六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: 六桩承台计算类型: 验算截面尺寸构件编号: CT-61. 几何参数矩形柱宽bc=400mm 矩形柱高hc=400mm圆桩直径d=400mm承台根部高度H=1000mm承台端部高度h=1000mmx方向桩中心距A=1400mmy方向桩中心距B=1400mm承台边缘至边桩中心距 C=400mm2. 材料信息柱混凝土强度等级: C30 ft_c=1.43N/mm2, fc_c=14.3N/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: C25 ft_p=1.27N/mm2, fc_p=11.9N/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=110mm4. 作用在承台顶部荷载标准值Fgk=2800.000kN Fqk=0.000kNMgxk=0.000kN*m Mqxk=0.000kN*mMgyk=0.000kN*m Mqyk=0.000kN*mVgxk=0.000kN Vqxk=0.000kNVgyk=0.000kN 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=2800.000+(0.000)=2800.000kNMxk=Mgxk+Fgk*(B2-B1)/2+Mqxk+Fqk*(B2-B1)/2=0.000+2800.000*(0.000-0.000)/2+(0.000)+0.000*(0.000-0.000)/2=0.000kN*mMyk=Mgyk+Fgk*(A2-A1)/2+Mqyk+Fqk*(A2-A1)/2=0.000+2800.000*(0.000-0.000)/2+(0.000)+0.000*(0.000-0.000)/2=0.000kN*mVxk=Vgxk+Vqxk=0.000+(0.000)=0.000kNVyk=Vgyk+Vqyk=0.000+(0.000)=0.000kNF1=rg*Fgk+rq*Fqk=1.20*(2800.000)+1.40*(0.000)=3360.000kNMx1=rg*(Mgxk+Fgk*(B2-B1)/2)+rq*(Mqxk+Fqk*(B2-B1)/2)=1.20*(0.000+2800.000*(0.000-0.000)/2)+1.40*(0.000+0.000*(0.000-0.000)/2) =0.000kN*mMy1=rg*(Mgyk+Fgk*(A2-A1)/2)+rq*(Mqyk+Fqk*(A2-A1)/2)=1.20*(0.000+2800.000*(0.000-0.000)/2)+1.40*(0.000+0.000*(0.000-0.000)/2) =0.000kN*mVx1=rg*Vgxk+rq*Vqxk=1.20*(0.000)+1.40*(0.000)=0.000kNVy1=rg*Vgyk+rq*Vqyk=1.20*(0.000)+1.40*(0.000)=0.000kNF2=1.35*Fk=1.35*2800.000=3780.000kNMx2=1.35*Mxk=1.35*(0.000)=0.000kN*mMy2=1.35*Myk=1.35*(0.000)=0.000kN*mVx2=1.35*Vxk=1.35*(0.000)=0.000kNVy2=1.35*Vyk=1.35*(0.000)=0.000kNF=max(|F1|,|F2|)=max(|3360.000|,|3780.000|)=3780.000kNMx=max(|Mx1|,|Mx2|)=max(|0.000|,|0.000|)=0.000kN*mMy=max(|My1|,|My2|)=max(|0.000|,|0.000|)=0.000kN*mVx=max(|Vx1|,|Vx2|)=max(|0.000|,|0.000|)=0.000kNVy=max(|Vy1|,|Vy2|)=max(|0.000|,|0.000|)=0.000kN四、计算参数1. 承台总长 Bx=C+2*A+C=0.400+2*1.400+0.400=3.600m2. 承台总宽 By=C+B+C=0.400+1.400+0.400=2.200m3. 承台根部截面有效高度 ho=H-as=1.000-0.110=0.890mho1=h-as=1.000-0.110=0.890mh2=H-h=1.000-1.000=0.000m4. 圆桩换算截面宽度 bp=0.8*d=0.8*0.400=0.320m五、内力计算1. 各桩编号及定位座标如上图所示:1号桩 (x1=-A=-1.400m, y1=-0.5*B=-0.700m)2号桩 (x2=0, y2=-0.5*B=-0.700m)3号桩 (x3=A=1.400m, y3=-0.5*B=-0.700m)4号桩 (x4=A=1.400m, y4=0.5*B=0.700m)5号桩 (x5=0, y5=0.5*B=0.700m)6号桩 (x6=-A=-1.400m, y6=0.5*B=0.700m)2. 各桩净反力设计值, 计算公式:【8.5.3-2】①∑x i=x12*4=7.840m∑y i=y12*6=2.940mN i=F/n-Mx*y i/∑y i2+My*xi/∑x i2+Vx*H *x i/∑x i2+(-Vy)*H *y1/∑y i2N1=3780.000/6-0.000*(-0.700)/2.940+0.000*(-1.400)/7.840+0.000*1.000*(-1.400)/7.840-0.000*1.000*(-0.700)/2.940=630.000kNN2=3780.000/6-0.000*(-0.700)/2.940+0.000*0.000/7.840+0.000*1.000*0.000/7.840-0.000*1.000*(-0.700)/2.940=630.000kNN3=3780.000/6-0.000*(-0.700)/2.940+0.000*1.400/7.840+0.000*1.000*1.400/7.840-0.000*1.000*(-0.700)/2.940=630.000kNN4=3780.000/6-0.000*0.700/2.940+0.000*1.400/7.840+0.000*1.000*1.400/7.840-0.000*1.000*0.700/2.940=630.000kNN5=3780.000/6-0.000*0.700/2.940+0.000*0.000/7.840+0.000*1.000*0.000/7.840-0.000*1.000*0.700/2.940=630.000kNN6=3780.000/6-0.000*0.700/2.940+0.000*(-1.400)/7.840+0.000*1.000*(-1.400)/7.840-0.000*1.000*0.700/2.940=630.000kN六、柱对承台的冲切验算【8.5.17-1】①1. ∑Ni=0=0.000kN2. αox=A-bc/2-bp/2=1.400-0.400/2-0.320/2=1.040m因为αox>ho, 所以αox=ho=0.890mαoy=B/2-hc/2-bp/2=1.400/2-0.400/2-0.320/2=0.340m3. λox=αox/ho=0.890/0.890=1.000λoy=αoy/ho=0.340/0.890=0.3824. βox=0.84/(λox+0.2)=0.84/(1.000+0.2)=0.700βoy=0.84/(λoy+0.2)=0.84/(0.382+0.2)=1.4435. 因 H=1.000m 所以βhp=0.983γo*Fl=γo*(F-∑Ni)=1.0*(3780.000-0.000)=3780.00kN2*[βox*(hc+αoy)+βoy*(bc+αox)]*βhp*ft_b*ho=2*[0.700*(400+340)+1.443*(400+890)]*0.983*1.43*890=5956.54kN≥γo*Fl=3780.00kN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】①1. Nl=max(N1, N3, N4, N6)=630.000kN2. a1x=A-bc/2-bp/2=1.400-0.400/2-0.320/2=1.040m因为 a1x>ho1 所以 a1x=ho1=0.890ma1y=(B-hc-bp)/2=(1.400-0.400-0.320)/2=0.340m3. λ1x=a1x/ho1=0.890/0.890=1.000λ1y=a1y/ho1=0.340/0.890=0.3824. β1x=0.56/(λ1x+0.2)=0.56/(1.000+0.2)=0.467β1y=0.56/(λ1y+0.2)=0.56/(0.382+0.2)=0.962 C1=C+1/2*bp=0.400+0.320/2=0.560mC2=C+1/2*bp=0.400+0.320/2=0.560m5. 因 h=1.000m 所以βhp=0.983γo*Nl=1.0*630.000=630.000kN[β1x*(C2+a1y/2.0)+β1y*(C1+a1x/2)]*βhp*ft_b*ho1 =[0.467*(560+340/2)+0.962*(560+890/2)]*0.983*1.43*890 =1636.496kN≥γo*Nl=630.000kN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bx1=Bx=C+2*A+C=0.400+2*1.400+0.400=3.600mbx2=bc=0.400mbxo=[1-0.5*h2/ho*(1-bx2/bx1)]*bx1=[1-0.5*0.000/0.890*(1-0.400/3.600)]*3.600=3.600mby1=By=C+B+C=0.400+1.400+0.400=2.200mby2=hc=0.400mbyo=[1-0.5*h2/ho*(1-by2/by1)]*by1=[1-0.5*0.000/0.890*(1-0.400/2.200)]*2.200=2.200m2.计算剪切系数因 0.800ho=0.890m<2.000m,βhs=(0.800/0.890)1/4=0.974ax=A-1/2*bc-1/2*bp=1.400-1/2*0.400-1/2*0.320=1.040m λx=ax/ho=1.040/0.890=1.169βx=1.75/(λx+1.0)=1.75/(1.169+1.0)=0.807ay=(B-hc-bp)/2=(1.400-0.400-0.320)/2=0.340mλy=ay/ho=0.340/0.890=0.382βy=1.75/(λy+1.0)=1.75/(0.382+1.0)=1.2663. 计算承台底部最大剪力【8.5.18-1】①因为 N16=N1+N6=630.000+630.000=1260.000kNN34=N3+N4=630.000+630.000=1260.000kN所以 Vx=max(|N16|, |N34|)=1260.000kN因为 N123=N1+N2+N3=630.000+630.000+630.000=1890.000kNN456=N4+N5+N6=630.000+630.000+630.000=1890.000kN所以 Vy=max(|N123|, |N456|)=1890.000kNγo*Vx=1.0*1260.000=1260.000kNβhs*βx*ft_b*byo*ho=0.974*0.807*1.43*2200*890=2200.110kN≥γo*Vx=1260.000kNγo*Vy=1.0*1890.000=1890.000kNβhs*βy*ft_b*bxo*h o=0.974*1.266*1.43*3600*890=5649.064kN≥γo*Vy=1890.000kN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】1. 承台底部弯矩最大值【8.5.16-1】【8.5.16-2】①因为 Mdx16=(N1+N6)*(A-1/2*bc)=(630.000+630.000)*(1.400-1/2*0.400)=1512.00kN*mMdx34=(N3+N4)*(A-1/2*bc)=(630.000+630.000)*(1.400-1/2*0.400)=1512.00kN*m所以 Mx=max(|Mdx16|, |Mdx34|)=max(|1512.00|,|1512.00|)=1512.00kN*m因为 Mdy123=(N1+N2+N3)*(B-hc)/2=(630.000+630.000+630.000)*(1.400-0.400)/2=945.00kN*mMdy456=(N4+N5+N6)*(B-hc)/2=(630.000+630.000+630.000)*(1.400-0.400)/2=945.00kN*m所以 My=max(|Mdy123|, |Mdy456|)=max(|945.00|,|945.00|)=945.00kN*m2. 计算配筋面积Asx=γo*Mx/(0.9*ho*fy)=1.0*1512.00*106/(0.9*890*360)=5243.4mm2Asx1=Asx/By=5243.4/2=2383mm2/mAsy=γo*My/(0.9*ho*fy)=1.0*945.00*106/(0.9*890.000*360)=3277.2mm2Asy1=Asy/Bx=3277.2/4=910mm2/m3. 计算最小配筋率受弯最小配筋率为ρmin=0.150%4. 承台最小配筋面积As1min=ρmin*H*1000=0.150%*1000*1000=1500mm2因As1min≤Asx1 所以承台底面x方向配筋面积为 2383mm2/m选择钢筋20@130, 实配面积为2417mm2/m。