dnv cn 32.2 container securing

CLASSIFICATION NOTES

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No. 32.2

Container SecuringJULY 2011

This Classification Note includes all amendments and corrections up to August 2011.DET NORSKE VERITAS AS

FOREWORDDET NORSKE VERITAS (DNV) is an autonomous and independent foundation with the objectives of safeguarding life,property and the environment, at sea and onshore. DNV undertakes classification, certification, and other verification andconsultancy services relating to quality of ships, offshore units and installations, and onshore industries worldwide, andcarries out research in relation to these functions.Classification NotesClassification Notes are publications that give practical information on classification of ships and other objects. Examplesof design solutions, calculation methods, specifications of test procedures, as well as acceptable repair methods for some

components are given as interpretations of the more general rule requirements.All publications may be downloaded from the Societys Web site http://www.dnv.com/.The Society reserves the exclusive right to interpret, decide equivalence or make exemptions to this Classification Note.The electronic pdf version of this document found through http://www.dnv.com is the officially binding version Det Norske Veritas AS July 2011

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Classification Notes - No. 32.2, July 2011Changes - Page 3

CHANGES

This revision replaces the October 2009 edition of the document.Text affected by the main changes is highlighted in red colour in the electronic pdf version. However, wherethe changes involve a larger section, only the title may be in red colour.Main ChangesThe strength ratings for typical pressure elements, and the corresponding transverse compressive strengthratings in containers, have been increased.Amendments 2011-08-03In addition to some editorial corrections, superfluous text on page 2 was removed.DET NORSKE VERITAS AS

Classification Notes - No. 32.2, July 2011 Page 4

CONTENTS1. General.................................................................................................................................................... 51.1 Introduction...............................................................................................................................................51.2 Procedure ..................................................................................................................................................51.3 Definitions.................................................................................................................................................61.4 Assumptions..............................................................................................................................................72. Design Loads........................................................................................................................................... 72.1 General......................................................................................................................................................72.2 Wind load..................................................................................................................................................72.3 Accelerations.............................................................................................................................................83. Loading Conditions................................................................................................................................ 83.1 General......................................................................................................................................................83.2 LC1: Transverse loading I ........................................................................................................................83.3 LC2: Vertical loading ...............................................................................................................................83.4 LC3: Transverse loading II .......................................................................................................................93.5 LC4: Longitudinal loading........................................................................................................................94. Acceptance Criteria ............................................................................................................................. 104.1 General....................................................................................................................................................104.2 Containers ...............................................................................................................................................104.3 Container securing devices .....................................................................................................................114.4 Ship structure ..........................................................................................................................................135. Direct Calculation using Beam Analysis............................................................................................ 135.1 General....................................................................................................................................................135.2 Modelling of geometry ...........................................................................................................................135.3 Boundary conditions ...............................................................................................................................145.4 Loading conditions..................................................................................................................................145.5 Results.....................................................................................................................................................146. Formula based Analysis, Basic Formulae.......................................................................................... 156.1 Rigid container securing arrangements (cell guides and similar) ...........................................................156.2 Non-rigid securing arrangements (lashings and similar) ........................................................................156.3 Container stack with four flexible horizontal supports...........................................................................166.4 Container stack with combined rigid and flexible horizontal supports ..................................................186.5 Container blocks .....................................................................................................................................187. Formula based Analysis, Derived Formulae ..................................................................................... 197.1 General....................................................................................................................................................197.2 Container stack with single rigid support ...............................................................................................207.3 Container stack with two rigid horizontal supports ................................................................................217.4 Container stack with three rigid horizontal supports ..............................................................................227.5 Container stack with single flexible support...........................................................................................237.6 Container stack with one rigid and one flexible support ........................................................................237.7 Container stack with two flexible horizontal supports ...........................................................................247.8 Container stack with one rigid and two flexible horizontal supports .....................................................257.9 Container stack with three flexible horizontal supports .........................................................................258. Special Container Arrangements ....................................................................................................... 278.1 General....................................................................................................................................................278.2 20' container in 40' cell guides................................................................................................................278.3 40' container in 45' cell guides................................................................................................................278.4 Effectiveness of lashings attached to lashing bridge ..............................................................................288.5 Vertical lashings wind lashing .............................................................................................................288.6 Block stowage in hold without cell guides .............................................................................................288.7 Platform-based containers with reduced stiffness...................................................................................288.8 Containers placed on two hatches or on hatches and side pillars ...........................................................28Appendix A.Approval of Lashing Computers/Software .................................................................................................. 29Appendix B.Calculated Examples...................................................................................................................................... 33DET NORSKE VERITAS AS

Classification Notes - No. 32.2, July 2011Page 5

1. General1.1 Introduction1.1.1 For ships intended for container transport the Rules for Classification of Ships require that approvedsecuring arrangements for the cargo containers are fitted.

1.1.2 The purpose of this publication is to serve as an aid to those responsible for the planning and strengthevaluation of securing arrangements for cargo containers on board ships. Acceptable assumptions andcalculation procedures supplementing the general requirements stated in the Rules for Classification of Shipsare given.

1.1.3 Principles of analysis have been outlined for normal types of securing arrangements, including cellularcontainment structures (rigid containment system).

1.1.4 For securing arrangements based on lashings or similar, calculation formulae taking into account theinteraction of containers and supports have also been included.

1.2 ProcedureThis classification note describes methods for performing calculations of container securing arrangements. Thecalculations are based on requirements given in Rules for Classification of Ships. Two different calculation methods are described Direct calculation using beam analysis and a Formula-based analysis these two methods are in general considered to be equivalent. Should there however bediscrepancies in the results of the two methods the direct calculation method will be decisive (this is also themethod used in approval).The flowchart in Figure 1-1 gives an overview of applicable sections, depending on the calculation method.The sections are briefly described in the following:Sec.2. Design loads, gives description or reference to the applicable local loads, like wind loads andaccelerations.Sec.3. Loading conditions, gives a description of the applicable loading conditions.Sec.4. Acceptance criteria, gives applicable strength ratings for the containers and recommendations for thelashing equipment.Sec.5. Direct calculation using beam analysis outlines the procedure for calculation of container arrangementswhere the containers and lashings are modelled as beam elements.Sec.6. Formula based analysis, basic formulae, outlines the basic formulae for the simplified calculation ofordinary container arrangements.Sec.7. Formula based analysis, derived formulae, gives derived formulae (from the Basic formulae describedin Sec.6) for simplified calculation of ordinary container arrangements.Sec.8. Special container arrangements, describes calculation methods for special container arrangementswhich are not necessarily covered by the other methods e.g. 20' containers in 40' cell guides.Appendix A. Approval of lashing computer/software gives guidance to procedure for type approval of computersoftware for determination of forces in lashing systems.Appendix B. Calculated examples, gives some calculated examples for easy reference.DET NORSKE VERITAS AS


Figure 1-1Flowchart of the calculation procedure

1.3 Definitions1.3.1 References to directions refer to the principal axis system of the ship. Thus the terms vertical, horizontal,longitudinal and transverse when used refer to the ships axes.

1.3.2 With regard to terms used in this note reference is made to Rules for Classification of Ships Pt.5 Ch.2Sec.6.

1.3.3 The following symbols are used:

av = combined vertical acceleration *at = combined transverse acceleration *al = combined longitudinal acceleration *g = acceleration of gravity = 9.81 m/s2 Pw = wind load according to the Rules for Classification of Ships Pt.5 Ch.2 Sec.6 Gkr = radius of gyration*GM = metacentric height* = roll angle*M = mass of container (Ma for variable container masses)bs = distance between bottom supports of container in mmh = height of container in mmnb = number of interconnected stacks in container blockn = number of tiers in stack or blocki = number of tiers of containers in stack or block below the level in question (also valid for j, k and m)Kc = racking stiffness in kN/mm of container wallKi = horizontal stiffness in kN/mm of container lashing connected to level iPh = horizontal force in kN acting per half container (Pha for variable forces)a = denominator of container in stack (from 1 to n)Pl i = lashing force in kN of lasing connected to level i, similar for k, j and mPri = horizontal support force in kN acting at level i, similar for k, j and mPsh = vertical support force in kN acting at bottom of container stack due to horizontal loadsPch = vertical support forces in kN acting in side posts of lower most container of stack due to horizontal loads

Ch.2Design loads

Ch.3Loading conditions

Ch.5Direct calculation

using beam analysis

Ch.6 and 7Formula based

analysis

Ch.8Special container

arrangements

Ch.4Acceptance

criteriaDET NORSKE VERITAS AS

= Psh Ph1 h / 2 bs


= assumed fraction of horizontal load acting on container end, which is transmitted through the containerwall, normally should be equal to VCG (min. 0.45) and 0.0 for end and side walls respectively

ic = clearance in mm of rigid transverse support at level i, similar at levels j, k and mio = calculated horizontal displacement in mm at level i of a horizontal unsupported stack of containers whensubjected to a uniform horizontal load, similar at levels j, k and m

ij = calculated horizontal displacement in mm at level i of a stack of containers when subjected to ahorizontal point load at level j, similar for other combinations of displacement and point load levels.

*For details see the Rules for Classification of Ships Pt.3 Ch.1 Sec.4 B.

1.4 Assumptions

1.4.1 Ship hull supports are normally assumed rigid. In special cases, e.g. shoring forces at ship sides, it maybe necessary to consider non-rigid supports. See also Sec. 8.

1.4.2 Calculations assume that containers have at least normal strength and stiffness, i.e. closed boxes, open-top boxes, tank containers. For platform-based containers see Sec. 8.

1.4.3 All containers in a stack or block are placed in the same directions, i.e. all containers have the doorlessend facing the same direction.

1.4.4 Friction effects are not taken into account.

1.4.5 Pretensioning of lashings is not considered.

2. Design Loads

2.1 General

2.1.1 Design loads applied in direct calculations are to be taken as given in the Rules for Classification of ShipsPt.5 Ch.2 Sec.6 E. Wind loads and accelerations are further specified in 2.2 to 2.3 in the following.

2.2 Wind load

2.2.1 For wind-exposed container stacks, a wind load of 1.171 kN/m2 is to be applied to the side and end walls.In accordance with the Rules for Classification of Ships Pt.5 Ch.2 Sec.6 E, the wind force, Pw, acting on ISOcontainer walls shall be taken as:

Figure 2-1

Sides 20 ft long, 8.5 ft high Pw = 18.5 kNSides 40 ft long, 8.5 ft high Pw = 37 kNEnds, 8.5 ft high Pw = 7.5 kN

Wind exposed container DET NORSKE VERITAS AS

Windload


2.3 Accelerations2.3.1 Accelerations should be computed according to the Rules for Classification of Ships Pt.5 Ch.2 Sec.6E300.The actual/realistic roll radius of gyration, kr, and metacentric height, GM, may be used in the calculationsinstead of the rule-defined values, provided that these have been computed for the actual condition.

Note:The rule-defined rolling angle is given in the Rules for Classification of Ships Pt.3 Ch.1 Sec.4. If rolling angles arespecified in excess of those defined in the rules, the accelerations should in general be computed in accordance withthe Rules for Classification of Ships Pt.3 Ch.1 Sec.4 B, utilising the specified roll angle and the rule-defined periodof roll. This will lead to very high accelerations unless the period of roll is increased.

---e-n-d---of---N-o-t-e---

3. Loading Conditions3.1 General3.1.1 Applicable loading conditions are listed in Table 3-1. In the subsequent sections the relevant loadingconditions will be described in more detail.

3.2 LC1: Transverse loading I3.2.1 For deck stowage extreme transverse accelerations are combined with the acceleration of gravity actingdownwards.Wind loads shall be added to wind exposed containers.See also Figure 3-1.

3.2.2 For hold stowage extreme transverse accelerations are combined with the acceleration of gravity actingdownwards.See also Figure 3-1.

Figure 3-1Load case 1

3.3 LC2: Vertical loading3.3.1 For deck stowage extreme vertical accelerations are combined with the acceleration of gravity actingdownwards.See also Figure 3-2.

3.3.2 For hold stowage extreme vertical accelerations are combined with the acceleration of gravity actingdownwards.

Table 3-1 Load case overviewLC Description Vertical Horizontal Wind1 Transverse loading I g at Yes2 Vertical loading g + av - No3 Transverse loading II g cos() at Yes4 Longitudinal loading g al Yes

Pw

M g

M

M at DET NORSKE VERITAS AS

See also Figure 3-2.



3.4 LC3: Transverse loading II

3.4.1 For deck stowage extreme transverse accelerations are combined with the vertical component ofacceleration of gravity acting downwards.Wind loads shall be added to wind exposed containers.See also Figure 3-3.

3.4.2 For hold stowage extreme transverse accelerations are combined with the vertical component ofacceleration of gravity acting downwards.See also Figure 3-3.


3.5 LC4: Longitudinal loading

3.5.1 For deck stowage extreme longitudinal accelerations are combined with the acceleration of gravityacting downwards.Wind loads shall be added to wind exposed containers.See also Figure 3-4.

3.5.2 For hold stowage extreme longitudinal accelerations, based on half the maximum service speed, arecombined with the acceleration of gravity acting downwards.See also Figure 3-4.

Figure 3-4

M (av+g)

M

Pw

M g cos

M

M at

M g

Pw

M g

M M al DET NORSKE VERITAS AS

Load case 4


4. Acceptance Criteria4.1 General4.1.1 Acceptance criteria for containers, securing equipment, support fittings and ship structures are outlinedin the Rules for Classification of Ships Pt.5 Ch.2 Sec.6 E. In the following sections, strength ratings for ISOcontainers and guidance as to the allow-able forces in the securing equipment are given.

4.2 Containers4.2.1 Container strength limits are normally to be in accordance with the required minimum (tested) strengthvalues and capabilities given in ISO-standard 1496/1. Strength ratings are given in Table 4-1.

Table 4-1 Strength ratingsStandard ISO

20 ft 40 ftRacking force door end 150 150Racking force doorless end 150 150Racking force side walls 75 (150*) 75 (150*)Corner post compression 848 848Vertical tension in top corner (from locking device) 250 250Vertical tension in bottom corner (from locking de-vice)

250 250

Lashing loads in corner casting (in plane of cont. wall)Horizontal 150 150Vertical 300 300Horizontal shoring forces on corners (perp. to cont. wall)Lower corner, tension 200 250Lower corner, compression 500 500Upper corner, tension 200 250Upper corner, compression 340 340* For closed box containersDET NORSKE VERITAS AS


Figure 4-1Strength ratings for 20'/40' containers

4.3 Container securing devices4.3.1 Working loads in container securing devices are in general not to exceed 50% of the minimum breakingload. Table 4-2 shows guidance values of maximum securing loads for selected types of the container securingdevices, for calculation purposes values for actual equipment are to be used.

150/150 kN

150/150 kN

150/150 kN

75/75 (150) kN

75/75 (150) kN

75/75 (150) kN

848/848 kN

848/848 kN

250/250 kN

250/250 kN

200/250 kN

200/250 kN

300/350 kN

300/350 kN

200/250 kN

200/250 kN

200/250 kN

200/250 kN

150/150 kN 150/150 kN

300/300 kN 300/300 kN DET NORSKE VERITAS AS


Table 4-2 Guidance values for container securing devices

Item Type Figure Typical MSL [kN] 1)

Lashings

1 Lashing rod

240

2 Turnbuckle

3 Penguin Hook

4 D-Ring

5 Lashing plate

Twistlocks and deck connections

6 Twist lock (single) 210

250

7 Twist-lock (linked) 210 2)

8 Flush ISO socket 250

9 Pedestal ISO socket 250

210

10 Dove tail socket with twist lock 250

210

Hold and block stowage

11 Stacker (single) 210

12 Stacker (double) 2103)

13 Linkage plate 210

14 Pressure element 840

15 Tension/pressure element 550/840

1) These values are selected to match the strength rating of the containers; for light-weight stacks smaller values may be accepted.2) As item 6 + horizontal tension as given3) As item 11 + horizontal tension as givenDET NORSKE VERITAS AS


4.4 Ship structure

4.4.1 The supporting structure for the containers such as hatch covers, decks, inner bottom and bulkheads shallbe evaluated according to the Rules for Classification of Ships Pt.5 Ch.2 Sec.6 and the acceptance criteria givenin E700.

5. Direct Calculation using Beam Analysis5.1 General

5.1.1 This section provides guidance on how to perform beam analysis for container lashing arrangements. Seealso Appendix B for examples.

5.1.2 The procedure described below represents the method used by the program NAUTICUS ContainerSecuring.

5.1.3 The container stacks are modelled as two independent 2-dimensional beam models, one for the door endand one for the doorless end, to incorporate the different racking stiffness.Each stack may be analysed separately unless there are connections between the stacks such as double stackersor similar, in which case the whole block needs to be analysed. Non-structural top bridge fittings are ignoredin the analysis.

5.1.4 Nonlinearities such as compression elements and gaps in horizontal supports must be included. Theanalysis is also to include the effects of clearances. For individual container stacks, clearances of stack fittingsmay be ignored. Stipulated clearances between container stacks and horizontal supports are to be taken intoaccount. For container blocks with horizontal supports, clearances of bridge fittings within the block are to betaken into account. Non-linearities such as compression elements and gaps in horizontal supports must beincluded.

5.2 Modelling of geometry

5.2.1 The analysis is to take into account the flexibility of the containers. Unless otherwise specified, theracking stiffness Kc of container end walls for normal closed box ISO containers may be taken as:

Kc = 10 kN/mm for doorless endsKc = 3.85 kN/mm for door ends

Unless otherwise specified, the racking stiffness of container sidewalls may be taken equal to doorlesscontainer end walls.The corner posts are modelled with a shear area so that the correct racking stiffness is obtained, according toFigure 5-1. The bending stiffness of the beams should be high in order to avoid introduction of bending stressesin the elements.

Figure 5-1Racking stiffness of container

When a force F (3.85 kN for the door end and 10 kN for the doorless end), is applied to the container thecalculated deflection should be 1 mm.

5.2.2 Twistlocks are to be modelled with an area sufficiently large to avoid large tensile deformations.The twistlocks must be modelled with a hinge at one end to avoid transfer of bending moments between the

F DET NORSKE VERITAS AS

containers, as shown in Figure 5-2.


Figure 5-2Hinge at end of twist lock

5.2.3 Stacking cones are modelled as twist locks with the difference that these must be modelled as non-linearelements capable of taking compression and shear but not tension.

5.2.4 Double stackers, linked twistlocks and linkage plates are modelled with the actual cross sectional area.The transverse elements should be positioned at the midpoint of the twistlock/stacking cone and in general befitted with hinges at both ends, as shown in Figure 5-3. For components that have the capability to transfervertical shear forces, these hinges should be omitted. Gaps in the bridges must be modelled as nonlinearities.

Figure 5-3Linking elements and double stackers

5.2.5 Buttress supports, compression and tension elements are modelled with the actual cross sectional area.Pure compression elements must be modelled as nonlinear elements taking compression only. In addition, thegap between the element and the supporting structure must be modelled as a nonlinearity.Hull deformations, if significant, are to be taken into account when determining the shoring forces.

5.2.6 For ordinary lashing units with one turnbuckle or lashing, the lashing should be modelled as beamelements with characteristics according to Table 5-1. The lashings elements shall be fitted with hinges at bothends to avoid transfer of bending moments.

For wind lashings please see section 8.4.

5.3 Boundary conditions5.3.1 Elements attached to the ship structure should be restricted from translation.

5.4 Loading conditions5.4.1 Loading conditions are to be in accordance with Sec. 2 and 3.

5.4.2 Loads should be applied as point loads in the corners of the containers. The distribution of transverseinertia forces between the top and bottom corners should be taken in relation to the centre of gravity of thecontainer, which should in no case be taken lower than 45% of the container height. Vertical inertia forces areonly applied to the bottom corners of the container. Wind loads may be equally distributed between the fourcorners of the container, on the windward side or distributed on all corners of the container.

5.5 Results5.5.1 Forces shall be extracted from the model to confirm that the loads in the securing devices between thecontainers and in the containers themselves do not exceed the safe working load of the securing devices or thecontainer strength limit, according to Sec. 4.

Table 5-1 Lashing rod characteristicsArea Modulus of elasticity [N/mm2]

Rod lashing Actual area of rod 14 (l+6500) maximum 2.06 105l = The length of lashing including turnbuckle, in mm

Twist lock

Hinge

Hinge

Linking elements

Twist lock Link

Hinge DET NORSKE VERITAS AS

In addition the reaction forces in the ship structure must be considered.


6. Formula based Analysis, Basic Formulae6.1 Rigid container securing arrangements (cell guides and similar)

6.1.1 The maximum vertical support force from corner base fitting may be taken as:

6.1.2 The maximum compressive force in container end posts may be taken as:

6.1.3 The stresses and forces in securing structures resulting from horizontal accelerations and wind forces, whererelevant, are to be calculated as M at + Pw and M al + Pw in transverse and longitudinal direction, respectively.

6.1.4 The analysis required for rigid container securing arrangements depends on the complexity of thearrangement. For complex cellular securing structures, direct analyses may be necessary. In other cases manualcalculations will be sufficient.

6.1.5 Hull deformations, if significant, are to be taken into account when determining the shoring forces.

6.2 Non-rigid securing arrangements (lashings and similar)

6.2.1 For non-rigid securing arrangements the vertical support forces, internal forces of the container stacks,horizontal support forces and lashing forces are all to be calculated, if relevant.

6.2.2 The analysis is to take into account the flexibility of the containers. Unless otherwise specified, theracking stiffness, Kc, of container end walls for normal closed-box ISO containers may be taken as:

Kc = 10 kN/mm for doorless endsKc = 3.85 kN/mm for door ends

Unless otherwise specified, the racking stiffness of container sidewalls may be taken equal to doorlesscontainer end walls.

6.2.3 Calculations of container stacks or blocks are to be performed for both doorless and door end walls.Normally maximum vertical and horizontal reaction forces at the stack base are found in doorless ends, whilstmaximum horizontal support forces and lashing forces are found in door ends.

6.2.4 The analysis is to be based on the elastic stiffness of lashings according to their type and dimensions, ref.Sec. 7.1.1.

6.2.5 The analysis is to include the effects of clearances. For individual container stacks, clearances of stackfittings may be ignored. Stipulated clearances between container stacks and horizontal supports are to be takeninto account. For container blocks with horizontal supports, clearances of bridge fittings within the block areto be taken into account as outlined in section 6.5.

6.2.6 The effects of vertical connections between the containers in a stack are to be taken properly intoaccount. The effects of possible tipping of container stacks without lock connection at bottom supports are ofspecial importance and must be especially considered. Reference is made to section 5.2.

6.2.7 The calculations are to be based on analysis methods applicable to structures in general. In the analysisthe container walls may be considered as shear panels. The interaction between the two ends, or sides, ofcontainers may normally be assumed negligible. See also section 8.2.

6.2.8 Generally, the horizontal force in each container end or side is to be taken as:

ah = at or al for transverse or longitudinal accelerations, respectively.

6.2.9 Maximum vertical support forces, racking forces, horizontal support forces and lashing forces maynormally be determined directly in accordance with chapter 7.

na

vas agMP1

25.0 [kN]

na

vas agMP2

25.0 [kN]

whh PaMP 5.0 [kN]DET NORSKE VERITAS AS

6.2.10 The combined maximum vertical support forces may be determined as the larger of:


On compression side (positive):

or

On tension side (negative):

If Pst becomes negative tipping will take place and locking cones or twistlocks are to be installed. See alsoRules for Classification of Ships Pt.5 Ch.2 Sec.6 F302, for stacks without lashing or shoring.

Psh = calculated vertical support force due to horizontal loads as given in Sec. 7.2.3Psl = sum of the vertical components of relevant lashing forces according to Sec.7On compression side Psl is only added when internal cross lashing is usedOn tension side Psl is only added when external lashing is used

6.2.11 The combined maximum compressive force in the lowermost container posts is normally determinedas the larger of:

and

Pch = calculated compressive force in post due to horizontal loadsPsl = as given in Sec. 6.2.106.2.12 The racking force in the wall of the lowermost container is determined by:

Pr = sum of horizontal lashing or supporting forces (Pri, Prj etc.) calculated in accordance with Sec.7.Ph1 = horizontal force in lowermost container end

In cases where there are two or more containers above the upper lashing or fixed support, the racking force inthe lower of these should also be checked.

6.3 Container stack with four flexible horizontal supports6.3.1 Consider a container stack supported by lashings at levels i, j, k and m in that order from the bottom.For the analysis in the following, reference is made to Figure 6-1.

slshn

aasc PPgMP

125.0 [kN]

n a

vasc agMP 1

25.0 [kN]

slshn

aast PPgMP

1cos25.0 [kN]

na

vac agMP2

25.0 [kN]

slchn

aac PPgMP

225.0 [kN]

na

rhhar PPPS2

1 [kN]DET NORSKE VERITAS AS


Figure 6-1Four flexible supports, general case

6.3.2 Disregarding the lashings, the free horizontal displacement at level i is given by:

and similar for other levels j, k and m.

6.3.3 The horizontal displacement at level i due to a horizontal force acting at the same level is given by:

and similar for other levels j, k and m.The displacement at levels below the force in question is proportional to the level number, e.g. the displacementat level i due to force acting at level k is given by:

The displacement at levels above the force in question is equal to the displacement at the force level.

6.3.4 The support force at level i is expressed as a function of the resulting horizontal displacement at the samelevel, i.e.:

and similar for levels j, k and m.

6.3.5 The horizontal forces as mentioned in 6.3.3 must be equal to the corresponding support forces given in2.3.4. Consequently the following linear equations may be derived, in matrix form:

Km

Kk

Kj

Ki

Pm

Pk

Pj

Pi

mm

kk

jj

ii

mo

ko

jo

io

Ph6

Ph5

Ph4

Ph3

Ph2

Phk n=6

i

a

i

a

n

abhbha

cio PPK 1 1 1

1

c

iii K

Pi

kkik ki

iiijikimioiri KP DET NORSKE VERITAS AS


From these equations the horizontal support forces Prm, Prk, Prj and Pri may be solved. If the number of lashingsis less than four, the system reduces correspondingly. E.g. for a system with two lashings the system reduces to:

6.4 Container stack with combined rigid and flexible horizontal supports6.4.1 Consider a stack of containers as in 2.3. Let one support be rigid, for example at level j. A clearance jcat that support is assumed.

6.4.2 The support forces at levels i, k and m are given by the formulae in 6.3.4. At level j the resultingdisplacement is given by:

Consequently the linear equations in 6.3.5 are modified as follows:

6.4.3 In this way the linear equations may be set up for an arbitrary combination of rigid and flexible supports.For example, with four rigid supports the horizontal support forces are given by:

6.5 Container blocks6.5.1 Container stacks connected by horizontal bridge stackers may be regarded as a block with respect tolashing and rigid horizontal supports. It is assumed that bridge stackers are fitted at each level of horizontalsupport and that the clearances at stackers normally are negligible. The block may be calculated on the basisof an analysis of single stacks with the same deflection (fixed support clearance). The resulting horizontalsupport force will be the sum of all support forces from the individual stacks.If the horizontal stackers are fitted with a clearance b at each stacker, the support clearances ic, jc, kc or lcare for each stack away from the rigid support to be increased by b. Arrangement with a single rigid supportis shown in Figure 6-2.

- The diagonal element

- The displacement

cio

cjo

cko

cmo

ri

rj

rk

rm

i

c

j

c

k

c

m

c

KKKK

PPPP

iKKiii

ijKKjj

ijkKKk

ijkmKK

cio

cjo

ri

rj

i

c

j

c

KK

PP

iKKi

ijKK

iijjkkmmjojc kj

mj

jjKK

j

c

jcjojo

cicio

cjcjo

ckcko

cmcmo

ri

rj

rk

rm

KKKK

PPPP

iiiiijjjijkkijkm

)()()()(

DET NORSKE VERITAS AS


Figure 6-2Block with single rigid horizontal support

6.5.2 If the number of stacks in a block is greater than 4 and bridge stackers are fitted at all levels in the block,a reduction in the horizontal support forces may be introduced due to the stackers giving a certain vertical shearrestraint. The final support forces may be found as:

Pri = calculated horizontal reaction force for blockCr = reduction factor as given in Table 6-1

The racking force, Sr, in the end wall of the lowermost container is to be calculated according to 6.2.12 withthe reduced Prif inserted in the formula. The vertical support forces may be calculated with the uncorrected Pri.

6.5.3 In order to reduce the horizontal support forces at rigid block supports, the supports may be arranged forabsorbing both compression and tension. If the clearances at the individual stackers are considered to benegligible, a 50% distribution between the compression and tension side may normally be used whencalculating the support forces according to 6.5.1 and 6.5.2.In case there is a clearance in each horizontal bridge stacker, redistribution towards 100% compression willtake place. A 50% distribution may be achieved by omitting all bridge stackers between middle stacks, thusobtaining two individual blocks.

7. Formula based Analysis, Derived Formulae7.1 General7.1.1 The following describes elementary formulae for the analysis of container stacks subjected to horizontalforces. In general, the formulae may be applied for the determination of vertical support forces, horizontalsupport forces and lashing forces. It should be noted that the formulae for vertical support forces do not includethe vertical component of possible lashing forces and vertical mass forces.

7.1.2 The calculation formulae are based on the following assumptions:

The bending stiffness of the container wall is assumed to be significantly higher than the shear stiffness;

Table 6-1 Reduction factorsnb 1 to 4 5 6 7 8 9 10Cr 1 0.98 0.95 0.91 0.85 0.79 0.75

ic

Pri

io Bridge stackers clearance: b

n=6

i=5

Psh

rirrif PCP DET NORSKE VERITAS AS

the container walls are therefore considered as shear panels


Internal clearances in stacking and locking members of individual stacks are ignored Tensile vertical forces are assumed taken by lock stackers; if lock stackers are not fitted and containers may

be subject to tilting, the lashing forces will have to be specially considered The flexibility of container walls and lashings are assumed to be linear Pre-stressing of lashings is not included in the consideration Containers subjected to horizontal acceleration forces are assumed homogeneously loaded, with the centre

of gravity in the centre point of the container. However a VCG of 45% of the container height may beutilised.

7.1.3 The horizontal spring stiffness of simple lashing rods supporting the container stack at level i may beexpressed as:

El = modulus of elasticity as per Table 5-1.

The modulus of elasticity of non-standardised lashing equipment, such as wires and chains, will be subject tospecial consideration, and may have to be determined experimentally.

Figure 7-1Stiffness of simple lashing

7.2 Container stack with single rigid support7.2.1 A container stack with single rigid support is shown in Figure 7-2.The clearance at the rigid support, ic, is assumed to be known. The unsupported displacement, io, may becalculated with the formula in 6.3.2.

7.2.2 The horizontal support force derived from the general formulae in 6.4.3 is given by:

Not valid for ic > io.

32122

sh

sAEK

l

llli

l

lli l

AEK 2sinor [kN/mm]

Pli

Kli

ll

sl

hl

i=3

iKP iciocri

)( [kN]DET NORSKE VERITAS AS


7.2.3 The vertical support force due to the horizontal forces is given by:

Figure 7-2Single rigid horizontal support

7.3 Container stack with two rigid horizontal supports7.3.1 A container stack with two rigid supports is shown in Figure 7-3.The clearances at the lower and higher supports, ic and jc respectively, are assumed to be known. Theunsupported displacements, io and jo, may be calculated in accordance with the formulae in 6.3.2.7.3.2 The horizontal support forces derived from the general formulae in 6.4.3 are given by:At level i:

At level j:

If any of the support forces becomes negative, this support will not be engaged. The calculation then has to berepeated with the remaining support only, according to 7.2.

s

n

ariha

sh b

hiPPaP

1

5.0[kN]

ic io

iji jiKP iciojcjocri 2 [kN]

ijK

P iciojcjocrj [kN]DET NORSKE VERITAS AS


7.3.3 The vertical support force is given by:

Figure 7-3Two rigid horizontal supports

7.4 Container stack with three rigid horizontal supports7.4.1 The clearances at the three supports, ic, jc and kc are assumed to be known. The unsupporteddisplacements, io, jo and ko, may be calculated in accordance with the formulae in 6.3.2.7.4.2 The horizontal support forces derived from the general formulae in 6.4.3 are given by:At level i:

At level j:

At level k:

If any of the support forces becomes negative, this support will not be engaged. The calculation then has to berepeated with the remaining supports, according to 7.3.

s

n

arjriha

sh b

hjPiPPaP

1

5.0[kN]

jc jo

ic

io

Prj

Pri

iji jiKP iciojcjocri 2 [kN]

jkijKP jcjokckoiciojcjocrj

[kN]

jk

KP jcjokckocrk

[kN]DET NORSKE VERITAS AS


7.4.3 The vertical support forces are given by:

7.5 Container stack with single flexible support7.5.1 A container stack with single flexible support is shown in Figure 7-4.The horizontal spring stiffness of the lashing, Ki, may be calculated in accordance with the formula in 7.1.3.The unsupported displacement, io, may be calculated in accordance with the formula in 6.3.2.7.5.2 The horizontal support force derived from the general formulae in 6.3.5 is given by:

7.5.3 The vertical support forces may be calculated as given in 7.2.3.

Figure 7-4Single flexible horizontal support

7.6 Container stack with one rigid and one flexible support7.6.1 A container stack with one rigid and one flexible support is shown in Figure 7-5.The horizontal spring stiffness of the lashing, Ki, may be calculated in accordance with the formula in 7.1.3.The clearance at the rigid support, ic, is assumed to be known.The unsupported displacements, io and jo, may be calculated in accordance with the formulae in 6.3.2.7.6.2 The horizontal support forces derived from the general formulae in 6.3.5 and 6.4.3 are given by:At level i:

s

n

arkrjriha

sh b

hkPjPiPPaP

1

5.0[kN]

i

KKKP

i

c

iocri

[kN]

Ki Pri

io

ji

KKi

jiKP

i

c

iojcjocri

2



At level j:


Figure 7-5One rigid and one flexible support

7.7 Container stack with two flexible horizontal supports

7.7.1 A container stack with two flexible horizontal supports is shown in Figure 7-6.The horizontal spring stiffness of the lashing, Ki and Kj, may be calculated in accordance with the formula in7.1.3.The unsupported displacements, io and jo, may be calculated in accordance with the formulae in 6.3.2.7.7.2 The horizontal support forces derived from the general formulae in 6.3.5 are given by:At level i:

At level j:

2iji

KK

iiKKK

P

i

c

iojcjoi

cc

rj

[kN]

Ki Pri

io

jc jo

Prj

j

KKi

KKi

jKKiK

P

j

c

i

c

ioj

cjoc

ri2

[kN]

2ijKKi

KK

iiKKK

Pcc

iojoi

cc

rj


ji



Figure 7-6Two flexible horizontal supports

7.8 Container stack with one rigid and two flexible horizontal supports7.8.1 A container stack with one rigid and two flexible supports is shown in Figure 7-7.The horizontal spring stiffness of the lashing, Ki and Kj, may be calculated in accordance with the formula in7.1.3.The clearance at the rigid support, kc, is assumed to be known.The unsupported displacements, io, jo and ko, may be calculated in accordance with the formulae in 6.3.2.7.8.2 The horizontal support forces derived from the general formulae in 6.3.5 and 6.4.3 are given by:At level i:

At level j:

At level k:

7.8.3 The vertical support forces due to the horizontal loads and forces may be calculated as given in 7.4.3.

7.9 Container stack with three flexible horizontal supports7.9.1 The horizontal spring stiffness of the lashing, Ki, Kj and Kk, may be calculated in accordance with theformula in 7.1.3.

Ki Pri

io

jo

Prj Kj

222

2 iCkjCjkC

kjijkCiCjKP

jij

jojiojkckocri

[kN]

2222

2 iCkjCjkC

ikCkjijCiKP

jij

ijoioikckocrj

[kN]

2222

2 iCkjCjkC

jCiCjiiCCKP

jij

ijojiojikckocrk

[kN]

iKKC

i

ci

jKKC

jc

j DET NORSKE VERITAS AS

The unsupported displacements, io, jo and ko, may be calculated in accordance with the formulae in 6.3.2.


7.9.2 The horizontal support forces derived from the general formulae in 6.3.5 are given by:At level i:

At level j:

At level k:

7.9.3 The vertical support forces due to horizontal loads and forces may be calculated as given in 7.4.3.

Figure 7-7Container stack with one rigid and two flexible supports

kjikji

kjiokjojkocri

CCjiCjCCC

jCCCjiCjiKP

222

2[kN]

kjikji

kiokijoikocrj

CCjiCjCCC

CjiiCCjCiKP

222

22 [kN]

kjikji

jioijojikocrk

CCjiCjCCC

CjijCiiCCKP

222

22 [kN]

iKKC

i

ci

jKKC

j

cj

kKKC

k

ck

Kj Prj

jo

kc ko

Prk

Ki Pri

io DET NORSKE VERITAS AS


8. Special Container Arrangements

8.1 General

8.1.1 In this section some special cases of container arrangements are presented with applicable analysismethods. The calculation methods described in the previous sections are not necessarily applicable to thesearrangements.

8.2 20' container in 40' cell guides

8.2.1 20' containers may be carried in cell guides designed for 40' containers provided that the following areconsidered:

Cones fixed to the tank top, or similar arrangements, are fitted at mid-hold, to prevent the lowermostcontainer from sliding in transverse direction.

Each tier of 20' containers is connected to the next by at least two stacking cones, one in each end, fitteddiagonally.

The uppermost 20' container is connected to the lowermost 40' container, if any, by two stacking cones inthe cell guide end.

The loads transferred to containers and securing devices do not exceed container strength ratings andmaximum securing load (MSL), respectively.

The 20' containers have steel walls and top, i.e. that they are not of open-frame type.

8.2.2 Maximum container weights in 20' stacks are determined by the racking force limit of the lowermostcontainer.The racking force in the lowermost 20' container is determined by summing the transverse forces from each 20'container. The contribution from the lowermost container should be taken equal to the fraction ,corresponding to the VCG. The transverse dynamic forces in each tier may be assumed distributed 35% to themid-hold end and 65% to the cell guide end, provided that the stack is topped by at least one 40' container.

8.2.3 If the 20' stack is not topped by a 40' container, the transverse force distribution is to be taken as 45% tothe mid-hold end and 55% to the cell guide end. Stacks with more than 10 tiers without a 40' container on topwill be specially considered.

8.2.4 The deformation of the container stack should also be analysed, taking into account the clearancesbetween the stacking cones and the corner castings, to verify that the different stacks will not come into contact.The analysis should be performed in longitudinal and transverse direction, and as a combination of both.

8.3 40' container in 45' cell guides

8.3.1 40' containers may be carried in cell guides designed for 45' containers provided that:

Cones fixed to the tank top, or similar arrangements, are fitted at mid-hold, to prevent the lowermostcontainer from sliding in transverse direction

Each tier of 40' containers is connected to the next by at least two stacking cones, one in each end, fitteddiagonally

The loads transferred to containers and securing devices do not exceed container strength ratings andmaximum securing load (MSL), respectively.

The 40' containers have steel walls and top, i.e. that they are not of open-frame type.

8.3.2 Maximum container weights in 40' stacks are determined by the racking force limit of the lowermostcontainer.The racking force in the lowermost 40' container is determined by summing the transverse forces from each 40'container. The contribution from the lowermost container should be taken equal to the fraction ,corresponding to the VCG. The transverse dynamic forces on each tier may be assumed distributed 50% to thefree end and 50% to the cell guide end.

8.3.3 Stacks more than 10 tiers high will be specially considered.

8.3.4 The deformation of the container stack should also be analysed, taking into account the clearancesbetween the stacking cones and the corner castings, to verify that the different stacks will not come into contact.DET NORSKE VERITAS AS

The analysis should be performed in longitudinal and transverse direction, and as a combination of both.


8.4 Effectiveness of lashings attached to lashing bridge

8.4.1 When a lashing is attached to a lashing bridge the relative movement of the hatch cover and the shipstructure will give rise to increased loads in the lashing. To account for this phenomenon in the calculations,the MSL of the lashing is in general to be reduced according to Table 8-1.

8.4.2 Specialised arrangements with extreme lashing angles or unusually long distance between lashing bridgeand container are to be specially considered.

8.5 Vertical lashings wind lashing

8.5.1 Vertical lashings cannot in general be included in the analysis but must be considered as a separate item.

8.5.2 Due to the clearances in the twistlocks the vertical lashing will carry the whole load until thedeformations of the stack have closed these clearances.

8.5.3 For vertical lashings fitted with special turnbuckles, in order to have the same clearance of the lashingas the twistlocks, the vertical tensile force may be assumed divided between the container corner post and thelashing, 1/3 in the lashing and 2/3 in the corner post.For lashings without such a device the method in B.3 of Appendix B can be used.

8.6 Block stowage in hold without cell guides

8.6.1 Care must be taken so that the vertical and transverse support points of the containers are aligned withthe areas of the ship structure which have been reinforced for this purpose.

8.6.2 The effects of stowing mixed container heights in the holds must be specially considered, taking intoaccount the support points in the transverse bulkhead and side structure.

8.6.3 The effects of hull deflections due to sea loading are to be taken into account when calculating transverseshoring forces. This is especially important for vessels with long holds and where the ship side deflections arelarge. If the hull deflections are unknown a conservative assumption should be made.

8.6.4 Clearances in securing equipment between the securing equipment and the supporting structure must bespecified.

8.6.5 Container blocks in holds without transverse connections, only compression i.e. pads (OSHA adaption)should be specially considered since this equipment does not give any vertical shear restraint and hence thehorizontal support forces will be increased.

8.7 Platform-based containers with reduced stiffness

8.7.1 Platform-based containers generally have reduced racking stiffness and longitudinal strength, whichmust be taken into account in the analysis.

8.8 Containers placed on two hatches or on hatches and side pillars

8.8.1 If containers are placed on two hatches or on hatches and side pillars the relative deformations must beaccounted for in the arrangement by fitting overlong ISO sockets, or by including this deformation in the

Table 8-1 Reduction of MSL

Length20' container stack 1) 40' container stackShort

lashing 2)Long

lashing 3)Short

lashing 2)Long

lashing 3)L < 270 m 10% 0% 15% 0%270 < L 315 20% 0% 25% 0%1) Assuming a lashing gap at mid-hold otherwise values as 40' should be utilised2) Lashing from lashing bridge to first tier above3) Lashing from lashing bridge to second tier aboveDET NORSKE VERITAS AS

lashing calculations.


Appendix AApproval of Lashing Computers/Software

A.1 IntroductionThis is guidance to those who are involved in approval and certification of lashing computers for a specific ship,i.e. software manufacturers who wish to have their software approved for a specific vessel.Guidance is also given for manufacturers who wish to have their software type approved.

A.2 DefinitionsLashing computer systemA lashing computer system is a computer-based system for calculation and control of container securingarrangements for compliance with the applicable strength requirements. The lashing computer system consistsof software (calculation program) and hardware (the computer on which it runs).Approval and certification for a specific vesselApproval of software means that DNV approves the software for a specific installation on board a specificvessel. The approval is based on a review and acceptance of design, calculation method, verification of storeddata and test calculation for the specific vessel.Approval of the software is to be carried out for each specific vessel where the software is to be installed.Approval of the software results in approved test conditions.If the software is type approved, the review and acceptance of design is not necessary for each specific vessel.Only verification of user manual, stored data and test calculations for the specific vessel will then be carriedout.Certification (installation testing) is carried out to ensure that the lashing computer system works properlyonboard the specific vessel, and to ensure that the correct approved version of the software has been installed.Certification is to be carried out for each vessel where a lashing computer system has been installed.Type approvalType approval means that DNV has approved the design methods and specifications of the software in general.The type approval is given based on a review and acceptance of design, calculation methods and documentedtest results for at least two test vessels. A type approval certificate is issued.In the type approval certificate it will be stated what kind of calculations the type approval covers.In connection with approval for a specific vessel with type approved software, less documentation will berequired, and a lower fee will be charged.

A.3 General requirementsThe approval and certification process includes the following procedures for each ship:

1) Approval of software which results in approved test conditions.2) Approval of computer hardware, where necessary.3) Certification of the installed lashing computer system, which results in a lashing computer certificate.

The approved test conditions are to be kept onboard together with the user manual and the lashing computercertificate.The approved software is either installed on a type approved hardware, or it is to be installed on two nominatedcomputers. If two nominated computers are available, approval of the hardware may be waived, but bothnominated computers are subject to certification. In addition, computers that are to be a part of a ships networkshould be approved in accordance with other relevant requirements imposed by the Society.The lashing computer is to be capable of producing printouts of the results numerically. These numeric valuesare to be presented both as absolute values and as a percentage of the allowable values.All screen and hardcopy output data are to be presented in a clear and unambiguous manner, with identificationof the version number of the calculation program.

A.4 General hardware requirementsDET NORSKE VERITAS AS

In case two nominated computers are used, these are to be equipped with separate screens and printers.


A.5 General software requirementsIt is recommended that the design and production of the calculation program be in accordance with appropriatequality standards.The software is to present the relevant parameters of each container arrangement. The following is to bepresented:

1) Draught2) GM value3) Each container weight4) Position of each container stack5) Lashing arrangement6) Forward visibility7) Accelerations of each container8) Strength limitation: Listing of obtained values compared with the limit values according to Sec. 4 (internal

forces in containers, forces in securing equipment and forces in supports)9) A clear warning is to be given if any of the strength limitations are not complied with10) The data is to be presented as screen and hard copy output to the user in a clear and unambiguous manner.

The software is to reject input errors by the user. For instance, negative weight input on containers or containerspositioned outside the ship is not to be accepted.The software and the stored characteristic data are to be protected against erroneous use. The software shouldbe written to ensure that these can not be altered by the user.The software is to be user-friendly, with a graphic presentation of the container arrangement.Any changes made to the software are to be made by the manufacturer or his appointed representative. TheSociety is to be informed immediately of any changes. Failure to advise of any modifications to the softwarewill invalidate the certificates issued. In such cases the modified software is to be reassessed in accordance withthe approval and certification procedure.

A.6 Documentation to submit for approval

A.6.1 Hardware documentationRequirements in Rules for Classification of Ships Pt.4 Ch.9 are to be complied with.If the hardware is to be type approved, documentation according to Rules for Classification of Ships Pt.4 Ch.9Sec.1 is to be submitted.

A.6.2 Software documentationApproval of the test conditions is mainly based on comparing the input and the results of the softwarecalculations with values calculated by DNV. The difference is not to be greater than 5%, calculated accordingto the following:((Value calculated by software) (Value calculated by DNV)) / (Allowable) The documentation must be prepared in a language understood by the users. If this language is not English, atranslation into English is to be included.All submitted documentation is to be identified with the following:

1) Name of vessel, name of yard, the yard building number and the DNV identification number of the ship forwhich the program applies

2) Program name, version number and version date3) Program manufacturer and address4) List of contents.

For each specific ship the following documentation is to be submitted:

1) User manual2) Program description (not required for type approved software)3) Test conditionsDET NORSKE VERITAS AS

4) Stored characteristic data.


The user manual is to contain:

1) A general description of the program denoting identification of the program and its version number stated2) Where applicable, a copy of the type approval certificate3) Hardware specification needed to run the program4) Listing of error messages and warnings with instructions for actions to be taken by the user in each case5) Listings of allowable strength limits with respect to the container, lashing equipment and ship6) Example of calculation procedure supported by illustrations and sample computer output7) Example of computer output of each screen display with explanatory text.

The program description is to contain the following:

1) Description of functionality, including flowcharts2) Descriptions of calculation methods and principles.

Program description is not required for type approved software.In some cases where the functionality and principles are not clear, the entire program may need to be submittedfor evaluation at the discretion of the Society.The test conditions are to be as follows:

1) Typical stowage in hold2) Mixed stowage, if applicable3) Typical stowage on deck4) Deck stowage with twistlocks only5) Case with exceeded stack weight6) Case with exceeded lashing force7) Case with exceeded lifting force8) An example where outboard stack is missing.

The stored characteristic data are to include the following:

1) Main dimensions of the ship2) The position of each bay from the aft perpendicular3) Strength limitations (for containers, lashing equipment and the ship)4) General loading limitations.

A.7 CertificationCertification is carried out to ensure that the lashing computer system works properly onboard, and to ensurethat the correct approved version of the software has been installed.The approved test conditions are to be tested on the lashing computer system in presence of a surveyor fromthe Society before the lashing computer certificate is issued.During the test, the securing arrangements calculated on the installed lashing computer system are to be verifiedto be identical to the approved test conditions. If numerical output from the lashing computer system is atvariance with the approved test conditions, a certificate cannot be issued.During the tests, at least one of the test conditions is to be built up from scratch, to ensure that the calculatingmethods function properly.Where the hardware is not type approved, the test is to be carried out on both the first and the second nominatedcomputer prior to the issuance of the lashing computer certificate. Both of the nominated computers are to beidentified on the certificate.After completion of satisfactory tests, the lashing computer certificate is to be issued.The following is to be listed in the lashing computer certificate:

1) Name of vessel, name of yard, yard number and year of built for the vessel2) Software name, software version3) Software manufacturer name and addressDET NORSKE VERITAS AS

4) Type approval certificate number, if relevant


5) Hardware name, serial number and manufacturer6) Name and serial number of the second nominated computer or type approval certificate number7) Identification of the approved test conditions used for the certification.

The lashing computer certificate and the approved test conditions are to be kept onboard attached to the usermanual.The certification is to be carried out onboard.DET NORSKE VERITAS AS


Appendix BCalculated ExamplesIn this appendix the following calculated examples are given using both the direct analysis method and theformula-based method:B.1 Three-tier stack with single lashing, no windloadB.2 Four-tier stack with two cross lashing, no windload (formula-based method).B.3 Wind lashing without special turnbuckle

B.1 Three-tier stack with single lashingFormula-based methodThree-tier 40' standard ISO container stack with single cross lashing to top of tier 1, no wind load included, seeFigure B-3.

Figure B-1Three-tier stack with single lashing, no wind load

Horizontal force per container end:Ph = 30 6.67 = 100 kNLashing (see Sec. 7.1.3):

General data:Container weights: 30 t (all tiers)Twistlocks: SWL 250 kN (between each tier)Lashing rods: Steel, diameter 25 mm

SWL 250 kNTransverse accelerations:Tier 1: 6.67 m/s2Tier 2: 6.67 m/s2Tier 3: 6.67 m/s2

Vertical acceleration:Tier 1-3 7.60 m/s2

Roll angle, 27

Al = 491 mm2

Ph

Ph

Ph n=3

i=1 Plsi

Pli

Ps Ps DET NORSKE VERITAS AS

hl = 2591 mm


Calculation for doorless end wallsEnd wall racking stiffness (see 6.2.2): Kc = 10 kN/mmFree displacement at level i (see 6.3.2):

Horizontal support force of lashing (see 7.5.2):

Vertical support force (see 7.2.3):

Lashing force:

Vertical component of lashing force:

Combined vertical support forces (see 6.2.10):Compression side

=> Psc = 727.0 kN (into ship structure)

Tension Side (Psl = 0))

Twistlock with SWL= 250 kN.Compressive force in lowermost container (see 6.2.11):

=> Pc = 596.1 kN (< 848)Racking force in lowest container (see 6.2.12):

sl = 2438 mmll = 3558 mmEl = 14(l + 6500) = 14(3558 + 6500) = 140 812 N/mm2 =

140.8 kN/mm2

mmkNK j /13.9)24382591(

24384918.140322

2

mm 25.0 1001001005.0101

0 i

)150(3.1191

13.910

2510

riP

kNPsh 5.379225825913.11911005.4

)250(1.1742438

243825913.11922

liP

)300(8.126243825913.119 slP

0.7278.1265.37981.930325.0 scP

)250(8.1825.37927cos81.930325.0 stP

kNPc 1.5968.1262258225911005.37981.930225.0 DET NORSKE VERITAS AS

)150(7.1303.1191005.01002 rS


Calculation for door end wallsEnd wall racking stiffness (see 6.2.2): Kc = 3.85 kN/mmFree displacement at level i (see 6.3.2):



Lashing force:




Tension Side (Psl = 0)

Twistlock with SWL = 250 kN.Compressive force in lowermost container (see 6.2.11):

=> Pc = 591.6 kN (


Compression side

Tension Side

B.2 Four-tier stack with two cross lashingsFour-tier 40' standard ISO container stack with two cross lashings, no wind load included, see Figure B-6.

Figure B-2Four-tier stack with two cross lashings, no wind load

Lashings (see 7.1.2):

General data:Twistlocks: SWL 250 kN

(between each tier)Lashing rods: Steel, diameter 25

mmSWL 250 kN

Mass Transverse acceleration, at:Pha

Tier 1: 30 6.10 m/s2 91.5 kNTier 2: 30 6.25 m/s2 93.8 kNTier 3: 30 6.40 m/s2 96.0 kNTier 4: 3 6.55 m/s2 9.8 kN

Vertical acceleration:Tier 1-3 4.20 m/s2

Roll angle, 25

kN 376.7 5.22981.930225.0 scP

250)( kN 98.4- 5.22927cos81.930225.0 stP

Ph4 n=4

i=1

j=2

Ph3

Ph2

Ph1

mm 3558 24382591 22 il

mm 5727 243825912 22 lDET NORSKE VERITAS AS

j


Ei = 14 (3 558 - 6500) = 140 812 N/mm2 = 140.8 kN/mm2Ej = 14 (l + 6500) = 14 (5727+6500) = 171 178 N/mm2

= 171.2 kN/mm2

Calculation for doorless end walls.End wall racking stiffness (see 6.2.2): Kc = 10 kN/mmFree displacement at level i and j (see 6.3.2):



Lashing force:



mmkNKi /13.9)24382591(

24384918.140322

2

mmkNK j /66.2)243825912(24384912.171

322

2

mm 24.5 8.90.968.935.915.0101

0 i

mm 39.8 8.90.968.938.90.968.935.915.0101

0 j

)150(5.912

66.2101

13.9101

5.24266.2

108.39110

2

kNPri

)150(2.5312

66.2101

13.910

5.2418.39113.9

1010

2

kNPrj

kNPrj 6.3012258

25912.5325.9118.95.3965.28.935.15.915.0

)250(5.1332438

243825915.9122 kNPli

)250(0.125

2438243825912

2.5322

kNPlj

)300(2.97243825915.91 kNPsli

)300(1.1132438

259122.53 kNPsljDET NORSKE VERITAS AS

kNPsc 0.7401.1132.976.30181.9330325.0



Tension Side (Psl = 0)

Twistlock with SWL = 250 kN.Compressive force in lowermost container (see 6.2.11):

=> Pc = 613.9 kN (


A = 22 mm; 380 mm2E = 14 (l + 6500) = 14 (5200+6500) = 1.64105 N/mm2 = 5 + 5 + 2.5 = 12.5 mmThe force in the wind lashing due to the elongation:

Force in wind lashing:

Force in twistlock/corner post:

kNx

LAE

F 1495200

3801064.15.12 5

kNFFF TOTSTACK 151149300

)250(19915131

14931

kNkNFFF STACKWL

)250(10115132

32 kNkNFF STACKT DET NORSKE VERITAS AS

1. General1.1 Introduction1.2 Procedure1.3 Definitions1.4 Assumptions

2. Design Loads2.1 General2.2 Wind load2.3 Accelerations

3. Loading Conditions3.1 General3.2 LC1: Transverse loading I3.3 LC2: Vertical loading3.4 LC3: Transverse loading II3.5 LC4: Longitudinal loading

4. Acceptance Criteria4.1 General4.2 Containers4.3 Container securing devices4.4 Ship structure

5. Direct Calculation using Beam Analysis5.1 General5.2 Modelling of geometry5.3 Boundary conditions5.4 Loading conditions5.5 Results

6. Formula based Analysis, Basic Formulae6.1 Rigid container securing arrangements (cell guides and similar)6.2 Non-rigid securing arrangements (lashings and similar)6.3 Container stack with four flexible horizontal supports6.4 Container stack with combined rigid and flexible horizontal supports6.5 Container blocks

7. Formula based Analysis, Derived Formulae7.1 General7.2 Container stack with single rigid support7.3 Container stack with two rigid horizontal supports7.4 Container stack with three rigid horizontal supports7.5 Container stack with single flexible support7.6 Container stack with one rigid and one flexible support7.7 Container stack with two flexible horizontal supports7.8 Container stack with one rigid and two flexible horizontal supports7.9 Container stack with three flexible horizontal supports

8. Special Container Arrangements8.1 General8.2 20' container in 40' cell guides8.3 40' container in 45' cell guides8.4 Effectiveness of lashings attached to lashing bridge8.5 Vertical lashings wind lashing8.6 Block stowage in hold without cell guides8.7 Platform-based containers with reduced stiffness8.8 Containers placed on two hatches or on hatches and side pillars

Appendix A Approval of Lashing Computers/SoftwareAppendix B Calculated Examples

dnv cn 32.2 container securing

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