43N/mm2, fc_b=14.3N/mm2桩混凝土强度等级: C30 ft_p=1.43N/mm2, fc_p=14.3N/mm2承台钢筋级别: HRB400 fy=360N/mm23. 计算信息结构重要性系数: γo=1.0纵筋合力点至近边距离: as=155mm4. 作用在承台顶部荷载标准值Fgk=4418.000kN Fqk=0.000kNMgxk=81.000kN*m Mqxk=0.000kN*mMgyk=6.000kN*m Mqyk=0.000kN*mVgxk=5.000kN Vqxk=0.000kNVgyk=57.000kN Vqyk=0.000kN永久荷载分项系数rg=1.20可变荷载分项系数rq=1.40Fk=Fgk+Fqk=4418.000+(0.000)=4418.000kNMxk=Mgxk+Fgk*(B2-B1)/2+Mqxk+Fqk*(B2-B1)/2=81.000+4418.000*(0.000-0.000)/2+(0.000)+0.000*(0.000-0.000)/2=81.000kN*mMyk=Mgyk+Fgk*(A2-A1)/2+Mqyk+Fqk*(A2-A1)/2=6.000+4418.000*(0.000-0.000)/2+(0.000)+0.000*(0.000-0.000)/2=6.000kN*mVxk=Vgxk+Vqxk=5.000+(0.000)=5.000kNVyk=Vgyk+Vqyk=57.000+(0.000)=57.000kNF1=rg*Fgk+rq*Fqk=1.20*(4418.000)+1.40*(0.000)=5301.600kNMx1=rg*(Mgxk+Fgk*(B2-B1)/2)+rq*(Mqxk+Fqk*(B2-B1)/2)=1.20*(81.000+4418.000*(0.000-0.000)/2)+1.40*(0.000+0.000*(0.000-0.000)/2) =97.200kN*mMy1=rg*(Mgyk+Fgk*(A2-A1)/2)+rq*(Mqyk+Fqk*(A2-A1)/2)=1.20*(6.000+4418.000*(0.000-0.000)/2)+1.40*(0.000+0.000*(0.000-0.000)/2)=7.200kN*mVx1=rg*Vgxk+rq*Vqxk=1.20*(5.000)+1.40*(0.000)=6.000kNVy1=rg*Vgyk+rq*Vqyk=1.20*(57.000)+1.40*(0.000)=68.400kNF2=1.35*Fk=1.35*4418.000=5964.300kNMx2=1.35*Mxk=1.35*81.000=109.350kN*mMy2=1.35*Myk=1.35*6.000=8.100kN*mVx2=1.35*Vxk=1.35*5.000=6.750kNVy2=1.35*Vyk=1.35*57.000=76.950kNF=max(|F1|,|F2|)=max(|5301.600|,|5964.300|)=5964.300kNMx=max(|Mx1|,|Mx2|)=max(|97.200|,|109.350|)=109.350kN*mMy=max(|My1|,|My2|)=max(|7.200|,|8.100|)=8.100kN*mVx=max(|Vx1|,|Vx2|)=max(|6.000|,|6.750|)=6.750kNVy=max(|Vy1|,|Vy2|)=max(|68.400|,|76.950|)=76.950kN四、计算参数1. 承台总长 Bx=C+A+C=0.600+1.800+0.600=3.000m2. 承台总宽 By=C+B+C=0.600+1.800+0.600=3.000m3. 承台根部截面有效高度 ho=H-as=1.250-0.155=1.095m4. 圆桩换算截面宽度 bp=0.8*d=0.8*0.600=0.480m五、内力计算1. 各桩编号及定位座标如上图所示:θ1=arccos(0.5*A/B)=1.047θ2=2*arcsin(0.5*A/B)=1.0471号桩 (x1=-A/2=-0.900m, y1=-B*cos(0.5*θ2)/3=-0.520m)2号桩 (x2=A/2=0.900m, y2=-B*cos(0.5*θ2)/3=-0.520m)3号桩 (x3=0, y3=B*cos(0.5*θ2)*2/3=1.039m)2. 各桩净反力设计值, 计算公式:【8.5.3-2】①∑x i=x12*2=1.620m∑y i=y12*2+y32=1.620mN i=F/n-Mx*y i/∑y i2+My*x i/∑x i2+Vx*H*x i/∑x i2-Vy*H*y1/∑y i2N1=5964.300/3-109.350*(-0.520)/1.620+8.100*(-0.900)/1.620+6.750*1.250*(-0.900)/1.620-76.950*1.250*(-0.520)/1.620=1983.134kNN2=5964.300/3-109.350*(-0.520)/1.620+8.100*0.900/1.620+6.750*1.250*0.900/1.620-76.950*1.250*(-0.520)/1.620=2001.509kNN3=5964.300/3-109.350*1.039/1.620+8.100*0.000/1.620+6.750*1.250*0.000/1.620-76.950*1.250*1.039/1.620=1979.656kN六、柱对承台的冲切验算【8.5.17-1】①1. ∑Ni=0=0.000kNho1=h-as=1.250-0.155=1.095m2. αox=A/2-bc/2-bp/2=1.800/2-1/2*0.500-1/2*0.480=0.410mαoy12=y2-hc/2-bp/2=0.520-0.550/2-0.480/2=0.005mαoy3=y3-hc/2-bp/2=1.039-0.550/2-0.480/2=0.524m3. λox=αox/ho1=0.410/1.095=0.374λoy12=αoy12/ho1=0.219/1.095=0.200λoy3=αoy3/ho1=0.524/1.095=0.4794. βox=0.84/(λox+0.2)=0.84/(0.374+0.2)=1.462βoy12=0.84/(λoy12+0.2)=0.84/(0.200+0.2)=2.100βoy3=0.84/(λoy3+0.2)=0.84/(0.479+0.2)=1.2386. 计算冲切临界截面周长AD=0.5*A+C/tan(0.5*θ1)=0.5*1.800+0.600/tan(0.5*1.047))=1.939mCD=AD*tan(θ1)=1.939*tan(1.047)=3.359mAE=C/tan(0.5*θ1)=0.600/tan(0.5*1.047)=1.039m6.1 计算Umx1Umx1=bc+αox=0.500+0.410=0.910m6.2 计算Umx2Umx2=2*AD*(CD-C-|y1|-|y3|+0.5*bp)/CD=2*1.939*(3.359-0.600-|-0.520|-|1.039|+0.5*0.480)/3.359=1.663m因Umx2>Umx1,取Umx2=Umx1=0.910mUmy=hc+αoy12+αoy3=0.550+0.219+0.524=1.293m因 Umy>(C*tan(θ1)/tan(0.5*θ1))-C-0.5*bpUmy=(C*tan(θ1)/tan(0.5*θ1))-C-0.5*bp=(0.600*tan(1.047)/tan(0.5*1.047))-0.600-0.5*0.480=0.960m7. 计算冲切抗力因 H=1.250m 所以βhp=0.963γo*Fl=γo*(F-∑Ni)=1.0*(5964.300-0.000)=5964.30kN[βox*2*Umy+βoy12*Umx1+βoy3*Umx2]*βhp*ft_b*ho=[1.462*2*0.960+2.100*0.910+1.238*0.910]*0.963*1.43*1.095*1000=8808.946kN≥γo*Fl柱对承台的冲切满足规范要求七、角桩对承台的冲切验算【8.5.17-5】①计算公式:【8.5.17-5】①1. Nl=max(N1,N2)=2001.509kNho1=h-as=1.250-0.155=1.095m2. a11=(A-bc-bp)/2=(1.800-0.500-0.480)/2=0.410ma12=(y3-(hc＋d)*0.5)*cos(0.5*θ2)=(1.039-(0.550-0.480)*0.5)*cos(0.5*1.047)=0.454m λ11=a11/ho=0.410/1.095=0.374β11=0.56/(λ11+0.2)=0.56/(0.374+0.2))=0.975C1=(C/tan(0.5*θ1))+0.5*bp=(C/tan(0.5*1.047))+0.5*0.480=1.279mλ12=a12/ho=0.454/1.095=0.415β12=0.56/(λ12+0.2)=0.56/(0.415+0.2))=0.911C2=(CD-C-|y1|-y3+0.5d)*cos(0.5*θ2)=(3.359-0.600-|-0.520|-1.039+0.5*1.047)*cos(0.5*0.480)=1. 247m3. 因 h=1.250m 所以βhp=0.963γo*Nl=1.0*2001.509=2001.509kNβ11*(2*C1+a11)*(tan(0.5*θ1))*βhp*ft_b*ho=0.975*(2*1279.230+410.000)*(tan(0.5*1.047))*0.963*1.43*1095.000=2518.101kN≥γo*Nl=2001.509kN底部角桩对承台的冲切满足规范要求γo*N3=1.0*1979.656=1979.656kNβ12*(2*C2+a12)*(tan(0.5*θ2))*βhp*ft_b*ho=0.911*(2*1247.077+453.997)*(tan(0.5*1.047))*0.963*1.43*1095.000*1000 =2337.378kN≥γo*N3=1979.656kN顶部角桩对承台的冲切满足规范要求八、承台斜截面受剪验算【8.5.18-1】①1. 计算承台计算截面处的计算宽度2.计算剪切系数因 0.800ho=1.095m<2.000m,βhs=(0.800/1.095)1/4=0.925ay=|y3|-0.5*hc-0.5*bp=|1.039|-0.5*0.550-0.5*0.480=0.524λy=ay/ho=0.524/1.095=0.479βy=1.75/(λy+1.0)=1.75/(0.479+1.0)=1.1833. 计算承台底部最大剪力【8.5.18-1】①bxo=A*(2/3+hc/2/sqrt(B2-(A/2)2))+2*C=1.800*(2/3+0.550/2/sqrt(1.8002-(1.800/2)2))+2*0.600=2.718mγo*Vy=1.0*3984.644=3984.644kNβhs*βy*ft_b*bxo*ho=0.925*1.183*1.43*2717.543*1095.000=4655.743kN≥γo*Vy=3984.644kN承台斜截面受剪满足规范要求九、承台受弯计算【8.5.16-1】【8.5.16-2】计算公式:【8.5.16-1.2】①1. 确定单桩最大竖向力Nmax=max(N1, N2, N3)=2001.509kN2. 承台底部弯矩最大值【8.5.16-1】【8.5.16-2】①M=Nmax*(A-(sqrt(3)/4)*bc)/3=2001.509*(1.800-(sqrt(3)/4)*0.500)/3=1056.459kN*m3. 计算系数C30混凝土α1=1.0αs=M/(α1*fc_b*By*ho*ho)=1056.459/(1.0*14.3*3.000*1.095*1.095*1000)=0.0214. 相对界限受压区高度ξb=β1/(1+fy/Es/εcu)=0.518ξ=1-sqrt(1-2αs)=0.021≤ξb=0.5185. 纵向受拉钢筋Asx=Asy=α1*fc_b*By*ho*ξ/fy=1.0*14.3*3000.000*1095.000*0.021/360=2708mm2最小配筋面积:B=|y1|+C=|-519.6|+600=1119.6mmAsxmin=Asymin=ρmin*B*H=0.200%*1119.6*1250=2799mm2Asx<Asxmin,取Asx=Asxmin=2799mm2Asy<Asymin,取Asx=Asymin=2799mm26. 选择Asx钢筋选择钢筋9 20, 实配面积为2827mm2/m。