HIGH SPEED AND LIGHT CRAFT

CLASSIFICATION NOTES No. 30.8 STRENGTH ANALYSIS OF HULL STRUCTURES IN HIGH SPEED AND LIGHT CRAFT AUGUST 1996 Veritasveien 1, N-1322 Høvik, Norway Tel.: +47 67 57 99 00 Fax: +47 67 57 99 11

FOREWORD (DNV) is an autonomous and independent Foundation with the object of safeguarding life, property and the environment at sea and ashore. AS (DNV AS), a fully owned subsidiary Society of the Foundation, undertakes classification and certification and ensures the quality of ships, mobile offshore units, fixed offshore structures, facilities and systems, and carries out research in connection with these functions. The Society operates a world-wide network of survey stations and is authorised by more than 120 national administrations to carry out surveys and, in most cases, issue certificates on their behalf. Classification Notes Classification Notes are publications which give practical information on classification of ships and other objects. Examples of design solutions, calculation methods, specifications of test procedures, as well as acceptable repair methods for some components are given as interpretations of the more general rule requirements. An updated list of Classification Notes is available on request. The list is also given in the latest edition of the Introductionbooklets to the "Rules for Classification of Ships", the "Rules for Classification of Mobile Offshore Units" and the "Rules for Classification of High Speed and Light Craft". In "Rules for Classification of Fixed Offshore Installations", only those Classification Notes which are relevant for this type of structure have been listed. Det Norske Veritas AS 1996 Data processed and typeset by Division Technology and Products, Det Norske Veritas AS 03/07/2003 10:43 AM - CN30-8.doc Printed in Norway by Det Norske Veritas AS 9.96.2000 ERROR! AUTOTEXT ENTRY NOT DEFINED.

CONTENTS 1. GENERAL...4 1.1 Introduction...4 1.2 Definitions...4 2. TRANSVERSE WEB FRAME ANALYSIS...5 2.1 Introduction...5 2.2 Procedure...5 2.3 Load conditions...5 2.4 Beam element modelling...8 2.5 Finite element modelling...10 2.6 Stress analysis...10 3. GLOBAL STRENGTH ANALYSIS...12 3.1 Introduction...12 3.2 Design loads...12 3.3 Modelling...14 3.4 Design criteria...15 3.5 Reporting... 15 4. WATERJET DUCTS... 16 4.1 Introduction... 16 4.2 Load conditions... 16 4.3 Modelling... 18 4.4 Results and stress analysis... 20 5. HIGH SPEED LIGHT CRAFT SUPPORTED BY FOILS... 22 5.1 Introduction... 22 5.2 Design loads on foil systems... 22 5.3 Strength analyses... 23 5.4 Local analysis... 23 5.5 Acceptance criteria... 23 6. APPENDIX A TYPICAL STRUCTURAL DETAILS... 24

4 Classification Notes- No. 30.8 1. GENERAL 1.1 Introduction These guidelines should be considered in connection with DNV Rules for Classification of High Speed and Light Craft, Pt.3 Ch.2 / Ch.3 Sec.9. The aim of these guidelines is to set a standard for various types of direct strength calculations performed in addition to or as a substitute to the specific rule requirements as given in the Rules for High Speed and Light Craft. The application of direct stress analysis may be required as: a) Part of rule scantling determination. In such cases where simplified formulations are not able to take into account special stress distributions, boundary conditions or structural arrangements with sufficient accuracy, direct stress analysis has been required in the rules. b) Alternative basis for the scantlings. In some cases direct stress calculations may give reduced scantlings, especially when optimisation routines are incorporated. 1.1.1 Due to complexity in design and extended need for direct strength calculations, guidelines are given in excess of direct rule requirements in some areas. Basis for class approval is related to the general rule requirements applicable for the response to specific load conditions. When direct calculations are intended as classification documentation, the class should in general be approached prior to submission of final documentation. The aim of this Classification Note is to establish an acceptable documentation standard with respect to direct strength calculations as basis for a class approval of a HSLC design. 1.2 Definitions 1.2.1 The following SI-units (International System of units) are used in this Note : Mass Length Time Force tonne (t) millimetre (mm) or meter (m), stated in each case seconds (s) kilonewton (kn) Acceleration meters per second square (m/s 2 ). 1.2.2 Notations L = length of the craft in m defined as the length between perpendiculars. Amidships is defined as the middle of L B = greatest moulded breadth in m D = moulded depth in m T = fully loaded draught in m with craft floating at rest in calm water = fully loaded displacement in tonnes in salt water at draught T C b = block coefficient V = Maximum speed in knots B wl = greatest moulded breath of the hull in m at the fully loaded water line, for multihull vessels B wl is the net sum of the waterline breadths g 0 = standard acceleration of gravity = 9,81 m/s 2 LCG = Longitudinal Centre of Gravity a cg = vertical design acceleration at LCG (m/s 2 ) a v = dynamic vertical design acceleration at different positions along the length of the craft (m/s 2 ). a t = dynamic transverse acceleration (m/s 2 ) a y, a ry = as given in the Rules for Classification of Ships, Pt.3 Ch.1 Sec.4 B ρh = specified uniform cargo load (t/m 2 ) p = design pressure (kn/m 2 ) E = modulus of elasticity of the material, = 69 000 N/mm 2 for aluminium, = 206 000 N/mm 2 for steel Cw = wave coefficient Hs = significant wave height in m θ = rolling angle (deg).

Classification Notes- No. 30.8 5 2. TRANSVERSE WEB FRAME ANALYSIS 2.1 Introduction 2.1.1 For girders which are part of a complex 2- or 3-dimensional structural system, the Rules for Classification of High Speed and Light Craft require a complete structural analysis to be carried out. The analysis is to show that the stresses are acceptable for the structure in question when loaded in accordance with the described load conditions. Any recognised calculation method or computer program may be applied, provided the effects of bending, shear, axial and torsional deformations are considered when relevant. Strength analysis in accordance with the guidelines outlined in this Classification Note will normally be accepted as basis for class approval. Guidance note: When web frame strength analysis is submitted as documentation for class approval of drawings, the following should be included: When a 3-dimensional analysis is performed, the loads, model and boundary conditions should correspond to the approach outlined in this Classification Note. 2.2.3 When pillars are fitted with regular intervals over the length of the cargo region, modelling of bottom and deck grillages may be necessary in addition to transverse web frame analysis. These additional calculations may involve an iteration process to obtain vertical force balance between the various grillage models. When this iteration process is necessary for simpler models, it is also valid to recommend a bigger 3 dimensional model to include frames, decks and pillars all together to make this iteration unnecessary. Bottom structures with longitudinal bottom girders and/or large fuel or ballast tanks, should be analysed by a 3- dimensional model. The model should preferably extend from middle of one compartment to middle of next compartment. reference to drawings description of model including boundary conditions description of loads description of results conclusion. See also 3.5. End of Guidance note 2.1.2 Strength analysis as described is generally related to a web frame structure of a High Speed and Light Craft, and unless otherwise stated related to a 2-dimensional beam element model. 2.2 Procedure 2.2.1 Calculations of the transverse web frame strength should generally be performed for a typical frame in the midship region for vessels less than 50 m. For larger vessels, and for vessels with unusual arrangement, several sections along the length of the vessel should be considered. 2.2.2 When maximum response for a transverse web frame is to be established, a frame in the middle of a compartment is normally analysed, see also Figure 2-1. Acceptable calculations may be performed by 2-dimensional beam element framework analysis 3-dimensional framework or finite element calculations. Figure 2-1 Frame or compartment for web frame analysis 2.3 Load conditions 2.3.1 Load Condition 1, sea pressure, maximum load on decks (LC1) This load condition is shown in Figure 2-2, and may be decisive for side and deck structures. The design pressures due to cargo loads (including structure) are to be taken as : pv = ρ H( g0 + 05, av) (kn/m 2 ) ρh = 0,35 t/m 2 for accommodation decks, see also the Rules Pt.3 Ch.1 Sec.2 C.

6 Classification Notes- No. 30.8 For wheel loaded decks, the actual wheel loads should be applied. The worst combination of wheel loads on one frame should be analysed. In addition to a load case with point loads representing wheel loads, an equivalent evenly distributed load should be considered (minimum 4 kn/m 2 ). Forces transferred to the analysed frame from surrounding structure should be applied as point loads (e.g. from longitudinal girder when considering frame in way of pillars). Design sea pressures are to be taken in accordance with the rules Pt.3 Ch.1 Sec.2 C500, and should be applied on all external surfaces. 2.3.2 Load Condition 2, symmetric bottom slamming (LC2) This load case is shown in Figure 2-3 and Figure 2-4, and may be decisive for the bottom structure. The load case investigates the effect of symmetric impact pressure on one frame, using the average impact pressure values as given by the Rules. The deck load distribution is the same as in LC1. The bottom slamming pressure is to be found from the Rules Pt.3 Ch.1 Sec.2 C200-C300, and be taken as the greatest of bottom slamming and pitching slamming. For frames positioned where the forebody side and bow impact pressure is largest, the loads must be applied up to main deck or vertical part of craft side. The design load area is normally taken as the frame spacing times the length of the frame between the chine or upper turn of bilge (m 2 ) for bottom slamming. For a 3-dimensional model, the bottom slamming pressure should be applied for one frame, and sea pressure on the bottom panels of the other frames. Figure 2-2 Load condition 1 (definition of point loads from surrounding structure indicated schematic for one pillar on one deck) Figure 2-3 Load condition 2. In midship region, bottom slamming pressure applied. In foreship area bow impact pressure applied

Classification Notes- No. 30.8 7 H L 08. = 022, L( kc L ) (m) 1000 k c = 0,3 for catamaran, wave-piercer, SES, ACV, and hydrofoil k c = 0,5 for SWATH, the tunnel top slamming pressure is to be replaced with sea pressure. Figure 2-4 Definition of turn of bilge/chine for different hull shapes. In a 3-dimensional model, tunnel top slamming pressure only needs to be applied to one frame (sea pressure on remaining frames). 2.3.3 Load condition 3 and 4, asymmetric bottom slamming (LC3 and LC4) This load case may be decisive for the bottom structure. The load case investigates the effect of asymmetric impact pressure on one frame, using the average impact pressure values as given by the Rules. In the bottom area design loads are applied on only one side at the time (inside slamming or outside slamming). The deck load distribution is the same as in LC1. The bottom slamming pressure is to be taken from the Rules Pt.3 Ch.1 Sec.2 C200-C300, and be taken as the greatest of bottom slamming, pitching slamming and forebody and bow impact pressure. The design load area is taken as half of the area used in LC2. In cases where a 3-dimensional analysis is performed, the slamming pressure only needs to be applied to one frame (sea pressure on other frames). 2.3.4 Load Condition 5, flat cross structure slamming (LC5) This load case is shown in Fig.2.5, and may be decisive for the cross structure of a multihull vessel. The load case investigates the effect of impact pressure on the wet deck, using the average impact pressure values as given by the Rules. The deck load distribution is the same as in LC1, and the sea pressure from water line to wet deck is taken from the Rules. The tunnel top slamming pressure is to be taken from the Rules Pt.3 Ch.1 Sec.2 C400. Design sea pressure is applied from centre line to design water line on the outside of the hull. The design load area is taken as the frame spacing times the distance between the hulls. Figure 2-5 Load condition 5 2.3.5 Load condition 6, transverse racking (LC6), monohull vessels only. This load case represents the vessel in heeled condition, and may be decisive for the lower side frames of a monohull. If a global racking calculation has been carried out, the transverse and vertical displacements of decks and side should be given as input, see also 3.3.10 regarding procedure for global racking calculations. A simplified check may be performed as indicated below. The deck vertical design load is taken as: pv = ρhg0 cos θ (kn/m 2 ) The deck horizontal design load is taken as: If the height from the water line to the wet deck is more than p h = 05, ρha t (kn/m 2 )

8 Classification Notes- No. 30.8 a t = design transverse acceleration (m/s 2 ), to be taken from the rules Pt.3 Ch.1 Sec.2 B302 for multihull vessels in forced roll, and from Rules for Classification of Ships for monohull vessels. See also 3.2.10. θ = maximum roll inclination. 2.3.6 Load condition 7, asymmetric deck load (LC7) This load case is shown in Figure 2-6 and Figure 2-7, and is only relevant for deck grillage including pillars. Deck load as for LC1. model transverse frame at pillars or between pillars model from side to side or half-model longitudinal position(s) of modelled frame(s). 2.4.2 It is assumed that correlation between individual 2- dimensional models is proven to be satisfactory (e.g. deck and transverse frame models). The symbols used are described in Figure 2-8. 2.4.3 Figure 2-9 and Figure 2-10 show typical models of transverse frames for a monohull and a multihull. Racking is not considered critical for a multihull vessel, and a halfmodel with symmetry conditions at centre line is normally modelled, while a full web frame is modelled for a monohull. 2.4.4 Areas of the web frame with large curvature should be modelled with increased number of elements. Structural discontinuities, as end connections with brackets or plate knuckles, should be modelled with rigid element ends offering similar section properties. See also Figure 2-11. Figure 2-6 Load condition 7, transversally asymmetric deck load Additional nodes may have to be modelled at side and decks in order to represent the loads properly. Figure 2-7 Load condition 7, longitudinally asymmetric deck load 2.4 Beam element modelling 2.4.1 Separate considerations must be made case by case to decide the extent and position of the model. The following should be considered when the extent of analysis is decided: Figure 2-8 Symbols 2.4.5 The efficiency of the girder flanges should be considered for girders with a large span

Classification Notes- No. 30.8 9 curved plate or face flanges. See also Fig.2.12. l n A s = distance between effective transverse bulkheads (fixed box ends) = number of loads along the box = actual shear area. Note that the spring stiffness calculations are based on the assumption that a frame in the middle of a compartment is analysed. The formula is only applicable for l / D < 5, else use 2.4.7. In areas where the shell plating is not tangential to a typical spring stiffness axis (program dependent), equivalent axial bar elements should be used. The length of the spring element may be found by : Figure 2-9 Transverse web frame model of monohull, complete frame modelled between pillars. A l s EA ls = (mm) K = cross-sectional area of spring element = length of spring element (lengths exceeding the length of the surrounding elements should be avoided). 2.4.7 Transverse frames are often connected by longitudinal deck girders, bottom girders and longitudinal bulkheads in the cross structure of multihull vessels. In a 2-dimensional model, this connection must be represented by springs. The spring stiffness of slender elements may be calculated by the following formula : K = 3 E ( n+ 1) l 26, ( n+ 1) l + 384I 8 A s (N/mm) Figure 2-10 Transverse web frame model of catamaran, only half of the frame modelled at pillar row. Valid only for symmetric load conditions 2.4.6 Vertical and horizontal springs corresponding to the stiffness of the shell and decks are to be applied. The stiffness coefficient for the springs representing the shell and the decks may normally be calculated by the following formula for l / D < 5: l n A s I = distance between effective transverse bulkheads (fixed box ends) or distance between pillars for deck beams supported by pillars = number of point loads along the box (e.g. number of frames between pillars) = actual shear area = actual moment of inertia. K = E 26,( n+ 1) l 8 A s (N/mm)

10 Classification Notes- No. 30.8 2.5.2 The mesh fineness and element types used in finite element models must be sufficient to allow the model to represent the deformation pattern of the actual structure with respect to matters such as: effective flange (shear lag) bending deformation of beam structures three dimensional response of curved regions. 2.5.3 In order to obtain sufficiently accurate results, the mesh fineness should represent the true web frame structure. This means modelling plating, webs and flanges as separate elements. It is acceptable that only one frame is modelled with a fine mesh (the highest loaded frame). Figure 2-11 Rigid element end 2.5.4 In order to properly consider shear and bending, 3 elements should be used over the height of the web of the frame, and with an element length to breadth ratio of 3. In areas with curved flanges, the element length should be approximately equal the stiffener spacing. 2.5.5 In areas with discontinuities (ends of flanges, knuckles, brackets), the model should represent the discontinuity with increased mesh fineness An alternative solution is to perform separate analysis by separate local models of such details. 2.5.6 Calculated stresses based on constant stress elements may have to be considered with respect to the stress variation within each element length. Figure 2-12 Effective flange consideration 2.5 Finite element modelling 2.5.1 A complex 3-dimensional finite element analysis may be applied to analyse the structural strength of a transverse web frame. 2.5.7 Symmetry conditions are to be applied at each end of the model. If the model only covers half of the breadth of the vessel, symmetry conditions should also be applied at centre line. Boundary conditions representing vertical support should be added as vertical shear forces at the end nodes of the model, in order to obtain a balanced model. 2.6 Stress analysis 2.6.1 For web frame analysis, the allowable stresses are normally taken as : Normally the model should cover the length of one compartment in the midship area from base line to upper deck, and extend from centre of one compartment to centre of next compartment.

Classification Notes- No. 30.8 11 Design loads Plating Stiffeners and girders Dynamic loads (slamming) equivalent stress bending stress Static loading (sea pressure) equivalent stress bending stress Allowable shear stress: 90 f 1. 220 f 1 200 f 1 200 f 1 180 f 1 200 f 1 180 f 1 180 f 1 160 f 1 The allowable stresses for dynamic loading are connected to impact loads. 2.6.4 Peak stresses as obtained by fine meshed finite element calculations may be allowed to exceed the values stated above in local areas close to stress concentration points. The allowable peak stress is subject to special consideration in each case. 2.6.5 The results from the web frame analysis should be evaluated with respect to plate buckling of the girder plate flange. 2.6.2 The allowable stresses given above assume that appropriate considerations and conditions are taken with respect to the model definition and result analysis. In particular the following should be noted: areas representing girder flanges must be adjusted for effective width in accordance with Pt.3 Ch.3 Sec.6 B200. structural details not modelled, as termination of flanges, bracket connections, pillar landings etc., should be separately evaluated based on forces taken from the analysis, see also Figure 2-13. Nominal stresses calculated by finite element calculations are to be related to the allowable stresses given above to the extent that such stresses do not refer to local stress concentrations in the structure or to local modelling deficiencies. 2.6.3 Shear stresses in girder webs as obtained by beam- or finite element calculation may only be related to the allowable shear stresses outside of areas with openings not modelled. Corrections for effective web area should be performed in the case of cut-outs for stiffeners or similar not being modelled, see also Figure 2-13. Figure 2-13 Local structural detail, effective web area adjusted for cut-outs

12 Classification Notes- No. 30.8 3. GLOBAL STRENGTH ANALYSIS Load 3.1 Introduction 3.1.1 In accordance with the rules Pt.3 Ch.3 Sec.4 A103, a complete 3-dimensional global analysis is to be performed for new designs of large and structurally complex craft. The requirement for global strength analysis normally applies for vessels more than 50 m in length. 3.1.2 The guidelines given in this Classification Note will provide a framework for the evaluation of the hull structure based on a global strength analysis, where the analysis may be accepted as basis for approval. 3.1.3 Calculations required to be performed are to be carried out by computer programs recognised by DNV. Recognised programs are considered programs used by shipyards where reliable results have been experienced and accepted by DNV. Condition Description Application LC 1 Still water condition Monohull/multihull vessels LC 2 Longitudinal ------- ------------ hogging moment LC 3 Longitudinal -------- ------------ sagging moment LC 4 Transverse split Multihull vessels force LC 5 Torsion moment / pitch connecting Monohull/multihull vessels moment LC 6 Combination Multihull vessels longitudinal bending and torsion LC 7 Transverse racking Monohull vessels Table 3-1 Global load conditions 3.2.4 Load Condition 1, still water condition (LC1) 3.1.4 General guidelines given by this Classification Note are only applicable for High Speed Light Craft, and references are given to the Rules for Classification of High Speed and Light Craft. 3.2 Design loads This load case is based on the difference between weight and buoyancy in still water condition at design draught. A loading manual is to be prepared to document the various still water conditions. The load condition should be accurately modelled to avoid trim of the model due to different position of Longitudinal Centre of Gravity and Longitudinal Centre of Buoyancy. The correct transverse and longitudinal mass distribution should be used. 3.2.1 The load case is a supplement to LC2, LC3 and LC4. The load calculations should be based on the Tentative Rules for the Classification of High Speed and Light Craft 1996. Design values should be agreed between designer and DNV prior to final analysis. 3.2.2 Alternative loads, i.e. from direct hydrodynamic calculations, may be used for design calculations. Alternative design load formulations must be agreed with DNV in each case. Wave load analysis programs and their application will only be accepted on a case to case basis. 3.2.3 Table 3-1 describes typical loading conditions and their applicability with respect to type of design. Each load case is described below. Additional load conditions may be considered relevant. 3.2.5 Load Condition 2, longitudinal hogging moment (LC2) This load case is shown in Figure 3-1 and will be decisive with regard to allowable longitudinal stresses and buckling capacity in the bottom area. The longitudinal hogging moment may be derived from : rule crest landing formula, Pt.3 Ch.1 Sec.3 A200 rule hogging moment, Pt.3 Ch.1 Sec.3 A500 direct calculations of hydrodynamic loads Only the largest needs to be analysed. An example of acceptable modelling of the load case is shown in Figure 3-1. The mass distribution of the vessel is given (g o +a cg ) vertical acceleration, and this load is balanced with buoyancy line loads around LCG. In order to verify that the loading is correct, regardless of modelling for design global moment, it is necessary to demonstrate that the following have been achieved :

Classification Notes- No. 30.8 13 the required maximum bending moment SPLIT LOAD CONDITION maximum shear at approximately quarter length of vessel the LCG is approximately in line with LCB y F y M split negligible reaction forces at supporting nodes. Correct transverse and longitudinal mass distribution is to be used. Longitudinal and transverse mass distribution multiplied by (g o + a cg ) LCG Aft 1 3 F y 1 3 2 4 F y 2 4 x + y = h 1 4 F y 3 M = F y + M split y s, keel 4 1 M = F x + y x s, keel y 4 x {( ) ~ } Boundary conditions only to prevent rigid body movement Bouyancy applied at bottom around LCG x+ y= h ~x BASELINE Figure 3-1 Load condition 2, only half of the vessel shown 3.2.6 Load Condition 3, global sagging moment (LC3) This load case may be decisive with regard to allowable longitudinal stresses and buckling capacity in the upper decks. Modelling of this load case may in principle be as for LC2. 3.2.7 Load Condition 4, transverse split force (LC4) This load case is shown in Figure 3-2 (split force acting outwards) and is decisive for the structure between the hulls, the side and bulkheads for a multihull vessel. The load case represents horizontal wave loads acting on the hulls. The horizontal transverse split force Fy is found from the Rules, Pt.3 Ch.1 Sec.3 B202. According to the rules, the split moment caused by the split force should be combined with the still water transverse bending moment. A combination of the transverse moments may be obtained by combining LC1 with this load condition. It is advised that both positive and negative split forces are combined with LC1 and analysed as two load conditions. ~x NOTE : = the mean offset line established by measuring the distance between the keel and the baseline - the sum of the horizontal forces is to act at 75% of the draught - no mass is required to be modelled in this condition Figure 3-2 Load condition 4, transverse split, split outwards shown 3.2.8 Load Condition 5, torsion moment / pitch connecting moment (LC5) This load case is shown in Figure 3-3, and may be decisive for the cross structure. As indicated in Figure 3-3, the torsion and pitch connecting moments are combined in the same load condition. The load condition may be modelled without a mass distribution. A full structural model should be applied. 3.2.9 Load Condition 6, combination of longitudinal bending and torsion (LC6) This load case is a combination of LC2 and LC5 or LC3 and LC5. Only the maximum longitudinal bending moment needs to be combined with LC5. The following combinations should be analysed: a) 80 % longitudinal bending and 60 % LC5. b) 80 % LC5 and 60% longitudinal bending.

14 Classification Notes- No. 30.8 p h q s q b b Figure 3-3 Possible modelling of Load condition 5, alternative ways may be used 3.2.10 Load Condition 7, transverse racking, dynamic loads only (LC7) This load case is shown if Figure 3-4, and may be decisive for the lower side frames and transverse bulkheads for a monohull vessel. A combination of vertical and transverse deck loads should be applied for the upper decks in accordance with: monohull vessel: Figure 3-4 Load condition 7 3.3 Modelling 3.3.1 The global finite element model should in general cover the complete ship. In particular it is necessary that the model covers the geometrical hull shape, transverse bulkheads, decks, and any torsional box structures. 3.3.2 Size, type and number of elements should be selected to ensure that the effects of bending, shear and torsion of the hull beam are fully accounted for. a t = g 0 sinθ + a ry m/s 2 Typical maximum element size may be influenced by θ, a ry, see Rules for Classification of Ships, Pt.3 Ch.1 Sec.4 B. multihull vessels: a t = rr r g 2π θ + 0 sinθ m/s 2 T R 2 T R, θ r, r r, see rules for HSLC, Pt.3 Ch.1 Sec.2 B. Dynamic horizontal deck loads are taken as p h = 0,5ρHa t (kn/m 2 ) where ρh is 0,35 t/m 2 for passenger deck. The transverse deck racking loads should be balanced by a horizontal line load (q s in Figure 3-4) at the design water line of the vessel. The resulting moment should be balanced by a counteracting vertical force couple (q b in Figure 3-4). All load components should be balanced in order to ensure that an equilibrium load condition is achieved, with minimised support node reaction forces. element type. If four noded elements are used, a typical element size is maximum three elements per frame spacing in the longitudinal direction and 3 elements for each tier. Normally a length to breadth ratio of 3 is acceptable as element size (normally not less than 1 m in breadth). An example of a global Finite Element Model is shown in Figure 3-5. 3.3.3 A basic description of the model is to be provided indicating the extent of the actual structure to be modelled, and stating that the model will represent the structural drawings adequately and which simplifications have been utilised. Drawings are to be referenced and, if possible, the modelled areas indicated on these drawings. Input units should be listed. Figure 3-5 Example of a Finite Element Model

Classification Notes- No. 30.8 15 3.3.4 buckling capacity of various panels, stiffeners and girder Simplified modelling compared to the real structure is systems, Pt.3 Ch.3 Sec.10 for aluminium and Pt.3 Ch.2 acceptable, but must be clearly identified. A list of Sec.10 for steel craft. assumptions and simplifications to be specified may include items such as: 3.4.3 representation of stiffeners as lumped to the nearest mesh line and inertia correcting techniques element connections curved plates modelled as straight representation and modelling of cut-outs transverse frame lumping techniques slight arrangement changes due to nodal locations 3.5.1 masses lumped as discrete points list of internal structure not included. 3.3.5 The correct choice of boundary conditions is essential in achieving reasonable results from an FEM analysis. The chosen boundary conditions should reflect symmetry (if so desired) and prevent numerical errors from occurring. Attention should always be paid to the stresses and deflections resulting from the modelled boundary conditions. Generally the boundary conditions are checked by verifying that they are in balance without reaction forces, and that only rigid body movements are prevented. 3.3.6 A verification of the model should be available for result evaluations. Plots of the model showing boundary conditions, shell thicknesses, co-ordinate axis orientation should be given. 3.4 Design criteria 3.4.1 Allowable global stresses are in general to be taken as given in Pt.3 Ch.3 Sec.4. Where shear-lag effects dominate, stress distribution and peak stresses should be carefully considered. Special attention should be given to structural discontinuities or areas where the stress flow is not properly taken into account due to a coarse element mesh or simplifications during modelling. 3.4.2 The results from the analysis should be evaluated with respect to: comparison of main results with simplified calculations reaction versus applied loads allowable global stresses according to Pt.3 Ch.3 Sec.4 for aluminium and Pt.3 Ch.2 Sec.4 for steel craft combination of global and local stresses according to Pt.3 Ch.3 Sec.9 for aluminium and Pt.3 Ch.2 Sec.9 for steel craft In areas with peak stresses exceeding the allowable rule values, such as at cut-outs or other structural discontinuities, the extent of the peak stresses and consequence of yield should be documented. 3.5 Reporting In order to accept the global FEM analysis as basis for approval, the analysis and the results must be reported to the class. 3.5.2 The following items should as a minimum be covered in the report from the FEM analysis: a) Basis for the work that is performed. This should include: description of analysis reference to program(s) used reference to drawings of the analysed structure reference to quality plan used during the work with the analysis. b) Description of model, including: model extent and reference drawings element description (type, coarseness of model) deviations between model and drawings boundary conditions input/output units global/local co-ordinate system. c) Description of loads and load conditions. d) Results from analysis. Based on the purpose of the analysis, relevant results to present may be: stress distribution for all load cases 1) stress components for documentation of local strength (shear, bending, buckling) principal stresses for fatigue analysis (separately agreed) pillar forces deflections (transverse racking, distortion of openings). 1) If contour plots are used instead of numerical plots, this will require: narrow bandwidth colour plots. e) Conclusion from the analysis: summary of the results from the analysis summary of modifications found necessary.

16 Classification Notes- No. 30.8 4. WATERJET DUCTS 4.1 Introduction 4.1.1 The reaction forces from the waterjet nozzles need to be transmitted into the hull structure in a manner for which adequate strength and fatigue life of critical details can be ensured through careful design. 4.1.2 For steerable jet units the reaction forces will typically arise from acceleration (thrust) and manoeuvring actions. For booster nozzles with no steering function reaction forces arise from acceleration (thrust) forces only. Additional to this vibration forces from impeller pulses/cavitation, turbulent waterflow in duct and around stator vanes, and various other possible sources (shaft misalignment, shaft/impeller imbalance etc.) will be present. Figure 4-1 shows a typical steering gear for a waterjet unit, which through manoeuvring actions will transmit reaction forces through the bolted connection at the transom to the duct and hull structure. Figure 4-2 Typical duct / jet nozzle configuration critical areas 4.1.5 The duct and the structural details of the duct must be considered to be experiencing high and low cycle loads and will therefore have to be considered for fatigue strength. For this reason it is recommended to design with few welded details and attachments on the duct itself, and that due attention is paid to the detail design and execution of welds (e.g. grinding of welds). 4.2 Load conditions 4.2.1 The critical details of the duct and connections to the hull structure should be dimensioned for the following static load conditions (LC) generally specified by the manufacturer of the waterjet: Load Condition Description Figure 4-1 Typical waterjet steering gear LC 1 LC 2 LC 3 Crash stop Maximum loads from reversing Maximum loads from steering LC 4 Waterjet unit weight accelerated as cantilever in pitching In addition, high cycle loads from impeller pulses should be considered, if available from the manufacturer. 4.1.3 Guidance note : The steering nozzle reaction forces should normally be transmitted into the hull structure in one of the following manners: through the duct and into transverse frames, bulkheads and bottom plating through additional stiffening structure at transom. 4.1.4 End of Guidance note For a jet unit assembly with the duct constructed from welded aluminium, where forces are transferred through the duct, some typical critical details which require attention during design are illustrated in Figure 4-2. High cycle loads and loadpaths are generally not specified by manufacturer and will vary with size and make, so a recommended way to take account for these loads in duct design is, for each critical detail, to design to the best possible fatigue class (see part four for typical details and fatigue classes). Also very important is shaft alignment at installation, balancing of shaft and impeller and condition of bearings during service.

Classification Notes- No. 30.8 17 Figure 4-3 shows typical application of forces to the duct as they may be split into horizontal and vertical forces and moments. 4.2.2 For fatigue life calculations, the long term load distributions in Table 4-1 should normally be considered: Long term load distribution Load distribution 1, Reversing loads (LD1) Description The accumulated sum of stresses will have the profile as shown. Maximum value, σ max, is taken from analysis of LC2. Assumption: maximum reversing load 20 times per day. Total number of cycles in 20 years is N reversing = 1,46 x 10 5 Load distribution 2, Steering loads (LD2) Assumption : Assuming steering cycle of 20 seconds 12 hours per day for all sea-states. The steering load varies with the angle ranging from corrective steering 5 (flat water) and full steering 30 (heavy seas). It may be assumed that steering at any angle varies from port to starboard at any one cycle, so that stress range at a detail is double that calculated from the static equivalent at any angle, Maximum values may be taken from the analysis of LC3 (for fatigue assessment of flanges stress range can be considered as the range from bending stresses and axial stresses when in tension to only axial stresses in compression). The total number of steering cycles; Nsteering= 1,57 x 10 7 corresponding to 5 steering (1/6 σ max ). Assuming full steering 40 hours per year for 20 years; Nfull steering= 1,44 x 10 5 corresponding to 30 steering (σ max ).

18 Classification Notes- No. 30.8 Load distribution 3, pitching load (LD3) The vertical accelerations at the stern will cause cyclic cantilever bending loads from the waterjet. The maximum value may be found from the analysis of LC4. The accumulated sum of stresses will have the profile as shown. Assumption : Assuming 12 hour operation per day. Assuming linear variation of pitching loads between 0 and maximum and a total number of cycles; Npitching= 2 x 10 7 Table 4-1 Long-term load distribution x v Such model should extend from the transom flange and at least to the first vertical support, though preferably to the second (web frame or bulkhead). Depending on the details involved (flange connections, discontinuities), the boundary conditions and load applications should be chosen according to the general principles described below. Steering Reversing / Crash-stop Figure 4-3 Manoeuvring force components 4.2.3 Limited data is available for the above load cycles and their distribution, but should generally be used for design fatigue calculations. The curves for steering and cantilever action is linked to a standard sea load distribution curve. 4.3.3 The loads on an axi-symmetric model may be applied as a unit linear load around the circumference. Results may be scaled to the correct values for forces and moments. Alternatively, if the modelling application used allows, the acting axial load and moment may be applied separately. That is, the moment may be applied as an asymmetric unit load with a sinusoidal distribution around the circumference. The resulting stresses may then be combined to give unit load stress at any point of interest. The steering curve does not take into account the long term distribution for angle of encounter of seas, nor seakeeping characteristics of particular ship types. 4.3 Modelling 4.3.1 Due to the complex structure, Finite Element Method analysis should normally be used for the assessment of the transom region. Linear unit load Sinusiodal unit load distribution 4.3.2 For waterjet ducts with flange connections and/or discontinuities along the length, an axi-symmetric model may be used to study and record the stresses in way of critical details. Figure 4-4 Axi-symmetric model, load application

Classification Notes- No. 30.8 19 4.3.4 Boundary conditions should be carefully selected. The duct, when continuous, should be held against axial and radial displacement at the forward end. If there are any transverse web frames with connections to the duct along the modelled section, these should be taken into account by restricting this particular point against displacement in the direction transverse to the duct, see Figure 4-5. 4.3.5 For alternative flange connections, it is in general recommended to design for a condition where the bolt pretension of the bolts is lost. This gives a model boundary condition where the flange is partly restricted to rotate. The stiffness of the rotational spring will depend on the size of facing jet bowl flange and size and material of bolts. This condition should be used as minimum fatigue design criteria. As the modelling of a partly stiff flange is uncertain, one may alternatively consider the two conditions where the flange is free to rotate (see Figure 4-6) and completely restricted against rotation (see Figure 4-7). This approach will give somewhat high stresses in way of the transom flange thickness transition, but the maximum stress will move from the inside of the duct to the outside of the duct and the difference in magnitude may not be very large. The condition giving the largest stress should be used as design criteria. The significance of these simplified boundary conditions may be considered negligible on the details further along the duct. 4.3.6 For a more detailed study of standard flange connections for dimensioning flange connections, bolt pretension, gaskets and washers with respective geometry and material quality, and local geometry such as fillet radii of transition between duct and flange etc., may be included in the model. Bolt pretension may be modelled using temperature loads or forced displacement. To study the non linear effects of gasket and washer compression more advanced methods need to be applied. 4.3.7 Non-continuous ducts with flange connections along the duct may be simplified by fixing nodes from the line of the flange bolts to the outside edge of the flange against axial and radial displacement, see Figure 4-8. F t F c Figure 4-5 Aft part of duct, actual boundary conditions (F t and F c are tensile and compressive load respectively). F t F c Figure 4-6 Aft part of duct, simplified boundary conditions (F t and F c is tensile and compressive load respectively, for top and bottom)

20 Classification Notes- No. 30.8 F t F c Figure 4-7 Aft part of duct, simplified boundary conditions (F t and F c is tensile and compressive load respectively, for top and bottom) F t F c Figure 4-8 Non-continuous duct, boundary conditions joining flange (F t and F c are tensile and compressive loads respectively) 4.4 Results and stress analysis 4.4.1 Stresses should be taken from the model as principal stresses along the local element axis. For static analysis (LC1 to LC4), the allowable stresses are: Load condition Combined axial-and bending Shear LC 1 180 f 1 100 f 1 LC2, LC3, LC4 160 f 1 90 f 1 For fatigue assessment the stress range at the detail, from maximum tension to maximum compression should be used. 4.4.2 The analysis results should be used to establish areas of high and low loading. Welded joints in the duct should typically be placed as far away from stress hot spots as possible. Results from an axisymmetric FEA, where linear stresses can be read at the actual position of the weld, should be used to position and design the welded connection with respect to fatigue. 4.4.3 The fatigue assessment may be based on the Miner-Palmgren method for accumulated fatigue damage. Where; η = Σ n i / N i η = fatigue damage ratio n i = number of cycles at stress range σ i N i = number of cycles to failure at stress range σ i. In general the damage ratio at one point is the sum of the damage ratio from each of the load effects. η total = η rev + η steer + η pitch For water jets the steering loads will not act in the same point as the others, therefore η steer = 0 when considering the top and bottom parts of the duct. The sum of the damage ratio from each of the load effects or in the case of steering the sum for steering alone should be kept less than one. i.e Σ η < 1 Guidance note : - The fatigue check for welded aluminium details should be based on the ECCS "EUROPEAN RECOMMENDATIONS FOR ALUMINIUM ALLOY STRUCTURES FATIGUE DESIGN" - Reference stress for fatigue check is the principal stresses in the main load carrying member.

Classification Notes- No. 30.8 21 - Stress concentrations due to the weld detail itself is included in the curve. - For practical purpose, using FEM analysis, the surface stress on the main member in the principal directions should be used. - Additional stress concentrations from geometrical effects may be included by the use of stress concentration factors K. Such effects may be cut-outs (not covered by an axe-symmetric FEM model), geometrical transitions or fillet radii. - For thicknesses of more than 25 mm a correction factor is to be used on the fatigue strength. - The reference curves in the ECCS guideline refer to dry environment. - Parts subjected to corrosion need to be specially evaluated (i.e parts not coated and exposed to sea-water). Figure 4-10 Critical areas steering with two adjacent jets End of Guidance note 4.4.4 When forces are transferred through the duct into the hull structure, the relative deflection between the duct and the hull structure may be most prominent at the connection to the transom. It is therefore necessary to allow this relative movement (mainly axial) between the transom flange connection and the vessel s bottom and sides without stresses in critical weld connections exceeding those given by the respective loadcases against yield and fatigue. A typical critical point in way of connection between transom and bottom plating is shown in Figure 4-9. Figure 4-9 Typical critical detail due to duct deflection in reversing/crash-stop 4.4.5 In situations where two steerable jets are located next to each other, the total relative displacement should be taken into account when estimating the stresses. Sufficient distance between such jets should be ensured to allow sufficient flexibility in the transom plating usually having a thickness dimensioned to take the vertical shear forces. The critical welds in this area should be considered with respect to fatigue when exposed to the distribution of steering actions over the lifetime of the vessel. Below is shown typical critical areas in way of transom for steering manoeuvres with two adjacent jets.

22 Classification Notes- No. 30.8 5. HIGH SPEED LIGHT CRAFT SUPPORTED BY FOILS 5.1 Introduction 5.1.1 As a part of the approval procedure, an extended safety evaluation compared to the conventional high speed light craft concept is required. In addition to the general safety aspects as covered by the rules, the following aspects are to be especially taken into consideration when the extent of required documentation is considered : consequence analysis to be documented for accidental events such as deflection/loss of foil/flaps, loss of active ride control (hull appendages and part of Failure Mode and Effect Analysis (FMEA) for vessel or also subject to structural evaluation) type of foils - if horizontal and completely submerged foils, the need for active stability control by flaps etc. is vital, hence the foil system is to be considered as an essential system and treated accordingly extent of lift - if hull completely out of water, the more severe consequences of accidental loss of lift forces, hence foil/strut connections to be considered both with respect to strength and performance of main function as per rules Pt.1 Ch.1. 5.1.2 It is considered important that well defined full scale test series of the vessel is to conclude the concept evaluation, verifying theoretical simulations, model testing and any important basic assumptions made during the earlier evaluation. Controlled prototype testing will provide a better reference for final definition of operational restrictions related to navigation in different sea states and manoeuvring characteristics at high speeds. 5.2 Design loads on foil systems 5.2.1 The builder should provide complete documentation of design loads for the foil system. Due to the fact that the profile shape and system configuration of the foil system affect the level of design loads, no empirical or simplified expressions should be used for design load calculations, and final load cases to be established case by case. The following parameters affecting the design loads should be considered: profile shape and lift coefficient speed/sea-state combinations and expected lift at various wave heights, corresponding speed loss at large wave heights physical limitation of profile lift due to ventilation or cavitation local distribution of loads on foil member (chordwise, spanwise) ratio between maximum values and in service values long term distribution of loads. 5.2.2 The hydrodynamic loading is generally to be based on extreme loads which may be considerably higher than design loads as expected during normal service. Normally the extreme loads are to be based on theoretical maximum values when cavitation or ventilation starts to occur. It is considered important that the angular movement of any rudder function of the foil system is limited at high speeds. 5.2.3 The loads on the foil system should as a minimum include the following: maximum positive lift maximum negative lift maximum side force maximum asymmetric loading (side wave, broaching, extreme rudder functions) drag forces obstruction loading secondary loading due to propulsion system (propeller induced forces, internal pressure in water inlets). Figure 5-1 Schematic example of loads on T-foil 5.2.4 Fatigue loading has to be established based on service notation and varying parameters, such as : sea condition headings vessel speed and frequency of encounter. 5.2.5 Global load cases for global analysis of hull strength will be considered individually based on size of vessel, level of design vertical acceleration and concept evaluation.