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1、ANIMPROVEDK-FACTORFORMULA1ByFrancoisCheong-Siat-Moy,MemberASCEABSTRACT:Theeffectivelengthfactor,K,ofacolumnisdependentonthelateralrestraintimposedonit.Theswayandno-swayalignmentchartK-factorsarespecialcaseswhenthelateralrestraintiszeroandin®nite,respectively.Therefore,theyarenotdirec
2、tlyapplicabletopracticalcolumns.Ageneralformulaisderivedthatisapplicabletocolumnsinfullybraced,partiallybraced,andunbracedframes,i.e.,tocasesinwhichthelateralrestraintcanvaryfromminusin®nitytoplusin®nity.Theadvantageofusingtheformulaisdemonstratedbycomparingitwithothermethods.Forexam
3、ple,theAISCLRFDSpeci®cationCommentarydoesnotallowK-factorslessthanthelimitimposedbyEq.C-C2-4btobeusedwhencalculatedbymeansofEq.C-C2-4a.Withtheproposedformulathisrestrictionisremoved,therebyincreasingthedesignrange.ItalsoshowsthatK-factorformulasbasedonthestiffnessconceptbecomeincreas
4、inglyunconservativeasthelateralrestraintbecomesverylarge.INTRODUCTIONwhereK9i=effectivelengthfactorwithstorystabilityeffectforithrigidcolumn;Ii=momentofinertiainplaneofbendingWhendesigninginaccordancewiththeAISCLRFD(Amer-forithrigidcolumn;Ki=effectivelengthforithrigid-columnicanInsti
5、tuteofSteelConstructionloadandresistancefactorfactorbasedonalignmentchartforunbracedframe;Pui=re-design)Speci®cation(1994),itiscommonpracticetoclassifyquiredaxialcompressivestrengthforithrigidcolumn;andasteelframeaseitherbracedorunbraced.Oneadvantageof(Pu=requiredaxialcompressivestre
6、ngthofallcolumnsinsuchaprocedureisthatitallowsanappropriatecolumnef-astory.[Note:(2)isactuallyEq.C-C2-4bofAISCSpeci®-fectivelengthfactor,K,tobereadilycalculated.Twoalign-cationCommentary.]mentchartshavebeenprovidedfordeterminingK-values,oneHowever,allsuchformulasarenotsuf®cientlyaccu
7、rateinfortheno-swaycaseandonefortheswaycase.Oftensuchmanycases.Forexample,substitutingthevalueofI2=`fromK-factorshavetobemodi®edtoimprovetheiraccuracy.SeeFig.1(b)into(1)givesKAB=K9i=0,whentheactualanswerEq.C-C2-4aofAISCLRFDSpeci®cationCommentaryforis0.7.ThedegradationofKABtozerowhenI
8、2=`isacom-ex