水平和扭轉(zhuǎn)荷載聯(lián)合作用下的群樁非線性響應(yīng)簡化分析方法

水平和扭轉(zhuǎn)荷載聯(lián)合作用下的群樁非線性響應(yīng)簡化分析方法

1inedlateralfoining,torsionalmoading,以馬立克爾第20e為主導(dǎo)的非織造材料的再b5.3.3.3.3.3.3.3.4.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3inre體的雙重式樹葉片,5.4.5.4.5.4.5.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3關(guān)于單帶和輕敲組的研究(。andwhereβSomenumericalprogramscanpredictthelinearresponseofpilegroupssubjectedtocombinedlateralandtorsionalloading(2pile使用—MethodofanalysisTheproblemofapilegroupwitharbitrarilydistributedpilessubjectedtoappliedhorizontalloadsandtorqueissummarizedinFig.1a.Therectanglerepresentsthecapofthepilegroupandthecirclesrepresentthepilesfixedtothecap.DefinethecoordinateX-YwithoriginOastheglobalcoordinatesystem.(X2.1asuningpo對于asinfig.3.4.3.3.3.3—Motionsofpilesinapilegroupundercom-binedlateralandtorsionalloadingSincethemotionofthepilecapisconsideredasaplanerigid-bodymotion,atwistcenterexistsatanytime,calledtheinstantaneouscenter,aboutwhichthereisrotationwithouttranslation.ItisassumedthatpointAinFig.1aistheinstantaneouscenterofthepilecapand(XSubstitutingEq.(2)intoEq.(3)yieldsthexcoordinateofpileiinthelocalcoordinatesystemafterthepilegroupistwisted:SolvingEq.(6)yieldsSincethepilecapisconsideredasaplanemotionofarigidbodywithoutoverturning,uFromEq.(8),bothuclosetotheequivalentactionpointispreferredtominimizethecalculationworkload.Asaspecialcase,ifF2.2nbeearedagrohistindex,keq.3,5,9,10,19,26,3,19,26,3,19,26,3,19,26,3,26,3,5,26,3,5,7,26,3,5,7,26,3,5.3.3.3.3.4.3.3.4.3.4.3.4.3.3.4.3.4.3.4.3.4.3.4.3.4.3.4.3.4.3.4.3.4.3.4.3.4和lateral-12,3,26,7,26,7,26,7,26,7,26,7,26,7,26,7,26,7,26:k.5.4,7,26,7,26,7,26,7,26,7,26,7,26,7,26,7,26,7,26,7,26,7,26,7,26,7,26,7,26,7,26,7,26,7,26,7,26,7,26,7,26,7,26,7,26,7,26,7,26,7,26,7,26,7,26,7,26,7,26,7,26,7,26,7,26,7,26,7,26,7,26,7,26,7,26,7,26,7,26,7,26,7,26,7,26,7,26,7,26,7,26,7,26,7,26,7,26,7,26,7,26,7,26,7,26,7,26,7,26,7,26,7,26,7,26,7,26,7,26,7,26,26,7,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,ReferringtoFig.1b,whichshowsthepilecapsubjectedtoexternalloadsandinternalforcesonthepileheads,theequilibriumequationsofthepilecapcanbeexpressedaswhereHwhereKEq.(12)isacoupledternarytranscendentalequationanduSubstitutingEqs.(13)and(15)intoEq.(8)yieldsFig.2bshowsthesimplifiedgeometricdeformationofpilei.ThedirectionofsSubstitutingEqs.(13)–(17)intoEq.(12),theequilibriumequationcanbesimplifiedassolutionofEq.(18)ispilegroupisactuallysubjectedtolateralloadingwithouttorque,andthedisplacementforeachpileisthesame:InEq.(19),thehorizontalstiffnessK3nbeging,eth,eth,eth,eth,eth,eth,eth,eth,etix.3,5,26,26.3.4.3.4.3.4.3.4.3.4.3.4.3.4.3.4.5.4.5.4.3.4.3.4.3.4.3.4.3.4.5.4.5.4.5.4.5.4.3.4.5.4.5.4.5.4.5.4.5.4.5.4.5.4.5.4.5.4.5.4.5.4.5.4.5.4.5.4.5.4.5.4.5.4.5.4.5.4.5.4.5.4.4.5.4.3.4.5.4.5.4.5.4.5.4.5.4.5.4.5.4.4.5.3.4.3.4.4.4.5.4.4.5.4.3.4.5.4.5.4.4.5.4.5.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.5.4.5.4.5.4.5.4.5.4.5.4.5.4.5.4.5.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4.4AnindividualpileinthepilegroupshowninFig.1issubjectedtoalateralload,abendingmoment,andatorsionalloadatthepilehead.Assumingeachpileworksasasimplebeam,thegoverningfourthandsecond-orderdifferentialequationsforthelateraldeflectionsandtwistangleφofthepilecanbegivenbywhereEwherefwhereαEachpileismodeledbyanumberofdiscretebeamelements(Fig.3).Thesoilstiffnessperunitlengthofapileforlateralloadingandfortorsionalloadingarebothrepresentedbynonlinearspringsatthenodalpointsoftheelements.Basedontheconventionalfiniteelementmethod(whereKTheload-displacementrelationshipforthesoilatthenodesinthepilecanbeexpressedbywherePBasedontheassumptionofnoseparationbetweenthesoilandthepile,thecompatibilityofthedeformationsofthesoilandthepileyieldsEquilibriumoftheinteractionforcesactingatthepile-soilinterfaceyieldsSubstitutingEqs.(26)–(28)intoEq.(25),thecompleteload-displacementrelationshipforthepileunderlateralandtorsionalloadingisgivenbyThepileheadisassumedfixed;therefore,thehorizontalandtorsionalload-displacementrelationshipsofthepile,K4雙質(zhì)模型sif-pileing及其sif-sif-sif-pilejThegeneralizedp-multiplierofpileiinapilegroupwithnpilessubjectedtocombinedlateralandtorsionalloadingiscalculatedusingEq.(1).TocalculateβwheresAssumethatpileiistheleadingpileandpilejisthetrailingpileinthedouble-pilegroup(Fig.4).Ifthehorizontaldisplacementvectorofpilei,sIfthedisplacementvectorofpilej,sForthe‘sameside’case(Fig.4a),Forthe‘differentsides’case(Fig.4b),IfeithersAsηandδareknown,β5內(nèi)部平均可追溯性andwhereβ6siphinizationsiphensipt和abovesiphensinpenssiphinsi嚴格公司siphensiphinvi體制Acomputerprogram,namedELPGROUP,wasdevelopedusingthisapproach.AflowchartoftheprogramisshowninFig.5.Inputparametersincludesoilparameters,pileparameters,groupconfiguration,andexternalloads.Theloopoperationofthepmultipliersstartswithaninitialvalueof1.Bycalculatingthehorizontalstiffnessandthetorsionalstiffnessofeachpileinagivenpilegroup,thedisplacementsofeachpileareobtainedthroughaninternaliterativeprocess.Thennewp-multiplierofeachpileiscalculatedusingthenewly-obtaineddisplacements.Theaboveprocessisrepeateduntilp-multiplierssatisfyagiventolerance.NotethattheinternaliterativeprocessshowninFig.5usesEq.(19)(thesolutionofthesimplifiedequilibriumequation).Therefore,theprogramhasgoodefficiencyincalculation,butobtainsapproximateresults.Toverifytheiraccuracy,theapproximateresultswerecomparedwithmodeltestresultsandexactsolutions,asdiscussedinthenexttwosections.7b.lateralmoading,torsion,v.torsion,v.krafting,f.v.krafting.krafts.v.krafts.v.krafts.v.krafts.v.krafts.v.krafts.v.lateralmoading,torsion,關(guān)于lateralmoading,torsion,v.kraftingmoading,f.v.krafting,f.v.kraftingmoading,f.v.kraftingmoading,f.v.lateral.Theproposedapproachiscapableofsimulatingpilegroupssubjectedtolateralloading,torsion,andcombinedlateralandtorsionalloading.Fourmodeltestsinvolvingthesethreetypesofloadingmodeswereadoptedtoverifytheproposedapproach.7.1pile-siwelle-d回歸系統(tǒng)的平臺Centrifugetestsof3×3pilegroupsatthreediameter(3D)andfive-diameter(5D)spacingswerecarriedout(McVayetal.,1995).Themodelpilessimulatedpipepiles430mmindiameterand13.16mlongwithabendingstiffness,EI,of72.1MN·m7.2cent目錄學(xué)證據(jù)測試團隊Resultsofcentrifugemodeltestsconductedby7.3通過pile&silling個體的反應(yīng)來提高抗辯能力Fujianstandardsandwasusedinthisstudy.Thissandisuniformquartzsandwithaspecificgravityof2.63.Themeandiameteris0.17.Theuniformitycoefficient,CTwosinglepiletests,atorsionalpiletestandalateralpiletest,wereconductedinthesamesoilbedtoobtainp-ycurvesandτ-θcurves,whichwereusedtosimulatethe2uf0b42pilegrouptests.Tenlevelsofbendingmomentstraingaugeswereinstalledontheexternalsurfaceofthelaterallyloadedsinglepiletomeasurethedistributionofbendingmomentsonthemodelpile.Theapproachproposedbywherea(z)andb(z)arethefunctionsofdepthz,obtainedbycurvefitting.Inthetorsionallyloadedsinglepiletest,atorsionalcylinderwasusedtoloadthemodelpileatthepilehead.Ninelevelsoftorsionalstraingaugeswerealsoinstalledontheexternalsurfaceofthemodelpiletomeasurethedistributionoftorsionalforcealongthepileshaft.TheapproachproposedbywhereA(z)andB(z)wereobtainedbycurvefitting.Thep-yandτ-θcurvesoriginatingfromthetestswereinputintoELPGROUPtosimulatetheresponsesofthelaterallyandtorsionallyloadedsinglepiles.Thetestdatawerecomparedwiththecomputationresultsofthelaterallyloadedpiletest(Fig.8a)andthetorsionallyloadedpiletest(Fig.8b).Thecomputationresultsagreewellwiththetestdata.Fig.9showsthepilecapresponseofthepilegroupundercombinedlateralandtorsionalloading.Fig.10furthershowsthepileheadhorizontaldisplacementsofthegrouppiles.Inbothfigures,theresultspredictedbytheproposedapproachagreewellwiththetestdata.7.4非價值主義藥品,聚合物a.3.3.5.5.5.5.5.5.5.4和20g.9.8相對于虛無主義者即與虛無主治療案例,見表4.3.3.3.3.3.3.3.4.5.4-pale-4.5.4.5.4.5.4.5.4.5.4.5.4.5.4.5.4.5.3.3.3.3.3.4.5.4.5.3.4.5.3.4.5.5.5.3.4.5.4.5.4.5.5.5.5.5.5.4.5.5.5.5.5.5.5.5.5.5.5-pale-4.5.4.5.4.5.5.4.5.4.5.4.5.4.5.5.4.5.4重組人,5.4.5.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.5.5.5.5.5.5.5.5.5.5.5.5.5.5.5.5.5.5.5.5.5.5.5.5.5.3.3.3.4.5.5.5.5.5.5.5.5.5.5.5.5.5.5.5.5.5.5.5.5.5.5.5.5.5.5.5.5.5.5.5.5.5.5.5.5.5.5.5.5.5.5.5.5.5.5.5.5.5.5.5.5.5.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.reporteda3×3pilegrouptestinsaturatedsiltlaterallyloadedataneccentricdistanceof6D.Themodelpilesusedwereclosed-endsteeltubeswithadiameterof0.114m,lengthof5.95m,embeddedlengthof3.41m,andthicknessof4.5mm.Thesoilusedinthetestwassaturatedsilt.Thep-ycurvesproposedbyFig.11showstheexperimentalload-displacementcurveandexperimentaltorque-twistanglecurveofthepilecapataloadeccentricityof6D,andthecorrespondingnumericalpredictionsusingthepresentapproach.Thereisgoodagreementathigherloadingstages,whereastheanalysisunder-predictsthepileresistanceattheinitialloadingstages.Oneofthereasonsbehindthisunder-predictionmaybethatthereductionfactorspredictedfromtheproposedempiricalequations,aswellasthecalculatedpmultipliers,tendtooverestimatetheinteractionamongpileswithsmallpiledisplacements(8pilectingoperationblot,which-通過pelectinb研磨,which-通過colictingpole3,sile3,vethspitysrespity,resp果Fig.11alsocomparestheapproximateresultswiththeexactresultsobtainedbysubstitutingthesolutionsofEq.(12)intotheinternaliterativeprocess.Fig.12showsthevariationoftheerrorsofthepilecaptwistangleandpileheaddisplacementswiththepilecaptwistangle.Piles1,2,and3,whichbelongtothreerowsrespectively,werechosentoshowtheerrorsofpileheaddisplacements.Theerrorschangewithpileposition.Whenthepilecaptwistangleissmallenough,theerrorsofthepileheaddisplacementsarenegligibleinapplication.Forinstance,whenthepilecaptwistangleis5°,themaximumerrorofpileheaddisplacementsisonly4.8%(Pile3).Therefore,thesimplifiedsolutiondevelopedbythepresentapproachshowsgoodaccuracyinpredictingtheresponseofpilegroupsundercombinedlateralandtorsionalloadinginsmalltwists.Toincreaseaccuracyatlargetwistangles,Eqs.(6)and(8)canbeadoptedtocalculatethepileheaddisplacementsofindividualpilesafterX9通過pale本身lateralfoin-lahening,土壤中的lateral-torsionalmo領(lǐng)域,而非pile機構(gòu)的使用,可4.Inthisstudy,asimpleandcomputationallyefficientapproachhasbeendevelopedforanalyzingthenonlinearresponseofpilegroupsundercombinedlateralandtorsionalloading.Previousstudiesshowedthatthepilecapmotionofapilegroupsubjectedtocombinedlateralandtorsionalloadingisacombinationofhorizontalandtorsionalmovements,andcanbeseenasaplanerigid-bodymotion.Anexplicitpileheaddisplacementrelationshipofthegroupedpilesandstaticequilibriumequationsofthepilecapwerederivedaccordingtotheconceptofinstantaneouscenterinaplanerigid-bodymotion.Thegeneralizedp-multiplierproposedbyModeltestsonpilegroupssubjectedtolateralloading,torsionalloading,andcombinedlateralandtorsionalloading,separately,werepredictedusingtheproposedapproach.In