shipright sda sloshingloadsandscantlingassessment

Structural DesignAssessment

Sloshing Loads andScantling Assessment

May 2004

ShipRightDesign and construction

ABCD Lloyds Register Marine Business Stream 71 Fenchurch Street London EC3M 4BS Telephone 020 7709 9166 Telex 888379 LR LON G Fax 020 7488 4796

Lloyd's Register, its affiliates and subsidiaries and their respective officers, employees or agents are, individually and collectively, referred to in this clause as the Lloyd's Register Group. The Lloyd's Register Group assumes no responsibility and shall not be liable to any person for any loss, damage or expense caused by reliance on the information or advice in this document or howsoever provided, unless that person has signed a contract with the relevant Lloyd's Register Group entity for the provision of this information or advice and in that case any responsibility. Lloyds Register Marine Business Stream is a part of Lloyds Register.

Lloyds Register,2004

Document History

Document Date: Notes:

October 1994 New document

November 2001 Intranet user review version

July 2002 General release.

Notice 1 October 2002

Revisions as identified in History of Development up to January 2004.

May 2004 Revisions as identified in Structural Design Assessment Sloshing Loads and Scantling Assessment, Changes incorporated in May 2004 version.

LLOYDS REGISTER

Chapter Contents

Sloshing Loads and Scantling Assessment, May 2004

1 Introduction

2 Scope of Procedure

3 Fluid Sloshing Phenomena

4 Definitions

5 Units

6 Data Requirements

7 Levels of Assessment

8 Loading Conditions and Ship Motions Sloshing Analysis

9 Level 1 Sloshing Pressure Determination



12 Post-Processing of SDA Fluids Data

13 Strength Assessment

PROCEDURES MANUAL

Chapter Contents


PROCEDURES MANUAL

LLOYDS REGISTER

14 Acceptance Criteria

15 Applications

References

Appendices

A Examples

B Natural Frequencies of Structural Components

C Determination of Equivalent UniformlyDistributed Loading

D SDA Fluids Data FileDYN_STAT Data File & Output

LLOYDS REGISTER

Contents


CHAPTER 1 INTRODUCTION 1

Summary

Section 1 Introduction

CHAPTER 2 SCOPE OF PROCEDURE 3

Section 1 Scope of Procedure

CHAPTER 3 FLUID SLOSHING PHENOMENA 5

Section 1 Sloshing Waves

Section 2 Sloshing Induced Loads

CHAPTER 4 DEFINITIONS 9

Section 1 Filling Factor Coefficient

Section 2 Fluid Natural Period

Section 3 Tank Depth

Section 4 Maximum Lifetime Ship Motions4.1 Ships Natural Rolling Period4.2 Ships Natural Pitching Period4.3 Maximum Lifetime Roll Angle4.4 Maximum Lifetime Pitch Angle4.5 Maximum Lifetime Heave Amplitude4.6 Maximum Lifetime Sway Amplitude4.7 Maximum Lifetime Vertical Acceleration4.8 Centre of rotation

Section 5 Effect of Wash Bulkhead on Sloshing Pressures

Section 6 Pressure at Tank Corners

Section 7 Pressure in Tapered Tanks

CHAPTER 5 UNITS 17

Section 1 Units

CHAPTER 6 DATA REQUIREMENTS 19

Section 1 Data Requirements

PROCEDURES MANUAL

Contents


PROCEDURES MANUAL

LLOYDS REGISTER

CHAPTER 7 LEVELS OF ASSESSMENT 21

Section 1 Pressure Determination

Section 2 Sloshing Criteria

Section 3 Critical Fill Range

Section 4 Level 1 Assessment



Section 7 Structural Capability

CHAPTER 8 LOADING CONDITIONS AND SHIP 23MOTIONS FOR SLOSHING ANALYSIS

Section 1 General Considerations

Section 2 Loading Conditions2.1 Unrestricted Filling Levels -

Unspecified Sea-Going Loading Conditions2.2 Restricted Filling Levels -

Unspecified Sea-Going Loading Conditions2.3 Unrestricted Filling Levels -

Specified Sea-Going Loading Conditions2.4 Restricted Filling Levels -

Sea-Going Loading Conditions

Section 3 Level 2 Sloshing Assessment Parameters3.1 Level 2 Ship Motions3.2 Level 2 Fill Range

Section 4 Level 3 Assessment Parameters4.1 Level 3 Ship Motions4.2 Level 3 Investigation Fill Range

CHAPTER 9 LEVEL 1 SLOSHING PRESSURE 27DETERMINATION

Section 1 Level 1 Sloshing Pressure Determination


Section 1 Smooth Rectangular Tanks

Section 2 Smooth Hopper Tanks

Contents

LLOYDS REGISTER


PROCEDURES MANUAL


Section 1 General

Section 2 Limitations and Assumptions of SDA FluidsProgram

Section 3 Data Preparation3.1 Mesh Spacing3.2 Fitting the mesh to the tank3.3 Boundary Conditions3.4 Including Internal Tank Structure3.5 Properties of the Fluid3.6 Pressure Output Sampling Points3.7 Ullage Pressure3.8 Sloshing Excitation Spectrum3.9 Time Control

CHAPTER 12 POST-PROCESSING OF SDA FLUIDS DATA 41

Section 1 Sloshing Simulation Quality Assurance Procedure1.1 General1.2 Minimum Quality Assurance Post Processing

Requirements1.3 Inconsistencies and Applied Results

Section 2 Pressure Pulse Time Averaging Scheme

Section 3 Dynamic and Static Pressures3.1 Conversion of Dynamic Pressure to Static

Pressure3.2 Response Calculation3.3 Pressure Conversion Procedure

Section 4 Structure Natural Frequency Calculation

Section 5 Force and Couple

Section 6 Pressure Applied to Internal Structural Members

CHAPTER 13 STRENGTH ASSESSMENT 47

Section 1 Pressure and Stresses

Section 2 Collapse Analysis Procedures for ClampedStiffened Panels

2.1 Description2.2 Assumptions and Limitations2.3 Applied Loads2.4 Output

Section 3 Minimum Factors of Safety

Contents


PROCEDURES MANUAL

LLOYDS REGISTER

Section 4 Girder Structural Analysis Procedure4.1 Finite Element Analysis4.2 Analytical Structural Analysis4.3 Applied Loads

CHAPTER 14 ACCEPTANCE CRITERIA 55

Section 1 Strength based acceptance criteria

Section 2 Service based acceptance criteria

CHAPTER 15 APPLICATIONS 57

REFERENCES 59

APPENDICES

APPENDIX A EXAMPLES 61

Section 1 Level 1 Investigation



APPENDIX B NATURAL FREQUENCIES OF 85STRUCTURAL COMPONENTS

Section 1 Natural Frequency of Plate

Section 2 Natural Frequency of Plate Stiffener

Section 3 Effect of Submergence

Section 4 Dynamic Load Factor Charts4.1 Gradually Applied Load4.2 Triangular Pulse Load

APPENDIX C DETERMINATION OF EQUIVALENT 93UNIFORMLY DISTRIBUTED LOADING

Section 1 General

Section 2 Determination of Equivalent UniformlyDistributed Loading

2.1 Trapezoidal Distributed Loading2.2 Arbitrary Distributed Loading

APPENDIX D SDA FLUIDS DATA FILE 97DYN_STAT FILE & OUTPUT

1LLOYDS REGISTER 1

Introduction


Chapter 1SUMMARY

SummarySection 1: Introduction

Summary

This document describes the ShipRight SDA Sloshingprocedure for the assessment of boundary structures ofpartially filled tanks and liquid carrying holds. Three levelsof assessment are defined, each requiring a differentapproach to the estimation of likely maximum sloshingpressures.

Level 1 assessment is based on equivalent static loadsresulting from lifetime angular motions.

Level 2 assessment uses the SDA Tank Assessment program(10603) to determine the pressure on the tank boundaries.

Level 3 assessment uses the SDA Fluids finite differenceprogram to determine sloshing pressures on the tankboundaries and internal structural elements.

The strength assessment is based on safety against collapse.The calculations may be carried out using the SDA UltimateStrength program (10604).

Section 1: Introduction

1.1 Where partial filling of tanks and liquid carryingholds is required, the likelihood of sloshing from both theship rolling and pitching is to be investigated. Sloshing isdefined as a dynamic magnification of internal pressuresacting on the boundaries of the tank to a level greater thanobtained from static considerations alone.

1.2 For any tank design, dimensions, internal stiffeningand filling level, a resonant period (or frequency) of thefluid exists, which, if excited by ship motions, can result invery high pressure magnifications.

1.3 The purpose of this procedure is to enable thedetermination of lifetime maximum design sloshingpressures for anticipated filling levels, tank position withinthe ship and ships loading conditions.

1.4 The estimated dynamic pressures may then be usedto determine the scantlings necessary to prevent structuralcollapse using appropriate structural collapse theory inassociation with defined criteria.

1.5 A typical sloshing investigation is illustrated in theflow chart in Figure 1.1.

1.6 The procedure is divided in two parts :

1. Assessment of pressures on tank boundaries2. Scantling determination and acceptance criteria

Note:LNG tanks in partial filling conditions exhibit a complexbehaviour of the fluid as a result of the possible change ofphase of the fluid under high velocity impacting with aboundary, and 3D effects resultings from the chamferedgeometry of the tank top. It is considered that both theSDA Tank Assessment program (10603) and SDA Fluidsyield a realistic behaviour of the fluid flow level ofpressures, for fill LNG levels which do not involve impactson the tank top.

Sloshing Loads and Scantling Assessment forTanks Partially Filled with Liquids


Chapter 1SECTION 1

LLOYDS REGISTER2

Figure 1.1

Sloshing Investigation Flow Chart

SHIP DATA

PERIODS CALCULATION

LEVEL OF ASSESSMENTDETERMINATION

LEVEL 1 LEVEL 2 LEVEL 3

SDA Fluids

DYN_STAT

PROCEDUREGUIDELINES

ACCEPTANCECRITERIA

STRENGTH ACCEPTANCECRITERIA

SE

RV

ICE

AC

CE

PT

AN

CE

CR

ITE

RIA

SDA Tank AssessmentProgram (10603)

SDA Ultimate StrengthProgram (10604)

SDA Tank AssessmentProgram (10603)

SDA Ultimate StrengthProgram (10604)

PRESSURECONVERSION

?

SATISFIED?

YES

YES

NO

NO

2LLOYDS REGISTER 3

Scope of Procedure


Chapter 2SECTION 1

Section 1: Scope of Procedure

Section 1: Scope of Procedure

1.1 The procedure applies to tanks and liquid carryingholds of arbitrary shape filled with liquids with theexception of spherical or cylindrical tanks which need to bespecially considered. In addition, some tanks, by virtue oftheir shape, size or degree of internal stiffening, will not besubjected to sloshing loads. If any such tank is likely to bepartially filled, the reasons for exclusion from theinvestigation should be stated and agreed by LloydsRegister. In general, sloshing calculations need not beperformed for peak tanks or bunkers.

1.2 Any scantlings derived as a result of this procedureare to be regarded as additional to the Rule requirementsfor full tanks and liquid carrying holds.


LLOYDS REGISTER4

3LLOYDS REGISTER 5

Fluid Sloshing Phenomena


Chapter 3SECTION 1

Section 1: Sloshing WavesSection 2: Sloshing Induced Loads

Section 1: Sloshing Waves

1.1.1 As the tank oscillates, different sloshing waves will becreated depending on the fill depth and frequency ofoscillations. An infinite number of different modes of liquidmotion may occur depending upon the conditions ofexcitation and fill depth. However, it is possible to dividethe sloshing phenomena into the following four categoriesto describe the observed modes shown on Figure 1.1.

Standing Wave

The movements of the liquid particles on the surface areessentially vertical, the surface having one or more nodeswhere practically no vertical surface displacement takesplace. Standing waves generally occur when F/Ls 0,2 andimpart high impact pressures mainly to the tank top.

whereF = Fill height (m)

Ls = Effective horizontal free surface length in thedirection of angular motion (m)

Travelling Wave

The surface has no nodes, a wave crests travels back andforth between vertical tank boundaries. Travelling wavesgenerally occur when F/Ls < 0,2 and impart high impactpressures to both side walls and tank top.

Hydraulic Jump

This Phenomena, which might be considered as a specialcase of a travelling wave, is characterised by a discontinuity(jump) in the surface, forming a vertical front which travelsperiodically back and forth in the tank.

Combination Wave

A combination of standing waves and travelling waves.

For low filling, a standing wave is formed when the tank isoscillating at a frequency far below the fluid naturalfrequency. As the excitation frequency increases, thistransforms into a train of progressive waves having a veryshort wavelength. A hydraulic jump is formed due to asmall disturbance at a range of frequency around the fluidresonance frequency. With further increase in frequencybeyond resonance, the hydraulic jump transforms into asolitary wave. In general, hydraulic jumps are formed onlywhen the fill level is 20 per cent of the horizontal freesurface length of the tank or less.

For high fill levels, the sloshing phenomenon nearresonance is characterised by the formation of standingwaves of large amplitudes. These waves are non symmetricand may be combined with travelling waves at largeamplitude of excitation.



Chapter 3SECTIONS 1 & 2

LLOYDS REGISTER6

Section 2: Sloshing Induced Loads

2.1.1 Liquid sloshing involves different types ofhydrodynamic loads upon the tank and its internalstructure. There are two types of dynamic pressure whichcan arise from liquid sloshing, namely non-impulsive andimpulsive pressure. Typical time histories for the followingsloshing induced loads are shown in Figure 2.1.

Non Impulsive Dynamic Pressure

These are slowly varying loads, pulsating with a period ofthe order of the sloshing wave period, i.e. period of theorder of the fluid natural period and/or excitation period.

Impulsive dynamic pressure type I

These are due to a rapid but continuous build up of liquidand liquid pressure on the surface of a member which isgradually being immersed. The impulse duration istypically in the order of 1/10 of the sloshing wave period.

Impulsive dynamic pressure type II

These are due to localised impact pressure arising from thecollision between the fluid and the solid surface. Suchpressures can be extremely high and of extremely short risetime duration in the range 1/100 to 1/1000 of the sloshingwave period.

Total Dynamic Forces and Moments

These loads arise from the slowly varying non impulsivehydrodynamic pressure distribution on the tank boundarieswith a period of the order of the sloshing wave period.

Drag and Inertial Forces

These non impulsive forces act on submerged memberswith time fluctuations related to the sloshing wave period.

Vortex Induced Pressure Field

These pressure fields develop around slender memberslocated in the field of oscillating liquid. Interactionbetween the generated pressure fluctuations and naturalmodes of structural vibrations in the member may becomecritical.

Standing Wave

Travelling Wave

Hydraulic Jump

Combination Wave

Fig 1.1

Typical Sloshing Waves


LLOYDS REGISTER 7


Chapter 3SECTION 2

Figure 2.1

Sloshing Induced Loads and Typical Time Trace


LLOYDS REGISTER8

4LLOYDS REGISTER 9

Definitions


Chapter 4SECTIONS 1, 2 & 3

Section 1: Filling Factor CoefficientSection 2: Fluid Natural Period

Section 3: Tank DepthSection 4: Maxiumum Lifetime Ship MotionsSection 5: Effect of Wash Bulkhead on Sloshing

PressuresSection 6: Pressure at Tank Corners

Section 7: Pressure in Tapered Tanks

Section 1: Filling FactorCoefficient

1.1.1 The filling factor, Fc is defined as follows :

Fc = F/H + 6,0 o /cosh (Fr) (4.1)

whereF = fill height (m)H = total tank depth (m) = max or max as appropriate (radian)o = the greater of 1 or 21 = e-(Tn Sn)

2/k

2 = 0,105 for roll= 0,052 for pitch

k = 4 for roll= 6 for pitch

Fr = the effective filling ratio= {F b-[n/(n+1]}/Ls

b = height of internal primary bottom stiffeners (m)n = number of internal primary bottom stiffenersLs = effective horizontal free surface length in the

direction of angular motion (m)g = gravity constant (9,81 m/s2).

A low fill is defined as a filling level for which the factor Fcis less or equal than 1,02. However, when the fluid andship natural periods are close, Fc will invariably be greaterthan 1,02; in this case, a low fill is defined for F/Ls less orequal to 0,21. Any other filling is defined as high.

Section 2: Fluid Natural Period

2.1.1 The fluid natural period in pitch or roll, Tnp or Tprrespectively is given by :

Tn = - 4Ls/(gtanh(Fr)) (4.2)

Section 3: Tank Depth

3.1.1 The depth of a tank H is measured from the bottomof the tank to the underside of the deck at side. In the caseof holds, the depth is measured from the inner bottom tothe underside of the deck at hatch side, except in doubleskin ships with hatch coaming in line with the inner skin, inwhich case, the depth is measured from the top of thehatch.



Chapter 4SECTION 4

LLOYDS REGISTER10

Section 4: Maximum LifetimeShip Motions

When possible, direct calculation procedures capable oftaking into account the ships actual form and weightdistribution should be performed in order to determine theship motions. Such methods will involve the derivation ofthe response to regular waves using strip theory, thederivation of the short term response to irregular wavesusing the concept of sea spectrum, and the derivation oflong term response predictions using statisticaldistributions of sea states.

Otherwise, the following expressions should be used todetermine the approximate maximum lifetime shipmotions. These expressions derived on a statistical basiscorrespond to extreme ship motions and accelerations witha probability of occurrence of once in a ship lifetime of 20years for ships of normal proportions.

4.1 Ships Natural Rolling Period

The ships natural rolling period Snr is given by :

Snr = 2,35 r/ GM (4.3)

wherer = the radius of gyration of roll and may be taken as

0,34 B (m)GM = transverse metacentric height with free surface

correction (m).

For ships for which either r or GM varies significantlybetween loading conditions (for example, bulk carriers andtankers), Snr should be evaluated for each representativeloading condition considered.

4.2 Ships Natural Pitching Period

The ships natural Pitching period Snp is given by :

Snp = 3,5 TCb = 3.5 (4.4)LB

whereT = the mean draught (m)

Cb = the block coefficientL = the lenght between perpendiculars (m)B = the ship breadth (m) = the ship displacement (m3)

Similarly, for ships for which either T or Cb variessignificantly between loading conditions (for example, bulkcarriers and tankers), Snp should be evaluated for eachrepresentative loading condition considered.

4.3 Maximum Lifetime Roll Angle

The maximum lifetime roll angle in degrees is given by :

max = (14,8 + 3,7 L/B)e-0,0023.L (4.5)

whereL = the length between perpendiculars (m)B = the ship breadth (m).

4.4 Maximum Lifetime Pitch Angle

The maximum lifetime pitch angle in degrees is given by :

max = (32,7 - 8,2 Cb)e-0,001L(4,9+Cb/2) (4.6)

4.5 Maximum Lifetime HeaveAmplitude

The maximum lifetime heave amplitude in metres is givenby :

Zmax = 10e-0,0032L (4.7)

but need not be taken greater than 4 metres.

4.6 Maximum Lifetime SwayAmplitude

The maximum lifetime sway amplitude, in metres, is givenby :

Ymax = 5e-0,0025L (4.8)

but need not be taken greater than 2,50 metres.


LLOYDS REGISTER 11


Chapter 4SECTIONS 4, 5 & 6

4.7 Maximum Lifetime VerticalAcceleration

The maximum lifetime acceleration, in m/s2, at alongitudinal position x from midships is given by :

a = gao 1+(5,3 45/L)2 (x/L + 0,05)2 (0,6/Cb)3/2

(4.9)

whereao = 0,2 V/ L + (34 600/L)/Lx = the longitudinal distance from midships to centre

of the tank being considered, with x positiveforwards (m)

V = the ship service speed (knots)g = the acceleration due to gravity (m/s2).

4.8 Centre of rotation

The vertical centre of rotation is to be taken to be at theVCG for the loading condition under consideration. Whenthis is unavailable, the vertical centre of rotation may betaken as at depth (moulded)/2,0 from the keel.

The longitudinal centre of rotation is to be taken to be atthe LCG for the loading condition under consideration.When this is unavailable, the centre longitudinal of rotationmay be taken as at midship.

Section 5: Effect of WashBulkhead on SloshingPressures

Wash bulkheads which represent more than 85% of thetank cross sectional area are taken as being effective assloshing barriers which limits the free surface length.

The effect of a wash bulkhead may be estimated using atotal energy approach applied to the load distribution ascalculated for the tank. The total pressure on the bulkheadwith the estimated effect of the wash bulkhead may beexpressed as follows :

P = Ps + PD /(1 + ) (4.10)

whereP = the total pressure on bulkhead with estimated

effect of wash bulkheadPs = the static pressure without wash bulkheadPD = (PT Ps) is the dynamic pressure without wash

bulkhead

PT = the computed total pressure without washbulkhead

= (area of openings in wash bulkhead)/(area ofwash bulkhead)

= (1)/1+).

In the case where frames or transverse members areinstalled instead of wash bulkhead, the pressure on thewatertight bulkhead is observed to decrease to about 80%of the dynamic pressure without frames or transversemembers when only two or three members are installed,but the dynamic pressure no longer decreases withincreasing number of frames or transverse members.

Section 6: Pressure at TankCorners

The pressure at the tank corners may be derived bycombining the corner pressure Proll and PPitch obtainedfrom a level 3 investigation for both rolling and pitchingmotions. The pressure at tank corners is expressed asfollows:

Pcorner = Max [ (Cpp()P2pitch + Cpr()P2roll)] (4.11)for 0 = Heading 180

whereCpp() = the pitch pressure coefficient at given in

Figure 6.1 and Table 6.1.Cpr() = the roll pressure coefficient based on the ratio

L/B at given in Figure 6.2 and Table 6.2. Forintermediate values of L/B, the factor is to bedetermined by linear interpolation.

The pressure at the corners is to be applied to a distanceextending 0,10 [Tank Breadth] and 0,10 [Tank Length] onthe transverse boundary and longitudinal boundaryrespectively. The pressure value then decreases linearlyover a distance 0,05 [Tank Breadth] or 0,05 [Tank Length]to the pressure value obtained from 2D solution.

The factors Cpp and Cpr are based on the short termmotion responses in long crested irregular seas for pitchand roll. These expressions incorporates both the effect ofmotion amplitude and phase between the components ofmotion.



Chapter 4SECTION 6

LLOYDS REGISTER12

Coefficient

Cpp

1

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

00 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180

Heading (o)

Pitch Pressure Coefficient Cpp

Figure 6.1

Pitch Pressure Coefficient Cpp

Figure 6.2

Roll Pressure Coefficient Cpr

Coefficient

Cpr

1

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

00 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180

Heading (Degrees)

Roll Pressure Coefficient Cpr

L/B = 5,50 - L/B = 6,25 ..... L/B = 7,00 - L/B = 7,75 -- L/B = 8,50


LLOYDS REGISTER 13


Chapter 4SECTION 6

Cpr Cpr Cpr Cpr Cpr

L/B 5,50 6,25 7,00 7,75 8,50

0 0,000 0,000 0,000 0,000 0,058

5 0,075 0,072 0,078 0,054 0,117

10 0,142 0,139 0,143 0,121 0,221

15 0,229 0,213 0,234 0,186 0,347

20 0,322 0,311 0,334 0,294 0,479

25 0,457 0,451 0,469 0,438 0,604

30 0,614 0,610 0,619 0,597 0,716

35 0,764 0,760 0,758 0,745 0,809

40 0,882 0,878 0,867 0,870 0,900

45 0,958 0,958 0,978 0,975 0,950

50 1,000 1,000 1,000 1,000 0,990

55 0,950 0,941 0,941 0,983 1,000

60 0,852 0,862 0,861 0,900 0,980

65 0,744 0,761 0,774 0,818 0,960

70 0,623 0,647 0,675 0,727 0,920

75 0,503 0,533 0,575 0,635 0,879

80 0,395 0,429 0,483 0,549 0,834

85 0,306 0,344 0,406 0,475 0,785

90 0,240 0,280 0,345 0,415 0,735

95 0,197 0,237 0,301 0,369 0,684

100 0,173 0,211 0,270 0,335 0,634

105 0,162 0,198 0,247 0,307 0,585

110 0,152 0,185 0,229 0,283 0,538

115 0,142 0,171 0,211 0,258 0,494

120 0,129 0,159 0,196 0,231 0,452

125 0,121 0,146 0,181 0,208 0,413

130 0,110 0,133 0,165 0,183 0,378

135 0,100 0,121 0,150 0,167 0,345

140 0,088 0,108 0,135 0,149 0,315

145 0,079 0,096 0,121 0,133 0,288

150 0,067 0,083 0,105 0,117 0,265

155 0,056 0,068 0,088 0,096 0,244

160 0,046 0,058 0,071 0,083 0,226

165 0,033 0,046 0,058 0,069 0,210

170 0,021 0,029 0,040 0,050 0,193

175 0,013 0,021 0,025 0,029 0,175

180 0,000 0,005 0,013 0,013 0,160

Cpp

0 0,600

5 0,600

10 0,600

15 0,600

20 0,600

25 0,600

30 0,600

35 0,594

40 0,575

45 0,547

50 0,510

55 0,466

60 0,416

65 0,363

70 0,310

75 0,262

80 0,222

85 0,194

90 0,181

95 0,186

100 0,210

105 0,253

110 0,313

115 0,389

120 0,474

125 0,565

130 0,654

135 0,734

140 0,800

145 0,860

150 0,915

155 0,955

160 0,980

165 0,995

170 1,000

175 1,000

180 1,000

Table 6.1 Table 6.2



Chapter 4SECTION 7

LLOYDS REGISTER14

Section 7: Pressure in TaperedTanks

Where tanks are tapered in plan view such as foremost oraftermost tanks, limited model experiments indicated thatin pitching the dynamic pressure on the bulkhead at thenarrow end can be magnified when compared with a tankof uniform section. Lloyds Register Fluids two-dimensionalfluid computational procedure cannot take into accountthis aspect. The pressure at the narrow end of the tank canbe expressed in terms of the pressure obtained for a tank ofuniform breadth by using the following expression.

Ptapered = Kt.Pmax.breadth (4.12)

whereKt = 0,8e(0,2235ARb)

ARb = the ratio of the maximum breath to the taperedbreadth.

Kt is also given in Figure 7.1 and Table 7.1.


LLOYDS REGISTER 15


Chapter 4SECTION 7

Figure 7.1

Tapered Tank Coefficient Kt

ARb 2,100 2,200 2,300 2,400 2,500 2,600 2,700 2,800 2,900 3,000 3,100

Kt 1,279 1,308 1,338 1,368 1,399 1,430 1,463 1,496 1,530 1,564 1,600

1.600

1.500

1.400

1.300

1.200

1.100

1.000

Coefficient

Kt

1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3

Tank Breadth Aspect Ratio ARb

Table 7.1


LLOYDS REGISTER16

5LLOYDS REGISTER 17

Units


Chapter 5SECTION 1

Section 1: Units

Section 1: Units

The units used throughout are consistent with the SIstandard where the basic quantities are the metre,Kilogram and Second (MKS system), except for angularmeasurement which is in degrees.


LLOYDS REGISTER18

6LLOYDS REGISTER 19

Data Requirements


Chapter 6SECTION 1

Section 1: Data Requirements

Section 1: Data Requirements

The following plans and informations are required toperform a sloshing and scantling investigation:

- General Arrangement- Midship Section Drawing- Longitudinal Bulkhead Drawing- Transverse Bulkhead Drawing- Trim & Stability and Loading Manuals- Material Properties.


LLOYDS REGISTER20

7LLOYDS REGISTER 21

Levels of Assessement



Section 1: Pressure DeterminationSection 2: Sloshing Criteria

Section 3: Critical Fill RangeSection 4: Level 1 AssessmentSection 5: Level 2 AssessmentSection 6: Level 3 Assessment

Section 7: Structural Capability

Section 1: Pressure Determination

Three levels of assessment are defined below, eachrequiring a different approach to the estimation of likelymaximum sloshing pressures.

Significant dynamic magnification is considered unlikelyfor the following cases:

- For internally stiffened tanks with two or moredeck girders (rolling)/transverses (pitching)wherethe girder/transverse location is less or equal to25% of the tank breadth/length from thedeck/tank corner, and/or the girder/transverseheight is less than 10% of the tank depth with filllevels greater than the tank depth minus height ofdeck girders/transverses.

or - For fill levels lower than height of any bottomgirders

or - For fill levels in excess of 97 % full for smoothtanks

or - For fill levels less than 10 % for smooth tanks.

Section 2: Sloshing Criteria

Based on Lloyd's Registers experience, and numericalstudies of a number of cases, it is considered thatsignificant magnification of the fluid motions can occur ifthe following conditions are found:

- The natural rolling period of the fluid and the shipnatural rolling period are within 5 seconds of eachother.

- The natural pitching period of the fluid is greaterthan a value of 3 seconds below the ship naturalpitching period.



Chapter 7SECTIONS 3, 4 , 5 , 6 , & 7

LLOYDS REGISTER22

Section 3: Critical Fill Range

The critical fill range may be determined by using thefollowing formula, or using the SDA Tank Assessmentprogram (10603).

Fcrit =100{Ls 1n [(1 + )]+ b n } (%)H 2 (1 ) (n+1)

whereLs = effective horizontal free surface length in direction

of angular motion (m)H = total tank depth (m)b = see Ch 4, 1.1.1g = gravity constant (m/s2) = 4Ls/[(Snr-5)2g] for fill level at Snr-5 seconds

to upper bound roll critical fill levelor = 4Ls/[(Snr+5)2g]for fill level at Snr+5 seconds

to lower bound roll critical fill levelor = 4Ls/[(Snp-3)2g] for fill level at Snp-3 seconds

to upper bound pitch critical fill level.

If 1,0 Fcrit is the maximum/minimum value of theupper/lower fill level bound [100%/0%].

If Fcrit 100,0 Then Fcrit = 100%.

Section 4: Level 1 Assessment

This level of assessment is appropriate where the shipsnatural period in roll differs from the fluid natural periodfor transverse oscillatory flow by more than 5 seconds; andwhere the ships natural pitching period exceeds that forthe fluid oscillating longitudinally by more than 3 seconds.


Where the separation of periods defined above is not met,but filling levels are such that impacts on the top of thetank are unlikely, then a level 2 investigation may be usedto assess the sloshing pressures on the tank bulkheads. Thislevel of assessment may also be used for low fill caseswhere the tank has internal stiffening, but the resultingpressures would be considered somewhat conservative. Alow fill is defined when the filling factor coefficient Fcdefined in Ch 4,1.1.1 is equal or less than 1,02. Where Sn(ship natural period) and Tn ( tank natural period) areclose, Fc will invariably give a high fill. In the case thatsuch a filling height is equal to or less than 0,21 Ls, a lowfill may be assumed and the case treated as a level 2assessment, otherwise, a level 3 assessment should be used.


Where significant dynamic magnification of fluid pressuresinvolving impacts on the top of the tank is likely, or wherethe effect of internal stiffening is to be taken into account,then a level 3 assessment is required.

Section 7: Structural Capability

The structural capability of the tank boundaries towithstand the dynamic sloshing pressures is to bedetermined using SDA Ultimate Strength program (10604).This program considers the lateral pressure on a stiffenedpanel comprising a single stiffener and attached plating.The ultimate strength of the plating is calculated on thebasis of a defined allowable permanent set taking intoaccount the membrane stress induced in the panel as itdeforms. For the stiffeners, a classical plastic collapsemethod is used taking into consideration both shear andbending strains. Allowance is made for the smallproportion of the pressure load transmitted directly fromthe plating to the supporting primary structure.

8LLOYDS REGISTER 23

Loading Conditions and ShipMotions for Sloshing Analysis



Section 1: General ConsiderationsSection 2: Loading Conditions

Section 3: Level 2 Sloshing Assessment ParametersSection 4: Level 3 Assessment Parameters

Section 1: General Considerations

Where partial fillings are contemplated in all tanks of aship, the following tanks are to be considered in theanalysis together with associated sea conditions given inTable 1.1 provided the following conditions are satisfiedtogether with the relevant level of assessment conditions.

The natural periods of the ship for a given motion typeshould be determined for the service loading conditionsagreed between the builder and the society. When a ship isto be approved for arbitrary tank filling, all approved safeloading conditions should be investigated and the estimationof significant dynamic pressure magnification consideredaccording to the guidelines provided in Chapter 7.

Section 2: Loading Conditions

The following loading conditions are provided as aguideline to the most critical conditions:

- Storm Ballast condition- Segregated ballast condition- All tanks partially filled.

Experience indicates that the shorter the ship naturalperiod, the greater the impact pressure. The procedure for the selection of the critical loadingconditions would therefore suggest that the loadingconditions with the shortest ship natural period shouldtherefore be considered as a production case.

Sea Condition Head Quartering Beam Stern Quartering

Table 1.1

Foremost

Aftermost

Closest to Amidship

Largest



Chapter 8SECTION 2

LLOYDS REGISTER24

2.1 Unrestricted Filling Levels - Unspecified Sea-Going Loading Conditions

When a ship is to be approved for Unrestricted FillingLevels - Unspecified Loading Conditions, many arbitraryship loading conditions are possible. In order to cover thecomplete range of loading conditions, the fully loaded andballast condition are to be considered. These twoconditions gives an upper and lower limit for the possiblerange of ship natural period as shown in Figure 2.1. Boththe roll and pitch motion modes are to be examined.

Because of the unrestricted filling level requirement, thecritical sloshing ranges extend from [SnrBallast-5] to[SnrLoaded+5] seconds in roll and from [SnpBallast-3] toinfinity in pitch. Also, because of unrestricted filling levelsthe ship natural period range extends from SnBallast toSnLoaded for both pitch and roll.

For sloshing in the Roll motion mode shown in Figure2.1.a, the critical fill range extends from F1 to F4. All filllevels between F1 to F4 are to be investigated.

- For fill levels between F1 and F2, SnrBallast is to beused.

- For fill level between F3 and F4, SnrLoaded is to beused.

- For fill levels between F2 and F3, Snr is to be equal toTn.

Similarly, for sloshing in the Pitch motion mode shown inFigure 2.1.b, the critical fill range extends from F1 to F4where F4 = 0,1%. All fill levels between F1 and F4 are to beinvestigated.

- For fill levels between F1 and F2, SnpBallast is to beused.

- For fill levels between F2 and F3, Snp is to be equal toTn.

- For fill levels between F3 and F4 Snploaded is to beused.

2.2 Restricted Filling Levels - Unspecified Sea-Going Loading Conditions

When a ship is to be approved for Restricted Filling Levels -Unspecified Loading conditions, many arbitrary shiploading conditions are possible within the restrictionsimposed. In order to cover the complete range of loadingconditions, the fully loaded and ballast conditions are to beconsidered. These two conditions gives an upper andlower limit for the possible range of ship natural period. Itis recognised that there might be ship natural period bands which will not be applicable as a result of the limitations ofthe fill levels. However, it is recommended to apply theUnrestricted Filling Levels - Unspecified Sea-Going LoadingConditions procedure outlined in Chapter 8, Section 2.1.

2.3 Unrestricted Filling Levels -Specified Sea-Going Loading Conditions

When a ship is to be approved for Unrestricted FillingLevels - Specified Loading Conditions, each specifiedloading conditions is to be examined for the complete fillranges to determine the critical sloshing fill range for eachtank in both roll and pitch motion modes.

2.4 Restricted Filling Levels -Specified Sea-Going LoadingConditions

When a ship is to be approved for Restricted Filling Levels -Specified Loading Conditions, each specified loadingconditions is to be examined for the restricted fill ranges todetermine the critical sloshing fill range for each tank inboth roll and pitch motion modes.


LLOYDS REGISTER 25


Chapter 8SECTION 2

Fill (%)

Period(s)

100

F1

F2

F3

0

Snr Ballast

Snr Loaded

5 seconds Range of OperatingShip Natural Periods

F4

5 seconds

Figure 2.1.a

Natural Periods Diagram Roll Motion

Figure 2.1.b

Natural Periods Diagram Pitch Motion

Fill (%)

Period(s)

100

F1

F2

F3

0

Snp Ballast

Snp Loaded

3 seconds Range of OperatingShip Natural Periods

F4 = 0,1%




LLOYDS REGISTER26

Section 3: Level 2 SloshingAssessmentParameters

3.1 Level 2 Ship Motions

The Combination of accelerations and motions to beconsidered for the sea conditions given in Table 1.1 are asfollows and are to be used with the critical loadingconditions:

- Head Seas Vertical acceleration and pitchangle

- Quartering Seas Vertical acceleration and 50% rollangle

- Beam Seas Vertical acceleration and roll angle- Stern Quartering 75% vertical acceleration and roll

angle.

3.2 Level 2 Fill Range

Where a tank is to be approved for arbitrary fillings, fillheights to be investigated are in 5% increments from 15%to 30% and then 10% increments until the low fill heightcriterion Fc defined in Chapter 4, Section 1 is exceeded. Ifa tank is to be approved for particular fillings, these,together with fillings 5% above and below the particularfillings are to be investigated.

Section 4: Level 3 AssessmentParameters

4.1 Level 3 Ships Motions

The combination of acceleration and motion to beconsidered for the sea conditions given in Table 1.1 are asfollows and are to be used with the critical loadingconditions:

Head Seas Heave and 70% pitch angle Beam Seas Heave, sway and 70% roll angle.

The investigation of sloshing in head seas requires thatboth aftermost and foremost tank be examined ifhorizontal internal structure are present, as well as thetank closest to amidship.

4.2 Level 3 Investigation Fill Range

Where a tank is to be approved for arbitrary fillings, theupper and lower bound of critical fill heights are to bedetermined according to level 1 procedure. The fill heightsto be investigated are to be taken in 10% increments fromthe lower bound fill height. The fill height at which thefluid natural period matches the ship natural period shouldalso be investigated together with fill level 5% on eachsides.

If a tank is to be approved for particular fillings, togetherwith fillings 5% above and below the particular fillings areto be investigated.

Where horizontal internal structure members are present,fill height coinciding with the location of the girder andwithin a range of 5% above and below the horizontalgirder should be investigated.

9LLOYDS REGISTER 27

Level 1 Sloshing PressureDetermination


Chapter 9SECTION 1

Section 1: Level 1 Sloshing Pressure Determination

Section 1: Level 1 SloshingPressure Determination

Where a level 1 assessment is indicated in accordance withChapter 7, Section 1, the following points need to beobserved:- For oil carrying cargo tanks with dimensions not

departing from standard practice, no furtherevaluation is needed.

- For LNG/LPG ships, sloshing pressures on tankboundaries should be determined according to theRules for LNG/LPG ships.

Otherwise, an equivalent static head is to be obtained byassuming the tank to be rolled or pitched to the lifetimeangles = max or = max respectively defined in Section 4.4, and the equivalent pressure is given by:

P = 11,75 (h + (Ls/2)tan ) KN/m2 (9.1)

where h = the static head in upright position (m).

It is not considered necessary to take translational motionsinto account.


LLOYDS REGISTER28

LLOYDS REGISTER 29


Section 1: Smooth RectangularTanks

Where a level 2 assessment is indicated in accordance withChapter 8, Section 1.2, pressures on the tank boundary areto be derived using SDA Tank Assessment program(10603) (Ref. 1) in association with the lifetime angles ofroll and pitch and the vertical acceleration defined inChapter 4, Section 4.

The transverse and longitudinal boundaries are to bestudied separately:

- Transverse bulkheads in association with pitch plusvertical acceleration.

- Longitudinal bulkheads in association with roll plusvertical acceleration.

The centre of rotation is defined in Chapter 4, Section 4.8.

Section 2: Smooth Hopper Tanks

In the case of tanks having upper and/or lower hoppertanks, the output pressures from the SDA Tank Assessmentprogram (10603) have to be corrected by applying thecorrelation factors derived from experiments (Ref. 2)shown in Figure 2.1.

No correlation factors are given for the knuckle or corner ofthe tank ceiling, as this would be equivalent to a high fillwhich is excluded from a level 2 assessment.

The pressure at the junction of the upper hopper tank andthe vertical tank side, position B shown in Figure 2.1 isgiven by:

PB = K2.P (10.1)

whereK2 = a correction factor depending on filling height F,

the minimum height of the upper hopper tank h,and the angle of the upper hopper tank with thehorizontal.

K2 = (1 + 2,5 F/h)(1 + 2cos)/3 for 0,0 < F < 0,8h P = the output pressure from SDA Tank Assessment

program (10603).

The pressure at the junction of the lower hopper tank andthe vertical tank side, position C shown in Figure 2.1, isgiven by:

PC = K3.P (10.2)

whereK3 = a correction factor depending on filling height F,

and the width of the lower hopper tank w, ifw>0,25Ls. If w 0,25Ls then no correction isnecessary.

K3 = 1 + 4F/Ls for 0,0 < F Ls/4K3 = 1 + (H-F)/(H Ls /4) for Ls/4 < F < H

P = the output pressure from SDA Tank Assessmentprogram (10603)

w = the width of the lower hopper tank (w>Ls /4).

10Level 2 Sloshing PressureDeterminationSection 1: Smooth Rectangular TanksSection 2: Smooth Hopper TanksChapter 10

SECTIONS 1 & 2



Chapter 10SECTION 2

LLOYDS REGISTER30

The higher corner pressures are considered to extend overone stiffener spacing from the corner. When this is notapplicable, the extent of influence may be taken as 0,04Heither sides of the corner. Corrected pressure increases atthe corners from equation (10.1) and (10.2) may bereduced linearly to the limit of corner effect defined above.


LLOYDS REGISTER 31


Chapter 10SECTION 2

Figure 2.1Maximum Pressure Correction Factor Ki

Position B

Correction Factor K2

0.8 h h

1.0

1.0

3.0

H

Position C

Ls

w

0.25 Ls

Correction Factor K3

1.0

1.0

2.0


LLOYDS REGISTER32

LLOYDS REGISTER 33


Section 1: General

Where level 3 assessment is indicated in accordance withChapter 7, Section 6, sloshing pressures are to be obtainedusing a finite difference or similar numerical solution to theone implemented in the SDA Fluids program described inReference 1. Alternatively, agreed model experimentswould be accepted as a means of obtaining the maximumdesign pressures.

The excitation is to cover conditions that would produce amaximum design pressure envelope on the tankboundaries, taking into account the significantcombinations of ship motions, amplitudes and periods andliquid natural period which could occur simultaneously inthe ships lifetime.

Section 2: Limitations andAssumptions of SDAFluids Program

SDA Fluids is based on the Marker And Cell (MAC)method and uses a two dimensional finite differencecalculation scheme. Details of the theory can be found inReferences 3, 4 and 5.

The following limitations and assumptions apply to theSDA Fluids program:

a) Any model is idealised as a uniform mesh ofrectangular cells and any attempted modelling isinfluenced by this limitation. Associated with thismesh are the three sets of independent variablesnamely, the pressure at the centre of each mesh cell,

the fluid velocities normal to the horizontal andvertical cell edges (Figure 2.1)Various methods are contained within the logic ofSDA Fluids to reduce the effect of limiting the scopeof modelling to a rectangular mesh and carefulimplementation by the user will render theselimitations insignificant in most cases.

b) Pressures are calculated at the centre of each meshcell only and this must be borne in mind whenhydrostatic loads are of considerable importance suchas when the mesh spacings are large.

c) SDA Fluids does not use a two phase fluid model atthe free surface; the ullage volume is treated as avacuum. Also, the free surface is only representableas a single valued function and consequently cannotexhibit features such as breaking waves. This mayaffect the simulation of low fill, large amplitudeexcitation cases.

d) In cases where the depth is such that the tank bottomis exposed due to the motion of the ship, the sloshingprogram output should be considered with care sincenumerical instability may arise in the solutionprocess. The behaviour of the free surface motionshould therefore be examined to detect anyincongruities.

11Level 3 Sloshing PressureDeterminationSection 1: GeneralSection 2: Limitations and Assumptions of SDA FLUIDS programSection 3: Data PreparationChapter 11

SECTIONS 1 & 2



Chapter 11SECTION 2

LLOYDS REGISTER34

Figure 2.1

JMAX

IMAX

NX

NY

1

I

y

x

dydx

J

1

Ui1,j Ui,jPi,j

Vi,j

Vi,j1

Finite Difference Mesh Arrangement with Fictitious Boundary Cells

Finite Difference Field Variables and their Location


LLOYDS REGISTER 35


Chapter 11SECTION 3

Section 3: Data Preparation

Further reference may be made to the software usermanual (Ref 1).

3.1 Mesh Spacing

Data Card : PMESH

There is one constant mesh spacing associated with each ofthe two principal axes of the mesh.

For a rectangular tank, it is an easy matter to fit a suitablerectangular grid exactly over the dimensions of the tank.However, if the tank is prismatic in shape, then care mustbe exercised in selecting mesh spacings that enable theslope of any chamfered wall of the tank to be adequatelymodelled. Due to the nature of the discretisation process,chamfers can only be modelled as stepwise boundaries andthe best configuration of mesh to chamfer is such that theboundary of the idealised tank coincides with the modelledtanks wall at the centre of each appropriate horizontal celledge, or the idealised structure bisects horizontal celledges.

If some internal structure such as stiffeners or deck girdersare to be included, further complications are added sincethese too may only have dimensions corresponding to anintegral number of mesh spacings.

Ideally, each mesh spacing should be a factor of all theimportant tank dimensions in its associated principal axistogether with a cell aspect ratio close to unity.Unfortunately, the mesh spacings cannot usually adopttheir ideal values since this will almost mean that thenumber of mesh cells used by the simulation will beprohibitively expensive in computer time. A compromisehas to be made and it is in this area that the skill of themodeller can be most gainfully employed.

For most applications, using 20-30 cells in the horizontal(i) direction and 15-20 cells in the vertical (j) direction is agood compromise. The minimum number of cells is 20 x15. The maximum number of cells allowed by the programis 60 x 40. It must be borne in mind that modelling with ahigher number of cells than the range recommended willtend to give conservative pressure estimates.

3.2 Fitting the mesh to the tank

Data Card : MESH

The relationship of the tank to the mesh may be bestappreciated by drawing the tank on a coarsely ruled sheetof paper, the ruled spacings reflecting the relativedimensions of each mesh cell as illustrated on Figure 3.1.

The first step is to identify the mesh cells that form the areaof the mesh in which fluid will be present if the tank isconsidered to be completely full. These are the active cellsand all active cells together form the idealised tank.

The bottom left hand cell of the calculation grid containedwithin the idealised tank will always have i,j co-ordinatesof (1,1). Cell numbering is carried out in a similar fashionto the grid-squares on a map.

3.3 Boundary Conditions

Data Card : MESH

The next stage is to identify the active cells through whichor on the edge of which the tank boundary passes. Theseactive cells are also boundary cells. The idealised tank isdefined by specifying the boundary cells on MESH cards.Each mesh card defining one section of the tank boundary.

There are four separate regions of the mesh boundary: theleft and right, which include only the vertical regions at theextreme edge of the mesh, and the top and bottom, whichinclude all other parts (See Figure 3.2). A boundarycondition type may be specified for each region. Care mustbe taken when fitting the mesh to chamfered sections oftank wall to avoid overlapping tank boundary sections.Boundary cells must be defined in a consistent direction,that is anticlockwise round the perimeter of the tank, withthe interior of the tank to the left.

The fluid flow conditions at the tank boundaries imposezero velocity normal to a tank wall, either free flow or zerovelocity normal to a tank wall, and either free flow or zerovelocity along a wall. The former, referred to as free slip,is the default boundary condition for all mesh boundaryregions and should be used unless the boundary layer isgreater than 2 or 3 mesh divisions thick. Otherwise, thelatter no slip condition may be used to force fluid to becompletely stationary on a mesh boundary region.



Chapter 11SECTION 3

LLOYDS REGISTER36

3.4 Including Internal Tank Structure

Data Card : BAFFLE

Many tanks have internal stiffeners, transverses or deckgirders. The main effect of such structure is to slow downthe fluid motions but sometimes its effects are moreimportant and less obvious.

Conceptually, the effect of this form of construction is toprevent the passage of fluid through an imaginary linedrawn in the fluid imparting zero fluid velocity across thisline. The modelling of the internal structure is based onmesh cell edges and vertical and horizontal baffles can bemodelled using the appropriate switch in the BAFFLE card.

The cell edge on which the structure lies is to the right orat the top of the specified cells with the tank viewedupright.

If a corner of the tank has a high angle of chamfer, anartificially large effective wave slope may be inducedleading to problems of solution stability. This is particularlylikely if the base of the tank becomes exposed and thenumber of mesh spacings for the chamfer in the verticaldirections exceeds the number in the horizontal direction.This may be overcome by modelling the tank as if it wererectangular at the bottom and using BAFFLE cards tospecify chamfers.

3.5 Properties of the Fluid

Data Card : PFLUID

The properties of the fluid and the amount of fluid in thetank affect the pressure loads obtained from sloshing. Theinitial static fill depth and all the physical properties of theidealised fluid used in the calculation are specified on theFLUID card.

The fill depth is specified as a percentage of the maximumdepth of the tank as defined in Chapter 4, Section 3.

The physical properties of the idealised fluid can bespecified using density, speed of sound in the fluid andkinematic viscosity.

It should also be noted that SDA Fluids does not use a twophase fluid model at the free surface; the ullage volume istreated as a vacuum. Also, the free surface is onlyrepresentable as a single valued function and consequentlycannot exhibit features such as breaking waves. This mayaffect the simulation of low fill, large amplitude excitationcases.

3.6 Pressure Output Sampling Points

Data Card : MESH

The most usual form of analysis required for any tank is anassessment of the maximum pressure loads exerted on itswalls. Pressure data may be calculated and output for everycell referenced on MESH cards. However, the number ofsampling points may be reduced by specifying a samplingrate other than unity.

Pressure data for internal structure defined on BAFFLEcards may be requested by specifying MESH cards for therequired cells and switching off the boundary option.

Similarly, velocity data may be calculated and output forevery cell referenced on the MESH cards.

If the tank structure, the applied excitation and inertialforces are all symmetrical, the calculations may be reducedby requesting output for only half of the tank.

3.7 Ullage Pressure

Data Card : PARAM

A constant pressure may be added to each mesh cellpressure to reflect a difference between the ullage pressureand the pressure of the surroundings.


LLOYDS REGISTER 37


Chapter 11SECTION 3

Figure 3.1

Mesh Co-ordinate System

18

17

16

15

14

13

1211109876

5

4

321

18

17

16

15

14

13

1211109876

5

4

321

1 2 3 4 5 6 7 8 9 10 11 12 13

J

I

J

I

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

BOUNDARY CELLS



Chapter 11SECTION 3

LLOYDS REGISTER38

BAFFLE, 18, 9, 20, 9, HBAFFLE, 1, 9, 3, 9, H

BAFFLE, 6, 1, 6, 4, V BAFFLE, 14, 1, 14, 4, V

Cells Defining Horizontal Bending

Cells Defining Vertical Baffles

Figure 3.2

Boundary Conditions Examples

MESH, 4, 18, 1, 15

MESH, 1, 14, 1,4

MESH, 1, 3, 3, 1MESH, 4, 1, 10, 1

MESH, 11, 1, 13, 3

MESH, 13, 4, 13, 14

MESH, 13, 15, 10, 18MESH, 9, 18, 5, 18

(cells marked: )

MESH, M-2, N-1, M-3, N

MESH, M-4, N, .., N

*MESH, M-2, -(N-2), M-2, N-2

*MESH, M-1, -(N-4), M-1, N-4

MESH, M, .., M, N-5

MESH, M-1, -(N-3), -(M-1), N-3*

MESH, M, N-5, -(M), N-5*

* - Single Cell, use negative cell number to indicate direction, right hand side forms boundary

J=N

I=M

(cells marked: )


LLOYDS REGISTER 39


Chapter 11SECTION 3

3.8 Sloshing Excitation Spectrum

Data Cards: PMESHANGLVERTHORISPEC

These data cards generate sinusoidal components ofmotion according to the following representative equation:

A = Aosin (wt + ) (11.1)

The motion is imparted to the idealised tank by the use ofthe relevant motion data cards. The degree of freedomapplied to the tank can be generated using the followingdata cards:

- ANGL Constant amplitude, angular motionabout an axis perpendicular to the meshthrough the centre of rotation as definedin Chapter 4, Section 4.8 and specified inthe PMESH data card.

- VERT Constant amplitude vertical (heave)motion

- HORI Constant amplitude horizontal (sway)motion

- SPEC Special form for varying amplitudemotion with the period of excitationaccording to the following equation:

Ao = Amax.e-(Tp-Tpn)2/2Q but not less than specified Amin

(11.2)

WhereAmin and Amax are specified amplitudes according toChapter 4, Section 4.Tpn and Q are the specified natural period and decayconstant.Tp is the current period.

The amplitude, period and relative phase of the forcedmotions are also specified on the motion card, togetherwith a period increment and an incrementation interval ifthe period is to be varied with time.

For ALL card type :

The initial period may be specified as follows :

Sn = Sn + 1 for Tn Sn < 1Sn = Sn + 2 for 1 Tn Sn 1 (11.3)Sn = Sn + 3 for Tn Sn >1

Period increment = - 0,001

Increment interval = Tr ( reference time step).

For SPEC (SPECial) card type :

The maximum amplitude is as defined in Chapter 4,Section 4 and Chapter 8, Section 4.1.

The minimum amplitude should be taken as follows :

Amin = 6 for roll= 3 for pitch.

The decay constant should be taken as follows :

Q = 2 for roll= 3 for pitch.

The natural period is taken as Snr for roll , or Snp for pitch.

Initial phase angle = 0,0

For VERT (VERTical heave) card type :

Required for assessment of longitudinal and transverseboundaries.Amplitude as defined in Chapter 4, Section 4 and Chapter8, Section 4.

Initial phase angle = both 90,0 and 90 for pitchGravity vector = -9,81 m/s2

For HORI (HORIzontal sway) card type :

Required for assessment of longitudinal boundaries.Amplitude as defined in Chapter 4, Section 4 and Chapter 8,Section 4.Initial phase angle = 180,0



Chapter 11SECTION 3

LLOYDS REGISTER40

3.9 Time Control

Data Card : TIMING

Since SDA Fluids is a transient method of analysis, resultsare obtained in the time domain. One of the mostimportant features of a simulation performed by SDAFluids is the selection of the reference timestep which isdefined on the TIMING card.

The reference time step chosen should not be too small asto make computational time excessive or too large so thatimportant features may be missed out in the datacollection.

The default reference time step is given by:

Tr = (Sn 2 )/200 (11.4)

The length of the simulation is such as to give a finalperiod of excitation 4 seconds less than the initial period,thus the total simulation time is given by:

Tsimul = 4000 Tr (11.5)

The following formula may be used to select the outputwindow. The data output may be stored for a simulationtime range of (kSn) the simulation time at which theperiod of excitation is equal to the tank natural period, theoutput time range is given by:

t (kSn) = Tsimul(Sn Tn)/4 (KSn) (11.6)

(kSn) represents the output window where k is thenumber of oscillations on each side of the time instantduring the simulation where the instantaneous excitationperiod is equal to the tank natural period. A typical k valueof 2 is usually adequate.

The following formula may be used to determine thespectrum period Tp at a given time of the simulation ts:

Tp = Sn + (ts.inc)/t (11.7)

whereinc = the period increment [-0,001]t = the time step [Tr].

The following formula may be used to determine thespectrum amplitude Apn at a given time of the simulationts:

Apn = Amaxexp[-(Sn Sn (ts inc)/t)2/2Q] (11.8)

If Ao is less than specified Amin, then Ao = Amin

Equation (11.8) may be rewritten as follows depending onthe starting period.

IfSn = Sn + 1 Ao = Amax exp[-(1 + (ts inc)/t)2/2Q]Sn = Sn + 2 Ao = Amax exp[-(2 + (ts inc)/t)2/2Q]Sn = Sn + 3 Ao = Amax exp[-(3 + (ts inc)/t)2/2Q]

(11.9)

LLOYDS REGISTER 41


Section 1: Sloshing SimulationQuality AssuranceProcedure

1.1 General

It should be borne in mind that the solution to the sloshingphenomenon is obtained using a complex mathematicalformulation of the fluid flow solved in an iterative method,and that the tank geometry, intervals and fluid aremodelled as cells of finite size over which thevelocities/pressures are evaluated. As a consequence, it ispossible that certain tank geometries and internalstructural arrangements and/or sloshing parametersoutside the extensive range covered during the testing andvalidation of this procedure may present some irregularitiesin terms of fluid flow motion, velocities or boundarypressure.

For these reasons which are solely due to the combinationof modelling assumptions and the type of numericalsolution, the following guidelines have been developed inorder to assist both the novice and experienced user of SDAFluids to detect inconsistencies.

1.2 Minimum Quality Assurance PostProcessing Requirements

The following procedure represents the minimum level ofpost-processing for quality assurance of the simulation. It isrecommended to adhere to these guidelines in order todetect any inconsistencies or unexpected behaviour whichmay occur during the simulation as a result of wrong inputdata or limitations due to assumptions or numericalinstabilities. The following output items are to beexamined:

a) Angular Horizontal Vertical Amplitude and PeriodTime History

The excitation spectrum should be examined to confirmthat the applied amplitudes and periods are in accordancewith the intended values specified in the proceduresmanual.

b) Free surface motion simulation

The examination of the free surface motion should beperformed both with and without the ZOOM facility.ZOOM OFF(0)/ON(1-10) allows to observe the behaviourof the free surface with the tank fixed/moving. The freesurface motions should be consistent with applied tankmotion. The types of waves formed during the simulationcan be identified be referring to Chapter 3, Section 1. Thefree surface behaviour is to be examined carefully when thetank bottom is exposed and internal members areimmersed.

12Post-Processing of SDA FluidsDataSection 1: Sloshing Simulation Quality Assurance ProcedureSection 2: Pressure Pulse Time Averaging SchemeSection 3: Dynamic and Static PressuresSection 4: Structure Natural Frequency CalculationSection 5: Force and Couple

Section 6: Pressure Applied to Internal Structural Members

Chapter 12SECTION 1



Chapter 12SECTION 1

LLOYDS REGISTER42

Since the free surface position is obtained at the cell centrealongside the cell vertical j axis, and the free surface isrepresented by line segments joining adjacent cells,excessive free surface slope can be identified. In general,the free surface slope should not exceed the cell aspectratio y/x.

c) Free surface envelope

The free surface envelope allows the visualisation of theboundary which is in contact with the fluid over the wholeduration of the simulation. The amplitude of fluid motionon the vertical boundaries, the extent of top boundarypotentially subjected to impulsive pressure, and eventuallythe extent of bottom boundary exposed can be observed.

When the centre of rotation is located on the tankcentreline, e.g. roll and the tank structure is symmetricalabout the tank centreline, the free surface envelope shouldbe approximately symmetrical about the centreline.

Note:Differences in the extent of the free surface envelope onopposite tank side in roll arise from the nature of themotion spectrum which is not linear and symmetric withrespect to time. When harmonic excitation is used, thisbehaviour is still occurring, because of the starting motionand computational round off errors inherent to all finitedifference schemes. Perfect symmetry of the free surface isvery rarely attained, but the difference is often negligible.

d) The velocity animation

The velocity vector animation during the simulation timewindow at which maximum magnification of sloshingeffects occurs, allows the visualisation of both the fluidparticle flow, and the velocity magnitude variations. Forcells adjacent to the boundary, the magnitude of thevelocity vector and its direction reflects the relativemagnitude of the boundary pressure. The behaviour of thefluid particle velocity during fluid/boundary interactioncan also be examined. The velocity vector are given at thecentre of the cell. The flow around internal structure andcorners also needs to be observed for consistency in termsof behaviour and input data.

e) Pressure envelope

The pressure envelope shows the distribution of maximumaverage pressure (see Chapter 12, Section 2) for the rangeof cells selected in the input data (MESH Cards). Ingeneral, it is more explicit to display only the cellsbelonging to one boundary, i.e. vertical RHS/LHS, Top,Bottom or Baffle LHS/RHS.

In general, the following pressure envelope behaviour areshown:

The pressure envelope on the bottom boundaryshould be fairly uniform except when deep girdersprevent fluid motion. This pressure is mainly due tothe hydrostatic term (gF), the heave accelerationand a small angular motion component.

On vertical boundaries, the pressure envelope belowthe still free surface is mainly hydrostatic with adynamic pressure component due to angular motionand heave and sway (if applicable) motion. Abovethe still free surface, the pressure envelope may risesharply if impacts on the ceiling occur during thesimulation. If deep girders are present, the pressureon the vertical boundary may drop close to thebottom as a result of fluid flow damping due to thegirders.

On the top boundaries, the pressure envelope mayshown high localised pressure, this may be due to thebehaviour of the free surface, or the interaction of thefluid with an internal structural element.

It is recommended to display simultaneously the pressureenvelope of opposite symmetrical boundaries insymmetrical motion.

e) Pressure time histories at cells exhibiting highpressure values

Cells exhibiting high pressures both on the tank top andvertical boundaries should be examined. Pressure types canbe identified by zooming on the pressure pulses in the timehistory. The occurence of high pressure values should beconsistent with the fluid natural period and the spectrumperiod, so that the maximum pressures occur within theoutput window with a range of ~kSn with respect to thesimulations timescale. In certain cases where the tanknatural period is away from the ship natural period, thepressure time history may exhibit two peak regionscorresponding to excitation at ship natural period andexcitation at tank natural period.

These recommendations are not a self-limiting and the useris encouraged to develop its own post-processing schemebased on these guidelines.


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1.3 Inconsistencies and AppliedResults

As mentioned in Chapter 12, Section 1.1, due to thecomplexity and assumptions of the mathematical solutionand idealisation, some unexpected results may occurdespite the extensive range of parameters covered duringboth the validation of this procedure and the softwarealgorithm. Certain problems are known to occur andsymptoms/remedy are shown in Table 12.1.

Section 2: Pressure Pulse TimeAveraging Scheme

During a sloshing simulation, high fluid velocities arise dueto the motion of the tank which require a smaller time stepthan the output time step t in order to satisfy the solutionalgorithm conditions. The program uses an auto time-stepping facility whereby the number of time cycles duringtime interval t (simulation cycle) is normally more thanone and typically about 10. The pressure value of one ofthese simulation cycles therefore would be taken torepresent the pressure values over the time interval t. Thisshould not matter if the pressure distribution is consideredas a whole, but quite often the user considers only the peakvalues without taking the characteristics of the pressureimpulses into account. Consequently this would lead tomisinterpretation of the results, that is, very large pressuresoccurring over very small time intervals being taken torepresent the average pressure over the required timeinterval t.

To overcome this problem of excessively large sampledpressure values, a pressure pulse averaging scheme has beendevised to give more realistic impact pressures (Ref 1).

The pressure pulse time averaging technique is illustratedin Figure 2.1. The instantaneous pressures which are thedirect solution from the algorithm are replaced by theaveraged pressure of the instantaneous pressure over onetime step. This averaged pressure is referred to as thecomputed pressure in this procedure, and is the pressurewhich is used as the sloshing load for capability assessmentof the structure.

Under certain circumstances, low fluid velocity will makethe solution converge for the reference time step withoutrequirement for smaller time step. However for consistencyof the pressure averaging scheme, SDA Fluids version 3.3and above implement a scheme by which a minimum offour values has to be sampled over each time step toperform the averaging scheme.

Table 12.1 Symptoms and Remedy

Symptoms

Exponential increase of pressure towards end of simulation

Unreasonable behaviour of free surface around horizontal baffle

With a fill level near the baffle level.

Unexpected high pressure on bottom, sides and top boundary

Impulse pressure for all boundary occurring at approx. the same

time instants

Other unexpected phenomenon

Remedy

Set minimum amplitude motion of SPEC card to zero

Model horizontral baffle as a step in the deck ignoring volume

above horizontal baffle

Water Hammer Effect Refer to Lloyds Register London

Modify Idealisation of tank Refer to Lloyds Register London



Chapter 12SECTION 3

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Section 3: Dynamic and StaticPressures

Since the pressures determined by SDA Fluids are dynamicin nature and the assessment of the response of thestructure is based on a static analysis, it is required incertain cases to convert the dynamic pressures toequivalent static pressures. This conversion to staticloading is necessary when the load time history is such thatthe impact period is close to the natural period of theloaded structural component. Then, the equivalent staticpressures can be up to twice the magnitude of the dynamicpressure. Figure 3.1 illustrates the dynamic load factordependence on the natural frequency of the structuralcomponent subjected to dynamic loading of triangularshape and duration t1.

The following guidelines are provided to determine if theconversion of dynamic to static pressure is required :

a) If the factor of safety given by the plastic collapseanalysis (SDA Ultimate Strength 10604) is superioror equal to 2, No pressure transformation is required.

b) If the impact pressure pulse is approximated to atriangular pressure pulse of duration t1 as shown inFigure 3.1, the impact pressure can be considered tobe quasi-static if t1/T>2, where T is the naturalperiod of the structural component. In general, thiscase applies for conventional structures subjected tosloshing pressures.

c) If none of the conditions above are satisfied,conversion of the dynamic to static pressure may berequired.

Figure 2.1

Pressure Time History and Pressure Pulse Averaging Scheme

Figure 3.1

Dynamic Load Factor for Triangular Pulse Load


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Chapter 12SECTION 3

3.1 Conversion of Dynamic Pressureto Static Pressure

The response of structures to dynamic loads can be quitecomplicated. It must be borne in mind that couplingbetween structural components can and does occur incomplex structures. For these cases, the analyst mustdecide whether or not the various components of the tankwall can be analysed individually or should a multi degreeof freedom system be used.

If each component of the tank structure is to be analysedindividually then it is usually conservative to assume rigidsupport for each element (neglecting flexibility in thesupporting structure) and that the sloshing forces aretransferred undistorted from one member to the next.Often, the response is attenuated by coupling, but it can beincreased as well.

However, using an equivalent single degree of freedomsystem computed from energy principles (Ref 8 & 9), asimple response calculation method for elasto-plasticbehaviour of tank boundaries has been developed, andimplemented in a computer program DYN_STAT (Ref 10).

The reduction of the dynamic pressure data to a staticpressure data for assessment of the structure is based onthe following points :

a) Solution for plastic behaviour can be based on aDynamic Load Factor (DLF) which is a function of theload time history and the natural period of thestructure.

b) The dynamic load factor when multiplied by the peakpressure gives an equivalent static pressure to beused for design purposes.

c) For plastic behaviour of structures which aresubjected to loads of long duration relative to thestructure fundamental period, the equivalent staticpressure gives good estimates of maximum shearreactions in the structures.

DYN_STAT is a development program restricted at presentto Lloyds Register TPDD/ASRD, and SDA Fluids usersmay contact TPDD/ASRD if required. Alternatively, DLFcharts may be used to convert dynamic pressure to staticpressure.

For the remaining part of this procedure, DYN_STAT refersto the process of converting dynamic pressure to staticpressure using either the software or the charts available inAppendix B5. It should be noted that these charts are basedon an elastic response model whilst DYN_STAT software isbased on an elasto-plastic response model.

3.2 Response Calculation

The design pressure to be used for the assessment of thestructural capability is given as follows :

Pstatic = Pdynamic x DLF (12.1)

3.3 Pressure Conversion Procedure

Generally, the worst case sloshing load for a structuralcomponent is one which has the following properties:

- Highest pressure- Shortest rise time

To establish whether or not a dynamic load factor shouldbe used for a given structural component, the followingprocedure may be used:

1) Calculate collapse strength of all structuralcomponents according to the guidelines provided inChapter 13.

2) Compute the sloshing pressure envelope using SDAFluids.

3) Apply a factor of 2 to the sloshing pressure values forthe structural components which satisfy condition c)of Chapter 12, Section 3 (this is equivalent toapplying the maximum possible dynamic load factor).

4) Identify the areas which require further investigation(i.e. 2 x sloshing pressure is greater than the collapsestrength, in association with the factors of safetygiven in Chapter 13, Section 3).

5) Examine the sloshing pressure time history, andidentify critical impacts according to the guidelinesprovided above.

6) Use the DYN_STAT program or charts to convert thedynamic sloshing pressure into equivalent staticsloshing pressure where required.



Chapter 12SECTIONS 3, 4 , 5 & 6

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7) Verify that the equivalent static sloshing pressure isless than the collapse pressure of the structuralcomponents where required with the associatedfactors of safety (Chapter 13, Section 3).

Section 4: Structure NaturalFrequency Calculation

Fundamental frequency of structural component may becalculated using LR.PASS desktop computer program LR20301 (Ref 7), or the formulae available in Appendix B andimplemented in the pressure conversion programDYN_STAT (Ref 10). Charts to determine the naturalfrequency of clamped plates in air and with one sideimmersed are also available in Appendix B.

Section 5: Force and Couple

For some type of analysis, it may be required to obtain theforces acting on the structure. This is particularly importantfor independent cargo tanks for which the forces on thetank supports may be found.

The force and couple are found by integrating the pressureon all cell boundary edges. The centre of integration forcouple calculation may be different from the centre ofrotation for angular motions, and may be used, forinstance, to find the shear force and tripping moment onselected internal structure.

Section 6: Pressure Applied toInternal StructuralMembers

When internal structural members represented by bafflesare present, the sloshing pressure applied to the internalmember is the maximum differential pressure at discretetime instant over the simulation period. The differentialpressure is calculated as the difference between thepressures acting at time instant t at opposite cells about theaxis of the structural element.

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Section 1: Pressure andStresses

The SDA Fluids program is used to determine themaximum lifetime sloshing pressures. When it isappropriate, to determine the design pressures, theresponse of the structural members also has to be takeninto account. Generally, from the standpoint of structuraldesign, the pressure is important not only for its value butas pressure multiplied by area; that is, even high pressurecauses no damage to the structural member and henceposes no problem in terms of structural strength as long asthe area acted upon is very small. The panel areasurrounded by stiffeners is usually taken as being thesmallest unit area.

Structural members must be strong enough to withstandthese effective loads. The plastic collapse load is used inmany instances to indicate the strength, commonly of bothpanel and stiffener, taking into account their collapsemechanism. For example, the strength of the panelfastened in way of primary and secondary members isobtained as the load required to form a roof shaped hinge.As for the primary members, it is necessary to pay attentionalso to the buckling of panel which composes their girders.

Also an allowance should be made for global bendingstresses which might occurs as a lifetime value and beadded to the sloshing load component.

Section 2: Collapse AnalysisProcedures forClamped StiffenedPanels

2.1 Description

The desk-top program SDA Ultimate Strength (10604) (Ref 1) requires information about the following for theevaluation:

- Bulkhead type- Direction of stiffening- Material properties- Applied pressure envelope- Thickness of plate panels- Spacing, spans and scantlings of stiffeners

The program considers a single stiffener and a breadth ofpanel between that and the next stiffener, or a corner of atank. The panel length is taken as the distance betweenframes, see Figure 2.1.

Stiffeners with the following cross sections may beexamined: angle, bulb plate, flat bar or T cross section, seeFigure 2.2.

Stiffeners are continuous and effectively supported at everyfloor, or girder.

Where brackets are used to reduce the effective length ofthe stiffener, it is assumed that these are arrangedsymmetrically either side of the primary member web, andadequately stiffened.

13Strength AssessmentSection 1: Pressure and StressesSection 2: Collapse Analysis Procedures for Clamped Stiffened PanelsSection 3: Minimum Factors of SafetySection 4: Girder Structural Analysis ProcedureChapter 13

SECTIONS 1 & 2



Chapter 13SECTION 2

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Figure 2.1

Panel Geometry

Figure 2.2

Stiffener Sections & Dimensions

Note: Bulb sections are to be represented as anglesections with dimensions given in accordancewith chapter 4 of the DCPD

Flat bar section T section Angle sectiontp tp

tp

tw

tf

tf

bf

tw

tw

dwdw dw

bf

tp = uniform panel thickness

s = panel breadth (stiffener spacing)l = panel length (frame spacing)pu = uniform pressure applied to

unstiffened side of panelx = applied axial stress acting in the

panely = applied transverse stress acting in

the panel = applied shear stress acting in the

panel

s

y z

x

l

y

x

PuPu

Pu

tp


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Chapter 13SECTION 2

The plate thickness used in the calculation are to be Rulethickness. When a plate panel consist of two or morestrakes, then the plate thickness is to be taken as follows:

t = 0.75 t12 + 0.25 t22

wheret1 is the thickness of the major area of the panel,

greater than 2/3 of the panel breadth.t2 is the thickness of the minor area.

Different yield stresses may be specified for the plating,stiffener web and stiffener flange. These are to be taken asthe minimum specified yield stress or 0.5 per cent proofstress. For normal and higher tensile steel or aluminium,Poissons ratio is to be taken as 0.3. The modulus ofelasticity is to be taken as 20.6 E4 N/mm2 for normal andhigher tensile steel and 6.89 E4 N/mm2 for aluminium. Forcargoes carried at cryogenic, or elevated temperatures. Theminimum material properties at the correspondingoperating temperatures of the structure are to be taken.

The panel is allowed an initial shape imperfection and apermanent set. These are the maximum deviations of thepanel from a plane surface for the undeformed panel, priorto the application of the forces, and the deformed panel,respectively.

2.2 Assumptions and Limitations

The initial shape imperfection and the allowablepermanent set are determined by the program from thespecified stiffener spacing. Initial shape imperfection andpermanent set are measured positive towards the stiffenerand negative away from the stiffener.

Default values of panel characteristics are:

- Initial panel imperfectio

shipright sda sloshingloadsandscantlingassessment

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