Effective Stiffness of the Engine Room Structure in Large Container Ships

Transcription

1 UDC : I. SENJANOVIĆ N. VLADIMIR M. TOMIĆ Ivo SENJANOVIĆ Nikola VLADIMIR Marko TOMIĆ Effecive Siffne of he Engine Room Srucure in Large Conainer Ship Original cienific paper Very large conainer hip are raher flexile due o he large deck opening. Therefore hydroelaic re analyi i required a a ai for a reliale rucural deign. In he early deign age he coupling of he eam model ih a D hydrodynamic model i raional and preferale. The calculaion i performed uing he modal uperpoiion mehod o naural hull mode have o e deermined in a reliale ay. Therefore he advanced hin-alled girder heory hich ake he influence of hear on oh ending and orion ino accoun i applied for calculaing he hull flexural and orional iffne properie. A characeriic of very large conainer hip i he quie hor engine room hoe cloed rucure ehave a an open hold rucure ih increaed orional iffne due o he deck effec. The paper deal ih he calculaion of i effecive orional iffne parameer y uilizing he energy alance approach. Alo eimaion of diorion of ranvere ulkhead a a reul of orion and arping i given. The procedure i checked y he D FEM analyi of a hip-like ponoon. Such a modified eam model of he engine room rucure can e included in he general eam model of a hip hull for he need of hydroelaic analyi here only a fe fir naural frequencie and mode hape are required. For pracical ue in he preliminary deign age of hip rucure he impliciy of he eam model preen an advanage over D FEM model. Keyord: conainer hip engine room rucure orion arping diorion hin-alled girder analyical oluion FEM hydroelaiciy Auhor Addre (Adrea auora): Univeriy of Zagre Faculy of Mechanical Engineering and Naval Archiecure I. Lučića Zagre Croaia ivo.enjanovic@f.hr Received (Primljeno): Acceped (Prihvaćeno): Open for dicuion (Ovoreno za rapravu): Efekivna kruo konrukcije rojarnice velikih konejnerkih rodova Izvorni znanveni rad Veliki konejnerki rodovi podložni u uvijanju zog relaivno male orzijke kruoi kao poljedica velikih palunih ovora. Soga je provođenje hidroelaične analize nužno kao onova za racionalno i pouzdano projekiranje konrukcije. U ranoj fazi onivanja preferira e prezanje grednog rukurnog modela D hidrodinamičkim modelom. Proračun e provodi meodom uperpozicije prirodnih olika viriranja e proračun prirodnih viracija u zraku rea ii pouzdan. Soga je uavršena eorija ankoijenih noača primijenjena za proračun flekijke i orzijke kruoi koja uzima u ozir i ujecaj mika na uvijanje. Jedna od značajki velikih konejnerkih rodova je relaivno kraka rojarnica ako da e njena zavorena konrukcija ponaša kao ovorena konrukcija erenog kladiša povećane orzijke kruoi ulijed ujecaja palua. U članku e razmara određivanje efekivnih parameara kruoi korieći energeki priup. Također procjenjuje e diorzija poprečnih pregrada rojarnice ulijed uvijanja i vioperenja poprečnog prejeka. Poupak je provjeren D MKE analizom ponona ličnog rodkoj konrukciji. Ovako modificirani model konrukcije rojarnice može e jednoavno uključii u opći gredni model rodkog rupa za poree hidroelaične analize za koju je poreno odredii nekoliko prvih prirodnih frekvencija i olika viriranja. Jednoavno grednog modela daje određenu predno u preliminarnom projekiranju rodke konrukcije pred uporeom D MKE modela. Ključne riječi: konejnerki rod konrukcija rojarnice uvijanje vioperenje diorzija ankoijeni noač analiičko rješenje MKE hidroelaično Inroducion Increae in ea ranpor require uilding of very large conainer hip (VLCS) []. Due o heir flexiiliy he convenional rengh analyi aed on rigid ody ave load i no reliale enough [ ]. Thee hip have o e umied o hydroelaic analyi and in he early deign age coupling of FEM eam rucural model ih D hydrodynamic model i a reaonale choice [4 5]. Hydroelaic analyi i performed y he modal uperpoiion mehod [6]. Thu he eam rucural model ha o e ufficienly reliale o decrie he hip hull dry naural mode equally ell a he D FEM model doe. For hi purpoe he advanced heory of hin-alled girder i ued o deermine he 6(0) 5-7 5

2 I. SENJANOVIĆ N. VLADIMIR M. TOMIĆ EFFECTIVE STIFFNESS OF THE ENGINE ROOM STRUCTURE IN LARGE... ending and hear iffne and orional and arping iffne ih hear influence [7 8 9]. In medium-ize conainer hip here are only a couple of ranvere ulkhead ha rei hull diorion. Hull orion and conequenly cro-ecion arping i reduced ih ool inegraed a he op of ranvere ulkhead. The ool are modelled a dicreiized rerain elemen [0 4]. In he cae of large conainer hip he ranvere ulkhead are quie rou. The heigh of heir girder i equal o he frame pacing i.e. ca. m. Thu he ranvere ulkhead ogeher ih he ool rei hull diorion and conequenly reduce hull orion. Due o heir large numer coninuou influence can e aumed hrough he increaed value of he S. Venan orional iffne proporionally o he ulkhead rain energy and he open hull rain energy [5]. Anoher prolem relaed o large conainer hip i a relaively hor engine room rucure hich i no compleely effecive. I complex deformaion i illuraed in cae of a 400 TEU conainer hip Figure [6]. The deck hear deformaion i predominan hile he ool on he hold ranvere ulkhead i expoed o ending. Due o he hor engine room i ranvere ulkhead are keed u omeha le pronouncedly han he arping of he hold ulkhead. Warping of he ranom i negligile and ha i an imporan fac hen pecifying oundary condiion. ( )= ( ) +. Diconinuiy of i angle derivaive ψ x ψ x and coupling eeen ending angle and i angle + ϕ( x )= ϕ( x )+ ψ ( x ); equilirium of ending momen + and imomen B x B x M x ( )= ( ) ( ) here and are he arping compaiiliy facor hich depend on arping funcion [0 ]. Efficiency of he aove join condiion i illuraed in he cae of a primaic ponoon ih an open middle par and cloed end: L B H = m l + l + l = m cl op cl = mm []. The ponoon i expoed o he end orque of knm. The oained i angle for he aove o compaiiliy condiion a ell a he hird one aed on he effecive iffne deermined y he heory of elaiciy [8] are correlaed in Figure. The hird oluion i he cloe one o he D FEM reul [7] and herefore i i preferale for he pracical ue due o he reaon of impliciy. Figure Bird -eye vie of he 400 TEU conainer hip afody he 5 h naural mode Slika Pičji pogled na krmu konejnerkog roda od 400 TEU pei olik prirodnih viracija Figure Ti angle of open ox girder ih cloed end a (B ψ') compaiiliy (B ψ') diconinuiy c effecive iffne d FEM Slika Ku uvijanja ovorenog kuijaog noača a zavorenim krajevima a (B ψ') kompaiilno (B ψ') dikoninuie c efekivna kruo d FEM A couple of prolem arie in he eam modelling of conainer hip rucure: connecion of he cloed fore and af peak and he cloed engine room ih he open hold and accouning for he effec of ranvere ulkhead. Due o differen verical poiion of he hear cenre coupling eeen orion and horizonal ending exi ihin diplacemen and ecional force; ( SC SC ) = + ( SC SC ) Y = Y + ψ z z T T Q z z here Y i deflecion ψ i i angle T i orque and Q i hear force z c i coordinae of hear cenre hile (.) * and (.) o deignae cloed and open cro-ecion. Warping compaiiliy in he join of he open and cloed cro-ecion preen anoher prolem hich can e olved in one of he folloing hree ay: a. Equilirium of imomen B and compaiiliy of i angle derivaive ψ [7]. Thi paper aim o deermine he effecive value of iffne parameer of a hor engine room rucure in he eam model uilizing he energy approach. Due o he mall apec raio lengh/readh he engine room rucure ehave a an open hold rucure ih increaed orional iffne. Therefore orionally induced horizonal ending i mall and can e negleced hich make he deerminaion of he effecive value of orional iffne parameer much eaier. In addiion diorion of he engine room ranvere ulkhead i conidered aed on he knon orional and arping repone. The aic formulae of he hinalled girder heory are ued and he procedure i verified y a D FEM analyi of a hip-like ponoon. Ouline of he hin-alled girder heory In he hin-alled girder heory i i aumed ha he rucure ehave a a memrane and ha here i no diorion of he cro-ecion [0 9 0]. Alo in he advanced heory hear influence on orion i aken ino accoun imilarly a in he flexural eam heory [7 8]. A a reul here i analogy eeen ending and orion. The i angle coni of a pure i angle and a hear conriuion ψ ψ ψ = + () 6 6(0) 5-7

3 I. SENJANOVIĆ N. VLADIMIR M. TOMIĆ here he laer i ψ EI = GI d ψ E and G are Young modulu and hear modulu hile I and I are arping modulu and hear momen of ineria repecively. The girder ecional orque coni of a pure orional par and a arping conriuion [4] The orque T and T are he reul of hear re τ and τ due o pure orion and fixed end again arping repecively. Conrained arping alo caue normal re. dψ T = T + T T = GI dψ d ψ T = GI = EI d ψ σ = E (4) x d here i he arping funcion (relaive axial diplacemen due o uni orional deformaion ψ ). The normal re diriuion per cro-ecion i condened in he arping imomen hich repreen he re ork on he relaive diplacemen B = EI (5) σ d d ψ = here I = d.. () () (6) here I oluion read ψ = A + A x + Achαx+ Ah αx+ ψ 0 p l α = GI EI and ψ p i a paricular oluion. Thu he oal i angle () ake he folloing form ψ = + + α (0) + A A x I I EI A ch x A hαx + ψ ψ n. 0 p π l I I GI No i i poile o derive formulae for he cro ecion arping and ecional momen Equaion () and (5) dψ u A = = + A x+ A x+ x αhα αchα ψ d l T Torion of primaic girder (8) (9) () () () (4) (5) The girder i loaded ih orque M a he end hile μ x = 0. The end are fixed again arping. The i angle i an ani-ymmeric funcion and herefore conan A 0 = A = 0. The remaining conan A and A are deermined y aifying he relevan oundary condiion p A = GI + A x+ A x+ αhα αchα ψ l p T = GI A x A x EI ( αhα + αchα ) ψ p A T = GI + EI ψ l ψ p m p B = GI A x A x EI ( ch α + hα )+ ψ n p. m x = l T = M u = 0. (6) Thu one find ha Figure Girder orion Slika Uvijanje noača The equilirium of he oal ecional orque ih he diriued exernal load dt = - μ x lead o he differenial equaion Figure 4 d ψ d ψ EI GI = μ. (7) 4 x Ml Ml A = A =. (7) GI GI αlchαl Diplacemen and force Equaion (0) (5) ake he folloing form: Ml x I α h x ψ = GI l I αlchαl M x u = GI ch α chαl T x = M ch α chα l (8) (9) (0) 6(0) 5-7 7

4 I. SENJANOVIĆ N. VLADIMIR M. TOMIĆ EFFECTIVE STIFFNESS OF THE ENGINE ROOM STRUCTURE IN LARGE... 4 Torion of egmened girder B T = M = M chα x chα l hα x αchα l. () () here GI GI α = β =. EI EI The oluion of he yem (5) read A DD B DD B D A B B = = = D (7) (8) here Figure 4 Torion of egmened girder Slika 4 Uvijanje egmennog noača Le u conider a girder coniing of hree egmen Figure 4. The econd egmen i locaed in he middle o ha he girder i ymmeric. The girder load and he oundary condiion are he ame a in he previou cae Secion. Each egmen i pecified in i local coordinae yem Figure 4. The properie of he middle and end egmen are deignaed y (*) and ( ) and ymol A i and B i are ued for he inegraion conan repecively. Conan A 0 and A are zero ecaue of aniymmeric deformaion. The compaiiliy condiion a he egmen join and he oundary condiion are he folloing: ( )= ( ) ( ) = ( ) ( )= ( 0) B a B ( ) = η ( 0) ( )= 0 ( )=. ψ a ψ 0 ψ a εψ 0 T a T u l T l M () The arping compaiiliy facor ε and η are inroduced in order o make handle of all hree e of join condiion pecified in he Inroducion poile i.e. Poin a and cae 0 and = 0. From he hird and la condiion () one find Ma Ml A = (4) GI B = GI. The remaining four condiion () lead o he folloing yem of algeraic equaion: ε αchαa 0 εβ A I I M I hαa hi 0 B = 0 (5) 0 βhβl βchβl G B I I I B = A + A a B 0 I hα I (6) M η I D = l A ε β ch ε G I M ε I ε I D = hαa chβl B + G I I M I D = ε ηα h αa hβl chαa B G I β D = ηi αch αa chβl + εi βh αa h βl. 5 Siffne of engine room rucure (9) Conainer hip hull i raher eak again orion due o large deck opening [0 ]. The engine room i quie hor he apec raio lengh/readh i ca. :. Therefore he hold doule kin i coninued hrough he engine room o enure ha he arping and ending ree have a coninuou re flo hrough he ranvere ulkhead urrounding he engine room. The upper deck in he large cro-ecion arping field i expoed o oundary hear load hile he doule oom roae around he verical axi a a rigid ody Figure. Thu he hear deformaion of he loer deck in he engine room i decreaing from he upper deck o he oom. Due o he aove fac he relevan iffne parameer of he engine room cloed cro-ecion are no fully effecive. Therefore i can e aumed a in he cae of ranvere ulkhead [5] ha he effecive arping modulu and he hear ineria modulu are equal o hoe of he open cro-ecion (ihou deck) i.e. I I and I I repecively hile only he orional modulu i increaed due o he deck influence. I value i omehere eeen hoe of he open and cloed cro-ecion depending on he deck apec raion I < I < I. The equivalen orional modulu I can e deermined y he energy approach and preened in he form I = + C I (0) here C i he raio of he deck rain energy and he rain energy of he correponding hull porion ihou deck. The relaive axial diplacemen of he upper deck oundarie ih repec o he doule oom i he reul of heir arping Eq. () ( ) U = U + U = D B ( + D B )ψ. () 8 6(0) 5-7

5 I. SENJANOVIĆ N. VLADIMIR M. TOMIĆ I caue deck in-plane (memrane) deformaion. The prolem can e olved in an approximae analyical ay y conidering he deck a a eam. I horizonal ani-ymmeric deflecion coni of pure ending and hear conriuion Figure 5. a 4 ( + ν) G E = U a + ( + ) ν (6) On he oher hand he rain energy of he engine room hull porion ihou deck and ranvere ulkhead read a E = T x GI a H ψ d = ψ a (7) Figure 5 Upper deck deformaion and doule oom roaion a ird -eye vie laeral vie Slika 5 Deformacija gornje palue i zakreanje dvodna a pičji pogled očni pogled The former i aumed in he form u y y = U () hich aifie he relevan oundary condiion: u (0) and u ( 0)= 0 here U i he oundary ending deflecion. Shear deflecion depend on ending deflecion u EI d u a y = = ( + ) ν GA y U d () here deck cro-ecion area A = a i momen of ineria I = a and he relaion E = (+ν)g are aken ino accoun Figure 5. The oal deflecion i oained y umming up Eq. () and () i.e. u = u + u. The relaion eeen he oal oundary deflecion and he ending oundary deflecion read a U = + ( + ) ν U. (4) The oal deck rain energy coni of he ending and hear conriuion E = EI d u y GA d + dy (5) By uiuing Eq. () () and (4) ino Eq. (5) e oain du y d. y d here T i pecified in Eq. () and for ψ he conan value ihin a hor pan a i aumed. Finally y aking he rain energy of all deck ino accoun a ell a Eq. () one find for coefficien C in Eq. (0) ( ) a 4 ( + ν) k D B E i + C = = (8) E H a + ( + ν) Ia here V h i i k = (9) V h i he um of he deck influence coefficien. I i oained y auming ha heir rain energy i proporional o he volume V and deformaion i linearly increaing ih he deck diance from he inner oom h Figure 5. In pie of he high deck apec raio ca. : he applied eam heory for deermining he deck in-plane deformaion give quie good reul. Performing an FEM analyi ih he deck memrane model hoed ha he eam model i only 6% iffer han he FEM model. 6 Diorion of egmened ponoon The open and cloed cro-ecion egmen are conneced a he ranvere ulkhead hich i ujeced o diorion due o differen hear flo on i fron and ack ide induced y he orque M Figure 6. The hear flo of he open cro-ecion o i paraolic hile ha of he cloed cro-ecion * i uniform. The reuling ide force are S S = S o - S * and he deck and oom S S force read S D = S * and S = S * ince S o = 0 for he open ecion D B B D and S o = 0 due o elf equilirium for he given oom flo B o Figure 6. The aove hear force aify he aic equilirium condiion. The inernal re equilirium lead o he diorion of he ranvere ulkhead δ. The hear flo hon in Figure 6 are realiic for he long open and cloed ponoon egmen. Hoever in cae of hor cloed egmen a he engine room rucure he deck i eakly effecive and i hear flo i conideraly reduced Figure 7. A a reul he remained par of he cro-ecion ehave imilarly o he open one. Difference of he hear flo o - * i quie mall u ill caue ulkhead diorion δ hich can e eimaed in he folloing ay. 6(0) 5-7 9

6 I. SENJANOVIĆ N. VLADIMIR M. TOMIĆ EFFECTIVE STIFFNESS OF THE ENGINE ROOM STRUCTURE IN LARGE... axi in he oppoie direcion due o arping of cro-ecion Figure 8. The oal ranvere gap eeen he deck corner and he ulkhead op yield Figure 8 Figure 6 Shear force a he join of open and cloed cro-ecion egmen Slika 6 Smične ile na poju ovorenog i zavorenog egmena Figure 7 Shear force a he join of long open and hor cloed cro-ecion egmen (qualiaive preenaion) Slika 7 Smične ile na poju dugog ovorenog i krakog zavorenog egmena (kvaliaivni prikaz) Tendency of he deck and doule oom of he engine room rucure ujeced o orion i roaion around he verical Figure 8 Deck and ulkhead diplacemen and in-plane deformaion Slika 8 Pomaci i memranke deformacije palue i pregrade a V = V + V = (40) U D B here relaive axial deck diplacemen ih repec o doule oom U i given y Eq. (). Gap V i cancelled y he deck corner ranvere diplacemen ν D and he ulkhead op diplacemen ν in he oppoie direcion a a reul of equiliraed inernal hear force S D and S Figure 8. The hear force depend on he hear deformaion γ D = ν D /a and δ = ν /H repecively here δ i diorional angle Figure 8. Thu one can rie for he deck hear force S = G k a v D D (4) here i he upper deck hickne hile k ake conriuion of all deck o he reuling deck force S D ino accoun. I i oained y auming a proporional increae of he deck hear deformaion ih he deck diance from he inner oom and momen equilirium of he hear forced S i and S D. Tha give he ame definiion of k a ha eimaed y energy alance Eq. (9). In he imilar ay he ulkhead hear force read S = G (4) H v. The force equilirium lead o he raio of he deck and ulkhead ranvere diplacemen v v D a = kh (4) hich i reciprocal o heir iffnee. On he oher hand ν D + ν = V and y aking Eq. () (40) and (4) ino accoun one oain δ v = H (44) If he ulkhead hickne increae he diorion angle decreae and vice vera. Figure 9 Deck oxe a eam on elaic uppor Slika 9 Paluni kuijai noači kao grede na elaičnoj podlozi ( + ψ D B ) = H. + a k 0 6(0) 5-7

7 I. SENJANOVIĆ N. VLADIMIR M. TOMIĆ Figure 0 Definiion of deck ox uppor iffne Slika 0 Definiranje kruoi elaične podloge palunih noača Diriuion of he diorion angle δ ihin he engine room i almo linear. Along he open hold i caue ending of he upper deck oxe a eam on elaic uppor Figure 9 [8]. The uppor iffne k e i deermined a he raio of he impoed deck load q and he reponded diplacemen v Figure 0. To deck oxe can e conidered a one girder ih doule ending and uppor iffnee I and k e repecively. Since he open hold i quie long l 0 muual oundary influence i negligile and herefore only he decreaing erm of homogenou oluion for he eam on elaic uppor can e ued. By aifying he relevan oundary condiion Figure 9 e ge here ϑx ϕ v = e v coϑ x+ v + x in ϑ ϑ ϑ = ke 4EI 4 (45) (46) ϕ = ν /a hile ν i founded from Eq. (44). Finally funcion of diorion angle read δ = ν/h. Baed on he knon deflecion of he deck ox v i i poile o deermine he ending momen M = -EIv and re σ = My/I here y i he diance of a conidered poin on he ox cro-ecion from he neural line. By employing (45) one oain Ek ϕ e ϑx σ = y e ϑ ϑ I v + ϑ co x v in x (47). The complee re coni of he memrane par due o rerained arping Eq. (4) and he aove ending re Eq. (47). Lengh overall L oa = 4 m Lengh eeen perpendicular L pp = 9 m Breadh B = 4.8 m Deph H = 4.6 m Draugh T = 4.5 m Diplacemen = 550. Maerial properie are he folloing: Young modulu E = kn/m Shear modulu G = kn/m Poion raio ν = 0.. The hip laeral plan and midhip ecion are hon in [5]. The engine room i locaed ca. 0. L from he af perpendicular here he cro-ecion i reduced. Hoever in hi numerical inveigaion he engine room i exended o he full midhip profile o ha a primaic hip-like ponoon can e creaed and analyed. The geomerical properie of he open and cloed hip croecion are deermined uing compuer program STIFF [] aed on he rip heory of hin-alled girder [ 4] Tale. I i eviden ha he cro-ecion area of he cloed ecion i 50% higher han ha of he open ecion. Torional modulu of he cloed ecion i much higher han ha of he open ecion. The hear cenre of he cloed ecion i in he middle of he croecion hile ha of he open ecion i elo he keel. Tale Geomeric properie of hip cro-ecion Talica Geomerijke značajke poprečnih prejeka roda Quaniy Symol uni Open ecion ( ) Cloed ecion (*) Cro-ecion area A m Horizonal hear area A h m Verical hear area A v m Verical poiion of neural line z NL m Verical poiion of hear cenre z SC m Horizonal momen of ineria I h m Verical momen of ineria I v m Torional modulu I m Warping modulu I m Shear polar momen of ineria I m Figure Warping funcion of he open cro-ecion Slika Vioperenje ovorenog poprečnog prejeka 7 Geomeric properie of hip-like ponoon A 7800 TEU Conainer Veel of he folloing main paricular i aken ino conideraion: 6(0) 5-7

8 I. SENJANOVIĆ N. VLADIMIR M. TOMIĆ EFFECTIVE STIFFNESS OF THE ENGINE ROOM STRUCTURE IN LARGE... are aken from Tale. Warping a he oundarie i rerained according o Figure and commen a he end of Secion. Torional momen M = knm i impoed a he ponoon end. The ponoon i conidered free in he pace and he prolem i olved analyically in Secion. The oal i angle ψ = ψ + ψ and he derivaive of he orional conriuion ψ Eq. (8) and (9) neceary for arping deerminaion are hon in Figure. Figure Deformaion funcion of uniform ponoon Slika Funkcija deformacije jednolikog ponona 8. Ponoon ih a cloed egmen Figure Warping funcion of he cloed cro-ecion Slika Vioperenje zavorenog poprečnog prejeka The arping funcion of he open and cloed cro-ecion are hon in Figure and. The relaive axial diplacemen of he inide poin of he upper deck and ilge a he level of he inner oom a he repreenaive quaniie read D = - m and B = 67 m repecively. The relaive momen of ineria of he deck volume Eq. (9) i calculaed in Tale. The analyical oluion for he orion of a ponoon coniing of hree egmen i preened in Secion 4 here compaiiliy facor for he convenional compaiiliy condiion (a) are ued ε = η =. The lengh of he middle cloed egmen i a = 0. m. The geomerical parameer of he open cro-ecion are lied in Tale. Diagram of he oal i angle ψ and derivaive of he pure i angle ψ are hon in Figure 4. Tale Relaive momen of ineria of deck rucure volume Talica Relaivni momen inercije volumena konrukcije palue Iem i Surucure V i (m ) h i (m) V h i i V h Upper deck.78.6 Deck Deck Deck k = Ponoon orion 8. Uniform open ponoon Torion of he uniform ponoon of he lengh L = 00 m ih he open cro-ecion i conidered. The iffne parameer Figure 4 Deformaion funcion of egmened ponoon acual parameer Slika 4 Funkcija deformacije egmennog ponona akualni parameri 8. Ponoon ih effecive parameer of a cloed egmen The procedure for orional analyi i he ame a in he previou cae. The reducion of he orional modulu of he cloed egmen due o i horne i.e. deck conriuion o he orional modulu of he open ecion i elaoraed in Secion 5. 6(0) 5-7

9 I. SENJANOVIĆ N. VLADIMIR M. TOMIĆ The folloing value of he aic parameer are ued: a = 0. m = 9.7 m = m D = - m B = 67 m Figure and I O m4 Tale k =.894 Tale. A a reul C =.4 Eq. (8) and accordingly I = 8.4 m 4 Eq. (0) are oained. Since I = 0.6I * he effec of he hor engine T room rucure on i orional iffne i oviou. Tale Ponoon diplacemen Talica Pomaci ponona Segmened ponoon Uniform ponoon Acual Effecive parameer parameer ψ (L/) rad ψ (0) rad Diriuion of diorion angle δ i deermined y employing he procedure decried in Secion 6 ih he folloing inpu daa: ψ = H =.6 m = m = 0.0 m in Eq. (44); momen of ineria of he deck ox cro-ecion I = 0.7 m 4 iffne of he elaic uppor k e = 7 kn/m. The value of k e i oained y FEM for a ponoon egmen Figure 6. 9 FEM analyi Figure 5 Deformaion funcion of egmened ponoon effecive parameer Slika 5 Funkcija deformacije egmennog ponona efekivni parameri The oained ponoon deformaion funcion are hon in Figure 5. There are large difference eeen he reul oained for he acual and effecive parameer Figure 4 and 5. The maximum diplacemen for all hree conidered cae i.e. he uniform ponoon and he egmened ponoon ih acual and effecive parameer are compared in Tale. Figure 6 A ypical hold uperelemen Slika 6 Tipični uperelemen kladiša Figure 7 Engine room uperelemen Slika 7 Superelemen rojarnice Figure 8 Load on he model end Slika 8 Runo operećenje modela In order o verify he numerical procedure for orional analyi y he eam model ih effecive iffne parameer deignaed a (+)D for hor he D FEM model of he uniform and egmened ponoon are creaed uing ofare [5]. 6(0) 5-7

10 I. SENJANOVIĆ N. VLADIMIR M. TOMIĆ EFFECTIVE STIFFNESS OF THE ENGINE ROOM STRUCTURE IN LARGE... The former coni of open uperelemen Figure 6 hile in he laer o cenral uperelemen are exchanged ih he one engine room uperelemen Figure 7. The ponoon end are cloed ih ranvere ulkhead. The hell finie elemen are ued. The ponoon are loaded a heir end ih he verical diriued force in he oppoie direcion generaing oal orque M = knm Figure 8. The midhip ecion i fixed again he ranvere and verical diplacemen and he ponoon end are conrained again he axial diplacemen (arping). Figure Laeral axial ird -eye and fih vie on deformed engine room uperelemen Slika Bočni uzdužni pičji i rilji pogled na deformirani uperelemen rojarnice Figure 9 Deformaion of uniform ponoon laeral and ird -eye vie Slika 9 Deformacije jednolikog ponona očni i pičji pogled Figure Shear ree in he fron engine room ulkhead Slika Smična naprezanja u pramčanoj pregradi rojarnice Figure Shear ree a he inernal oundary of he fron engine room ulkhead Slika Smična naprezanja na unuarnjem ruu pramčane pregrade rojarnice Figure 0 Deformaion of egmened ponoon laeral and ird eye vie Slika 0 Deformacije egmennog ponona očni i pičji pogled Laeral and ird eye vie on he deformed uniform and egmened ponoon are hon in Figure 9 and 0 repecively. In he former preenaion he deformaion i monoonou hile in he laer one he influence of he more rigid engine room rucure i eviden. A deailed vie of hi ponoon porion i preened in Figure. I i apparen ha he doule oom and 4 6(0) 5-7

11 I. SENJANOVIĆ N. VLADIMIR M. TOMIĆ ide roae a a rigid ody hile he deck and ranvere ulkhead are expoed o hear deformaion. The hear re diriuion in he fron engine room ulkhead i hon in Figure. The oundary ree hich caue diorion of he croecion are preened in Figure. The aumed hear force in he heoreical conideraion of diorion Figure 7 are imilar o he acual oundary hear re diriuion in Figure. 0 Comparaive analyi 0. Uniform ponoon If one dra he i angle diagram aed on D FEM reul almo he ame hape a ha from he ( + )D analyi i oained Figure. The raio of he maximum diplacemen in he o model i.e. heir i angle and axial diplacemen read ψ ( + ) D x = L/ : = = ψ D u. 878 x = 0 ( + ) D upper deck: = mm = u mm x = 0 ilge: u ( ) + D u D D = mm mm = Dicrepancie in hi imple cae are ihin % hich i quie good. The maximum i angle a he ponoon end are alo compared in Figure 4. The oal i angle of he analyical oluion ψ (+)D i almo equal o ha of he FEM analyi ψ D. The value of ψ (+)D coni of pure orional par ψ and hear conriuion ψ. The former caue he cro-ecion roaion around he hear cenre S.C. hile he laer coninue i roaion around poin P a he level of he doule oom neural line. A a reul he i cenre i oained T.C. Figure 4 [5] hich i no he ame poin a S.C. 0.. Segmened ponoon ih effecive iffne The i angle deermined y he analyical eam oluion and he FEM analyi for he ponoon oom and ide are compared in Figure 5. A can e noiced here are ome mall dicrepancie eeen ψ (+)Doom and ψ Doom hich are reduced o a negligile value a he ponoon end: ψ ( + ) Doom x = L/ : = = ψ Doom The diorion curve of he (+)D oluion δ ( ψ ψ + ) = ( + ) D Dide ( + ) alo follo quie ell ha of Doom he D FEM analyi. Figure 4 Ti angle a he ponoon end Slika 4 Ku uvijanja na kraju ponona Figure 5 Ti angle of he egmened ponoon Slika 5 Kuevi uvijanja egmennog ponona Warping of cro-ecion i evaluaed y comparing axial diplacemen of he ilge and upper deck a repreenaive poin Fig. 6. Correlaion of he reul oained y he eam heory and FEM analyi i quie good from engineering poin of vie. There are ome dicrepancie eeen he axial diplacemen a he deck level in he engine room area a a reul of large hear deformaion Figure. Hoever hi i a local phenomenon hich canno eaily e capured y he eam heory. In order o have eer inigh ino he rucural deformaion he longiudinal diriuion of he verical poiion of he i cenre i hon in Figure 7. I value i omeha reduced in 6(0) 5-7 5

12 I. SENJANOVIĆ N. VLADIMIR M. TOMIĆ EFFECTIVE STIFFNESS OF THE ENGINE ROOM STRUCTURE IN LARGE... he engine room area u i i ill oo far from he i cenre of he cloed egmen hich ould induce coniderale horizonal ending. Anoher crierion for recognizing ending in he orional repone i he value of he inegral I = yd A hich i zero in cae of no ending. Depending on ha value he arping cenre (defined a he poin a he inner ide hell ih zero axial diplacemen Figure and ) i moved from he open o he cloed cro-ecion poiion Figure 8. Since ha change i quie mall ihin he engine room area one can conclude ha horizonal ending i negligile. Baed on he aove fac he inroduced aumpion ha he hor engine room rucure ehave a an open one ih increaed orional iffne i accepale. y A Figure 6 Axial diplacemen of he deck and oom Slika 6 Uzdužni pomaci palue i dna Figure 7 Verical poiion of he i cenre Slika 7 Verikalni položaj cenra uvijanja Figure 8 Verical poiion of he arping cenre Slika 8 Verikalni položaj cenra vioperenja Figure 9 Ti and diorion angle of he join cro-ecion of he open and cloed egmen Slika 9 Kuevi uvijanja i diorzije poja ovorenog i zavorenog egmena Deformaion of he join cro-ecion i hon in Figure 9 here he poiion of he i cenre for he open and cloed cro-ecion i indicaed and compared ih he poiion of he i cenre for he real D rucure. Alo he i angle ψ D and ψ (+)D and he diorion angle δ hich are of he ame order of magniude are dran. Concluion Hydroelaic analyi of large conainer hip i currenly ecoming a prolem [6]. For reaon of impliciy and epecially in he early deign age he eam model of he hull girder i coupled ih a D hydrodynamic model. Tranvere ulkhead increae he hull orional modulu conideraly. Thi prolem i olved ih he energy approach conidering he ulkhead a an orhoropic plae. In hi paper a imilar approach i ued o deermine he effecive orional iffne parameer of he hor engine room rucure. I ha een found ha mo of he rain energy i due 6 6(0) 5-7

13 I. SENJANOVIĆ N. VLADIMIR M. TOMIĆ o he deck in-plane ending and hear deformaion caued y he hull cro-ecion arping. The deck deformaion increae ih i diance from he doule oom hich mainly roae a a rigid ody. By modelling he deck a a eam ih hear influence on deflecion he prolem i implified and focued on he deerminaion of he deck plaing volume. Ponoon diorion i a reul of differen hear flo diriuion of he open and cloed ponoon egmen conneced a he engine room ulkhead. In he conidered cae diorion doe no have a ig influence on orion and herefore i i eimaed in addiion a he econd ep of calculaion aed on he orional reul. Diorion i reduced y increaing he ulkhead hickne. Adopion of cloed cro-ecion iffne moduli and he aifacion of compaiiliy condiion a he join of he cloed engine room egmen ih he hold rucure of he open cro-ecion preen a real prolem relaed o he applicaion of he eam model of a hip hull. The offered oluion for he engine room rucure modelling i quie imple and i correlaion ih he D FEM reul in he cae of hip-like ponoon ho accepale agreemen. Therefore i can e generally ued for improving he eam rucural model in a hydroelaic analyi of relaively flexile hip uch a large conainer veel. Due o variale cro-ecion properie he eam finie elemen mehod i preferale. Acknoledgmen Thi reearch a uppored y he Miniry of Science Educaion and Spor of he Repulic of Croaia (Projec No ). The auhor expre heir graiude o Sipe Tomašević DSc Univeriy of Zagre for hi uppor in generaing he D FEM model. Reference [] PAYER H.: Technological and economic implicaion of mega-conainer carrier SNAME Tranacion Vol. 09 (00) p [] VALSGÅRD S. SVENSEN T.E. THORKILDSEN H.: A compuaional mehod for analyi of conainer veel SNAME Tranacion Vol. 0 (995) p [] SHI B. LIU D. WIERNICKI C.: Dynamic loading approach for rucural evaluaion of ulra large conainer carrier SNAME Tranacion (005) p [4] MALENICA Š. SENJANOVIĆ I. TOMAŠEVIĆ S. STUMPF E.: Some apec of hydroelaic iue in he deign of ulra large conainer hip The nd Inernaional Workhop on Waer Wave and Floaing Bodie IWWWFB Plivice Lake Croaia; 007. [5] TOMAŠEVIĆ S.: Hydroelaic model of dynamic repone of conainer hip in ave (in Croaian) Ph.D. Thei Univeriy of Zagre Zagre 007. [6] BISHOP R.E.D. PRICE W.G.: Hydroelaiciy of Ship Camridge Univeriy Pre 979. [7] PAVAZZA R.: Bending and orion of hin-alled eam of open ecion on elaic foundaion Ph.D. Thei (in Croaian). Univeriy of Zagre Zagre 99. [8] PAVAZZA R.: Inroducion o hin-alled girder analyi (in Croaian) Univeriy of Spli 007. [9] PAVAZZA R.: Torion of hin-alled eam of open cro-ecion ih influence of hear Inernaional Journal of Mechanical Science p [0] HASLUM K. TONNESSEN A.: An analyi of orion in hip hull European Shipuilding 97; 5/6 p [] PEDERSEN P.T.: A eam model for he orional-ending repone of hip hull RINA Tranacion 98 p.7-8. [] PEDERSEN P.T.: Torional repone of conainerhip. Journal of Ship Reearch 985; 9 p [] STENEROTH E.R ULFVARSON A.Y.J.: The naking of open hip Inernaional Shipuilding Progre p. -9. [4] PAVAZZA R. PLAZIBAT B. MATOKOVIĆ A.: Idealiaion of hip ih large hach opening y a hin-alled rod of open ecion on many elaic uppor Thin-Walled Srucure 998 p [5] SENJANOVIĆ I. TOMAŠEVIĆ S. RUDAN S. SENJANOVIĆ T.: Role of ranvere ulkhead in hull iffne of large conainer hip Engineering Srucure 008; 0(9) p [6] URŠIĆ J.: Ship Srengh II (in Croaian) Univeriy of Zagre Zagre 98. [7] SENJANOVIĆ I. FAN Y.: Ponoon orional rengh analyi relaed o hip ih large deck opening Journal of Ship Reearch 99; 5(4) p [8] SENJANOVIĆ I. FAN Y.: On orional and arping iffne of hin-alled girder Thin-Walled Srucure 99 p [9] SENJANOVIĆ I. TOMAŠEVIĆ S. VLADIMIR N.: An advanced heory of hin-alled girder ih applicaion o hip viraion Marine Srucure (009) : p [0] VLASOV V.Z.: Thin-alled elaic eam Irael Program for Scienific Tranlaion Ld Jerualem 96. [] SENJANOVIĆ I.: One oluion of he orion prolem on conainer hip Par I and II (in Croaian) Brodogradnja 97 () [] : STIFF Uer Manual. FAMENA Zagre 990. [] SENJANOVIĆ I. FAN Y.: A higher-order heory of hin-alled girder ih applicaion o hip rucure Compuer & Srucure 99; 4():-5. [4] SENJANOVIĆ I. Fan Y.: A finie elemen formulaion of hip croecional iffne parameer Brodogradnja; 4(99) p [5]...: SESAM Uer Manual. De Norke Veria Høvik; 007. [6] Proceeding of Inernaional Conference on Deign & Operaion of Conainer Ship RINA London; 006. Nomenclaure A cro-ecion area A c common cro-ecion area A i B i inegraion conan a one half of engine room lengh B arping imomen C energy coefficien D deerminan E Young modulu E i rain energy G hear modulu I I I eam hear orional and arping moduli L eam and ponoon lengh l egmen lengh M exernal orque conour coordinae compaiiliy facor T orque T T iing and arping orque plae hickne u axial diplacemen arping funcion xyz coordinae z S.C. ordinae of hear cenre α ( β ϑ coefficien of funcion argumen δ diorion angle ε η compaiiliy facor μ diriued orque υ Poion raio σ normal re ψ i angle ψ i deformaion ( o ) open ecion ( * ) cloed ecion ( ) effecive value 6(0) 5-7 7