混凝土專業(yè)畢業(yè)設(shè)計(jì)外文翻譯混合物配合比設(shè)計(jì)

附錄外文翻譯MIXDESIGN&PROPORTIONING（一）MIXDESIGNTheconcretemixdesign(CMD)forQC/QAsuperstructureconcretemustproduceaworkableconcretemixturehavingpropertiesthatwillnotexceedthemaximumand/orminimumvaluesdefinedinthespecialprovision.Workabilityinconcretedefinesitscapacitytobeplaced,consolidated,andfinishedwithoutharmfulsegregationorbleeding.Workabilityisaffectedbyaggregategradation,particleshape,proportioningofaggregate,amountandqualitiesofcementitiousmaterials,presenceofentrainedair,amountandqualityofhighrangewaterreducer,andconsistencyofmixture.Consistencyoftheconcretemixtureisitsrelativemobilityandismeasuredintermsofslump.Thehighertheslumpthemoremobiletheconcrete,affectingtheeasewithwhichtheconcretewillflowduringplacement.Consistencyisnotsynonymouswithworkability.Twodifferentmixdesignsmayhavethesameslump;however,theirworkabilitymaybedifferent.Selectionoftargetparametersbythecontractorforanymixdesignmustconsidertheinfluenceofthefollowing:1.materialavailabilityandeconomics2.variabilityofeachmaterialthroughoutperiodofusage3.controlcapabilityofproductionplant4.ambientconditionsexpectedatthetime(s)ofconcreteplacement5.logisticsofconcreteproduction,delivery,andplacement6.variabilityintestingconcreteproperties7.generationofheatinlargestructuralelementsanddifferentialinthermalgradientThequalitiesofthecementitiouspasteprovideaprimaryinfluenceonthepropertiesofconcrete.Properselectionofthecementitiouscontentandwater/cementitiousratioisdependentontheexperienceoftheconcreteproducerandbecomesaveryimportantfirststepinpreparingadesign.Forworkableconcrete,ahigherwatercementitiousratioistypicallyrequiredwhenaggregatebecomesmoreangularandroughtextured.Thepresenceofair,certainpozzolans,andaggregateproportioningwillworktolowerthewatercementitiousratio;howeverthemostsignificantreductioninwaterdemandcomesthroughtheuseofahighrangewaterreducingchemicaladmixture.Water/cementitiousratioisdeterminedfromthenet,perunit,quantityofwaterandtotalcementitiousmaterials.Thenetwatercontentexcludeswaterthatisabsorbedbytheaggregates.Foragivensetofmaterialsandconditions,aswater/cementitiousratioincreases,strengthandunitweightwilldecrease.Compressivestrengthisaconcreteparameterusedincombinationwithunitweightandaircontenttoevaluatethedurabilityofthesuperstructureconcrete'sexposuretofreeze/thawaction,andexposuretodeicingsalts.Itisimportanttonotethatthedesignerofthebridgestructuredoesnotrecognizethebenefitofincreasedcompressivestrength.Theslabstillreliesonaminimumdesigncompressivestrength(f'c)of4000psiat28-days.Proportioningofaggregatesisdefinedbythevolumeoffineaggregatetothevolumeofcoarseaggregate,asapercent.Thelowerpercentageoffinetototalaggregateprovidesanincreaseincompressivestrengthattheexpenseofworkability.Thegradation,particleshapeandtextureofthecoarseaggregatealongwithfinenessmodulusofthefineaggregatewilldeterminehowlowthefinetototalaggregatepercentagecanbeforagivenworkabilityrequirement.（二）MIXINGPROPORTIONINGOncethecementcontent,pozzolancontent,water/cementitiousratio,andfinetototalaggregatepercentagearedefinedfortheconcrete'sintendeduseinthesuperstructure,proportioningofthemixintermsofdesignbatchweightscanbegin.Specificgravitiesmustbeaccuratelydefinedforeachmaterialbeingutilizedinordertoproportionthemixproperlybytheabsolutevolumemethod.Cementistypicallyacceptedashavingaspecificgravityof3.15.Pozzolanswilltypicallyvarybetween2.22and2.77.Pozzolansuppliersshouldreadilybeabletoprovidecurrentvaluesfortheirmaterial.ApproximatespecificgravitiesareidentifiedforeachsourceontheDepartment'sApproved/PrequalifiedMaterialslist;however,theyshouldnotbeconsideredthemostcurrent.Bulkspecificgravity,inthesaturatedsurfacedrycondition,mustbeusedtoproportionthefineandcoarseaggregate.AccuratetestingofoneormoresamplesoffineandcoarseaggregatemustbeaccomplishedbytheContractoraspartofanyproportioningforamixdesign.Subsequentshiftsinbenchingattheaggregatesourcemaycausesignificantshiftsinbulkspecificgravityandabsorption.Theseareimportantaggregatepropertiestomonitoraspartofconcretequalitycontrol.Proportioningconcretebytheabsolutevolumemethodinvolvescalculatingthevolumeofeachingredientanditscontributiontomakingoneyd3or27ft3ofconcrete.Volumesaresubsequentlyconvertedtodesignweights,whichthenbecomethebasisforactualproductionofconcretefromtheplant.Forcementitiousmaterialsandwater,theweighttovolumeconversionisaccomplishedbydividingtheweight(lbs)bythespecificgravityofthematerialandagaindividingbythedensityofwater.Convertingfromvolumetoweightisaccomplishedsimplybytakingtheknownvolumeoftheingredientandmultiplyingbythespecificgravityoftheingredientandagainmultiplyingbythedensityofwater.Volumetoweightconversionsforaggregatesareaccomplishedbythesameseriesofcomputations;however,bulkspecificgravity(SSD)mustbeused.Thetargetaircontentisestablishedat6.5%bythespecialprovision,whichconvertstoavolumeof1.76f（三）LINEAREQUATIONOFUNITWEIGHTvs.AIRCONTENTItisknownthattheunitweightofplasticconcreteisinverselyproportionaltoaircontent.Thatistosay,asaircontentincreasesunitweightdecreases.Thisrelationshipbecomesaveryusefultoolwhenevaluatingplasticconcrete.Unitweightandaircontentarepropertiesofplasticconcretethatcanbeeasilyandquicklymeasuredinthefield.Aunitweightmeasurement,ataknownaircontent,thatdeviatesexcessivelyfromthelinearrelationshipprovidesinformationastothepossibledeficienciesinthemixandpotentialeffectsonpropertiessuchasworkability,durability,andstrength.Thelinearequationtopredictunitweightbasedonagivenaircontentispresentedbelowindirectionalform:UW=m(Air)+bWhere:mistheslopeoflineAiristheplasticconcreteaircontent(independentvariable,xcoordinateorabscissaofpoint)bisthey-interceptUWistheplasticconcreteunitweight(dependentvariable,ycoordinate,orordinateofpoint)Ifallpoints(Air,UW)associatedwiththesolutionsetofthislinearequationwereplottedonagraph,therewouldbeastraightlineasillustratedbyFigure3.1.Thislinearrelationshipcanbedeterminedforanyconcretemixdesign.（四）THRESHOLDFORMAXIMUMALLOWABLEWATER/CEMENTITIOUSRATIOJustasconcreteunitweightisaffectedbychangesinaircontent,itisalsoaffectedbytheamountofwaterthatisavailabletoreactwithcementitiousmaterials.Astheamountofwaterincreasesthewater/cementitiousratioalsoincreases,producingconcreteofinferiorquality.Thisservestolowertheconcreteunitweightatanygivenaircontent.Sincethemaximumallowablewater/cementitiousratioforQC/QAsuperstructureconcreteis0.420,athresholdlineorlimitcanbedetermined.Thisthresholdlinewouldbeparalleltothelinearequationforthemixdesign;however,theunitweightwouldbelower.ThethresholdlimithasrelevancytoresultsfromqualitycontrolaswellasAcceptancesamplingandtesting.Shouldthemeasuredunitweightatanygivenaircontentbeatorlowerthanthethreshold,itcouldindicatethatthemaximumallowablewatercementitiousratiowasexceeded.Itisimportanttounderstandthatqualitycontrolworkstocenterproductionaboutthelinearequationforthemixdesign.Thereareseveralwaysinwhichadditionalwatercouldenteraconcretemix.Themethodologypresentedinthischapterassumesthattheincreaseinwater/cementitiousratioisduesoleytoexcessivebatchwater.Thisprovidesasimpleandaccuratedeterminationofthethresholdlimitequation.Themethodologybeginswiththelinearequationalreadyestablishedforthemixdesign.Byestablishingasinglepointbelowthelinearequation,representingconcretewithexcessivewater,theequationforthresholdlimitcanbedetermined.Theeasiestpointtoselectisatthey-intercept,wheretheconcretehasnoentrappednorentrainedair.ThispointisdefinedasPoint3,havingcoordinates(x3,y（五）MixDesign&ProportioningWorksheetsIfatleasttwopointsareknowntobeasolutiontotheequation,algebracanbeutilizedtosolveforthetwounknownvariables(i.e.slopeandy-intercept).TheforminAppendixD(undertab11)entitled"WORKSHEETFORCMDLINEAREQUATION"providestheformatinwhichtwopointscanbedefinedandtheequationdetermined.TheCartesiancoordinatesofonesolutionpointisalreadyavailablefromthemixdesign.WecandefinethisasPoint2withcoordinates(x2,y2).Thevalueofx2isthetargetaircontentofthemixdesign(i.e.xabsolutevolumeswhichwillalwaysbe27.00ftExample:xyy2y2AplotofthecoordinatesforPoint2(x2=6.5,yPoint1,representingthey-intercepthavingcoordinates(x1,y1),mustnowbedetermined.Thisisaccomplishedbytheoreticallyremovingalltheentrappedandentrainedairfromthemixtureandcalculatingtheconcreteunitweight.Thevalueofx1is0.0%aircontent.ThevalueofycalculatesthecoordinatesforPoint1.Example:xyyy1TheCartesiancoordinatesofPoint1,(x1=0.0,yItisimportanttorememberthatasairisremovedfromconcretetheindividualweightsofcementitiousmaterials,fineaggregate,coarseaggregate,andwaternolongerrepresentamountsrelativeto1.000yd3ofconcrete.Concretewithoutthe6.5%targetaircontent(1.76ft3)wouldonlyyield0.9348ydFromthexandycoordinatesofPoints1&2,thereisnowenoughinformationtosolveforthevariablesofslopeandy-interceptinthelinearequation.Theworksheetcalculationforslope,alsoknownas"rise/run",isexemplifiedasfollows:Example:m=?Itisimportanttonotethatslopewillalwaysbenegativesinceunitweightisinverselyproportionaltoaircontent.They-interceptvalue(b)issimplytheordinateofPoint1,whichhasalreadybeendetermined.Intheexampleproblem,theworksheetwouldshowthesolutionbasfollows:Example:Thecalculatedandroundedvaluesforslopeandy-interceptcannowbeinsertedinthelinearequationforthevariablesmandb,respectively.Thelinearequationcannowbewrittenfortheconcretemixdesign.Thenumbersfromtheexampleresultinthefollowing:Example:（六）DEPARTMENTCONCURRENCEOFMIXDESIGNItistheresponsibilityoftheDepartment'sProjectEngineer/ProjectSupervisortoconductacompleteandthoroughreviewofeverymixdesignandproportioningforQC/QASuperstructureConcrete.ThereisasubstantialamountofworkthatisbasedonthetargetsestablishedbytheCMD,nottheleastofwhichisthelinearequationforthethresholdlimitthatrepresentsthemaximumallowablewater/cementitiousratio.ThisthresholdlimitisofcriticalimportanceindeterminingwhetheradditionalcylindersaretobecastaspartofanacceptancesamplefortestingperAASHTOT277andsubsequentaction,whichmayinvolveafailedmaterialinvestigation.ThefirststepinproperreviewofaCMDistoverifythatthematerialsarefromcurrentapprovedsources.ThelistofApprovedand/orPrequalifiedMaterialsistobeusedtoverifyapprovedsourcesofcement,flyash,GGBFS,silicafume,chemicaladmixturesandairentrainingagents.ThefineandcoarseaggregateingredientsoftheconcretemixmustbematerialsfromanapprovedCertifiedAggregateProducer.Thegradationandqualityrequirementfortheaggregatesmustalsobeverified,particularlyifstay-in-placemetaldeckformsareusedtofacilitateconstructionofthedeck.IfAPQualitycoarseaggregateisrequiredinthesuperstructure,thePE/PSwillsubstantiatethequalitystatus.Thiswouldincludethenatureoftheminingoperationsthatproduceaggregatesofthedesiredquality.ThePE/PSshouldcontacttheDistrictMaterials&TestsEngineerortheDistrictGeologistforconfirmation.InadditiontotheaggregatesgradationsthePE/PSmustverifythebulkspecificgravity(SSD)andabsorptionforthefineandcoarseaggregateasbeingreasonableforthesource.IftheContractor'svalueforabsorptiondiffersbymorethanthemultilabortoryprecisiondefinedwithintheappropriatetestmethod,thediscrepancywillbeinvestigated.ThebulkspecificgravityandabsorptionforaggregatesaremeasuredbytheDepartmentaspartoftheannual"SummaryofProductionQualityResults",andperiodicPoint-Of-Usesamples.Thisdataprovidesthecorrectbasisforcomparisonofabsorptionandspecificgravity.Figures3.5and3.6aregraphsofbulkspecificgravity(ssd)vs.absorptionforafineandcoarseaggregateandarepresentedasexamplesofwhathistoricaldatamightlooklikeforspecificproductsatanaggregatesource.Usuallysourceswilldemonstrateatrendofbulkspecificgravity(SSD)beinginverselyproportionaltoabsorption;however,suchmaynotalwaysbethecase.Figure3.6representsdatafromtheINDOTSummaryofProductionQualityResultsforaspecificsourceof#8coarseaggregate.TheAPqualitystonecomesfromledges1803,1804,19,&20processedasoneworkingbench.Thesefourledgeshavethicknessesof7.9ft,8.9ft,5.9ft,and12.1ft,respectively.Sincetheseledgesrangeinabsorptionfrom2%to4%,theconsistencyofbulkspecificgravityandabsorptiondependsontheaggregatesource'sabilitytoprocessthebenchinauniformmanner.TheDistrictGeologististhebestsourceforobtaininghistoricaldatafrom"SummaryofProductionQualityResults"and"Point-of-Use"samplesobtainedfromtheaggregatesource.TheywillassistthePE/PSintheproperreviewofcontractortestresultsforaggregates.ItisimportanttounderstandthatINDOThistoricalrecordsforbulkspecificgravity(dryorSSD)fromcoarseaggregatesourcesarebasedonprocedure8.1ofAASHTOT85.TheContractormustthereforetestthecoarseaggregateaccordingtothesameprocedureeventhoughtheresultistypicallynotappropriateforconcretemixdesign.Ifthemixdesignissubmittedwithenoughadvancenotice,itbecomespreferablefortheDepartmenttoobtainaPoint-Of-Usesampleofthecoarseaggregateandtestforbulkspecificgravity(SSD)byprocedure8.2ofAASHTOT85,whichisappropriateforconcretemixdesign.SplittingasamplebetweentheContractorandtheDepartmenttocomparetestresultswouldbeevenbetter.TheairentrainingandchemicaladmixturesthatareapprovedforuseareasstatedinthespecialprovisionandtheApproved/PrequalifiedMaterialsListreferencedtherein.ItisimportanttorecognizethelimitationsofTypeFadmixturesorHRWRAdmixtureSystems.Thesechemicaladmixtureshavenoretardingcapabilityandwouldnotbeappropriateforsuperstructureconcretethatisplacedinconditionswhereconcreteandambienttemperaturesareabove65°F,andwheredeadloaddeflectionsareofconcern.Afterverifyingthematerialsasbeingapprovedfortheconcrete,theinitialparametersfortheMixDesignmustbecheckedagainstthespecificationrequirements.TheremainderofthePE/PScheckinvolvescheckingthemathforproportioning,andthelinearequationsfortheCMDandthresholdlimit.UseoftheformsandworksheetsbythecontractorwillprovidethequickestandmostcompletereviewbytheDepartmentandthereforehelpeliminateunnecessarydelaysbyrecognizingproblemsearlyon.混合物配合比設(shè)計(jì)（一）混合物設(shè)計(jì)混凝土配合比設(shè)計(jì)混凝土質(zhì)量保證上層建筑（CMD）用于QC/QA必須出示有一個(gè)和易性好的混凝土混合物的性能，將不會(huì)超過最大和/或最低的特別規(guī)定定義的值。在具體的工作性定義它的的能力，放置，鞏固，無離析或泌水。可操作性是受骨料級(jí)配，顆粒形狀，配料總量，數(shù)量和質(zhì)量的膠凝材料減速氣流，空氣的含量，高效減水劑的數(shù)量和質(zhì)量，及混和料的和易性?；炷粱旌衔锏暮鸵仔杂孟鄳?yīng)的流動(dòng)性，和坍落度衡量。坍落度越高，混凝土流動(dòng)性就越好，對(duì)混凝土將流動(dòng)過程中的具體位置影響更好。和易性和可操作性不等同。兩種不同的配合比設(shè)計(jì)可能有相同的坍落度，但其工作性能可能會(huì)有所不同。目標(biāo)參數(shù)的選擇，承包商的任何配合比的設(shè)計(jì)必須考慮下面的影響：1.材料供應(yīng)和經(jīng)濟(jì)狀況2.在整個(gè)使用期間每一種材料的變化3.生產(chǎn)廠的管理能力4.預(yù)期在混凝土澆筑時(shí)的環(huán)境條件5.混凝土產(chǎn)品的物流，配送與安置6.在測(cè)試中混凝土性能變化7.熱產(chǎn)生在大型構(gòu)件和在熱梯度的差別。水泥粘貼性的質(zhì)量起到了對(duì)混凝土主要性能的影響。正確選擇水泥含量和水灰比依賴于生產(chǎn)的經(jīng)驗(yàn)，準(zhǔn)備工作是完成一個(gè)非常重要的設(shè)計(jì)的第一步。對(duì)于和易性好的混凝土，水灰比較高的水時(shí)，通常需要更多的角度和總體變得粗糙質(zhì)感的集料。空氣的存在，一定的火山灰，集料配料凈漿降低水灰比；然而，最顯著降低用水量求是通過使用一種高化學(xué)減水劑的外加劑。水灰比由每單，水的重量和總膠凝材料重量決定。水凈含量不包括由集料所吸收的水量。對(duì)于一個(gè)給定的材料和條件，水灰比增大，強(qiáng)度和單位重量將減少?？箟簭?qiáng)度是在單位重量和空氣含量具體的參數(shù)組合使用，以評(píng)估暴露結(jié)構(gòu)的耐久性混凝土的凍結(jié)/解凍的行為，以及接觸除冰鹽。重要的是要注意到，在橋梁結(jié)構(gòu)設(shè)計(jì)不會(huì)增加抗壓強(qiáng)度。該板仍然依賴抗壓強(qiáng)度（f'c）28天最低設(shè)計(jì)4000psi。集料配合比是指由細(xì)骨料量與粗骨料量，以百分比。損失可工作性下，低比例的集料總額合計(jì)使抗壓強(qiáng)度增加。級(jí)配，顆粒形狀和質(zhì)地優(yōu)良的總和粗骨料模量隨細(xì)度低，將決定如何將集料比例可以為一個(gè)給定的可操作性的要求。（二）混合配料一旦水泥含量，火山灰含量，水灰比，集料總額百分比意味著混凝土將用于上層建筑，就設(shè)計(jì)一批混凝土而言，配合比設(shè)計(jì)就可以開始了。具體的比重，必須準(zhǔn)確界定每個(gè)材料被利用，以絕對(duì)體積法的比例處理。水泥是典型的被認(rèn)為為具有比重的3.15?；鹕交彝ǔＴ?.22和2.77之間各有不同，火山灰供應(yīng)商應(yīng)隨時(shí)能夠?yàn)樗麄兲峁┑奈镔|(zhì)的當(dāng)前值。近似比重都確定了每個(gè)部門的批準(zhǔn)/資格預(yù)審材料清單源，但是，他們不應(yīng)該被認(rèn)為是最近的。容重，在飽和表面干燥狀態(tài)下，必須使用一定比例的粗細(xì)骨料。準(zhǔn)確的測(cè)試一個(gè)或多個(gè)細(xì)和粗骨料樣品必須完成由承包商作為任何一個(gè)混合配料設(shè)計(jì)的一部分。總源頭在隨后的變化可能導(dǎo)致在容重和吸收的重大變化。以監(jiān)測(cè)為總量控制混凝土質(zhì)量的一部分，這些都是重要的屬性。混凝土配合比的方法涉及的絕對(duì)量計(jì)算的各成分含量及其對(duì)取決于1yd3或27ft3的混凝土含量。其后體積轉(zhuǎn)換為設(shè)計(jì)重量，然后成為工廠的基礎(chǔ)上生產(chǎn)的具體實(shí)際。對(duì)于膠凝材料和水，轉(zhuǎn)化為體積和重量完成的比重材料除以體重（磅）再除以水的密度。從體積重量轉(zhuǎn)換完成的，是僅僅通過已知的體積成分和乘以成份比重，并再次磅乘以水的密度之間。體積與重量都聚集轉(zhuǎn)換為計(jì)算完成的系列相同，但是，容重法（SSD）必須使用。我們的目標(biāo)是建立空氣含量在6.5％的特別規(guī)定，它轉(zhuǎn)換為一個(gè)具體的量1.76ft3（三）單位重量空氣含量線性方程據(jù)了解，塑性混凝土的單位重量與空氣含量成反比的。這就是說，由于空氣含量的增加，單位重量下降。這種關(guān)系成為評(píng)估塑性混凝土?xí)r一個(gè)非常有用的工具。單位重量和空氣含量的塑料混凝土，可以很容易地和迅速地在現(xiàn)場(chǎng)實(shí)測(cè)其性能。一個(gè)單位重量的測(cè)量，在已知的空氣含量，即通過分偏離線性關(guān)系，提供有關(guān)信息，如耐久性、可操作性和強(qiáng)度，對(duì)可能出現(xiàn)的缺陷結(jié)構(gòu)和性能的潛在影響等。線性方程來預(yù)測(cè)單位重量的基礎(chǔ)上給定的空氣含量的形式如下：UW=m(空氣)+b其中：M——直線的斜率空氣是塑性混凝土含氣量b——y軸截距UM——塑性混凝土的單位重量如果所有的點(diǎn)的線性方程與此相關(guān)聯(lián)的解集分別繪于一圖，將有一條直線，由圖3.1所示。這種線性關(guān)系，可以決定對(duì)任何混凝土配合比設(shè)計(jì)解到，代數(shù)可以用來解決這兩個(gè)未知變量（即斜率和y軸截距）。在附錄D的形式（在選項(xiàng)卡11），題為“線性方程加利福尼亞的工作表”確定的格式提供，其中有兩點(diǎn)可以定義和公式。直角坐標(biāo)（點(diǎn)空氣的一個(gè)解決方案，威斯康星大學(xué)）已經(jīng)可以從結(jié)構(gòu)設(shè)計(jì)。我們可以定義為2點(diǎn)與點(diǎn)的坐標(biāo)（x2，y2）的。的x2=6.5％的目標(biāo)空氣含量的配合比設(shè)計(jì)（即x2）的。在y2型價(jià)值是混合設(shè)計(jì)單位在規(guī)定的具體重量。這是由樓總結(jié)取得一批權(quán)重的設(shè)計(jì)絕對(duì)再除以總結(jié)了設(shè)計(jì)容量將永遠(yuǎn)是27.00，為工作表下面的例子計(jì)算的基礎(chǔ)上配合比設(shè)計(jì)及配比值本章前面介紹的這一點(diǎn)。（四）水灰比的臨界值正如混凝土的單位重量是受空氣中含量的變化，也受水與膠凝材料反應(yīng)影響。由于用水量增加了，水灰比也增加了，混凝土生產(chǎn)質(zhì)量下降。這降低了在任何具體空氣含量下單位混凝土重量。由于最高允許水/用于QC/QA上層建筑混凝土膠凝比例是0.420，臨界線或限度可確定。這個(gè)臨界線將與配合比設(shè)計(jì)線性方程平行；但是，單位重量將降低。這極限值與質(zhì)量控制和進(jìn)料抽樣與測(cè)試有關(guān)，以控制結(jié)果的質(zhì)量以及驗(yàn)收取樣和測(cè)試。如果測(cè)量單位重量在任何特定的空氣含量等于或低于閾值，它可能表明，已超過最大水灰比。重要的是要明白，工程質(zhì)量控制中心關(guān)于為線性方程的生產(chǎn)配合比設(shè)計(jì)。有幾種方法，使更多的水可以進(jìn)入混凝土混合料。本章提出的方法在此假定加的水灰比，完全是由于過量的水。這提供了一個(gè)簡(jiǎn)單的準(zhǔn)確測(cè)定極限值的方程。該方法首先假設(shè)的混合求解線性方程組已經(jīng)成立。通過建立一個(gè)線性方程單點(diǎn)以下，占混凝土與水過多，限制方程的極值確定。最簡(jiǎn)單的一點(diǎn)是選擇在y軸截距，其中混凝土并沒有夾雜空氣。這一點(diǎn)是指第3點(diǎn)，有坐標(biāo)（x3,y3）。該方程的臨界線與線性方程平行，斜率相同。知道了斜率和y軸截距的極限方程就可以完成。（五）配合比設(shè)計(jì)及配料工作頁(yè)如果至少有兩個(gè)點(diǎn)，知道是一對(duì)方程的解，代數(shù)可用來解決這兩個(gè)未知變數(shù)（即斜率和y截距）。在附錄D表（在標(biāo)簽11）題為“加利福尼亞線性方程表”中提供了兩點(diǎn)可以定義和公式確定格式。直角坐標(biāo)已經(jīng)從結(jié)構(gòu)設(shè)計(jì)提供了一種解決方案點(diǎn)。我們可以確定點(diǎn)2的坐標(biāo)（x2,y2）。x2的值配合比設(shè)計(jì)的目標(biāo)空氣含量（即x2=6.5%）。在y2型的值是一定配合比設(shè)計(jì)中的單位重量。這視由設(shè)計(jì)總和除以求和絕對(duì)量將永遠(yuǎn)是27.00立方英尺而定。為工作表下面的例子計(jì)算的基礎(chǔ)上配合比設(shè)計(jì)及配比值本章前面介紹的這一點(diǎn)。例：x2=6.5％y2=Σ設(shè)計(jì)批次重量÷27.00ft3y2=3871lbs÷27.00ft3y2=143.4lbs/ft3（四舍五入至小數(shù)點(diǎn)第一位）關(guān)于點(diǎn)2的坐標(biāo)為（x2=6.5，y2=143.4），如圖3.2所示。重要的是要注意，第2點(diǎn)為單位的重量計(jì)算至最接近的0.1lbs/ft3。點(diǎn)1，現(xiàn)在必須確定代表截距坐標(biāo)（x1，y1）。這是通過從理論上消除所有缺陷和夾帶的空氣混合對(duì)混凝土的單位重量計(jì)算。這個(gè)x1的值是0.0％的空氣含量。y1的值取決于再次獲得一批設(shè)計(jì)重總和除以設(shè)計(jì)除了夾帶或夾帶空氣的絕對(duì)量，本卷將永遠(yuǎn)27.00立方英尺-1.76立方英尺=25.24立方英尺。下面的例子說明了在工作表如何。計(jì)算一坐標(biāo)點(diǎn)例如：x1=0