new methods for ponding analysis of open web steel joist roofs · aisc appendix 2 “this appendix...

Presentedby:

Copyright©2018SteelJoistInstitute.AllRightsReserved.

F E B R U A R Y 2 1 , 2 0 1 8

MarkD.Denavit,P.E.,Ph.D.JamesM.Fisher,Ph.D.,P.E.,Dist.M.ASCE

NewMethodsforPondingAnalysisofOpenWebSteelJoistRoofs

PollingQuestion

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•  NewrequirementtoearnPDHcredits

•  Twoquestionswillbeaskedduringthedurationoftoday’spresentation

•  ThequestionwillappearwithinthepollingsectionofyourGoToWebinarControlPaneltorespond

Disclaimer

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Theinformationpresentedhereinisdesignedtobeusedbylicensedprofessionalengineersandarchitectswhoarecompetenttomakeaprofessionalassessmentofitsaccuracy,suitabilityandapplicability.TheinformationpresentedhereinhasbeendevelopedbytheSteelJoistInstituteandisproducedinaccordancewithrecognizedengineeringprinciples.TheSJIanditscommitteeshavemadeaconcertedefforttopresentaccurate,reliable,andusefulinformationonthedesignofsteeljoistsandJoistGirders.ThepresentationofthematerialcontainedhereinisnotintendedasarepresentationorwarrantyonthepartoftheSteelJoistInstitute.Anypersonmakinguseofthisinformationdoessoatone’sownriskandassumesallliabilityarisingfromsuchuse.

LearningObjectives

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1. RecalltheroofpondingrequirementswithinASCE7,IBC,andFMGlobal.

2. DescribethelimitationsofthemethodofpondinganalysisgiveninAppendix2oftheAISCSpecification.

3. InvestigatethestabilityofsimpleroofsystemsforpondingusingtheSJIRoofBayAnalysisTool.

4. Identifythemainfactorsinfluencingthepondingstabilityofopen-websteeljoistroofs.


•  ReviewofroofpondingrequirementsandintroductiontotheSJIRoofBayAnalysisTool

–  PresentedbyJimFisher

•  ThedirectanalysismethodforpondingandusingtheSJIRoofBayAnalysisTooltoevaluatesusceptiblebays

–  PresentedbyMarkDenavit

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RoofPonding

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SJITechnicalDigestNo.3

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STRUCTURALDESIGNOFSTEELJOISTROOFSTORESISTPONDINGLOADSORDERFROMsteeljoist.org$25.00

RoofPonding

•  Commentson:

–  IBC2015–  ASCE7-2016–  FMGlobal1-54,2016

–  ANSI/AISC360-16–  ANSI/SJI100-2015

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InternationalBuildingCode1503.4RoofDrainage.

“DesignandinstallationofroofdrainagesystemsshallcomplywithSection1503ofthiscodeandSections1106and1108,asapplicable,oftheInternationalPlumbingCode.”

1503.4.1Secondary(emergencyoverflow)drainsorscuppers.

“Whereroofdrainsarerequired,secondary(emergencyoverflow)roofdrainsorscuppersshallbeprovidedwheretheroofperimeterconstructionextendsabovetheroofinsuchamannerthatwaterwillbeentrappediftheprimarydrainsallowbuildupforanyreason.Theinstallationandsizingofsecondaryemergencyoverflowdrains,leadersandconductorsshallcomplywithSections1106and1108,asapplicable,oftheInternationalPlumbingCode.”

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InternationalBuildingCode

1503.4.2Scuppers.

“Whenscuppersareusedforsecondary(emergencyoverflow)roofdrainage,thequantity,size,locationandinletelevationofthescuppersshallbesizedtopreventthedepthofpondingwaterfromexceedingthatforwhichtheroofwasdesignedasdeterminedbySection1611.1.Scuppersshallnothaveanopeningdimensionoflessthan4inches(102mm).Theflowthroughtheprimarysystemshallnotbeconsideredwhenlocatingandsizingscuppers.”

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1507.10Built-uproofs.

“Theinstallationofbuilt-uproofsshallcomplywiththeprovisionsofthissection.”

1507.10.1Slope.

“Built-uproofsshallhaveadesignslopeofaminimumofnotlessthanone-fourthunitverticalin12unitshorizontal(2-percentslope)fordrainage,exceptforcoal-tarbuilt-uproofsthatshallhaveadesignslopeofaminimumnotlessthanone-eighthunitverticalin12unitshorizontal(1-percentslope).”

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1608.3“SusceptiblebaysofroofsshallbeevaluatedforpondinginstabilityinaccordancewithSection7.11ofASCE7.”

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1611.1Designrainloads.

“Eachportionofaroofshallbedesignedtosustaintheloadofrainwaterthatwillaccumulateonitiftheprimarydrainagesystemforthatportionisblockedplustheuniformloadcausedbywaterthatrisesabovetheinletofthesecondarydrainagesystematitsdesignflow.Thedesignrainfallshallbebasedonthe100-yearhourlyrainfallrateindicatedinFigure1611.1oronotherrainfallratesdeterminedfromapprovedlocalweatherdata.

R=5.2(ds+dh) (Equation16-36)”

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where:

dh=Additionaldepthofwaterontheundeflectedroofabovetheinletofsecondarydrainagesystematitsdesignflow(i.e.,thehydraulichead),ininches.

ds=Depthofwaterontheundeflectedroofuptotheinletofsecondarydrainagesystemwhentheprimarydrainagesystemisblocked(i.e.,thestatichead),ininches.

R=Rainloadontheundeflectedroof,inpsf.Whenthephrase"undeflectedroof"isused,deflectionsfromloads(includingdeadloads)shallnotbeconsideredwhendeterminingtheamountofrainontheroof.”

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1611.2Pondinginstability

“SusceptiblebaysofroofsshallbeevaluatedforpondinginstabilityinaccordancewithSection8.4ofASCE7.”

1611.3Controlleddrainage.

“Roofsequippedwithhardwaretocontroltherateofdrainageshallbeequippedwithasecondarydrainagesystematahigherelevationthatlimitsaccumulationofwaterontheroofabovethatelevation.SuchroofsshallbedesignedtosustaintheloadofrainwaterthatwillaccumulateonthemtotheelevationofthesecondarydrainagesystemplustheuniformloadcausedbywaterthatrisesabovetheinletofthesecondarydrainagesystematitsdesignflowdeterminedfromSection1611.1.SuchroofsshallalsobecheckedforpondinginstabilityinaccordancewithSection1611.2.”

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ASCE7-16Criteria

•  7.11PondingInstability–  Susceptiblebaysshallbedesignedtoprecludepondinginstability.Roofdeflectionscausedbythefullsnowloadsshallbeevaluatedwhendeterminingthelikelihoodofpondinginstability(seeSection8.4)

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ASCE7-16Criteria•  8.4PONDINGINSTABILITYANDPONDINGLOADSusceptiblebaysshallbeinvestigatedbystructuralanalysistoassurethattheypossessadequatestiffnesstoprecludeprogressivedeflection(i.e.,instability)andadequatestrengthtoresisttheadditionalpondingloadAnyofthefollowingconditionsshallbedeemedtocreatesusceptiblebays:

•  1)Bayswitharoofslopelessthan1/4inchperfootwhenthesecondarymembersareperpendiculartothefreedrainingedge.

•  2)Bayswitharoofslopelessthan1inchperfootwhenthesecondarymembersareparalleltothefreedrainingedge.

•  3)Bayswitharoofslopeof1inchperfootandaspantospacingratioforthesecondarymembersgreaterthan16whenthesecondarymembersareparalleltothefreedrainingedge.

•  4)Baysonwhichwateraccumulates(inwholeorinpart)whentheprimarydrainsystemisblockedbutthesecondarydrainsystemisfunctional.Thelargerofthesnowloadortherainloadequaltothedesignconditionforablockedprimarydrainsystemshallbeusedinthisanalysis.

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Susceptiblebays-ASCE7

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FMGlobal1-54

•  SECTION2.5.4.1.6.5

•  “A.Providesecondarydrainagetopreventanypossibilityofrainwateroverload.Theoverflowreliefprovisionestablishesthemaximumpossiblewaterlevelbasedonblockageoftheprimarydrainagesystem.Ensuretheprovisionisintheformofminimalheightroofedges,slotsinroofedges,overflowscuppersinparapetsoroverflowdrainsadjacenttoprimarydrains.

•  B.Ensuretheoverflowreliefprotectionprovidespositiveanduniformdrainagereliefforeachroofsection.

•  C.Whendesigningandsizingthesecondarydrainagesystem(overflowdrainsorscuppers),assumetheprimarydrainsare100%blockedandcannotflowwater.

•  D.Ensuretheinletelevationofoverflowdrainsandtheinvertelevation(seesketchesinTable6aand8d)ofoverflowscuppersarenotlessthan2in.(50mm)normorethan3in.(75mm)abovethelowpointofthe(adjacent)roofsurfaceunlessasaferwaterdepthloading,includingtherequiredhydraulicheadtomaintainflow,hasbeendeterminedbytheroof-framingdesigner.”

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AISCSpecifications-SectionB3DESIGNBASIS

B3.10.DesignforPonding

“Theroofsystemshallbeinvestigatedthroughstructuralanalysistoensurestrengthandstabilityunderpondingconditions,unlesstheroofsurfaceisconfiguredtopreventtheaccumulationofwater.MethodsofevaluatingstabilityandstrengthunderpondingconditionsareprovidedinAppendix2.”

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AISCAppendix2

“Thisappendixprovidesmethodsfordeterminingwhetheraroofsystemhasadequatestrengthandstiffnesstoresistponding.Thesemethodsarevalidforflatroofswithrectangularbayswherethebeamsareuniformlyspacedandthegirdersareconsideredtobeuniformlyloaded.

Theappendixisorganizedasfollows:

–  2.1.SimplifiedDesignforPonding

–  2.2.ImprovedDesignforPonding

ThemembersofaroofsystemshallbeconsideredtohaveadequatestrengthandstiffnessagainstpondingbysatisfyingtherequirementsofSections2.1or2.2.”

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AISCAppendix2

2.1.SIMPLIFIEDDESIGNFORPONDING

Theroofsystemshallbeconsideredstableforpondingandnofurtherinvestigationisneededifbothofthefollowingtwoconditionsaremet:

Cp+0.9Cs≤0.25 (A-2-1)

Id≥25(S4)10-6 (A-2-2)

Id≥3940S4 (A-2-2M)

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AISCAppendix2

2.2.IMPROVEDDESIGNFORPONDING

ItispermittedtousetheprovisionsinthissectionwhenamoreaccurateevaluationofframingstiffnessisneededthanthatgivenbyEquationsA-2-1andA-2-2.

Definethestressindexes

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0 8

0 8

. for primary member (A-2-5)

. for secondary member (A-2-

y op

o p

y os

o s

F fU

f

F fU

f

−⎛ ⎞= ⎜ ⎟⎝ ⎠

−⎛ ⎞= ⎜ ⎟⎝ ⎠

6)

AISCSPECIFICATION

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ImprovedDesign:

Up,thestressindexfortheprimarymemberUs,thestressindexforthesecondarymemberCp,thestiffnessindexfortheprimarymemberCs,thestiffnessindexforthesecondarymemberfo,thestressatinitiationofponding

0.8 for the primary member (Eq. A-2-5)

0.8for the secondary member (Eq. A-2-6)

y op

o p

y os

o s

F fU

f

ffF

U

−⎛ ⎞= ⎜ ⎟⎝ ⎠

⎛ ⎞⎜ ⎟⎝ ⎠

−=

AISCAppendix2PondingAssumptions

•  Framingisflat.

•  Membersarenotcambered.

•  Taperedinsulationnotconsidered.

•  Baysarerectangular.

•  Adjacentbaysareidentical.

•  Beamsareuniformlyspaced.

•  Allbeamshaveequalstiffness.

•  Allmembersaresimplysupported.

•  Axialloadsnotpresent.

•  Waterloadcoverstheentirebay.

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PondingLoadStrategiesbasedontheAISCprovisions:•  Provideroofsystemstoavoidpondingbyslopingroofmembers,orbythe

useoftaperedinsulationorslopingfill.

•  Stiffentheroof’sstructuralmembersbyselectingacombinationoflowflexibilityconstantswhichsatisfyEquationA-2-1oftheAISCSpecificationAppendix2(AISC2016).

•  ConductamoreexactanalysisforpondingfollowingtheproceduresgivenintheAISCSpecificationAppendix2.

•  Counteractthepondingmechanismbyprovidingupwardcamberinthejoists,providedthatdrainsareinstallednearcolumns(seeFMGlobal1-54FM(2016).

•  Whendesigningroofswithlowslopes,parallelchordjoistswithendsupportsatdifferentelevationsaremoreeconomicalthanprovidingpitchintothejoisttopchords.Thewebsystemofanon-parallelchordjoistandthejoistasawholeismoreexpensivetomanufacture……”

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ANSI/SJI100-2015

•  StandardSpecificationforK-Series,LH-Series,andDLH-SeriesOpenWebSteelJoistsandforJoistGirders.

•  TheSJISpecificationsinSection5.11containsthefollowingrequirementrelativetoponding:

– “Thepondinginvestigationshallbeperformedbythespecifyingprofessional.”

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COMMENTSONTHECITEDDOCUMENTS:

•  Allroofsrequireasecondarydrainagesystem.

•  Allroofsmustbedesignedforimpoundedwaterbasedontheprimarydrainsbeingblocked.

•  Impoundedwaterheightsaretoincludethehydraulicheadabovethesecondarydrainagesystem.

•  Pondinginstabilitychecksaretobemadeusingthelargerofsnowloadorrainload(impoundedwater).

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COMMENTSONTHECITEDDOCUMENTS:

•  Forroofswithsnowloadsof20psforless,anadditional5psfofrainonsnowmustbeusedindesign.

•  FollowIBCrequirementsinSection1507.10.1Slope.“Built-uproofsshallhaveadesignslopeofnotlessthanone-fourthunitverticalin12unitshorizontal(2-percentslope)fordrainage,exceptforcoal-tarbuilt-uproofsthatshallhaveadesignslopeofnotlessthanone-eighthunitverticalin12unitshorizontal(1-percentslope).”

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RoofPonding-Maintenance

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RoofPonding-Construction

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RoofPonding-UniqueGeometry

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RoofPonding-UniqueGeometry

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Slope TypicalDrainWater

Flow

Parapet

SJIRoofBayAnalysisTool

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https://steeljoist.org

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“Free”downloadavailableforSJIspreadsheettools.


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GeneralInfoTab

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Copyright©2018

GeneralInfoTab-ASDorLRFD

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GeneralInfoTab-Notes•  GoverningcodeisIBC2012.

•  BaysizesarelimitedtoJoistandJoistGirderLoadTables.

•  Decksizeselectedbyminimumweightanddeflectionlimits,fromSDITables.

•  DeckdeflectionisbasedonminimumofIporIn,perdirectionofSDI.

•  SDIminimumbearinglengthsassumed.

•  JoistsizeselectedbyminimumweightanddeflectionlimitsfromSJILoadTables.

•  DLHjoistdataislimitedtospansgreaterthanthe“safeload”spansintheSJILoadTables.

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LoadInput

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NewinVersion3.0

SteelDeckandJoistSpacingInput

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Joist/JoistGirderDepths&DeflectionChecks

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OPTIONAL INCREASED LOAD DATA Member I Ieff = I/1.15

Joist Load lb / ft 18K 3 85 74 in.4

JG Panel Point Load kips 60G10N4.6F 2484 2160 in.4 NEW

Suggestdoingthis.

DesignSummaries

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CostDataInput

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Cost&DesignSummary

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RunDataSummary

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RunComparisons

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PollingQuestion

WhichofthefollowingisNOToneoftheassumptionsmadeforthepondingprovisionsinAppendix2oftheAISCSpecification?

A.  TheroofsatisfiestheIBCminimumsloperequirements.

B.  Themembersarenotcambered.

C.  Thebeamsareuniformlyspaced.

D.  Thebeamshaveequalstiffness.

E.  Waterloadcoverstheentirebay.

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•  ReviewofroofpondingrequirementsandintroductiontotheSJIRoofBayAnalysisTool

–  PresentedbyJimFisher

•  ThedirectanalysismethodforpondingandusingtheSJIRoofBayAnalysisTooltoevaluatesusceptiblebays

–  PresentedbyMarkDenavit

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LimitationsoftheAISCAppendix2Method

•  Flatroofconstruction–  ThemethodinAISCAppendix2assumesaperfectlyflatroof

•  Noroofslopeandnocamber

•  Momentandshearenvelopes–  ThemethodinAISCAppendix2checksonlythemaximummoment

•  Nocheckformomentandshearstrengththatvaryalongthelength•  Nolocalchecks(e.g.,bendingbetweenpanelpoints)

•  Levelofloading–  ThemethodinAISCAppendix2isonlyintendedforusewithASD

•  NoprovisionsforusewithLRFD

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DirectAnalysisMethodforPonding

•  Anewmethodtoevaluateroofsforponding

•  SimilarinconcepttothedirectanalysismethoddescribedinChapterCoftheAISCSpecification,buttherearemanydifferences

•  Load-effectsduetoimpoundedwaterarecomputeddirectlybasedonthedeformedshapeoftheroofsystem

•  Checkperformedbycomparingrequiredstrengthstoavailablestrengths

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RequiredStrengths

•  Determinedfromananalysisthatcapturesthenonlinearloadingfromtheimpoundedwater

–  Closed-formsolutionsavailableforsimplecases

–  Iterativeanalysisforgeneralcases

•  Geometricnonlinearity(second-ordereffects)andmaterialnonlinearity(inelasticity)neednotbecaptured

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LoadCombinations

•  ForthepondingcheckSJIrecommendsusing:

–  D+0.75P+0.75S forASD

–  1.2D+1.2P+1.2S forLRFD

•  NotethattheIBCstrengthcombinationsstillneedtobechecked

–  D+(LrorSorR) forASD

–  1.2D+1.6(LrorSorR) forLRFD

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D =DeadLoadP =ImpoundedWaterLoadS =SnowLoadLr =RoofLiveLoadR =RainLoad

ForceLevelAdjustmentFactor

•  RequirementfromChapterCoftheAISCSpecification:

“Allload-dependenteffectsshallbecalculatedatalevelofloadingcorrespondingtoLRFDloadcombinationsor1.6

timesASDloadcombinations.”

•  FordesignbyASD,theanalysisisconductedunder1.6timestheASDloadcombination,andtheresultinginternalforcesaredividedby1.6toobtaintherequiredstrengthsofcomponents

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Loads

•  Waterandsnowactatthesametime,butaccountforthephysicaloverlapofmaterial–  Densityofwateronly=62.4lb/ft3–  Densityofsnowonly=γ (14-30lb/ft3,ASCE7-16Equation7.7-1)–  Densityofwaterandsnow=62.4lb/ft3

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Water Level

Water Only

AvailableStrengths

•  MomentandshearenvelopespertheSJISpecification

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0

wL2/8

0

wL/2

-wL/2

wL/8 (25% of end reaction, per SJI Specification)

wL/16 (12.5% of end reaction,assumed)

Shear diagram for simply supported beam under uniformly

distributed load

JoistMomentEnvelope JoistShearEnvelope

NotethattheSJISpecificationdoesnotrequireanystrengthforshearreversals.12.5%ofendreactionisassumedandactionmustbetakentoensurethatcapacity

AvailableStrengths

•  MomentandshearenvelopespertheSJISpecification

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JoistGirderMomentEnvelope JoistGirderShearEnvelope

0

Mmax

0

R

R

R/4 (25% of end reaction, per SJI Specification)

Shear diagram for simply supported beam with equal point loads

25% of shear envelope in reverse direction per SJI Specification


59

Thesesheetsallowyoutocheckabayforponding

NewinVersion3.0

GeneralInput

•  GeneraldatareferencedfromRoofBayAnalysissheet

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General Input (Defined in Roof Bay Analysis Spreadsheet)

Design Methodology ASD40.00 ft40.00 ft24K 7253 lb/ft

36G8N6.2K6.2 k8

18.00 psf36.00 lb/ft12.00 psf

Joist SpanJoist Girder SpanJoist Size

Dead Load on Joists

Snow Load

Joist Girder Size

Number of Joist Spaces

Joist Girder Self Weight

Joist Allowable Load

Joist Girder Allowable Load

PondingSpecificInput

•  Additionaldatabeyondwhatisdefinedonthe“RoofBayAnalysis”sheet

•  Defines:–  Waterload–  Loadfactors–  Undeformedshapeof

theroof(slopeandcamber)

–  Adjacentbays–  etc.

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Ponding Specific Input

-3.00 inCompute load on deformed roof: Y (Y or N)

15.30 lb/ft3

Force level adjustment factor (α ): 1.60override:

Load factors:1.00

override:0.75

override:0.75

override:

0.000 in0.000 in

-10.000 in-10.000 in

Camber:0.625 in

override: in0.000 in


override: inBay is mirrored:

Y (Y or N)Y (Y or N)N (Y or N)Y (Y or N)

Joist support is wall:Y (Y or N)N (Y or N)

N (Y or N)N (Y or N)

Effective moment of inertia:215.1 in4

(Values include override: in4

1.15 factor for 1,677 in4

shear deformations) override: in4

Joist is rigid:

Bottom Joist Girder

Top Joist Girder

Top

Joist Girder

Joist 1 (Leftmost)Joist 9 (Rightmost)

Snow

Dead

Top of roof elevation:

Bottom Right

Snow density:

BottomTop

Bottom

Right

Joist

Left

Bottom LeftTop RightTop Left

Water level relative to zero datum:

Joist

Ponded Water

AnalysisProcedure

•  Readinputandsetupanalysis(e.g.,computejoistandjoistgirderstiffnessmatrices)

•  Loopuntilconvergence:–  Computepondedwaterloads

–  Analyzeeachjoist

–  Analyzejoistgirders(ifnecessary)

–  Checkforconvergencebasedonpondedwaterloadvector

•  Computeanddisplayandmoments,shears,andequivalentloads

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RUN ANALYSIS

Convergence!

Iteration ΣW# (kips)1 14.7852 30.3473 34.1714 35.1135 35.3486 35.4077 35.4218 35.4259 35.42610 35.4261112131415

ComputingPondingLoads

•  Thebaydiscretizedintoagridofcellstocomputepondingloads.

–  Furthersubdivisionintoa4x4girdwithineachcell–  Colombi,P.(2006).“ThePondingProblemonFlatSteelRoofGrids.”JournalofConstructionalSteelResearch,62(7),647–655.

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JoistOutput

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Joist Output

Joist Max Shear Equiv. Load Max Moment Equiv. Load Strength StrengthNumber kips lb/ft kip-ft lb/ft Ratio Check

1 4.29 214.3 39.10 212.9 0.85 OKAY2 4.44 222.0 40.32 220.3 0.88 OKAY3 4.64 232.2 41.97 230.3 0.92 OKAY4 4.78 239.2 43.10 237.2 0.95 OKAY5 4.83 241.7 43.49 239.7 0.96 OKAY6 4.78 239.2 43.10 237.2 0.95 OKAY7 4.64 232.2 41.97 230.3 0.92 OKAY8 4.44 222.0 40.32 220.3 0.88 OKAY9 4.29 214.3 39.10 212.9 0.85 OKAY

NOTES: 1. Loads and load effects correspond to ASD load combinations.2. Strength ratio computed assuming shear capacity equal to 12.5% of the end reaction for shear reversals, see Note 14 on the Ponding Instructions spreadsheet.

RUN ANALYSIS

JoistOutput

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JoistNumber 0' 0" 2' 0" 4' 0" 6' 0" 8' 0" 10' 0" 12' 0" 14' 0" 16' 0" 18' 0" 20' 0" 22' 0" 24' 0" 26' 0" 28' 0" 30' 0" 32' 0" 34' 0" 36' 0" 38' 0" 40' 0"

1 243 241 239 236 233 229 225 220 214 208 200 192 183 173 163 152 141 135 135 135 1352 253 251 248 245 242 238 233 228 222 215 207 198 188 178 167 155 143 136 135 135 1353 267 265 261 258 254 249 244 238 231 224 215 206 195 184 172 160 147 137 135 135 1354 277 274 270 266 262 257 252 245 238 230 221 211 200 188 176 163 149 137 135 135 1355 281 278 273 269 265 260 254 248 241 232 223 213 202 190 177 164 150 138 135 135 1356 277 274 270 266 262 257 252 245 238 230 221 211 200 188 176 163 149 137 135 135 1357 267 265 261 258 254 249 244 238 231 224 215 206 195 184 172 160 147 137 135 135 1358 253 251 248 245 242 238 233 228 222 215 207 198 188 178 167 155 143 136 135 135 1359 243 241 239 236 233 229 225 220 214 208 200 192 183 173 163 152 141 135 135 135 135

NOTES: 1. Loads correspond to ASD load combinations.2. Highlighted distributed loads may cause a local overstress, see notes on Ponding Instructions spreadsheet.

Total Distributed Load on Joist as a Function of Distance from Bottom Support (lb/ft)

JoistOutput

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JoistNumber 0' 0" 2' 0" 4' 0" 6' 0" 8' 0" 10' 0" 12' 0" 14' 0" 16' 0" 18' 0" 20' 0" 22' 0" 24' 0" 26' 0" 28' 0" 30' 0" 32' 0" 34' 0" 36' 0" 38' 0" 40' 0"

12 03 14 12 8 5 14 24 21 17 13 9 45 28 25 20 16 12 7 16 24 21 17 13 9 47 14 12 8 5 18 09

Total Distributed Load in Excess of Allowable Load on Joist as a Function of Distance from Bottom Support (lb/ft)

JoistGirderOutput

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Joist Girder Output

Joist Joist React. Joist React.Number kips kips

2 3.48 4.443 3.58 4.644 3.65 4.785 3.68 4.836 3.65 4.787 3.58 4.648 3.48 4.44

N/A (WALL) 9.78N/A (WALL) 9.62N/A (WALL) 1.58N/A (WALL) NO GOOD

NOTES: 1. Loads and load effects correspond to ASD load combinations.2. Highlighted panel point loads may cause a local overstress, see notes in Ponding Instructions.

Joist Girder size can be revised by inputting larger loads in the ''optional increased load data'' section of the Roof Bay Analysis spreadsheet

Top Joist GirderPanel Point Load

kips

Strength Check:

Bottom Joist GirderPanel Point Load

kips9.069.479.75

Strength Ratio:Strength Check:

Equiv. Load for Shear (kips):

Strength Ratio:

Equiv. Load for Shear (kips):Equiv. Load for Moment (kips): Equiv. Load for Moment (kips):

9.859.759.479.06

Procedure

1.CompleteinitialdesignofroofsystemforprimarydesignloadsandidentifysusceptiblebaysinaccordancewithSection8.4ofASCE7-16.

•  Theremainingstepswillneedtobecompletedforeachuniquesusceptiblebay.

2.DeterminethejoistandJoistGirderpreliminarydesignusingtheroofbayanalysisspreadsheet.

3.Determinethehydraulicheadbasedontheflowrate,Q,andthedrainagesystem.

•  TheflowratecanbedeterminedusingASCE7-16EquationC8-1.

•  ThehydraulicheadcanbedeterminedbasedonASCE7-16TableC8.3-1(overflowdamsorstandpipes),C8.3-3(scuppers),orC8.3-5(circularscuppers)

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Procedure

4.Determinethewaterlevelabovetheprimarydrain(dh+ds).

•  ChecktheBuildingCodetoseeifaminimumheightforsecondarydrainsisprovided.ASCE7-16providesnominimumheightexceptthattheheightshouldbehigherthantheprimarydrain.Aminimumof2inchesabovetheprimarydrainisoftenusedandisrequiredbyFMGlobal.

•  Somecodesrequirethatscuppersbeaminimumof2inchesabovetherooflevel,butshouldnotexceed4inchesabovetherooflevel.

5.Inputtherequireddataintothepondinganalysisspreadsheet.Thedatafromtheroofbayanalysisisautomaticallytransferredtothepondinganalysis.

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Procedure6.Runthepondinganalysis.

•  Ifstabilityisachieved,theanalysisiscomplete.PondingstabilityisachievedwhentheshearandmomentenvelopesforthejoistsandJoistGirdersarenotexceeded.

•  Ifstabilityisnotachieved,returntotheroofbayanalysisandselectalargerjoist,JoistGirder,orbothbyinputtingincreasedloadsinthe“optionalincreasedloaddata”section(ordecreasethejoistspacing).Rerunthepondinganalysisuntilstabilityisachieved.

•  Iflocalloadeffectsareindicated(loadshighlightedwithredfont)determinebasedonanalysisorjudgementwhethertheindicatedappliedloadswillcausealocalizedoverstress.Iftheloadsaredeterminedtocauseoverstress,reruntheanalysiswithlargerjoistsorJoistGirders.

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Procedure

7.Determineifloadingonthejoistsissymmetricorcouldcauseshearreversals.IfthereispotentialforshearreversalinthejoistsandshearreversalisnotaddressedviaotherdesignloadingcriteriasuchasNetUpliftorSnowDrift,specifythatjoistmanufacturerisrequiredto“designjoistsandJoistGirderwebsforaminimumverticalshearequalto12.5%oftheendreactionincompression.”

71

0

wL/2

-wL/2

wL/8 (25% of end reaction, per SJI Specification)

wL/16 (12.5% of end reaction,assumed)

Shear diagram for simply supported beam under uniformly

distributed load

Example

•  Example2fromSJITechnicalDigest3

•  StructurelocatedinMemphis,TN

•  DrainElevation=-10in.

•  OverflowScupperElevation=-8in.

–  Secondarydrainsare24in.wideopenchannelscuppers

72

Controllingsusceptiblebay

ProjectDescriptionandLoading

•  GirderLength,Lg=40ft•  GirderDepth=36in.•  NumberofGirderTopChordPanelPointSpaces,N=8•  JoistLength,Lj=40ft•  JoistSpacing,S=5ft•  DeadLoad,wD=18psf•  GirderDeadLoad,wD=1psf•  LiveLoad,wL=20psf(reducible)•  SnowLoad,ws=7psf(requires5psfrain-on-snowsurcharge

load;seeIBC1611.2andSection7.10ofASCE7-16)

73

PreliminaryDesign

•  EntertherelevantdataintotheRoofBayAnalysissheet

–  SetmaximumJoistGirderdepthto36in.

•  DataautomaticallytransferredtothePondingAnalysissheet

•  Designsatisfactoryfordead,live,andsnowloads

–  Stillneedtocheckrainloadcombinationandpondingstability

74



36G8N6.2K6.2 k8

18.00 psf36.00 lb/ft12.00 psf

Dead Load on Joists

Snow Load

Joist Girder Size






DetermineHydraulicHead

•  Therearetwooverflowsuppers,eachhasatributaryareaofhalfthetotalareaoftheroof:

A=(60ft.)(80ft.)=4800ft.2

•  The100-yearhourlyrainfallrateforMemphis,TNis3.75in./hr.asdeterminedfromFigure1611.1inthe2015IBC

i=3.75in./hr

75


•  DeterminetheflowrateusingEquationC8-1inASCE7-16:

Q=0.0104Ai,gals/min.(ASCE7-16Eq.C8.3-1)

Q=(0.0104)(4800ft.2)(3.75in./hr)=187.2gals/min.

76


•  Aflowrateof187.2gals/min.correspondstoahydraulicheadbetween1and2in.forthe24in.widescupperaccordingtoTableC8.3-3ofASCE7-16.

•  Interpolatingyieldsdh=1.9in. Usedh=2in.

77

DetermineSnowDensity

•  ThegroundsnowloadforMemphis,TNis10psfasdeterminedfromFigure7.2-1ofASCE7-16

pg=10psf

•  DeterminethesnowdensityusingEquation7.7-1ofASCE7-16

γ=0.13pg+14≤30lb/ft3

γ=15.3lb/ft3

78


•  Waterlevel2in.abovesecondarydrain

–  -8in.+2in.=-6in.

•  Computeloadondeformedroof:Yes

•  SJIRecommendedLoadCombination

–  D+0.75P+0.75S–  α=1.6

79


-6.00 inCompute load on deformed roof: Y (Y or N)

15.30 lb/ft3


Load factors:1.00

override:0.75

override:0.75

override:

0.000 in0.000 in

-10.000 in-10.000 in

Camber:0.625 in











Joist is rigid:

Bottom Joist Girder

Top Joist Girder

Top

Joist Girder


Snow

Dead


Bottom Right

Snow density:

BottomTop

Bottom

Right

Joist

Left



Joist

Ponded Water

JoistOutput

80

Joist Output

Joist Max Shear Equiv. Load Max Moment Equiv. Load Strength StrengthNumber kips lb/ft kip-ft lb/ft Ratio Check

1 3.36 167.8 30.37 166.3 0.66 OKAY2 3.46 172.8 31.08 171.2 0.68 OKAY3 3.59 179.6 32.08 177.8 0.71 OKAY4 3.69 184.3 32.78 182.4 0.73 OKAY5 3.72 186.0 33.03 184.1 0.74 OKAY6 3.69 184.3 32.78 182.4 0.73 OKAY7 3.59 179.6 32.08 177.8 0.71 OKAY8 3.46 172.8 31.08 171.2 0.68 OKAY9 3.36 167.8 30.37 166.3 0.66 OKAY

NOTES: 1. Loads and load effects correspond to ASD load combinations.2. Strength ratio computed assuming shear capacity equal to 12.5% of the end reaction for shear reversals, see Note 14 on the Ponding Instructions spreadsheet.

RUN ANALYSIS

JoistOutput

81

JoistNumber 0' 0" 2' 0" 4' 0" 6' 0" 8' 0" 10' 0" 12' 0" 14' 0" 16' 0" 18' 0" 20' 0" 22' 0" 24' 0" 26' 0" 28' 0" 30' 0" 32' 0" 34' 0" 36' 0" 38' 0" 40' 0"

1 197 194 190 186 182 177 172 166 160 154 146 139 135 135 135 135 135 135 135 135 1352 204 201 197 193 188 183 178 172 165 158 151 142 136 135 135 135 135 135 135 135 1353 214 211 207 202 197 192 186 179 172 165 157 148 139 135 135 135 135 135 135 135 1354 221 218 213 208 203 197 191 184 177 169 161 151 142 136 135 135 135 135 135 135 1355 223 220 215 210 205 199 193 186 179 171 162 153 143 136 135 135 135 135 135 135 1356 221 218 213 208 203 197 191 184 177 169 161 151 142 136 135 135 135 135 135 135 1357 214 211 207 202 197 192 186 179 172 165 157 148 139 135 135 135 135 135 135 135 1358 204 201 197 193 188 183 178 172 165 158 151 142 136 135 135 135 135 135 135 135 1359 197 194 190 186 182 177 172 166 160 154 146 139 135 135 135 135 135 135 135 135 135

NOTES: 1. Loads correspond to ASD load combinations.


Appliedloadsgreatestatlocationofgreatest

deflection

Constantappliedloadwheretheroofis

abovethewaterlevel

JoistGirderOutput

82

Joist Girder Output


2 2.90 3.463 2.95 3.594 2.99 3.695 3.00 3.726 2.99 3.697 2.95 3.598 2.90 3.46

N/A (WALL) 7.58N/A (WALL) 7.47N/A (WALL) 1.22N/A (WALL) NO GOOD

NOTES: 1. Loads and load effects correspond to ASD load combinations.2. Highlighted panel point loads may cause a local overstress, see notes in Ponding Instructions.

Joist Girder size can be revised by inputting larger loads in the ''optional increased load data'' section of the Roof Bay Analysis spreadsheet


kips

Strength Check:


kips7.097.377.55



Strength Ratio:


7.627.557.377.09

ReviseDesign

•  The36G8N6.2Kwhichwasselectedbytheroofbayanalysissheetbasedondead,live,andsnowloadingisinsufficientforthepondingcondition.

–  Itneedstobestrengthenedorstiffened.

•  TheJoistGirderwillbebothstrengthenedandstiffenedifthepanelpointloadisincreased.

•  Revisethedesignto36G8N7.5Kusingtheoptionalincreasedloaddataintheroofbayanalysissheet

83

OPTIONAL INCREASED LOAD DATA Member I Ieff = I/1.15Joist Load lb / ft 24K 7 247 215 in.4

JG Panel Point Load 7.5 kips 36G8N7.5K 2333 2029 in.4

JoistGirderOutput

84

Joist Girder Output


2 2.89 3.423 2.93 3.524 2.95 3.595 2.96 3.616 2.95 3.597 2.93 3.528 2.89 3.42

N/A (WALL) 7.37N/A (WALL) 7.29N/A (WALL) 0.98N/A (WALL) OKAY

NOTES: 1. Loads and load effects correspond to ASD load combinations.


kips

Strength Check:


kips7.017.227.36



Strength Ratio:


7.417.367.227.01

CheckIBCStrengthLoadCombination

•  Differencesinpondingspecificinput

–  Computeloadondeformedroof:No

–  Loadfactors(D+R)

•  Bayfoundtobeadequate

85


-6.00 inCompute load on deformed roof: N (Y or N)

15.30 lb/ft3


Load factors:1.00

override:0.00

override:1.00

override:

0.000 in0.000 in

-10.000 in-10.000 in

Camber:0.625 in











Joist is rigid:

Bottom Joist Girder

Top Joist Girder

Top

Joist Girder


Snow

Dead


Bottom Right

Snow density:

BottomTop

Bottom

Right

Joist

Left



Joist

Ponded Water

Example

•  Example4fromSJITechnicalDigest3

•  Determineiftheroofisfreedrainingunderthetotalsuperimposedloads–  DeadLoad=14psf–  DeadLoad=1psf(JoistGirder)–  SnowLoad=25psf

•  Donotconsidercamber•  Duetowallattachmentassume

theedgejoistdoesnotdeflect.•  Theroofhasaslopeof1/4in./ft.

downwardtotheright.

86

PreliminaryDesign

•  Usetheroofbayanalysistabtodesignthebayfordeadandsnowload

–  26K6Joist–  56G8N10KJoistGirder

87



56G8N10K10 k8

14.00 psf42.00 lb/ft25.00 psf

Dead Load on Joists

Snow Load

Joist Girder Size







•  Setwaterlevelaselevationofedgejoist

•  Overrideloadfactorstoanominalloadconditionforthisserviceabilitycheck

–  D+P+S–  α=1.0

•  Overridecambertozero(perproblemstatement)

88


0.00 inCompute load on deformed roof: Y (Y or N)

0.00 lb/ft3

Force level adjustment factor (α ): 1.00override: 1.00

Load factors:1.00

override:1.00

override: 1.001.00

override: 1.00

12.500 in0.000 in12.500 in0.000 in

Camber:0.000 in

override: 0 in0.000 in


override: 0 inBay is mirrored:

Y (Y or N)N (Y or N)Y (Y or N)Y (Y or N)

Joist support is wall:N (Y or N)N (Y or N)

N (Y or N)Y (Y or N)





Joist is rigid:

Bottom Joist Girder

Top Joist Girder

Top

Joist Girder


Snow

Dead


Bottom Right

Snow density:

BottomTop

Bottom

Right

Joist

Left



Joist

Ponded Water

Output

89

Iteration ΣW# (kips)1 0.0002 0.6013 0.6984 0.7135 0.7166 0.7167 0.7168 0.7169 0.716

JoistNumber 0' 0" 2' 0" 4' 0" 6' 0" 8' 0" 10' 0" 12' 0" 14' 0" 16' 0" 18' 0" 20' 0" 22' 0" 24' 0" 26' 0" 28' 0" 30' 0" 32' 0" 34' 0" 36' 0" 38' 0" 40' 0"

1 244 244 244 244 244 244 244 244 244 244 244 244 244 244 244 244 244 244 244 244 2442 244 244 244 244 244 244 244 244 244 244 244 244 244 244 244 244 244 244 244 244 2443 244 244 244 244 244 244 244 244 244 244 244 244 244 244 244 244 244 244 244 244 2444 244 244 244 244 244 244 244 244 244 244 244 244 244 244 244 244 244 244 244 244 2445 244 244 244 244 244 244 244 244 244 244 244 244 244 244 244 244 244 244 244 244 2446 244 244 244 244 244 244 244 244 244 244 244 244 244 244 244 244 244 244 244 244 2447 244 244 244 244 244 245 246 248 250 251 251 251 250 248 246 245 244 244 244 244 2448 244 244 244 245 249 255 260 265 269 271 271 271 269 265 260 255 249 245 244 244 2449 122 122 122 122 124 125 126 127 128 129 129 129 128 127 126 125 124 122 122 122 122

NOTES: 1. Loads correspond to ASD load combinations.2. Highlighted distributed loads may cause a local overstress, see notes on Ponding Instructions spreadsheet.


Convergeswithwater

Waterpresentonfirsttwoupslopejoistsasindicated

byload>244lb/ftTHEROOFISNOTFREEDRAINING


0.00 inCompute load on deformed roof: Y (Y or N)

0.00 lb/ft3

Force level adjustment factor (α ): 1.00override: 1.00

Load factors:1.00

override:1.00

override: 1.001.00

override: 1.00

12.500 in0.000 in12.500 in0.000 in

Camber:0.000 in



override: 0 inBay is mirrored:

Y (Y or N)N (Y or N)Y (Y or N)Y (Y or N)

Joist support is wall:N (Y or N)N (Y or N)

N (Y or N)Y (Y or N)


(Values include override: 485 in4



Joist is rigid:

Bottom Joist Girder

Top Joist Girder

Top

Joist Girder


Snow

Dead


Bottom Right

Snow density:

BottomTop

Bottom

Right

Joist

Left



Joist

Ponded Water


•  Revisedesignbyincreasingthesizeofthejoist

•  Determinetherequiredmomentofinertiabytrialanderror

90

JoistNumber 0' 0" 2' 0" 4' 0" 6' 0" 8' 0" 10' 0" 12' 0" 14' 0" 16' 0" 18' 0" 20' 0" 22' 0" 24' 0" 26' 0" 28' 0" 30' 0" 32' 0" 34' 0" 36' 0" 38' 0" 40' 0"

1 244 244 244 244 244 244 244 244 244 244 244 244 244 244 244 244 244 244 244 244 2442 244 244 244 244 244 244 244 244 244 244 244 244 244 244 244 244 244 244 244 244 2443 244 244 244 244 244 244 244 244 244 244 244 244 244 244 244 244 244 244 244 244 2444 244 244 244 244 244 244 244 244 244 244 244 244 244 244 244 244 244 244 244 244 2445 244 244 244 244 244 244 244 244 244 244 244 244 244 244 244 244 244 244 244 244 2446 244 244 244 244 244 244 244 244 244 244 244 244 244 244 244 244 244 244 244 244 2447 244 244 244 244 244 244 244 244 244 244 244 244 244 244 244 244 244 244 244 244 2448 244 244 244 244 244 244 244 244 244 244 244 244 244 244 244 244 244 244 244 244 2449 122 122 122 122 122 122 122 122 122 122 122 122 122 122 122 122 122 122 122 122 122

NOTES: 1. Loads correspond to ASD load combinations.


Output

91

Convergeswithoutwater

Uniformtotalloadindicatesnoimpounded

waterpresentTHEROOFISFREEDRAININGSelectajoistwithIe≥485in4

Iteration ΣW# (kips)1 0.0002 0.0003456789

SummaryandConclusions

•  Provisionsrelatedtopondingexistinseveralcodes

•  ThecommonlyusedAISCAppendix2methodforevaluatingpondinghasseverallimitations,especiallyforopen-websteeljoistroofs

•  Anewmethod,directanalysisforponding,hasbeendevelopedandimplementedwithintheSJIRoofBayAnalysisTool

•  TherecentlyupdatedSJITechnicalDigest3providesadditionalbackgroundinformationanddetails.

92

PollingQuestion

WhichofthefollowingstatementsisNOTtrueforpondingevaluationusingtheSJIRoofBayAnalysisTool?

A.  JoistsandJoistGirderscanbesloped.B.  JoistsandJoistGirderscanbecambered.

C.  Spacingbetweenjoistsdoesnothavetobeequal.

D.  LoadsonjoistsandJoistGirderscanbecalculatedonundeformedroofs.

E.  ASDandLRFDsolutionsarepossible.

93

PollingQuestionAnswers

WhichofthefollowingisNOToneoftheassumptionsmadeforthepondingprovisionsinAppendix2oftheAISCSpecification?

A.Theroofisassumedtobeflat

WhichofthefollowingstatementsisNOTtrueforpondingevaluationusingtheSJIRoofBayAnalysisTool?TheroofsatisfiestheIBCminimumsloperequirements.

C.TheSJIRoofBayAnalysisToolcanonlymodeluniformlyspacedjoists.

94

new methods for ponding analysis of open web steel joist roofs · aisc appendix 2 “this appendix...

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