the development of trimaran rules
TRANSCRIPT
by Dr F. Cheng, Mrs C. Mayoss and Mr T. Blanchard
Lloyd’s Register Technical Papers
The development of TrimaranRules
The authors of this paper retain the right of subsequent
publication, subject to the sanction of the Committee of
Lloyd’s Register. Any opinions expressed and statements
made in this paper and in the subsequent discussions are
those of the individuals and not those of Lloyd’s Register.
© Lloyd’s Register 2006. All rights reserved. Except as
permitted under current legislation no part of this work
may be photocopied, stored in a retrieval system,
published, performed in public, adapted, broadcast,
transmitted, recorded or reproduced in any form or means,
without the prior permission of the copyright owner.
Enquiries should be addressed to Lloyd’s Register,
71 Fenchurch Street, London EC3M 4BS, England.
The development of Trimaran Rulesby Dr F. Cheng, Mrs C. Mayoss and Mr T. Blanchard
Dr Fai Cheng is a Senior Principal Surveyorto Lloyd’s Register. He joined Lloyd’sRegister in 1984 after a lecturingappointment. He is Manager and Head ofRules and is responsible for thedevelopment, maintenance and publicationof Lloyd’s Register Rules and Regulations for
Classification. Dr. Cheng is a member of theRoyal Institution of Naval Architects and afellow of the Institute of Marine Engineers,Scientists and Technologists.
Mrs Catherine Mayoss is a Specialist toLloyd’s Register. She joined Lloyd’s Registerin 2002 after working in the designdepartment of Herbert Engineering in theUSA as a Naval Architect. She is the lead
engineer in the development of the TrimaranRules. Mrs. Mayoss is a member of theRoyal Institution of Naval Architects.
Mr Tim Blanchard is a Surveyor to Lloyd’sRegister. He joined Lloyd’s Register in 1995after graduation, and has worked as a fieldand plan approval surveyor before joiningthe Research and Development Departmentin 2002. He is a project engineer in the
development of the Trimaran Rules.Mr Blanchard is a member of the RoyalInstitution of Naval Architects.
Table of Contents
Summary1 Introduction2 Rule structure3 Philosophy for Rule formulation and direct calculations4 Classification of loads5 Rule formulation for primary loads6 Rule formulations for secondary and tertiary loads7 Advanced calculation procedure8 Load combinations and acceptance criteria9 Acknowledgements10 References
Summary
The trimaran design has generated intense interest in recentyears and the subject has been investigated around theworld with a combination of design studies, numericalsimulation, model testing and the construction of the largeocean-going technology demonstrator, RV Triton. It isbecoming a viable option for both military and commercialapplications.
With funding from the Ministry of Defence (MoD) andtechnical support by QinetiQ (QQ), Lloyd’s Register (LR) isdeveloping Rules for Classification of Trimaran Ships(Trimaran Rules). The Trimaran Rules includedevelopment of design loads applicable to the unique hullform of a trimaran, as well as a direct calculation procedurefor analysis of new trimaran designs.
This paper describes briefly the structure and content of theTrimaran Rules, the rule development process involved andhighlights some of the assumptions made. The emphasis ofthe paper is placed on the development of primary loadswhich are the main dimensional loads and the data utilisedfor calibrations.
Nomenclature
ah Heave acceleration ( g )
az Vertical acceleration due to roll and heave ( g )
Bmh Greatest moulded breadth of the main hull ( m )
Bwl Total moulded breadth of hulls at design waterline (m )
Cbmh Block coefficient of the main hull
Df Longitudinal distribution factor
D Depth of main hull ( m )
Ff Hogging or sagging correction factor based on theamount of bow flare, stern flare, length and effectivebuoyancy of the after portion end of the ship abovethe waterline.
Ffh Hogging correction factor
Ffs Sagging correction factor
fserv Service group factor depending on sea area ofoperations
g Acceleration due to gravity and is to be taken as 9.81( m s-2 )
Lf Factors varying with length
Lsh Length of side hulls (m)
LTf Longitudinal torsional moment distribution factor
L Rule length (m)
Mh Horizontal wave bending moment ( kNm )
Mlt Longitudinal torsional moment ( kNm )
Msph Splitting moment in hog ( kNm )
Msps Splitting moment in sag ( kNm )
Mswh Still water bending moment in hog ( kNm )
Msws Still water bending moment in sag ( kNm )
Mtt Transverse torsional moment ( kNm )
Mwh Vertical wave bending moment in hog ( kNm )
Mws Vertical wave bending moment in sag ( kNm )
Mo Wave bending moment ( kNm )
Mw Vertical wave bending moment ( kNm )
Ømax Maximum roll angle (degrees) in beam sea conditions
Water density ( tonnes m-3 )
Vcd Volume of the cross-deck structure ( m3 ) on one sideof the ship. The inside and outside boundaries of thecross-deck structure are to be taken as the verticallines extending upward from points O and I, seeFigure 6.
Vmhs Volume of the main hull ( m3 ), which extends thelength of the side hull. The outside boundary of themain hull is to be taken as a vertical line extendingupwards from point O, see Figure 6
Vsh Volume of one side hull ( m3 ). The inside boundaryof the side hull is to be taken as a vertical lineextending upward from the point O, see Figure 6.
Wsh Total weight of one side hull including lightshipweight and deadweight (tonnes).
x longitudinal distance ( m ) from aft perpendicular,positive forward.
y Transverse distance ( m ), from the centreline to thecentre of gravity of the item being considered. y ispositive to port and negative to starboard.
yo Distance between the centreline of the main hull andpoint O, as depicted in Figure 6.
ysh Distance between the centreline of the main hull andthe centreline of the side hull, see Figure 6.
z Vertical distance, in metres, from the baseline to theposition or centre of gravity of the item underconsideration. z is positive above the baseline.
1 Introduction
1.1 General
Lloyd’s Register has already published extensive sets ofrules to cover a multitude of ship types depending on theirapplication, size, materials of construction and regulatoryframework.
1.2 Existing Rules and Regulations
1.2.1 Rules and Regulations for the Classificationof Ships (Ship Rules)
These rules cater for major commercial ships such astankers, bulk carriers and container ships regulated underthe framework of Safety of Life at Sea (SOLAS). These shipsare generally large steel mono-hulls of robust constructionand are typically ocean-going [1].
1.2.2 Rules and Regulations for the Classificationof Special Service Craft (SSC Rules)
These rules cater for small to medium size craft with anemphasis on high speed and highly optimizedconstruction, generally regulated under the framework ofIMO International Code for High Speed Craft. These craftcan be mono-hulls or catamarans of highly optimisedconstruction with steel, aluminium or composite materials.Special Service Craft are generally operated in a restrictedsea environment [3].
1.2.3 Rules and Regulations for the Classificationof Naval Ships (Naval Ship Rules)
These rules cater for naval ships of all different sizes withvarying operational environment. These ships areessentially steel mono-hulls and are regulated by the naviesconcerned. A distinct naval element is added in the form ofmilitary features to the hull structural requirements,machinery, electrical and control systems [2].
2 Rule structure
2.1 General
In general, classification rules cover a multitude ofrequirements for the design, construction and maintenanceof ships. The elements described in 2.1 (a) to 2.1 (f) aretypically included.
A trimaran design may fit within the framework of any ofthe three existing Rules listed in 1.2. Obviously a set oftrimaran rules that encompass the following elements foreach possible vessel type would be very extensive andvoluminous indeed. A new approach for rule constructionis therefore necessary.
2.1.1 Regulations
The regulations detail the relationships between variousparties, builders, owners, class, flag and regulatoryauthorities. They also detail requirement for newconstruction surveys and periodic surveys that are requiredfor the maintenance of class.
2.1.2 Materials
Rules for Materials provide detail requirements for materialtesting, certification and approvals.
2.1.3 Hull Structures
Hull structure rules provide requirements for the design ofhull structures and they cover:
• Specification of loadings;• Capability of structures to withstand the specified
loadings; and • Acceptance Criteria.
The load specification, capability assessment andacceptance criteria can either be expressed implicitly, as inthe case of Ship Rules, or explicitly, as in the case of the SSCRules, or a combination of both as in the case of Naval ShipRules. They are usually referred to as prescriptiverequirements.
Additionally, direct calculation procedures may also beprovided and required to enable further checks to becarried out, for cases where prescriptive rules areconsidered to be inappropriate, or for cases where moreadvanced analysis is deemed to be more suitable, on anequivalent basis.
2.1.4 Machinery, Electrical and ControlEngineering Systems
Machinery, Electrical and Control Engineering Rules detailthe requirements for the safe installation, testing andoperation of these systems.
2.1.5 Military Features
These requirements are important for naval ships and areessential features of the Naval Ship Rules.
2.1.6 Fire Protection and Stability
These aspects are generally covered by InternationalConventions and Regulations and are pre-requisites forclassification.
2.2 Overlay Rule structure
From the discussion in Section 2.1 above, it is obvious thatit would be impossible to develop a trimaran rule set tocater for ships that are covered by any of the three mainrules listed in 2.1. The Trimaran Rules are thereforedeveloped as an overlay set of requirements to Lloyd’sRegister’s Rules and Regulations described above and theywill focus on essential elements that are unique to trimaranhull forms.
The relationship between the Trimaran Rules and the ShipRules, SSC Rules and Naval Ship Rules is illustrated inTable 1. As it may be observed, the development of theTrimaran Rules is centred upon the hull structure aspectswith particular emphasis in loads and capabilityassessment. Other aspects such as rules and regulations formaterials are already covered by existing rules.
Many sources of data, as illustrated in Figure 1, are beingused in developing environmental loads and in scantlingdetermination. These include a full ship finite elementanalysis, local detailed finite element models, segmentedmodel tests, MoD research vessel Triton sea trials data,hydro-elastic analysis and computational methods. Thisdata, combined with Lloyd’s Register’s experience in ruledevelopment, will contribute to a rationally based set ofTrimaran Rules.
For conventional ships, parametric formulae which arebased on extensive service experience and theoreticalexperience, coupled with model test results, are available toprovide a basis for Rule formulation. For trimaran vessels,there is very little service experience and design is mainlybased on direct calculations verified by model experiments.Whatever the approach adopted, there is a need to provideguidance as to the range of validity of the various formulaeand direct calculation methods, and they should be based
on a unified philosophy and lead to a consistent level ofsafety.
In the development of the Trimaran Rules, major effort hasbeen put in the development of empirical formulae toprovide initial design solutions, an advanced calculationprocedure is then provided by which a detailed analysismay be performed. These include procedures fordeveloping loads, suitable modelling and loadingtechniques for structural analyses and appropriateacceptance criteria.
Figure 1: Data sources for load calibrations
2.1.1 Common Common Common
2.1.2 Common Common Common
2.1.3 Trimaran Rules Trimaran Rules Trimaran Rules
2.1.4 Common Common Common
2.1.5 Common Not applicable Not applicable
2.1.6 Common Common Common
Table 1 Relationship between Rule sets
RRuullee NNaavvaall sshhiippSShhiipp RRuulleess SSSSCC RRuulleess
eelleemmeenntt RRuulleess
Calibration
Parametric RuleFormula
Direct CalculationProcedures
Segmented ModelResults
TheoreticalStudies
HydrodynamicSoftware
Existing DataService
Experience
Full ScaleMeasurement
Data
Fatigue Loads
3 Philosophy for Ruleformulation and directcalculations
3.1 Rule development process
The design procedure, in the broad sense, involves theentire process from the initial concept to the final approveddesign ready for fabrication/manufacture. An importantpart of this process is the design control, or structuralanalysis, to ensure reliability against structural failure.
The design control consists of a number of steps:
• evaluation of environmental conditions,• analysis of loads,• analysis of response,• evaluation of strength, and• control of safety.
The rule development process will have to take all theseelements into account. The analysis methods used may bebased on theory, experiments or full scale measurements.An additional essential step in this development process isthe calibration of the result against service experience asillustrated in Figure 2.
Figure 2: Rule Development Process
Conventional monohull ship structural design has, as itsbasis, about a hundred years of combined data andexperience. This background allows the structural design ofthe hull to be pursued by relatively wellproven designmethods. Within limits, one hull form is similar to previoushull forms, and the design is relatively forgiving to under oroverestimation of the loads. Any radical departure from thenormal hull forms would severely de-value the usefulnessof accumulated expertise, as knowledge of the loads isessential for design of the hull structure.
The key element in the development of design proceduresfor trimaran vessels is the prediction of the loads acting onthe hull structure. For trimarans, an initial emphasis must beplaced on theory and experimental data in the absence ofexperimental data. Consequently, a level of conservatismmust be applied in order to maintain an acceptable risk level.
3.2 Demand and capability approach
Trimaran ships can experience a combination of all theloads, described in Section 3, acting on the hull and theirprediction is extremely complex. It is considered necessaryto adopt a modern approach to the development of theseRules as illustrated in Figure 3.
Figure 3: A modern rule format
This decoupling of load, strength and acceptance criteriaopens the possibility to base new design approval on directcalculations using a similar approach, as illustrated inFigure 4.
Figure 4: Load determination
From a class point of view, this is important as while theclassification rules should be as simple as possible to use,the direct calculation approach should provide the sameuniform technical standard for all kinds of hullconfigurations and sizes thus allowing for optimisation bymore detailed analysis.
It is obvious that while the strength assessment techniques(finite element analysis, for example) can be applieddirectly to conventional designs, it is more difficult toestablish design load formulations that are equally welladapted to different hull configurations, speed ranges andship sizes. Therefore the main emphasis for ruledevelopment would be the determination of loads.
Environment
Theory &Experiment
CalculationModel
StrengthCriteria
ResponseLoads
Evaluation ofSafety
ServiceExperience
Rules
Acceptanceof
Risk Level
Operational Envelope(Environment)
Demand(Loads)
Capability(Strength)
Criteria(Acceptance Criteria)
RulesModel
ExperimentsSemi-analytical
ApproachMotion
Program
LOADS(Demand)
STRENGTH ASSESSMENT(Capability)
ACCEPTANCE CRITERIA FORDIFFERENT FAILURE MODES
4 Classification of loads
4.1 General
The overall load on a trimaran, or indeed any ship,consists of four components: namely; primary, secondary,tertiary and internal loads as illustrated in Figure 5. Theclassification of loads as primary, which affect the hull asa whole; secondary, which affect large panels of the hullsuch as bulkheads; and tertiary or local, which have alocal effect only, has been made for convenience inrelation to structural considerations. It has developed tosatisfy the needs of the structural engineers requiring asimplified approach to structural analysis problems. Allloads, with the exception of thermal loads, originate fromforces or pressures applied over small areas. Whetherthese loads are subsequently treated in a local or anintegrated form is largely a matter of analyticalconvenience. However, such a classification has found tobe useful in identifying the dominating forces for directcalculation purposes.
Figure 5: Classification of loads
4.2 Primary loads
The primary loads which must be considered for the designof trimaran are:
4.2.1 Wave Induced Bending Moment, and StillWater Bending Moment
For mono-hull ship, the longitudinal wave inducedbending moments are the most important primary loadsacting on the vessel and are most severe in head seas.
Likewise, the longitudinal wave induced bending momentacting on a trimaran will be of significance and ismaximised in the head sea condition. This primary loadwill drive the design of the longitudinal hull girder. Thereare, however, additional primary loads influencing thedesign of the transverse structure.
4.2.2 Splitting Loads
A splitting moment occurs when the side hull is beingpushed away or towards the centre hull by wave actions.Consideration of the splitting loads is of particularimportance in determining the scantlings of the cross-deckstructure.
Available model data and theoretical studies have providedsome insight into the nature and magnitude of theseloadings on catamarans and SWATH ships. Further modeltests and Triton trials data have been more recentlyavailable for derivation of these loads for trimarans.
4.2.3 Torsional Loads
The torsional loads acting on the trimaran are of similarimportance to the splitting loads, especially for the strengthassessment of the cross-deck structure. The most severeheading for torsional loads is quartering (bow or stern)seas. Though the responses are similar, the torsional loadmay be considered to act about the transverse orlongitudinal axis.
The transverse torsional load, together with the splittingloads, drives the scantling design of the cross deckstructure.
The longitudinal torsional load acts on the longitudinal hullgirder, particularly the centre hull. In most cases, this loadwill not be of great significance as the hull girder is a closedsection. However, in cases where the centre hull isextremely slender, the side hulls are relatively small and/orthe transverse distance between the side hulls and centrehull is large, this load may become significant.
4.2.4 Horizontal Bending Moment
As with the longitudinal torsional moment, the horizontalbending moment is not likely to be of great significance.However, in combination with other global loads, asprescribed in the Advanced Calculation Procedure, thehorizontal bending moment may influence some localstructure, such as the connection of the cross-deck structureto the main and side hulls.
4.2.5 Fatigue Loads
Because the majority of the loads imposed on trimaranships are cyclic in nature, the possibility of failure by fatiguemust never be forgotten. Indeed most structural failuresthat occur in service life of a ship result from fatigue. Whilethere is a large body of knowledge on the fatigueperformance of conventional designs, there is very littlework done and little knowledge in relation to trimaranships. The most important task in the question of fatigueperformance of trimaran ships is the determination of thefatigue loading.
4.3 Secondary and tertiary loads
The secondary load and tertiary loads which must beconsidered for the design of large high speed craft are:
PRIMARYLOADS
SECONDARYLOADS
TERTIARYLOADS
OTHERLOADS
CLASSIFICATION OF LOADS
Affect hullgirder
strength
Affect globalstructural
components
Affect localstructural
components
In general,affect internal
structuralcomponents
4.3.1 Loads in a Seaway due to External WaterPressures, including Slamming and GreenWater Loads.
This category of loads is probably the most important froma local strength point of view, and in fact, is often thegoverning criteria for the design of the small to mediumsize vessels. In general, these loads can be sub-dividedfurther into the following components:
• Bottom slammingBottom slamming arises as the result of the pitchingand heaving motion of the ship at speed where itusually undergoes a severe hydrodynamic impact onre-entry. The impact is typically rapid and intense togenerate a high pressure impulse on the bottomplating. This event is often accompanied by a loudbooming sound, particularly apparent for largerships. The duration of this type of slamming force isin general less than 100 milliseconds. Bottomslamming has been the most common cause of hullstructural damage. The magnitude and duration ofthe impact pressure depend on, or are sensitive to, theangle and relative shape of the hull and the watersurface, and the encounter velocity and frequency.
• Bow flare slammingBow flare slamming is the rapid immersion of theupper flared portion of the bow deeper into the water.This is a more gradual phenomenon than bottomslamming, usually without any sound unless the flareis very concave. This event lasts for less than asecond, but nevertheless imparts a relatively suddenand intensive force to the forward part of the ship.The bow flare slamming is an importantconsideration for fine hull form ships. The maindifference between bottom and bow flare slamming isthat the forward bottom slamming is alwaysassociated with the emergence of the forebody, whilebow flare slamming is not.
• Cross-deck slammingThis type of slamming arises as a result of the heavingand pitching motion of the ship causing the impact ofwaves on the flat underside centre body and leadingedge of the cross-deck structure. This phenomena isexacerbated by the ‘funnelling effect’ between theside and main hull. Such forces can result in largeaccelerations and related structural loads acting onthe ship which must be accounted for in thedetermination of the local strength of the cross deckstructure.
• Green sea loadingThe green sea loading of the wet deck forward isanother source of transient loading that excitesvibratory response and is caused primarily by therelative ship motion to the water’s surface. In manycases, this load may simply be the static head of waterscooped up by the bow as it submerges downwarduntil it runs off. The duration of this load is thereforerelatively long. However, there may be a dynamiccomponent, especially if the ship is moving forwardat high speed into head sea, particularly common for
fine form ships. In some instances, the whippingstress generated can constitute a sizable percentage ofthe sagging bending moment.
4.3.2 Load due to the Impact of Solid Objects andRobustness Considerations
These types of loads are very difficult to quantify.Traditionally, they have been taken care of by specifyingminimum scantlings based upon service experience. It hasbeen argued by many that existing robustness requirementsdo not allow the full use of advanced materials andtechnology. However, until more service experience isgathered for trimarans, these type of requirements areconsidered necessary.
4.4 Other loads
Other types of secondary loads include thermal loads, loadsarising as a result of cargo (weight and distribution) andvessel motions, and due to sloshing of liquids. These loadsare important and are required to be taken into account indesign. However these types of loading are common to alltypes of vessels and are therefore not uniquely specified inthe Trimaran Rules.
5 Rule formulation forprimary loads
Major efforts have been devoted to the derivation ofprimary load components as these loads are the principaldimensional loads for structural synthesis. Empiricalformulae are provided for the loads based on a database ofexisting designs with calibration carried out using thedirect analysis results provided by QinetiQ. The data setsused for direct analysis are those from numericalsimulations, model test data and Triton sea trialmeasurements. Sign conventions and definitions used areshown in Figure 6.
Figure 6: Sign conventions and definitions
5.1 Vertical bending moment [CAM5]
The vertical bending moment formulae implemented in theTrimaran Rules have similar form to that of a mono-hullship. The premise is that the trimaran behaves similarly toa mono-hull. All available trimaran data against which themoment values are validated suggest that the magnitude isreasonable. A comparison of the maximum Rule valuescalculated for the designs in the database versus theQinetiQ parametric analysis results is provided in Figure 7.
The rule formulae are given as:
Mw = FfDfMo
Mwh = FfhDfMo (Hog)
Mws = FfsDfMo (Sag)
Mo = 0,1LffservL2Bwl(Cbmh + 0,7)
Figure 7: Vertical bending moment comparisons
The distribution factors for vertical wave bending momentsvary according to the side hull position. This distributionfactor is given by:
Df = 0 at aft end of L
It is assumed that the side hull position has a greaterinfluence on the longitudinal distribution of the verticalbending moment than the relative displacement of the sidehull. The distribution factors were tested against resultsfrom QinetiQ’s parametric assessment as depicted inFigure 8. This plot is provided to represent only the foreand aft distribution of the moment, the magnitudes of themoment have been normalised.
= 1 from ( 0,35 - — ) L to ( 0,6 - — ) L
= 0 at forward end of L
x4L
x4L
(a)
(b)
(c)
Vertical Bending Moment
y = 110.04xR2 = 0.9809
y = 135.42xR2 = 0.9844
y = 87.319xR2 = 0.9561
y = 72.107xR2 = 0.9513
0
500000
1000000
1500000
2000000
2500000
3000000
3500000
4000000
0 5000 10000 15000 20000 25000 30000 35000 40000 45000 50000
Overall displacement (tonnes)
Ver
tical
ben
ding
mom
ent
(kN
-m)
Rule Sag VBM QQ Zero Speed QQ 12 Knots Rule Hog VBM
Linear (QQ Zero Speed) Linear (QQ 12 Knots) Linear (Rule Sag VBM) Linear (Rule Hog VBM)
Figure 8: Vertical bending momentdistribution factors
5.2 Horizontal bending moment
The horizontal bending moment was derived on the samebasis as the vertical bending moment except that thepressure distribution is integrated over the depth ratherthan the breadth of the ship. The factor, Lf, used for thisequation was then derived using QinetiQ’s parametricresults and comparing this to the calculated Rule values,see Figure 9. A comparison of the horizontal bendingmoment versus overall displacement is given as Figure 10.The magnitude of the horizontal bending moment is givenas follows:
Mh = Df Lf fservL2D(Cbmh + 0,7)
Figure 9: Determination of factor, Lf
Figure 10: Horizontal bending moment comparison
The distribution factor is taken to be the same as for thevertical bending moment as the premise of the calculationis the same.
5.3 Longitudinal torsional moment
The longitudinal torsional moment is derived using aconservative equivalent static wave to that occurring in aquarterting sea. This mass is multiplied by the heaveacceleration. Potential pitch and roll accelerationcomponents are assumed to cancel within the scope of thissimplified calculation. A distribution factor was thenderived using the parametric data from QinetiQ, seeFigure 11.
Figure 11: Distribution Factor LTf
Comparison of results is shown in Figure 12. It should benoted that this comparison is made versus side hulldisplacement, resulting in a significant spread in the plot.This spread may not exist if a volumetric comparison isplotted.
Lf = - [ 70 ( — )2+ 5L ] x103L
100
Mlt = 7,5LTf fservρ ( Vsh + Vcd + — ) yshahVmhs
2
HBM factor - HBM Thafts Value/ Rule value [L2D(CB+0.7)]
y = -0.072x2 + 0.465xR2 = 0.675
0.00
0.20
0.40
0.60
0.80
1.00
0 0.4 0.8 1.2 1.6 2 2.4
Rule length/100 (m)
CH
QQ Zero and 12 knots Poly. (QQ Zero and 12 knots)
150m - Vertical bending moment at zero speedRule distribution versus THAFTS distribution
0
50
100
150
200
250
300
350
400
450
500
0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150
Cut position - X coord.
Mom
ent [
MN
m]
Medium displacement - 0-speed Aft outriggers - medium - 0-speed Fw d. outriggers - medium - 0-speed
Horizontal Bending Moment
y = 42.778x
y = 45.993x y = 36.668x
0
300000
600000
900000
1200000
1500000
1800000
2100000
2400000
2700000
0 10000 20000 30000 40000 50000 60000 70000
Overall displacement (tonnes)
Hor
izon
tal b
endi
ng m
omen
t(k
N-m
)
QQ Zero Speed QQ 12 Knots Rule Value
Linear (QQ Zero Speed) Linear (QQ 12 Knots) Linear (Rule Value)
0.10
0.23
0.37
0.62
0.881.000.96
0.82
0.66
0.40
0.10
Distance from aft end of L in terms of L
LT f
Figure 12: Longitudinal torsional moment comparison
5.4 Splitting moment
The splitting moment is also derived from first principles ina similar manner to those currently used for a twin hulledship. In the case of the trimaran, there is a hog and sagsplitting moment. The hogging moment assumes the sidehulls are completely out of the water, while the saggingassumes complete submersion of the side hulls.
The rule formulae for splitting moment at point I are givenas follows (see Figure 6 for definitions):
The rule formulae for splitting moment at point O are givenas follows (see Figure 6 for definitions):
Msph = 25 fservWshaz(ysh- yO) (Hog)
The magnitudes of the splitting moments are compared toQinetiQ’s parametric values, as well as to design values forTriton and the two frigate designs. The factors for thesplitting moments were calibrated against the parametricvalues, see Figures 13 and 14. A factor of 2,5 was calculatedfor the hogging splitting which is coincidentally the same asthe factor applied for the catamaran splitting moment. Thesagging factor obtained is 1,5. The comparison of splittingloads to design values resulted in reasonable agreement.
Long term analysis of QinetiQ’s model tests was alsoperformed for splitting loads. Load gauges were fitted tofour locations on the models; at the connection of the crossdeck beams to the main hull, forward and aft. Althoughthese models were not segmented models, but rigidmodels, they gave a good indication of the generalmagnitude of the computed values. The general magnitudeof the long term splitting moment is in the order of thatobtained using the Rules.
Figure 13: Hog splitting moment comparison
Figure 14: Sag splitting moment comparison
5.5 Transverse torsional moment
The transverse torsional moment is calculated in a similarmanner to the longitudinal torsional moment except thatthe moment is calculated about the transverse axis of theship. The mass is also multiplied by the heave acceleration.Factors are again calculated using QinetiQ’s parametricresults. Comparisons are provided in Figure 15.
Mtt = 3,75fservρ(Vsh + Vcd)Lshab
Figure 15: Transverse torsional moment comparison
Longitudinal Torsional Moment
y = 585.28xR2 = 0.8607
y = 564.39xR2 = 0.7392
y = 591.58xR2 = 0.8342
0
100000
200000
300000
400000
500000
600000
700000
800000
900000
1000000
0.0 300.0 600.0 900.0 1200.0 1500.0
Side hull displacement (tonnes)
Long
itudi
nal t
orsi
onal
mom
ent
(kN
-m)
QQ Zero Speed QQ 12 Knots
Rule Longitudinal Torsional Moment Linear (QQ Zero Speed)
Linear (QQ 12 Knots) Linear (Rule Longitudinal Torsional Moment)
Hog Splitting Moment
y = 349.49x
R2 = 0.8976
y = 389.06x
R2 = 0.7317 y = 371.72x
R2 = 0.915
0
100000
200000
300000
400000
500000
600000
0 200 400 600 800 1000 1200 1400 1600
Displacement of side hull (tonnes)
Hog
Spl
it M
omen
t at I
(kN
-m)
Rule Hog Splitting Moment QQ Zero Speed QQ 12 Knots
Linear (QQ Zero Speed) Linear (QQ 12 Knots) Linear (Rule Hog Splitting Moment)
Sag Splitting Moment
y = 15.021x
R2 = 0.9741
y = 17.512x
R2 = 0.9454
y = 18.048x
R2 = 0.9759
0
100000
200000
300000
400000
500000
600000
0 5000 10000 15000 20000 25000 30000
Overall displacement (tonnes)
Sag
Spl
it m
omen
t at
I (k
N-m
)
Rule Sag Splitting Moment QQ Zero Speed QQ 12 Knots
Linear (QQ Zero Speed) Linear (QQ 12 Knots) Linear (Rule Sag Splitting Moment)
Transverse Torsional Moment
y = 701.6x
R2 = 0.7487
y = 965.23x
R2 = 0.7005y = 794.42x
R2 = 0.6187
0
200000
400000
600000
800000
1000000
1200000
1400000
1600000
1800000
0 200 400 600 800 1000 1200 1400 1600
Displacement of side hull (tonnes)
Tran
sver
se t
orsi
onal
mom
ent
(kN
-m)
Rule Values Zero Speed 12 Knots
Linear (Zero Speed) Linear (12 Knots) Linear (Rule Values)
Msph = 25 fservWshaz ( ysh - — ) (Hog)
Msps = 15 fserv— ah ( ysh - — ) (Sag)
Bmh2
Bmh2
(Δ - 2Wsh)2
Msps = 15 fserv — ah (ysh- yO) (Sag)(Δ - 2Wsh)2
6 Rule formulations forsecondary and tertiaryloads
Secondary and tertiary loads are considered local in natureand they were mainly derived from existing ruleformulations from the Ship Rules, SSC Rules and the NavalShip Rules. Thus far, they have been calibrated against thescantlings of RV Triton and two MoD frigate designs.Validation against other designs is ongoing and UniversityCollege of London (UCL) is contracted by MoD to providesome of this validation.
Scantlings for RV Triton are calculated based on theempirical formulae and compared with those fitted. Thecomparisons for tertiary structures are shown in Figures 16and 17. It can be observed the robustness criteria in theform of minimum requirements are, in some cases,governing. These comparisons do not include scantlingrequirements for impact loads. In all cases the as builtscantlings are in compliance with the rule requirements.
Figure 16: Comparison of rule and as built scantlings
Figure 17: Comparison of rule and as built scantlings
7 Advance calculationprocedure
After obtaining an initial design using the empiricalformulae given in the Rules, the designer, builder or owneris to undertake a detailed analysis of the structureaccording to the Advanced Calculation Procedure. Thisprocedure consists of Structural Strength Analysis andVerification section which is mandatory, as well as anoptional Load Development Procedure. A flow diagramdescribing the overall analysis is provided as Figure 17.
Figure 18: Advanced Calculation ProcedureFlow Diagram
Plating Thickness Comparison
0
1
2
3
4
5
6
7
8
Main Hull
Bottom
Main Hull
Bilg
e
Main Hull
WL
Main Hull
Side
Side
Hull B
ottom In
bd
Side
Hull W
L Inbd
Side
Hull S
ide Inbd
Side
Hull B
ottom O
utbd
Side
Hull W
L Outbd
Side
Hull S
ide Outbd
Side
Hull 2
Dec
k Outbd
Side
Hull 1
Dec
k Outbd
Wet
Dec
k
Wea
ther D
eck
Thic
knes
s (m
m)
tbuilt(mm)tmin(mm)trule(mm)
Secondary Member Modulus Comparison
01020304050607080
Main Hull
Bottom
Main Hull
Bilg
e
Main Hull
WL
Main Hull
Side
Side
Hull W
L Lo
ngInbd
Side
Hull W
L Lo
ng O
utbd
Side
Hull 2
Dec
k Lon
gOutbd
Side
Hull 1
Deck L
ongOutbd
Wet
Dec
k
Wea
ther D
eckLo
ng
Mod
ulus
(cm
3 )
Zrule (cm3)Zbuilt (cm3)
Global FE Model
Are Rule loadsused?
Loads from alternateprocedure applied,
Chapter 3
Rule loads applied,Chapter 2
Boundary conditions applied
Full ship global finite elementanalysis
Critical areas selected fromglobal FE results
Analysis Complete
Apply loads
no yes
Fine mesh analysis
Assess againstacceptance criteria
Structure meetscriteria
Modifications toglobal model
Structure doesnot meet criteria
Assess againstacceptance criteria
Structure meetscriteria
Structure doesnot meet criteria
Refine local model
7.1 Structural strength analysis andverification
This portion of the Advanced Calculation Proceduredescribes how to undertake a finite element analysis of thetrimaran structure. This includes guidance on modelling ofglobal and local structure, as well as details on applicationof loads for each of the primary loads. Figure 19, forexample, depicts the application of load for the longitudinaland transverse torsional moments.
Also included in this procedure are requirements forboundary conditions, as depicted in Figure 20, as well asdetails on load combinations to be evaluated andacceptance criteria against which to evaluate the structure.
Figure : Load Application for Torsional Moments
Figure 20: Boundary Conditions for Global Model
7.2 Load development procedure
This portion of the Advanced Calculation Proceduredescribes how to undertake the development of wave-induced loads acting on the structure by a ìfirst principlesîapproach. The procedure provides more realistic loadingscenarios, improving the user’s confidence in the loadswhich are to be applied to the finite element model. Itprovides a method to derive the design loads using directcalculation techniques. These loads may be used as the
design loads instead of the Rule loads in all aspects ofstructural assessment provided that the proposed loads aresubmitted and approved by LR. The procedure thendescribes how to apply these loads to the finite elementmodel. An overview of the steps of the Load DevelopmentProcedure is given in Figure 21.
Figure 21: Load Development Procedure
BHD
x
yz
BHDBHD
BHD
BHD
BHD
(a) Longitudinal Torsional Moment
(b) Transverse Torsional Moment
Loading conditions,
RAO calculations,
Short term response,
Long term response,
Derive designvalue
RAOs formotion and
loadparameters
ω range,ψ range,
Operationalprofile,
Scatter diagram,wave spectrum,
spreading function,
Calibrationmodel, tank
test, full scalemeasurements
Select characteristic wave byidentifying RAO with maximum
amplitude, A
Motion andload
parameters
For each load andmotion parameter
For each load andmotion parameter
Obtain phase angle, φ and time, tr,
Derive value of all pressures and inertialloads for application to the FE
Check ship motion balance
Check FE load balance
Apply load case to FE according to StructuralStrength Analysis and Verification
8 Load combinations andacceptance criteria
Parametric formulae for primary, secondary and tertiaryloads are provided for the initial derivation of scantlings. Itis then required that a three dimensional finite elementanalyses be carried to examine the adequacy of the globalstrength in accordance to the acceptance criteria given inthe Rules.
The loads applied to the finite element model may either bederived according to the Advanced Calculation Procedureor the Rule values may be used. If the Rule values are usedfor the primary loads, then the load combinations describedin 7.1 are to be evaluated. If the loads are obtained fromdirect calculation, pressures, which inherently include acombination of primary responses, will have been derived.
8.1 Load combinations
There are four sea conditions for which the primaryresponses are maximised. These are as follows:
8.1.1 Head Seas
The head sea conditions correspond to the maximumhogging and sagging bending moments. The main areasthat require examination are the mid-ship structure, deckand keel longitudinal stresses and maximum shear at theside hull termination.
For the hogging condition, the following load combinationsare to be applied to the model:
Mswh + Mwh + 0,3Msph + 0,2Mtt
For the sagging condition, the following load combinationsare to be applied to the model:
Msws + Mws + 0,3Msps + 0,2Mtt
8.1.1 Bow Quartering Seas
The bow quartering sea conditions correspond to themaximum longitudinal torsional moment and themaximum horizontal bending moment. Main areas thatrequire examination include the torsional strength of themain hull, warping of the cross deck, as well as theconnections of the side hulls to the main hull through thecross deck structure.
For the examination of the longitudinal torsional strength,the following load combination is to be applied to themodel:
-0,3Mh + 0,3Msph + Mlt + 0,3Mtt ± Msw
where Msw is the still water bending moment (Mswh orMsws) that gives the highest stress for the combination.
For the examination of the horizontal bending strength, thefollowing load combination is to be applied to the model:
Mh + 0,4Msph -0,3Mtt ± Msw
where Msw is the still water bending moment (Mswh orMsws) that gives the highest stress for the combination.
8.1.3 Beam Seas
The main areas that require examination are the bendingand shear strength of cross deck structures, and connectionsof side hulls to the main hull.
For the splitting hog condition, the following loadcombination is to be applied to the model:
Mswh + 0,1Mwh + Msph + 0,2Mlt
For the splitting sag condition, the following loadcombination is to be applied to the model:
Msws + 0,1Mws + Msps + 0,2Mlt
For the maximum roll condition, the following loadcombination is to be applied to the model:
Msws + Mws + θmax
is determined from simplified formulae given in the Rulesor from direct computations.
8.1.4 Stern Quartering Seas
The main areas that require examination are the torsionalstrength of the hull, warping of the cross deck and theconnections of the side hulls to main hull through the crossdeck structures.
For the examination of the transverse torsional strength, thefollowing load combination is to be applied to the model:
Mswh + 0,2Mwh - 0,2Mh + 0,5Msph + Mtt
8.2 Acceptance criteria
The results from the finite element analysis are to beassessed against acceptance criteria on yield, buckling anddeflection as given in the Rules. Similar acceptance criteriaare used to assess the structure using the empiricalformulae, thus maintaining a consistent safety margin.
9 Conclusions
The trimaran design has now become a viable option forboth military and commercial applications. With fundingfrom the MoD and support by QinetiQ and more recentlyUniversity College London, Lloyd’s Register is developingRules for Classification of these vessels. The TrimaranRules development involves principally the developmentof design loads applicable to the unique hull form of atrimaran, as well as a direct calculation procedure foranalysis of new trimaran designs.
The development of the these rules has been a verycomplex task as there is relatively little data and serviceexperience available for calibration in comparison withconventional mono-hull ships. Efforts have been put in thearea of load development, in particular, the development ofprimary loads. It is recognised that it is not sufficient just toprovide prescriptive design formulae, but it is alsoimportant to provide the necessary framework to achieve asafe and economic design through direct analysis. TheTrimaran Rules adopt a modern demand and capabilityapproach which enables direct analyses to be performed forboth load computation and strength analysis. The overallphilosophy of the Rules is to ensure that a consistent levelof safety is achieved whatever route the design isgenerated, through a consistent set of acceptance criteria.
It is anticipated the Trimaran Rules will be publishedformally in 2005.
10 Acknowledgements
The authors wish to express their sincere thanks to theMinistry of Defence for their financial support and toQinetiQ for their technical support during the developmentof the Trimaran Rules. Colleagues in Lloyd’s Register whocontributed to these Rules are gratefully acknowledged.
Views expressed in this paper are solely those of theauthors and they do not represent necessarily the views ofLloyd’s Register and any supporting organisations.
11 References
1. Lloyd’s Register Rules and Regulations for theClassification of Ships, 2003.
2. Lloyd’s Register Rules and Regulations for theClassification of Naval Ships, 2003.
3. Lloyd’s Register Rules and Regulations for theClassification of Special Service Craft, 2003.