ISOGRID DESIGN HANDBOOK - NASA

1 NASACONTRACTORREPORTNASACR-124075 REVISIONAISOGRIDDESIGNHANDBOOKMcDonnellD ouglasAstronauticsCompany5301 BotsaAvenueHuntingtonBeach,Ca92647 February1973[NASA-CR-12_075)150 GRIDDESIGNHANDBOOK(McDonnell-DouqlasAstr onauticsCo.)222pHC$ .) ,GRIDDESIGNHANDBOOKMDCG4295 APREPAREDBY,V1 CDONNELLDOUGLASASTRONAUFIL;SCO_.,1 PANYFOR:NASAMARSHALLSPACEFLIGItTCEN] FOREWORDT hisprogram,thedevelopmentoftheisogriddes ignhandbook,wasconductedbytheMcDonnellDo uglasAstronauticsCompanyatHuntingtonBeac h,Cal.;forniaund_, ,MarshallSpaceFlightCenter, ,Direct:or,ResearchandDevelopment, ,beingresponsibleforSections2and4, :(1)theresultsofanalysis,test,andadvance dmanufacturingstudiesofIndependentResear chandDevelopmentprogcams,(2)aphaseBspace shuttleboosterstudyfundedbytheNASAM arshallSpaceFlightCenter,(3)anisogridtan ktestprogramfundedbytheNASAM arshallSpaceFlightCenter,and(4)theDeltap rogramisogridstructuraltestsfundedbytheN ASAG oddardSpaceFlightCenter, ' :: ,BendingCylindersUnderTorsionalShearCyli nderUnderUniformExternalPressureln-Plane ConcentratedIx}adinInfiniteSheetIn-Plane ConcentratedLoadatEdgeofSheetCutoutReinf orcementOpenIsogridShearWebs()penIsogrid CylindersinCompression,BendingOpenandSki nnedIsogridtqatesMinimumOverallWeightfor CylinderSubjectedtoAxialCompressionandBe ndingNoteonUseofx,y;o,,(.

2 ' ' '.001ill,? ] [m----_? (a,6)CurvesIsogridisSimpletoAnalyzeDistr ibutingConcentratedLoadEquipmentAttached toNodesSkylabFloorandWallGridReinforcedH oleforConcentratedLoadFail-SafeConceptAc cessDoorDesignsSpeedBrakesManufacturingS amplesofIsogridFormingIsogridSampleOptim umCurvesforSphericalCapwithReversePressu reDesignofIsogridSphericalBulkheadsLengt hDependenceofTheoreticalAxialCompression andBendingBucklingSolutionsInteractionCu rveShowingtheEffectofLengthWeightofOptim izedCompression-CriticalIsogridCylinders DesignofIsogridCylindersX,Y,a, ,Y,a,5 CurvesforCylindersUnderUniformExternalPr essureMasterCurvesforUniformExternalPres sureMasterCurvesforUniformExternalPressu reConcentratedLoadShearPanelk1,a,6 Curvesk2,a,5,.,-esX,Y,a,6 CurvesIsogridNodeMachiningIsogridwithUnf langedRibsMachiningIsogridwithFlangedRib sATankWallConfigurationElectricalDischar ge(EDM)orElectrochemical(ECM) , , , ! :a=[32 ISOGRIDDEFINITIONS thicknessofskinwidthofribwebdepthofwebde pthofflangewidthofflanget+d=platethickne ssofunflangedisogridheightoftrianglelego ftriangle, ,d:=mt'KDteffdistancecentertocenterofnod esTcbdwc =_'_-W'_:t-ffnon-dimensionalparameters(l +_+_I[3(I+6_z+-3_I* )z+I+_62*_ z]3[(1+6)-b_(l+k)]2bendingstiffnessparam eter.)]

3 (Forunflangedisogrid, ,_z:[3_(1+6)z+(1+_)(1+_62)].)Et2(1+a+_)1 -visogrid):extensionalstiffness(Iz=0foru nflanged=(Et312)(( )1+a+ ISOGRID ):t(I+a+_)bendingstiffness(g :0forunflanged:equivalentthicknessformem branestresses(1_=0forunflangedisogrid)t( 1+3a 3t_)=equivalentweightthickness(_:0forunf langedisogrid)vlll_LtE_=01t1+_+_Equivale ntthicknessandYoung'smodulus=toobtaincor rectKandD(_=0forunflangedE(1+a+_)Zisogri d)UseofE*andt*inmonocoqueequationsgivesc orrectstressresultants,couples,strains, ,lightweight,economical, ,compression-load-carryingstructuresform partofallair-craft,booster, ,frame,anctskinconstruction,whichareofco urse9' ,however,weredesignedasint(:graliystiffe nec} ,theS-IIsecondstageduplicatedaircraft0-t o90-degreepat=ernswithanintegral, ,aswellastheThor, ;reeand45-degreestiffeningpatternsu_edin thestagesoftheSaturnvehi, ,theyareinherentlyfourbarlin,< , ,Reference1-1, , , ,,' ,thisstiffeningconceptisnowbeingusedasst ructureforDeltavehicletanksandinterstage s(Reference1o2),Deltashrouds,orbitalshro uds, " ISOGRID " , ISOGRID (triangularintegralstiffening) (1)thecapabilityofcarryinghightorquesfro mthewings,(2)supplyingmultipleattachpoin tsforanexternalthermalprotectionsystem,a nd(3) (1)hightorsional_'esistance,(2)manynodal points,whichcouldbeusedasattachpointsfor thethermalprotectionsystem3tandoffstruct ures,and(3)thecapabilityofresistingtheor biterattachloadswithlocalstiffeningofthe isog_' ,Figure1-1, , ,bothbuiltinthesamestructuralstyle,mustb eattributedmainlytotheinstallationofequi pmentinnon-standardfashionintheformercom partment(seeFig ure1-2).))

4 Evidently, ,muchasisogrid, "-'-----C) (CONICAL)AFTSKIRTSKINAND"; ,-USEOFTIIEtL,kNI)t_()C)t,,.Thishandhoot<pr,,suntsinforr;_,;t:o:llu't'e!_,dtodesignis,)firid,triangularintegralstiffenedstructur4, ,,'>-pointsal)()utis(,uri({ar,,.,,t_)\ ('(},.' ,.:,_.(',_tndflaF=_vrlis()_t'idwiththvin l(_rzll,,tioz'ionflangediso_ri(lh_,in,,: soct,. ,, \11()th,,riIlt'(_rzl,nli_,nnpt)li,,sl(,u nflanRediso, ,,rth,, ,s()_'.'idispr,'_,_' ,,rtin,":,_'cti(>n2,"]h 'usershouldacquaintIzill_s,,ltxxllhthi_a nalysisnnditsa, ()llSl)('i'Ol'("usinRthehandl)n()l<.B()t htlllIl;tllt2_,(']all(ll'lnn_ediso, ) (-basicth(,oryi-su,'_11_ilrix_,datth{,cn ([()tth,,._,cti(_i1t_)s(,r\_,asareadyr,' f(,renc(, ,dkli(Itii_'I,_N,_iii,l,ll,,lllllllt,,I, i!l,i!,l,i_,,I|iIt_,l,ill,'lll1,0,004 Tablei-1 ISOGRID00 Alatticeofintersectingribsforminganarray ofequilateraltriangh,sCharacteristics:-I sotropic(nodirectionsofinst,,bilitvt)rwe akness)-Poisson'sratio1/-Efficientinconl p,,-cssi_nandbcndint,Advantages:-Easilya nalyzed-Canbeoptimizedforwiderang_, ,_a:'commodateequipm,,nt_nountine,witlmu tchan_t.))))))))))}

5 -Readilyreinforcedforconccntratt,dloadsa nticutouts-Redundantloadpaths-Lessstruct uraldt, ,,,_ccproorams,'lilot'-l)cltaandSkylal_, andcxtunsix'clyinvcsti_aludandtestedonsp aceshuttlestudyeffortSection3describt,st hechl,raclt'risticsandadvantal2,'sofisog rid,includingsomecurrentandlttlurt,appli cation:,!orvt,hiclt, ,,Ihodsfo,"typicalstruclurufoundiraat,to -spacevehicles,l'ypicaltit,signsiluatit, nsat,,describedfor"eachtypeofstructure,a ntinwthods_foptiTr:i.<in,.:thestruclttr' t,fornainimutalw,'ightart,Rivenwheresuch mvthedsexist."lh,,nwthodofanalx'sisisfol lowedbyworkedexamples,whichart,gix',,nto ,e,,,fi(l_,tht,trs,,rinllu,applicationof theequationsandofthegraphs,"Ih,,tzraphs, ,nal)luthe,u,-,,rtoquicklyandaccuratelys izeisogridslruclur,,."l'h,,structuralIx, pusprest,nt,,darc: Sphericalcat)withr,,','(,rs(,prt,ssuru Cylindersincotlq) )_, Cylindersund_,rtorsion,_! ' , ,tethesections.,informationisgivenon:(1) theminimumoverallweightforcylinderssubje ctedtoaxialcompres,_ionandbending,and(2) .

6 ,amodel,sub-scale, , : Machining Powerbrakeforming Creepandageforming CompoundcurvaturesReferenctsusedintht, ' "Section2 BASICTHEORYT heisogridrib-gridsareanalyzedby"smearing out",averaging, ,thesmeared-outelasticconstantsareidenti cal' ,theco,npositeconstructionistreatedasani sotropiclayeredmaterial,withappropriatee lasticconstantsforeachlayer,viz., ,thestressesinth." , , 'SLAWFORISOGRIDRIB-GRIDT heisogridribpatternconsistsofanetworkofe quilateral(60degree) 'slawrelationsaredevelopedbyisolatingane len_entofthegridworkandassumingthatthein dividualbarsareir, /\ElementofIsogridRibCridXBymeansofthest raintransformationlaw, +YsinOcosO.+eeixxxyixYx( )oneobtainatherela:ionbetweentheuniaxial barstrains,ei,andthex,yand_ gridcoordinatestrains,ex,eyxyele2'3!40I- q_( ) ,known(forexamplefromstraingagereadings} then(ex,Infact,eyt'Oi'''102q'_-2 2-1Ze3sothatif(el,e2,e3)areYxy'ey)maybe( ,_) ,2,3{ }Resolutesofthebarloadsinthexandydirecti onsdividedbytheperiodiclengths,aand_tTag ivethe"smeared-out" +(P2+P3}cos60 4Pl+P2+P3( )Ha2_a(P_+P_)sin60 _(P2+P3}ya2a( )(P2-P3)sin60 P2-P3( )--T----TXyyX'_a2aUsingeq.)))

7 ( ),thrsebecome,{x}yih33]{} ( )whert_h-_-a, ( )and( }withtheHooke'slawrelationforisotropicma terialsinplanestress,(ry1-v2vyxyEryx-2(l +v}Xxyitisevidentthateq.( ),( }areaspecialcaseof( ),whe"e13b( )( )( )( )andthebarredquantitiesindicatetheequiva lentPoisson'sratioandYoung' , , (loadingonthcsurfaceisconsidLredtoberesi stedbystressresultantsantistres_couph'so btainodbyintegratingthestressesand,laome ntsinthethicknessdirection,OvNyMyiy_Y_i' iyxZNxZMxxMxv$ *lThesearecomputedperunitlengthoftherefe rencesurfacecoordinates, ,thesestressresultantsandcour) "xTxy_yTZX"rzy:f'le:YJZdz( )ZdZ( )whereN=NandM=MxyyxxyyxByuseoftheKirchho ff-Loveassumptionoflinearstrain,(z)x^(z) {YfIEXI_xyEYL-Z_x2 xyXy( )\vhere(_x,_xy'Ey)arereferencesurfacestr ainsand( x'2 Xxy'X_)arereferencesurfacechangesofcurva ture,togetherwiththeappropriateHooke' :/[i0o0:=ltx]0vDYXy/,.v[:ol,,_xyj=_MyxJ_ Kistheextension_isti'fness,K"--L-ll-v2fE (z)dzzDisthebendingstiffness( )( )( )D-1----_vlJE(z)z2dz!))))

8 Zandthereferencesurfacehasbeenchosensoth at( )JE(z)zdz:0Z( )E(z)ofcourseistheappropriateYoung'amodu lusofribsorskinasafunctionofthethickness coordinate, ( )-( )maybeevaluatedgeometricallybyadevicekno wnasthemethodofthe"transformedsection." ( ) ( )0--/_z2dz,Eo( ,11)ThequantityE(z)/E maynowbethoughtofasa"transformedwidth" "-I_Li ]_i d12bib_d/2 TRANSFORMEDSECTIONOFhSOGRIDWITHFLANGELet t:skinthicknessb,d=:ribwebthicknessandde pthw,c: ,g, ,z,willbechosentosatisfythecondition,_EE -_zdz= {X--thUsingtheparallelaxistheorem, !Ai_iZPart1-t2t3 Qtt(1+5)(1+5)--(1+5)2T4 Qta000tt23t__(l+x)--f_(l+_l__(l+ (tz)t3_-_[l+ab2 vk2] ".. "!Then_iAi_iAS2_ioi= (1*a_u/[(1+ (l+kl]__t__21+,_+t_tZIZ,)3(1+812+_,p.( +1+o,_2+pk"_[_l_-,(!_>,I]2[I+c*4bttOFt3_ zI-12(l+_.+..'_'where(1+a+-g)_( )"_3t*(1+kl+1+c,t,v} (1+6} :a,b,k, { (=( )and( )oneobtains_8 EoIEoA( )sincev:1 'sratiooftheskinmaterialisalso1 ,itwillnotbepossibletoexpresseq.( )and( )inthesimpleformshown, ( )and( ).)))))))))))

9 Forthinrib,thesetermsarenegligible, ,3 NON-DIMENSIONALSTIFFNESSESFORUNFLANGEDIS OGRIDF orunflangedisogrid,k=_t= :_(_,a):[3_(1+6)2+(1+_,)(l+,_a2)]( )Forconstructionconsistingofskinalone(mo nocoque),a=:b:o,13=1( ) [3,EtoK:_(l+a)1-v( )Et3oLD=12( )l+a( )ItwillbenotedthatEt/1-v2andEt3/12(1-v2) aretheextensionalandoobendingstiffnesses oftheskinalone,whilethenon-dimensionalfa ctors(l+a)and[52/(1+a) (a,b) [ ,forexample, ,[52=C1+ [3,Ifthisrelationisplottedontransparentp apertothesame[3,ascaleasthe[3(a,6)grapha ndsuperimposedonthe[5(a,6)graph, [5(a,6) , (a,dl) ,Reference2= ,Nxy, ( )reducesto,Ny[.1/31e( )while1 Nxy=_-K_xy( )andK=9Et(l+a)solvingforthestrains,( )}11-1/3exEt(l+a)Nyey=1/31( )N8 y_xy="3Et(l+a)( ) 'slawrelationfortheskin.{x)[3]{}exOy=_1/ 31ey( )E_y2(l+u)_xy( ) ;SByuseof( )and( )oneobtainstheskinstresses,_yt(l+a)N_x'O 'y,rxy"( )1 1"-IXlxyt(1+_)xy( )Ifthequantityteff=t(l+a)isdefined,then, ( )NNN_0"t,0:,T-"xeffYxy( ) , , , , ,theskinthickness,thestressfieldintheski n,Young' ,inturn, ' , Fromeq.]]]]]]]]]]

10 ( )and( ),P1=_= "_-2132bE4(ex+ff-_'_xy+3ey)133 "3-b-E(ex__, +3e)4'xyyUsingeq.( }and( )thesebecome,1-N,) l:3t(l+a)(3Nx2a2:3t(1+a)(Ny+,J3 Nxy)2#3Na3:3t(l+a)(Nyxy)( )andNareprincipalstressresultants, :t(l+=='=='=_),x-' :0"3:3t(14Ny( )If,inaddition,Ny::0, ::telf( )Noteintheapplicationofeq.( )thatthe1barisorientedinthedirec-tionoft hexaxisandthatthe,2and_barsareat 60degreestothe axis, , , ,xN=0xyand,= *ANDt::"Becauseoftheisotropicpropertieso ftheconstruction,itispossibletouseallthe establishedisotropicsolutionsfromextensi velydevelopedtheoryforplatesandshells, , ,however, ,itispossibletodetermineanequivalentmono coquethickness,t*andYoung'smodulus,E":', _hichwillgivethesamebendingandextensiona lstiffnessesas( )and( ). ,EAEtK=E":"t_:_oo:2--z(i+_)1-v1-vl-v( )DE':-"t::'-3 EIEt3oo--2I+_i2(l_v2)l-v212(l-v)( )whereAandIarethetransformedareaandmomen tofinertiaandwheretheexpressionsinaand[ ( )and( )fort::'andE::',t-':-":_=t--_l+_( )A_( )E':-"-E_,:,=ENotethatonceagain, ,t',_=tE': =ESincec_=0and_= ( )and( ) :_andE':'reproducetherequir(dbendingande xtensionalstiffnesses,DandK, ,theequationsintowhicht':"andE*aretobesu bstitutedmustbeexpressedintermsofstressr esultants_andcouples, !)))]