极差，极差一、单桩承载力例题1条件：有一批桩,经单桩竖向静载荷试验得三根试桩的单桩竖向极限承载力分别为830kN、860kN和880kN。要求:单桩竖向承载力容许值。答案：根据《建筑地基与基础规范》附录Q(6),(7)进行计算。其单桩竖向极限承载力平均值为:830+860+8802575==858.3kN33858.3R=8583=429.3kNa2例题2求单桩竖向极限承载力942条件：某工程柱下桩基础,采用振动沉管灌注桩,桩身设计直径为377mm,桩身有效计算长度13.6m。地质资料如右图。要求：确定单桩竖向承载力容许值。答案：[R]=丄(u工alq+aAq)a2iiikrprki=1查表粉质黏土，粉土,黏性土摩阻力标准值分别为45kPa、55kPa、53kPa。'」=—(u乙alq+aAq)a2iiikrprki=1=丄[3.14x0.377(0.7x2.3x45+0.9x8.6x55+0.6x2.7x53)+0.6x3.14x0.3772x2200]24=1[1.18x(72.45+425.7+85.86)+147.27]=418.2kPa二、单排桩桩基算例设计资料：某直线桥的排架桩墩由2根1。0m钢筋混凝土钻孔桩组成，混凝土采用C20,承台底部中心荷载2N=5000kN，工H=l00kN，工M=320kN-m。其他有关资料如图所示，桥下无水。试求出桩身弯矩的分布、桩顶水平位移及转角(已知地基比例系数m=8000kPa/m2,m=50000kPa/m2)02答案：(i)桩的计算宽度bb=kk(d+1)二1.0x0.9(1+1)二1.8(m)1f80000x1.i'mb1"=5方=5m=8000kPa/m2,b=1.8(m),E-2.7x107kN/m21c=如==0.049m464■mb=5=0.4234/m10.8EI1'0.8x2.7x107x0.049c桩的换算深度h=ah=0.4234x16=6.76>2.5，属弹性桩。*二■JLJX砂夹卿M解(3)桩顶受力N5000P===2500kNi—M、,=320=160kN•m22Q=H=100=50kNin2(4)地面处桩的内力P二P二2500kN0iM二M+QI=160+50x4二360kN-m0ii0Q=Q=50kN0i(5)桩在地面处的横向位移和转角MQx=4B+—Aza2EIxa3EIxMQ申=亠B+—AzaEI申a2EI申其中无量纲系数查附表1、2、5、6A=2.44066A=-1.62100B=1.62100B=-1.75058,x9x9MQ36050x=—B+0A=x1.62100+x2.44066za2EIxa3EIx0.42342x8640000.42343x864000=0.00376+0.00186=0.0056(m)MQ360509=4B+0—A=—(x1.75058+x1.62100)zaEI9a2EI90.4234x8640000.42342x864000=—(0.00172+0.00052)=-0.00224(rad)(6)底面以下深度z处桩截面的弯矩MzM=MB+QA=360B+—50A=360B+118.09Az0MaMM0.4234MMM无量纲系数A、B查附表3、7MMz=azzAMBM118・09A“360B^MZ000103603600。30。70。29010.9938234.25791357o7752392o03310.61.40.529380.9586162。51448345.0996407o61410。92.10.689260。8860781.39471318.9852400.37991。22.80.761830.7741589.9645278.694368o65851。53.50.754660.6408189.1178230o6916319.80941.84。30.684880.4988980.87748179o6004260o47792。25。20.53160。3202562。77664115.2917&06662。66.10.354580。1754641.8723563.1656105o03837.10。193050.0759522o7972727o34250.139273。58.30。050810.013546.0001534o874410o8745549。40。000050。000090.0059050.03240o038305a2EIx1"i__(aEI竹+-^—Aa3EIxi+-^A)a2EI竹其中A二AB广B"查附表14—16/=al=0.4234x4.0=1.69200m=3.0485及h=ah=0.4234x16=6.7744查附=0.658=1.554(m)0.4234表13得J=°658，故由公57）桩顶水平位移及转角h=ah=0.4234x16=6.76>2.5，取h=4,A=14.58671,B=A=6.01938；B=3.44258xix1"1'"1EI=0.8EI=0.8x2.7x107x0.049=864000m2cx=—B+-QA=160x6.01938+50x14.586711a2EI坷a3EI珀0.42342x8640000.42343x864000=0.00621+0.01112=0.01733(m)"=-(—B+-QA)=-(160x3.44258+50x6.019381aEI"1a2EI",0.4234x8640000.42342x864000=—(0.00151+0.00194)=-0.00345(rad（8）桩身最大弯矩M及最大弯矩位置计算max厂aM0.4234x360(4—70)得C===3-0485Q0由z=0.658及h=6.7744查附表13得K=U。22MMmaxM=KM=1.1022x360=396.80(kN-m)maxM0（9）桩身配筋计算及桩身材料截面强度验算-0因为长细比：10.=32<17.5—M—Brf+Cpgr3广—3364.18(kN・m)>M—720.17kN・m)—0.5898x8253x9.2+1.1212x0.002x0.9x8253x280满足要求所以偏心距增大系数：c）计算截面实际偏心距e0nM720.17e—max—0N3017.11maxd）根据《公路桥涵地基与基础设计规范》（JTGD63—2007）求得轴向力的偏心距e0：e_Bfj+Dpgf:e—cdsd0Af+Cpf'cdsd其中：r—825mm，p—0.002；并设g—0.9则9.2B+0...
