1 SteelDesignGuide BasePlateand AnchorRodDesign SecondEdition 1 SteelDesignGuide BasePlateand AnchorRodDesign SecondEdition JAMESM.FISHER,Ph.D.,P.E. ComputerizedStructuralDesign,S.C. Milwaukee,Wisconsin and LAWRENCEA.KLOIBER,P.E. LeJueneSteelCompany Minneapolis,Minnesota AM ERI CAN I NST I T UT E O F ST EEL CO NST RUCT I O N, I NC. Copyright©2006 by AmericanInstituteofSteelConstruction,Inc. Allrightsreserved.Thisbookoranypartthereof mustnotbereproducedinanyformwithoutthe writtenpermissionofthepublisher. Theinformationpresentedinthispublicationhasbeenpreparedinaccordancewithrecognized engineeringprinciplesandisforgeneralinformationonly.Whileitisbelievedtobeaccurate, thisinformationshouldnotbeusedorrelieduponforanyspecificapplicationwithoutcompetentprofessionalexaminationandverificationofitsaccuracy,suitability,andapplicabilitybya licensedprofessionalengineer,designer,orarchitect.Thepublicationofthematerialcontained hereinisnotintendedasarepresentationorwarrantyonthepartoftheAmericanInstitute ofSteelConstructionorofanyotherpersonnamedherein,thatthisinformationissuitablefor anygeneralorparticularuseoroffreedomfrominfringementofanypatentorpatents.Anyone makinguseofthisinformationassumesallliabilityarisingfromsuchuse. Cautionmustbeexercisedwhenrelyinguponotherspecificationsandcodesdevelopedbyother bodiesandincorporatedbyreferencehereinsincesuchmaterialmaybemodifiedoramended fromtimetotimesubsequenttotheprintingofthisedition.TheInstitutebearsnoresponsibilityforsuchmaterialotherthantorefertoitandincorporateitbyreferenceatthetimeofthe initialpublicationofthisedition. PrintedintheUnitedStatesofAmerica FirstPrinting:May2006 Acknowledgements The authors would like to thank Robert J. Dexter from the University of Minnesota, and Daeyong Lee from the SteelStructureResearchLaboratory,ResearchInstituteof Industrial Science & Technology (RIST), Kyeonggi-Do, SouthKorea,fortheirwritingofAppendixAandthefirst draftofthisGuide.Theauthorsalsorecognizethecontributionsoftheauthorsofthefirsteditionofthisguide,John DeWolf from the University of Connecticut and David Ricker (retired) from Berlin Steel Construction Company, andthankChristopherHewittandKurtGustafsonofAISC fortheircarefulreading,suggestions,andtheirwritingof AppendixB.SpecialappreciationisalsoextendedtoCarol T.WilliamsofComputerizedStructuralDesignfortyping themanuscript. AISCwouldalsoliketothankthefollowingindividuals whoassistedinreviewingthedraftsofthisDesignGuidefor theirinsightfulcommentsandsuggestions. VictoriaArbitrio ReidarBjorhovde CrystalBlanton CharlesJ.Carter BradDavis RobertO.Disque JamesDoyle RichardM.Drake SamuelS.Eskildsen DanielM.Falconer MarshallT.Ferrell RogerD.Hamilton JohnHarris AllenJ.Harrold v DonaldJohnson GeoffreyL.Kulak BillR.LindleyII DavidMcKenzie RichardOrr DavisG.ParsonsII WilliamT.Segui DavidF.Sharp VictorShneur BozidarStojadinovic RaymondTide GaryC.Violette FloydJ.Vissat vi TableofContents 1.0 INTRODUCTION..................................................... 1 2.0 MATERIAL,FABRICATION, INSTALLATION,ANDREPAIRS.......................... 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 2.10 2.11 2.12 MaterialSpecifications...................................... 2 BasePlateMaterialSelection............................ 2 BasePlateFabricationandFinishing................ 3 BasePlateWelding............................................ 4 AnchorRodMaterial......................................... 5 AnchorRodHolesandWashers........................ 6 AnchorRodSizingandLayout......................... 7 AnchorRodPlacementandTolerances............ 7 ColumnErectionProcedures............................. 8 2.9.1 SettingNutandWasherMethod............. 8 2.9.2 SettingPlateMethod.............................. 9 2.9.3 ShimStackMethod................................ 9 2.9.4 SettingLargeBasePlates....................... 9 GroutingRequirements..................................... 9 AnchorRodRepairs........................................ 10 2.11.1AnchorRodsintheWrongPosition.... 10 2.11.2AnchorRodsBentorNotVertical....... 10 2.11.3AnchorRodProjectionTooLong orTooShort.......................................... 10 2.11.4AnchorRodPatternRotated90°.......... 12 DetailsforSeismicDesignD.......................... 12 3.1 3.2 3.3 3.3.3 BasePlateFlexuralYielding atTensionInterface............................... 25 3.3.4 GeneralDesignProcedure.................... 25 DesignofColumnBasePlateswith LargeMoments................................................ 25 3.4.1 ConcreteBearingand AnchorRodForces............................... 25 3.4.2 BasePlateYieldingLimit atBearingInterface.............................. 26 3.4.3 BasePlateYieldingLimit atTensionInterface............................... 27 3.4.4 GeneralDesignProcedure.................... 27 DesignforShear.............................................. 27 3.5.1 Friction.................................................. 27 3.5.2 Bearing.................................................. 27 3.5.3 ShearinAnchorRods........................... 29 3.5.4 InteractionofTensionand ShearintheConcrete........................... 30 3.5.5 HairpinsandTieRods.......................... 30 4.0 DESIGNEXAMPLES............................................31 3.0 DESIGNOFCOLUMNBASE PLATECONNECTIONS.......................................13 3.4 3.5 ConcentricCompressiveAxialLoads............. 14 3.1.1 ConcreteBearingLimit........................ 14 3.1.2 BasePlateYieldingLimit (W-Shapes)........................................... 15 3.1.3 BasePlateYieldingLimit (HSSandPipe)................................... 16 3.1.4 GeneralDesignProcedure.................... 16 TensileAxialLoads......................................... 18 3.2.1 AnchoreRodTension........................... 19 3.2.2 ConcreteAnchoragefor TensileForces....................................... 19 DesignofColumnBasePlateswith SmallMoments................................................ 23 3.3.1 ConcreteBearingStress....................... 24 3.3.2 BasePlateFlexuralYielding LimitatBearingInterface.................... 24 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 4.10 4.11 Example:BasePlateforConcentricAxial CompressiveLoad (Noconcreteconfinement).............................. 31 Example:BasePlateforConcentrixAxial CompressiveLoad (Usingconcreteconfinement)......................... 32 Example:AvailableTensileStrengthofa w-in.AnchorRod............................................ 34 Example:ConcereteEmbedmentStrength..... 34 Example:ColumnAnchoragefor TensileLoads................................................... 34 Example:SmallMomentBasePlateDesign.. 37 Example:LargeMomentBasePlateDesign.. 38 Example:ShearTransferUsingBearing......... 40 Example:ShearLugDesign............................ 40 Example:EdgeDisttanceforShear................ 42 Example:AnchorRodResistingCombined TensionandShear........................................... 42 REFERENCES...............................................................45 APPENDIXA.................................................................47 APPENDIXB.................................................................55 vii viii 1.0INTRODUCTION Column base plate connections are the critical interface betweenthesteelstructureandthefoundation.Theseconnectionsareusedinbuildingstosupportgravityloadsand functionaspartoflateral-load-resistingsystems.Inaddition, theyareusedformountingofequipmentandinoutdoorsupportstructures,wheretheymaybeaffectedbyvibrationand fatigueduetowindloads. Base plates and anchor rods are often the last structural steel items to be designed but are the first items required onthejobsite.Thescheduledemandsalongwiththeproblems that can occur at the interface of structural steel and reinforcedconcretemakeitessentialthatthedesigndetails takeintoaccountnotonlystructuralrequirements,butalso include consideration of constructability issues, especially anchor rod setting procedures and tolerances. The importance of the accurate placement of anchor rods cannot be over-emphasized.Thisistheoneofthekeycomponentsto safelyerectingandaccuratelyplumbingthebuilding. ThematerialinthisGuideisintendedtoprovideguidelines for engineers and fabricators to design, detail, and specify column-base-plateandanchorrodconnectionsinamanner thatavoidscommonfabricationanderectionproblems.This Guideisbasedonthe2005AISCSpecificationforStructuralSteelBuildings(AISC,2005),andincludesguidancefor designsmadeinaccordancewithloadandresistancefactor design(LRFD)orallowablestressdesign(ASD). ThisGuidefollowstheformatofthe2005AISCSpecification, developing strength parameters for foundation system design in generic terms that facilitate either load and resistance factor design (LRFD) or allowable strength design (ASD). Column bases and portions of the anchorage designgenerallycanbedesignedinadirectapproachbased on either LRFD orASD load combinations. The one area ofanchoragedesignthatisnoteasilydesignedbyASDis theembedmentofanchorrodsintoconcrete.Thisisdueto the common use ofACI 318Appendix D, which is exclusivelybasedonthestrengthapproach(LRFD)forthedesign ofsuchembedment.Othersteelelementsofthefoundation system, including the column base plate and the sizing of anchordiametersareequallyproficienttoevaluationusing LRFDorASDloadmethods.Incasessuchasanchorssubjectedtoneithertensionnorshear,theanchoragedevelopmentrequirementmaybearelativelyinsignificantfactor. The generic approach in development of foundation designparameterstakeninthisGuidepermitstheuserachoice todeveloptheloadsbasedoneithertheLRFDorASDapproach.Thederivationsoffoundationdesignparameters,as presentedherein,aretheneithermultipliedbytheresistance factor,φ,ordividedbyasafetyfactor,Ω,basedontheappropriate load system utilized in the analysis; consistent withtheapproachusedinthe2005Specification.Manyof theequationsshownhereinareindependentoftheloadapproachandthusareapplicabletoeitherdesignmethodology. Theseareshowninsingularformat.Otherderivedequations arebasedontheparticularloadapproachandarepresented inaside-by-sideformatofcomparableequationsforLRFD orASDapplication. The typical components of a column base are shown in Figure1.1. Material selection and design details of base plates can significantly affect the cost of fabrication and erection of steel structures, as well as the performance under load. Relevant aspects of each of these subjects are discussed brieflyinthenextsection.Notonlyisitimportanttodesign thecolumn-base-plateconnectionforstrengthrequirements, it is also important to recognize that these connections affect the behavior of the structure. Assumptions are made in structural analysis about the boundary conditions representedbytheconnections.Modelscomprisingbeamor trusselementstypicallyidealizethecolumnbaseconnection as either a pinned or fixed boundary condition. Improper characterization can lead to error in the computed drifts, leading to unrecognized second-order moments if the stiffness is overestimated, or excessive first-floor column sizes if the stiffness is underestimated. If more accurate analysesaredesired,itmaybenecessarytoinputthestiffness ofthecolumn-base-plateconnectionintheelasticandplastic ranges, and for seismic loading, possibly even the cyclic force-deformation relations. The forces and deformations fromthestructuralanalysesusedtodesignthecolumn-baseplateconnectionaredependentonthechoiceofthecolumnbase-plateconnectiondetails. Figure1.1.Columnbaseconnectioncomponents. DESIGNGUIDE1,2NDEDITION/BASEPLATEANDANCHORRODDESIGN/1 Table2.1.BasePlateMaterials Thickness(tp) PlateAvailability tp≤4in. ASTMA36[a] ASTMA572Gr42or50 ASTMA588Gr42or50 4in.<tp≤6in. ASTMA36[a] ASTMA572Gr42 ASTMA588Gr42 tp>6in. ASTMA36 Preferredmaterialspecification [a] The vast majority of building columns are designed for axialcompressiononlywithlittleornouplift.Forsuchcolumns,thesimplecolumn-base-plateconnectiondetailshown inFigure1.1issufficient.Thedesignofcolumn-base-plate connectionsforaxialcompressiononlyispresentedinSection 3. The design is simple and need not be encumbered withmanyofthemorecomplexissuesdiscussedinAppendixA,whichpertainstospecialstructures.Anchorrodsfor gravity columns are often not required for the permanent structureandneedonlybesizedtoprovideforcolumnstabilityduringerection. Columnbaseplateconnectionsarealsocapableoftransmittingupliftforcesandcantransmitshearthroughtheanchorrodsifrequired.Ifthebaseplateremainsincompression, shear can be transmitted through friction against the groutpadorconcrete;thus,theanchorrodsarenotrequired tobedesignedforshear.Largeshearforcescanberesisted by bearing against concrete, either by embedding the columnbaseorbyaddingashearlugunderthebaseplate. Column base plate moment connections can be used to resistwindandseismicloadsonthebuildingframe.Moment atthecolumnbasecanberesistedbydevelopmentofaforce couplebetweenbearingontheconcreteandtensioninsome oralloftheanchorrods. Thisguidewillenablethedesignertodesignandspecify economicalcolumnbaseplatedetailsthatperformadequatelyforthespecifieddemand.TheobjectiveofthedesignprocessinthisGuideisthatunderserviceloadingandunderextremeloadinginexcessofthedesignloads,thebehaviorof columnbaseplatesshouldbeclosetothatpredictedbythe approximatemathematicalequationsinthisDesignGuide. Historically,twoanchorrodshavebeenusedinthearea boundedbycolumnflangesandweb.Recentregulationsof the U.S. Occupational Safety and Health Administration (OSHA)SafetyStandardsforSteelErection(OSHA,2001) (SubpartRof29CFRPart1926)requirefouranchorrodsin almostallcolumn-base-plateconnectionsandrequireallcolumnstobedesignedforaspecificbendingmomenttoreflect thestabilityrequiredduringerectionwithanironworkeron the column. This regulation has essentially eliminated the typical detail with two anchor rods except for small posttype structures that weigh less than 300 lb (e.g., doorway portalframes). ThisGuidesupersedestheoriginalAISCDesignGuide1, ColumnBasePlates.InadditiontotheOSHAregulations, there has been significant research and improved design guidelines issued subsequent to the publication of Design Guide1in1990.TheACIBuildingCodeRequirementsfor Structural Concrete (ACI, 2002) has improved provisions for the pullout and breakout strength of anchor rods and otherembeddedanchors.Designguidanceforanchorrods basedontheACIrecommendationsisincluded,alongwith practicalsuggestionsfordetailingandinstallinganchorrod assemblies.These guidelines deal principally with cast-inplaceanchorsandwiththeirdesign,installation,inspection, andrepairincolumn-base-plateconnections. TheAISCDesignGuide7,2ndedition,IndustrialBuildings: Roofs to ColumnAnchorage (Fisher, 2004), contains additionalexamplesanddiscussionrelativetothedesignof anchorrods. 2.0MATERIALS,FABRICATION, INSTALLATION,ANDREPAIRS 2.1MaterialSpecifications TheAISCSpecificationlistsanumberofplateandthreaded rod materials that are structurally suitable for use in base plateandanchorroddesigns.Basedoncostandavailability, thematerialsshowninTables2.1and2.2arerecommended fortypicalbuildingdesign. 2.2BasePlateMaterialSelection BaseplatesshouldbedesignedusingASTMA36material unless the availability of an alternative grade is confirmed 2/DESIGNGUIDE1,2NDEDITION/BASEPLATEANDANCHORRODDESIGN Table2.2.AnchorRodMaterials F1554 Material ASTM Gr36[d] Tensile Strength, Fu(ksi) NominalShear NominalShearStress Maximum NominalTensile Diameter, (Ntype),[a,c] Stress(Xtype),[a,b] Stress,[a] Fnv=0.40Fu(ksi) in. Fnv=0.50Fu(ksi) Fnt=0.75Fu(ksi) 58 43.5 29.0 23.2 4 Gr55 75 56.3 37.5 30.0 4 Gr105 125 93.8 62.5 50.0 3 120 90.0 60.0 48.0 1 A449 105 78.8 57.5 42.0 1� 90 67.5 45.0 36.0 3 A36 58 43.5 29.0 23.2 4 A307 58 43.5 29.0 23.2 4 A354 GrBD 150 112 75.0 60.0 2� 140 105 70.0 56.0 4 Nominalstressonunthreadedbodyforcutthreads(basedonmajorthreaddiameterforrolledthreads) [b] Threadsexcludedfromshearplane [c] Threadsincludedintheshearplane [d] Preferredmaterialspecification [a] priortospecification.SinceASTMA36plateisreadilyavailable,theplatescanoftenbecutfromstockmaterial.There is seldom a reason to use high-strength material, since increasingthethicknesswillprovideincreasedstrengthwhere needed.Platesareavailablein8-in.incrementsupto14in. thicknessandin4-in.incrementsabovethis.Thebaseplate sizesspecifiedshouldbestandardizedduringdesigntofacilitatepurchasingandcuttingofthematerial. Whendesigningbaseplateconnections,itisimportantto considerthatmaterialisgenerallylessexpensivethanlabor and,wherepossible,economymaybegainedbyusingthicker plates rather than detailing stiffeners or other reinforcementtoachievethesamestrengthwithathinnerbaseplate. Apossibleexceptiontothisruleisthecaseofmoment-type basesthatresistlargemoments.Forexample,inthedesign ofacranebuilding,theuseofaseatorstoolatthecolumn basemaybemoreeconomical,ifiteliminatestheneedfor large complete-joint-penetration (CJP) groove welds to heavyplatesthatrequirespecialmaterialspecifications. Mostcolumnbaseplatesaredesignedassquaretomatch thefoundationshapeandmorereadilyaccommodatesquare anchor rod patterns. Exceptions to this include momentresistingbasesandcolumnsthatareadjacenttowalls. Many structural engineers have established minimum thicknessesfortypicalgravitycolumns.Forpostsandlight HSScolumns,theminimumplatethicknessistypically2in., andforotherstructuralcolumnsaplatethicknessofwin.is commonlyacceptedastheminimumthicknessspecified. 2.3BasePlateFabricationandFinishing Typically,baseplatesarethermallycuttosize.Anchorrod andgroutholesmaybeeitherdrilledorthermallycut.Section M2.2 of theAISC Specification lists requirements for thermalcuttingasfollows: “…thermallycutfreeedgesthatwillbesubjecttocalculated static tensile stress shall be free of round-bottom gouges greater than x in. deep … and sharp V-shaped notches. Gougesdeeperthanxin.…andnotchesshallberemoved bygrindingandrepairedbywelding.” Becausefreeedgesofthebaseplatearenotsubjecttotensile stress,theserequirementsarenotmandatoryfortheperimeter edges;however,theyprovideaworkmanshipguidethatcan beusedasacceptancecriteria.Anchorrodholes,whichmay besubjecttotensilestress,shouldmeettherequirementsof SectionM2.2.Generally,round-bottomgrooveswithinthe limits specified are acceptable, but sharp notches must be repaired.Anchorrodholesizesandgroutingarecoveredin Sections2.6and2.10ofthisdesignguide. Finishing requirements for column bases on steel plates are covered in Section M2.8 of theAISC Specification as follows: “Steelbearingplates2in.…orlessinthicknessarepermittedwithoutmilling,providedasatisfactorycontactbearing isobtained.Steelbearingplatesover2in.…butnotover4 in.…inthicknessarepermittedtobestraightenedbypress- DESIGNGUIDE1,2NDEDITION/BASEPLATEANDANCHORRODDESIGN/3 ing or, if presses are not available, by milling for bearing surfaces … to obtain a satisfactory contact bearing. Steel bearingplatesover4in.…inthicknessshallbemilledfor bearingsurfaces….” Twoexceptionsarenoted:Thebottomsurfaceneednotbe milledwhenthebaseplateistobegrouted,andthetopsurfaceneednotbemilledwhenCJPgrooveweldsareusedto connectthecolumntothebaseplate. AISCSpecification,SectionM4.4,definesasatisfactory bearingsurfaceasfollows: betweenthewebandflangeaddverylittlestrengthand areverycostly. • Formostwide-flangecolumnssubjecttoaxialcompressiononly,weldingononesideofeachflange(seeFigure2.1) with c-in. fillet welds will provide adequate strength and the most economical detail. When these welds are notadequateforcolumnswithmomentoraxialtension, consideraddingfilletweldsonallfacesuptowin.insize beforeusinggroovewelds. “Lackofcontactbearingnotexceedingagapofzin.… regardlessofthetypeofspliceused…ispermitted.Ifthe gapexceedszin.…butislessthan�in.…andifanengineeringinvestigationshowsthatsufficientcontactareadoes notexist,thegapshallbepackedoutwithnontaperedsteel shims.Shimsneednotbeotherthanmildsteel,regardlessof thegradeofmainmaterial.” • ForrectangularHSScolumnssubjecttoaxialcompressiononly,weldingontheflatsofthefoursidesonlywill avoid having to make an out-of-position weld on the corners.Note,however,thatcornersmustbeweldedfor HSScolumnsmomentoraxialtensionandanchorrods atthecornersofthebaseplatesincethecriticalyieldline willformintheplateatthecornersoftheHSS. WhiletheAISCSpecificationrequirementsforfinishing areprescriptiveinform,itisimportanttoensurethatasatisfactorycontactbearingsurfaceisprovided.Byapplyingthe provisionsofSectionM4.4,itmaynotbenecessarytomill platesover4in.thickiftheyareflatenoughtomeetthegap requirementsunderthecolumn.Standardpracticeistoorder allplatesoverapproximately3in.withanextra4in.to2 in.overthedesignthicknesstoallowformilling.Typically, onlytheareadirectlyunderthecolumnshaftismilled.The base elevation for setting the column is determined in this casebytheelevationatthebottomofthecolumnshaftwith thegroutspaceandshimsadjustedaccordingly. • Theminimumfilletweldrequirementshavebeenchanged inthe2005AISCSpecification.Theminimum-sizefillet weldisnowbasedonthethinnerofthematerialsbeing joined. 2.4BasePlateWelding Mostcolumnbaseplatesareshopweldedtothecolumn shaft.Inthepastitwascommontodetailheavybaseplates formulti-storybuildingasloosepiecestobesetandgrouted beforeerectingthecolumnshaft.Thebaseplatewasdetailed withthreeadjustingscrews,asshowninFigure2.2,andthe milledsurfacewascarefullysettoelevation. Thisapproachhadtheadvantageofreducingtheweight ofheavymembersforhandlingandshippingandprovideda fullygroutedbaseplateinplacetoreceiveaveryheavycol- The structural requirements for column base plate welds may vary greatly between columns loaded in compression only and columns in which moment, shear, and/or tension forces are present.Welds attaching base plates to columns areoftensizedtodevelopthestrengthoftheanchorrodsin tension,whichcanmostoftenbeachievedwitharelatively small fillet weld. For example, a c-in., 22-in.-long fillet weldtoeachcolumnflangewillfullydevelopa1-in.-diameter ASTM F1554 Grade 36 anchor rod when the directional strengthincreaseforfilletweldsloadedtransverselyisused, Alternativecriteriamaybeadvisablewhenroddiametersare largeormaterialstrengthlevelsarehigh. Afewbasicguidelinesonbaseplateweldingareprovided here: • Filletweldsarepreferredtogrooveweldsforallbutlarge moment-resistingbases. • Theuseoftheweld-all-aroundsymbolshouldbeavoided, especiallyonwide-flangeshapes,sincethesmallamount of weld across the toes of the flanges and in the radius Figure2.1.Typicalgravitycolumnbaseplateweld. 4/DESIGNGUIDE1,2NDEDITION/BASEPLATEANDANCHORRODDESIGN umnshaft.Thecolumnmayormaynotbeweldedaftererectiondependingonthestructuralrequirementsandthetypeof erectionaidprovided.Mosterectorsnowprefertohavethe baseplateshopweldedtothecolumnwheneverpossible. 2.5AnchorRodMaterial AsshowninTable2.2,thepreferredspecificationforanchor rodsisASTMF1554,withGrade36beingthemostcommon strengthlevelused.Theavailabilityofothergradesshould beconfirmedpriortospecification. ASTMF1554Grade55anchorrodsareusedwhenthere arelargetensionforcesduetomomentconnectionsoruplift fromoverturning.ASTMF1554Grade105isaspecialhighstrengthrodgradeandgenerallyshouldbeusedonlywhen itisnotpossibletodeveloptherequiredstrengthusinglarger Grade36orGrade55rods. Unlessotherwisespecified,anchorrodswillbesupplied withunifiedcoarse(UNC)threadswithaClass2atolerance, aspermittedinASTNF1554.WhileASTMF1554permits standardhexnuts,allnutsforanchorrods,especiallythose usedinbaseplateswithlargeoversizeholes,shouldbefurnishedasheavyhexnuts,preferablyASTMA563GradeA orDHforGrade105. ASTMF1554anchorrodsarerequiredtobecolorcoded toalloweasyidentificationinthefield.Thecolorcodesare asfollows: Grade36............................................................... Blue Grade55............................................................Yellow Grade105.............................................................. Red In practice, Grade 36 is considered the default grade and oftenisnotcolorcoded. TheASTMspecificationallowsF1554anchorrodstobe supplied either straight (threaded with nut for anchorage), bentorheaded.Rodsuptoapproximately1in.indiameter are sometimes supplied with heads hot forged similar to a structuralbolt.Thereafter,itismorecommonthattherods willbethreadedandnutted. Hooked-type anchor rods have been extensively used in thepast.However,hookedrodshaveaverylimitedpullout strengthcomparedwiththatofheadedrodsorthreadedrods withanutforanchorage.Therefore,currentrecommended practiceistouseheadedrodsorthreadedrodswithanutfor anchorage. The addition of plate washers or other similar devices doesnotincreasethepulloutstrengthoftheanchorrodand can create construction problems by interfering with reinforcingsteelplacementorconcreteconsolidationunderthe plate.Thus,itisrecommendedthattheanchoragedevicebe limitedtoeitheraheavyhexnutoraheadontherod.Asan exception,theadditionofplatewashersmaybeofusewhen high-strengthanchorrodsareusedorwhenconcreteblowout couldoccur(seeSection3.22ofthisGuide).Inthesecases, calculationsshouldbemadetodetermineifanincreasein thebearingareaisnecessary.Additionally,itshouldbeconfirmedthattheplatesizespecifiedwillworkwiththereinforcingsteelandconcreteplacementrequirements. ASTMF1554Grade55anchorrodscanbeorderedwith a supplementary requirement, S1, which limits the carbon equivalentcontenttoamaximumof45%,toprovideweldability when needed. Adding this supplement is helpful shouldweldingbecomerequiredforfixesinthefield.Grade 36istypicallyweldablewithoutsupplement. Therearealsotwosupplementalprovisionsavailablefor Grades55and105regardingCharpyV-Notch(CVN)toughness.TheseprovideforCVNtestingof15ft-lbsateither40°F(S4) orat−20°F(S5).Note,however,thatanchorrodstypically havesufficientfracturetoughnesswithoutthesesupplementalspecifications.Additionalfracturetoughnessisexpensive andgenerallydoesnotmakemuchdifferenceinthetimeto failureforanchorrodssubjectedtofatigueloading.Although fracturetoughnessmaycorrespondtoagreatercracklength atthetimeoffailure(becausecracksgrowatanexponential rate)95%ofthefatiguelifeoftheanchorrodisconsumed whenthecracksizeislessthanafewmillimeters.Thisis alsothereasonitisnotcosteffectivetoperformultrasonic testingorothernondestructivetestsonanchorrodstolook forfatiguecracks.Thereisonlyasmallwindowbetweenthe timecracksarelargeenoughtodetectandsmallenoughto notcausefracture.Thus,itgenerallyismorecosteffective todesignadditionalredundancyintotheanchorrodsrather thanspecifyingsupplementalCVNproperties. Figure2.2.Baseplatewithadjustingscrews. DESIGNGUIDE1,2NDEDITION/BASEPLATEANDANCHORRODDESIGN/5 Table2.3.RecommendedSizesforAnchorRodHolesinBasePlates AnchorRod Diameter,in. Hole Diameter,in. Min.Washer Dimension,in. Min.Washer Thickness,in. w 1c 2 � d 1b 2� c 1 1m 3 a 1� 2z 3 � 1� 2c 3� � 1w 2w 4 s 2 3� 5 w 2� 3� 5� d Notes:1.Circularorsquarewashersmeetingthesizeshownareacceptable. 2.Adequateclearancemustbeprovidedforthewashersizeselected. 3.Seediscussionbelowregardingtheuseofalternate1z-in.holesizeforw-in.-diameteranchorrods,withplateslessthan1�in.thick. Galvanizedanchorrodsareoftenusedwhenthecolumnbase-plate assembly is exposed and subject to corrosion. Eitherthehot-dipgalvanizingprocess(ASTM153)orthe mechanical galvanizing process (ASTM B695) is allowed inASTMF1554;however,allthreadedcomponentsofthe fastenerassemblymustbegalvanizedbythesameprocess. Mixingofrodsgalvanizedbyoneprocessandnutsbyanother may result in an unworkable assembly. It is recommendedthatgalvanizedanchorrodsandnutsbepurchased fromthesamesupplierandshippedpreassembled.Because thisisnotanASTMrequirement,thisshouldbespecifiedon thecontractdocuments. Notealsothatgalvanizingincreasesfrictionbetweenthe nutandtherodandeventhoughthenutsareovertapped, speciallubricationmayberequired. ASTMA449,A36 andA307 specifications are listed in Table2.2forcomparisonpurposes,becausesomesuppliers aremorefamiliarwiththesespecifications.NotethatASTM F1554gradesmatchupcloselywithmanyaspectsofthese oldermaterialspecifications.Notealsothattheseoldermaterialspecificationscontainalmostnoneoftheanchorrod specificrequirementsfoundinASTMF1554. Drilled-in epoxy-type anchor rods are discussed in severalplacesinthisDesignGuide.Thiscategoryofanchorrod doesnotincludewedge-typemechanicalanchors,whichare notrecommendedforanchorrodsbecausetheymustbetensionedtosecurelylockinthewedgedevice.Columnmovementduringerectioncancausewedge-typeanchorrodsto loosen. 2.6AnchorRodHolesandWashers Themostcommonfieldproblemisanchorrodplacements that either do not fit within the anchor rod hole pattern or donotallowthecolumntobeproperlypositioned.Because OSHA requires any modification of anchor rods to be approvedbytheEngineerofRecord,itisimportanttoprovide as large a hole as possible to accommodate setting tolerances.TheAISC-recommended hole sizes for anchor rods aregiveninTable2.3. TheseholesizesoriginatedinthefirsteditionofDesign Guide 1, based on field problems in achieving the column settingtolerancesrequiredfortheprevioussomewhatsmallerrecommendedsizes.TheywerelaterincludedintheAISC SteelConstructionManual. ThewasherdiametersshowninTable2.3aresizedtocovertheentireholewhentheanchorrodislocatedattheedge ofthehole.Platewashersareusuallycustomfabricatedby thermalcuttingtheshapeandholesfromplateorbarstock. Thewashermaybeeitheraplaincircularwasherorarectangularplatewasheraslongasthethicknessisadequatetopreventpullingthroughthehole.Theplatewasherthicknesses showninthetablearesimilartotherecommendationinDesign Guide 7, that the washer thickness be approximately one-thirdtheanchorroddiameter.ThesamethicknessisadequateforallgradesofASTMF1554,sincethepull-through criterionrequiresappropriatestiffnessaswellasstrength. Foranchorrodsforcolumnsdesignedforaxialcompression only, the designer may consider using a smaller hole diameterof1zin.withw-in.-diameterrodsandbaseplates lessthan14in.thick,asallowedinFootnote3inTable2.3. Thiswillallowtheholestobepuncheduptothisplatethickness,andtheuseofASTMF844(USSStandard)washersin lieuofthecustomwashersofdimensionsshowninthetable. Thispotentialfabricationsavingsmustbeweighedagainst possibleproblemswithplacementofanchorrodsoutoftolerance. 6/DESIGNGUIDE1,2NDEDITION/BASEPLATEANDANCHORRODDESIGN Foranchorrodsdesignedtoresistmomentoraxialtension,theholeandwashersizesrecommendedinTable2.3 shouldbeused.Theaddedsettingtoleranceisespeciallyimportantwhenthefullornear-fullstrengthoftherodintensionisneededfordesignpurposes,becausealmostanyfield fixinthiscasewillbeverydifficult. Additional recommendations regarding washers and anchorrodholesareasfollows: • Washersshouldnotbeweldedtothebaseplate,except whentheanchorrodsaredesignedtoresistshearatthe columnbase(seeSection3.5). • ASTMF436washersarenotusedonanchorrodsbecause theygenerallyareofinsufficientsize. • Washersforanchorrodsarenot,anddonotneedtobe, hardened. 2.7AnchorRodSizingandLayout Use w-in.-diameter ASTM F1554 Grade 36 rod material wheneverpossible.Wheremorestrengthisrequired,considerincreasingroddiameteruptoabout2in.inASTMF1554 Grade36materialbeforeswitchingtoahigher-strengthmaterialgrade. Anchorroddetailsshouldalwaysspecifyamplethreaded length.Wheneverpossible,threadedlengthsshouldbespecifiedatleast3in.greaterthanrequired,toallowforvariations insettingelevation. Anchorrodlayoutsshould,wherepossible,useasymmetricalpatterninbothdirectionsandasfewdifferentlayouts aspossible.Thus,thetypicallayoutshouldhavefouranchor rodsinasquarepattern. Anchorrodlayoutsshouldprovideampleclearancedistanceforthewasherfromthecolumnshaftanditsweld,as wellasareasonableedgedistance.Whentheholeedgeis notsubjecttoalateralforce,evenanedgedistancethatprovidesacleardimensionassmallas2in.ofmaterialfrom theedgeoftheholetotheedgeoftheplatewillnormally suffice,althoughfieldissueswithanchorrodplacementmay necessitatealargerdimensiontoallowsomeslottingofthe baseplateholes.Whentheholeedgeissubjecttoalateral force,theedgedistanceprovidedmustbelargeenoughfor thenecessaryforcetransfer. Keeptheconstructionsequenceinmindwhenlayingout anchorrodsadjacenttowallsandotherobstructions.Make suretheerectorwillhavetheaccessnecessarytosetthecolumnandtightenthenutsontheanchorrods.Wherespecial settings are required at exterior walls, moment bases, and other locations, clearly identify these settings on both the columnscheduleandfoundationdrawings. Anchorrodlayoutsmustbecoordinatedwiththereinforcingsteeltoensurethattherodscanbeinstalledintheproper locationandalignment.Thisisespeciallycriticalinconcrete piersandwallswherethereislessroomforadjustmentin thefield.Anchorrodsinpiersshouldneverextendbelowthe bottomofthepierintothefootingbecausethiswouldrequire thattheanchorrodsbepartiallyembeddedpriortoforming thepier,whichmakesitalmostimpossibletomaintainalignment.Whenthepierheightislessthantherequiredanchor rodembedmentlength,thepiershouldbeeliminatedandthe columnextendedtosetthebaseplateonthefooting. 2.8AnchorRodPlacementandTolerances Properplacementofanchorrodsprovidesforthesafe,fast, andeconomicalerectionofthestructuralsteelframe. Theplacementprocessbeginswiththepreparationofan anchor rod layout drawing.While it is possible to lay out anchor rods using the foundation design drawings and the columnschedule,therewillbefewerproblemsifthestructuralsteeldetailercoordinatesallanchorroddetailswiththe column-base-plateassembly.Theanchorrodlayoutdrawing willshowallanchorrodmarksalongwithlayoutdimensions andelevationrequirements.Becauseofschedulepressures, thereissometimesarushtosetanchorrodsusingadrawing submittedforapproval.Thisshouldbeavoided;onlyplacementdrawingsthathavebeendesignatedas“Releasedfor Construction”shouldbeusedforthisimportantwork. Layout(andafter-placementsurveying)ofallanchorrods should be done by an experienced construction surveyor. Thesurveyorshouldbeabletoreadstructuraldrawingsand knowledgeableofconstructionpractices.Atypicallicensed landsurveyormayormaynothavethenecessaryknowledge andexperienceforthistypeofwork. Templates should be made for each anchor rod setting pattern.Typically, templates are made of plywood on site. The advantage of plywood templates is they are relatively inexpensive to make and are easy to fasten in place to the woodfoundationforms.Theanchorrodscanbeheldsecurely inplaceandrelativelystraightbyusinganutoneachside ofthetemplate.Steeltemplatesconsistingofflatplatesor angle-typeframesaresometimesusedforverylargeanchor rodassembliesrequiringclosesettingtolerances.Provisions shouldbemadetosecurethetemplateinplace,suchaswith nailingholesprovidedinthesteelplate.Steelplatetemplates canalsobereusedassettingplates. Embedded templates are sometimes used with large anchorrodassembliestohelpmaintainalignmentoftherods duringconcreteplacement.Thetemplateshouldbekeptas smallaspossibletoavoidinterferencewiththereinforcing steelandconcreteplacement.Whenusingasingleexposed template,thereinforcingsteelcanbeplacedbeforepositioning the anchor rods in the form.With the embedded template,theanchorrodassemblymustbeplacedfirstandthe reinforcingsteelplacedaroundorthoughthetemplate.Care must be taken to consolidate the concrete around the tem- DESIGNGUIDE1,2NDEDITION/BASEPLATEANDANCHORRODDESIGN/7 platetoeliminatevoids.Thisisespeciallyimportantifthe templateservesaspartoftheanchorage. Whenthetemplatesareremoved,theanchorrodsshould besurveyedandgridlinesmarkedoneachsetting.Theanchorrodsshouldthenbecleanedandcheckedtomakesure thenutscanbeeasilyturnedandthattheverticalalignmentis proper.Ifnecessary,thethreadsshouldbelubricated.OSHA requiresthecontractortoreviewthesettingsandnotifythe EngineerofRecordofanyanchorrodsthatwillnotmeetthe tolerancerequiredfortheholesizespecified. Asexceptionstotheforgoingrecommendations,fast-track projectsandprojectswithcomplexlayoutsmayrequirespecialconsiderations.Inafast-trackproject,thesteeldesign anddetailingmaylagbehindtheinitialfoundationworkand thestructurallayoutchangedasthejobprogresses.Aproject with complex layouts may be such that even the most accurateplacementpossibleofanchorrodsinconcreteforms doesnotfacilitateproperfit-up.Ontheseprojects,itmaybe bettertousespecialdrilled-inepoxy-typeanchorrodsrather thancast-in-placerods. Forfast-trackprojects,thishastheadvantageofallowing thefoundationworktostartwithoutwaitingforanchorrods andanchorrodlayoutdrawings.Forcomplexlayouts,this hastheadvantageofprovidingeasierandmoreaccurateanchorrodlayoutformoreaccuratecolumnerection. CoordinationofAISCanchorrodsettingtolerancesand ACI tolerances for embedded items can be an issue. ACI 117-90,Section2.3,Placementofembeddeditems,allows a tolerance on vertical, lateral, and level alignment of ±1 in.AISCCodeofStandardPractice(AISC,2005),Section 7.5.1,liststhefollowingtolerances: “(a)Thevariationindimensionbetweenthecentersofany twoAnchorRodswithinanAnchor-RodGroupshallbe equaltoorlessthan 8in.” “(b)ThevariationindimensionbetweenthecentersofadjacentAnchor-RodGroupsshallbeequaltoorlessthan 4in.” “(c)ThevariationinelevationofthetopsofAnchorRods shallbeequaltoorlessthanplusorminus2in.” “(d)TheaccumulatedvariationindimensionbetweencentersofAnchor-RodGroupsalongtheEstablishedColumn LinethroughmultipleAnchor-RodGroupsshallbeequal toorlessthan4in.per100ft,butnottoexceedatotal of1in.” “(e)ThevariationindimensionfromthecenterofanyAnchor-RodGrouptotheEstablishedColumnLinethrough thatgroupshallbeequaltoorlessthan4in.” Thus,ACI117ismuchmoregenerousforembeddeditems thantheAISCCodeofStandardPractice(AISC,2005)is for anchor rod tolerances. Furthermore, since each trade willworktotheirownindustrystandardunlessthecontract documents require otherwise, it is recommended that the projectspecifications,typicallyCSIDivision3,requirethat theanchorrodsbesetinaccordancewiththeAISCCodeof StandardPractice(AISC,2005)tolerancerequirements,in ordertoclearlyestablishabasisforacceptanceoftheanchor rods.Itmaybehelpfultoactuallylistthetolerancerequirementsinsteadofsimplyprovidingareference. 2.9ColumnErectionProcedures OSHArequiresthegeneralcontractortonotifytheerector in writing that the anchor rods are ready for start of steel erection. This notice is intended to ensure that the layout hasbeenchecked,anyrequiredrepairshavebeenmade,and theconcretehasachievedtherequiredstrength.Theerector then,dependingonprojectrequirements,rechecksthelayout andsetselevationsforeachcolumnbase. There are three common methods of setting elevations: setting nuts and washers, setting plates, and shim stacks. Projectrequirementsandlocalcustomgenerallydetermine whichofthesemethodsisused.Itisimportantinallmethods thattheerectortightenalloftheanchorrodsbeforeremovingtheerectionloadlinesothatthenutandwasheraretight against the base plate. This is not intended to induce any levelofpretension,butrathertoensurethattheanchorrod assemblyisfirmenoughtopreventcolumnbasemovement duringerection.Ifitisnecessarytoloosenthenutstoadjust columnplumb,careshouldbetakentoadequatelybracethe columnwhiletheadjustmentismade. 2.9.1.SettingNutandWasherMethod The use of four anchor rods has made the setting nut and washer method of column erection very popular, as it is easy and cost effective. Once the setting nuts and washers are set to elevation, there is little chance they will be disturbed.Thefour-rodlayoutprovidesastableconditionfor erection,especiallyiftheanchorrodsarelocatedoutsideof thecolumnarea.Theelevationandplumbnessofthecolumn canbeadjustedusingthenuts.Whendesigninganchorrods usingsettingnutsandsashers,itisimportanttoremember theserodsarealsoloadedincompressionandtheirstrength shouldbecheckedforpushoutatthebottomofthefooting. It is recommended that use of the setting nut and washer method be limited to columns that are relatively lightly loadedduringerection.Evenafterthebaseplateisgrouted, thesettingnutwilltransferloadtotheanchorrod,andthis shouldbeconsideredwhenselectingthemethodtosetthe columnelevation. 8/DESIGNGUIDE1,2NDEDITION/BASEPLATEANDANCHORRODDESIGN 2.9.2SettingPlateMethod Settingplates(sometimescalledlevelingplates)areavery positivemethodforsettingcolumnbaseelevationsbutare somewhatmorecostlythansettingnutsandwashers. Setting plates are usually about 4 in. thick and slightly largerthanthebaseplate.Becauseaplatethisthinhasatendencytowarpwhenfabricated,settingplatesaretypically limitedtoamaximumdimensionofabout24in. If the setting plate is also to be used as a template, the holesaremadezin.largerthantheanchorroddiameter. Otherwise,standardanchorrodholesizesareused. After the anchor rods have been set, the setting plate is removedandtheanchorrodsarecheckedasnotedearlier. Thebearingareaisthencleaned,andtheelevationsareset usingeitherjamnutsorshims.Groutisspreadoverthearea, andthesettingplatetappeddowntoelevation.Theelevation shouldberecheckedaftertheplateissettoverifythatitis correct.Ifnecessary,theplateandgroutcanberemovedand theprocessstartedover. Oneproblemwithusingsettingplatesisthatwarpingin either the setting plate or the base plate, or column movementduring“bolt-up,”mayresultingapsbetweenthesettingplateandbaseplate.Generally,therewillstillbeadequatebearingandtheamountofcolumnsettlementrequired toclosethegapwillnotbedetrimentaltothestructure.The acceptabilityofanygapscanbedeterminedusingtheprovisionsinAISCSpecificationSectionM4.4. Setting plates provide a positive check on anchor rod settings prior to the start of erection and provide the most stableerectionbaseforthecolumn.Theuseofsettingplates shouldbeconsideredwhenthecolumnisbeingerectedinan excavationwherewaterandsoilmaywashunderthebase plateandmakecleaningandgroutingdifficultafterthecolumniserected. 2.9.3ShimStackMethod Columnerectiononsteelshimstacksisatraditionalmethod forsettingbaseplateelevationsthathastheadvantagethat all compression is transferred from the base plate to the foundation without involving the anchor rods. Steel shim packs, approximately 4 in. wide, are set at the four edges ofthebaseplate.Theareasoftheshimstacksaretypically largeenoughtocarrysubstantialdeadloadpriortogrouting ofthebaseplate. 2.9.4SettingLargeBasePlates Baseplatesizeandweightmaybesuchthatthebaseplate must be preset to receive the column.When crane capacities or handling requirements make it advantageous to set theplateinadvanceofthecolumn,theplatesarefurnished witheitherwedge-typeshimsorlevelingoradjustingscrews toallowthemtobesettoelevationandgroutedbeforethe column is set, as illustrated in Figure 2.2. Leveling-screw assembliesconsistofsleevenutsweldedtothesidesofthe plateandathreadedrodscrewthatcanbeadjusted.These platesshouldbefurnishedwithholesizesasshowninTable2.3. Thecolumnshaftshouldbedetailedwithstoolsorerection aids,asrequired.Wherepossible,thecolumnattachmentto thebaseplateshouldavoidfieldweldingbecauseofthedifficultyinpreheatingaheavybaseplateforwelding. 2.10GroutingRequirements Groutservesastheconnectionbetweenthesteelbaseplate andtheconcretefoundationtotransfercompressionloads. Accordingly, it is important that the grout be properly designedandplacedinaproperandtimelymanner. Groutshouldhaveadesigncompressivestrengthatleast twicethestrengthofthefoundationconcrete.Thiswillbe adequatetotransferthemaximumsteelbearingpressureto thefoundation.Thedesignthicknessofthegroutspacewill dependonhowfluidthegroutisandhowaccuratetheelevationofthetopofconcreteisplaced.Ifthecolumnisseton afinishedfloor,a1-in.spacemaybeadequate,whileonthe topofafootingorpier,normallythespaceshouldbe12in. to 2 in. Large base plates and plates with shear lugs may requiremorespace. Grout holes are not required for most base plates. For plates24in.orlessinwidth,aformcanbesetupandthe groutcanbeforcedinfromonesideuntilitflowsouttheoppositeside.Whenplatesbecomelargerorwhenshearlugs areused,itisrecommendedthatoneortwogroutholesbe provided.Groutholesaretypically2to3in.indiameterand aretypicallythermallycutinthebaseplate.Aformshould beprovidedaroundtheedge,andsomesortoffillingdevice shouldbeusedtoprovideenoughheadpressuretocausethe grouttoflowouttoallofthesides. It is important to follow the manufacturer’s recommendations for mixing and curing times. When placing grout in cold weather, make sure protection is provided per the manufacturer’sspecification. Grouting is an interface between trades that provides a challengeforthespecificationwriter.Typically,thegroutis furnishedbytheconcreteorgeneralcontractor,butthetimingisessentialtotheworkofthesteelerector.Becauseof this, specification writers sometimes place grouting in the steelsection.Thisonlyconfusestheissuebecausetheerectorthenhastomakearrangementswiththeconcretecontractortodothegrouting.Groutingshouldbetheresponsibility oftheconcretecontractor,andthereshouldbearequirement togroutcolumnbasespromptlywhennotifiedbytheerector thatthecolumnisinitsfinallocation. DESIGNGUIDE1,2NDEDITION/BASEPLATEANDANCHORRODDESIGN/9 2.11AnchorRodRepairs Anchor rods may require repair or modification during installation or later on in service. OSHA requires that any modificationofanchorrodsduringconstructionbereviewed andapprovedbytheEngineerofRecord.Onacase-by-case basis,theEngineerofRecordmustevaluatetherelativemeritsofaproposedrepairasopposedtorejectingthefoundation andrequiringthecontractortoreplacepartofthefoundation withnewanchorrodspertheoriginaldesign. Recordsshouldbekeptoftherepairprocedureandtheresults.TheEngineerofRecordmayrequirespecialinspection ortestingdeemednecessarytoverifytherepair. Most of these repairs are standard simple modifications thatdonotrequirecalculations.Themostcommonanchor rodproblemsareaddressedinthefollowingsections. 2.11.1AnchorRodsintheWrongPosition For anchor rods in the wrong position, the repair method dependsonthenatureoftheproblemandwhenintheconstructionprocessitisfirstnoted.Istherepairrequiredfor onlyonerodorfortheentirepatternofrods?Howfarout ofpositionistherodorpattern,andwhataretherequired strengthsoftherods? Iftheerrorisdiscoveredbeforethecolumnbaseplatehas beenfabricated,itmightbepossibletouseadifferentpattern orevenadifferentbaseplate.Iftherodpositionsinterfere withthecolumnshaft,itmaybenecessarytomodifythecolumnshaftbycuttingandreinforcingsectionsoftheflange orweb. Ifoneortworodsinapatternaremisplacedafterthecolumnhasbeenfabricatedandshipped,themostcommonrepairistoslotthebaseplateanduseaplatewashertospan the slot. If the entire pattern is off uniformly, it might be possibletocutthebaseplateoffandoffsetthebaseplateto accommodatetheoutoftolerance.Itisnecessarytocheck the base plate design for this eccentricity.When removing thebaseplate,itmayberequiredtoturntheplateoverto haveacleansurfaceonwhichtoweldthecolumnshaft. Iftheanchorrodorrodsaremorethanacoupleofinches outofposition,thebestsolutionmaybetocutofftheexistingrodsandinstallnewdrilled-inepoxy-typeanchorrods. Whenusingsuchrods,carefullyfollowthemanufacturer’s recommendationsandprovideinspectionasrequiredinthe applicablebuildingcode.Locatetheholestoavoidreinforcingsteelinthefoundation.Ifanyreinforcingsteeliscut,a checkoftheeffectonfoundationstrengthshouldbemade. mayendupatanangletotheverticalthatwillnotallowthe baseplatetobefitovertherods. Rodscanalsobedamagedinthefieldbyequipment,such aswhenbackfillingfoundationsorperformingsnowremoval.Anchor rod locations should be clearly flagged so that theyarevisibletoequipmentoperatorsworkinginthearea. TheanchorrodsshowninFigure2.3weredamagedbecause theywerecoveredwithsnowandthecraneoperatorcould notseethem. ASTMF1554permitsbothcoldandhotbendingofanchorrodstoformhooks;however,bendinginthethreaded areacanbeaproblem.ItisrecommendedthatonlyGrade 36rodsbebentinthefieldandthebendlimitedto45°or less. Rods up to about 1 in. in diameter can be cold bent. Rodsover1in.canbeheatedupto1,200ºFtomakebendingeasier.Itisrecommendedthatbendingbedoneusinga rod-bendingdevicecalledahickey.Afterbending,therods shouldbevisuallyinspectedforcracks.Ifthereisconcern aboutthetensilestrengthoftheanchorrod,therodcanbe loadtested. 2.11.3AnchorRodProjectionTooLongorTooShort Anchorrodprojectionsthataretooshortortoolongmust beinvestigatedtodetermineifthecorrectanchorrodswere installed.Iftheanchorrodistooshort,theanchorrodmay beprojectingbelowthefoundation.Iftherodprojectionis toolong,theembedmentmaynotbeadequatetodevelopthe requiredtensilestrength. Often, when the anchor rod is short, it may be possible to partially engage the nut.A conservative estimate of the resultingnutstrengthcanbemadebasedonthepercentage ofthreadsengaged,aslongasatleasthalfofthethreadsin 2.11.2AnchorRodsBentorNotVertical Care should be taken when setting anchor rods to ensure theyareplumb.Iftherodsarenotproperlysecuredinthe template,orifthereisreinforcingsteelinterference,therods Figure2.3.Anchorrodsrunoverbycrane. 10 / DESIGN GUIDE 1, 2ND EDITION /BASEPLATEANDANCHORRODDESIGN Table2.4.HexCouplingNutDimensions Diameter ofRod,in. Width AcrossFlats,in. Width AcrossCorners,in. Height ofNut,in. w 18 1c 2� d 1c 1� 2s 1� 1w 3 1 1� 1d 2x 3w 1� 2� 38 4� 1w 2w 3x 5� 2 38 3s 6 2� 3d 4� 7� DimensionsbasedonIFI#128ofIndustrialFastenerInstitute.MaterialconformstoASTMA563GradeA. thenutareengaged.Weldingthenuttotheanchorrodisnot aprequalifiedweldedjointandisnotrecommended. Iftheanchorrodistooshortandtherodsareusedonlyfor columnerection,thenthemostexpedientsolutionmaybeto cutordrillanotherholeinthebaseplateandinstalladrilledin epoxy-type anchor rod.When the rods are designed for tension,therepairmayrequireextendingtheanchorrodby usingacouplingnutorweldingonapieceofthreadedrod. Figure2.4showsadetailofhowacouplingnutcanbeused toextendananchorrod.Thisfixwillrequireenlargingthe anchorrodholetoaccommodatethecouplingnutalongwith using oversize shims to allow the plate washer and nut to clearthecouplingnut.Table2.4liststhedimensionsoftypi- calcouplingnutsthatcanbeusedtodetailtherequiredhole size and plate fillers.ASTM F1554 Grade 36 anchor rods andASTMF1554Grade55withsupplementS1anchorrods canbeextendedbyweldingonathreadedrod.Buttwelding two round rods together requires special detailing that usesarunouttabinordertomakeapropergrooveweld. Figure2.5ashowsarecommendeddetailforbuttwelding. Therun-outtabcanbetrimmedoffafterwelding,ifnecessary,andtherodcanevenbegroundflushifrequired.For more information on welding to anchor rods, see AISC DesignGuide21,WeldedConnections,APrimerforEngineers(Miller,2006). Figure2.4.Couplingnutdetailforextendinganchorrod. Figure2.5a.Grooveweldsplice. DESIGNGUIDE1,2NDEDITION/BASEPLATEANDANCHORRODDESIGN/11 Itisalsopossibletoextendananchorbyusingsplicebars toconnectathreadedrodextension.Detailssimilartothat showninFigure2.5bwillrequireenlargingtheanchorrod holesimilartowhatisrequiredforthethreadedcoupler.Either of these welded details can be designed to develop a full-strengthspliceoftheanchorrod. When anchor rods are too long, it is easy to add plate washers to attain an adequate thread length to run the nut downtothebaseplate.Asnotedearlier,anchorroddetails shouldalwaysincludeanextra3in.ormoreofthreadbeyondwhatthedetaildimensionrequirestocompensatefor somevariationinanchorrodprojection. 2.11.4AnchorRodPatternRotated90° Nonsymmetricalanchorrodpatternsrotated90ºareverydifficulttorepair.Inspecialcases,itmaybepossibletoremove thebaseplateandrotateittoaccommodatetheanchorrod placement. In most cases, this will require cutting off the anchorrodsandinstallingdrilled-inepoxy-typeanchors. 2.12DetailsforSeismicDesignD The 2005 AISC Seismic Provisions for Structural Steel Buildings (AISC, 2005) govern the design of structural Figure2.5b.Lapplatesplice. steelmembersandconnectionsintheseismicloadresisting system(SLRS)forbuildingsandotherstructureswherethe seismicresponsemodificationcoefficient,R,istakengreater than3,regardlessoftheseismicdesigncategory. Thebaseplateandanchorroddetailsforcolumnsthatare partoftheSLRSmusthaveadequatestrengthtoachievethe requiredductilebehavioroftheframe.Columnbasestrength requirementsforcolumnsthatarepartoftheSLRSaregiven inSection8.5oftheAISCSeismicProvisions.Seismicshear forcesaresometimesresistedbyembeddingthecolumnbase andprovidingforsheartransferintothefloorsystem.Reinforcingsteelshouldbeprovidedaroundthecolumntohelp distributethishorizontalforceintotheconcrete. The available strength for the concrete elements of columnbaseconnectionisgiveninACI318,AppendixD,exceptthatthespecialrequirementsfor“regionsofmoderate orhighseismicriskorforstructuresassignedtointermediateorhighseismicperformanceordesigncategories”need notbeapplied.TheAISCSeismicProvisionsCommentary explainsthatthese“specialrequirements”arenotnecessary becausetherequiredstrengthsinSections8.5aand8.5bof theAISCSeismicProvisionsarecalculatedathigherforce levels.TheAISCSeismicProvisionsCommentary,Section8.5, isarecommendedsourceforinformationonthedesignof columnbasesintheSLRS. Braced frame bases must be designed for the required strengthoftheelementsconnectedtothebase.Thecolumn baseconnectionmustbedesignednotonlyfortherequired tension and compression strengths of the column, but also for the required strength of the brace connection and base fixity or bending resistance for moments that would occur atthedesignstorydrift(inelasticdriftsaspredictedbythe buildingcode).Alternatively,wherepermitted,thecolumn basemaybedesignedfortheamplifiedforcesderivedfrom the load combinations of the applicable building code, includingtheamplifiedseismicload. Moment frame bases can be designed as rigid fully restrained (FR) moment connections, true “pinned bases” or, more accurately, as “partially restrained (PR) moment connections.” The intent of the discussion provided in the AISC Seismic Provisions regarding this issue is to design thisconnectionconsistentwiththeexpectedbehaviorofthe joint,accountingfortherelativestiffnessandstraincapability of all elements of the connection (the column, anchor rods, base plate, grout, and concrete). Depending on the connectiontype,thecolumnbasemusteitherhaveadequate strengthtomaintaintheassumeddegreeoffixityormustbe able to provide the required shear strength while allowing theexpectedrotationtooccur.Momentbasedetailsshown inFigures2.6and2.7arefromtheCommentarytotheAISC SeismicProvisions. Thebaseplateconnectioncanbedesignedusingconcepts similartobeam-to-columnconnections.However,theCom- 12 / DESIGN GUIDE 1, 2ND EDITION /BASEPLATEANDANCHORRODDESIGN mentarytotheAISCSeismicProvisionsnotessomesignificantdifferences: 1. Longanchorrodsembeddedinconcretewillstrainmuch morethanhigh-strengthboltsorweldsinbeam-to-column connections. 2. Column base plates are bearing on grout and concrete, whichismorecompressiblethanthecolumnflangesof thebeam-to-columnconnections. 3. Columnbaseconnectionshavesignificantlymorelongitudinalloadintheplaneoftheflangesandlesstransverse loadwhencomparedtobeam-to-columnconnections. 4. Theshearmechanismbetweenthecolumnbaseandthe groutorconcreteisdifferentfromtheshearmechanism betweenthebeamendplateandthecolumnflange. 5. AISC standard hole diameters for column base anchor rods are different than AISC standard holes for highstrengthbolts. 6. Foundationrockingandrotationmaybeanissue,especiallyonisolatedcolumnfootings. AstheCommentarytotheAISCSeismicProvisionssuggests,researchislackingregardingtheperformanceanddesignofbasedetailsforhighseismicloading.However,the Commentaryalsoacknowledgesthatthesedetailsarevery important to the overall performance of the SLRS. Therefore, careful consideration must be given to the design of thesedetails. Figure2.6.Typicalmomentbasedetail. 3.0DESIGNOFCOLUMNBASEPLATE CONNECTIONS This section of the Design Guide provides the design requirements for typical column base plate connections in buildings,suchastheoneshowninFigure1.1. Fivedifferentdesignloadcasesincolumnbaseplateconnectionsarediscussed: • Section3.1ConcentricCompressiveAxialLoads • Section3.2TensileAxialLoads • Section3.3BasePlateswithSmallMoments • Section3.4BasePlatesLargeMoments • Section3.5DesignforShear Incolumnbaseconnections,thedesignforshearandthe designformomentareoftenperformedindependently.This assumes there is no significant interaction between them. Severaldesignexamplesareprovidedinthefollowingsectionsforeachloadingcase. Thegeneralbehavioranddistributionofforcesforacolumnbaseplateconnectionwithanchorrodswillbeelastic until either a plastic hinge forms in the column, a plastic mechanismformsinthebaseplate,theconcreteinbearing crushes, the anchor rods yield in tension, or the concrete pullout strength of the anchor rod group is reached. If the concretepulloutstrengthoftheanchorrodgroupislarger thanthelowestoftheotheraforementionedlimitstates,the behaviorgenerallywillbeductile.However,itisnotalways necessaryorevenpossibletodesignafoundationthatpreventsconcretefailure. Figure2.7.Embeddedmomentbasedetail. DESIGNGUIDE1,2NDEDITION/BASEPLATEANDANCHORRODDESIGN/13 Forexample,instaticallyloadedstructures,ifthestrength ismuchlargerthanthedemand,theductilityisnotnecessary anditisacceptabletodesignwiththelimitstateoftensileor shearstrengthoftheanchorrodgroupgoverningthedesign. However,framesdesignedforseismiclateralloadresistance areexpectedtobehaveinaductilemannerand,inthiscase, it may be necessary to design the foundation and the column-base-plateconnectionsothattheconcretelimitstates oftensileorshearstrengthoftheanchorrodgroupdonot governthedesign.SeeACIAppendixD,SectionD3.3.4. EquationJ8-2: OSHARequirements Alternatively,ACI 318-02 stipulates a φ factor of 0.65 for bearingonconcrete.Thisapparentconflictexistsduetoan oversight in the AISC Specification development process. TheauthorsrecommendtheuseoftheACI-specifiedφfactorindesigningcolumnbaseplates. Thenominalbearingstrengthcanbeconvertedtoastress formatbydividingouttheareatermPpequationssuchthat, Onthefullareaofaconcretesupport: TheregulationsoftheOccupationalSafetyandHealthAdministration (OSHA) Safety Standards for Steel Erection (OSHA, 2001) require a minimum of four anchor rods in column-base-plate connections. The requirements exclude post-type columns that weigh less than 300 lb. Columns, baseplates,andtheirfoundationsmusthavesufficientmoment strength to resist a minimum eccentric gravity load of300lblocated18in.fromtheextremeouterfaceofthe columnineachdirection. TheOSHAcriteriacanbemetwitheventhesmallestof anchorrodsona4-in.×4-in.pattern.Ifoneconsidersonly the moments from the eccentric loads (since including the gravityloadsresultsinnotensileforceintheanchorrods), and the resisting force couple is taken as the design force ofthetwoboltstimesa4-in.leverarm,thedesignmoment strengthforw-in.anchorrodsequals(2)(19.1kips)(4in.)= 306 kip-in. For a 14-in.-deep column, the OSHA required momentstrengthisonly(1.6)(0.300)(18+7)=12.0kip-in. A Pp = (0.85 f c′A1 ) 2 ≤ 1.7 f c′A1 A1 Theseequationsaremultipliedbytheresistancefactor,φ,for LRFDordividedbythesafetyfactor,Ω,forASD.Section J8 stipulates the φ and Ω factors (in the absence of Code Regulations)forbearingonconcreteasfollows: φ=0.60(LRFD) fp(max)=0.85fc′ Whentheconcretebaseislargerthantheloadedareaon allfoursides: A f p(max) = (0.85 f c′) 2 ≤ 1.7 f c′ A1 The conversion of the generic nominal pressure to an LRFDorASDavailablebearingstressis fpu(max)=φfp(max)(LRFD) 3.1.ConcentricCompressiveAxialLoads Whenacolumnbaseresistsonlycompressivecolumnaxial loads,thebaseplatemustbelargeenoughtoresistthebearingforcestransferredfromthebaseplate(concretebearing limit), and the base plate must be of sufficient thickness (baseplateyieldinglimit). f pa(max) = The 2005 AISC Specification, Section J8, provides the nominalbearingstrength,Pp,asfollows: Ω (ASD) ( f p(max) = φ 0.85 fc′ ) A2 A1 A2 ≤2 A1 where fp(max) = maximumconcretebearingstress,ksi EquationJ8-1: Pp=0.85fc′A1onthefullareaofaconcretesupport. f p(max) Theconcretebearingstrengthisafunctionoftheconcrete compressivestrength,andtheratioofgeometricallysimilar concreteareatobaseplatearea,asindicatedinSection10.17 ofACI318(ACI,2002),asfollows: 3.1.1ConcreteBearingLimit The design bearing strength on concrete is defined in ACI 318-02, Section 10.17, as φ(0.85fc′A1) when the supportingsurfaceisnotlargerthanthebaseplate.Whenthe supportingsurfaceiswideronallsidesthantheloadedarea, thedesignbearingstrengthaboveispermittedtobemultipliedby A2 A1 ≤2. Ω=2.50(ASD) φ = strength reduction factor for bearing, 0.65 per Section9.3,ACI318-02 fc′ = specifiedcompressivestrengthofconcrete,ksi 14 / DESIGN GUIDE 1, 2ND EDITION /BASEPLATEANDANCHORRODDESIGN A1 = areaofthebaseplate,in.2 A2 = maximumareaoftheportionofthesupporting surfacethatisgeometricallysimilartoandconcentricwiththeloadedarea,in.2 Theincreaseoftheconcretebearingcapacityassociated withtheterm A2 A1 accountsforthebeneficialeffectsof the concrete confinement. Note that A2 is the largest area thatisgeometricallysimilarto(havingthesameaspectratio as)thebaseplateandcanbeinscribedonthehorizontaltop surfaceoftheconcretefooting,pier,orbeamwithoutgoing beyondtheedgesoftheconcrete. Thereisalimittothebeneficialeffectsofconfinement, whichisreflectedbythelimitonA2(toamaximumoffour timesA1)orbytheinequalitylimit.Thus,foracolumnbase platebearingonafootingfarfromedgesoropenings, A2 A1 = 2. =2. The bearing stress on the concrete must not be greater thanfp(max): Manycolumnbaseplatesbeardirectlyonalayerofgrout. Because,thegroutcompressivestrengthisalwaysspecified higherthantheconcretestrength—theauthorsrecommend thatthegroutstrengthbespecifiedastwotimestheconcrete strength—itisconservativetousetheconcretecompressive strengthforfc′intheaboveequations. Theimportantdimensionsofthecolumn-baseplateconnectionareshowninFigure3.1.1. 3.1.2BasePlateYieldingLimit(W-Shapes) Foraxiallyloadedbaseplates,thebearingstressunderthe baseplateisassumeduniformlydistributedandcanbeexpressedas f pu = Pu (LRFD) BN f pa = Pa (ASD) BN Thisbearingpressurecausesbendinginthebaseplateat theassumedcriticalsectionsshowninFigure3.1.1(b).This Pu ≤ f pu(max) (LRFD) A1 Pa ≤ f pa(max) (ASD) A1 Thus, Pu A1( req ) = f pu(max) A1( req ) = (LRFD) Pa (ASD) f pa(max) WhenA2=A1,therequiredminimumbaseplateareacan bedeterminedas A1( req ) = Pu (LRFD) φ0.85 f c′ A1( req ) = ΩPa (ASD) 0.85 f c′ WhenA2≥4A1,therequiredminimumbaseplateareacan bedeterminedas 1 Pu (LRFD) A1( req ) = 2 φ0.85 f c′ 1 ΩPa (ASD) A1( req ) = 2 0.85 f c′ Figure3.1.1.Designofbaseplatewithaxialcompressiveload. DESIGNGUIDE1,2NDEDITION/BASEPLATEANDANCHORRODDESIGN/15 bearingpressurealsocausesbendinginthebaseplateinthe area between the column flanges (Thornton, 1990; Drake andElkin,1999).Thefollowingprocedureallowsasingle proceduretodeterminethebaseplatethicknessforbothsituations. Therequiredstrengthofthebaseplatecanbedetermined as l 2 M pl = f pu (LRFD) 2 Itisconservativetotakeλas1.0. Fortheyieldinglimitstate,therequiredminimumthicknessofthebaseplatecanbecalculatedasfollows(Thornton, 1990)(AISC,2005): tmin = l tmin = l l 2 M pl = f pa (ASD) 2 Wherethecriticalbaseplatecantileverdimension,l,isthe largerofm,n,andλn′, m= n= N − 0.95d 2 2 db f where φ = resistancefactorforflexure,0.90 Ω = factorofsafetyforASD,1.67 Fy = specifiedminimumyieldstressofbaseplate,ksi 3.1.3BasePlateYieldingLimit(HSSandPipe) 4 N = baseplatelength,in. B = baseplatewidth,in. bf = columnflangewidth,in. d = overallcolumndepth,in. n′ = yield-line theory cantilever distance from columnweborcolumnflange,in. 2 X λ= ≤1 1 + 1− X 4db P u f (LRFD) X = (d + b f ) 2 φc Pp 4db f Ω P c a (ASD) X = (d + b f ) 2 Pp where Pu = therequiredaxialcompressiveload(LRFD),kips Pa = therequiredaxialcompressiveload(ASD),kips Pp = 0.85 f c′A1 2ΩPa (ASD) Fy BN Sincelisthemaximumvalueofm,n,andλn′,thethinnestbaseplatecanbefoundbyminimizingm,n,andλ.This isusuallyaccomplishedbyproportioningthebaseplatedimensionssothatmandnareapproximatelyequal. B − 0.8b f λn ′ = λ 2 Pu (LRFD) φFy BN A2 A1 ForHSScolumns,adjustmentsformandnmustbemade (DeWolf and Ricker, 1990). For rectangular HSS, both m andnarecalculatedusingyieldlinesat0.95timesthedepth andwidthoftheHSS.ForroundHSSandPipe,bothmand narecalculatedusingyieldlinesat0.8timesthediameter. TheλtermisnotusedforHSSandPipe. 3.1.4GeneralDesignProcedure Threegeneralcasesexistforthedesignofbaseplatessubjecttoaxialcompressiveloadsonly: CaseI: CaseII: CaseIII: A2=A1 A2≥4A1 A1<A2<4A1 ThemostdirectapproachistoconservativelysetA2equal toA1(CaseI);however,thisgenerallyresultsinthelargest baseplateplandimensions.Thesmallestbaseplateplandimensionsoccurwhentheratiooftheconcretetobaseplate areaislargerthanorequalto4,i.e.,A2≥4A1(CaseII).Base platesrestingonpiersoftenmeetthecasethatA2islarger thanA1butlessthan4A1,whichleadstoCaseIII. Whenabaseplatebearsonaconcretepedestallargerthan thebaseplatedimension,therequiredminimumbaseplate areacannotbedirectlydetermined.ThisisbecausebothA1 andA2areunknown. As mentioned before, the most economical base plates usuallyoccurwhenmandn,showninFigure3.1.1(b),are 16 / DESIGN GUIDE 1, 2ND EDITION /BASEPLATEANDANCHORRODDESIGN equal.ThissituationoccurswhenthedifferencebetweenB andNisequaltothedifferencebetween0.95dand0.8bf. Inselectingthebaseplatesizefromastrengthviewpoint, thedesignermustconsiderthelocationoftheanchorrods within the plate and the clearances required to tighten the boltsontheanchorrods. Steps for obtaining base plates sizes for these cases are suggested below.Anchor rod design is covered in Section 3.2. CaseI:A2=A1 N = baseplatelength,in. B = baseplatewidth,in. bf = columnflangewidth,in. d = overallcolumndepth,in. n′ = yield-line theory cantilever distance from columnweborcolumnflange,in. λ= ThelargestbaseplateisobtainedwhenA2=A1. A1( req ) = ΩPa (ASD) 0.85 f c′ where φPP = φ0.85 f c′ A1 (LRFD) 0.85 f c′ A1 PP = (ASD) Ω Ω 3. Optimizethebaseplatedimensions,NandB. N ≈ A1( req ) + ∆ where∆ = ≤1 4db f ΩP a (ASD) X = (d + b f ) 2 Pp 2. Calculatetherequiredbaseplatearea. Pu (LRFD) φ0.85 f c′ 1 + 1− X 4db f P u (LRFD) X = (d + b f ) 2 φPp 1. Calculate the required axial compressive strength, Pu (LRFD)orPa(ASD). A1( req ) = 2 X Findlmax(m,n,λn′) 0.95d − 0.8b f tmin = l 2 then B= tmin = l A1( req ) N Notethatthebaseplateholesarenotdeductedfromthe baseplateareawhendeterminingtherequiredbaseplate area.AsmentionedearlierintheGuide,fromapractical viewpointsetNequaltoB. 4. Calculatetherequiredbaseplatethickness. N − 0.95d m= 2 n= B − 0.8b f λn ′ = λ 2 2 Pu (LRFD) φFy BN 2 Pa Ω (ASD) Fy BN 5. Determinetheanchorrodsizeandthelocationoftheanchorrods.Anchorrodsforgravitycolumnsaregenerally notrequiredforthepermanentstructureandneedonlyto besizedforOSHArequirementsandpracticalconsiderations. CaseII:A2≥4A1 ThesmallestbaseplateisobtainedwhenA2≥4A1forthis case. 1. Calculatethefactoredaxialcompressiveload,Pu(LRFD) orPa(ASD). db f 2. Calculatetherequiredbaseplatearea. 4 A1( req ) = Pu (LRFD) 2φ0.85 f c′ DESIGNGUIDE1,2NDEDITION/BASEPLATEANDANCHORRODDESIGN/17 A1( req ) = ΩPa (ASD) 2 (0.85 f c′) 3. Optimizethebaseplatedimensions,NandB. UsethesameprocedureasinStep3fromCaseI. 4. Checkifsufficientarea,A2existsforCaseIIapplicability (A2≥4A1). Basedonthepierorfootingsize,itwilloftenbeobvious iftheconditionissatisfied.Ifitisnotobvious,calculate A2geometricallysimilartoA1.WithnewdimensionsN2 andB2,A2thenequals(N2)(B2).IfA2≥4A1,calculatethe requiredthicknessusingtheprocedureshowninStep4of CaseI,exceptthat φPp = φf c′2 A1 (LRFD) Pp Ω = f c′2 A1 (ASD) Ω 5. Determinetheanchorrodsizeandlocation. CaseIII:A1<A2<4A1 1.Calculatethefactoredaxialcompressiveload,Pu(LRFD) orPa(ASD). 2.Calculatetheapproximatebaseplateareabasedonthe assumptionofCaseIII. A1( req ) = Pu (LRFD) 2φ0.85 f c′ A1( req ) = ΩPa (ASD) 2 (0.85 f c′) 3. Optimizethebaseplatedimensions,NandB. UsethesameprocedureasinStep3fromCaseI. 4. CalculateA2,geometricallysimilartoA1. 5.Determinewhether Pu ≤ φPp = φ0.85 f c′A1 Pa ≤ A2 (LRFD) A1 0.85 f c′A1 A2 (ASD) = A1 Ω Ω Pp Iftheconditionisnotsatisfied,reviseNandB,andretry untilcriterionissatisfied. 6. DeterminethebaseplatethicknessusingStep4,asshown inCaseI. 7. Determinetheanchorrodsize,andtheirlocations. 3.2TensileAxialLoads Thedesignofanchorrodsfortensionconsistsoffoursteps: 1. Determinethemaximumnetupliftforthecolumn. 2. Selecttheanchorrodmaterialandthenumberandsizeof anchorrodsrequiredtoresistuplift. 3. Determinetheappropriatebaseplatesize,thickness,and weldingtotransfertheupliftforces. 4. Determinethemethodfordevelopingthestrengthofthe anchorrodintheconcrete(i.e.,transferringthetension forcefromtheanchorrodtotheconcretefoundation). Step1—Themaximumnetupliftforthecolumnisobtained fromthestructuralanalysisofthebuildingfortheprescribed building loads. When the uplift due to wind exceeds the dead load of a roof, the supporting columns are subjected to net uplift forces. In addition, columns in rigid bents or braced bays may be subjected to net uplift forces due to overturning. Step2—Anchorrodsshouldbespecifiedtoconformtothe material discussed in Section 2.5. The number of anchor rodsrequiredisafunctionofthemaximumnetupliftonthe columnandthestrengthperrodfortheanchorrodmaterial chosen. Pryingforcesinanchorrodsaretypicallyneglected.This isusuallyjustifiedwhenthebaseplatethicknessiscalculatedassumingcantileverbendingabouttheweband/orflange ofthecolumnsection(asdescribedinStep3below),andbecausethelengthoftherodsresultinlargerdeflectionsthan for steel to steel connections. The procedure to determine therequiredsizeoftheanchorrodsisdiscussedinSection 3.2.1below. Step3—Baseplatethicknessmaybegovernedbybending associatedwithcompressiveortensileloads. Fortensileloads,asimpleapproachistoassumetheanchorrodloadsgeneratebendingmomentsinthebaseplate consistent with cantilever action about the web or flanges ofthecolumnsection(one-waybending).SeeFigure3.1.1. Ifthewebistakingtheanchorloadfromthebaseplate,the webanditsattachmenttothebaseplateshouldbechecked. Alternatively,amorerefinedbaseplateanalysisforanchor rods positioned inside the column flanges can be used to considerbendingaboutboththewebandthecolumnflanges (two-waybending).Forthetwo-waybendingapproach,the derived bending moments should be consistent with com- 18 / DESIGN GUIDE 1, 2ND EDITION /BASEPLATEANDANCHORRODDESIGN patibility requirements for deformations in the base plate. Ineithercase,theeffectivebendingwidthforthebaseplate canbeconservativelyapproximatedusinga45°distribution fromthecenterlineoftheanchorrodtothefaceofthecolumnflangeorweb. Step4—MethodsofdeterminingtherequiredconcreteanchoragearetreatedinSection3.2.2. 3.2.1AnchorRodTension Thetensilestrengthofananchorrodisequaltothestrength oftheconcreteanchorageoftheanchorrodgroup(orthose anchor rods participating in tension in the case of tension duetomoment)orthesumofthesteeltensilestrengthsof thecontributinganchorrods. Foranchorrodconnectionsintension,thedesigntensile strengthofcontributinganchorrodsistakenasthesmallest ofthesumofthesteeltensilestrengthsofthecontributing individualanchorrodsortheconcretetensilestrengthofthe anchorgroup.Concretetensilestrengthandorthedevelopment length of deformed bars is calculated in accordance with currentAmerican Concrete Institute (ACI, 2002) criteria. The limiting tension on a rod is based on the minimum areaalongthemaximumstressedlengthofthatrod.Foran anchorrod,thisistypicallywithinthethreadedportion(exceptwhenupsetrodsareused).ANSI/ASMEB1.1defines thisthreadedareaas 2 0.7854 Tensilestressarea = D − n D = majordiameter n = numberofthreadsperin. Rn=0.7FuAb ToobtainthedesigntensilestrengthforLRFD,useφ=0.75, thus, Designtensilestrength=(0.75)(0.75)FuAb=0.5625FuAb To obtain the allowable tensile strength forASD use Ω = 2.00,thus, Allowabletensilestrength= 0.75 Fu Ab =0.375Fu Ab 2.00 ACI318,AppendixD,stipulatesthedesigntensilestrength ofananchoras Designtensilestrength=φFuAts=0.75FuAts whereφ=0.75 ShowninTable3.1arethedesignandallowablestrengths forvariousanchorrods. 3.2.2ConcreteAnchorageforTensileForces where strength of a particular anchor analyzed by either method willproduceaconsistentendresult. Strengthtablesforcommonlyusedanchorrodmaterials andsizesareeasilydevelopedbytheproceduresthatfollow, foreitherdesignmethod.Table3.1includedhereinhasbeen developedforASTMF1554rodsbasedonthenominalbolt diameterapproachofAISC.(Note:ASTMF1554isthesuggestedstandardandpreferredanchorrodmaterial.) The2005AISCSpecificationstipulatesthenominaltensilestrengthofafasteneras Table7–18intheAISCSteelConstructionManuallistthe tensilestressareafordiametersbetween�in.and4in. Two methods of determining the required tensile stress areaarecommonlyused.OneisbaseddirectlyontheANSI/ ASME-stipulatedtensilestressareaasdescribedabove.The other is to add a modifying factor that relates the tensile stress area directly to the unthreaded area as a means of simplifyingthedesignprocess.Thelattermethodisstipulatedinthe2005AISCSpecification. Thestrengthofstructuralfastenershashistoricallybeen based on the nominal bolt diameter, and the direct tensile stressareaapproachisstipulatedinACI318AppendixD. The designer should be aware of the differences in design approachesandstayconsistentwithinonesystemwhendeterminingtherequiredanchorarea.However,thecalculated ItispresumedthatASCE7loadfactorsareemployedinthis Guide.TheφfactorsusedhereincorrespondtothoseinAppendixD4.4andSection9.3ofACI318-02. Appendix D of ACI 318-02 (ACI, 2002) addresses the anchoringtoconcreteofcast-inorpost-installedexpansion orundercutanchors.Theprovisionsincludelimitstatesfor concrete pullout, and breakout strength [concrete capacity design(CCD)method]. ConcretePulloutStrength ACIconcretepulloutstrengthisbasedontheACIAppendix Dprovisions(SectionD5.3): φNP=φψ4Abrg8fc′ where Np = thenominalpulloutstrength φ = 0.7 DESIGNGUIDE1,2NDEDITION/BASEPLATEANDANCHORRODDESIGN/19 Table3.1.AnchorRod(RodOnly)AvailableStrength,kips LRFD φRn,φ=0.75 ASD Rn/Ω,Ω=2.00 Rod Diameter,in. RodArea, Ar,in2 s 0.307 10.0 12.9 21.6 6.7 8.6 14.4 w 0.442 14.4 18.6 31.1 9.6 12.4 20.7 d Grade36, Grade55, Grade105, Grade36, Grade55, Grade105, kips kips kips kips kips kips 0.601 19.6 25.4 42.3 13.1 16.9 28.2 1 0.785 25.6 33.1 55.2 17.1 22.1 36.8 18 0.994 32.4 41.9 69.9 21.6 28.0 46.6 1� 1.23 40.0 51.8 86.3 26.7 34.5 57.5 1� 1.77 57.7 1w 2.41 78.5 2 3.14 2� 124 38.4 49.7 102 169 52.3 67.6 113 103 133 221 68.3 88.4 147 3.98 130 168 280 86.5 2� 4.91 160 207 345 2w 5.94 194 251 418 3 7.07 231 298 3� 8.30 271 350 3� 9.62 74.6 82.8 112 186 107 138 230 129 167 278 497 154 199 331 583 180 233 389 314 406 677 209 271 451 3w 11.0 360 466 777 240 311 518 4 12.6 410 530 884 273 353 589 ψ4 = 1.4 if the anchor is located in a region of a concrete member where analysis indicates no cracking(ft–fr)atservicelevels,otherwiseψ4= 1.0 Abrg = thebearingareaoftheanchorrodheadornut, andfc′istheconcretestrength ShowninTable3.2aredesignpulloutstrengthsforanchor rodswithheavyhexheadnuts.The40%increaseinstrength has not been included. Notice that concrete pullout never controlsforanchorrodswithFy=36ksi,andconcretewith fc′ = 4 ksi. For higher strength anchor rods, washer plates maybenecessarytoobtainthefullstrengthoftheanchors. Thesizeofthewashersshouldbekeptassmallaspossible todeveloptheneededconcretestrength.Unnecessarilylarge washerscanreducetheconcreteresistancetopullout. Hookedanchorrodscanfailbystraighteningandpulling out of the concrete.This failure is precipitated by a localizedbearingfailureoftheconcreteabovethehook.Ahook is generally not capable of developing the required tensile strength.Therefore,hooksshouldonlybeusedwhentension intheanchorrodissmall. Appendix D ofACI 318-02 provides a pullout strength forahookedanchorofφψ4(0.9fc′ehdo),whichisbasedonan anchorwithdiameterdobearingagainstthehookextension ofeh;φistakenas0.70.Thehookextensionislimitedtoa maximumof4.5do;ψ4=1iftheanchorislocatedwherethe concreteiscrackedatserviceload,andψ4=1.4ifitisnot crackedatserviceloads. ConcreteCapacityDesign(CCD) IntheCCDmethod,theconcreteconeisconsideredtobe formed at an angle of approximately 34° (1 to 1.5 slope). Forsimplification,theconeisconsideredtobesquarerather thanroundinplan.SeeFigure3.2.1. The concrete breakout stress (ft in Figure 3.2.1) in the CCDmethodisconsideredtodecreasewithanincreasein size of the breakout surface. Consequently, the increase in strengthofthebreakoutintheCCDmethodisproportional totheembedmentdepthtothepowerof1.5(ortothepower of5/3fordeeperembedments). TheCCDmethodisvalidforanchorswithdiametersnot exceeding2in.andtensileembedmentlengthnotexceeding 25in.indepth. 20 / DESIGN GUIDE 1, 2ND EDITION /BASEPLATEANDANCHORRODDESIGN Table3.2.AnchorRodConcretePulloutStrength,kips Rod Diameter,in. RodArea, Ar,in2 Bearing Area,in2 s 0.307 w 0.442 ConcretePulloutStrength,φNp Grade36, kips Grade55, kips Grade105, kips 0.689 11.6 15.4 19.3 0.906 15.2 20.3 25.4 d 0.601 1.22 20.5 27.3 34.1 1 0.785 1.50 25.2 33.6 42.0 18 0.994 1.81 30.4 40.5 50.7 1� 1.23 2.24 37.7 50.2 62.8 1� 1.77 3.13 52.6 70.1 1w 2.41 4.17 70.0 93.4 2 3.14 5.35 90.0 2� 3.98 6.69 2� 4.91 2w 5.94 3 7.07 3� 8.30 3� 9.62 87.7 117 120 150 112 150 187 8.17 137 183 229 9.80 165 220 274 11.4 191 254 318 13.3 223 297 372 15.3 257 343 429 3w 11.0 17.5 294 393 491 4 12.6 19.9 334 445 557 Anchorroddesignforstructuressubjecttoseismicloads anddesignedusingaresponsemodificationfactor,R,greater than3,shouldbeinaccordancewithSection8.5ofthe2005 AISCSeismicProvisionsforStructuralSteelBuildings. Per ACI 318-02, Appendix D, the concrete breakout strengthforagroupofanchorsis φ N cbg =φψ 3 24 f c′ hef 1.5 AN forhef < 11in. ANo φ N cbg =φψ 316 f c′ hef 5 / 3 AN forhef ≥ 11in. ANo and where Figure3.2.1.FullbreakoutconeintensionperACI318-02. φ = 0.70 ψ3 = 1.25consideringtheconcretetobeuncrackedat serviceloads,otherwise=1.0 hef = depthofembedment,in. AN = concretebreakoutconeareaforgroup ANo = concretebreakoutconeareaforsingleanchor DESIGNGUIDE1,2NDEDITION/BASEPLATEANDANCHORRODDESIGN/21 AppendixDofACI318-02alsolistscriteriaforanchor rodstoprevent“failureduetolateralburstingforcesatthe anchor head.” These lateral bursting forces are associated with tension in the anchor rods. The failure plane or surfaceinthiscaseisassumedtobeconeshapedandradiating from the anchor head to the adjacent free edge or side of the concrete element.This is illustrated in Figure 3.2.4. It isrecommendedtouseaminimumsidecoverc1ofsixanchordiametersforanchorrodsconformingtoASTMF1554 Grade36toavoidproblemswithsidefacebreakout.Aswith thepulloutstresscones,overlappingofthestressconesassociated with these lateral bursting forces is considered in Appendix D ofACI 318-02. Use of washer plates can be beneficial by increasing the bearing area, which increases theside-faceblowoutstrength. Theconcretebreakoutcapacitiesassumethattheconcrete is uncracked. The designer should refer toACI 318-02 to determineiftheconcreteshouldbetakenascrackedoruncracked.Iftheconcreteisconsideredcracked,(ψ3=1.0)and 80%oftheconcretecapacityvaluesshouldbeused. DevelopmentbyLappingwithConcreteReinforcement Theextentofthestressconeisafunctionoftheembedment depth, the thickness of the concrete, the spacing between adjacentanchors,andthelocationofadjacentfreeedgesin theconcrete.Theshapesofthesestressconesforavarietyof situationsareillustratedinFigures3.2.1,3.2.2and3.2.3. Figure3.2.2.Breakoutconeforgroupanchorsinthinslab. Thestressconechecksrelyonthestrengthofplainconcrete for developing the anchor rods and typically apply when columns are supported directly on spread footings, concretemats,orpilecaps.However,insomeinstances,the projectedareaofthestressconesoroverlappingstresscones is extremely limited due to edge constraints. Consequently, the tensile strength of the anchor rods cannot be fully developed with plain concrete. In general, when piers are used, concrete breakout capacity alone cannot transfer the significantleveloftensileforcesfromthesteelcolumntothe concretebase.Intheseinstances,steelreinforcementinthe concreteisusedtocarrytheforcefromtheanchorrods.This reinforcementoftendoublesasthereinforcementrequiredto accommodatethetensionand/orbendingforcesinthepier. Thereinforcementmustbesizedanddevelopedfortherequiredtensilestrengthoftheanchorrodsonbothsidesofthe potentialfailureplanedescribedinFigure3.2.5. Ifananchorisdesignedtolapwithreinforcement,theanchorstrengthcanbetakenasφAseFyasthelapsplicelength willensurethatductilebehaviorwilloccur.Aseistheeffectivecross-sectionalarea,whichisthetensilestressareafor threadedrods.φ=0.90,asprescribedinChapter9ofACI 318-02. Figure3.2.3.Breakoutconeintensionnearanedge. 22 / DESIGN GUIDE 1, 2ND EDITION /BASEPLATEANDANCHORRODDESIGN Theanchorrodembedmentlengthsaredeterminedfrom the required development length of the spliced reinforcement.Hooksorbendscanbeaddedtothereinforcingsteel tominimizedevelopmentlengthinthebreakoutcone.From ACI318,anchorrodembedmentlengthequalsthetopcover to reinforcing plus Ld or Ldh (if hooked) plus 0.75 times g (seeFigure3.2.5).Theminimumlengthis17timestherod diameter. 3.3DesignofColumnBasePlateswithSmallMoments Drake and Elkin (1999) introduced a design approach usingfactoredloadsdirectlyinamethodconsistentwiththe equationsofstaticequilibriumandtheLRFDmethod.The procedurewasmodifiedbyDoyleandFisher(2005).Drake andElkinproposedthatauniformdistributionoftheresultant compressive bearing stress is more appropriate when utilizingLRFD.Thedesignisrelatedtotheequivalenteccentricitye,equaltothemomentMu,dividedbythecolumn axialforcePu. Forsmalleccentricities,theaxialforceisresistedbybearingonly.Forlargeeccentricities,itisnecessarytouseanchor rods.The definition of small and large eccentricities, based on the assumption of uniform bearing stress, is discussedinthefollowing.ThevariablesTu,Pu,andMuhave beenchangedfromtheoriginalworkbyDrakeandElkinto T,Pr,andMr,sothatthemethodisapplicabletobothLRFD andASD.Atriangularbearingstressapproachcanalsobe used,asdiscussedinAppendixB. ConsidertheforcediagramshowninFigure3.3.1.TheresultantbearingforceisdefinedbytheproductqY,inwhich q=fp×B (3.3.1) where fp = bearingstressbetweentheplateandconcrete B = thebaseplatewidth Theforceactsatthemidpointofbearingarea,orY/2tothe leftofpointA.Thedistanceoftheresultanttotherightofthe centerlineoftheplate,ε,is,therefore ε= N Y − 2 2 (3.3.2) ItisclearthatasthedimensionYdecreases,εincreases.Y willreachitssmallestvaluewhenqreachesitsmaximum: Ymin = Figure3.2.4.Lateralburstingforcesforanchorrods intensionnearanedge. Figure3.2.5.Theuseofsteelreinforcementfor developinganchorrods. Pr qmax (3.3.3) Figure3.3.1.Baseplatewithsmallmoment. DESIGNGUIDE1,2NDEDITION/BASEPLATEANDANCHORRODDESIGN/23 where q=fp(max)×B Thebearingstresscanthenbedeterminedas (3.3.4) Theexpression,forthelocationoftheresultantbearingforce giveninEquation3.3.2showsthatεreachesitsmaximum valuewhenYisminimum.Therefore ε max = P N Ymin N − = − u 2 2 2 2 qmax (3.3.5) q= for the small moment case, e ≤ ecrit. Therefore, as noted above,q≤qmax.FromEquations3.3.1and3.3.4,itfollows thatfp≤fp(max). Fortheconditione=ecrit,thebearinglength,Y,obtained byuseofEquations3.3.7and3.3.8is For moment equilibrium, the line of action of the applied load,Pu,andthatofthebearingforce,qYmustcoincide;that is,e=ε. Iftheeccentricity e= Mr Pr (3.3.6) exceeds the maximum value that ε can attain, the applied loads cannot be resisted by bearing alone and anchor rods willbeintension. Insummary,forvaluesofelessthanεmax,Yisgreaterthan Yminandqislessthanqmax,andobviously,fpislessthanfp(max). For values of e greater than εmax, q = qmax.Thus, a critical valueofeccentricityoftheappliedloadcombinationis ecrit = ε max P N = − r 2 2 qmax (3.3.7) Whenanalyzingvariousloadandplateconfigurations,in casee≤ecrit, therewillbenotendencytooverturn,anchor rodsarenotrequiredformomentequilibrium,andtheforce combinationwillbeconsideredtohaveasmallmoment.On the other hand, if e > ecrit, moment equilibrium cannot be maintainedbybearingaloneandanchorrodsarerequired. Suchcombinationsofaxialloadandmomentarereferredto aslargemomentcases.ThedesignofplateswithlargemomentsisoutlinedinSection3.4. N P P Y = N − 2 − r = r 2 2 qmax q max (3.3.9) 3.3.2BasePlateFlexuralYieldingLimitatBearing Interface Thebearingpressurebetweentheconcreteandthebaseplate willcausebendinginthebaseplateforthecantileverlength, m,inthecaseofstrongaxisbendingandcantileverlength, n,inthecaseofweakaxisbending.Forthestrongaxisbending,thebearingstressfp(ksi),iscalculatedas fp = Pr Pr = BY B ( N − 2e ) (3.3.10) The required strength of the base plate can be then determinedas ForY≥m: m 2 M pl = f p 2 (3.3.11) Y M pl = f p(max)Y m − 2 (3.3.12) ForY<m: where 3.3.1ConcreteBearingStress TheconcretebearingstressisassumedtobeuniformlydistributedovertheareaY×B.Equation3.3.2,for the case of e = ε, provides an expression for the length of bearing area,Y: Mpl = platebendingmomentperunitwidth Thenominalbendingresistanceperunitwidthoftheplate isgivenby N Y − =e 2 2 therefore, Y=N−(2)(e) Pr P ;fromwhichf p = r Y BY Rn = Fy t 2p 4 where (3.3.8) Fy = specifiedyieldstressoftheplatematerial tp = platethickness 24 / DESIGN GUIDE 1, 2ND EDITION /BASEPLATEANDANCHORRODDESIGN Theavailablestrength,perunitwidth,oftheplateis φb Rn = φb Fy t 2p 4 (LRFD) (3.3.13a) Fy t 2p Rn (ASD) = Ω Ω 4 (3.3.13b) where 3.3.3BasePlateFlexuralYieldingatTensionInterface Withthemomentsuchthate≤ecrit,therewillbenotension intheanchorrodsandthustheywillnotcausebendinginthe baseplateatthetensioninterface.Therefore,bearingatthe interfacewillgovernthedesignofthebaseplatethickness. 3.3.4GeneralDesignProcedure 1. Determinetheaxialloadandmoment. φb = strengthreductionfactorinbending=0.90 2. Pickatrialbaseplatesize,N×B. Ω = thesafetyfactorinbending=1.67 3. Determinetheequivalenteccentricity, To determine the plate thickness, equate the right-hand sidesofEquations3.3.11or3.3.12and3.3.13andsolvefor tp(req): ForY≥m: t p( req ) = t p( req ) = (3.3.14a) m 2 4 f p 2 = 1.83m f p (ASD) Fy / 1.67 Fy (3.3.14b) andthecriticaleccentricity, P N − r 2 2 qmax Ife≤ecrit,gotonextstep(designofthebaseplatewith small moment); otherwise, refer to design of the base platewithlargemoment(Section3.4). 4. Determinethebearinglength,Y. ForY<m: Y f p Y m − 2 (ASD) t p( req ) = 2.58 Fy e=M r/P r, ecrit = m 2 4 f p 2 = 1.5m f p (LRFD) Fy 0.90 Fy Y f p Y m − 2 (LRFD) t p( req ) = 2.11 Fy 5. Determine the required minimum base plate thickness tp(req). 6. Determinetheanchorrodsize. (3.3.15a) (3.3.15b) where tp(req) = minimumplatethickness Note:When n is larger than m, the thickness will be governedbyn.Todeterminetherequiredthickness,substituten forminEquations3.3.14,and3.3.15.Whilethisapproach offersasimplemeansofdesigningthebaseplateforbending,whenthethicknessoftheplateiscontrolledbyn,the designermaychoosetouseothermethodsofdesigningthe plateforflexure,suchasyield-lineanalysisoratriangular pressuredistributionassumption,asdiscussedinAppendixB. 3.4DesignofColumnBasePlateswithLargeMoments Whenthemagnitudeofthebendingmomentislargerelative to the column axial load, anchor rods are required to connectthebaseplatetotheconcretefoundationsothatthe basedoesnottipnorfailtheconcreteinbearingatthecompressed edge.This is a common situation for rigid frames designedtoresistlateralearthquakeorwindloadingsandis schematicallypresentedinFigure3.4.1. Asdiscussedintheprevioussection,largemomentconditionsexistwhen e > ecrit = P N − r 2 2 qmax (3.3.1) 3.4.1ConcreteBearingandAnchorRodForces Thebearingpressure,q,isequaltothemaximumvalue,qmax, foreccentricitiesgreaterthanecrit.Tocalculatethetotalconcretebearingforceandtheanchorrodforces,considerthe forcediagramshowninFigure3.4.1. DESIGNGUIDE1,2NDEDITION/BASEPLATEANDANCHORRODDESIGN/25 Verticalforceequilibriumrequiresthat 2 2 P e + f ) f + N ≥ r ( 2 q max ∑ Fvertical = 0 T=qmaxY−Pr (3.4.2) whereTequalstheanchorrodrequiredtensilestrength. Also,thesummationofmomentstakenaboutthepointB mustequalzero.Hence, N Y qmaxY − + 2 2 f − Pr ( e + f ) = 0 After rearrangement, a quadratic equation for the bearing length,Y,isobtained: 2 Pr (e + f ) N Y 2 − 2 + f Y + =0 2 qmax N Y = f + ± 2 2 2 P e + f ) f + N − r ( 2 qmax willthequantityundertheradicalinEquation3.4.3bepositiveorzeroandprovidearealsolution.Iftheexpressionin Equation3.4.4isnotsatisfied,alargerplateisrequired. SubstitutionofthecriticalvalueofefromEquation3.3.7 intoEquation3.4.3resultsinthefollowingexpressionforY: N Y = f + ± 2 f f + N − Pr 2 P r 2 2 2qmax N + − qmax 2 Rearrangingterms: N Y = f + ± 2 andthesolutionforYis (3.4.4) 2 2 f + N − 2 Pr f + N + Pr 2 2 qmax qmax P N N = f + ± f + − r 2 2 qmax (3.4.3) TheconcretebearingforceisgivenbytheproductqmaxY.The anchorrodtensileforce,T,isobtainedbysolvingEquation 3.4.2. Forcertainforce,moment,andgeometrycombinations,a realsolutionofEquation3.4.3isnotpossible.Inthatcase, an increase in plate dimensions is required. In particular, onlyifthefollowingholds Finally,useofthenegativesignbeforethelasttermgives thevalueforY: Y= Pr q max 3.4.2BasePlateYieldingLimitatBearingInterface For the case of large moments, the bearing stress is at its limitingvalue: fp=fp(max) Therequiredplatethicknessmaybedeterminedfromeither Equation3.3.14or3.3.15: IfY≥m: t p( req ) = 1.5m t p( req ) = 1.83m f p(max) Fy (LRFD) f p(max) Fy (ASD) (3.3.14a) (3.3.14b) IfY<m: Y f p(max)Y m − 2 (LRFD) t p( req ) = 2.11 Fy Figure3.4.1.Baseplatewithlargemoment. 26 / DESIGN GUIDE 1, 2ND EDITION /BASEPLATEANDANCHORRODDESIGN (3.3.15a) Y f p(max)Y m − 2 (ASD) t p( req ) = 2.58 Fy andthecriticaleccentricity, (3.3.15b) ecrit = P N − r 2 2 qmax Note:When n is larger than m, the thickness will be governedbyn.Todeterminetherequiredthickness,substituten forminEquations3.3.14and3.3.15. Ife>ecrit,gotonextstep(designofthebaseplatewith largemoment);otherwise,refertodesignofthebaseplate withsmallmomentdescribedinSection3.3. 3.4.3BasePlateYieldingLimitatTensionInterface ChecktheinequalityofEquation3.4.4.Ifitisnotsatisfied,chooselargerplatedimensions. ThetensionforceTu(LRFD),Ta(ASD)intheanchorrods will cause bending in the base plate. Cantilever action is conservatively assumed with the span length equal to the distancefromtherodcenterlinetothecenterofthecolumn flange,x.Alternatelythebendinglinescouldbeassumedas showninFigure3.1.1.Foraunitwidthofbaseplate,therequiredbendingstrengthofthebaseplatecanbedeterminedas M pl = M pl Tu x (LRFD) B T x = a (ASD) B (3.4.5a) (3.4.5b) (3.4.6) d = depthofwideflangecolumnsection(seeFig.3.1.1) tf = columnflangethickness t p( req ) = 2.58 Ta x (ASD) BFy 3.4.4GeneralDesignProcedure 1. Determinetheaxialloadandmoment. 2. Pickatrialbaseplatesize,N×B. 3. Determinetheequivalenteccentricity There are three principal ways of transferring shear from columnbaseplatesintoconcrete: 1. Frictionbetweenthebaseplateandthegroutorconcrete surface. 3. Shearintheanchorrods. 3.5.1Friction Theavailablestrengthperunitlengthfortheplateisgiven inEquation3.3.13.Settingthatstrengthequaltotheapplied momentgivenbyEquation3.4.5providesanexpressionfor therequiredplatethickness: Tu x (LRFD) BFy 6.Determinetheanchorrodsize. 2. Bearingofthecolumnandbaseplate,and/orshearlug, againstaconcretesurface. with t p( req ) = 2.11 5. Determine the required minimum base plate thickness tp(req)atbearingandtensioninterfaces.Choosethelarger value. 3.5DesignforShear where d tf x= f − + 2 2 4. Determine the equivalent bearing length, Y and tensile forceintheanchorrod,Tu(LRFD),Ta(ASD). (3.4.7a) In typical base plate situations, the compression force betweenthebaseplateandtheconcretewillusuallydevelop shear resistance sufficient to resist the lateral forces. The contribution of the shear should be based on the most unfavorable arrangement of factored compressive loads, Pu, thatisconsistentwiththelateralforcebeingevaluated,Vu. TheshearstrengthcanbecalculatedinaccordancewithACI criteria, φVn=φµPu≤0.2fc′Ac (3.4.7b) Thefrictioncoefficientµis0.55forsteelongrout,and0.7 forsteelonconcrete. 3.5.2Bearing Shearforcescanbetransferredinbearingbytheuseofshear lugsorbyembeddingthecolumninthefoundation.These methodsareillustratedinFigure3.5.1. e=Mr/Pr DESIGNGUIDE1,2NDEDITION/BASEPLATEANDANCHORRODDESIGN/27 Whenshearlugsareused,AppendixBofACI349-01permits use of confinement in combination with bearing for transferring shear from shear lugs into the concrete. The commentarytoACI349-01suggeststhismechanismisdevelopedasfollows: 1. Shear is initially transferred through the anchor rods to thegroutorconcretebybearingaugmentedbyshearresistancefromconfinementeffectsassociatedwithtension anchorsandexternalconcurrentaxialload. 2. Shearthenprogressesintoashear-frictionmode. TherecommendedbearinglimitφPubrgperSectionB.4.5.2 ofACI349-01,AppendixB,isφ1.3fc′A1.Usingaφconsistent withASCE 7 load factors (φ = 0.60), φPubrg ≈ 0.80fc′ A1andA1=embeddedareaoftheshearlug(thisdoesnot includetheportionofthelugincontactwiththegroutabove thepier). For bearing against an embedded base plate or column section where the bearing area is adjacent to the concrete surface,ACI 318-02 recommends that φPubrg = 0.55fc′Abrg, andAbrg=contactareabetweenthebaseplateand/orcolumn againsttheconcrete,in2. AccordingtotheCommentaryofAppendixBofACI34901,theanchorageshearstrengthduetoconfinementcanbe takenasφKc(Ny−Pa),withφequalto0.75,whereNyisthe yield strength of the tension anchors equal to nAseFy, and Paisthefactoredexternalaxialloadontheanchorage.(Pa is positive for tension and negative for compression.)This shearstrengthduetoconfinementconsiderstheeffectofthe tensionanchorsandexternalloadsactingacrosstheinitial shearfractureplanes.WhenPaisnegative,onemustverify thatPawillactuallybepresentwhiletheshearforceisoccurring.BasedonACI349-01Commentary,Kc=1.6. Insummary,thelateralresistancecanbeexpressedas φPn = 0.80fc′A+1.2(Ny−Pa)forshearlugs φPn = 0.55fc′ Abrg+1.2(Ny−Pa)forbearingonacolumnorthesideofabaseplate If the designer wishes to use shear-friction strength as well,theprovisionsofACI349-01canbefollowed.Additionalcommentsrelatedtotheuseofshearlugsareprovided here: 1. Forshearlugsorcolumnembedmentsbearinginthedirectionofafreeedgeoftheconcrete,AppendixBofACI 349-01statesthat,inadditiontoconsideringbearingfailure in the concrete, “the concrete design shear strength forthelugshallbedeterminedbasedonauniformtensile stressof 4φ f c′ actingonaneffectivestressareadefined by projecting a 45° plane from the bearing edge of the shear lug to the free surface.” The bearing area of the shearlug(orcolumnembedment)istobeexcludedfrom theprojectedarea.Useφ=0.75.Thiscriterionmaycontrolorlimittheshearcapacityoftheshearlugorcolumn embedmentdetailsinconcretepiers. 2. Consideration should be given to bending in the base plateresultingfromforcesintheshearlug.Thiscanbeof specialconcernwhenthebaseshears(mostlikelydueto bracingforces)arelargeandbendingfromtheforceon theshearlugisabouttheweakaxisofthecolumn.Asa ruleofthumb,theauthorsgenerallyrequirethebaseplate tobeofequalorgreaterthicknessthantheshearlug. 3. Multiple shear lugs may be used to resist large shear forces.Appendix B ofACI 349-01 provides criteria for thedesignandspacingofmultipleshearlugs. 4. Groutpocketsmustbeofsufficientsizeforeaseofgrout placement. Nonshrink grout of flowable consistency shouldbeused. ThedesignofashearlugisillustratedinExample4.9. Figure3.5.1.Transferofbaseshearsthroughbearing. 28 / DESIGN GUIDE 1, 2ND EDITION /BASEPLATEANDANCHORRODDESIGN 3.5.3ShearinAnchorRods It should be noted that the use of anchor rods to transfer shearforcesmustbecarefullyexaminedduetoseveralassumptions that must be made. Particular attention must be paidtothemannerinwhichtheforceistransferredfromthe baseplatetotheanchorrods. UsingtheAISC-recommendedholesizesforanchorrods, which can be found in Table 2.3, considerable slip of the baseplatemayoccurbeforethebaseplatebearsagainstthe anchorrods.Theeffectsofthisslipmustbeevaluatedbythe engineer.Thereaderisalsocautionedthat,duetoplacement tolerances,notalloftheanchorrodswillreceivethesame force. Theauthorsrecommendacautiousapproach,suchasusingonlytwooftheanchorrodstotransfertheshear,unless specialprovisionsaremadetoequalizetheloadtoallanchor rods(Fisher,1981).Lateralforcescanbetransferredequally to all anchor rods, or to selective anchor rods, by using a platewasherweldedtothebaseplatebetweentheanchorrod nutandthetopofthebaseplate.Theplatewashersshould haveholeszin.largerthantheanchorroddiameter.Alternatively, to transfer the shear equally to all anchor rods, a settingplateofproperthicknesscanbeusedandthenfield weldedtothebaseplateafterthecolumniserected.Itcannotbeemphasizedenoughthattheuseofshearintheanchor rodsrequiresattentioninthedesignprocesstotheconstructionissuesassociatedwithcolumnbases. Oncetheshearisdeliveredtotheanchorrods,theshear must be transferred into the concrete. If plate washers are usedtotransfersheartotherods,somebendingoftheanchorrodscanbeexpectedwithinthethicknessofthebase plate. If only two anchor rods are used for shear transfer, assuggestedearlier,theshearistransferredwithinthebase plate, and bending of the rods can be neglected. Based on shearfrictiontheory,nobendingoftheanchorrodwithinthe grout need be considered.The moment in the anchor rods canbedeterminedbyassumingreversecurvaturebending. Theleverarmcanbetakenasthehalfdistancebetweenthe centerofbearingoftheplatewashertothetopofthegrout surface.Whereanchorsareusedwithabuilt-upgroutpad, ACI318-02requiresthattheanchorcapacitybemultiplied by0.8.Noexplanationofthereductionisprovided;however,itistheauthors’understandingthattherequirementisto adjustthestrengthtoaccountforbendingoftheanchorrods withinthegroutpad.Limitationsongroutpadthicknesses are not provided. It is the authors’ opinion that the reductionisnotrequiredwhenAISCcombinedbendingandshear checksaremadeontheanchorrods,andtheresultingareaof theanchorrodis20%largerthantherodwithoutshear. AppendixDofACI318-02employstheCCDmethodto evaluate the concrete breakout capacity from shear forces resistedbyanchorrods. Forthetypicalcast-in-placeanchorgroupusedinbuildingconstruction,theshearcapacitydeterminedbyconcrete breakoutasillustratedinFigure3.5.2isevaluatedas φVcbg = φ Av ψ 5 ψ 6 ψ 7Vb ,kips Avo where 0.2 do Vb = 7 d o f c′ c11.5 c1 = theedgedistance(in.)inthedirectionofloadas illustratedinFigure3.5.2 fc′ = concretecompressivestrength,ksi = theembedmentdepth,in. do = theroddiameter,in.(Typically,/dobecomes8 sincetheloadbearinglengthislimitedto8do.) φ = 0.70 ψ5 = 1(allanchorsatsameload) ψ7 = 1.4(uncrackedorwithadequatesupplementary reinforcement). Figure3.5.2.Concretebreakoutconeforshear. DESIGNGUIDE1,2NDEDITION/BASEPLATEANDANCHORRODDESIGN/29 Substituting, φVcbg = 10.4 Av ψ 6 do Avo f c′ c11.5 Avo = 4.5c12(theareaofthefullshearconeforasingle anchorasshowninViewA-AofFigure3.5.2) Av = thetotalbreakoutshearareaforasingleanchor, oragroupofanchors ψ6 = amodifiertoreflectthecapacityreductionwhen sidecoverlimitsthesizeofthebreakoutcone Itisrecommendedthattheroddiameter,do,usedinthesquare roottermoftheVbexpression,belimitedtoamaximumof 1.25in.,basedonresearchresultsconductedattheUniversityofStuttgart.Iftheedgedistancec1islargeenough,then theanchorrodshearstrengthwillgovern.Thenominalshear strengthofasingleanchorrodequals0.4FuAr,ifthethreads are not excluded from the shear plane, and 0.5FuAr, if the threadsareincluded;φ=0.55andΩ=2.75.ACI318-02AppendixDrecognizesthebenefitofthefrictionandallowsthe sharingoftheanchorrodshearwiththefrictiondeveloped fromfactoredaxialandflexuralload. Inevaluatingtheconcretebreakoutstrength,thebreakout eitherfromthemostdeeplyembeddedanchorsorbreakout ontheanchorsclosertotheedgeshouldbechecked.When breakoutisbeingdeterminedontheinnertwoanchors(those farthestfromtheconcreteedge)theoutertwoanchors(those closesttotheconcreteedge)shouldbeconsideredtocarry the same load. When the concrete breakout is considered fromtheoutertwoanchors,allofshearistobetakenbythe outeranchors.ShowninFigure3.5.3arethetwopotential breakout surfaces and an indication of which will control, basedonanchorlocationrelativetotheedgedistance. Inmanycasesitisnecessarytousereinforcementtoanchorthebreakoutconetoachievetheshearstrengthaswell astheductilitydesired.Tiesplacedatoppiersasrequiredin Section7.10.5.6ofACI318-02canalsobeusedstructurally totransfertheshearfromtheanchorstothepiers. In addition to the concrete breakout strength, ACI also containsprovisionsforalimitstatecalledpryoutstrength. The authors have checked several common situations and havenotfoundpryoutstrengthtocontrolfortypicalanchor roddesigns.ACIdefinesthepryoutstrengthas Ncp = nominalconcretebreakoutstrengthintensionof asingleanchor,kips hef = effectiveanchorembedmentlength,in. 3.5.4InteractionofTensionandShearintheConcrete Whentheconcreteissubjectedtoacombinationofpullout andshear,ACI318,AppendixD,usesaninteractionequation solution.The reader is referred toACI for further explanation. 3.5.5HairpinsandTieRods Tocompletethediscussiononanchoragedesign,transferof shearforcestoreinforcementusinghairpinsortierodswill beaddressed.Hairpinsaretypicallyusedtotransferloadto thefloorslab.Thefrictionbetweenthefloorslabandthesubgradeisusedinresistingthecolumnbaseshearwhenindividualfootingsarenotcapableofresistinghorizontalforces. Thecolumnbaseshearsaretransferredfromtheanchorrods to the hairpin (as shown in Figure 3.5.4) through bearing. Problems have occurred with the eccentricity between the baseplateandthehairpinduetobendingintheanchorrods afterthefrictioncapacityisexceeded.Thisproblemcanbe avoidedasshowninFigure3.5.5orbyprovidingshearlugs. Sincehairpinsrelyuponthefrictionalrestraintprovidedby thefloorslab,specialconsiderationshouldbegiventothe locationandtypeofcontrolandconstructionjointsusedin thefloorslabtoensurenointerruptioninloadtransfer,yet stillallowingtheslabtomove.Inaddition,avaporbarrier shouldnotbeusedundertheslab. Vcp=kcpNcp where kcp = 1.0forhef≤2.5in.and = 2.0forhef>2.5in. Figure3.5.3.Concretebreakoutsurfacesforgroupanchors. 30 / DESIGN GUIDE 1, 2ND EDITION /BASEPLATEANDANCHORRODDESIGN Tierods(continuousrodsthatrunthroughtheslabtothe oppositecolumnline)aretypicallyusedtocounteractlarge shear forces associated with gravity loads on rigid frame structures.When using tie rods with large clear span rigid frames,considerationshouldbegiventoelongationofthe tierodsandtotheimpactoftheseelongationsontheframe analysisanddesign.Inaddition,significantamountsofsagging or bowing should be removed before tie rods are encased or covered, since the tie rod will tend to straighten whentensioned. Tierodsandhairpinbarsshouldbeplacedasclosetothe top surface of the concrete slab as concrete cover requirementsallow. 4.0DESIGNEXAMPLES 4.1Example:BasePlateforConcentricAxial CompressiveLoad(Noconcreteconfinement) AW12×96columnbearsona24-in.×24-in.concretepedestal.Theminimumconcretecompressivestrengthisfc′=3 ksi,andthebaseplateyieldstressisFy=36ksi.Determine thebaseplateplandimensionsandthicknessforthegiven requiredstrength,usingtheassumptionthatA2=A1(CaseI). 1. Therequiredstrengthduetoaxialloads. LRFD ASD Pu=700kips Pa=430kips 2. Calculatetherequiredbaseplatearea. LRFD A1( req ) = = ASD Pu φ0.85 f c′ 700 kips (0.65)(0.85)(3ksi) = 422in.2 Figure3.5.4.Typicaldetailusinghairpinbars. A1( req ) = = ΩPa 0.85 f c′ 430 kips × 2.50 (0.85)(3ksi) = 422in.2 Note: Throughout these examples a resistance factor for bearingonconcreteofφ=0.65hasbeenapplied,perACI 318-02. This resistance factor is more liberal than the resistance factor of φ = 0.60 presented in the 2005 AISC Specification.AlthoughitwasintendedthattheAISCprovision would match theACI provision, this deviation was overlooked. As both documents are consensus standards endorsed by the building code, andACI 318-02 has been adoptedbyreferenceintothe2005AISCSpecificationfor Structural Steel Buildings, the authors consider a φ factor of0.65appropriateforuseindesign.However,ACI318is writtenusingstrengthdesignonlyanddoesnotpublishan equivalentΩfactor.Therefore,anΩ=2.50hasbeenused intheASDcalculationspresentedheretoremainconsistent withthevaluepublishedintheAISCSpecification. 3. Optimizethebaseplatedimensions,NandB. ∆= 0.95d − 0.8b f 2 0.95 (12.7 in.) − 0.8 (12.2 in.) = 2 = 1.15in. N ≈ A1( req ) + ∆ Figure.3.5.5Alternatehairpindetail. ≈ 422 in.2 + 1.15in. ≈ 21.7 in. DESIGNGUIDE1,2NDEDITION/BASEPLATEANDANCHORRODDESIGN/31 ∆= 0.95d − 0.8b f 2 ( 0.95 12.7 in.) − 0.8 (12.2 in.) = 2 = 1.15in. N ≈ A1( req ) + ∆ λ= 2 ≈ 422 in. + 1.15in. ≈ 21.7 in. TryB=20 A1=(22)(20)=440in.2>422in.2 Pa ≤ ) × 440in.2 2 440in. = 729 kips > 700kipso.k. Pp Ω 0.85 f c′A1 = A2 A1 2.50 440in.2 (0.85)(3ksi) 440in. 440in.2 = 2.50 = 499 kips > 430 kipso.k. ( 2 N − 0.95d 2 22 in. − 0.95 (12.7 in.) = 2 = 4.97 in. B − 0.8b f 700 kips 4(12.7 in.)(12.2 in.) = (12.7 in. + 12.2 in.) 2 729kips = 0.96 = max(4.97in.,5.12in.,3.11in.) = 5.12in. LRFD tmin = l 2 Pu φFy BN (2)(700) (0.9)(36)(20)(22) = 1.60in. Usetp=1win. ASD tmin = l tmin = 5.12 2ΩPa Fy BN (2)(430) (1.67) (36)(20)(22) = 1.54 in. Usetp=1win. 7. Determinetheanchorrodsize,andtheirlocations. Sincenoanchorrodforcesexist,theanchorrodsizecan be determined based on the OSHA requirements, and practicalconsiderations. 2 2 in. − 0.8 (12.2 in.) = 2 = 5.12 in. P 4db f u X = 2 φP d b + ( ) f p l = max(m,n,λn′) tmin = 5.12 m= LRFD 4 ) 6. Calculaterequiredbaseplatethickness. n= 4 (12.7 in.)(12.2 in.) = 3.11 ASD A2 A1 db f = (1) 5. Determineifthefollowinginequalityismet. ( 2 0.96 λn ′ = λ LRFD ≤ 1.0 1 + 1− 0.96 = 1.63 ⇒ 1 TryN=22in. B=422/22=19.2in. = (0.65)(0.85)(3ksi) 440in.2 1 + 1− X = 4. CalculateA2geometricallysimilartoA1. Pu ≤ φPp = φ0.85 f c′A1 2 X Use4w-in.-diameterrods,ASTMF1554,Grade36. Rodlength=12in. ASD ΩP 4db a f X = (d + b f ) 2 Pp 4(12.7 in.)(12.2 in.) 430 kips = 2 449kips (12.7 in. + 12.2 in.) = 0.96 4.2Example:BasePlateforConcentricAxial CompressiveLoad(Usingconcreteconfinement) Determine the base plate plan dimensions from Example 4.1,usingconcreteconfinement(CaseIII). 1. Calculatetherequiredaxialcompressivestrength. LRFD ASD Pu=700kips Pa=430kips 2.Calculatetherequiredbaseplateareausingthestrength increaseforconcreteconfinement. 32 / DESIGN GUIDE 1, 2ND EDITION /BASEPLATEANDANCHORRODDESIGN LRFD A1( req ) = = ASD Pu 2φ0.85 f c′ 700 kips (2)(0.65)(0.85)(3ksi) A1( req ) = = Pa Ω 2× 0.85 f c′ 430 kips × 2.50 (2)(0.85)(3ksi) LRFD 6.DetermineifPu≤φcPp,if 6. DetermineifPa≤Pp /Ω, if not revise N and B, and not revise N and B, and retry until criterion is retry until criterion is satisfied. satisfied. φPp = φ0.85 f c′A1 2 2 = 211in. = 211in. 3. Optimizethebaseplatedimensions,NandB. ∆= 0.95d − 0.8b f N ≈ A1( req ) + ∆ 2 = (0.65)(0.85)(3ksi)(360in. ) 518in.2 360in.2 Basedonthe24-in.pier, B2 = (0.88)(24)=21.12in. A2 = (24)(21.12)=507 518in.2 360in.2 2.50 Pa ≤ Pp Ω 700kips≤716kipso.k. 430kips≤400kipso.k. UseN=20in.,B=18in. UseN=20in.,B=18in. N − 0.95d 2 20 in. − 0.95(12.7 in.) = 2 =3.97in. 5. Usetrialanderrorsolution. TryN = 20in. B = 18in. A1 = (20)(18)=360in.2 N2= 24in. B − 0.8b f 2 18.5in. − 0.8(12.2 in.) = 2 =4.37in. 507 ≤ 4A1=(4)(211)=844in.2 CaseIIIapplies. Ω (0.85)(3ksi)(360in.2 ) Pu≤φPp n= A2 A1 = 440 kips 4. CalculateA2geometricallysimilartoA1. RatioB/N = 14/16=0.88 = = = 716 kips TryB=14in. 0.85 f c′A1 m= TryN=16in. B=211/16=13.2 N2 = 24in. Pp 7. Calculaterequiredbaseplatethickness. ≈ 211in.2 + 1.15in. ≈ 15.7 in. A2 A1 Ω × 2 0.95(12.7 in.) − 0.8(12.2 in.) = 2 = 1.15in. ASD LRFD ASD 4db P u f X = 2 φP ( ) + d b f p 4db f ΩPa X = 2 (d + b f ) P p 4(12.7 in.)(12.2 in.) 700 kips = (12.7 in. + 12.2 in.) 2 716 kips = 0.98 4(12.7 in.)(12.2 in.) 700 kips = 2 (12.7 in. + 12.2 in.) 716 kips = 0.98 λ= RatioB/N = 18/20=0.9 = B2 = (0.9)(24)=21.6in. A2 = (24)(21.6)=518in. 2 2 X 1 + 1− X 2 0.98 1 + 1− 0.98 = 1.73 ⇒ 1 DESIGNGUIDE1,2NDEDITION/BASEPLATEANDANCHORRODDESIGN/33 λn ′ = λ Assuminguncrackedconcrete,ψ3=1.25.Forasinglerod, AN=ANo. db f = (1) 4 (12.7 in.)(12.2 in.) 1.5 φN cbg = 0.7(1.25) 24 4, 000 (6) 4 = 19, 500 lbor19.5kips = 3.11 l = max(m,n,λn′) = max(3.97in.,4.37in.,3.11in.) = 4.37in. LRFD tmin = l 2 Pu φFy BN (2)(700) (0.90)(36)(18)(20) = 4.37 = 1.5in. Usetp=12in. ASD tmin = l 2 Pa Ω Fy BN (2)(430) (1.67) (36)(18)(20) = 4.37 = 1.5in. Usetp=12in. 4.3Example:AvailableTensileStrengthofaw-in. AnchorRod Calculatetheavailabletensilestrengthofaw-in.-diameter ASTMF1554Grade36anchorrod. Rn=(0.75)FuAr=(0.75)(58)(0.442)=19.2kips where Fu = 58ksi Ar = 0.442in.2 Notethatthebreakoutstrengthistheoreticallyindependentofthesizeoftheanchorrod.Thisembedmentatonly6in. isenoughtomakethedesigntensilestrengthofaGrade36 anchorroduptow-in.-diametergovernthedesign. As discussed in Section 3.2.2, theACI pullout strength equationsdonottypicallycontrolprovidedthattheanchor rodyieldstrengthdoesnotexceed36ksi.Inthiscase,the pulloutstrengthshowninTable3.2maybemultipliedby1.4 toobtainthepulloutstrength,astheconcreteisuncracked. Theresultingpulloutstrengthis φNp=1.4×15.2=21.3>19.5 NoequivalentASDsolutiontothischeckexistsinACI318-02. 4.5Example:ColumnAnchorageforTensileLoads DesignabaseplateandanchorageforaW10×45columnsubjectedtoanetuplift,asaresultofthenominalloadsshownin Figure4.5.1. Procedure: 1. Determinetherequiredstrengthduetoupliftonthecolumn. 2. Selectthetypeandnumberofanchorrods. Theavailabletensilestrengthisdeterminedas LRFD ASD φRn=(0.75)(19.2) =14.4kips Rn/Ω=19.2/2.00 =9.6kips 3. Determinetheappropriatebaseplatethicknessandwelding to transfer the uplift forces from the column to the anchorrods. 4. Determinethemethodfordevelopingtheanchorrodsin theconcreteinthespreadfooting. 5. Reevaluatetheanchorageifthecolumnisona20-in.× 20-in.pier. Alternatively the rod strength could be obtained in accordancewithACIAppendixD. 4.4Example:ConcreteEmbedmentStrength Calculate the tensile design strength of the concrete for a single smooth w-in.-diameter headed anchor rod with an embedment length of 6 in.TheACI concrete breakout designstrength(usingequationforhef≤11in.)foruncracked 4,000=psiconcreteis A φ N cbg =φψ 3 24 f c′ hef 1.5 N ANo Figure4.5.1.NominalloadingdiagramforExample4.5. 34 / DESIGN GUIDE 1, 2ND EDITION /BASEPLATEANDANCHORRODDESIGN 1. Determine the required strength due to uplift on the column. Therequiredmomentstrengthofthebaseplateequalsthe rodforcetimestheleverarmtothecolumnwebface. LRFD ASD LRFD ASD Uplift=1.6WL−0.9DL Uplift=WL–0.6(DL) =1.6(56)−0.9(22) =69.8kips =56−(0.6)22=42.8kips 0.350 M u = 17.5 2 − 2 0.350 M a = 10.7 2 − 2 = 31.9 in.-kips = 19.5in.-kips 2. Selectthetypeandnumberofanchorrods.Usefouranchorrods(minimumperOSHArequirements). LRFD ASD T/rod=69.8/4=17.5kips T/rod=42.8/4=10.7kips Theeffectivewidthofbaseplateforresistingtherequired momentstrengthatthefaceofweb=beff. Usinga45°distributionfortherodloads(widthshown betweenthedashedlinesinFigure4.5.2), 0.350 beff = 2 − (2) = 3.65in. 2 UsinganASTMF1554Grade36material,selectad-in.diameterrod. Z= 4 Fy = 36 ksi Rn=0.75FuAr=(0.75)(58)(0.6013)=26.1kips LRFD ASD Thedesignstrengthoftherod Theallowablestrengthofthe =φRn anchorrod=Rn/Ω φRn = (0.75)(26.1) = 19.6 kips/rod > 17.5o.k. Rn / Ω = (26.1) / 2.00 = 13.1kips/rod > 10.7 o.k. 3. Therodsarepositionedinsidethecolumnprofilewitha 4-in.squarepattern.Pryingforcesarenegligible.Tosimplifytheanalysis,conservativelyassumethetensileloads intheanchorrodsgenerateone-waybendinginthebase plate about the web of the column. This assumption is illustratedbytheassumedbendinglinesshowninFigure 4.5.2.Ifthecolumnwebstrengthcontrolsthedesign,then considerdistributingtheforcestotheflangesaswellas theweb.Iftheboltsareplacedoutsideoftheflanges,the 45°loaddistributioncanbeusedtodistributetheforces totheflanges. beff t 2 LRFD treq’ d = = ASD M u ( 4) treq’ d = beff (φFy ) (31.9)(4) = 1.04 in. (3.65)(0.90)(36) = M a ( 4) Ω beff ( Fy ) (19.5)(4)( 1.67 ) = 0.991in. (3.65)(36) Usea1-in.-thickplate (Fy=36ksi). Usea14-in.-thickplate (Fy=36ksi). Forweldingofthecolumntothebaseplate: Maximumweldload = LRFD = T / Bolt beff ASD 17.5 = 4.79 kips/in . 3.65 = 10.7 = 2.93kips/in . 3.65 Minimumweldfor0.35in.columnweb=xin.(Table J2.4ofAISCSpecification). Nominal weld strength per inch for a x-in. fillet weld withE70electrode(usingthe50%directionalincrease): Rn = Fw Aw Figure4.5.2.Rodloaddistribution. = (1.5)(0.60)(70)(0.707)(3 / 16) = 8.35kips/in. DESIGNGUIDE1,2NDEDITION/BASEPLATEANDANCHORRODDESIGN/35 LRFD ASD φRn=(0.75)(8.35)=6.26kips/in. Rn/Ω=(8.35)/2.0=4.16kips/in. 4.79<6.26 2.93<4.16 x-in.filletweldoneachsideof thecolumnwebiso.k. x-in.filletweldoneachsideofthe columnwebiso.k. Checkweb: Webstress=Forceperin./Areaofwebperin. LRFD ASD 2× 4.79kips/in. 2× 2.93kips/in. Webstress = 0.35in. 0.35in. = 27.4 ksiinweb = 16.7 ksiinweb < Fy / 1.67 ofcolumn,o.k. < 0.9 Fy ofcolumn,o.k. Thus,a32-in.hookisnotcapableofdevelopingtherequiredtensileforceintherod. Therefore, use a heavy hex nut to develop the anchor rod. Thepulloutstrengthofad-in.-diameteranchorrodfrom Table3.2is20.5kips,whichisgreaterthantherequired strengthperanchorrod. The required embedment depth to achieve a concrete breakoutstrength,φNcbg,thatexceedstherequireduplift of69.8kipscanbedeterminedbytrialanderror.Thefinal trialwithanembedmentlengthof13in.isshownbelow. Webstress = 4. Asnotedearlier,thiscolumnisanchoredinthemiddle of a large spread footing. Therefore, there are no edge constraintsontheconcretetensileconesandthereisno concernregardingedgedistancetopreventlateralbreakoutoftheconcrete. Try using a 32-in. hook on the embedded end of the anchor rod to develop the rod.As mentioned earlier in this Guide, the use of hooked anchor rods is generally notrecommended.Theirusehereistodemonstratetheir limitedpulloutstrength. NotethatnoequivalentASDsolutionexistsforconcrete bearingcapacity. Basedonuniformbearingonthehook,thehookbearing capacityperACI318-02AppendixD =φ(0.9)(fc′)(do)(eh)(ψ4) Per ACI 318-02, Appendix D, the concrete breakout strength: AN forhef ≤ 11in. ANo φ N cbg =φψ 316 f c′ hef 5 / 3 AN forhef > 11in. ANo and where φ = 0.70 ψ3 = 1.25consideringtheconcretetobeuncracked hef = 13in. AN = concretebreakoutconeareaforgroup =[3(13)+(4)(3)(13)+4]=1,849in.2 where φ N cbg =φψ 3 24 f c′ hef 1.5 ANo = concretebreakoutconeareaforsingleanchor= 9(13)2=1,521in.2 1850 φN cbg = 0.70(1.25)(16) 4, 000 (13)5 / 3 1520 φ = 0.70 f′c = concretecompressivestrength do = hookdiameter eh = hookprojection Withthed-in.-diameteranchors,a13-in.embedmentis adequatetoachievetheanchorcapacityconsideringthe fullbreakoutcapacity. ψ4 = cracking factor (1.0 for cracked, 1.4 for uncrackedconcrete) Hookbearingcapacity= = = 0.70(0.9)(4,000) ×(7/8)(3.5−0.875)(1.4) 8,100lb 8.10kips<17.50kipsn.g. = 77,400lb=77.4kips>69.8kipso.k. 5. Iftheanchorswereinstalledina20-in.squarepier,the concretebreakoutstrengthwouldbelimitedbythepier cross section. With an 8-in. maximum edge distance, theeffectivehefneedbeonly8/1.5=5.33in.tohavethe breakout cone area equal the pier cross sectional area. 36 / DESIGN GUIDE 1, 2ND EDITION /BASEPLATEANDANCHORRODDESIGN Thisleadsto N>d+(2)(3.0in).=18.7in. 202 φN cbg = 0.70(1.25)(24) 0.004 (5.33)1.5 9(5.33) 2 B>df+(2)(3.0in.)=18.2in. = 25.5kips<69.8kipsn.g. TryN=19in.andB=19in. 3. Determineeandecrit. Thus, it is necessary to transfer the anchor load to the verticalreinforcingsteelinthepier.Therequiredareaof steelAS=69.8kips/0.9(60)=1.29in.2Theminimum4-#7 barsrequiredperACI318-02inthepierareadequateto takethistension.Withthebarslocatedinthecornersof thepiers,usealateraloffsetdistance,g=[(20in.−4in.)/ (2−2.4in.)]√2.UsingaClassBsplicefactorwitha1.3 LRFD e= ASD Mu 940 = = 2.5in. 376 Pu A2 A1 f p ( max ) = φc (0.85 f c′) 1.3 d e 1.3(24.9) = = 69.8 nAs φFy 4(0.6)(0.9)(60) qmax M 650 = 2.5in. e= a = 260 Pa f p (max) = = (0.65)(0.85)(4)(1) = 2.21ksi = f p ( max ) × B qmax P N − u 2 2 qmax ecrit = = 1 / 2[19 − 376 / 42.0] whichleadsto (0.85)(4)(1) 2.50 = 1.36 ksi = f p ( max ) × B = (1.36)(19) = 25.8kips/in. = 42.0 kips/in. ecrit = A2 A1 = = (2.21)(19) valueandwithadevelopmentlengthofthe#7barequal to24.9in.,computeefromtheratio (0.85 f c′) Ωc P N − a 2 2 qmax = 1 / 2[19 − 260 / 25.8] = 4.46 in. = 5.02 in. e = 17.4in. where Therefore,e<ecrit,andthedesignmeetsthecriteriafor thecaseofabaseplatewithsmallmoment. eistheeffectivesteelreinforcementlaprequiredtodeveloptheloadinthereinforcingsteel. 4. Determinebearinglength,Y. Therefore minimum required hef = 17.4 + 1.5 (concrete cover)+7.9/1.5=24.2in.asillustratedinFigure3.2.5. Select25-in.embedmentforanchors. Y=N−2e=19–(2)(2.50)=14in. Verifybearingpressure: LRFD 4.6Example:SmallMomentBasePlateDesign Designabaseplateforaxialdeadandliveloadsequalto100 and160kips,respectively,andmomentsfromthedeadand liveloadsequalto250and400kip-in.,respectively.Bending isaboutthestrongaxisforthewideflangecolumnW12×96 withd=12.7in.andbf=12.2in.Theratiooftheconcreteto baseplateareaisunity;Fyofthebaseplateis36ksiandf′c oftheconcreteis4ksi. Pu = 376 kips/14 in. Y = 26.9 kips/in. < 42.0 = qmax o.k. q= LRFD Pa = 260 kips/14 in. Y = 18.6 kips/in. < 25.8 = qmax o.k. q= 5. Determineminimumplatethickness. Atbearinginterface: N − 0.95d 2 19 − 0.95(12.7) = 2 = 3.47 in. m= 1. Computetherequiredstrength. Pu=1.2(100)+1.6(160) =376kips ASD ASD Pa=100+160=260kips Ma=250+400=650kip-in. Mu=1.2(250)+1.6(400) =940kip-in. LRFD 2. Choosetrialbaseplatesize. fp = ThebaseplatedimensionN×Bshouldbelargeenoughfor theinstallationoffouranchorrods,asrequiredbyOSHA. Pu 376 = 1.41ksi = BY (19)(14) ASD fp = Pa 260 = = 0.977 ksi BY (19)(14) DESIGNGUIDE1,2NDEDITION/BASEPLATEANDANCHORRODDESIGN/37 The minimum thickness may be calculated from Equation3.3.14sinceY≥m: t p( req ) = 1.5m B>bf+(2)(3.0in.)=18.2in. Fy TryN=19in.andB=19in. 3. Determineeandecrit;checkinequalityinEquation3.4.4 todetermineifasolutionexists. ASD 1.41 36 = (1.83)(3.47) 0.977 36 = 1.04 in. = 1.03in. N>d+(2)(3.0in.)=18.7in. fp LRFD = (1.5)(3.47) 2. Choosetrialbaseplatesize. LRFD ASD qmax = 24.0 kips/in. qmax = 25.8kips/in. (SeeExample4.6) M 3, 600 kip-in. e= u = Pu 376 kips Checkthethicknessusingthevalueofn. n = B − 0.8b f 2 19 − (0.8)(12.2) = = 4.62 in. 2 LRFD ASD 1.41 t p( req ) = (1.5)(4.62) 36 t p( req ) = 1.36 in.controls 0.977 t p( req ) = (1.83)(4.62) 36 t p( req ) = 1.39 in.controls Useabaseplate12"×19"×1'-7". Useabaseplate12"×19"×1'-7". ecrit = 9.57 in. P N = − u 2 2 qmax = (SeeExample4.6) e= ecrit 19 376 − 2 (2)(42.0 ) = 5.02 in. e > ecrit Ma 2,500kip-in. = Pa 260 kips = 9.62 in. P N = − a 2 2 qmax = 19 260 − 2 (2)(25.8 ) = 5.03in. e > ecrit Therefore, this is the case of base plate with large moment. ChecktheinequalityofEquation3.4.4: 6. Determinetheanchorrodsize. Sincenoanchorrodforcesexist,theanchorrodsizecan be determined based on the OSHA requirements and practicalconsiderations. Usefourw-in.-diameterrods,ASTMF1554,Grade36; rodlength=12in. Assume that the anchor rod edge distance is 1.5 in. Therefore, N f = −1.5 2 f = 9.5 - 1.5 = 8in. 2 f + N = (8 + 9.5)2 = 306 2 4.7Example:LargeMomentBasePlateDesign Design a base plate for axial dead and live loads equal to 100and160kips,respectively,andmomentsfromthedead andliveloadsequalto1,000and1,500kip-in.,respectively. BendingisaboutthestrongaxisforaW12×96wideflange columnwithd=12.7in.andbf=12.2in.Conservatively, considertheratiooftheconcretetobaseplateareaisunity; Fyofthebaseplateis36ksiandfc′ofconcreteis4ksi. 1. Computetherequiredstrength. LRFD Pu = 1.2(100) + 1.6(160) = 376 kips M u = 1.2(1, 000) + 1.6(1,500) = 3, 600 kip-in. ASD Pa = 100 + 160 = 260 kips M a = 1, 000 + 1,500 = 2 ,500 kip-in. LRFD 2 Pu (e + f ) qmax = ASD (2)(376)(9.57 + 8) 2 Pa (e + f ) 42 qmax = 315 = (2)(260)(9.62 + 8) 25.8 = 355 Since315>306,theinequality Since 315 > 306, the inequality isnotsatisfied. isnotsatisfied. Hence,alargerplatedimension Hence,alargerplatedimension isrequired. isrequired. Astheseconditeration,trya20×20plate. The increased dimensions cause a modification in the maximumbearingpressure,qmax,f,andecrit.Thenewvaluesbecome 38 / DESIGN GUIDE 1, 2ND EDITION /BASEPLATEANDANCHORRODDESIGN LRFD BecauseY≥m: ASD qmax = (1.36)( B ) qmax = (2.21)( B ) = (2.21)(20) = 44.2 kips/in. 20 −1.5 = 8.5in. f = 2 20 376 ecrit = − 2 (2)(44.2) = 27.2 kips/in. 20 −1.5 f = 2 = 8.5in. ecrit = 20 260 − 2 (2)(27.2) = 5.75in. = 5.22 in. The eccentricity, e, still exceeds Theeccentricity,e,stillexceedsecrit; ecrit;therefore,theloadcombination therefore,theloadcombinationisfor isforlargemoments.Also: largemoments.Also: 2 f + N = (8.5 + 10)2 2 = 342 2 f + N = (8.5 + 10)2 2 = 342 2 Pu (e + f ) qmax = (2)(376)(9.57 + 9.5) 2 Pa (e + f ) 44.2 qmax = (2)(260)(9.62 + 9.5) LRFD 4. Determinebearinglength,Y,andanchorrodtension,Tuor Ta. LRFD ASD N Y = f + 2 N Y = f + 2 2 2 Pa (e + f ) N ± f + − 2 qmax 2 2 Pu (e + f ) N ± f + − 2 qmax 20 Y = 9.5 + 2 20 Y = 9.5 + 2 2 2 (376)(9.57 + 9.5) 20 ± 9.5 + − 2 44.2 = 19.5 ± 7.47 Y = 12.0 in. Tu = qY − Pu = (44.2)(12.0) − 376 = 156 kips 2 (260)(9.62 + 9.5) 20 ± 9.5 + − 2 29.9 2 = 19.5 ± 6.90 t p( req ) = 1.83m Fy = (1.5)(3.97) 2.21 36 t p( req ) = 1.48in. Ta = qY − Pa = (29.9)(12.6) − 260 = 117 kips 5. Determineminimumplatethickness. Atbearinginterface: Fy = (1.83)(3.97) 1.36 36 t p( req ) = 1.41in. N d 20 12.7 − −1.5 = − −1.5 2 2 2 2 = 2.15in. x= LRFD t p ( req ) = 2.11 = 2.11 ASD Tu x BFy t p( req ) = 2.58 (156 )(2.15) (20)(36) t p ( req ) = 1.44 in = 2.58 Ta x BFy (117)(2.15) (20)(36) n. t p( req ) = 1.52 in Checkthethicknessusingthevalueofn. n = B − 0.8b f 2 = LRFD Y = 12.6 in. f p(max) Attensioninterface: 29.9 324<342,thereforetheinequality 332<342,thereforetheinequalityin inEquation3.4.4issatisfiedanda Equation3.4.4issatisfiedandareal solutionforYexists. realsolutionforYexists. f p(max) t p( req ) = 1.5m = 332 = 324 ASD 2.21 36 = 1.90 in.controls t p( req ) = (1.5)(5.12) 20 − 0.8(12.2) =5.12in. 2 ASD 1.36 36 = 1.82 in.controls t p( req ) = (1.83)(5.12) Bearinginterfacegovernsthedesignofbaseplatethickness.Use2-in.plate. N − 0.95d 2 20 − 0.95(12.7) = 2 = 3.97 in. m= 6. Determine the anchor rod size and embedment (LRFD only). LRFD ASD fp=fp(max)=2.21ksi fp=fp(max)=1.36ksi Fromtheabove,Tu=156kips.Ifthreeanchorrodsare usedoneachfaceofthecolumn,theforceperrodequals 52kips.FromTable3.1,thedesignstrengthof12-in.diameterGrade36anchorrodsis57.7kips.Therecommended hole size for the 12-in. rod is 2c in. (AISC, 2005).Usinganedgedistancetothecenteroftheholeof 24in.,theinitialassumptionof12in.mustbeadjusted. DESIGNGUIDE1,2NDEDITION/BASEPLATEANDANCHORRODDESIGN/39 Usingtheadjustededgedistancethe1�-in.rodsarestill adequate. Thus,therequiredflangeembedmentdepthis 10.2in.2 8.08in. =1.26in. The pullout strength of each anchor rod with a heavy hexnutisselectedfromTable3.2as52.6kips,whichis greaterthantherequiredstrengthperrod=52kips. For completeness determine the embedment length for theanchorrods. Use a total embedment of 4 in. for the flange and base plate. 4.9Example:ShearLugDesign Try18in.ofembedment. Thedesignconcretebreakoutstrengthis A φ N cbg =φψ 316 f c′ hef 5 / 3 N forhef > 11in. ANo Iftherodsareplaced6in.apart,theplanareaofthefailureconeis(3)(18)=54in.inwidthand(2)(18)+12=48in. inlength,thusthetotalareaAN=2,590in.2Theplanarea of the failure cone for a single anchor rod embedded to 18 in. is (3)(18)2 = 972 in.2The ratio of these areas is2.67,soforuncracked4,000psiconcrete,thedesign concretebreakoutstrengthis 5/ 3 φN cbg = 0.70 (1.25)16 4 , 000 (18) (2.67) = 295, 000 lbor = 295kipsso.k. Formoderateorhighseismicrisk,inACI318indicates thatthestrengthofanchorsistobemultipliedby0.75.In thiscase,thesteelstrengthwouldbe0.75times57.7= 43.1kipsperrod.Largeranchorrodswouldberequired. Design a shear lug detail for the W10×45 column consideredinExample4.6,butwithanadditionalshearof23kips (nominal load) due to wind. See Figure 4.9.1.The anchor rods in this example are designed only to transfer the net upliftfromthecolumntothepier.Theshearlugwillbedesignedtotransfertheentireshearloadtothepierwiththe confinementcomponentbeingignored. Procedure: 1. Determine the required embedment for the lug into the concretepier. 2. Determinetheappropriatethicknessforthelug. 3. Sizetheweldsbetweenthelugandthebaseplate. Solution: 1. Twocriteriaareusedtodeterminetheappropriateembedmentforthelug.Thesecriteriaarethebearingstrength oftheconcreteandtheshearstrengthoftheconcretein frontofthelug.Theshearstrengthoftheconcreteinfront of the lug is evaluated (in ultimate strength terms) as a 4.8Example:ShearTransferUsingBearing Calculate the minimum embedment depth of a shallowly embeddedW12×50in6,000-psigroutforafactoredshear loadof100kips.Thebaseplateis15in.×15in.andis1.5 in.thick.TheprojectedareaoftheplateAbrg=(1.5)(15)= 22.5 in2.The design shear strength in bearing on the base plateedgeperACI318-02is 0.6 (0.85) f c′Abrg = 0.6 (0.85)(6)(22.5) = 68.8kips The remaining 31.2 kips must be taken by bearing of the flangeoftheW12×50againsttheconcrete.Thewidthofthe flangeis8.08in.Therequiredbearingareais Abrg = 31.2kips = 10.2 in.2 0.6(0.85)(6 ksi) Figure4.9.1Shearlugdesign. 40 / DESIGN GUIDE 1, 2ND EDITION /BASEPLATEANDANCHORRODDESIGN uniformtensilestressofwithφ=0.75actingon 4φ f c′ aneffectivestressareadefinedbyprojectinga45°plane fromthebearingedgeoftheshearlugtothefreesurface (thefaceofthepier).Thebearingareaofthelugistobe excludedfromtheprojectedarea.Sincethiscriterionis expressedinultimatestrengthterms,thebearingstrength oftheconcreteisalsoevaluatedwithanultimatestrength approach.Theultimatebearingstrengthoftheconcretein contactwiththelugisevaluatedas0.8fc′A. Theprojectedareaofthisplane(Av),excludingtheareaof thelug,isthencalculatedas Av=(20)(11.0)–(1.5)(9)=207in.2 Usingthisarea,theshearcapacityoftheconcreteinfront ofthelug(Vu)iscalculatedas Vu = 4φ f c′ Av 4(0.75) 4, 000 (207) 1, 000 =39.2kips>36.8kipso.k. = Sincetheanchorrodsaresizedforonlytherequireduplift tension,the1.2(Ny−Pa)termaddressedinSection3.5.2 willbesmallandthusisignoredinthisexample. Thefactoredshearload=(1.6)(23)=36.8kips Equatingthisloadtothebearingcapacityoftheconcrete, thefollowingrelationshipisobtained: (0.8)(4,000)(A)req’d=36,800 Assumingthebaseplateandshearlugwidthtobe9in., therequiredembeddeddepth(d)ofthelug(intheconcrete)iscalculatedas d=11.5/9=1.28in. Use12in. Usingthisembedment,theshearstrengthoftheconcrete infrontofthelugischecked.Theprojectedareaofthe failureplaneatthefaceofthepierisshowninFigure4.9.3. Assumingthelugispositionedinthemiddleofthepier andthelugis1in.thick, B = 1.5in.+9.5in.=11.0in. Ml = V(G+d/2) = (36.8)(2+1.5/2)=101kip-in. Z= bt 2 4 M l = φFy Z = φFy bt 2 4 = (0.90)(36)(9)t 2 = 72.9t 2 4 treq ’d = 1.18iin. Usea14-in.-thicklug(Fy=36ksi). SeeFigure4.9.2. a = 5.5in.inthe20-in.-widepier Note:G=2in.=thicknessofgroutbed. (A)req’d=11.5in.2 2. Usingacantilevermodelforthelug, Figure4.9.2.Shearlugdepth. Based on the discussion in Section 3.5.2, it is recommendedtouseabaseplateof14-in.minimumthickness withthisshearlug. 3. Most steel fabricators would prefer to use heavy fillet weldsratherthanpartialorfullpenetrationweldstoat- Figure4.9.3.Lugfailureplane. DESIGNGUIDE1,2NDEDITION/BASEPLATEANDANCHORRODDESIGN/41 tachthelugtothebaseplate.Theforcesontheweldsare asshowninFigure4.9.4. ForallfourrodsφRn=30.8kips: φVcbg = 10.4 Considerc-in.filletwelds: s = 1.25+0.3125(1/3)(2)=1.46in. 101.2 = 7.71kips/in. 1.46(9) 1.6(23) fv = = 2.05kips/in. 9(2) fc = Theresultantweldload(fr)iscalculatedas fr = 2 (7.71) + ( 2.05 )2 = 7.98kips/in. DesignStrength=(0.3125)(0.707)(31.5)=6.96kips/in. 6.69kips/in.<7.98kips/in.n.g. Usea-in.filletwelds. 4.10Example:EdgeDistanceforShear Determine the required concrete edge distance to develop theshearstrengthoffourw-in.-diameteranchorrods.A4-in. ×4-in.patternisusedfortherods.Theconcretestrengthis 4,000psi. f c′ c11.5 where Trialc1 = 14in.(distancetotheedgeofconcrete) s = 4in.(rodspacing) c1/s = 14/4 = 3.5 > 1.5, therefore the total group controls ψ6 = 1(notlimitedbysideencroachment) Avo = 4.5c12=4.5(14)2=882in2(theareaofthefull shearconeforasingleanchorasshowninView A-AofFigure3.5.4) Av = 4.5c12+s(1.5c1)=882+84=966in2(thetotal breakoutshearareaforagroupofanchors) Forac-in.filletweldusingE70electrode: Fw=φ(0.60)FExx=(0.75)(0.60)(70)=31.5ksi Av ψ 6 do Avo 966 1.5 1 0.75 4000 (14) = 32 , 700 lb φVcbg = 10.4 882 ( ) = 32.7kips Approximately 14-in. clearance in plain concrete is required. The reader is referred toAISC Design Guide 7 (AISC, 2005)foradiscussiononthereinforcementofconcrete pierstoresistlateralthrusts. Rodshearstrength: φRn = φ(0.4)FuAb(threadsincluded) φRn = (0.75)(0.4)(58ksi)(0.4418in.2)=7.69kips 4.11Example:AnchorRodResistingCombinedTension andShear Determine the required size of four anchor rods for the W10×45columnexaminedinExample4.9,usingtheanchor rodstoresistwindshear. Wind shear force is 23 kips, therefore, the required shear strengthis LRFD ASD =1.6×23kips=36.8kips =23.0kips Solution: 1. AsdeterminedinExample4.5,therequiredstrengthdue toupliftonthecolumn. Figure4.9.4.Forcesonshearlugwelds. LRFD ASD =69.8kips =46.5kips 42 / DESIGN GUIDE 1, 2ND EDITION /BASEPLATEANDANCHORRODDESIGN 2. A total of four anchor rods is used. Use plate washers weldedtothetopofthebaseplatetotransfertheshear toallfouranchorrods.Tryfour18-in.-diameterF1554 Grade 36 anchors. For combined shear and tension the anchorrodsmustmeettheAISCprovision. LRFD ASD F ft ≤ φFnt′ = φ 1.3Fnt − nt f v ≤ φFnt F φ nv whereφ = 0.75 1.3Fnt − ΩFnt f v F Fnv Fnt′ ≤ nt = ft ≤ Ω Ω Ω whereΩ = 2.00 Stressesinrods: where Ml , Z 3 S= d 3 (1.125) = = 0.237 in.3 6 6 LRFD ftb = ASD 5.18 = 21.9 ksi 0.237 ftb = 3.24 = 13.7 ksi 0.237 Theaxialstressequals LRFD ASD Shearstress: 36.8 fv = = 10.5ksi 4(0.994) Shearstress: 23.0 f v = = 5.78ksi 4(0.994) Tensilestress:Thetensilestressintherodscomesfromtwo sources: 1. tensionfrombending,and 2. axialtension. Thebendingmomentineachrodequalstheshearperrod timesthehalfdistancefromthecenteroftheplatewasherto thetopofthegrout. Determinetheplatewasherthickness: Thebearingforceperrodis LRFD fta = Pu A fta = Pa A fta = 69.8 = 17.6 ksi 4(0.994) fta = 46.5 = 11.7 ksi 4(0.994) Thetensilestress,ft=21.9+17.6 =39.5ksi. Fnt=0.75Fu=(0.75)(58)= 43.5ksi Fnv=0.4Fu=(0.4)(58)=23.2ksi (threadsincluded) 23.0 =5.75kips 4 Thedeformationattheholeatserviceloadisnotadesign consideration,butthenominalbearingstrengthis Rn=1.5LctFu≤3.0dtFu LRFD 4 = 5.18kip-in. 1.3Fnt − ΩFnt f v F F Fnt′ nv ≤ nt = Ω Ω Ω (1.3)(43.5) − 2.00( 43.5 )(6.16) . 23 2 ( ) = 2.00 = 16.7 ksi 43.5(10.5) = 0.75 (1.3)(43.5) − (0.75)(23.2) = 22.7 ksi (43.5) Fnt′ = 21.8ksi ≤ Ω 2.00 ASD Ml = 23.0 (0.563) 4 = 3.24 kip-in. 25.4 > 16.7 n.g. 39.1 > 22.7 n.g. Tryfour12-in.-diameterrods. LRFD 36.8 Shearstress:f v = = 5.20 ksi 4(1.77) 3 By inspection, �-in. plate washers will suffice even with minimaledgedistance.Thus,theleverarmcanbetakenas one-halfofthesumofthebaseplatethicknessand0.125in. (1in.+0.125in.=1.125in./2=0.563in.).Thus, 36.8 (0.563) Thetensilestress,ft=13.7+11.7= 25.4ksi. Fnt=0.75Fu=(0.75)(58)= 43.5ksi Fnv=0.4Fu=(0.4)(58)=23.2ksi (threadsincluded) F φFnt′ = φ 1.3Fnt − nt f v ≤ φFnt F φ nv ASD 1.6× 23 =9.20kips 4 ASD φFnt′ ≤ (0.75)(43.5) = 32.6 ksi LRFD Ml = Thestressduetobendingequalsftb = d 3 (1.5) = = 0.563in.3 6 6 5.18 ftb = = 9.20 ksi 0.563 P Theaxialstressequalsfta = u A S= fta = 69.8 = 9.86 ksi 4(1.77) Thetensilestress, ft = 9.20 + 9.86 = 19.1ksi ASD Shearstress:f v = 23.0 = 3.25ksi 4(1.77) 3 d 3 (1.5) = = 0.563in.3 6 6 3.45 = 6.13ksi ftb = 0.563 P Theaxialstressequalsfta = a A 46.5 fta = = 6.57 ksi 4(1.77) S= Thetensilestress, ft = 6.13 + 6.57 = 12.7 ksi DESIGNGUIDE1,2NDEDITION/BASEPLATEANDANCHORRODDESIGN/43 43.5 (5.20) φFnt′ = 0.75 (1.3)(43.5) − (0.75)(23.2) = 32.7 ksi ≤ (0.75)(43.5) = 32.6 ksi =32.6ksi 30.1<32.6o.k. Usefour12-in.-diameterrods. (1.3)(43.5) − 2.00( 43.5 )(3.25) (23.2) Fnt′ = 2.00 Ω = 22.2 ksi (43.5) = 21.8ksi ≤ 2.00 = 21.8ksi 20.1<21.8o.k. Usefour12-in.-diameterrods. Duetothesizeoftherodstheywillhavetobepositioned beyondthecolumnflanges. Asamatterofinterest,assumethatweldedwashersare notprovided.Itshouldbenotedthataslipofwin.couldoccurbeforetheanchorrodsgointobearing.Checkthe12-in. anchorrodsusingtheauthor’ssuggestionthatonlytwoanchorrodsbeconsideredtocarrytheshear;however,bending canbeneglectedintherods,butthe0.8reductioninshear capacityperACI318isincluded.Ratherthanusingthe0.8 reduction,usea1.25magnifierontheshearload. LRFD fv = (1.25)(36.8) = 13.0 ksi 2(1.77) 69.8 fta = = 9.9 ksi 4(1.77) F φFnt′ = φ 1.3Fnt − nt f v ≤ φFnt φFnt ASD fv = (1.25)(23) = 8.12 ksi 2( 1.77 ) 46.5 fta = = 6.6 ksi 4( 1.77 ) ΩFnt 1.3Fnt − fv Fnt Fnt Fnt′ ≤ = Ω Ω Ω ( )( ) (1.3)(43.5) − 2.00 43.5 8.12 (23.2) 43.5 (13.0) = 0.75 (1.3)(43.5) − (0.75)(23.2) = = 18.0 ksi = 13.1ksi 9.9ksi<18.0ksio.k. 44 / DESIGN GUIDE 1, 2ND EDITION /BASEPLATEANDANCHORRODDESIGN 2.00 6.6ksi<13.1ksio.k. REFERENCES ACI117(1990),StandardSpecificationsforTolerancesfor Concrete Construction and Materials (ACI 117-90 (Reapproved2002),FarmingtonHills,MI. ACI 349 (2001), Code Requirements for Nuclear Safety RelatedConcreteStructuresandCommentary(ACI34901/349R-01),FarmingtonHills,MI. ACI Committee 318 (2002), Building Code Requirements for Structural Concrete (ACI 318-02) and Commentary (ACI318R-02),FarmingtonHills,MI. AmericanInstituteofSteelConstruction(2001),Manualof SteelConstruction,LoadResistanceFactorDesign,Chicago,IL. AmericanInstituteofSteelConstruction(2005),SpecificationforStructuralSteelBuildings,Chicago,IL. American Institute of Steel Construction (2005), Seismic ProvisionsforStructuralSteelBuildings,Chicago,IL. American Institute of Steel Construction (2005), Code of StandardPracticeforSteelBuildingsandBridges,Chicago,IL. DeWolf,J.T.andRicker,D.T.(1990),DesignGuideNo.1, Column Base Plates, Steel Design Guide Series,AISC, Chicago,IL. Drake, R.M. and Elkin, S.J. (1999), “Beam-Column Base PlateDesign—LRFDMethod,”EngineeringJournal,Vol. 36,No.1,FirstQuarter,AISC,Chicago,IL. Fisher,J.M.(2004),DesignGuideNo.7,IndustrialBuildings—RoofstoAnchorRods,2ndEd.,SteelDesignGuide Series,AISC,Chicago,IL. Fisher,J.M.(1981),“StructuralDetailsinIndustrialBuildings,” EngineeringJournal,ThirdQuarter,AISC,Chicago,IL. Fisher,J.M.andWest,M.A.(1997),DesignGuideNo.10, Erection Bracing of Low-Rise Structural Steel Frames,” SteelDesignGuideSeries,AISC,Chicago,IL. Fisher, J.M. and Doyle, J.M. (2005), “Discussion: BeamColumnBasePlateDesign—LRFDMethod,”Engineering Journal,Vol. 36, No. 1, Fourth Quarter,AISC, Chicago,IL. Frank, K.H. (1980), “Fatigue Strength of Anchor Bolts,” ASCE Journal of the Structural Division,Vol. 106, No. ST,June. Kaczinski, M.R., Dexter, R.J., and Van Dien, J.P. (1996), “Fatigue-Resistant Design of Cantilevered Signal, Sign, andLightSupports,”NationalCooperativeHighwayResearchProgram,NCHRPReport412,TransportationResearchBoard,WashingtonD.C. Koenigs, M.T., Botros,T.A., Freytag, D., and Frank, K.H. (2003), “Fatigue Strength of Signal MastArm Connections,”ReportNo.FHWA/TX-04/4178-2,August. Occupational Safety and Health Administration (2001), OSHA,SafetyStandardsforSteelErection,(SubpartRof 29CFRPart1926),Washington,D.C. ResearchCouncilonStructuralConnections(2004),SpecificationforStructuralJointsUsingASTMA325orA490 Bolts,availablefromAISC,Chicago,IL. Thornton, W.A. (1990), “Design of Small Base Plates for Wide-Flange Columns,” Engineering Journal, Vol. 27, No.3,ThirdQuarter,AISC,Chicago,IL. Till, R.D. and Lefke, N.A. (1994), “The Relationship BetweenTorque,Tension,andNutRotationofLargeDiameterAnchor Bolts,” Materials and Technology Division, MichiganDepartmentofTransportation,October. Wald,F.,Sokol,Z.,andSteenhuis,M.(1995),“Proposalof the Stiffness Design Model of the Column Bases,” ProceedingsoftheThirdInternationalWorkshoponConnectionsinSteelStructures,Trento,Italy. DESIGNGUIDE1,2NDEDITION/BASEPLATEANDANCHORRODDESIGN/45 46 / DESIGN GUIDE 1, 2ND EDITION /BASEPLATEANDANCHORRODDESIGN APPENDIXA SPECIALCONSIDERATIONSFOR DOUBLE-NUTJOINTS,PRETENSIONED JOINTS,ANDSPECIALSTRUCTURES A1.DesignRequirements Anchorrodsaresometimesusedinspecialapplicationsthat requirespecialdesigndetails,suchasanchorrodsdesigned withoutagroutbase(double-nutanchorrods),anchorrods in sleeves, pretensioned applications, and special moment basesorstools. Double-nutanchorrods,aredifferentfrombuildingcolumnanchorrodsthatmayuseasettingnutbutarenotdesignedforcompressioninthecompletedstructure.Doublenutjointsareverystiffandreliablefortransmittingmoment tothefoundation.Becausetallpole-typestructuresarenonredundantandaresubjecttofatigueduetowindflutterspecial inspection and tightening procedures should be used. Studieshaveshownthatpretensionintherodbetweenthe two nuts improves fatigue strength and ensures good load distributionamongtheanchorrods(Frank,1980;Kaczinski etal.,1996).Thebaseplatesoflightandsignstandardsare notgroutedaftererection,andtherodcarriestheallofthe structuralload.Theanchorrodsmustbedesignedfortension, compression, and shear, and the foundation must be designedtoreceivetheseloadsfromtheanchorrods. Machinery bases and certain columns may require very closealignmentoftheanchorrods.Oversizedsleevescanbe usedwhensettingtherodstoprovidesubstantialflexibility intherodsothatitcanbeadjustedtofitthemachinerybase. The anchorage at the bottom of the rod must be designed tospanthesleeveanddeveloptherequiredbearingonthe concrete. FigureA1.1.Anchorrodswithsleeves. Oftenmachinery,processequipment,andcertainbuilding columnsmaybesubjecttovibrationorcyclicalloads,which may in turn subject the anchor rod to fatigue. Pretensioningtherodcanimproveitsfatiguelife,butanchorrodscan effectively be pretensioned only against steel. Even when tensioningaGrade55rod24in.long,itonlytakesconcrete creep/shrinkageof0.05in.torelieveallofthepretension. Thus,itisrecommended,whenitisnecessarytopretension anchorrods,thatasteelsleevebeusedthatisadequateto transfertheanchorrodpretensionfromtheanchorplateto thebaseplate.SeeFigureA1.1. Largemillbuildingcolumnsthathavetobesetaccurately andhavelargemomentsatthebasecanbedesignedusinga stool-typedetailasshowninFigureA1.2.Theadvantageof thistypeofdetailisthatthebaseplatecanbesetinadvance usinglargeoversizedholes.Theuseofthefilletweldedstool avoidshavingtocompletejointpenetrationgrooveweldthe columnbasetotheheavybaseplate.Ifthecolumnandbase plateareover2in.thick,usingacompletejointpenetration weld detail would require special material toughness. The useofthestoolhastheaddedadvantagethattheextended anchorrodlengthwillalloweasieradjustmenttomeetthe holesinthestoolcapplate. A1.1CompressionLimitStateforAnchorRods With the usual short length involved, the nominal steel compressivestrengthforanchorrodsindouble-nutmoment joints is the product of its yield stress and the gross area. Yielding could initiate at lower load levels on the reduced areaofthethreads,butitisassumedthattheconsequences of this yielding would be relatively minor. The available strength,φRcorRc/Ω,isdeterminedwith Rc=FyAg φ=0.90 Ω=1.67 FigureA1.2.Columnmomentbaseusingstool. DESIGNGUIDE1,2NDEDITION/BASEPLATEANDANCHORRODDESIGN/47 where Rc = nominalsteelcompressivestrengthofananchor rod,kips Fy = specifiedminimumyieldstress,ksi Ag = grossareabasedonthenominaldiameterofthe anchorrodforcutthreadsorthepitchdiameter forrolledthreads,in.2 Typically,thecleardistanceunderthebaseplateshould notexceed2.5in.Ifthecleardistancebetweenthebottom ofthebottomlevelingnutandthetopofconcreteisgreater than four rod diameters, buckling of the anchor rod shall beconsideredusingthecolumndesigncriteriaoftheAISC Specification. Headedanchorrodstransferthecompressiveforcetothe concretebybearingofthehead,anddeformedbarstransfer thecompressiveforcetotheconcretealongtheirlength.The compressivestrengthoftheanchorrodduetoconcretefailureshouldbecalculatedusingtheAmericanConcreteInstitute(ACI318-02)criteria. A1.2TensileFatigueLimitStateforAnchorRods Column base connections subject to more than 20,000 repeatedapplicationsofaxialtensionand/orflexuremustbe designed for fatigue. When the maximum fatigue stress range is less than the threshold fatigue stress range, 7 ksi, anchorrodsneednottobefurthercheckedforfatigue. Four anchor rod joints are of low cost and suitable for small sign, signal, and light supports and other miscellaneousstructures.Inothercases,althoughonlyfouranchor rodsmayberequiredforstrength,thereshouldideallybeat leastsixandpreferablyeightanchorrodsinajointinanonredundantstructuresubjecttofatigue. Thereisatrendtowardusingfewerverylargeanchorrods inhigh-demanddynamicallyloadedstructures.Whenthere areeightanchorrodsinajoint,andthefirstonefailsfrom fatigue, the stress range on the neighboring rods increases onlyabout25%.Theserodswouldthenbeexpectedtolast anadditional35to50%ofthetimeittooktofailthefirst rod,assumingtheloadingremainsapproximatelyconstant. Thisgivesthecolumnbaseplateconnectionsomemeasure ofredundancy,evenifthestructureisnonredundant.Fatigue ofanchorrodjointswithonlyfourrodswillfailcompletely onlyashorttimeafterthefirstrodfailure. Forcircularpatternsofsixormoredouble-nutanchorrods, testinghasshownthatthethicknessofthebaseplatemust atleastequalorexceedthediameteroftheanchorrods,and alsothatthebendingintheanchorrodisnegligiblewhenthe distancebetweenthebottomofthelevelingnutandthetop oftheconcreteislessthantheanchorroddiameter(Kaczinskietal.,1986).However,testsonfouranchorrodpatterns show that neither of these simple rules is sufficient when determinetheproperbaseplatethicknessandthebendingin theanchorrods. In column-base-plate connections subject to fatigue, the anchor rod will fail before the concrete fatigue strength is reached.Therefore,itisnotnecessarytoconsiderthefatigue strengthoftheconcrete. Corrosionprotectionisparticularlyimportantforfatiguecriticalanchorrods,sincecorrosionpittingcandegradethe fatigueresistance.Itisgenerallyacceptedthatgalvanizing doesnotdecreasethefatiguestrengthsignificantly. Stresses in anchor rods for fatigue analysis should be based on elastic distribution of service loads. The tensile stressareashouldbeusedinthecomputationofstressesin threadedanchors.Thestressrangeshouldbecalculatedincluding the external load range due to repeated live loads andanypryingactionduetothoseloads.Thebendingstress rangeshouldbeaddedtotheaxialstressrangetodetermine thetotalstressrangetocheckforfatigue. The S-N curve for galvanized nonpretensioned anchor rodscorrespondstodetailCategoryE′;however,thefatigue thresholdismuchgreaterthanforotherCategoryE′details. Inthecaseofanchorrods,7ksiisthethresholdassociated with Category D. If the anchor rod in double-nut moment and pretensioned joints is properly pretensioned, the S-N curve for finite life increases to Category E, however the fatigue threshold is not significantly increased.When tests wereconductedwithaneccentricityof1:40,theappropriate categoryforbothpretensionedandnonpretensionedanchor rods was Category E′. Therefore, for design, it is recommended that Category E′ be used with a fatigue threshold of7ksi,regardlessofthepretension.Thisdesignwouldbe tolerantoflimitedmisalignmentupto1:40. Since the fatigue resistance of various grades of anchor rodisthesame,itisnotadvantageoustousegradeshigher than Grade 55 in fatigue applications. The fracture toughnessofthehighergradesisgenerallysomewhatless. Base plates, nuts, and other components need not be checkedforfatigue,unlessrequiredbytheinvokingspecification.Axialforcesintheanchorrodsfromtension,compression, and flexure must be considered. For all types of joints,theentireforcerangeisassumedtobeappliedtothe anchorrods,eveniftheyarepretensioned.Bendingofthe anchor rods need not be considered, with the exception of double-nut joints when there are only four anchor rods or whenthecleardistancebetweenthebottomoftheleveling nutandtheconcreteexceedsthediameteroftheanchorrods. Incaseswherethebendingstressrangemustbecalculated, theminimumbendingmomentistheshearforceintheanchorrodtimesthedistancebetweenthebottomofthebase plateandthetopofconcrete.Shearforcesmaybeignored forpurposesofcalculatingthefatigueeffect,eveniftheyact incombinationwiththeaxialforces. 48 / DESIGN GUIDE 1, 2ND EDITION /BASEPLATEANDANCHORRODDESIGN anchorrodswithoutbending.Inthinnerbaseplates,thelocal baseplatebendingresultsinsignificantbendingmomentsin thetubewallattheconnection. For the 1-in.-thick base plate, there are stress concentrationsatthebendlines,whichmeansthatthemembrane stresses are not well distributed around the perimeter, but ratherconcentratedatthebendsinthetube.Thisobservation is consistent with crack initiation locations observed incrackedtowers.However,withincreasingthickness,the base plate becomes less flexible, and the influence of the stressconcentrationsislesspronounced. Thisfindingisconsistentwithfatiguetestdatafromthe UniversityofTexas(Koenigsetal.,2003).Inthesetests,a socket joint detail with a 2-in.-thick base plate performed much better in fatigue than one with a 12-in.-thick base plate. Toassesstherelativeeffectofbaseplatethickness,longitudinalstressesontheoutersurfacefromthemodelarecomparedinFigureA1.3at12in.abovethetopofthebaseplate. Thestresseswerenormalizedtothestressesextractedfrom the model of the actual “as-built” 14-in.-thick base plate. The results of interest are labeled “outer stress at 12 in.” Theresultsforthecasewith“12-in.hole”maybeignored.It canbeseenthat,forabaseplate24in.thick,theouterstress atthislocationdecreasestoabout65%ofwhatitwouldbe fora14-in.-thickbaseplate.Forabaseplate3in.thick,the stressdecreasesfurtherbutnotmuch,downtoabout60%of whatitwouldbefora14-in.-thickbaseplate. Stressrangeisdefinedasthemagnitudeofthechangein servicestressduetotheapplicationorremovaloftheservice liveload.Theentirerangeinstressmustbeincluded,even if during part of the cycle the stress is in compression. In thecaseofaloadreversal,thestressrangeinanindividual anchorrodiscomputedasthealgebraicdifferencebetween thepeakstressduetotheliveloadappliedinonedirection andthepeakstressduetotheliveloadappliedintheother direction.Ifthebaseplatethicknessislessthanthediameter oftheanchorrods,theappliedstressrangesshouldinclude anyadditionaltensionresultingfrompryingactionproduced bytheunfactoredliveload. Theappliedstressrangeiscomputedbydividingtheaxial forcerangesbythetensilestressarea.Ifbendingoftheanchorrodsisincludedintheanalysis,thebendingstressrange mustbeaddedtothestressrangefromtheaxialforcesfrom aconsistentloadcase.Thestressrangeneednotbeamplifiedbystressconcentrationfactors. Nofurtherevaluationoffatigueresistanceisrequiredif thestressintheanchorrodremainsincompressionduring theentirecycle(includingtheminimumdeadload),orifthe stressrangeislessthanthethresholdstressrange,FTH.The maximum applied stress range must not exceed the allowablestressrangecomputedasfollows: Cf N FSR = 0.333 ≥ FTH where A2.InstallationRequirementsforPretensionedJoints FSR = allowablestressrange,ksi Cf = constantequalto3.9×108 N = numberofstressrangecyclesduringthelifeof thestructure ProperinstallationisusuallytheresponsibilityoftheContractor.However,theEngineerofRecord,ortheirrepresentative,maywitnesstheinspectionandtesting. FTH = thresholdstressrangeequalto7ksi Forpostsandpoles,thebaseplatethicknesscaninfluence thefatigueresistanceofthinposts.Asshownbelow,3in.is theoptimumthickness,butaslongasthethicknessisgreater than2in.,thefatigueresistanceisgenerallyadequate. Finite-elementanalysesillustratetheeffectofbaseplate thickness. In the model generated by the authors, the base platethicknesswasvariedfrom1to6in.Obviously,a6-in.thickbaseplateisunreasonableformostcommonapplications,butitwasusedtoshowtheeffectoveralargerange ofthickness.Theresultsofthestudyindicatethatincreasing thethicknessofthebaseplatecansignificantlydecreasethe stressesimmediatelyadjacenttothepole-to-base-plateweld. Thereductioninstressisduetothedecreaseinbaseplate flexibilitythatoccursasthebaseplatebecomesthicker(i.e., greater than 1.5 in.).As the base plate gets thicker, it can moreefficientlydistributethestressesfromthetowertothe 1.50 OuterStress@1.5in 1.25 NormalizedStress OuterStress@1.5inw/12inHole 1.00 0.75 0.50 0.25 0.00 1 2 3 4 5 6 7 BasePlateThickness(in) FigureA1.3.Stressesinbaseplate. DESIGNGUIDE1,2NDEDITION/BASEPLATEANDANCHORRODDESIGN/49 Inanyanchorrodinstallationtherewillbesomeamount of misalignment. It is assumed that the tolerances will be stated in the invoking specification and that the tolerances correspondwiththetolerancesspecifiedintheAISCCode of Standard Practice for Steel Buildings and Bridges. For anchor rods subjected to fatigue loading, it is also recommended that a tolerance for vertical misalignment of anchorrodsbespecifiedaslessthan1:40.Provisionsshould be made to minimize misalignments and to meet required tolerances.Thebestwaytomaintainalignmentistheuseof a template. Templates comprising rings with nuts on both sidesattwolocationsalongthelengthoftheanchorrodsare recommended. Vibratorymachinejointsanddouble-nutjointsdesigned for Seismic Design Category D or greater, according to ASCE 7, or designed for fatigue as described herein, require pretensioning. Failure to follow the nut tightening procedure can lead to inadequately pretensioned anchor rods and associated uneven distribution of loads among the contributing anchor rods. Inadequately tightened bolts canalsoleadtofatiguefailuresandfurtherlooseningofthe nutsundercyclicloading.Alesslikelyoutcomeoffailureto followthetighteningprocedureistighteningtothepointof damage—plasticdeformationandstrippingofthethreads— whichmayrequireremovalandreplacement. Thestartingpointfortighteningproceduresisbetween20 to30%ofthefinaltension.Foranchorrods,thisisdefined asafunctionoftorque,as Tv=0.12dbTm where Tv = verificationtorque(in.-kips) db = nominalbodydiameteroftheanchorrod(in.) Tm = minimuminstallationpretension(kips)givenin TableA1 Till(1994)hasshownthatamultiplierof0.12inthisrelationshipisadequateforcommonsizesandcoatingsofanchorrods.Otherresearchershavesuggestedavalueof0.20 forless-well-lubricatedrods. Ifananchorrodhasanutheadortheheadisfastenedwith nuts, the nut should be prevented from rotation while the anchorrodistightened.Thiscanbeachievedwithajamnut oranothertypeoflockingdevice.Thejamnutwillaffectthe ultimateorfatiguestrengthoftherod. Verylargetorquesmayberequiredtoproperlytightenanchorrodsgreaterthan1in.indiameter.Asluggingwrench or a hydraulic torque wrench is required. For the leveling nuts,anopen-endsluggingwrenchmaybeused. A2.1Double-NutJoints Priortoinstallationofanchorrodsinadouble-nut-moment joint, an anchor-rod rotation capacity test should be performedwithatleastoneanchorrodfromeachlot.Thistest attemptstorecreatetheconditionstowhichtheanchorrod willbesubjectedduringinstallation. Afterthetestandbeforeplacingtheconcrete,anchorrods should be secured to a template or other device to avoid movement during placing and curing of the concrete that may lead to misalignments larger than what may be tolerated.Theholepatterninthetemplateshouldbeverifiedby comparingthetoptemplatetothebaseplatetobeerectedif itisonsite. Beveledwashersshouldbeused: 1. Underthelevelingnutiftheslopeofthebottomfaceof thebaseplatehasaslopegreaterthan1:20. 2. Underthelevelingnutifthelevelingnutcouldnotbe broughtintofirmcontactwiththebaseplate. 3. Underthetopnutiftheslopeofthetopfaceofthebase platehasaslopegreaterthan1:20. 4. Under the top nut if the top nut could not be brought intofirmcontactwiththebaseplate. Ifabeveledwasherisrequired,thecontractorshoulddisassemblethejoint,replacenuts,addthebeveledwasher(s), andretighteninastarpatterntotheinitialcondition.Beveledwasherscantypicallyaccommodateaslopeupto1:6. Topnutsshouldbepretensioned.Theprocedureforpretensioningisaturn-of-nutprocedure,althoughtheyareinspected using torque. Pretensioning the nuts should be accomplished in two full tightening cycles following a star pattern. Experienceindicatesthatevenproperlytightenedgalvanizedanchorrodscansubsequentlybecomeloose,especially inthefirstfewdaysafterinstallation,presumablybecauseof creepinthegalvanizing.Therefore,afinalinstallationcheck should be made after at least 48 hours using a calibrated wrenchand110%ofthetorquecalculatedusingthetorque equation.Itisexpectedthatproperlytightenedjointswillnot moveevenif110%oftheminimuminstallationtorqueisapplied.Ifarodassemblycannotachievetherequiredtorque, isverylikelythatthethreadshavestripped. Whenitisrequiredthatthenutsbepreventedfromloosening,ajamnutorothersuitabledevicecanbeused.Any other method for preventing nut loosening should be approvedbytheEngineerofRecord.Tackweldingthetopside ofthetopnuthasbeenused,althoughthisisnotconsistent withtheAWSStructuralWeldingCode.Whiletackwelding totheunstressedtopoftheanchorrodisrelativelyharmless, undernocircumstanceshouldanynutbetackweldedtothe washerorthebaseplate. 50 / DESIGN GUIDE 1, 2ND EDITION /BASEPLATEANDANCHORRODDESIGN Thefollowingstepsareinsequence: 1. Thetorquewrenchusedfortighteningthenutsorfinal torqueverificationshouldhaveatorqueindicatorthatis calibrated annually.A certification of such calibration shouldbeavailabletotheEngineerofRecord.Atorque multipliermaybeused. 2. Theverificationtorqueiscomputedusing, Tv=0.12dbTm where Tv = verificationtorque(in.-kips) db = nominalbodydiameteroftheanchorrod(in.) Tm = minimuminstallationpretension(kips)givenin TableA1 3. Prior to placing the anchor rods in the concrete, an anchor rod rotation capacity test should be conducted with at least one anchor rod from every lot. This test shouldbeconductedusingthebaseplateoraplateof equivalentgrade,thickness,andfinish.Theplatemust be restrained against movement from the torque that willbeapplied.ThetestconsistsofSteps11through19 below,withtheexceptionofStep13(sincethereisonly oneanchorrod).Thenutshouldberotatedtoatleast therequiredrotationgiveninTableA2.Afterthetest, thenutsshouldberemovedandinspectedfordamageto theirthreads.Then,theanchorrodisremovedfromthe testplateandrestrainedwhilethenutsshouldbeturned ontotheboltsatleastoneroddiameterpastthelocation ofthelevelingnutandtopnutinthetest,thenbacked off by one worker using an ordinary wrench (without acheaterbar).Thethreadsareconsidereddamagedif an unusual effort is required to turn the nut. If there isnodamagetotheanchorrodornutduringthistest, theymaybeusedinthejoint.Ifthereisdamagetothe threadsoraninabilitytoattainatleasttheverification torque,thelotofanchorrodsshouldberejected. 4. Anchorrodsshouldbesecuredagainstrelativemovementandmisalignment. 5. A template is required for leveling the leveling nuts. Theholepatterninthetemplateshouldbeverified.Any deviationbetweentheholepositionsoutsideofthetolerancesmustbereportedtotheEngineerofRecord.The templateset(orotherdevice)withanchorrodsshould besecuredinitscorrectpositioninaccordancewiththe contractdocuments. 6. Theconcreteshouldbeplacedandcured. 7. Ifatoptemplateisabovetheconcretesurface,itmaybe removed24hoursafterplacingtheconcrete. 8. Theexposedpartoftheanchorrodsshouldbecleaned withawirebrushorequivalentandlubricatedifgalvanized. 9. Theanchorrodsshouldbeinspectedvisuallytoverify thatthereisnovisibledamagetothethreadsandthat theirposition,elevation,andprojectedlengthfromthe concretearewithinthetolerancesspecifiedinthecontractdocuments.Intheabsenceofrequiredtolerances, the position, elevation, and projected length from the concreteshouldbeaccordingtotheAISCCodeofStandard Practice for Steel Buildings and Bridges. If the jointisrequiredtobedesignedforfatigue,themisalignmentfromverticalshouldbenomorethan1:40.Nuts shouldbeturnedontotheboltswellpasttheelevation ofthebottomofthelevelingnutandbackedoffbya workerusinganordinarywrenchwithoutacheaterbar. Threaddamagerequiringunusuallylargeeffortshould bereportedtotheEngineerofRecord. 10. If threads of galvanized anchor rods were lubricated morethan24hoursbeforeplacingthelevelingnut,or havebeenwetsincetheywerelubricated,theexposed threadsoftheanchorrodshouldberelubricated.Leveling nuts should be cleaned and threads and bearing surfaces lubricated (if galvanized) and placed on the anchorrods. 11. Leveling nut washers should be placed on the anchor rods.Beveledwashersshouldbeusedifthenutcannot bebroughtintofirmcontactwiththebaseplate. 12. The template should be placed on top of the leveling nutstocheckthelevelofthenuts.Insomecases,ifindicatedinthecontractdocuments,itispermittedtosetthe baseplateatsomeotherangleotherthanlevel.Ifthis angle exceeds 1:40, beveled washers should be used. Verifythatthedistancebetweenthebottomofthebottomlevelingnutandthetopofconcreteisnotmorethan oneanchorroddiameter(unlessspecifiedotherwisein thecontractdocuments). 13. Thebaseplateandstructuralelementtowhichitisattachedshouldbeplaced. 14. Top nut washers should be placed. Beveled washers shouldbeusedifthenutcannotbebroughtintofirm contactwiththebaseplate. 15. Threadsandbearingsurfacesofthetopnutsshouldbe lubricated,placedandtightenedtobetween20and30% oftheverificationtorquefollowingastarpattern. DESIGNGUIDE1,2NDEDITION/BASEPLATEANDANCHORRODDESIGN/51 TableA1.MinimumAnchorRodPretensionforDouble-Nut-MomentJoints AnchorRod Diameter,in. MinimumAnchorRodPretensionTm,kips ASTMF1554 RodGrade36a ASTMF1554 RodGrade55b ASTMF1554 RodGrade105b ASTMA615andA706 BarsGrade60b � 4 6 11 7 s 7 10 17 11 w 10 15 25 16 d 13 21 35 22 1 18 27 45 29 18 22 34 57 37 1� 28 44 73 47 1� 41 63 105 67 1w 55 86 143 91 2 73 113 188 – 2� 94 146 244 156 2� 116 180 300 – 2w 143 222 370 – 3 173 269 448 – 3� 206 320 533 – 3� 242 375 625 – 3w 280 435 725 – 4 321 499 831 – Equalto50%ofthespecifiedminimumtensilestrengthofrods,roundedtothenearestkip. Equalto60%ofthespecifiedminimumtensilestrengthofrods,roundedtothenearestkip. a b TableA2.NutRotationforTurn-of-NutPretensioningofUNCThreads NutRotationa,b,c AnchorRodDiameter,in. ≤1� >1� F1554Grade36 F1554Grades55and105 A615Grade60and75andA706 Grade60 6 turn 3turn 1 /12turn 6turn 1 Nutrotationisrelativetoanchorrod.Thetoleranceisplus20°. b ApplicableonlytoUNCthreads. c Beveledwashershouldbeusedif:1)thenutisnotintofirmcontactwiththebaseplate;or2)theouterfaceofthebaseplateisslopedmorethan1:40. a 52 / DESIGN GUIDE 1, 2ND EDITION /BASEPLATEANDANCHORRODDESIGN 16. Leveling nuts should be tightened to between 20 and 30%oftheverificationtorquefollowingastarpattern. 17. Before further turning the nuts, the reference position ofthetopnutintheinitialconditionshouldbemarked on an intersection between flats with a corresponding referencemarkonthebaseplateateachbolt.Topnuts shouldbeturnedinincrementsfollowingastarpattern (usingatleasttwofulltighteningcycles)tothenutrotation specified inTableA2 if UNC threads are used. If 8UN threads are used, the appropriate nut rotation should be shown in the contract documents or specifiedbytheEngineerofRecord.Aftertightening,thenut rotationshouldbeverified. 18. Atorquewrenchshouldbeusedtoverifythatatorque at least equal to the verification torque is required to additionallytightenthelevelingnutsandthetopnuts. Aninabilitytoachievethistorquemeansitislikelythat thethreadshavestrippedandthismustbereportedto theEngineerofRecord. 19. Afteratleast48hours,thetorquewrenchshouldagain beusedtoverifythatatorqueatleastequalto110percentoftheverificationtorqueisrequiredtoadditionally tightenthelevelingnutsandthetopnuts.Forcantilever or other nonredundant structures, this verification shouldbemadeatleast48hoursaftererectionofthe remainder of the structure and any heavy attachments tothestructure. 20. IfthejointwasdesignedforSeismicDesignCategory D or greater according to ASCE 7, or designed for fatigue, the nut should be prevented from loosening unlessamaintenanceplanisinplacetoverifyatleast everyfouryearsthatatorqueequaltoatleast110%of theverificationtorqueisrequiredtoadditionallytighten thelevelingnutsandthetopnuts. A2.2PretensionedJoints Theinstallationproceduresforpretensionedjointsarevery similartothefirststepsfordouble-nut-momentjoints,except fortheinclusionofthesleeve.Thesleevemustbecleaned andsealedofftopreventinclusionofdebris. Anchor rods are typically tensioned using a center-hole ramwithaccesstothenutforretightening.Thenutistightened down while the tension is maintained on the anchor rod,andtheanchorrodtensionisreleased.Itisrecognized that part of the tension will be lost to relaxation after the tensionisreleased.Sincetherearemanyvariationsofpretensionedjoints,theEngineerofRecordshouldprovidethe specificproceduresfortighteningthesejoints. Installationsequence: 1. The assembly of sleeve and anchor rod should be securedinitscorrectpositioninaccordancewiththecontractdocuments. 2. Ifatemplateisused,theholepatternshouldbeverified bycomparingthetoptemplatetothebaseplatetobe erected and any deviation between the hole positions outsideofthetolerancesmustbereportedtotheEngineerofRecord. 3. Theconcreteshouldbeplacedandcured. 4. Ifatoptemplateisabovetheconcretesurface,itmay beremovednosoonerthan24hoursafterplacingthe concrete. 5. Theexposedpartoftheanchorrodsshouldbecleaned withawirebrushorequivalentandlubricated. 6. Theopeningofthesleeveshouldbecleanedofdebris andsealedoff. 7. Afterremovalofthetemplate,ifany,theanchorrods should be inspected visually to verify that there is no visible damage to the threads and that their position, elevation, and projected length from the concrete are within the tolerances specified in the contract documents.Intheabsenceofrequiredtolerances,theposition,elevation,andprojectedlengthfromtheconcrete should be within the tolerances specified in theAISC Code of Standard Practice for Steel Buildings and Bridges.Thenutsshouldbeturnedontotheboltsatleast oneroddiameterpasttheelevationofthebottomofthe baseplateandbackedoffbyaworkerusinganordinary wrenchwithoutacheaterbar.Anydamageresultingin unusualefforttoturnthenutshouldbereportedtothe EngineerofRecord. 8. Thebaseplateandattachedstructuralelement,orpiece ofequipmentormachinery,shouldbeplaced. 9. Washersshouldbeplaced. 10. Ifthreadsofanchorrodswerelubricatedmorethan24 hoursbeforeplacingthenutorhavebeenwetsincethey werelubricated,theexposedthreadsoftheanchorrod shouldberelubricated.Nutsshouldbecleanedandthe threadsandbearingsurfaceslubricated. 11. Thepretensionandpretensioningmethodshouldbeas specifiedinthecontractdocuments,alongwiththeproceduresandrequirementsforaninstallationverification test,ifnecessary. DESIGNGUIDE1,2NDEDITION/BASEPLATEANDANCHORRODDESIGN/53 A3.InspectionandMaintenanceAfterInstallation Regularinspectionandmaintenanceshouldbeconductedfor jointsthataredesignedforthefatigue.Alljointsdesignedfor SeismicDesignCategoryDorgreater,accordingtoASCE 7,shouldalsobeinspectedandmaintainedasfollowsaftera significantseismicevent. 1. Anchor rod appearance—Draw a diagram of the anchorrodpatternandnumberinaclockwisepattern. Checkeachanchorrodforcorrosion,gouges,orcracks. Suspectedcracksmaybemorecloselyexaminedusing thedye-penetranttechnique.Ifthereisheavycorrosion neartheinterfacewiththeconcrete,theremaybemore severecorrosionhiddenbelowtheconcretewherethe pocket around the anchor rod stays wet. Verify that all the anchor rods have top nuts with washers. Lock washersshouldnotbeused.Galvanizednutsorwashersshouldnotbeusedwithunpaintedweatheringsteel. Checkforinadequatelysizedwashersforoversizeholes. Ifthereisnogroutpad,verifythatalltheanchorrods havelevelingnutswithwashers.Checkforloosenuts, gouges,threaddamage,orcorrosion.Noteanyanchor rodsthataresignificantlymisalignedorbenttofitinthe baseplatehole.Noteanyanchorrodsthatarenotflush withorprojectingpastthenut.Iftheanchorrodisnot projectingpastthenut,measurethedistancefromthe topofthenuttothetopoftheanchorrod. 2. Sounding the anchor rods—Anchor rods may be struckbyahammer(alargeballpeenhammerissuggested)todetectbrokenbolts.Strikethesideofthetop nutandthetopoftherod.Goodtightanchorrodswill allhaveasimilarring.Brokenorlooseanchorrodswill haveadistinctlydifferentanddullersound. 3. Tightness of anchor rod nuts—It should be verified that the top nuts still have a sound tack weld (at the topofthetopnutonly)orajamnut.Tackweldstothe washerorthebaseplateareundesirableandshouldbe reported.Ifoneoftheseisnotusedtopreventloosening ofthenut,thetightnessshouldbeverifiedbyapplying atorqueequalto110%ofthetorquecomputedusing thetorqueequation,inaccordancewithstep20ofthe installationprocedurefordouble-nutjoints. Ifmorethanonenutinajointisloose,theentirejoint should be disassembled, all the anchor rods visually inspected, and the joint reassembled with new nuts. Ifmorethanonenutisloose,thejointmayhavebeen poorlyinstalledorfatigueproblemsmayexist.Aclose following of the performance of the joint should be made. 4. Ultrasonictestofanchorrods—Anultrasonictestof anchorrodsneedbeperformedonlyif • Weldedrepairshavebeenmade. • Similarstructuressubjecttosimilarloadinghave hadfatigueproblems. • Anchor rods were not adequately designed for fatigueinaccordancewiththisSpecification. Theinspectionshouldincludeatleast a. Verification that the joint is kept free of debris, waterandvegetation. b. Verification that there is not severe corrosion, gouges,orcracks. c. Verificationthatthegroutandconcreteinthevicinityoftheanchorrodsisingoodcondition. d. Ahammersoundtestofanchorrods. e. Verificationofthetightnessofnuts.Itshouldbe verifiedthatthenutsstillhaveajamnutorother lockingdeviceorthetightnessshouldbeverified byapplying110%oftheverificationtorque. f. Retighteningofanchorrods,ifneeded. If similar structures subject to similar loading have had anchorrodfatiguecrackingproblems,anultrasonictestof anchorrodsshouldbeperformed.Thetopoftherodorextension should be ground flush and the ultrasonic test and itsinterpretationshouldbeinaccordancewithaprocedure approvedbyaqualifiedengineer. Ifonenutinajointisloose(thetackweldisfractured orthenutdoesnotreachtherequiredtorque),itshould be unscrewed, cleaned, inspected for possible thread stripping, lubricated, placed and brought to the initial condition,andretightenedtothepretensionspecifiedin TableA1usingtheturn-of-nutmethod. 54 / DESIGN GUIDE 1, 2ND EDITION /BASEPLATEANDANCHORRODDESIGN APPENDIXB B.3DeterminationofRequiredStressandEffectsof Eccentricity TRIANGULARPRESSUREDISTRIBUTION Theaxialandflexuralcomponentsoftheappliedloadsare treated separately to determine the resulting stresses betweenthebaseplateandfoundationandthencombinedby superpositiontocalculatethepressuredistributionacrossthe plate. Assumingthatthesupportedcolumnandbaseplatehave coincidentcentroids,if B.1Introduction Whenacolumnissubjectedtoeitheraneccentricityofaxial loadoramomentduetobaserigidity,asimplifyingassumptionmustbemadetodetermineadesignpressureonthebase plate. Throughout this Design Guide, design procedures andexampleshavebeenpresentedusinganassumptionof auniformpressuredistributiononthebaseplate,whichis consistentwithproceduresadoptedbyACI.Alternatively,it ispermissibletoassumeatriangularpressuredistributionon thebaseplate. ThisalternativedoesnotinandofitselfrepresentanelasticdesignoranASDapproachtodesign.Rather,bothtriangularanduniformdistributionsrepresentsimplifyingapproximationsthatareequallyapplicableforLRFDandASD applications. The use of a triangular pressure distribution, as shown in Figure B.1, will often require slightly thicker baseplatesandslightlysmalleranchorrodsthantheuniform pressureapproach,sincethecentroidofthepressuredistributionisclosertothecantileveredgeoftheplate. fpa=Pr/A fpb=Mr/Spl where Pr = appliedaxialcompressiveload Mr = appliedbendingmoment A = areaofbaseplateplandimensions(B×N) Spl = sectionmodulusofbaseplateareawithrespect todirectionofappliedmoment;forbendingofa rectangularplate,Spl=BN2/6 B.2DeterminingRequiredBasePlateThicknessfrom RequiredStrength At times the base plate designer may wish to determine thebasepressureseparatelyfromdeterminingtherequired thickness.To facilitate this approach, a general format for sizingthebaseplatethicknessbasedontheflexuralmoment causedbythepressureontheplatesurfacecanbederivedby settingtherequiredflexuralmomentstrengthoverthewidth ofthebaseplateequaltotheavailableflexuralstrengthand solvingfort: LRFD treq = 4 M u pl φBFy ASD treq = 4 M a pl Ω BFy whereφ=0.90andΩ=1.67. The designer may wish to solve directly for the plate thicknessbasedontheappliedloadsandthegeometryofthe baseconditions.However,anassumptionofpressuredistributionmustbemadetodeterminethemomentusedinthe aboveequations.Thisprocessisillustratedinthefollowing sections. FigureB.1.Elasticanalysisforaxialload plusmoment,triangulardistribution. DESIGNGUIDE1,2NDEDITION/BASEPLATEANDANCHORRODDESIGN/55 Equatingfpa=fpbwillresultinatriangularpressuredistributionacrossthelengthofthebaseplateinthedirection oftheappliedmoment,withthemaximumpressureonthe compressive side of the moment and zero pressure on the tensilesideofthemoment.Thisisthetheoreticalcondition where no tension exists on the interface between the base plateandfoundation,andanyappliedadditionalmomentat thesameaxialcompressiveloadwillresultintension. Theappliedbendingmomentcanbeexpressedasanaxial compressiveforceappliedatadistancefromthecentroidof thecolumn/baseplate.Thisdistance,designatedastheeccentricity(e),canbedeterminedas e=Mr/Pr Thebalancepointwherethebaseplatepressurechanges fromzerotensiontopositivetensioncanbedefinedbyarelationshipbetweentheeccentricityandthebaseplatelength orwidthasapplicable.Itwaspreviouslyindicatedthatthis transitionpointoccurswhenfpa=fpb.Therefore,setting P M = A S pl P Pe = BN BN 2 6 (assumingappliedmomentisparalleltoN) e=N/6 Thispointwheree=N/6iscommonlycalledthekernof thebaseplate. B.4.1DesignProcedureforaSmallMomentBase 1. Choosetrialbaseplatesizes(BandN)basedongeometryofcolumnandfour-anchorrequirements. N>d+(2×3in.) B>bf+(2×3in.) 2. Determineplatecantileverdimension,morn,indirectionofappliedmoment. m=(N−0.95d)/2 n=(B-0.80bf)/2 3. Determine applied loads, P and M (Pu and Mu for LRFD, Pa and Ma for ASD) based on ASCE 7 load combinations. 4. Determineeccentricityeandekern. e=M/P ekern=N/6 Ife≤ekern,thisisasmallmomentbase,notensionexists betweenbaseplateandfoundation,seeFigureB.2a. If e > ekern, this is a large moment base, and must be designedfortensionanchorage.SeeSectionB4.2. FigureB.2.Effectofeccentricityonbearing. 56 / DESIGN GUIDE 1, 2ND EDITION /BASEPLATEANDANCHORRODDESIGN 5. Determinebasepressures. B.4.2DesignProcedureforaLargeMomentBase Whentheeffectiveeccentricityislarge(greaterthanekern), there is a tensile force in the anchor rods due to the moment,seeFigureB.2b.Tocalculatethisforce,theanchorrod force,T,andthelengthofbearing,A,mustbedetermined, asshowninFigureB.3. By static equilibrium, the following equations can be derived. Duetoaxialcompression: f pb = P P = A BN whereP=PuforLRFD,PaforASD Duetoappliedmoment: f pb = whereP=PuforLRFD,PaforASDandM=Mufor LRFD,MaforASD. P 6e 1 + ≤ f p avail BN N whereP=PuforLRFD,PaforASD f p avail = A′ = thedistancebetweentheanchorrodandthecolumncenter T = TuforLRFD,TaforASD P = PuforLRFD,PaforASD M = MuforLRFD,MaforASD 0.85 f c′ Ω iffp(max)≥fpavail,adjustthebaseplatedimensions f p(max) = f pa − f pb = ASD f p avail = φ0.85 f c′ where Combinedpressure: LRFD f p AB 2 f p AB N ′ − A PA′ + M = 2 3 6 Pe M = S pl BN 2 f p(max) = f pa + f pb = T + P= P 6e 1− BN N whereP=PuforLRFD,PaforASD. 6. Determinepressureatmdistancefromfp(max). fpm=fp(max)–2fpb(m/N) 7. DetermineMplatm. m m 2 m m 2 M pl = f p(max) − 2 f pb + 2 f pb N 3 N 2 8. Determinerequiredplatethickness. LRFD treq = 4 M u pl φBFy ASD whereφ=0.90andΩ=1.67 treq = 4 M a pl Ω BFy FigureB.3.Generaldefinitionofvariables. DESIGNGUIDE1,2NDEDITION/BASEPLATEANDANCHORRODDESIGN/57 Bysummingthemomentsabouttheresultingboltforce andsolvingasaquadraticfunction,thefollowingexpression canbedeterminedforcalculatingthebearingdistance,A: 6. Determine the plate thickness based on the required flexuralstrengthperinchofplate: LRFD f ′± A= f p B ( PA′ + M ) f ′ 2 − 4 6 fpB tp = ASD 4 M u pl tp = φFy 4 M a pl Ω Fy 3 where B.5Example:SmallMomentBasePlateDesign, TriangularPressureDistributionApproach f′ = fpBN′/2 P = PuforLRFD,PaforASD M = MuforLRFD,MaforASD Theresultingtensileforceintheanchorrodsisthen T= f p AB 2 −P whereT=TuforLRFD,TaforASD,andP=PuforLRFD, PaforASD. Thedesignprocedureisasfollows: 1. Determinetheavailablebearingstrength,φPporPp /Ω with Pp = 0.85 f c′A1 A2 / A1 ≤ 1.7 f c′A1 φ = 0.90 Ω = 1.67 2. Choosetrialbaseplatesizes(BandN)basedongeometryofcolumnandthefour-anchorrequirement. 3. Determinethelengthofbearing,A,equaltothesmallest positive value from the equation in Section B.4.2. Ifthevalueisreasonable,goontothenextstep.Ifit isclosetothevalueofN′,thesolutionisnotpractical sincethisimpliesthatbearingexistsinthevicinityof theanchorrod.Ifthiswereso,theanchorrodcouldnot developitsfulltensilestrength.Itisthennecessaryto returntoStep2andchooseanother,largerplatesize. 4. Determinetheresultantanchorboltforce,T,fromthe aboveequation.Ifitisreasonable,gotothenextstep. OtherwisereturntoStep2. 5. Determine the required moment strength per inch of plateasthegreaterofthemomentduetothepressure andthemomentduetotensionintheanchorrods.Each istobedeterminedattheappropriatecriticalsection. Designabaseplateforaxialdeadandliveloadsequalto100 and160kips,respectively,andmomentsfromthedeadand liveloadsequalto250and400kip-in.,respectively.Bending isaboutthestrongaxisforthewideflangecolumnW12×96 withd=12.7in.andbf=12.2in.Theratiooftheconcrete tobaseplateareaisunity;Fyofthebaseplateis36ksiand fc′oftheconcreteis4ksi. 1. Choosetrialbaseplatesizes(BandN)basedongeometryofcolumnand4-anchorrequirements. N>d+(2×3.0in.)=12.7+6=18.7in. B>bf+(2×3.0in.)=12.2+6=18.2in. TryN=19in.,B=19in. 2. Determineplatecantileverdimension,morn,indirectionofappliedmoment. ( N − 0.95d ) 19.0 − 0.95(12.7 in.) = = 3.47 in. 2 2 B − 0.80b f 19 − 0.80(12.2 in.) n = = =4.62in. 2 2 (Notindirectionofappliedmoment) m = 3. Determine applied loads, P and M, based onASD or LRFDloadcombinations. LRFD ASD Pu=1.2(100)+1.6(160)= 376kips Pa=100+160=260kips Mu=1.2(250)+1.6(400)= 940kip-in. Ma=250+400=650kip-in. 4. Determineeccentricityeandekern. LRFD eu = Mu 940 = = 2.5in. 376 Pu 58 / DESIGN GUIDE 1, 2ND EDITION /BASEPLATEANDANCHORRODDESIGN ASD ea = Mu 650 = = 2.5in. 260 Pu eker n = 6. Determinepressureatcriticalbendingplane[mdistance fromfp(max)]. N 19.0 = = 3.17in. 6 6 Thus,e=2.5in.<ekern=3.17in.,thisisasmallmoment base,notensionexistsbetweenbaseplateandfoundation. LRFD m f pu ( m ) = f pu(max) − 2 f p (b )u N 5. Determinebasepressuresfora1-in.stripofplate. Duetoaxialcompression: P P f p( ax ) = = A BN LRFD 2(0.822)(3.47 in.) 19 in. = 1.56 kips/in. = 1.86 − ASD Pu P f p(ax) = a BN BN 260 kips 376 kips = 0.720 ksi = 1.04 ksi = = 19 in.×19 in. 19 in.×19 in. LRFD m 2 +( f pu(max) − f pu ( m ) ) 3 Duetoappliedmoment: f p(ax) =f p (bu) = = M u pl =(1.56 kips/in.) ASD 6 Pu e BN 2 6(376 kips)(2.50 in.) 2 19 in.×(19 in.) = 0.822 kips/in. (3.47 in.) 2 2 (3.47 in.) 2 +(1.86 −1.56 kips/in.) 3 = 10.6 kip-in. M 6 Pe = S pl BN 2 LRFD f p ( ax ) = f p (ba ) = = 6 Pa e BN 2 6(260 kips)(2.50 in.) 2 = 0.569 kips/in. ASD f pu(max) = f p ( ax )u +f p (b )u f pa(max) = f p ( ax )u +f p (b )u = 1.042 − 0.822 = 0.220 kips/in. n 2 M u pl = f p ( ax )u 2 (4.62 in.) 2 2 = 11.1kip-in./in. = 1.04 kips/in. = 0.720 + 0.569 = 1.29 kips/in. f pa(min) = f p ( ax )u +f p (b )u = 0.720 − 0.569 = 0.151kips/in. ASD m 2 M a pl =( f pa ( m ) ) 2 m 2 +( f pa(max) − f pa ( m ) ) 3 (3.47 in.) 2 2 (3.47 in.) 2 +(1.29 −1.08kips/in.) 3 = 7.34 kip-in. M u pl =(1.08kips/in.) Bending about a plane at n, perpendicular to applied moment. For the case of axial loads plus small moments,theprocedureshownbelowcanbeused(using theaxialloadonly).Foraxialloadspluslargemoments, amorerefinedanalysisisrequired. LRFD LRFD f pu(min) =f p ( ax )u + f p (b )u 19 in.×(19 in.) Combinedpressure: = 1.042 + 0.822 = 1.86 kips/in. 2(0.569)(3.47in.) 19 in. = 1.08kips/in. = 1.29 − Bendingofa1-in.-widestripofplateaboutaplaneatm, inthedirectionofappliedmoment: m 2 M u pl =( f pu ( m ) ) 2 f p( b ) = m f pa ( m ) = f pa(max) − 2 f p (b ) a N 7. Determine Mpl for bending about critical planes at m andn. f p( ax ) = ASD ASD n 2 M a pl = f p ( ax ) a 2 (4.62 in.) 2 2 = 7.68kip-in./in. = 0.720 kips/in. ThecriticalmomentisthelargerofMplaboutmandn criticalplanes. LRFD ASD Mucrit=11.1kip-in./in. Macrit=7.68kip-in./in. DESIGNGUIDE1,2NDEDITION/BASEPLATEANDANCHORRODDESIGN/59 8. Determinerequiredplatethickness: Note:SincetheMplisexpressedinunitsofkip-in./in., theplatethicknessexpressionscanbeformattedwithouttheplatewidth(B)assuch: LRFD tu req = 4 M ucrit φFy 4×11.1kip-in. 0.90×36 ksi = 1.17 in. = 2. Assumea14-in.×14-in.baseplate.Theeffectiveeccentricityis LRFD ASD e=720kip-in./90kips=8.00in. e=480kip-in./60kips=8.00in. ASD ta req = 4 M acrit Ω Fy 4× 7.68kip-in.×1.67 36 ksi = 1.19 in. = 3. Determinethelengthofbearing. LRFD N =19in. B =19in. t =14in. ASD 3.06 ksi ×14 in.×12.5in. ′ 2.04 ksi ×14 in.×12.5in. f = 2 2 = 178kips = 268kips f′= 9. Useplatesize: Then, e > ekern; therefore, anchor rods are required to resistthetensileforce.Theanchorrodsareassumedto be1.5fromtheplateedge. thus, LRFD B.5.2Example:LargeMomentBasePlateDesign, TriangularPressureDistributionApproach DesignthebaseplateshowninFigureB.4foranASDand LRFDrequiredstrengthof60and90kips,respectively,and momentsfromthedeadandliveloadsequalto480and720 kip-in.,respectively.Theratiooftheconcretetobaseplate area(A2/A1)is4.0.Bendingisaboutthestrongaxisforthe wideflangecolumnW8×31withd=bf=8in.;Fyofthe baseplateandanchorrodsis36ksiandfc′oftheconcrete is3ksi. 3.06×14 2682 − 4 6 268 − × (90×5.5) + 720 A= 3.06×14 3 = 5.27 in. ASD A= 2.04×14 1782 − 4 6 178 − × (60×5.5) + 480 2.04×14 3 = 5.27 in. 1. LRFD Pu = 90 kips M u = 720 kip-in. φPp A1 = 0.60(0.85)(3.0)(2) ASD Pa = 60 kips M a = 480 kip-in. Pp ΩA1 ≤ 0.60(1.7)((3.0) φPp A1 = 3.06 ksi Pp ΩA1 = (0.85)(3.0)(2) 2.50 ≤ (1.7)(3.0) 2.50 = 2.04 ksi FigureB.4.Designexamplewithlargeeccentricity. 60 / DESIGN GUIDE 1, 2ND EDITION /BASEPLATEANDANCHORRODDESIGN 4. Determine the required tensile strength of the anchor rod. LRFD Anchorrodsareplacedata12-in.edgedistance.The requiredmomentstrength,MuplorMapl,fora1-in.strip ofplateduetothetensionintheanchorrodsis ASD 2.04ksi ×5.27in.×14in. 3.06ksi ×5.27in.×14in. − 60 kips − 90 kips Ta = 2 2 = 15.2 kips = 22.8kips 60kips Trod = Ta / 2 = 7.6 = Tu / 2 = 11.4kips Tu = Trod LRFD ASD 22.8kips(3.2 in. −1.5in.) 2(3.2 in. −1.5in.) = 11.4 in.-kips/in. 15.2 kips(3.2 in. −1.5in.) M a pl = 2(3.2 in. −1.5in.) = 7.60 in.-kips/in. M u pl = 5. Determinetherequiredplatethickness. Themomentforthisdeterminationistobetakenatthe criticalplatewidth.Thisisdeterminedbyassumingthat theloadspreadsat45°toalocation0.95dofthecolumn.Thewidthisthentakenastwicethedistancefrom the bolt to the critical section for each bolt, provided thatthecriticalsectiondoesnotintersecttheedgeofthe plate. Thecriticalsection,asshowninFigureB.5,isat14− 0.95(8)/2=3.2in. Therequiredmomentstrength,MuplorMapl,fora1-in. stripofplate,determinedfromthebearingstressdistributioninFigureB.4,is LRFD Therequiredmomentstrengthduetothebearingstress distributioniscritical. Therequiredplatethicknessis: LRFD tp = 4(12.5in.-kips) = 1.24 in. 0.90×36 ksi ASD tp = 4(8.33in.-kips)(1.67) = 1.24 36 ksi Usea14×14×1�-in.baseplate. ASD 2 M u pl = 1.20 ksi ×(3.2 in.) 2 2 (3.06 ksi −1.20 ksi) × (3.2 in.) 2 + 3 2 =12.5in-kips/in. 2 M a pl = 0.80 ksi ×(3.2 in.) 2 2 ( 2.04 ksi − 0.80 ksi) × (3.2 in.) 2 3 + 2 =8.33in-kips/in. FigureB.5.Criticalplatewidthforanchorbolt(tensionside). DESIGNGUIDE1,2NDEDITION/BASEPLATEANDANCHORRODDESIGN/61 62 / DESIGN GUIDE 1, 2ND EDITION /BASEPLATEANDANCHORRODDESIGN