RECOMMENDED PRACTICE
DNVGL-RP-C204
Edition August 2017
Design against accidental loads
The electronic pdf version of this document, available free of charge
from http://www.dnvgl.com, is the officially binding version.
DNV GL AS
FOREWORD
DNV GL recommended practices contain sound engineering practice and guidance.
©
DNV GL AS August 2017
Any comments may be sent by e-mail to rules@dnvgl.com
This service document has been prepared based on available knowledge, technology and/or information at the time of issuance of this
document. The use of this document by others than DNV GL is at the user's sole risk. DNV GL does not accept any liability or responsibility
for loss or damages resulting from any use of this document.
General
This document supersedes the October 2010 edition of DNV-RP-C204.
The purpose of the revision of this service document is to comply with the new DNV GL document reference
code system and profile requirements following the merger between DNV and GL in 2013. Changes mainly
consist of updated company name and references to other documents within the DNV GL portfolio.
Some references in this service document may refer to documents in the DNV GL portfolio not yet published
(planned published within 2017). In such cases please see the relevant legacy DNV or GL document.
References to external documents (non-DNV GL) have not been updated.
Editorial corrections
In addition to the above stated changes, editorial corrections may have been made.
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Changes - current
CHANGES – CURRENT
Changes – current.................................................................................................. 3
Section 1 General.................................................................................................... 6
1.1 Introduction......................................................................................6
1.2 Application........................................................................................ 6
1.3 Objectives......................................................................................... 6
1.4 Normative references....................................................................... 6
1.5 Definitions.........................................................................................7
1.6 Symbols............................................................................................ 8
Section 2 Design philosophy................................................................................. 12
2.1 General........................................................................................... 12
2.2 Safety format..................................................................................12
2.3 Accidental loads..............................................................................13
2.4 Acceptance criteria......................................................................... 13
2.5 Analysis considerations.................................................................. 13
Section 3 Ship collisions....................................................................................... 15
3.1 General........................................................................................... 15
3.2 Design principles............................................................................ 15
3.3 Collision mechanics.........................................................................16
3.4 Dissipation of strain energy............................................................18
3.5 Ship collision forces........................................................................19
3.6 Force-deformation relationships for denting of tubular
members............................................................................................... 24
3.7 Force-deformation relationships for beams.................................... 25
3.8 Strength of connections..................................................................31
3.9 Strength of adjacent structure....................................................... 31
3.10 Ductility limits.............................................................................. 31
3.11 Resistance of large diameter, stiffened columns...........................36
3.12 Energy dissipation in floating production vessels......................... 38
3.13 Global integrity during impact...................................................... 38
Section 4 Dropped objects.................................................................................... 39
4.1 General........................................................................................... 39
4.2 Impact velocity............................................................................... 39
4.3 Dissipation of strain energy............................................................41
4.4 Resistance/energy dissipation........................................................ 42
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Contents
CONTENTS
Section 5 Fire........................................................................................................ 44
5.1 General........................................................................................... 44
5.2 General calculation methods...........................................................44
5.3 Material modelling.......................................................................... 44
5.4 Equivalent imperfections................................................................ 45
5.5 Empirical correction factor..............................................................45
5.6 Local cross sectional buckling........................................................ 45
5.7 Ductility limits................................................................................ 46
5.8 Capacity of connections.................................................................. 46
Section 6 Explosions............................................................................................. 47
6.1 General........................................................................................... 47
6.2 Classification of response............................................................... 47
6.3 Recommended analysis models for stiffened panels....................... 48
6.4 Single degree of freedom system analogy...................................... 50
6.5 Dynamic response charts for SDOF system.....................................55
6.6 Multi degree of freedom analysis....................................................55
6.7 Classification of resistance properties............................................ 56
6.8 Idealisation of resistance curves.................................................... 57
6.9 Resistance curves and transformation factors for plates................ 57
6.10 Resistance curves and transformation factors for beams............. 61
Section 7 References.............................................................................................73
7.1 References...................................................................................... 73
Section 8 Commentary.......................................................................................... 74
8.1 Commentary....................................................................................74
Section 9 Examples............................................................................................... 91
9.1 Design against ship collisions......................................................... 91
9.2 Design against explosions.............................................................. 93
9.3 Resistance curves and transformation factors................................ 95
9.4 Ductility limits................................................................................ 99
9.5 Design against explosions - girder............................................... 100
Changes – historic.............................................................................................. 113
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Contents
4.5 Limits for energy dissipation.......................................................... 43
SECTION 1 GENERAL
1.1 Introduction
This recommended practice deals with design to maintain the load-bearing function of the structures during
accidental events. The overall goal of the design against accidental loads is to achieve a system where the
main safety functions of the installation are not impaired.
The recommended practice has been developed for general world-wide application. Governmental legislation
may include requirements in excess of the provisions of this recommended practice depending on type,
location and intended service of the unit/installation.
The design accidental loads and associated performance criteria are given in DNVGL-OS-A101. The accidental
loads in this standard are prescriptive loads. This recommended practice may also be used in cases where
the design accidental loads are determined by a formal safety assessment (see DNVGL-OS-A101) or
quantified risk assessment (QRA).
The following main subjects are covered:
—
—
—
—
—
design philosophy
ship collisions
dropped objects
fire
explosions.
1.2 Application
The recommended practice is applicable to all types of floating and fixed offshore structures made of steel.
The methods described are relevant for both substructures and topside structures.
The document is limited to load-carrying structures and does not cover pressurised equipment.
1.3 Objectives
The objective with this recommended practice is to provide recommendations for design of structures
exposed to accidental events.
1.4 Normative references
The following standards include requirements which, through reference in the text constitute provisions
of this recommended practice. Latest issue of the references shall be used unless otherwise agreed.
Other recognised standards may be used provided it can be demonstrated that these meet or exceed the
requirements of the standards referenced below.
Any deviations, exceptions and modifications to the codes and standards shall be documented and agreed
between the supplier, purchaser and verifier, as applicable.
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1.4.1 DNV GL offshore standards (OS)
The latest revision of the following documents applies:
Table 1-1 DNV GL offshore standards
Document code
Title
DNVGL-OS-A101
Safety principles and arrangements
DNVGL-OS-C101
Design of offshore steel structures, general - LRFD method
DNVGL-OS-C102
Structural design of offshore ships
DNVGL-OS-C103
Structural design of column stabilised units - LRFD method
DNVGL-OS-C104
Structural design of self-elevating units - LRFD method
DNVGL-OS-C105
Structural design of TLPs - LRFD method
DNVGL-OS-C106
Structural design of deep draught floating units - LRFD method
DNVGL-OS-C301
Stability and watertight integrity
1.4.2 DNV GL recommended practices (RP)
The latest revision of the following documents applies:
Table 1-2 DNV GL recommended practices
Document code
Title
DNVGL-RP-C201
Buckling strength of plated structures
DNVGL-RP-C202
Buckling strength of shells
1.5 Definitions
Table 1-3 Definitions of terms
Term
Definition
accidental event
an undesired incident or condition which, in combination with other conditions (e.g.:
weather conditions, failure of safety barrier, etc.), determines the accidental effects
accidental effect
the result of an accidental event, expressed in 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, which results in effects that, the platform should be designed to
sustain
acceptance criteria
functional requirements, which are concerned with the platforms' resistance to accidental
effects
This should be in accordance with the authority's definition of acceptable safety levels.
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Term
Definition
active protection
operational loads and mechanical equipment which are brought into operation when an
accident is threatening or after the accident has occurred, in order to limit the probability
of the accident and the effects thereof, respectively
Some examples are safety valves, shut down systems, water drenching systems, working
procedures, drills for coping with accidents, etc.
passive protection
protection against damage by means of distance, location, strength and durability of
structural elements, insulation, etc.
event control
implementation of measures for reducing the probability and consequence of accidental
events, such as changes and improvements in equipment, working procedures, active
protection devices, arrangement of the platform, personnel training, etc.
indirect design
implementation of measures for improving structural ductility and resistance without
numerical calculations and determination of specific accidental effects.
direct design
determination of structural resistance, dimensions, etc. on basis of specific design
accidental effects
load
any action causing load effect in the structure
load-bearing structure
that part of the facility whose main function is to transfer loads
characteristic load
reference value of a load to be used in determination of load effects when using the
partial coefficient method or the allowable stress method
load effect
effect of a single load or combination of loads on the structure, such as stress, stress
resultant (internal force and moment), deformation, displacement, motion, etc.
resistance
capability of a structure or part of a structure to resist load effect
characteristic resistance
the nominal capacity that may be used for determination of design resistance of a
structure or structural element The characteristic value of resistance is to be based on a
defined percentile of the test results.
The characteristic value of resistance is to be based on a defined percentile of the test
results.
design life
the time period from commencement of construction until condemnation of the structure
limit state
a state where a criterion governing the load-carrying ability or use of the structure is
reached
1.6 Symbols
A
cross-sectional area
Ae
effective area of stiffener and effective plate flange
As
area of stiffener
Ap
projected cross-sectional area
Aw
shear area of stiffener/girder
B
width of contact area
CD
hydrodynamic drag coefficient
D
diameter of circular sections, plate stiffness
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E
Young's modulus of elasticity, (for steel 2.1#10 N/mm )
Ep
plastic modulus
Ekin
kinetic energy
Es
strain energy
F
lateral load, total load
G
shear modulus
H
non-dimensional plastic stiffness
I
moment of inertia, impulse
J
mass moment of inertia
Kl
load transformation factor
Km
mass transformation factor
Klm
load-mass transformation factor
L
girder length
M
total mass, cross-sectional moment
MP
plastic bending moment resistance
NP
plastic axial resistance
Sd
design load effect
T
fundamental period of vibration
N
axial force
NSd
design axial compressive force
NRd
design axial compressive capacity
NP
axial resistance of cross-section
R
resistance
RD
design resistance
R0
plastic collapse resistance in bending
V
volume, displacement
WP
plastic section modulus
W
elastic section modulus
a
added mass
as
added mass for ship
ai
added mass for installation
b
width of collision contact zone
bf
flange width
c
factor
cf
axial flexibility factor
clp
plastic zone length factor
5
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cs
shear factor for vibration eigenperiod
cQ
shear stiffness factor
cw
displacement factor for strain calculation
d
smaller diameter of threaded end of drill collar
dc
characteristic dimension for strain calculation
generalised load
fu
ultimate material tensile strength
fy
characteristic yield strength
g
acceleration of gravity, 9.81 m/s
hw
web height for stiffener/girder
i
radius of gyration
k
stiffness, characteristic stiffness, plate stiffness, factor
2
generalised stiffness
ke
equivalent stiffness
kl
bending stiffness in linear domain for beam
stiffness in linear domain including shear deformation
kQ
shear stiffness in linear domain for beam
temperature reduction of effective yield stress for maximum temperature in connection
plate length, beam length
m
distributed mass
ms
ship mass
mi
installation mass
meq
equivalent mass
generalised mass
p
explosion pressure
r
radius of deformed area, resistance
rc
plastic collapse resistance in bending for plate
rg
radius of gyration
s
distance, stiffener spacing
sc
characteristic distance
se
effective width of plate
t
thickness, time
td
duration of explosion
tf
flange thickness
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tw
web thickness
vs
velocity of ship
vi
velocity of installation
vt
terminal velocity
w
deformation, displacement
wc
characteristic deformation
wd
dent depth
non-dimensional deformation
x
axial coordinate
y
generalised displacement, displacement amplitude
yel
generalised displacement at elastic limit
z
distance from pivot point to collision point
zplast smaller distance from flange to plastic neutral axis
α
plate aspect parameter
β
cross-sectional slenderness factor
ε
yield strength factor, strain
εcr
critical strain for rupture
εy
yield strain
η
plate eigenperiod parameter
displacement shape function
reduced slenderness ratio
μ
ductility ratio
ν
Poisson's ratio, 0.3
θ
angle
ρ
density of steel, 7860 kg/m
ρw
density of sea water, 1025 kg/m
τ
shear stress
τcr
critical shear stress for plate plugging
ξ
interpolation factor
ψ
plate stiffness parameter
3
3
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SECTION 2 DESIGN PHILOSOPHY
2.1 General
The overall goal for the design of the structure against accidental loads is to prevent an incident to develop
into an accident disproportional to the original cause. This means that the main safety functions should not
be impaired by failure in the structure due to the design accidental loads. With the main safety functions is
understood:
— usability of escapeways
— integrity of shelter areas
— global load bearing capacity.
In this section the design procedure that is intended to fulfil this goal is presented.
The design against accidental loads may be done by direct calculation of the effects imposed on the
structure, or indirectly, by design of the structure as tolerable to accidents. Examples of the latter are
compartmentation of floating units which provides sufficient integrity to survive certain collision scenarios
without further calculations.
The inherent uncertainty of the frequency and magnitude of the accidental loads, as well as the approximate
nature of the methods for determination of accidental load effects, shall be recognised. It is therefore
essential to apply sound engineering judgement and pragmatic evaluations in the design.
Typical accidental events are:
—
—
—
—
ship collision
dropped objects
fire
explosion.
2.2 Safety format
The requirements to structures exposed for accidental loads are given in DNVGL-OS-C101.
The structure should be checked in two steps:
— First the structure will be checked for the loads to which it is exposed due to the accidental event
— Secondly in case the structural capacity towards ordinary loads is reduced as a result of the accident then
the strength of 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
accidental limit states (ALS). The requirement may be written as
(2.1)
Sd ≤ Rd
where:
Sd
=
design load effect
Rd
=
design resistance
Sk
=
characteristic load effect
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γf
=
partial factor for loads
R
=
characteristic resistance
γM
=
material factor.
For check of accidental limit states (ALS) the load and material factor should be taken as 1.0.
The failure criterion needs to be seen in conjunction with the assumptions made in the safety evaluations.
The limit states may need to be alternatively formulated to be on the form of energy formulation, as
acceptable deformation, or as usual on force or moment.
2.3 Accidental loads
The accidental loads are either prescriptive values or defined in a formal safety assessment. Prescriptive
values may be given by authorities, the owner or found in DNVGL-OS-A101.
Usually the simplification that accidental loads need not to be combined with environmental loads is valid.
For check of the residual strength in cases where the accident lead to reduced load carrying capacity in the
structure the check should be made with the characteristic environmental loads determined as the most
probable annual maximum value.
2.4 Acceptance criteria
Examples of failure criteria are:
— Critical deformation criteria defined by integrity of passive fire protection. To be considered for walls
resisting explosion pressure and shall serve as fire barrier after the explosion.
— Critical deflection for structures to avoid damage to process equipment (Riser, gas pipe, etc). To be
considered for structures or part of structures exposed to impact loads as ship collision, dropped object
etc.
— Critical deformation to avoid leakage of compartments. To be considered in case of impact against floating
structures where the acceptable collision damage is defined by the minimum number of undamaged
compartments to remain stable.
2.5 Analysis considerations
The mechanical response to accidental loads is generally concerned with energy dissipation, involving large
deformations and strains far beyond the elastic range. Hence, load effects (stresses forces, moments etc.)
obtained from elastic analysis and used in ultimate limit state (ULS) checks on component level are generally
not applicable, and plastic methods of analysis should be used.
Plastic analysis is most conveniently based upon the kinematical approach, taking into account the effect
of the strengthening (membrane tension) or softening (compression) caused by finite deformations, where
applicable.
The requirements in this RP are generally derived from plastic methods of analysis, including the effect of
finite deformations.
Plastic methods of analysis are valid for materials that can undergo considerable straining and during
this process exhibit considerable strain hardening. If the material is ductile as such, i.e. it can be strained
significantly, but has little strain hardening, the member tends to behave brittle in a global sense (i.e. with
respect to energy dissipation), and plastic methods should be used with great caution.
A further condition for application of plastic methods to members undergoing large, plastic rotations is
compact cross-sections; typically type I cross-sections (see DNVGL-OS-C101 ). The methods may also be
utilised for type II sections provided that the detrimental effect of local buckling is taken into account. Note
that for members subjected to significant tensile straining, the tendency for local buckling may be overridden
by membrane tension for large deformations.
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The straining, and hence the amount of energy dissipation, is limited by fracture. This key parameter is
associated with considerable uncertainty, with respect to both physical occurrence as well as modelling
in theoretical analysis. If good and validated models for prediction of fracture are not available, safe and
conservative assumptions for ductility limits should be adopted.
If non-linear, dynamic finite elements analysis is applied, it shall be verified that all behavioural effects and
local failure modes (e.g. strain rate, local buckling, joint overloading, and joint fracture) are accounted for
implicitly by the modelling adopted, or else subjected to explicit evaluation.
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SECTION 3 SHIP COLLISIONS
3.1 General
The requirements and methods given in this section have historically been developed for jackets. They are
generally valid also for jack-up type platforms, provided that the increased importance of global inertia
effects are accounted for. Column-stabilised platforms and floating production and storage vessels (FPSOs)
consist typically plane or curved, stiffened panels, for which methods for assessment of energy dissipation
in braced platforms (jackets and jack-ups) sometimes are not relevant. Procedures especially dedicated to
assessment of energy dissipation in stiffened plating are, however, also given based on equivalent beamcolumn models.
The ship collision load is characterised by a kinetic energy, governed by the mass of the ship, including
hydrodynamic added mass and the speed of the ship at the instant of impact. Depending upon the impact
conditions, a part of the kinetic energy may remain as kinetic energy after the impact. The remainder of the
kinetic energy has to be dissipated as strain energy in the installation and, possibly, in the vessel. Generally
this involves large plastic strains and significant structural damage to the installation, the ship or both. The
strain energy dissipation is estimated from force-deformation relationships for the installation and the ship,
where the deformations in the installation shall comply with ductility and stability requirements.
The load bearing function of the installation shall remain intact with the damages imposed by the ship
collision load. In addition, damaged condition should be checked if relevant, see [2.2].
The structural effects from ship collision may either be determined by non-linear dynamic finite element
analyses or by energy considerations combined with simple elastic-plastic methods.
If non-linear dynamic finite element analysis is applied all effects described in the following paragraphs
shall either be implicitly covered by the modelling adopted or subjected to special considerations, whenever
relevant.
Often the integrity of the installation can be verified by means of simple calculation models.
If simple calculation models are used the part of the collision energy that needs to be dissipated as strain
energy can be calculated by means of the principles of conservation of momentum and conservation of
energy, see [3.3].
It is convenient to consider the strain energy dissipation in the installation to take part on three different
levels:
— local cross-section
— component/sub-structure
— total system.
Interaction between the three levels of energy dissipation shall be considered.
Plastic modes of energy dissipation shall be considered for cross-sections and component/substructures in
direct contact with the ship. Elastic strain energy can in most cases be disregarded, but elastic axial flexibility
may have a substantial effect on the load-deformation relationships for components/sub-structures. Elastic
energy may contribute significantly on a global level.
3.2 Design principles
With respect to the distribution of strain energy dissipation there may be distinguished between, see Figure
3-1:
— strength design
— ductility design
— shared-energy design.
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Figure 3-1 Energy dissipation for strength, ductile and shared-energy design
Strength design implies that the installation is strong enough to resist the collision force with minor
deformation, so that the ship is forced to deform and dissipate the major part of the energy.
Ductility design implies that the installation undergoes large, plastic deformations and dissipates the major
part of the collision energy.
Shared energy design implies that both the installation and ship contribute significantly to the energy
dissipation.
From calculation point of view strength design or ductility design is favourable. In this case the response
of the soft structure can be calculated on the basis of simple considerations of the geometry of the rigid
structure. In shared energy design both the magnitude and distribution of the collision force depends upon
the deformation of both structures. This interaction makes the analysis more complex.
In most cases ductility or shared energy design is used. However, strength design may in some cases be
achievable with little increase in steel weight.
3.3 Collision mechanics
3.3.1 Strain energy dissipation
The collision energy to be dissipated as strain energy may - depending on the type of installation and the
purpose of the analysis - be taken as:
Compliant installations
(3.1)
Fixed installations
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(3.2)
Articulated columns
(3.3)
ms
as
vs
mi
ai
vi
J
z
= ship mass
= ship added mass
= impact speed
= mass of installation
= added mass of installation
= velocity of installation
= mass moment of inertia of installation (including added mass) with respect to effective pivot point
= distance from pivot point to point of contact.
In most cases the velocity of the installation can be disregarded, i.e. vi = 0.
The installation can be assumed compliant if the duration of impact is small compared to the fundamental
period of vibration of the installation. If the duration of impact is comparatively long, the installation can be
assumed fixed.
Floating platforms (semi-submersibles, TLP’s, production vessels) can normally be considered as compliant.
Jack-ups may be classified as fixed or compliant. Jacket structures can normally be considered as fixed.
3.3.2 Reaction force to deck
In the acceleration phase the inertia of the topside structure generates large reaction forces. An upper bound
of the maximum force between the collision zone and the deck for bottom supported installations may be
obtained by considering the platform compliant for the assessment of total strain energy dissipation and
assume the platform fixed at deck level when the collision response is evaluated.
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Figure 3-2 Model for assessment of reaction force to deck
3.4 Dissipation of strain energy
The structural response of the ship and installation can formally be represented as load-deformation
relationships as illustrated in Figure 3-3. The strain energy dissipated by the ship and installation equals the
total area under the load-deformation curves.
Figure 3-3 Dissipation of strain energy in ship and platform
(3.4)
As the load level is not known a priori an incremental procedure is generally needed.
The load-deformation relationships for the ship and the installation are often established independently of
each other assuming the other object infinitely rigid. This method may have, however, severe limitations;
both structures will dissipate some energy regardless of the relative strength.
Often the stronger of the ship and platform will experience less damage and the softer more damage than
what is predicted with the approach described above. As the softer structure deforms the impact force is
distributed over a larger contact area. Accordingly, the resistance of the strong structure increases. This may
be interpreted as an upward shift of the resistance curve for the stronger structure (refer Figure 3-3).
Care should be exercised that the load-deformation curves calculated are representative for the true,
interactive nature of the contact between the two structures.
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3.5 Ship collision forces
3.5.1 Recommended force-deformation relationships
Force-deformation relationships for supply vessels with a displacement of 5000 tons are given in Figure 3-4
for broad side -, bow-, stern end and stern corner impact for a vessel with stern roller.
The curves for broad side and stern end impacts are based upon penetration of an infinitely rigid, vertical
cylinder with a given diameter 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 of an infinitely rigid cylinder and may be used
for large diameter column impacts.
In lieu of more accurate calculations the curves in Figure 3-4 may be used for square-rounded columns.
The curve for bow impact is based upon collision with an infinitely rigid, plane wall and may be used for
large diameter column 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 jacket braces all energy shall normally be assumed
dissipated by the brace, refer Ch.8, Comm. 3.5.2.
For bow impacts against jacket braces, see [3.5.3].
For supply vessels and merchant vessels in the range of 2-5000 tons displacement, the force deformation
relationships given in Figure 3-5 may be used for impacts against jacket legs with diameter 1.5 m – 2.5 m.
Figure 3-4 Recommended deformation curve for beam, bow and stern impact
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Figure 3-5 Force deformation relationship for bow with and without bulb (2-5.000 dwt)
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Figure 3-6 Force deformation relationship for tanker bow impact app.(~ 125.000 dwt)
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Figure 3-7 Force deformation relationship and contact area for the bulbous bow of a VLCC (~
340.000 dwt)
Force-deformation relationships for tanker bow impact are given in Figure 3-6 for the bulbous part and the
superstructure, respectively, and for the bulb of a VLCC in Figure 3-7. The curves may be used provided that
the impacted structure (e.g. stern of floating production vessels) does not undergo substantial deformation
i.e. strength design requirements are complied with. If this condition is not met interaction between the bow
and the impacted structure shall be taken into consideration. Non-linear finite element methods or simplified
plastic analysis techniques of members subjected to axial crushing shall be employed, see Ch.7 /3/, /4/.
3.5.2 Force contact area for strength design of large diameter columns.
The basis for the curves in Figure 3-4 is strength design, i.e. limited local deformations of the installation at
the point of contact. In addition to resisting the total collision force, large diameter 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.
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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
3.0
0.35
1.65
6.4
0.20
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
5.6
0.9
0.5
7.5
2.0
1.1
10
If strength design is not aimed for - and in lieu of more accurate assessment (e.g. nonlinear finite element
analysis) - all strain energy has to be assumed dissipated by the column, corresponding to indentation by an
infinitely rigid stern corner.
3.5.3 Energy dissipation is ship bow
For typical supply vessels bows and bows of merchant vessels of similar size (i.e. 2-5000 tons displacement),
energy dissipation in ship bow may be taken into account provided that the collapse resistance in bending for
the brace, R0, see [3.7] is according to the values given in Table 3-3. The figures are valid for normal bows
without ice strengthening and for brace diameters < 1.25 m. The values should be used as step functions,
i.e. interpolation for intermediate resistance levels is not allowed. If contact location is not governed by
operation conditions, size of ship and platform etc., the values for arbitrary contact location shall be used.
(see also Ch.8, Comm. 3.5.3).
Table 3-3 Energy dissipation in bow versus brace resistance
Energy dissipation in bow
Contact location
if brace resistance R0
> 3 MN
> 6 MN
> 8 MN
> 10 MN
Above bulb
1 MJ
4 MJ
7 MJ
11 MJ
First deck
0 MJ
2 MJ
4 MJ
17 MJ
First deck - oblique brace
0 MJ
2 MJ
4 MJ
17 MJ
Between forcastle/first deck
1 MJ
5 MJ
10 MJ
15 MJ
Arbitrary location
0 MJ
2 MJ
4 MJ
11 MJ
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In addition, the brace cross-section must satisfy the following compactness requirement
(3.5)
where factor is the required resistance in [MN] given in Table 3-3.
See [3.6] for notation.
If the brace is designed to comply with these provisions, special care should be exercised that the joints and
adjacent structure is strong enough to support the reactions from the brace.
3.6 Force-deformation relationships for denting of tubular members
The contribution from local denting to energy dissipation is small for brace members in typical jackets and
should be neglected.
The resistance to indentation of unstiffened tubes may be taken from Figure 3-8. Alternatively, the resistance
may be calculated from Equation (3.6):
Figure 3-8 Resistance curve for local denting
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(3.6)
NSd
NRd
B
wd
= design axial compressive force
= design axial compressive resistance
= width of contactarea
= dent depth.
The curves are inaccurate for small indentation, and they should not be used to verify a design where the
dent damage is required to be less than wd / D > 0.05.
The width of contact area is in theory equal to the height of the vertical, plane section of the ship side that is
assumed to be in contact with the tubular member. For large widths, and depending on the relative rigidity
of the cross-section and the ship side, it may be unrealistic to assume that the tube is subjected to flattening
over the entire contact area. In lieu of more accurate calculations it is proposed that the width of contact
area 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 General
The response of a beam subjected to a collision load is initially governed by bending, which is affected by
and interacts with local denting under the load. The bending capacity is also reduced if local buckling takes
place on the compression side. As the beam undergoes finite deformations, the load carrying capacity may
increase considerably due to the development of membrane tension forces. This depends upon the ability of
adjacent structure to restrain the connections at the member ends to inward displacements. Provided that
the connections do not fail, the energy dissipation capacity is either limited by tension 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
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—
—
—
—
local buckling
strength of connections
strength of adjacent structure, and
fracture.
3.7.2 Plastic force-deformation relationships including elastic, axial
flexibility
Relatively small axial displacements have a significant influence on the development of tensile forces in
members undergoing large lateral deformations. An equivalent elastic, axial stiffness may be defined as
(3.7)
knode
= axial stiffness of the node with the considered member removed. This may be determined by
introducing unit loads in member axis direction at the end nodes 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:
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
c1 = 1
for pinned beams
characteristic deformation for tubular beams
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characteristic deformation for stiffened plating
WP
=
plastic section modulus
=
member length.
For non-central collisions the force-deformation relationship may be taken as the mean value of the forcedeformation curves for central collision with member half length equal to the smaller and the larger portion of
the member length, respectively.
For members where the plastic moment capacity of adjacent members is smaller than the moment capacity
of the impacted member the force-deformation relationship may be interpolated from the curves for pinned
ends and clamped ends:
For non-central collisions the force-deformation relationship may be taken as the mean value of the forcedeformation curves for central collision with member half length equal to the smaller and the larger portion of
the member length, respectively.
For members where the plastic moment capacity of adjacent members is smaller than the moment capacity
of the impacted member the force-deformation relationship may be interpolated from the curves for pinned
ends and clamped ends:
(3.8)
where:
(3.9)
=
plastic resistance by bending action of beam accounting for actual
bending resistance of adjacent members
(3.10)
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(3.11)
i
j
MPj,i
= adjacent member no i
= end number {1,2}
= Plastic bending resistance for member number i at App.end j.
Elastic, rotational flexibility of the node is normally of moderate significance.
Figure 3-9 Force deformation relationship for tubular beam with axial flexibility
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Figure 3-10 Force deformation relationship for stiffened plate with axial flexibility
3.7.3 Support capacity smaller than plastic bending moment of the beam
For beams where the plastic moment capacity of adjacent members is smaller than the moment capacity of
*
the impacted beam, the force-deformation relationship, R , may be derived from the resistance curve, R, for
beams where the plastic moment capacity of adjacent members is larger than the moment capacity of the
impacted beam ([3.7.2]), using the expression:
,
(3.12)
where:
R0
= plastic bending resistance with clamped ends (c1 = 2) – moment capacity of adjacent members
larger than the plastic bending moment of the beam
= plastic bending resistance - moment capacity of adjacent members at one or both ends smaller than
the plastic bending moment of the beam.
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(3.13)
(3.14)
= adjacent member no i
i
= end number {1,2}
j
MPj,i = Plastic bending resistance for member no. i
wlim = 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 = ∞,
tubular beams and
for
for stiffened plate.
3.7.4 Bending capacity of dented tubular members
The reduction in plastic moment capacity due to local denting shall be considered for members in
compression or moderate tension, but can be neglected for members entering the fully plastic membrane
state.
Conservatively, the flat part of the dented section according to the model shown in Figure 3-11 may be
assumed non-effective. This gives:
(3.15)
wd
= dent depth as defined in Figure 3-11.
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Figure 3-11 Reduction of moment capacity due to local dent
3.8 Strength of connections
Provided that large plastic strains can develop in the impacted member, the strength of the connections that
the member frames into should be checked.
The resistance of connections should be taken from ULS requirements in relevant standards.
For braces reaching the fully plastic tension state, the connection shall be checked for a load equal to the
axial capacity of the member. The design axial stress shall be assumed equal to the ultimate tensile strength
of the material.
If the axial force in a tension member becomes equal to the axial capacity of the connection, the connection
has to undergo gross deformations. The energy dissipation will be limited and rupture should be considered
at a given deformation. A safe approach is to assume failure (disconnection of the member) once the axial
force in the member reaches the axial capacity of the connection.
If the capacity of the connection is exceeded in compression and bending, this does not necessarily mean
failure of the member. The post-collapse strength of the connection may be taken into account provided that
such information is available.
3.9 Strength of adjacent structure
The strength of structural members adjacent to the impacted member/sub-structure must be checked to see
whether they can provide the support required by the assumed collapse mechanism. If the adjacent structure
fails, the collapse mechanism must be modified accordingly. Since, the physical behaviour becomes more
complex with mechanisms consisting of an increasing number of members it is recommended to consider a
design which involves as few members as possible for each collision scenario.
3.10 Ductility limits
3.10.1 General
The maximum energy that the impacted member can dissipate will – ultimately - be limited by local buckling
on the compressive side or fracture on the tensile side of cross-sections undergoing finite rotation.
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If the member is restrained against inward axial displacement, any local buckling must take place before the
tensile strain due to membrane elongation overrides the effect of rotation induced compressive strain.
If local buckling does not take place, fracture is assumed to occur when the tensile strain due to the
combined effect of rotation and membrane elongation exceeds a critical value.
To ensure that members with small axial restraint maintain moment capacity during significant plastic
rotation it is recommended that cross-sections be proportioned to section type I requirements, defined in
DNVGL-OS-C101 .
Initiation of local buckling does, however, not necessarily imply that the capacity with respect to energy
dissipation is exhausted, particularly for type I and type II cross-sections. The degradation of the crosssectional resistance in the post-buckling range may be taken into account provided that such information is
available, refer Ch.8, Comm. 3.10.1.
For members undergoing membrane stretching a lower bound to the post-buckling load-carrying capacity
may be obtained by using the load-deformation curve for pure membrane action.
3.10.2 Local buckling
Tubular cross-sections:
Buckling does not need to be considered for a beam with axial restraints if the following condition is fulfilled:
(3.16)
where:
(3.17)
axial flexibility factor
(3.18)
dc
= characteristic dimension
c1
= 2 for clamped ends
c
= non-dimensional spring stiffness, see [3.7.2].
κ
≤ 0.5
= D for circular cross-sections
= 1 for pinned ends
= the smaller distance from location of collision load to adjacent joint.
If this condition is not met, buckling may be assumed to occur when the lateral deformation exceeds
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(3.19)
For small axial restraint (c < 0.05) the critical deformation may be taken as
(3.20)
Stiffened plates/ I/H-profiles:
In lieu of more accurate calculations the expressions given for circular profiles in Equation (3.19) and
Equation (3.20) may be used with
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).
For flanges subjected to compression;
(3.21)
type I cross-sections
(3.22)
type II and type III cross-sections
For webs subjected to bending
(3.23)
type I cross-sections
(3.24)
type I and type III cross-sections
bf
tf
hw
tw
= flange width
= flange thickness
= web height
= web thickness.
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3.10.3 Tensile fracture
The degree of plastic deformation or critical strain at fracture will show a significant scatter and depends
upon the following factors:
—
—
—
—
material toughness
presence of defects
strain rate
presence of strain concentrations.
The critical strain for plastic deformations of sections containing defects need to be determined based
on fracture mechanics methods. Welds normally contain defects and welded joints are likely to achieve
lower toughness than the parent material. For these reasons structures that need to undergo large plastic
deformations should be designed in such a way that the plastic straining takes place outside the weld. In
ordinary full penetration welds, the overmatching weld material will ensure that minimal plastic straining
occurs in the welded joints even in cases with yielding of the gross cross section of the member. In such
situations, the critical strain will be in the parent material 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 strains as such. Therefore, strain levels should be
assessed by means of adequate analytic models of the strain distributions in the plastic zones or by nonlinear finite element analysis with a sufficiently detailed mesh in the plastic zones. (For information about
mesh size see Ch.8, Comm. 3.10.4.)
When structures are designed so that yielding take place in the parent material, the following value for
the critical average strain in axially loaded plate material may be used in conjunction with nonlinear finite
element analysis or simple plastic analysis
(3.25)
where:
t
= plate thickness
= length of plastic zone. Minimum 5t.
3.10.4 Tensile fracture in yield hinges
When the force deformation relationships for beams given in [3.7.2] are used rupture may be assumed to
occur when the deformation exceeds a value given by
(3.26)
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where the following factors are defined;
Displacement factor
(3.27)
plastic zone length factor
(3.28)
axial flexibility factor
(3.29)
non-dimensional plastic stiffness
(3.30)
c1
=
2 for clamped ends
=
1 for pinned ends
c
=
non-dimensional spring stiffness, see [3.7.2]
κ
≤
0.5
W
=
elastic section modulus
WP
=
plastic section modulus
εcr
=
critical strain for rupture (see Table 3-4 for recommended values)
=
yield strain
=
yield strength
fy
the smaller distance from location of collision load to adjacent joint
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fcr
=
strength corresponding to
εcr.
The characteristic dimension shall be taken as:
dc
=D
diameter of tubular beams
= 2hw
twice the web height for stiffened plates (se·t > As)
=h
height of cross-section for symmetric I-profiles
= 2 (h − zplast)
for unsymmetrical I-profiles
zplast = smaller distance from flange to plastic neutral axis of cross-section.
For small axial restraint (c < 0.05) the critical deformation may be taken as
(3.31)
The critical strain εcr and corresponding strength fcr should be selected so that idealised bi-linear stressstrain relation gives reasonable results, see Ch.8, Commentary. For typical steel material grades the following
values are proposed:
Table 3-4 Proposed values for εcr and H for different steel grades
Steel grade
εcr
H
S 235
20 %
0.0022
S 355
15 %
0.0034
S 460
10 %
0.0034
3.11 Resistance of large diameter, stiffened columns
3.11.1 General
Impact on a ring stiffener as well as midway between ring stiffeners shall be considered.
Plastic methods of analysis are generally applicable.
3.11.2 Longitudinal stiffeners
For ductile design the resistance of longitudinal stiffeners in the beam mode of deformation can be calculated
using the procedure described for stiffened plating, [3.7].
For strength design against stern corner impact, the plastic bending moment capacity of the longitudinal
stiffeners has to comply with the requirement given in Figure 3-12, on the assumption that the entire load
given in Table 3-1 is taken by one stiffener.
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Figure 3-12 Required bending capacity of longitudinal stiffeners
3.11.3 Ring stiffeners
In lieu of more accurate analysis the plastic collapse load of a ring-stiffener can be estimated from:
(3.32)
where:
= characteristic deformation of ring stiffener
D
MP
WP
Ae
= column radius
= plastic bending resistance of ring-stiffener including effective shell flange
= plastic section modulus of ring stiffener including effective shell flange
= area of ring stiffener including effective shell flange.
Effective flange of shell plating: Use effective flange of stiffened plates, see Sec.6.
For ductile design it can be assumed that the resistance of the ring stiffener is constant and equal to the
plastic collapse load, provided that requirements for stability of cross-sections are complied with, see
[3.10.2].
3.11.4 Decks and bulkheads
Calculation of energy dissipation in decks and bulkheads has to be based upon recognised methods for plastic
analysis of deep, axial crushing. It shall be documented that the collapse mechanisms assumed yield a
realistic representation of the true deformation field.
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3.12 Energy dissipation in floating production vessels
For strength design the side or stern shall resist crushing force of the bow of the off-take tanker. In lieu of
more accurate calculations the force-deformation curve given in [3.5.2] may be applied. (See Sec.8, Comm.
3.12 on strength design of stern structure)
For ductile design the resistance of stiffened plating in the beam mode of deformation can be calculated using
the procedure described in [3.7.2]. (See Sec.8, Comm. 3.12 on resistance of stiffened plating)
3.13 Global integrity during impact
Normally, it is unlikely that the installation will turn into a global collapse mechanism under direct collision
load, because the collision load is typically an order of magnitude smaller than the resultant design wave
force.
Linear analysis often suffices to check that global integrity is maintained.
The installation should be checked for the maximum collision force.
For installations responding predominantly statically the maximum collision force occurs at maximum
deformation.
For structures responding predominantly impulsively the maximum collision force occurs at small global
deformation of the platform. An upper bound to the collision force is to assume that the installation is fixed
with respect to global displacement. (e.g. jack-up fixed with respect to deck displacement).
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SECTION 4 DROPPED OBJECTS
4.1 General
The dropped object load is characterised by a kinetic energy, governed by the mass of the object, including
any hydrodynamic added mass, and the velocity of the object at the instantof impact. In most cases the
major part of the kinetic energy has to be dissipated as strain energy in the impacted component and,
possibly, in the dropped object. Generally, this involves large plastic strains and significant structural damage
to the impacted component. The strain energy dissipation is estimated from force-deformation relationships
for the component and the object, where the deformations in the component shall comply with ductility and
stability requirements.
The load bearing function of the installation shall remain intact with the damages imposed by the dropped
object load. In addition, damaged condition should be checked if relevant, see [2.2].
Dropped objects are rarely critical to the global integrity of the installation and will mostly cause local
damages. The major threat to global integrity is probably puncturing of buoyancy tanks, which could impair
the hydrostatic stability of floating installations. Puncturing of a single tank is normally covered by the
general requirements to compartmentation and watertight integrity given in DNVGL-OS-C301.
The structural effects from dropped objects may either be determined by non-linear dynamic finite element
analyses or by energy considerations combined with simple elastic-plastic methods as given in [4.2] - [4.5].
If non-linear dynamic finite element analysis is applied all effects described in the following paragraphs
shall either be implicitly covered by the modelling adopted or subjected to special considerations, whenever
relevant.
4.2 Impact velocity
The kinetic energy of a falling object is given by:
(4.1)
(in air)
and
(4.2)
(in water)v
a
= hydrodynamic added mass for considered motion
For impacts in air the velocity is given by
(4.3)
s
v
= travelled distance from drop point
= vo at sea surface.
For objects falling rectilinearly in water the velocity depends upon the reduction of speed during impact with
water and the falling distance relative to the characteristic distance for the object.
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Figure 4-1 Velocity profile for objects falling in water
The loss of momentum during impact with water is given by
(4.4)
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 in water is of drag type the velocity in water can be
taken from Figure 4-1 where:
=
terminal velocity for the object (drag force and buoyancy force balance
the gravity force)
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= characteristic distance
ρw
Cd
m
Ap
V
= density of sea water
= hydrodynamic drag coefficient for the object in the considered motion
= mass of object
= projected cross-sectional area of the object
= object displacement.
The major uncertainty is associated with calculating the loss of momentum during impact with sea surface,
given by Equation (4.4). However, if the travelled distance is such that the velocity is close to the terminal
velocity, the impact with sea surface is of little significance.
Typical terminal velocities for some typical objects are given in Table 4-1.
Table 4-1 Terminal velocities for objects falling in water
Item
Drill collar
Mass
[kN]
Terminal velocity
28
23-24
Winch,
250
Riser pump
100
BOP annular preventer
Mud pump
[m/s]
50
16
330
7
Rectilinear motion is likely for blunt objects and objects which do not rotate about their longitudinal axis.
Bar-like objects (e.g. pipes) which do not rotate about their longitudinal axis may execute lateral, damped
oscillatory motions as illustrated in Figure 4-1.
4.3 Dissipation of strain energy
The structural response of the dropped object and the impacted component can formally be represented as
load-deformation relationships as illustrated in Figure 4-2. The part of the impact energy dissipated as strain
energy equals the total area under the load-deformation curves.
(4.5)
As the load level is not known a priori an incremental approach is generally required.
Often the object can be assumed to be infinitely rigid (e.g. axial impact from pipes and massive objects) so
that all energy is to be dissipated by the impacted component.
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Figure 4-2 Dissipation of strain energy in dropped object and installation
If the object is assumed to be deformable, the interactive nature of the deformation of the two structures
should be recognised.
4.4 Resistance/energy dissipation
4.4.1 Stiffened plates subjected to drill collar impact
The energy dissipated in the plating subjected to drill collar impact is given by
(4.6)
where:
: stiffness of plate enclosed by hinge circle
fy = characteristic yield strength
R=
πdtτ = contact force for τ ≤τ cr see [4.5.1] for τ cr
= mass of plate enclosed by hinge circle
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m
= mass of dropped object
ρp
= mass density of steel plate
d
= smaller diameter at threaded end of drill collar
r
= smaller distance from the point of impact to the plate boundary defined by adjacent
stiffeners/girders, refer Figure 4-3.
For validity range of design formula reference is given to Ch.8, Comm. 4.4.1.
Figure 4-3 Definition of distance to plate boundary
4.4.2 Stiffeners/girders
In lieu of more accurate calculations stiffeners and girders subjected to impact with blunt objects may be
analysed with resistance models given in [6.10].
4.4.3 Dropped object
Calculation of energy dissipation in deformable dropped objects shall be based upon recognised methods
for plastic analysis. It shall be documented that the collapse mechanisms assumed yield a realistic
representation of the true deformation field.
4.5 Limits for energy dissipation
4.5.1 Pipes on plated structures
The maximum shear stress for plugging of plates due to drill collar impacts may be taken as
(4.7)
f u = ultimate material tensile strength.
4.5.2 Blunt objects
For stability of cross-sections and tensile fracture, see [3.10].
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SECTION 5 FIRE
5.1 General
The characteristic fire structural load is temperature rise in exposed members. The temporal and spatial
variation of temperature depends on the fire intensity, whether or not the structural members are fully or
partly engulfed by the flame and to what extent the members are insulated.
Structural steel expands at elevated temperatures and internal stresses are developed in redundant
structures. These stresses are most often of moderate significance with respect to global integrity. The
heating causes also progressive loss of strength and stiffness and is, in redundant structures, accompanied
by redistribution of forces from members with low strength to members that retain their load bearing
capacity. A substantial loss of load-bearing capacity of individual members and subassemblies may take
place, but the load bearing function of the installation shall remain intact during exposure to the fire load.
In addition, damaged condition should be checked if relevant, see [2.2].
Structural analysis may be performed on either:
— individual members
— subassemblies
— entire system.
The assessment of fire load effect and mechanical response shall be based on either:
— simple calculation methods applied to individual members
— general calculation methods
or a combination.
Simple calculation methods may give overly conservative results. General calculation methods are methods
in which engineering principles are applied in a realistic manner to specific applications.
Assessment of individual members by means of simple calculation methods should be based upon the
provisions given in Sec.7 /2/ Eurocode 3 Part 1.2. /2/ .
Assessment by means of general calculation methods shall satisfy the provisions given in Sec.7 /2/
Eurocode 3 Part1.2, Section 4.3.
In addition, the requirements given in this section for mechanical response analysis with nonlinear finite
element methods shall be complied with.
Assessment of ultimate strength is not needed if the maximum steel temperature is below 400°C, but
deformation criteria may have to be checked for impairment of main safety functions.
5.2 General calculation methods
Structural analysis methods for non-linear, ultimate strength assessment may be classified as
— stress-strain based methods
— stress-resultants based (yield/plastic hinge) methods.
Stress-strain based methods are methods where non-linear material behaviour is accounted for on fibre level.
Stress-resultants based methods are methods where non-linear material behaviour is accounted for on
stress-resultants level based upon closed form solutions/interaction equation for cross-sectional forces and
moments.
5.3 Material modelling
In stress-strain based analysis temperature dependent stress-strain relationships given in Sec.7 /2/
Eurocode 3, Part 1.2, Section 3.2 may be used.
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For stress resultants based design the temperature reduction of the elastic modulus may be taken as kE,θ
according to Sec.7 /2/ Eurocode 3. The yield stress may be taken equal to the effective yield stress, fy,θ. The
temperature reduction of the effective yield stress may be taken as ky,θ.
Provided that the above requirements are complied with creep does need explicit consideration.
5.4 Equivalent imperfections
To account for the effect of residual stresses and lateral distortions compressive members shall be modelled
with an initial, sinusoidal imperfection with amplitude given by
Elastic-perfectly plastic material model, refer Figure 6-4:
Elasto-plastic material models, refer Figure 6-4:
α
i
z0
WP
W
A
I
e*
= 0.5 for fire exposed members according to column curve c, Sec.7 /2/ Eurocode 3
= radius of gyration
= distance from neutral axis to extreme fibre of cross-section
= plastic section modulus
= elastic section modulus
= cross-sectional area
= moment of inertia
= amplitude of initial distortion
= member length.
The initial out-of-straightness should be applied on each physical member. If the member is modelled by
several finite elements the initial out-of-straightness should be applied as displaced nodes.
The initial out-of-straightness shall be applied in the same direction as the deformations caused by the
temperature gradients.
5.5 Empirical correction factor
The empirical correction factor of 1.2 should be accounted for in calculating the critical strength in
compression and bending for design according to Sec.7 /2/ Eurocode 3, refer Ch.8, Comm. A.5.5.
5.6 Local cross sectional buckling
If shell modelling is used, it shall be verified that the software and the modelling is capable of predicting local
buckling with sufficient accuracy. If necessary, local shell imperfections have to be introduced in a similar
manner to the approach adopted for lateral distortion of beams
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If beam modelling is used local cross-sectional buckling shall be given explicit consideration.
In lieu of more accurate analysis cross-sections subjected to plastic deformations shall satisfy compactness
requirements given in DNVGL-OS-C101:
Type I:
Type II:
Locations with plastic hinges (approximately full plastic utilization)
Locations with yield hinges (partial plastification).
If this criterion is not complied with explicit considerations shall be performed. The load-bearing capacity will
be reduced significantly after the onset of buckling, but may still be significant. A conservative approach is to
remove the member from further analysis.
Compactness requirements for type I and type I cross-sections may be disregarded provided that the
member is capable of developing significant membrane forces.
5.7 Ductility limits
5.7.1 General
The ductility of beams and connections increase at elevated temperatures compared to normal conditions.
Little information exists.
5.7.2 Beams in bending
In lieu of more accurate analysis requirements given in [3.10] shall be complied with.
5.7.3 Beams in tension
In lieu of more accurate analysis an average elongation of 3% of the member length with a reasonably
uniform temperature can be assumed.
Local temperature peaks may localise plastic strains. It is considered to be to the conservative side to use
critical strains for steel under normal temperatures. See [3.10] and [3.10.4].
5.8 Capacity of connections
In lieu of more accurate calculations the capacity of the connection can be taken as:
Rθ = ky,θ R0
where:
R0
ky,θ
= capacity of connection at normal temperature
= temperature reduction of effective yield stress for maximum temperature in connection.
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SECTION 6 EXPLOSIONS
6.1 General
Explosion loads are characterised by temporal and spatial pressure distribution. The most important temporal
parameters are rise time, maximum pressure and pulse duration.
For components and sub-structures the explosion pressure shall normally be considered uniformly
distributed. On global level the spatial distribution is normally non-uniform both with respect to pressure and
duration.
The response to explosion loads may either be determined by non-linear dynamic finite element analysis
or by simple calculation models based on single degree of freedom (SDOF) analogies and elastic-plastic
methods of analysis.
If non-linear dynamic finite element analysis is applied all effects described in the following paragraphs
shall either be implicitly covered by the modelling adopted or subjected to special considerations, whenever
relevant.
In the simple calculation models the component is transformed to a single spring-mass system exposed to an
equivalent load pulse by means of suitable shape functions for the displacements in the elastic and elasticplastic range. The shape functions allow calculation of the characteristic resistance curve and equivalent mass
in the elastic and elastic-plastic range as well as the fundamental period of vibration for the SDOF system in
the elastic range.
Provided that the temporal variation of the pressure can be assumed to be triangular, the maximum
displacement of the component can be calculated from design charts for the SDOF system as a function of
pressure duration versus fundamental period of vibration and equivalent load amplitude versus maximum
resistance in the elastic range. The maximum displacement must comply with ductility and stability
requirements for the component.
The load bearing function of the installation shall remain intact with the damages imposed by the explosion
loads. In addition, damaged condition should be checked if relevant, see [2.2].
6.2 Classification of response
The response of structural components can conveniently be classified into three categories according to the
duration of the explosion pressure pulse, td, relative to the fundamental period of vibration of the component,
T:
impulsive domain
td/T < 0.3
dynamic domain
0.3 < td/T < 3
quasi-static domain
3 < td/T.
Impulsive domain:
The response is governed by the impulse defined by
(6.1)
Hence, the structure may resist a very high peak pressure provided that the duration is sufficiently small. The
maximum deformation, wmax, of the component can be calculated iteratively from the equation
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(6.2)
where:
R(w) = force-deformation relationship for the component
meq = equivalent mass for the component.
Quasi-static-domain:
The response is governed by the peak pressure and the rise time of the pressure relative to the fundamental
period of vibration. If the rise time is small the maximum deformation of the component can be solved
iteratively from the equation:
(6.3)
If the rise time is large the maximum deformation can be solved from the static condition.
(6.4)
Dynamic domain:
The response has to be solved from numerical integration of the dynamic equations of equilibrium.
6.3 Recommended analysis models for stiffened panels
Various failure modes for a stiffened panel are illustrated in Figure 6-1. Suggested analysis model and
reference to applicable resistance functions are listed in Table 6-1. application of a SDOF model in the
analysis of stiffeners/girders with effective flange is implicitly based on the assumption that dynamic
interaction between the plate flange and the profile can be neglected.
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Figure 6-1 Failure modes for two-way stiffened panel
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Table 6-1 Analysis models
Simplified
analysis
model
Resistance models
Elastic-plastic deformation of
plate
SDOF
Section [6.9]
Stiffener plastic
SDOF
Stiffener: Section
[6.10.1]-[6.10.2].
Failure mode
– plate elastic
Stiffener plastic
SDOF
SDOF
SDOF
– stiffener elastic
– plate plastic
Girder and stiffener plastic
Stiffener: Section
[6.10.1]-[6.10.2].
Effective width of plate at mid span.
Elastic, effective flange of plate at ends.
Plate: Section [6.9]
– stiffener and plating elastic
Girder plastic
Elastic, effective flange of plate
Plate: Section [6.9.1]
– plate plastic
Girder plastic
Comment
MDOF
– plate elastic
Girder: Section
[6.10.1]-[6.10.2]
Plate: Section [6.9]
Elastic, effective flange of plate with
concentrated loads (stiffener reactions).
Stiffener mass included.
Girder: Section
[6.10.1]-[6.10.2]
Effective width of plate at girder mid span
and ends.
Plate: Section [6.9]
Stiffener mass included
Girder and stiffener:
Dynamic reactions of stiffeners
Section
[6.10.1]-[6.10.2]
→ loading for girders
Plate: Section [6.9]
Girder and stiffener plastic
– plate plastic
MDOF
Girder and stiffener:
Dynamic reactions of stiffeners
Section
[6.10.1]-[6.10.2]
→ loading for girders
Plate: Section [6.9]
By girder/stiffener plastic is understood that the maximum displacement wmax exceeds the elastic limit wel
6.4 Single degree of freedom system analogy
Biggs method:
For many practical design problems it is convenient to assume that the structure - exposed to the dynamic
pressure pulse - ultimately attains a deformed configuration comparable to the static deformation pattern.
Using the static deformation pattern as displacement shape function, i.e.
the dynamic equations of equilibrium can be transformed to an equivalent single degree of freedom system:
(6.5)
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φ(x)
= displacement shape function
y(t)
= displacement amplitude
= generalized mass
= generalized load
= generalized elastic bending stiffness
= generalized plastic bending stiffness
(fully developed mechanism)
= generalized membrane stiffness
(fully plastic: N = NP)
m
= distributed mass
Mi
= concentrated mass
q
= explosion load
Fi
= concentrated load (e.g. support reactions)
xi
= position of concentrated mass/load.
The equilibrium equation can alternatively be expressed as:
(6.6)
where:
= load-mass transformation factor for uniform mass
= load-mass transformation factor for concentrated mass
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= mass transformation factor for uniform mass
= mass transformation factor for concentrated mass
= 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.
The natural period of vibration for the equivalent system in the linear resistance domain is given by
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(6.7)
The response, y(t), is - in addition to the load history - entirely governed by the total mass, load-mass factor
and the characteristic stiffness.
For a linear system, the load mass factor and the characteristic stiffness are constant k = k1. The response is
then alternatively governed by the eigenperiod and the characteristic stiffness.
For a non-linear system, the load-mass factor and the characteristic stiffness depend on the response
(deformations). Non-linear systems may often conveniently be approximated by equivalent bi-linear or
tri-linear systems, see [6.8]. In such cases the response can be expressed in terms of (see Figure 6-6 for
definitions):
k1
yel
T
= characteristic stiffness in the initial, linear resistance domain
= displacement at the end of the initial, linear resistance domain
= eigenperiod in the initial, linear resistance domain
and, if relevant,
k3
= normalised characteristic resistance in the third linear resistance domain.
Characteristic stiffness is given explicitly or can be derived from load-deformation relationships given in
[6.10]. If the response is governed by different mechanical behaviour relevant characteristic stiffness must
be calculated.
For a given explosion load history the maximum displacement, ymax, is found by analytical or numerical
integration of Equation (6.6).
For standard load histories and standard resistance curves maximum displacements can be presented in
design charts. Figure 6-2 shows the normalised maximum displacement of a SDOF system with a bi- (k3 = 0)
or tri-linear (k3 > 0) resistance function, exposed to a triangular pressure pulse with zero rise time. When the
duration of the pressure pulse relative to the eigenperiod in the initial, linear resistance range is known, the
maximum displacement can be determined directly from the diagram as illustrated in Figure 6-2.
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Figure 6-2 Maximum 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 resistance curves subjected to a triangular pressure pulse with
0.5 td rise time is given in Figure 6-3. Curves for different rise times are given in Sec.8, Commentary Figure
8-15 to Figure 8-17.
Baker's method
The governing Equations (6.1) and Equation (6.2) for the maximum response in the impulsive domain and
the quasi-static domain may also be used along with response charts for maximum displacement for different
Fmax/Rel ratios to produce pressure-impulse (Fmax, I) diagrams - iso-damage curves - provided that the
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
histories and eliminate those that obviously lie in the admissible domain. This will reduce the need for large
complex simulation of explosion scenarios.
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6.5 Dynamic response charts for SDOF system
Transformation factors for elastic–plastic-membrane deformation of beams and one-way slabs with different
boundary conditions are given in Table 6-2.
Maximum displacement for a SDOF system exposed to a triangular pressure pulse with rise time of 0.5td is
displayed in Figure 6-3. Maximum displacement for a SDOF system exposed to different pressure pulses are
given in Sec.8, Commentary Figure 8-15 to Figure 8-17.
The characteristic response of the system is based upon the resistance in the linear range, k = k1, where the
equivalent stiffness is determined from the elastic solution to the actual system.
Figure 6-3 Dynamic response of a SDOF system to a triangular load (rise time = 0.50 td)
6.6 Multi degree of freedom analysis
SDOF analysis of built-up structures (e.g. stiffeners supported by girders) is admissible if
— the fundamental periods of elastic vibration are sufficiently separated
— the response of the component with the smallest eigenperiod does not enter the elastic-plastic domain so
that the period is drastically increased.
If these conditions are not met, then significant interaction between the different vibration modes is
anticipated and a multi degree of freedom analysis is required with simultaneous time integration of the
coupled system.
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6.7 Classification of resistance properties
6.7.1 Cross-sectional behaviour
Figure 6-4 Bending moment-curvature relationships
Elasto-plastic : The effect of partial yielding on bending moment is accounted for
Elastic-perfectly plastic: Linear elastic up to fully plastic bending moment
The simple models described herein assume elastic-perfectly plastic material behaviour.
Note: Even if the analysis is based upon elastic-perfectly plastic behaviour, the material has to exhibit strain
hardening in practice for the theory to be valid. The effect of strain hardening on the plastic, cross-sectional
resistances may be accounted for by using an equivalent (increased) yield stress. If this is considered
relevant, and the material is utilised beyond ultimate strain, it is often justified to use an equivalent yield
stress equal to the mean of the lower yield stress and the ultimate stress.
In the clauses for the ductility limits the effect of strain hardening is accounted for.
Component behaviour
Figure 6-5 Resistance curves
Elastic: Elastic material, small deformations
Elastic-plastic (determinate): Elastic-perfectly plastic material. Statically determinate system. Bending
mechanism fully developed with occurrence of first plastic hinge(s)/yield lines. No axial restraint.
Elastic-plastic (indeterminate): Elastic perfectly plastic material. Statically indeterminate system. Bending
mechanism develops with sequential formation of plastic hinges/yield lines. No axial restraint. For simplified
analysis this system may be modelled as an elastic-plastic (determinate) system with equivalent initial
stiffness. In lieu of more accurate analysis the equivalent stiffness should be determined such that the area
under the resistance curve is preserved.
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Elastic-plastic with membrane: Elastic-perfectly plastic material. Statically determinate (or indeterminate).
Ends restrained against axial displacement. Increase in load-carrying capacity caused by development of
membrane forces.
6.8 Idealisation of resistance curves
The resistance curves in 6.7 are idealised. For simplified SDOF analysis the resistance characteristics of a real
non-linear system may be approximately modelled. An example with a tri-linear approximation is illustrated
in Figure 6-6. The stiffness in the k3 phase may have some contribution from strain hardening, but in most
cases the predominant effect is development of membrane forces when member ends are restrained form
inward displacement.
Figure 6-6 Representation of a non-linear resistance by an equivalent tri-linear system
In lieu of more accurate analysis the resistance curve of elastic-plastic systems may be composed by an
elastic resistance and a rigid-plastic resistance as illustrated in Figure 6-7.
Figure 6-7 Construction of elastic -plastic resistance curve
6.9 Resistance curves and transformation factors for plates
6.9.1 Elastic - rigid plastic relationships
In lieu of more accurate calculations rigid plastic theory combined with elastic theory may be used.
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In the elastic range the stiffness and fundamental period of vibration of a clamped plate under uniform lateral
pressure can be expressed as:
r = k1w
= resistance-displacement relationship for plate centre
= plate stiffness
= natural period of vibration
= plate bending stiffness.
The factors
ψ and η are given in Figure 6-8.
Figure 6-8 Coefficients ψ and η.
In the plastic range the resistance (r) of plates with edges fully restrained against inward displacement and
subjected to uniform pressure can be taken as:
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(6.8)
Pinned ends:
Clamped ends:
= plate aspect parameter
l (>s)
s
t
rc
= plate length
= plate width
= plate thickness
= plastic resistance in bending for plates with no axial restraint
= non-dimensional displacement parameter.
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Figure 6-9 Plastic load-carrying capacities of plates as a function of lateral displacement
6.9.2 Axial restraint
In Equation (6.8) the beneficial effect of membrane stiffening is represented by the term containing the nondimensional displacement parameter
. Great caution should be exercised when assuming the presence of
the membrane effect, because the membrane forces must be anchored in the adjacent structure. For plates
located in the middle of a continuous plate field, the boundaries have often considerable restraint against
pull-in. If the plate is located close to the boundary, the edges are often not sufficiently stiffened to prevent
pull-in of edges.
Unlike stiffeners no simple method with a clear physical interpretation exists to quantify the effect of
flexibility on the resistance of plates under uniform pressure. In the formulations used in this RP the flexibility
may be split into two contributions:
1)
2)
pull-in of edges
elastic straining of the plate.
The effect of flexibility may be taken into account in an approximate way by means of plate strip theory
and the procedure described in [3.7.2]. The relative reduction of the plate’s plastic resistance, with respect
to the values given in Equation (6.8), is taken equal to the relative reduction of the resistance for a beam
with rectangular cross-section (plate thickness x unit width) and length equal to stiffener spacing, using
nd
the diagram for α = 2 (Figure 6-12). The elastic straining of the plate is accounted for by the 2 term in
Equation (6.8). In lieu of more accurate calculation, the effect of pull-in, given by the first term in Equation
(6.8) may be estimated by removing the plate and apply a uniformly distributed unit in-plane force normal to
the plate edges. The axial stiffness should be taken as the inverse of the maximum in-plane displacement of
the long edge.
In lieu of more accurate calculation, it should be conservatively assumed that no membrane effects exist for
a plate located close to an unsupported boundary, i.e. the resistance should be taken as constant and equal
to the resistance in bending, r = rc over the allowable displacement range.
In lieu of more accurate calculations, it is suggested to assess the relative reduction of the resistance for a
uniformly loaded plate located some distance from an unsupported boundary with c = 1.0.
If membrane forces are taken into account it must be verified that the adjacent structure is strong enough to
anchor the fully plastic membrane tension forces.
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6.9.3 Tensile fracture of yield hinges
In lieu of more accurate calculations the procedure described in [3.10.4] may be used for a beam with
rectangular cross-section (plate thickness x unit width) and length equal to stiffener spacing.
6.10 Resistance curves and transformation factors for beams
Provided that the stiffeners/girders remain stable against local buckling, tripping or lateral torsional buckling
stiffened plates/girders may be treated as beams. Simple elastic-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
fracture.
6.10.1 Beams with no- or full axial restraint
Equivalent springs and transformation factors for load and mass for various idealised elasto-plastic systems
are shown in Table 6-2. For more than two concentrated loads, equal in magnitude and spacing, use values
for uniform loading.
Shear deformation may have a significant impact on the elastic flexibility and eigenperiod of beams and
girders with a short span/web height ratio (L/hw), notably for clamped ends. The eigenperiod and stiffness in
the linear domain including shear deformation may be calculated as:
(6.9)
and
(6.10)
where:
cs
= 1.0 for both ends simply supported
= 1.25 for one end clamped and one end simply supported
= 1.5 for both ends clamped
L
E
G
A
= length of beam/girder
= elastic modulus
= shear modulus
= total cross-sectional area of beam/girder
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Aw
kQ
k1
rg
Mps
Mpm
= shear area of beam/girder
= shear stiffness for beam/girder
= bending stiffness of beam/girder in the linear domain according to Table 6-2
= radius of gyration
= plastic bending capacity of beam at support
= plastic bending capacity of beam at midspan
and regardless of rotational boundary conditions the following values 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 increasingly inaccurate for loads with short duration
and/or high magnitudes.
Table 6-2 Transformation factors for beams with various boundary and load conditions
Mass factor
Load-mass factor
Km
Klm
Load
Load case
Resistance
Factor
domain
Kl
ConcenConcenUniform
trated
trated
mass
mass
mass
Elastic
0.64
0.50
0.78
Plastic
bending
0.50
0.33
0.66
Plastic
membrane
0.50
0.33
0.66
Uniform
mass
Elastic
1.0
1.0
0.49
1.0
0.49
Plastic
bending
1.0
1.0
0.33
1.0
0.33
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Maximum
resistance
Linear
stiffness
Rel
k1
Dynamic reaction
V
0
0
Page 62
Mass factor
Load-mass factor
Km
Klm
Load
Load case
Resistance
Factor
domain
Kl
Plastic
membrane
ConcenConcenUniform
trated
trated
mass
mass
mass
1.0
0.33
1.0
0.33
0.87
0.76
0.52
0.87
0.60
Plastic
bending
1.0
1.0
0.56
1.0
0.56
Plastic
membrane
1.0
1.0
0.56
1.0
0.56
Loadmass factor
Mass factor
Load case
Load
Km
Resistance
Factor
domain
Kl
Elastic
0.53
0.41
0.77
Elastoplastic
bending
0.64
0.50
0.78
Plastic
bending
0.50
0.33
0.66
Plastic
membrane
0.50
0.33
0.66
Concentrated
mass
Klm
Uniform
mass
ConcenUniform
trated
mass
mass
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Linear
stiffness
Rel
k1
Uniform
mass
1.0
Elastic
Maximum
resistance
Dynamic reaction
V
0
Maximum Linear
resistance stiffness
Rel
k1
Equivalent
linear
stiffness
ke
Dynamic
reaction
V
0
Page 63
Loadmass factor
Mass factor
Load case
Load
Km
Resistance
Factor
domain
Kl
Concentrated
mass
Uniform
mass
Elastic
1.0
1.0
0.37
1.0
0.37
Plastic
bending
1.0
1.0
0.33
1.0
0.33
Plastic
membrane
1.0
1.0
0.33
1.0
0.33
Elastic
080
0.64
0.41
0.80
0.51
Elastoplastic
bending
0.87
0.76
0.52
0.87
0.60
Plastic
bending
1.0
1.0
0.56
1.0
0.56
Plastic
membrane
1.0
1.0
0.56
1.0
0.56
Elastic
0.58
0.45
0.78
Elastoplastic
bending
0.64
0.50
0.78
Klm
ConcenUniform
trated
mass
mass
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Maximum Linear
resistance stiffness
Rel
k1
Equivalent
linear
stiffness
ke
Dynamic
reaction
V
0
0
Page 64
Loadmass factor
Mass factor
Load case
Load
Km
Resistance
Factor
domain
Kl
Plastic
bending
0.50
Plastic
membrane
0.50
0.33
Elastic
1.0
1.0
0.43
1.0
0.43
Elastoplastic
bending
1.0
1.0
0.49
1.0
0.49
Plastic
bending
1.0
1.0
0.33
1.0
0.33
Plastic
membrane
1.0
1.0
0.33
1.0
0.33
Elastic
0.81
0.67
0.45
0.83
0.55
Elastoplastic
bending
0.87
0.76
0.52
0.87
0.60
Concentrated
mass
Klm
Uniform
mass
ConcenUniform
trated
mass
mass
0.33
0.66
Maximum Linear
resistance stiffness
Rel
k1
Equivalent
linear
stiffness
ke
Dynamic
reaction
V
0
0.66
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0
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Loadmass factor
Mass factor
Load case
Load
Km
Resistance
Factor
domain
Kl
Concentrated
mass
Uniform
mass
Plastic
bending
1.0
1.0
0.56
1.0
0.56
Plastic
membrane
1.0
1.0
0.56
1.0
0.56
Klm
ConcenUniform
trated
mass
mass
Maximum Linear
resistance stiffness
Rel
k1
Equivalent
linear
stiffness
ke
Dynamic
reaction
V
0
Where:
q
= explosion load per unit length
= ps for stiffeners
= p
for girders.
m1, m2 and m3 are factors for deriving the equivalent stiffness:
6.10.2 Beams with partial end restraint
Relatively small axial displacements have a significant influence on the development of tensile forces in
members undergoing large lateral deformations. Equivalent elastic, axial stiffness may be defined as
(6.11)
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knode = axial stiffness of the node with the considered member removed. This may be determined by
introducing unit loads in member axis direction at the end nodes with the member removed.
Plastic force-deformation relationship for a beam under uniform pressure may be obtained from Figure
6-10, Figure 6-11 or Figure 6-12 if the plastic interaction between axial force and bending moment can be
approximated by the following equation:
(6.12)
α = 1.2 can be assumed for stiffened plates and H or I beams. For members
with tubular section α = 1.5. For rectangular sections and plates α = 2.0 can be assumed.
In lieu of more accurate analysis
= plastic collapse resistance in bending for the member with uniform load.
= member length
= non-dimensional deformation
=
characteristic beam height for beams described by plastic interaction Equation
(6.12).
= non-dimensional spring stiffness
c1 = 2
= for clamped beams
c1 = 1
= for pinned beams
WP
= plastic section modulus for the cross-section of the beam
Wp = zgAg
= plastic section modulus for stiffened plate for set > As
A = As + st
= total area of stiffener and plate flange
Ae = As + set
= effective cross-sectional area of stiffener and plate flange,
zg
= distance from plate flange to stiffener centre of gravity.
As
= stiffener area
s
= stiffener spacing
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se
= effective width of plate flange see [6.10.4].
Figure 6-10 Plastic load-deformation relationship for beam with axial flexibility (α = 1.2)
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Figure 6-11 Plastic load-deformation relationship for beam with axial flexibility (α = 1.5)
Figure 6-12 Plastic load-deformation relationship for beam with axial flexibility (α = 2)
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For members where the plastic moment capacity of adjacent members is smaller than the moment capacity
of the exposed member the force-deformation relationship may be interpolated from the curves for pinned
ends and clamped ends:
(6.13)
where:
(6.14)
= collapse load in bending for beam accounting for actual bending resistance of adjacent
members
(6.15)
(6.16)
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 moderate significance.
6.10.3 Beams with partial end restraint - support capacity smaller than
plastic bending moment of member
For beams where the plastic moment capacity of adjacent members is smaller than the moment capacity of
the impacted beam, the force-deformation relationship, R*, may be derived from the resistance curve, R, for
beams where the plastic moment capacity of adjacent members is larger than the moment capacity of the
impacted beam ([3.7.2]), using the expression:
(6.17)
,
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,
where:
R0
= plastic bending resistance with clamped ends (c1 = 2) – moment capacity of adjacent members
larger than the plastic bending moment of the beam
= plastic bending resistance - moment capacity of adjacent members at one or both ends smaller than
the plastic bending moment of the member
(6.18)
(6.19)
i
j
MPj,i
= adjacent member no i
wlim
= 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 = ∞,
= end number {1,2}
= plastic bending resistance for member no. i.
for tubular beams and for stiffened plate.
6.10.4 Effective flange
In order to analyse stiffened plate as a beam the effective width of the plate between stiffeners need to be
determined. The effective width needs to be reduced due to buckling and/or shear lag.
Shear lag effects may be neglected if the length is more than 2.5 times the width between stiffeners. For
guidance see Ch.8, Commentary.
Determination of effective flange due to buckling can be made as for buckling of stiffened plates see DNVGLRP-C201.
The effective width for elastic deformations may be used when the plate flange is on the tension side.
In most cases the flange will experience varying stress with parts in compression and parts in tension. It
may be unduly conservative to use the effective width for the section with the largest compression stress to
be valid for the whole member length. For continuous stiffeners it will be reasonable to use the mean value
between effective width at the section with the largest compression stress and the full width. For simple
supported stiffeners with compression in the plate it is judged to be reasonable to use the effective width at
midspan for the total length of the stiffener.
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6.10.5 Strength of adjacent structure
The adjacent structure must be checked to see whether it can provide the support required by the assumed
collapse mechanism for the member/sub-structure
6.10.6 Strength of connections
The capacity of connections can be taken from recognised codes.
The connection shall be checked for the dynamic reaction force given in Table 6-2.
For beams with axial restraint the connection should also be checked for lateral - and axial reaction in the
membrane phase:
— If the axial force in a tension member exceeds the axial capacity of the connection the member should be
assumed disconnected.
— If the capacity of the connection is exceeded in compression and bending, this does not necessarily mean
failure of the member. The post-collapse strength of the connection may be taken into account provided
that such information is available.
6.10.7 Ductility limits
See [3.10].
The local buckling criterion in [3.10.2] and tensile fracture criterion given in [3.10.3] may be used with:
dc
= characteristic dimension equal to twice the distance from the plastic neutral axis in bending to the
extreme fibre of the cross-section
c
= non-dimensional axial spring stiffness calculated in [6.10.2].
Alternatively, the ductility ratios
Table 6-3 Ductility ratios
Boundary
conditions
in Table 6-3 may be used.
μ - beams with no axial restraint
Cross-section type
Load
1)
Type I
Type II
Type III
Cantilevered
Concentrated distributed
67
45
22
Pinned
Concentrated distributed
6 12
48
23
Fixed
Concentrated distributed
64
43
22
1)
Cross-section types are defined in DNVGL-OS-C101.
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SECTION 7 REFERENCES
7.1 References
/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,
Norwegian 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 Collision 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 Collision with Jacket Legs, ISOPE, Stavanger, 2001.
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SECTION 8 COMMENTARY
8.1 Commentary
Comm. 2.3 General
The structural design is seen as having acceptable safety against accidental loads when the design accidental
loads are less than the design resistance. This is similar to the check of the structure for ordinary loads
but with the following differences: As ordinary loads are either permanent or occur frequent it will not
be acceptable that the load lead to reduced load carrying capacity while the short duration and the low
probability of accidental loads make this an acceptable assumptions. E.g. a blast wall need not be capable of
resisting another explosion after a blast, but if the wall is used as a fire barrier it need to serve as such after
the blast.
Comm. 3.1 General
For typical installations, the contribution to energy dissipation from elastic deformation of component/
substructures in direct contact with the ship is very small and can normally be neglected. Consequently,
plastic methods of analysis apply.
However, elastic elongation of the hit member as well as axial flexibility of the nodes to which the member
is connected, have a significant impact on the development of membrane forces in the member. This effect
has to be taken into account in the analysis, which is otherwise based on plastic methods. The diagrams in
[3.7.2] are based on such an approach.
Depending on the structure size/configuration as well as the location of impact elastic strain energy over the
entire structure may contribute significantly.
Comm. 3.2 Design principles
The transition from essentially strength behaviour to ductile response can be very abrupt and sensitive to
minor changes in scantlings. E.g. integrated analyses of impact between the stern of a supply vessel and
a large diameter column have shown that with moderate change of (ring - and longitudinal) stiffener size
and/or spacing, the energy dissipation may shift from predominantly platform based to predominantly vessel
based. Due attention should be paid to this sensitivity when the calculation procedure described in [3.5] is
applied.
Comm. 3.3 Collision mechanics
The added mass is due to the hydrodynamic pressure induced by the forced motion of water particles on the
wet surface of the ship. By solving the velocity potential for the fluid on the body surface, the added mass is
determined by means of 2-D (strip theory) or 3-D techniques. The added mass is frequency dependent, and
thus varies with time during a collision, but a constant value is recommended for simple analysis.
The fraction of collision energy to be dissipated as strain energy for shuttle tanker impact on FPSO stern is
shown in Figure 8-1. Note the strong dependency of the mass ratio; the larger the mass of shuttle tanker, the
lesser of the collision energy must be dissipated as strain energy. (However, provided that the speed of the
shuttle tanker is constant, the absolute value of the strain energy increases)
The relative size may differ considerably for the approach phase (shuttle tanker in ballast, FPSO fully loaded)
and the departure phase (shuttle tanker fully loaded, FPSO in ballast). To illustrate this, possible values are
listed in Table 8-1. In this example both the FPSO and shuttle tanker are large compared to typical North
Sea conditions. The same added mass coefficient applies to both vessels. It is observed that the fraction of
energy to be dissipated as strain energy varies between 0.33 (departure) and 0.71 (approach). This indicates
that the approach phase may be particularly critical with respect to the consequences of collision.
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Table 8-1 Fraction of collision energy for strain energy dissipation
Vessel size [dwt]
Approach phase
Departure phase
Shuttle tanker
150.000
370.000
FPSO
320.000
160.000
0.71
0.33
Strain energy fraction
Figure 8-1 Fraction of collision energy to be dissipated as strain energy for shuttle tanker impact
on an FPSO.
Comm. 3.5.1 Recommended force-deformation relationships
The force-deformation relationship for impacts from supply vessels/merchant vessels against jacket legs
have been elaborated because of the need to consider high-energy impacts (collision energy ~50 MJ) for
some installations in the North Sea. The likelihood of a central impact against a leg is obviously not very
large, but has still been considered because loss of a leg could be critical for some platforms. Experience has
shown, however, that many large North Sea jackets have sufficient strength to crush the bow. See Amdahl
and Johansen (2001).
The curve for bow impact in Figure 3-4 has been derived on the assumption of impacts against an infinitely
rigid wall. Sometimes the curve has been used erroneously to assess the energy dissipation in bow-brace
impacts.
Experience from small-scale tests Ch.7, /3/ indicates that the bow undergoes very little deformation until
the brace becomes strong enough to crush the bow. Hence, the brace absorbs most of the energy. When the
brace is strong enough to crush the bow the situation is reversed; the brace remains virtually undamaged.
On the basis of the tests results and simple plastic methods of analysis, force-deformation curves for bows
subjected to (strong) brace impact were established in Ch.7, /3/ as a function of impact location and brace
diameter. These curves are reproduced in Figure 8-2. In order to fulfil a strength design requirement the
brace should at least resist the load level indicated by the broken line (recommended design curve). For
braces with a diameter to thickness ratio < 40 it should be sufficient to verify that the plastic collapse load in
bending for the brace is larger than the required level. For larger diameter to thickness ratios local denting
must probably be taken into account.
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Normally sized jacket braces are not strong enough to resist the likely bow forces given in Figure 8-2, and
therefore it has to be assumed to absorb the entire strain energy. For the same reasons it has also to be
assumed that the brace has to absorb all energy for stern and beam impact with supply vessels.
Figure 8-2 Load-deformation curves for bow-bracing impact, Ch.7, /3/
Comm. 3.5.2 Force contact area for strength design of large diameter columns.
Figure 8-3 Distribution of contact force for stern corner/large diameter column impact
Figure 8-3 shows an example of the evolution of contact force intensity during a collision between the stern
corner of a supply vessel and a stiffened column. In the beginning the contact is concentrated at the extreme
end of the corner, but as the corner deforms it undergoes inversion and the contact ceases in the central
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part. The contact area is then, roughly speaking, bounded by two concentric circles, but the distribution is
uneven.
The force-deformation curves given in Figure 3-4 relate to total collision force for stern end - and stern
corner impact , respectively. Table 3-1 and Table 3-2 give the anticipated maximum force intensities (local
force and local contact areas, i.e. subsets of the total force and total area) at various stages of deformation.
The basis for the design curves is integrated, non-linear finite element analysis of stern/column impacts.
The information given in 3.5.2 may be used to perform strength design. If strength design is not achieved
numerical analyses have shown that the column is likely to undergo severe deformations and absorb a major
part of the strain energy. In lieu of more accurate calculations (e.g. non-linear FEM) it has to be assumed
that the column absorbs all strain energy.
Comm. 3.5.3 Energy dissipation is ship bow.
The requirements in this paragraph are based upon considerations of the relative resistance of a tubular
brace to local denting and the bow to penetration of a tubular beam. A fundamental requirement for
penetration of the brace into the bow is, first - the brace has sufficient resistance in bending, second - the
cross-section does not undergo substantial local deformation. If the brace is subjected to local denting,
i.e. undergoes flattening, the contact area with the bow increases and the bow inevitably gets increased
resistance to indentation. The provisions ensure that both requirements are complied with.
Figure 8-8 indicates the level of the various contact locations.
Figure 8-4 shows the minimum thickness as a function of brace diameter and resistance level in order to
achieve sufficient resistance to penetrate the ship bow without local denting. It may seem strange that
the required thickness becomes smaller for increasing diameter, but the brace strength, globally as well as
locally, decreases with decreasing diameter.
Local denting in the bending phase can be disregarded provided that the following relationship holds true:
(8.1)
Figure 8-5 shows brace thickness as a function of diameter and length diameter ratio that results from
Equation (8.1). The thickness can generally be smaller than the values shown, and still energy dissipation
in the bow may be taken into account, but if Equation (8.1) is complied with denting does not need to be
further considered.
The requirements are based upon simulation with LS-DYNA for penetration of a tube with diameter 1.0 m.
Great caution should therefore be exercised in extrapolation to diameters substantially larger than 1.0 m,
because the resistance of the bow will increase. For brace diameters smaller than 1.0 m, the requirement is
conservative.
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Figure 8-4 Required thickness versus grade and resistance level of brace to penetrate ship bow
without local denting
Figure 8-5 Brace thickness yielding little local deformation in the bending phase
Comm. 3.7.3 Support capacity smaller than plastic bending moment of the beam
The procedure is illustrated in Figure 8-6.
Elastic, rotational flexibility of the node is normally of moderate significance.
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Figure 8-6 Derivation of force-deformation relationship for beam with end moments less than
beam plastic moment.
The procedure given is essentially the same as the one used in NORSOK N-004, but is formulated differently.
The bending moment 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 is used.
Comm. 3.10.1 General
If the degradation of bending capacity of the beam cross-section after buckling is known the load-carrying
capacity may be interpolated from the curves with full bending capacity and no bending capacity according to
the expression:
(8.2)
= collapse load with full bending contribution
= collapse load with no bending contribution
= plastic collapse load in bending with reduced cross-sectional capacities. This has to be
updated along with the degradation of cross-sectional bending capacity.
Comm. 3.10.4 Tensile fracture in yield hinges
The rupture criterion is calculated using conventional beam theory. A linear strain hardening model is
adopted. For a cantilever beam subjected to a concentrated load at the end, the strain distribution along the
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beam can be determined from the bending moment variation. In Figure 8-7 the strain variation,
,
is shown for a circular cross-section for a given hardening parameter. The extreme importance of strain
hardening is evident; with no strain hardening the high strains are very localised close to the support (x = 0),
with strain hardening the plastic zone expands dramatically.
On the basis of the strain distribution the rotation in the plastic zone and the corresponding lateral
deformation can be determined.
If the beam response is affected by development of membrane forces it is assumed that the membrane strain
follows the same relative distribution as the bending strain. By introducing the kinematic relationships for
beam elongation, the maximum membrane strain can be calculated for a given displacement.
Figure 8-7 Axial variation of maximum strain for a cantilever beam with circular cross-section
Adding the bending strain and the membrane strain allows determination of the critical displacement as a
function of the total critical strain.
Figure 8-8 shows deformation at rupture for a fully clamped beam as a function of the axial flexibility factor
c.
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Figure 8-8 Maximum 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 stiffness shall be determined such that the total area under the stress-strain curve up to the critical
strain is preserved (the two portions of the shaded area shall be equal), see Figure 8-9. It is un-conservative
and not allowable to use a reduced effective yield stress and a plastic stiffness factor as illustrated in Figure
8-10.
Figure 8-9 Determination of plastic stiffness
Figure 8-10 Erroneous determination of plastic stiffness
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The accuracy of the calculation model for tensile fracture in yield hinges has been investigated by Amdahl
and Skallerud (2002). The maximum strain as a function of lateral displacement (Equation (3.22)) for a
tubular beam is compared with the maximum strain from finite element calculations in Figure 8-11. The
beam is assumed to be clamped and fixed against inward 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 at ultimate strain εu = 0.15). The mesh size
for USFOS shell and ABAQUS is 0.25 · 0.39 m and for ABAQUS fine mesh 0.05 · 0.195 m. The element used
in ABAQUS analyses is the S4R reduced integration element.
Figure 8-11 Strain versus displacement of clamped beam
It is observed that the strain estimated in ABAQUS analysis depend significantly on the mesh size evidencing
the need for a mesh-size-dependent fracture strain criterion. The NORSOK criterion agrees fairly well with
FEM calculations when a fine mesh is used. The criterion is conservative, as desired. The strain calculation
in the USFOS beam element assumes a yield plateau followed by parabolic type hardening. Only the fine
ABAQUS mesh captures the yield plateau effect.
Comm. 3.12 Energy dissipation in floating production vessels
Figure 8-12 Design of an impact resistant stern – collision with a VLCC
Calculation of energy dissipation in stringers, decks and bulkheads subjected to gross, axial crushing shall be
based upon recognised methods for plastic analysis, e.g. Ch.7, /3/ and Ch.7, /4/. It shall be documented that
the folding mechanisms assumed yield a realistic representation of the true deformation field.
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The force deformation relationships given in Figure 3-6 may be used to design a collision resistant stern of
an FPSO. In order to be impact resistant, stringers and frames must be fairly closely spaced, typically in
the range of 1.5 – 2 m. Given the relative dimensions of the girder system and the bulb cross-section, as
illustrated in Figure 8-12, it is reasonable to apply the total collision force as uniformly distributed line loads
on the stringers and frames. The integrity of the stringers and frames can then be checked in a FEM analysis.
Moderate local yielding should be accepted.
The stern structure must resist the collision force during all stages of the collision process. Normally, it
suffices to analyse a few collision force and contact area situations.
It is normally neither practical nor necessary to design the plating and stiffeners such that their response
is elastic. Large plastic deformations can be accepted, but fracture of the plating should not occur (Note:
provided that strength design is aimed for). In lieu of more accurate calculations, the contact force may be
considered uniformly distributed over the plate field, and the resistance may be assessed using the provisions
given for the resistance of plates and stiffeners to explosion loads.
Even if the stiffeners are allowed to deform under extreme collision loads, they should be sufficiently robust
to initiate crushing of the bulb. Engineering judgment must be applied, but it is recommended to design the
stiffeners according to requirements for ships navigating in ice.
With respect to deformation resistance of stiffened plating, see next paragraph.
The ductile resistance of stiffened plates may be analysed considering the side as an assembly of plate/
stiffeners. The resistance of individual stiffeners with associated plate flange can be calculated with the
methods given in [6.3] using relationships for a concentrated force, see example in Ch.8, Comm. 9.3. The
resistance of the various stiffeners will be mobilised according to the geometry (raking) of the impacting bow.
Unless the frame spacing is long or the stiffener height is small, fracture will take place before noticeable
membrane stiffening has taken place. The initiation of fracture does not necessarily imply that the resistance
is totally lost, because fracture takes place in the top flange while the strain on the plate side is considerably
smaller .
The above procedure neglects the effect of membrane forces transverse to the stiffeners. Depending on the
geometry of the panel this contribution may be substantial.
Collisions with FPSOs have been studied in-depth in a paper by Moan et.al. (2002). Force-deformation
relationships are given for supply vessels/merchant vessels, 18.000 tons chemical tanker and a 42.000
tons tanker and a shuttle tanker. The collision risk for all categories of vessels is discussed extensively. The
consequences of a collision with a shuttle tanker servicing the FPSO are especially considered.
Figure 8-13 shows the force-deformation relationship for supply vessel/merchant vessel colliding with the
side of an FPSO. It is interesting to see that the force level for bow without bulb is smaller than the bow
force-deformation curve given in Figure 3-4.
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Figure 8-13 Force-deformation relationship for supply vessel/merchant vessel impact against
FPSO side
Comm. 4.4.1 Stiffened plates subject to drill collar impact
The 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 be added as Eloc = R·0.2 t.
In case of hit near the plate edges the energy dissipation will be low and may lead to unreasonable plate
thickness. The failure criterion used for the formula is locking of the plate. In many cases locking may be
acceptable as long as the falling object is stopped. If the design is based on a hit in the central part of a plate
with use of the smaller diameter in the treaded part in the calculations, no penetration of the drill collar will
take place at any other hit location due to the collar of such dropped objects.
Comm. 5.1 General
For redundant structures thermal expansion may cause buckling of members below 400°C. Forces due to
thermal expansion are, however, purely internal and will be released once the member buckles. The net
effect of thermal expansion is therefore often to create lateral distortions in heated members. In most cases
these lateral distortions will have a moderate influence on the ultimate strength of the system.
As thermal expansion is the source of considerable inconvenience in conjunction with numerical analysis it
would tempting to replace its effect by equivalent, initial lateral member distortions. There is however, not
sufficient information to support such a procedure at present.
Comm. 5.5 Empirical correction factor
In Ch.7 /2/ Eurocode 3 an empirical reduction factor of 1.2 is applied in order to obtain better fit between
test results and column curve c for fire exposed compressive members. In the design check this is performed
by multiplying the design axial load by 1.2. In non-linear analysis such a procedure is impractical. In nonlinear space frame, stress resultants based analysis the correction factor can be included by dividing the yield
compressive load and the Euler buckling load by a factor of 1.2. (The influence of axial force on member’s
stiffness is accounted for by the so-called Livesly’s stability multipliers, which are functions of the Euler
buckling load.) In this way the reduction factor is applied consistently to both elastic and elasto-plastic
buckling.
The above correction factor comes in addition to the reduction caused by yield stress and elastic modulus
degradation at elevated temperature if the reduced slenderness is larger than 0.2.
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Comm. 6.2 Classification of response
Equation (6.2) is derived using the principle of conservation of momentum to determine the kinetic energy
of the component at the end of the explosion pulse. The entire kinetic energy is then assumed dissipated as
strain energy.
Equation (6.3) is based on the assumption that the explosion pressure has remained at its peak value during
the entire deformation and equates the external work with the total strain energy. In general, the explosion
pressure is not balanced by resistance, giving rise to inertia forces. Eventually, these inertia forces will be
dissipated as strain energy.
Equation (6.4) is based on the assumption that the pressure increases slowly so that the static condition
(pressure balanced by resistance) applies during the entire deformation.
Comm. 6.4 SDOF system analogy
The displacement at the end of the initial, linear resistance domain yel will generally not coincide with the
displacement at first yield. Typically, yel represents the displacement at the initiation of a plastic collapse
mechanism. Hence, yel is larger than the displacement at first yield for two reasons:
i)
ii)
Change from elastic to plastic stress distribution over beam cross-section.
Bending moment redistribution over the beam (redundant beams) as plastic hinges form.
Figure 8-14 Iso-damage curve for ymax/yel = 10. Triangular pressure
Figure 8-14 is derived from the dynamic response chart for a SDOF system subjected to a triangular load
with zero rise time given in Figure 6-3.
In the example it is assumed that from ductility considerations for the assumed mode of deformation a
maximum displacement of ten times elastic limit is acceptable. Hence the line
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represents the upper limit for the
displacement of the component. From the diagram it is seen that several combinations of pulses
characterised by Fmax and td may produce this displacement limit. Each intersection with a response curve
(e.g. k3 = 0) yields a normalized pressure
and a normalised impulse
By plotting corresponding values of normalised impulse and normalised pressure the iso-damage curve given
in Figure 8-14 is obtained.
If the displacement shape function changes as a non-linear structure undergoes deformation the
transformation factors change. In lieu of accurate analysis an average value of the combined load-mass
transformation factor can be used:.
(8.3)
μ = ymax/yel ductility ratio
Since μ is not known a priori iterative calculations may be necessary.
Dynamic response charts for a SDOF system with triangular pressure pulses with rise time different from td/2
are given in Figure 8-15 to Figure 8-17.
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Figure 8-15 Dynamic response of a SDOF system to a triangular load (rise time=0)
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Figure 8-16 Dynamic response of a SDOF system to a triangular load (rise time = 0.15td)
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Figure 8-17 Dynamic response of a SDOF system to a triangular load (rise time = 0.30td)
Comm.6.7.1.1 Component behaviour
For beams the characteristic linear stiffness given for the elasto-plastic resistance domain in Table 6-2 is
derived from the equal area principle on the assumption that the support moment 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 (shear lag effect) of the plate flange, se, of simply
supported or clamped stiffeners/girders may be taken from Figure 8-18.
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Figure 8-18 Effective flange for stiffeners and girders in the elastic range
Comm. 6.10.7 Ductility limits
The table is taken from Sec.7, Reference /4/. The values are based upon a limiting strain, elasto-plastic
material and cross-sectional shape factor 1.12 for beams and 1.5 for plates. Strain hardening and any
membrane effect will increase the effective ductility ratio. The values are likely to be conservative.
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SECTION 9 EXAMPLES
9.1 Design against ship collisions
9.1.1 Jacket subjected to supply vessel impact
The location of contact is at brace mid-span and the force acts parallel to global x-axis. The brace dimensions
are 762 x 28.6 mm. From linear elastic analysis it is found that the stiffness of nodes 508 and 628 against
displacement in the brace direction is 736 MN/m and 51 MN/m respectively, when the brace is removed. The
unequal stiffness may be represented by two equal springs, each with stiffness:
Figure 9-1 Jacket subjected to ship impact
The axial stiffness of the brace is given by
and is large compared to the stiffness of the node. This yields an effective stiffness of
Assuming clamped ends (c1 = 2) the non-dimensional spring stiffness comes out to be
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The resulting end restraint is quite flexible. This is particularly due to low stiffness in node 628, in spite of the
support by the adjacent braces. Hence, the build-up of tension force will be delayed compared to a full axial
fixity.
The collapse load in bending is calculated assuming clamped conditions at both ends. This is a good
approximation at the lower end but slightly optimistic at the upper end.
The load-deformation characteristics for the brace are obtained by interpolation of the curves given in Figure
3-7. The result is depicted in Figure 9-2. The response predicted by means of the nonlinear analysis program
USFOS is also plotted. It appears that the simplified approach performs very well when axial flexibility is
taken into account. The loss of stiffness predicted by USFOS at large displacements is due to initiation of
failure of adjacent members at node 628. Collapse of these members takes place at a load level of 2.8 MN.
It must also be verified that the capacity of the joints is sufficient to support the force state in the brace both
in the bending mode of deformation and in the membrane tension state. Figure 9-3 displays the simulated
bending moment-axial force interaction history in the brace and shows that the membrane force becomes
substantial, but doe not attain the fully plastic axial force. In lieu of accurate calculations, it should be
assume that the fully plastic tension is developed.
Provided that the joints and adjacent structure are capable of supporting the brace ends, the energy
dissipation is limited by fracture due to excessive straining of the brace. Fracture criteria are given in
[3.10.3]. Using the fracture criterion in [3.10.3] there is obtained wcrit = 2.2 m and a corresponding energy
dissipation E = 6 MJ.
Figure 9-2 Load versus lateral deformation of the contact point
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Figure 9-3 Axial force-bending moment interaction in brace
Tensile fracture in jacket brace
Tensile fracture of the brace considered in is estimated. The characteristic dimension is, dc = D = 0.762 m.
For steel grade S 355 a strain hardening coefficient of H = 0.0034 is used, refer Table 3-3. c1 = 2 (clamped
ends are assumed), the collision occurs at mid span, hence κ = 0.5, and κ /dc = 15.3. The non-dimensional
spring stiffness is c = 0.18 and W/WP =
Because of the large
κ
π /4. This yields wcrit = 2.2 m.
/dc – ratio, the brace is capable of deforming almost three times its diameter.
9.2 Design against explosions
9.2.1 Geometry
The geometry of the structure is outlined in Figure 9-4. The plate, stiffeners and girders will be assessed. The
main dimensions are:
t
s
l
= 10 mm
= 500 mm
= 2000 mm.
Stiffener dimension Hp 180.
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Figure 9-4 Geometry
9.2.2 Calculation of dynamic response of plate
The dynamic response of the plate considered in [9.3.1] is studied. The plate is subjected to a triangular
pressure pulse with duration of 20 msecs. The peak pressure is fmax = 2.5 MPa. Assume that the resistance
curve for c = 1.0 in Figure 9-7 applies. This yields rel/fmax = 0.3. The curve is redrawn below along with
approximate relationships
Alternative 1- static analysis: The eigenperiod of the plate according to [9.3.1] with η = 25 is T = 4.0 msecs.
Hence td/T = 5. This is a fairly long duration and static behaviour can be assumed. The maximum deflection
is determined directly from Figure 9-7, i.e. wmax = 27 mm.
Alternative 2 - tri-linear resistance: By inspection of the dynamic response charts and the resistance curve
for the plate it is noticed that none of the tri-linear curves apply very well. The best fit is obtained with k3 =
0.5 k1, but this underestimates the resistance for large deformations. From the response chart for 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 deformations the stiffness is fairly linear. Assume that
the average stiffness 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 arbitrarily, but it should be ensured that the response is such that ymax/yel < 1.0,
and it is practical to select a given rel/fmax ratio for 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
to account for less stiffness. This yields td/Tmod = 4.0. From the response chart there is obtained ymax/yel ~
0.7. This yields wmax = 0.7 · 47,3 = 33 mm.
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All these methods yield approximately the same result. The static approach is quite good, but there is a slight
dynamic amplification > 1 in the present case.
The plate must be checked with respect to rupture, see [9.4.1].
It is noticed that if no membrane force can be taken into account, i.e. c = 0, then ymax/yel >> 100 and the
plate will fail completely.
9.2.3 Calculation of dynamic response of stiffened plate
The dynamic response of the stiffened plate considered in [9.3.2], subjected to a triangular explosion pulse
with duration 20 msecs and peak pressure fmax = 2.5 MPa, is studied. The collapse resistance is R0 = Rel =
0.58 MN, and no membrane stiffening can be assumed, i.e. k3 = 0. As the plate/stiffener undergoes a phase
with elasto-plastic bending, the resistance is approximated by a linear elastic-perfectly plastic model, with
equivalent stiffness of 208 MN/m and wel = 2.8 mm. The critical deformation at rupture wcrit = 36 mm, hence
the ductility ratio is μ = ymax/yel = 36/2.8 = 13.
The total mass is 108 kg. The load-mass factor is ~ 0.77 and 0.66 in the elastic/elasto-plastic and
plastic bending phase, respectively. Using Equation (8.3) the average load-mass factor becomes
and the eigenperiod is:
This gives td/T = 5.4. By inspection of Figure 6-3 it is found that for μ = 13 and td/T =5.4 → Rel/Fmax # 0.75
(in other words, because of limited pulse duration it is possible to “overload” the stiffener by 33% compared
to the static collapse resistance in bending).
The maximum peak pressure the stiffener can resist is:
Consequently; the stiffener is not strong enough to resist the explosion pressure without rupture (see
discussion in [9.3.2] as concerns rupture of stiffener).
It is a fairly common experience that stiffeners are more likely to be critical with respect to explosion loads
than the plating between stiffeners.
9.3 Resistance curves and transformation factors
9.3.1 Plates
Generation of elastic–plastic resistance curve is illustrated for a plate with the following particulars: Length,
l = 2 m, width, s = 0.5 m, thickness, t = 10 mm, yield stress f y = 355 MPa. It is assumed that the plate
is a part of a continuous plate field. Large deformations are expected so that the plate will yield along the
boundaries. Then clamped boundaries are assumed.
The rigid – plastic curve is given by Equation (8.3). The collapse resistance in bending is rc = 0.76 MPa. The
resistance curve for fully fixed boundaries are indicated by the line “Plate c = inf” in Figure 9-6. Below, the
curve will be adjusted for the effect of in-plane flexibility using the procedure described in [6.8.2].
First, the resistance of a plate-strip is calculated, using information given in [6.9.2] with α = 2 (rectangular
cross-section). Clamped boundaries with c1 = 2 are assumed also for the plate strip. The collapse resistance
in bending for the plate strip is rc = 0.57 MPa.
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The characteristic beam height is
The resistance curve for the plate strip is shown in Figure 9-6 for fully fixed boundaries
, and for
two values of the non-dimensional spring stiffness, c = 1.0 and c = 0.3. It is observed that the difference
between the plate strip and the plate solution is small for the present fairly large aspect ration, notably when
the membrane effect predominates
On the assumption that the plate experiences the same relative reduction of the resistance due to axial
flexibility as does the plate strip, resistance curves for the plate with non-dimensional spring stiffness, c =
1.0, and c = 0.3 can be generated as shown in Figure 9-6.
The next step is to assess the flexibility factor c:
nd
If the flexibility of the adjacent structure is neglected, accounting only for the 2
there is obtained
term in Equation (6.11),
This yields a non-dimensional spring stiffness, c = 0.95.
Figure 9-5 Approximate determination of flexibility by means of membrane analysis
In order to assess the influence of the flexibility of the adjacent structure, a membrane analysis is
performed with the plate removed, see Figure 9-5. A constant stress of 100 MPa is applied perpendicular the
boundaries. The maximum deformation obtained, at the mid-point of the long edges, is 0.25 mm. This yields
-3
an equivalent stiffness of knode = 100·0.010·1/0.25·10 = 4000 MN/m. When both effects are accounted
-1
for, the resulting stiffness becomes k = (1/8400 +1/4000) = 2710 MN/m and c = 0.31. Hence, the plate
resistance may be assessed 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 resistance in bending, rc, is added to the rigidplastic solution. Using the information given in [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.
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Figure 9-6 Derivation of rigid-plastic resistance curves for a plate
Figure 9-7 Elastic-plastic resistance for a plate with various degrees of axial flexibility
9.3.2 Calculation of resistance curve for stiffened plate
The plate considered in [9.3.1] is stiffened with HP 180x 8 stiffeners with yield stress fy = 355 MPa. The
girder spacing is 2.0 m. It is assumed that the stiffener is continuous, so that yield hinges can form at the
-2
2
connections to the girder, hence c1 = 2. The area of the stiffener As= 1.88·10 m and the distance to the
centroid is zg = 0.109 m.
From Figure 8-18 it is found that the plate flange is approximately 80% for a uniformly distributed load when
-3
2
/s = 0.6·2.0/0.5 = 2.4. The effective area of the plate flange is 0.8 s t = 4·10 m > As. Hence, it may
be assumed that the plastic neutral axis for the effective section lies at the stiffener web toe. This yields the
-3
3
plastic section modulus WP = As zg = 2.05·10 m and collapse resistance in bending
The characteristic beam height is:
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The moment of inertia for stiffener with effective plate flange is I = 2.28 10
is taken from Table 6-2:
-5
4
m . The initial elastic stiffness
This yields a lateral elastic deformation of wel = 2.5 mm for R = R0.
The resistance curve for the stiffener with associated plate flange is shown in Figure 9-8 for various degrees
of axial flexibility (Note elastic part not included!).
For uniformly loaded, clamped beams there will be an elasto-plastic bending phase between the occurrence
of first plastic hinge and final formation of final collapse mechanism. To account for this effect, the initial
stiffness may be modified on the basis of equal area principle. The equivalent elastic stiffness 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 plastic deformation before membrane
strengthening becomes significant according to the present model. Whether this is achievable depends on the
ductility of the stiffener, see [9.4.2].
Recent investigations indicate that the model adopted for stiffened plate is considerably conservative, which
may warrant a more accurate nonlinear finite element analysis if the stiffener response becomes critical.
Figure 9-8 Resistance curve for stiffener with associated plate flange
9.3.3 Calculation of resistance curve for girder
What is the maximum pressure a steel girder can resist prior to rupture, when the explosion load is
triangular, with equal rise and 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 thickness ttop = 19 mm. The girder spacing is 2 m and the plate thickness is 10 mm. For simplicity
2
it is assumed that the plate flange is fully effective. The girder has a distributed load of intensity 10 kN/m
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5
and mounted equipment with mass 1.8·10 kg. The equipment load acts equally at two points located L/3
from member ends. The girder is simply supported at one end and clamped at the other end. At the clamped
end fully plastic bending moment of the girder can be assumed. There is no axial restraint. Yield stress fy =
2
3
3
355 MPa, acceleration of gravity g = 10 m/s , density of steel 7.86·10 kg/m .
The following is obtained for the girder:
-2
4
-2
3
Moment of inertia I = 1.84·10 m , elastic section modulus, W = 1.96·10 m , plastic section modulus, WP
-2
3
2
= 2.51·10 m , total cross-sectional area 0.048 m . The total distributed mass, including mass of girder is
-5
0.29·10 kg, so the concentrated mass predominates. Hence, transformation factors for two concentrated
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 to 1.8 + 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 elastic range. The limiting deformation for rupture calculated in 9.4.3 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 transformation factor from the elastic to plastic regime
may be accounted for, see Sec.8, Comm. 6.4. The factor for distributed mass and concentrated mass is
average,u
klm
= (0.55 + (6.7 − 1) · 0.56) / 6.7 = 0.56
and
average,c
klm
= (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 read Rel/Fmax = 0.7 for coordinates (2,6.7).
Hence, the girder can resist a dynamic load of Fmax = 3.86/0.7 = 5.5 MN, corresponding to a peak pressure
of fmax= 0.23 MPa.
Example girder:
The neutral axis for the girder studied in [9.3.3] is located 0.315 m from the plate flange. This yields a
characteristic dimension dc = 2 · (1.5 − 0.315) = 2.37 m. The critical location is at the clamped side,
whereby κ =1/3. Clamped end yields 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 Ductility limits
9.4.1 Plating
Rupture of the plating for the example considered in [9.2.2] may be estimated by means of the procedure
given in [3.10.4], using the plate strip analogy. The characteristic dimension is, dc = t = 10 mm. For steel
grade S 355 a strain hardening coefficient of H = 0.0034 is used, see Table 3-4. κ = 0.5, c1 = 2 (clamped
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ends) and κ /dc = 0.5 s/t = 25. This yields the following values for the critical deformation, wcrit, depending
on the spring stiffness c, see Table 9-1 (Note: the elastic deformation rel = 6.15 mm is added to the values
obtained). By inspection of Figure 9-7 it is noticed that the fully plastic membrane state according to this
procedure is attained in all cases but c = 0.
Table 9-1 Ductility limit as a function of the spring stiffness
c
∞
1.0
0.3
0
wcrit [mm]
35
51
59
76
9.4.2 Stiffener
Rupture is calculated for the stiffened plate considered in [9.3.2] using the procedure given in [3.10.4]. The
steel grade is S 355 with a strain hardening coefficient of H = 0.0034, see Table 3-3. Clamped conditions
are assumed, i.e. c1 = 2. The shape factor (somewhat arbitrarily) set to 1.5. The characteristic dimension
of the stiffened plate is dc = 2hw = 0.36 m. This yields λ/dc = 5.56, only. This critical deformation becomes
wcrit = 0.1dc = 36 mm, almost independent of the spring stiffness c (Note: ductility ratio is
μ = 36/2.2 =
16). This fairly small value is due to the low κλ/dc – ratio for the stiffener. The stiffener is far from entering
the membrane stiffening phase, so that any discussion of the possibility for membrane forces to develop is
irrelevant.
If the stiffener is free against rotation and/or has a longer span membrane effects may become important
prior to rupture.
Observe that rupture is calculated for the location subjected to the largest strains, i.e. at the stiffener top
flange. Rupture in the top flange is not necessarily critical with respect to intactness to explosion loads,
because the plate side experiences far less strains. It is likely that the plate will remain intact beyond
the deformation limit corresponding to rupture in the top flange. A significant part of the contribution
to resistance from the stiffener is lost, but the plating between girders may have a significant residual
resistance after failure of stiffeners provided that the plate does not disintegrate. It is, however, difficult to
provide validated, closed form solution for this situation.
A stiffener subjected to pressure on the plate side may trip about the weld toe at mid span. In this case the
assumptions used 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 is located 0.315 m from the plate flange. This
yields a characteristic dimension dc = 2 · (1.5 − 0.315) = 2.37 m. The critical location at the clamped side,
whereby κ =1/3. Clamped end yields 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 loads
The geometry of the structure is outlined in Figure 9-4. The main dimensions are:
Plate thickness:
t = 14 mm
Stiffener dimension:
HP240x10, simulated as an L-profile with dimension L240x39x10x29
Stiffener spacing:
s = 800 mm
Stiffener length:
l = 3200 mm
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Girder dimension:
T-girder with dimension: 870x300x10 x20
Girder length:
L = 12000 mm .
The material properties are as follow:
Yield strength:
fy = 420 MPa
Strain rate factor:
γε = 1.0
Effective yield strength:
fy = fy· γε = 420 MPa
Modulus of elasticity:
E = 2.1·10 MPa
Material density:
ρ = 7850 kg/m3
Poisson’s ratio:
ν = 0.3
Max. plastic strain:
1.0% (maximum allowable, correspond to cross-section class 3 or 4, see
sub-section 9.5.2).
5
Permanent loads and live loads are as follow:
Permanent loads:
pP = 10.0 kN/m
Live loads:
pL = 5.0 kN/m
Explosion pulse period:
td = 0.15 sec
2
2
(triangular load with a rise time = 0.50·td).
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Figure 9-9 Geometry
9.5.2 Cross-sectional of properties for the girder
Effective plate flange according to DNV Classification Note 30.1 (July 1995), sub-section 3.4.3 and 3.5.4:
Determination of cross section class, see NS3472:2001, section [12.1]:
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Web:
, i.e. class 3 (bending considered)
Bottom flange:
, i.e. class 2 (bending & axial)
Plate flange:
, i.e. class 4 (bending & axial)
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 mm
Area of girder flange: Af = bfg·tfg = 300·20 = 6000.0 mm
2
2
Total area of girder web: Aw = hwg·twg = 850·10 = 8500.0 mm
2
Total area (gross section): AG = Ap+Af+Aw = 4245.1+6000+8500 = 18745.1 mm
2
Distance to neutral axis (from bottom of girder flange):
Web height in tension: ht = z0-tfg = 403.6-20.0 = 383.6mm
Web height in compression: hc = hwg-ht = 850.0-383.6 = 466.4mm.
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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:
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Figure 9-10 Effective Girder section
Effective girder cross section properties
Reduction 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 mm
2
Distance to neutral axis from bottom of girder flange:
Effective elastic moment of inertia:
Effective elastic section modulus:
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Plastic section modulus:
Web areas:
Eccentricities (see figure):
Plastic section modulus if Ap > Aw1 + Aw2 + Af :
Plastic section modulus if Ap + Aw1 > Aw2 + Af :
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Plastic section modulus if Ap + Aw1 < Aw2 + Af :
Plastic section modulus:
Ratio between plastic and elastic section modulus:
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9.5.3 Mass
Mass from plate:
Mass from stiffener, see figure:
Mass from girder:
Mass from permanent loads and possible live loads (to be evaluated in each case):
Total mass:
9.5.4 Natural period
Linear stiffness, see Table 6-2 in [6.10]:
Natural period assuming uniformly distributed mass (Klm,u is taken from Table 6-2):
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Ratio of pulse load period versus natural period:
9.5.5 Ductility ratio
The maximum lateral deformation prior to buckling can be calculated according to Equation (3.19) in 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)=
1089mm
c1 is 2 for clamped beams
κL 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, see [3.7];
knode is axial stiffness of the node with the considered member removed, here assumed infinitely.
Calculation of cross sectional slenderness factor, see [3.10], i.e. the maximum of the following:
Plate flange:
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Bottom flange:
Web (bending):
Based on these input parameters, the maximum plastic deformation is calculated to:
The maximum elastic deformation is found from:
Ductility ratio:
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9.5.6 Maximum blast pressure capacity
From Figure 9-11, the dynamic load factor is found:
With reference to Figure 9-11, k3 was set to 0, which ensures conservative results.
Figure 9-11 Dynamic response of a SDOF system due to a triangular pulse load profile (rise time =
0.50td)
Maximum resistance for a fixed supported beam, see Figure 9-12:
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Figure 9-12 Moment 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 following two equations:
The maximum blast pressure capacity is then:
Note that the maximum resistance (Rm) given above does not include a capacity check with respect to shear.
The shear capacity can be determined from sub-section 12.4.4 in NS3472-2001.
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Changes – historic
CHANGES – HISTORIC
There are currently no historical changes for this document.
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