某某小桥桩基薄壁桥台计算

1、- 1 -某某小小桥桥桩桩基基薄薄壁壁桥桥台台计计算算( (一一) ) 设设计计资资料料1、总体情况结构重要性系数0 =1.0桥梁计算跨径l =16m环境类别类2、地震资料桥梁抗震设防类别:C类地震动峰值加速度A =0.10g阻尼比 =0.053、汽车荷载汽车荷载等级:公路级汽车荷载提高或折减系数1行驶方向:双向行驶设计车道数2车道折减系数1桥台传递的制动力比例0.54、上部构造一孔上部结构重力7400kN上部结构混凝土强度等级C40上部结构跨中处延米结构重力G =15kN/m上部结构跨中截面惯矩Ic =0.04m45、桥台尺寸桥梁斜度0 桥台正宽度13m桥台斜宽度13.000m背墙高度1.2

2、5m背墙顶宽度0.4m置搭板背墙高0.31m置搭板背墙宽0.25m台帽高度1.3m台帽宽度1.45m台帽支撑宽度0.8m台帽前缘帽檐0.35m台身高度4.08m台身厚度0.8m承台高度1.6m- 2 -承台顺桥向宽度2.2m台身前缘与承台前缘垂直距离0.7m桥台桩基个数n桩 =4桥台桩径d =1.5m桥台桩长10m桩基类型嵌岩桩6、桥头搭板搭板长度8m搭板宽度13m搭板厚度0.3m7、支座数据支座中心与背墙前缘线正距离0.32m支座种类：板式橡胶支座(与混凝土接触)支座摩擦系数 =0.3支座+垫石高度0.2m8、地基及填土桥梁工程场地类别类场地地基土的比例系数m =30000kN/m4台后土的

3、重力密度 =19kN/m3台后土的内摩擦角 =359、建筑材料桥台混凝土的重力密度25kN/m3台身混凝土强度等级C30台身主筋种类HRB335台身主筋直径25mm台身主筋中心至混凝土表面的距离0.06m桩基混凝土强度等级C25桩基主筋种类HRB335桩基主筋直径25mm桩基主筋中心至混凝土表面的距离0.075m10、其他计算数据是否考虑支撑梁作用考虑构件计算长度系数(台身)2.0构件计算长度系数(桩基)0.511、技术标准与设计规范1)中华人民共和国行业标准公路桥涵设计通用规范(JTG D602004)2)中华人民共和国行业标准公路钢筋混凝土及预应力混凝土桥涵设计规范(JTG D622004

4、)- 3 -3)中华人民共和国行业标准公路桥涵地基与基础设计规范(JTG D632007)4)中华人民共和国行业推荐性标准公路桥梁抗震设计细则(JTG/T B02-012008)( (二二) ) 竖竖向向恒恒载载计计算算1、恒载重力计算1)上部构造恒载反力竖向力P1 =3700kN对台身中心偏心距e1 =0.27m对承台中心偏心距e1 =0.27m2)桥台背墙重竖向力P2 = 162.5 +76.4 =238.9kN对台身中心偏心距e2 =-0.25m ，-0.575m对承台中心偏心距e2 =-0.25m ，-0.575m3)桥台台帽重竖向力P3 =612.6kN对台身中心偏心距e3 =0.0

5、25m对承台中心偏心距e3 =0.025m4)桥台台身重竖向力P4 = 1060.8kN对承台中心偏心距e4 =0m5)桥台承台重竖向力P5 = 1144.0kN6)承台上土重竖向力P6 = 705.4 +221.3 =926.7kN对承台中心偏心距e6 =-0.75m ，-0.9m7)桥头搭板反力按跨径为搭板长度的0.7倍的简支梁计算竖向力P7 =273.0kN对台身中心偏心距e7 =-0.575m对承台中心偏心距e7 =-0.575m2、恒载对各截面所产生的垂直力及弯矩1)对台身底截面竖向力P恒 = P1+P2+P3+P4+P7 = 5885.3kN弯矩M恒 = P1e1+P2e2+P3e

6、3+P7e7 =772.8kNm2)对承台底截面竖向力P恒 = P1+P2+P3+P4+P5+P6+P7 = 7956.0kN弯矩M恒 = P1e1+P2e2+P3e3P4e4+P6e6+P7e7 =44.5kNm- 4 -( (三三) ) 水水平平土土压压力力计计算算1、台后填土自重引起的土压力土的内摩擦角 =35 桥台与竖直面的夹角 =0 填土表面与水平面的夹角 =0 台背与填土间的摩擦角 =/2 = 17.5 主动土压力系数 = 0.2461主动土压力标准值E = BH2/2土的重力密度 =19kN/m3桥台的计算宽度B = 13.000m对台身底截面计算土层高度H1 =6.63m主动土

7、压力E1 = 1336.1kN自计算土层底面算起土压力的着力点C1 = H1/3 =2.210m弯矩ME = E1C1 = 2952.8kNm对承台底截面计算土层高度H2 = H1 =6.63m主动土压力E2 = E1 = 1336.1kN自计算截面算起土压力的着力点C2 = C1+ 1.6 =3.810m弯矩ME = E2C2 = 5090.6kNm2、汽车荷载引起的土压力桥台与竖直面的夹角 =0 土的内摩擦角 =35 台背与填土间的摩擦角 =/2 = 17.5 = += 52.5 破坏棱体破裂面与竖直线间夹角tan = 0.5835填土高度H =6.63m破坏棱体长度l0 = H(tan+

8、tan) =3.868m破棱体上作用轴数2 轴车道系数2车轮的总重力G =560.0kN桥台横向全宽B = 13.000m土的重力密度 =19.0kN/m3车辆荷载等代均布土层厚度h = G/(Bl0) =0.586m主动土压力系数 = 0.2461()()()()()222coscossinsin1coscoscos-+-+-()()tantantancottan-+- 5 -主动土压力标准值E = BHh对台身底截面计算土层高度H1 =6.63m汽车引起的主动土压力E1 =236.2kN自计算土层底面算起土压力的着力点C1 = H1/2 =3.315m弯矩Me = E1C1 =783.1k

9、Nm对承台底截面计算土层高度H2 = H1 =6.63m汽车引起的主动土压力E2 = E1 =236.2kN自计算截面算起土压力的着力点C2 = C1+ 1.6 =4.915m弯矩Me = E2C2 = 1161.0kNm( (四四) ) 汽汽车车荷荷载载计计算算1、汽车荷载反力计算车道荷载的均布荷载标准值qK =7.9kN/m车道荷载的集中荷载标准值PK =168.0kN车道系数2桥梁计算跨径l =16m汽车荷载反力P汽 = (qKl/2+1.2PK)*车道系数 =529.2kN对台身中心偏心距e1 =0.27m对承台中心偏心距e1 =0.27m汽车荷载对台身底截面产生的弯矩M汽 =142.

10、9kNm汽车荷载对承台底截面产生的弯矩M汽 =142.9kNm2、汽车冲击力计算上部结构跨中处的单位长度质量mc =G/g = 1529.1kg/m上部结构混凝土的弹性模量Ec = 3.25E+10 N/m2上部结构跨中截面惯矩Ic =0.04m4桥梁计算跨径l =16m结构基频f =5.66Hz冲击系数当f1.5Hz，=0.05当1.5Hzf14Hz，=0.1767lnf-0.0157当f14Hz，=0.45 =0.291汽车冲击力P冲 = P汽 =153.7kN汽车冲击力对台身底截面产生的弯矩cccmIEl22- 6 -M冲 =41.5kNm汽车冲击力对承台底截面产生的弯矩M冲 =41.5

11、kNm( (五五) ) 汽汽车车荷荷载载制制动动力力、支支座座摩摩阻阻力力计计算算1、汽车荷载制动力计算车道荷载的均布荷载标准值qK =7.9kN/m车道荷载的集中荷载标准值PK =168.0kN一个设计车道总重力的10%29.4kN 17.5 考虑偏心距增大系数偏心矩增大系数 =式中：轴向力对截面重心轴的偏心距e0 = Md/Nd =0.883m截面有效高度h0 = h-a =0.74m荷载偏心率对截面曲率的影响系数1 = 0.2+2.7e0/h0 =3.4231.0212000)(/140011xxhlhe+hAI121=承载能力极限状态基本组合- 11 -1 =1.000构件长细比对截面

12、曲率的影响系数2 = 1.15-0.01l0/h =1.0111.02 =1.000 =1.116e0 =0.986m轴向力至受拉边纵向钢筋合力点的距离e =e0+h/2-a =1.326m轴向力至受压边纵向钢筋合力点的距离台身混凝土轴心抗压强度设计值fcd =13.8MPa纵向钢筋的抗拉、抗压强度设计值fsd = fsd =280MPa截面受压区矩形应力图高度与实际受压区高度的比值 =0.80矩形截面对称配筋，As = As假定为大偏心受压，s=fsd，则0Nd fcdbx 截面受压区高度x =0.043m相对受压区高度 = x/h0 =0.058b =0.56 为大偏心受压构件0Nde f

13、cdbx(h0-x/2)+fsdAs(h0-as)As = As = 0.0247m2矩形截面对称配筋的钢筋混凝土小偏心受压构件，其钢筋截面面积可按下式计算As = As =式中相对受压区高度 = 0.5589As = As = -0.1539m2 最小受拉或受压区纵向钢筋面积As = As = 0.0247m2桥台台身纵向主筋直径为 25 mm 持久状况承载能力极限状态计算台身一侧所需最小纵向钢筋根数为5151根2、构造规定根据公路钢筋混凝土及预应力混凝土桥涵设计规范(JTG D622004)第9.1.12条，偏心受压构件全部纵向钢筋的配筋百分率不应小于0.5桥台台身纵向主筋直径为 25 m

14、m 构造规定台身一侧最小纵向钢筋根数为53根3、正常使用极限状态台身裂缝宽度验算1)作用台身底面处短期效应组合作用台身底面处正常使用极限状态短期效应组合以组合控制设计轴向力Ns = 6255.7kN最大弯矩Ms = 5110.9kNm()()bcdsbcddcdbdbhfahbhfeNbhfN+-002000043. 0()()5 . 010200ssdcddahfbhfeN- 12 -台身正常使用极限状态作用效应以台身底截面(-截面)组合控制设计。2)作用作用台身底面处长期效应组合作用于台身底面处长期效应组合轴向力为Nl = 6097.0kN3)裂缝宽度验算按公路钢筋混凝土及预应力混凝土桥涵

15、设计规范(JTG D622004)第6.4.3、6.4.4条计算轴向力Ns的偏心距e0 = Ms/Ns =0.817m截面高度h =0.80m截面有效高度h0 =0.74m构件的计算长度l0 =11.160m使用阶段的偏心距增大系数s = 1.0441l0/h =13.95014取s =1.0000截面重心至纵向受拉钢筋合力点的距离ys =0.34m轴向压力作用点至纵向受拉钢筋合力点的距离es = se0+ys =0.340m受压翼缘截面面积与腹板有效截面面积的比值f =0纵向受拉钢筋合力点至截面受压区合力点的距离z = 0.87-0.12(1-f)(h0/es)2h0=0.2230.87h0

16、 =0.644m取z =0.223m纵向钢筋直径d =25mm一侧纵向钢筋设计采用根数53根受拉区纵向钢筋截面面积As =0.0260m2 钢筋应力ss = Ns(es-z)/(Asz) =125.91MPa纵向受拉钢筋配筋率 = As/bh0 = 0.00270.022.5 m根据公路桥涵地基与基础设计规范附录P第P.0.4条，按表P.0.4计算作用效应及位移。影响系数kh =0桩顶水平位移x0 =桩顶转角0 =取h4.0，由公路桥涵地基与基础设计规范表P.0.8查得= 2.4007= 1.5998= 1.5998= 1.7322桩顶水平位移x0 = 0.0040m桩顶转角0 = -0.00

17、18rad桩身弯矩Mz =A3、B3、C3、D3由公路桥涵地基与基础设计规范表P.0.8查得，计算见下表h=zA3B3C3D3zMz(m)(m)(kNm)00.000000.000001.000000.0000002404.92404.90.1-0.00017-0.000011.000000.100000.2422404.3FALSE0.2-0.00133-0.000130.999990.200000.4832400.3FALSE0.3-0.00450-0.000670.999940.300000.7252390.3FALSE0.4-0.01067-0.002130.999740.399980

18、.9672372.1FALSE0.5-0.02083-0.005210.999220.499911.2082344.6FALSE0.6-0.03600-0.010800.998060.599741.4502306.8FALSE0.7-0.05716-0.020010.995800.699351.6922258.3FALSE)(33032030302DEIHCEIMBAxEIaaafa+51EImb2112211220211221123011BABACBCBEIMBABADBDBEIH-+-aa)11(2112211202112211220BABACACAE IMBABADADAE IH-+-a

19、a21122112BABADBDB-21122112BABACBCB-21122112BABACACA-21122112BABADADA- 15 -0.8-0.08532-0.034120.991810.798541.9342199.1FALSE0.9-0.12144-0.054660.985240.897052.1752129.9FALSE1-0.16652-0.083290.975010.994452.4172051.1FALSE1.1-0.22152-0.121920.959751.090162.6591963.8FALSE1.2-0.28737-0.172600.937831.1834

20、22.9001868.8FALSE1.3-0.36496-0.237600.907271.273203.1421767.6FALSE1.4-0.45515-0.319330.865731.358213.3841661.2FALSE1.5-0.55870-0.420390.815041.436803.6251561.8FALSE1.6-0.67629-0.543480.738591.506953.8671438.3FALSE1.7-0.80848-0.691440.646371.566214.1091324.3FALSE1.8-0.95564-0.867150.529971.611624.350

21、1210.2FALSE1.9-1.11796-1.073570.385031.639694.5921097.0FALSE2-1.29535-1.313610.206761.646284.834985.8FALSE2.2-1.69334-1.90567-0.270871.575385.317772.3FALSE2.4-2.14117-2.66329-0.948851.352015.801574.9FALSE2.6-2.62126-3.59987-1.877340.916796.284396.4FALSE2.8-3.10341-4.71748-3.107910.197296.767237.7FAL

22、SE3-3.54058-5.99979-4.68788-0.891267.25197.8FALSE3.5-3.91921-9.54367-10.34040-5.854028.459-189.8FALSE4-1.61428-11.73066 -17.91860 -15.075509.668-436.4FALSE由上表得知最大弯矩处z =0.000m最大弯矩Md = 2404.9kNm该处轴力Nd = 2554.1kN4)桩基配筋计算轴向力偏心距e0 = Md/Nd =0.942m构件计算长度系数0.5构件的计算长度l0= 0.5 4/ =4.834m惯性半径i= d/4 =0.375m长细比l0

23、/i = 12.89017.5 不考虑偏心距增大系数偏心矩增大系数 =式中：圆截面半径r =0.75m纵向钢筋所在圆周的半径rs =0.675m截面有效高度h0 = r+rs =1.425m截面高度h = 2r =1.5m荷载偏心率对截面曲率的影响系数1 = 0.2+2.7e0/h0 =1.9841.0212000)(/140011xxhlhe+AI- 16 -1 =1.000构件长细比对截面曲率的影响系数2 = 1.15-0.01l0/h =1.1181.02 =1.000 =1.000e0 =0.942m由公路钢筋混凝土及预应力混凝土桥涵设计规范(JTG D62-2004)附录C有配筋率

24、=桩的混凝土轴心抗压强度设计值fcd =11.5MPa普通钢筋的抗压强度设计值fsd =280MPag = rs/r =0.900假定 =0.27A =0.4992B =0.3717C = -1.1254D =1.6584 = 0.0036Ar2fcd+Cr2fsd = 2590.2kN Nd = 2554.1kNBr3fcd+Dgr3fsd = 2438.9kN Nde0 = 2404.9kN 最小纵向钢筋面积As = r2 = 0.0064m2桥台桩基纵向主筋直径为 25 mm 持久状况承载能力极限状态计算桩基所需最小纵向钢筋根数为1313根3、构造规定根据公路钢筋混凝土及预应力混凝土桥涵

25、设计规范(JTG D622004)第9.1.12条，偏心受压构件全部纵向钢筋的配筋百分率不应小于0.5桥台台身纵向主筋直径为 25 mm 构造规定桩基最小纵向钢筋根数为19根4、正常使用极限状态桩基裂缝宽度验算1)作用短期效应组合作用于承台底面处正常使用极限状态短期效应组合以组合控制设计竖向力P短 = 8326.5kN水平力H短 = 1662.3kN最大弯矩M短 = 7042.4kNm单桩顶作用短期效应桥台桩基个数n桩 =4单桩顶竖向力P0短 = P短/n桩 = 2081.6kN单桩顶水平力H0短 = H短/n桩 =415.6kN单桩顶弯矩M0短 = M短/n桩 = 1760.6kNmDgrC

26、eAeBrffsdcd-00- 17 -考虑支撑梁作用，则桩顶水平力H0短 =0.0kN桩基最大弯矩计算桩顶水平位移x0 = 0.0030m桩顶转角0 = -0.0013rad桩身弯矩Mz计算见下表h=zA3B3C3D3zMz(m)(m)(kNm)00.000000.000001.000000.0000001760.61760.60.1-0.00017-0.000011.000000.100000.2421760.2FALSE0.2-0.00133-0.000130.999990.200000.4831757.2FALSE0.3-0.00450-0.000670.999940.300000.7

27、251749.9FALSE0.4-0.01067-0.002130.999740.399980.9671736.6FALSE0.5-0.02083-0.005210.999220.499911.2081716.5FALSE0.6-0.03600-0.010800.998060.599741.4501688.7FALSE0.7-0.05716-0.020010.995800.699351.6921653.2FALSE0.8-0.08532-0.034120.991810.798541.9341609.9FALSE0.9-0.12144-0.054660.985240.897052.1751559

28、.3FALSE1-0.16652-0.083290.975010.994452.4171501.6FALSE1.1-0.22152-0.121920.959751.090162.6591437.6FALSE1.2-0.28737-0.172600.937831.183422.9001368.1FALSE1.3-0.36496-0.237600.907271.273203.1421294.0FALSE1.4-0.45515-0.319330.865731.358213.3841216.1FALSE1.5-0.55870-0.420390.815041.436803.6251143.4FALSE1

29、.6-0.67629-0.543480.738591.506953.8671053.0FALSE1.7-0.80848-0.691440.646371.566214.109969.5FALSE1.8-0.95564-0.867150.529971.611624.350886.0FALSE1.9-1.11796-1.073570.385031.639694.592803.1FALSE2-1.29535-1.313610.206761.646284.834721.7FALSE2.2-1.69334-1.90567-0.270871.575385.317565.4FALSE2.4-2.14117-2

30、.66329-0.948851.352015.801420.9FALSE2.6-2.62126-3.59987-1.877340.916796.284290.2FALSE2.8-3.10341-4.71748-3.107910.197296.767174.0FALSE3-3.54058-5.99979-4.68788-0.891267.25171.6FALSE3.5-3.91921-9.54367-10.34040-5.854028.459-138.9FALSE4-1.61428-11.73066 -17.91860 -15.075509.668-319.4FALSE由上表得知最大弯矩处z =

31、0.000m最大弯矩Ms = 1760.6kNm- 18 -该处轴向力Ns = 2081.6kN2)作用长期效应组合作用于承台底面处长期效应组合竖向力为P长 = 8167.7kN单桩顶竖向力P0长 = P长/n桩 = 2041.9kN作用短期效应组合最大弯矩处z =0.000m该处长期效应组合轴向力Nl = 2041.9kN3)裂缝宽度验算按公路钢筋混凝土及预应力混凝土桥涵设计规范(JTG D622004)第6.4.5条计算按作用短期效应组合计算的轴向力Ns = 2081621 N轴向力Ns的偏心距e0 = Ms/Ns =846mm截面高度h = 2r =1.5m截面有效高度h0 = r+rs

32、 =1.425m构件的计算长度l0 =4.834m使用阶段的偏心距增大系数s = 1.0044l0/h =3.22314取s =1.0000构件的截面半径r =750mm混凝土强度等级fcu,k =25MPa纵向钢筋直径d =25mm设计采用钢筋根数19根截面配筋率 = As/r2 = 0.0053截面受拉区最外缘钢筋应力ss =144.8MPa 24 MPa 应验算裂缝宽度钢筋表面形状系数C1 =1.0作用长期效应影响系数C2 =1+0.5Nl/Ns =1.490钢筋的弹性模量Es =200000MPa混凝土的保护层厚度C =60.8mm 最大裂缝宽度Wfk = C1C20.03+ss/Es

33、(0.004d/+1.52C)=0.165mm 0.20 mm 满足规范裂缝宽度要求( (十十) ) 计计算算结结果果汇汇总总2000/400011+hlhe320,265. 10 . 180. 242.59-refrNskcus- 19 -项目台身厚度或桩径(m)混凝土 强度等级主筋种类主筋直径(mm)计算所需主筋根数构造最小主筋根数构造最大主筋根数(超过可采用束筋)设计采用 主筋根数钢筋间距(cm)裂缝宽度(mm)台身(一侧)0.8C30HRB3352551531645324.80.136桩基1.5C25HRB335251319391922.30.165桩长 (m)10#DIV/0!- 20 -P (kN)H (kN)8018.51870.6基本组合6841.41870.6基本组合7062.42201.3基本组合5885.322