api-rp c204 2010-10

RECOMMENDED PRACTICE

DET NORSKE VERITAS

DNV-RP-C204

DESIGN AGAINSTACCIDENTAL LOADS

OCTOBER 2010

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Recommended Practice DNV-RP-C204, October 2010Changes –

CHANGES• General

As of October 2010 all DNV service documents are primarilypublished electronically.In order to ensure a practical transition from the “print” schemeto the “electronic” scheme, all documents having incorporatedamendments and corrections more recent than the date of thelatest printed issue, have been given the date October 2010.An overview of DNV service documents, their update statusand historical “amendments and corrections” may be foundthrough http://www.dnv.com/resources/rules_standards/.

• Main changesSince the previous edition (November 2004), this documenthas been amended, most recently in April 2005. All changeshave been incorporated and a new date (October 2010) hasbeen given as explained under “General”.

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Recommended Practice DNV-RP-C204, October 2010 – Changes

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Recommended Practice DNV-RP-C204, October 2010 Contents –

CONTENTS

1. GENERAL .............................................................. 71.1 Introduction .............................................................71.2 Application ...............................................................71.3 Objectives .................................................................71.4 Normative references ..............................................71.4.1 DNV Offshore Standards (OS)........................................... 71.4.2 DNV Recommended Practices (RP)................................... 71.5 Definitions ................................................................71.6 Symbols.....................................................................8

2. DESIGN PHILOSOPHY ....................................... 92.1 General .....................................................................92.2 Safety format............................................................92.3 Accidental loads .......................................................92.4 Acceptance criteria..................................................92.5 Analysis considerations .........................................10

3. SHIP COLLISIONS............................................. 103.1 General ...................................................................103.2 Design principles....................................................103.3 Collision mechanics ...............................................113.3.1 Strain energy dissipation................................................... 113.3.2 Reaction force to deck ...................................................... 113.4 Dissipation of strain energy ..................................113.5 Ship collision forces ...............................................113.5.1 Recommended force-deformation relationships............... 113.5.2 Force contact area for strength design of large diameter

columns............................................................................. 133.5.3 Energy dissipation is ship bow ......................................... 133.6 Force-deformation relationships for denting of

tubular members ...................................................143.7 Force-deformation relationships for beams........143.7.1 General.............................................................................. 143.7.2 Plastic force-deformation relationships including elastic,

axial flexibility.................................................................. 143.7.3 Support capacity smaller than plastic bending moment of

the beam............................................................................ 163.7.4 Bending capacity of dented tubular members .................. 163.8 Strength of connections.........................................173.9 Strength of adjacent structure .............................173.10 Ductility limits........................................................173.10.1 General.............................................................................. 173.10.2 Local buckling ................................................................. 173.10.3 Tensile fracture ................................................................. 183.10.4 Tensile fracture in yield hinges......................................... 183.11 Resistance of large diameter, stiffened columns.193.11.1 General.............................................................................. 193.11.2 Longitudinal stiffeners...................................................... 193.11.3 Ring stiffeners................................................................... 193.11.4 Decks and bulkheads ........................................................ 193.12 Energy dissipation in floating production

vessels......................................................................193.13 Global integrity during impact ............................19

4. DROPPED OBJECTS ......................................... 194.1 General ...................................................................194.2 Impact velocity.......................................................204.3 Dissipation of strain energy ..................................214.4 Resistance/energy dissipation ...............................21

4.4.1 Stiffened plates subjected to drill collar impact ............... 214.4.2 Stiffeners/girders .............................................................. 214.4.3 Dropped object ................................................................. 214.5 Limits for energy dissipation ............................... 214.5.1 Pipes on plated structures ................................................. 214.5.2 Blunt objects ..................................................................... 21

5. FIRE ...................................................................... 215.1 General ................................................................... 215.2 General calculation methods................................ 225.3 Material modelling................................................ 225.4 Equivalent imperfections...................................... 225.5 Empirical correction factor.................................. 225.6 Local cross sectional buckling.............................. 225.7 Ductility limits ....................................................... 225.7.1 General.............................................................................. 225.7.2 Beams in bending ............................................................. 235.7.3 Beams in tension............................................................... 235.8 Capacity of connections ........................................ 23

6. EXPLOSIONS...................................................... 236.1 General ................................................................... 236.2 Classification of response ..................................... 236.3 Recommended analysis models for stiffened

panels...................................................................... 236.4 SDOF system analogy ........................................... 256.5 Dynamic response charts for SDOF system ....... 266.6 MDOF analysis ...................................................... 276.7 Classification of resistance properties ................ 276.7.1 Cross-sectional behaviour................................................. 276.8 Idealisation of resistance curves .......................... 286.9 Resistance curves and transformation factors

for plates ................................................................ 286.9.1 Elastic - rigid plastic relationships.................................... 286.9.2 Axial restraint ................................................................... 296.9.3 Tensile fracture of yield hinges ........................................ 296.10 Resistance curves and transformation factors

for beams................................................................ 296.10.1 Beams with no- or full axial restraint ............................... 296.10.2 Beams with partial end restraint. ...................................... 326.10.3 Beams with partial end restraint - support capacity

smaller than plastic bending moment of member............. 346.10.4 Effective flange................................................................. 346.10.5 Strength of adjacent structure ........................................... 346.10.6 Strength of connections .................................................... 346.10.7 Ductility limits .................................................................. 34

7. REFERENCES..................................................... 35

8. COMMENTARY ................................................. 35

9. EXAMPLES ......................................................... 439.1 Design against ship collisions ............................... 439.1.1 Jacket subjected to supply vessel impact.......................... 439.2 Design against explosions ..................................... 449.2.1 Geometry .......................................................................... 449.2.2 Calculation of dynamic response of plate: ....................... 449.2.3 Calculation of dynamic response of stiffened plate.......... 449.3 Resistance curves and transformation factors .. 449.3.1 Plates................................................................................. 449.3.2 Calculation of resistance curve for stiffened plate ........... 459.3.3 Calculation of resistance curve for girder......................... 46

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Recommended Practice DNV-RP-C204, October 2010 – Contents

9.4 Ductility limits ..................................................... 469.4.1 Plating ...............................................................................469.4.2 Stiffener: ...........................................................................469.4.3 Girder: ...............................................................................479.5 Design against explosions - girder ....................... 47

9.5.1 Geometry, material and loads ...........................................479.5.2 Cross sectional of properties for the girder.......................489.5.3 Mass ..................................................................................519.5.4 Natural period ...................................................................519.5.5 Ductility ratio ....................................................................529.5.6 Maximum blast pressure capacity.....................................52

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Recommended Practice DNV-RP-C204, October 2010

1. General1.1 IntroductionThis Recommended Practice deals with design to maintain theload-bearing function of the structures during accidentalevents. The overall goal of the design against accidental loadsis to achieve a system where the main safety functions of theinstallation are not impaired.The Recommended Practice has been developed for generalworld-wide application. Governmental legislation may includerequirements in excess of the provisions of this RecommendedPractice depending on type, location and intended service ofthe unit/installation.The Design Accidental Loads and associated performance cri-teria are given in DNV-OS-A101. The Accidental Loads inthis standard are prescriptive loads. This Recommended Prac-tice may also be used in cases where the Design AccidentalLoads are determined by a formal safety assessment (seeDNV-OS-A101, Appendix C) or Quantified Risk Assessment(QRA).The following main subjects are covered:

— Design philosophy— Ship Collisions— Dropped Objects— Fire— Explosions.

1.2 ApplicationThe Recommended Practice is applicable to all types of float-ing and fixed offshore structures made of steel. The methodsdescribed are relevant for both substructures and topside struc-tures. The document is limited to load-carrying structures and doesnot cover pressurised equipment.

1.3 ObjectivesThe objective with this Recommended Practice is to providerecommendations for design of structures exposed to acciden-tal events.

1.4 Normative referencesThe following standards include requirements which, throughreference in the text constitute provisions of this Recom-mended Practice. Latest issue of the references shall be usedunless otherwise agreed. Other recognised standards may beused provided it can be demonstrated that these meet or exceedthe requirements of the standards referenced below. Any deviations, exceptions and modifications to the codes andstandards shall be documented and agreed between the sup-plier, purchaser and verifier, as applicable.

1.4.1 DNV Offshore Standards (OS)The latest revision of the following documents applies:

1.4.2 DNV Recommended Practices (RP)The latest revision of the following documents applies:

1.5 DefinitionsLoad-bearing structure: That part of the facility whose mainfunction is to transfer loads.Accidental Event: An undesired incident or condition which, incombination with other conditions (e.g.: weather conditions,failure of safety barrier, etc.), determines the accidentaleffects.Accidental Effect: The result of an accidental event, expressedin terms of heat flux, impact force and energy, acceleration,etc. which is the basis for the safety evaluations.Design Accidental Event (DAE): An accidental event, whichresults in effects that, the platform should be designed to sus-tain.Acceptance criteria: Functional requirements, which are con-cerned with the platforms' resistance to accidental effects. Thisshould be in accordance with the authority's definition ofacceptable safety levels.Active protection: Operational loads and mechanical equip-ment which are brought into operation when an accident isthreatening or after the accident has occurred, in order to limitthe probability of the accident and the effects thereof, respec-tively. Some examples are safety valves, shut down systems,water drenching systems, working procedures, drills for cop-ing with accidents, etc.Passive protection: Protection against damage by means ofdistance, location, strength and durability of structural ele-ments, insulation, etc.Event control: Implementation of measures for reducing theprobability and consequence of accidental events, such aschanges and improvements in equipment, working procedures,active protection devices, arrangement of the platform, person-nel training, etc.Indirect design: Implementation of measures for improvingstructural ductility and resistance without numerical calcula-tions and determination of specific accidental effects.Direct design: Determination of structural resistance, dimen-sions, etc. on basis of specific design accidental effects.Load: Any action causing load effect in the structure.Characteristic load: Reference value of a load to be used indetermination of load effects when using the partial coefficientmethod or the allowable stress method.Load effect: Effect of a single load or combination of loads onthe structure, such as stress, stress resultant (internal force andmoment), deformation, displacement, motion, etc.Resistance: Capability of a structure or part of a structure toresist load effect.Characteristic resistance: The nominal capacity that may beused for determination of design resistance of a structure orstructural element. The characteristic value of resistance is tobe based on a defined percentile of the test results.Design life: The time period from commencement of construc-tion until condemnation of the structure.Limit state: A state where a criterion governing the load-carry-ing ability or use of the structure is reached.

DNV-OS-A101 Safety Principles and ArrangementsDNV-OS-C101 Design of Offshore Steel Structures,

General (LRFD Method)DNV-OS-C102 Structural Design of Offshore ShipsDNV-OS-C103 Structural Design of Column Stabilised

Units (LRFD)DNV-OS-C104 Structural Design of Self-Elevating Units

(LRFD)DNV-OS-C105 Structural Design of TLPs (LRFD)DNV-OS-C106 Structural Design of Deep Draught

Floating Units (LRFD)

DNV-OS-C301 Stability and Watertight Integrity of Offshore Units

DNV-RP-C201 Buckling Strength of Plated StructuresDNV-RP-C202 Buckling Strength of Shells

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1.6 Symbols

A Cross-sectional areaAe Effective area of stiffener and effective plate flangeAs Area of stiffenerAp Projected cross-sectional areaAw Shear area of stiffener/girderB Width of contact areaCD Hydrodynamic drag coefficientD Diameter of circular sections, plate stiffnessE Young's Modulus of elasticity,

(for steel 2.1⋅105 N/mm2) Ep Plastic modulusEkin Kinetic energyEs Strain energyF Lateral load, total loadG Shear modulusH Non-dimensional plastic stiffnessI Moment of inertia, impulseJ Mass moment of inertiaKl Load transformation factorKm Mass transformation factorKlm Load-mass transformation factorL Girder lengthM Total mass, cross-sectional momentMP Plastic bending moment resistanceNP Plastic axial resistanceSd Design load effectT Fundamental period of vibrationN Axial forceNSd Design axial compressive forceNRd Design axial compressive capacityNP Axial resistance of cross sectionR ResistanceRD Design resistanceR0 Plastic collapse resistance in bending V Volume, displacementWP Plastic section modulusW Elastic section modulusa Added massas Added mass for shipai Added mass for installationb Width of collision contact zonebf Flange widthc Factorcf Axial flexibility factor

clp Plastic zone length factorcs Shear factor for vibration eigenperiodcQ Shear stiffness factorcw Displacement factor for strain calculationd Smaller diameter of threaded end of drill collardc Characteristic dimension for strain calculation

Generalised loadfu Ultimate material tensile strengthfy Characteristic yield strengthg Acceleration of gravity, 9.81 m/s2

hw Web height for stiffener/girderi Radius of gyrationk Stiffness, characteristic stiffness, plate stiffness, factor

Generalised stiffnesske Equivalent stiffnesskl Bending stiffness in linear domain for beam

Stiffness in linear domain including shear deformationkQ Shear stiffness in linear domain for beam

Temperature reduction of effective yield stress for maximum temperature in connection

Plate length, beam lengthm Distributed massms Ship massmi Installation massmeq Equivalent mass

Generalised massp Explosion pressurer Radius of deformed area, resistancerc Plastic collapse resistance in bending for platerg Radius of gyrations Distance, stiffener spacing sc Characteristic distancese Effective width of platet Thickness, timetd Duration of explosion tf Flange thicknesstw Web thicknessvs Velocity of shipvi Velocity of installationvt Terminal velocityw Deformation, displacementwc Characteristic deformationwd dent depth

Non-dimensional deformationx Axial coordinate

f

k

'1k

θy,k

l

m

w

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2. Design Philosophy2.1 GeneralThe overall goal for the design of the structure against acciden-tal loads is to prevent an incident to develop into an accidentdisproportional to the original cause. This means that the mainsafety functions should not be impaired by failure in the struc-ture due to the design accidental loads. With the main safetyfunctions is understood:

— usability of escapeways,— integrity of shelter areas,— global load bearing capacity

In this section the design procedure that is intended to fulfilthis goal is presented. The design against accidental loads may be done by direct cal-culation of the effects imposed on the structure, or indirectly,by design of the structure as tolerable to accidents. Examplesof the latter are compartmentation of floating units which pro-vides sufficient integrity to survive certain collision scenarioswithout further calculations.The inherent uncertainty of the frequency and magnitude of theaccidental loads, as well as the approximate nature of the meth-ods for determination of accidental load effects, shall be recog-nised. It is therefore essential to apply sound engineeringjudgement and pragmatic evaluations in the design.Typical accidental events are:

— Ship collision— Dropped objects— Fire— Explosion

2.2 Safety formatThe requirements to structures exposed for accidental loads aregiven in DNV-OS-C101 Section 7.The structure should be checked in two steps:

— First the structure will be checked for the loads to which itis exposed due to the accidental event

— Secondly in case the structural capacity towards ordinaryloads is reduced as a result of the accident then the strengthof the structure is to be rechecked for ordinary loads.

The structure should be checked for all relevant limit states.The limit states for accidental loads are denoted AccidentalLimit States (ALS). The requirement may be written as

where:

For check of Accidental limit states (ALS) the load and mate-rial factor should be taken as 1.0. The failure criterion needs to be seen in conjunction with theassumptions made in the safety evaluations.The limit states may need to be alternatively formulated to beon the form of energy formulation, as acceptable deformation,or as usual on force or moment.

2.3 Accidental loadsThe accidental loads are either prescriptive values or definedin a Formal Safety Assessment. Prescriptive values may begiven by authorities, the owner or found in DNV OffshoreStandard DNV-OS-A101. Usually the simplification that accidental loads need not to becombined with environmental loads is valid.For check of the residual strength in cases where the accidentlead to reduced load carrying capacity in the structure thecheck should be made with the characteristic environmentalloads determined as the most probable annual maximum value.

2.4 Acceptance criteriaExamples of failure criteria are:

— Critical deformation criteria defined by integrity of pas-sive fire protection. To be considered for walls resistingexplosion pressure and shall serve as fire barrier after theexplosion.

— Critical deflection for structures to avoid damage to proc-ess equipment (Riser, gas pipe, etc). To be considered forstructures or part of structures exposed to impact loads asship collision, dropped object etc.

— Critical deformation to avoid leakage of compartments. Tobe considered in case of impact against floating structureswhere the acceptable collision damage is defined by theminimum number of undamaged compartments to remainstable.

y Generalised displacement, displacement amplitude yel Generalised displacement at elastic limitz Distance from pivot point to collision pointzplast Smaller distance from flange to plastic neutral axisα Plate aspect parameterβ Cross-sectional slenderness factorε Yield strength factor, strainεcr Critical strain for ruptureεy Yield strainη Plate eigenperiod parameter

Displacement shape functionReduced slenderness ratio

μ Ductility ratioν Poisson's ratio, 0.3θ Angleρ Density of steel, 7860 kg/m3

ρw Density of sea water, 1025 kg/m3

τ Shear stressτcr Critical shear stress for plate pluggingξ Interpolation factorψ Plate stiffness parameter

φ

λ

(2.1)

Sd = Design load effect

Rd = Design resistance

Sk = Characteristic load effectγf = partial factor for loadsR = Characteristic resistanceγM = Material factor

dd RS ≤

fkγS

M

k

γR

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2.5 Analysis considerationsThe mechanical response to accidental loads is generally con-cerned with energy dissipation, involving large deformationsand strains far beyond the elastic range. Hence, load effects(stresses forces, moments etc.) obtained from elastic analysisand used in ultimate limit state (ULS) checks on componentlevel are generally not applicable, and plastic methods of anal-ysis should be used. Plastic analysis is most conveniently based upon the kinemat-ical approach, taking into account the effect of the strengthen-ing (membrane tension) or softening (compression) caused byfinite deformations, where applicable. The requirements in this RP are generally derived from plasticmethods of analysis, including the effect of finite deforma-tions. Plastic methods of analysis are valid for materials that canundergo considerable straining and during this process exhibitconsiderable strain hardening. If the material is ductile as such,i.e. it can be strained significantly, but has little strain harden-ing, the member tends to behave brittle in a global sense (i.e.with respect to energy dissipation), and plastic methods shouldbe used with great caution.A further condition for application of plastic methods to mem-bers undergoing large, plastic rotations is compact cross-sec-tions; typically type I cross-sections (refer DNV-OS-C101,Table A1). The methods may also be utilised for type II sec-tions provided that the detrimental effect of local buckling istaken into account. Note that for members subjected to signif-icant tensile straining, the tendency for local buckling may beoverridden by membrane tension for large deformations.The straining, and hence the amount of energy dissipation, islimited by fracture. This key parameter is associated with con-siderable uncertainty, with respect to both physical occurrenceas well as modelling in theoretical analysis. If good and vali-dated models for prediction of fracture are not available, safeand conservative assumptions for ductility limits should beadopted.If non-linear, dynamic finite elements analysis is applied, itshall be verified that all behavioural effects and local failuremodes (e.g. strain rate, local buckling, joint overloading, andjoint fracture) are accounted for implicitly by the modellingadopted, or else subjected to explicit evaluation.

3. Ship Collisions3.1 GeneralThe requirements and methods given in this section have his-torically been developed for jackets. They are generally validalso for jack-up type platforms, provided that the increasedimportance of global inertia effects are accounted for. Column-stabilised platforms and floating production and storage ves-sels (FPSOs) consist typically plane or curved, stiffened pan-els, for which methods for assessment of energy dissipation inbraced platforms (jackets and jack-ups) sometimes are not rel-evant. Procedures especially dedicated to assessment of energydissipation in stiffened plating are, however, also given basedon equivalent beam-column models.The ship collision load is characterised by a kinetic energy,governed by the mass of the ship, including hydrodynamicadded mass and the speed of the ship at the instant of impact.Depending upon the impact conditions, a part of the kineticenergy may remain as kinetic energy after the impact. Theremainder of the kinetic energy has to be dissipated as strainenergy in the installation and, possibly, in the vessel. Generallythis involves large plastic strains and significant structuraldamage to the installation, the ship or both. The strain energydissipation is estimated from force-deformation relationships

for the installation and the ship, where the deformations in theinstallation shall comply with ductility and stability require-ments.The load bearing function of the installation shall remain intactwith the damages imposed by the ship collision load. In addi-tion, damaged condition should be checked if relevant, seeSection 2.2.The structural effects from ship collision may either be deter-mined by non-linear dynamic finite element analyses or byenergy considerations combined with simple elastic-plasticmethods.If non-linear dynamic finite element analysis is applied alleffects described in the following paragraphs shall either beimplicitly covered by the modelling adopted or subjected tospecial considerations, whenever relevant. Often the integrity of the installation can be verified by meansof simple calculation models.If simple calculation models are used the part of the collisionenergy that needs to be dissipated as strain energy can be cal-culated by means of the principles of conservation of momen-tum and conservation of energy, refer Section 3.3.It is convenient to consider the strain energy dissipation in theinstallation to take part on three different levels:

— local cross-section— component/sub-structure— total system

Interaction between the three levels of energy dissipation shallbe considered.Plastic modes of energy dissipation shall be considered forcross-sections and component/substructures in direct contactwith the ship. Elastic strain energy can in most cases be disre-garded, but elastic axial flexibility may have a substantialeffect on the load-deformation relationships for components/sub-structures. Elastic energy may contribute significantly ona global level.

3.2 Design principlesWith respect to the distribution of strain energy dissipationthere may be distinguished between, see Figure 3-1:

— strength design— ductility design— shared-energy design

Figure 3-1Energy dissipation for strength, ductile and shared-energy design

Strength design implies that the installation is strong enough toresist the collision force with minor deformation, so that theship is forced to deform and dissipate the major part of theenergy.Ductility design implies that the installation undergoes large,plastic deformations and dissipates the major part of the colli-sion energy.

Strength design

Shared-energy design

Ductile design

Relative strength - installation/ship

ship

installation

Ene

rgy

diss

ipat

ion

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Shared energy design implies that both the installation andship contribute significantly to the energy dissipation.From calculation point of view strength design or ductilitydesign is favourable. In this case the response of the «soft»structure can be calculated on the basis of simple considera-tions of the geometry of the «rigid» structure. In shared energydesign both the magnitude and distribution of the collisionforce depends upon the deformation of both structures. Thisinteraction makes the analysis more complex.In most cases ductility or shared energy design is used. How-ever, strength design may in some cases be achievable with lit-tle increase in steel weight.

3.3 Collision mechanics

3.3.1 Strain energy dissipationThe collision energy to be dissipated as strain energy may -depending on the type of installation and the purpose of theanalysis - be taken as:Compliant installations

Fixed installations

Articulated columns

ms = ship massas = ship added massvs = impact speedmi = mass of installationai = added mass of installationvi = velocity of installationJ = mass moment of inertia of installation (including

added mass) with respect to effective pivot pointz = distance from pivot point to point of contact

In most cases the velocity of the installation can be disre-garded, i.e. vi = 0. The installation can be assumed compliant if the duration ofimpact is small compared to the fundamental period of vibra-tion of the installation. If the duration of impact is compara-tively long, the installation can be assumed fixed. Floating platforms (semi-submersibles, TLP’s, productionvessels) can normally be considered as compliant. Jack-upsmay be classified as fixed or compliant. Jacket structures cannormally be considered as fixed.

3.3.2 Reaction force to deckIn the acceleration phase the inertia of the topside structuregenerates large reaction forces. An upper bound of the maxi-mum force between the collision zone and the deck for bottomsupported installations may be obtained by considering theplatform compliant for the assessment of total strain energydissipation and assume the platform fixed at deck level whenthe collision response is evaluated.

Figure 3-2Model for assessment of reaction force to deck

3.4 Dissipation of strain energyThe structural response of the ship and installation can for-mally be represented as load-deformation relationships asillustrated in Figure 3-3. The strain energy dissipated by theship and installation equals the total area under the load-defor-mation curves.

Figure 3-3Dissipation of strain energy in ship and platform

As the load level is not known a priori an incremental proce-dure is generally needed. The load-deformation relationships for the ship and the instal-lation are often established independently of each other assum-ing the other object infinitely rigid. This method may have,however, severe limitations; both structures will dissipatesome energy regardless of the relative strength.Often the stronger of the ship and platform will experience lessdamage and the softer more damage than what is predictedwith the approach described above. As the softer structuredeforms the impact force is distributed over a larger contactarea. Accordingly, the resistance of the strong structureincreases. This may be interpreted as an "upward" shift of theresistance curve for the stronger structure (refer Figure 3-3 ).Care should be exercised that the load-deformation curves cal-culated are representative for the true, interactive nature of thecontact between the two structures.

3.5 Ship collision forces

3.5.1 Recommended force-deformation relationshipsForce-deformation relationships for supply vessels with a dis-placement of 5000 tons are given in Figure 3-4 for broad side-, bow-, stern end and stern corner impact for a vessel withstern roller.The curves for broad side and stern end impacts are based upon

(3.1)

(3.2)

(3.3)

ii

ss

2

s

i

2ssss

amam1

vv1

)va(m21E

++

+

⎟⎟⎠

⎞⎜⎜⎝

⎛−

+=

2ssss )va(m

21E +=

Jzm

1

vv

1)a(m

21E 2

s

2

s

i

sss

+

⎟⎟⎠

⎞⎜⎜⎝

⎛−

+=

(3.4)

Collision response Model

dws dwi

RiRs

Ship Installation

Es,sEs,i

∫∫ +=+= maxi,maxs, w

0 ii

w

0 ssis,ss,s dwRdwREEE

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penetration of an infinitely rigid, vertical cylinder with a givendiameter and may be used for impacts against jacket legs (D =1.5 m) and large diameter columns (D = 10 m).The curve for stern corner impact is based upon penetration ofan infinitely rigid cylinder and may be used for large diametercolumn impacts.In lieu of more accurate calculations the curves in Figure 3-4may be used for square-rounded columns.The curve for bow impact is based upon collision with an infi-nitely rigid, plane wall and may be used for large diameter col-umn impacts, but should not be used for significantly different

collision events, e.g. impact against tubular braces. For beam -, stern end – and stern corner impacts against jacketbraces all energy shall normally be assumed dissipated by thebrace, refer Ch.8, Comm. 3.5.2.For bow impacts against jacket braces, reference is made toSection 3.5.3. For supply vessels and merchant vessels in the range of 2-5000 tons displacement, the force deformation relationshipsgiven in Figure 3-5 may be used for impacts against jacket legswith diameter 1.5 m – 2.5 m.

Figure 3-4Recommended-deformation curve for beam, bow and stern impact

Figure 3-5Force -deformation relationship for bow with and without bulb (2-5.000 dwt)

0

10

20

30

40

50

0 1 2 3 4Indentation (m)

Impa

ct fo

rce

(MN

)

Broad sideD = 10 m = 1.5 m

Stern end D = 10 m = 1.5 m

Bo

Stern corner

D

D

Bow0

10

20

30

40

50

0 1 2 3 4Indentation (m)

Impa

ct fo

rce

(MN

)

Broad sideD = 10 m = 1.5 m

Stern end D = 10 m = 1.5 m

Bo

Stern corner

D

D

Bow

0

20

40

60

80

0 1 2 3 4 5

Deformation [m]

Ener

gy [M

J]

0

10

20

30

Forc

e [M

N]

Contact force

Energy

no bulb

with bulb

curve - plane wall

0

20

40

60

80 40

Energy

Design -

0

20

40

60

80

0 1 2 3 4 5

Deformation [m]

Ener

gy [M

J]

0

10

20

30

Forc

e [M

N]

Contact force

Energy

no bulb

with bulb

curve - plane wall

0

20

40

60

80 40

Energy

Design -

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Figure 3-6Force -deformation relationship for tanker bow impact (~ 125.000 dwt)

Figure 3-7Force -deformation relationship and contact area for the bulbousbow of a VLCC (~ 340.000 dwt)

Force-deformation relationships for tanker bow impact aregiven in Figure 3-6 for the bulbous part and the superstructure,respectively, and for the bulb of a VLCC in Figure 3-7. Thecurves may be used provided that the impacted structure (e.g.stern of floating production vessels) does not undergo substan-tial deformation i.e. strength design requirements are compliedwith. If this condition is not met interaction between the bowand the impacted structure shall be taken into consideration.Non-linear finite element methods or simplified plastic analy-sis techniques of members subjected to axial crushing shall beemployed, see Ch.7 /3/, /4/.

3.5.2 Force contact area for strength design of large diam-eter columns.The basis for the curves in Figure 3-4 is strength design, i.e.limited local deformations of the installation at the point ofcontact. In addition to resisting the total collision force, largediameter columns have to resist local concentrations (subsets)of the collision force, given for stern corner impact in Table 3-1 and stern end impact in Table 3-2.

If strength design is not aimed for - and in lieu of more accurateassessment (e.g. nonlinear finite element analysis) - all strainenergy has to be assumed dissipated by the column, corre-sponding to indentation by an infinitely rigid stern corner.

3.5.3 Energy dissipation is ship bowFor typical supply vessels bows and bows of merchant vesselsof similar size (i.e. 2-5000 tons displacement), energy dissipa-tion in ship bow may be taken into account provided that thecollapse resistance in bending for the brace, R0, see Section 3.7is according to the values given in Table 3-3. The figures arevalid for normal bows without ice strengthening and for bracediameters < 1.25 m. The values should be used as step func-tions, i.e. interpolation for intermediate resistance levels is notallowed. If contact location is not governed by operation con-ditions, size of ship and platform etc., the values for arbitrarycontact location shall be used. (see also Ch.8, Comm. 3.5.3).

In addition, the brace cross-section must satisfy the following

0

10

20

30

40

50

60

70

0 1 2 3 4 5 6

Deformation [m]

Forc

e [M

N]

0

2

4

6

8

10

12

Con

tact

dim

ensi

on [m

]Bulb force

a

b

a

b

0

10

20

30

40

50

60

70

0 1 2 3 4 5

Deformation [m]

Forc

e [M

N]

0

2

4

6

8

10

12

14

16

18

Con

tact

dim

ensi

on [m

]

Force superstructure

a

b

a

b

020406080

100120140160

0 1 2 3 4 5 6 7 8Deformation [m]

Forc

e [M

N]

0100200300400500600700800

Ener

gy [M

J]

ForceEnergy

0

2

4

6

8

10

12

0 1 2 3 4 5 6 7 8Deformation [m]

Cont

act d

imen

sion

s [m

]

ab

a

b

Table 3-1 Local concentrated collision force -evenly distributed over a rectangular area. Stern corner impact

Contact area Force (MN)a (m) b (m)0.35 0.65 3.00.35 1.65 6.40.20 1.15 5.4

Table 3-2 Local concentrated collision force -evenly distributed over a rectangular area. Stern end impact

Contact area Force (MN)a (m) b (m)0.6 0.3 5.60.9 0.5 7.52.0 1.1 10

Table 3-3 Energy dissipation in bow versus brace resistance

Contact locationEnergy dissipation in bow

if brace resistance R0 > 3 MN > 6 MN > 8 MN > 10 MN

Above bulb 1 MJ 4 MJ 7 MJ 11 MJFirst deck 0 MJ 2 MJ 4 MJ 17 MJFirst deck - oblique brace 0 MJ 2 MJ 4 MJ 17 MJBetween forcastle/first deck

1 MJ 5 MJ 10 MJ 15 MJ

Arbitrary location 0 MJ 2 MJ 4 MJ 11 MJ

a

b

b

a

DET NORSKE VERITAS


compactness requirement

where factor is the required resistance in [MN] given in Table3-3.See Section 3.6 for notation.If the brace is designed to comply with these provisions, spe-cial care should be exercised that the joints and adjacent struc-ture is strong enough to support the reactions from the brace.

3.6 Force-deformation relationships for denting of tubular membersThe contribution from local denting to energy dissipation issmall for brace members in typical jackets and should beneglected.The resistance to indentation of unstiffened tubes may be takenfrom Figure 3-8. Alternatively, the resistance may be calcu-lated from Equation (3.6):

Figure 3-8Resistance curve for local denting

NSd = design axial compressive forceNRd = design axial compressive resistanceB = width of contactareawd = dent depth

The curves are inaccurate for small indentation, and theyshould not be used to verify a design where the dent damage isrequired to be less than wd / D > 0.05.The width of contact area is in theory equal to the height of thevertical, plane section of the ship side that is assumed to be incontact with the tubular member. For large widths, anddepending on the relative rigidity of the cross-section and theship side, it may be unrealistic to assume that the tube is sub-jected to flattening over the entire contact area. In lieu of moreaccurate calculations it is proposed that the width of contactarea be taken equal to the diameter of the hit cross-section (i.e.B/D = 1).

3.7 Force-deformation relationships for beams

3.7.1 GeneralThe response of a beam subjected to a collision load is initiallygoverned by bending, which is affected by and interacts withlocal denting under the load. The bending capacity is alsoreduced if local buckling takes place on the compression side.As the beam undergoes finite deformations, the load carryingcapacity may increase considerably due to the development ofmembrane tension forces. This depends upon the ability ofadjacent structure to restrain the connections at the memberends to inward displacements. Provided that the connectionsdo not fail, the energy dissipation capacity is either limited bytension failure of the member or rupture of the connection.Simple plastic methods of analysis are generally applicable.Special considerations shall be given to the effect of:

— elastic flexibility of member/adjacent structure,— local deformation of cross-section,— local buckling,— strength of connections,— strength of adjacent structure, and— fracture.

3.7.2 Plastic force-deformation relationships including elastic, axial flexibilityRelatively small axial displacements have a significant influ-ence on the development of tensile forces in members under-going large lateral deformations. An equivalent elastic, axialstiffness may be defined as

knode = axial stiffness of the node with the considered mem-ber removed. This may be determined by introduc-ing unit loads in member axis direction at the endnodes with the member removed.

Plastic force-deformation relationship for a central collision(midway between nodes) may be obtained from:

— Figure 3-9 for tubular members — Figure 3-10 for stiffened plates in lieu of more accurate

analysis.

The following notation applies:

(3.5)

(3.6)

factor32Dtf 0.51.5

y ⋅≥

0

2

4

6

8

10

12

14

16

18

20

0 0.1 0.2 0.3 0.4 0.5

wd/D

R/(k

Rc)

2 1 0.5 0

b/D =

Rd

Sd

Rd

Sd

Rd

Sd

Rd

Sd

2

1

2

yc

cd

1c

NN

0.60k

0.6NN

0.20.2NN

21.0k

0.2NN

1.0k

DB3.5

1.925c

DB1.222c

tD

4tfR

Dw

kcRR 2

≤=

<<⎟⎟⎠

⎞⎜⎜⎝

⎛−−=

≤=

+=

+=

=

⎟⎟⎠

⎞⎜⎜⎝

⎛= (3.7)

plastic collapse resistance in bending for the member, for the case that contact point is at midspan

non-dimensional deformation

non-dimensional spring stiffness

c1 = 2 for clamped beams

2EAk1

k1

node

l+=

lP1Mc4R 0 =

cwcww

1

=

lAfkw4c

cy

2c1=

DET NORSKE VERITAS


For non-central collisions the force-deformation relationshipmay be taken as the mean value of the force-deformationcurves for central collision with member half length equal tothe smaller and the larger portion of the member length,respectively.For members where the plastic moment capacity of adjacentmembers is smaller than the moment capacity of the impactedmember the force-deformation relationship may be interpo-lated from the curves for pinned ends and clamped ends:For non-central collisions the force-deformation relationshipmay be taken as the mean value of the force-deformationcurves for central collision with member half length equal tothe smaller and the larger portion of the member length,respectively.For members where the plastic moment capacity of adjacentmembers is smaller than the moment capacity of the impacted

member the force-deformation relationship may be interpo-lated from the curves for pinned ends and clamped ends:

where

i = adjacent member no ij = end number {1,2}MPj,i = Plastic bending resistance for member number i at

end j.Elastic, rotational flexibility of the node is normally of moder-ate significance.

Figure 3-9Force-deformation relationship for tubular beam with axial flexibility

c1 = 1 for pinned beams

characteristic deformation for tubular beams

characteristic deformation for stiffened plating

WP = plastic section modulus= member length

2Dw c =

AW2.1

w Pc =

l

(3.8)

(3.9)

= Plastic resistance by bending action of beam account-ing for actual bending resistance of adjacent members

(3.10)

(3.11)

pinnedclamped Rζ)(1RR −+= ζ

11M4

Rξ0P

actual0 ≤−=≤

l

actual0R

lP2P1Pactual

02M2M4M

R++

=

∑ ≤=i

PiPj,Pj MMM

Bending & membraneMembrane only

k k

F (collision load)

w

0

0,5

1

1,5

2

2,5

3

3,5

4

4,5

5

5,5

6

6,5

0 0,5 1 1,5 2 2,5 3 3,5 4

Deformation

R/R

0

1

0.1

0.2

0,3

0.5

0.05c=∞

w


k k

F (collision load)

w


k k

F (collision load)

w

0

0,5

1

1,5

2

2,5

3

3,5

4

4,5

5

5,5

6

6,5

0 0,5 1 1,5 2 2,5 3 3,5 4

Deformation

R/R

0

1

0.1

0.2

0,3

0.5

0.05c=∞

w

0

0,5

1

1,5

2

2,5

3

3,5

4

4,5

5

5,5

6

6,5

0 0,5 1 1,5 2 2,5 3 3,5 4

Deformation

R/R

0

1

0.1

0.2

0,3

0.5

0.05c=∞

w

DET NORSKE VERITAS


Figure 3-10Force-deformation relationship for stiffened plate with axial flexibility

3.7.3 Support capacity smaller than plastic bending moment of the beamFor beams where the plastic moment capacity of adjacentmembers is smaller than the moment capacity of the impactedbeam, the force-deformation relationship, R*, may be derivedfrom the resistance curve, R, for beams where the plasticmoment capacity of adjacent members is larger than themoment capacity of the impacted beam (Section 3.7.2), usingthe expression:

where

R0 = Plastic bending resistance with clamped ends (c1 = 2)– moment capacity of adjacent members larger thanthe plastic bending moment of the beam

= Plastic bending resistance - moment capacity of adja-cent members at one or both ends smaller than the plas-tic bending moment of the beam

i = adjacent member no ij = end number {1,2}MPj,i= Plastic bending resistance for member no. iwlim = limiting non-dimensional deformation where the

membrane force attains yield, i.e. the resistance curve,R, with actual spring stiffness coefficient, c, intersects

with the curve for c = ∞. If c = ∞, fortubular beams and for stiffened plate

3.7.4 Bending capacity of dented tubular membersThe reduction in plastic moment capacity due to local dentingshall be considered for members in compression or moderatetension, but can be neglected for members entering the fullyplastic membrane state.Conservatively, the flat part of the dented section according tothe model shown in Figure 3-11 may be assumed non-effec-tive. This gives:

wd = dent depth as defined in Figure 3-11.

0

0,5

1

1,5

2

2,5

3

3,5

4

4,5

5

0 0,5 1 1,5 2 2,5 3 3,5 4

Deformation

R/R

0

1

0

0.1

0.20.5

w


k k

F (collision load)

w∞=c

0

0,5

1

1,5

2

2,5

3

3,5

4

4,5

5

0 0,5 1 1,5 2 2,5 3 3,5 4

Deformation

R/R

0

0

0,5

1

1,5

2

2,5

3

3,5

4

4,5

5

0 0,5 1 1,5 2 2,5 3 3,5 4

Deformation

R/R

0

1

0

0.1

0.20.5

ww


k k

F (collision load)

w∞=c


k k

F (collision load)

w


k k

F (collision load)

ww∞=c ∞=c ∞=c

,

(3.12)

(3.13)

(3.14)

lim

*00

* )R(RRRw

w−+= 0.1

lim

≤w

w

RR * = 0.1lim

≥w

w

*0R

lP2P1P*

02M2M4M

R++

=

∑ ≤=i

PiPj,Pj MMM

(3.15)

lim 2w wπ

=

lim 1.2w w=

⎟⎠⎞

⎜⎝⎛ −=

=

−=

D2w1arccosθ

tDfM

sinθ21

2θcos

MM

d

2yP

P

red

DET NORSKE VERITAS


Figure 3-11Reduction of moment capacity due to local dent

3.8 Strength of connectionsProvided that large plastic strains can develop in the impactedmember, the strength of the connections that the memberframes into should be checked.The resistance of connections should be taken from ULSrequirements in relevant standards. For braces reaching the fully plastic tension state, the connec-tion shall be checked for a load equal to the axial capacity ofthe member. The design axial stress shall be assumed equal tothe ultimate tensile strength of the material.If the axial force in a tension member becomes equal to theaxial capacity of the connection, the connection has to undergogross deformations. The energy dissipation will be limited andrupture should be considered at a given deformation. A safeapproach is to assume failure (disconnection of the member)once the axial force in the member reaches the axial capacityof the connection.If the capacity of the connection is exceeded in compressionand bending, this does not necessarily mean failure of themember. The post-collapse strength of the connection may betaken into account provided that such information is available.

3.9 Strength of adjacent structureThe strength of structural members adjacent to the impactedmember/sub-structure must be checked to see whether theycan provide the support required by the assumed collapsemechanism. If the adjacent structure fails, the collapse mecha-nism must be modified accordingly. Since, the physical behav-iour becomes more complex with mechanisms consisting of anincreasing number of members it is recommended to considera design which involves as few members as possible for eachcollision scenario.

3.10 Ductility limits

3.10.1 GeneralThe maximum energy that the impacted member can dissipatewill – ultimately - be limited by local buckling on the compres-sive side or fracture on the tensile side of cross-sections under-going finite rotation. If the member is restrained against inward axial displacement,any local buckling must take place before the tensile strain dueto membrane elongation overrides the effect of rotationinduced compressive strain.If local buckling does not take place, fracture is assumed to

occur when the tensile strain due to the combined effect ofrotation and membrane elongation exceeds a critical value.To ensure that members with small axial restraint maintainmoment capacity during significant plastic rotation it is recom-mended that cross-sections be proportioned to section type Irequirements, defined in DNV-OS-C101.Initiation of local buckling does, however, not necessarilyimply that the capacity with respect to energy dissipation isexhausted, particularly for type I and type II cross-sections.The degradation of the cross-sectional resistance in the post-buckling range may be taken into account provided that suchinformation is available, refer Ch.8, Comm. 3.10.1.For members undergoing membrane stretching a lower boundto the post-buckling load-carrying capacity may be obtainedby using the load-deformation curve for pure membraneaction.

3.10.2 Local buckling Tubular cross-sections: Buckling does not need to be considered for a beam with axialrestraints if the following condition is fulfilled:

where

axial flexibility factor

dc = characteristic dimension = D for circular cross-sectionsc1 = 2 for clamped ends = 1 for pinned endsc = non-dimensional spring stiffness, refer Section 3.7.2.

κ ≤ 0.5 = the smaller distance from location of collisionload to adjacent jointIf this condition is not met, buckling may be assumed to occurwhen the lateral deformation exceeds

For small axial restraint (c < 0.05) the critical deformation maybe taken as

Stiffened plates/ I/H-profiles:In lieu of more accurate calculations the expressions given forcircular profiles in Equation (3.19) and (3.20) may be usedwith

0

0,2

0,4

0,6

0,8

1

0 0,2 0,4 0,6 0,8 1

wd/D

Mre

d/MP

Dwd

(3.16)

(3.17)

(3.18)

(3.19)

(3.20)

dc = characteristic dimension for local buckling, equal to twice the distance from the plastic neutral axis in bending to the extreme fibre of the cross-section

= h height of cross-section for symmetric I –profiles= 2hw for stiffened plating (for simplicity)

31

2

c1

yf

dκ

cf14c

β ⎟⎟

⎠

⎞

⎜⎜

⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛≤

l

yf235tD

β =

2

fc1

cc ⎟⎟⎠

⎞⎜⎜⎝

⎛

+=

l l

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

⎟⎟⎠

⎞⎜⎜⎝

⎛−−=

2

c3

1

yf

fc dκ

βc

f14c11

2c1

dw l

2

c3

1

y

c dκ

βc

3.5fdw

⎟⎟⎠

⎞⎜⎜⎝

⎛=

l

DET NORSKE VERITAS


For flanges subjected to compression;

For webs subjected to bending

bf = flange widthtf = flange thicknesshw = web heighttw = web thickness

3.10.3 Tensile fractureThe degree of plastic deformation or critical strain at fracturewill show a significant scatter and depends upon the followingfactors:

— material toughness— presence of defects— strain rate— presence of strain concentrations

The critical strain for plastic deformations of sections contain-ing defects need to be determined based on fracture mechanicsmethods. Welds normally contain defects and welded jointsare likely to achieve lower toughness than the parent material.For these reasons structures that need to undergo large plasticdeformations should be designed in such a way that the plasticstraining takes place outside the weld. In ordinary full penetra-tion welds, the overmatching weld material will ensure thatminimal plastic straining occurs in the welded joints even incases with yielding of the gross cross section of the member.In such situations, the critical strain will be in the parent mate-rial and will be dependent upon the following parameters:

— stress gradients— dimensions of the cross section— presence of strain concentrations— material yield to tensile strength ratio— material ductility

Simple plastic theory does not provide information on strainsas such. Therefore, strain levels should be assessed by meansof adequate analytic models of the strain distributions in theplastic zones or by non-linear finite element analysis with asufficiently detailed mesh in the plastic zones. (For informa-tion about mesh size see Ch.8, Comm. 3.10.4.)When structures are designed so that yielding take place in theparent material, the following value for the critical averagestrain in axially loaded plate material may be used in conjunc-tion with nonlinear finite element analysis or simple plasticanalysis

where:

3.10.4 Tensile fracture in yield hingesWhen the force deformation relationships for beams given inSection 3.7.2 are used rupture may be assumed to occur whenthe deformation exceeds a value given by

where the following factors are defined;Displacement factor

plastic zone length factor

axial flexibility factor

non-dimensional plastic stiffness

The characteristic dimension shall be taken as:

For small axial restraint (c < 0.05) the critical deformation may

type I cross-sections (3.21)

type II and type III cross-sections (3.22)

type I cross-sections (3.23)

type I and type III cross-sections (3.24)

(3.25)

t = plate thickness= length of plastic zone. Minimum 5t

y

ff

f235tb

2.5β =

y

ff

f235tb

3β =

y

ww

f235th

0.7β =

y

ww

f235th

0.8β =

l

t65.00.02 +=crε

l

(3.26)

(3.27)

(3.28)

(3.29)

(3.30)

c1 = 2 for clamped ends= 1 for pinned ends

c = non-dimensional spring stiffness, refer Sec-tion 3.7.2

κ ≤ 0.5 the smaller distance from location of collision load to adjacent joint

W = elastic section modulusWP = plastic section modulusεcr = critical strain for rupture (see Table 3-4 for

recommended values)

= yield strain

fy = yield strengthfcr = strength corresponding to εcr

dc = D diameter of tubular beams= 2hw twice the web height for stiffened

plates (se·t > As)= h height of cross-section for symmet-

ric I-profiles= 2 (h − zplast) for unsymmetrical I-profiles

zplast = smaller distance from flange to plastic neutral axis of cross-section

⎟⎟⎠

⎞⎜⎜⎝

⎛−+= 1

cεc4c

12cc

dw

1

crfw

f

1

c

2

ccr

y

Plplp

1w d

κεε

WW14c

311c

c1c ⎟⎟

⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛−+⎟

⎠⎞

⎜⎝⎛ −=

l

1HWW1

εε

HWW1

εε

c

Py

cr

Py

cr

lp

+⎟⎟⎠

⎞⎜⎜⎝

⎛−

⎟⎟⎠

⎞⎜⎜⎝

⎛−

=

2

fc1

cc ⎟⎟⎠

⎞⎜⎜⎝

⎛

+=

⎟⎟⎠

⎞⎜⎜⎝

⎛

−

−==

ycr

ycrp

εεff

E1

EE

H

l l

Ef

ε yy =

DET NORSKE VERITAS


be taken as

The critical strain εcr and corresponding strength fcr should beselected so that idealised bi-linear stress-strain relation givesreasonable results, see Ch.8, Commentary. For typical steelmaterial grades the following values are proposed:

3.11 Resistance of large diameter, stiffened columns

3.11.1 GeneralImpact on a ring stiffener as well as midway between ring stiff-eners shall be considered. Plastic methods of analysis are generally applicable.

3.11.2 Longitudinal stiffenersFor ductile design the resistance of longitudinal stiffeners inthe beam mode of deformation can be calculated using the pro-cedure described for stiffened plating, Section 3.7. For strength design against stern corner impact, the plasticbending moment capacity of the longitudinal stiffeners has tocomply with the requirement given in Figure 3-12, on theassumption that the entire load given in Table 3-1 is taken byone stiffener.

Figure 3-12Required bending capacity of longitudinal stiffeners

3.11.3 Ring stiffenersIn lieu of more accurate analysis the plastic collapse load of aring-stiffener can be estimated from:

where

=characteristic deformation of ring stiffener

D = column radius MP = plastic bending resistance of ring-stiffener including

effective shell flangeWP = plastic section modulus of ring stiffener including

effective shell flangeAe = area of ring stiffener including effective shell flange

Effective flange of shell plating: Use effective flange of stiff-ened plates, see Chapter 6.For ductile design it can be assumed that the resistance of thering stiffener is constant and equal to the plastic collapse load,provided that requirements for stability of cross-sections arecomplied with, refer Section 3.10.2.

3.11.4 Decks and bulkheadsCalculation of energy dissipation in decks and bulkheads hasto be based upon recognised methods for plastic analysis ofdeep, axial crushing. It shall be documented that the collapsemechanisms assumed yield a realistic representation of the truedeformation field.

3.12 Energy dissipation in floating production ves-selsFor strength design the side or stern shall resist crushing forceof the bow of the off-take tanker. In lieu of more accurate cal-culations the force-deformation curve given in Section 3.5.2may be applied. (See Ch.8, Comm. 3.12 on strength design ofstern structure)For ductile design the resistance of stiffened plating in thebeam mode of deformation can be calculated using the proce-dure described in Section 3.7.2. (See Ch.8, Comm. 3.12 onresistance of stiffened plating)

3.13 Global integrity during impactNormally, it is unlikely that the installation will turn into a glo-bal collapse mechanism under direct collision load, becausethe collision load is typically an order of magnitude smallerthan the resultant design wave force.Linear analysis often suffices to check that global integrity ismaintained. The installation should be checked for the maximum collisionforce.For installations responding predominantly statically the max-imum collision force occurs at maximum deformation.For structures responding predominantly impulsively the max-imum collision force occurs at small global deformation of theplatform. An upper bound to the collision force is to assumethat the installation is fixed with respect to global displace-ment. (e.g. jack-up fixed with respect to deck displacement).

4. Dropped Objects4.1 GeneralThe dropped object load is characterised by a kinetic energy,governed by the mass of the object, including any hydrody-namic added mass, and the velocity of the object at the instan-tof impact. In most cases the major part of the kinetic energyhas to be dissipated as strain energy in the impacted componentand, possibly, in the dropped object. Generally, this involveslarge plastic strains and significant structural damage to theimpacted component. The strain energy dissipation is esti-mated from force-deformation relationships for the componentand the object, where the deformations in the component shallcomply with ductility and stability requirements.The load bearing function of the installation shall remain intactwith the damages imposed by the dropped object load. In addi-tion, damaged condition should be checked if relevant, seeSection 2.2.Dropped objects are rarely critical to the global integrity of the

(3.31)

Table 3-4 Proposed values for εcr and H for different steel grades

Steel grade εcr HS 235 20 % 0.0022S 355 15 % 0.0034S 460 10 % 0.0034

(3.32)

crwc

εcdw

=

0

1

2

3

1 2 3 4

Distance between ring stiffeners (m)

Plas

tic b

endi

ng c

apac

ity(M

Nm

)

0

1

2

3

1 2 3 4

Distance between ring stiffeners (m)

Plas

tic b

endi

ng c

apac

ity(M

Nm

)

Dw

MF

c

P240 =

e

Pc A

Ww =

DET NORSKE VERITAS


installation and will mostly cause local damages. The majorthreat to global integrity is probably puncturing of buoyancytanks, which could impair the hydrostatic stability of floatinginstallations. Puncturing of a single tank is normally coveredby the general requirements to compartmentation and water-tight integrity given in DNV-OS-C301.The structural effects from dropped objects may either bedetermined by non-linear dynamic finite element analyses orby energy considerations combined with simple elastic-plasticmethods as given in Sections 4.2 - 4.5.If non-linear dynamic finite element analysis is applied alleffects described in the following paragraphs shall either beimplicitly covered by the modelling adopted or subjected tospecial considerations, whenever relevant.

4.2 Impact velocityThe kinetic energy of a falling object is given by:

and

a = hydrodynamic added mass for considered motion

For impacts in air the velocity is given by

s = travelled distance from drop pointv = vo at sea surface

For objects falling rectilinearly in water the velocity dependsupon the reduction of speed during impact with water and thefalling distance relative to the characteristic distance for theobject.

Figure 4-1Velocity profile for objects falling in water

The loss of momentum during impact with water is given by

F(t) = force during impact with sea surface

After the impact with water the object proceeds with the speed

Assuming that the hydrodynamic resistance during fall inwater is of drag type the velocity in water can be taken fromFigure 4-1 where

ρw = density of sea waterCd = hydrodynamic drag coefficient for the object in the

considered motionm = mass of objectAp = projected cross-sectional area of the objectV = object displacement

The major uncertainty is associated with calculating the loss ofmomentum during impact with sea surface, given by Equation(4.4). However, if the travelled distance is such that the veloc-ity is close to the terminal velocity, the impact with sea surfaceis of little significance. Typical terminal velocities for some typical objects are given

(in air) (4.1)2

kin mv21E =

(in water) (4.2)

(4.3)

( ) 2kin vam

21E +=

2gsv =

s

-3

-2

-1

0

1

2

3

4

5

6

7

0 0,5 1 1,5 2 2,5 3 3,5 4

Velocity [v/vt]

In water

In air

Dis

tanc

e [s

/sc]

ss

-3

-2

-1

0

1

2

3

4

5

6

7

0 0,5 1 1,5 2 2,5 3 3,5 4

Velocity [v/vt]

In water

In air

Dis

tanc

e [s

/sc]

-3

-2

-1

0

1

2

3

4

5

6

7

0 0,5 1 1,5 2 2,5 3 3,5 4

Velocity [v/vt]

In water

In air

Dis

tanc

e [s

/sc]

(4.4)

=terminal velocity for the object (drag force and buoyancy force balance the gravity force)

∫=Δ dt

0F(t)dtvm

Δvvv 0 −=

pdw

wt ACρ

V)ρ2g(mv

−=

= characteristic distance)

mVρ2g(1

)ma(1v

ACρams

w

2t

pdw −

+=

+=c

DET NORSKE VERITAS


in Table 4-1.

Rectilinear motion is likely for blunt objects and objects whichdo not rotate about their longitudinal axis. Bar-like objects(e.g. pipes) which do not rotate about their longitudinal axismay execute lateral, damped oscillatory motions as illustratedin Figure 4-1.

4.3 Dissipation of strain energyThe structural response of the dropped object and the impactedcomponent can formally be represented as load-deformationrelationships as illustrated in Figure 4-2. The part of the impactenergy dissipated as strain energy equals the total area underthe load-deformation curves.

As the load level is not known a priori an incremental approachis generally required. Often the object can be assumed to be infinitely rigid (e.g. axialimpact from pipes and massive objects) so that all energy is tobe dissipated by the impacted component.

Figure 4-2Dissipation of strain energy in dropped object and installation

If the object is assumed to be deformable, the interactive natureof the deformation of the two structures should be recognised.

4.4 Resistance/energy dissipation

4.4.1 Stiffened plates subjected to drill collar impactThe energy dissipated in the plating subjected to drill collarimpact is given by

where:

fy = characteristic yield strength

R = πdtτ = contact force for τ ≤τ cr refer Section 4.5.1 for τ cr

For validity range of design formula reference is given to Ch.8,Comm. 4.4.1.

Figure 4-3Definition of distance to plate boundary

4.4.2 Stiffeners/girdersIn lieu of more accurate calculations stiffeners and girders sub-jected to impact with blunt objects may be analysed withresistance models given in Section 6.10.

4.4.3 Dropped objectCalculation of energy dissipation in deformable droppedobjects shall be based upon recognised methods for plasticanalysis. It shall be documented that the collapse mechanismsassumed yield a realistic representation of the true deformationfield.

4.5 Limits for energy dissipation

4.5.1 Pipes on plated structuresThe maximum shear stress for plugging of plates due to drillcollar impacts may be taken as

f u = ultimate material tensile strength

4.5.2 Blunt objectsFor stability of cross-sections and tensile fracture, refer Sec-tion 3.10.

5. Fire5.1 GeneralThe characteristic fire structural load is temperature rise inexposed members. The temporal and spatial variation of tem-perature depends on the fire intensity, whether or not the struc-tural members are fully or partly engulfed by the flame and towhat extent the members are insulated. Structural steel expands at elevated temperatures and internalstresses are developed in redundant structures. These stresses

Table 4-1 Terminal velocities for objects falling in waterItem Mass

[kN]Terminal velocity

[m/s]Drill collarWinch,Riser pump

28250100

23-24

BOP annular preventer 50 16Mud pump 330 7

(4.5)

(4.6)

: stiffness of plate enclosed by hinge circle

∫∫ +=+= max,maxo, w

0 ii

w

0 oois,os,s dwRdwREEE i

dwo dwi

RiRo

Object Installation

Es,oEs,i

2i

2

sp mm

0.4812kRE ⎟⎟

⎠

⎞⎜⎜⎝

⎛+=

( )⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜

⎝

⎛

+

⎟⎠⎞

⎜⎝⎛+−+

= 2

22

y c12rd6.256c

rd51

tπf21k

= mass of plate enclosed by hinge circle

m = mass of dropped objectρp = mass density of steel plated = smaller diameter at threaded end of drill

collarr = smaller distance from the point of impact to

the plate boundary defined by adjacent stiffeners/girders, refer Figure 4-3.

(4.7)

⎟⎟⎠

⎞⎜⎜⎝

⎛ −−

−= 2rd

12.5ec

tπrρm 2pi =

rr r

⎟⎠⎞

⎜⎝⎛ +=

dt0.410.42fτ ucr

DET NORSKE VERITAS


are most often of moderate significance with respect to globalintegrity. The heating causes also progressive loss of strengthand stiffness and is, in redundant structures, accompanied byredistribution of forces from members with low strength tomembers that retain their load bearing capacity. A substantialloss of load-bearing capacity of individual members and sub-assemblies may take place, but the load bearing function of theinstallation shall remain intact during exposure to the fire load.In addition, damaged condition should be checked if relevant,see Section 2.2.Structural analysis may be performed on either

— individual members— subassemblies— entire system

The assessment of fire load effect and mechanical responseshall be based on either

— simple calculation methods applied to individual mem-bers,

— general calculation methods,

or a combination.Simple calculation methods may give overly conservativeresults. General calculation methods are methods in whichengineering principles are applied in a realistic manner to spe-cific applications.Assessment of individual members by means of simple calcu-lation methods should be based upon the provisions given inCh.7 /2/ Eurocode 3 Part 1.2. /2/ .Assessment by means of general calculation methods shall sat-isfy the provisions given in Ch.7 /2/ Eurocode 3 Part1.2, Sec-tion 4.3.In addition, the requirements given in this section for mechan-ical response analysis with nonlinear finite element methodsshall be complied with.Assessment of ultimate strength is not needed if the maximumsteel temperature is below 400°C, but deformation criteria mayhave to be checked for impairment of main safety functions.

5.2 General calculation methodsStructural analysis methods for non-linear, ultimate strengthassessment may be classified as

— stress-strain based methods — stress-resultants based (yield/plastic hinge) methods

Stress-strain based methods are methods where non-linearmaterial behaviour is accounted for on fibre level. Stress-resultants based methods are methods where non-linearmaterial behaviour is accounted for on stress-resultants levelbased upon closed form solutions/interaction equation forcross-sectional forces and moments.

5.3 Material modellingIn stress-strain based analysis temperature dependent stress-strain relationships given in Ch.7 /2/ Eurocode 3, Part 1.2, Sec-tion 3.2 may be used.For stress resultants based design the temperature reduction ofthe elastic modulus may be taken as kE,θ according to Ch.7 /2/ Eurocode 3. The yield stress may be taken equal to the effec-tive yield stress, fy,θ. The temperature reduction of the effec-tive yield stress may be taken as ky,θ.Provided that the above requirements are complied with creepdoes need explicit consideration.

5.4 Equivalent imperfectionsTo account for the effect of residual stresses and lateral distor-

tions compressive members shall be modelled with an initial,sinusoidal imperfection with amplitude given byElastic-perfectly plastic material model, refer Figure 6-4 :

Elasto-plastic material models, refer Figure 6-4 :

α = 0.5 for fire exposed members according to columncurve c, Ch.7 /2/ Eurocode 3

i = radius of gyrationz0 = distance from neutral axis to extreme fibre of cross-

sectionWP = plastic section modulusW = elastic section modulusA = cross-sectional areaI = moment of inertiae* = amplitude of initial distortion

= member length

The initial out-of-straightness should be applied on each phys-ical member. If the member is modelled by several finite ele-ments the initial out-of-straightness should be applied asdisplaced nodes. The initial out-of-straightness shall be applied in the samedirection as the deformations caused by the temperature gradi-ents.

5.5 Empirical correction factorThe empirical correction factor of 1.2 should be accounted forin calculating the critical strength in compression and bendingfor design according to Ch.7 /2/ Eurocode 3, refer Ch.8,Comm. A.5.5.

5.6 Local cross sectional bucklingIf shell modelling is used, it shall be verified that the softwareand the modelling is capable of predicting local buckling withsufficient accuracy. If necessary, local shell imperfectionshave to be introduced in a similar manner to the approachadopted for lateral distortion of beamsIf beam modelling is used local cross-sectional buckling shallbe given explicit consideration.In lieu of more accurate analysis cross-sections subjected toplastic deformations shall satisfy compactness requirementsgiven in DNV-OS-C101:

type I: Locations with plastic hinges (approximately fullplastic utilization)

type II: Locations with yield hinges (partial plastification)If this criterion is not complied with explicit considerationsshall be performed. The load-bearing capacity will be reducedsignificantly after the onset of buckling, but may still be signif-icant. A conservative approach is to remove the member fromfurther analysis.Compactness requirements for type I and type I cross-sectionsmay be disregarded provided that the member is capable ofdeveloping significant membrane forces.


5.7.1 GeneralThe ductility of beams and connections increase at elevatedtemperatures compared to normal conditions. Little informa-

απ 0

y*

zi

Ef1e

=l

αAI

WEf1α

zi

Ef1

W

We py

0

y*

p

ππ==

l

l

DET NORSKE VERITAS


tion exists.

5.7.2 Beams in bendingIn lieu of more accurate analysis requirements given in Section3.10 shall be complied with.

5.7.3 Beams in tensionIn lieu of more accurate analysis an average elongation of 3%of the member length with a reasonably uniform temperaturecan be assumed.Local temperature peaks may localise plastic strains. It is con-sidered to be to the conservative side to use critical strains forsteel under normal temperatures. See Section 3.10 and 3.10.4.

5.8 Capacity of connectionsIn lieu of more accurate calculations the capacity of the con-nection can be taken as:Rθ = ky,θ R0where

R0 = capacity of connection at normal temperatureky,θ = temperature reduction of effective yield stress for max-

imum temperature in connection

6. Explosions6.1 GeneralExplosion loads are characterised by temporal and spatial pres-sure distribution. The most important temporal parameters arerise time, maximum pressure and pulse duration. For components and sub-structures the explosion pressureshall normally be considered uniformly distributed. On globallevel the spatial distribution is normally non-uniform both withrespect to pressure and duration.The response to explosion loads may either be determined bynon-linear dynamic finite element analysis or by simple calcu-lation models based on Single Degree Of Freedom (SDOF)analogies and elastic-plastic methods of analysis.If non-linear dynamic finite element analysis is applied alleffects described in the following paragraphs shall either beimplicitly covered by the modelling adopted or subjected tospecial considerations, whenever relevant.In the simple calculation models the component is transformedto a single spring-mass system exposed to an equivalent loadpulse by means of suitable shape functions for the displace-ments in the elastic and elastic-plastic range. The shape func-tions allow calculation of the characteristic resistance curveand equivalent mass in the elastic and elastic-plastic range aswell as the fundamental period of vibration for the SDOF sys-tem in the elastic range. Provided that the temporal variation of the pressure can beassumed to be triangular, the maximum displacement of thecomponent can be calculated from design charts for the SDOFsystem as a function of pressure duration versus fundamentalperiod of vibration and equivalent load amplitude versus max-imum resistance in the elastic range. The maximum displace-ment must comply with ductility and stability requirements forthe component.

The load bearing function of the installation shall remain intactwith the damages imposed by the explosion loads. In addition,damaged condition should be checked if relevant, see Section2.2.

6.2 Classification of responseThe response of structural components can conveniently beclassified into three categories according to the duration of theexplosion pressure pulse, td, relative to the fundamental periodof vibration of the component, T:

Impulsive domain:The response is governed by the impulse defined by

Hence, the structure may resist a very high peak pressure pro-vided that the duration is sufficiently small. The maximumdeformation, wmax, of the component can be calculated itera-tively from the equation

where

R(w)= force-deformation relationship for the componentmeq = equivalent mass for the component.

Quasi-static-domain:The response is governed by the peak pressure and the risetime of the pressure relative to the fundamental period of vibra-tion. If the rise time is small the maximum deformation of thecomponent can be solved iteratively from the equation:

If the rise time is large the maximum deformation can besolved from the static condition

Dynamic domain:The response has to be solved from numerical integration ofthe dynamic equations of equilibrium.

6.3 Recommended analysis models for stiffened pan-elsVarious failure modes for a stiffened panel are illustrated inFigure 6-1. Suggested analysis model and reference to applica-ble resistance functions are listed in Table 6.1. Application ofa Single Degree of Freedom (SDOF) model in the analysis ofstiffeners/girders with effective flange is implicitly based onthe assumption that dynamic interaction between the plateflange and the profile can be neglected.

Impulsive domain td/T < 0.3Dynamic domain 0.3 < td/T < 3Quasi-static domain 3 < td/T

(6.1)

(6.2)

(6.3)

(6.4)

( )∫= dt

0dttFI

( )∫= maxw

0eq dwwR2mI

( )∫= maxw

0max

max dwwRF

1w

)R(wF maxmax =

DET NORSKE VERITAS


Figure 6-1Failure modes for two-way stiffened panel

Table 6-1 Analysis models

Failure modeSimplified analysis model Resistance models

Comment

Elastic-plastic deformation of plate SDOF Section 6.9 Stiffener plastic – plate elastic

SDOF Stiffener: Section 6.10.1-2.Plate: Section 6.9.1

Elastic, effective flange of plate

Stiffener plastic– plate plastic

SDOF Stiffener: Section 6.10.1-2.Plate: Section 6.9

Effective width of plate at mid span. Elastic, effective flange of plate at ends.

Girder plastic– stiffener and plating elastic

SDOF Girder: Section 6.10.1-2Plate: Section 6.9

Elastic, effective flange of plate with concentrated loads (stiffener reactions). Stiffener mass included.

Girder plastic– stiffener elastic– plate plastic

SDOF Girder: Section 6.10.1-2Plate: Section 6.9

Effective width of plate at girder mid span and ends.Stiffener mass included

Girder and stiffener plastic – plate elastic

MDOF Girder and stiffener: Section 6.10.1-2Plate: Section 6.9

Dynamic reactions of stiffeners→ loading for girders

Girder and stiffener plastic– plate plastic

MDOF Girder and stiffener: Section 6.10.1-2Plate: Section 6.9

Dynamic reactions of stiffeners→ loading for girders

By girder/stiffener plastic is understood that the maximum displacement wmax exceeds the elastic limit wel

DET NORSKE VERITAS


6.4 SDOF system analogyBiggs method:For many practical design problems it is convenient to assumethat the structure - exposed to the dynamic pressure pulse - ulti-mately attains a deformed configuration comparable to thestatic deformation pattern. Using the static deformation patternas displacement shape function, i.e.

the dynamic equations of equilibrium can be transformed to anequivalent single degree of freedom system:

The equilibrium equation can alternatively be expressed as:

where

The natural period of vibration for the equivalent system in thelinear resistance domain is given by

The response, y(t), is - in addition to the load history - entirelygoverned by the total mass, load-mass factor and the character-istic stiffness.For a linear system, the load mass factor and the characteristicstiffness are constant k = k1. The response is then alternativelygoverned by the eigenperiod and the characteristic stiffness.For a non-linear system, the load-mass factor and the charac-teristic stiffness depend on the response (deformations). Non-linear systems may often conveniently be approximated byequivalent bi-linear or tri-linear systems, see Section 6.8. Insuch cases the response can be expressed in terms of (see Fig-ure 6-6 for definitions):

k1 = characteristic stiffness in the initial, linear resistancedomain

yel = displacement at the end of the initial, linear resistancedomain

T = eigenperiod in the initial, linear resistance domain

and, if relevant,

k3 = normalised characteristic resistance in the third linearresistance domain.

Characteristic stiffness is given explicitly or can be derivedfrom load-deformation relationships given in Section 6.10. Ifthe response is governed by different mechanical behaviourrelevant characteristic stiffness must be calculated.For a given explosion load history the maximum displacement,ymax, is found by analytical or numerical integration of equa-tion (6.6). For standard load histories and standard resistance curvesmaximum displacements can be presented in design charts.Figure 6-2 shows the normalised maximum displacement of aSDOF system with a bi- (k3 = 0) or tri-linear (k3 > 0) resistancefunction, exposed to a triangular pressure pulse with zero risetime. When the duration of the pressure pulse relative to theeigenperiod in the initial, linear resistance range is known, themaximum displacement can be determined directly from thediagram as illustrated in Figure 6-2.

(6.5)

φ(x) = displacement shape func-tion

y(t) = displacement amplitude= generalized mass

= generalized load

= generalized elastic bend-ing stiffness

= generalized plastic bend-ing stiffness(fully developed mecha-nism)

= generalized membrane stiffness (fully plastic: N = NP)

m = distributed massMi = concentrated massq = explosion loadFi = concentrated load (e.g.

support reactions)xi = position of concentrated

mass/load

(6.6)

= load-mass transformation factor for uniform mass

= load-mass transformation factor for concentrated mass

= mass transformation factor for uni-form mass

= mass transformation factor for concentrated mass

( ) ( ) ( )tyxt,xw φ=

( )tfykm =+y&&

( ) ∑∫ +=i

2ii

2 φMdxxmφml

( )∫ ∑+=l i

iiφFdxxq(t)φ)t(f

( )∫=l

dxxEIφk 2xx,

0k =

( )∫=l

dxxNφk 2x,

( )ii xxφφ ==

F(t)K(y)yy)MKM(K ccm,uum, =++ &&ll

l

l KK

K um,um, =

l

l KK

K um,um, =

u

2

um, M

dx(x)mK

∫= l

ϕ

c

i

2

cm, M

MK

∑=

ϕi

= load transformation factor for uniformly distributed load

= load transformation factor for concentrated load

= total uniformly, distributed mass

= total concentrated mass

= total load in case of uniformly distributed load

= total load in case of concentrated load

= equivalent stiffness

(6.7)

F

(x)dxqK

∫= l

l

ϕ

F

FK i

∑=

iiϕ

l

∫=l

mdxMu

c ii

M M= ∑

∫=l

qdxF

ii

F F= ∑

lkkk e =

e

ccm,uum,

kMKMK

2km2T ll +

== ππ

DET NORSKE VERITAS


Figure 6-2Maximum response a SDOF system to a triangular pressure pulse with zero rise time. Fmax / Rel = 2

Design charts for systems with bi- or tri-linear resistancecurves subjected to a triangular pressure pulse with 0.5 td risetime is given in Figure 6.3. Curves for different rise times aregiven in Ch.8, Commentary Figure 8-15 to Figure 8-17.Baker's methodThe governing equations (6.1) and (6.2) for the maximumresponse in the impulsive domain and the quasi-static domainmay also be used along with response charts for maximum dis-placement for different Fmax/Rel ratios to produce pressure-impulse (Fmax, I) diagrams - iso-damage curves - provided thatthe maximum pressure is known. The advantage of using iso-damage diagrams is that "back-ward" calculations are possible:The diagram is established on the basis of the resistance curve.The information may be used to screen explosion pressure his-tories and eliminate those that obviously lie in the admissible

domain. This will reduce the need for large complex simula-tion of explosion scenarios.

6.5 Dynamic response charts for SDOF systemTransformation factors for elastic–plastic-membrane deforma-tion of beams and one-way slabs with different boundary con-ditions are given in Table 6-2.Maximum displacement for a SDOF system exposed to a tri-angular pressure pulse with rise time of 0.5td is displayed inFigure 6.3. Maximum displacement for a SDOF systemexposed to different pressure pulses are given in Ch.8, Com-mentary Figure 8-15 to Figure 8-17. The characteristic response of the system is based upon theresistance in the linear range, k = k1, where the equivalent stiff-ness is determined from the elastic solution to the actual sys-tem.

0,1

1

10

100

0,1 1 10td/T

Impulsive asymptote, k 3=0.2k 1

Elastic-perfectly plastic, k 3=0

Static asymptote, k 3=0.2k 1

k 3=0.2k 1

k 3=0.1k 1

td/T for system

ymax/yel

for system

td

F(t)

0,1

1

10

100

0,1 1 10td/T

Impulsive asymptote, k 3=0.2k 1

Elastic-perfectly plastic, k 3=0

Static asymptote, k 3=0.2k 1

k 3=0.2k 1

k 3=0.1k 1

td/T for system

ymax/yel

for system

td

F(t)

DET NORSKE VERITAS


Figure 6-3Dynamic response of a SDOF system to a triangular load (rise time = 0.50 td)

6.6 MDOF analysisSDOF analysis of built-up structures (e.g. stiffeners supportedby girders) is admissible if

— the fundamental periods of elastic vibration are suffi-ciently separated

— the response of the component with the smallest eigenpe-riod does not enter the elastic-plastic domain so that theperiod is drastically increased

If these conditions are not met, then significant interactionbetween the different vibration modes is anticipated and amulti degree of freedom analysis is required with simultaneoustime integration of the coupled system.

6.7 Classification of resistance properties

6.7.1 Cross-sectional behaviour

Figure 6-4Bending moment-curvature relationships

Elasto-plastic : The effect of partial yielding on bendingmoment is accounted forElastic-perfectly plastic: Linear elastic up to fully plastic bend-ing moment The simple models described herein assume elastic-perfectlyplastic material behaviour. Note: Even if the analysis is based upon elastic-perfectly plas-tic behaviour, the material has to exhibit strain hardening inpractice for the theory to be valid. The effect of strain harden-ing on the plastic, cross-sectional resistances may beaccounted for by using an equivalent (increased) yield stress.If this is considered relevant, and the material is utilisedbeyond ultimate strain, it is often justified to use an equivalentyield stress equal to the mean of the lower yield stress and theultimate stress.In the clauses for the ductility limits the effect of strain hard-ening is accounted for.

0.1

1

10

100

0.1 1 10

td/T

y max

/yel

= 1.1

Rel/Fmax= 0.8

= 1.0

= 0.9

= 1.2= 1.5

=0.1= 0.7

= 0.6= 0.5Rel/Fmax=0.05 = 0.3

yel y

R

Rel

FFmax

td0.50td

k1

k3 = 0.5k1 =0.2k1 =0.1k1k3 = 0k3 = 0.1k1

k3 = 0.2k1

k3 = 0.5k1

Elastic-perfectly plastic

elasto-plastic

Moment

Curvature

DET NORSKE VERITAS


Component behaviour

Figure 6-5Resistance curves

Elastic: Elastic material, small deformationsElastic-plastic (determinate): Elastic-perfectly plastic mate-rial. Statically determinate system. Bending mechanism fullydeveloped with occurrence of first plastic hinge(s)/yield lines.No axial restraint.Elastic-plastic (indeterminate): Elastic perfectly plastic mate-rial. Statically indeterminate system. Bending mechanismdevelops with sequential formation of plastic hinges/yieldlines. No axial restraint. For simplified analysis this systemmay be modelled as an elastic-plastic (determinate) systemwith equivalent initial stiffness. In lieu of more accurate anal-ysis the equivalent stiffness should be determined such that thearea under the resistance curve is preserved.Elastic-plastic with membrane: Elastic-perfectly plastic mate-rial. Statically determinate (or indeterminate). Ends restrainedagainst axial displacement. Increase in load-carrying capacitycaused by development of membrane forces.

6.8 Idealisation of resistance curvesThe resistance curves in 6.7 are idealised. For simplifiedSDOF analysis the resistance characteristics of a real non-lin-ear system may be approximately modelled. An example witha tri-linear approximation is illustrated in Figure 6-6. The stiff-ness in the k3 phase may have some contribution from strainhardening, but in most cases the predominant effect is devel-opment of membrane forces when member ends are restrainedform inward displacement.

Figure 6-6Representation of a non-linear resistance by an equivalent tri-lin-ear system

In lieu of more accurate analysis the resistance curve of elastic-plastic systems may be composed by an elastic resistance anda rigid-plastic resistance as illustrated in Figure 6-7.

Figure 6-7Construction of elastic -plastic resistance curve

6.9 Resistance curves and transformation factors for plates

6.9.1 Elastic - rigid plastic relationshipsIn lieu of more accurate calculations rigid plastic theory com-bined with elastic theory may be used.In the elastic range the stiffness and fundamental period ofvibration of a clamped plate under uniform lateral pressure canbe expressed as:

The factors ψ and η are given in Figure 6-8.

Figure 6-8Coefficients ψ and η.

RRR R

w w w w

k 1k 1k 1k 1k 3

k 2k 2k 2

Elastic Elastic-plastic(determinate)

Elastic-plastic(indeterminate)

Elastic-plasticwith membrane

RRR R

w w w w

k 1k 1k 1k 1k 3

k 2k 2k 2

Elastic Elastic-plastic(determinate)

Elastic-plastic(indeterminate)

Elastic-plasticwith membrane

k 2=0

k 1

Rk 3

w

Rel

wel

k 2=0

k 1

Rk 3

w

Rel

wel

r = k1w = resistance-displacement relationship for plate centre

= plate stiffness

= natural period of vibration

= plate bending stiffness

Elastic

+ =

Rigid-plastic Elastic-plastic with membrane

41 sDψk =

Dtsρ

η2πT

4

=

( )2

3

ν112

tED−

=

0

100

200

300

400

500

600

700

800

1 1.5 2 2.5 3l/s

ψ

0

5

10

15

20

25

30

35

40

ηψ

η

DET NORSKE VERITAS


In the plastic range the resistance (r) of plates with edges fullyrestrained against inward displacement and subjected to uni-form pressure can be taken as:

l (>s) = plate lengths = plate widtht = plate thicknessrc = plastic resistance in bending for plates with no axial

restraint= non-dimensional displacement parameter

Figure 6-9Plastic load-carrying capacities of plates as a function of lateraldisplacement

6.9.2 Axial restraintIn Equation (6.8) the beneficial effect of membrane stiffeningis represented by the term containing the non-dimensional dis-placement parameter . Great caution should be exercisedwhen assuming the presence of the membrane effect, becausethe membrane forces must be anchored in the adjacent struc-ture. For plates located in the middle of a continuous platefield, the boundaries have often considerable restraint againstpull-in. If the plate is located close to the boundary, the edgesare often not sufficiently stiffened to prevent pull-in of edges. Unlike stiffeners no simple method with a clear physical inter-pretation exists to quantify the effect of flexibility on the resist-ance of plates under uniform pressure. In the formulations usedin this RP the flexibility may be split into two contributions

1) Pull-in of edges2) Elastic straining of the plate

The effect of flexibility may be taken into account in anapproximate way by means of plate strip theory and the proce-dure described in Section 3.7.2. The relative reduction of theplate’s plastic resistance, with respect to the values given inEquation (6.8), is taken equal to the relative reduction of theresistance for a beam with rectangular cross-section (platethickness x unit width) and length equal to stiffener spacing,using the diagram for α = 2 (Figure 6-12). The elastic strainingof the plate is accounted for by the 2nd term in Equation (6.8).In lieu of more accurate calculation, the effect of pull-in, givenby the first term in Equation (6.8) may be estimated by remov-ing the plate and apply a uniformly distributed unit in-planeforce normal to the plate edges. The axial stiffness should betaken as the inverse of the maximum in-plane displacement ofthe long edge. In lieu of more accurate calculation, it should be conserva-tively assumed that no membrane effects exist for a platelocated close to an unsupported boundary, i.e. the resistanceshould be taken as constant and equal to the resistance in bend-ing, r = rc over the allowable displacement range.In lieu of more accurate calculations, it is suggested to assessthe relative reduction of the resistance for a uniformly loadedplate located some distance from an unsupported boundarywith c = 1.0.If membrane forces are taken into account it must be verifiedthat the adjacent structure is strong enough to anchor the fullyplastic membrane tension forces.

6.9.3 Tensile fracture of yield hingesIn lieu of more accurate calculations the procedure describedin Section 3.10.4 may be used for a beam with rectangularcross-section (plate thickness x unit width) and length equal tostiffener spacing.

6.10 Resistance curves and transformation factors for beamsProvided that the stiffeners/girders remain stable against localbuckling, tripping or lateral torsional buckling stiffened plates/girders may be treated as beams. Simple elastic-plastic meth-ods of analysis are generally applicable. Special considerationsshall be given to the effect of:

— Elastic flexibility of member/adjacent structure— Local deformation of cross-section— Local buckling — Strength of connections— Strength of adjacent structure— Fracture

6.10.1 Beams with no- or full axial restraintEquivalent springs and transformation factors for load andmass for various idealised elasto-plastic systems are shown inTable 6-2. For more than two concentrated loads, equal inmagnitude and spacing, use values for uniform loading.Shear deformation may have a significant impact on the elasticflexibility and eigenperiod of beams and girders with a shortspan/web height ratio (L/hw), notably for clamped ends. Theeigenperiod and stiffness in the linear domain including sheardeformation may be calculated as:

and

where

(6.8)

Pinned ends:

Clamped ends:

= plate aspect parameter

( ) 1w3α92α3αw1

rr 2

2

c

≤⎟⎟⎠

⎞⎜⎜⎝

⎛

−−+

+=

( ) 1w1w3

1α3α2α1w2

rr

2c

>⎟⎟

⎠

⎞

⎜⎜

⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛−

−−

+=

22

2y

c αt6f

rtw2w

l==

22

2y

c αt12f

rtww

l==

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛−⎟

⎠⎞

⎜⎝⎛+=

lllss3sα

2

w

0

1

2

3

4

5

6

0 0.5 1 1.5 2 2.5 3Relative displacement

Res

ista

nce

[r/r c

]

l/s = 100

5 3 2 1

w

w

(6.9)

(6.10)

⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛+

+==

w

2g

s'1

ccm,uum,

AA

GE1

Lrπ

c1k

MKMK2

km2T llππ

LGA

ck,k1

k1

k1 w

QQQ1

'1

=+=

DET NORSKE VERITAS


cs = 1.0 for both ends simply supported = 1.25 for one end clamped and one end simply sup-

ported = 1.5 for both ends clampedL = length of beam/girderE = elastic modulusG = shear modulusA = total cross-sectional area of beam/girderAw = shear area of beam/girderkQ = shear stiffness for beam/girderk1 = bending stiffness of beam/girder in the linear domain

according to Table 6-2rg = radius of gyration

Mps = plastic bending capacity of beam at supportMpm= plastic bending capacity of beam at midspan

and regardless of rotational boundary conditions the followingvalues may be used

cQ = 8 for uniformly distributed loads = 4 for one concentrated loads = 6 for two concentrated loads

The dynamic reactions according to Table 6-2 become increas-ingly inaccurate for loads with short duration and/or high mag-nitudes.

Table 6-2 Transformation factors for beams with various boundary and load conditions

Load caseResistancedomain

LoadFactor

Kl

Mass factor Km

Load-mass factor Klm Maximum

resistanceRel

Linear stiffness

k1

Dynamic reaction

VConcen-trated mass

Uni-form mass

Concen-trated mass

Uniform mass

Elastic 0.64 0.50 0.78

Plastic bending 0.50 0.33 0.66 0

Plastic membrane 0.50 0.33 0.66

Elastic 1.0 1.0 0.49 1.0 0.49

Plastic bending 1.0 1.0 0.33 1.0 0.33 0

Plastic membrane 1.0 1.0 0.33 1.0 0.33

Elastic 0.87 0.76 0.52 0.87 0.60

Plastic bending 1.0 1.0 0.56 1.0 0.56 0

Plastic membrane 1.0 1.0 0.56 1.0 0.56

Load caseResist-ance

domain

LoadFac-torKl

Mass factor Km


resistanceRel

Linear stiffness

k1

Equiva-lent lin-

ear stiffness

ke

Dynamic reaction

VConcen-trated mass

Uniform mass

Con-cen-

trated mass

Uniform mass

Elastic 0.53 0.41 0.77

Elasto-plastic

bending0.64 0.50 0.78


Plastic mem-brane

0.50 0.33 0.66

F=pL

L

8ML

p 3845 3

EIL

0 39 011. .R F+

8ML

p 0 38 012. .R Fel +

4NL

P

LyN maxP2

L/2

F

L/2

4 ML

p 483EI

L0 78 0 28. .R F−

4 ML

p 0 75 0 25. .R Fel −

4NL

P

LyN maxP2

L/3 L/3 L/3

F/2 F/2

6ML

p 56 43

. EIL

0 525 0 025. .R F−

6ML

p 0 52 0 02. .R Fel −

6NL

P

LyN maxP3

F=pL

L

12 ML

ps 3843EI

L FR 14.036.0 +

( )8 M M

Lps Pm+ 384

5 3EI

L 0 39 011. .R Fel +

( )8 M M

Lps Pm+ 0 38 012. .R Fel +

4NL

P

LyN maxp2

DET NORSKE VERITAS


Where:

q = explosion load per unit length = ps for stiffeners = p for girders

m1, m2 and m3 are factors for deriving the equivalent stiffness:

Elastic 1.0 1.0 0.37 1.0 0.37

Plastic bending 1.0 1.0 0.33 1.0 0.33 0

Plastic mem-brane

1.0 1.0 0.33 1.0 0.33

Elastic 080 0.64 0.41 0.80 0.51

Elasto-plastic

bending0.87 0.76 0.52 0.87 0.60

Plastic bending 1.0 1.0 0.56 1.0 0.56 0

Plastic mem-brane

1.0 1.0 0.56 1.0 0.56

Elastic 0.58 0.45 0.78

Elasto-plastic

bending0.64 0.50 0.78


Plastic mem-brane

0.50 0.33 0.66

Elastic 1.0 1.0 0.43 1.0 0.43

Elasto-plastic

bending1.0 1.0 0.49 1.0 0.49

Plastic bending 1.0 1.0 0.33 1.0 0.33 0

Plastic mem-brane

1.0 1.0 0.33 1.0 0.33

Elastic 0.81 0.67 0.45 0.83 0.55

Elasto-plastic

bending0.87 0.76 0.52 0.87 0.60

Plastic bending 1.0 1.0 0.56 1.0 0.56 0

Plastic mem-brane

1.0 1.0 0.56 1.0 0.56

Load caseResist-ance

domain

LoadFac-torKl

Mass factor Km


resistanceRel

Linear stiffness

k1

Equiva-lent lin-

ear stiffness

ke

Dynamic reaction

VConcen-trated mass

Uniform mass

Con-cen-

trated mass

Uniform mass

F

L/2 L/2

( )4 M M

Lps Pm+ 192

3EI

L13

48 mLEI

⋅⎟⎠⎞

⎜⎝⎛

0 71 0 21. .R F−

( )4 M M

Lps Pm+ 0 75 0 25. .R Fel −

4NL

P

LyN maxP2

L/3 L/3 L/3

F/2 F/29 psM

L 3260EI

L13

212m

LEI

⋅⎟⎠

⎞⎜⎝

⎛

0.48 0.02R F+

( )6 ps PmM ML+

356.4EI

L0.52 0.02elR F−

( )6 ps PmM ML+ 0.52 0.02elR F−

6 PNL

V2 V1

F=pL

L

8ML

ps 1853EI

L23

160m

LEI

⋅⎟⎠

⎞⎜⎝

⎛

V R F1 0 26 0 12= +. .V R F2 0 43 019= +. .

( )4 2M M

Lps Pm+ 384

5 3EI

L

0 39 011. .R FM LPs

+±

( )4 2M M

Lps Pm+ 0 38 012. .R F

M LPs

+±

4NL

PLyN maxP2

V1

L/2 L/2

F

V2

163ML

Ps 1073EI

L23

160m

LEI

⋅⎟⎠

⎞⎜⎝

⎛

V R F1 0 25 0 07= +. .V R F2 054 014= +. .

( )2 2M M

Lps Pm+ 48

3EI

L

0 78 0 28. .R FM LPs

−±

( )2 2M M

Lps Pm+ 0 75 0 25. .R F

M LPs

−±

4NL

PLyN maxP2

V1

L/3 L/3 L/3

F/2 F/2

V2

6ML

Ps 1323EI

L33

122m

LEI

⋅⎟⎠

⎞⎜⎝

⎛

V R F1 017 017= +. .V R F2 0 33 0 33= +. .

( )2 3M M

Lps Pm+ 56

3EI

L

0 525 0 025. .R FM LPs

−±

( )2 3M M

Lps Pm+ 0 52 0 02. .R F

M Lel

Ps

−±

6NL

PLyN maxP3

l

25.05.1

1 ++

=pmps

ps

MMM

m

5.02

5.12 +

+=

pmps

ps

MMM

m

5.03

23 +

+=

pmps

ps

MMM

m

DET NORSKE VERITAS


6.10.2 Beams with partial end restraint.Relatively small axial displacements have a significant influ-ence on the development of tensile forces in members under-going large lateral deformations. Equivalent elastic, axialstiffness may be defined as

knode = axial stiffness of the node with the considered memberremoved. This may be determined by introducing unit loads inmember axis direction at the end nodes with the memberremoved.Plastic force-deformation relationship for a beam under uni-form pressure may be obtained from Figure 6-10, Figure 6-11or Figure 6-12 if the plastic interaction between axial force andbending moment can be approximated by the following equa-tion:

In lieu of more accurate analysis α = 1.2 can be assumed forstiffened plates and H or I beams. For members with tubularsection α = 1.5. For rectangular sections and plates α = 2.0 canbe assumed.

Figure 6-10Plastic load-deformation relationship for beam with axial flexibility (α = 1.2)

(6.11)

(6.12)

= plastic collapse resistance in bending for the member with uniform load.

= member length

2EAk1

k1

node

l+=

21for1NN

MM

α

pp

<<=⎟⎟⎠

⎞⎜⎜⎝

⎛+ α

l

py10

Wf8cR =

l

= non-dimensional deformation

=characteristic beam height for beams described by plastic interaction equation (6.12).

= non-dimensional spring stiffness

c1 = 2 = for clamped beamsc1 = 1 = for pinned beamsWP = plastic section modulus for the cross sec-

tion of the beamWp = zgAg = plastic section modulus for stiffened

plate for set > AsA = As + st = total area of stiffener and plate flangeAe = As + set = effective cross-sectional area of stiffener

and plate flange,zg = distance from plate flange to stiffener

centre of gravity.As = stiffener areas = stiffener spacingse = effective width of plate flange see Sec-

tion 6.10.4

c1wcww =

AαW

w pc =

lAfkw4c

cy

2c1=

α = 1.2

0

1

2

3

4

5

6

0 0,5 1 1,5 2 2,5 3 3,5 4Deformation

1

0

0.10.20.5

c = ∞

w


k k

F (explosion load)

w

R/R

0

α = 1.2

0

1

2

3

4

5

6

0 0,5 1 1,5 2 2,5 3 3,5 4Deformation

1

0

0.10.20.5

c = ∞

w


k k

F (explosion load)

w

R/R

0

DET NORSKE VERITAS


Figure 6-11Plastic load-deformation relationship for beam with axial flexibility (α = 1.5)

Figure 6-12Plastic load-deformation relationship for beam with axial flexibility (α = 2)

For members where the plastic moment capacity of adjacentmembers is smaller than the moment capacity of the exposedmember the force-deformation relationship may be interpo-lated from the curves for pinned ends and clamped ends:

where

α = 1.5

0

1

2

3

4

5

6

7

0 0,5 1 1,5 2 2,5 3 3,5 4

Deformation

0.10.20.51

0

w

c = ∞


k k

F (explosion load)

w

R/R

0

α = 1.5

0

1

2

3

4

5

6

7

0 0,5 1 1,5 2 2,5 3 3,5 4

Deformation

0.10.20.51

0

w

c = ∞


k k

F (explosion load)

w

R/R

0

α = 2

0

1

2

3

4

5

6

7

8

9

0 0,5 1 1,5 2 2,5 3 3,5 4

Deformation

1

0.50.2 0.1

0

w

c = ∞


k k

F (explosion load)

w

R/R

0

α = 2

0

1

2

3

4

5

6

7

8

9

0 0,5 1 1,5 2 2,5 3 3,5 4

Deformation

1

0.50.2 0.1

0

w

c = ∞


k k

F (explosion load)

w

R/R

0

(6.13)pinnedclamped ζ)R(1ζRR −+=(6.14)11

M8

Rζ0

p

actual0

≤−=≤

l

DET NORSKE VERITAS


i = adjacent member no i j = end number {1,2}MPj,i = Plastic bending moment for member no. i.Elastic, rotational flexibility of the node is normally of moder-ate significance

6.10.3 Beams with partial end restraint - support capacity smaller than plastic bending moment of memberFor beams where the plastic moment capacity of adjacentmembers is smaller than the moment capacity of the impactedbeam, the force-deformation relationship, R*, may be derivedfrom the resistance curve, R, for beams where the plasticmoment capacity of adjacent members is larger than themoment capacity of the impacted beam (Section 3.7.2), usingthe expression:

where

R0 = Plastic bending resistance with clamped ends (c1 = 2)– moment capacity of adjacent members larger thanthe plastic bending moment of the beam

= Plastic bending resistance - moment capacity of adja-cent members at one or both ends smaller than the plas-tic bending moment of the member

i = adjacent member no ij = end number {1,2}MPj,i = Plastic bending resistance for member no. i.wlim = limiting non-dimensional deformation where the

membrane force attains yield, i.e. the resistancecurve, R, with actual spring stiffness coefficient, c,intersects with the curve for c = ∞. If c = ∞,

for tubular beams and for stiffened plate

6.10.4 Effective flangeIn order to analyse stiffened plate as a beam the effective widthof the plate between stiffeners need to be determined. Theeffective width needs to be reduced due to buckling and/orshear lag. Shear lag effects may be neglected if the length is more than2.5 times the width between stiffeners. For guidance see Ch.8,

Commentary. Determination of effective flange due to buckling can be madeas for buckling of stiffened plates see DNV-RP-C201.The effective width for elastic deformations may be used whenthe plate flange is on the tension side.In most cases the flange will experience varying stress withparts in compression and parts in tension. It may be undulyconservative to use the effective width for the section with thelargest compression stress to be valid for the whole memberlength. For continuous stiffeners it will be reasonable to use themean value between effective width at the section with thelargest compression stress and the full width. For simple sup-ported stiffeners with compression in the plate it is judged tobe reasonable to use the effective width at midspan for the totallength of the stiffener.

6.10.5 Strength of adjacent structureThe adjacent structure must be checked to see whether it canprovide the support required by the assumed collapse mecha-nism for the member/sub-structure

6.10.6 Strength of connectionsThe capacity of connections can be taken from recognisedcodes. The connection shall be checked for the dynamic reactionforce given in Table 6-2.For beams with axial restraint the connection should also bechecked for lateral - and axial reaction in the membrane phase:

— If the axial force in a tension member exceeds the axialcapacity of the connection the member should be assumeddisconnected.

— If the capacity of the connection is exceeded in compres-sion and bending, this does not necessarily mean failure ofthe member. The post-collapse strength of the connectionmay be taken into account provided that such informationis available.

6.10.7 Ductility limitsReference is made to Section 3.10.The local buckling criterion in Section 3.10.2 and tensile frac-ture criterion given in Section 3.10.3 may be used with:

dc = characteristic dimension equal to twice the distancefrom the plastic neutral axis in bending to the extremefibre of the cross-section

c = non-dimensional axial spring stiffness calculated inSection 6.10.2.

Alternatively, the ductility ratios in Table 6-3 maybe used.

= Collapse load in bending for beam accounting for actual bending resistance of adjacent members

(6.15)

(6.16)

, (6.17)

,

(6.18)

(6.19)

actual 0R

l

p2p1pactual 0

4M4M8MR

++=

∑ ≤=i

PPj,iPj MMM

lim

*00

* )R(RRRww

−+= 0.1lim

≤ww

RR* = 0.1lim

≥w

w

*0R

* P P1 P20

4M 2M 2MR + +=

l

∑ ≤=i

PiPj,Pj MMM

lim 2w wπ

= Table 6-3 Ductility ratios μ - beams with no axial restraint

Boundaryconditions

Load Cross-section type 1)

Type I Type II Type III

Cantilevered ConcentratedDistributed

67

45

22

Pinned ConcentratedDistributed

612

48

23

Fixed ConcentratedDistributed

64

43

22

1) Crossecton types are defined in DNV-OS-C101, Table A3, Appendix A

elyymax=μ

DET NORSKE VERITAS


7. References

8. CommentaryComm. 2.3 GeneralThe structural design is seen as having acceptable safetyagainst accidental loads when the design accidental loads areless than the design resistance. This is similar to the check ofthe structure for ordinary loads but with the following differ-ences: As ordinary loads are either permanent or occur fre-quent it will not be acceptable that the load lead to reduced loadcarrying capacity while the short duration and the low proba-bility of accidental loads make this an acceptable assumptions.E.g. a blast wall need not be capable of resisting another explo-sion after a blast, but if the wall is used as a fire barrier it needto serve as such after the blast.Comm. 3.1 GeneralFor typical installations, the contribution to energy dissipationfrom elastic deformation of component/substructures in directcontact with the ship is very small and can normally beneglected. Consequently, plastic methods of analysis apply.However, elastic elongation of the hit member as well as axialflexibility of the nodes to which the member is connected, havea significant impact on the development of membrane forces inthe member. This effect has to be taken into account in theanalysis, which is otherwise based on plastic methods. The dia-grams in Section 3.7.2 are based on such an approach.Depending on the structure size/configuration as well as thelocation of impact elastic strain energy over the entire structuremay contribute significantly.Comm. 3.2 Design principlesThe transition from essentially strength behaviour to ductileresponse can be very abrupt and sensitive to minor changes inscantlings. E.g. integrated analyses of impact between the sternof a supply vessel and a large diameter column have shownthat with moderate change of (ring - and longitudinal) stiffenersize and/or spacing, the energy dissipation may shift from pre-dominantly platform based to predominantly vessel based.Due attention should be paid to this sensitivity when the calcu-lation procedure described in Section 3.5 is applied.Comm. 3.3 Collision mechanics

The added mass is due to the hydrodynamic pressure inducedby the forced motion of water particles on the wet surface ofthe ship. By solving the velocity potential for the fluid on thebody surface, the added mass is determined by means of 2-D(strip theory) or 3-D techniques. The added mass is frequencydependent, and thus varies with time during a collision, but aconstant value is recommended for simple analysis. The fraction of collision energy to be dissipated as strainenergy for shuttle tanker impact on FPSO stern is shown inFigure 8-1. Note the strong dependency of the mass ratio; thelarger the mass of shuttle tanker, the lesser of the collisionenergy must be dissipated as strain energy. (However, pro-vided that the speed of the shuttle tanker is constant, the abso-lute value of the strain energy increases)The relative size may differ considerably for the approachphase (shuttle tanker in ballast, FPSO fully loaded) and thedeparture phase (shuttle tanker fully loaded, FPSO in ballast).To illustrate this, possible values are listed in Table 8-1. In thisexample both the FPSO and shuttle tanker are large comparedto typical North Sea conditions. The same added mass coeffi-cient applies to both vessels. It is observed that the fraction ofenergy to be dissipated as strain energy varies between 0.33(departure) and 0.71 (approach). This indicates that theapproach phase may be particularly critical with respect to theconsequences of collision.

Figure 8-1Fraction of collision energy to be dissipated as strain energy forshuttle tanker impact on an FPSO.

Comm. 3.5.1 Recommended force-deformation relationshipsThe force-deformation relationship for impacts from supplyvessels/merchant vessels against jacket legs have been elabo-rated because of the need to consider high-energy impacts (col-lision energy ~50 MJ) for some installations in the North Sea.The likelihood of a central impact against a leg is obviously notvery large, but has still been considered because loss of a legcould be critical for some platforms. Experience has shown,however, that many large North Sea jackets have sufficientstrength to crush the bow. Reference is made to Amdahl andJohansen (2001).

/1/ NORSOK Standard N-003 Action and Action Effect/2/ NS-ENV 1993-1 Eurocode 3: Design of Steel structures

Part 1-2. General rules - Structural fire design/3/ Amdahl, J.: “Energy Absorption in Ship-Platform

Impacts”, UR-83-34, Dept. Marine Structures, Norwe-gian Institute of Technology, Trondheim, 1983.

/4/ SCI 1993: Interim Guidance Notes for the Design and Protection of Topside Structures against Explosion and Fire

/5/ Amdahl, J.: “Mechanics of Ship-Ship Collisions- Basic Crushing Mechanics”. West Europene Graduate School of Marine Technology, WEGEMT , Copenhagen, 1995

/6/ Skallerud, B. and Amdahl, j.: “Nonlinear Analysis of Offshore Structures”, Research studies Press, UK 2002

/7/ Amdahl, J. and Johansen, A.: “High-Energy Ship Colli-sion with Jacket Legs” ISOPE, Stavanger, 2001

/8/ Moan, T., Amdahl, J., Wang, X. and Spencer, J.: “ Risk Assessment of FPSOs, with Emphasis on Collisions”, SNAME Annual Meeting, Boston, 2002

/9/ Skallerud, B. and Amdahl, j.: “Nonlinear Analysis of Offshore Structures”, Research studies Press, UK 2002

/10/ Amdahl, J. and Johansen, A.: “High-Energy Ship Colli-sion with Jacket Legs” ISOPE, Stavanger, 2001 Table 8-1 Fraction of collision energy for strain energy

dissipationVessel size [dwt]

Approach phase Departure phaseShuttle tanker 150.000 370.000FPSO 320.000 160.000Strain energy fraction 0.71 0.33

0

0,2

0,4

0,6

0,8

1

1,2

0 1 2 3 4

Mass ratio [(ms+ as)/(mi+ ai)]

Stra

in e

nerg

y fr

actio

n

DET NORSKE VERITAS


The curve for bow impact in Figure 3-4 has been derived on theassumption of impacts against an infinitely rigid wall. Some-times the curve has been used erroneously to assess the energydissipation in bow-brace impacts.Experience from small-scale tests Ch.7, /3/ indicates that thebow undergoes very little deformation until the brace becomesstrong enough to crush the bow. Hence, the brace absorbs mostof the energy. When the brace is strong enough to crush thebow the situation is reversed; the brace remains virtuallyundamaged. On the basis of the tests results and simple plastic methods ofanalysis, force-deformation curves for bows subjected to(strong) brace impact were established in Ch.7, /3/ as a func-tion of impact location and brace diameter. These curves arereproduced in Figure 8-2. In order to fulfil a strength designrequirement the brace should at least resist the load level indi-cated by the broken line (recommended design curve). Forbraces with a diameter to thickness ratio < 40 it should be suf-ficient to verify that the plastic collapse load in bending for thebrace is larger than the required level. For larger diameter tothickness ratios local denting must probably be taken intoaccount.Normally sized jacket braces are not strong enough to resist thelikely bow forces given in Figure 8-2, and therefore it has to beassumed to absorb the entire strain energy. For the same rea-sons it has also to be assumed that the brace has to absorb allenergy for stern and beam impact with supply vessels.

Figure 8-2Load-deformation curves for bow-bracing impact, Ch.7, /3/

Comm. 3.5.2 Force contact area for strength design of largediameter columns.

Figure 8-3Distribution of contact force for stern corner/large diameter col-umn impact

Figure 8-3 shows an example of the evolution of contact forceintensity during a collision between the stern corner of a supplyvessel and a stiffened column. In the beginning the contact isconcentrated at the extreme end of the corner, but as the cornerdeforms it undergoes inversion and the contact ceases in thecentral part. The contact area is then, roughly speaking,bounded by two concentric circles, but the distribution is une-ven.The force-deformation curves given in Figure 3-4 relate tototal collision force for stern end - and stern corner impact ,respectively. Table 3-1 and Table 3-2 give the anticipatedmaximum force intensities (local force and local contact areas,i.e. subsets of the total force and total area) at various stages ofdeformation.The basis for the design curves is integrated, non-linear finiteelement analysis of stern/column impacts.The information given in 3.5.2 may be used to performstrength design. If strength design is not achieved numericalanalyses have shown that the column is likely to undergosevere deformations and absorb a major part of the strainenergy. In lieu of more accurate calculations (e.g. non-linearFEM) it has to be assumed that the column absorbs all strainenergy.Comm. 3.5.3 Energy dissipation is ship bow.The requirements in this paragraph are based upon considera-tions of the relative resistance of a tubular brace to local dent-ing and the bow to penetration of a tubular beam. Afundamental requirement for penetration of the brace into thebow is, first - the brace has sufficient resistance in bending,second - the cross-section does not undergo substantial localdeformation. If the brace is subjected to local denting, i.e.undergoes flattening, the contact area with the bow increasesand the bow inevitably gets increased resistance to indentation.The provisions ensure that both requirements are compliedwith. Figure 8-8 indicates the level of the various contact locations.Figure 8-4 shows the minimum thickness as a function of bracediameter and resistance level in order to achieve sufficientresistance to penetrate the ship bow without local denting. Itmay seem strange that the required thickness becomes smallerfor increasing diameter, but the brace strength, globally as wellas locally, decreases with decreasing diameter.Local denting in the bending phase can be disregarded pro-vided that the following relationship holds true:

Figure 8-5 shows brace thickness as a function of diameter andlength diameter ratio that results from Equation (8.1). Thethickness can generally be smaller than the values shown, andstill energy dissipation in the bow may be taken into account,but if Equation (8.1) is complied with denting does not need tobe further considered.The requirements are based upon simulation with LS-DYNAfor penetration of a tube with diameter 1.0 m. Great cautionshould therefore be exercised in extrapolation to diameterssubstantially larger than 1.0 m, because the resistance of thebow will increase. For brace diameters smaller than 1.0 m, therequirement is conservative.

4

2.01.51.00.50

8

12

Indentation [m]

Impact force [MN]

Between stringers (D= 0.75) m

On a stringer (D= 0.75 m)

Between a stringer (D= 1.0 m)

Recommended design curve for brace impact

Total collision force

distributed over this

Area with high forceintensity

Deformed stern corner

(8.1)2

21

D 10.14t c D

⎛ ⎞≤ ⎜ ⎟⎝ ⎠

l

DET NORSKE VERITAS


Figure 8-4Required thickness versus grade and resistance level of brace topenetrate ship bow without local denting

Figure 8-5Brace thickness yielding little local deformation in the bendingphase

Comm. 3.7.3 Support capacity smaller than plastic bendingmoment of the beamThe procedure is illustrated in Figure 8-6.Elastic, rotational flexibility of the node is normally of moder-ate significance.

Figure 8-6Derivation of force-deformation relationship for beam with endmoments less than beam plastic moment.

The procedure given is essentially the same as the one used inNORSOK N-004, but is formulated differently. The bendingmoment boundary condition is important in the bending phase,but has no influence on the resistance in the pure membrane

phase. Between these extremities, simple linear interpolation isused.Comm. 3.10.1 GeneralIf the degradation of bending capacity of the beam cross-sec-tion after buckling is known the load-carrying capacity may beinterpolated from the curves with full bending capacity and nobending capacity according to the expression:

= Collapse load with full bending contribution = Collapse load with no bending contribution

Comm. 3.10.4 Tensile fracture in yield hingesThe rupture criterion is calculated using conventional beamtheory. A linear strain hardening model is adopted. For a can-tilever beam subjected to a concentrated load at the end, thestrain distribution along the beam can be determined from thebending moment variation. In Figure 8-7 the strain varia-tion, , is shown for a circular cross-section for agiven hardening parameter. The extreme importance of strainhardening is evident; with no strain hardening the high strainsare very localised close to the support (x = 0), with strain hard-ening the plastic zone expands dramatically.On the basis of the strain distribution the rotation in the plasticzone and the corresponding lateral deformation can be deter-mined.If the beam response is affected by development of membraneforces it is assumed that the membrane strain follows the samerelative distribution as the bending strain. By introducing thekinematic relationships for beam elongation, the maximummembrane strain can be calculated for a given displacement.

Figure 8-7Axial variation of maximum strain for a cantilever beam with cir-cular cross-section

Adding the bending strain and the membrane strain allowsdetermination of the critical displacement as a function of thetotal critical strain.Figure 8-8 shows deformation at rupture for a fully clampedbeam as a function of the axial flexibility factor c.

0

20

40

60

80

0,6 0,8 1 1,2 1,4

Diameter [m]

Thic

knes

s [m

m]

fy = 235 MPa, 6 MN

fy = 235 MPa, 3 MN

fy = 355 MPa, 6 MN

fy = 355 MPa, 3 MN

fy = 420 MPa, 6 MN

fy = 420 MPa, 3 MN

0

20

40

60

80

100

0,6 0,8 1 1,2 1,4Diameter [m]

Thic

knes

s [m

m]

L/D =20L/D =25L/D =30

α = 1.5

0

1

2

3

4

5

6

7

0 1 2 3 4

Deformation w

R/R

0 R

*/R 0

c =0.5

wlim

R/R0

R*/R0

*0 0R / R

(8.2)

= Plastic collapse load in bending with reduced cross-sectional capacities. This has to be updated along with the degradation of cross-sectional bending capacity.

)1)(()()( 01 ξξ −+= == wRwRwRPMPM

)(1 wRPM =

)(0 wRPM =

)0(1

,

==

= wRR

PM

redPMξ

red,PMR

Ycr εεε =

0

5

10

15

20

25

30

35

40

45

50

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35x/l

Stra

in ε

Hardening parameter H = 0.005

Maximum strain εcr/εY

= 50 = 40 = 20

No hardening

P

l

x

DET NORSKE VERITAS


Figure 8-8Maximum deformation for a tubular fully clamped beam(H=0.005)

The plastic stiffness factor H is determined from the stress-strain relationship for the material. The equivalent linear stiff-ness shall be determined such that the total area under thestress-strain curve up to the critical strain is preserved (The twoportions of the shaded area shall be equal), refer Figure 8-9. Itis un-conservative and not allowable to use a reduced effectiveyield stress and a plastic stiffness factor as illustrated in Figure8-10.

Figure 8-9Determination of plastic stiffness

Figure 8-10Erroneous determination of plastic stiffness

The accuracy of the calculation model for tensile fracture inyield hinges has been investigated by Amdahl and Skallerud(2002). The maximum strain as a function of lateral displace-ment (Equation (3.22)) for a tubular beam is compared with themaximum strain from finite element calculations in Figure8-11. The beam is assumed to be clamped and fixed againstinward axial displacement, l = 25 m, D = 1 m, t = 0.06 m, fy =300 MPa, H = 0.00287 (i.e. ultimate stress fu = 390 MPa for atultimate strain εu = 0.15). The mesh size for USFOS shell andABAQUS is 0.25 ⋅ 0.39 m and for ABAQUS fine mesh 0.05 ⋅ 0.195 m. The element used in ABAQUS analyses is theS4R reduced integration element .

Figure 8-11Strain versus displacement of clamped beam

It is observed that the strain estimated in ABAQUS analysisdepend significantly on the mesh size evidencing the need fora mesh-size-dependent fracture strain criterion. The NORSOKcriterion agrees fairly well with FEM calculations when a finemesh is used. The criterion is conservative, as desired. Thestrain calculation in the USFOS beam element assumes a yieldplateau followed by parabolic type hardening. Only the fineABAQUS mesh captures the yield plateau effect. Comm. 3.12 Energy dissipation in floating production vessels

Figure 8-12Design of an impact resistant stern – collision with a VLCC.

Calculation of energy dissipation in stringers, decks and bulk-heads subjected to gross, axial crushing shall be based uponrecognised methods for plastic analysis, e.g. Ch.7, /3/ andCh.7, /4/. It shall be documented that the folding mechanismsassumed yield a realistic representation of the true deformationfield.The force deformation relationships given in Figure 3-6 maybe used to design a collision resistant stern of an FPSO. Inorder to be impact resistant, stringers and frames must be fairlyclosely spaced, typically in the range of 1.5 – 2 m. Given therelative dimensions of the girder system and the bulb cross-section, as illustrated in Figure 8-12, it is reasonable to applythe total collision force as uniformly distributed line loads onthe stringers and frames. The integrity of the stringers andframes can then be checked in a FEM analysis. Moderate localyielding should be accepted.The stern structure must resist the collision force during allstages of the collision process. Normally, it suffices to analysea few collision force and contact area situations.It is normally neither practical nor necessary to design the plat-ing and stiffeners such that their response is elastic. Large plas-tic deformations can be accepted, but fracture of the platingshould not occur (Note: provided that strength design is aimedfor). In lieu of more accurate calculations, the contact forcemay be considered uniformly distributed over the plate field,and the resistance may be assessed using the provisions givenfor the resistance of plates and stiffeners to explosion loads.

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0 20 40 60 80 100 120

εcr/εy

w/D

l/D = 30

c= 0 = 0.05 = 0.5 = 1000

l/D = 20

c = 0 = 0.05 = 0.5 = 1000

E

H E

εcr

fcr

E

H E

εcr

fcr

H E

f

ε

0%

5%

10%

15%

20%

0.0 0.5 1.0 1.5 2.0

Displacement [m]

Stra

in

NORSOK

ABAQUS fine

USFOS beam

ABAQUS

USFOS shell

1600

1600

1600

DET NORSKE VERITAS


Even if the stiffeners are allowed to deform under extreme col-lision loads, they should be sufficiently robust to initiate crush-ing of the bulb. Engineering judgment must be applied, but itis recommended to design the stiffeners according to require-ments for ships navigating in ice; DNV Ice Class POLAR.With respect to deformation resistance of stiffened plating, seenext paragraph.The ductile resistance of stiffened plates may be analysed con-sidering the side as an assembly of plate/stiffeners. The resist-ance of individual stiffeners with associated plate flange can becalculated with the methods given in Section 6.3 using rela-tionships for a concentrated force, see example in Ch.8,Comm. 9.3. The resistance of the various stiffeners will bemobilised according to the geometry (raking) of the impactingbow. Unless the frame spacing is long or the stiffener height is small,fracture will take place before noticeable membrane stiffeninghas taken place. The initiation of fracture does not necessarily

imply that the resistance is totally lost, because fracture takesplace in the top flange while the strain on the plate side is con-siderably smaller .The above procedure neglects the effect of membrane forcestransverse to the stiffeners. Depending on the geometry of thepanel this contribution may be substantial.Collisions with FPSOs have been studied in-depth in a paperby Moan et.al. (2002). Force-deformation relationships aregiven for supply vessels/merchant vessels, 18.000 tons chemi-cal tanker and a 42.000 tons tanker and a shuttle tanker. Thecollision risk for all categories of vessels is discussed exten-sively. The consequences of a collision with a shuttle tankerservicing the FPSO are especially considered.Figure 8-13 shows the force-deformation relationship for sup-ply vessel/merchant vessel colliding with the side of an FPSO.It is interesting to see that the force level for bow without bulbis smaller than the bow force-deformation curve given in Fig-ure 3-4.

Figure 8-13Force-deformation relationship for supply vessel/merchant vessel impact against FPSO side

Comm. 4.4.1 Stiffened plates subject to drill collar impactThe validity for the energy equation 4.6 is limited to 7 < 2 r/d < 41, t/d < 0.22 and mi/m < 0.75.The formula neglect the local energy dissipation which can beadded as Eloc = R·0.2 t. In case of hit near the plate edges the energy dissipation will below and may lead to unreasonable plate thickness. The failurecriterion used for the formula is locking of the plate. In manycases locking may be acceptable as long as the falling object isstopped. If the design is based on a hit in the central part of aplate with use of the smaller diameter in the treaded part in thecalculations, no penetration of the drill collar will take place atany other hit location due to the collar of such dropped objects.Comm. 5.1 General For redundant structures thermal expansion may cause buck-ling of members below 400°C. Forces due to thermal expan-sion are, however, purely internal and will be released once themember buckles. The net effect of thermal expansion is there-fore often to create lateral distortions in heated members. Inmost cases these lateral distortions will have a moderate influ-ence on the ultimate strength of the system.As thermal expansion is the source of considerable inconven-ience in conjunction with numerical analysis it would tempting

to replace its effect by equivalent, initial lateral member distor-tions. There is however, not sufficient information to supportsuch a procedure at present.Comm. 5.5 Empirical correction factor In Ch.7 /2/ Eurocode 3 an empirical reduction factor of 1.2 isapplied in order to obtain better fit between test results and col-umn curve c for fire exposed compressive members. In thedesign check this is performed by multiplying the design axialload by 1.2. In non-linear analysis such a procedure is imprac-tical. In non-linear space frame, stress resultants based analysisthe correction factor can be included by dividing the yieldcompressive load and the Euler buckling load by a factor of1.2. (The influence of axial force on member’s stiffness isaccounted for by the so-called Livesly’s stability multipliers,which are functions of the Euler buckling load.) In this way thereduction factor is applied consistently to both elastic andelasto-plastic buckling.The above correction factor comes in addition to the reductioncaused by yield stress and elastic modulus degradation at ele-vated temperature if the reduced slenderness is larger than 0.2.Comm. 6.2 Classification of response Equation (6.2) is derived using the principle of conservation ofmomentum to determine the kinetic energy of the componentat the end of the explosion pulse. The entire kinetic energy is

0

5

10

15

20

25

30

0 1 2 3Bow Displacement [m]

Ene

rgy

[MJ]

0

5

10

15

20

25

30

For

ce [M

N]

Energy superstr.Energy bulbTotal forceForce superstr.Force bulb

DET NORSKE VERITAS


then assumed dissipated as strain energy.Equation (6.3) is based on the assumption that the explosionpressure has remained at its peak value during the entire defor-mation and equates the external work with the total strainenergy. In general, the explosion pressure is not balanced byresistance, giving rise to inertia forces. Eventually, these iner-tia forces will be dissipated as strain energy.Equation (6.4) is based on the assumption that the pressureincreases slowly so that the static condition (pressure balancedby resistance) applies during the entire deformation.Comm. 6.4 SDOF system analogy The displacement at the end of the initial, linear resistancedomain yel will generally not coincide with the displacement atfirst yield. Typically, yel represents the displacement at the ini-tiation of a plastic collapse mechanism. Hence, yel is largerthan the displacement at first yield for two reasons:

i) Change from elastic to plastic stress distribution overbeam cross-section

ii) Bending moment redistribution over the beam (redundantbeams) as plastic hinges form

Figure 8-14Iso-damage curve for ymax/yel = 10. Triangular pressure

Figure 8-14 is derived from the dynamic response chart for aSDOF system subjected to a triangular load with zero rise timegiven in Figure 6-3.In the example it is assumed that from ductility considerationsfor the assumed mode of deformation a maximum displace-ment of ten times elastic limit is acceptable. Hence the line

represents the upper limit for the displacement of the component. From the diagram it is seenthat several combinations of pulses characterised by Fmax andtd may produce this displacement limit. Each intersection witha response curve (e.g. k3 = 0) yields a normalized pressure

and a normalised impulse

By plotting corresponding values of normalised impulse andnormalised pressure the iso-damage curve given in Figure 8-14is obtained.If the displacement shape function changes as a non-linearstructure undergoes deformation the transformation factorschange. In lieu of accurate analysis an average value of thecombined load-mass transformation factor can be used:.

μ = ymax/yel ductility ratioSince μ is not known a priori iterative calculations may be nec-essary.Dynamic response charts for a SDOF system with triangularpressure pulses with rise time different from td/2 are given inFigure 8-15 to Figure 8-17.

0

1

2

3

4

5

6

7

8

9

10

11

0 1 2 3 4 5 6 7 8 9 10 11

Impulse I/(RT)

Pre

ssur

e F

/R

Pressure asymptote

Impu

lsiv

e as

ympt

ote

Iso-damage curve for ymax/yelastic = 10Elastic-perfectly plastic resistance

(8.3)

10y

yy

y

el

max

el

allow ==

el

max

RF

RF

=

Tt

FR

2

1TR

tF21

RTI d

max

elel

dmax⋅==

( )μμ plastic

melastic

maveragem

kkk ll

l

1−+=

DET NORSKE VERITAS


Figure 8-15Dynamic response of a SDOF system to a triangular load (rise time=0)

Figure 8-16Dynamic response of a SDOF system to a triangular load (rise time = 0.15td)

0.1

1

10

100

0.1 1 10

td/T

y max

/yel

=0.1 = 0.7= 0.6= 0.5Rel/Fmax=0.05 = 0.3

= 1.1

= 1.0

= 0.9

Rel/Fmax= 0.8

= 1.2

= 1.5

yel y

R

Rel

F

Fmax

td

k1

k3 = 0.5k1 =0.2k1 =0.1k1k3 = 0k3 = 0.1k1

k3 = 0.2k1

k3 = 0.5k1

0.1

1

10

100

0.1 1 10

td/T

y max

/yel

=0.1 = 0.7= 0.6= 0.5Rel/Fmax=0.05 = 0.3

= 1.1= 1.0

= 0.9

Rel/Fmax= 0.8

= 1.2= 1.5

yel y

R

Rel

F

Fmax

td0.15td

k1

k3 = 0.5k1 =0.2k1 =0.1k1k3 = 0k3 = 0.1k1

k3 = 0.2k1

k3 = 0.5k1

DET NORSKE VERITAS


Figure 8-17Dynamic response of a SDOF system to a triangular load (rise time = 0.30td)

Comm.6.7.1.1 Component behaviourFor beams the characteristic linear stiffness given for theelasto-plastic resistance domain in Table 6-2 is derived fromthe equal area principle on the assumption that the supportmoment is equal to the plastic bending moment of the beam. Comm. 6.7.1.1 Component behaviour For deformations in the elastic range the effective width (shearlag effect) of the plate flange, se, of simply supported orclamped stiffeners/girders may be taken from Figure 8-18.

Figure 8-18Effective flange for stiffeners and girders in the elastic range

Comm. 6.10.7 Ductility limitsThe table is taken from Ch.7, Reference /4/. The values arebased upon a limiting strain, elasto-plastic material and cross-sectional shape factor 1.12 for beams and 1.5 for plates. Strainhardening and any membrane effect will increase the effectiveductility ratio. The values are likely to be conservative.

9. Examples9.1 Design against ship collisions

9.1.1 Jacket subjected to supply vessel impactThe location of contact is at brace mid-span and the force actsparallel to global x-axis. The brace dimensions are 762 x 28.6mm. From linear elastic analysis it is found that the stiffness ofnodes 508 and 628 against displacement in the brace directionis 736 MN/m and 51 MN/m respectively, when the brace isremoved. The unequal stiffness may be represented by twoequal springs, each with stiffness:

0.1

1

10

100

0.1 1 10

td/T

y max

/yel

=0.1 = 0.7= 0.6= 0.5Rel/Fmax=0.05 = 0.3

= 1.1= 1.0

= 0.9

Rel/Fmax= 0.8

= 1.2= 1.5

yel y

R

Rel

FFmax

td0.30td

k1

k3 = 0.5k1 =0.2k1 =0.1k1k3 = 0k3 = 0.1k1

k3 = 0.2k1

k3 = 0.5k1

0

0.2

0.4

0.6

0.8

1

1.2

0 2 4 6 8

/s

s e/s

n > 6n = 5n = 4n = 3

Uniform distribution or

nFi

= L

nFi

�= 0.6L

DET NORSKE VERITAS


Figure 9-1Jacket subjected to ship impact

The axial stiffness of the brace is given by

and is large compared to the stiffness of the node. This yieldsan effective stiffness of

Assuming clamped ends (c1 = 2) the non-dimensional springstiffness comes out to be

The resulting end restraint is quite flexible. This is particularlydue to low stiffness in node 628, in spite of the support by theadjacent braces. Hence, the build-up of tension force will bedelayed compared to a full axial fixity.The collapse load in bending is calculated assuming clampedconditions at both ends. This is a good approximation at thelower end but slightly optimistic at the upper end.

The load-deformation characteristics for the brace are obtainedby interpolation of the curves given in Figure 3-7. The result isdepicted in Figure 9-2. The response predicted by means of thenonlinear analysis program USFOS is also plotted. It appearsthat the simplified approach performs very well when axialflexibility is taken into account. The loss of stiffness predictedby USFOS at large displacements is due to initiation of failureof adjacent members at node 628. Collapse of these memberstakes place at a load level of 2.8 MN.

It must also be verified that the capacity of the joints is suffi-cient to support the force state in the brace both in the bendingmode of deformation and in the membrane tension state. Fig-ure 9-3 displays the simulated bending moment-axial forceinteraction history in the brace and shows that the membraneforce becomes substantial, but doe not attain the fully plasticaxial force. In lieu of accurate calculations, it should be assumethat the fully plastic tension is developed. Provided that the joints and adjacent structure are capable ofsupporting the brace ends, the energy dissipation is limited byfracture due to excessive straining of the brace. Fracture crite-ria are given Section 3.10.3. Using the fracture criterion in Sec-tion 3.10.3 there is obtained wcrit = 2.2 m and a correspondingenergy dissipation E = 6 MJ.

Figure 9-2Load versus lateral deformation of the contact point

Figure 9-3Axial force-bending moment interaction in brace

Tensile fracture in jacket braceTensile fracture of the brace considered in is estimated. Thecharacteristic dimension is, dc = D = 0.762 m. For steel gradeS 355 a strain hardening coefficient of H = 0.0034 is used, referTable 3-3. c1 = 2 (clamped ends are assumed), the collisionoccurs at mid span, hence κ = 0.5, and κ /dc = 15.3. The non-dimensional spring stiffness is c = 0.18 and W/WP = π /4. Thisyields wcrit = 2.2 m. Because of the large κ /dc – ratio, the brace is capable ofdeforming almost three times its diameter.

628

508

762 x 28.6 mml= 23.3 m

mMNKnode /95511

73612

1

=⎟⎠⎞

⎜⎝⎛ +=

−

mMNEA /12343.23

0286.0762.0101.222 5

=⋅⋅⋅⋅⋅

=π

l

MN/m881234

19511

=+=K

18.03.230286.0355

762.08822Af

Kw4cc

y

2c1 ≅

⋅⋅⋅⋅⋅

===ππ ll tf

Kd

y

MN9.13.23

0286.0)0286.0762.0(355244R2

10 =⋅−⋅⋅⋅==

lPMc

0

2

4

6

8

10

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Displacement [m]

Impa

ct fo

rce

[MN

]

0

2

4

6

8

10

Ener

gy d

issip

atio

n [M

J]

USFOS

Simple model

Energy dissipation

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.0Normalised moment M/MP

Nor

mal

ised

forc

e N

/NP

l

l

DET NORSKE VERITAS


9.2 Design against explosions

9.2.1 GeometryThe geometry of the structure is outlined in Figure 9-4. Theplate, stiffeners and girders will be assessed. The main dimen-sions are:

t = 10 mms = 500 mml = 2000 mm

Stiffener dimension Hp 180

Figure 9-4Geometry

9.2.2 Calculation of dynamic response of plate:The dynamic response of the plate considered in Section 9.3.1is studied. The plate is subjected to a triangular pressure pulsewith duration of 20 msecs. The peak pressure is fmax = 2.5MPa. Assume that the resistance curve for c = 1.0 in Figure 9-7 applies. This yields rel/fmax = 0.3. The curve is redrawnbelow along with approximate relationships

Alternative 1- static analysis: The eigenperiod of the plateaccording to Section 9.3.1 with η = 25 is T = 4.0 msecs. Hencetd/T = 5. This is a fairly long duration and static behaviour canbe assumed. The maximum deflection is determined directlyfrom Figure 9-7, i.e. wmax = 27 mm. Alternative 2 - tri-linear resistance: By inspection of thedynamic response charts and the resistance curve for the plateit is noticed that none of the tri-linear curves apply very well.The best fit is obtained with k3 = 0.5 k1, but this underestimatesthe resistance for large deformations. From the response chartfor td/T = 5 there is read ymax/yel ~ 4.8. This yields wmax = 4.8· 6.15 = 30 mm.Alternative 3 – equivalent linear resistance: For large defor-mations the stiffness is fairly linear. Assume that the averagestiffness is linear and equal to 65 % of the elastic stiffness, i.e.k = 0.65 · 123 = 80 MPa/m. In this case the rel can be set arbi-trarily, but it should be ensured that the response is such thatymax/yel < 1.0, and it is practical to select a given rel/fmax ratiofor which a response curve is provided. Hence assume rel/fmax= 1.5, which gives rel = 47.3 mm and then it follows r. The

eigenperiod is adjusted by toaccount for less stiffness. This yields td/Tmod = 4.0. From theresponse chart there is obtained ymax/yel ~ 0.7. This yieldswmax = 0.7 · 47,3 = 33 mm.All these methods yield approximately the same result. Thestatic approach is quite good, but there is a slight dynamicamplification > 1 in the present case. The plate must be checked with respect to rupture, see Section9.4.1.It is noticed that if no membrane force can be taken intoaccount, i.e. c = 0, then ymax/yel >> 100 and the plate will failcompletely.

9.2.3 Calculation of dynamic response of stiffened plateThe dynamic response of the stiffened plate considered in Sec-tion 9.3.2, subjected to a triangular explosion pulse with dura-tion 20 msecs and peak pressure fmax = 2.5 MPa, is studied.The collapse resistance is R0 = Rel = 0.58 MN, and no mem-brane stiffening can be assumed, i.e. k3 = 0. As the plate/stiff-ener undergoes a phase with elasto-plastic bending, theresistance is approximated by a linear elastic-perfectly plasticmodel, with equivalent stiffness of 208 MN/m and wel = 2.8mm. The critical deformation at rupture wcrit = 36 mm, hencethe ductility ratio is μ = ymax/yel = 36/2.8 = 13. The total mass is 108 kg. The load-mass factor is ~ 0.77 and0.66 in the elastic/elasto-plastic and plastic bending phase,respectively. Using Equation (8.3) the average load-mass fac-tor becomes and theeigenperiod is:

This gives td/T = 5.4. By inspection of Figure 6-3 it is foundthat for μ = 13 and td/T =5.4 → Rel/Fmax ≅ 0.75 (in otherwords, because of limited pulse duration it is possible to “over-load” the stiffener by 33% compared to the static collapseresistance in bending). The maximum peak pressure the stiffener can resist is:

Consequently; the stiffener is not strong enough to resist theexplosion pressure without rupture (see discussion in Section9.3.2 as concerns rupture of stiffener).It is a fairly common experience that stiffeners are more likelyto be critical with respect to explosion loads than the platingbetween stiffeners.

9.3 Resistance curves and transformation factors

9.3.1 Plates.Generation of elastic–plastic resistance curve is illustrated fora plate with the following particulars: Length, l = 2 m, width,s = 0.5 m, thickness, t = 10 mm, yield stress f y = 355 MPa. Itis assumed that the plate is a part of a continuous plate field.Large deformations are expected so that the plate will yieldalong the boundaries. Then clamped boundaries are assumed.The rigid – plastic curve is given by Equation (8.3). The col-lapse resistance in bending is rc = 0.76 MPa. The resistancecurve for fully fixed boundaries are indicated by the line “Platec = inf” in Figure 9-6. Below, the curve will be adjusted for theeffect of in-plane flexibility using the procedure described inSection 6.8.2. First, the resistance of a plate-strip is calculated, using infor-mation given in Section 6.9.2 with α = 2 (rectangular cross-section). Clamped boundaries with c1 = 2 are assumed also for

t = 10

Stiffener Hp180

Girder

0

1

2

3

4

5

0 10 20 30 40 50D eform ation [m m ]

Res

ista

nce

[Mpa

]

P late c = 1.0

Tri-linear

Eq. linearStatic

msecs0.565.01mod == TT

( )( )0.77 13 1 0.66 /13 0.67averagelmk = + − =

smk

MkT

averagelm sec7.32

1== π

.MPa8.075.01

==ls

Rf elcrit

DET NORSKE VERITAS


the plate strip. The collapse resistance in bending for the platestrip is rc = 0.57 MPa.The characteristic beam height is.

The resistance curve for the plate strip is shown in Figure 9.6for fully fixed boundaries , and for two values of the non-dimensional spring stiffness, c = 1.0 and c = 0.3. It is observedthat the difference between the plate strip and the plate solutionis small for the present fairly large aspect ration, notably whenthe membrane effect predominatesOn the assumption that the plate experiences the same relativereduction of the resistance due to axial flexibility as does theplate strip, resistance curves for the plate with non-dimen-sional spring stiffness, c = 1.0, and c = 0.3 can be generated asshown in Figure 9-6.The next step is to assess the flexibility factor c: If the flexibility of the adjacent structure is neglected, account-ing only for the 2nd term in Equation (6.11), there is obtained

This yields a non-dimensional spring stiffness, c = 0.95.

Figure 9-5Approximate determination of flexibility by means of membraneanalysis

In order to assess the influence of the flexibility of the adjacentstructure, a membrane analysis is performed with the plateremoved, see Figure 9-5. A constant stress of 100 MPa isapplied perpendicular the boundaries. The maximum deforma-tion obtained, at the mid-point of the long edges, is 0.25 mm.This yields an equivalent stiffness of knode = 100·0.010·1/0.25·10-3 = 4000 MN/m. When both effects are accounted for,the resulting stiffness becomes k = (1/8400 +1/4000)-1 =2710 MN/m and c = 0.31. Hence, the plate resistance may beassessed reasonably well by means of the curves for either c =1.0 or c = 0.3.Finally, the linear elastic solution up to the collapse resistancein bending, rc, is added to the rigid-plastic solution. Using theinformation given in Section 6.9.1, ψ = 400, and k1 = 123 MPa/m. The deformation corresponding to r = rc is wel = 6.15 mm.The resulting resistance curves are shown in Figure 9.7.

Figure 9-6Derivation of rigid-plastic resistance curves for a plate

Figure 9-7Elastic-plastic resistance for a plate with various degrees of axialflexibility.

9.3.2 Calculation of resistance curve for stiffened plateThe plate considered in Section 9.3.1 is stiffened with HP 180x8 stiffeners with yield stress fy = 355 MPa. The girder spacingis 2.0 m. It is assumed that the stiffener is continuous, so thatyield hinges can form at the connections to the girder, hence c1= 2. The area of the stiffener As= 1.88·10-2 m2 and the distanceto the centroid is zg = 0.109 m. From Figure 8-18 it is found that the plate flange is approxi-mately 80% for a uniformly distributed load when

/s = 0.6⋅2.0/0.5 = 2.4. The effective area of the plate flangeis 0.8 s t = 4·10-3 m2 > As. Hence, it may be assumed that theplastic neutral axis for the effective section lies at the stiffenerweb toe. This yields the plastic section modulus WP = As zg =2.05·10-3 m3 and collapse resistance in bending

The characteristic beam height is.

The moment of inertia for stiffener with effective plate flangeis I = 2.28 10-5 m4. The initial elastic stiffness is taken fromTable 6-2:

This yields a lateral “elastic” deformation of wel = 2.5 mm forR = R0.The resistance curve for the stiffener with associated plateflange is shown in Figure 9.8 for various degrees of axial flex-ibility (Note elastic part not included!).

21412 2 t

tt

AWw P

c =⋅⋅

==α

∞=c

mMNs

EtEAk /8400122=

⋅==

l

Inwarddisplacement

Uniform stress field applied alongboundary of removed plate

0

1

2

3

4

5

0 10 20 30 40 50

Deformation [mm]

Res

ista

nce

[Mpa

]

Plate c = infPlate c = 1.0Plate c = 0.3Strip c = infStrip c = 1.0Strip c = 0.3

0

1

2

3

4

5

0 10 20 30 40 50

Deformation [mm]

Res

ista

nce

[Mpa

]Plate c = infPlate c = 1.0Plate c = 0.3

l

MN58.08 1

0 ==l

PyWfcR

wcαWP

A------------ αzg 1.2 0.109⋅ 0.13m= = = =

MN/m230L

384EIk3

==

DET NORSKE VERITAS


For uniformly loaded, clamped beams there will be an elasto-plastic bending phase between the occurrence of first plastichinge and final formation of final collapse mechanism. Toaccount for this effect, the initial stiffness may be modified onthe basis of equal area principle. The equivalent elastic stiff-ness is obtained from Table 6-2 with m1 = 1:

and wel = 3.2 mm for R = R0.It is noticed that the stiffener must undergo a substantial plasticdeformation before membrane strengthening becomes signifi-cant according to the present model. Whether this is achievabledepends on the ductility of the stiffener, refer Section 9.4.2.Recent investigations indicate that the model adopted for stiff-ened plate is considerably conservative, which may warrant amore accurate nonlinear finite element analysis if the stiffenerresponse becomes critical.

Figure 9-8Resistance curve for stiffener with associated plate flange.

9.3.3 Calculation of resistance curve for girderWhat is the maximum pressure a steel girder can resist prior torupture, when the explosion load is triangular, with equal riseand decay time, and the duration is 0.33 s? The girder has the following dimensions: Length L = 12 m, web height, hw = 1.5 m, web thickness, tw =13 mm, top flange breadth, btop = 0.45 m, top flange thicknessttop = 19 mm. The girder spacing is 2 m and the plate thicknessis 10 mm. For simplicity it is assumed that the plate flange isfully effective. The girder has a distributed load of intensity 10kN/m2 and mounted equipment with mass 1.8·105 kg. Theequipment load acts equally at two points located L/3 frommember ends. The girder is simply supported at one end andclamped at the other end. At the clamped end fully plasticbending moment of the girder can be assumed. There is noaxial restraint. Yield stress fy = 355 MPa, acceleration of grav-ity g = 10 m/s2, density of steel 7.86⋅103 kg/m3.The following is obtained for the girder: Moment of inertia I = 1.84⋅10-2 m4, elastic section modulus, W= 1.96⋅10-2 m3, plastic section modulus, WP = 2.51⋅10-2 m3,total cross-sectional area 0.048 m2. The total distributed mass,including mass of girder is 0.29⋅10-5 kg, so the concentratedmass predominates. Hence, transformation factors for two con-centrated loads in Table 6.2 are used.The equivalent stiffness in the elasto-plastic range (m3 = 1) is.

The plastic bending resistance is

and wel* = 21.8 mm. However, the functional loads amount to1.8 + 0.29 = 2.09 MN (including steel weight), so 21.8·2.09/5.95 = 7.6 mm is already utilised and only Rel = 5.95-2.09 =3.86 MN and wel = 14.1 mm is available in the equivalent elas-tic range. The limiting deformation for rupture calculated in9.4.3 is wmax = 95 mm, yielding ductility ratio μ = w/max / wel= 95/14.1 = 6.7. When calculating the load-mass factor the change in transfor-mation factor from the elastic to plastic regime may beaccounted for, see Ch.8, Comm. 6.4. The factor for distributedmass and concentrated mass is

klmaverage,u = (0.55 + (6.7 − 1) ⋅ 0.56) / 6.7 = 0.56

and klm

average,c = (0.83 + (6.7 − 1) ⋅ 1.0) / 6.7 = 0.975,respectively. The eigenperiod becomes

and hence td/T= 0.33/0.166 ~ 2. From Figure 6-3 there is readRel/Fmax = 0.7 for coordinates (2,6.7). Hence, the girder canresist a dynamic load of Fmax = 3.86/0.7 = 5.5 MN, corre-sponding to a peak pressure of fmax= 0.23 MPa.Example girder:The neutral axis for the girder studied in Section 9.3.3 islocated 0.315 m from the plate flange. This yields a character-istic dimension dc = 2 ⋅ (1.5 − 0.315) = 2.37 m. The criticallocation is at the clamped side, whereby κ =1/3. Clamped endyields c1 = 2 for the fracture check. With H = 0.0034 and c =0, there is obtained w/dc = 0.069 and w = 0.095 m.


9.4.1 PlatingRupture of the plating for the example considered in Section9.2.2 may be estimated by means of the procedure given inSection 3.10.4, using the plate strip analogy. The characteristicdimension is, dc = t = 10 mm. For steel grade S 355 a strainhardening coefficient of H = 0.0034 is used, refer Table 3-4. κ= 0.5, c1 = 2 (clamped ends) and κ /dc = 0.5 s/t = 25. Thisyields the following values for the critical deformation, wcrit,depending on the spring stiffness c, see Table 9.1 (Note: theelastic deformation rel = 6.15 mm is added to the valuesobtained). By inspection of Figure 9-7 it is noticed that thefully plastic membrane state according to this procedure isattained in all cases but c = 0.

9.4.2 Stiffener:Rupture is calculated for the stiffened plate considered in sec-tion 9.2.3 using the procedure given in Section 3.10.4. Thesteel grade is S 355 with a strain hardening coefficient of H =0.0034, refer Table 3-3. Clamped conditions are assumed, i.e.c1 = 2. The shape factor (somewhat arbitrarily) set to 1.5. Thecharacteristic dimension of the stiffened plate is dc = 2hw =0.36 m. This yields λ/dc = 5.56, only. This critical deformationbecomes wcrit = 0.1dc = 36 mm, almost independent of thespring stiffness c (Note: ductility ratio is μ = 36/2.2 = 16). Thisfairly small value is due to the low κλ/dc – ratio for the stiff-ener. The stiffener is far from entering the membrane stiffen-ing phase, so that any discussion of the possibility formembrane forces to develop is irrelevant.

MN/m184L

307EIk3

==

α = 1.2

0.0

0.5

1.0

1.5

2.0

0 0.1 0.2 0.3 0.4 0.5Deformation w [m]

R [M

N]

c = infc = 1.0c = 0.5c = 0.2c = 0.1

MN/m274L

122EIk3

==

Table 9-1 Ductility limit as a function of the spring stiffnessc ∞ 1.0 0.3 0

wcrit [mm] 35 51 59 76

*8 5.95 MNPm

elMRL

= =

T 2p 0.56 2.9 104⋅⋅ 0.975 1.8 105⋅ ⋅+

274 106⋅----------------------------------------------------------------------------------- 0.166s= =

l

DET NORSKE VERITAS


If the stiffener is free against rotation and/or has a longer spanmembrane effects may become important prior to rupture. Observe that rupture is calculated for the location subjected tothe largest strains, i.e. at the stiffener top flange. Rupture in thetop flange is not necessarily critical with respect to intactnessto explosion loads, because the plate side experiences far lessstrains. It is likely that the plate will remain intact beyond thedeformation limit corresponding to rupture in the top flange. Asignificant part of the contribution to resistance from the stiff-ener is lost, but the plating between girders may have a signif-icant residual resistance after failure of stiffeners provided thatthe plate does not disintegrate. It is, however, difficult to pro-vide validated, closed form solution for this situation. A stiffener subjected to pressure on the plate side may tripabout the weld toe at mid span. In this case the assumptionsused in the strain calculation model are no longer valid.

9.4.3 Girder:The neutral axis for the girder studied in Ch.8, Comm. 6.10 islocated 0.315 m from the plate flange. This yields a character-istic dimension dc = 2 ⋅ (1.5 − 0.315) = 2.37 m. The criticallocation at the clamped side, whereby κ =1/3. Clamped endyields c1 = 2 for the fracture check. With H = 0.0034 and c =0, there is obtained w/dc = 0.069 and w = 0.095 m.

9.5 Design against explosions - girder

9.5.1 Geometry, material and loadsThe geometry of the structure is outlined in Figure 9-4. Themain dimensions are:

Plate thickness: t = 14 mmStiffener dimension: HP240x10, simulated as an L-profile

with dimension L240x39x10x29Stiffener spacing: s = 800 mmStiffener length: l = 3200 mmGirder dimension: T-girder with dimension: 870x300x10

x20Girder length: L = 12000 mm

The material properties are as follow:

Permanent loads and live loads are as follow:

Figure 9-9Geometry

Yield strength: fy = 420 MPaStrain rate factor: γε = 1.0Effective yield strength: fy = fy· γε = 420 MPaModulus of elasticity: E = 2.1·105 MPaMaterial density: ρ = 7850 kg/m3

Poisson’s ratio: ν = 0.3Max. plastic strain: 1.0% (maximum allowable, corre-

spond to cross section class 3 or 4, see sub-section 9.5.2)

Permanent loads: pP = 10.0 kN/m2Live loads: pL = 5.0 kN/m2Explosion pulse period:

td = 0.15 sec (triangular load with a rise time = 0.50·td)

t = 14

Bulkhead

Girder:

800 (typ.)

10

Stiffener: Hp240

Girder: TG870x300x10x20

Bulkhead

12000

Stiffener:

870

300

20

10 240

39

29

3200(typ.)

DET NORSKE VERITAS


9.5.2 Cross sectional of properties for the girderEffective plate flange according to DNV Classification Note30.1 (July 1995), sub-section 3.4.3 and 3.5.4:

Determination of cross section class, Ref. NS3472:2001, Sec- tion 12.1:

In the following calculations, a plate flange width larger than cross sectional class 3 will not be considered, i.e.:

Gross sectional properties:Effective area of plate flange:Ap = le·t = 303.2·14 = 4245.1 mm2

Area of girder flange:Af = bfg·tfg = 300·20 = 6000.0 mm2

Total area of girder web:Aw = hwg·twg = 850·10 = 8500.0 mm2

Total area (gross section):AG = Ap+Af+Aw = 4245.1+6000+8500 = 18745.1 mm2

Distance to neutral axis (from bottom of girder flange):

Web height in tension:ht = z0-tfg = 403.6-20.0 = 383.6mmWeb height in compression:hc = hwg-ht = 850.0-383.6 = 466.4mm

56.251.2

42014800

=⋅=⋅=EE

fts yβ

58.056.2

8.056.28.18.08.1

22=−=−=

ββxC

mmslCsl xe 6.784

56.2111

80032001.058.08001111.0

2

2

2

2 =⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ +⋅⎟

⎠⎞

⎜⎝⎛ −⋅+⋅=

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛+⋅⎟

⎠⎞

⎜⎝⎛ −⋅+⋅=

β

Web: , i.e. class 3 (bending considered)

Bottom Flange: , i.e. class 2 (bending & axial)

Plate Flange: , i.e. class 4 (bending & axial)

6.113420/235

)10/850(/235

)/(==

y

wgwg

f

th

7.9420/235

)20

)10300(5.0(

/235

))(5.0

(=

−⋅

=

−⋅

y

fg

wgfg

f

ttb

0.37420/235

)14

)106.784(5.0(

/235

))(5.0

(=

−⋅

=

−⋅

y

wge

ft

tl

mmtftl wgye 2.30310)420/2351414(2)/23514(2 =+⋅⋅⋅=+⋅⋅⋅=

mmA

thtAth

At

Az

G

fgwgpfgwg

wfg

f

6.403222

0 =⎟⎠⎞

⎜⎝⎛ ++⋅+⎟⎟

⎠

⎞⎜⎜⎝

⎛+⋅+⋅

=hwg = 870-20

= 850

twg = 10

le = 303.2

bfg = 300

t = 14

z0

tfg = 20

hc

ht

DET NORSKE VERITAS


Elastic moment of inertia (gross section):

Effective girder web according to NS3472:Elastic buckling stress

Web slenderness:

Effective compression web height, see Figure 9-10:

Figure 9-10Effective Girder Section

Effective girder cross section propertiesReduction in web height:Δh = hc -hce = 466.4 – 430.8 = 35.6 mm Effective cross section area:Ae = AG -Δh ·twg = 18745.1 – 35.6·10.0 = 18389.1 mm2 Distance to neutral axis from bottom of girder flange:

Effective elastic moment of inertia:

( ) 4920

222

222 10407.222212

1 mmzAthtAth

At

AtAhAtAI Gfgwgpfgwg

wfg

fpwgwfgfG ⋅=⋅−⎟⎠⎞

⎜⎝⎛ ++⋅+⎟⎟

⎠

⎞⎜⎜⎝

⎛+⋅+⎟⎟

⎠

⎞⎜⎜⎝

⎛⋅+⋅+⋅+⋅⋅=

( ) ( ) MPahtEf

wg

wge 9.627

85010

3.0112101.29.23

1129.23

2

2

522

2

2

=⎟⎠⎞

⎜⎝⎛⋅

−⋅⋅⋅

⋅=⎟⎟⎠

⎞⎜⎜⎝

⎛⋅

−⋅⋅

⋅=π

νπ

818.09.6270.420

===e

yp f

fλ

⎪⎩

⎪⎨

⎧

>⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛

⋅−⋅

≤

= 724.05

11

724.0

ppp

c

pc

ce ifh

ifh

hλ

λλ

λ

mmhce 8.430818.05

11818.0

2.341=⎥

⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛

⋅−⋅=

½ hcehwg = 870-20

= 850twg = 10

le = 303.2

bfg = 300

t = 14

e

z0

hc

ht

½ hce

tfg = 20

Δh

ht

mmA

thhh

thzAz

e

fgtce

wgG

e 1.3991.18389

206.3832

8.4306.35106.356.4031.1874520

0 =⎟⎠⎞

⎜⎝⎛ ++

+⋅−⋅

=⎟⎠

⎞⎜⎝

⎛++

+Δ⋅Δ−⋅

=

2

03

2121

⎟⎠⎞

⎜⎝⎛ −++⋅⋅Δ−⋅Δ⋅−= e

ctfgwgwgGGe z

hhtththII

492

39 10387.21.3992

4.4666.38320106.35106.3512110407.2 mmI Ge ⋅=⎟

⎠⎞

⎜⎝⎛ −++⋅⋅−⋅⋅−⋅=

DET NORSKE VERITAS


Effective elastic section modulus:

Plastic section modulus:

Plastic section modulus if Ap > Aw1 + Aw2 + Af :

Plastic section modulus if Ap + Aw1 > Aw2 + Af :

Plastic section modulus if Ap + Aw1 < Aw2 + Af :

369

0

10923.41.3991485020

10387.2 mmztht

IW

ewgfg

Geeo ⋅=

−++⋅

=−++

=

369

0

10982.51.39910387.2 mm

zI

We

Geeu ⋅=

⋅==

3610923.4),min( mmWWW eueoe ⋅==

Web areas:

Eccentricities (see figure):

21 0.215410

28.430

2mmt

hA wg

cew =⋅=⋅=

½ hce

Aw1½ hce

ht

e1

e3

Aw2

22 0.5990106.383

28.430

2mmth

hA wgt

cew =⋅⎟

⎠⎞

⎜⎝⎛ +=⋅⎟

⎠

⎞⎜⎝

⎛+=

mmt

AAAAe

wg

pwwf 9.494102

1.42450.59900.215460002

211 =

⋅−++

=⋅

−++=

mmt

AAAAe

wg

pwwf 5.279102

1.42450.59900.214560002

213 =

⋅−+−

=⋅

−+−=

⎪⎩

⎪⎨

⎧

+≤

+>+=

tc

tc

tc

hh

eife

hh

eifhh

e

2

222

33

23

2

2 mme 5.2792 =

36211 10719.8

22

422mm

hh

hAh

Aht

AtAWt

ce

wgwce

wwgfg

fpp ⋅=

⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛+

−⋅+⋅+⎟⎟⎠

⎞⎜⎜⎝

⎛+⋅+⋅=

( ) 3612

2

121

112 10392.62

22

222

mmeh

h

hAte

h

te

ehtAetAWt

ce

wgwwg

ce

wgwgfgfpp ⋅=

⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

−+

−⋅+⋅⎟⎠

⎞⎜⎝

⎛−

+⋅+−+⋅+⎟⎠⎞

⎜⎝⎛ +⋅=

362231 10259.4

2222mme

thhAeh

htAW fcetf

cepp ⋅=⎟⎟

⎠

⎞⎜⎜⎝

⎛−++⋅+⎟

⎠

⎞⎜⎝

⎛+Δ++⋅=

36

2

222

2132 10812.12

224

mmteh

h

te

ehh

AW wg

tce

wgce

wp ⋅=⋅⎟⎠

⎞⎜⎝

⎛−+

+⋅+⎟⎠

⎞⎜⎝

⎛+Δ+⋅=

36213 10070.6 mmWWW ppp ⋅=+=

DET NORSKE VERITAS


Plastic section modulus:

Ratio between plastic and elastic section modulus:

9.5.3 Mass

Mass from permanent loads and possible live loads (to be evaluated in each case):

Total mass:

9.5.4 Natural periodLinear Stiffness, Ref. Table 6-2 in Section 6.10:

Natural period assuming uniformly distributed mass (Klm,u istaken from Table 6-2):

Ratio of pulse load period versus natural period:

36

213

212

211

10070.6 mmAAAAifWAAAAifWAAAAifW

W

fwwpp

fwwpp

fwwpp

p ⋅=⎪⎩

⎪⎨

⎧

+<++>+++>

=

23.1=e

p

WW

Mass from plate:

Mass from stiffener, see figure:

Mass from girder:

mkgltwp 7.3517850200.314 =⋅⋅=⋅⋅= ρ

hws = 240-29= 211

tws = 10

bfs = 39

tfs = 29

23241293910211 mmtbthA fsfswswss =⋅+⋅=⋅+⋅=

mkg

slAw ss 8.101

80032007850

103241

6 =⋅⋅=⋅⋅= ρ

mkg

Aw Gg 1.147785010

1.187456

=⋅=⋅= ρ

mkgl

gp

w PPL 1.3263200.3

807.91010 3

=⋅⋅

=⋅=

mkg

wwwww PLgsp 7.38631.32631.1478.1017.351 =+++=++⋅+=

mN

mmN

LIE

k Gel

853

95

310114.110114.1

1200010387.2101.2384384

⋅=⋅=⋅⋅⋅⋅

=⋅⋅

=

sec113.010114.1

0.127.386377.0277.0228

, =⋅

⋅⋅⋅⋅=

⋅⋅⋅⋅=

⋅⋅⋅= πππ

ll

uulm

kLw

kMK

T

33.1113.015.0

==Ttd

DET NORSKE VERITAS


9.5.5 Ductility ratioThe maximum lateral deformation prior to buckling can be cal-culated according to equation 3.19 in sub-section 3.10.2:

where;dc is characteristic dimension for local buckling, i.e.2·(t+½hce+dh+e3) = 2·(14+½·430.8+35.6+279.5)= 1089mmc1 is 2 for clamped beamsκL is the smaller the distance from load to adjacent joint (0.5).Here set to 0.5·L, i.e. 6000

,and c is non-dimensional spring stiffness, ref Section 3.7;

knode is axial stiffness of the node with the considered memberremoved, here assumed infinitely.

Calculation of cross sectional slenderness factor, ref. Section3.10, i.e. the maximum of the following:Plate flange:

Bottom flange:

Web (bending):

Based on these input parameters, the maximum plastic defor-mation is calculated to:

The maximum elastic deformation is found from:

Ductility ratio:

9.5.6 Maximum blast pressure capacityFrom Figure 9-11, the dynamic load factor is found:

With reference to Figure 9-11, k3 was set to 0, which ensuresconservative results.

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

⎟⎟⎠

⎞⎜⎜⎝

⎛⋅

⋅

⋅⋅−−⋅

⋅=

2

31

1411

21

c

yf

fc

p

dL

c

fccd

w κβ

994.01066241

1066241

22

=⎟⎟⎠

⎞⎜⎜⎝

⎛

+=⎟⎟

⎠

⎞⎜⎜⎝

⎛

+=

ccc f

106624120001.18389420

1.40610873.7244 2921 =

⋅⋅⋅⋅⋅⋅

=⋅⋅

⋅⋅⋅=

lAfwkc

cey

c

9

520

10873.7

1.18745101.221

1011

1

211

1⋅=

⋅⋅⋅+

⋅

=

⋅⋅+

=

Gnode AEk

k

1.3961.1838910070.62.12.1 6

=⋅⋅

=⋅

=e

pc A

Ww

9.86420/23514/2.3033

/235/

3 ===y

e

ftl

β

2.60420/23520/3003

/235

/3 ===

y

fgfg

f

tbβ

9.90420/23510/8508.0

/235

/8.0 ===

y

wgwg

f

thβ

mmw p 37.3310896000

9.902420994.01411

994.021089 2

3 =⎟⎟

⎠

⎞

⎜⎜

⎝

⎛⎟⎠⎞

⎜⎝⎛⋅

⋅⋅⋅

−−⋅⋅

=

mmIELWf

wGe

eye 56.18

10387.2101.2321200010923.4420

32 95

262

=⋅⋅⋅⋅

⋅⋅⋅=

⋅⋅

⋅⋅=

Maximum elastic deformation:

p

L

12

2Lp

WfM eye

⋅=

⋅=

IELpwe ⋅

⋅⋅=

4

3841

IELWf

IELM

IELLpw ey

ee ⋅⋅

⋅⋅=

⋅⋅⋅=

⋅⋅

⋅⋅

⋅=3232

11212384

1 2222

80.156.1837.33

===e

p

ww

μ

99.0)( ==l

m

FR

DLF μ

DET NORSKE VERITAS


Figure 9-11Dynamic Response of a SDOF system due to a triangular pulse load profile (rise time = 0.50td)

Maximum resistance for a fixed supported beam, see Figure9-12:

Figure 9-12Moment diagram (elastic and fully plastic)

Resistance utilised in order to take the permanent and live load:

The maximum blast pressure capacity is obtained from the fol-lowing two equations:

The maximum blast pressure capacity is then:

Note that the maximum resistance (Rm) given above does notinclude a capacity check with respect to shear. The shearcapacity can be determined from sub-section 12.4.4 inNS3472-2001.

0.1

1

10

100

0.1 1 10

td/T

y max

/yel

= 1.1

Rel/Fmax= 0.8

= 1.0

= 0.9

= 1.2= 1.5

=0.1= 0.7

= 0.6= 0.5Rel/Fmax=0.05 = 0.3

yel y

R

Rel

FFmax

td0.50td

k1

k3 = 0.5k1 =0.2k1 =0.1k1k3 = 0k3 = 0.1k1

k3 = 0.2k1

k3 = 0.5k1

μ = 1.80

td/T = 1.33

kNNL

fWLM

R yppm 2.3399102.3399

1200042010070.6161616 3

6

=⋅=⋅⋅⋅

=⋅⋅

=⋅

=

Plastic

pP

Elastic

M = pL2/24

p

Rm = pPL = 16MP/L

M = pL2/12 MP = pPL2/16

MP = pPL2/16

LL

( ) ( ) kNNLlppLgwR lpg 3.593103.593122.31051012807.91.147 330 =⋅=⋅⋅⋅++⋅⋅=⋅⋅++⋅⋅=

LlpFandDLF

RRF lm

l ⋅⋅=−

= max0

)(μ

barMPaLlDLF

RRp m 74.0074.01200032001

99.010)3.5932.3399(1

)(

30

max ==⋅

⋅⋅−

=⋅

⋅−

=μ

DET NORSKE VERITAS

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