SLOSHING ANALYSIS OF LNG MEMBRANE TANKS

Transcription

1 CLASSIICATION NOTES No SLOSHING ANALYSIS O LNG EBRANE TANKS JUNE 006 Veritasveien, NO-3 Høvik, Norway Tel.: ax:

2 OREWORD (DNV) is an autonomous and independent foundation with the objetives of safeguarding life, property and the environment, at sea and onshore. DNV undertakes lassifiation, ertifiation, and other verifiation and onsultany servies relating to quality of ships, offshore units and installations, and onshore industries worldwide, and arries out researh in relation to these funtions. Classifiation Notes Classifiation Notes are publiations that give pratial information on lassifiation of ships and other objets. Examples of design solutions, alulation methods, speifiations of test proedures, as well as aeptable repair methods for some omponents are given as interpretations of the more general rule requirements. A list of Classifiation Notes is found in the latest edition of Pt.0 Ch. of the Rules for Classifiation of Ships and the Rules for Classifiation of High Speed, Light Craft and Naval Surfae Craft. The list of Classifiation Notes is also inluded in the urrent Classifiation Servies Publiations issued by the Soiety, whih is available on request. All publiations may be ordered from the Soiety s Web site INTRODUCTION This Classifiation Note was first issued in June 006. Comments may be sent by to rules@dnv.om or subsription orders or information about subsription terms, please use distribution@dnv.om Comprehensive information about DNV and the Soiety's servies is found at the Web site Det Norske Veritas Computer Typesetting (+SGL) by Det Norske Veritas Printed in Norway. If any person suffers loss or damage whih is proved to have been aused by any negligent at or omission of Det Norske Veritas, then Det Norske Veritas shall pay ompensation to suh person for his proved diret loss or damage. However, the ompensation shall not exeed an amount equal to ten times the fee harged for the servie in question, provided that the maximum ompensation shall never exeed USD million. In this provision "Det Norske Veritas" shall mean the oundation Det Norske Veritas as well as all its subsidiaries, diretors, offiers, employees, agents and any other ating on behalf of Det Norske Veritas.

3 Classifiation Notes - No June 006 CONTENTS. GENERAL Introdution...4. embrane type LNG tanks Purpose of this Classifiation Note Doumentation DNV Classifiation of LNG arriers Design basis Design priniples...8. APPLICATION O THE PRINCIPLES.... Limit state appliations.... Strength assessment methodology SLOSHING IPACT DESIGN LOADS Environmental modelling Ship motion alulation for sloshing tests Sloshing model experiments Sloshing design loads PUP TOWER DESIGN LOADS Identifiation of relevant loads Sloshing loads Inertia and gravity loads Thermal loads Hull girder loads Internal tank pressure and external sea pressure Combination of loads STRUCTURAL RESPONSE ANALYSIS O CONTAINENT SYSTES General ark III system NO96 system aterial stiffness parameters asti Simplified assessment of dynami response ULTIATE STRENGTH O CONTAINENT SYSTES General Capaity assessment ark III system NO96 system Plywood strength data RPU strength data STINESS AND STRENGTH O HULL STRUCTURE General Comparative basis (referene ase) Stiffness of hull plating Strength of hull struture RESPONSE AND STRENGTH O PUP TOWER AND SUPPORTS General Response analysis of main struture Response analysis of base support Response analysis of liquid dome area ULS assessment LS assessment Vibration hek REERENCES... 49

4 4 Classifiation Notes - No June 006. General. Introdution The sea-borne LNG transportation is inreasing dramatially. Not only is the industry inreasing in size, it develops new trade routes, new ship designs and new operations. Traditionally LNG arriers operate in a fully loaded ondition or in a ballast ondition to their next port-of-all. Presently key tehnial developments are the large inrease in vessel size (from ~ m 3 to ~ m 3 and above) and the disharge of argo in offshore waters. These developments imply a hange in argo dimensions and the operation with partially filled tanks in a wave environment. or the strutural integrity of the argo insulation, the hull support struture and the pump tower and supports the loads indued by the motions of the liquid argo inside the tanks need to be evaluated. These motions of the liquid argo inside the tanks is alled sloshing. Sloshing an indue various types of loads. Slowly varying motions ause a smooth hange of pressure distributions inside the tanks and a stati pressure model an be applied. Larger motions and/or more rapidly varying motions, ausing higher aelerations, indue dynami effets. The pressure fields inside the tanks an still be desribed by smoothly varying pressure distribution funtions and the strutural response an be alulated in a quasi-stati manor. In ase of more severe motions the fluid behaviour beomes violent, ausing breaking waves and high veloities of the fluid surfae. In this ase the fluid an ause impat loads on the ontainment system. These loads an be haraterised by a high load with a short duration ating on a limited area. Violent sloshing an be haraterised by various fluid flow phenomena illustrated in igure - - igure -5. In the high filling range (>90% H) the impats typially our on the tank roof at the onnetion with the transverse bulkheads. Typially a flat fluid surfae hits at high veloity the roof ausing the impat. Tank roof Impat loation Tank roof Keel igure - Typially high-filling (~60-70% H) impat due to a run-up against the longitudinal and or transverse bulkhead Tank roof Keel igure -3 Typially high-filling (~70-80% H) impat due to a run-up along the longitudinal bulkhead and hamfer or fillings in the range of ~0% to ~40% the largest impats our at the longitudinal and transverse bulkheads due to breaking waves. Tank roof CL CL Hopper Chamfer Chamfer Impat loation Impat loation Chamfer knukle Chamfer knukle Transverse BH Impat loation Transverse BH Upper hopper knukle Hopper knukle Keel igure - Typial high-filling (>90% H) impat in near head sea onditions or fillings in the range of ~60% to ~80% the largest impats our in the orners and knukles of the hamfer. These impats an be aused by run-ups against the longitudinal or transverse bulkheads or by a flat fluid surfae impat. Keel igure -4 Typial low-filling impat in near head sea onditions A harateristi phenomenon, whih an our at lower fillings is the so-alled hydrauli jump or bore. This wave phenomena is haraterised by a jump in the free surfae level, whih travels at high speed, whih an ause a large impat.

5 Classifiation Notes - No June 006 Tank roof CL Chamfer Impat loation speify the DNV requirements for approval of membrane type LNG arriers and floating strutures exposed to liquid sloshing in their argo tanks provide the LNG industry with the neessary methodology to assess sloshing impat loads, and to evaluate its impat on the design of membrane type ontainment systems for LNG, the supporting hull struture, and the pump tower struture provide the LNG industry with guidane on how to use this methodology to omply with the DNV lass requirements. Keel igure -5 Shemati illustration of an hydrauli jump or hydrauli bore Sloshing model experiments are required in order to assess the violent sloshing ausing impat loads. Setion 3 gives a detailed desription on how to ondut sloshing experiments and how to determine sloshing design load preditions. The sloshing loads vary in size, duration and load area. In addition, the ontainment system and hull struture have different failure modes. Consequently, a areful analysis of the strutural response and strength needs to be onduted for the various loads to assess the strutural integrity. A detailed disussion on the response preditions, the failure modes and the strength are given in Setion 5 to Setion 8. In traditional diret wave load analysis of ships the load and strength assessments are onduted in an absolute approah. Due to unertainties in the sloshing impat load assessment a omparative approah is used for the ontainment system and hull strength, whih is desribed in detail in Setion. or the pump tower, an absolute approah may be used. The basis for a omparative approah lies in the appliation of the equivalent safety priniple as outlined in the DNV Rules for the Classifiation of Ships. In the omparative approah the sloshing load and strength of a new LNG arrier design or a new operation of an LNG arrier is ompared with the sloshing load and strength of the existing fleet of membrane type LNG arriers that have traded in a safe and damage free operation. The former is referred to as the target vessel, whereas the latter is referred to as the referene ase. The remaining of this setion outlines in more detail the purpose and bakground of this Classifiation Note as well as the design basis and the design priniples, whih are used for the sloshing load, response and strength assessment of membrane LNG tanks.. embrane type LNG tanks This Classifiation Note onsiders Liquefied Natural Gas (LNG) membrane tanks as used in LNG arriers and LNG floating prodution and/or storage units. embrane type LNG tanks are defined aording to the International Code for the Constrution and Equipment of Ships Carrying Liquefied Gases in Bulk, see the IGC Code //, and the DNV Rules for Classifiation of Ships Pt.5 Ch.5 Liquefied Gas Carriers, //. They are non-self-supporting tanks whih onsists of a thin layer (membrane) supported through insulation by the adjaent hull struture. The membrane is designed in suh a way that thermal and other expansion and ontration is ompensated for without undue stressing of the membrane..3 Purpose of this Classifiation Note The purpose of this Classifiation Note an be summarised as follows: The Classifiation Note is mainly intended to be used for the approval of LNG arrier designs and operations that deviate from the designs and operations for whih operational experiene is available. This operational referene is defined in more detail in.6.. The methodology presented in this Classifiation Note an also be applied in the sloshing load and strength assessment of other marine strutures where sloshing is an important design parameter, suh as floating LNG terminals and prodution units..4 Doumentation The following doumentation is to be provided and submitted to the Classifiation Soiety as part of the design review and approval: the design basis used for the design of the vessel, i.e. the target ase the sloshing experimental programme, inluding the ship motion preditions, the test set-up, the test sope, the postproessing and the results the analysis of the sloshing experimental programme load and/or strength omparative analysis for ontainment system and hull strength, omparing the target ase with the referene ase load and strength alulations for the pump tower and supports drawings of ontainment system, pump tower, and supports..5 DNV Classifiation of LNG arriers.5. Appliable Rules and Classifiation Notes The lassifiation of LNG arriers is governed by the following rules and regulations in addition to the requirements to ain Class: DNV Rules for Classifiation of Ships Pt.5 Ch.5 Liquefied Gas Carriers //. International aritime Organisation: International Code for the Constrution and Equipment of Ships Carrying Liquefied Gases in Bulk (IGC Code) //. In addition to these douments, the Classifiation Soiety enfore limits on the allowable tank filling levels and limits on the allowable argo tanks dimensions. These limits are subjet to ontinuous onsiderations, and the appliable limits an be obtained upon request to the Soiety..5. Approval proedure for non-standard ships or ship operations The main purpose of this Classifiation Note is to provide guidane to assess sloshing in inreased size LNG arriers and/ or in partially filled onditions. Both require at present a diret sloshing assessment for approval if the appliations are not within the standard approved tank dimensions, ship size and/or filling restritions. A vessel with normal size and regasifiation failities is an example of a non-standard ship operation, sine it will involve partial filling during the regasifiation proess.

6 6 Classifiation Notes - No June 006 The present Classifiation Note desribes how a sloshing load and strength assessment an be onduted. The basi approah as outlined in this Classifiation Note is illustrated in igure -6. A short summary is given of the nd olumn desribing the sloshing load and strength assessment. The first step starts by desribing the design basis and the limit states for the vessel. The result of this is a detailed list desribing the speifiations, whih are used to develop a sope of work for the sloshing experiments. It is strongly reommended that this first phase is disussed with DNV Classifiation. Sloshing experiments are onduted resulting in a set of sloshing loads, whih are used in the omparative sloshing load and strength approah. or the omparative approah sloshing loads for the referene vessel and the target vessel are needed. The strutural strength of the ontainment system(s) is needed in ase of a strength omparative approah. or the known GTT systems, i.e. NO96 and ark III this is established and desribed in this Classifiation Note. If a new ontainment system is under onsideration a strength assessment is to be onduted. General proedure Sloshing load & strength assessment Review by Classifiation Prismati membrane tank? yes Design basis and limit state analysis (design vessel and operational speifiations) Design & operational onditions (sloshing test sope) Intermediate review by Classifiation Referenes to Classifiation Note.6 Design basis.7 Design Priniples. Limit state appliations 3. Environmental modelling Need sloshing assessment yes Sloshing Analysis 3. Ship motion alulation 3.3 Sloshing model experiments Apply Classifiation Note 30.9 Sloshing loads Intermediate review by Classifiation 3.4 Sloshing design loads 4 Pump tower design loads Known ontainment system? no Approval request yes Strength Assessment no Approval? yes Sloshing strength omparative assessment 5 Strutural reponse analysis 6 Ultimate strength of ont. systems. Strength assessment methodology 7 Stiffness and strength of hull struture 8 Response and strength of pump tower and supports Analysis report inal review by Classifiation.4 Doumentation igure -6 Shemati desription of the appliation of Classifiation Note 30.9 to assess sloshing in membrane LNG tanks for the ontainment system load&strength assessment.5.3 Guidane for qualifiation assessments.5.3. Inreased size LNG arrier The size of LNG arriers has gradually inreased in the past period of time from ~0 000 m 3 to ~ m 3, with m 3 often designated as the standard or onventional size. Sizes of m 3 and m 3 are being built (005/006) and vessels in the size of around ~ m 3 are being ordered. Regarding the building osts a minimum number of tanks is desired. However an inreasing tank size implies inreasing sloshing loads, whih need to be assessed. In addition the ship sizes are signifiantly larger, whih imply different ship motions. Consequently, an optimum ship design needs to be developed balaning the number of tanks and their dimensions with aeptable sloshing loads Offshore loading/unloading By onstruting LNG terminals offshore, where off-loading an take plae far from densely populated areas and busy ports and estuaries, the risk to the environment and the people at large is redued. However, disharging offshore implies that LNG arriers and LNG floating reeiving terminals will experiene all filling levels inside their tanks while operating in a wave environment. A liquefied disharge offshore implies a rather short period of time having to operate with partially filled tanks, the required weather window is thus more easily predited. An on-board re-gasifiation and a diret send-out to the onshore gas grid implies that the vessel will be on-site for several days. This poses different requirements to the weather window, while the availability should be high as there is no storage but diret grid supply Low-partially filled tank on a partiular trade route or for restrited operation or some partiular trades, argo maybe disharged at more than one terminal during one vessel voyage. Hene the arrier will be sailing with a partially filled tank(s) after having delivered part of its argo at the first terminal. ost obvious would be to re-distribute the argo to arrive at a situation suh that the filling levels in all tanks are within the approved filling range. Re-distribution takes time and is an extra ost fator. It is therefore of interest to investigate whether approval an be obtained for a speifi filling ase on a speifi route. If partial filling is an operational requirement for the owner, but this operation is not speified as a site-speifi offshore disharge operation nor a trade on a partiular route, the partial filling onditions may be assessed aording to this Classifiation Note in order to determine an environmental envelope for safe operation of the arrier.

7 Classifiation Notes - No June Guidane for sloshing load assessments The main fous of the Classifiation Note is to provide guidane to assess sloshing for: inreased size LNG arriers offshore loading/unloading partially filled LNG tanks on a partiular trade route. However, this Classifiation Note provides detailed information on the speifiation, exeution and analysis of sloshing experiments. Consequently, the Classifiation Note may be used to assess other appliations than the speifi appliations listed above. It is strongly reommended to inform the Class Soiety at an early stage and disuss and agree on the following key issues: design basis design priniples appliation of the priniples sloshing analysis sope of work strutural response and strength assessment proedure doumentation. Any alternative proedure to assess sloshing and its effets is to be agreed upon with the Class Soiety before ommenement of the studies..5.5 Guidane for novel ontainment system strength assessments The omparative strength assessment methodology used throughout this Classifiation Note is based on operational experiene with membrane type LNG tank systems, and this limits its appliation to the Gaztransport & Tehnigaz liensed ark III and NO96 membrane type LNG insulation systems. It is, however, believed that the methodology in some ases may be extended to over novel systems based on a similarity onsideration with the existing systems. This possibility must be disussed and agreed with the Class Soiety based on a review of the system. The strength aeptane riteria doumented in the Classifiation Note are speifi to the ark III and NO96 membrane type tank systems. The struture and formulation of the riteria may be useful in the formulation of the strength riteria for novel systems..6 Design basis.6. aterials The methodology for the assessment of the hull struture and the pump tower presented in this Classifiation Note is based on the presumption that materials are seleted in aordane with the requirements of the DNV Rules Pt.5 Ch.5. The methodology for the strength assessment of the ontainment systems is based on the presumption that the materials satisfy the requirements speified by the liense owner, Gaztransport & Tehnigaz S.A.s..6. Comparative basis (referene ase) The basis for the safety equivalene assessment of new LNG arrier designs and operations must be onsistent with the ship designs and operations that represent the safe and damage free operation experiened with the fleet of membrane type LNG arriers so far. The latter is referred to as the referene ase. The referene vessel is a 4-tank LNG arrier with a total argo apaity of to m 3 utilising the Gaztransport & Tehnigaz ark III or NO96 type ontainment system. The ontainment system should be of the same type for the referene ase as for the target ase. The seletion of an appropriate referene vessel may be subjet to disussion with DNV Classifiation. A design speed of 9.5 knots is assumed. It is assumed that the vessel trades on a world wide basis. A design life of 0 years is assumed. The tank fillings are between 90% and 98.5% of the tank height or below 0% of the tank length..6.3 Containment systems or the purpose of this Classifiation Note, the target LNG arrier utilises a membrane type ontainment system applied in prismati hamfered tank onfigurations. The strutural strength assessment methods desribed in this Classifiation Note is appliable to the Gaztransport & Tehnigaz ark III and NO96 tank insulation systems, and moderate evolutions of these systems in terms of modified plate thikness, modified support spaings, and modified onfigurations of internal load bearing struture..6.4 Cargo tank environment The strength of the insulation system should be evaluated on the basis of a argo temperature of -63 C, and a temperature of 0 C at the level of the steel struture in the argo tank ompartment. In the omparative approah equal densities of the argo are to be assumed. A density of 500 kg/m 3 is reommended to be used in the analyses..6.5 Normal operation of LNG arriers With the exeption of vessels trading as speified in.6.8, and the loading/unloading operational phase of vessels desribed in.6.7, it is assumed in this Classifiation Note that LNG arriers mainly trade with tank filling levels above 90% H, and only oasionally at filling levels between 90% H and the minimum aeptable upper range. With this as a basis, it is not orret to diretly ompare the frequently ourring referene ase (95% H) and a less frequently ourring target ase at fillings below 90% H at the same exeedane probability level. Corretions shall be made for the fat that the relationship between the short term and the long term (lifetime) expeted extreme sloshing load is expeted to be larger for the 95% H referene ase than for a target ase with filling levels below 90% H, see Inreased size LNG arrier An inreased size LNG arrier is an LNG arrier with a total argo apaity larger than the urrently approved standard size, see The number of tanks may be speified by the designer. The design speed is to be speified by the designer. It is assumed that the vessel trades on a world wide basis, but the vessel may be sailing on a dediated route, whih may be more severe than a general trade on a world wide basis. A minimum design life of 5 years is assumed. The design life is used to define the sea state ontour in order to identify the ritial sea states for ship motion alulation and sloshing model experiments. The design life is also used for the fatigue alulations of the pump tower. The tank filling restritions are to be speified by the designer..6.7 Offshore loading/unloading The operation of the vessel while trading to and from a disharge loation is onsidered to be a normal trading pattern, for whih the design basis is overed by.6., onerning a onventionally sized LNG arrier, or.6.6, if the target vessel onerns an inreased size LNG arrier intended for offshore disharge. At the disharge site the vessel will approah the mooring site by positional DP and/or tug assistane. Different mooring onfigurations may be used, like spread mooring or moored by a bow-turret. The vessel may be moored along

8 8 Classifiation Notes - No June 006 side a fixed or floating struture or moored to a subsea buoy. The vessel may be moored on-site for hours or several days. Liquefied or re-gasified disharge may be onduted, through the midship manifold, flexible hoses or risers. The number of tanks may be speified by the designer. While on-site no forward speed is assumed. While on-site the LNG arrier might be disonneted at any stage of the disharge operation due to an emergeny. The total design life of the vessel is divided into a period moored on-site and a trading period. or the on-site operation a minimum design life of 5 years is assumed when disharging is onduted by re-gasifiation or year when liquefied disharging is onduted. While disharging, the vessel will experiene all filling levels inside the argo tanks..6.8 Low-partially filled tank on a partiular trade route or for restrited operation The operation of the vessel while trading with tank filling levels within the approved filling range is onsidered to be a normal trading pattern, for whih the design basis is overed by.6., or.6.6 if the target vessel onerns an inreased size LNG arrier. The number of tanks may be speified by the designer. The design speed is to be speified by the designer. It is assumed that the vessel trades on a world wide basis, but the vessel may be sailing on a dediated route, whih may be more or less severe than a general trade on a world wide basis. A minimum design life of 5 years is assumed. The tank fillings are to be speified by the designer..7 Design priniples.7. Limit state design priniples The sloshing assessment is to be based on the priniples of limit state design. A limit state is defined as a ondition beyond whih the struture, or part of the struture, no longer satisfies its funtional requirements. The limit states onern the safety of life, property (ship+argo) and the environment. The following limit states should in general be onsidered. ) ULS Ultimate Limit State The ULS onerns the ability of the struture to resist the ation of the maximum expeted loads or load effets during the design life of the ship. The limit state orresponds to the maximum load-arrying apaity (or strain or deformation) under intat onditions. ) ALS Aidental Limit State The ALS onerns the ability of the struture to resist aident situations. The limit state onerns the safety of life, property and the environment in a) Intat onditions under the ation of abnormal loads. b) Damaged ondition under the ation of normal loads. 3) LS atigue Limit State The LS onerns the ability of the struture to resist timevarying (yli or repeated) loading. No abnormal environmental onditions are onsidered for the ALS, e.g. freak waves, tsunamis, years storms. The possible severe onsequenes of loss of ontainment of the membrane system, and the severe eonomial onsequenes of damages to the system impliates that the funtional requirements defining the Aidental Limit State will be the same as the ones defining the Ultimate Limit State and the atigue Limit State. The overall funtional requirements that define the limit states for the strutures governed by this Classifiation Note are: integrity of the primary and the seondary membranes the insulation system should be able to withstand the sloshing impat loads without suffering damages or exessive deformations ompromising the support of the primary and seondary membranes the inner hull struture should be able to withstand the ombined effet of global hull stresses and sloshing impat loads without ompromising the support of the tank insulation system the pump tower inluding its supports should be able to withstand the ombined effet of gravity, temperature loads, inertia loads, and drag fores indued by liquid sloshing without suffering damage..7. Safety equivalent approah.7.. General The methodology presented in this Classifiation Note is based on the priniples of safety equivalene as outlined in the DNV Rules for Classifiation of Ships Pt. Ch. Se. B305 and B306. or the sloshing exposed insulation system and hull struture omponents of membrane type LNG arriers, the equivalent safety priniple will be satisfied on a omparative basis, where the requirements to the sloshing exposed strutures of the investigated ship design or operating profile (target ase) is determined based on a omparison with similar strutures installed in onventional LNG arriers (referene ase). The details of the omparative basis, the referene ase, are speified in.6.. The hoie of a omparative approah is motivated, in partiular, by the unertainty identified in the determination of the sloshing impat loads, but also by ertain aspets of the strutural response and apaity assessment. It has the advantage that it allows for a simplified treatment of design parameters that exhibit similar qualitative behaviour in both the referene ase and the target ase. Design parameters that exhibit different qualitative behaviour in the referene and the target ase must be inluded with its orret qualitative behaviour, or the omparative assessment must be designed in suh a way that potential differenes in the qualitative behaviour of the design parameters an be disregarded..7.. Containment system and hull struture The safety equivalene assessment an be arried out on two levels of sophistiation, depending on the similarity in impat harateristis and strutural arrangement between the referene and the target ases, as well as the relationship between the sloshing impat load level in the two ases, as follows: Load omparative approah: The assessment of the target ase is arried out based on a omparison of the sloshing impat load level between the referene and the target ase. It is required that the strutural arrangement is idential between the referene ase and the target ase, and that it an be demonstrated that the sloshing impat events an be onsidered idential in terms of load area, impat pressure time histories and statistial harateristis. Appliation of the load omparative approah is limited to ases where the sloshing impat load level for the target ase is lower than for the referene ase. Strength omparative approah: The assessment of the target ase is in general based on an assessment of the strutural strength margin for the target, assuming that the strength is fully utilised for the referene ase. ore details about the two methods, and the onditions under whih they an be applied, are given in.. The ontainment system and its supporting hull struture

9 Classifiation Notes - No June 006 should be treated onsistently by utilising the same load data for the two strutures. The load level should be derived from the load apaity of the ontainment systems installed in the referene LNG arriers. The supporting inner hull struture should be dimensioned to provide at least the same support for the ontainment systems in the target LNG arrier as in the referene LNG arrier. This is to ensure that potential interation effets between the hull and the ontainment system are equal or less severe in the target ase as in the referene ase Pump tower and supports or the pump tower main struture and supports, an absolute strength approah is feasible. The sloshing loads on the pump tower are due to sloshing motion rather than sloshing impat, and the loads an therefore be assessed with a larger degree of auray than for the ontainment system and the hull struture. The response assessment is also expeted to be more aurate, sine the response of the pump tower is expeted to be quasi-stati and linear elasti. The sloshing assessment of the pump tower may therefore be arried out using either the omparative approah as desribed above, or by a diret strength assessment..7.3 Sloshing design loads The determination of the sloshing loads for assessment of ontainment system and hull strength should be based on irregular sloshing model experiments. or the pump tower, the sloshing loads may be determined from analysis. The ship motions as used for the sloshing experiments are to be determined using a verified ship motion program. The sloshing loads used in the omparative assessment are based on the worst short-term loads as enountered by the vessel during operation at sea. The sloshing loads onsidered for the assessment of the ontainment system are impat loads ating on small areas, typial box or panel sizes and smaller. Larger areas may be relevant for assessment of the hull struture. urther details of the exeution of sloshing experiments is given in Setion 3. No load ombinations are onsidered for the sloshing impat loads when assessing the ontainment system strutural integrity..7.4 Strutural response analyses To be onsistent with the priniples of the omparative assessment, the strutural response analysis methodology needs to be apable of aurately prediting the strutural response in the response range up to where damages are likely to our in the struture. Depending on the response harateristis of the onsidered struture, it may be required to onsider non-linear strutural response. The strutural response assessment needs to onsider and inlude all physial effets that affets the relative strutural response between loations relevant for the assessment of the individual failure modes, and effets that potentially give different results for the referene and the target ases. The most important effets that must be inluded are: effets of the temperature variations through the thikness of the insulation system dynami response effets. Details on how to handle these effets are given in Setion Ultimate apaity models The ultimate apaity models should be able to predit the limit states assoiated with damages to the ontainment system. All physial effets that signifiantly affets the relative strutural strength between the individual failure modes, and effets that may give different results for the referene and the target ases should be inluded in the apaity models. The most important effets that must be inluded are: effets of the temperature variations through the thikness of the insulation system strength differenes aused by differenes in the dynamis of the response. Details on how to handle these effets are given in Setion 6 for the ontainment systems..7.6 atigue apaity models The fatigue assessment of the ontainment system must be arried out using a semi-diret alulation. or onsisteny with the omparative ultimate strength assessment of the ontainment system the long term response spetrum for the target ase should be saled so that the maximum response in the spetrum orresponds to the design load used in the ultimate strength assessment. Aeptane is, however, based on diret evaluation of the alulated damage for the target ase without onsideration of the referene ase. The umulative damage (D) from repeated sloshing impats should be alulated aording to the iner-palmgren theory in ombination with S-N urves, a harateristi stress range, and a long term response distribution urve, as follows: where the summation is over a number of i stress intervals, n i is the number of load yles within eah stress interval, and N i is the number of yles to failure for the onstant stress range of that interval..7.7 Design format ni D = N i.7.7. Load omparative approah The following aeptane riterion should be satisfied in ases where the load omparative safety equivalent approah is appliable. p tar γ p tar is the sloshing impat pressure for the target LNG arrier. p ref is the sloshing impat pressure for the referene LNG arrier. γ is the partial load fator, defined in γ is the partial resistane fator, defined in The riterion should be satisfied for the entire range of load areas relevant for the unit dimensions of the ontainment system Strength omparative approah The riteria for the assessment of the equivalent safety of the argo ontainment system and hull struture between the referene and the target ase are formulated on a partial safety fator format, as follows: S is the strutural response, in general a non-linear funtion of the dynami load. p is the sloshing impat pressure saled aording to the om- i p γ ref R S( p DA γ ) γ

10 0 Classifiation Notes - No June 006 parative proedure desribed in.. DA is the dynami load fator. R is the apaity in terms of the onsidered response parameter. γ is the partial load fator, defined in γ is the partial resistane fator, defined in Pump tower assessment The strength assessment of the pump tower and supports may be arried out using either a omparative approah or an absolute approah. The absolute approah will usually be most onvenient, sine the load and strength need to be alulated for the target ase LNG arrier only. The strength is satisfatory if: Sγ S is the strutural response R is the apaity in terms of the onsidered response parameter γ is the partial load fator, defined in γ is the partial resistane fator, defined in In a diret strength assessment, the absolute magnitude of the loads is of major importane, and a thorough investigation of the loads is neessary. Larger load fators need to be used in the absolute approah than in the omparative approah, in order to aount for the unertainties related to the load level. If the omparative approah is followed, as reommended for the ontainment system and the hull strength, the load and strength of the pump tower in the referene ase are ompared with the load and strength of the pump tower in the target ase. The utilization for the target ase, multiplied with a safety fator, should be lower than for the referene ase. The strength is satisfatory if: S R tar S is the strutural response R is the apaity in terms of the onsidered response parameter γ ompare is a load fator that reflets the statistial unertainty in the omparative load assessment In the omparative approah, the unertainty related to load level is redued, sine the main onern is the load inrease from the referene ase to the target ase, rather than the absolute load level..7.8 Partial safety fators γ R γ ompare.7.8. Unertainties in the omparative approah The load and resistane fators shall be applied in the strength assessment of the target ase to reflet the unertainties in the omparative proedure and hene make sure that the safety level in the referene ase is maintained in the target ase. The main unertainties involved in the omparative strength assessment of the tank systems of the membrane type LNG arriers are: unertainties in the relative impat load assessment between the referene ase and target ase S R ref inherent unertainties in the determination of design loads from statistial analysis of sloshing impat load time histories unertainties in the determination of (long-term representative) design loads due to a limited test possibilities. (Physial limitations simply prohibit that all ship and sea state onditions an be assessed) potential differenes in saling from model to full sale in the referene and the target ase (model saling law, hydro-elasti effets) differenes in statistial distribution of sloshing impat loads between the referene and the target ase unertainies in the relative response assessment between the referene and the target ases. Applies only if the dimensioning impat area differs signifiantly between the two ases. differenes in aeptane level between the failure modes in the proedure. Applies if the governing failure mode is hanged between the referene ase and the target ase, and is aused by either: differenes in onfidene level for the governing strutural apaity differenes in the auray of the governing strutural response Load fators for strength assessment of ontainment system The load fator to be used in the strength assessment of the ontainment system for the target ase should be determined as: γ = γ γ γ 0 γ 0 reflets the inherent statistial unertainty in the experimental load assessment. γ reflets the potential differene in the saling law between impat areas of different sizes. (Saling fator is expeted to be higher for small impat areas than for large. The effet is therefore relevant only if the design area for the target ase is larger than for the referene ase.) γ reflets the possible differene in the sloshing load probability distributions between the referene and the target ase, and should in general be determined based on proessing of the load data, see 3.4, as well as a onsideration of the operational profile. Two main reasons for the possible differene are: ) The sloshing loads as derived from a short-term assessment are not onsidered identially representative for the long-term sloshing loads. ) The short-term sloshing load exeedane probability funtions for the referene and the target ase show signifiant different trends, suh that the reliability of expeted extreme values is not the same. 3) Combination of ) and ). The following paragraph explains these issues in more detail. In standard wave load analysis a wave satter diagram is used to desribe the long-term wave environment. Using linear response transfer funtions a omplete wave satter-diagram an be assessed and the long-term response amplitude distribution an be alulated. rom this distribution, the lifetime expeted extremes an be determined, e.g. with a 5 years return period or at 0-8 probability level. Another approah is to determine the most ritial sea state from the satter-diagram and assess only the short-term statistis for that sea state. or linear responses this typially leads to a differene of 0 to 0 perent. Or in other words this shortterm expeted extreme is some 0% to 0% lower than the long-term expeted extreme. However, for nonlinear respons-

11 Classifiation Notes - No June 006 es the response behaviour may be haraterised by response amplitude distributions having more flat tails (i.e. Weibull fitted funtion with low values for the slope fator). This is further disussed in Resistane fators for strength assessment of ontainment system The resistane fator to be used in the strength assessment of the ontainment system for the target ase should be determined as: γ 0 reflets the general unertainty in the response assessment proedure. γ reflets the differene in strutural redundany between impat areas of different sizes. It is expeted that the insulation systems are more redundant (have larger potential for redistribution of loads) for impats on small areas of the struture than for impats on large areas. The effet is therefore relevant only if the design load area for the target ase is larger than for the referene ase. γ reflets potential differene in statistial onfidene level in the aeptane riteria between the referene and the target ase. The fator is relevant only if the ritial failure mode hanges between the referene and the target ase Design values of load and resistane fators for ontainment system and hull struture The values of the basi load and resistane fators γ 0 and γ 0 appliable to the strength assessment of the target ase are summarised in Table -. Table - Appliable values of the basi load and resistane fators for ontainment system ULS ALS LS γ γ The remaining load and resistane fators are not speified in advane and need to be determined from the analyses Load and resistane fators for stiffness and strength assessment of hull struture The load fator to be used in the stiffness and strength assessment of the hull struture is to be taken as: γ = γ 0 γ = γ γ DA γ γ DA is a partial fator aounting for potential differene in dynami response amplifiation between the target and the referene ase. Appliable load and resistane fators for the hull struture are given in Table -. Table - Appliable values of the load and resistane fators for the hull struture ULS γ DA, hull stiffness.5 γ DA, hull strength.3 γ Load and resistane fators for pump tower and supports Appliable load and resistane fators for the pump tower and supports are given in Table -3. Table -3 Appliable values of the load and resistane fators for pump tower and supports ULS LS γ, sloshing loads.3.0 γ, wave indued loads (inertia, hull girder, pressure).5.0 γ, other loads (gravity, thermal).0.0 γ.5.0 γ ompare..0 or LS assessment, a design fatigue fator shall be used. The alulated damage, multiplied with the design fatigue fator (D), should be less than or equal to.0: D D.0 The design fatigue fator should be taken as //: D =.0 for parts aessible for inspetion D = 3.0 for parts not aessible for inspetion, but not substantial onsequene of failure D = 0.0 for parts not aessible for inspetion, and substantial onsequene of failure. Appliation of the Priniples This setion desribes the appliation of the design priniples as outlined in.7 using the design basis as given.6.. Limit state appliations This setion desribes the appliation of the limit states, as desribed in.7., to speifi LNG arrier appliations. Consideration of fatigue limit states (LS) will normally not be required for the membrane insulation systems. This onlusion is based on tehnial investigations arried out by DNV that an be generalised as a onsequene of both the harateristis of the sloshing phenomenon as well as properties of the omparative strength assessment methodology. The following harateristis of the sloshing phenomenon is important: ) Signifiant liquid sloshing motion requires a ertain level of ship motions ombined with motion periods in the same range as the natural period for the sloshing motion in the tank (resonane). The number of sloshing impats during the lifetime of a vessel is therefore low ompared to what is ommon for fatigue exposed strutures. ) Extreme sloshing impat loads do not only require the presene of extreme sloshing motion in the tank, but also requires a ertain unfavourable fluid surfae geometry at impat to avoid gas ushioning. The few high impat loads of this harater ourring during the lifetime of the vessel are signifiantly higher than the other impat loads. The long term sloshing load distribution will therefore show a rapid derease in load level with inreasing number of umulative impats. 3) Variations in wave heading and filling levels will lead to variations in the sloshing exposed loations in the tank. This will further limit the number sloshing impats per impat loation in the LNG tank. A typial shape of the long term sloshing load distribution is shown in igure -.

12 Classifiation Notes - No June 006 Saled 0 years vs 40 years response spetra 0 years operation 40 years operation Impat pressure LOG(number of yles) igure - Typial long term distribution of sloshing impat loads or load distribution like this, representative for 0 years operation, DNV investigations have shown that: the main ontribution to the umulative fatigue damage omes from the upper range of the response spetrum (the highest loads) fatigue is not a relevant failure mehanism when the hot spot stress level is governed by the ultimate strength requirements as is ensured by the omparative strength assessment. This overs most of the relevant hot-spots for the onsidered insulation systems the fatigue damage at hot spots not governed by the ultimate strength requirements is aeptable for load levels up to what is onsidered the limits for strengthening of the insulation systems. These onlusions an be extended to govern longer operational times for the target ase, e.g. 40 years operation by the following argument. A key omponent of the omparative strength assessment is the saling of the sloshing impat load distribution to math the ultimate apaity of the ontainment system for the referene ase, followed by a strengthening of the ontainment system to sustain the higher load in the target ase as is expeted when the servie life is inreased from 0 to 40 years. Consequently, the extreme response in the long term response distributions for the target ase will either be equal to or smaller than the extreme response in the referene ase (onsidering the same governing failure mode). In fat, the differene in partial safety fators between the ULS and the LS will ensure that the target ase extreme response is smaller than the referene ase extreme response. It follows from this that the long term response spetrum governing the fatigue of the target ase will be almost equal to or lower than the long term response spetrum for the referene ase in the governing upper part of the distribution. This is illustrated in igure -, whih shows a omparison of saled long term response distributions for 0 and 40 years operation. The effet of inreased servie life on the fatigue performane of the insulation systems is hene be small. These onlusions apply to vessels and operations where the long term distribution of strutural response for the target ase is governed for normal trade operation of an LNGC. This is speified in more detail in the following setions. Vessels involved in offshore loading and disharge operations as well as vessels oasionally trading with redued fillings are onsidered to fall into this ategory. Long term response distributions for the redued filling operations are onsidered governed by the less severe short term distributions..0e+00.0e+0.0e+0.0e+03.0e+04.0e+05.0e+06 Number of yles igure - Comparison of saled long term response distributions for 0 years and 40 years North Atlanti operation... Comparative design referene ase Only an ULS ondition is onsidered for this ase. No LS and ALS onditions are onsidered. Drifting in beam seas due to an engine blak-out is onsidered to our in a less severe sea state that the ULS requirements for beam seas.... ULS ondition The maximum ULS ondition to be onsidered is 0 years world-wide operation. DNV Classifiation Note 30.5 /3/ provides a wave satter diagram, whih an be used to represent the long-term world-wide wave limate. The short-term sea states are to be modelled by the two-parameter Pierson-oskowitz spetrum, see referene /3/. Waves are to be modelled as long-rested waves. Wave headings from stern quartering (45 degrees) to head waves (80 degrees) are to be onsidered. A minimum stepsize of 5 degrees is reommended. or beam sea onditions (60-0 degrees) the 0-years ontour of signifiant wave heights may be redued by 0% to reflet voluntary heading hanges in severe beam seas. or quartering sea onditions (30-60 and 0-50 degrees) the 0-years ontour of signifiant wave heights may be redued with a linear varying redution starting from 0% at 30 and 50 degrees to a redution of 0% at 60 and 0 degrees wave hading. A ballast loading ondition and a loaded ondition are to be onsidered. or the latter a fully loaded or partly loaded ondition maybe used. The loading ondition giving the severest ship motions is to be used to determine the ship motions for the sloshing analyses. The speed of the vessel is to be redued to ½ design speed. A more refined speed-sea-state urve may be used, as for example depited in igure -3. Suh alternative speed-sea-state urves are to be disussed with the Class Soiety. There are two aspets whih are of importane to onsider when applying a stepwise speed-sea-state urve in a omparative analysis. irstly, the speed an have an important effet on the sloshing impat loads. In standard wave load analysis a large ship speed gives onservative design motions and loads in an absolute strength assessment. In the present guideline a omparative approah is followed, not an absolute sloshing load and strength assessment. This implies that the hoie of a onservatively high ship speed for the referene ship implies that large sloshing loads are allowed for the target ase. Seondly, the sloshing proedure, as reommended in Setion 3, identifies the worst sea state on a ontour of signifiant wave heights and periods. Applying this proedure for the referene and the target ase

13 Classifiation Notes - No June 006 may lead to a situation where the ship speed for referene ase is higher than for the target ase, whih for some ases is unreasonable or unaeptable. Ship speed Design speed igure -3 Example speed-sea-state urve anoeuvring speed Signifiant wave height.. Inreased size LNG arrier Only an ULS ondition is onsidered for this ase, no LS and ALS onditions are onsidered.... ULS ondition The minimum ULS ondition to be onsidered is 5 years North-Atlanti operation. IACS Re. No. 34, see /4/, or DNV Classifiation Note 30.5, see /3/, provide wave satter diagrams for the North-Atlanti oean, whih an be used to represent the long-term North-Atlanti wave limate. The short-term sea states are to be modelled by the two-parameter Pierson-oskowitz spetrum, see referene /3/. Waves are to be modelled as long-rested waves. Wave headings from stern quartering (45 degr) to head waves (80 degrees) are to be onsidered. A minimum stepsize of 5 degrees is reommended. or beam sea onditions (60-0 degrees) the 5-years ontour of signifiant wave heights may be redued by 0% to reflet voluntary heading hanges in severe beam seas. or quartering sea onditions (30-60 & 0-50 degrees) the 5- years ontour of signifiant wave heights may be redued with a linear varying redution starting from 0% at 30 and 50 degrees to a redution of 0% at 60 and 0 degrees wave hading. A ballast loading ondition and a loaded ondition are to be onsidered. or the latter a fully loaded or partly loaded ondition maybe used. The loading ondition giving the severest ship motions is to be used to determine the ship motions for the sloshing analyses. The speed of the vessel is to be redued to half design speed. A more refined speed-sea-state urve may be used as disussed in Offshore loading/unloading Only ULS and ALS onditions are onsidered for this ase, no LS ondition is onsidered...3. ULS ondition The minimum ULS ondition to be onsidered is 0 years sitespeifi operation. The site speifi wave environment is to be used for the modelling of the long-term wave limate. This data should be derived from at least a 0 years wave measurement period. The short-term sea states are to be modelled by a wave spetrum, whih is representative for the offloading site. If no speifi wave spetral information is available the JONSWAP wave spetrum may be used with a peakness parameter of 3.3, see /3/. Waves are to be modelled as long-rested waves. or a bow-turret moored LNG arrier wave headings from beam seas (90 degrees) to head waves (80 degrees) are to be onsidered. A minimum stepsize of 5 degrees is reommended. A bow-turret moored LNG arrier, freely able to weathervane, is likely to experiene predominantly a head waves onditions. A low-frequeny drift study may be used to determine the probability distribution for headings from beam to head waves. Suh a study needs areful modelling or assessment of at least the following aspets: draft and trim variations joint modelling of wave, urrent and wind mooring harateristis shallow water effets (if present) (wave and ship dynamis). or an LNG arrier, whih is moored in suh a way that she is not able to weathervane, wave headings from following (0 degrees) to head waves (80 degrees) are to be onsidered. A minimum stepsize of 5 degrees is reommended. or an LNG arrier that maintains a near head waves ondition by using DP assisted mooring it is reommended to ontat the Classifiation Soiety in order to disuss a relevant set of wave headings that need to be onsidered in the sloshing experiments. A ballast loading ondition, fully loaded and intermediate loading onditions are to be onsidered. The loading ondition giving the severest ship motions is to be used to determine the ship motions for the sloshing analyses. While on-site no forward speed is to be onsidered...3. ALS ondition drifting in beam seas An emergeny situation may fore an emergeny disonnetion of the vessel from its mooring, leading to a situation where the vessel is drifting in beam seas without propulsion and manoeuvring apabilities. The minimum ALS ondition to be onsidered is year sitespeifi operation. The site speifi wave environment is to be used for the modelling of the long-term wave limate. The short-term sea states are to be modelled by a wave spetrum, whih is representative for the offloading site. If no speifi wave spetral information is available the JONSWAP wave spetrum may be used with a peakness parameter of 3.3, see /3/. Waves are to be modelled as long-rested waves. The vessel is onsidered in a beam waves ondition without forward speed. A ballast loading ondition, fully loaded and intermediate loading onditions are to be onsidered. The loading ondition giving the severest ship motions, espeially roll and sway, is to be used to determine the ship motions for the sloshing analyses ALS ondition maintaining a head sea ondition at manoeuvring speed An emergeny may give an emergeny disonnetion of the vessel from its mooring leading to a situation where it will, as soon as possible, maintain a head sea ondition with a low forward speed to maintain manoeuvrability. The minimum ALS ondition to be onsidered is years sitespeifi operation. The site speifi wave environment is to be used for the modelling of the long-term wave limate. The short-term sea states are to be modelled by a wave spetrum, whih is representative for the offloading site. If no speifi wave spetral information is available the JONSWAP wave spetrum may be used with a peakness parameter of 3.3, see /3/.

14 4 Classifiation Notes - No June 006 Waves are to be modelled as long-rested waves. The vessel is onsidered in a head waves ondition with a minimum forward speed of 5 knots. A ballast loading ondition, fully loaded and intermediate loading onditions are to be onsidered. The loading ondition giving the severest ship motions, espeially roll and sway, is to be used to determine the ship motions for the sloshing analyses...4 Low-partially filled tank on a partiular trade route or for restrited operation Only ULS and ALS onditions are onsidered for this ase, no LS ondition is onsidered...4. ULS ondition The minimum ULS ondition to be onsidered is 5 years route-speifi operation. The wave environment to be modelled is to represent the route-speifi onditions. Referene / 3/ provide wave satter-diagrams that an be used to develop a route-speifi satter diagram. If no speifi route is speified a North-Atlanti operation is to be used. IACS re.34, see /4/, or DNV Classifiation Note 30.5, see /3/, provide wave satter diagrams for the North-Atlanti oean, whih an be used to represent the long-term North-Atlanti wave limate. The short-term sea states are to be modelled by the two-parameter Pierson-oskowitz spetrum, see referene /3/. Waves are to be modelled as long-rested waves. Wave headings from stern quartering (45 degr) to head waves (80 degrees) are to be onsidered. A minimum stepsize of 5 degrees is reommended. A ballast loading ondition and a loaded ondition are to be onsidered. or the latter a fully loaded or partly loaded ondition maybe used. The loading ondition giving the severest ship motions is to be used to determine the ship motions for the sloshing analyses. The speed of the vessel is to be redued to ½ design speed. A more refined speed-sea-state urve may be used as disussed in ALS ondition drifting in beam seas An emergeny or damage may lead to a situation where the vessel is drifting in beam seas without propulsion and or manoeuvring apabilities. The minimum ALS ondition to be onsidered is year routespeifi operation. The route-speifi wave environment is to be used for the modelling of the long-term wave limate. If no speifi route is speified a North-Atlanti operation is to be used as desribed in..4.. The short-term sea states are to be modelled by a wave spetrum, whih is representative for the speifi route. If no speifi wave spetral information is available the Pierson- oskowitz wave spetrum may be used for open oean onditions and the JONSWAP wave spetrum may be used with a peakness parameter of 3.3, for sheltered and or near shore waters, see /3/. Waves are to be modelled as long-rested waves. The vessel is onsidered in a beam waves ondition without forward speed. A ballast loading ondition, fully loaded and intermediate loading onditions are to be onsidered. The loading ondition giving the severest ship motions, espeially roll and sway, is to be used to determine the ship motions for the sloshing analyses.. Strength assessment methodology The overall methodology for the omparative strength assessment of the membrane type insulation systems and its supporting hull struture are summarised in the following. The omparative aspet of the methodology lies in the assessment of the referene ase, whih is used to harmonise the load and the apaity to be onsistent with the operational experiene of membrane type LNG arriers operated to date. In pratie this is ahieved by saling the sloshing design loads, but the harmonisation also overs other systemati unertainties in the proedure. The sloshing impat load is, however, onsidered to represent the largest unertainty in the proedure. The methodology an be summarised as follows: Referene ase (see igure -4): ) Establish a urve relating sloshing impat pressure and sloshing exposed area based on experimental results as desribed in more detail in Setion 3. Load fators should be disregarded in this step. ) Establish a urve relating the impat load apaity of the insulation system and the sloshing exposed surfae area of the struture as desribed in Setion 6. Resistane fators should be disregarded in this step. 3) Establish the ratio between the load and the apaity for the entire range of load areas, and identify the maximum ratio between load and apaity. Denote this ratio by α omp. 4) Sale the load uniformly for all load areas using the maximum identified ratio between the load and the apaity. The saled load will now for any load area size be lower than the ultimate apaity of the insulation panels. This step is motivated by the damage free operational experiene with the membrane type LNG arriers. The resulting load urve should be the basis for the strength assessment of the insulation system and its supporting hull struture. Load/ Capaity igure -4 Saling of loads for referene ase to the ULS apaity Target ase (see igure -5): easured load Saled load Capaity standard Saling of load to ULS apaity Load exposed area ) Establish a urve relating sloshing impat pressure and sloshing exposed area based on experimental results as desribed in more detail in Setion 3. ) Sale the load using the maximum ratio, α omp, between load and response determined from the referene ase. 3) Carry out a strength assessment of the insulation system aording to the proedure speified in Setion 6. 4) Carry out the neessary reinforement of the insulation system so that the load for any load area is lower than the ultimate apaity of the insulation panels. 5) Carry out a strength assessment of the supporting hull struture aording to the proedure speified in Setion 6.

15 Classifiation Notes - No June 006 going through the above mentioned parameter ombination. Load/ Capaity Reinforement of insulation sysetm easured load Saled load Capaity standard Capaity reinfored Saling of load aording to referene ase igure -5 Saling of loads for target ase using the same sale fator as for the referene ase. Strengthen ontainment system aording to the saled load urve The omparative strength assessment should be arried out for all insulation struture elements that will experiene sloshing impat loads in the argo tank. In pratie this means the dediated transverse and longitudinal orner/knukle struture and standard flat wall struture adjaent to the orner/knukles. The speifi loations are determined by the appliable tank filling limitations and the operation of the vessel. A single omparative load saling fator, α omp, representative for the weakest element of the onsidered insulation strutures should be applied in the assessment of all relevant insulation strutures of the target vessel. This means that potential strength margins determined for the referene ase an be utilised in the target ase. 3. Sloshing Impat Design Loads Load exposed area 3. Environmental modelling The wave environment is to be desribed by a wave satter diagram. The satter diagram gives the probability of ourrene of short-term sea states. The basis for the satter diagram, i.e. measurements and/or observation period, is to represent the long-term wave limate. The number of ourrenes in the satter diagram should therefore be suffiiently large; for example ourrenes onsidering a duration of 3 hours per ourrene. This reveals a total duration of ~34 years. Contours with a fixed return period an be established from the wave satter diagram, like a 5 or 40 years ontour. If a return period is to be determined while the satter-diagram is established based on a lesser period of time, an extrapolation of the wave statistial data may be applied. Standard ontours are given in Table 3-. One method for establishing the ontour is the onstant probability density approah.. This is outlined in the following. irst, the joint environmental model of the sea state variables of interest is determined. Seond, the extreme value for the governing variable for the presribed return period and assoiated values for other variables are estimated, e.g. the 00-year value for H s and the onditional median for T z. Third, the ontour line is estimated from the joint model or satter diagram as the ontour of onstant probability density Table 3- Standard sea state ontours for the North-Atlanti and for world-wide operations North Atlanti IACS Re.34, /4/ North Atlanti IACS Re.34, /4/ DNV CN30.5 World-Wide, /3/ 40 years 5 years 0 years T z (s) H s (m) T z (s) H s (m) T z (s) H s (m) If another return period ontour is needed for the North-Atlanti or the world-wide satter diagram the following Weibullonditional log-normal distributions may be used to establish new ontours. f f ( H, T ) = ( H ) ( T H ) s z ( ) H s = e ( T H ) z ( H ) s s = T β H γ = s α α µ = a + a 0 z = b + 0 Table 3- Standard sea state ontours for the North-Atlanti and for world-wide operations North Atlanti IACS Re.34, /4/ DNV CN30.5 World-Wide, /3/ α β γ a a a b b b s z β H γ s α ln T z µ e π β β H γ s α e a H s b b H s s

16 6 Classifiation Notes - No June 006 The short-term sea states are desribed by a wave spetrum, whih is a funtion of the mean wave period and a signifiant wave height. Different wave spetra may be used depending on the ondition that is investigated, see.. Reommendations for wave spetral formulation are given in /3/. 3. Ship motion alulation for sloshing tests The motions for a sloshing test are to be determined by a dediated ship motion analysis using a verified and validated omputer ode reognized by the Class Soiety. The preditions are to provide linear ship motion transfer funtions, whih an be used to generate tank motions for speified short-term sea states. The ship motion alulations are to be onduted for the loading ondition and speed as speified for the assoiated sloshing test. In head and near head waves the surge motion is an important motion or exitation mode for sloshing. The surge motion equation is to be modelled properly in the ode. It is therefore reommended to use a 3-dimensional ship motion program. In quartering and beam seas the roll motion is an important motion or exitation mode for sloshing. Roll damping, additional to the potential damping, is to be aounted for in the roll motion predition. The effets of bilge keels, eddies, fins, skegs, et. and their possible speed dependene is to be inluded. This inlusion an be done using linearization tehniques. This linearization may be done for varying sea state severities. The oupled motion effet due to partially filled tanks may be inluded in the motion preditions. In ase of a vessel moored side-by-side with another vessel the hydrodynami interation is to be taken into aount in the motion preditions. Irregular time series of the ship in a seaway are to be alulated by ombining a speified wave spetrum with the motion transfer funtions. The alulated motions are to be alulated for the motion referene point of the sloshing rig. The motions are to be roude-saled for input to the sloshing rig. Repetition of the irregular motions of the tank are to be avoided. This an easily be ahieved by using an inverse ourier approah using a very small frequeny stepsize, i.e. a large number of frequeny omponents. Alternatively, the irregular time series an be omposed by a linear superposition of harmoni omponents with unequidistant frequeny stepsizes. 3.3 Sloshing model experiments Sloshing model experiments are tests where a model of a ship tank is plaed on a motion platform, whih simulates the motions of a ship in a seaway. The model tank is filled with liquid and is equipped with pressure transduers to measure the fluid pressures inside the tank. Sloshing model experiments are to be arried out in a laboratory environment with the neessary safety failities and regulations Sloshing experimental lay-out Sloshing experiments require a motion platform apable or simulating the motions of the tank on-board a ship in a seaway. The motion platform should be able to simulate both regular and irregular motions as speified by time series from a ship motion analysis. The maximum strokes and angles for the motion platform are to be designed suh that the worst ship motions antiipated for the intended sloshing tank model size an be simulated. It is reommended not to dimension the rig apabilities only by regular maximum expeted motion amplitudes. Espeially in beam sea onditions, the ombination of large heave, large sway and large roll angles is expeted to set apability envelope for the rig. The motion ontrol needs to be designed suh that the speified ship motions an aurately be simulated. The motion platform, loaded with its maximum payload, is to be equipped with a motion response unit to verify if the generated tank motions orrespond with the input motion signals. The size of the motion platform is preferably as large as possible. At least a sale of :50 for the sloshing model test tank should be used. Preferably a six-degrees of freedom motion platform is to be used. or a proper omparative approah the sloshing tests need to be exeuted at the same model sale and model test set-up for the referene ase and the target ase. The sloshing model tank is to be made suffiiently stiff suh that natural frequenies of the tank and its parts do not interfere with the sloshing impat pressures. It is reommended to manufature the sloshing model test tank of transparent material suh that the behaviour of the fluid motions in the tank an be observed. The sloshing model tank is to be prepared for the mounting of pressure sensors, single and luster-wise, at various loations throughout the tank in order to be able to measure sloshing pressures at possible ritial areas. The loal struture of the tank, where pressure transduers an be positioned, are to be suffiiently stiff to avoid fluid-struture interation. The sloshing model test tank should be equipped with filling and emptying taps, suh that level adjustments are made easily and aurately. At high filling (~95% of tank height) signifiant differenes in impat pressures an be measured for small filling differenes. Consequently, the auray of the filling level is an important aspet. In ase sloshing tests are to be onduted with varying ullage gas onditions the sloshing model tank struture should be designed for depressurisation. The sloshing model tank should be prepared with taps for gas filling and emptying. When using different gases or fluids to vary the ullage or fluid onditions inside the tank, preparations must be made to ontain the gases or fluids after testing to onform with environmental regulations if appliable Saling of sloshing pressures ullage gas and fluid onditions The appliation of a omparative approah as outlined in. for the assessment of the ontainment strutural strength does not require a saling of the sloshing model-test pressures to full-sale. Sloshing model-test studies investigating sloshing impat pressures for various ullage onditions, see e.g. /5/, indiate that the saling may be a funtion of, among other aspets, the load area. In ase the omparative approah results in different ritial load areas for the referene and the target ase the potential differene in saling is to be addressed addresses this aspet with the load fator γ. In order to be onsistent in a omparative approah the model sale for the referene ase and the target ase is to be equal as well as the fluid and ullage onditions. Sloshing impats may show an osillating behaviour in the time history of the sloshing impat pressure, aused by entrapped gas. It is reommended to apply a similar saling for sloshing impats with or without this osillating behaviour, unless experiments and doumentation may argument a hange of saling Instrumentation and data aquisition Pressure transduers are to be mounted to measure the fluid pressures inside the tank. The sensing area should be positioned flush with the inner tank wall. The shok resistane of pressure sensors should be suffiient not to interfere with the impats and aelerations expeted.

17 Classifiation Notes - No June 006 The pressure sensors should be appliable in a wet and/or orrosive environment. The rated pressures and the maximum measurable pressure should be suffiiently above the expeted pressures, whih will be measured inside the tank. The frequeny response of the pressure sensor and signal amplifier must be suffiiently high to apture the pressure flutuations at least at the intended sampling frequeny, i.e. the signal should not be onditioned. The pressure sensors should preferably be suffiiently insensitive to temperature flutuations or this should be orreted for in the testing. The sensing area should be in diret ontat with the medium inside the tank. No protetive over or similar aps are to be used, whih an affet the dynamis of the measurements. Pressure transduers should be alibrated before use. In addition to a stati alibration, a dynami alibration is reommended. This an be aomplished by use of drop-tests, where the pressure sensors are mounted in a wedge-shaped setion being dropped down onto a flat water surfae. The temporal and spatial shapes of the pressure pulse are funtions of the impat veloity and wedge deadrise angle. They an easily be aurately alulated for a small deadrise angle, and provide an exellent means of assessing the pressure sensor performane. The size of pressure transduers should be small to be able to measure loal impat pressures and to be able to position several pressure transduers lose together. At least 9 sensors should over a full-sale square area of.5 m. Common hotspots for impat loads are at intersetions between the tank roof or hamfers and the tank walls. The sensors should be plaed suffiiently lose to these intersetions so that the orner panels are overed. A 4x4 luster of sensors (6 total) should be used in order to failitate a load versus area estimate based on 9 sensors for both the perimeter zone and the internal area exluding orner boxes. The data aquisition system should be able to sample the pressure sensors at a suffiiently high sampling rate to apture short impat pressure time histories. Typially sampling rates of ~0 khz to ~0 khz are required for sloshing tests at sales of :5 to :50 respetively. The pressure time histories and the tank motion histories are to be stored as raw data for further post-proessing. Video apturing of the sloshing tests is reommended in order to study the resulting fluid behaviour inside the tank for speifi onditions, like for example the wave heading, the sea state, the filling level, etetera Data analysis statistial post-proessing The stored pressure time histories are to be statistially postproessed to determine impat pressure statistis. The sloshing impat peaks in the time series are to be identified. A peak-over-threshold method is reommended to identify the impat peaks and separate them from noise in the signal. axima are to be identified as illustrated in igure 3-. A moving time window may be used to identify only these global maxima within the window settings. Alternatively a minimum required time-step between global impat peaks may be set. A variation of the moving window size and the threshold is reommended to identify parameters for these suh that reliable results and onverging results are obtained. Pressure Threshold oving window Identified maximum igure 3- Identifiation of loal sloshing impat maxima Time A histogram of the identified sloshing impat is to be determined. A large number of bins are defined from zero to the largest impat pressure measured. All the identified peaks are sorted in these bins in order to establish the histogram. When normalising the area under the histogram the disrete probability density funtion (pdf) is obtained. Integration of the PD gives the umulative distribution funtion (CD). Given the ourrene of an impat peak, the CD gives the probability that this peak is lower than a given pressure value. Sine the main interest is in the extreme values the CD is preferably presented in the form of the Exeedane Probability untion (EP) on a logarithmi sale. igure 3- illustrates the various probability funtions. or further details about the theory of probability funtions one is referred to handbooks on statistis and stohastis.

18 8 Classifiation Notes - No June 006 Number of impats mathematial funtions has a fundamental relation to the physis dominating the randomness of the impats. A mathematial fit should be plotted together with the disrete data. A mathematial fit may be easy to use for further mathematial proessing. When omparing two different ases the response periods may differ and hene the EP plots may be diffiult to ompare. It is then reommended to normalise the EP by dividing the probabilities by the response period. The EP then gives the probability that a peak exeeds a given pressure value per unit time. A return period level in this figure has the same probability level irrespetive of the response period. PD Normalising Pressure Expeted extreme to our in h Expeted extreme to our in 3 h Expeted extreme to our in 30 hours 0.0 Sloshing impat pressure peaks Pressure Partial integration CD.0 Exeedane probability (/s) hour return i d 3 hours 30 hours Inverse Pressure Pressure igure 3-3 Example EP with 3 different return periods EP igure 3- Shemati proedure to determine sloshing impat peak pressure probability funtions rom the peak identifiation proess the total number of identified sloshing impat peaks is obtained. The total time duration in whih these peaks ourred is known as well, hene the average time between suessive sloshing impat peaks an be alulated. This average time is often alled the response period. The response period is to be used to determine probability levels in the EP plot for speified return period(s), sine for large N the probability of exeedane is given as /N. Using the mean enounter wave period or the mean enounter period of a typial ship motion mode as response period an give erroneous results. or example in some onditions only the severest wave or motion sequenes may give impat reordings, whih leads to only a small number of identified sloshing impat peaks per time, whih implies a muh larger response period than for example the mean wave period. Expeted extremes to our in a speified return period may be estimated when defining return periods in the EP plots. An example plot is given in igure 3-3. itting of the disrete statistial data may be done using a mathematial funtion, like the Weibull or the Pareto distribution. It should be remembered however that none of those When onduting a series of irregular sloshing experiments for an idential ondition, the probability funtions per test run may be obtained. These an be ombined using statistial theory to determine the probability funtions for the entire test duration, whih is the sum of the individual runs. An aurate estimation of the expeted extremes for large return periods require that sloshing tests are onduted for suffiiently long duration. A test duration of X hours is normally not suffiient to estimate the expeted extreme to our in X hours. But this is highly dependent on the unertainty in the extreme value data. igure 3-4 shows two example EP plots for different ases. As seen the data is believed to be suffiiently aurate to estimate the expeted extremes in and 3 hours, but for a 30 hours period the slopes of the two urves are very muh different and by that the unertainty in the extreme value estimates. Exeedane probability (/s) Sloshing impat pressure peaks Referene ase Target ase hour return period 3 hours 30 hours igure 3-4 Two example EPs illustrating the variation in extreme value unertainty The statistial post-proessing proedures as outlined in this

19 Classifiation Notes - No June 006 paragraph applies to the measurements of single pressure sensor but is likewise to be applied to the pressure histories resulting from a summation/integration of a luster of pressure sensors. The average pressure history on an area may be determined by a (weighed) sum of the individual pressure sensor time histories positioned in the speified area. It is to be noted that the appliation of this pressure history in a strutural response dynami analysis may give different results than a diret appliation of the individual pressure sensor time histories. After onduting a statistial post-proessing of single sensors and lusters of sensors the expeted extreme impat pressures are to be plotted as a funtion of load area. igure 3-5 gives an example. Pressure Peak value Threshold Impulse=?p(t)dt Time Expeted extreme impat pressure Referene ase Target ase igure 3-6 Charaterisation of sloshing impat peak Pressure ½ Peak value Rise time Load area (m) igure 3-5 Example urves of expeted extreme impat pressures as a funtion of load area Peak value rom the pressure sensor time histories the harateristis of the single impats an be determined. igure 3-6 shows the main harateristis, whih are to be determined. The rise-time is the time from the start of the impat to the time of the maximum peak. or some impats this definition is not straightforward enough, as the slope of the impat may vary signifiantly. In order to avoid suh ases it may be more appropriate to define the rise time as twie the time from half the peak value to the peak value, see igure 3-7. The impulse is defined as the pressure integration of the impat. It is reommended to plot the sloshing impat peak values and the assoiated rise times for both the target and referene ase in one figure. See an example in igure 3-8. Suh a figure gives information on the possible differenes in rise times between the referene and target ase, whih might have an effet on the strutural responses. The alulated rise-time should be verified for the 0 largest impats for the design ases by a visual inspetion of the pressure time traes. ½ rise time igure 3-7 Alternative definition of rise time Time igure 3-8 Comparison of sloshing impat peak values and assoiated rise times for a referene and a target ase. The impat pressure peak values are normalized by the expeted extreme impat pressure 3.4 Sloshing design loads Based on the set of ship and environmental onditions a sloshing test experimental programme is omposed. The testing is divided into a sreening phase and a design phase. The sreen-

20 0 Classifiation Notes - No June 006 ing phase is to evaluate all the possible ombinations of filling levels, wave headings, etetera to identify the sea state giving the worst sloshing impat loads. The sreening proess is not straightforward. The number of test ases needs to be limited, and the seletion of ritial ases is based on a slowly onverging statistial estimate of the impat load indiator This indiator an be seleted in different ways. One option is to look at the harateristi impat pressure from eah sensor separately. This is onsistent with how the design loads are found. The obvious drawbak of this approah is that a single test with a duration of 5 hours full-sale gives a large unertainty of the expeted extreme single-sensor pressure, and thus is a weak basis for ritial ase seletion. An alternative is to ombine the single sensor measurements, i.e. the event maximum from eah sensor luster is used a basis for the statistial expeted extreme estimate. Only the maximum peak pressure reorded among the sensors in the luster is ounted eah time an impat ours. This approah impliitly assumes that the position of the high pressure is of seondary importane. The benefit is a muh larger number of reorded peak pressures whih gives a smaller variability in the expeted extreme pressure. A third alternative is to look at the average pressure over a larger area, for instane a grid of sensors in a orner hot-spot. Ideally, both single-sensor and larger area based expeted extreme pressures should be found during sreening. If the trends vary with area, the ritial ase seletion should reflet any previous experiene regarding ritial loading area size. Based on the results from the sreening phase the design ondition(s) are determined. These design onditions are tested for a long duration in order to obtain suffiient data for proper statistial analysis of the sloshing impat loads. Signifiant wave height Sreening tests Wave period Long-term ontour of H s and T z igure 3-9 Sloshing sreening proedure to identify worst sea state Signifiant wave height igure 3-0 Identified sloshing design ases Design ase Wave period Additional design ases Long-term ontour of H s and T z In.7.8. load fators are disussed, where γ is introdued to reflet the differene in the statistial distribution between the referene and the target ase. In igure 3-4 the expeted extremes for the referene and target ase are nearly similar, however the unertainty in both is signifiantly different, hene a load fator larger than.0 should be applied in this ase. In order to determine a proper load fator, γ, a number of aspets needs to be onsidered: ) It should be investigated if the likelihood that the referene vessel will enounter the design sea state is equal to the likelihood that the target ase enounters its design sea state. Let s onsider for example that the referene ase in igure 3-4 represents a 95% H filling ase in a head waves situation, whereas the target ase represents a 5% H filling ase in beam sea ondition for a weather-vaning offshore disharging vessel. It an then be argued that the likelihood for the target ase meeting this partiular ase is lower than the likelihood for the referene ase. ) It should be investigated if the sloshing loads from the short-term design sea state assessment for the referene and target ase are likewise long-term representative. It is reommended to determine as well the sloshing design impats for idential ship and sea state onditions but with lower sea state severity, as illustrated in igure 3-0. Alternatively a sreening proedure is redone for a lower ontour, resulting in possibly a different design sea state. This testing an give information on the expeted extreme impat pressures as a funtion of sea states severity for the referene and the target ase. Combining this information with the sea state probabilities it an be investigated if the ratio between the short-term extreme values an be assumed to be lifetime representative. How well the sloshing load estimate based on a short-term assessment represents the sought long-term value will be illustrated in the following. Nonlinear responses like sloshing indued impat pressures may be haraterised by response amplitude distributions having flat tails (i.e. Weibull fitted funtion with low values for the slope fator). The figure below shows some example urves with varying slope parameters. or linear responses the amplitude distribution is given by the Rayleigh distribution.

21 Classifiation Notes - No June 006 Exeedane probability.0e+00.0e-0.0e-0.0e-03.0e-04.0e-05.0e-06.0e-07.0e-08 Amplitude Rayleigh (slope=.0) Weibull (slope=.4) Weibull (slope=0.8) igure 3- Example figure showing effet of the Weibull slope fator When the response is haraterised by more flat tails the differene in determining a short-term or a long-term extreme is larger than 0% to 0%. Typially the sloshing impat pressure amplitude distribution an be modelled by a Weibull funtion with a slope less than.0. Consequently, by testing only the worst sea state the short-term expeted extreme is not representative for the lifetime expeted extreme but signifiantly lower. The example below desribes this harater in more detail. Note: Consider the North Atlanti wave satter diagram as given by IACS Reommendation No. 34, see /4/. Assume that sloshing sreening tests have been done along the 40 years ontour of H s and T z. The worst sea state is found to be given by T z = 8.5 s and H s =.8 m (as an example). It is assumed that the expeted short-term extreme is 5 bar and that the impat pressure amplitude exeedane probability urve an be modelled by a -parameter Weibull funtion Q(p a ) with a sale fator α = and a slope fator β = 0.6, whih typially an be observed from sloshing experiments. β p α a Q p = a e ( ) rom the IACS Reommendation No. 34 satter diagram a seletion of sea states is taken, see Table 3-3. (NOTE: The number of observations is adjusted in order to math a 40 years duration, i.e observations orresponds to 34 years) Table 3-3 Sea state seletion from IACS re.34 H s Number of observations during 40 years (T z = 8.5 s) SU rom sloshing tests it is observed that expeted short-term extremes vary more-or-less linearly with the signifiant wave height. Seondly, the slope parameter varies little for varying signifiant wave heights. Hene Weibull funtions an be modelled for lower signifiant wave height with idential slopes and with sale fators linearly saled by the signifiant wave height. (Note: expeted extremes are linearly related to the sale fator for Weibull distributed responses). These Weibull funtions are modelled for the seleted sea states of Table 3-3. The resulting long-term exeedane probability urve is then determined by the weighted sum of these individual Weibull funtions aording to: Qlong term ( p ) w Q ( p H ) p( H ) a = j= Hs, j s, j s, j Q( p a ) is the exeedane probability funtion of sloshing impat peak values T wh = s, j TH is the weighing fator to aount for relative number of yles (= sine all response periods are taken equal to 8.5 seonds) T is the average period between impats (long-term) T H s, j = average period between impats for sea state j p(h s,j ) = short-term sea state probability Here it is assumed that the number of impats per time is equal for all sea states and is taken equal to the wave period, i.e. 8.5 seonds. or the 40 years storm ondition a return period of 3 hours results in an exeedane probability level of 7.87 E-4. The sum of observation from Table 3-3 is 3 65 for a 40 years period. This orresponds then to a return period of 3 months, whih results in an exeedane probability level of.49 E-7. igure 3- shows the short-term exeedane probability urve for the 40 years storm ondition (H s =.8 m) and the long-term exeedane probability urve as the weighted sum of the seletion of sea states. When deriving the expeted extremes it is seen that the long-term value is almost twie as large as the short-term value (.93). rom this example it is believed that the testing of only the worst 40 years storm ondition and determining the expeted 3 hours extreme is a signifiant underpredition of the expeted lifetime extreme. Exeedane probability.0e-0.0e-0.0e-03.0e-04.0e-05.0e-06.0e-07.0e-08 igure 3- Short-term and long-term exeedane probability urves (Weibull slope = 0.6) or ompleteness an additional example is shown, where the Weibull funtion is modelled with a slope fator β =.0, whih orresponds to the Rayleigh distribution as usually applied for linear ship responses. igure 3-3 shows the results from whih it is seen that the long-term extreme is only slightly larger than the short-term extreme (.04). st s, j E+00 Short-term urve - 40 years sea state 5 bar a Pressure (bar) 3 hours return period 'Long-term' urve 3 months return period 9 bar

22 Classifiation Notes - No June 006 Exeedane probability E+00 Short-term urve - 40 years sea state.0e-0.0e-0.0e-03.0e-04.0e-05.0e-06.0e-07.0e-08 5 bar 5.6 b Pressure (bar) igure 3-3 Short-term and long-term exeedane probability urves (Weibull slope =.0) ---e-n-d---of---n-o-t-e Pump Tower Design Loads 4. Identifiation of relevant loads The loads relevant for the dimensioning of the pump tower are due to the ship motion, the motion of the LNG in the argo tanks, and the temperature of the argo. Loads that may need to be inluded in the strength assessment are hene: sloshing loads gravity and inertia loads thermal loads hull girder loads (for liquid dome area and for base support) internal tank pressure and external sea pressure (for base support). A desription of eah load type is given in the following setions. 4. Sloshing loads Sloshing loads on the pump tower struture our due to motion of the liquid inside the argo tanks. Usually, tank no. is onsidered to be ritial for sloshing, i.e. having the maximum sloshing motion, due to size and distane from the ship s enter of rotation. However, both tank no. and tank no. need to be onsidered, to determine whih one is most ritial with respet to the ombined effet of sloshing loads and inertia loads. The sloshing loads are to be determined using model testing or numerial analyses by omputational fluid dynamis (CD). Irregular motions are to be onsidered. 4.. Load onditions and filling levels The sloshing loads should be onsidered for various filling levels aording to the ship s filling restritions. or normal filling restritions (less than 0% L, above 70% H), the following filling levels should be onsidered: 0% L 70% H, 80% H, 90% H and 95% H. or unrestrited filling, the following intermediate filling levels should also be onsidered: 0% H, 30% H, 40% H, 50% H, 60% H. 3 hours return period 'Long-term' urve 3 months return period The ship loading onditions that are onsidered to be ritial for sloshing motion in the tanks must be determined. Loading onditions that may need to be onsidered are: full load ondition ballast ondition part load ondition, with all tanks equally filled part load ondition, with one tank partly filled and other tanks empty. 4.. Environmental onditions The speed of the vessel is to be redued to ½ design speed. A more refined speed-sea-state urve may be used, as depited in igure -3. If a omparative approah is used, there are two aspets whih are of importane to onsider when applying a stepwise speed-sea-state urve. irstly, the speed an have an important effet on the sloshing loads. In standard wave load analysis a large ship speed gives onservative design motions and loads in an absolute strength assessment. Seondly, the sloshing proedure identifies the worst sea state on a ontour of signifiant wave heights and periods. Applying this proedure for the referene and the target ase may lead to a situation where the ship speed for referene ase is higher than for the target ase, whih for some ases is non-onservative. or alulation of LS loads, an operational profile through the lifetime of the ship must be assumed. Critial wave headings must be determined. In priniple, all headings 0º to 80º should be onsidered for all filling levels. The sea states that are ritial for sloshing motion in the tanks must be determined. A satter diagram is used to desribe the probability of ourrene of short-term sea states. The North Atlanti satter diagram should be used, as given in /3/. The short-term sea states are desribed by a wave spetrum. The Pierson-oskowitz spetrum may be used, in ombination with a osine squared wave spreading funtion. or the relevant loading onditions, ship motion analyses are to be arried out. The analyses are to provide linear ship motion transfer funtions, whih an be used to generate ship motions for speified sea states. The tank motions are then alulated by aounting for the distane from the ship s rotational enter to the enter of the tank. or the sea states assumed to be ritial with respet to sloshing motion, irregular time series of motion are to be alulated using the ship motion transfer funtions. The sloshing loads on the pump tower frame struture due to the irregular tank motions are then determined, using experiments or analyses. Expeted extreme loads are to be determined for a duration of not less than 3 hours Load predition Based on the set of ship and environmental onditions a sloshing test experimental or alulation programme is omposed. The testing is divided into a sreening phase and a design phase. The sreening phase is to evaluate all the relevant ombinations of loading ondition, filling level and wave heading to identify the sea state giving the worst sloshing loads. Based on the results from the sreening phase the design ondition(s) are determined. These design onditions are tested or alulated for a long duration in order to obtain suffiient data for proper statistial analysis of the sloshing loads. The proedure desribed in is reommended for statistial post-proessing of the load time histories. The 5 years ontour of signifiant wave height and period of this satter diagram may be used to identify the worst onditions for the sloshing motion. or beam sea onditions, the 5 years ontour may be redued by 0% to reflet voluntary heading hanges in severe beam seas. The sloshing load for the ULS assessment should be taken as the load ourring one during the lifetime of the ship, as determined from the long-term load distribution. The atual longterm distribution of sloshing loads should in priniple be determined as a weighted sum over all the sea states given in the satter diagram and all headings onsidered, as explained in The proedure may also be found in the DNV Classi-

23 Classifiation Notes - No June 006 fiation Note 30.7 /6/. If no evaluation of the long term distribution is made, the ULS load may be determined by inreasing the load alulated for the ritial short-term sea state by a fator of.5: The short term values are based on a 5 years ontour. The fator may be used in ase of normal filling operations. or evaluation of unrestrited filling, speial onsiderations are to be made of the long term distribution Establish long term distribution In order to establish the long-term distribution of sloshing loads, the umulative distribution may be estimated by a weighted sum over the sea states used for estimating the sloshing load. The long-term stress range distribution is then alulated from, p ij r ij =ν ij /ν 0 seastates headings ν 0 = ν ν = ij p ij i= j= π m m p long term =. 5 seastates headings ij i= j= short term is the probability of ourrene of a given sea state i ombined with a heading j. is the ratio between the response rossing rates in a given sea state and the average rossing rate. is the average rossing rate. is the response zero-rossing rate in sea state i and heading j. Q() ij is the Weibull distribution from the experiment or CD alulation in sea state i ombined with heading j. or the ase of unrestrited filling, speial onsideration of the long term value of the load should be made. The LS assessment is to be arried out using the same longterm load distribution as applied for the ULS assessment Simplified long term distribution Alternatively, the long-term distribution for LS may for simpliity be assumed as a Weibull distribution: where Q() is the probability of exeedane of the stress, h is the shape parameter, and q is the sale parameter, defined as where 0 is the referene stress value exeeded one out of n 0 yles. The shape fator should be taken as h = Sloshing experiments and analysis The sloshing loads on the pump tower resulting from the applied tank motion are a funtion of the liquid veloities and aelerations. The veloities and if possible aelerations should be determined at several vertial loations along the midpoint p Q ( ) = r Q ij 0ij ij ij Q( ) = exp q 0 q = / h (ln n0 ) ( ) p h ij of the tower, i.e. along the z-axis indiated in igure 4-. Transverse bulkhead Disharge pipe Disharge pipe y loat level gauge illing pipe Emergeny pipe igure 4- Illustration of pump tower lay-out and oordinate system The fluid fores on the pump tower struture may be assumed to be drag dominated, so that the fluid aeleration is of seondary importane relative to the fluid veloity. The veloities and aelerations may be determined by one of the following methods: experimental tests analysis with omputational fluid dynamis (CD). The fores ating on the atual pump tower an then be alulated using orison s equation, as explained in luid veloities and aelerations based on experiments The experiments should failitate veloity estimates at least ten points along the vertial axis. A diret flow veloity measurement an be ahieved by use of Partile Image Veloimetry (PIV). The fluid is seeded with tiny refletive partiles with density lose to that of the fluid. The partiles are assumed to follow the flow, and they are illuminated by e.g. a laser sheet. One or more ameras are used to apture two frames within a short instant. With two ameras in a stereosopi setup, partile displaements along all three axes an be found. The veloity field in the imaged part of the laser sheet is typially found based on partile displaements from a ross-orrelation analysis and the time separation between the images. The hallenge of light refletion from the free surfae an be partly overome by use of fluoresent partiles. PIV an also be used to estimate fluid aelerations. An alternative to a diret veloity measurement method is given in the following example. The setup is illustrated in igure 4-. The bending moment in a pipe loated in the tank is measured with strain gauges positioned to measure vertial strain. ore transduers should be fitted at top and bottom, in order to measure the total reation fores on the pipe. By fitting for instane a spline funtion to the measured bending moments, the shear fore is found as the derivative of the moment. By requiring fore balane for a pipe segment, the differene in shear fore at the end of the segment equals the external fore on the segment. This external fore ontains gravity, inertia, buoyany and hydrodynami omponents. The inertia effet may be found by measuring the aeleration by an aelerometer. The gravity and buoyany must also be aounted for. Then the fluid fore on the segment is obtained. or estimation of the fluid veloities and aelerations, orison s equation an be used. Again, drag may be assumed to dominate the fluid fores on the pump tower struture. x

24 4 Classifiation Notes - No June 006 The post-proessing desribed in should be arried out on eah of these time series, in order to determine design bending moment and reation fores. rom these, the ritial time instants for top and bottom support and main struture may be determined. The veloity fields at eah of these time instants should be seleted for the strutural analysis, and the sloshing loads ating on all strutural members at these instanes should be applied to the strutural model. Pumptower loation Tank roof Chamfer igure 4- Example of test setup for pump tower loads onitoring loations for veloity and aeleration luid veloities and aelerations from CD If analyses are arried out using CD, the following requirements should be fulfilled: The adequay of the program used is to be doumented, espeially for low filling heights where breaking waves are expeted. The adequay is strongly related to the treatment of the free surfae. To ensure that the software is apable of desribing the physial sloshing phenomenon, the CD software should be verified with model tests. The program should be apable of handling irregular tank motions and long simulation length. Requirements related to modelling, mesh, and time step are to be given areful onsideration. The requirements are important for numerial stability and an adequate disretisation of the problem whih an provide a physial solution. or alulations with an Eulerian grid, the disretisation is reommended to be at least 40 elements in lengthwise diretion, 40 elements along the tank breadth and 30 elements in the vertial diretion. Veloities and aelerations in the liquid at the loation of the pump tower is to be determined. The veloities and aelerations may be alulated for a vertial axis loated on the mean distane between the disharge pipes and the emergeny pipe. The loads will vary in the vertial diretion, but for eah vertial position the veloities and aelerations may be taken as equal for all the pipes. The number of positions should be suffiient to desribe the flow field along the pump tower length aurately. Typially more than 0 positions should be used Load alulation from fluid veloity and aeleration Based on the time series of the veloity field, the time instant of maximum bending moment and upper and lower reation fore are determined. aximum bending moment and reation fore should be onsidered both for the longitudinal diretion and the transverse diretion. igure 4-3 onitoring loations for veloities and aelerations The loads on the pump tower segment are then alulated using orison s equation, as desribed in /3/. The fore ating on a part of a member is where ρ L is liquid density, C m is added mass oeffiient, V is volume of liquid displaed by the part, a is partile aeleration normal to the member axis, C D is drag oeffiient, v is liquid partile veloity normal to the member axis, and A is area of the part projeted onto a plane normal to fore diretion. Values of C D and C m should be determined for eah strutural member aording to reommendations given in /3/. or a ylindrial tube C m is to be taken as.0. It should be noted that for osillatory motions, C D is a funtion of the K C -number, Keel = ρ L ( + Cm ) Va + ρ LC Dv v A K C = U T / D D = diameter of pipe T = sloshing wave period U = maximum sloshing veloity The drag oeffiient may be taken from igure 4-4, /3/.

25 Classifiation Notes - No June 006 igure 4-4 Drag oeffiient C D as funtion of K C for ylinders in waves, Re > or ylinders that are lose together, suh as the emergeny pipe and the filling pipe, group effets may be taken into aount when determining the drag oeffiients. If no doumentation of the group effet is available, the drag oeffiients for the individual ylinders should be used. When the load on eah segment is determined, a beam model may be used to determine top and bottom support fores and bending moments. The boundary ondition of this model should reflet the atual boundary onditions of the pump tower. 4.3 Inertia and gravity loads Inertia loads on the pump tower are due to the aelerations of the vessel. Translational tank aelerations due to the pith and roll aelerations of the ship is to be aounted for. Weight of liquid inside the pipes should be inluded in the alulation of inertia loads. Gravity loads are due to the self-weight of the pump tower, and due to the roll and pith motion of the ship. When the gravity loads are alulated, the buoyany of the pipes should be deduted. or inertia and gravity loads, the pump tower in tank no. is usually the most ritial, due to its distane from the ship enter of motion. However, both tank no. and tank no. need to be onsidered, in order to determine whih one is most ritial with respet to the ombined effet of sloshing loads and inertia loads. The ombined effet of sloshing and inertia load is to be summed as a total load. or both inertia load and gravity load alulation, the weight of additional elements (strutural members and equipment) that are not inluded in the finite element model used for the response analysis should be inluded as lumped or distributed masses. The ship loading onditions that are onsidered to be ritial with respet to ship aelerations and motions must be determined. The loading onditions that need to be onsidered are given in 4... or alulation of LS loads, an operational profile through the lifetime of the ship must be assumed. The sea states that are onsidered to be ritial for ship aelerations and motions must be determined. A satterdiagram is used to desribe the probability of ourrene of short-term sea states. The North Atlanti satter diagram should be used, as given in /3/. The short-term sea states are desribed by a wave spetrum. The Pierson-oskowitz spetrum may be used. A osine squared wave spreading funtion may be assumed. Critial wave headings must be determined. All headings between 0º and 80º should be onsidered for all relevant loading onditions. The long-term distribution of inertia and gravity loads should be determined as a weighted sum over all sea states given in the satter diagram and all headings, as explained in DNV Classifiation Note 30.7 /6/. The loads to be used for the ULS assessment are to be taken as the load ourring one during the lifetime of the ship. The LS assessment is to be arried out using the atual long-term load distribution. or the relevant loading onditions, ship motion analyses are to be arried out. The analyses are to provide linear ship motion transfer funtions, whih an be used to generate ship motions for speified sea states. The inertia and gravity loads may be alulated for a vertial axis loated on the mean distane between the disharge pipes and the emergeny pipe. The loads will vary in the vertial diretion, but for eah vertial position the aelerations may be taken as equal for all pipes. 4.4 Thermal loads Thermal loads are due to thermal shrinkage of the pump tower material in the low temperature ondition, relative to the room temperature ondition. The temperature effet is most important for the upper and lower supports of the pump tower. or eah filling level onsidered, the temperature distribution over the height of the pump tower is to be determined. or filling levels above 70%H, the temperature an be taken as onstant and equal to -63ºC. or filling levels below 0% L, the temperature of the submerged part of the pump tower an be taken as -63ºC, while the temperature of the non-submerged part an be assumed to vary linearly from -63ºC at the liquid surfae to -30ºC at the top of the pump tower. The initial temperature of the steel an be taken as 0ºC. Thermal expansion oeffiients relevant for the pump tower material should be applied. Stainless steel is usually applied. aterial properties for the stainless steel 304L are given in 8.. The temperature field should be applied to the E model used for the response analysis, in order to determine the stress field in the struture resulting from the thermal shrinkage. Low-yle fatigue due to yli variation of the thermal stresses between the empty and loaded ondition may need to be inluded in the fatigue life alulations. Thermal stresses ating in the base support due to the thermal gradient from the level of the primary membrane to the level of the inner bottom plating should also be alulated. 4.5 Hull girder loads The global bending moment ating on the ship hull girder auses a stress field in the liquid dome area. The stress field resulting from the still water and wave bending moment should be determined, and applied to the E model used for analysis of the liquid dome area. The maximum bending moment ating along the ship length should be onsidered. The global stress should inlude the stress onentration due to the liquid dome opening. Similarly, the longitudinal stress ating in the bottom due to the global bending moment should be determined, and applied to the E model used for analysis of the base support. 4.6 Internal tank pressure and external sea pressure The double bottom stress resulting from the internal tank pressure and external sea pressure ating on the double bottom should be determined, and applied to the E model used for analysis of the base support.

26 6 Classifiation Notes - No June Combination of loads or ULS assessment, the worst possible ombination of sloshing load and inertia load on the pump tower should be determined. In priniple, this an be done by investigating a time series of irregular tank motion, and monitoring the ombined effet of sloshing load and inertia load. By post-proessing the ombined load effet, the maximum load may be determined. Alternatively, a onservative approah is to add together the maximum values of sloshing loads and inertia loads: = + tower slosh The atual apaity may be governed either by exessive deinertia When the total pump tower loads are ombined with hull girder loads and pressure loads for analysis of the pump tower supports, quadrati summation may be applied for the fore omponents: = + + x, dyn x, tower x, hull x, press The stati loads due to gravity and thermal gradients should be added: = + stati gravity thermal The total load is found by adding the stati loads to the total dynami load: = + total dyn stati The summation of fores should be arried out omponentwise, i.e. = x, total x, dyn + x, stati y, total = y, dyn + y, stati z, total = z, dyn + z, stati It should be noted that both positive and negative values of the dynami loads must be onsidered when the total load is alulated, i.e. ± inertia, ± hull, and ± press. or the yield hek, the maximum stress is of interest, while for the bukling hek the maximum ompression stress is of interest. or LS assessment, four long-term load distributions should be determined; one for the full load ondition, one for the ballast ondition, one for the part load ondition with all tanks equally filled, and one for the part load ondition with one tank partly filled and the other tanks empty. The fatigue damage should be alulated for eah ondition, and the total damage is found by addition of the four ontributions. An operational profile for the ship must be assumed. In priniple, the long-term load distributions should be determined for the total load, onsisting of all load effets. or simpliity, however, the sloshing loads and inertia loads may be ombined by assuming that the number of ourrenes are approximately the same for both ontributions. The long-term stress distribution may then be determined for the dominating load, i.e. either the inertia or sloshing load, and the referene stress level is found by adding the stress distribution due to the sloshing load and the inertia load. or ULS assessment and LS assessment, both tank no. and tank no. should be onsidered, in order to determine whih one is most ritial with respet to the ombined effet of sloshing loads and inertia loads. A simplified approah inluding the use of a dynami load fator along with quasi-stati response analyses should be used to assess the dynami responses of the membrane type insulation systems. The requirements and guidelines for the quasi-stati response analyses are desribed in 5. for the ark III system and 5.3 for the NO96 system. The dynami fator is defined in 5.6. Analysis should be arried out for transverse orner/longitudinal knukle insulation strutures and for the flat wall insulation struture adjaent to orners and knukles. Note that the response analysis methodology speified for the ark III system in 5. is also appliable to the CS system, but that the omparative strength assessment methodology an not be applied to this system. 5. ark III system 5.. General A shemati representation of the quasi-stati load-displaement response of a ark III insulation panel is shown in igure 5-. The elasti response limit of the struture is reahed at Point on the urve, where the elasti apaity of the reinfored polyurethane foam (RPU) is reahed at the masti support loations as illustrated in the upper right hand sketh on igure 5-. This is not onsidered to represent the apaity of the struture. Loading past Point on the response urve requires that the inremental load is transferred to the masti supports as shear fore in the plate, and given suffiient strength of the bottom plywood plate, the stress in the foam will reah a distribution as shown in the lower right hand sketh of igure 5-. Loading beyond this limit will lead to exessive deformation of the panel, and it onsequently represents an upper bound on the apaity of the insulation panel. Load Displaement 5. Strutural Response Analysis of Containment Systems 5. General The strength assessment of strutures exposed to transient dynami loads suh as those generated by sloshing impats generally requires the assessment of the dynami response of the struture. igure 5- Shemati illustration of the load-displaement response and stress states in the polyurethane foam at the foam/plywood interfae of a ark III/ insulation panel

27 Classifiation Notes - No June 006 formation of the insulation panel at the load level identified at Point, or shear or bending failure of the bottom plywood plate at an intermediate load level between Point and Point. It is lear that an assessment of the bottom plate apaity requires a determination of its strutural response in the non-linear response range of the insulation panel. The non-linear response assessment should be arried out using linear elasti finite element response analysis to determine the elasti stress and deformation state at Point (5..), in ombination with a simplified analytial model based on linear elasti beam theory to assess the inremental shear fore and bending moment in the bottom plywood plate (5..3 and 5..4). 5.. inite element analyses The finite element response analyses should be arried out using a finite element model overing a suffiiently large portion of the insulation panel to make sure that the strutural response is well onfined within the interior of the model. The model need not reflet the full length and width of the insulation panel. Symmetry in geometry and/or strutural response of the insulation panel may be exploited. or the orner/knukle panels it is suffiient to model only one side of the orner/knukle as illustrated in igure 5-. The model should inlude a suffiiently large portion of the adjaent flat insulation panel to avoid signifiant effets of boundary onditions for the onsidered load areas. The model should be built up using a mix of ontinuum, shell, and membrane elements, as follows: The polyurethane foam, the masti strips, and the hardwood key of the orner/knukle panels should be modelled using eight node 3D ontinuum elements. Elements using a redued integration sheme may be used. The upper and lower plywood plates as well as the seondary barrier level plywood plate of the orner/knukle panel an be modelled using four-node shell elements. The primary orrugated steel membrane may be modelled using membrane elements with small in-plane stiffness, but with a representative mass per unit area to inlude its inertia effets on the dynamis of the panel. The seondary triplex membrane may be disregarded. The shell and the ontinuum omponents of the model should be onstrained to enfore kinemati ontinuity between the omponents, taking into aount the thikness of the plates. The membrane elements representing the primary membrane should be onstrained to follow the deformation of the mm top plywood plate. The finite element mesh requirements are given in the following. esh densities deviating from these requirements will be aepted provided that the adequay of the mesh an be demonstrated with a mesh onvergene test. In regions of the model where the strutural response will be extrated: 3 elements should be used aross the width of the masti supports at least 7 elements should be used aross the free span of the bottom plywood plate the element edge length in the diretion of the masti supports and in the through thikness diretion of the panel should be determined so that the elements are pratially square. In other parts of the model: igure 5- Required model extent for orner panel An example finite element model omprising half the width of a flat wall ark III panel (495 mm) and approximately a quarter length of a panel is shown in igure 5-3. elements should be used aross the width of the masti supports at least 5 elements should be used aross the free span of the bottom plywood plate the element edge length in the diretion of the masti supports and in the through thikness diretion of the panel an be retangular, with a maximum aspet ratio of 3.0. In the ase the three planes of symmetry in geometry and response of the panel is exploited, the boundary onditions for the panel should be taken as follows: restrained translations of the bottom nodes of the masti support symmetry onditions on seondary foam, bottom plywood plate and entre masti at panel symmetry planes (see igure 5-4) symmetry onditions on primary foam and top plywood plate at ross-panel boundaries (see igure 5-4). igure 5-3 Example finite element model of a ark III panel The far end plane of the model may be kept free. All path loads should be applied away from this boundary, and even in the ase of uniform load the results are taken at the opposite end of the model.

28 8 Classifiation Notes - No June 006 ) or a referene path load, establish the elasti through thikness stress on top of the masti support loated as far as possible diretly below the entre of the loaded area (see igure 5-6). If the load path overs more than one masti support, the average of the stress at all the masti p supports may be used. Let this be 0. ) Establish the elasti through thikness stress on top of the same masti support(s) for the ase of a uniform referene load with the same magnitude as above (see igure 5-6). u Let this be 0. p 0 3) Calulate the ratio r = u 0 4) Calulate the average through thikness stress as = r p igure 5-4 Symmetry planes for the example ark III insulation panel model The plywood and the reinfored polyurethane foam materials may be modelled as homogeneous linear orthotropi elasti materials. In this ase the bending stiffness moduli should be used to represent the plywood stiffness. Alternatively the plywood may be modelled as a 0-90 laminate of layers of orthotropi elasti materials. The masti may be modelled as a homogeneous linear elasti material. aterial properties are given in 5.4, and should be seleted based on the material diretions speified in igure 5-5. u 0 p p 0 igure 5-6 Definition of the stress quantities used to define the average through thikness stress igure 5-5 Definition of RPU and plywood material diretions relative to the ark III insulation panel 5..3 Average through thikness stress in foam The average through thikness stress may for a path load ase be interpreted as the equivalent uniform stress applied to the surfae of the panel. It follows that for a uniform load situation the stress is diretly defined by the applied load, p: = The average through thikness stress for the seondary foam insulation at the interfae with the bottom plywood plate should be assessed as follows: p 3 The proedure outlined above implies that the average ompressive stress is defined based on the linear elasti through thikness load dispersion in the model. This is onservative, sine inelasti deformations below the loaded region of the panel will result in a hange in the relative stiffness between this area and the adjaent areas, and thus also inrease the load distribution to adjaent areas. Another soure of onservatism in this alulation is the seletion of the peak elasti stress in the path load ase to enter the alulation of the ratio r Shear fore and bending moment in bottom plate In the ase of simple load situations where the load on the panel surfae extends over an area spanning several masti support spaings, the strutural system for assessment of the inremental shear fore at the supports is statially determinate. The additional fore applied to the system beyond the elasti response limit (Point in igure 5-) an not be transferred through the foam into the supports beause the elasti limit of the foam has been reahed at the masti support loations. The entire fore must hene be transferred to the supports as shear fore in the plywood plate.

29 Classifiation Notes - No June 006 λ el, = λ el, = λ el, 3 = ref foam ref Q Q ref λ el = min( λ el,i ) el (x), Q el (x) el-pl (x), Q el-pl (x) pl (x), Q pl (x) igure 5-7 Illustration of the onept of ombining linear finite element response analyses for the linear elasti response range and simplified analytial models for the elasto-plasti load range of the insulation panel An assessment of the bending moment in the plate is more ompliated, and requires that an assumption is made with respet to the distribution of inremental vertial stress exerted by the foam on the plywood plate. The inremental bending moment will therefore be a more unertain quantity than the inremental shear fore. or path load situations the assessment of the shear fore will be approximate, sine the proedure will not aount for the redistribution of fores that will take plae in the struture as soon as the stiffness loally beneath the load derease as a result of inelasti material response. The approah outlined above is illustrated in igure 5-7, where the seleted paraboli additional foam stress funtion q pl (x) is also speified. The amplitude q 0 pl is a funtion of the magnitude of the inremental load, as outlined in more detail in the following. The response assessment requires the exeution of the following analysis steps: ) Linear elasti strutural response analysis using a referene load amplitude, p ref. ) Extrat the ritial response parameters from the model. This involves (see igure 5-7): a) The vertial stress in the reinfored polyurethane foam at the enter of the most highly loaded masti ref support,. foam

30 30 Classifiation Notes - No June 006 b) The bending moment per unit plate width of the bottom plywood plate at masti supports and mid span, ref ref ref,, 3. ) The shear fore per unit plate width of the bottom plywood plate at masti supports, Q ref ref, Q. d) The rotations of the bottom plywood plate at the masti supports,, ref ref. The strutural response should be output at loations of maximum response entred below the applied load. When the bending moment and the shear fore is obtained at the integration points of the shell elements adjaent to the masti supports the orretions shown in igure 5-8 and igure 5-9 should be made to make the results representative for the plate ross-setion adjaent to the masti support. L int is the distane from the integration point of the element to the edge of the masti. igure 5-8 Corretion of E alulated plate shear fore to obtain a better estimate of the plate end value igure 5-9 Corretion of E alulated plate bending moment to obtain a better estimate of the plate end value 3) Determine the minimum elasti pressure apaity of the insulation panel (Point in igure 5-7) in terms of a proportionality fator λ el on the applied referene load. This is the minimum of the load proportionality fators λ el,i satisfying the following equations: a) b) oam oam el, Q Q ref foam θ L int L int Q E E λ = λ ref = el, θ Q = Q L ) ref λel,3 Q = Q where is the rushing strength of the polyurethane foam in the through thikness diretion of the insulation panel E oam = E Q L int int speified in Table 6-7, and and Q is the bending moment apaity the shear fore apaity of the bottom plywood plate in the relevant ross-setion diretion, speified in Table 6-6. If min(λ el,i )= λ el, the next step is to alulate the inremental shear fore. If not, the apaity is governed by plywood plate failure in the linear elasti response range of the struture, and an be estimated using either the bending moment or shear fore strength riterion. The remaining steps are presented under the assumption that min(λ el,i )= λ el,. The inremental shear fore and bending moment are alulated under the assumption that an inremental pressure (λ-λ el )p ref is applied to the panel, where λ is the load proportionality fator desribing the ratio between the design sloshing impat pressure inluding dynami effets ( p D ) and the referene pressure used in the finite element analyses. 4) As mentioned earlier in this setion, the inremental load must be transferred to the masti support as shear fore in the plywood plate. It is assumed that the shear fore is equally distributed to eah end of the plate, and the inremental shear fore at the end of the plate is therefore: Q = ( λ λ ) p L pl el ref ref 5) The total plate end shear fore per unit plate width in the non-linear response range an be estimated as: ref Q = λ Q + ( λ λ ) p L el el ref ref 6) or the assessment of the inremental bending moment per unit plate width, the inremental load speified above is assumed to be distributed aording to the paraboli funtion shown in igure 5-7, as follows: Lref q pl ( x) = 6( λ λel ) pref ( x Lx) 3 L The bending moments for the ase of (λ-λ el ) = at end, mid span and end (see igure 5-7) are: 0 pl, 0 pl, pref Lref L k (6EI + kl) = 90(3( EI ) + EIL( k + k ) + k k L ) pref Lref L k(6ei + kl) = 90(3( EI ) + EIL( k + k ) + k k L ) p L L k (6EI + k L) ref ref = 90(3( EI ) + EIL( k + k ) + k k L ) 0 pl, 3 The elasti modulus E should represent the bending modulus of the bottom plate in the diretion transverse to the masti supports, and the area moment of inertia I should be alulated for a unit width plate strip. The support bending stiffness k and k are alulated from the plate end bending moment and rotation obtained from the linear finite element analyses, as follows: ref ref k =, k = ref ref θ θ The sign onventions for the bending moment are indiated in the upper left hand sketh in igure 5-7. The total plate end and mid point bending moments per unit plate width in the non-linear response range an be estimated as: ref 0 = λ + λ λ ), i =,, 3 i el i ( el pl, i 5p ref L ref 3EI L

31 Classifiation Notes - No June Shear fore and bending moment in the seondary barrier plywood plate in orners/knukles The plate shear fore and bending moments should be output at high stress loations at the edges of the hardwood key (transition between the hardwood key and the softer primary foam). When the bending moment and the shear fore is obtained at the integration points of the shell elements adjaent to the hardwood key, similar orretions as speified for the bottom plate should be made (igure 5-8 and igure 5-9) to make the results representative for the plate ross-setion adjaent to the hardwood key. oam should in this ase be taken as the differential stress between the foam on the primary and seondary insulation side of the plate. 5.3 NO96 system The primary and seondary invar membranes may be disregarded inite element analyses The primary and the seondary insulation boxes should be modelled as separate entities. Both the primary box and the seondary box may be modelled as ontinuous strutures, meaning that full translational and rotational ontinuity may be assumed between the bulkheads and the top and bottom plates. The disontinuous stapled onnetion between the plates are hene disregarded. In the ase of the reinfored primary box with double over plates, the upper and lower plates should be modelled as separate entities. The plates should be onneted using elasti springs at the positions of the staples, as indiated in igure 5-0, and the interation between the plates should otherwise be treated as ontat in the normal diretion and free sliding in the tangential diretion. The stiffness of the onneting springs should be taken as N/mm. The over plates should be modelled as three individual parts in order to aount for the disontinuity of the plating at the invar tongue slits. Analysis of the orner boxes should inlude the adjaent flat wall boxes and the plywood plate that overs the gap between the orner struture and the flat wall struture. igure 5- Cut through the 3D model igure 5- odelling of staples in the E model Spring Node The NO96 insulation boxes should be modelled using 4 node shell elements. The mesh requirements are as follows: Cover plates: at least 7 elements between the vertial bulkheads of the primary box the element aspet ratio for the over plate should not exeed.0, and should be determined based on the bulkhead plate mesh requirements given below. Primary box bulkheads: igure 5-0 Loation of staples in the E model The interation between the primary and the seondary box should be modelled as a ontat onstraint. In addition the primary box should be onneted to the seondary box in eah orner using elasti springs to prevent undesired relative displaement of the boxes relative to eah other. This is a simplifiation of the stud bolt arrangement that seures both boxes to the hull struture. The stiffness of the onnetion springs should be taken as N/mm. The resin ropes may be disregarded, and the support boundary onditions may be diretly imposed at the intersetion lines between the bulkhead plates and the bottom plate of the seondary box. the element mesh should be ongruent with the mesh in the over plates at least 7 elements should be used aross the height of the bulkhead plates the elements in the bulkheads should as far as possible be square. Seondary box: at least 9 elements should be used aross the height of the seondary bulkheads the elements in the bulkhead plates should as far as possible be square. The following displaement restraints shall be imposed on the model: the seondary box are to be fixed in the vertial diretion at the intersetion lines between the bulkhead plates and

32 3 Classifiation Notes - No June 006 the bottom plate of the seondary box. In ase the resin ropes are inluded in the model the same ondition should be enfored at the bottom of the resin rope elements a minimum restraint against in-plane translation and rigid body rotation of the model should be imposed at two of the bottom orners of the seondary box. The plywood material may either be modelled as a homogeneous linear orthotropi elasti material, or as a 0-90 laminate of layers of orthotropi elasti materials. In the former ase the over plate stiffness should be represented by the bending stiffness moduli of the plate, whereas the membrane stiffness moduli should be used for all other omponents. aterial properties are given in 5.4, and should be seleted based on the material diretions speified in igure 5-3 unless other diretions are speified on the drawings Shear fore and bending moment in the over plates The output parameters should be the bending moment and shear fore per unit width of the plate ross-setion at loations of maximum response entred below the applied load. In ase the bending moment and the shear fore are obtained at the integration points of the shell elements adjaent to the masti supports, the orretions shown in igure 5-4 and igure 5-5 should be made to make the results representative for the plate ross-setion adjaent to the primary box bulkheads. L int is the distane from the integration point of the element to the edge of the masti. Note that the orretions are speified under the assumptions of double over plates, and that the shear fore and bending moment orretions are relevant for eah individual plate. No orretion of the bending moment is required if the maximum moment our at mid span of the unsupported plate field, and the element mesh ontains an element row entred on the plate field. Q p L int Q E Q = QE p L igure 5-4 Corretion of E alulated plate shear fore to obtain a better estimate of the plate end value int Q p L int E = E + Q L 0 p L int. 5 int Cover plates, primary Cover plates, seondary 3 3 Bulkhead plates seondary, transverse end plates primary Bulkhead plates primary, transverse end plates seondary igure 5-3 Definition of material diretions relative to the NO96 insulation panel 3 3 igure 5-5 Corretion of E alulated plate bending moment to obtain a better estimate of the plate end value Referene stress for bukling strength assessment The in-plane referene stress to be used in the bukling strength assessment of the vertial bulkheads of the primary and the seondary box should be seleted at mid height of the bulkheads and in line with the intersetion between the bulkheads in the primary and the seondary box as illustrated in igure 5-6 for the primary box bulkhead and in igure 5-7 for the seondary box bulkhead. Referene stress output loation igure 5-6 Seletion of vertial in-plane membrane stress for bukling strength assessment of the primary bulkhead

33 Classifiation Notes - No June aterial stiffness parameters 5.4. Plywood The material stiffness properties for the plywood laminate and the individual wood layers of the laminate are given in Table 5- and Table 5-, respetively. The properties are given in terms of the material oordinate systems shown in igure 5-9. Subsript m denotes the in-plane (membrane) stiffness properties of the plates, and subsript b denotes the bending stiffness properties. Referene stress output loation igure 5-7 Seletion of vertial in-plane membrane stress for bukling strength assessment of the seondary bulkhead Surfae grain diretion Grain diretion If the element mesh ontains an even number of elements aross the height of the bulkhead and thus does not allow for seletion of an element at the entre of the bulkhead, the element farthest away from the stress onentration at the primary and seondary bulkhead intersetions should be seleted. This implies the element just above the entreline should be seleted for the primary bulkhead and the element just below the entreline should be seleted for the seondary bulkheads. The stress should be seleted from the most highly loaded bulkhead for the onsidered load ondition Referene stress for bulkhead intersetion rushing assessment The in-plane referene stress to be used in the strength assessment of the bottom plate of the primary box, the over plate of the seondary box, and the bulkhead plate edges should be obtained at mid height of the primary box bulkhead and in line with the intersetion between the bulkheads in the primary and the seondary box as illustrated in igure 5-7. This is the same stress as should be used in the bukling strength assessment of the primary box bulkheads Referene stress for bottom plate rushing assessment The referene stress for the rushing strength assessment of the bottom plate of the seondary box at the intersetion with the vertial bulkheads should be seleted at the bottom element row of the seondary bulkhead, as illustrated in igure 5-8. This should be the vertial membrane stress omponent in the bulkhead. Referene stress output loation igure 5-8 Seletion of vertial in-plane membrane stress for rushing strength assessment of the bottom plate of the seondary box igure 5-9 aterial oordinate systems for the plywood laminate(left) and the individual layers of wood The relationship between the individual layer and the integrated laminate properties are: t / E = E ( x ) dx m, i 3 3, i =, t i t / t / G, i =, j =, 3 m, ij = G ( x3) dx3 t ij t / t / E = E ( x ) x dx, i =, b, i 3 i t t / The loal E i and G ij of the individual layers should be evaluated in the material oordinate system of the laminate. Table 5- Integrated orthotropi material stiffness properties for the plywood plates Parameter 0ºC -63ºC E m, [Pa] E m, [Pa] E m3 [Pa] G m, [Pa] G m,3 [Pa] G m,3 [Pa] υ [-] υ 3 [-] υ 3 [-] E b, 9 mm [Pa] E b, 9 mm [Pa] E b, mm [Pa] E b, mm [Pa] Density [ton/mm 3 ] Table 5- aterial properties for the individual wood layers Parameter 0ºC -63ºC E [Pa] E [Pa] E 3 [Pa] G [Pa] G 3 [Pa] G 3 [Pa]

34 34 Classifiation Notes - No June 006 υ [-] υ 3 [-] υ 3 [-] Density [ton/mm 3 ] Reinfored polyurethane foam The orthotropi linear elasti material properties for the reinfored polyurethane foam are summarised in Table 5-3. Table 5-3 aterial stiffness properties for the reinfored polyurethane foam Parameter 0ºC -63ºC E [Pa] E [Pa] 80 5 E3 [Pa] G [Pa] 7 G3 [Pa] 7 G3 [Pa] 7 υ [-] υ3 [-] υ3 [-] Density [ton/mm 3 ] asti The material stiffness properties for masti is summarised in Table 5-4. Table 5-4 aterial stiffness properties for masti Parameter 0ºC E [Pa] 900 υ [-] 0.3 Density [ton/mm 3 ] Simplified assessment of dynami response 5.6. General The dynami response is determined from the quasi-stati response desribed above through the appliation of a dynami amplifiation fator, denoted DA. The fator is a funtion of the ratio between the pressure pulse rise time t r defined in igure 3-6 in and the natural period T n of the insulation system. Natural periods to be used in the seletion of the dynami load fator are speified in 5.6. and for the ark III and the NO96 systems, respetively. Note that the natural period in general varies with the loaded area. However, the onsequenes of the expeted variations is onsidered to be within the unertainty limits inherent in the present approah to determine the dynami load fator. A piee-wise linear urve is used beause of the unertainties involved in determining the rise time of the pressure pulse. Due to this unertainty, the design urve is speified to envelope the maximum-points on the atual alulated DAurves. The design DA urve is illustrated in igure 5-0, and is defined as follows: Tr < 0.5 : DA = f T n Tr (0.5,.0) : DA = f T n Tr T n >.0 : DA = max(.0, f Tr ( T n 0.5)( f f Tr 0.33 ( T n ).0)( f.0)) f f DA (-) Rise time/natural period igure 5-0 Illustration of the urve to be used in the simplified assessment of the dynami amplifiation fator The fators f and f relevant for the ark III and the NO96 systems are given below ark III system The fators f and f are given as a funtion of the vertial position of the onsidered response variable: At the bottom plywood plate (furthest away from the load) the following values apply: f =.65 f =.5 At the upper plywood plate (losest to the load) the following values apply: f =.5 f =. Linear interpolation may be applied when response variables in between the top and bottom are onsidered. or moderate design modifiations of the system inluding hanges of the masti support spaing and the bottom plate thikness the natural period to be used in the assessment of the dynami load fator an be taken as.0 milliseonds. ore radial design modifiations requires that the natural period is established by dynami finite element analyses NO96 system The fators f and f are funtions of the vertial position of the onsidered response variable, as given in the following. At the mid part of the seondary box bulkhead: f =.6 f =. At the mid part of the primary box bulkhead: f =. f =.05 At the over plywood plates (losest to the load): f =.4 f =. Linear interpolation may be applied when response variables in between the top and bottom are onsidered. or moderate design modifiations of the system inluding hanges of the internal bulkhead plate thikness the natural period to be used in the assessment of the dynami load fator an be taken as.3 milliseonds. ore radial design modifiations requires that the natural period is established by dynami finite element analyses.

35 Classifiation Notes - No June Ultimate Strength of Containment Systems 6. General Aeptane riteria for the ultimate strength assessment of the ark III and the NO96 insulation systems are given in 6.3 and 6.4, respetively. Note that the aeptane riteria speified for the ark III system in 6.3 is also appliable to the CS system, but that the omparative strength assessment methodology an not be applied to this system. 6. gives guidane on how to use the aeptane riteria to alulate the load apaity of the insulation system as needed to determine the load level for the referene ase in the omparative assessment (see.). 6. Capaity assessment The load apaity of the insulation systems in terms of peak impat pressure for a given impat area size should be alulated based on the strength aeptane riteria given in this setion, as follows: ) Calulate the design apaity of eah relevant response parameter inluding dynami effets by solving the limit state equations for the maximum allowable dynami response parameter. ) Invert the quasi-stati response analysis to determine the surfae pressures orresponding to the ritial response. This will be the maximum effetive dynami pressure the insulation system an sustain. 3) Calulate the peak pressure apaity for eah onsidered impat area by dividing the effetive dynami pressure apaity by the relevant dynami fator. If the statistial proessing of the load data does not distinguish between foot print orientations and 4, 3 and 5, and 7 and 8, it is suffiient to onsider only one from eah pair for the flat wall panels. Table 6- Definition of load foot prints for the orner panels oot Print Width (mm) Length (mm) Area (mm ) P P P P P P P 7 >600 >680 > mm masti spaing P 50x50mm P 50x400mm P3 50x800mm P4 400x50mm P5 800x50mm P6 400x400mm 4 P7 400x800mm P8 800x400mm P 9 50x50mm ark III system Impat areas The strength of the ark III insulation system should be heked for the impat load foot prints identified in igure 6- and igure 6-, and defined in Table 6-. Table 6- Definition of load foot prints for the flat wall panels oot Print Width (mm) Length (mm) Area (mm ) P P P P P P P P P P P 0 Uniform Load 0 7 igure 6- Load footprints for strength assessment of the flat wall ark III insulation panel

36 36 Classifiation Notes - No June mm masti spaing P 0x340mm P 0x340mm P3 0x680mm 6) Bending failure of the seondary barrier level plywood plate (orner/knukle) at the edge of the hardwood key P4 0x680mm P5 40x340mm P6 40x680mm P 7 Uniform Load igure 6- Load footprints for strength assessment of the orner/knukle ark III insulation panels 6.3. ailure modes The ultimate strength assessment of the ark III insulation panel should onsider the following set of ritial failure modes (see igure 6-3 and igure 6-4): igure 6-3 Visual identifiation of loations of ritial failure modes for the flat wall ark III insulation panel ) Crushing of primary foam ) Crushing of seondary foam at plywood interfae 3) Shear failure of plywood plate at support 4) Bending failure of plywood plate. 5) Shear failure of the seondary barrier level plywood plate (orner/knukle) at the edge of the hardwood key igure 6-4 Visual identifiation of loations of ritial failure modes for the orner/knukle ark III insulation panel Crushing of primary foam The strength riterion for this failure mode is a stress ontrol riterion for the average through thikness ompressive stress in the foam on the form: p DA γ γ p is the peak impat pressure ating on the panel. DA is the dynami amplifiation fator as defined in γ is a partial load fator, if appliable. is the rushing strength of the reinfored polyurethane for the relevant temperature and load rate onditions, as defined in 6.6. γ is a partial resistane fator, if appliable Crushing of seondary foam The strength riterion for this failure mode is a stress ontrol riterion for the average through thikness ompressive stress in the foam on the form: DA γ γ is the average through thikness stress in the panel. The foam rushing riterion will ensure that the loads do not reah levels where the struture will experiene total ollapse or exessive deformations. A main issue with this kind of strength riteria is that it is not unique in terms of the loal state of stress and strain in the struture for different masti support onditions or other relevant design modifiations. This is not believed to be a big issue for the ultimate strength, sine the foam appears to be robust and able to sustain rather large ranges of inelasti deformations without any observable differenes in strength and damage Shear failure of bottom plywood plate The maximum shear fore in the bottom plywood plate in the most highly loaded ross setion adjaent to the masti support should fulfil the following requirement: Q Q( p DA γ ) γ Q is the alulated dynami shear fore per unit plate width at the most highly loaded ross-setion of the bottom plywood plate for a quasi-stati pressure p DA. The alulation of this quantity is desribed in more detail in 5..4.

37 Classifiation Notes - No June 006 Q is the shear fore apaity per unit plate width of the plywood plate for the onsidered material orientation, as defined in 6.6. Unless a speifi orientation of the plywood plate with respet to the masti support an be guaranteed the value should be representative for the weakest ross-setional diretion of the laminate Bending failure of bottom plywood plate The maximum bending moment in the bottom plywood plate in the most highly loaded ross-setion should fulfil the following requirement: ( p DA γ ) γ is the alulated dynami bending moment per unit plate width at the most highly loaded ross-setion of the bottom plywood plate for a quasi-stati pressure p DA. This is most likely at a ross-setion adjaent to the masti support. The alulation of this quantity is desribed in more detail in is the bending moment apaity of the plywood plate for the onsidered material orientation, as defined in 6.6. Unless a speifi orientation of the plywood plate with respet to the masti support an be guaranteed the value should be representative for the weakest ross-setional diretion of the laminate Shear failure of seondary barrier level plywood plate (orner/knukle) The maximum shear fore in the bottom plywood plate in the most highly loaded ross-setion adjaent to the masti support should fulfil the following requirement: Q Q DA γ γ Q is the alulated stati shear fore per unit plate width at the most highly loaded ross-setion of the plywood plate for a quasi-stati pressure p. The alulation of this quantity is desribed in more detail in Q is the shear fore apaity per unit plate width of the plywood plate for the onsidered material orientation, as defined in 6.6. Unless a speifi orientation of the plywood plate with respet to the onsidered ross-setion of the plate an be guaranteed, the value should be representative for the weakest ross-setional diretion of the laminate Bending failure of seondary barrier level plywood plate (orner/knukle) The maximum bending moment in the bottom plywood plate in the most highly loaded ross-setion should fulfil the following requirement: is the alulated stati bending moment per unit plate width at the most highly loaded ross-setion of the plywood plate for a stati pressure p. The alulation of this quantity is desribed in more detail in is the bending moment apaity of the plywood plate for the onsidered material orientation, as defined in 6.6. Unless a speifi orientation of the plywood plate with respet to the DA γ γ onsidered ross-setion of the plate an be guaranteed, the value should be representative for the weakest ross-setional diretion of the laminate. 6.4 NO96 system 6.4. Impat areas The strength of the NO96 insulation system should be heked for the impat load foot prints identified in igure 6-5 and igure 6-6 and defined in Table 6-3. oot print overs the entire insulation box surfae and is not shown in the figures. The foot prints have been arefully seleted to obtain lower bound strength values for all relevant omponents of the primary and the seondary insulation box. oot prints -8 are seleted to primarily over the strength of the seondary box. Of these, foot prints -5 over the strength of the external members of the insulation box, whereas foot prints 6-8 over the internal members. oot prints 9-3 are seleted to primarily over the strength of the primary box. Of these, foot prints 9- over the strength of the external members of the insulation box, whereas foot prints and 3 over the internal members. Table 6-3 Definition of load foot prints oot Print Width (mm) Length (mm) Area (m ) P (full box) P P P P P P P P P P P P Bulkhead diretion in primary box igure 6-5 Load foot prints primarily intended for assessment of seondary box members 7 3 6

38 38 Classifiation Notes - No June Bulkhead diretion in primary box igure 6-6 Load foot prints primarily intended for assessment of primary box members 6.4. ailure modes The strength assessment of the NO96 insulation boxes is based on the following set of ritial failure modes (see igure 6-7): ) Shear failure of the over plate(s) of the primary insulation box. ) Bending failure of the over plate(s) of the primary insulation box. 3) Bukling of internal and external bulkheads of the primary insulation box. 4) Bukling of internal and external bulkheads of the seondary insulation box. 5) Through thikness rushing of the bottom/over plates of the primary/seondary boxes at the intersetion between the bulkheads of the primary and seondary boxes. The rushing deformation will lead to failure of the same plates in bending or shear. Shear failure of the over plates Bukling of seondary box bhds igure 6-7 ailure modes onsidered for the NO96 system Shear failure of over plate(s) The strength riterion for this failure mode is a stress ontrol riterion for the through thikness shear fore in the over plates in the most highly loaded ross-setion adjaent to the Bending failure of the over plates Bukling of primary box bhds Crushing of plates at bulkhead intersetions vertial bulkheads: Q is the alulated setion shear fore per unit plate width at the most highly loaded ross-setion of the over plates. The alulation of this quantity is desribed in more detail in Q is the setion shear fore apaity of the plywood plate for the onsidered material orientation Bending failure of over plate(s) The strength riterion for this failure mode is a stress ontrol riterion for the bending stress in the over plates in the most highly loaded ross-setion adjaent to the vertial bulkheads: is the alulated bending moment per unit plate width at the most highly loaded ross-setion of the over plates, most likely to be at a ross-setion adjaent to vertial box bulkheads. The alulation of this quantity is desribed in more detail in is the bending moment apaity of the plywood plate for the onsidered material orientation Bukling of plywood bulkheads General This setion presents the formulas and proedures to be used for bukling strength assessment of the internal and external bulkheads of both the primary and seondary insulation box. The setion is organised into three subsetions desribing the assessment of the stati bukling apaity of the plywood bulkheads, how to aount for the additional edge bending moment load potentially experiened by the external primary bulkheads, and last how to utilise the bulkheads in the dynami and unstable load regime during rapid load events. The bukling strength hek should be based on the following strength equation: Q Q DA γ γ is the nominal in-plane stress in the bulkhead plate, as desribed in D is the nominal in-plane bukling apaity of the bulkhead onsidering both dynami and temperature effets. The temperature dependent material stiffness and strength parameters should be evaluated at the mid-height of the primary and seondary bulkheads aording to the proedure desribed in 5.4 and Stati apaity assessment The proposed bukling strength design urve is shown in the figure below, inluding results from finite element analyses for room temperature and uniform load for different slenderness. The bukling strength design urve is given as: where is the stati bukling strength at room temperature, λ DA γ γ DA γ.05 + λ = λ γ D (.05 + λ ) 4λ

39 Classifiation Notes - No June 006 is the redued slenderness defined as λ = E is the material ompressive strength in the diretion of the load (measured as average stress over the plate ross-setion) and E is the elasti bukling strength of the plate. A graphial presentation of the bukling strength design urve is shown in igure 6-8. /f Design urve λ igure 6-8 Graphial representation of the bukling strength design urve The elasti bukling stress for a simply supported bulkhead subjeted to loads over parts or all of its edge an be expressed as: E = k E, + k E, is the elasti bukling stress for a simply supported bulkhead subjeted to uniform load, k is a fator depending on the size of the load exposed region of the bulkhead, k is a fator to aount for the inreased bukling strength of slender bulkheads aused by the rotational restraint resulting from the finite thikness of the bulkheads, and is the material ompressive strength as defined above. The fators k, k, and E, are desribed in more detail below. The elasti bukling stress for a simply supported bulkhead subjeted to uniform load, E, may be taken as: E, π D * = Where t is the thikness, h is the height of the bulkhead plate, and D* is the generalised bending modulus of the bulkhead plate, defined as: 4 Eb, Eb, D* = h + + ( ν E, + G ) 4 4 b h B h B where E b,, E b, are bending stiffness properties of the laminate, ν is the in-plane Poissons ratio, and G is the in-plane shear modulus of the plate, all defined in Table 5-. When the bulkheads are subjeted to ompressive loading over a limited area only, the slenderness is modified using the fator k defined as: t h k =, minimum.0 b ( h B) where h is the height of the bulkhead, B is the width of the bulkhead, and b is the width of the loaded area (all given in mm). The k -fator as a funtion of load width b is shown in igure 6-9. The width b may be taken as the width of the zone where the vertial stress is larger than half of the maximum stress at mid height of the bulkhead, as illustrated in igure 6-0. k b/(h*b) igure 6-9 The part load elasti bukling stress orretion fator k load width b = 0 / = 0 / = 0 igure 6-0 Illustration of the riterion for seletion of the load width b The ase of a part load loated towards the end of the bulkhead has been onsidered, but found not to be ritial. In this ase, the redistribution of the load will be smaller, sine the stress an redistribute in one diretion only. However, the restraining effet of the end bulkhead will be larger when the load is lose to the restraint, and some of the loading will be taken up by the end bulkhead. If E is less than 0.5, the elasti bukling stress may be inreased by k. The fator k is defined to aount for the inreased bukling strength of slender bulkheads aused by the rotational restraint resulting from the finite thikness of the bulkheads, as illustrated in igure 6-.

40 40 Classifiation Notes - No June 006 igure 6- Illustration of the end restraint effet experiened by slender bulkheads during bukling deformations The rotational restraint is a funtion of the through-thikness stiffness of the top and bottom plywood plates onneted to the bulkheads, and is taken to be linearly dereasing with the applied stress, as follows: k E, > 0.5 : k = 0 k E, < 0.8 : k = 0. k = E else : k The k -fator as a funtion of the normalised elasti bukling strength is illustrated in igure 6-. In the ase that dynami strengthening is aounted for, as defined in , the rotational restraint effet must be re-evaluated after alulation of the dynami strength. The k -fator must then be re-alulated, using the dynami strength d instead of E, in the formula above. Using the modified k -fator, the modified stati and dynami strength is alulated. urther iterations are not neessary. k E / igure 6- Graphial presentation of the end restraint orretion fator k as a funtion of the normalised elasti bukling strength, Corretion of stati apaity due to bending moment The outer bulkheads in the primary box will be subjeted to bending moment due to the deformation of the top plate, while the outer bulkheads in the seondary box will be subjeted to bending moment due to deformation of the entire primary box. The bending stress in the bulkheads is alulated by linear finite element analysis. If bending is signifiant, the ritial bukling stress must be redued as a result of the bending moment using a bukling-bending interation equation. In this ase, the rotational restraint orretion should not be applied, i.e. k = 0. The bending stress resulting from linear analyses indiates that the bending moment in the outer bulkhead in the seondary box is relatively small. or uniform load, the bending stress in the outer bulkhead is approximately 0% of the total stress, whih means that it may be negleted. This is also supported by the apaity tests arried out by GTT, whih gives a apaity in exess of the one alulated by the design formulas proposed, without onsidering the bending moment effet. or the end bulkheads in the primary box, the bending effet is muh larger. or a strip load on the edge of the box, the bending stress is approximately 37% of the total stress, whih means that the bending moment must be aounted for. The following interation equation is used for the external bulkheads in the primary box: where b is the bending stress in the bulkhead, is the yield stress of the outer veneer, and is the ritial average stress under ombined axial load and bending. The values to be used for the bending stress and the yield stress in the above equation depends on whether the plywood plates are modelled as laminate plates or equivalent homogeneous orthotropi plates, as summarised in Table 6-4. Table 6-4 Definition of bending and yield stress values depending on plate modelling approah Parameter Plate modelling approah Equivalent Laminate plate homogeneous orthotropi plate b b + = ( ) The parameters referred to in the table are defined as follows: E veneer and E average are the elasti moduli of the surfae veneer and the entire laminate, respetively, in the material diretion oiniding with the load. max is the maximum alulated stress at the extreme fibre of the plate. av is the average stress over the plate ross-setion, alulated t as av = dz in the ase that the z axis is oriented in the 0 through thikness diretion of the plate. avg is the material strength of the laminate plate speified in Table 6-6. Sine the bending moment is proportional to the load, b may be replaed by b = C b, where C b is the ratio between bending stress and average stress in the bulkhead, as determined from finite element analysis. The solution to the interation equation is then: E E veneer = b max av E b = max av average = E veneer avg veneer = avg = E average

41 Classifiation Notes - No June 006 where = ( E + + C K K A B = = C b E b E ) + K = K A + K B E + K Cb E E + + Cb E exeeding.0 ms. Table 6-5 Relationship between impat pressure rise time and vertial stress response rise times for the primary and seondary box bulkheads response load t [ms] t [ms] r r Primary box Seondary box The bending moment applied to the external bulkheads of the primary box due to bending of the over plate need not to be taken greater than the value implied by the rotational restraint limit as defined by the above. This means that the maximum moment is defined for the load level giving a nominal ompressive stress in the bulkhead plate equal to Dynami strength orretion Bukling failure is a dynami event, and it is lear that inertia will allow a bukling exposed struture to sustain in-plane loads beyond the stati bukling apaity without suffering damage given that the load event is suffiiently rapid. This effet is aounted for by multiplying the ritial bukling stress D by a dynami strength fator (DS= ) defined as a funtion of the slenderness of the bulkhead and the ratio of the rise / time of the sloshing impat stress response (t r ) and the natural period relevant for lateral osillation of the bulkhead plate (T e ), as follows: DS = f ( λ) t t = ( ),0.55 < r r DS f λ 0.95 T T e e tr DS =.0, >.50 T f (λ) and f (λ) are given as: e f ( λ) f ( λ) t r 0.55 T tr, T f f ( λ) = 3, maximum 4 (see igure 6-4) r f 3 = safety fator =0.95 f (λ) = min(f (λ),.5) A graphial representation of the dynami strength fator as a funtion of the ratio between rise time and natural period, t r /T e, is shown in igure 6-3. The natural period relevant for lateral osillation of the bulkhead plate an for all load ases be alulated as: T e h = tπ ρ E where t is the thikness of the bulkhead plate, h is the height of the bulkhead, ρ is the density of the plywood, and E b is the bending stiffness of the plate about its stiffest axis, ref. Table 5-. The relationship between the rise time of the impat pressure and the rise time of the stress response in the bulkheads of the primary and the seondary insulation boxes are summarised in Table 6-5. Response rise times for impat pressure rise times between the values given in the table should be obtained by linear interpolation. The response rise time an be taken as equal to the impat pressure rise time for impat pressure rise times b e e DS f (λ) f (λ) igure 6-3 Definition of the DS as a funtion of the ratio between the rise time of the sloshing stress response and the natural period of the bulkhead plates in the lateral bending deformation mode The dynami bukling strength is then found as: = DS D The dynami low temperature bukling strength is limited by the material ompression strength: D ax( ) = igure 6-4 Graphial representation of the slenderness dependent fator f Crushing of plates at bulkhead intersetions The rushing strength is measured in terms of the nominal stress in the vertial bulkhead of the seondary insulation box, av av, measured against a ritial value of this parameter, assoiated with through thikness rushing of the insulation box over plates and more importantly the assoiated bending failure of these over plates. The apaity has been determined from laboratory tests and numerial simulations. The strength hek should be arried out using the following equation: Dynami fator λ t r /T e 4.5 f av DA γ av γ is the nominal stress in the bulkhead of the primary insu- av

42 4 Classifiation Notes - No June 006 lation box in the region of the bulkhead intersetions. av is the through thikness ompressive strength of the plywood plate measured in terms of the nominal stress in the seondary box bulkhead. 6.5 Plywood strength data Strength data for 9 mm and mm thik plywood plates are summarised in Table 6-6. The first subsript identifies that this is a limit value (ritial), and the seond and potentially third alphanumeri subsript refers to the material diretions of the laminate, as defined in igure 5-9. or bending moments the subsript refers to the vetorial diretion of the moment, i.e. denotes bending about the -axis and denotes bending about the -axis. Table 6-6 ean strength properties for the 9 mm and mm plywood laminates 9 mm mm 0 C -63 C 0 C -63 C,t, tension (Pa) ,, ompr. (Pa) ,t, tension (Pa) ,, ompr. (Pa) av ompr. (Pa) , (Nmm/mm) * ,, (Nmm/mm) * Q,3 (N/mm) Q,3 (N/mm) * Calulated based on the veneer tensile strength. 6.6 RPU strength data The temperature and strain rate dependent through thikness rushing strength of the reinfored polyurethane foam is given in Table 6-7. Table 6-7 Temperature and strain rate dependent strength for through thikness ompression of the RPU Strain rate Temperature 0* 0./s 4/s 00/s 0 C C * Quasi-stati loading Evaluation of temperature dependent strength It should be assumed that the temperature at the hull struture side of the ontainment system is 0 C, with a linear variation down to -63 C at the primary barrier of the system. The material strength an be taken as a linear funtion of the temperature between the limits given in Table 6-6 and Table 6-7. The material strength for temperatures between the limits given in should thus be obtained by linear interpolation between these limits based on the through thikness oordinate at the loation being investigated Evaluation of strain rate dependent strength The strain rate dependent material strength should be determined based on linear interpolation between the values given in Table 6-7 using a strain rate alulated as follows: DA ε& = E response 3 t r is the average through thikness stress in the foam as defined in DA is the dynami amplifiation fator as defined E 3 is the relevant temperature dependent through thikness elasti modulus of the reinfored polyurethane foam as defined in 5.4. response t r is the estimated rise time of the average through thikness stress, and should be alulated as follows: or the upper part of the foam the response is onsidered to follow the load, and the response of the rise time should onsequently be taken equal as the load rise time. or the foam adjaent to the bottom the response rise time should be taken equal to the load rise time for load rise times larger than.5 ms. or shorter load rise times the response rise time should be obtained by interpolation between the values given in Table 6-8. Table 6-8 Relationship between load and response rise times for bottom foam for load rise times below.5 ms load response [ms] [ms] t r t r Stiffness and Strength of Hull Struture 7. General The sloshing impat loads ating on the ontainment system inside the argo tanks must be transferred into the supporting hull struture. It is therefore neessary to ensure that the hull struture has the suffiient stiffness and strength to arry the sloshing loads. The hull struture assessment should be arried out in two steps in order to make sure that: ) The stiffness of the hull struture is suffiient to provide adequate support for the ontainment system. ) The strength of the hull struture is suffiient to arry the sloshing loads without suffering large permanent deformations. or assessment of the hull struture stiffness, it is suffiient to onsider the plate stiffness only. The stiffener span is muh longer than the stiffener spaing, whih means that the urvature of the plate during defletion is muh smaller in the stiffener diretion than in the ross-stiffener diretion. The assessment of the hull plating stiffness is disussed in 7.3. or assessment of the hull struture strength, it is suffiient to onsider the stiffener strength only. The stiffness riterion presented in 7.3 will be dimensioning for the hull plating. The hull plating will not be ritial from a strength point of view, sine the ontainment system will redistribute the sloshing loads into the stiffeners when the plate is defleting. Hene, the load will eventually be arried by the stiffeners. When the plate deforms, the ontainment system will re-distribute the sloshing impat load from the plating and diretly into the stiffeners, and the strength of the plating will therefore not be ritial. The assessment of the stiffener strength is disussed in 7.4. The hull stiffness and strength should be onsidered for the most sloshing exposed regions of the tank. or normal filling operations, partiular attention should be paid to the following areas, igure 7-: the inner dek and hamfer area at loations lose to the transverse bulkheads the transverse bulkheads at loations lose to the inner dek the inner dek and hamfer area lose to the upper hamfer knukle along the entire length of the tank the hamfer area lose to the lower hamfer knukle along the entire length of the tank.

43 Classifiation Notes - No June 006 CL Upper hamfer knukle Lower hamfer knukle rame spaing igure 7- Part of inner shell whih should be speially onsidered with respet to sloshing (top view) The extent of the areas is to be determined based on results from sloshing tests for the atual tank onfiguration. As for the membrane ontainment system, the assessment of the hull struture is arried out using a omparative approah. Hene, the stiffness and strength of the hull struture for the target ase is ompared with the orresponding stiffness and strength for the referene ase. The referene ase to be onsidered is defined in the next Setion. 7. Comparative basis (referene ase) The basis for the omparative assessment of the hull struture of the new LNG arrier should be taken as the referene ase vessel speified in.6.. Sine tank fillings between 90% and 98.5% of the tank height are assumed for the referene ase, a typial dek panel is onsidered as the basis for the omparative assessment. A stiffened panel with the dimensions listed in the following is taken as representative for the referene ase: Vessel with ark III ontainment system: igure 7- Illustration of stress onentration in the foam of the ark III ontainment system above the stiffener It is worth noting that the stress onentration due to the hull defletion is not a very loalized effet, ompared to the dimensions of the insulation system. Sine the stiffener spaing is large ompared to the spaing of the masti strips supporting the ontainment system, the stress onentration due to the hull defletion ats over a large area of the insulation boxes. The effet of the plate defletion may therefore be onsidered as relevant for several of the failure modes in the ontainment system. or assessment of the stiffness of the hull struture, it is normally suffiient to onsider the stiffness of the plating between the stiffeners. or an insulation box loated above a stiffener and lose to the transverse bulkhead, the stiffener santlings will also influene the stress distribution, sine some of the load is transferred diretly into the transverse bulkhead. The amount of loading transferred into the transverse bulkhead inreases with inreasing stiffener defletion, i.e. with dereasing stiffener santlings. This means that inreasing the stiffener santlings will inrease the stress onentration in the insulation box at the loation of the stiffener. In pratie the most ritial ase will be an insulation box loated above a longitudinal girder, whih may be onsidered as an infinitively stiff longitudinal. Hene, for the stiffness assessment, the insulation box may be onsidered as rigidly supt (mm) s (mm) L (mm) Profile (mm) /8 Vessel with NO96 ontainment system: t (mm) s (mm) L (mm) Profile (mm) /4 where t is plate thikness, s is stiffener spaing, L is stiffener span, and Profile is stiffener santlings. The yield stress for the hull struture material for the referene ase is 35 Pa. 7.3 Stiffness of hull plating 7.3. General In the response and strength assessment of the membrane ontainment system, desribed in Setion 5 and 6, it is assumed that the struture supporting the ontainment system is flat and rigid. In reality the hull struture is flexible, and the hull defletion will affet the stress distribution in the ontainment system. The stiffness of the hull struture must therefore be assessed in order to ensure that the sloshing impat loads do not lead to unaeptable defletion of the hull, whih will lead to stress onentration and possible damage to the ontainment system. As the shell plate below the insulation boxes deflets due to the sloshing loads, the stress in the ontainment system will redistribute towards the stiffeners. An illustration of the stress onentration ourring in the ontainment system at the position of the stiffener is shown in igure 7- for the ark III system and in igure 7-3 for the NO96 system. igure 7-3 Illustration of stress onentration in the seondary bulkhead of the NO96 ontainment system above the stiffener

44 44 Classifiation Notes - No June 006 ported at the position of the stiffener/girder. The hull stiffness should be ontrolled by assessment of the stress onentration ourring in the ontainment system due to the flexible hull plating, relative to the ase of rigid support onditions. The stresses need to be assessed by use of finite element analysis, as desribed in the next setion Response assessment In order to assess the stress onentration in the ontainment system due to the flexible support, two sets of finite element analyses need to be arried out for eah of the target ase and the referene ase: ) The first analysis is arried out with the atual hull plating supporting the ontainment system ) The seond analysis is arried out with rigid support onditions, i.e. with the ontainment system resting on a flat plate Both analyses should be stati or quasi-stati, and linear elasti. The non-linear effets related to the plate defletion are assumed to be rather small for the expeted load magnitudes, and an be negleted. The dynami effet is aounted for by applying a dynami fator in the aeptane riterion desribed in The finite element models should inlude one full box of the ontainment system. The models used for response assessment of the ontainment system may be used also for these analyses. However, it is essential that the mesh density is the same for the two analyses, sine the stress will be mesh sensitive. If the same mesh density is used for both analyses, the alulated stress onentration will be less dependent on the mesh density. or the rigid support ase, only the ontainment system itself is needed in the finite element model, sine the bottom of the mastis are onsidered as fixed in the vertial diretion. or the flexible support ase, the part of the hull plating loated between primary strength members should be inluded in the model. The masti should be onneted to the plating, and the stiffeners should be represented by fixing the plating in the vertial diretion at the positions of the stiffeners. The ontainment system should be positioned as the first flat panel away from the transverse bulkhead, i.e. one orner panel distane from the bulkhead. The load area onsidered for the analyses should be the area that is ritial with respet to the stress onentration. A quadrati load path with width and length equal to the stiffener spaing may be onsidered, unless information from sloshing tests indiate that other areas are more ritial. Uniform pressure should be applied over the load area. Sine the analyses are linear, the stress onentration will be independent of the load magnitude. Hene, a unit load may be applied for all ases. The load area should be entered above the stiffener, as illustrated in igure 7-4. igure 7-4 Illustration of loation of ontainment system and load area for analysis of ark III panel In ase of ark III ontainment system, the resulting vertial stress is measured in the foam diretly above the middle stiffener and middle masti. In ase of NO96 ontainment system, the resulting vertial stress is measured as the membrane stress in the mid part of the middle bulkhead of the seondary box. The stress onentration due to the flexible support is then alulated for the referene ase and the target ase as SC ref SC tar Load area = = Stiffeners flex 3 fix 3 flex 3 fix 3 Trv. Bulkhead asti SC = Stress onentration fator. 3 = maximum vertial stress in the ritial part of the ontainment system, as defined above. fix = Containment system with fixed support. flex = Containment system with flexible support Aeptane riterion The stiffness assessment of the hull struture is arried out under the presumption that the strength of the ontainment system has already been assessed for the ase of a rigid support ondition. A potential load inrease from the referene ase to the target ase should therefore already be aounted for by a apaity inrease of the ontainment system. Hene, the hull stiffness riterion shall only ensure that the stress onentration due to the hull defletion is not larger for the target ase than the referene ase. The dynami amplifiation in the ontainment system is largest for the smaller rise times, but for suh small rise times the effet of the hull defletion is found to be less important. The stress onentration due to the hull defletion is larger for somewhat larger rise times, where dynami effets are less signifiant. or this reason, the assessment of the hull stiffness may be arried out using a stati approah, using a safety fator to aount for the potential differene in dynami effets on the stress onentration between the referene ase and the target ase. Using the omparative approah, the aeptane riterion for the target ase is determined by the referene ase. The SC alulated for the target ase should satisfy the following re- ref tar

45 Classifiation Notes - No June 006 quirement: SC γ DA is a partial fator aounting for potential differene in dynami amplifiation between the target and the referene ase γ is the partial resistane fator The following values may be used, as speified in.7.8: γ DA =.5 γ =.0 The suggested value of the fator γ DA have been determined based on results from a large number of dynami analyses arried out for various hull geometries. The fator may alternatively be determined by arrying out dynami analyses for the referene ase and the target ase for various rise-times, and omparing with results for the quasi-stati ase. If the aeptane riterion is not fulfilled, the stiffness of the hull plating needs to be inreased. The stiffness is a funtion of stiffener spaing and plate thikness. Hene, the plate stiffness may be inreased by reduing the stiffener spaing or by inreasing the plate thikness. 7.4 Strength of hull struture tar γ DA SC γ 7.4. General The strength of the hull struture must be onsidered in order to ensure that the sloshing impat loads do not lead to exessive permanent deformations in the hull. An illustration of plasti strains remaining in the stiffener after loading and offloading of the sloshing impat pressure is shown in igure 7-5, where the pressure has been applied to the top of the ontainment system. The ontainment system is indiated with grey olour in the figure. or this speifi ase, the most highly utilized part of the stiffener is lose to the transverse bulkhead, where large shear stresses our. ref 7.4. Response assessment or assessment of the stiffener strength, linear elasti and stati finite element analyses should be arried out for the referene ase and the target ase. A single stiffener with attahed plating may be onsidered. Three stiffener spans should be inluded in the model, one on eah side of the span where the load is ating. The number of elements over the stiffener web height and along the plate flange should be suffiient to properly apture the representative shear and bending stress distribution. The refinement of the model should generally be the same for the referene and target ase. The sloshing load may be applied diretly to the stiffener as a line load. The stress distribution through the ontainment system does not need to be onsidered for the stiffener assessment. The load area should be taken as the ritial area aording to the load-area urve determined from sloshing tests. A load width equal to the stiffener spaing and a length of approximately.5 m may be onsidered, unless information from sloshing tests indiate that other areas are more ritial. The load should be applied at a loation of one orner panel distane away from the transverse bulkhead. The transverse bulkhead and girders may be aounted for by speifying simple supports, as illustrated in igure 7-6. L igure 7-6 Illustration of sloshing load applied to stiffener The longitudinal stress L ourring in the stiffener due to the maximum global bending moment should be onsidered to at simultaneously with the sloshing load p. Hene, a uniform axial stress orresponding to the global bending stress should be superimposed on the stress due to the sloshing load. The value of the stress L should be taken aording to the design bending moment both for the referene ase and for the target ase. The value of the sloshing pressure for the referene ase and the target ase may be taken as: p Cofferdam L p ref = 0. 5Pa p tar = λ λ load is the load inrease fator for the target ase relative to the referene ase, determined from sloshing tests: load p ref igure 7-5 Illustration of plasti strains in the stiffener resulting from sloshing pressure on ontainment system The strength of the stiffeners in the inner hull struture is assessed using a omparative approah. Response analyses should therefore be arried out both for the referene ase and for the target ase, as desribed in the next setion. λ load p = p The pressures p tar and p ref should be evaluated for the most ritial load area. Boundary onditions may be applied as shown in igure 7-7. The longitudinal stress L may be inluded diretly in the analysis by prestressing of preompressing the model. When suh applied, any orresponding stresses in the transverse diretion should be eliminated. Alternatively the longitudinal stress may be superposed as follows: x = x, loal where x,loal is the loal bending stress due to the sloshing path load. tar ref + L

46 46 Classifiation Notes - No June 006 z y x z-dir. fixed z-dir. fixed Clamped Symmetry Clamped igure 7-7 Proposed boundary onditions for strength assessment of stiffener The strength of the pump tower main struture, the base support and the liquid dome area shall then be heked with respet to ULS and LS. In addition, a vibration hek of the main struture should be arried out. 8. Response analysis of main struture 8.. inite element model The finite element analysis of the main struture of the pump tower should be arried out as a 3D analysis. The analysis may be linear elasti. A priniple sketh of the tower struture is shown in igure 8-. The maximum von ises equivalent stress e ourring in the stiffener web or the stiffener flange should be extrated from the analyses. Only membrane stress, i.e. the stress in the middle of the plate, needs to be onsidered. It should be noted that modelling only one stiffener is a simplifiation, and the response obtained from this analysis will not be realisti in an absolute sense. In the real ase, the load will redistribute to the surrounding stiffeners when the loaded stiffener starts to deflet, and the stress and deformation will therefore be redued. Hene, the simplified model is only relevant in a omparative strength assessment Aeptane riterion Using the omparative approah, the aeptane riterion for the target ase is determined by the referene ase. The von ises stress in the stiffener for the target ase should satisfy the following requirement: γ e, tar DA e, ref γ DA is a partial fator aounting for potential differene in dynami amplifiation between the target and the referene ase. γ is the partial resistane fator. The von ises equivalent stress is alulated as: The following values may be used for the partial safety fators: γ DA =.3 γ =.0 The suggested value of the fator γ DA have been determined based on results from a large number of dynami analyses arried out for various hull geometries. The fator may alternatively be determined by arrying out dynami analyses for the referene ase and the target ase for various rise-times, and omparing with results for the quasi-stati ase. 8. Response and Strength of Pump Tower and Supports 8. General inite element analyses of the pump tower struture shall be arried out in order to determine the response in the struture due to the loads ating for the ULS and the LS assessment. Separate analyses should be arried out for the main struture, for the base support, and for the liquid dome area, as desribed in the following setions τ γ e = x y x y Disharge pipes Tubular joint Guiding system igure 8- Illustration of pump tower main struture Emergeny pipe Braes Base plate The main strength members of the pump tower are the emergeny pipes and the two disharge pipes. The olumns are onneted by intermediate braes, and are fitted to the base plate at the bottom of the tower. The filling pipe and the float level gauge are onneted to the tower by supports. The members that should be inluded in the finite element model are: emergeny pipe disharge pipes (port and starboard) filling pipe float level gauge supports for filling pipe and float level gauge braes base plate. The olumns and braes may be modelled with beam elements, while the base plate should be modelled with shell elements. The beam elements should be positioned in the at the entre of eah olumn/brae, as indiated by the dashed lines in igure 8-, with the finite element nodes at the intersetion between the elements. The restraining effet of the joint on the braes may be aounted for by speifying rigid ends of the elements. Loads should only be applied to the free span part of the brae elements.

47 Classifiation Notes - No June 006 The filling pipe and the float level gauge should be onneted to the emergeny pipe and the horizontal bak struts, respetively. The onnetion should be modelled so that vertial displaement and rotation of the pipes are allowed aterial properties Charateristi values of the material properties are to be applied in the response analysis. The pump tower is usually onstruted by stainless steel, and typially of qualities in the 300- series. Properties for the 304L stainless steel are given in Table 8-. igure 8- Illustration of beam element modelling 8.. Load appliation Sloshing loads should be applied to the olumns and braes loated below the liquid dome. Gravity, inertia loads and thermal loads should be applied to all elements. The mass and load/drag fore effet of additional elements should be inluded (suh as pumps, platforms, ladders and valves), by distributing the masses and modifying the drag oeffiients to the main members of the tower. The mass of liquid inside the olumns must also be inluded for alulation of inertia fores. The mass may be applied to the olumns as an additional distributed mass. However, the amount of liquid will depend on the filling level, and a separate model will therefore be required for eah filling level onsidered. Therefore, the fore due to the inertia ating on the additional mass may alternatively be inluded diretly by a distributed load Boundary onditions At the top, the emergeny pipe and the disharge pipes are onneted to the liquid dome over plate. The boundary onditions at the top of eah olumn may be taken as: T x = T y = T z = R z = fixed R x = R y = free where T is translation, R is rotation, x is longitudinal diretion, y is transverse diretion, and z is vertial diretion, ref. igure 4-. Alternatively, translational (k x and k y ) and rotational (k rx, k ry, k rz ) springs may be used. The spring stiffnesses should then be doumented from the finite element analysis of the liquid dome area. The sliding joints of the three upper horizontal struts should be modelled so that axial displaement and rotation about the axial diretion of the strut are allowed: T x = R x = free where the x-diretion is in the length diretion of the strut. At the bottom, the emergeny pipe and the disharge pipes are onneted to the base plate. In order to aount for the sliding pads between the base plate and the base support, the boundary onditions of the base plate are taken as: T x = T y = R z = fixed T z = R x = R y = free where x is longitudinal diretion, y is transverse diretion, and z is vertial diretion. Alternatively, translational (k x and k y ) and rotational (k rz ) springs may be used. The spring stiffness should then be doumented from the finite element analysis of the base support. Table 8- aterial properties for 304L stainless steel E (Pa) odulus of elastiity ν ( ) 0.3 Poisson s rato ρ (kg/m 3 ) Density y,0 (Pa) 70 Yield limit at 0ºC y,-78 (Pa) 80 Yield limit at -78ºC y,-63 (Pa) 0 Yield limit at -63ºC α 0 (0-6 /ºC) 6.3 Thermal exp. oeffiient at 0ºC α -63 (0-6 /ºC) 3.5 Thermal exp. oeffiient at -63ºC or intermediate temperatures, the yield limit and the thermal expansion oeffiient may be interpolated linearly between the speified values. The referene temperature for the thermal expansion is 0ºC Response parameters or tubular members, the following result parameters should be determined for ritial setions along the length of the member: axial fore (or tension/ompression stress) vertial bending moment (or bending stress) horizontal bending moment (or bending stress) torsional moment (or torsional stress). or joints, the following result parameters should be determined: axial load horizontal bending moment vertial bending moment. In addition, total reation fores at the top and at the bottom of the tower is to be determined. 8.3 Response analysis of base support The finite element analysis of the base support of the pump tower should be arried out as a 3D analysis using shell elements. The analysis may be linear elasti. The finite element model should inlude the base support itself, and a portion of the double bottom. The portion of the double bottom should be large enough to provide realisti restraint onditions to the base support. esh density may be hosen aording to reommendations given in /6/ and /7/. The reation fores determined from the analysis of the pump tower main struture should be applied to the model, and ombined with hull girder loads due to global bending moment, double bottom stresses due to external sea pressure, and thermal stresses due to the thermal gradient in the base support. The temperature variation through the height of the base support should be determined by a separate assessment. The resulting stress field in the base support should be determined, and applied for the ULS and LS strength assessment. Areas of speial onern for the base support is the onnetion between the base support and the inner bottom, the onnetion to the primary membrane and the onnetion to the seondary membrane.

48 48 Classifiation Notes - No June 006 In addition, the reinforements in the inner bottom underneath the base support should be onsidered. The omplete set of hot spots to be onsidered should be agreed with the Classifiation Soiety. 8.4 Response analysis of liquid dome area The finite element analysis of the liquid dome area should be arried out as a 3D analysis using shell elements, as illustrated in igure 8-3. The top over plate and the onnetion to the pump tower should be inluded in the analysis. The analysis may be linear elasti. esh density may be hosen aording to reommendations given in /6/ and /7/. The reation fores determined from the analysis of the pump tower main struture should be applied to the model, and ombined with hull girder loads due to global bending moment. The resulting stress field in the liquid dome area should be determined, and applied for the ULS and LS strength assessment. Areas of speial onern are the onnetion between the pump tower struture and the liquid dome over plate, and the orner areas of the liquid dome. igure 8-3 Example of E-model of liquid dome area 8.5 ULS assessment The main struture, the base support and the liquid dome area should be heked with respet to yielding, using the von ises yield riterion: R Sγ γ S R = e = where is the yield stress of the material, and e is the von ises equivalent stress: + + 3τ e = x y x y In addition, the tubular members of the main struture should be heked with respet to bukling and ombinations of bending and bukling. The tubular joints should be heked with respet to shear apaity. The bukling/bending hek of the tubular members may be arried out aording to DNV Classifiation Note 30. /8/ or API-RP-A /9/. Strength heks should be arried out for several setions along the length of eah brae, in order to make sure that the most ritial setion is heked, i.e. the worst ombination of axial and bending stress. The shear apaity of the tubular joints should be heked aording to API RP A /9/. or eah failure mode, it should be heked that the strength of the struture is aeptable aording to the requirements given in LS assessment The fatigue damage should be alulated for relevant parts of the struture. It should be heked that the maximum damage is aeptable aording to the requirements given in.7. or LS assessment of a vessel with ordinary operation, loading and offloading at shore terminals, the ship s operational profile through its lifetime may be assumed as 0% in harbour, 50% in full load and 40% in ballast. or the full load ondition, a ertain ratio of the life time should be assumed to be in the range of 70-98% filling. or ballast ondition, filling ratios between 5-0% should be assumed. The ship s operating profile ould be taken from Table 8- for ships intended for normal world wide trading. Table 8- ration of time at sea in loaded, ballast and part load ondition Operating ondition ration of design life ull load, 95% tank filling 0.40 Ballast, 0% of tank length filling 0.40 Part load, 70% tank filling 0.0 Harbour 0.0 All wave headings (0-80º) should be onsidered, with equal probability. Long term stress distributions are to be determined for inertia loads and sloshing loads. The long-term LS stress distribution may be desribed by a two parameter Weibull distribution, haraterised by a referene stress range and the Weibull slope parameter. or inertia loads, the ordinary Weibull-distribution for ship motion should be used. or sloshing loads, the long term distribution must be determined by ombination of short-term results. In priniple, the long term stress distribution for the ombined stress effet should be established. However, if it an be doumented that that inertia fores are the main ontributor to fatigue damage for high fillings, and sloshing loads are the main ontributor for low fillings, the LS assessment may be arried out by onsidering the two effets separately. The fatigue life may be alulated based on the SN fatigue approah under the assumption of linear umulative damage (iner-palmgren rule): D = i= where D is aumulated fatigue damage, n i is number of stress yles within stress range i, and N i is number of yles to failure at onstant stress range i, aording to the appropriate SN-urve. The umulative damage for a design fatigue life of 40 years should not exeed the aeptable damage. The total damage is found by summing the damage for eah sea state (aording to the North Atlanti satter diagram) for eah sea state: all load onditions (full load/ballast) for eah sea state and load onditions: all headings (0-80º) k ni N i