Some aspects to consider when analysing mat foundations
Question:
I am using STAAD.Pro to analyze a mat foundation that supports a steel frame. I have used the PLATE MAT command and set the springs to COMPRESSION only. I encounter 2 problems :- a) Instability warnings b) Some springs still go into tension
How do I go about correcting these problems?
Answer:
Inordertosolveproblemsofthistype,therearetwoaspectsthatoneneedstopayattentionto.
1.Solvingpurecomponentloadcases
Letusassumethatthereare4primaryloadcases.Loadcases1and2areverticalloadcases(downwardloadsalongGY),3iswindalongX(NodalforcesalongglobalX),4iswindalongZ(NodalforcesalongglobalZ).
Considertheloadcases3and4.Theycontainonlylateralforces.Casessuchasthesearecalledcomponent-typeprimarycasesbecausetheyrepresentonlyonetypeofload-windonly,seismiconly,etc.Intherealworld,acomponenttypeloadactsinconjunctionwithothercasessuchasgravity.Thus,solvingapurecomponentcaseisusefulonlywhentheresultsforthatcasecanbecombinedwiththosefromgravityandotherloadcasesforasteeldesignforexample.Butthisrequirestheprincipleofsuperpositiontobeapplicableforthatanalysisrun.Theprincipleofsuperpositionstatesthat
Resultsofcase
A +ResultsofcaseB=Resultsof(caseA+caseB)
Thisprincipleworksonlyforstaticlinearconditions.
Loadcases3and4produceanoverturningmoment.Tosatisfyequilibrium,arestoringmomentneedstobemobilizedtocounteractthisoverturningmoment.Intheseloadcases,inadditiontothehorizontalforces,hadtherebeenloadsactingverticallydownwards,theywouldhavecontributedtowardsarestoringmoment.Butsuchloadsarenotpresent.
So,thecontributiontorestoringmustcomesolelyfromthesoilsprings.Normally,thisisformedwhensomespringsgointo compressionandothersgointotensionthusformingacouple.But,bydeclaringthesoilspringsascompression-only,thetensileforceinthespringsaredisallowed.Thus,arestoringmomentcannotbeformedsolelybythespringforces.Itleadstotheinstabilitywarnings.
Consequently,acomponentloadcasecontainingonlyhorizontalforcesthatproduceanoverturningmomentcannotberesistedbyasystemofsoilspringsinwhichatensileforceinthesoilspringisdisallowed.
Therearetwowaystoaddressthissituation.
1.Instructtheprogramto"not"solvesuchloadcases.Themeanstodothatistoconverttheminto"REFERENCELOADDATA"whichisexplainedinsection5.31.6oftheTechnicalReferencemanual.
2.Instructtheprogramtosolveloadcases1through4withoutthe"COMPRESSION"attribute.Thatattributecanbespecifiedlaterwhenthecombinationcasesaresolved,asexplainednext.ThePERFORMANALYSISandCHANGEcommandsshouldalsobespecifiedafterloadcase4.Sincetheresultsofthesecomponentcasesareofnousetous,wewilldis-regardthem.Thus,wewillhavesomethinglikethis.
MEMBERPROPERTIES
..
CONSTANTS
..
MEMBERRELEASE
..
SUPPORTS
1TO126 PLATEMATDIRECTIONYSUBGRADE12.0
LOAD1DEADLOAD
SELFY-1.0
LOAD2LIVELOAD
MEMBERLOAD
LOAD3WINDINX
JOINTLOAD
35TO46FX0.6
LOAD4WINDINZ
JOINTLOAD
31TO67FZ0.35
PERFORMANALYSIS
CHANGE
2.Solvingcombinationloadcases
Thesecondaspecttoconsiderinthesemodelsisthetypeofcommandtousewhencombiningtheindividualcasestoformcombinationcases.MostpeopletypicallyusethesyntaxLOADCOMBINATIONnnn.ThisinstructsSTAADtofindtheresultforacombinationcasebyaddingtheresultsofthecomponentprimarycasesthatmakeupthatcombinationcase.Inotherwords,
LOADCOMBINATION7
11.021.0
instructstheprogramtofetchtheresultsofloadcases1and2andaddthemalgebraicallytoproducetheresultsofloadcase7.Ananalysisinvolvingtheequation[K]{d}={P}isnotbeingdonewhendetaileddiscussionon this syntaxisused.
Thisapproachtopic is OKtouseonlyunderlinearconditionsinwhichthelawsofsuperpositionwork.
Innon-linearconditionssuchaswhenCOMPRESSION-onlyspringsarepresentavailable in themodel,thisprincipledoesnotwork.
So,insteadofaddingtheresults,theprogrammustbeinstructedtoformaphysicalloadcasecalled7whichcontainstheloaditemsofcases1and2factoredby1.0andperformtheoperation[K]{d}={P} where{P}isloadcase7.Thisisthecorrectwaytoanalyzethemodelfortheloadsofcases1and2actingsimultaneously.
ThemeanstoachieveitistousetheREPEATLOADsyntaxinsteadoftheLOADCOMBINATIONsyntax.Forexample,thecommands
LOADCOMB7COMBINATIONLOADCASE7
11.021.0
LOADCOMB8COMBINATIONLOADCASE8
11.021.031.0
LOADCOMB9COMBINATIONLOADCASE9
11.021.041.0
LOADCOMB12COMBINATIONLOADCASE12
11.041.0
LOADCOMB13COMBINATIONLOADCASE13
10.6720.6730.67
LOADCOMB14COMBINATIONLOADCASE14
10.6720.6740.67
mustbechangedto
LOAD7COMBINATIONLOADCASE7
REPEATLOAD
11.021.0
LOAD8COMBINATIONLOADCASE8
REPEATLOAD
11.021.031.0
LOAD9COMBINATIONLOADCASE9
REPEATLOAD
11.021.041.0
LOAD12COMBINATIONLOADCASE12
REPEATLOAD
11.041.0
LOAD13COMBINATIONLOADCASE13
REPEATLOAD
10.6720.6730.67
LOAD14COMBINATIONLOADCASE14
REPEATLOAD
10.6720.6740.67
Additionally,since the COMPRESSION-onlyattributewasremovedforcases1to4,theSUPPORTSneedtobere-specifiedjustbeforeloadcase7andarticlepostedat the COMPRESSIONattributemustbeincludedinthatcommand.Thedatawillthenlooklike
LOAD4WINDINZ
JOINTLOAD
31TO67FZ0.35
PERFORMANALYSIS
CHANGE
SUPPORTS
1TO126 PLATEMATDIRECTIONYSUBGRADE12.0COMPRESSION
LOAD7COMBINATIONLOADCASE7
REPEATLOAD
11.021.0
..
..
..
LOAD14COMBINATIONLOADCASE14
REPEATLOAD
10.6720.6740.67
PERFORMANALYSIS
CHANGE
LOADLIST7TO14
..
PARAMETER
CODEAISCUNIFIED2010
METHODASD
..
........followinglink