GUIDELINES FOR DIRECT STRENGTH ANALYSIS OF DOUBLE SIDE SKIN BULK CARRIERS

Transcription

1 GUIDANCE NOTES GD CHINA CLASSIFICATION SOCIETY GUIDELINES FOR DIRECT STRENGTH ANALYSIS OF DOUBLE SIDE SKIN BULK CARRIERS 004 Bejng

2 Contents 1 General General requrements Defntons... Drect Loads Analyss General requrements...3. Stll water loads Wave loads Desgn loads pressure n hold Eternal sea pressure Bendng moment on end planes Structural model Coordnate defntons Model meshng Boundary condtons Loadng Condtons Strength Crtera Evaluaton of Bucklng Strength General requrements Methods of bucklng evaluaton...1

3 1 General 1.1 General requrements For double sde skn (DSS) bulk carrers by assgnng correspondng harmonsed notatons of IACS UR S5, drect strength analyss of hull structure s to be carred out n accordance wth the Gudelnes. If other requrements are nvolved, the correspondng Rules and Regulatons for the Constructon and Classfcaton of Sea-gong Steel Shps (herenafter referred to as the Rules) and Gudelnes of can be referred For bulk carrers of 150m or more n length, whch are arranged wth the double sde skn wthn the cargo holds and the dstance between the outer and nner sde skn beng 1000mm or more, drect strength analyss of hull structure s to be carred out n accordance wth the Gudelnes For the double sde skn structure, the net breadth between the face plates of the transverse frames (for transverse frame type) on the outer and nner skn s not less than 600mm, and that between the face plates of the longtudnal stffeners (for longtudnal frame type) s not less than 800mm wthn the parallel mddle body and not less than 600mm for the others The Gudelnes present detaled requrements and methods for drect strength analyss of prmary structural members of DSS bulk carrers Harmonzed notatons, addtonal notatons and annotatons Ths resoluton s applcable to "Bulk Carrer" as defned n UR Z11.., havng length as defned n UR S.1 of 150 m or above and contracted for new constructon on or after 1 July 003, harmonzed notatons as followng (1)~(3) and annotatons as (4)~(5): (1) BC-A: for bulk carrers desgned to carry dry bulk cargoes of cargo densty 1.0 tonne/m 3 and above wth specfed holds empty at mamum draught n addton to BC-B condtons. () BC-B: for bulk carrers desgned to carry dry bulk cargoes of cargo densty 1.0 tonne/m 3 and above wth all cargo holds loaded n addton to BC-C condtons. (3) BC-C: for bulk carrers desgned to carry dry bulk cargoes of cargo densty less than 1.0 tonne/m 3. (4) Addtonal notatons: {mamum cargo densty.y (n tonnes/m 3 )} for notatons BC-A and BC-B f the mamum cargo densty s less than 3.0 tonnes/m 3. {no MP}for all notatons when the vessel has not been desgned for loadng and unloadng n multple ports. (5) Annotatons: {allowed combnaton of specfed empty holds a, b, }for notaton BC-A. -1-

4 1.1.6 The structural FE model and appled loads are to be capable of fully reflectng the followng responses of the structure resultng from the local loads and the global longtudnal bendng moment: (1) stresses of longtudnal members ; () stresses of prmary transverse members, ncludng transverse bulkheads; and (3) bucklng of prmary members Documents of drect strength analyss submtted for approval: (1) lst of drawngs used; () detaled descrpton of FE model of hull structure; (3) the structural model and relevant physcal propertes; (4) materal propertes ; (5) detaled descrpton of boundary condtons; (6) detals of appled loads; (7) fgures and results showng responses of loads-related wth structural FE model; (8) summary, ncludng fgures, of the global and local deformatons ; (9) summary, ncludng fgures, showng von Mses stress, stresses n and y drectons, and shear stresses of all structural members n complance wth the strength crtera; (10) nalyss and results of plate bucklng; (11) utput of the strength assessment; (1) proposed structure modfcatons, ncludng yeldng and bucklng strength, f necessary. 1. Defntons 1..1 Unts : t; Length: m; Tme: s; Force: N or kn; Stress: N/mm ; Pressure: kn/m. 1.. Symbols L length of shp, n m, as defned n Secton 1, Chapter 1, Part two of the Rules; B breadth of shp, n m, as defned n Secton 1, Chapter 1, Part two of the Rules; D moulded depth, n m, as defned n Secton 1, Chapter 1, Part two of the Rules; d draft, n m, as defned n Secton 1, Chapter 1, Part two of the Rules; C b block coeffcent, as defned n Secton 1, Chapter 1, Part two of the Rules; V speed, n kn; --

5 g gravtatonal acceleraton, g = 9.81m/s ; C w wave coeffcent; ρ seawater specfc gravty, ρ = 1.05t/m 3 ; σ e von Mses stress (N/mm ),= σ + σ σ σ + 3τ ; σ stress of element n drecton (N/mm ); σ y stress of element n y drecton (N/mm ); τ y shear stress of element n y planes (N/mm ); σ l stress n longtudnal drecton of hull grder (N/mm ); σ w stress n transverse or vertcal drecton of hull grder (N/mm ); τ mean shear stress of full depth of the web plate (N/mm ); k materal converson factor; E elastc modulus of materal, E = N/mm for steel; υ Posson s rato of materal, υ = 0.3 for steel. Drect Loads Analyss.1 General requrements.1.1 Whle at sea, shps are subjected to wave-nduced load, n addton to buoyancy, cargo loads and correspondng nertal loads. Ths secton defnes the basc prncples for calculaton of stll water loads and wave loads. The stll water loads and wave loads may be calculated by the codes approved by the Socety.. Stll water loads..1 Weght dstrbuton curve Breakng up the weght of varous tems (hull steel, equpments, fttngs and cargoes) along shp s length nto the trapezod weght dstrbuton blocks and supermposng the blocks, the weght dstrbuton curve w() wll be formed n the gven condtons. y y y In general, for bulk carrers of 150 m n length and over, frame spacng s to be as a block for calculatng weght dstrbuton curve... Buoyancy curve In the balanced floatng condton of the shp, the buoyancy of the shp n stll water can be determned by the draft. Therefore the buoyancy curve b() along shp s length can be obtaned based on the shp s lnes...3 Shear and bendng moment curves The stll water shear force N s () and stll water bendng moment M s () actng on hull grder are obtaned from followng equatons: N ( ) = [ w( ) b( )] d kn s 0 M s N s ( ) d = [ w( ) ( ) = b( )] d d kn m As both fore and aft ends of the hull are free ends, the shear and bendng moment curves -3-

6 are to be corrected whle shear force and bendng moment at end ponts are not equal to zero..3 Wave loads.3.1 Applcatons The methods recommended n ths secton are appled to the shps of: L 500 m L/D Methods and assumed condtons (1) Wave loads may be calculated by two-dmensonal strp theory or three- dmensonal theory. () Sea condtons: 1 The P-M spectrum s recommended, descrbed by the followng epresson: S( ω, H 1 3, T 14H, θ ) = π 0 T 4 1/ ω ep cos θ 4 4 T ω π π - θ θ as other value where: θ relatve spreadng around the man wave leadng, n rad; cosθ energy spreadng functon; π H sgnfcant wave heght, n m; 1 3 T the average zero up-crossng wave perod, n s; ω angular wave frequency, n rad/s. For makng a long-term predcton of wave loads, the dstrbuton of wave heght for each perod s assumed as Raylegh dstrbuton and all wave headngs can be assumed to have an equal probablty of occurrence. () Speed s assumed as 0 knot when calculatng wave bendng moment and as /3 the shp s desgn speed when calculatng wave pressure. (3) Eceedance probablty level s taken as 10-8 when calculatng wave bendng moment and as 10-4 when calculatng wave pressure..3.3 Shp s roll radus of gyraton and crtcal roll dampng coeffcent: For desgn of the shp, the roll radus of gyraton may be taken as: 0.35 B (full load) 0.3 B (ballast) the crtcal roll dampng coeffcent may be taken as:

7 .3.4 Wave loads (1) Vertcal wave bendng moment M v and shear force F v Base on the above method and defntons, the vertcal wave bendng moment M W n way of md-shp secton can be obtaned, and the desgn wave bendng moment M v along shp s length obtaned from the followng equatons: hoggng saggng M M V V ( ) = M C M kn m + HB W ( ) = M C M kn m SB W where: M W: vertcal bendng moment n way of mdshp secton by the codes, n kn m; M: dstrbuton factor of bendng moment along shp s length, generally by the Rules; C HB, C SB: nonlnear correcton coeffcent, to be obtaned from the followng equatons: C C SB HB 110( Cb + 0.7) = 95C + 55( C + 0.7) b = 95C b 190C b b + 55( C b + 0.7) where: C b block coeffcent, but not less than 0.6. The vertcal wave shear force F W s to be obtaned by the codes, so the desgn vertcal wave shear force F v along shp s length can be obtaned from followng equatons: hoggng F V ( + ) = F1 CsFW kn saggng FV ( ) = FC sfw kn Where: F W: vertcal wave shear force n way of md-shp secton, to be obtaned by the codes, n kn; F 1, F : dstrbuton factor of shear force, to be obtaned by the Rules; C s: correcton coeffcent, to be determned by Table.3.4. Shp s length (m) C s Shp s length (m) Correcton Coeffcent C s Table.3.4 C s Shp s length (m) C s Shp s length (m) C s -5-

8 3 Desgn loads 3.1 pressure n hold The cargo pressure n hold s to be obtaned by the followng equaton: a0 P = 10ρ c( ) kbhd kn/m C b Where: ρ c cargo densty, n t/m 3 ; L 1. a [10.75 ( ) 5 0 = V L] 150m L <300 m L = [ V L] 300m L <350 m L k b = addtonal requrement 350m L <500 m o = sn α tan (45 0.5δ ) + cos α a ncluded angle between plate and horzontal plane, e.g. 90 for bulkhead and sde plate, and 0 for nner bottom platng. δ repose angle of cargoes, 35 for ore and coal cargoes, 30 for salt, sand, stone and gran cargoes, and 5 for bulk cement. h d vertcal dstance from calculatng pont to cargo top surface, n m. For transverse shape of cargo top surface, see Fg. 3.1, t s assumed that the cargo n hold s unformly dstrbuted along shp s length. On cargo top surface, t s unformly dstrbuted longtudnally; and t s dstrbuted as parabolc curve of the followng equaton transversely: where: b=b/ B s the breadth of shp; z s = h (1 y s ) b mamum dstance (h) between top surface and connecton lne, see Fg 3.1: h = tan δ (δ =35 ) area(a) between the parabolc curve and the connecton lne : A = b 3 b tanδ h d = zs + h0 + h db z where: h d : dstance from cargo top surface to calculatng pont, n m; -6-

9 z s : dstance from cargo top surface to connecton lne, n m; h db : heght of double bottom, n m; z: vertcal heght of calculatng pont, measured from baselne, n m; h o : to be calculated accordng to loadng capacty, cargo densty and shape of cross secton of the hold, but to be not less than dstance from top of slopng plate n hopper tank to nner bottom platng, n m. Fgure 3.1 Shape of cargo top surface The pressure-head s up to the top of the ar ppe for the ballast tank or fuel ol tank, and the top of the hatch coamng for the cargo hold. 3. Eternal sea pressure The eternal sea pressure may be determned by drect strength analyss as requred n.3 or by ether of the followng methods Method 1 (1) Full loadng condton Eternal sea pressure ncludes hydrostatc pressure and dynamc pressure, and s determned as follows: At baselne: P b = 10d + 1.5C w kn/m At waterlne: P w = 3C w kn/m At sde top: P s = 3 P 0 kn/m Dynamc pressure on deck: P s =.4P 0 kn/m where: P = Cw 0.67( D ) C w 0 d 300 L = ( ) m L 300m = m < L < 350m L 350 = ( ) m L 500m -7-

10 () Other loadng condtons: At baselne: P b = 10d a kn/m At waterlne: P w = 0.0 kn/m Where: d a s actual draft correspondng to the loadng condton, n m. The formula for dynamc pressure at baselne, waterlne and sde top are gven above. The eternal sea pressure at other sde postons s to be determned by lnear nterpolaton. 3.. Method (1) Hydrostatc pressure At baselne: At waterlne: Pb 10d a kn/m = = 0.0 kn/m P w () Dynamc pressure 1 Dynamc pressure at waterlne(kn/m ): f P WL = ma(, ) 4 p 1 p y p1 = p ( T1 Zw) B + 75 p11 = 3ks C + k 50c y + k f Z p = 13 y + C w B ( B + 75) 14 T1 at waterlne y = B /; = T Zw 1 Dynamc pressure at blge(kn/m ): f P BS = ma(, ) 4 p 1 p p 1 and p are the same as n the formula for waterlne, but y = B /; Z =0.0. w 3 Dynamc pressure at bottom (kn/m ): 1 PB = l f f ma(, ) 4 p 1 p p and p are the same as n the formula for waterlne, but y = B /4; Z = Dynamc pressure above sde waterlne h f PDK sde = P WL 4 where: h : heght from stll waterlne to the pont consdered, n m. 5 Dynamc pressure on deck (hatch cover) w -8-

11 P dk = H where: H = A V L C B d where: A coeffcent dependng on the longtudnal poston of the hatch md length gven n Table 3..()5 V L f Table 3..()5 Dstance to A FP FP.70 desgn speed, n kn, but not less 0.05 L.16 than 13 kn; 0.10 L 1.70 rule length of shp, n m, as defned 0.15 L 1.43 n URS; 0.0 L 1. C B block coeffcent; 0.5 L 1.00 d f vertcal dstance from summer load lne to the top of hatch coamng, n m. where: T l draft, n m; C = [(300-L)/100] 3/ 90m L 300m = m< L 350m = [(L-350)/150] 3/ 350m<L 500m; A R 0.75c roll angle, taken as 0.34 ; B kr c=( ) k; GM k = 1. (wthout blge keel ) k r = 1.0 (wth blge keel ) = 0.8 (wth actve roll dampng facltes); roll radus of gyraton; GM metacentrc heght, n m; k r = 0.39 B (even dstrbuton of mass) = 0.5 B (ore carrers); GM = 0.1 B ; y transverse horzontal dstance from centerlne to the load pont, B/4 y B/; k v speed factor; V mnmum servce speed, n kn; f ndcator of probablty level = 4 (at probablty 10-4 per cycle) = 8(at probablty 10-8 per cycle, appromately the largest pressure n 0 years); -9-

12 k s = C B (at AP and aft) C B = C B (between 0. L and 0.6 L from AP) = C B (at FP and forward ) C B Between the specfc pont, k s s to be vared lnearly; l f = 1.0 (at AP and aft ) = 0.5 (between 0. L and 0.6 L from AP) = 1.0 (at FP and forward) Between the specfc pont, l f s to be vared lnearly; k f Mnmum of T l and T f ; T f vertcal dstance from the waterlne to the sde top at the consdered cross secton, but not greater than 0.8C. 3.3 Bendng moment on end planes The bendng moment appled on end planes of the FE model s to be the actual moment of the planes, ncludng stll water bendng moment M s and wave bendng moment M w. When the actual bendng moment s not avalable, alternatve one may be taken as The wave bendng moment M w s to be determned n accordance wth the Rules, postve as hoggng Stll water bendng moment M s s to take the mamum bendng moment of the model correspondng to the loadng condton. If the condton s not avalable, the condton wth full load draft of mamum (or mnmum) bendng moment that occurs s to be appled subject to correcton accordng to 3.3.4, postve as hoggng The bendng moment appled on the end planes of the FE model s composed of the stll water bendng moment M s, wave bendng moment M w and corrected bendng moment Mγ: M = M s + M w -M r Corrected bendng moment Mγ: The corrected bendng moment s an addtonal bendng moment due to local loads. (1) When L 1 L 0.5 L m as shown n Fgure 4.1 Q m as the unformly dstrbuted lnear pressure of mddle hold model, and Q e as the unformly dstrbuted lnear pressure of both end holds, postve n upwards drecton along vertcal coordnate Z: Q m = Pb b Wmcagro / L m -10-

13 Q e = Pb b Wecagro / L e where: P b : eternal pressure on bottom, n kn/m, see 3.; W mcargo cargo weght, ncludng weght of ballast water, n the mddle : hold, takng half of total weght n the hold for half-breadth model, n kn; W ecargo : cargo weght, ncludng weght of ballast water, n end holds, takng half of total weght n the hold for half-breadth model, n kn; L e : Length of end hold correspondng to W ecargo, n m; L m : Length of mddle hold, n m; L 0 : overall length of FE model, n m; b: breadth of model, b= B/ when half-breadth model s appled, where B s moulded breadth of shp, n m; 3 1 M r = QmL0 + QeL0 3 3 kn m () When L 1 L 0.5 Lm as shown n Fgure 4.1, the smple beam calculaton method may be appled. In ths case the pressure may be obtaned by tem(1) n the secton, and the mamum M r s to be taken. 4 Structural model 4.1 Coordnate defntons the longtudnal drecton, postve forward; y the transverse drecton, postve to port from the center lne; z the vertcal drecton, postve upwards from the baselne. 4. Model meshng 4..1 The 3-D FE model s appled for drect strength analyss of prmary members strength of bulk carrers. The etent of 1/ hold length forward and 1 hold length n the mddle and 1/ hold length aft wthn md-shp cargo area n longtudnal drecton, and full depth of the shp n vertcal drecton, (see fgure 4.1&4.). In general, the results of the mddle hold, ncludng bulkhead, are appled for strength assessment. The lght cargo hold, heavy cargo hold and heavy ballast hold are assessed respectvely. 4.. Whle both prmary members and loads are symmetrcal to longtudnal centerlne plane, only half breadth, port or starboard sde, of the shp hull s requred to be modeled. In the case of the asymmetrcal loads appled, t can be equvalently dvded nto symmetrcal and ant-symmetrcal loads (see Fg.4.); otherwse, a full-breadth model s to be requred The meshng of the 3-D FE model of hull structure s to be carred out as the longtudnal spacng or smlar spacng transversely along the hull envelop, and the frame spacng or smlar spacng along hull length. The meshes are to be as square as possble. -11-

14 4..4 In general, all areas of shell plates, deep webs of transverse rngs, strngers, plane bulkhead web stffeners, frames, other members as well as corrugaton bulkheads and bulkhead stools are to be modeled by 4-node plate (shell) elements. Trangular elements are to be mnmzed. In hgh stress areas and areas of sgnfcant stress changes, such as lghtenng holes, manholes, connecton of stool to bulkhead, postons adjacent to brackets or structural dscontnutes, trangular elements are to be avoded as practcable as possble All stffeners of plates, whch are subject to eternal sea pressure and cargo pressure, are modeled by eccentrc beam elements. The stffeners and/or face plates of web transverses, frames, floors, grders and brackets may be modeled by rod elements. In vew of dffculty n meshng, one lne element may represent more than one beam or rod elements Not less than 3 plate elements are to be arranged n vertcal drecton for bottom grders and floors. In general, the elements at the lowest end of bulkhead are to be dvded as square as possble In general, the web of sde frame may be modeled by plate element. In case the rato of web heght of frame aganst sze of grd at sde s less than 1/3, beam element may be appled Corrugated bulkhead and bulkhead stools: each flange plate or web plate s to be taken at least as a plate element; for the plate elements at the lower end of corrugated bulkhead n the vcnty of lower stool and for the elements adjacent to stool plate, the aspect rato of sdes of grd s to be close to For lghtenng holes and manholes of prmary members, n partcular the openngs on grders adjacent to bulkhead and bracket floors adjacent to lower stool n double bottom, plate elements of equvalent plate thckness may be used to consder the effect of these openngs One ndependent pont s set respectvely n way of ntersecton of neutral as wth longtudnal centerlne n fore and aft end planes, and the degree of freedomδ,δz, θy,θz for nodes of longtudnal members n end planes are related to the relevant ndependent ponts The bult scantlngs are to be appled for the FE model Membrane stress,.e. md-surface stress of bendng plate element, s appled as permssble stress crtera for plate element. Aal stress s employed for beam element. -1-

15 Fgure 4.1 Etent of 3D FE Model Fgure 4. 3D FE Model 5 Boundary condtons 5.1 If the loads are symmetrcal on port and starboard sdes, the dsplacements n transverse drecton of nodes on longtudnal centerlne plane are constraned, and the rotatons about the two coordnate aes on longtudnal centerlne plane are constraned,.e.δy =θ =θz = If the loads are ant-symmetrcal on port and starboard sdes, the dsplacements n the drectons along the two coordnate aes of nodes on longtudnal centerlne plane are constraned, and the rotatons about the coordnate as perpendcular on longtudnal centerlne are constraned,.e.δ =δz =θy = Constrant of end planes: the ndependent pont at one end constrantδ,δy,δz,θ -13-

16 ,θz, and the ndependent pont at the other end constrantδy,δz,θ,θz, as ndcated n Table 5.1. Fgure 5.1 Constrant of End Planes Applcaton of Boundary Condtons (Boundary wth Symmetrcal Load) Table 5.1 dsplacement constrant rotaton constrant Poston δ δy δz θ θy Θz Longtudnal centerlne secton - Cons. - Cons. - Cons. End plane A Lnk - Lnk - Lnk Lnk End plane B Lnk - Lnk - Lnk Lnk Rgd pont A Cons. Cons. Cons. Cons BM Cons Rgd pont B - Cons. Cons. Cons BM Cons Notes:Cons. constrant correspondng to dsplacement; Lnk dsplacement of relevant nodes wthn end plane lnked to ndependent node BM global bendng moment appled on end plane 6 Loadng Condtons 6.1 Desgn loadng condtons (General) General (1) BC-C Homogeneous cargo loaded condton where the cargo densty corresponds to all cargo holds, ncludng hatchways, beng 100% full at mamum draught wth all ballast tanks empty. -14-

17 () BC-B As requred for 6.1.1(1), plus: Homogeneous cargo loaded condton wth cargo densty 3.0 tonnes/m 3, and the same fllng rate (cargo mass/hold cubc capacty) n all cargo holds at mamum draught wth all ballast tanks empty. In cases where the cargo densty appled for ths desgn loadng condton s less than 3.0 tonnes/m 3, the mamum densty of the cargo that the vessel s allowed to carry s to be ndcated wth the addtonal notaton {mamum cargo densty.y tonnes/m 3 } (see 1.1.5(4)), and the actual cargo densty s appled. (3) BC-A As requred for 6.1.1(), plus: At least one cargo loaded condton wth specfed holds empty, wth cargo densty 3.0 tonnes/m 3, and the same fllng rate (cargo mass/hold cubc capacty) n all loaded cargo holds at mamum draught wth all ballast tanks empty. The combnaton of specfed empty holds shall be ndcated wth the annotaton {holds a, b, may be empty}. In such cases where the desgn cargo densty appled s less than 3.0 tonnes/m 3, the mamum densty of he cargo that the vessel s allowed to carry shall be ndcated wthn the annotaton, e.g. {holds a, b, may be empty, wth mamum cargo densty.y tonnes/m 3 }, and the actual cargo densty s appled condtons (1) Normal ballast condton 1) The ballast tanks may be full, partally full or empty. Where partally full opton s eercsed, the condtons n the last paragraph of S are to be compled. ) Any cargo hold or holds adapted for the carrage of water ballast at sea are to be empty. 3) The propeller s to be fully mmersed 4) The trm s to be by the stern and s not to eceed 0.015L, where L s the length between perpendculars of the shp. () Heavy ballast condton 1) The ballast tanks may be full, partally full or empty. Where partally full opton s eercsed, the condtons n the last paragraph of S are to be compled. ) At least one cargo hold adapted for carrage of water ballast at sea, where requred or provded, s to be full. 3) The propeller mmerson I/D s to be at least 60%, where I =the dstance from propeller centerlne to the waterlne D =propeller dameter. 4) The trm s to be by the stern and s not to eceed 0.015L, where L s the length between perpendculars of the shp. -15-

18 5) The moulded forward draught n the heavy ballast condton s not to be less than the smaller of 0.03L or 8 m. 6. Desgn loadng condtons (for local strength) 6..1 mass defntons M H : the actual cargo mass n a cargo hold correspondng to a homogeneously loaded condton at mamum draught. M Full : the cargo mass n a cargo hold correspondng to cargo wth vrtual densty (homogeneous mass/hold cubc capacty, mnmum 1.0 tonne/m 3 ) flled to the top of the hatch coamng. M Full s n no case to be less than M H. M HD : the mamum cargo mass allowed to be carred n a cargo hold accordng to desgn loadng condton(s) wth specfed holds empty at mamum draft. 6.. Besdes the load condtons of the loadng manual, the followng condtons should be consdered: Load condton 1: General condtons applcable for all notatons. Load condton : Condton applcable for all notatons, ecept when notaton {no MP} s Assgned. Load condton 3: Addtonal condtons applcable for BC-A notaton only. Load condton 4: Addtonal condtons applcable for ballast hold(s)only. Load condton 5: Addtonal condtons applcable durng loadng and unloadng n harbour only The wave loads (pressure and bendng moment) are not appled to the load condtons n harbour. 6.3 Load cases Correspondng to the harmonsed notatons BC-C, BC-B and BC-A, the load cases nclude the load condtons n Accordng to the load condton requrement, detaled load cases appled to the hull structure strength assessment are n table

19 Load cases Table 6.1 Load condton No. Load Case General 1 LC01 condtons applcable for all notatons LC0a -1 M Full M Full +1 M Full %M H M H d=t Fgures +1 M H d=t 3 LC0b -1 M H 50%M H +1 M H d=t Condton applcable for all notatons, ecept when notaton {no MP} s assgned 4 LC03 5 LC04 6 LC M Full M FO +1 0 d=0.67t -1 M Full 0 d= the deepest ballast draught +1 M Full 0 7 LC06a +1 0 d=0.83t M Full +1 M Full M FO +1 M FO d=0.67t -17-

20 8 LC06b M BW +1 M Full M FO +1 M FO d=0.67t 9 LC06c M Full +1 M BW M FO +1 M FO d=0.67t 10 LC07 0 Addtonal condtons applcable for BC-A notaton only 11 LC08 1 LC09 13 LC10 +1 M Full M HD 0 +1 M HD MHD+10%MH +1 0 M FO +1 0 MHD+10%MH d=0.75t d=t Only for hold beng lght cargo hold d=t Only for hold beng heavy cargo hold +1 MHD+10%MH M FO Addtonal condtons applcable for ballast hold(s) only 14 LC11 +1 M FO d=t Only ths case n desgn load condton +1 0 M BW M DHBW +1 0 d= any heavy ballast draught Only for hold beng heavy ballast hold -18-

21 Addtonal condtons applcable durng loadng and unloadng n harbour only 15 LC1a (BC-A) 16 LC1b 17 LC1c M HD M Full d=0.67t Only for hold beng heavy cargo hold d=0.67t 18 LC13 +1 M Full M Full d=0.67t +1 M Full M FO +1 M FO d=0.67t Note:M BW =ballast mass n the heavy ballast hold, M DHBW =ballast mass n the ballast tank, M FO =fuel ol mass n the fuel ol tank. 7 Strength Crtera 7.1 Stresses at the md surface of plate bendng elements, and aal stress of beam elements are to be appled for assessment. 7. In general, the stress of prmary members n the typcal loadng condtons should not eceed permssble stresses (or allowable stresses) specfed n Table For bulkheads, the stress n way of corrugaton end may be obtaned by etrapolaton of average stresses of bulkhead platng. 7.4 The average shear stress τ means the average shear stress over depth of the web of prmary members. 7.5 For those elements of concentrated stress and poor shape, the stresses should not be taken nto consderaton. -19-

22 Mamum Permssble Stresses Table 7.1 Permssble stresses Type of Structure σ e σ l σ w τ N/mm N/mm N/mm N/mm Man deck platng 0/k 10/k - - Inner and outer bottom platng 0/k 10/k 145/k - Slope plate of top sde tanks and hopper tanks, outer and nner sde 0/k 10/k 145/k 115/k shell, sde strnger or platform platng Double bottom grder 35/k 10/k - 115/k Floor and transverse bulkhead 175/k /k Stool plate, transverse web frame 195/k /k others 195/k - - Symbols σ e = von Mses stress, gven by σ e = y σ + σ σ σ + 3τ y y where: σ = stress of element n drecton ; σ y = stress of element n drecton y; τ y = shearng stress of element n y planes. In ths table:σ l = stress n longtudnal drecton of hull grder σ w = stress n transverse or vertcal drecton of hull grder. τ= shear stress; taken by the average shear stress full depth of the web for grders and floors; k = converson rato of materal Aal stress of beam element (N/mm ) Beam on transverse members 176/k Beam on longtudnal members 06/k 8 Evaluaton of Bucklng Strength 8.1 General requrements All prmary members are to be subjected to flat plate bucklng evaluaton. Specal attenton shall be gven to followng areas: (1) double-bottom floors, especally those n md-length of hold () double-bottom grders, especally those n way of both ends of hold adjacent to bulkhead or stool and the plate n way of the frst openng from bulkhead or stool n double bottom md-length of hold (3) top sde tank, deck and sde shell plate (4) bottom plate and nner-bottom platng, especally those n way of both ends of hold adjacent to bulkhead or stool and md-length of hold (5) bulkhead and stool, especally those n way of md-span and area adjacent to stool and sde platng of stool 8.1. The evaluaton of plate bucklng s based on the standard thckness deducton as -0-

23 gven n Table Whle determnng bucklng, b-drectonal aal compressng stress and shear stress are to be consdered, and the stress at md surface of the plate s generally appled for bucklng evaluaton Whle determnng bucklng safety factor, boundary constrant coeffcent c as defned n paragraph..7, Part two of the Rules, s taken nto consderaton The requred mnmum bucklng safety coeffcentλgven n Table 8.1. should be satsfed for bucklng check. Standard Thckness Deducton for Crtcal Bucklng Strength Table Locaton Thckness deducton (mm) tank wthn 1.5m of weather deck Connected wth ballast water on one sde 1.0 Connected wth ballast.0 water on both sdes Other areas 1.0 Requred Safety Factor λ for Bucklng Table 8.1. Structure Bucklng safety factorλ Deck and top sde tank platng 1.0 Bottom platng, nner bottom and hopper tank platng 1.0 Double bottom grder 1.0 Double-bottom floor and web transverse n top sde tank and hopper tank 1.1 Transverse water-tght bulkhead and stool 1. Transverse bulkhead and stool n deep tank 1. Note:λ= crtcal bucklng stress/appled stress 8. Methods of bucklng evaluaton Ether of the followng methods may by appled: 8..1 Method 1: FE Method (1) Modelng When addressng the ssue of stablty based on the net scantlngs, the thckness of the panel selected for bucklng s deduced as specfed n Table The requrements of meshng are not less than 8 meshes at each sde, preferably n square shape. () Loads and boundary condtons -1-

24 Loads: the results of σ, σ y, τ y (.e. appled stress) for stresses at md surface of the panel, as calculated by FE model, are taken n the specfed condtons and multpled respectvely by the orgnal thckness wthout deducton to get the correspondng loads. N=σ t o Ny=σ y t o Ny=τ y t o where: t o s orgnal plate thckness. The loads are to be appled on relevant boundares. Where compressve stresses beng sgnfcantly varable between plate panels, the loads may be appled as lnearly dstrbuton, and the average shear stress s to be taken. Boundary condtons: The dsplacements n -drecton at the mdponts of longtudnal boundares and n y-drecton at the mdponts of transverse boundares should be constraned. The dsplacement n z-drecton at the 4 sdes boundares should be constraned, as shown n Fgures 8..1 and 8... Fgure 8..1 Model where b-drectonal loads and shear force are appled Fgure 8.. Model where b-drectonal loads are appled --

25 Notes: 1. Ether of appled pressures as shown n both Fgure 8..1 and Fgure 8.. are acceptable.. Fgure 8..1 ndcates the nodal loads, and Fgure 8.. ndcates the edge pressure of the boundary loads. (3) Bucklng evaluaton The factor shown n FE analyss post-processng of s the crtcal bucklng factor λ. The results can be obtaned by multplyng wth the boundary constrant coeffcent as defned n 8.1.4, and should not be less than the safety factor specfed n Table Method : Smplfed Method (1) The stresses at md surface of the panel, by FE method, are corrected by the standard thckness deducton specfed n Table 8.1.1: σ A =σt/(t-t r ) where: σ A workng stress n bucklng evaluaton; σ stress obtaned by FE analyss; t orgnal plate thckness appled n FE analyss; t r standard thckness deducton as specfed n Table () Crtcal bucklng stress and elastcty correcton 1 The elastc crtcal bucklng stress σ cr_e of the plate panel, of whch the shorter sde s subjected to compresson, s defned as follows: σ π E 1(1 ν ) t s cr _ e = k C1 ( ) N / where: k bucklng coeffcent for shorter sde subjected to compresson and bendng specfed n Table 8..1; C 1 boundary constrant coeffcent specfed n Table 8..; t thckness of plate panel, n mm; s length of shorter sde of plate panel, n mm, taken as spacng of longtudnals or stffeners; defned as aal drecton of longer sde of plate panel. mm -3-

26 Bucklng Coeffcents of Plate Panel Table 8..1 Mechancal model of plate panel subjected to compresson, bendng and shearng Bucklng coeffcent 1 y k = ϕ Compresson on shorter sdes 1 s l where: 0 φ 1 y s 1 k = ϕ + 10ϕ l where: -1 φ<0 y y y1 k y s.1 = 1 + ( ) l ϕ y s l Compresson on longer sdes y y y1 where: 0 φ 1 y y y1 s y l y y y1 where: -1 φ<0 s k y = 1.909(1 + ϕ) 1 + ( ) l s + 10ϕ (1 + ϕ)( ) l where: s 4( ) k = l p s s ( ) + 8( ) l l k ϕ p l 3 s l 3 > s Shearng on sdes s y y l s k t = ( 4 ) l -4-

27 Boundary Constrant Coeffcents C 1 and C of Plate Panel Table 8.. C Boundary C 1 Wthn double bottom or Other locatons double hull Angel or T-bar Flat plate or bulb bar The elastc crtcal bucklng stress σ ycr_e of the plate panel, of whch the longer sde s subjected to compresson, s defned as follows: σ π E 1(1 ν ) t s ycr _ e = k y C ( ) N / where: K y bucklng coeffcent for longer sde subjected to compresson and bendng specfed n Table 8..1; C boundary restrant coeffcent specfed n Table 8..; y defned as aal drecton of shorter sde of plate panel; Others are the same as those n 1. mm 3 The elastc crtcal bucklng stress τ cr_e of the plate panel, whch s subjected to shearng, s defned as follows: τ π E 1(1 ν ) t s cr _ e = k t C1 ( ) N / mm where: K t shear bucklng coeffcent specfed n Table 8..1; Others are the same as those n 1 and. 4 The elastc crtcal bucklng stress of plate panel s to be corrected as follows: σ cr ( ycr) τ cr σ ( = σ S σ S (1 4σ cr ( ycr cr _ e ycr _ e) _ e τ cr = τ S τ S (1 ) 4τ cr _ e _ e) _ e ) when when when when τ σ σ cr _ e ( ycr _ e) cr _ e ( ycr _ e) cr _ e τ cr _ σ S σ S > τ S τ S e > where: σ cr_e, σ ycr_e, τ cr_e elastc crtcal bucklng compressve stress and crtcal bucklng shear stress of plate panel along aes X and Y respectvely, wth referred to 1, and 3; σ S Yeld strength of materal, n N/mm ; τ S σ S 3-5-

28 (3) Bucklng strength evaluaton 1 The rato λ of the crtcal bucklng stress of plate panel wth composte stress to the actual compressve stress, determned by Table 8..3, s not to be less than the safety factor specfed n Table The absolute values of σ, σ y and τ y are appled for the evaluaton and they are taken as zero when the workng stress along as or y s tensle. Rato of plate panel Stress status B-drectonal compresson Compresson along as X + shear Compresson along as Y + shear B-drectonal compresson + shear λ Calculaton Table 8..3 l 1 s (1 1 σ l < 8 s cr cr + k1) σ (1+ k1 ) σ 1 σ (1+ k ) σ 1 (1+ k 1 3 ) σ σ cr ycr 1 σ (1+ k + k ) σ y cr 1 σ Where: σ y σ ycr k 1 =, σ σ cr τy τcr k =, σ σ cr k 3 τ = σ y y σ τ cr ycr Notes: 1 σ 1 and σ y1 are the greater values of workng stresses actng on sdes of plate panel along aes X and Y; σ and σ y are the smaller values of such stresses, and σ and σ y are to be taken as the average values of σ 1, σ andσ y1, σ y and σ y respectvely; τ y s the average shear stress. σ 1, σ, σ y1, σ y and τ y, as shown n Table σ cr, σ ycr and τ cr are the elastcally corrected crtcal bucklng compressve stresses and crtcal bucklng shear stress of plate panel along aes X an Y respectvely. -6-