预应力混凝土简支小箱梁桥设计

桥梁工程课程设计预应力混凝土简支小箱梁桥设计计算书姓名学号班级指导教师成绩二一二年七月第一章设计依据1公路钢筋混凝土及预应力混凝土桥涵设计规范（JTGD622004）（以下简称公预规）2公路桥涵设计通用规范（JTGD602004）（以下简称桥规3公路工程技术标准（JTGB012003）第二章设计资料及上部结构主要尺寸21设计资料1桥梁跨径及桥宽标准跨径35M；主梁全长3494M；计算跨径3419M；桥面宽度05M（防撞栏杆）159（净行车道宽度）M05M（防撞栏杆）169M。分幅单幅行车方向单向行车2设计荷载公路I级，无人群荷载，单侧防撞护栏重78KN/M。3材料及工艺混凝土小箱梁梁的预制部分及现浇接缝部分均采用C50（容重为26KN/M3）；铺装层为10CM厚沥青混凝土混凝土（容重为24KN/M3）；沥青铺装层下设置8CM厚的C40防水混凝土调平层（容重为25KN/M3）。预应力钢筋152S钢绞线，1860PKFMPA，单根面积140MM2。普通钢筋直径12MM采用HRB335钢筋；直径053772号梁图268620017110187601998021680227023690241024380502CQM按照2车道加载47440227023690241024380501CQM067086205775047443号梁816302038021140215002128020850200501944018620503CQM按照2车道加载3948020850200501944018620501CQM067081630546903948根据对称性关系8620024CQCQMM8859015CQCQMM322支座处用杠杆原理法1号梁图27078912827066970205415010QM2号梁图28132310882047060161760088205020QM3号梁图29132310882047060161760088205030QM根据对称性关系132312040QQMM078911050QQMM表34各梁横向分布系数梁号跨中支座10885910789208621132330816311323408621132350885910789322活载计算荷载值MKNQK/510KNPK300折减系数0671号梁Z4525697548010453193421432102HMEILFCC143001570LN17670F弯矩横向分布系数图210剪力横向分布系数图211支座处弯矩M0剪力图212Q1143107893000671143（05（1078910885908571）3419/7088590563419/7）10506738835KN1/8跨处弯矩图213M114308859374300067114308859053743419105067121664MKN剪力图214Q11430913000671143（05（09108750885908571）061088590563419/7）10506731726KN1/4跨处弯矩图215M114308859641300067114308859056413419105067208521MKN剪力图216Q11430753000885906711430885905075075341910506722105KN3/8跨处弯矩图217M11430885980133000671143088590580133419105067260667MKN剪力图218Q11430625300088590671143088590506250625341910506717477KN跨中处弯矩图219M1143300854750885906711430534198547510508859067278055MKN剪力图220Q12937KN2号梁弯矩横向分布系数图221剪力横向分布系数图222支座处M0Q39845KN1/8跨处M118382MKNQ31184KN1/4跨处M202896MKNQ21518KN3/8跨处M253635MKNQ17006KN跨中处M270554MKNQ12864KN3号梁弯矩横向分布系数图223剪力横向分布系数支座处M0Q39229KN1/8跨处M112106MKNQ29635KN1/4跨处M192391MKNQ20375KN3/8跨处M240188MKNQ16104KN跨中处M256179MKNQ12182KN4,5号梁活载内力分别于2，1号梁相同表35各梁活载内力值梁号支座处1/8跨处1/4跨处3/8跨处跨中处MKNMQKNMKNMQKNMKNMQKNMKNMQKNMKNM1038835121664317262085212210526066717477278055203984511838231184202896215182536351700627055430392291121062963519239120375240188161042561794039845118382311842028962151825363517006270554503883512166431726288521221052606671747727805533内力组合表361号梁内力组合1号梁序号荷载类别支座处1/8跨处1/4跨处3/8跨处跨中处QMQMQMQMQKNKNMKNKNMKNKNMKNKNMKN1自重66277742479497084248383313925310818888856650502二期恒载292497310942193718749146252343778336022500103恒载955274835737164561232747764276545727224881651504活载38835121664317262085212210526066717477278055129375承载力极限状态组合1,690005,990901,3039010,26720882612,83480571413,6910018116正常使用短期组合1,193104,3181091077,400306139,2510037939,868007927正常使用长期组合1,091203,9988082756,853005558,5668033349,138204538正常使用标准组合1,343604,789601,033708,20850698710,2612044710,945701294表372号梁内力组合2号梁序号荷载类别支座处1/8跨处1/4跨处3/8跨处跨中处QMQMQMQMQKNKNMKNKNMKNKNMKNKNMKN1自重6716625120250374643053633583853820419141857410402二期恒载2925109393219371187491462512343778335872500103恒载9641636059572311861802548208977258127477782411404活载39845118382311842028962151825363517006270554128645承载力极限状态组合1,714805,984501,3043010,25680879812,82190567813,6771018016正常使用短期组合1,208204,3309091417,4228061399,2791037899,898107887正常使用长期组合1,103604,0202083226,8903055748,6134033439,18800458正常使用标准组合1,362604,789801,035008,20920697310,26220444810,946701286表383号梁内力组合3号梁序号荷载类别支座处1/8跨处1/4跨处3/8跨处跨中处QMQMQMQMQKNKNMKNKNMKNKNMKNKNMKN1自重6716625120250374643053633583853820419141857410402二期恒载2925109393219371187491462512343778335872500103恒载9641636059572311861802548208977258127477782411404活载39229112106296351923912037524018816104256179121825承载力极限状态组合1,706205,896601,2826010,10980863812,63360555213,4759017056正常使用短期组合1,204404,2925090467,3585060699,1968037349,810007467正常使用长期组合1,101403,9983082686,8535055348,5664033119,137704268正常使用标准组合1,356504,727001,019508,10420685810,12770435810,802901218第四章预应力钢筋估束和布置41预应力钢束的估束由于边梁的内力最大，所以预应力钢筋的布置一边梁为准，其他梁预应力布置与边梁相同。对于预应力钢筋混凝土简支梁桥，控制结构设计的通常是抗裂性验算。因而，可按照抗裂性验算原则完成估束工作。根据公路钢筋混凝土及预应力混凝土桥涵设计规范JTGD622004的第631条P58规定全预应力混凝土构件，在作用或荷载短期效应组合下预制构件0850PCST41式中，ST为作用或荷载短期效应组合下构件抗裂验算边缘混凝土的拉应力，PC为扣除全部预应力损失后预加力在构件抗裂验算边缘产生的预压应力。本课程设计，抗裂验算边缘为截面下边缘。根据材料力学知识，作用或荷载短期效应组合下构件抗裂验算边缘混凝土的拉应力ST按下式求得BSTSTYIM042其中，STM是弯矩短期效应组合值，0I是毛截面抗弯惯性矩，BY是下边缘距截面中性轴的距离。预加力在构件抗裂验算边缘产生的预压应力的计算按如下方式计算。将预加力等效为作用在截面中性轴位置处的轴力和一外加弯矩，如图41所示。NENNE图41预加力等效则，预加力在构件抗裂验算边缘产生的预压应PC按下式计算BPCYINEAN0043上式中，0A是毛截面面积，E是预应力钢绞线合力作用点距截面中性轴的距离，0I和BY的定义与式42一致，N是预加力，按下式计算PEFFAN44其中，EFF和PA分别为预应力钢束的有效预应力和面积。将式4244代入式41，并将式41取等号，得到预应力钢束面积估算公式000850IEYAYIMABEFFEFFBSTP45上式中，预应力钢束的有效预应力EFF及预应力钢绞线合力作用点距截面中性轴的距离E需要预先假定。一般而言，对于MPAFPK1860的预应力钢绞线的控制张拉应力取MPAFPKCON13951860750750，在估束阶段，根据经验，考虑25的预应力损失，则有效预应力的估计值为MPACONEFF10461395750750。对于跨中截面，可假设预应力钢绞线合力作用点距截面下边缘18CM进行试算。MKNMST810459205520MIMYB171ME990代入45得28365MMAP选配12束5152的钢束实际28400MMAP图41预应力钢束布置图表41钢束尺寸钢束号长度（CM）半径（M）弯起角度（）钢束中心到梁底距离支座处1/8截面处1/4截面处3/8截面处跨中处N1173804300021259999N217399830007521102999N317403445007742932202020N41740696000796497231093131N517410675007118704145074242N617414290007140916861725353表42截面特性计算点截面积（2MM）截面重心至底面（MM）WN3MM梁自重弯矩（KNM）IN（4MM）I0（4MM）截面重心至到钢束质心距离（MM）NA0ANY0YNE0E跨中13725045141864571188611588452610856650553810115761011915688581/8跨1372504514186457118861158845261085310853810115761011915688581/4跨13725045141864571188211591454510842483854010115761011895286613/8跨1372504514186457118531160846061082479546101157210117507255支点15995045164564571105109735620108062110116171011284276342预应力损失计算421磨阻损失11XCONLE00150220MPACON1395表431L计算表422由锚具变形及钢束回缩引起的预应力损失2L按公预规2L计算公式如下反向摩擦影响长度计算点钢束X（）（RAD）MMPA跨中N130052361738003758900368915146314N27012217173800529470051577194013N37012217173800529470051577194013N47012217173800529470051577194013N57012217173800529470051577194013N670122171738005294700515771940131/8跨N130052361300500310260030554261719N27012217130050046385004532563229N37012217130050046385004532563229N47012217130050046385004532563229N57012217130050046385004532563229N670122171300500463850045325632291/4跨N13005236863002446400241673371299N2701221786300398220039045446051N3701221786300398220039045446051N4668011659863003859400378585281241N553600935586300335250032974599255N64480078198630030146002969741426743/8跨N13005236463001846400182942552072N2493008604463002587400255423563166N3331005777463001965400194622714981N42590045246300168900167482336313N5201003508463001466300145562030513N6167002915463001335700132681850933支点N1000120000180000180251077N2000120000180000180251077N3000120000180000180251077N4000120000180000180251077N5000120000180000180251077N6000120000180000180251077X1XE1XCONEDPFELLMML6LLD0MPAEP510951其中MPA13950L为预应力钢筋扣除磨阻损失后锚固端应力L为张拉端至锚固端的距离FDLL22在反影响长度内，距张拉端X处的锚具变形、钢筋回缩损失22XLFDL；在反影响长度外，锚具变形、钢筋回缩损失02L表442L计算表计算点钢束影响长度XMPAMMMMMPA跨中N100029611987786173801479261N20004139168125173800N30004139168125173800N40004139168125173800N50004139168125173800N600041391681251738001/8跨N10003277188953813005386054N200048621551279130052438526N300048621551279130052438526N400048621551279130052438526N500048621551279130052438526N6000486215512791300524385261/4跨N10003906173061286306778631N20006311136162586306293248N30006311136162586306293248N4000612138270886306360836N50005329148168186306594368D2LN6000481561198863067031433/8跨N1K0005512145692446301095709N20007696123300746301185167N30005864141253846301113597N40005046152271346301069469N50004386163335546301026532N60003998171075646309976298支点N100020922364721209845247N200020922364721209845247N300020922364721209845247N400020922364721209845247N500020922364721209845247N600020922364721209845247423钢筋松弛引起的预应力损失4L4935PN28400MMAP表454L计算表计算点钢束平均COSNNNWEA1COS111NNAPPWEANNNN1PE4LMPAMPAMPA/MM跨中N113287441275E061061,255687307N21323061275E061061,250307276N31323061275E061061,250307276N41323061275E061061,250307276N51323061275E061061,250307276N61323061275E061061,2503072761/8跨N113137771275E061061,241537225N213073861275E061061,235497189N313073861275E061061,235497189N413073861275E061061,235497189N513073861275E061061,235497189N613073861275E061061,23549718921LLCON1/4跨N1129350109998270E061061,223696981N2127760709998270E061061,208656895N3127760709998270E061061,208656895N4127857909998270E061061,209576901N5128306409998270E061061,213816925N6128654209998270E061061,2171069443/8跨N1125990809977236E061051,200225969N2124085209977236E061051,182075878N3125649109977236E061051,196975952N412646909977236E061051,204785991N5127204209977236E061051,211786026N6127672809977236E061051,216246048支点N1129629609936113E061021,266223008N2129629609936113E061021,266223008N3129629609936113E061021,266223008N4129629609936113E061021,266223008N5129629609936113E061021,266223008N6129629609936113E061021,266223008424由钢筋应力松弛引起的预应力损失L5公预规规定，钢绞线由松弛引起的预应力损失的终极值，按下式计算PEPKPEF2605205L0130表46L5计算表计算点钢束MPAPE5MPAL跨中N11,25568343N21,250303359N31,250303359N41,250303359N51,250303359N61,2503033591/8跨N11,241533244N21,235493166N31,235493166N41,235493166N51,235493166N61,2354931661/4跨N11,223693014N21,208652825N31,208652825N41,209572836N51,213812889N61,2171029313/8跨N11,20022272N21,182072499N31,19697268N41,204782777N51,211782864N61,21624292支点N11,266223571N21,266223571N31,266223571N41,266223571N51,266223571N61,266223571425混凝土收缩徐变引起的预应力损失根据公预规规定，由混凝土收缩徐变引起的预应力损失可按下式计算PPCEPCSPLTTTTE151,90006221IEPP其中MPAEP510951支座处2322UA00021360,0TTEP62761,0TT跨中处1942UA000220,0TTEP65361,0TT4935EP60NPAA表476L计算表计算点钢束C,9000TTTTEPCEPCSPP6LMPAMPA跨中N127072598728720655N226942588528720574N326942588528720574N426942588528720574N526942588528720574N6269425885287205741/8跨N12674257228720443N22662560628720352N32662560628720352N42662560628720352N52662560628720352N626625606287203521/4跨N125822497227919966N225482469327919743N325482469327919743N4255247127919757N52562478927919819N625672485279198683/8跨N12213219542261824N221772166122617997N322072190122618197N422222202822618301N522362214122618395N622452221322618455支点N1114612551211329N2114612551211399N3114612551211399N4114612551211329N5114612551211329N6114612551211329表48钢束预应力损失一览表计算点钢束预加应力阶段正常使用阶段锚固前的预应力损失锚固时的预应力损失锚固后的预应力损失钢束有效应力12456跨中N15146314147926173071,25568343206551,01483N27194013072761,250303359205741,01097N37194013072761,250303359205741,01097N47194013072761,250303359205741,01097N57194013072761,250303359205741,01097N67194013072761,250303359205741,010971/8跨N1426171938605472251,241533244204431,00466N263229243852671891,235493166203521,00031N363229243852671891,235493166203521,00031N463229243852671891,235493166203521,00031N563229243852671891,235493166203521,00031N663229243852671891,235493166203521,000311/4跨N13371299677863169811,2236930141996699389N25446051629324868951,2086528251974398297N35446051629324868951,2086528251974398297N45281241636083669011,2095728361975798364N54599255659436869251,2138128891981998673N64142674670314369441,21710293119868989113/8跨N12552072109570959691,20022272182499062N23563166118516758781,1820724991799797711N32714981111359759521,19697268181979882N42336313106946959911,20478277718301994N52030513102653260261,2117828641839599919N61850933997629860481,21624292184551,00249支点N10251077984524730081,266223571113291,11722N20251077984524730081,266223571113291,11722N30251077984524730081,266223571113291,11722N40251077984524730081,266223571113291,11722N50251077984524730081,266223571113291,11722N60251077984524730081,266223571113291,11722第五章小箱梁梁验算51正截面抗弯验算对于箱型截面，可按T型截面进行验算。KNNAFPPD105841058400084001260PPDFFCDAFKNNHBF213507135072001803350422中性轴在翼缘板内设中性轴到截面上缘距离为X，则MMBFAFXFCDPPD14133504221058400040B由公预规正截面承载力按下式计算2000XHXBFMFCD010跨中截面MMH152727318000XMMHB8610000M13,6910KNM000615415105415701527105840002MMKNMMNEXHXBFFCD合格1/4截面MMH150729318000XMMHB8602000M10,2672KNM000915203105215701507105840002MMKNMMNEXHXBFFCD合格支座处不用进行抗弯验算。52正截面抗裂验算根据公预规，对预制的A类预应力混凝土构件，在作用短期荷载效应组合下，应符合MPAPCST861在长期荷载效应组合下，应符合0PCSTXPNXGSTWMWM01NXPNPPCWMAN下表出示了正截面抗裂验算的计算过程和结果，可见其结果符合规范要求。表49应力部位跨中下缘1/4跨下缘支点下缘PN（01KN）849755282870349384648MPNM752713167177400124929782CMAN3CMWNX1372504137250415995043CMWOX4526004545005620001MNMG497065496937562289MNML566505042483800MNMS913820068530000MPAANNP986800074003000NXPWM（MPA）61912766746037894245867224PC（MPA）16630869641579185944435904NXGWM1（MPA）22822146322182975371030313OXGSWMM11251668149347370740（MPA）OXGLWMM1（MPA）84555339846342695350LT（MPA）6987315542524134850ST（MPA）19503996941458871920PCST（MPA）20972215381569006610PCLT（MPA）18499309461396876103031PN（01KN）3318149387241034410303153混凝土正截面压应力和预应力钢筋拉应力验算1正截面混凝土压应力验算根据公预规，使用阶段正截面应力应符合下列要求21650MPAFCKPTKC表410正截面混凝土压应力验算