Longitudinal Strength Standard for Container Ships

Transcription

1 (June 05) Longitudinal Strength Standard or Container Ships. General.. Application... Application This UR applies to the ollowing types o steel ships with a length L o 90 m and greater and operated in unrestricted service:. Container ships. Ships dedicated primarily to carry their load in containers.... Load limitations The wave induced load requirements apply to monohull displacement ships in unrestricted service and are limited to ships meeting the ollowing criteria: (i) Length 90 m L 500 m (ii) Proportion 5 L/B 9; B/T 6 (iii) Block coeicient at scantling draught 0.55 C B 0.9 For ships that do not meet all o the aorementioned criteria, special considerations such as direct calculations o wave induced loads may be required by the Classiication Society....3 Longitudinal extent o strength assessment The stiness, yield strength, buckling strength and hull girder ultimate strength assessment are to be carried out in way o 0.L to 0.75L with due consideration given to locations where there are signiicant changes in hull cross section, e.g. changing o raming system and the ore and at end o the orward bridge block in case o two-island designs. In addition, strength assessments are to be carried out outside this area. As a minimum assessments are to be carried out at orward end o the oremost cargo hold and the at end o the at most cargo hold. Evaluation criteria used or these assessments are determined by the Classiication Society. Note:. This UR is to be uniormly implemented by IACS Societies or ships contracted or construction on or ater July 06.. The contracted or construction date means the date on which the contract to build the vessel is signed between the prospective owner and the shipbuilder. For urther details regarding the date o contract or construction, reer to IACS Procedural Requirement (PR) No. 9. Page o IACS Req. 05

2 .. Symbols and deinitions... Symbols L B Rule length, in m, as deined in UR S Moulded breadth, in m C Wave parameter, see.3. T C B C w Scantling draught in m Block coeicient at scantling draught Waterplane coeicient at scantling draught, to be taken as: AW CW (LB) A w Waterplane area at scantling draught, in m R eh Speciied minimum yield stress o the material, in N/mm k E M S M Smax, M Smin M W F S F Smax, F Smin F W q v Material actor as deined in UR S4 or higher tensile steels, k.0 or mild steel having a minimum yield strength equal to 35 N/mm Young s modulus in N/mm to be taken as E.06*0 5 N/mm or steel Vertical still water bending moment in seagoing condition, in knm, at the cross section under consideration Permissible maximum and minimum vertical still water bending moments in seagoing condition, in knm, at the cross section under consideration, see.. Vertical wave induced bending moment, in knm, at the cross section under consideration Vertical still water shear orce in seagoing condition, in kn, at the cross section under consideration Permissible maximum and minimum still water vertical shear orce in seagoing condition, in kn, at the cross section under consideration, see.. Vertical wave induced shear orce, in kn, at the cross section under consideration Shear low along the cross section under consideration, to be determined according to Annex NL-Hog Non-linear correction actor or hogging, see.3. NL-Sag Non-linear correction actor or sagging, see.3. Page o IACS Req. 05

3 R Factor related to the operational proile, see.3. t net Net thickness, in mm, see.3. t res I net Reserve thickness, to be taken as 0.5mm Net vertical hull girder moment o inertia at the cross section under consideration, to be determined using net scantlings as deined in.3, in m 4 σ HG Hull girder bending stress, in N/mm, as deined in.5 τ HG Hull girder shear stress, in N/mm, as deined in.5 x z Longitudinal co-ordinate o a location under consideration, in m Vertical co-ordinate o a location under consideration, in m z n Distance rom the baseline to the horizontal neutral axis, in m.... Fore end and at end The ore end (FE) o the rule length L, see Figure, is the perpendicular to the scantling draught waterline at the orward side o the stem. The at end (AE) o the rule length L, see Figure, is the perpendicular to the scantling draught waterline at a distance L at o the ore end (FE). T Figure : Ends o length L...3 Reerence coordinate system The ships geometry, loads and load eects are deined with respect to the ollowing righthand coordinate system (see Figure ): Origin: X axis: Y axis: Z axis: At the intersection o the longitudinal plane o symmetry o ship, the at end o L and the baseline. Longitudinal axis, positive orwards. Transverse axis, positive towards portside. Vertical axis, positive upwards. Page 3 o IACS Req. 05

4 Figure : Reerence coordinate system..3 Corrosion margin and net thickness..3. Net scantling deinitions The strength is to be assessed using the net thickness approach on all scantlings. The net thickness, t net, or the plates, webs and langes is obtained by subtracting the voluntary addition t vol_add and the actored corrosion addition t c rom the as built thickness t as_built, as ollows: t net tas _ built tvol _ add αt c where α is a corrosion addition actor whose values are deined in Table. The voluntary addition, i being used, is to be clearly indicated on the drawings. Table : Values o corrosion addition actor Structural requirement Property / analysis type α Strength assessment (.3) Section properties 0.5 Section properties (stress Buckling strength 0.5 determination) (.4) Buckling capacity.0 Hull girder ultimate strength Section properties 0.5 (.5) Buckling / collapse capacity Determination o corrosion addition The corrosion addition or each o the two sides o a structural member, t c or t c is speciied in Table. The total corrosion addition, t c, in mm, or both sides o the structural member is obtained by the ollowing ormula: t ) + t c ( tc + tc res Page 4 o IACS Req. 05

5 For an internal member within a given compartment, the total corrosion addition, t c is obtained rom the ollowing ormula: t ) + t c ( tc res The corrosion addition o a stiener is to be determined according to the location o its connection to the attached plating. Table : Corrosion addition or one side o a structural member Compartment type One side corrosion addition t c or t c [mm] Exposed to sea water.0 Exposed to atmosphere.0 Ballast water tank.0 Void and dry spaces 0.5 Fresh water, uel oil and lube 0.5 oil tank Accommodation spaces 0.0 Container holds.0 Compartment types not mentioned above Determination o net section properties The net section modulus, moment o inertia and shear area properties o a supporting member are to be calculated using the net dimensions o the attached plate, web and lange, as deined in Figure 3. The net cross-sectional area, the moment o inertia about the axis parallel to the attached plate and the associated neutral axis position are to be determined through applying a corrosion magnitude o 0.5 αt c deducted rom the surace o the proile cross-section. Page 5 o IACS Req. 05

6 Figure 3: Net sectional properties o supporting members Page 6 o IACS Req. 05

7 . Loads.. Sign convention or hull girder loads The sign conventions o vertical bending moments and vertical shear orces at any ship transverse section are as shown in Figure 4, namely: The vertical bending moments M S and M W are positive when they induce tensile stresses in the strength deck (hogging bending moment) and negative when they induce tensile stresses in the bottom (sagging bending moment). The vertical shear orces F S, F W are positive in the case o downward resulting orces acting at o the transverse section and upward resulting orces acting orward o the transverse section under consideration. The shear orces in the directions opposite to above are negative. Bending moments: Shear orces: Figure 4: Sign conventions o bending moments and shear orces Page 7 o IACS Req. 05

8 .. Still water bending moments and shear orces... General Still water bending moments, M S in knm, and still water shear orces, F S in kn, are to be calculated at each section along the ship length or design loading conditions as speciied in Design loading conditions In general, the design cargo and ballast loading conditions, based on amount o bunker, resh water and stores at departure and arrival, are to be considered or the M S and F S calculations. Where the amount and disposition o consumables at any intermediate stage o the voyage are considered more severe, calculations or such intermediate conditions are to be submitted in addition to those or departure and arrival conditions. Also, where any ballasting and/or de-ballasting is intended during voyage, calculations o the intermediate condition just beore and just ater ballasting and/or de-ballasting any ballast tank are to be submitted and where approved included in the loading manual or guidance. The permissible vertical still water bending moments M Smax and M Smin and the permissible vertical still water shear orces F Smax and F Smin in seagoing conditions at any longitudinal position are to envelop: The maximum and minimum still water bending moments and shear orces or the seagoing loading conditions deined in the Loading Manual. The maximum and minimum still water bending moments and shear orces speciied by the designer The Loading Manual should include the relevant loading conditions, which envelop the still water hull girder loads or seagoing conditions, including those speciied in UR S Annex. Page 8 o IACS Req. 05

9 ..3 Wave loads..3. Wave parameter The wave parameter is deined as ollows:.50 L Lre. C or L L re 0.45 L L re.7 C or L > L re L re Reerence length, in m, taken as: re 35C.3 W L or the determination o vertical wave bending moments according to.3. re 330C.3 W L or the determination o vertical wave shear orces according to Vertical wave bending moments The distribution o the vertical wave induced bending moments, M W in knm, along the ship length is given in Figure 6, M W Hog +.5 R 3 L CC W B L 0.8 NL Hog M W Sag.5 R 3 L CC W B L 0.8 NL Sag R : NL-Hog : NL-Sag : Factor related to the operational proile, to be taken as: R 0.85 Non-linear correction or hogging, to be taken as: CB NL Hog 0. 3 T, not to be taken greater than. C W Non-linear correction or sagging, to be taken as: + 0. Bow NL Sag 4.5, not to be taken less than C C L W B Page 9 o IACS Req. 05

10 Bow : A DK : A WL : z : Bow lare shape coeicient, to be taken as: ADK AWL Bow 0.Lz Projected area in horizontal plane o uppermost deck, in m including the orecastle deck, i any, extending rom 0.8L orward (see Figure 5). Any other structures, e.g. plated bulwark, are to be excluded. Waterplane area, in m, at draught T, extending rom 0.8L orward Vertical distance, in m, rom the waterline at draught T to the uppermost deck (or orecastle deck), measured at FE (see Figure 5). Any other structures, e.g. plated bulwark, are to be excluded. Figure 5: Projected area A DK and vertical distance z Page 0 o IACS Req. 05

11 M W M W Hog 0.5 M W Hog 0.5 M W Hog AE 0.L 0.35L 0.55L 0.8L 0.35L 0.6L FE M W Sag Figure 6: Distribution o vertical wave bending moment M W along the ship length Page o IACS Req. 05

12 ..3.3 Vertical wave shear orce The distribution o the vertical wave induced shear orces, F W in kn, along the ship length is given in Figure 7, where, F F F F F W W W W At Hog Fore Hog At Sag Fore Sag Mid W RL CCW R L CC W RL CCW RL CCW B L B L B L B L B 4.0 RL CCW L ( NL Hog ( NL Hog NL Sag ( ) ) NL Sag ) F W Fore Fw Sag At Fw Hog Fw Mid AE 0.5L 0.3L 0.4L 0.55L 0.65L 0.85L 0.5L 0.3L 0.4L 0.5L 0.6L 0.75L FE At 0.5 Fw Sag Fw Mid Fore Fw Hog At Fw Sag Figure 7: Distribution o vertical wave shear orce F W along the ship length Page o IACS Req. 05

13 ..4 Load cases For the strength assessment, the maximum hogging and sagging load cases given in Table 3 are to be checked. For each load case the still water condition at each section as deined in. is to be combined with the wave condition as deined in.3, reer also to Figure 8. Table 3: Combination o still water and wave bending moments and shear orces Load case Bending moment Shear orce M S M W F S F W Hogging M Smax M WH Smax F Smin or x > 0.5L Wmax F Wmin or x > 0.5L F or x 0.5L F or x 0.5L Sagging M Smin M WS F Smin or x 0.5L F Wmin or x 0.5L F Smax or x > 0.5L F Wmax or x > 0.5L M WH : Wave bending moment in hogging at the cross section under consideration, to be taken as the positive value o M W as deined in Figure 6. M WS : F Wmax : F Wmin : Wave bending moment in sagging at the cross section under consideration, to be taken as the negative value o M W as deined Figure 6. Maximum value o the wave shear orce at the cross section under consideration, to be taken as the positive value o F W as deined Figure 7. Minimum value o the wave shear orce at the cross section under consideration, to be taken as the negative value o F W as deined Figure 7. Figure 8: Load combination to determine the maximum hogging and sagging load cases as given in Table 3 Page 3 o IACS Req. 05

14 ..5 Hull girder stress The hull girder stresses in N/mm are to be determined at the load calculation point under consideration, or the hogging and sagging load cases deined in.4 as ollows: Bending stress: σ HG γ M + γ M I ( Z Z s s W W n net )0 3 Shear stress: τ HG γ sfs + γ W F tnet q v W 3 0 γ s, γ W : Partial saety actors, to be taken as: γ s.0 γ W.0.3 Strength Assessment.3. General Continuity o structure is to be maintained throughout the length o the ship. Where signiicant changes in structural arrangement occur adequate transitional structure is to be provided..3. Stiness criterion The two load cases hogging and sagging as listed in.4 are to be checked. The net moment o inertia, in m 4, is not to be less than: I net.55l M s + M W 0 7 Page 4 o IACS Req. 05

15 .3.3 Yield strength assessment.3.3. General acceptance criteria The yield strength assessment is to check, or each o the load cases hogging and sagging as deined in.4, that the equivalent hull girder stress σ eq, in N/mm, is less than the permissible stress σ perm, in N/mm, as ollows: σ eq < σ perm σ eq σ x + 3τ σ perm R eh γ γ γ : Partial saety actor or material, to be taken as: γ R eh k 35 γ : Partial saety actor or load combinations and permissible stress, to be taken as: γ. 4, or bending strength assessment according to γ. 3, or shear stress assessment according to Bending strength assessment The assessment o the bending stresses is to be carried out according to 3.3. at the ollowing locations o the cross section: At bottom At deck At top o hatch coaming At any point where there is a change o steel yield strength The ollowing combination o hull girder stress as deined in.5 is to be considered: σ x σ HG τ Shear strength assessment The assessment o shear stress is to be carried out according to 3.3. or all structural elements that contribute to the shear strength capability. The ollowing combination o hull girder stress as deined in.5 is to be considered: σ x 0 Page 5 o IACS Req. 05

16 τ τ HG.4 Buckling strength.4. Application These requirements apply to plate panels and longitudinal stieners subject to hull girder bending and shear stresses. Deinitions o symbols used in the present article.4 are given in Annex Buckling Capacity..4. Buckling criteria The acceptance criterion or the buckling assessment is deined as ollows: η act η act : Maximum utilisation actor as deined in Buckling utilisation actor The utilisation actor, η γ c, see igure 9. η act γ c act Failure limit states are deined in:, is deined as the inverse o the stress multiplication actor at ailure Annex, or elementary plate panels, Annex, 3 or overall stiened panels, Annex, 4 or longitudinal stieners. Each ailure limit state is deined by an equation, and γ c is to be determined such that it satisies the equation. Figure 9 illustrates how the stress multiplication actor at ailure γ c, o a structural member is determined or any combination o longitudinal and shear stress. Where: σ,τ x : Applied stress combination or buckling given in.4.4. c τ c σ, : Critical buckling stresses to be obtained according to Annex or the stress combination or buckling σ x and τ. Page 6 o IACS Req. 05

17 Figure 9: Example o ailure limit state curve and stress multiplication actor at ailure.4.4 Stress determination.4.4. Stress combinations or buckling assessment The ollowing two stress combinations are to be considered or each o the load cases hogging and sagging as deined in..4. The stresses are to be derived at the load calculation points deined in.4.4. a) Longitudinal stiening arrangement: Stress combination with: σ x σ HG σ y 0 τ 0. 7τ HG Stress combination with: σ 0. 7 σ y 0 τ τ HG x σ HG b) Transverse stiening arrangement: Stress combination with: σ x 0 σ y σ HG τ 0. 7τ HG Stress combination with: Page 7 o IACS Req. 05

18 σ x 0 σ 0. 7 y σ HG τ τ HG.4.4. Load calculation points The hull girder stresses or elementary plate panels (EPP) are to be calculated at the load calculation points deined in Table 4. Table 4: Load calculation points (LCP) coordinates or plate buckling assessment LCP coordinates x coordinate y coordinate z coordinate Hull girder bending stress Non horizontal plating Horizontal plating Mid-length o the EPP Both upper and lower ends Outboard and inboard o the EPP ends o the EPP (points A and A in Figure (points A and A in 0) Figure 0) Corresponding to x and y values Hull girder shear stress Mid-point o EPP (point B in Figure 0) Figure 0: LCP or plate buckling assessment, PSM stands or primary supporting members The hull girder stresses or longitudinal stieners are to be calculated at the ollowing load calculation point: at the mid length o the considered stiener. at the intersection point between the stiener and its attached plate. Page 8 o IACS Req. 05

19 .5.5. General Hull girder ultimate strength The hull girder ultimate strength is to be assessed or ships with length L equal or greater than 50m. The acceptance criteria, given in 5.4 are applicable to intact ship structures. The hull girder ultimate bending capacity is to be checked or the load cases hogging and sagging as deined in Hull girder ultimate bending moments The vertical hull girder bending moment, M in hogging and sagging conditions, to be considered in the ultimate strength check is to be taken as: M γ M + γ M s s w w M s Permissible still water bending moment, in knm, deined in.4 M w Vertical wave bending moment, in knm, deined in.4. γ s γ s Partial saety actor or the still water bending moment, to be taken as: γ s.0 Partial saety actor or the vertical wave bending moment, to be taken as: γ w..5.3 Hull girder ultimate bending capacity.5.3. General The hull girder ultimate bending moment capacity, M U is deined as the maximum bending moment capacity o the hull girder beyond which the hull structure collapses Determination o hull girder ultimate bending moment capacity The ultimate bending moment capacities o a hull girder transverse section, in hogging and sagging conditions, are deined as the maximum values o the curve o bending moment M versus the curvature χ o the transverse section considered (M UH or hogging condition and M US or sagging condition, see Figure ). The curvature χ is positive or hogging condition and negative or sagging condition. Page 9 o IACS Req. 05

20 Figure : Bending moment M versus curvature χ The hull girder ultimate bending moment capacity M U is to be calculated using the incremental-iterative method as given in o Annex 3 or using an alternative method as indicated in 3 o Annex Acceptance criteria The hull girder ultimate bending capacity at any hull transverse section is to satisy the ollowing criteria: M γ M U M γ DB M Vertical bending moment, in knm, to be obtained as speciied in 5.. M U γ M γ DB Hull girder ultimate bending moment capacity, in knm, to be obtained as speciied in 5.3. Partial saety actor or the hull girder ultimate bending capacity, covering material, geometric and strength prediction uncertainties, to be taken as: γ M.05 Partial saety actor or the hull girder ultimate bending moment capacity, covering the eect o double bottom bending, to be taken as: For hogging condition: γ DB.5 For sagging condition: γ DB.0 For cross sections where the double bottom breadth o the inner bottom is less than that at amidships or where the double bottom structure diers rom that at amidships (e.g. engine room sections), the actor γ DB or hogging condition may be reduced based upon agreement with the Classiication Society. Page 0 o IACS Req. 05

21 .6.6. General Additional requirements or large container ships The requirements in.6. and.6.3 are applicable, in addition to requirements in.3 to.5, to container ships with a breadth B greater than 3.6 m..6. Yielding and buckling assessment Yielding and buckling assessments are to be carried out in accordance with the Rules o the Classiication Society, taking into consideration additional hull girder loads (wave torsion, wave horizontal bending and static cargo torque), as well as local loads. All in-plane stress components (i.e. bi-axial and shear stresses) induced by hull girder loads and local loads are to be considered..6.3 Whipping Hull girder ultimate strength assessment is to take into consideration the whipping contribution to the vertical bending moment according to the Classiication Society procedures. Page o IACS Req. 05

22 Annex Calculation o shear low. General This annex describes the procedures o direct calculation o shear low around a ship s cross section due to hull girder vertical shear orce. The shear low q v at each location in the cross section, is calculated by considering the cross section is subjected to a unit vertical shear orce o N. The unit shear low per mm, q v, in N/mm, is to be taken as: q q + q v D I q D : Determinate shear low, as deined in. q I : Indeterminate shear low which circulates around the closed cells, as deined in 3. In the calculation o the unit shear low, q v, the longitudinal stieners are to be taken into account.. Determinate shear low The determinate shear low, q D, in N/mm at each location in the cross section is to be obtained rom the ollowing line integration: q D ( s) 0 s ( z zn ) t 6 net I 0 y net d s s : Coordinate value o running coordinate along the cross section, in m. I y-net : Net moment o inertia o the cross section, in m 4. t net : Net thickness o plating, in mm. z n : Z coordinate o horizontal neutral axis rom baseline, in m. It is assumed that the cross section is composed o line segments as shown in Figure : where each line segment has a constant plate net thickness. The determinate shear low is obtained by the ollowing equation. t net q Dk ( zk + zi zn ) IY net q Di q Dk, q Di : Determinate shear low at node k and node i respectively, in N/mm. Page o 4 IACS Req. 05

23 l : Length o line segments, in m. y k, y i : Y coordinate o the end points k and i o line segment, in m, as deined in Figure. z k, z i : Z coordinate o the end points k and i o line segment, in m, as deined in Figure. Where the cross section includes closed cells, the closed cells are to be cut with virtual slits, as shown in Figure : in order to obtain the determinate shear low. These virtual slits must not be located in walls which orm part o another closed cell. Determinate shear low at biurcation points is to be calculated by water low calculations, or similar, as shown in Figure. Figure : Deinition o line segment Figure : Placement o virtual slits and calculation o determinate shear low at biurcation points 3. Indeterminate shear low The indeterminate shear low around closed cells o a cross section is considered as a constant value within the same closed cell. The ollowing system o equation or determination o indeterminate shear lows can be developed. In the equations, contour integrations o several parameters around all closed cells are perormed. Page o 4 IACS Req. 05

24 w q Ic ds qim ds C t net N m c& m t net q t D c net ds N w : Number o common walls shared by cell c and all other cells. c&m : Common wall shared by cells c and m q Ic, q Im : Indeterminate shear low around the closed cell c and m respectively, in N/mm. Under the assumption o the assembly o line segments shown in Figure and constant plate thickness o each line segment, the above equation can be expressed as ollows: q N t N c w m c q Im N t Ic j net j m j j net j m N φ j φ j I Y net ( z k + z i 3z n ) + t net q Di j N c : Number o line segments in cell c. N m : Number o line segments on the common wall shared by cells c and m. q Di : Determinate shear low, in N/mm, calculated according to Annex,. The dierence in the directions o running coordinates speciied in Annex, and in this section has to be considered. Figure 3: Closed cells and common wall 4. Computation o sectional properties Properties o the cross section are to be obtained by the ollowing ormulae where the cross section is assumed as the assembly o line segments: Page 3 o 4 IACS Req. 05

25 y + zk zi ( ) ( ) a k net 0 3 t net y i A net a net anet s y net ( zk + zi ) y net y net anet i y net ( zk + zk zi + z 3 0 i I y0 net i y0 net ) s a net, A net : Area o the line segment and the cross section respectively, in m. s s y-net, s y-net : i y0-net, I y0-net : First moment o the line segment and the cross section about the baseline, in m 3. Moment o inertia o the line segment and the cross section about the baseline, in m 4. The height o horizontal neutral axis, z n, in m, is to be obtained as ollows: z n s y net A net Inertia moment about the horizontal neutral axis, in m 4, is to be obtained as ollows: I y net I y0 net z n A net Page 4 o 4 IACS Req. 05

26 Annex Buckling Capacity Symbols x axis : Local axis o a rectangular buckling panel parallel to its long edge. y axis : Local axis o a rectangular buckling panel perpendicular to its long edge. σ x : Membrane stress applied in x direction, in N/mm. σ y : Membrane stress applied in y direction, in N/mm. τ : Membrane shear stress applied in xy plane, in N/mm. σ a : Axial stress in the stiener, in N/mm² σ b : Bending stress in the stiener, in N/mm² σ w : Warping stress in the stiener, in N/mm² σ cx,σ cy,τ c : Critical stress, in N/mm, deined in [..] or plates. R eh_s : Speciied minimum yield stress o the stiener, in N/mm² R eh_p : Speciied minimum yield stress o the plate, in N/mm² a : Length o the longer side o the plate panel as shown in Table, in mm. b : Length o the shorter side o the plate panel as shown in Table, in mm. d : Length o the side parallel to the axis o the cylinder corresponding to the curved plate panel as shown in Table 3, in mm. σ E : Elastic buckling reerence stress, in N/mm to be taken as: For the application o plate limit state according to [..]: π E ( ν ) t p b σ E For the application o curved plate panels according to [.]: π E ( ν ) t p d σ E ν : Poisson s ratio to be taken equal to 0.3 t p : Net thickness o plate panel, in mm t w : Net stiener web thickness, in mm t : Net lange thickness, in mm b : Breadth o the stiener lange, in mm : Stiener web height, in mm h w e : Distance rom attached plating to centre o lange, in mm, to be taken as: e h w or lat bar proile. e h w 0.5 t or bulb proile. e h w t or angle and Tee proiles. α : Aspect ratio o the plate panel, to be taken as α a b β : Coeicient taken as β ψ α ψ : Edge stress ratio to be taken as ψ σ σ σ : Maximum stress, in N/mm² σ : Minimum stress, in N/mm² R : Radius o curved plate panel, in mm l : Span, in mm, o stiener equal to the spacing between primary supporting members s : Spacing o stiener, in mm, to be taken as the mean spacing between the stieners o the considered stiened panel. Page o 7 IACS Req. 05

27 . Elementary Plate Panel (EPP). Deinition An Elementary Plate Panel (EPP) is the unstiened part o the plating between stieners and/or primary supporting members. All the edges o the elementary plate panel are orced to remain straight (but ree to move in the in-plane directions) due to the surrounding structure/neighbouring plates (usually longitudinal stiened panels in deck, bottom and inner-bottom plating, shell and longitudinal bulkheads).. EPP with dierent thicknesses.. Longitudinally stiened EPP with dierent thicknesses In longitudinal stiening arrangement, when the plate thickness varies over the width, b, in mm, o a plate panel, the buckling capacity is calculated on an equivalent plate panel width, having a thickness equal to the smaller plate thickness, t. The width o this equivalent plate panel, b eq, in mm, is deined by the ollowing ormula: b eq l + l t t l l.5 : Width o the part o the plate panel with the smaller plate thickness, t, in mm, as deined in Figure. : Width o the part o the plate panel with the greater plate thickness, t, in mm, as deined in Figure. Figure : Plate thickness change over the width.. Transversally stiened EPP with dierent thicknesses In transverse stiening arrangement, when an EPP is made o dierent thicknesses, the buckling check o the plate and stieners is to be made or each thickness considered constant on the EPP. Page o 7 IACS Req. 05

28 . Buckling capacity o plates. Plate panel.. Plate limit state The plate limit state is based on the ollowing interaction ormulae: a) Longitudinal stiening arrangement: γ β0.5 Cσ x p σ cx + γ β0.5 p C τ τ c b) Transverse stiening arrangement: γ Cσ y σ cy β0.5 p + γ β0.5 p C τ τ c σ x, σ y : Applied normal stress to the plate panel in N/mm², as deined in 4.4, at load calculation points o the considered elementary plate panel. τ : Applied shear stress to the plate panel, in N/mm², as deined in 4.4, at load calculation points o the considered elementary plate panel. : Ultimate buckling stress in N/mm² in direction parallel to the longer edge o σ cx σ cy the buckling panel as deined in..3 : Ultimate buckling stress in N/mm² in direction parallel to the shorter edge o the buckling panel as deined in..3 τ c :Ultimate buckling shear stress, in N/mm² as deined in..3 β p : Plate slenderness parameter taken as: β p b t p R eh_p E.. Reerence degree o slenderness The reerence degree o slenderness is to be taken as: λ R eh _ P Kσ E K : Buckling actor, as deined in Table and Table Ultimate buckling stresses The ultimate buckling stress o plate panels, in N/mm², is to be taken as: σ cx C x R eh_p σ cy C y R eh_p The ultimate buckling stress o plate panels subject to shear, in N/mm², is to be taken as: Page 3 o 7 IACS Req. 05

29 τ c C τ R eh _ P 3 C x, C y, Cτ : Reduction actors, as deined in Table The boundary conditions or plates are to be considered as simply supported (see cases, and 5 o Table ). I the boundary conditions dier signiicantly rom simple support, a more appropriate boundary condition can be applied according to the dierent cases o Table subject to the agreement o the Classiication Society...4 Correction Factor F long The correction actor F long depending on the edge stiener types on the longer side o the buckling panel is deined in Table. An average value o F long is to be used or plate panels having dierent edge stieners. For stiener types other than those mentioned in Table, the value o c is to be agreed by the Society. In such a case, value o c higher than those mentioned in Table can be used, provided it is veriied by buckling strength check o panel using non-linear FE analysis and deemed appropriate by the Classiication Society. Table : Correction Factor F long Structural element types F long c Unstiened Panel.0 N/A Stiened Panel () Stiener not ixed at both ends.0 N/A Stiener Flat bar () t 0.0 w ixed at Bulb proile F long c + or > t 0.30 p both Angle proile ends T proile tw tw F long c + or 0.30 t p t p Girder o high rigidity (e.g. bottom transverse).4 N/A t w is the net web thickness, in mm, without the correction deined in Page 4 o 7 IACS Req. 05

30 σ x Table : Buckling Factor and reduction actor or plane plate panels Stress Aspect Case Buckling actor K Reduction actor C ratio ψ ratio α C x or 8.4 λ λ c K x F long ψ +. C 0. c x λ λ or λ > λ c c (.5 0.ψ ).5 K x F long [ 7.63 ψ (6.6 0ψ )] c 0.88 λ + c c σ x ψ 0 0 > ψ > - ψ σ x t p a ψ σ x b ψ - K x F long [ 5.975( ψ ) ] ψ 0 K y + α ( ψ ).4 + ψ α α 6 ( ψ )( α ) α > 6 6ψ α α α But not greater than α R + F ( H R) C y c λ λ c (.5 0.ψ ).5 R λ( λ / c) or λ < λc R 0. or λ λc ( c ) λc 0.5 c / K F / λp c λ p λ 0.5 λ or p 3 σ y σ y t p a ψ σ y b ψ σ y 0 > ψ -4α/3 00( + β ) ( )( β ) K y + α > 6(- ψ) 3(- ψ) α 6(- ψ) β β 4 but not greater than β 3 0 β 3 0 c 0 α λ H λ c( T + T 4 T λ + + 5λ 3 R 4).5(- ψ) α < 3(- ψ) 4 β β ( ωβ ) 9( ωβ ) Page 5 o 7 IACS Req. 05

31 Case Stress ratio ψ Aspect ratio α For α >.5: Buckling actor K Reduction actor C - ψ α <.5(- ψ) 0.75(- ψ) α < - ψ 4 ω 6 β 3 β 3β 3 0 For α.5:.5 ψ β ψ ( 6 4 ) α (.5-Min(.5;α)) β 48 β 3 ( ) (.5-Min(.5;α)) α.3 ( β ) 4 ψ < -4α/3 β K y ψ Max( ; ψ ) 6 ( ) 3 ψ 0 K x 4( / α ) 3ψ + σ x σ x ψ σ x 4 t a ψ σ x b 0 > ψ - K x 4 ( / α ) ( +ψ ) 5ψ ( 3.4ψ ) C x C x λ or λ 0. 7 or λ > 0. 7 ψ σx σ x a t p ψ σ x σ x b ψ - K x 3 ψ.45 + α 0 Page 6 o 7 IACS Req. 05

32 Case Stress ratio ψ Aspect ratio α Buckling actor K Reduction actor C 5 α.64 K x.8 σ x σ x t p b x a α <.64 K x α α 6 ψ 0 K y 4( α ) (3ψ + )α 0 > ψ - K y 4( α )( + ψ) α 5ψ( 3.4ψ) α 7 C y or λ 0.7 C y λ or λ > ψ - (3 K y ( α ψ) ) α 8 - K y α α 4 Page 7 o 7 IACS Req. 05

33 Case Stress ratio ψ Aspect ratio α Buckling actor K Reduction actor C 9 σ x t p σ x b - K x x a 0 K α + α - y 4 C x C x or λ ,3 λ λ or λ > α 4 K x 4 σ x x t p a σ x b - α < 4 K x 4 α K y K y determined as per case For α < : C y C y For α : Cy 0α C y C y determined as per case.06 + Cy 3 α 4 K x 6.97 C x or λ σ x x t p a σ x b - α < 4 K x 4 α C x 0.,3 λ λ or λ > K y 6.97 α + 3. α 4 α 3 4 C y or λ 0.83 C y.3 λ 0. or λ > 0.83 λ Page 8 o 7 IACS Req. 05

34 Case Stress ratio ψ Aspect ratio α Buckling actor K Reduction actor C 5 τ t p a τ b - K τ α 6 7 d b τ d a a t p τ b - - K Max ;. α α τ 5 K K r K K according to case 5. r opening reduction actor taken as r d a a d b b with d a 0.7 and d b 0.7 a b C τ 0.84 Cτ λ or λ or λ > K τ ( α ) 9 C τ 0.84 Cτ λ or λ or λ > K τ 8 Edge boundary conditions: Plate edge ree. Plate edge simply supported. Plate edge clamped. Notes: ) Cases listed are general cases. Each stress component (σx, σy) is to be understood in local coordinates. Page 9 o 7 IACS Req. 05

35 . Curved plate panels This requirement or curved plate limit state is applicable when R/t p 500. Otherwise, the requirement or plate limit state given in.. is applicable. The curved plate limit state is based on the ollowing interaction ormula: γ cσ ax C ax R eh_p.5 + γ cτ 3.0 C τ R eh_p σ ax : Applied axial stress to the cylinder corresponding to the curved plate panel, in N/mm². In case o tensile axial stresses, σ ax 0. C ax, C τ : Buckling reduction actor o the curved plate panel, as deined in Table 3. The stress multiplier actor γ c o the curved plate panel needs not be taken less than the stress multiplier actor γ c or the expanded plane panel according to... Table 3: Buckling Factor and reduction actor or curved plate panel with R/t p 500 Case Aspect ratio Buckling actor K Reduction actor C d 0.5 R d > 0.5 R R t p R t p K d + 3 Rt p d d t p K Rt R R p d 0.4 Rt p For general application: C ax or λ 0.5 C ax λ or 0.5<λ C ax 0.3/λ³ or <λ.5 C ax 0./λ² or λ>.5 For curved single ields, e.g. bilge strake, which are bounded by plane panels: C ax 0.65/λ².0 d 8.7 R d > 8.7 R R t p R t p d K C R τ or λ 0.4 K 0.8d 3 R Rt p.5.5 t p C τ λ or 0.4 < λ. C τ 0.65/λ² or λ >. Explanations or boundary conditions: Plate edge simply supported. 3 Buckling capacity o overall stiened panel The elastic stiened panel limit state is based on the ollowing interaction ormula: Pz c where P z and c are deined in Page 0 o 7 IACS Req. 05

36 4 Buckling capacity o longitudinal stieners 4. Stieners limit states The buckling capacity o longitudinal stieners is to be checked or the ollowing limit states: Stiener induced ailure (SI). Associated plate induced ailure (PI). 4. Lateral pressure The lateral pressure is to be considered as constant in the buckling strength assessment o longitudinal stieners. 4.3 Stiener idealization 4.3. Eective length o the stiener l e The eective length o the stiener l e, in mm, is to be taken equal to: l e l or stiener ixed at both ends. 3 l e 0.75l or stiener simply supported at one end and ixed at the other. l e l or stiener simply supported at both ends Eective width o the attached plating b e The eective width o the attached plating o a stiener b e, in mm, without the shear lag eect is to be taken equal to: b e C xb + C x b C x, C x : Reduction actor deined in Table calculated or the EPP and EPP on each side o the considered stiener according to case. b, b : Width o plate panel on each side o the considered stiener, in mm Eective width o attached plating b e The eective width o attached plating o stieners, b e, in mm, is to be taken as: b e min b e, χ s s χ s : Eective width coeicient to be taken as: χ s min. ; l e or +.75 χ s l e s l e s.6 or l e s < s Page o 7 IACS Req. 05

37 4.3.4 Net thickness o attached plating t p The net thickness o plate t p, in mm, is to be taken as the mean thickness o the two attached plating panels Eective web thickness o lat bar For accounting the decrease o stiness due to local lateral deormation, the eective web thickness o lat bar stiener, in mm, is to be used or the calculation o the net sectional area, A s, the net section modulus, Z, and the moment o inertia, I, o the stiener and is taken as: t π ² hw tw 3 s w _ red b e s Net section modulus Z o a stiener The net section modulus Z o a stiener, in cm 3, including eective width o plating b e is to be taken equal to: the section modulus calculated at the top o stiener lange or stiener induced ailure (SI). the section modulus calculated at the attached plating or plate induced ailure (PI) Net moment o inertia I o a stiener The net moment o inertia I, in cm 4, o a stiener including eective width o attached plating b e is to comply with the ollowing requirement: I s t p Idealisation o bulb proile Bulb proiles may be considered as equivalent angle proiles. The net dimensions o the equivalent built-up section are to be obtained, in mm, rom the ollowing ormulae. h w h w h w 9. + b α t w + h w 6.7 t h w 9. t w t w h w, t w : Net height and thickness o a bulb section, in mm, as shown in Figure. α : Coeicient equal to: Page o 7 IACS Req. 05

38 α. + 0 h w 3000 or h w 0 α.0 or h w > 0 Bulb Equivalent angle Figure : Idealisation o bulb stiener 4.4 Ultimate buckling capacity 4.4. Longitudinal stiener limit state When σ σ + σ > 0, the ultimate buckling capacity or stieners is to be checked a + b w according to the ollowing interaction ormula: γ c σ a + σ b + σ w R eh σ a : Eective axial stress, in N/mm², at mid-span o the stiener, deined in σ b : Bending stress in the stiener, in N/mm, deined in σ w : Stress due to torsional deormation, in N/mm, deined in R eh : Speciied minimum yield stress o the material, in N/mm : R eh R eh S or stiener induced ailure (SI). R eh R eh P or plate induced ailure (PI). Page 3 o 7 IACS Req. 05

39 4.4. Eective axial stress σ a The eective axial stress σ a, in N/mm², at mid-span o the stiener, acting on the stiener with its attached plating is to be taken equal to: σ σ a x b st p e t + A p s + A s σ x : Nominal axial stress, in N/mm, acting on the stiener with its attached plating, calculated according to a) at load calculation point o the stiener. A s : Net sectional area, in mm, o the considered stiener Bending stress σ b The bending stress in the stiener σ b, in N/mm², is to be taken equal to: σ b M 0 + M 0 3 Z M : Bending moment, in Nmm, due to the lateral load P: P sl M C i or continuous stiener P sl M C i 0 3 or sniped stiener 8 P : Lateral load, in kn/m, to be taken equal to the static pressure at the load calculation point o the stiener. C i : Pressure coeicient: C i C SI or stiener induced ailure (SI). C i C PI or plate induced ailure (PI). C PI : Plate induced ailure pressure coeicient: C PI i the lateral pressure is applied on the side opposite to the stiener. C PI - i the lateral pressure is applied on the same side as the stiener. C SI : Stiener induced ailure pressure coeicient: C SI - i the lateral pressure is applied on the side opposite to the stiener. C SI i the lateral pressure is applied on the same side as the stiener. : Bending moment, in Nm, due to the lateral deormation w o stiener: M 0 Pz w M 0 F E with c c P P z > 0. z F E : Ideal elastic buckling orce o the stiener, in N. F E π l EI 0 4 P z : Nominal lateral load, in N/mm, acting on the stiener due to stresses σ x and τ, in the attached plating in way o the stiener mid span: Page 4 o 7 IACS Req. 05

40 P z t p σ π s s xl l + τ σ xl γ c σ x + A s st p but not but not less than 0 m m τ γ c τ t p ReH p E + 0 but not less than 0 a s m, m : Coeicients taken equal to: w m.47, m 0.49 or α. m.96, m 0.37 or α <. : Deormation o stiener, in mm, taken equal to: w w 0 + w w 0 w na : Assumed imperection, in mm, taken equal to: w l 0 3 in general w0 w or stieners sniped at both ends, considering stiener induced ailure (SI) na w 0 w or stieners sniped at both ends, considering plate induced ailure (PI) na : Distance, in mm, rom the mid-point o attached plating to the neutral axis o the stiener calculated with the eective width o the attached plating b e. w c c p c p c xa : Deormation o stiener at midpoint o stiener span due to lateral load P, in mm. In case o uniormly distributed load, w is to be taken as: P s l w C 4 i 384 EI 0 7 in general 5 P s l w C 4 i 384 EI 0 7 or stiener sniped at both ends : Elastic support provided by the stiener, in N/mm, to be taken equal to: c F E π l + c p : Coeicient to be taken as: I0 c 3 xa st p 4 : Coeicient to be taken as: c xa l s + s l c xa + l s or l s or l < s Page 5 o 7 IACS Req. 05

41 4.4.4 Stress due to torsional deormation σ w The stress due to torsional deormation σ w, in N/mm, is to be taken equal to: σ w E y w t + h w Φ 0 π l 0.4 R eh S σ ET or stiener induced ailure (SI). σ 0 or plate induced ailure (PI). w γ w : Distance, in mm, rom centroid o stiener cross-section to the ree edge o stiener lange, to be taken as: y γ w t w h t t b or lat bar. w w + w b or angle and bulb proiles. As b y w or Tee proile. Φ 0 l 0 3 h w σ ET : Reerence stress or torsional buckling, in N/mm : I P σ ET E ε π I ω I P l I T : Net polar moment o inertia o the stiener about point C as shown in Figure 3, as deined in Table 4, in cm 4. I T : Net St. Venant s moment o inertia o the stiener, as deined in Table 4, in cm 4. I ω : Net sectional moment o inertia o the stiener about point C as shown in Figure 3, as deined in Table 4, in cm 6. ε : Degree o ixation. ε + l π 0 3 I 0.75 s ω tp 3 +e 0.5t tw 3 Page 6 o 7 IACS Req. 05

42 Table 4: Moments o inertia Flat bars Bulb, angle and Tee proiles 3 h I w t w A ( 0.5 ) w e t 4 P + A e 3 3 ( e 0.5t ) tw tw e 0.5t h IT wtw t w hw 3 b t t b A e b A +. 6Aw h I w t 0 w A + Aw ω b t e or bulb and angle proiles. 6 0 or Tee proiles. A w : Net web area, in mm. A : Net lange area, in mm. Figure 3: Stiener cross sections Page 7 o 7 IACS Req. 05

43 (Cont) Annex 3 - Hull girder ultimate bending capacity Symbols I y-net : Z B-net, Z D-net : R eh_s : R eh_p : A s-net : A p-net : Net moment o inertia, in m 4, o the hull transverse section around its horizontal neutral axis Section moduli, in m 3, at bottom and deck, respectively, Minimum yield stress, in N/mm, o the material o the considered stiener. Minimum yield stress, in N/mm, o the material o the considered plate. Net sectional area, in cm, o stiener, without attached plating. Net sectional area, in cm, o attached plating.. General Assumptions. The method or calculating the ultimate hull girder capacity is to identiy the critical ailure modes o all main longitudinal structural elements.. Structures compressed beyond their buckling limit have reduced load carrying capacity. All relevant ailure modes or individual structural elements, such as plate buckling, torsional stiener buckling, stiener web buckling, lateral or global stiener buckling and their interactions, are to be considered in order to identiy the weakest inter-rame ailure mode.. Incremental-iterative method. Assumptions In applying the incremental-iterative method, the ollowing assumptions are generally to be made: The ultimate strength is calculated at hull transverse sections between two adjacent transverse webs. The hull girder transverse section remains plane during each curvature increment. The hull material has an elasto-plastic behaviour. The hull girder transverse section is divided into a set o elements, see.., which are considered to act independently. According to the iterative procedure, the bending moment M i acting on the transverse section at each curvature value χ i is obtained by summing the contribution given by the stress σ acting on each element. The stress σ corresponding to the element strain, ε is to be obtained or each curvature increment rom the non-linear load-end shortening curves σ-ε o the element. These curves are to be calculated, or the ailure mechanisms o the element, rom the ormulae speciied in.3. The stress σ is selected as the lowest among the values obtained rom each o the considered load-end shortening curves σ-ε. Page o 4 IACS Req. 05

44 The procedure is to be repeated until the value o the imposed curvature reaches the value χ F in m -, in hogging and sagging condition, obtained rom the ollowing ormula: M y X F ± EI y net M y : Lesser o the values M Y and M Y, in knm. M Y 0 3 R eh Z B-net. M Y 0 3 R eh Z D-net. I the value χ F is not suicient to evaluate the peaks o the curve M -χ, the procedure is to be repeated until the value o the imposed curvature permits the calculation o the maximum bending moments o the curve.. Procedure.. General The curve M -χ is to be obtained by means o an incremental-iterative approach, summarised in the low chart in Figure. In this procedure, the ultimate hull girder bending moment capacity, M U is deined as the peak value o the curve with vertical bending moment M versus the curvature χ o the ship cross section as shown in Figure. The curve is to be obtained through an incrementaliterative approach. Each step o the incremental procedure is represented by the calculation o the bending moment M i which acts on the hull transverse section as the eect o an imposed curvature χ i. For each step, the value χ i is to be obtained by summing an increment o curvature, χ to the value relevant to the previous step χ i-. This increment o curvature corresponds to an increment o the rotation angle o the hull girder transverse section around its horizontal neutral axis. This rotation increment induces axial strains ε in each hull structural element, whose value depends on the position o the element. In hogging condition, the structural elements above the neutral axis are lengthened, while the elements below the neutral axis are shortened, and vice-versa in sagging condition. The stress σ induced in each structural element by the strain ε is to be obtained rom the load-end shortening curve σ-ε o the element, which takes into account the behaviour o the element in the non-linear elasto-plastic domain. The distribution o the stresses induced in all the elements composing the hull transverse section determines, or each step, a variation o the neutral axis position due to the nonlinear σ-ε, relationship. The new position o the neutral axis relevant to the step considered is to be obtained by means o an iterative process, imposing the equilibrium among the stresses acting in all the hull elements on the transverse section. Once the position o the neutral axis is known and the relevant element stress distribution in the section is obtained, the bending moment o the section M i around the new position o the Page o 4 IACS Req. 05

45 neutral axis, which corresponds to the curvature χ i imposed in the step considered, is to be obtained by summing the contribution given by each element stress. The main steps o the incremental-iterative approach described above are summarised as ollows (see also Figure ): a) Step : Divide the transverse section o hull into stiened plate elements. b) Step : Deine stress-strain relationships or all elements as shown in Table. c) Step 3: Initialise curvature χ and neutral axis or the irst incremental step with the value o incremental curvature (i.e. curvature that induces a stress equal to % o yield strength in strength deck) as: χ. χ R 0.0 E eh z D z n z D : z n : Z coordinate, in m, o strength deck at side. Z coordinate, in m, o horizontal neutral axis o the hull transverse section with respect to the reerence coordinate system deined in...3 d) Step 4: Calculate or each element the corresponding strain, ε i χ(z i - z n ) and the corresponding stress σ i e) Step 5: Determine the neutral axis z NA_cur at each incremental step by establishing orce equilibrium over the whole transverse section as: ΣA i-net σ i ΣA j-net σ j (i-th element is under compression, j-th element under tension). ) Step 6: Calculate the corresponding moment by summing the contributions o all elements as: M σ A z z ) U Ui i net ( i NA _ cur g) Step 7: Compare the moment in the current incremental step with the moment in the previous incremental step. I the slope in M -χ relationship is less than a negative ixed value, terminate the process and deine the peak value M U. Otherwise, increase the curvature by the amount o χ and go to Step 4. Page 3 o 4 IACS Req. 05