ANALYSIS OF FLAT PLATE STRUCTURES BY EQUIVALENT GRID METHOD

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1 VOLUME, NO., EDISI XXXI PEBRUARI 005 ANALYSIS OF FLAT PLATE STRUCTURES BY EQUIVALENT GRID METHOD Ilhm Nurhu, Hn Ay Lie ABSTRAK Penggunn moel ler efektif lok untuk mengnlisis struktur flt-plte yng ikeni en lterl suh sering ilkukn. Nmun emikin, smpi st ini moel terseut msih terts penggunnny p moel-moel struktur imensi. Anlisis ini memperlus penggunn moel gri ekuivlen untuk mengnlisis struktur ser imensi. Ler efektif gri inlisis ser empirik ersrkn hsil eksperimen. Perilku struktur itinju engn melkukn nlisis struktur ser linier n non linier. Keywors : flt-plte, moel, reinfore onrete. INTRODUCTION A reinfore onrete floor is generlly plte fixe y mens of ems, long its four sies. This onventionl system is the elest system n universlly well known. However, this plte-em system hs some weknesses espeilly in its effiieny n eonomi spets. Formwork for exmple, is time onsuming n ostly. Due to tehnology evolvement, the use of this olumn-line-ems system reues, eveloping in n vne system where sls onsist of soli pltes supporte iretly y olumns. This is lle the flt plte []. This kin of struture s evelopment is se on the unerstning tht sl not only istriute lo to the em ut lso funtions s struture unity, rrying lo. Diffiulty fe in usge of this flt-plte system is in its ehvior nlysis, espeilly relte to the effet of lterl loing when the struture is esigne to resist strong win or erthquke. Sttil nlysis with lssil mehnis is not equte euse of the omplex stress istriution tht ourre in these pltes. Avne omputer tehnology evelopment le to fst progress in solving the prolem numerilly. The numeril metho most ommon use in struture nlysis is the Finite Element Metho. The struturl moel wiely use in struturl nlysis is the Frme Element Moel or Br Element. This moel is often preferre euse simpliity n ese pplition. In the flt-plte struture n nlysis y using frme elements is generlly rrie out y the Effetive Bem- With Moel. In this metho, the plte is moele s n equivlent em with ertin effetive with. This nlysis generlly mkes use of two-imensionl nlysis. Bse on the unerstning tht the nlysis requires moeling of flt-pltes s two-iretionl-single-lo supporting unity, the use of gri moel for moelling flt-plte strutures, will e stuie. This moelling nlysis is se on the ssumption tht sls onsist of gri formtions tht re le to istriute lo to every iretion. Effetive gri istne will e exmine y vrying the istne etween gris n ompring the result to Pengjr Jurusn Teknik Sipil Universits Diponegoro Semrng MEDIA KOMUNIKASI TEKNIK SIPIL 7

2 Anlysis Of Flt Plte Strutures By Equivlent Gri Metho experiment t. The effet of gri-to-slefletion numer of is lso oserve y ompring numeril nlysis to experimentl result. GRID MODELING OF FLAT PLATE STRUCTURES Generl Behvior of Flt Plte Strutures A flt-plte is struturl system where sls re supporte iretly y olumns without the existne of ems. A flt-plte system is nlyze similrely s two-wy sl ut iffers in ehvior to the two-wy sl in sl-em strutures. In slem system, the positive elsti moment of plte ourre in the mile of the plte, n the negtive moment ourre in the mile of the plte ege onnete to the em. On the ontrry, in flt-plte struture the mximum positive n negtive moments ourre t the olumn line. In the retngulr pnel, sls on rigi ems spn preominntly etween the long ems, n for n spet rtio of two the entrl region is urve prtilly only in the short spn iretion. In flt-plte the entrl setion spns in the longer iretion, n the trnsverse moments re onfine to limite with on either sie of the olumns, s inite y fig. Fig. Behvior of Elongte Pnels of Continuous Sls When the two-wy sl is supporte y wll or em, then sher will not govern the esign. Generlly, this is euse the ftore sher fore is preominntely smller thn the onrete sher pity. On the ontrry, in two-wy sl system where the sl is supporte iretly y the olumn, the sl rries the entire lo n istriutes it iretly to the olumn. Here sher roun the olumn governs the esign. In this se, struture sher esign nees speil onsiertions from the esigner [5]. Two types of sher ehvior requires to e onsiere in esigning flt-plte strutures. These re em sher n punhing sher. Bem sher type one-wy-sher eomes ritil in thin n long pltes. While punhing sher, whih is often the most ommon moe of filure, is ue to the reltively smll sher re roun the olumn, inle to etin olumn point loing. The ritil re of punhing sher filure is t istne ½ from the olumn fe, where is the effetive sl epth. Effetive-Bem-With Moel Conerning the sl-olumn onnetion, not ll portions of the sl-with work effetively s is the se in flexurl element frme to the olumn. This ehvior is ue to the ft tht the sls o 7 MEDIA KOMUNIKASI TEKNIK SIPIL

3 VOLUME, NO., EDISI XXXI PEBRUARI 005 not experiene the sme rottion long its entire with. To overome this, it is ommon prtie to moel the sl simply t esign phse. The simplest wy is y moeling the sl in r elements known s sl-em element. This sl-em element rottes uniformly ross its trnsverse with. The em epth generlly is tken equl to the sl thikness. Wheres the effetive em with hs een stuie n propose y mny reserhers. Bnhik (987), s quote y Hwng n Moehle [], presents the effetive em with y using finite element tehniques. The solutions pply to interior, ege, n orner onnetions, for olumn with squre ross setions, n for omintions of l n l l, efine s follows l = 0.06, 0.09, 0. l l = 0.67,.00,.50 Where: is the olumn with. l is the olumn istne in the lterl lo iretion. l is the olumn istne in the trnsverse iretion. Bnhik presente his result using l the min geometri vriles. The results re ivie into two groups: one for the interior frme, n nother for the exterior frme. The vritions of effetive em with for n interior frme, whih inlues interior onnetions n ege onnetions ening perpeniulr to the ege, n e represente s: l.... () The effetive em with for n exterior frme, whih inlues orner onnetions n ege onnetions ening prllel to the ege, n e represente s s l 6...() Aoring to Hwng n Moehle [], the influene of setion rkes is ommote y mens of reution ftor to the element stiffness, tken s /. Improving Moels y implementing Gri Moel for D Anlysis Bse on the stuy onute y Hwng n Moehle [], the moel propose y Bnhik is fir enough to moel strutures two imensionlly. However, this moel fils to represents omprehensive unerstning of struturl ehvior. Behvior of struture suh s plte eformtion, internl fore istriution, influene of struture n loing onfigurtion n e oserve only y using three-imension nlysis. Moreover, y using nonliner proeure in the threeimension nlysis, struture inelsti ehvior n e exmine. To simplify, the gri moel where the sl is reple y n rrngement of equivlent ems in gri moel with ertin with, is propose. The questions is how wie the pproprite effetive-gri-with shoul e, n how the numer of gris influene the nlytil result. To nswer this question, numeril experiments re onute. Detils of the numeril experiments re expline in the following hpter. NUMERICAL EXPERIMENTAL PROGRAM Configurtion n Properties The Test sl onfigurtion n geometries re pte from the experiment onute y Hwng n Moehle []. This test sl is n ieliztion of flt-plte floor on n intermeite multistory offie uiling level. The sl hs three ys in eh iretion with enter-to-enter spn of.6 m n 6.9 m in eh iretion. Sl thikness is MEDIA KOMUNIKASI TEKNIK SIPIL 7

4 Anlysis Of Flt Plte Strutures By Equivlent Gri Metho 0 mm n story height is.0 m. Grvity loing onsists of self-weight n live lo. The lterl los re ue to win. For experimentl purpose the struture is sle to :5, thus enter to enter spns in the two prinipl iretions eome.8 n.7 m. Sl thikness eomes 8 mm, the olumns exten 05 mm ove the sl n 0 mm elow the sl. The olumn is pin supporte to the moel infletion point of moment roun olumn miheight. Configurtion n imension of test sl in m re s shown in figure x6. 6.x m 8. m x6..x. m CL.5x6..x..x..x. Fig. Configurtion n Dimension of Test Sl Struture properties re: ultimte ompressive strength of onrete (f ).8 MP, Splitting tension (f tr ).6 MP, with sent moulus of 7860 P. Sl reinforement re eforme rs No., with the yiel strength (f y ) of 50 MP. Loings The test sl is loe with omintion of vertil n lterl lo. The vertil lo hs mgnitute of 5650 P. Lterl loing ws pplie in the north-south n estwest iretion seprtely, n pplie til the struture ollpse. In the north-south iretion, the lterl lo is pplie to sl ege t two points, one miwy etween frme lines n, n the other etween lines n. In the est-west iretion, the lterl lo is pplie to sl ege t miwy etween frme Lines n, n Lines n, s shown in fig. B U S T CL Fig. Lterl Loing Diretion in Test Sl 7 MEDIA KOMUNIKASI TEKNIK SIPIL

5 VOLUME, NO., EDISI XXXI PEBRUARI 005 Struture Moelling y the Gri Moel For the numeril investigtion, four gri moels with ifferent gri-spes re me. The olumn is moelle s frme element with its setion properties s onstnt for ll the four moels. The illustrtion of the four gri moels n e seen in fig (,,, ): () () () () Fig. Illustrtion of Gri Moels () Moel ; () Moel ; () Moel ; () Moel The istne etween gris of eh gri moel is shown in tles. Tle. Gri-spe Moel Distne Between Column (l ) Gri-spe (l g) N S E W N - S E - W 8.8 m 7. m 8.8 m 7. m 8.8 m 7. m 9. m 7. m 8.8 m 7. m 9. m 68.6 m 8.8 m 7. m 5.7 m 68.6 m MEDIA KOMUNIKASI TEKNIK SIPIL 75

6 Anlysis Of Flt Plte Strutures By Equivlent Gri Metho The vrition of the effetive-gri-with will e erive empirilly from the four gri moels ove. The effetive-gri-with will e the funtion of gri-spe (l g) n istne etween olumn in the gri iretion (l ), or =f (l, l g ). Metho Of Anlysis Numeril nlysis ws governe y two methos, i.e. liner nlysis n mterilnonlinerity nlysis. Liner nlysis ws one to investigte the effetive-gri-with. Nonliner nlyses tht ount for the mteril nonlinerity, ws governe to oserve inelsti ehvior of struture fter yiel our, n how the moels meet the experimentl result. Behviors of struture evlute here re the reltion of the lo to lterl isplement, vertil efletion of sl, n sher stress istriution roun olumn. The nlysis ws onute y using the MASTAN progrm [,6]. RESULTS AND DISCUSSION Effetive Bem With Anlysis result of effetive-gri-with for eh moel is present in tle. The result is ivie into two groups tht is for the interior n the exterior gri. Tle.. Anlysis of Effetive-gri-with of Interior Gri l l g l g / l / l g Tle.. Anlysis of Effetive-gri-with of Exterior Gri l l g l g / l / l g MEDIA KOMUNIKASI TEKNIK SIPIL

7 VOLUME, NO., EDISI XXXI PEBRUARI 005 Results of nlysis re plotte in figure 5, in terms of l g / l. The effetive-gri-with is erive y urve fitting. 0.8 / l g y = 0.9. e -X Interior Gri Exterior Gri 0. y = 0.5. e l g / l Fig 5. Plot of Effetive-gri-with From the grph ove, the vritions of the effetive-em-with for n interior gri, whih inlues interior onnetions n ege onnetions, ening perpeniulr to the ege, n e represente s 0,9.Lg.e Lg L Wheres the effetive em with for n exterior gri, whih inlues orner onnetions n ege onnetions, ening prllel to the ege, n e represente s 0,5.Lg.e Lg L Aoring to these expressions, the effetive-gri-with in exterior gri is hlf the vlue of the interior gri. Anlysis of Vertil Sl Defletion Vertil efletion is n importnt ftor in the struture esign, espeilly in servie loing onitions. Therey efletion estimtion tht my our, plys n essentil rule in the esign proess. In the fig 6, the vertil efletion resulte from numeril nlysis of the three moels is plotte together with the experimentl result. Due to the limite numer of t, the efletion is only ontrolle t the mile of olumn line. Aoring to the nlysis result, it is seen (fig 6) tht moel gives the est preition ompre to the other moels. Moel n moel shown to overestimte the lterl rift rtio to /50. The inresing of gri numer in the moel will improve the preition of previling vertil efletion. Lrge numer of gri will mke the tht the stiffness oes not hnge immeitely. In moel, ue to its few numer of gri, yieling in one element uses the glol stiffness rop n mkes the vertil efletion to inrese fst. Another onlusion is tht the three moels present goo preition until lterl rift rtio of /00. MEDIA KOMUNIKASI TEKNIK SIPIL 77

8 Anlysis Of Flt Plte Strutures By Equivlent Gri Metho Vertil Defletion (mm) Experiment Moel moel moel L/60 /800 /00 /00 /00 /50 Lterl Drift Rtio Fig 6. Clulte vertil efletion n experimentl result Sher in Sl Effet of lterl loing to sher fore in the sl is nlyze y gri moel. The sher fore roun the olumn is otine from sher fore t the en of eh gri element onnete to the olumn joint. Sher strength is lulte in one sie of the olumn where the sher with (o) is equl to olumn with () plus the effetive sl height (h). Sher strength is lulte using n empiril formul [] s follows: V * f' * o *...() Result of nlysis of the sher fore in three lotions tht is B, B, A, to its orresponing lterl rift rtio re shown in figure 7(,,, ) Sher Fore(kN) V est V w est V north V roun Lterl Drift Rtio(%) () V est V north V roun V south Lterl Drift Rtio( %) Sher ForekN) C o l u m n J o i n t V est V w est V north V roun V south Lterl Drift Rtio(%) () () S h e r S t r e n g t h o f S l o B 6 m m 6 0 k N B 6 m m k N A 6 m m k N () Fig 7. () Sher Fore in Sl t Joint B; () Sher Fore in Sl t Joint B () Sher Fore in Sl t Joint A; () Sher Strength of Sl t one olumn sie 78 MEDIA KOMUNIKASI TEKNIK SIPIL

9 VOLUME, NO., EDISI XXXI PEBRUARI 005 B Joint (fig. ) is in south ege, wheres B joint (fig. ) is in the mile of the plte, n A joint (fig. ) is on the west ege. During nlysis, vertil loing remin onstnt while the lterl loing inrese. It n e seen from fig. 7 tht shows the omprison to sher strength, to lterl rift vlue rtio of % tht the lulte sher fore remins elow its sher strength pity. These results re ongruent with the experimentl results y Hwng n Moehle [] where the sher filure ours t % lterl rift rtio. CONCLUSION Bse on the result of numeril nlysis, the following onlusions re me.. The result of numeril simultion shows tht the three-imension gri moel n e use to moel ehvior of flt-plte strutures.. Aoring to the nlysis result, there re reltions etween the effetive-griwith, gri-spe, n gri-length from olumn to olumn. This nlysis erives the vritions of effetive-gri-with s follows: 0,9.Lg.e Lg L n 0,5.Lg.e for the interior gri, Lg L for the exterior, Where is the effetive-gri-with, Lg is gri-spe n L is gri-length from olumn to olumn.. Anlysis result shows tht until lterl rift rtio of %, the three moels (moel, moel, n moel ) still perform goo preition. For the elsti nlysis purpose, moel n e use. Wheres for the inelsti nlysis, inresing of gri numer is suggeste.. In this nlysis, sher filure is voie y esigning the sher strength pity lmost times of sher from grvittionl lo. It n e seen tht y this wy the struture onut high egree of utility. 5. Anlysis shows tht gri moel n e use to rekon sher fore n meet the experimentl result. ACKNOWLEDGEMENTS This reserh is rrie out with the finnil support of the Diretorte Generl of Higher Eution, Repuli of Inonesi through Tehnologil n Professionl Skills Development Setor Projets (TPSDP), ADB Lon No 79-INO, uner ontrt No. 568/TPSDP/TS/K/XII/0. This pper is prepre with the finnil i of Deprtment of Civil Engineering, Diponegoro University. REFERENCES Ghosh, S.K., Fnell, D.A., Rt, B.G, Notes on ACI 8-95, pp , Portl Cement Assoition, 996 Hwng, S.J., Moehle, J.P., Vertil n Lterl Lo Tests of Nine Pnel Flt-Plte Frme, ACI Struturl journl, vol 97, no., pp. 9-0, Amerin Conrete Institute, 000. Hwng, S.J., Moehle, J.P., Moels for Lterlly Loe Sl-Column Frmes, ACI Struturl journl, vol 97, no., pp. 5-5, Amerin Conrete Institute, 000. MGuire, W., Gllgher, R.H., Ziemin, R.D., Mtrix Struturl Anlysis, n Eition, pp. 6-5, John Willey & Sons In, 000 Regn, P.E., Behvior of Reinfore Conrete Flt Sl, pp. -9, Constrution Inustry Reserh n Informtion Assoition, 98 Ziemin, R.D., M Guire, W., MASTAN, Version, John Willey & Sons In, 00. MEDIA KOMUNIKASI TEKNIK SIPIL 79