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deflection limit state

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  A Beginner's Guide to the Steel Construction Manual, 13 th  ed. (old) Chapter 8 - Bending Members © 2006, 2007, 2008 T. Bartlett Quimby Introduction Flexure Flexural Limit State Behavior Determining  A pplicable Limit States Flexural Yielding Limit State Lat eral Torsional Buckling Limit State Flange Local Buckling Limit State Shear Shear Behavior Shear Strength Limit State Deflection Deflection Behavior Deflection Limit State Misc. Limit States Web Local  Yieldin g Web Crippling Beam Design  Section 8.4.2 Deflection Limit State Last Revised: 11/04/2014 In the abse nce of more specific criteria, criteria for structures with brittle finishes (as found in code documents for years) is frequently used. This simplistic crit eria puts a limit of the span divided by 360 on the incremental deflection due to live (or transient) load only and a limit of the span divided by 2 40 on deflecti on under total load. These limit states are mathematic expressed as: LL  < L/360 TL  < L/240 These limits were originally developed for members with "brittle" finishes, such a s plaster. Plaster is not commonly used as a finishing material anymore. The goal of th e limits wa s to minimi ze the possibility of damage to the finish and provide reasonable comfort for the building occ upants. The criteria has persisted in practice. Other criteria has been used that more explicitly addresses the use of the beam un der consideration. For example, the Timber Construction Manual [ref. 12], page 66 suggests the values given in Table 8.4.2.1 and 8.4.2.2. Other references give different, but similar, crit eria. Table 8.4.2.1  AITC Recommended Deflection Limits Used with Permission Use Classification  Applied Loa d Only  Applied Load + Dead Load Roof Beams - Industrial L/180 L/120 - Commercial and institutional - Without plaster ceiling L/240 L/180  - With plaster ceiling L/360 L/240

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deflection limit theorem

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  • ABeginner'sGuidetotheSteelConstructionManual,13thed.(old)

    Chapter8BendingMembers2006,2007,2008T.BartlettQuimby

    Introduction

    Flexure

    FlexuralLimitStateBehaviorDeterminingApplicableLimitStatesFlexuralYieldingLimitStateLateralTorsionalBucklingLimitStateFlangeLocalBucklingLimitState

    Shear

    ShearBehaviorShearStrengthLimitState

    Deflection

    DeflectionBehaviorDeflectionLimitState

    Misc.LimitStates

    WebLocalYieldingWebCrippling

    BeamDesign

    Section8.4.2

    DeflectionLimitStateLastRevised:11/04/2014

    Intheabsenceofmorespecificcriteria,criteriaforstructureswithbrittlefinishes(asfoundincodedocumentsforyears)isfrequentlyused.Thissimplisticcriteriaputsalimitofthespandividedby360ontheincrementaldeflectionduetolive(ortransient)loadonlyandalimitofthespandividedby240ondeflectionundertotalload.Theselimitstatesaremathematicexpressedas:

    LL

  • Figure8.4.2.1FrozenScupper

    SelectingSectionsCoverPlatesTransverseStiffenersforShearBearingPlatesTransverseStiffenersforConcentratedLoadsContinuousBeams

    ChapterSummary

    ExampleProblems

    HomeworkProblems

    References

    ReportErrorsorMakeSuggestions

    PurchaseHardCopy

    MakeDonation

    FloorBeams Ordinaryusagea L/360 L/240Highwaybridgestringers L/200toL/300 Railwaybridgestringers L/300toL/400 aOrdinaryusageclassificationforfloorsisintendedforconstructioninwhichwalkingcomfortandminimizedplastercrackingarethemainconsiderations.Theserecommendeddeflectionlimitsmaynoteliminateallobjectionstovibrationssuchasinlongspansapproachingthemaximumlimitsorforsomeofficeandinstitutionalapplicationswhereincreasedfloorstiffnessisdesired.Fortheseusages,thedeflectionslimitsoftable8.4.2.2havebeenfoundtoprovideadditionalstiffness.

    Table8.4.2.2AITCDeflectionLimitsforUsesWhereIncreasedFloorStiffnessisDesired

    UsedwithPermission

    UseClassification AppliedLoadOnlyAppliedLoad+DeadLoada

    FloorBeamsCommercial,Office&InstitutionalFloorJoists,spansto26ftb

    LL

  • pondingwater.Pondingisaprogressiveevent.Themorewaterontheroof,themoredeflectionyouget,whichmeansthatevenmorewatercanberetained,whichleadstomoredeflection,etc...Ifthebeamisstiffenough,thenpondingcanbeminimized.

    Thebestsolutiontothepondingproblemisarchitectural.Itisstronglyrecommendedthatsufficientslopebegiventoroofsystems(aminimumof1/4"perfoot)topreventponding.Appropriatedrainagemustalsobeprovided.

    Roofsincoldregionsthatusescupperstodrainarooflocatedbehindaparapetmaybecomepluggedwithice,resultinginunintentionalponding,leadingtodisastrousresults.Figure8.4.2.1showssuchafrozenscupper.Scuppersmustalsobemadelargeenoughtoallowwatertoescapeduringadelugeandtominimizeblockagebydebris.

    TolerancesofAttachedElementsorNonStructuralElementsBelow

    Oftentimes,nonstructuralelementshavespecificdeflectiontolerancesthataremorerestrictivethanthegeneralcriteriagivenabove.Thesetolerancesgenerallyareexpressedintermsasamaximumdeflectionvalueandmustbeconsideredindesign.

    Forexample,afloorgirderspanning36ftmaydeflectupto1.2inchesunderaliveloadonlydeflectionlimitofL/360.Anynonstructuralpartitionunderthebeammustbeabletoaccommodatethisdeflection.However,ifitcannot,thentheamountofliveloaddeflectionthatcanbeaccommodatedbecomesthenewdeflectioncriteriaforthisbeam.

    Vibrations

    Certainvibrationshavebeenfoundtobeobjectionableinmostoccupancyclassifications.Vibrationsareoftenlumpedtogetherwithdeflectionsincebotharestiffnessrelated.Vibrationsareafunctionof

  • stiffnessandmass.Thefrequencyofthevibrationsisofmoreconcernthantheamplitude.Thetreatmentofvibrationsisbeyondthecurrentscopeofthistext.

    SelectionofCriteria

    Thechoiceofdeflectioncriteriaisaprojectdependent.Othercriteriamaybeencounteredthathavebeendevelopedforspecialstructuresand/orsituations.Thesemaybeconsideredasneeded.

    Fortheproblemsinthistext,theequationslistedatthestartofthissectionwillbeusedunlessotherwisespecified.


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