Document 1792152

OTH 92 365
A REVIEW OF THE ULTIMATE
STRENGTH OF TUBULAR
FRAMED STRUCTURES
Authors
H M Bolt, C J Billington and J K Ward
Billington Osborne-Moss Engineering Limited
Ledger House, Forest Green Road
Maidenhead
Berkshire SL6 2NR
HSE BOOKS
Health and Safety Executive OffshoreTechnology Report
Crown copyright 1996
Applications for reproduction should be made to HMSO
First published
ISBN 0-7176-1040-3
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written permission of the copyright owner.
Thisreport is published by the Health and Safety Executive as part of
a series of reports of work which has been supported by funds
provided by the Executive. Neither the Executive,or the contractors
concerned assume any liabilityfor the report nordo they necessarily
reflect the views or policy of the Executive.
Results, including detailed evaluation and, where relevant,
stemming from their research projects are
published in the
series of reports.
from these research projects
Backgroundinformationand
are published in the
seriesof reports.
CONTENTS
Page
SUMMARY
1. INTRODUCTION
1 . 1 Background
1.2 Objectives and Scope of the Review
1.3 Development of the Review
2. DEFINITIONS AND PRACTICAL CONSIDERATIONS
2.1 Reserve Strength
2.2 Design Procedures
2.3 Redundancy
2.4 Residual Strength
2.5 Ductile Versus Brittle Responses
2.6 Reliability Based Versus Deterministic Approaches
2.7 Pushover Analysis and Cyclic Loading
2.8 Treatment of Loads and Safety Margins in Reserve Strength Assessment
2.9 Conclusion
3. EXPERIMENTAL INVESTIGATIONS
3.1 Background to Test Programmes
3.2 Comparison of Results
3.2.1 Single versus two-bay plane frames
3.2.2 Role of redundant members
3.2.3 K versus X bracing
3.2.4 Effective length factors
3.2.5 Joint versus member failures
3.2.6
3.2.7 Initial imperfections and the effects of scale
3.2.8 Comparison with jacket structures
3.2.9 Materials
3.2.10 Conclusion
4.
FOR PUSHOVER ANALYSIS
4.1 Analysis Methods
4.1
Member removal
4.1.2 Member replacement
4.1.3 Linear superposition - strain based
4.1.4 Linear superposition - load based
4.1.5 Limit equilibrium analysis
4.1.6 Nonlinear collapse analysis software
4.1.7 Appropriate analysis approaches
4.2 Description of Nonlinear Software
4.3 Software Comparisons
iii
Page
5. ANALYTICAL INVESTIGATIONS
5.1 Background to Analyses
5.1.1 Simple 2D frame analyses
5.1.2 Idealised 3D jacket analyses
5.1.3 Structural jacket analytical investigations
loading investigations
5.1.4 Jacket
5.1.5 Jacket hindcasting calculations
5.1.6 Reliability analyses
5.2 Comparison of Results
5.2.1 Quantification of RSR
5.2.2 Bracing configuration
5.2.3 Joint behaviour
5.2.4
5.2.5 Foundation modelling
5.2.6 The role of comparative analysis
6. DISCUSSION
6.1 Summary of Review
6.1.1 Experimental results
6.1.2 Numerical results
6.2 Reserve Strength of Frames
6.2.1 Background to evaluating reserve strength
6.2.2 Redundancy beyond first member failure
6.2.3 Alternative loadpaths and sources of reserve
6.2.4 Relation between 2D and 3D structures
6.3 Reserve Strength Considerations for Offshore Jacket Structures
6.3.1 Complexity of 3D jacket structures
6.3.2 Modelling of jacket loads
Influences on RSR
6.3.4 Role of tubular joint failures
6.3.5 Role of foundation failure
6.3.6 Cyclic loading effects
6.3.7 Accounting for damage
6.3.8 Target system reserve
6.4 Calculation of Reserve Strength
6.4.1 Analytical tools for pushover analysis
6.4.2 Validation
7. CONCLUSIONS AND RECOMMENDATIONS
7.1 Conclusions
7.2 Recommendations
REFERENCES
-
APPENDIX A REVIEW UPDATE AUGUST 1993 MAY 1995
A l Introduction
A2 Developments in Reserve Strength Technology
A3 API RP 2A Section 17.0
- Acceptance and Interpretation of System Reserve Strength
A4
the Use of Ultimate Strength Analysis Techniques
A5 Conclusions
A REVIEW OF THE ULTIMATE STRENGTH
OF TUBULAR FRAMED STRUCTURES
SUMMARY
This review of the ultimate strength of tubular framed structures has been prepared for the
Health and Safety Executive (HSE) by Billington Osborne-Moss Engineering Limited
(BOMEL). A numerical capability to predict the nonlinear response of jacket structures
has been developed over the last decade in parallel with experimental investigations. It is
now being applied to assure the continued integrity of installations beyond the design event
in circumstances of extreme environmental loading or damage. A recent investigation has
confirmed that an extreme event static pushover analysis generally suffices to demonstrate
a structure's resistance to the cyclic loading of the full storm.
This report draws together the results from published investigations and identifies key
factors contributing to system reserve. It is shown that bracing configurations and relative
member properties are important influences. From the work presented, it is demonstrated
that many jacket analyses embody simplifying assumptions, and features such as loading
asymmetry, joint nonlinearity, foundation interactions, global deflection criteria etc, are
neglected. Specific examples highlighted in the review illustrate their potential importance
and systematic sensitivity evaluations are therefore recommended.
Differences in the definition of reserve strength ratio are noted, underlining difficulties in
drawing comparisons between structures. Nevertheless, jacket examples are cited where
first failure precipitates global collapse. Other structures are sufficiently redundant to
sustain loads well in excess of the design value, with collapse occurring only after a
sequence of component failures under increasing load.
The facilities of specific software programs are compared. Analyses using different
programs are shown not always to give consistent results and discrepancies in terms of
capacity and failure mode for the same jacket structure are found. Further benchmarking
and detailed comparison of software predictions is recommended.
This review was completed in 1993. Since that time and prior to publication of the review
in 1995 a number of important developments have taken place in relation to both the
understanding and the application of ultimate system strength technology.
A supplementary review in Appendix A brings the document up to date reflecting the
insight to frame behaviour derived from Hurricane
analyses, the
experience of recent benchmarking activities and the acceptance of ultimate strength
analyses in API RP 2A for the assessment of existing offshore structures.
Note
The illustrations, provided by BOMEL,in this report are only intended to be indicative of
actions that have been taken and not to be clear representations of the subject matter.
1. INTRODUCTION
1
BACKGROUND
The design of jacket structures is generally based on the expected response of components
to the applied loads anticipated. There is uncertainty on both the loading and resistance
sides of this equation so characteristic values are derived from the available data.
Furthermore, safety factors are introduced explicitly to ensure that an 'adequate' safety
margin exists.
Simplifying assumptions are inherent in the derivation of component forces from global
loads. An elastic frame analysis is performed, typically with elements rigidly connected.
Components are sized to ensure that the acting loads do not exceed the allowable values
designated by the codes for each component. Any potential of the structure to yield and
redistribute loads is neglected, giving an inherent 'reserve' capacity beyond the design event
year return period storm wave). The risk of exceptional loading beyond
(typically the
the 100 year event is not negligible however and modem codes (eg. ECCS and NPD) are
taking account of 10,000 year loadings but with plastic responses permitted. In November
1993 an API preliminary draft for RP 2A-WSD Section 17.0 for the assessment of existing
platforms was circulated, in which a sequence of analysis from screening, through design
level to ultimate strength assessment is advocated to demonstrate structural adequacy. At
the ultimate strength level it is proposed that 'a platform may be assessed using inelastic,
static pushover analysis' [see also Appendix A].
This review is concerned primarily with the reserve strength of jacket structures as
evaluated in pushover analysis. The frame action and system redundancy are implicit
sources of reserve strength which are not generally controlled or quantified in design.
Similarly, conservatism embodied within codes, material yield strengths exceeding the
minimum criteria specified, component limit states less onerous than ultimate strength and
overdesign for non-structural requirements, may be considered as implicit sources of
reserve. By contrast, overdesign by exceeding minimum requirements or by conservative
combinations of loads are sources of explicit reserve and can be controlled by the designer.
(1984) present a discussion of these various sources of reserve and
Lloyd and
residual strength but the focus of this review is on the important contribution of frame
behaviour. Marshal1(1979) demonstrates that this difference between elastic single element
behaviour and ultimate strength system behaviour is a major source of reserve strength.
Marshal1 and Bea (1976) demonstrated that a reserve strength factor of the order of 2 on
the design capacity may be found in offshore structures. Kallaby and
(1975)
published one of the first applications of inelastic analysis to demonstrate the energy
absorption capacity of the Maui A platform under earthquake loading.
Reserve strength should not be soley considered as overdesign of structures, rather it is
required to cope with loads which have not been foreseen in the design process or loads
which cannot be economically designed for on an elastic basis (eg. seismic or accidental
loads). The risks of these are not negligible and whilst traditional elastic design approaches
might preclude economic structural solutions for all conceivable loads, it is essential to
demonstrate that extreme events can be sustained without endangering human life or the
environment.
It is also important that a structure can sustain damage without collapse, ie. that it has
sufficient remaining or 'residual' strength. Such damage may result from extreme
overloading of the structure as a whole or from localised damage (eg. from impact). If
alternative load paths exist, the forces may be redistributed safely.
These requirements are not stipulated in quantitative terms within design codes although,
as noted above, traditional design practices have embodied inherent reserves. The attention
to safety in the post Cullen era has underlined the need to consider hazards such as extreme
environmental conditions or accidental loading scenarios which present a significant risk
to structural survival but which may not have been considered in the traditional design
process. Therefore there has been the requirement to develop an understanding and the
corresponding analytical tools to be able to predict system reserves beyond individual
component failure capacities, in order to demonstrate integrity in the event of such extreme
loading scenarios occurring.
Trends for lighter, liftable jackets and new concepts for deeper waters provide additional
impetus to the study. Fewer members in the splash zone may increase the risk to topsides
safety in the event of impact, and the deletion of members with low elastic utilisations to
save weight reduces the capacity for redistribution along alternative load paths.
Comparative calculations of reserve capacity for different structural configurations can help
ensure that levels of reserve strength and safety embodied within older designs are
maintained.
Reserve strength calculations may therefore be required in the course of the service life or
may be used to optimise a configuration or compare different concepts at the design stage
to ensure efficient structural forms are adopted.
However, the ultimate strength of a structure is not simple to calculate. It depends on the
nonlinear responses of components within a frame and the interaction between those
components. Figure 1.1 illustrates the three primary bracing types (a, b, d) used alone or
in combination in jacket structures. The presence of alternative load paths within a panel
ensures that (d) the X-bracing offers greater reserves than either (b) the K-bracing, or (a)
the single diagonal bracing. However, the degree of reserve depends on the slenderness
of the braces and redundancy throughout the structure. The hybrid structure (c) is not
whereas for (e) failure of one
therefore considered satisfactory in API RP 2A
member could be tolerated without structural collapse. Furthermore, the structural reserve
depends on alternative load paths through other panels within the frame, (Figure
as
well as on three-dimensional framing between planes (Figure 1.3).
Linear analysis of the first structure in Figure 1.2 would show there to be negligible load
in the horizontals between the panels. However, in the event of damage (diagonal braces
removed), these horizontals would be essential for maintaining framing action through the
structure. The idealised structures in Figure 1.3 were used by Lloyd (1982) to determine
the minimum structural weight to achieve a desired residual capacity beyond primary
member failure. A simple linear programming technique was adopted. Elastic analysis
again showed the face frame horizontals and diagonal plan framing in A to be redundant
for the applied loading regime, but in the event of a brace 'failure' these members provide
important alternative load paths to distribute the forces efficiently down through the
structure.
Since the 1970s experimental programmes have been implemented to provide data on the
collapse behaviour of frames (see Section 3). In addition to revealing the response
characteristics, the results enable reserve strength to be quantified and provide physical data
against which nonlinear software can be verified. Indeed, in parallel with the experimental
work, a number of 'pushover' analysis programs have been developed, embodying not only
material nonlinearity but also large displacement behaviour inherent in structural collapse
(see Section 4). These programs have been applied to a number of frames, representative
of jacket structures. In some instances the full ultimate response has been evaluated; in
others, a simplified approach in which 'damaged' members are removed has been taken to
evaluate the residual capacity (see Section 5).
The investigations (particularly numerical) have often been motivated by specific problems
in the field. Nevertheless, sufficient results now exist for the findings to be drawn together
to start to give an overview and comparison of the reserve strengths of different structural
forms. Reserve strength is an important yardstick of safety and the results of this work will
be useful in both the design of new structures and requalificationand assessment of existing
installations.
It is on this basis that the Health Safety Executive commissioned Billington
Moss Engineering Limited (BOMEL) to undertake the present review of the reserve
strength of framed structures. The principal research effort in the UK in relation to reserve
and residual strength has been undertaken within the Joint Industry Funded Tubular Frames
Project, first at the Steel Construction Institute (Phase I, 1990) and then by Billington
Osborne-Moss Engineering Limited (Phase 1992) to whom the project was transferred.
The project, described more fully in Sections 3, 4 and 5, encompassed collapse tests on
large scale tubular frames as well as the development of advanced nonlinear software for
the pushover analysis of 2D and 3D frames and jackets. This review presents the test
results and places them in the context of other research findings.
1.2
OBJECTIVES AND SCOPE OF THE REVIEW
The principal objective of this review is to draw together all available data on the reserve
strength of frames from experimental and analytical sources, to provide the offshore
industry with a base reference for assessing the ultimate response of different structural
configurations.
The focus of the review is on system behaviour and the contribution of frame action to
reserve strength. The information is largely deterministic, based on collapse tests or static
pushover analyses, however results from reliability based investigations are introduced.
The intent was to encompass both joint and member failures within the review but the
greater emphasis is on member dominated responses, reflecting the bias within the
literature.
Sources of implicit and explicit reserves listed in Section 1.1, other than system behaviour,
are not considered in depth in the study. It was noted in Section 1.1 that uncertainty in
environmental criteria and load generation also influence the overall reliability. These are
important issues but are beyond the scope of this review.
1.3
DEVELOPMENT OF THE REVIEW
The main text of this Review was completed by February 1993. The document was
expanded in August 1993 specifically to include a series of papers examining the validity
of static pushover analyses to evaluate ultimate structural response characteristics in a cyclic
storm loading environment. In reformatting the review in anticipation of publication in
January 1994, reference was included to the first draft of a Section 17.0 to API RP
WSD for the assessment of existing platforms which was first published in December 1993.
A final appendix was added in May 1995 to describe the principal developments in relation
to industry's understanding of ultimate system strength and its application of the technology
in the intervening period.
DETERMINATE
WEAKLY REDUNDANT
STRONGLY REDUNDANT
STRONGLY REDUNDANT
Figure 1
Principal bracing configurations-adoptedin offshore jacket structures
'NO
LOAD IN
THESE MEMBERS
figure 1.2
Alternative load paths through bracing
figure 1.3
Alternative plan bracing to distribute loads in
2. DEFINITIONS AND PRACTICAL
CONSIDERATIONS
In assessing the ability of a structure to withstand loads in excess of the design load or to
sustain loading in the damaged state, some measure of this ability is required. Terms such
as reserve and residual strength, and redundancy are used and it is appropriate that this
review should begin with a clear definition of these terms and their usage.
2.1
RESERVE STRENGTH
Concepts of reserve strength were introduced in relation to seismic assessment where
Blume's 'Reserve Energy Technique' (Blume, 1960) defines the reserve capacity B, as:
Energy Capacity
Energy Demand
Eqn 2.1
Reserve strength is now more commonly defined as the ability of a structure to sustain
loads in excess of the design value. Care should be taken in comparing alternative
safety factors and
structural configurations with respect to the design basis
the reserve strength definition adopted (see also Section 2.2). For example, in working
stress design (WSD) the ultimate platform resistance should exceed the design load by a
margin equivalent to the required safety factor and reserve strength should perhaps only be
taken as any additional capacity.
Reserve strength exists at the component level to allow for uncertainties in both the
resistance of the component and the loading to which it is subjected. Based on statistical
data, characteristic values are adopted to ensure that the probabilityof failure is acceptable.
Beyond that, safety factors are applied to improve the certainty of survival and to allow for
factors for which no statistical data are available (eg. for inaccuracies in structural analysis
techniques). It is clear that the actual capacity of a component is likely to exceed the
allowable loads for which it is designed.
At the system level, however, there are additional sources of reserve strength. The failure
of one component may not limit the capacity of the structure as a whole, provided there is
adequate ductility and redundancy such that loads can be redistributed. For more complex
(highly redundant) structures, a sequence of component failures may occur before the
ultimate strength is reached. Elastic design capacities are limited by the theoretical
occurrence of first component failure. The Reserve Strength Ratio (RSR) (eg.
and
1988) may be defined as:
RSR =
Ultimate Platform Resistance
Design Load
Eqn 2.2
This is comparable to the Reserve Resistance Factor (REF) defined by Lloyd and
(1984) as:
REF =
Environmental Load at Collapse (undamaged)
Design Environmental Load
Eqn 2.3
The term 'RSR' will be adopted in this review.
In the literature RSR is measured in a variety of ways and, other than the ratio of the
ultimate platform resistance to the design load, RSR is also quoted as ratios of platform
base shear or overturning moment. It should also be recognised that for a single platform
there is a separate RSR for each load case or load combination. Indeed, in many instances
the loading case which produces the highest component utilisation at the design load level
is not the loading case which produces the lowest RSR. Therefore, as illustrated later,
when assessing the RSR a full range of load cases must be considered in order to ensure
that the most critical case is identified.
Figure 2.1 illustrates the reserve strength of a test structure. The ratio of the peak load
is the reserve
sustained by the intact structure compared with the design load
strength.
2.2
DESIGN PROCEDURES
Concepts of reserve strength as noted above are inextricably linked to design criteria and
it is therefore necessary that typical design procedures should be reviewed. For existing
structures, and the design of some conventionaljacket structures in the near future, working
stress principles apply. From a working stress view-point, design loadings (eg. from a
year return period storm) are applied to the structure and the forces and moments in the
components are compared with the 'allowable' values taken from the prevailing Codes of
Practice or Guidance, encompassing the appropriate factor of safety. In simplistic terms,
so long as the design loads do not exceed the allowable capacities on a component by
component basis (ie. the utilisations are less than unity) the structure may be deemed
adequate. Typical guidelines therefore address how the elements of a structure should be
proportioned, but not how the assembled elements or structural system should perform.
These are left to engineering judgement.
In Section 1 it was shown how members which carry negligible load under elastic loading,
can provide a significant contribution to maintaining overall resistance in the event of
damage to other parts of the structure. This concept has been formally embodied in API
RP 2A (1993) where earthquakes are a necessary inelastic design consideration for US
waters. The RP 2A commentary relates to the proportioning of members (and joints) to
provide adequate ductility and diagrams, reproduced in Figure 2.2, illustrate structural
configurations which do and do not comply with the guidelines. In addition, clause
of the commentary refers to members with low utilisation:
..These horizontals
have small loads for elastic analysis but are required to pick
main
up substantial compressive loads to prevent the structure from "unzipping"
diagonals buckle.
Although introduced to cover earthquake loading scenarios, these concepts are also clearly
related to considerations of the ultimate structural response under extreme storm loading.
Load and resistance factor (LRFD) limit state design codes are now in place and although
these still focus primarily on component adequacy, in some instances they also contain
explicit provisions for system behaviour. However, the LRFD formulation may first be
compared with a working stress design (WSD) approach at the component level. The WSD
acceptance criteria for components may be given by the following inequality:
Eqn 2.4
where R =
D =
E =
F =
characteristic ultimate resistance or strength
stillwater loads
environmental loading due to wave, wind and current in the event of storm
conditions
factor of safety which varies with component and loading mode. (In
storm conditions given by E, a
overstress is generally
allowed. In the case of a tubular joint, for example, the normal safety
factor of 1.7 is thereby reduced, so F = 1.711.33 = 1.28.)
By contrast with the all-encompassingsafety factor, F, in WSD, a range of partial factors,
are adopted for LRFD to reflect the respective uncertainties on individual elements of
loading and resistance:
Eqn 2.5
where
=
=
=
=
material coefficient
structural coefficient
stillwater load coefficient
environmental load coefficient.
The above comparison becomes important to considerations of reserve strength where
reference is made to the design load. Under WSD, a significant margin, corresponding to
the safety factor F, is required between the applied loads, D and E, and the available
resistance. However, for an LRFD structure, the design loads are the factored values,
and
thus the required margin between the resistance and design loads relates only to
structural and modelling uncertainties contained in
and y,. Given this discrepancy, an
RSR relating ultimate platform resistance to design load needs careful qualification to
prevent confusion in identifying a target RSR.
With regard to design requirements for system behaviour beyond specific earthquake
provisions, the NPD rules (1990) mark a significant advance. Section 5 of the document
identifies the 'Progressive collapse limit state' and begins with the general statements:
"In
progressive collapse limit state the structure is checked against design accidental
loads or abnormal environmental loads. These loads are assessed in relation to the risk
for extensive damage to or collapse of the structure. Because these loads are large and
their probability of occurrence very low, it is normally not practical to design the structure
such that the local capacity can resist the loads. In some cases increased local strength
may even reduce safety against total collapse.
It is required that abnormal loads should be withstood with only local damage and that in
the damaged state the structure should be able to withstand defined environmental loads
without further collapse. The only quantified guidance given is that:
"Where a large characteristic resistance is unfavourable with respect to the safety, the
rather than the 5% fractile.
characteristic capacity should be based on the 95%
The design resistance shall be
with the material coefficient,
set to 1.0, and,
in accordance with Section 3.1.3.
for the design of shells, a structural
This reduction in
from 1.15 to 1.0 reflects the lesser probability of, for example, poor
material combined with the extreme or abnormal loads and the uncertainty already
embodied in the rare event (104). For guidance on the assessment of the structure, the
designer is referred to the technical literature, and similarly API RP 2A-LRFD (1993)
Moses (1982).
makes reference in this context to papers by Lloyd and
Gates et al (1977) and Lloyd (1982). It is clear that consideration of concepts such as
reserve strength, redundancy and ductility is now required of the designer and the following
subsections define these additional terms.
2.3
REDUNDANCY
Fixed offshore structures generally have a multiplicity of load paths such that failure of a
single member does not necessarily lead to catastrophic structural collapse. This is
attributable to the 'redundancy' of the system but it is demonstrated below that careful
definition of the term is required.
In conventional deterministic structural engineering, redundancy is generally equated to the
degree of indeterminacy, ie. the number of unknown internal member forces in excess of
the number of degrees of freedom of the system. However, this definition is not
satisfactory for evaluating the ability of a structure to withstand overloads in the intact or
damaged condition. It does not account for the existence of a weak link in an otherwise
highly redundant system or the distribution of redundancy (or under utilisation) throughout
the system. See Figure 1 for an example of such a 'weakly redundant' system. Lloyd
and
(1984) suggest that, in practice, each member should systematically be
removed so that the consequences, in terms of the remaining capacity beyond which
progressive collapse occurs, can be evaluated. In this way the concept of residual strength
was developed. They present the hierarchy reproduced in Table 2.1 to demonstrate the
gradation in redundancy that can be afforded by different members. Such an approach can
be used as a basis for sizing members to give adequate redundancy.
Table 2.1
Member redundancy hierarchy for indeterminate structures given by Lloyd and
Member
Redundancy
Level
Member Classification
-
p
-
A member whose failure leads to
-
-
collapse for dead weight load conditions.
A member whose failure leads to progressive collapse for dead plus some fraction of live
weight load conditions.
A member whose failure leads to progressive collapse for a limited set of load conditions
that include dead and live loads in combination with some fraction of the design
environmental load.
A member whose failure leads to progressive collapse for a limited set of load conditions
that include dead and live loads in combination with some multiple of the design
environmental load.
A member whose failure has
effect on the design strength, but whose presence
enhances the redundancy of nearby members, ie. a normally lightly loaded member that
provides an alternative load path when a nearby member fails.
A member whose failure has no bearing on the design, reserve or residual strength, ie. a
member.
In 1979 Marshal1 proposed two alternative measures of redundancy. For simple systems
a redundancy factor (RF)
with a number of identical parallel load carrying elements
was defined as:
Values of RF less than unity therefore imply a high likelihood that initial failure will lead
to collapse, whereas very high values relate to damage tolerant structures.
The alternative measure is the damaged strength rating (DSR) given by:
damaged strength
intact strength
-
Eqn 2.7
is not directly available, the effect of damage is
For more complex structures where
established by comparing the results of structural analyses for the intact and damaged
structures. This will be illustrated in examples presented in Section 5.
In later work by
is defined as:
RF =
et al (1988) another definition of redundancy, again denoted RF,
Ultimate structure resistance
Structure resistance at which first member fails
Eqn 2.8
In some ways this definition may be considered to be more akin to the foregoing definitions
of reserve strength. Nevertheless, the notation indicates the strong correlation between
redundancy and system reserve. Use of this measure of redundancy, RF, will be
demonstrated in the presentation of specific results which follows. Caution in determining
first member failures is also required, however. It might be considered as the first
occurrence of plasticity which needs to be defined in terms of complete section or extreme
fibre conditions, or otherwise might be linked to buckling and a loss of a component
capacity. Recent use of the term 'System Redundancy Factor' (SRF)
has
referred to first major member failure, to avoid reference to early failure of a secondary
component which plays no part in the overall system response. It should be noted that in
some instances first component failure may not necessarily be related to a member and
tubular joints and foundations may need to be considered.
In the jacket study by Nordal et al (1988) probabilistic measures were introduced and
and
respectively,
additional consideration of these is given in Section 2.6. Taking
as the safety index for the full system and for the union of first member failures (ie. the
combined probability of any member failing first), a redundancy measure:
is proposed. For a statically determinate system P,,,, = P, and therefore redundancy is
given as zero, whereas for a highly redundant system P,,,,
P,, such that this
redundancy measure would approach unity.
Nordal et al also present a more direct measure of redundancy based on the conditional
probability of system failure given any first member failure. This latter definition relates
the failure probabilities for the system and union of first member failures, as for the safety
index approach above. The authors also suggest that in some circumstances the conditional
failure probability can be approximated by the ratio of probabilities associated with the
most-likely-failure-pathto the most-likely-to-fail-first-memberwhich is easier to obtain than
the combined probabilities.
On the basis of the various redundancy measures proposed to date it is difficult to draw
generalised conclusions. It should be noted that many of these measures are load case
dependent and any structure may exhibit very different redundancy properties for different
loading directions. For example, in one direction the structure may be able to mobilise out
of plane bracing to shed load whereas for an orthogonal direction this may not be the case.
Further consideration of structural configurations and orientation will be given in the
reviews that follow.
2.4
RESIDUAL STRENGTH
The concept of residual strength is particularly important in assessing the capacity of a
structure which has been damaged, be it due to accidental loading, fatigue, fracture or
(1984) define residual strength in terms
extreme environmental loads. Lloyd and
of a Residual Resistance Factor (RIF) given by:
=
Load
Load
Collapse
Eqn 2.10
The ability of alternative load paths to carry applied loads in the presence of damage
governs the residual strength of the structure as a whole (see Section 2.3).
Figure 2.1 illustrates an alternative representation of the residual strength for a test
structure. The remaining capacity once a component has failed compared with the peak
load sustained
is taken to represent the residual strength. The two measures would
be the same if the damaged structure sustained applied loads up to the post-ultimate plateau
level (Z). Generally this will be the case but loads are not necessarily shed from damaged
components to give the same force distribution as if the loads were applied to the damaged
structure from an unloaded state. This distinction should be recognised. It can be seen
from the figure that if the product of the reserve and residual strength factors
exceeds unity, the structure is able to sustain the design load even in the damaged condition
(ie.
Nordal et al (1988) adopted an alternative probabilistic view of residual strength, termed
'robustness'. The probability of system failure in the presence of damage compared with
the intact structure, is defined as the robustness factor. The lower the robustness factor,
the less effect the component failure has had on the system.
to compare the post-ultimate and
The term robustness is also used by
ultimate system strengths as a measure of resilience or a structure's ability to dissipate
energy through nonlinear hysteretic cycles.
It will be seen in the sections that follow that in published work to date, little attention has
been paid to residual strength or robustness in the overload condition and this may in part
be due to the analytical complexity of modelling load shedding beyond the peak load.
Frequently residual strength is estimated by removing 'damaged' members (eg. Piermattei
et al, 1990) or by introducing damaged member properties (eg. Martindale et al, 1989) and
performing a new analysis. If adequate data are available the latter approach is to be
preferred as it will more accurately reflect the load distribution through the structure. In
the first instance the concern is that, although the approach may be conservative from a
local viewpoint, it may not lead to conservatism in predicting the overall nonlinear collapse
behaviour of the structure. Furthermore it may be necessary to consider the sequence of
loading, component failure and redistribution, as removing members and repeating the
analysis from the unloaded state may not yield the same load distribution and hence ultimate
response.
2.5
DUCTILE VERSUS BRITTLE RESPONSES
In the context of overall structural performance, the terms 'ductile' and 'brittle' are used
to identify the stiffness characteristics of the responses. If the global capacity is maintained
or continues to increase despite a component 'failure', the behaviour is said to be ductile.
If rapid unloading (ie. a reduction in capacity) occurs, the response is described as brittle.
At a component level ideal tensile yield is clearly ductile (provided the material is ductile)
as shown in Figure 2.3, whereas rapid load shedding associated with fracture is brittle.
The more gradual unloading of tubular beam-columns is an intermediate case where the
for
reduced residual capacity is described as semi-brittle. Marshal1 and Bea
example, use the terms further in the descriptions of 'brittle-redundant' and
redundant' structures and responses.
Concepts of ductility and brittleness lead on to considerations of reliability, ie. if two
systems have the same reserve strength but one is ductile and the other brittle, can the
system reliabilities be equal? This is explored with the following example due to
and
illustrated in Figure 2.4.
Two simple systems are considered: single X- and K-braced panels. Compression and
tension members are denoted C and T, the applied load is Q and the member load F. If
failure occurs in a K brace the load path through the panel is lost - the tension and
compression braces are effectively in series and the response is brittle (see Figure 2.4).
In the X-braced case, if the compression brace buckles additional load can still be carried
through the panel via the tension brace. So long as the stiffness of the tension brace
exceeds the rate of unloading from the compression brace, the panel as a whole can take
increasing global load. The members may be considered to act in parallel and the response
is ductile.
If the braces are designed to the same codes the reserve strength of the K panel will equal
the safety factor adopted, whereas for the X panel (depending on the brace slendernesses)
it may be greater due to the tension brace contribution. This is a result of frame action,
ignored in traditional elastic design. Using first order second moment reliability techniques
the example indicates an annual failure probability of 4x104 for the K-braced panel
(an order of magnitude lower) for the X bracing. It may also be
compared with
concluded that the reserve strength factor increases as the tension to compression strength
ratio increases (see Section 2.1 above).
The term ductility is also used in another context for problems such as seismic loading or
impact. Ductility is an important property for consideration of energy absorption. A
ductility ratio is used to characterise plastic deformation capability and is the ratio of total
available deformation to initial peak elastic deformation (see Figure 2.5). Energy
absorbtion capacity is equivalent to the area under the
curve for the
structure and is also related to the post-peak capacity as discussed in Section 2.4 above.
2.6
RELIABILITY BASED VERSUS DETERMINISTIC APPROACHES
Both deterministic and reliability based approaches are being adopted to investigate the
collapse behaviour of jacket structures. The deterministic approach is to perform a static
pushover analysis, using specific nonlinear software, to evaluate the peak and post-ultimate
capacities of the structure for comparison with the design load. The member properties,
geometry and loading are considered to have unique values.
In reliability based approaches member properties, geometry and loading are considered as
variables with known or assumed distributions. Simplified structural assessments are
performed to identify 'important' sequences of component failures, ie. sequences which
have a high probability of occurrence. The results are generally presented in terms of
The two measures may be
either the probability of occurrence, P, or the safety index,
considered to be equivalent based on the relation:
Eqn 2.11
where
) is the cumulative normal distribution.
Although the details are beyond the scope of this review, it has been found that for intact
structures, the failure mode and capacity established by a deterministic pushover analysis
is usually an adequate representation of the structure for a system reliability analysis. The
reason is attributed to the far higher uncertainty in environmental load than for resistance
1994).
2.7
PUSHOVER ANALYSIS AND CYCLIC LOADING
Reserve strength is assessed in terms of a structure's ability to resist a load in excess of the
design value (Section 2.1). For a jacket structure it is typically evaluated by applying the
maximum loading from the extreme event and performing a so-called 'pushover' analysis.
Although this static approach to collapse is now widely adopted, the relation between the
models and the real situation needs to be reviewed. For an extreme storm the
environmental loading is cyclic, imposed on an underlying dominant direction. The
maximum wave is unlikely to be an isolated event, but will be a peak in a series of extreme
loads. The possibility of cyclic degradation of components which have failed, or are near
failure even though the overall structural resistance may remain adequate, therefore needs
to be considered. Low cycle-high stress fatigue from either the same or different events
et al, 1991) where the effects of shakedown were
is the subject of work at SINTEF
initially studied using nonlinear FE analysis. Results published in 1993, based on studies
of North Sea jackets, suggest that an extreme event static analysis generally suffices to
demonstrate a structure's resistance to the cyclic loading of a full storm. These important
findings are reviewed here.
The jacket studies conclude a set of four papers presented by investigators drawn largely
from SINTEF and Shell Research at the Offshore Mechanics and Arctic Engineering
Conference in 1993
et
and Tromans, Eberg et al and
et al) to
establish whether strength estimates based on pushover analyses are suitable measures of
system capacity. Without this work significant questions regarding the applicability of
ultimate strength 'pushover' analyses to offshore structures might remain. For this reason
the methodology and modelling of cyclic loads is reviewed in this section and the resistance
nonlinear collapse analysis program USFOS are covered
models developed for
before the presentation and discussion of the case studies in Section 5.
The principal concern is whether cumulative damage due to cyclic loading will reduce
system capacity below predictions from the single 'worst' event. In this regard cyclic
loading may be associated with the sequence of loading in a given storm or with the
occurrence of storms over a longer time period.
and Tromans examined both short
term and long term wave statistics and established that one extreme storm may be
considered to dominate the load history and this may be represented by factoring the
year 'design storm' to give a rare event with a notional 10,000 year return period. The
sequence of the diminishing waves within the design storm is shown to be modelled
conservatively by a 'pseudo-storm' comprising the most probable largest waves in the
storm, thereby ignoring short term effects. Were these taken into account, it is shown that
the second and subsequent waves in the storm would be smaller than those given by the
pseudo-storm.
The environmental load history proposed for a cyclic assessment is shown in Figure 2.6.
This storm loading history for cyclic analysis parallels the single storm load applied in static
pushover analysis. Within the sequence, the 100 year wave loading is applied initially to
identify alternating plasticity at low storm intensities. The above extreme storm is then
factored (a factor of 1.5 corresponding to the 10,000 year event) with the application of
waves in descending order having been shown to be most damaging. Finally the 100 year
loading is re-applied as a stability check after the passage of the storm.
The bias in the load history results from the forward action of the combined wave crest,
current and wind and reverse action of the wave trough opposed by the forward current in
the absence of wind.
et al report the ratio between reverse and forward loads to be
in the range 0.23 to 0.37 for the North Sea jacket study which is much less damaging than
if alternating plasticity were to be generated by complete load reversals.
Having established a representative loading scenario the potential responses of a structure
to cyclic loading need also to be considered. When a structure is loaded into the
plastic range yielding occurs reducing the stiffness and introducing permanent plastic
deformations. Under cyclic loads the yielding repeats and can result in three different
forms of response as shown in Figure 2.7:
Low cycle fatigue or fracture is associated with large inelastic straining locally within
a structure. The global structural response presented in Figure
shows how low
cycle fatigue does not necessarily trigger global instability, although this may follow
further cyclic loading.
Incremental collapse occurs as loading cycles impose significant overloads,
continuously exceeding the elastic recovery until the excessive deformations lead to
structural collapse (Figure
Shakedown imparts a linear (desirable) characteristic to the subsequent response of the
structure. It is associated with moderate overloads whereby the structure yields less
until the elastic state is achieved. This
and less with each loading cycle (Figure
is associated with permanent plastic deformations but the associated residual stress field
counteracts the effect of the wave loads.
The maximum load intensity at which a structure shakes down to an elastic state (ie. the
divide between the conditions in Figures
and
is defined as the cyclic capacity.
The critical question in the assessment of reserve strength is therefore to determine whether
the system strength demonstrated in a static pushover analysis will be degraded due to the
repeated action of extreme waves, or whether shakedown can satisfactorily occur. Based
on a series of case studies as noted above,
et al (1993) and
et al (1993)
conclude that pushover analysis does generally suffice to assess a structure's integrity.
Detailed results are discussed in Section 5 and, although verification work is continuing,
the investigations increase the confidence that can be placed in reserve strength assessments.
2.8
TREATMENT OF LOADS AND SAFETY MARGINS IN RESERVE
STRENGTH ASSESSMENT
It is clear that reserve strength is an important measure of structural system performance.
However, in most practical cases combinations of different types of load (eg. permanent,
functional, environmental, accidental) produce the critical case for calculation of reserve
strength. Furthermore in structures where ultimate load is reached after significant
plasticity and redistribution have occurred, the sequence of load application can affect the
final result. In such circumstances the order in which loads are applied and the choice of
partial factors used to interpret the results require careful consideration and will vary
according to the purpose of the analysis being undertaken. The following scenarios may
be considered illustrative:
a. An existing jacket structure, for which, for various reasons, some existing components
year design condition.
fail to meet current code criteria for the
b. A new structure under design for which the relative contribution from framing to
reserve strength is to be assessed.
c. A structure, designed on the basis of 100 year storm criteria, for which additional
consideration of less likely but more onerous events is now required.
It will be shown in Section 5 that typically still water loads are applied and held constant
whilst environmental loads are increased until ultimate capacity is reached. This approach
is implicit in the definition of reserve strength presented in Section 2.1 above. This may
be useful in providing a relative measure of reserve strength, for example in consideration
of Case b.
However, within this approach, the proportion of stillwater and environmental loads in the
components changes and the effect will vary with water depth, platform geometry and
bracing patterns. The relative load contribution at the ultimate load may not be meaningful
or realistic. If such an approach is adopted, some decision as to the percentage of
identified reserve strength which can be utilised in a reassessment exercise needs to be
taken
and Edwards, 1992). Alternatively, all loads could be increased by a
constant factor but it may be considered that greater confidence can be placed in predicting
the stillwater loads than environmental. On that basis different factors may be considered
applicable - perhaps based on the partial factors now embodied in limit state design
(LRFD), where
exceeds
on a rational basis. Such an approach may give a better
confidence measure that a given structure, be it damaged or
code provisions, will
be able to mobilise structural reserve and withstand the extreme event.
In general terms the ultimate strength check may be formulated as in Equation 2.5.
of 1.3 with
Norwegian Petroleum Directorate limit state criteria require a load factor
equal to unity. The appropriate material factor, y,, depends on the critical component
but for member failure a blanket value of 1.15 may be assumed. It is convenient for
pushover analysis to combine the factors on the applied loads for comparison with the
calculated resistance. Therefore, for compliance with the NPD limit state safety criteria,
and
pushover analysis should be undertaken with stillwater loads factored by 1.15
= 1.15 1.3).
environmental loading increased to a factor beyond 1.5 (ie.
The relation between base shear and wave height for drag dominated structures indicates
that 1.5 times the
year wave loading corresponds approximately to the 10,000 year
et al, 1993).
wave giving a notional failure probability of
A further consideration in reserve strength analysis is the confidence level in the accuracy
of the analytical results. In nonlinear analysis there are many more options in the ways in
which the various types of nonlinearity are represented and the ways in which the structure
is modelled. As is shown later in this report, there has to date (1993) been little
opportunity for benchmarking of different software packages against representative test
results for offshore tubular frame structures and there have been few comparative analyses.
Therefore, in considering RSR values obtained from analysis, the level of validation of both
the program and analysis technique should be allowed for. [Appendix A is an update to
this review and presents benchmark analyses reported between 1993 and May 1995.1
Where an extreme condition is being addressed, as in Case c, it is less appropriate to factor
the design wave. Instead a meaningful prediction of the loads is required which may for
example include direct loads in the deck due to wave impact. In such cases the load
distribution will be determined for the critical load case (eg. blast, ship impact, earthquake,
abnormal environmental loads such as hurricanes, typhoons, etc). The proportion of this
load causing first yield will be calculated and beyond this value the loads will be
incremented in the same proportion until ultimate load is reached. There is likely to be
significant uncertainty in the loading and an appropriate target RSR for the structure will
need to be assessed. In addition, the combined probability of the extreme event and
minimum material properties is lower than for each individuallyand reduced partial factors
on resistance may therefore be permitted.
An alternative approach being taken by the API Assessment Process Workgroup, (API
draft, 1993) is the specification of the return period loading which the structure should be
able to sustain if it is to be deemed satisfactory. The criteria are differentiated according
to geographical region, exposure category (environmental safety and life safety
combination) and type of analysis (screening, design level or ultimate strength).
The importance of dynamic transient loading effects on the ultimate response of offshore
jacket structures can be demonstrated by deriving an appropriate modification factor. Bea
and Young (1993) separate imposed 'loadings' and 'loading effects' which are determined
by performance characteristics of the structure-foundation system. Based on comparative
results of static collapse and time domain nonlinear analyses for Gulf of Mexico structures
in hurricane environments, an apparent increase in RSR by a factor of 1.2 is suggested.
In addition, extreme events such as impact or accidental loads may need separate
effects.
consideration of the dynamic load and
A further key difference from practice is the performance of analysis and tests under
displacement control. This enables control of tests to be maintained and the mechanisms
of load shedding and redistribution to be modelled analytically. In practice however, if the
environmental loads are increasing, once the peak platform resistance is exceeded, the
platform deflects to collapse.
As an introduction it can be seen that the strategy of assessing reserve strength is complex
and remains an area for keen debate and further areas of uncertainty can be cited. Even
if a ductile response is maintained, the practical limits on deformation need to be
considered. Pushover analysis will be seen to focus largely on jacket models in which the
topside is simulated. In practice the need to maintain serviceability of piping, vessels or
equipment will limit the global deflection that can be safely sustained. The deflection
limits, for example for the operation of emergency equipment or the flexibility of risers,
will vary between structures. Deflection criteria therefore need to be developed.
2.9
CONCLUSION
In this section some key considerations in evaluating the reserve strength of jacket
structures have been introduced. Their simple definition has been shown to be complicated
by many factors arising from differences between design processes, structural configuration
and the purpose of assessments.
In order to provide some comparison in this review, the following terminology is adopted
wherever possible.
Reserve strength ratio
ultimate load at collapse
RSR =
design load
Eqn 2.12
Redundancy factor
RF
=
ultimate capacity
capacity at first member failure
Residual resistance factor
damaged structure capacity
RIF =
ultimate capacity
Eqn 2.13
Eqn 2.14
Responses are described as brittle when the overall load deflection curve for the structure
exhibits a rapid reduction, whereas ductility describes a gradual change in the resistance
curve.
In many instances sufficient information is not provided and alternative presentations are
necessarily adopted. Sometimes the obscurity is intentional as the results relate to
investigations for critical platforms. However, in all cases there is an attempt to explain
the work and its basis so that final comparisons can be made.
Having raised several areas of uncertainty at this early stage in the review, the relation with
the current literature can be explored and the various points are discussed further in Section
6.
Y
CAPACITY OF
FRAME
CAPACITY OF OAMAGEO FRAME
8
FRAME DESIGN LOAD
Measured
response
GLOBAL FRAME DISPLACEMENT
Figure 2.1
Definitions of reserve and residual strength
FIG.
FRAME CONFIGURATIONS NOT MEETINGGUIDELINES
CONFIGURATIONS
API
GUIDELINES
2.2
guidelines for ductile configurations
MAX.
CAPY.
I
IDEALLY DUCTILE
TENSION MEMBER
YIELD
BRITTLE FAILURE
AXIAL STRAIN
Ductile and
Figure 2.3
failure modes (taken from
and Bea)
F
K-BRACE
X-BRACE
X-BRACE
TENSION
MEMBER
COMPRESSION
MEMBER
DISPLACEMENT
(NOT TO SCALE FOR
Figure 2.4
Series and parallel K- and X-bracing analyses and illustration of X-bracing reserve
and
(due to
DUCTILITY RATIO
I
ID
3.0
20
(INCHES)
Figure 2.5
Ductility ratio quantifying plastic deformation capacity based on Gates et
100-year loading
(or
Extreme storm loading
storm loading)
Figure 2.6
Environmental load history for cyclic assessment due to
100-year loading
and Tromans
Load
Low cycle fatigue fracture
yield
a)
global
Low cyde fatigue
Load
, Single
yield
wave
deformations
Deck displacement
b)
collapse
Load
Initial
yield
Shake down state (elastic)
displacement
c) Shakedown
Figure 2.7
Failure and survival modes under cyclic loads
et
3. EXPERIMENTAL INVESTIGATIONS
A number of experimental programmes have provided physical data on the reserve and
residual strength of tubular frames representative of offshore jacket structures. Not all the
tests reported here were undertaken for this specific purpose, nevertheless relevant data (for
example from the first cycle in high stress seismic loading scenarios) have been extracted.
The available results are reviewed in turn in Section 3.1 below, and these are followed by
a comparison and discussion in Section 3.2.
In evaluating the reserve strength of test specimens, the allowable loading for a
to code requirements is calculated based on the specimen geometry.
The ratio of the ultimate capacity sustained to this design load then gives the reserve
strength ratio (RSR) for the structure. This approach is appropriate for simple test
structures but differs from the evaluation of offshore jackets. These are designed for a
range of loading scenarios and components are sized to give elastic utilisations less than
unity in all cases.
Furthermore, test investigations generally identify exact member properties in terms of
diameter, wall thickness and material yield stress based on tensile coupon test results. In
the assessment of jacket structures only nominal or minimum specified properties are
generally available. However, to adopt these in the assessment of test specimens, although
attractive for giving a comparative basis, may not be practical. For example, test
specimens are loaded slowly and the results from static tensile coupon tests are more
relevant than from conventional dynamic testing. Material grades at the scale of testing
may differ and the associated distribution of yield stresses may not be the same. Similarly
ERW pipe is often adopted but is annealed after delivery, the minimum specification would
therefore not be an appropriate reference.
Caution should therefore be exercised when comparing ultimate strength evaluations for test
structures (based on measured properties) with predictions for jacket structures (using
nominal values) to ensure that this source of reserve strength is properly accounted for.
3.1
BACKGROUND TO TEST PROGRAMMES
The presentation of the experimental programmes begins with the simplest, single bay twodimensional (2D) frame and continues, generally with increasing complexity, to the threedimensional (3D) test results.
The scope of the various experimental programmes completed to date, and their order of
presentation here, is summarised in Table 3.1.
3.1
Experimental frame test programmes
Principal Reference
Test Frame Configuration
Briggs and Maison (1978)
single-bay, X-braced
Ogawa et
(1987)
1
Grenda et
(1988)
single bay, K-braced
- member failure (4 frames)
single bay, K-braced
- joint failure (4 frames)
single bay, X-braced
- member failure (2 frames)
two bay, X-braced
- member failure (2 frames)
failure (2 frames)
BOMEL 992)
Popov et
(1980)
SCI (1990)
BOMEL (1992)
bay trusses (3 trusses)
2D, two bay, X-braced
Paik and Shin (1990)
two bay, K-braced
Inoue et
two bay, X-braced
Soreide et
(1984)
(1987)
single bay, X-braced
-joint failure (2 frames)
member failure
dented member failure
- member failures
frames)
- not tubular connections
fracture failure
dented member failure
Briggs and Maison
A set of tests were undertaken to complement the analysis of an offshore jacket face frame
(Gates et al, 1977) which will be described in Section 5. The jacket structure was
braced (see Figure 5.10) and the test model comprised a single primary bay as shown in
Figure 3.1. The member dimensions are noted on the figure, together with the coupon test
results for the API 5LB pipe. The test programme generally focused on the nonlinear
response of frames subject to earthquake (cyclic) loading, but one X frame was loaded
monotonically to failure and is presented here.
The load-displacement response of the frame is also plotted in Figure 3.1. The profile
indicates a gradual reduction in overall stiffness with no significant fall off in load carrying
capacity. This behaviour is in part a result of the low slenderness of the compression
braces. Indeed it is reported that the tension braces yielded before the compression brace
buckled. This strut exhibited overall ductile behaviour as an S curve column buckling
gradually developed along its length with the tension member providing mid point support.
Sudden local buckling eventually occurred when plastic hinges
at the upper end of
the compression member and was accompanied by a small drop in load. Thereafter,
deformation was concentrated in this buckled half of the brace with the other half
straightening out. Although slight cracking occurred in the tension member, it sustained
load at the yield plateau. The legs acquired the load shed by the compression brace and
enabled the overall structure resistance to increase as the deflections proceeded due to portal
frame action in the stiff squat legs. Throughout the test these legs remained elastic.
In Section 3.2.7 the possibility that locked-in pre-tension in the braces due to weld
shrinkage may have precipitated the tensile yield prior to compression buckling is
discussed.
Within the paper comparison is made with a finite element analysis conducted using the
DYNAS program (Section 4). It is notable that strut buckling is anticipated ahead of
tension member yielding which may result from the assumptions of effective length, the
flexibility of the joint or locked-in tension in the braces of the test specimen remaining after
fabrication. The test demonstrates the parallel action of the tension and compression brace
load paths through an X-braced panel, combined with portal frame behaviour.
Ogawa et
Cyclic tests were carried out on planar tubular trusses as shown in Figure 3.2 with
diameter chords and brace diameters of the order of
The trusses were fixed at
their left hand end with load being applied vertically in the plane of the page. Results were
reported by Ogawa et al (1987) and discussed further by Kurobane et al (1991).
The overall load deflection responses of the trusses for the first half loading cycle are
shown in Figure 3.3, together with a pictorial representation of the collapse condition
corresponding to the plateau. 'S' denotes localised shell bending deflection of the chord
wall in the joint. 'Y', in the B series specimens, signifies tensile yielding of the brace.
'B' denotes buckling of the brace which, except for specimen C, was out-of-plane. In all
cases, however, some in-plane movement preceded out-of-plane buckling of the braces.
Plastic hinges formed at both ends and the centre of the brace. The small circles denote
plastic hinge formation.
Within the A series specimens, A-2 had a thicker chord than A - l , whereas overlapping
joints in A-3 contrasted with the gap joints in A - l . Member buckling was the cause of
failure in all cases with a subsequent degradation of capacity and shell bending of the chord
wall at the joints shown. At the overlapped joints in A-3, this was accompanied by
localised shell bending deflections of the braces. From the load-deflection responses
shown, it can be seen that the thicker chord wall in A-2 has a positive contribution to
residual strength. The overlapped joints reduce the effective length of the compression
brace and defer buckling in A-3 compared with A - l .
The B series specimens were shallower than the A series and thus the effective length of
the compression members reduced. Specimens A-l and B-l were in all other respects
identical and the overall load-deflection responses may be contrasted as yielding of the
tension member in the latter case gives a more gradual failure mode. The thicker chord
in specimen B-2 enhanced the capacity of the truss such that on yielding of the tension
member, load was redistributed to the compression brace until that buckled precipitating
a small drop off in load in the response curve.
Specimen C was loaded to cause a buckling failure in the long compression brace. The
buckle occurred in-plane and was associated with a much lower overall capacity than the
capacities of the otherwise similar specimen A-l.
Table 3.2 compares the maximum load sustained with the load at which the critical brace
buckled.
Table 3.2
Comparison of reserve strength for different
Failure Mode
Specimen
Maximum
Load
Brace Buckling
Load
A-l
127.5
119.6
Brace 3 buckling
A-2
137.3
133.9
Brace 3 buckling
A-3
145.1
131.0
Brace 3 buckling
B- l
168.7
B-2
197.6
142.3
Brace 3 buckling
Brace 2 yielding
C-l
-83.8
182.4
Brace 2 buckling
Brace 2 yielding
It can be seen that the stockier members in the shallower B series trusses ensure that the
structural response is more ductile. There is additional reserve beyond first member failure
before the peak load is attained (B-2 versus A-2).
Grenda,
and Shinners
Static pushover tests were carried out at the Southwest Research Institute on six planar, Kbraced, single-bay tubular frames, some 9m by
in size, and with gravity acting out of
the plane of the frames. The configuration of the one-third scale test specimens of Bass
Strait platforms, is shown in Figure 3.4. Lateral load was applied at the top of the frame
and reacted at the base by pinned supports. In test specimens 2 and 3 the can thickness at
the K joint was 0.432 inches whereas in tests 1 and 4 the can was omitted, giving a chord
wall thickness of 0.156 inches, equivalent to the member geometry. The braces were
grouted in specimens 5 and 6. Table 3.3 summarises the test matrix for specimens 1 to 4.
Table 3.3
K-braced frame configurations and capacities
Test
number
Overlap K joint
configuration
Maximum applied
frame load
1
0.156" Can
170
2
0.432" Can
168
3
0.432" Can
157
4
Can
175
was governed by compression
In all four tests the ultimate frame load (given in Table
member buckling. The overall load deflection responses of the frames are given in Figure
3.4. It can be seen that as the compression brace diagonal subsequently sheds load, the
lateral load resistance of the frame declined with further frame displacement, with a
consistent post-failure stiffness from one test to another. The third frame was deformed
far enough to mobilise the portal strength of the legs which gave a residual strength some
two thirds of the peak value.
The insensitivity of the responses to the thickness of the K joint cans is attributed to the
degree of overlap; much of the compressive brace load was transferred directly into the
overlapped tension brace, thereby reducing the stresses in the can and thus its influence on
K brace strength. The response has in fact spawned further investigation of the relation
between frame behaviour and isolated joint capacities (Connelly and Zettlemoyer, 1989).
This latter numerical study is described in Section 5.1.
The effective lengths of the compression diagonals, which governed the buckling load and
thus the overall capacity of the test frames, were calculated from the measured curvatures
of the member. Details of the compression member responses are given in Table 3.4.
Table 3.4
K bracing behaviour in test frames
I
-Frame
test
1
2
3
4
Measured axial capacities - K brace compressiondiagonal
Brace yield
stress
54
52
52
51
Out of plane
k-value (5)
.63
.61
.57
.81
.77
.72
.67
Static stress at 0.2%offset strain
(2) In-plane k-value - Frame 4 diagonal buckled purely in-plane
(3) X =
(4)
= Fy Area of steel
(5) Calculated from measured curvature node to node
Peak brace
load (ksi)
Peak brace
112
116
112
1 16
.65
.71
.68
.72
At peak load the effective lengths for out-of-plane bending were slightly larger than the
factors for in-plane bending. The support conditions dictating the capacity of the
compression members, appeared from the curvature measurements to be nearly fixed at the
brace to leg joint and between fixed and pinned at the K node. Hence the measured
effective length values were slightly less than the theoretical fixed-pinned value of 0.70.
Figure 3.4 shows the rapid fall off in load from the compression braces once they had
buckled. Due to the small stiffness of the surrounding frame of a K brace (relative to an
X brace), analysis of K-braced jacket structures indicates a peak global load just a few
percent higher than that causing failure of the primary compression brace. The results
shown were used to assess the post-buckling stiffness occurring in practice. The steepness
of the gradient was attributed to the early formation of local buckles brought about by
nominal mismatch between cans and the girth weld residual stresses. The impact of this
finding would be greater for X-braced structures than for K-braced configurations, for
which the incremental platform strength beyond first failure is very small anyway.
Calculations to API RP 2A give a design storm capacity (ie. allowing a one third increase
in the allowable brace capacity) of 115 kips for the frames giving an average RSR of 1.46.
At the K brace component level the RSR is around 1.24 indicating that the frame action
from the legs contributes some 15% to the ultimate frame response.
The low reserve strength ratios are attributable to the high residual stresses in the ERW
tubulars used for the test frame. These precipitate earlier failure in response to applied
loads and invalidate the comparison with the API RP 2A design provisions which implicitly
assume steels of typical offshore grades and characteristics.
BOMEL
Within Phase of BOMEL's Frames Project, four single-bay K-braced frames (Figure 3.5)
in which the central K joints were the critical component were loaded monotonically to
collapse. Frames VII,
and X contained gap K joints, whereas the central node in
Frame IX was a concentric overlap joint (Table 3.5). Load was applied in displacement
control at the top of the frames and the supports were pinned at the base. Frame
is
shown prior to testing in Figure 3.6.
Table 3.5
Details of BOMEL's single bay K-braced test frames
Critical Joint
Frame
Test Objective
P
Critical gap K joint to investigate capacity variation
between isolated and frame mounted joint failures. K
joint failure to compare with previous critical X joint
frame tests.
Critical gap K joint with lesser to compare with
response of Frame VII.
Critical lap K joint to compare ultimate frame response
with gap failure.
Critical gap K joint with wider gap to compare with
and complete investigation of
response of Frame
typical K-braced frame configurations.
=
= chord
diameters
=
diameter =
= brace-chord angle
The global responses for the K-braced frames are presented together in Figure 3.7. It can
be seen that the frames with gap K joints continue to sustain increasing load until such time
as cracking occurs in the gap region due to shearing action across the joint (Figure 3.8).
Load is then rapidly shed as the load path through the K bracing is destroyed. Residual
capacity is dependent entirely on the surrounding structure, which for the test frames
constitutes only the frame legs. Table 3.6 compares the API RP 2A design loads for the
overstress, with the peak brace loads transmitted in
critical joints calculated allowing a
the tests. These values indicate the level of reserve implicit within the component design.
In Frame VII, for example, it can be seen that the maximum load sustained by the critical
joint was
compared with a design load to API RP 2A of
giving a 'component
RSR' of 2.89. On the basis of this 'reserve' implicit within the component design, it is
expected that the load sustained by the frame in the test would exceed the design value as
a result.
Table 3.6
Comparison of component and frame capacity reserves
Joint
Frame
Frame
API RSR
Joint
Frame
%ageFrame
Contribution
I
VIII
144 202
416
468
2.89 3.25
11.1
192 210
375
425
1.95 2.21
11.9
9.1
15.2
IX
298 318
562
621
1.89 2.08
X
105
381
449
3.63 4.28
185
For the
bracing and vertical legs of the K-framed tests, simplified assessment of axial
loads equates the design frame load to the design load for the component. On that basis
design load to API RP 2A is also
whereas in the test the peak frame
the Frame
giving an RSR of 3.25, exceeding the component value. However, as
load was
noted above, this significant reserve is due in part to the conservatism of the design criteria
for the critical joint. To obtain a measure of the system or frame contribution to the
ultimate frame response an alternative assessment is proposed. It is the frame RSR beyond
the component conservatism which reflects the frame contribution and in percentage terms
this is given by
Frame RSR - Component 'RSR'
Frame RSR
For Frame
the percentage frame contribution is therefore (3.25 - 2.89)
11.1 % as shown in the final column of Table 3.6.
10013.25 =
This presentation illustrates the difficulty in relying solely on the RSR to quantify the ability
of structural configurations to sustain loads in excess of the design value. The single bay
K frames in the BOMEL tests exhibit a high RSR but this is derived largely from the
conservatism in the design of the critical component and little contribution due to nonlinear
frame action is mobilised. An alternative frame configuration may offer alternative
loadpaths for redistribution contributing to an equivalent frame RSR but with lesser
conservatism in component design. The percentage is therefore a means to demonstrate the
contribution from nonlinear frame action to the ultimate system response.
There are significant differences in some joint capacity equations in API RP 2A (1993) and
the HSE Guidance Notes (1990). These arise due to factors such as different source
databases, the chosen lower bound or characteristic philosophies and definitions of first
crack or ultimate load failures. Depending which provisions are adopted, the apparent
RSRs vary. For Frame X, for example, the API joint and frame RSRs of 3.63 and 4.28
would become 2.06 and 2.43 if HSE Guidance were the base. This difference is
attributable to the accuracy of tubular joint equations rather than the inherent reserve
strength offered by the frame. By focusing on the reserve beyond the component
contribution the API ((4.28 = 15.2%) and HSE (2.43 - 2.06) 10012.43
= 15.2%) based assessments reveal a consistent level of system reserve due to frame
action. In this way the percentage frame contribution may be considered to give a robust
measure of system reserve.
In Figure 3.8 the brace loads for Frame
are compared with the global frame load. It
is clear that in the elastic region the components are equal, but the reserve capacity of the
regime to enhance the overall capacity.
portal action is utilised in the
By contrast, the overlapping joint in Frame IX failed in an unexpected mode, with local
buckling of the brace wall at the compression intersection (Figure 3.10). The joint
remained intact and therefore imparted much greater post-peak residual capacity than the
gap K frames, as shown in Figure 3.7.
It may be concluded that although component reserves or inherent conservatism are large,
the contribution of frame action is not very significant. Furthermore, the tests confirm the
importance of a proper understanding of tubular joint behaviour within the confines of a
frame for structural collapse predictions.
Popov et
The results of two two-bay X-braced frame tests undertaken at the University of California
Berkeley in the late 1970s are reported and discussed in a number of references (Mahin et
1980; Zayas et al, 1982; Popov et al, 1985). Two tests (Frames
1980; Popov et
I and
were undertaken as shown in Figure 3.11 with a prescribed sequence of cyclic
loads. Because the loads are reversed and incremented to collapse, direct comparison
cannot be made between these tests and other ultimate strength tests reported in this section
because of the uncertain influence of the development of plasticity on the peak load.
Nevertheless the influence of component slenderness on the response characteristics is
instructive. Table 3.7 presents the yield stress values based on tensile coupon tests and
section sizes from which the relative slenderness of Frame I compared with Frame is
evident. In the tests this was manifested in earlier and more severe local buckling and
tearing failures in Frame I whereas Frame was able to maintain its capacity for a greater
number of cycles and attain a larger lateral displacement thereby absorbing more energy
as required under seismic loading.
Table 3.7
Tubulars used in frames tested under
loads at University of Berkeley
Frame I
Member
Frame
D (mm) T (mm)
Top bay X-bracing and
D
2
48
Yield
T (mm)
3
33
250
Bottom bay X-bracing
114
5
42
130
3
24
250
X-joint cans
150
3
48
150
5
33
250
Legs
320
7
45
320
9
34
320
The tests demonstrate the significance of relative section sizes and not just bracing
configuration on the inelastic response of structures. Because of the manner of load
application the tests are not considered further in this review of static reserve strength,
neverthess note of the frames is made given the scale of testing and the wide recognition
of the tests in the offshore industry. The work demonstrated the value of large scale frame
tests and led into the SCI (1990) and BOMEL (1992) programmes to investigate ultimate
static responses.
SCI
The four two-bay X-braced frames shown in Figure 3.12 were tested to collapse with
lateral load applied to the top of the frame under displacement control (SCI, 1990;
Billington et al, 1991 and
Bolt et
The bases of the frames were
were designed for member failure. The horizontal brace was
hinged. Frames I and
omitted in the latter case to investigate the influence of the member which is lowly utilised
in elastic analysis on the collapse mechanism. Frame was specifically designed for the
compression X joint in the top bay to be critical. Frame IV included a fatigue crack to
demonstrate the influence on the collapse mechanism. Table 3.8 summarises the frame
configurations.
The primary bracing members were from BS 3601 ERW tubulars which were annealed to
remove residual stresses which had influenced the response of the K-braced frames tested
by Grenda et al. Stub column tests confirmed that the annealed tubulars gave a distinct
yield typical of offshore grade steels and that static coupon tests gave yield values
representative of member responses. The yield stress levels for the bracing averaged
287N/mm2, for the API 5L X52 legs 359N/mm2, and the thickened joint cans 324N/mm2.
The individual test results are described on the following pages.
Table 3.8
Details of SCI two-bay X-braced test frames
Critical Components
Test Objective
Critical member
18.7,
To investigate load shedding and redistribution in X bracing
associated with compressionbrace buckling.
Critical X joint
1.0
To investigate load shedding and redistribution associated with
compression X joint failure.
Critical member
18.7,
As Frame I but without mid-height horizontal to investigate the
role of redundancy.
Critical X joint
As Frame but with fatigue cracks at chord-side saddle of X
joint to quantify influence on frame response.
Frame I
Figure 3.13 shows Frame I at the start of the test. Frame I was designed with a thickened
joint can at the top bay X joint (Figure 3.12) so that the compression diagonal was the
critical component.
The global response during the test is shown in Figure 3.14. This figure presents the
overall displacement of the frame as measured by a transducer at the top of the frame
parallel to the application of load. Scan numbers are marked on each plot and will be used
in reference to discussion of the test. A similar format is adopted in the description of
subsequent frames. The design load for the frames, based on elastic assumptions and the
capacity of the critical component given by API RP 2A provisions, are also shown in the
figures. Extreme 'storm' loading is considered as the reference for reserve strength
calculations with a one third increase in the allowable capacities accounted for.
The response of Frame I remained linear up to Scan 7. Subsequently the stiffness of the
frame reduced with further application of load, as the stiffness of the tension brace reduced
with the onset of tensile yielding. This can be seen from the forces recorded by the
integral brace load cells (Figure 3.12) plotted in Figure 3.14. This yielding before buckling
of slender braces with the same nominal properties, indicates the presence of a locked-in
1978).
pre-tension from fabrication (see also Briggs and
The lower portion of the top bay compression braces buckled at Scan 11 (Figure 3.15) with
a drop in the sustainable load (Figure 3.14). The buckle was at approximately
to the
in-plane and out-of-plane directions. Two sudden drops in the load with increasing
displacement coincided with local brace wall buckling and crimping at the plastic hinge
locations at the leg tubular joint and at mid span of the buckled member.
Although the load in the tension member remained constant at yield and the load in the
damaged compression member reduced, the residual strength of the frame gradually
increased from Scans 13 to 17. Shear forces in the legs increased as portal action
developed and the axial load in the horizontal member increased. This illustrates the
importance of this member to the residual strength of the structure in the event of damage
or overload.
The comparisons between the design 'storm' loads that it is calculated the component and
frame can sustain in accordance with API RP 2A and the experimental capacities are
presented in Table 3.9. For Frames I and in which brace buckling dominates, the
for each would be the same whether API RP 2A or HSE Guidance Notes guidelines were
adopted. However, in cases where joints are the critical component (eg. Frames and IV)
the base design loads (capacities) are different giving apparent differences in the reserves.
1.0 X joints in Frames and IV the API and HSE provisions give
In fact, for the
almost identical capacities. However, for the general situation it should be noted that the
RSR calculated depends on the validity of the base formulation for predicting component
capacities.
Table 3.9
Comparison of component and frame capacity reserves from SCI tests
Frame
I
IV
API design load
Critical
Component
Frame
409
579
195
276
395
559
200
284
peak in joint response
Peak Load
Component
693
514
RSR
Frame
Component
Frame
%ageframe
contribution
922
1.69
1.59
+ NIA
1080
2.03
3.91
48.1
782
1.30
1.40
7.1
952
1.95
3.35
41.8
+ see text for discussion
The conservatism in the individual component designs (expressed here as the component
RSR) would be expected to result in a corresponding increase in the frame capacity. Any
increase in the RSR beyond the component value is therefore attributable to nonlinear frame
action, alternative loadpaths etc., arising from the redundancy of the frame configuration.
Expressed as a percentage of the frame RSR this gives the percentage frame contribution
in the final column of Table 3.9. Further discussion of this approach was given in
conjunction with the BOMEL K-braced frame test results.
The results for Frame I are unexpected as the component appears to have greater reserve
than the frame. However, the member properties and critical loads for brace buckling and
tensile yield are similar. The addition of locked-in tensile loads from fabrication
determines that tensile yield occurs first and gives an increase in the apparent load at which
compression buckling occurs. In this case it is not therefore appropriate to evaluate the
frame contribution with respect to this 'apparent' component capacity.
This may not be representative of offshore structures where the welds, degree of constraint
and therefore shrinkage differ from scaled test structures. However, understanding this
influence, the contribution of X bracing action can be revealed. First yield occurs between
Scans 7 and 8, nevertheless the frame sustains increasing load, albeit at a reduced stiffness
as load is carried by the alternative compression diagonal. It is only with the second
component failure (brace buckling), that the frame capacity is exceeded. The ratio of peak
load
to the frame load at first failure Scan 8
is 1.10, giving a measure
et al, 1988) due to the frame action.
of the redundancy factor
Frame
Frame was the first frame in which a joint was the critical component. The top bay X
joint can was of similar thickness to the brace but had a higher yield stress. In all other
respects Frame was nominally identical to Frame I as shown in Figure 3.12. The overall
response of the frame is shown in Figure 3.16. The top bay compression X joint response
softened from Scan 6 and chord wall ovalisation became visible. However, this is not
apparent from the global load deflection response (Figure 3.16). because the tension load
paths compensated for the softening compression joints, carrying a greater proportion of
load. The limiting load was reached across the joint at Scan 11. The apparent capacity
was some 40% higher than had been predicted by reference to the mean of test data (HSE,
1990). This unexpected behaviour was due to the membrane action of the frame including
symmetry, and locked-in tension in the compression braces from fabrication.
The frame test was continued beyond first joint failure and yielding of the tension chord
spread from Scan 12 giving rise to a plateau in the response curve, with local yielding of
the bottom bay compression member noted at Scan 13. From Scan 16 onwards, yielding
of the tension brace became extensive, portal action developed in the legs and the brace
welds came into contact across the flattening X joint (Figure 3.17) allowing the joint to
transmit greater loads.
Driven by in-plane bending arising from the leg moments associated with portal action, the
top bay compression brace buckled predominantly in-plane at Scan 22 and the frame
capacity reduced. Figure 3.18 shows Frame was extremely ductile and the process of
load redistribution led to a higher capacity than for Frame I, albeit achieved at larger
overall displacement, as shown in Figure 3.19. This was not an obvious result as Frame
with a thinner X joint chord, contained less steel than Frame I. This test demonstrates
the potential importance of nonlinear joint behaviour on ultimate structural responses.
The role of frame action on reserve strength can be seen from Figure 3.16. The joint
capacity is reached at Scan 11 yet the frame load continued to increase until the capacity
of the alternative tensile load path through the X bracing was also reached. Both
compression joint failure and tensile yield are ductile modes of failure without rapid
reductions in capacity. The global frame response is therefore for the capacity to increase
as portal action is mobilised. Additionally the deformations across the joint enable a new
stiff load path to be developed as the braces contact, until buckling and rapid unloading is
precipitated. This gross nonlinear response is not predicted in elastic analysis. Comparing
Frames I and (Figure 3.19) it can be seen that the joint failure protects the compression
brace from early buckling.
The deformations enable parallel load paths to be mobilised such that when brace buckling
occurs portal action in the legs develops whilst loads are transmitted simultaneously by the
braces. The reserve strength beyond the critical component load is therefore considerable
as demonstrated by the large percentage frame contribution in the final column of Table
3.9. This contrasts with the figures for Frame
below and the less redundant K-braced
frames (BOMEL) in which first member failure triggers frame collapse. It should be noted
that locked-in stresses have little influence on the global reserve. Tensile prestress exists
in both braces reducing the apparent tensile capacity and increasing the capacity in the case
of compression. The net effect on the global reserve is therefore negligible.
The important role of joint nonlinearity on frame behaviour is clearly revealed by this test.
Frame
Frame
was identical to Frame I, except that the mid-height horizontal was omitted
(Figure 3.20). The member carries negligible load in the elastic regime (Figure 3.14) and
might be omitted in practice to reduce structural weight. The implications of reduced
redundancy on reserve and residual strength were therefore examined in Frame
The global response is shown in Figure 3.21. The response was linear up to Scan 5. With
the next increment the top bay lower compression brace buckled, shedding load via the
alternative top bay (tension) diagonal directly into the bottom bay compression member,
which became visibly bowed. The alternative load path ensured that the overall frame
capacity was maintained with no rapid reduction in load. From Scan 8 the upper bay
tension member began to yield and the bottom bay compression member buckled with
increasing displacement at Scan 1 1 . Figure 3.22, looking down the top bay compression
brace, shows the dual member failures as well as the portal action mobilised in the frame
legs.
The sequence of failures, without the mid-height horizontal to evenly distribute loads to the
bottom bay, reduced the residual frame capacity below the design storm load. Figure 3.23
compares the Frame I and Frame results. Larger imperfections and compressive
in stresses, relating to the degree of restraint and specific fabrication procedure adopted,
also explain the difference in peak capacity. However, the role of the mid-height horizontal
in maintaining the residual strength is shown and this is also indicated in Table 3.9 by the
difference between the frame and component reserve strengths.
Frame IV
Frame IV was nominally identical to Frame
except that a fatigue crack had been
introduced at the critical top bay X joint (Figure 3.24). The global load-deflection response
of Frame IV is shown in Figure 3.25. At Scan 8 ovalisation of the X joint chord became
visible, there being relative displacement between the fatigue crack faces as the brace-side
crack face slid under the chord side. The X joint response is shown in Figure 3.25 from
which the capacity can be seen almost equal the uncracked joint capacity in Frame
(Figure 3.16). By Scan 1 1 the upper portion of the compression brace was pushing into
the chord under the existing crack and by Scan 13 the two braces were in contact (Figure
3.26).
As the crack propagated round the weld toe, the chord began yielding due to the reduction
in its cross sectional area. At Scan 20 a tear opened perpendicular to the axis of the chord
and rapidly propagated, rupturing the chord and the global load fell. This changed the
compliance, and with additional prescribed displacement the compression brace lifted at the
joint.
The crack had very little effect on the global response as seen in the comparison between
the Frame
and IV responses in Figure 3.27 and Table 3.9. However, the reserve
strength associated with joint failure, even with the presence of a crack, is confirmed. Had
the crack been oriented differently the effect may have been for fracture to occur earlier
action having been mobilised to
with a rapid reduction in capacity and with less
contribute to residual capacity.
BOMEL
In Phase of the Frames Project two additional double bay X-braced frame tests were
undertaken to further examine the influence of joint behaviour on system responses. The
frames are shown in Figure 3.28 and Table 3.10 summarises their purpose.
Table 3.10
Details of BOMEL two bay X-braced test frames
Critical Joint
Test Objective
Repeat of Frame to investigate unexpected behaviour and
capacity of compression X joint in that test.
Frame V with reserved X joint to investigateultimate frame
response associated with tension X joint failure.
Frame V was not tested to collapse. It confirmed the influences of locked-in stress as
postulated for the SCI tests above. The test was halted when the applied load gave a
multiple of 3.1 on the design load. The global response was ductile again indicating that
the RSR would considerably exceed 3.1.
Frame
Frame
was fabricated by replacing the failed joint in Frame V with a new joint of
reversed configuration (Figure 3.28). Figure 3.29 presents the global load-deflection
response and the member responses, showing the distribution of loading between the tension
and compression load paths within the top bay X-braced panel, are shown in Figure 3.30.
The response of the frame and joint were ductile, contrary to expectations for a tension
loaded X joint, in which crack initiation and fracture usually occur. These expectations are
derived from isolated tests where brace loads but no chord loads are generally applied.
However, a high level of chord compression was developed in the Frame
joint as the
tension path through the joint softened, and this contributed to the yielding and gross plastic
deformation at the joint. At the end of the test, although grossly distorted, the steel joint
remained intact.
The member forces in Figure 3.30 illustrate clearly the contribution of X-braced frame
action on redundancy in comparison with the K-braced frame responses in Figure 3.7. As
the tension joint softened initially, so additional load was carried by the alternative
compression diagonal, giving an imperceptible change to the stiffness of the global
response. However, as buckling of the compression chord took place, so the increased
deformation enabled greater loads to be transmitted in membrane action across the
1.0
tension X joint. Only when significant portal action, full brace yield and plastic buckling
of the compression braces were acting, was ultimate frame capacity attained. The frame
is shown at this stage in Figure 3.31. It should be noted that the X joint did not crack in
tension, possibly due to the presence of high chord loads, but deformed in a ductile manner
(as shown in Figure 3.32 where cracking of the paint is observed). The reserve strength
and comparison with frame design loads are given in Table 3.1 1.
1
Comparison of component and frame capacity reserves
Design storm load
Joint
Frame
Code
API RP
Peak Load
Joint*
Frame
RSR
Joint Frame
%ageframe
contribution
85.9
120
455
789
5.30
6.58
19.5
152.3
212
455
789
2.99
3.72
19.7
Peak load based on deformation limit and capacity for locked-in
Comparisons both for API RP 2A and the UK HSE Guidance Notes are presented,
illustrating the dependence of the RSR on the base design criteria. There are significant
for tension joints and these are manifested in RSRs of
differences between API and
6.58 compared with 3.72. However, isolating frame action by comparing the global and
component RSRs in both cases, reveals a consistent contribution of some 20%.
This strong influence of frame action ensuring system reserve is a function of the frame
being X-braced and first failure being joint related.
Paik and Shin
The influence of damage within plane and space frames of K-braced configuration was
investigated in the tests reported by Koreans Paik and Shin, 1990 and Shin, 1990. The
work was in support of numerical development of elements for modelling damage. The
program used is the Idealised Structural Unit Method (ISUM) developed by Ueda and
Rashed (eg. Ueda et al, 1986). The test structures are shown in Figure 3.33. The brace
WT tubulars with
OD by
WT tubular
members are 60mm OD by
legs. The respective yields are 319 and 286Nlmm2. The K joints were stiffened "by rigid
body" rectangular box sections to protect against local joint failure.
Three plane frame tests were undertaken and the results, in comparison with the ISUM
analytical predictions, are shown in the top part of Figure 3.33, where:
P-IC
Intact plane frame.
P-DC
Frame with dented member as indicated with an initial global deflection of
1.5% and a local dent depth 19.5% of the brace diameter.
P-RC
Frame with member completely removed (assumed to be the member damaged
in P-DC above).
The tests were run under displacement control applied at
per second. No
description of the tests is provided (Paik and Shin, 1990) although the load-deflection
response for the intact frame suggests member buckling may have occurred and the kink
on the unloading path may be due to failure of the compression brace in the other bay. The
residual strength factor is around 0.55.
It can be seen that all the load-deflection curves converge to a common load level,
associated with the portal frame capacity of the frame legs. It is remarkable that the
damage to the critical members has only a small influence on the peak load sustained. The
test demonstrates that analytical assumptions of complete member removal allow greater
deflections whilst giving a poor prediction of the peak capacity.
It has not been possible to quantify the RSR for the frames. Based on the dimensions and
material properties given in the paper the allowable frame load (to API RP 2A with a one
third concession for extreme loading) takes a design value around
In a test the
capacity would be expected to correspond to the capacity with the safety factor completely
removed giving
( - 10.7 ton) capacity in this instance. Based on the premise that
RSR relates the peak load to the design value, the intact frame has an RSR around unity.
This is not considered to be a reflection of the system behaviour, rather it is more likely
to be due to the unusual joint configuration, or other aspects of the materials or set up
which cannot be defined but may invalidate reference to API RP 2A provisions. For this
are not reported in the summary tables at the end of Section 3
reason the calculated
and discussion focuses on the behaviour characteristics and relative structure performances.
The space frame shown in the lower diagram of Figure 3.33 was tested in the damaged
condition (S-DC) with 2.5% global bending and 29.9% local denting of the member.
Analyses in the intact (S-IC) and member removed (S-RC) conditions were also undertaken.
The intact and damaged cases are again seen to give similar capacities with the test giving
a gradual softening characteristic although no description is given in the paper. In the
space frame, with greater redundancy than the plane frame, the removed member has
relatively less influenceand despite contributing to a reduction in overall stiffness the S-RC
analysis gives a reasonable representation of the performance of the damaged structure.
lnoue et
The effect of a horizontal brace on the performance of X-braced tubular frames was studied
in this series of ultimate load tests of two plane frames and two space truss specimens. The
structural configurations, together with the member dimensions and properties, are shown
in Figure 3.34. The members were manufactured from ERW pipe. The joints were not
tube-to-tube welded connections as used offshore; instead brace members were welded to
gusset plates attached to the chord. This method of attachment gives fixed end conditions
in the plane and pin-ended conditions out of the plane of the gusset. Nevertheless the
comparative tests with and without horizontals and in two and three dimensions are
instructive. The specimens were cycled beyond the attainment of a peak capacity but the
first half cycles are of relevance here.
The two dimensional frames were loaded in-plane, whereas the space frame was loaded
across the diagonal. Against each response curve, in Figure 3.34, the legend enables the
progress of failure to be followed.
Considering first the planar frame behaviour, it can be seen that buckling of the
compression braces initiated collapse but it was only with failure along the alternative load
path that the peak load was attained. The maximum load sustained by the frame with
horizontals was some 10% greater than that by the frame without horizontals.
Furthermore, the drop in load was more abrupt and resulted in a much smaller residual
capacity in the latter case. The different behaviour is attributable to the horizontal brace
which took significant load from the tension brace as redistribution from the buckled
compression brace occurred. Where the horizontal is omitted a second buckle in the lower
bay was precipitated. This correlates with the findings for Frames I and in the SCI tests
(SCI, 1990; Bolt et al, 1994).
The inelastic behaviour of the space frames subjected to
direction load was dominated
largely by buckling and yielding of the legs, rather than the braces as in the plane frame
tests. Accordingly the horizontal members made a less significant contribution to the
overall load-deflection response. Nevertheless in the absence of horizontals the peak load
was about 10% less than in the fully braced case. Direct comparison with the 2D tests is
not possible because of the re-orientation.
Tests (Soreide et all
Two X-braced three dimensional frames were tested by SINTEF to ultimate load as shown
in Figure 3.35 a and b. Load was applied along the axis of member EF whose wall
thickness was increased accordingly to obviate buckling. The frames, denoted S1 and S2,
ratios and brace slendernesses and in both cases the joint cans were
had different
thickened to ensure member failure dominated.
Soreide et al (1986) presented USFOS (analytical) predictions for the frame responses in
advance of the test work being carried out. These are shown in Figure 5.23 indicating
(factors on the design load) of around and 3.3 and 3.6 with a considerable margin
between first component failure and the peak frame capacity. The basis of the 'design
loads' indicated by the authors is not given and so absolute comparison with other test
programmes must be made with caution.
The actual test results reported by Soreide et al (1987) are also given by the dashed line in
Figure 3.35 in terms of the global load applied and the lateral displacement of the frame
at E. From the graphs in Figure
for Frame
it can be seen that the stiffness
degraded gradually prior to failure, when buckling occurred in member EB at an applied
load of about
At that point member IF, which was at yield, fractured, due to lack
of fusion in the weld to the can at Joint I, causing a sudden drop in the external load. With
redistribution some additional load was sustained but a similar fracture then occurred in
member JG at joint J precipitating another abrupt decrease in load bearing capacity. At this
point the test was terminated. Fracture did not occur throughout the second frame test, S2.
The diagonal bracing in Frame S2 was more slender than it had been in S1 and buckling
occurred first in member EI. A small local dent (about 2mm deep) had been introduced
ratio of 63, was vulnerable to
in this member during transportation which, given its
imperfections. Subsequently the frame continued to take load but with an ever reducing
stiffness.
Frame S1 demonstrated the 'brittle' response related to fracture where the rapid loss of
stiffness along the load path cannot be compensated by redundancy within the simple
structure. In comparison with the original Soreide et al (1986) prediction in Figure 5.23
(slightly higher than predicted for
it appears that the frame sustained a load around
the perfect structure), giving an apparent RSR of 3.3. However, it is likely that the
Soreide predictions were based on nominal material properties and dimensions whereas
other tests have been interpreted on the basis of actual properties. Furthermore the basis
of the 'design load' is not known. The deformation characteristics of the frame with initial
nonlinearity occurring around
and a peak load corresponding to a deflection in the
are similar in both initial analytical prediction (Figure 5.23) and test.
range
However the later analysis and test comparisons in Figure
offer less good agreement,
although the stages of rapid unloading associated with fracture have been tracked.
In Frame S2 however, the global response maintained a positive slope as alternative bracing
load paths compensated for the falling load. The original Soreide et al (1986) prediction
achieved at around 40mm deflection, whereas in the
indicated a peak load of
presence of the dent the ultimate load was associated with a deflection of some
It may therefore be concluded that the RSR was as predicted, ie. around 3.6, but the
reservations noted for Frame S1 apply together with concerns about the acceptable
shows the comparison between
deformations to be associated with the RSR. Figure
the 'dented' prediction and experiment. From the figures the responses at component level
provide no explanation for the apparently higher stiffness determined analytically, compared
with the gradual softening in the test.
Comparative analysis
Many of the frame tests described in this section have been used as a baseline for
calibrating nonlinear analysis programs. Discussion of these results would provide little
additional information on the reserve strength characteristics of tubular frames, however
Table 3.12 identifies references where test and analysis comparisons are presented. These
are clearly important stages in the validation of software for predicting the ultimate
responses of jacket structures (see also Section 4).
3.2
COMPARISON OF RESULTS
The individual experimental results described in Section 3.1 are summarised together in
Table 3.13. Measures of reserve strength are presented. The form depends on the
information given in particular references. Comparisons are made in the sub-sections
which follow.
Single versus two-bay plane frames
Single bay test structures enable the reserve strength due to portal action in the legs and
alternative bracing load paths within a panel to be identified. In two bay structures the
transmission of loads from one panel to another can be determined. In addition the role
of bracing members between panels can be investigated. The tests reveal the following:
The single bay tests by Briggs and Maison, Grenda et al and BOMEL reveal the
ultimate response of components within a frame. The Briggs and Maison test shows
a small component of X action. It also demonstrates the dependence of the reserve
strength, due to portal action, on the relative size of the legs. Had the leg members
in the Grenda and BOMEL tests been larger, the reserve capacity would have been
greater. For this reason comparison between different frame test programmes in
quantitative, rather than qualitative terms, needs to be undertaken with care.
The single bay tests demonstrate the reserve strength from panel action (eg. for the
Briggs and Maison X-braced bay) and the 'surrounding structure' (ie. frame legs). In
the two-bay structures the impact of load redistribution on other parts of the frame is
demonstrated. Both SCI and Inoue tests show that beyond first buckling in a
compression brace, the maximum capacity of the tension load path is utilised and that
load in turn is shed to the lower part of the structure through the K or KT joint into
which the member frames. In the latter case the load is distributed between K and T
branches. However, in the absence of a midheight horizontal all load is shed via the
compression diagonal. Depending on its size it may in turn buckle and a sequence of
failures and a significant reduction in load carrying capacity is triggered.
3.2.2 Role of redundant members
The above description of load redistribution between bays illustrates the role of a member
which carried negligible load initially, on the performance of the structure in the event of
overload or damage. The increase in structural weight is small but the post-ultimate
capacity is much greater.
K versus X bracing
Comparison of the Grenda and BOMEL K frame tests with the X-braced frames,
demonstrates that in the first case only the surrounding frame (ie. legs) can contribute to
the reserve strength. In the second case the bracing within the panel presents an additional
source of reserve and it is only when the limiting capacities of both brace load paths have
been reached, that reliance is placed on the legs.
The magnitude of the X-braced panel contribution, depends on the relative slenderness and
therefore the capacity of the braces with respect to yield and buckling. Similarly the
relative contribution from the legs depends on their stiffness. This is influenced by the
length of the legs and therefore the contribution from portal action would be different from
the BOMEL K frames and SCI-BOMEL X frames despite the leg tubulars being of the
same size.
for X and K frames is not meaningful. The
On this basis direct comparison of
important point demonstrated is that the X framing offers an additional source of reserve
strength over and above K action. This is reflected in the recommended bracing for
framing of structures in earthquake regions embodied in API RP 2A (Figure 2.2).
FAILURE MODE
BOMEL
et
Ogawa et
Briggs
Maison
REFERENCE
Table 3.13 Summ
LOAD-DEFLECTION
of experimental investigations of
RSR
%frame action
SYSTEM RESERVE
m reserve strength (Part 1 of 3)
Buckling insensitive to
changes in chord at K joint
Relatively large legs
Significant portal action
NOTES
MODE
and Shin
BOMEL*
SCI
REFERENCE
3.13 Summ
LOAD-DEFLECTION
V 3.1
6.58 API
3.72
RSR
of experimental investigations of system reserve
%frameaction
SYSTEM RESERVE
(Part 2 of 31
Little information in paper.
Heavily stiffened joints.
NOTES
3.2.4 Effective length factors
In both the SCI X-braced frames and the Grenda et al K-braced tests measurements of the
effective buckling length of compression members were based on the distance between
points of contraflexure out-of-plane. These are reproduced in Table 3.14 in relation to
node to node member lengths for comparison with the design values given in API RP 2A.
Initial analysis often applies these factors to node to node lengths and therefore the
comparison reveals the conservatism in conventional practice.
Table 3.14
Comparison of measured and code effective length factors
and Grenda et
Effective length factor
Source
SCI
SCI
SCI
SCI
Grenda
Grenda
Grenda
Grenda
I)
2)
3)
Measured
node to node
out-of-plane
API RP 2A
K factor
API RP 2A
/measured
X-braced Frame I
X-braced Frame
X-braced Frame
X-braced Frame
K-braced Frame 1
K-braced Frame 2
K-braced Frame 3
K-braced Frame 4
X joint
when member failed giving
Significant initial imperfection in-plane driving failure
In plane value corresponding to dominant failure mode
Aside from the experimental uncertainties noted, a consistent view of measured effective
length factors being some 30%less than values given in RP 2A is shown in Table 3.14.
Relating these experimental findings to those analysis methods (eg. INTRA) for which
the importance
effective length factors have to be specified by the analyst (see Section
of good data for reliable structural collapse load predictions is clear. A dependence on
code values would not give reliable reserve strength predictions.
3.2.5 Joint versus member failures
Within the K-braced framing, gap K joint failure and member failure impart similar
characteristics to the global load deflection curves. In the case of joint failure, fracture
generates a more rapid shedding of load. Nevertheless the effective loss of capacity
for the bracing load path through the panel is lost in both cases.
For the X-braced frames joint and member failures give quite different characteristics
to the global responses. Following buckling of one brace, the alternative diagonal may
sustain increasing load until yield is reached and the global capacity is determined.
Where ductile joint failure occurs, the load in the compression brace is limited until the
alternative braces have yielded in tension and the remaining stiffness of the
compression load path enables it to sustain increasing load albeit with large deflections.
When the brace eventually buckles the full yield load in the braces, combined with
portal action in the legs associated with the greater displacement, mean that the frame
can sustain a higher ultimate load than in the case where brace buckling precipitates
collapse. Continual integrity of the X joint and the dual load paths through it, ensure
that the frames have a high reserve strength when ultimate capacity is compared with
brace loading through the joint.
design based on
Ductile joint behaviour can be beneficial in terms of system reserve strength, despite
current design guidance in API RP 2A requiring joints to be stronger than the members
framing into them.
If failure of the primary joint in an X-braced panel abruptly reduces the capacity of one
load path, load may still be transmitted via the alternate diagonal (as demonstrated by
Frame IV of the SCI tests), depending on the degree of damage, for example,
associated with tensile cracking.
3.2.6
2D versus 3D
The degree of reserve that can be exhibited in the 2D tests is limited compared with 3D
jacket structures by their simplicity and the finite number of alternative load paths available.
In practice 2D analyses are more economical to perform than 3D and the correlation is
therefore important. Unfortunately, the available frame test data do not provide direct
comparison. However, it may be deduced from the SINTEF Frame S2 test that, suitably
braced, brace buckling and member yield in one panel does not necessarily compromise the
overall structural performance. Load can be shed to panels in other planes enabling greater
load to be sustained. The presence of initial defects (weld lack of fusion, denting) qualify
the reserve strengths exhibited.
The orientation of loading and symmetry of the Inoue frames precipitated failure in the legs
without significant loading in the braces. The dependence of failure mode as well as
reserve capacity on the direction of loading is instructive.
3.2.7 Initial imperfections and the effects of scale
The influence of initial imperfections has been illustrated by the tests in several ways. The
SINTEF frame in which a dent precipitated buckling in one member demonstrated the
susceptibility to damage. The failure at the weld due to lack of fusion in the other 3D box
frame showed how defects can compromise capacity. The presence of the defect may have
been a function of the weld procedures adopted, the extent of NDT performed or the ability
to inspect small scale specimens. These factors do not apply in the same way to new
offshore structures where quality control is particularly stringent. However in an overload
situation a jacket may contain small fatigue cracks due to the service history and these may
compromise the reserve strength in a similar way.
The Briggs and Maison test was unusual in that compression brace buckling was not abrupt
nor was it observed prior to yield in the nominally identical tension X brace. The
explanation may in part be due to the low slenderness of the members but it must also be
associated with a locked-in pre-tension. Such locked-in forces would clearly depend on the
fabrication sequence, but from Figure 3.1 it may be postulated that the large frame legs and
would be welded prior to introducing the braces. Having laid the
top and bottom
brace-leg welds, cooling and shrinkage would occur, with deformations restrained by the
legs such that a locked-in pre-tension would develop.
A similar fabrication sequence was adopted by the fabricator for the SCI frames (Figure
3.12). Evidence that a preload had been introduced could be seen from a discrepancy
between apparent tensile yield levels in brace members (from several independent
measurement sources) compared with true yield values from tensile coupons tested at a
comparable rate to the frames. For significant preload (which may be tensile or
compressive depending on the fabrication sequence), it can be shown that both the failure
mode and load may be influenced. However, the root gap in jacket structures may be of
but in a test structure this cannot be scaled in proportion with the
the order of
global geometry as a
minimum gap is required. It may therefore be concluded that
the axial shrinkage, and therefore the locked-in force, will be different in a test structure.
Furthermore the relative complexity of a jacket structure means that such locked-in forces
will be built up and mitigated in stages due not only to the fabrication sequence but also to
the temperature variations across the structure. In addition, the jacket structure is likely
to experience other extreme loads associated with the peak and these may develop local
plasticity enabling redistribution or shake-down of these locked-in forces. A series of full
scale fabrication measurements (BOMEL, 1993) and the discussion above indicate that
initial member preloads may not be an overriding consideration in establishing collapse
loads for jacket structures, nevertheless their potential significance in small scale tests, and
for the ability to obtain good agreement with analysis, needs to be accounted for.
tests were fabricated in accordance with AWS D1.l criteria. In
The
particular geometric and initial out-of-straightness tolerances were imposed. The initial
occurred at significantly different global
compression brace failures in Frames I and
which was on
loads (Figure 3.23) due largely to the initial out-of-straightness in Frame
the limit of acceptability whereas in Frame I the member was hardly bowed at all. It
should be noted that the difference is also due to the absence of the mid-height horizontal
is influenced by some initial
and the more gradual mode of failure in Frame
compression in the braces as described above. Nevertheless, unless these parameters are
recorded the validity of the test results for software calibration may be undermined.
In relation to full scale structures there is a need to consider the influence that
imperfections, which may be present, can have on capacity predictions. In jacket
structures, sensitivity analyses encompassing locked-in member forces in addition to other
aspects of uncertainty such as material properties, foundations, etc., are recommended
(BOMEL, 1993). The important point is that the lower bound, largest imperfection for the
member may not give the most conservative solution for the structure as a whole, and
sensitivity analyses for a range of reasonable pre-existing imperfections are strongly
recommended, although it will be seen in Section 5 that few are performed.
Comparison with jacket structures
It is important to note that although the tests by Ogawa et al, Inoue et al and Paik and Shin
are instructive in terms of the mechanisms and sequences of load redistribution, the
structures bear little direct resemblance to offshore jackets. The connections in the Inoue
and Paik and Shin tests mean that the effective lengths are not directly applicable and the
trusses tested by Ogawa do not develop the frame action anticipated in offshore structures.
The remaining tests however were configured specifically to mimic elements of jacket
construction. To this end non-dimensional geometric parameters and relative member sizes
were carefully selected and in the SCI, BOMEL and Grenda tests the frames were extended
so that the applied loads were distributed evenly into the test parts of the frames.
3.2.9 Materials
In configuring test frames to represent offshore jacket structures a principal constraint is
the type, grades and produced sizes of steel, given the limitation in terms of frame size and
capacity that can be accommodated for a reasonable budget. An additional factor is the
stress-strain characteristics of the chosen steel in relation to 'typical' offshore materials and
the influence of girth welds, longitudinal welds, etc., on component capacities.
The materials used in the test frames have been reviewed and are summarised in Table
3.15. In general the references give insufficient detail for conclusions about member
properties to be drawn. The exception is the interaction between the Grenda, SCI and
BOMEL tests.
3.15
Comparison of steels in test frames
Material Type
Reference
Maison (1978)
Inoue et
(1984)
API 5LB 42/52
Not given
Ogawa et
(1987)
Not given
Soreide et
(1987)
Not given
Grenda et
(1988)
API
Paik and Shin
ERW
Not given
BS 3601 ERW annealed at 690°C (braces), API 5L X52 (legs)
BOMEL (1992)
BS 3602 ERW annealed at 690°C (braces), API
X52 (legs)
hot rolled seamless
ERW: cold formed welded tube - electric resistance welded
From the Grenda tests it was recognised that the fabrication of tubulars in the electric
resistance welding (ERW) process introduces residual stresses which cause a larger portion
of a member cross-section to yield at a given applied load, thus reducing capacity. Having
quantified this effect in the Grenda tests, steps were taken to eliminate these residual
stresses in the SCI and BOMEL tests by annealing the tubulars prior to frame fabrication.
Stub column trials showed the annealing process to restore the onset of yield (nonlinearity)
from about 50% of the plateau stress in the as-welded condition to around
engendering the
yield characteristic of offshore structural steels. The series of stub
column tests also showed that girth welds (present in full scale jackets) had no apparent
effect on the response (Bolt et al, 1994).
The results presented by Grenda et al include a correction for the
ERW
properties. However, without further evidence for the treatment state of the Briggs and
Maison tubulars it remains a possibility that the early compression failure and ductility were
influenced by residual stresses from the ERW process.
Changes to the characteristic of the response of components and hence test frames, need
to be allowed for in the relation of the results to jacket structures. Furthermore in
performing calibration analyses, appropriate stress-strain characteristics need to be
modelled. This section therefore provides a caution to the immediate adoption of test
results unless full details of the geometry, material and fabrication are known.
As an alternative to material specifications some authors report specific tensile coupon
results. The rate of testing can influence the yield value recorded and therefore the coupon
testing procedure needs to be linked to the rate of load applicationto the structure. Practice
is not uniform across the test programmes, however.
0
Conclusion
The general findings from experimental work will be drawn together with numerical results
in the discussion in Section 6.
i
TO
GRADE
STRENGTHS ARE BASED ON DYNAMIC
TENSILE COUPON TEST RESULTS
LOAD CELL
PRESSURE
J
0
1.0
2.0
INCLUDE SUPPORT
2.5
3.0
FRAME DEFLECTION
AND RIG
Figure 3.1
and Maison single bay X-braced test frame
Brace Nos
figure 3.2
trusses tested by Ogawa et
Figure 3.3
Truss load deflection response (Ogawa et
Figure 3.4
Single bay K-braced frames tested by Grenda et
FRAME
FRAME
FRAME
FRAME X
Figure 3.5
Single bay K-braced frames tested by BOMEL
P
20
0
FRAME
FRAME
LOAD DISPLACEMENT RESPONSE
RESPONSE
FRAME
OVERALL
RESPONSE
FRAME X OVERALL LOAD-DISPLACEMENTRESPONSE
Figure 3.7
Global load-deflection responses for BOMEL K-braced frames
FRAME
Figure 3.1 1
Two bay X-braced frames tested under cyclic loading by Popov et
FRAME DISPLACEMENT (mm)
0
50
100
150
250
FRAME DISPLACEMENT (mm)
Figure 3.14
SCI Frame I global and local member responses
300
LOAD
W
X
0
m
W
F
FRAME V
I
V MODIFIED
FRAME
Figure 3.28
Two bay X-braced frames tested by BOMEL
P
-
Necking at joint.
brace bowed.
Frame design storm load
member buckling
--
Frame
storm load
joint failure
design storm load
API joint failure
50
100
Frame Displacement (mm)
Figure 3.29
BOMEL Frame
global response
TENSION BRACES
COMPRESSIONCHORD
150
50
200
300
250
Frame displacement (mm)
UCD
Frame
LCD
UTD
LTD
Frame
Figure 3.30
member forces showing X bracing load distribution and frame action
350
C
-: Present Experiment
Present
,
l
,
0.0
10
30
point
pin
40
SO
60
70
displacement
.
,
: Present Theory
a
0.0
20
70
displacement
Figure 3.33
Frames tested with and without damage by Paik and Shin
90
Oil
Reaction
PC
Oil
Cell
Figure 3.34
X-braced frames and towers tested by lnoue et
-- C
cc-
--*
Figure
3D X-braced box frame tested by
Frame S1
failure due to buckling and fracture due to lack of fusion
-
o
LOAD
LOAD
Figure
3D X-braced box frame tested by
Frame S2
buckling failure initiated by dent in member
-
4.
4.1
SOFTWARE FOR
PUSHOVER ANALYSIS
ANALYSIS METHODS
The reserve strength of a structure is derived from the nonlinear distribution of loads along
alternate paths as the capacity of individual components is exceeded. The process is
inherently nonlinear and, for accurate numerical predictions to be achieved, the ultimate
and post-ultimate responses of components need to be modelled. Sophisticated
software programs have been developed through the 1980s and advances continue today.
Before reviewing these advanced methods, however, simplified approaches may first be
considered, namely:
Member removal
Member replacement
Linear superposition - strain based load based
Limit equilibrium analysis
These are considered in turn below.
4.1
Member removal
To evaluate the influence of damage on a structure the simplest approach is to remove the
damaged member entirely and repeat the analysis. This avoids the uncertainty associated
with modelling post-bucklingor dented member characteristics, nevertheless it is likely to
give a lower bound to the residual capacity. This may be considered as a valuable
approach to determine rapidly the importance of specific members to structural integrity and
the ability of the configuration to redistribute loading in the event of damage. However,
although zero post-buckling capacity may be assumed for compression members, elastic
analysis programs will not generally enable the yield plateau response for failed tension
members or tubular joints to be modelled. The approach is therefore limited.
4.1.2 Member replacement
In this method a series of linear structural analyses are performed and as each member
fails, it is replaced by end forces representing the post-ultimate component response. The
method is straightforward to apply in situations where just a few members fail, but the
accuracy is entirely dependent on the modelling and post-ultimate characteristics (Pike and
Grenda, 1987). In brace buckling, for example, these depend on the surrounding structural
system as well as the properties of the member itself and this therefore limits the achievable
accuracy with the method. It is also criticised for being inefficient in
of both
and van de
1990).
computer time and
-
4 . 1 . 3 Linear superposition strain based
As an advance on the member replacement method Holnicki-Szulc and Gierlinski (1989)
proposed a method which uses constraint equations based on lack-of-fit member strains,
providing a phenomenological
capability. In combination with the linear solution,
the nonlinear structural response can be modelled. The concept uses the superposition
principle to combine the linear elastic solution with 'virtual' distortions introduced in the
structure, hence it is known as the Virtual Distortion Method(VDM). In addition to the
elastic stiffness matrix, a matrix representing the sensitivity of the structure to local damage
such as hinge formation or fracture is required. The matrix components are given by
deformations at a member end due to unit deformations at the other. The virtual state is
scaled such that global equilibrium and limit strength conditions are satisfied giving an
approximation to the condition within a progressively collapsing structure.
Failure is determined by the formation of a collapse mechanism when the permanent
deformations (virtual distortions) grow infinitely.
4.1.4 Linear superposition - load based
and van de Graaf (1990) developed the linear superposition method further and
their load based method enables additional constraining loadcases to be defined simply.
The method is restricted to axial nonlinear behaviour but can model cases of practical
importance where axial brace buckling or yielding, or axial pile failure dominate the
response. Instances of leg failure due to beam-column action cannot be simulated.
Figure 4.1 illustrates the method whereby the difference between the linear and nonlinear
responses of a component are identified. The difference is accounted for by applying end
force pairs to each nonlinear member. The constraint equations determine the correct
deformations and calculate the components of resistance to be derived from the member or
the surrounding frame. The nonlinear problem is reduced to finding a set of member end
forces, which, when combined with the applied loading, constrain the linear system to
follow the behaviour of the nonlinear system. The set of constraining forces can be quite
small as relatively few members (typically around ten) contribute to the collapse
mechanism. This approach is seen by
and van de Graaf to have several advantages
over more complex nonlinear analysis programs. The authors consider that because a
linear structural model and a suitable linear analysis program are generally readily
available, a full collapse analysis of a complex structure can be performed within a few
days, in contrast to the months required to regenerate the model and perform the analysis
using a more complex nonlinear analysis capability.
The method is advocated for sensitivity analyses or to determine critical scenarios for
complete nonlinear analysis (van de Graaf and Tromans, 1991).
4.1.5 Limit equilibrium analysis
Bea (1992) has recently proposed a 'limit equilibrium analysis' approach whereby simplified
analysis is performed of the principal structural components - deck, legs, jacket and
foundation (see also Bea and
1993). Storm loading profiles of horizontal shear
are developed and compared with the horizontal shear capacity of the platform to identify
the 'weak link' in the system. The level at which the weak link capacity is exceeded is
used to define the lateral static capacity for the platform. Modification factors to correct
static capacities for interactions of transient wave loading and nonlinear hysteretic structural
characteristics are applied.
The approach is advocated to investigate how the configuration and proportioning of
offshore structures influence the robustness. It is applied with an assessment of
uncertainties both in loading and resistance to determine failure probabilities. The authors
suggest that the true RSR can be predicted to within about 10% of a full nonlinear
assessment.
4.1.6 Nonlinear collapse analysis software
The most advanced techniques for collapse analysis incorporate explicit nonlinear modelling
to account for both material and geometric nonlinearity. Basic methods, of varying degrees
of efficiency and accuracy, have been used to model nonlinear member responses:
solutions of the exact differential equation of beam columns
finite element method
polynomial beam column modelling
finite segment method
physical models
phenomenological models.
In some instances nonlinear joint behaviour is modelled either explicitly with nonlinear
springs or else incorporating joint utilisation criteria underlying design codes in limiting
member capacities.
Many nonlinear analysis programs require specific division of the structure, which is
different from conventional modelling for elastic analysis. Some programs require the user
to anticipate regions where nonlinear behaviour will occur. The nature of the problem also
demands that small increments in both load and displacement control are applied to enable
the nonlinear response to be tracked as redistribution occurs. Displacement control is
required to trace unloading paths smoothly.
of engineering and computer time,
Nonlinear analysis can therefore be demanding in
nevertheless it offers the only accurate approach to evaluating the reserve strength of jacket
structures. A number of specific programs for the collapse analysis of jacket structures
have been developed since the early 1980s with the objective of improving computational
efficiency. The general basis of these is described below.
4.1.7 Appropriate analysis approaches
It is clear from the brief descriptions above that a variety of approaches can be taken to
predict the reserve strength of jacket structures. Full nonlinear analysis is demanding in
terms both of
requirements and computing capacity. However, simplified
methods necessarily introduce approximations in the ultimate and particularly post-ultimate
responses of components. In a redundant nonlinear system the difficulty is that
conservatism in modelling a component may not be
with respect to the global
capacity. Local failure may limit loads through one primary loadpath, placing reliance on
alternative components which may fail in rapid sequence.
Nevertheless it is important to recognise the insight that simple methods can give in
screening configurations so that accurate nonlinear modelling can be devoted to critical
scenarios. This has practical considerations in terms of economy and will be driven in part
by the purpose of analysis, be it to get a relative measure of system reserve or to requalify
a structure which fails to meet current elastic code provisions.
To this end a number of assessment methodologies are being proposed embodying different
(1992) has suggested that assessment needs to begin by
levels of assessment.
classifying structures in terms of:
failure consequences
increasing age - deterioration
decreasing quality of design
operational loads.
To determine the capacity, the appropriate calculation method should be chosen from:
back of the envelope
elastic (ie. utilisation)
nonlinear pushover analysis (eg. INTRA)
research level (detailed modelling of post-ultimate component responses).
This is not dissimilar from the approach advocated by Bea and Craig
although this
focuses more on what may be considered to be advanced simplified methods. The four
levels of analysis, with increasing detail and difficulty, for calculating the RSR are:
Level 1
Level 2
Level 3
Level 4
- scoring factor analyses
- simplified limit equilibrium analyses
- modified elastic state-of-the-art practice
- state-of-the-art nonlinear analysis.
It is suggested that a fitness for purpose evaluation should start at Level 1 and need only
proceed to higher levels if the acceptance criteria cannot be satisfied. As a backdrop to full
nonlinear analysis these approaches may be reviewed in detail.
Level 1 RSR is based on factors that address platform capacity (R) and environmental and
operational loadings (S):
RSR =
[S,,
where guidance on the scoring factors given by Bea and Craig is reproduced in Tables 4.1
and 4.2.
Table 4.1
Level 1 RSR capacity scoring factor guidelines
and Craig,
Guideline
Score
Structure and foundation design and construction criteria (in relation to API RP 2A)
- 1959
- 1964
1965- 1975
1976- 1993
Structure condition: corrosion, dentedlbent members, dropped objects, fouling, scour
poor
good
excellent
Structure and foundation modificationsdeveloped during installation. operations, or
reassessment that result in increases or decreases in capacity
decreases
no changes
increases
0.5 - 0.9
1
1.1 - 1.5
Structure and foundation configuration
low robustness (eg. caisson)
moderate robusmess (eg. 4 leg platform nonductile bracing)
high robusmess (eg. 8 leg platform with ductile bracing)
very high robusmess (eg. 8 leg platform with ductile bracing and excess capacity)
1.0- 1.1
1.2 - 1.3
1.4 - 1.5
1.6 - 2.0
Loading-capacity effects factor
waves
earthquakes
1.0 - 1.5
1.0 - 4.0
Table 4.2
Level 1 RSR storm and operational loadings scoring factor guidelines
and Craig, 1993)
Guideline
Factor
Score
Storm loadings design criteria (Ref. 1993 API RP 2A)
(Cd,,,
(dir. spread, shielding, blockage and current corrections)
Lower equipment deck elevation (not in design wave loading)
I
1.0- 1.5
1 . 0 - 1.5
1.0 - 1.5
Loading modifications: elements added or removed, marine growth management
0.5 - 1.5
S,
S,
Operating I gravity loading modifications
0.5 - 2.0
Level 2 is based on the limit equilibrium technique due to Bea and
(1993)
At Level 3 linear elastic analysis is used where WSD criteria
described in Section
are modified to give best estimate ultimate capacities and for LRFD structures the partial
resistance factors are set to unity. Platform capacity is based on the inverse of the largest
allowable stress ratios for the primary members (ie. those critical to ultimate capacity).
This is subject to a robustness factor to reflect the influences of system redundancy,
ductility and conservatism in primary components in terms of post yield and load
redistribution effects. Level 4 encompasses a full nonlinear analysis either within the
context of deterministic or reliability based approaches.
The focus in this review is on the reserve strength of jacket structures and to that end full
nonlinear analyses offer the route to the more accurate predictions. Nevertheless the
foregoing methods and other such simplified approaches to evaluating approximate estimates
of RSR offer a rational and cost-effective methodology for assessing system reserves.
Furthermore this sequential analysis is the methodology being proposed for the assessment
of existing platforms in the draft API RP 2A Section 17.0 (1993). There the progression
is from screening, through design level to ultimate strength level analysis, as required, to
demonstrate system adequacy. It is only at the third level that inelastic, static pushover
analysis 'may' be required. However, if nonlinear analysis is necessary it is likely that the
structure is at greater risk and therefore particular confidence in the analytical techniques
is required.
4.2
DESCRIPTION OF
SOFTWARE
The principal software programs developed for the nonlinear analysis of the ultimate static
and post-ultimateresponses of jacket structures are detailed in turn below. The presentation
is alphabetical by program name. The coverage of this section, the programs and
development organisations are listed in Table 4.3 below.
Table 4.3
Nonlinear software for pushover analysis of offshore structures detailed in this review
Full title
Program
Software development organisation
EDP
Extended
FACTS
Finite Element Analysis and for Complex
Three dimensional Systems
Structural Software Development, USA
INTRA
Developmentof
Analysis
ISEC, USA
SAFJAC
Strength
USFOS
Program
Digital Structures, USA
Tower Response
of
and
BOMEL, UK
Proprietary nonlinear dynamic analysis
program developmentof INTRA
PMB Systems Engineering, USA
Ultimate Strength of
Structures
SINTEF, Norway
Information on the various programs for ultimate strength analysis listed in Table 4.3 is
given below. The descriptions of each program have been provided by the associated
development or support organisations to the same specification. The specification asked
for a 500 word summary of the program describing the status as at the end of May 1993,
with information to be provided covering the following points:
Beam element formulations
Spring elements
Method of solution
Load application
creation facilities
processing facilities
Offshore code
facilities
Ongoing developmentslenhancements relevant to collapse analysis of jacket
structures
Date of original development, current status and contact details for further
information.
The organisations were also asked to confirm that the current report provides
comprehensive coverage of publications involving the use of the software. These are
included in the reference section and are discussed in Sections 4.3 and 5 which follow.
In addition to the software description, diagrams could be supplied and the material
provided for each program is reproduced below without modification.
Although not strictly a 'nonlinear analysis package', details of the VDM module within
RASOS are also included in this section as several North Sea operators are participating
in the development of the package. The information was supplied by WS Atkins to the
same specification as for the nonlinear programs presented above.
EDP
"The Extended Design Program, EDP, performs general nonlinear three dimensional
element analysis of structural systems including the effects of soil-structure interaction.
The program is suitable for static and dynamic analysis of steel and concrete structures such
as fixed and compliant offshore platforms.
Element formulations
The EDP element library consists of many formulations for modelling the
nonlinear response of offshore platforms, including linear and
beams, struts, plates, shells, solids, pipes, quadrilaterals, loading and matrix
elements. Nonlinear elements are hysteretic and all elements are three dimensional.
Geometric stiffness, large displacement and P-delta effects are included.
Two and three hinge beam-column elements capture plastic hinge formation due to
combined axial force and bending moment interaction for primary bending members. The
strut element is a multipurpose phenomenological element to represent buckling and tension
yield in primary braces or large deformation cable tension response. Special composite
tubular beam-joint elements combine the nonlinear response features of the strut buckling
or inelastic beam-column elements with the joint nonlinear behaviour.
Plates and solid elements enable the finite element analysis of tubular joints, concrete shells,
interaction and diaphragm response.
Spring elements
Spring algorithms enable any physical force deformation behaviour to be replicated.
pile interaction, structural joints or boundaries and their energy absorbing characteristics
are incorporated by use of nonlinear elastic or hysteretic spring elements. Soil axial and
lateral stiffness nonlinearity are modelled using a hysteretic soil element that includes
Spring elements also model impact, uplift and friction.
degradation and
Method of solution
EDP contains features which minimise the potential for numerical instability in static and
dynamic analyses. Constant stiffness and Newton Raphson iteration schemes are used for
both static and dynamic analyses to maintain internal equilibrium with the externally applied
loadings. Nonlinear dynamic response is determined by direct integration of the equations
of motion. Linear response is obtained from response spectrum or time history analyses.
EDP is capable of incorporating local failure with advancing time. The analysis then
continues with this revised state and thus simulates progressive collapse situations to the
point of ultimate instability. When considering such alternate load paths for redundant
structures, the failure criteria for brittle and ductile members may be defined by force
limits, or deformation limits, cumulative deformation or hysteretic energy dissipation.
A demonstrated characteristic of the program is a very high efficiency in numerical
solutions.
Load
Static and dynamic loads may be superimposed to replicate the actual instantaneous and
complicated loading sequence experienced by the
system. Static loads
are applied in a prescribed manner by the user or automatically by the program in
increments. Dynamic loads can be time varying forces (nodal or element), displacement
functions, wave loads or ground acceleration time histories. Multiple support excitation and
phased motions simulate the spatial variability of seismic motions for extended structures.
Code checking
Tubular steel structural members are checked to API RP 2A code requirements, even
during seismic time history analyses. AISC code checks are available for other sections.
facilities
EDP has an integrated comprehensive graphics capability to facilitate interpretation and
documentation of results.
Current status
First developed in 1980, and continually enhanced, EDP has been used extensively in
production analysis of complex offshore structures and has been checked against other
through
nonlinear programs. EDP versions exist for a range of computers from
mainframes.
A reference including the use of EDP is by Piermattei et al (1990).
For further information contact Digital Structures
2855 Telegraph Avenue, Suite 300,
Berkeley CA 94705, USA, Tel:
510 549 1565,
1 510 549 1600.
+
FACTS
"FACTS is an integrated library of programs for the linear and nonlinear
element
Systems under static and dynamic loads.
Analysis of
Element
The FACTS library includes both general purpose and application specific element types
and internal modelling features including:
3D linear:
truss
beam
straight and curved pipe
3-9 node
3-9 node shell element
8-20 node solid
membrane element
3D nonlinear:
truss
cable
beam-column, lumped plasticity
beam-column, distributed plasticity
degrading stiffness beam-column, lumped plasticity
straight pipe
effects
curved pipe with
8 node shell
8-20 node solid
gap friction
shear degrading link
free-field soil
near-field soil
2D nonlinear 4-8 node
membrane element
U-bar restraint
SSD nonlinear buckling strut
buckling strut
Method of solution
Linear static solution
Multiple static, thermal and pressure load cases.
Specification of loads at substructure level.
Automatic recovery of all substructure displacement and stresses.
Linear dynamic solution
Eigensolution using an efficient and reliable shifted
Component modes for linear substructures.
Response spectrum dynamic analysis.
Modal superposition time history dynamic analysis.
iteration scheme.
static solution
Ability to include linear as well as nonlinear elements and to specify that certain
analysis).
substructures remain linear
Newton-Raphson Iteration: Both load and displacement iteration options are
available.
Event-to-Event Strategy: Automatic subdivision of the load step based upon events,
strut buckling etc., to stabilise the analysis with minimal user interaction.
dynamic solution
Ability to specify linear elements and substructures.
Newton-Raphson Iteration: Step-by-step analysis with constant time step with or
without equilibrium iteration.
Automatic Event-to-Event Strategy: Automatic modificationof the integration time
step based on accuracy considerations to minimise equilibrium balance requiring
minimal user interaction.
Solution control
Pause and restart from any state.
Organisation as a series of computational models linked by commands which are
input as program data. This provides unlimited flexibility in ordering the input
data and computational sequence, while still allowing well-established sequences
to be 'hard-wired' by macro commands.
Load
ion
FACTS includes a hierarchial database management system which allows the FACTS
analysis programs to exist as stand alone modules. Access to the database is through an
easy-to-use interface language that allows users to develop and link their own applications.
Analysis of Structural and Mechanical Systems - GENLIB - For static and dynamic analysis
of structures with localised nonlinearities, including structures with nonlinear foundations
and general linear and nonlinear static and dynamic finite element stress analysis. Static
loads include: nodal applied forces, self-weight and temperature and pressure distributions.
Dynamic loads include: applied force functions and multiple support seismic excitation.
Inelastic buckling and postbuckling analysis of pipelines and stiffened shell structures made
of metallic or composite materials.
Hydrodynamic Analysis - Static and dynamic wave-structure interaction.
Frequency domain and time history analysis of the hydrodynamic response and wave force
distributions for floating or fixed based platforms in regular or random seas.
Seismic Analysis - SEISLIB - Seismic strength and ductility analysis.
Ice-Structure Analysis - ARTICLIB - Dynamic ice-structure interaction.
creation
- Automatic modelling of complex tubular joints in
Tubular Joint Analysis offshore platforms to capture the effects of joint flexibility and to estimate the stress
concentration factors.
Geometry definition - Includes point, line, grid and solid generation schemes. FACTS also
provides general kinematic constraints on nodal degrees of freedom.
Multi-level substructuring - Provides up to 25 levels of substructuring with up to
substructures in each level. FACTS includes automatic transfer of stiffness, loads,
recovery of displacement and recovery of stresses. Free
word input procedure.
Offshore code
Fatigue Analysis of Structure - A post-processor to
to
predict fatigue life and long term statistics. Performs stress determination, member
checking and joint can design subject to API RP 2A guidelines.
facilities
Full interactive with
options.
Interactive preview of results saved.
Initial geometry plotting.
Deformed geometry plotting.
Construction and plotting of result tables.
Graphical presentation of displacement and element results.
Current status
The FACTS package can be made available on a wide variety of computer systems
including IBM, CDC, CRAY,
and Sun SPARC.
Early application of the FACTS software is given in a reference by Bouwkamp et
FACTS is available for lease or purchase. For further information contact SSD Inc, 1930
510 849 3458.
Shattuck Avenue, Berkeley, California 94704, USA, Tel
KARMA
"The Computer program. KARMA, developed by ISEC Inc., is a three-dimensional,
inelastic, nonlinear, static and dynamic response analysis program. It is based on finite
element formulations for structures subjected to environmental loads. A coupled foundation
structure, 3D nonlinear dynamic failure analyses of land-based and offshore structures can
be performed. KARMA, an United States oil industry standard program, is a result of 14
years of in-house and oil industry sponsored research and development.
The program's capabilities can be effectively used to evaluate ductility, failure modes or
structural integrity of a variety of onshore structures (bridges, overpasses, high-rise
buildings, transmission towers, etc) and offshore structures (jacket type, jack-up rigs,
deepwater compliant structures, floating systems, tension leg platforms,
systems,
etc). Wherever possible, the program's methodology has been verified using model scale
and full scale experimental data.
Linear and nonlinear dynamic analyses are performed in the time domain. Alternatively,
linear dynamic analyses for earthquake loads may be performed in the frequency domain
(response spectrum analyses). Environmental loads may be wind, hurricane, wave,
earthquake, boat impact, or any generalised loading. Eigensolutions of large 3D complex
eigensolver. The
systems may be performed using a state of the art shifted
program can handle material (steel, concrete, reinforced concrete, soil) as well as geometric
nonlinearities. KARMA is computationally very efficient.
KARMA has an automated redesign capability for offshore structures based on a minimum
cost algorithm. Also, comprehensive fatigue analyses can be performed including all
nonlinear effects.
A comprehensive post-processor exists in KARMA. It performs member checks using API
19th Edition
approach for tubulars. Joint checks are performed using
RP
the AWS Alpha approach for joint classifications. Non-tubular member checks are
performed using the AISC recommendations. It also includes the interface to the 3D
general purpose visualisationand animation program, SWAMI. Thus results from KARMA
can be visualised and animated using SWAMI. Alternatively, KARMA models can be
interactively built with SWAMI'S 3D graphics capability.
Some of KARMA'S special features are listed:
1.
2.
3.
4.
5.
Conventional fixed format input or key word oriented input structure.
Input data echo and extensive data checking capability.
Automated generation of inelastic properties for truss and beam element types.
Profile minimiser to optimise storage and computations.
Flexible boundary conditions handling through
or multipoint constraints.
6. A generalised damping formulation to allow user specified damping ratios in as many
modes as desired.
7. Automated earthquake load profile generation for static pushover analysis.
8. Automated wave load profile generation for pushover analysis.
9. Marine growth and comprehensive hydrodynamic options.
10. Extensive element library for structure, soil, foundation and specialised applications.
11. Flexible and comprehensive load definition options including member loads, random
wave generation for unlimited durations and dynamic wind gust loads.
12. Automated self-tracking static and dynamic analysis capabilities.
13. State of the art fatigue analysis options which include all nonlinear effects.
14. Comprehensive post-processing and interfaces to 3D photoelastic graphics and
animation with lighting and shading (Program SWAMI).
and
Karma can be executed on workstations such as the Sun Micro Systems
minicomputers like the VAX series, mainframes such as the IBM, parallel
processors, or the super-computers such as the CRAY."
A reference including the use of KARMA is by Gidwani and Renault (1990).
Further information can be obtained from ISEC Inc., 505 Montgomery Street, Suite 680,
USA,
1 4 421 1692.
San Francisco, CA 94111
+
SAFJAC
- A program for the Strength
Analysis of Frames and
SAFJAC is a nonlinear analysis program for determining the reserve and residual strength
and the progressive collapse behaviour of offshore structures. The program is based on
conventional finite element analysis techniques but for purposes of efficiency and
friendliness it incorporates high-order beam-column elements and automatic mesh
refinement as plasticity develops.
Beam element formulation
The basic element of SAFJAC is an elastic high-order
beam-column element which
permits each member of the structure to be represented by a single element because it
models large deflection behaviour accurately and sub-divides automatically when plasticity
is detected at which point a cubic element is introduced within the original element. The
plastic hinge formulation is based on axial load-moment (P-M) interaction surfaces whilst
the cubic element simulates the gradual spread of plasticity (softening) through the
section and along the length of the member (Figure 4.2).
Spring elements
Linear and nonlinear spring elements may be introduced into any part of the structure to
model joint flexibility, pile-soil interaction and
The behaviour in tension and
compression may be different. A comprehensive library of P-6, M-0 joint characteristics
is provided linked to mean capacity equations underlying HSE Guidance.
Load
Proportional or non-proportional loads or prescribed displacements may be applied after the
application of, for example, initial loading corresponding to the still water condition.
proportional loading allows random-time-history of loading to be specified. Special
facilities also exist to apply and remove loading due to boat impact allowed by
environmental storm loading.
Method of solution
An incremental iterative solution procedure is employed based on the frontal technique
which assembles and reduces the global stiffness matrix according to an optimised element
order that minimises the bandwidth. Once optimised at the start of the analysis, no further
optimisation is required to accommodate the extra nodes and elements generated during
solution. To overcome convergence problems in the vicinity of the ultimate load, both load
and displacement control of the solution and automatic scaling of
increments is employed.
Code checking
At any stage of the incremental analysis tubular joints can be checked according to API.
Joint classification is automatic according to geometry and load path of coplanar members.
Model creation and
Data input is by an ASCII format file with recognisable headers and subheaders for ease
of data entry. Interfaces to IDEAS-FEM and
allow the model to be displayed
graphically.
facilities
allow the results to be displayed and plotted. A
Interfaces to IDEAS-FEM and
post processing program RESULTS allows the user to extract results (displacements,
forces, stresses) in a tabulated form suitable for input into PC graphics and plotting
programs.
Ongoing develovments
Developments at BOMEL include:
Integrated wave and current load generator.
Joint failure surfaces.
Integration of system into a fully integrated CFD, thermal and structural analysis
system for progressive collapse analysis of structures exposed to fires.
Graphical pre- and post-processing enhancements for displaying the sequence of
plastic hinge development and spread of plasticity.
Program
Development of the program began in 1987 as part of the Joint Industry Frames Project in
which experimental and theoretical investigations were carried out into the reserve and
residual strength of large scale tubular frames. SAFJAC has thus been fully calibrated
against experimental tests designed to fail as a system rather than at a component level
(Figure 4.3).
References citing the development and application of SAFJAC are by Ward and Izzuddin
Billington et al (1991) and Bolt et al (1994).
Further information can be obtained from BOMEL, Ledger House, Forest Green Road,
UK,
+44 1628 777877.
Fifield, Maidenhead, Berkshire, SL6
Introduction
PMB began its development of state-of-the-art nonlinear analysis software for the oil and
gas industry in 1978 with the introduction of the INTRA
Analysis) computer program. INTRA was originally developed through a joint industry
project to meet the challenge of analysing platforms in seismically active areas where
extensive nonlinearity is expected and confirmation of adequate ductility is essential for
good design.
INTRA was expanded for analysis of a wide range of structural types and thus became the
standard for nonlinear dynamic analysis in the oil and gas industry. Additional
enhancements included the development of advanced soil-pile modelling capabilities which,
was
in 1983, represented a capability that is still unique within the industry.
created in 1987 when the basic architecture of the program was updated with improved
solution schemes and computational efficiency.
General
is a comprehensive nonlinear static and dynamic analysis tool which can be used
to analyse a variety of offshore structures, including fixed platforms, compliant towers,
stiff and flexible risers, buoys and cable systems. It has been used
extensively to perform regular and random wave analyses, pushover (collapse) analyses,
ship impact analyses, and toppling analyses. Its basic capabilities include:
A library of linear and nonlinear finite elements.
Regular waves, irregular 2D and 3D waves, current, ice and earthquake loading.
Static, eigenvalue, frequency domain and explicit time domain analysis.
API code checks and fatigue life calculations through a graphic post-processor with
automatic redesign capability.
Interactive, graphical model generation and post-processing with colour animation.
Element library
In addition to the conventional linear beam, plate and truss element, SeaStar has an
extensive library of nonlinear finite elements which explicitly model material nonlinearity
and large deformations including, for example:
Beam column
bending failure surfaces are either generated automatically using an
extension of Mohr plasticity theory or user-specified.
Substructured beam-column
Represents material and geometric nonlinearity including explicit modelling of local
damage.
Pile-soil interaction
Discrete elements to model nonlinear axial and lateral interaction for both static
and dynamic loading including rate of loading effects, cyclic degradation, hysteretic
behaviour and
Properties are either generated automatically based on API formulations, using
algorithms calibrated to large-scale field tests, or are user specified.
Speciality elements
- A phenomenological model of brace buckling, post-buckling and cyclic
response.
Cable element - Represents nonlinear interacting components of cable response
with a single element.
element - Models contact problems such as riser-seafloor.
interaction
Wave, current and earthauake loading
Wave loading in SeaStar includes regular wave, irregular waves, current loading,
kinematics stretching and wave-current interaction effects. Regular waves can be modelled
using Airy waves, Stokes fifth order waves, or Stream Function waves. Irregular waves
can be modelled with either a user-defined or Pierson-Moskowitz spectra. Both
unidirectional and multidirectional seas can be modelled.
Ice loads can be applied statically (slowly mooring sheet ice) or dynamically (impacting ice
floes), with the nonlinear constitutive properties of the ice modelled explicitly.
Earthquake loading can be defined using either ground motion records or spectra, for use
in time domain or response spectra analyses, respectively.
Solution methods
Static solution schemes include self-sensing methods. Dynamic analysis methods include
a constant time step procedure using Newmark's integration method and a step by step
integration strategy which automatically adapts the time step to ensure accuracy.
Model generation and
and post processing (CAP)
CAP is an environment developed to access information which can help the user understand
a
model and its behaviour. This objective is achieved with an interactive,
graphical windowing system through which the user can build or import (from SeaStar,
SACS and STRUDL) structural models, performs queries on those models to highlight key
feature (ie. all flooded members, all pinned joints, etc), run analyses, and post-process
results.
In addition to presenting basic member and structure results (force histories, displaced
shapes, etc), CAP can animate an analysis on screen, while at the same time colour coding
member utilisation ratios and nonlinear events (buckling, hinging, etc). This capability is
extremely useful for helping to visualise and understand the behaviour of a structure
responding to various loading conditions.
The ability to access multiple types of information is demonstrated in Figures 4.4 through
4.6 which show examples of the information provided on-screen for static pushover,
dynamic failure and toppling analyses, respectively. Each of these figures are based on
'snapshots' from animated results of these analyses.
References including the use of
include Craig et al
et al
et
An-Nashif
Dolan et
Nordal (1991) and Bea et al (1988).
Pawsey
Dolan and
Further information can be obtained from: PMB Engineering Inc, 500 Sansome Street, San
Francisco, CA
11, USA, Fax: 1 415 986 2699.
+
USFOS
Main fields of application
USFOS is a computer program developed for nonlinear analysis of offshore structures in
steel and aluminium with special reference to progressive collapse. The direct damage
caused by accidental or abnormal environmental loads is assessed in addition to the residual
strength of the damaged structure. The following load conditions can be considered:
Functional loads
Environmental loads (wave, wind, current)
Ship collision
Dropped objects
Fire loads
Explosion loads
USFOS is based on a general, nonlinear continuums formulation for solids. The
formulation is then tailored to 3D frame analysis, based on familiar engineering concepts.
In addition to the nonlinear static analysis, nonlinear time-domain dynamic analysis as well
as eigenvalue analysis may be performed.
Beam element formulation
The beam column is the basic entity of USFOS (Figure 4.7). A coarse element mesh is
used, only one finite element is required per physical member of the structure.
The USFOS beam is valid for large lateral displacementsand moderate strains. An updated
Lagrange formulation is used based on Green strains. The axial force influence on bending
is represented by Livesly's stability functions. Nonlinear material behaviour is modelled
by means of plastic hinges which includes material hardening and the Bauschinger effect.
Spring elements
Linear and nonlinear - single and 2 noded springs are available.
Special features
load analysis:
The basic formulation is extended with special features for
Ship collision algorithm including local denting, overall structure deformation and
ship deformation.
Residual strength of tubulars with dents and permanent distortion.
Interaction with local buckling for thin walled tube and rectangular sections.
Tubular joint flexibility and ultimate strength models.
Non structural element option.
Internal, guided pile option.
Fracture criterion for tubulars based on a level 3 CTOD approach.
Degradation of yield stress and elastic modulus at elevated temperatures. Effect
of thermal expansion.
Effect of external hydrostatic pressure on plastic capacity.
Method of solution
An incremental iterative loading procedure employing arc-length iterations to a normal
plane is used. The post collapse behaviour is determined by the current stiffness parameter
and determinant. A bifurcation point analysis is optional. Automatic load step scaling is
offered.
Load avvlication
Proportional and non-proportional loading. Concentrated and linearly distributed loads,
temperature loads, collision loads, acceleration fields. Combination of load cases to load
combinations.
Offshore code checking
Plastic utilisation and von Mises stress check. Member buckling calibrated according to
ECCS code or other. Tubular joint capacity checked according to API and HSE. Ship
requirements.
collision according to
Pre-vrocessing and model creation facilities
USFOS may be used as a stand-alone program with ASCII format input files.
The geometry input defined according to the SESAM Interface File Format which may be
generated using the SESAM programs PREFRAME or PREFEM.
Wave and current load data may be generated by the SESAM program WAJAC.
Thermal loads input directly by the user, or generated by the SINTEF program FAHTS.
facilities
user interface. Results
Graphic post-processor, XFOS, based on a X
presented as colour fringes (eg. plastic structural utilisation, temperature distribution) on
images of the structure, deformed configurations, XY plots or printed result data tables.
Step by step of visualisation of material yielding, member buckling, force redistribution
etc., up to final collapse of the entire structure.
The USFOS development continues at
through several Joint Industry
Research Projects and includes:
Integrated, nonlinear dynamic analysis of ship collision
Nonlinear, dynamic analysis of ductility level earthquakes
Elasto-plastic cyclic analysis of jackets structures (incremental collapse vs
shakedown)
Integrated, progressive collapse of structures exposed to fire (fire development,
heat transfer, mechanical response)
Models for aluminium behaviour, including creep
Explosion response
Pre and post processing enhancements.
Development of the program was initiated at
in 1983. The ongoing program
development is supported by seven oil companies and 2 engineering companies."
References including the development and application of USFOS include Moan et
Soreide et al
Soreide et al
Moan and Taby
Moan and Amdahl
Moan et
van de Graaf and Tromans (1991).
Medenos and
Jacobs and Fyfe (1992). Tromans and van de Graaf
Logendra
et al
Eberg et al
Amdahl and Eberg
et al
et al (1993) and Eberg et al (1993).
USFOS is marketed by Det Norske Veritas Sesam AS, Head office address: Det Norske
Norway,
+47 67 57 72 72.
Veritas Sesam AS, Veritasveien l , N-1322
RASOS
Reliability Analysis System for Offshore Structures
RASOS is a software system specially developed for the system reliability analysis of fixed
offshore structures. Main analysis options embrace both extreme events and long term
effects such as fatigue. Included within the system are also modules for environmental load
generation due to wave, current and wind, pile foundation modelling, deterministic collapse
analysis of arbitrary 3D skeletal structures and fatigue-fracture analysis of tubular joints.
The summary information given below refers to a particular feature of RASOS concerned
with progressive collapse analysis and ultimate strength assessment of jacket structures.
The model creation is based on a standard data file input, including nodal coordinates,
topology, definition of member cross-section, elastic material properties and details of
suppressions and constraints. For nonlinear analysis relevant material properties and
definition of force moment interaction surface (limit surface) is required.
The loading types available in RASOS are user defined nodal loads, thermal loading, initial
strain loading, gravity loading and environmental loading. The environmental loading can
be user defined or calculated by a dedicated module using a response surface model based
on Airy's wave theory. Load combinations and unity checks can be performed. For
linear analysis non-proportional load history can be specified.
Two types of structural components available in RASOS: two noded beams and joints. Of
the first type tubular, beam and flange elements are available to the user, along with
secondary members designed to be used to model non-structural elements such as risers and
conductors. The linear analysis is formulated upon the engineer's beam theory, whereas
in the nonlinear collapse analysis critical members are replaced with a sophisticated
nonlinear beam column model. This nonlinear member model makes use of a range of
slopes, brittle
post-limit models, such as conventional plasticity with
or ductile failure and member buckling. Joints can be modelled as rigid or flexible, with
flexibility characteristics automatically calculated depending on the joint geometry. For
nonlinear analysis failure modes such as fracture, plastic failure and punching are available.
Component capacities in various modes can be user defined or calculated by a dedicated
module. During global collapse analysis member and joint failure modes are combined into
resultant limit surface.
RASOS has the capability to allow the user to use both nodal spring supports and pile
supports in the same structure. The pile support is defined using local stiffness matrix,
which includes lateral-rotational coupling terms and can be user specified or calculated by
a dedicated module.
The Virtual Distortion Method (VDM) is employed for global progressive collapse analysis
and has the capability to trace the nonlinear behaviour into post-critical domain. The
algorithm identifies overloaded locations within the structure based on a defined limit
surface. At the onset of damage, whether ductile or brittle, permanent deformations at
these locations are modelled by virtual distortions, which are the main degrees of freedom
of VDM. Consequently, only small system of equations, corresponding to the damaged
locations, has to be solved repetitively. Internal forces and displacements are calculated
separately through simple substitutions and only when needed.
The results from RASOS are presented in text files which give displacements and internal
member forces. Visual presentation of results from linear elastic and collapse analysis is
available through a dedicated graphical module or the FEMVIEW package.
The major developments currently being undertaken are mainly concerned with the
probabilistic approach and are following two independent directions: (i) structural reliability
under combined extreme loading and (ii) fire safety of offshore structures (jackets and
topsides).
The original development of RASOS was conducted under the BRITE P1270 project Reliability Methods for Design and Operation of Offshore Structures. BRITE P1270 ceased
in September 1991, and since them much progress has been made under collaborative
projects. Access to the code is currently available through membership of the RASOS User
Group.
References citing the development and application of the VDM within RASOS are
and Gierlinski
Gierlinski and Yarimer (1992) and Gierlinski and Shetty
(1993).
For further information please contact: Dr J T Gierlinski, Chairman RASOS User Group,
Grove, Ashley Road, Epsom, Surrey KT18
WS Atkins Science and Technology,
+44 1372 740055.
4.3
SOFTWARE COMPARISONS
In addition to specific nonlinear programs for analysis of structural collapse, conventional
finite element programs such as ABAQUS, FENRIS and MARC have been used to model
the collapse response of frames. Table 4.4 presents key references for the programs in
which results of collapse analyses are presented, so that the reader can readily identify
works of interest. These references are reviewed in turn in Section 5.1 to identify
information on the reserve strength of structures that the analyses reveal. It should be
noted that the references cited are examples and other publications of similar studies and
results are available. Furthermore, the review focuses more on static pushover analyses
rather than seismic assessments.
Modelling of members within programs falls generally into three categories:
conventional finite elements
phenomenological modelling
exact modelling of beam-column action.
When conventional finite elements are used (eg. ABAQUS, MARC, FENRIS), several
elements are required to model the nonlinear behaviour of members. This generates a large
problem size which is time consuming to solve. Furthermore, the element specification for
conventional elastic analysis cannot be adopted and specific modelling is required.
Phenomenological modelling (eg. CAP, KARMA, EDP, etc) requires significant input from
skilled engineers who are able to postulate potential failure sites and define appropriate
phenomenological characteristics for the struts relating to both the member properties and
influence of surrounding structure.
Using one element per member (eg. USFOS, SAFJAC) enables efficient solution of large
problems such as jacket analyses. Furthermore it enables typical elastic beam models from
conventional structural analysis to be adopted. The fact that each element can embody both
tension and compression member characteristics is a significant advantage, placing less
reliance on the experience of the analyst, or requiring remodelling for different loading
scenarios.
Table 4.5 highlights references where the same structures have been analysed using
different analysis programs. The comparisons are too few for general conclusions to be
drawn. Furthermore all analyses were performed with the assumption of rigid joints. The
Frames Project data
have been made available for benchmarking software
as part of an exercise being managed by the UK Health and Safety Executive (HSE, 1993).
This will enable the ability of programs to model both joint and member failures, as well
as load redistribution, to be demonstrated and will clearly be a valuable exercise.
Table 4.5
Comparative analyses of the same structure using different software
(Furtherdetails are given in
5.1)
E
Structure
References (Programs)
Comparisons
2D frame
et al, 1988 (MARC,
Ward and
1988 (SAFJAC)
et
1991
Global loaddeflection responses show good
correlation to peak load. SAFJAC and USFOS
also track post-ultimate curves.
Nordal, 1991
(FENRIS,
Good agreement for NW wave.
Discrepancy for
for N wave different
loads and sequence of collapse but different
analysis brief and modelling assumptions.
USFOS)
4.4
Application of nonlinear collapse analyses software in the literature
Paper - Authors
Program
ABAQUS
Zettlemoyer (1989)
EDP
Piermanei et
FACTS
Bouwkampet
FENRIS
(1980)
(1984)
MARC
Renault (1990)
et
Ueda et
SAFJAC
Ward
Plane frame and 3D jacket
(1988)
Gidwani
Idealised frame including joint flexibility
(1986)
Izzuddin (1988)
Veslefrikk platform
Maui A seismic reassessment and pushover
(1992)
Bea et
Example requalification assessment
(1988)
Veslefrikk platform
(1991)
USFOS
(1991)
Medenos
Jacobs
Fyfe (1992)
Soreide et
Moan et
Plane jacket frame - benchmarking against 2D
frame test
2D test calibration, including joint nonlinearity
(1991)
(1991)
Dolan et
Idealised jacket - impact
Plane jacket frame
(1988)
Billington et
Idealised 3D jacket
3D jacket - bracing study
(1988)
INTRA (KARMA)
Elastic 2D jacket frame with joint flexibility
(Program also has nonlinear capability)
Simple structures
Grenda (1987)
et
Goodwyn platform optimisation
Benchmarking against single bay 3D test
(1991)
Lloyd
Pike
Frame subassemblage - detailed joint model
Veslefrikk platform
(1991)
Moan et
INTRA
(1990)
Analysis
(1987)
Jacket impact
Jacket bracing study
jacket
against single bay 3D test
(1991)
van de Graaf
Tromans (1991)
3D platform hindcasting
van de Graaf (1
3D platform hindcasting
et
(1991)
Cyclic shakedown of plane jacket frame
et
(1993)
North Sea jackets - static and cyclic pushover
Tromans
DYNAS
(dynamic)
et
ADAPTIC
(dynamic)
and Gho (1992)
(1977)
Benchmarking against
Idealised
cyclic frame tests
including joint
(Note: example publications are cited - where related papers present results of the same or similar analysis, just
one reference is given.)
(a)
(b) pseudo
structure
axial load
additionalforce in
member caused by
axial deformation
(c)
response curve for member "I"
Figure 4.1
Basis of linear superposition method
and van de
a) P-M Interaction Surface
for Plastic Hinge Analysis
GAUSS INTEGRATION POINTS
NODE l
STRESS MONITORING
POSITIONS AT GAUSS
I
Distributed Plasticity
Two new
elements
Elasto-plasticcubic elements
node
Elastic
elements
Distributed Plasticity.
Plastic Hinge.
C)
Subdivision of Quartic Element
Figure 4.2
SAFJAC plastic hinge and cubic elements with automatic subdivision of
element
LATERAL
DISPLACEMENT
A
LOAD
Single Element Per Member and
Joint Flexibility Included
0
Upper compression
-----
EXPERIMENTAL RESULTS
ANALYTICAL RESULTS
LATERAL DISPLACEMENT
Comparison of Analytical and
Experimental Reponses
Figure 4.3
SAFJAC analysis correlation with Frames Project test result
CAP
Figure 4.4
static pushover analysis
R
W...
CAP
Figure 4.5
dynamic failure analysis
CAP
Figure 4.6
dynamic toppling analysis
P
Non-linear material
(Elastic)
Non-linear geometry
Figure 4.7
USFOS basic concepts
ANALYTICAL INVESTIGATIONS
The technical literature now contains a number of papers describing the ultimate response
of frames based on pushover analysis. The basis of the investigations differ, so
representative analyses are described in Section 5.1 before the results are compared in
Section 5.2. Analyses performed to calibrate software against experimental data and
presented in Section 3 are not reproduced, as the intent is to derive new information on the
reserve strength of structures.
5.1
BACKGROUND TO ANALYSES
Analytical investigations vary from the assessment of simplified structures to the analysis
of offshore jackets in a hurricane environment for hindcasting evaluations. The analyses
are presented in order of increasing complexity as summarised in Table 5.1 overleaf.
The developments in RSR assessment can be seen from the dates against the references in
Table 5.1. Work was driven initially by the assessment needs for 3D jacket structures and
hence the idealised approaches were adopted (eg. Lloyd, 1982). The move was then to 2D
frames, either as representations of offshore platforms (eg.
et al, 1988) or as a
influences on ultimate response characteristics
means to elucidate some of the key
(eg. Pike and Grenda, 1987). As RSR has begun to play a role in offshore practice so
examples of the application of nonlinear software to real structures have been published (eg.
Piermattei et al, 1990; Jacobs and Fyfe, 1992). Specific
evaluations utilising
more advanced knowledge of hurricane driven hydrodynamic load in conjunction with
and Tromans, 1991). Indeed as US
pushover analysis are now emerging (eg. van de
attention turns increasingly to platform requalification for both earthquake and hurricane
environments (API draft, 1993). and North Sea regimes require ongoing reassessment for
the number of papers in the literature has proliferated.
extreme loads (Sharp et al,
The results presented in the following sections indicate the information about platform
reserve strength that can be learned from analysis.
Table 5.1
Summary of presentation of analytical work
Type of Investigation
Authors
2D frames
Pike
Grenda (1987)
(1980)
Bouwkamp et
Elastic influence of joint flexibility
Illustration of importance of nonlinear joint
(1986)
Ueda et
Demonstrationof buckling algorithm
Influence of joint flexibility on seismic response
Elnashai
Connelly
Zettlemoyer (1989)
et
(1988)
Influence of frame
Comparative analyses
Izzuddin (1988)
Ward
et
(1991)
Gates et
on joint behaviour
et
frame, different program
et
frame. different program
Contribution of redundant bracing to reserve
(1977)
Idealised 3D jacket
Demonstrationof redundancy in different framing
Lloyd
(1984)
Intact and damaged structure calculations
Lloyd (1982)
Alternative plan bracing configurations
Paik and Shin
Intactldamagedlmemberremoval analyses
Jacket (structure investigation)
Jacobs
Fyfe (1992)
Alternative bracing configurations
(1988)
Alternative bracing configurations
et
Comparative analyses using three programs
Nordal (1991)
et
(1990)
(1992)
Dolan et
(1987)
Soreide et
Optimisation to achieve target RSR
Pushover as part of seismic investigation
versus damage investigations
Jacket pushover and 3D frame
Moan et
Bea et
interactions
(1988)
Example requalification assessment
(1988)
Shinners et
(1988)
Evaluation of upgrading options
Jacket
investigations)
Cyclic loading comparisonswith pushover results
Jacket
Tromans
van de Graaf (1992)
van de Graaf
Tromans (1991)
Jacket reassessment
Comparison of predicted damage with observations
Reliability
Edwards et
Holm et
Nordal et
(1985)
(1988)
(1988)
Jacket case study to evaluate techniques
Role of
Comparison of
variability
influences
5.1.1
Simple 2D frame analyses
Pike and Grenda (1987)
The paper presents an algorithm to model buckling and its use is demonstrated with two
simple structures. For the two bay X-braced frame in Figure 5.1, it is shown that the RSR
increases for increasing brace slenderness and for lower rates of compression brace load
shedding. Allowing for the restraining stiffness of the mid-height horizontal, the member
was shown to increase the frame RSR by 6% compared with the case where it was omitted.
Exact agreement was obtained from comparative analyses with INTRA.
The reserve strength of a parallel system of K-braced frames was also investigated (Figure
5.2). Plan bracing, although not shown, was provided to distribute loading between the
panels. For central loading, failure is governed by buckling in the compression braces,
there being no redundancy within individual panels. For eccentric loading, denoted by
(the ratio of the loads carried by each panel before failure), load shedding from the panel
to fail first is redistributed to the parallel panel. The reserve strength for the system
beyond first member (panel) failure is given as
Eqn 5.1
where p is the rate of unloading following compression brace buckling. The figure
demonstrates the system reserve associated with eccentricity or lack of symmetry which is
inherent in real offshore structures but absent in many simplified models.
Bouwkarnp, Hollings. Maison and Row
Both static and dynamic analysis of the 2D jacket frame in Figure 5.3 were performed
using FACTS incorporating joint flexibilities (see Section 4). A complete nonlinear
pushover analysis is not undertaken, neither are limit loads incorporated for the tubular
joints. Nevertheless the influence of non-rigid joint behaviour on the frame response is
demonstrated in the paper although the results do not enable the influence on reserve
strength to be assessed. However, the paper is a milestone in the recognition of joint
flexibility effects on static performance.
Ueda, Rashed, lshiharna and Nakacho
In place of rigid joints, idealised elastic perfectly plastic models were incorporated in the
analysis of the five bay K-braced frame shown in Figure 5.4 subject to lateral loading. The
model simulates the flexibility and ultimate capacity of the joints. Where the joints are
rigid, failure is in the braces. For high joints joint failure can dominate the response,
limiting the global capacity. This introductory paper is used to illustrate the importance
that joint failure can play in overall structural responses. The analysis was performed with
a program 'NOAMAS'.
Elnashai and Gho
Although focusing on the influence of joint flexibility and seismic responses, the authors
performed a static pushover analysis of the 2D jacket frame shown in Figure 5.5. The
configuration determined that brace buckling preceded joint failure so just the effects of
linear flexibility compared with rigidity are assessed. Little influence on capacity was
therefore found, although the sequence of failure and ductility were affected, as shown in
the figure. This latter observation is particularly serious for ductility based design of
offshore structures. The 'rigid' structure was also able to redistribute loading more
effectively in the dynamic case. The factored load is arbitrary and the relation of the
failure sequence to the global response is not given so further discussion of reserve strength
cannot be presented.
and Elnashai
In contrast to the above, the analysis of the frame in this paper involved joint failure prior
to brace buckling. This afforded the structure significant ductility.
and Zettlemoyer
The K-brace subassemblage in Figure 5.6 was analysed using ABAQUS with a shell
element model of the central K joint incorporated explicitly. The same K joint model was
analysed in isolation with typical boundary conditions. Joints with brace angles of 45" and
and overlap configurations. It was found that
60" were considered, both with
restraints in the frame enabled the joints to sustain substantially higher loads than
determined from isolated analysis. The results are presented in Table 5.2.
5.2
Comparison of apparent joint capacities within the frame and in
K joint type
of ioint in frame
Capacity of joint in isolation
1.20
eccentric overlap
concentric overlap
45" eccentric overlap
I
1.11
1.26
It was also
that the capacity for the joint at that point in the frame was not
strongly influenced by changes to the frame geometry (eg. leg stiffnesses, etc).
The implication from the work is that differences between boundary restraints for joints
tested in isolation and existing in real structures may influence capacity. The work
indicates that 'frame effects' may therefore contribute additional conservatism to
components, which in turn will add to the reserve strength of jacket structures but the
converse could also be the case so further investigation is ongoing.
The experimental programme in Phase of the Frames Project has investigated this aspect
and is being followed by further finite element analyses in Phase IIA (BOMEL, 1992).
Efthymiou and Vugts
The authors present results for the X-braced plane frame, shown in Figure 5.7, typical of
an offshore jacket structure, which was analysed using MARC and INTRA to quantify the
differences in the brace modelling. Within MARC, six distributed plasticity elements per
member were used to obtain a good representation of bucklingand post-bucklingbehaviour.
The phenomenological approach of INTRA allows the brace to be modelled by one element
with a single degree of freedom in the axial direction. The nonlinear characteristics to
represent buckling are prescribed by the user. Close correlation between the MARC and
INTRA results is obtained, as shown.
Details of the failure sequence are not presented. However, a 'redundancy factor' is
considered by the authors (see Section 2.3) indicating that the ultimate structural resistance
is 1.36 times the resistance at which the first member fails. Comparison with the elastic
design load is not possible because the paper is based on a limit state approach with partial
factors on loading. Specific calibration would be required. Factored vertical loads were
state design requires
applied and held constant whilst lateral loads were incremented.
a factor of 1 and 1.7 was sustained indicating a reserve strength margin. Nevertheless
it is clear that a sequence of member failures is required before the structural capacity is
limited, and further the reserve strength will be in excess of 1.36. The global post-ultimate
(1988) and
responses are not traced. The structure is also analysed by Ward and
et al (1991).
Ward and lzzuddin
988)
The plane frame analysed by
et al (1988) was subjected to a pushover analysis
elements which automatically subusing SAFJAC. Analysis was performed using
divide introducing hinges to model plasticity due to buckling or tensile yield. Vertical dead
loads were applied and held constant whilst the lateral loads were increased proportionally.
The compression brace in the bottom bay was the critical component, as shown in the
plastic hinge sequence in Figure 5.8. Analysis with an initial 0.3% imperfection had little
effect on the ultimate load.
The agreement between the SAFJAC, INTRA and MARC analyses is generally good,
although SAFJAC predicts a higher peak load corresponding to an environmental load
et al. However,
factor of 1.85 compared with the figure around 1.7 calculated by
in that analysis a partial factor of 1.15 was applied to the initial dead loads and this is likely
to account for the discrepancy. This highlights a problem in basing reserve strength on
measures of applied loads when not all components, ie. dead and environmental are being
factored together.
Finally, the analysis by Ward and Izzuddin was continued beyond the peak. The residual
strength of the structure is
= 0.89 and is well in excess of the design load.
Skallerud, Amdahl and Moan
An analysis of the jacket plane frame, analysed previously by
et al (1988) and
was performed using USFOS. The static pushover formed part
Ward and Izzuddin
of a study of cyclic loading and shakedown. Dead loading, without partial factors, was
applied first and environmental loads were then incremented. Damage was simulated by
removal of member 36 and additionally 37. The sequence of failures is not described but
the ultimate response curve is shown with the Ward and
analysis in Figure 5.8.
Table 5.3 gives the load factor at first yield and ultimate load and on that basis the margin
beyond first yield, RF, is calculated. The value of 1.44 for the intact structure compares
with 1.36 calculated by
et al.
Table 5.3
Load factors at first yield and ultimate load for
Analysis
jacket frame
Ultimate load
factor
Load factor
at first yield
Intact
1.79
1.24
1.44
36 removed
1
0.81
1.96
-0.65
1.69
36
-1.1
37 removed
Use of the redundancy factor with respect to first yield is demonstrated in this analysis but
the analytical definition of a single plastic hinge is straightforward compared with the
detection of plasticity in a structure in practice.
The USFOS analysis is in close agreement with the SAFJAC results reported by Ward and
Izzuddin under the same loading regime. Ultimate load factors of 1.79 and 1.85 were
and
These values are scaled from
achieved respectively, at displacementsof
figures in the papers, and therefore agreement may be considered to be very good. The
results of all three analyses are plotted together in Figure 5.9.
Gates,
and Mahin
In recognition of the need to account rationally for the post-elastic behaviour of tubular
steel structures from the viewpoint of earthquake loading, the computer program DYNAS
was developed as a derivative of INTRA, to perform nonlinear time domain response
analyses. In this paper the authors apply the program to a face frame of the offshore
platform, shown in Figure 5.10, and compare the ultimate static response with predictions
from simplified design methods.
All cross braces and horizontal braces were modelled using the 'Marshal1 element' which
is a single component, one-dimensional,axial force resisting member, with user prescribed
degrading force deflection relationships for buckling and tensile yielding. The
element failure criteria is based on energy limits and the failure algorithm removes the
member stiffness from the structural model. The deck girders, jacket legs and piles were
modelled with tubular beam-column elements which are capable of inelastic
deformations through concentrated plastic hinge formation at the member ends.
Whilst a full earthquake analysis was undertaken by the authors, the DYNAS program was
also used to perform a pseudo static incremental analysis directly. The resulting structural
force deflection plot is shown in Figure 5.10. From initiation of nonlinear behaviour at
step 1 to sudden and drastic loss of strength at step 6, the structure exhibited a deflection
ductility of 1.36 (see Section 2.5 for energy absorption definition of ductility). Once the
horizontal struts buckled, (steps 5 and 6) all the diagonal braces in levels and buckled
or yielded, unzipping the primary lateral resistance. Portal frame action of the jacket legs
and stiff deck members prevented the structure from collapsing until a complete double
hinge mechanism developed in the piles (step 8). Design loads are not given but the ratio
for the peak load to the load at first yield (RF) is approximately 1.2.
The abrupt fall in lateral resistance at step 6 is typical of braced frames with members
designed to a comparable level of utilisation. The lack of ductility and energy absorbing
capacity led the authors to double the cross-sectional area of the horizontal braces at levels
B, C and D and rerun the structural analysis. From the resulting force deflection plot given
in the lower diagram in Figure 5.10,it can be seen that whilst the early nonlinear response
was little changed, a more gradual degradation of capacity occurs. From the first nonlinear
behaviour to the sudden loss of capacity at step 9, the total ductility ratio was 3.0. Thus,
doubling the volume of steel (weight) in just the three horizontal braces, more than doubled
the inelastic deflection and plastic energy absorbing capacity of the structure as a whole.
As in the first case it was the eventual buckling of the horizontal braces at levels C and D
which brought about unzipping of the bracing system and the major drop in resistance from
steps 9 to l l. It should be noted that these horizontals are typically given nominal
design which indicate that the members carry
properties within the criteria of
negligible load under elastic situations.
5.1.2 Idealised 3D jacket analyses
976)
Marshall's definition of a redundancy factor and damaged strength rating were presented
in Section 2.3. These state:
RF =
damaged strength
strength loss
and
DSR =
damaged strength
intact strength
Eqn 5.2
Eqn 5.3
Simplified calculations were performed for an eight leg Gulf of Mexico jacket to indicate
the role of redundancy (Figure 5.11). It can be seen that the end K frames offer little
redundancy.
1984)
To illustrate their treatise on the reserve and residual strength of piled offshore structures,
a jacket with diagonally braced face frames and X-braced transverse frames was devised
water depth as shown in Figure 5.12.
for
Lloyd and
A storm loading condition was considered (allowing a one third increase in allowable stress
wave height with a 60%
in component design). The design loads were based on a
increase to account for simplifications in the model (eg. absence of current, appurtenances
etc). The structural design was in accordance with API but was not optimised, therefore
members had elastic ultilisations well below unity introducing an implicit reserve.
Nonlinear analysis was performed using INTRA. Modelling of the structure was as shown
in Table 5.4.
Table 5.4
Modelling of jacket structure with
Members
Element type
Piles (PL)
Legs
& X-bracing (XB)
Diagonal
Horizontal bracing (HB)
Piles below
Nonlinear beam-columns with plastic hinges
Struts
Nonlinear truss elements
Linear beams
Design wave loading was increased until the global stiffness decayed. The results for
conventional and grouted pile models indicate the reserve strengths, ie. the ratio of the
environmental load at collapse to the design environmental load. These are presented in
Table 5.5 in which the controlling members in the collapse mechanism are also indicated.
Load deflection curves are not given and loads at which first failure occured are not cited.
Table 5.5
Comparison of collapse and design loads for
Direction
Design load
Collapse load
and
jacket
RSR
Critical
members
(a) Conventional Pile Model
S
SE
E
W
SW
2630
2410
2290
2300
2410
9150
7810
6050
5600
7960
3.48
3.24
2.64
2.43
3.30
Piles and Legs
Struts
Struts
Struts
Struts
I
(b) Grouted Pile Model
3.50
4.36
3.29
2.93
3.84
XBI Struts
Struts
Struts
Struts
Struts
As an illustration, the elastic design utilisation in the
struts was around 0.55 for the
South East wave design load. It was clear therefore that significant loading beyond the
design load was required to overcome this implicit reserve at the component level, before
global structural reserves were mobilised. On this basis the levels of reserve capacity are
not unreasonable.
To simulate damage, a series of analyses were performed with members removed. Elastic
analyses revealed the redistribution of loading and in particular higher utilisations for
horizontal bracing which experienced very low loading in the intact state. Furthermore,
nonlinear analyses demonstrated the capacity of the damaged structures which, compared
with the intact capacities, give a measure of residual strength as shown in Table 5.6. The
failure scenarios also reveal the remaining redundancy and the sequence of failures required
to cause collapse.
Table 5.6
Residual strength of damaged jacket structure
Member Removed
Level 2 diagonal brace
Level 2 face frame
Level 2 transverse horiz
Level 2-3 half X brace
Ultimate Resistance (kips)
Damaged
Undamaged
4900
5450
9150
8350
6050
6050
9150
9150
Residual
0.81
0.90
0.91
Lloyd
The examples in this paper illustrate the role of redundancy in optimising the material
distribution within a 3D four-legged X-braced frame (Figure 5.13) to achieve a target
residual capacity. It also demonstrates how different structures designed to the same code,
do not necessarily have the same reserve strength above the design load level.
The frame bracing members are idealised as elastic-perfectly plastic with compression to
tension capacities in the ratio a. The vertical members are assumed to have equal tension
and compression capacities. The three frames are subjected to point loads at the top of the
and 0". For the three frames the following redundancy study
structure from
was performed:
Minimal intact structural weight configuration adopted.
Target residual strength less than original loading set.
Capacity of a primary member deleted.
Member sizes increased.
Repeated for different 'damaged' members.
Structural weights compared.
The work demonstrates that two mechanisms of load redistribution occur simultaneously:
1. The loads formerly carried by the failed diagonal are transferred by means of the
horizontals to the diagonal pair in the same plane as the failed diagonal.
2. The loads are transferred by framing shear and system torsion to the other parallel
bent. The shear is transferred by the framing members, and the torsion is developed
by diagonals on the remaining three faces of the frame.
These mechanisms cannot be mobilised without adequate horizontal or framing braces. The
results of this example simply establish the sizes of these members necessary to achieve the
desired redundancy at minimum structure weight.
For the intact structure, when the compression to tension strength ratio for members is
the optimum solution shows that horizontal and framing members are
unity
unnecessary. This result is consistent with conventional elastic analysis. However, when
the ratio a is less than one as is representative of slender bracing in offshore structures, the
optimum solution requires horizontals and framing members. Also, the diagonal braces
must be stronger than given by the case
1.O. It was shown that framing and horizontal
braces are "interchangeable" with no weight penalty in the intact structure.
In terms of optimising the redundancy solution there was little difference between cases A
and B shown in the figure. It was also shown that to achieve residual strengths greater than
60 it was necessary to increase the system weight considerably. The quantities presented
in the figure are a function of the simplified structure and its specific geometry,
nevertheless the role of redundancy and comparisons of plan bracing configurations are
instructive.
990)
Associated with plane and space frame tests reported in Section 3, Paik and Shin undertook
a series of corresponding analyses for the structures in the intact (IC) and damaged (DC)
conditions and with a member removed (RC). The idealised structural unit method (ISUM)
was adopted (see also Ueda et al, 1986) and elements to model damaged member properties
were employed. The results, shown in Figure 3.25, demonstrate the significant
contribution to the global response that the damaged member can make to the global
response. For the plane frame, with little redundancy, member removal contributed to a
gross under estimate of the frame stiffness and capacity. For the 3D space frame, where
the contribution of the individual member was proportionally less, complete removal of the
member gave a reasonable representation of the damaged response.
Paik and Shin
Structural jacket analytical investigations
Jacobs and Fyfe
The authors used USFOS to analyse a series of different structures for impact and pushover
loads as shown in Table 5.7. Cases D and F are of particular relevance here.
For Case D, vertical loads were applied to the structure in Figure 5.14 and storm wave
loading was distributed, as shown, and incremented to collapse. The applied loading
causing collapse was 107.
compared with the base shear of
generated by the
extreme storm loading. The RSR is therefore 2.96. The lateral displacements at various
levels in the structure are presented in the figure and failure was reported in the X bracing
between elevations -71 and
Table 5.7
Nonlinear analyses performed by Jacobs and Fyfe
8 leg jacket with topsides damage scenarios members removed
Topsides module - explosion
Integrated deck - dropped object
- Impact and damage scenarios - Intact pushover analysis
4 leg X-braced jacket in
Tripod - impact
4 leg jacket in
Pushover of plane frames for different bracing.
The plots of member forces, which are also reproduced in Figure 5.14, indicate that
buckling in the compression brace was preceded by load shedding from another
compression member which was redistributed within the redundant structure. Details of
the plan bracing are not given. From the information presented, comparison between peak
load and load at first failure gives an RF of about 1
Case F was a four leg jacket in
water depth for which the plane face frame was
analysed with different bracing configurations, as shown in Figure 5.15. Bracing was sized
from elastic analysis with equivalent interaction ratios for extreme storm conditions.
Design loads and member sizes are not given, nor are failure modes described in detail, so
and RF factors cannot be calculated. However, comparison of the framing reported
in the paper indicates:
The diamond bracing gives the least reserve strength as first member failure limits the
full load path through the structure. (This is not shown in the figure but it is not
certain whether the plateau was plotted or drawn).
The fully X-braced system with horizontals is the most ductile, offering the greatest
reserve capacity as load is redistributed through the bracing.
Substitution of K bracing in place of X bracing causes more sudden failure once the
local capacity is exceeded. This is relevant to the use of K bracing in potential impact
zones or may determine that K bracing should be over-designed to force initial failure
in X panels.
and
The analysis of a platform is presented to illustrate the value of the reserve strength method
water depth,
in platform optimisations and requalifications. The four leg platform, in
year design wave.
in both the jacket and foundation
was analysed for the
were modelled using the element types shown in Table 5.8. The analysis method is not
cited but it is believed to be INTRA.
5.8
Element selection for jacket
Components
Element Type
Vertical diagonals
legs and piles
Launch trusses
Struts
Beam-columns
Elastic beams
Soil resistance
Nonlinear springs
Reason
Buckling anticipated so moments ignored
Controlled by axial loads and bending
Expected to remain elastic
Different configurations were analysed as shown in Table 5.9 where the results are also
presented. In all cases failure and the reserve strength were apparently governed by the
first failure cited as loading was shed to the legs which rapidly developed plastic hinges.
Gravity and live loads were applied initially and maintained at a constant level.
Environmental storm loads (wave, wind, current and dynamic loads) were applied
incrementally and increased by a common factor until the global failure mechanism was
developed.
The conclusions from the paper may be presented, with reference to Table 5.9, as follows:
Cases 1 and 2 Clearly the higher the design utilisation of the critical component the lower
is the relative reserve strength ratio.
Cases 3 and 2 Adopting X braces in place of K braces and not affecting structural
weight, a significant increase in reserve strength is achieved and the failure
mode is changed from brittle to ductile.
Cases 4 and 3 Reconfiguration of the X bracing maintains the reserve strength whilst
saving on bracing weight.
Cases 5 and 4 Case 5 similar to Case 4, difference in RSR due to "slightly lower design
unity checks for Case 5".
This is an important demonstration of the role of ultimate strength analysis in optimising
structural configurations for a desirable level of system reserve without compromising
important commercial factors such as steel weight and cost. The point will be discussed
further in Section 6.
Efthymiou and Vugts 988)
Following the verification of INTRA against MARC by the authors reported in Section
5.1.1, the program was used for the nonlinear analysis of a Southern North Sea platform
to demonstrate the use of the limit state assessment criterion with partial factors. The
of water with topsides loading of 4700 tonnes and a design base
structure stands in
shear for the North wave of 2150 tonnes. The geometry and elements used in various parts
of the structure are shown in Figure 5.16. Influences of wave loading on member
capacities was accounted for and bending elements were included in parallel with
phenomenological strut elements. A two pass analysis thereby allowed end moment effects
caused by framing action to be accounted for. Three cases were analysed:
Nonlinear structure with linear foundations
Nonlinear structure with nonlinear foundations
Nonlinear damaged structure with nonlinear foundations.
Analyses were performed with 1.15 times the dead loading applied, before environmental
loading was incremented until non convergence occurred at
It was then confirmed that
a collapse mechanism had formed. Five wave directions were analysed. The results are
presented in Table 5.10 as in the paper, where the environmental factor at collapse (A,,,,)
is compared with that at which first member failure occurs (X,) to give a measure of the
redundancy factor (RF), where A,,, = X, RF.
Table 5.10
Results from jacket analyses for different structure and foundation conditions
*
X,
Does not meet requirement.
Environmental load factor at first member failure.
Redundancy factor =
load
In terms of the limit state criterion of the paper, requiring:
Eqn 5.4
where R is the nonlinear ultimate strength, D are dead loads and E environmental loads
which are multiplied by appropriate partial factors, the limit state criterion demands that
X should exceed 1.5 (ie. 1.15 1.3) for acceptance (NPD, 1990). An approximate
measure of reserve strength may therefore be given by comparison of
with
1.5.
This is shown in the table with factors in the range 0.93 to 2.07.
Again the style of presentation and absence of member properties precludes direct
calculation of reserve strength in the terms defined in Section 2.3. However, in all cases
it is clear that redundancy gives a factor of 1.3 on the environmental loading beyond first
failure for the intact structure. This is attributable to the X bracing in the face frames.
the foundation is explicitly modelled this dictates the collapse load and the authors
note that for most intact structures designed to API standards, the foundation will be an
important factor in collapse. For the damaged structures considered, where critical
members are removed, the jacket was again critical.
991
Three static pushover analyses of the four leg Veslefrikk jacket in 175m waterdepth are
(see Section 4). The structure is shown in
presented using USFOS, FENRIS and
Figure 5.17. The ultimate strength analyses were driven by concerns that eliminating the
horizontal X bracing to save weight might reduce the system reserve capacity unacceptably.
year
Environmental loading was based on 28m wave height, 13.5 second period,
Stoke's wave with a superimposed 10 year current. Although this specification was the
same in all cases, the structural modelling differed as shown in Table 5.11 below.
Nordal
Table 5.1 1
Alternative modelling of Veslefrikk jacket
MODELLING COMPARISONS
Components
USFOS
FENRIS
Members
Beams with insertion of
hinges
Beams with
hinges
Piled foundation
Equivalent
beam elements
* text ambiguous
Linear springs
Nonlinear springs
Grouted pile inserts
Equivalent linear beams
Equivalent linear beams
Composite sections
Not included
Included
Included
39.2
45.7
39.6
Wind loading
N wave design
base shear (MN)
of
Braces: struts with
prescribed
Leg: nonlinear beams
NW wave design
base shear (MN)
Furthermore, the analyses were performed at different stages of the structure design and
details of the member slendernesses differed. The analyses were not commissioned as a
benchmarking exercise (ie. not with the same brief) and there was no attempt to reconcile
the different results. The
analysis was undertaken first and the USFOS and
FENRIS studies were performed later at the detailed design stage (PMB, 1993). The
comparison presented by Nordal is therefore more illustrative of the different approaches
to pushover analysis that can be adopted and of the importance of careful definition of all
parameters, than a fair comparison of the software packages. It is on this basis that the
findings of the paper are presented.
Analyses of the intact and damaged structure were performed. Damage by removal of one
simulated incidence
diagonal of the top bay X bracing, simulated ship impact and at
of a dropped object. Collapse was defined by a reduction in global stiffness but the cut off
levels varied in the analyses. In no case was the post failure response traced. Other
differences in the modelling are highlighted in Table 5.11.
The results for the North and North West waves are then compared in Tables 5.12 and 5.13
which follow. The reserve strength ratios relate the environmental load at collapse to the
environmental design load which includes no code load factor. In accordance with
et al
a load factor of 1.5 (minimum RSR) is needed to satisfy limit state code
provisions.
Table 5.12
comparisons for
under N wave
NORTH WAVE COMPARISONS
USFOS
FENRIS
Design Base shear
in MN (load factor)
Base shear in MN
(load factor)
Failure mode
Yield at lower end of
compression legs (2.2).
Global stiffness reducing with
extreme yielding in
compression legs (2.7).
Leg capacity reached at
and
(3.1).
As for USFOS.
Buckling of compression
braces and yielding of
tension braces in upper
bay followed by
yielding in compression
legs at
Damaged:
Base shear in MN
Failure Mode
Yielding and tension in upper
part of jacket. Grouted insert
piles prevent failure. Failure
involves intact failure mode in
lower pan of jacket.
Base shear in MN
Failure mode
Load deflection
Deflected shape
* Damaged at
Intact failure mode with
additional global torsion.
Buckling of compression
braces in upper bays.
Figure 5.13
comparisons for
under NW wave
NORTH WEST WAVE COMPARISONS
USFOS
SeaStar
Design Base shear in MN
(load factor)
Base shear in MN
(load factor)
Failure mode
4s wave initial failure in lower
eg sections. Failure in compression
egs (2.0). Tension failure in
legs (2.4).
Leg capacities critical
at
Base shear in MN
(load factor)
Load deflection
Deflected shape
In addition to the tabulated data, the narrative indicates that the USFOS N wave analysis
= 1.4 on the load at first failure.
shows the peak load is achieved with a factor of
After adjustment for base shear, it may be concluded that the USFOS and FENRIS analyses
agree well, whereas the SeaStar analysis for the N wave shows marked differences in terms
of failure mode
dominated rather than leg failures) and load factors at collapse (1.8
compared with 3.1). The differences listed in the table are highlighted and the author also
suggests the differences may indicate that the structure is 'well balanced with competing
failure mechanisms'. This conclusion also needs qualificaitonin light of the different stages
at which the analyses were performed and the fact that the basis of foundation modelling
was quite different for the SeaStar analysis. Without resolution of this key factor in
determining the system response it may be concluded that the comparison was invalid.
However, the paper does illustrate the significant value of performing comparative analyses
so that methodologies for structural modelling as well as the performance of different
software can be assessed. The discrepancy between the analyses was large and it is
essential that such factors in relation to jacket performance are verified. For jacket
structures direct calibration is clearly not possible and such comparisons are an important
part of developing a consistency and accuracy across the industry.
Pierrnattei, Ronalds and Stock
The Goodwyn A steel jacket in 131m water depth off Western Australia had a specific
requirement for an RSR of 2.0 for lateral storm loading, where the RSR equals the ratio
of the ultimate platform resistance to the design load, based on base shear or overturning
moment. The conceptual designs were based on working stress criteria in API RP 2A.
Nonlinear analysis to verify RSRs for the concepts was then performed using the Extended
Design Program (EDP).
Initial 2D analysis of the first four legged jacket structure shown in Figure 5.18 gave RSRs
of 1.60 and 1
for linear and nonlinear foundations, respectively, and the worst case
westerly storm direction. Dimensions of critical braces were increased and a subsequent
3D analysis gave an RSR of 2.0. Before the structural members were resized, load
redistributed to the tension brace following buckling in the compression brace at one level,
caused an immediate buckling of the compression brace in the bay above. The mechanism
proceeded up the structure causing collapse. Once resized, the initial compression failure
at the same location (Figure 5.18) was followed by leg and tension brace yielding such that
the target RSR of 2.0 was achieved. Based on the results of the intact analyses and an
elastic redundancy study, three critical members were removed in turn. RSRs between 1
and 1.7 were achieved in the damaged condition which were considered to be satisfactory.
For the alternative eight legged concept shown in Figure 5.19, 3D nonlinear pushover
analyses were performed and member sizes optimised until RSRs in excess of 2.0 were
achieved. The south direction wave was the most critical giving sequential failure in the
diagonal bracing. Missing member analyses were also performed to demonstrate adequate
RSRs.
Dolan, Crouse and
(1992)
The four-legged Maui A platform off New Zealand was analysed using
primarily
to demonstrate adequate seismic performance. However, as part of the work a static
pushover analysis was undertaken. Sufficient details are not given for comparison with
design capacities to be made but the load deflection curve and damage sequence shown in
Figure 5.20, confirm the lack of any reserve beyond first failure associated with the single
diagonal bracing and the rapid decay of any residual capacity.
Soreide, Arndahl and
The six leg jacket structure for
water depth with a combination of X and K braces
shown in Figure 5.21 was analysed using USFOS. The configuration is shown in Figure
5.21. Gravity loads were applied and environmental loads, based on a
year return
period 3 wave with a parallel current and CO-acting wind, were incremented. Four cases
were analysed for the intact and damaged structures as shown in Table 5.14.
Local loading from the conductors to the structure was shown to contribute to the collapse
mechanism. In all cases significant additional capacity existed beyond the first component
is useful
failure as shown by the RF values in the table. The distinction between P, and
in distinguishing the partial factor contribution to the RSR.
Table 5.14
Progressive collapse analysis results
First
Yield
Hinge
1.81
Corner leg in splash zone
removed
1.59
0.87
Collision simulation
Damaged structure
1
0.88
2.49
Dropped object simulation
Lower horizontal removed
P,,
P,
P,
-
Intact
0.85
= design load
with partial safety factors
= ultimate collapse load of intact structure
= ultimate strength of damaged structure
= design load
=
yield hinge
= residual strength factor =
= reserve strength factor =
Engseth and Granli (1985)
Moan,
An 8-leg jacket for 70m water depth with X-bracing in plan, longitudinal and transverse
framing is analysed using USFOS. The structure is shown in Figure 5.22. The
year
design loads for each of three directions are incremented whilst still water loads remain
constant. A typical failure sequence for diagonal and transverse seas begins in the bottom
bay end row bracing. Loads are shed through the conductor frame bracing to parallel rows
and so on, until intermediate horizontal bracings fail and the global load is limited by the
extent of plasticity (Figure 5.22). It can be seen from Table 5.15 below, that the
redistribution imparts significant reserve strength to the structure beyond first yield.
Table 5.1 5
Reserve strength in X-braced jacket structure
Load factor on 100 year return
Load Case
First Hinge
Max. Load
REF
Diagonal wave
Longitudinal wave
2.60
4.39
4.39
1.69
2.49
3.71
3.71
1.49
Transverse wave
2.99
4.32
4.32
1.44
In addition to the analysis of the jacket structure, a 3 D box frame of similar configuration
to the structure tested by SINTEF (Section 3.1 and Figure 3.35) was analysed using
FENRIS. The member properties and dimensions are detailed in Table 5.16 and differ
from the final test structure.
Table 5.16
3D box frame member properties
Member Type
Legs
System
S2
S2
Horizontal X brace
Vertical X braces
S2
S1
S2
Vertical loading was held constant and lateral point loading at nodes (NPL) and in some
cases element loads (EL) were incremented. This differentiated between loading regimes
near the base and top of a jacket structure, respectively. Design loads were calculated to
API and these are compared with the ultimate frame loads for the different brace
slenderness in Table 5.17. Details of the failure modes and redistribution are not given.
Table 5.17
Comparison of reserve strengths for 3D box structure
System
S1
= 97)
S2
= 1.95)
Loading
Frame Loads
Design
Collapse
RSR
NPL
(no initial imperfection)
NPL
44.0
82
1.86
44.0
80.4
1.83
NPL + EL
40.0
88.8
2.22
NPL
8.0
16.9
2.11
NPL + EL
8.0
18.9
2.36
The analyses were repeated with USFOS and good agreement was achieved. In USFOS
one element was adopted per member whereas FENRIS required 108 beam elements and
93 nodal points. Comparative computing times were 1 hour and 2 minutes (see Section 6.3
for further discussion of analysis efficiency). Subsequent USFOS analyses performed by
Soreide et al (1986) for the test structures are shown in Figure 5.23.
Bea, Puskar, Smith and Spencer
The authors outline a general AIM (Assessment, Inspection and Maintenance) approach for
requalifying offshore installations and demonstrate the application to an example Gulf of
Mexico platform. In developing the approach the importance of evaluating platform
capacities and determining the implications of defects was identified. Linear elastic analysis
were shown to be inadequate and potentially misleading giving either conservative or
unconservative predictions. The absence of guidelines or evaluation procedures was noted
but the usefulness of the RSR as a quantified reserve was recognised. Furthermore a
capacity-consequence relation with RSR was introduced as shown in Figure 5.24 and has
been developed further by Bea and Young (1993).
The example platform analysed by the authors shown in Figure 5.25 is a 5 leg (4 corner,
water depth which was installed in 1962. The
1 centre), fixed drilling platform in
with inelastic beam-column elements modelling the
structure was analysed using
plastic performance of legs, piles and conductors at their load-carrying limit. Braces were
modelled with 'strut' elements to account for buckling in compression or yielding in tension
and the capacities were modified to account for premature punching or tearing at the leg
is ungrouted and there are no joint cans this frequently controlled the
joint. As the
capacities. The force deformation of the pile and conductor soil interfaces was modelled
and the authors emphasise the need to account for conductor lateral capacity in order to
model the system capacity realistically. In other words, although such factors are neglected
with a view to conservatism in elastic design, for modelling the nonlinear ultimate response
their influence should be accounted for.
Analysis was performed with environmental loads incremented to failure. Alternative
scenarios were considered, in which:
ALT
ALT
ALT
ALT
1 - platform left as is
2 - 'repair' missing braces and cracked joints
3 - repair as 2 and grout legs to piles
4 - repair and raise deck
Figure 5.25 shows the ultimate responses predicted by the
analyses but details of
the failure modes were not given. With respect to the 100-year design load of 1200 kips,
to 1988 standards, the structure in the as is and repaired states, was shown to exhibit
of
l and 1.25, respectively. The paper proceeds to discuss the relative
benefit considerations in upgrading the platform.
Shinners, Edwardes, Lloyd and Grill (1988)
In upgrading five Bass Strait platforms, installed in the late 1960s (Figure
Esso
Australia recognised that it was not practicable for all components of the platform to satisfy
late 1980s design standards and a target RSR philosophy was therefore adopted. In addition
to more stringent code criteria, the foundation conditions had been found to be worse and
the environmental loads higher than in the original designs.
A study showed that RSRs of recent platforms fell between 1.6 and 2.5, and an optimised
Given more
structure could meet current code requirements but have an RSR of only 1
exact knowledge of actual materials, and fabrication and installation events, a target RSR
of 1.5 was adopted, see also
and
1988. Supporting research programmes
tubular joint
were undertaken into soil conditions, K-brace behaviour (Grenda et al,
characteristics and material testing.
To determine RSRs, a nonlinear computer model of the jacket was initially loaded with
year load were progressively applied as
dead and live loads. Then, increments of the
static steps to collapse. Typically, members with high axial loads and high slenderness
ratios were modelled with nonlinear strut elements; low slenderness ratio members with a
significant component of bending loading were modelled with inelastic beam-column
elements. Strut elements were pin ended and account for post-buckling strength
degradation in compression and strain hardening in tension. The beam-column elements
allow for bending moments at the member ends and account for buckling strength
limitations but do not model post buckling strength degradation. Nonlinear strut and
column elements were also developed to model joint behaviour. Elastic elements were used
for members which were not highly stressed. Special elements were required to model the
sliding of the piles within the legs and preserve lateral compatibility. The deck structures
were replaced by simplified elastic equivalents to reduce computer time. Linearity
assumptions were verified at calculated collapse.
The authors felt that the complexity and multiplicity of failure modes that could occur, as
well as the "judgement required by the analyst", meant that an exact measure of platform
strength could not be achieved although the RSR gave a useful measure.
Analyses for the critical east-northeast direction showed Barracouta and Marlin installations
to be foundation limited, Halibut (right of Figure 5.25) to have equivalent structure and
foundation resistances, and
A and B (left of Figure 5.25) to be structure
controlled.
Where structural failure was calculated (and this applied to the strengthened structures as
well) the controlling feature was failure of the east-west K braces and more specifically,
buckling of the compression member or joint within the K brace. The post-buckling, load
shedding behaviour of the K braces leads to an almost "brittle" failure of the jackets. The
shedding of load to adjacent already highly loaded K braces triggered rapid progressive
collapse. The longer diagonally braced north-south column rows were significantly
stronger and did not shed load as rapidly as compression members in K braces.
The need for a
increase in capacity was reported for all but Barracouta platforms,
which may be interpreted as RSRs of 0.9-1.0 in the unstrengthened condition.
Alternative upgrading and load reduction options were considered and evaluated using the
RSR approach. Marine growth control and pile struts were recommended although
were shown to be feasible. However, these only became effective when deflections were
large and the dependence on foundation failure to mobilise the
action was therefore
not acceptable. The explicit consideration of deflections is unusual however in analyses of
RSR.
5.1.4 Jacket
et
loading investigations
(1993)
In Section 2.7 the investigation, largely by SINTEF and Shell Research into cyclic
degradation of offshore structures in extreme seastates was introduced. A key question was
whether static pushover assessments were a suitable measure of system capacity. To
answer this 32 static pushover and 37 cyclic analyses were undertaken using six North Sea
jacket structures. The structures, shown in Figure 5.27, encompass older launch installed
structures as well as more slender lift installed jackets. The water depths, number of legs,
bracing patterns, member geometries etc., differ as shown in Table 5.18 and may be
and A2
considered to be representative of the North Sea jacket population. Structures
are subjected to similar environmental conditions, and A l , B1 and B2 are also subject to
approximately the same environment.
Table 5.18
Structures analysed in pushoverlcyclic investigation
et
Structure
Wellhead
Field
terminal
Hotel
Compressor
station
Quarter
Water depth
Number of legs
Longitudinal
bracing
Diagonal
bracing
Double X
Foundation
4 legs
skirt
piles
Internal
leg piles,
grouted
Diagonal1
Double X
X without
horizontals
K
Diagonal
Double X
X without
horizontals
K
Diagonal
+ K
4 legs
Skin
piles
Internal
leg piles,
grouted
Internal
leg piles,
grouted
Internal
leg piles,
not
grouted
Analysis was performed using USFOS by SINTEF and consulting engineers Offshore
and Aker Engineering Bergen
Modelling was as follows:
Design
Soil was represented by linear springs.
All primary members were given initial
imperfections in the dominant
wave direction.
Conductors, conductor framing and topsides were simplified from linear analysis
model.
Tubular joints were not explicitly modelled.
Under cyclic loading the new facility within the USFOS beam element to account for cyclic
plasticity (Eberg et al, 1993) was employed. It is derived from potential energy
considerations and uses a Green strain formulation that allows large local lateral rotations.
The plastification of the cross section is modelled by means of plastic hinges utilising two
yield surfaces in the generalised force space. One surface represents first fibre yield and
the other fully plastic utilisation. Kinematic hardening models are employed for these two
surfaces to account for cyclic material behaviour. The element model was verified by
comparison with a large number of tests on tubular beam-columns and plane frames
subjected to cyclic loading (see Section 3) giving good agreement between measured and
calculated responses provided local buckling or fracture does not occur.
For the pushover analyses, characteristic stillwater loads were applied with the
environmental loads (100 year wind and waves with 10 year current) factored to collapse.
The load factors corresponding to first fibre yield, first member failure (buckling or tensile
yield) and ultimate collapse were recorded enabling redundancy and reserve strength factors
to be derived from the analyses. The loading envelopes for eight directions were reportedly
evaluated but only four or six results are presented in the paper. It is assumed that the least
heavily loaded directions were omitted.
Given the number of load cases in this paper the results are divided into subsections.
Pushover analvsis results
Table 5.19 overleaf, reproduces the results of the pushover analyses. The characteristic
load factors at collapse are presented for comparison with the design value of 1.5 but the
load factors at yield and first member failure are non-dimensionalised with respect to the
collapse load. Within the table the load cases for each structure generating the lowest
redundancy factor (RF) beyond first member failure to collapse are highlighted, as are the
lowest characteristic load factors. It can be seen that these do not necessarily occur for
corresponding loadcases. Nevertheless in all cases the minimum reserve strength (lowest
characteristic load factor 1 is associated with very little margin between first member
failure and collapse. This is demonstrated in Table 5.20 where comparison is also made
with the bracing configuration in the transverse plane. The highest margin between first
member failure and collapse is associated with the only X-braced frame.
Table 5.20
Reserve strength and ultimate response characteristics from pushover analyses by
Structure
A2
B1
B2
B3
Loading
Direction
Min RSR
Broadside
Broadside
End-on
End-on
End-on
Broadside
et
RF at min RSR
Bracing in
transverse frame
1 .OO
1.02
1.04
1.12
1.06
1.01
K
K
Diagonal
X
K
strength
The structure exhibited a range of system reserves beyond the design events. This is shown
more clearly in Table 5.21 in which the load factors on the 100 year design load are
divided by 1.5 (product of partial factors 1.3 and 1.15) to give a measure of the capacity
beyond the design event. The basis of the original structure designs is not known so it is
difficult to dra firm conclusions with respect to the absolute RSR values. However, it is
clear that an RSR based on one direction may not be a reliable measure of the structural
system reserve. This can be illustrated
by examining the results for structure
in further detail (Table 5.19) and comparing the South (S) and West (W) directions.
Table 5.21
Ranges of reserve strength and redundancy for pushover analyses by
RF
et
Indicative
Structure
Max
Min
Max
A2
B1
B2
B3
1.28
1.03
1.39
1.13
1.36
1.10
1.00
1
1
1 .O1
1.06
1.00
6.04
2.94
5.47
5.27
2.81
3.08
1.69
1.91
1.63
2.25
2.11
1.37
The characteristic load factor at collapse for W is 2.81 and the load factor at first member
failure was 2.50 (2.81 0.89). For S at collapse the factor is 2.54 which also corresponds
to first member failure. Thus the load factor at first member failure was slightly greater
than for the W case. In elastic assessment it may therefore by postulated that these critical
members in the W and S load cases would have had similar utilisation. To select a single
load case on the basis of elastic analysis (highest utilisation) for detailed pushover
assessment may not therefore reveal the minimum collapse load factor for the structure as
a whole. Although the W wave would be likely to have generated the higher utilisation,
the ultimate RSR was in fact higher than for the S case. The point is made by way of
structure design would be
illustration and further information regarding the original
required for firm conclusions to be drawn in the specific case.
,,
Table 5.19
Results for structures analysed in pushoverlcyclic investigation
STRUCT
LOADING
DIRECTION
0.65
0.81
1.00
N
0.79
0.96
1.00
Diagonal NW
0.56
0.86
1.00
2.63
SE
0.55
0.78
1.00
3.63
S
0.65
0.99
1.00
4.41
W
0.87
0.98
1.00
E
0.77
NW
0.78
SE
0.45
0.87
1.00
3.48
Broadside SW
0.57
0.72
1.00
4.90
NE
0.51
0.73
1.00
8.20
N
0.63
0.96
1.00
4.80
S
0.61
0.98
1.00
7.39
W
0.51
0.98
1.00
5.10
E
0.45
1.00
7.90
NW
0.72
0.89
1.00
SE
0.66
0.99
1.00
5.87
N
0.73
0.88
1.00
3.36
Al
Broadside
A2
Diagonal
Diagonal
End-on
End-on
LIMIT LOAD
cyclic
Amplitude
E
Broadside
B1
PUSHOVER LOAD LEVEL CHAR'C
FACTOR ON
First
Collapse
Extreme
member
LOADS AT
COLLAPSE
et
9.06
0.98
0.98
0.98
4.17
1.00
0.98
0.84
0.93
0.98
B2+
I-
* Alternating plasticity due to local bending. 'Cyclic capacity' 98% if four members are clamped
+ Results may not be totally representative
112
It should be noted that the
account for conservatism in the initial component designs
(eg. member effective lengths) and it is the redundancy factor, RF, the ratio for ultimate
load to load at first member failure, which provides additional information on the system
reserve characteristics.
Although Table 5.21 reveals a range in RSR, the redundancy factors are low and indeed
in only 13 of the 32 cases in Table 5.19 does the margin beyond first failure exceed 10%
of the collapse load, and only seven exceed 20%. The statistic will in part reflect the
configuration of the jackets adopted, nevertheless the structures are reasonably
representative. Focusing only on the lowest ultimate load factor for each platform, the
corresponding margins between first and ultimate failure are in the range 0-12%. However
the load factors at which first member failure occurs are in the range 2.34 to 3.00 which
is significantly higher than the 1.3 to 1.5 range anticipated. The expectation is based on
the limit state factors which are required to produce adequate component designs and the
additional capacity exhibited by the jacket structures is attributed to:
differences in wave theory and current used in design and assessments,
conservatism in design codes and designer's selection of member sizes,
governing design criteria other than environmental loading.
Structure A2 with X and additional cross-bracing in the transverse frames, offers significant
capacity for redistribution (RF, = 1.39). The K-braced jacket B2 also appears to exhibit
good redundancy (RF, = 1.36) for diagonal loading but details of the plan bracing and
the capacity for redistribution cannot therefore be interpreted. However, it is noted in the
paper that first failure occurs in non-critical members which do not play a subsequent role
in the global collapse mechanism. From a system point of view the high RF factors are
therefore misleading although at a local level the component failures may be unacceptable
and require separate assessment.
With regard to determinacy the determinate configurations generally give low RF factors.
Conversely indeterminate systems would be expected to offer capacity for redistribution and
although this is confirmed for end-on loading of structure AO, for broadside of A2 and
partly for end-on loading of A2, insignificant strength reserves are observed for end-on
and B3, and for one end-on loading direction of A2. This is attributed to
loading of
the tension members having insufficient capacity to accommodate the load shedding from
the compression braces. Relative member properties as well as bracing configuration are
clearly important.
Although not demonstrated in the paper, it is reported that for non-redundant framing
governed by brace compression failure, there was a dramatic drop in capacity at peak load.
For redundant framing systems, and in particular those having equal number of tension and
compression members, the drop in load was not as pronounced, and the behaviour was
more ductile. In all systems, the energy dissipation in the post collapse range depended on
the yield capacity (or the number) of tensile members, the residual capacity of the buckled
braces and the portal capacity of the legs.
The margin between first yield and first member failure and collapse is also instructive
although it is noted that the USFOS two surface plasticity model underpredicts yield for
components under pure axial loading (Eberg et
1993). In all cases the load factor at
first yield is at or exceeds the target value of around 1.5. Little correlation between first
yield and subsequent member failure can be found, in that early development of a zone of
plasticity does not necessarily lead rapidly to a mechanism of three hinges to precipitate
buckling. Structure B1-East wave gives load factors of
and 0.99 respectively, whereas
for structure B2-South wave initial yield at 0.83 is followed by first member failure at 0.94.
No information on the location of initial yield with respect to first member failure is given
to enable further investigation.
Static
analysis
et al present details of the pushover structural responses for two of the platform
analysed,
and Al. The load deflection curves for three wave attack directions are
shown in Figures 5.28 and 5.29. The load axis represents the characteristic load factor on
year environmental loads.
the
Under broadside loading the four compression K-braces in the transverse frames at Level
buckle in rapid succession giving a residual capacity plateau associated
3 in structure
For end-on loading (Figure
sequential
with portal action in the legs (Figure
compressive and tensile failure of the diagonal bracing gives a softening characteristic and
eventual decay in capacity to portal action in the legs. The progressive failures for diagonal
resemble the end-on characteristic.
loading (Figure
Structure
with K-braced transverse frames exhibit a more brittle response to broadside
It is approximately linear up to a peak load, followed by a sudden
loads (Figure
collapse due to extensive brace failure as two compression braces fail over elevation 2 and
the remaining braces at that level fail at the next peak. The platform has heavy legs with
insert piles, so instead of developing a portal frame mechanism between Levels 2 and 3,
further loading leads to failure of the braces above elevation 3. These braces fail at the
next two P-6 'peaks', leading to the failure mechanism shown in the first and second
deflected shapes. From this stage, a portal frame mechanism is developed in the legs over
two elevations (between three horizontal framings) as shown in the third plot.
consists of two diagonal and one X-braced row. The behaviour
Longitudinal framing of
under end-on loading is linear up to a peak defined by first member failure. The load then
but to a much higher post-collapse capacity than under transverse
drops (Figure
loading. A portal frame mechanism develops in the legs, before further brace failure is
initiated at other levels of the structure.
enters into a predominantly transverse failure mode,
Under diagonal loading, structure
and the load-deformation curves (Figure
resemble the behaviour under broadside
loading.
Cyclic
results
The corresponding results for cyclic loading of the structures were shown in Table 5.19.
Three analyses were performed. In the first the variable amplitude pseudo-storm was
applied. Secondly, constant amplitude cycles were applied to investigate the shakedown
which is in part obscured by the reducing amplitude of the first scenario. Finally the
year and extreme storm
representative long term cyclic load history incorporating
loading sequences (Figure 2.6) was adopted. In all but two cases under application of the
cyclic extreme event scenario (Section 2.7) shakedown of the structures occurred, even with
a peak load at 98% of the static collapse value.
Typical results, for structure
under broadside loading, are reproduced in Figure 5.30
indicate the cyclic load
and are described in the authors' words as follows.
history, with forward and reverse loading on the y-axis and cycle number on the x-axis.
Occurrence of yield hinges are marked on the plot. Some members yield under the first
year' loading.
'100 year' loading (incoming wave), no members yield under reverse
year' extreme storm cycle, but no
Further plastic deformations occur under initial '10,
year' cycles, some yielding
member yield under reverse loading. Under the final
occurs the first time the load is reversed. In the final cycles, the response is purely elastic.
are observed."
No members experience repeated yielding, and very little cyclic
The linearity of the global response is evident and the authors report that few cycles (as
shown) are required to verify shakedown or indicate incremental collapse. It is on the basis
of responses such as these that it is concluded that pushover analysis is an acceptable
measure of the ultimate response of an offshore structure.
However, less satisfactory results were obtained for structures A2 under broadside loading
and B3 end-on. There were strong indications of incremental collapse when loads were
factored to the 98% level, with several members experiencing repeated yielding and global
deformations increasing in each cycle. The structures did shakedown for a load factored
to 90% and 93% of the collapse load, respectively.
Taking structure A2 as an example, Figure 5.31 illustrates that significant plastic
deformations (nonlinearity in the response curve) occur within the first cycle of constant
amplitude loading to 98% of collapse. In the static pushover, first member failure was
reported to occur at 72% of collapse. Several members yield under reverse loading, and
in both directions of the remaining cycles. This is indicated in Figure
with the
occurrence of yield hinges marked on the plot. Global deformations increase for each
cycle, as shown in Figure 5.3 and Figure 5.3 shows bending moment and axial force
interaction of the critical compression brace as it undergoes severe cyclic yielding.
Shakedown only occurs when the constant amplitude cyclic loading is factored to 84% of
collapse. Under the long-term cyclic load history, shakedown occurred when the cyclic
load was factored to 90% of collapse.
It is emphasised that cyclic degradation is due to the extent of plastic deformations rather
than the absolute value of the external loading above first member buckling. For structure
A2 buckling occurred at 72 % of the collapse load and shakedown was obtained 18 % above
this level. For structure B3 first member failure was at 91 % of collapse but cyclic loads
at only a 2% higher load level could be sustained. The role of alternating plasticity in
exacerbating cyclic degradation is also stressed.
Further discussion of the importance of cyclic loading considerations in relation to static
collapse analysis is presented in Section 6.3.6.
5.1.5 Jacket hindcasting calculations
Tromans and van de Graaf
Analysis of the Gulf of Mexico Platform South Pass SP62-B, shown in Figure 5.32 was
and the risk of failure under that
performed. The platform survived Hurricane
extreme loading was assessed by hindcasting. The structure's long term reliability was also
studied by Marshal1 and Bea (1976).
water depth. Diagonal bracing sizes range from
The eight leg platform, stands in
in the top bay to
in the bottom bay. The jacket was
analysed for the calculated
loading for seven attack directions covering
The total lateral load was 6080 kips, 1.7 times the original design base shear.
Wave loading on the deck was not included. Lateral distributed loading on the braces was
accounted for but the vertical diagonals are stocky so the reduction in compressive capacity
was slight. Environmental loading was incremented until the peak capacity was
determined. No mention is made of gravity loads although it is expected that they were
applied and held constant.
The resulting platform failure surface is related to the total hurricane base shear, 6080 kips,
since the system failure modes involve diagonal members as a result of shear transfer down
the structure. Three failure modes are noted: two broadside and one end-on. In all cases
the ultimate strength was achieved at first member failure, the system offering no additional
reserve, see Figure 5.32. Further details of the critical end on failure mode are given as
follows. The three compression diagonals in Row A between Levels IV and V failed,
followed by the three compression diagonals in Row B between Levels and IV. The top
of the structure was undermined and essentially sheared over two bays in the end-on
direction. The same failure mode occurred for all wave attack directions between
and
The reserve strength is approximately 1.4 1.7 = 2.38, given that the 1.4 ratio
shown relates to the hurricane base shear which is 1.7 times greater than the original design
value.
The USFOS analysis would not track the post buckling equilibrium path, but repeating the
analysis without the six members, revealed that the residual strength was around 70% of
the ultimate capacity.
van de Graaf and Tromans (1991
A pushover analysis of the Gulf of Mexico platform shown in Figure 5.33 was performed
with loading from a probabilistic assessment of the extreme hurricane. The purpose was
to validate the use of probabilistic models for environmental loading and strength for
evaluating the reliability of offshore platforms. The example presented also offers insight
into jacket reserve strength.
The eight leg diagonally braced jacket, designed in the early sixties, stands in
water
welded off at the jacket top. The jacket was modelled using
with piles penetrating to
USFOS (see Section 4) and account was taken of the foundation. Using the nonlinear
of constraint loads, due to
and
simulation approach based on linear
(1990) and described in Section 4, the critical wave attack angle,
from
van de
end-on, was determined.
The pushover analysis was performed for this direction which in the first case caused lateral
failure in the piles below the
but in the second, where lateral failure was
suppressed, a sequence of member failures developed. This is shown in Table 5.22, the
final column indicating whether the same damage was actually observed. In this case not
only bracing but leg members were damaged by the environmental load, yet the structure
was still able to take increasing load.
Table 5.22
Member failure sequence in analysis with lateral foundation failure suppressed
Member
Load Factor
Predicted
failure mode
Leg B4
First yielding due to tension
Pile B4
Pile punch through
Leg
Leg global buckling
Diagonal - Row 2
Level I -
Member buckling
Leg A2
Leg global buckling
Diagonal Row B
between Rows 1&2
Level I -
Member buckling
Failure
observed?
Table 5.23 compares the overturning moments at various stages of the analysis with the
design loads.
Table 5.23
Comparison of jacket capacity with design criteria
Overturning moment
'
Load factor
Original design
Original design
API RP 2A design
API RP 2A design
(8" on diameter for marine growth)
At 1st member failure
At
collapse
In comparison with the original design, the reserve ratio on loads is 3.77 but this is a result
of the low wave height
and drag coefficient
adopted in the early 1960s.
wave height and C, of 0.6, reduces the
Adopting the API RP 2A criterion for a
and if the presence of marine growth is accounted for this
reserve to
further reduces to 1.3310.78 = 1.71.However, the allowable design capacity is reduced by
a factor of about 1.48 when code safety factors and differences in material properties
between actual or specified yields are accounted for. Therefore, the system reserve
strength ratio is between 1.39 and 1.16 but it can be seen that first failure occurs below the
current acceptance levels, (ie 1
= 1.38
1.48).
In the
adopted by the authors, relating the load at complete collapse to the load at
first failure, the redundancy factor is 1.23 which is quite low but considered to be 'typical'
of such older structures.
5.1.6 Reliability analyses
Edwards, Heidweiller, Kerstens and Vrouwenvelder (1985)
This paper presents the results of a case study into the reliability of a typical jacket
structure under extreme wave loading. Analysis was performed using the Plastic Frame
Analysis option in the Dutch version of ICES-STRUDL. From 60 Monte Carlo runs with
different wave heights, two dominant failure modes (shown in Figure 5.34) emerged,
however a level reliability analysis gave a much higher probability of mode I occurring
The authors demonstrate that Monte Carlo analyses alone are not
than mode
appropriate, and an approach combining with level reliability analysis is put forward.
Load deflection characteristics are presented for only a few unspecified loadings and
failures, so conclusions regarding reserve strength cannot be drawn.
Holm, Bjerager, Olesen and Madsen (1988)
A systems reliability program is used to determine the reliability with respect to initial
yielding. Upper and lower bounds with respect to plastic collapse are determined for a
spatial truss with elastic-ideal plastic members, shown in Figure 5.35. A sensitivity study
with respect to loading parameters was conducted and to check the robustness of the jacket,
the yield force in compression was reduced for two different members. The influence
depends strongly on which member is affected. For member 244 the role of redistribution
to the surrounding structure beyond first yield can be seen in the figure.
Nordal,
and Kararnchandani
As part of the joint industry project on offshore structural systems reliability, the steel
jacket analysed deterministically by Lloyd and
(1984) was assessed (Figure 5.12).
For the critical broadside storm wave loading the following effects were considered:
X versus K bracing in transverse frames.
Wave load variability (Gulf of Mexico cf North Sea).
Damage.
Contribution of plan X bracing.
Members were assumed to be semi-brittle with a peak strength R and post failure capacity
with = 1.0 for tensile yield and = 0.4 for compression buckling, see Figure 5.36.
The reliability approach adopted was to identify the important failure paths, with the results
or probability of occurrence, P. For the base
given in terms of the safety index,
braced case, failures leading to system collapse all involve the members in the vertical X
braces at one level.
In the deterministic analysis, brittle system failure was observed. Even with the assumption
that the compression members are ductile = 1.0 the system failure load is only 5 % above
that to cause first member failure. The reserve strength factors comparing the ultimate and
design loads are in good agreement for deterministic and probabilistic assessments of the
X-braced structure. The reliability analysis gives values of 3.3 and 3.45 for values of
of 0.4 and 1.0 respectively, in comparison with 3.5 given by the deterministic analysis by
Lloyd and
For the alternative K-braced framing shown in Figure 5.37 the members were sized to give
comparable utilisations to the API code as for the X bracing. As in the base X-braced
case, system collapse corresponded to the first K bracing failure. From the
analysis a reserve strength factor of 2.3 was calculated for the K-braced frame, significantly
below the X-braced frame result. The reliability level was found to be two orders of
magnitude less. This is due largely to greater conservatism in code buckling factors for X
bracing and the fact that the utilisation of X bracing arises partly to dead loads whereas the
K bracing takes only lateral shear. This highlights the inconsistencies in the reliability of
the structures designed to the same code but with different bracing configurations.
Both X and K-braced structures were assessed in Gulf of Mexico and North Sea
environments, where in the latter case the variation in possible loading is less, but the mean
value is higher. The results are all shown together in Table 5.24. It was found that
probability of first member failure and system collapse are lower in the North Sea case but
the 'system effect' is larger with a greater difference between the union of first member
failures and the probability of system collapse. A measure of redundancy as the
'conditional probability of system failure given any first member failure' is defined. This
demonstrates that the redundancy of an X-braced system in a Gulf of Mexico environment
is an order of magnitude better than K bracing. In the North Sea environment the measure
is two orders of magnitude better for X-braced configurations.
Structural damage was examined by removing X and K bracing and the structures
'robustness' was quantified in terms of the relative probabilities of system failures in the
damaged and intact conditions. These are
in Table 5.25. In the X case the
factor was 20 and in the K case 40, ie. of similar magnitude. It was also demonstrated that
the non-uniformity from removing a member, leads to a higher reserve beyond first
member failure to system collapse. This is more representative of real offshore structures
even in the intact state, where member sizes and configurations are generally not entirely
symmetric. Indeed, the idealism in the structural configuration and loading is stressed by
the authors, nevertheless the demonstration of the methodology and the insight it affords
are instructive.
Table 5.24
Comparison of performance of intact X and K-braced structures in different environments
J
Environment
Gulf of Mexico
Most likely
to fail member
Union of any
1st failure
Most likely
failure path
System
failure
3.96
3.71
4.40
5.4x10 6
4.20
Probability
1.3x10 5
Redundancy
5.10
Sea
4.97
3.0x10 7
Probability
5.94
0.8x10 3
Probability
Redundancy
= 0.7
3.84
3.75
8.8x10
Probability
North Sea
5.98
1
1.1x10 9 3.0x10 7 = 0.003
Redundancy
Gulf of Mexico
l.lx10 4 = 0.12
J
Redundancy
4.09
5.4x10 6
3.95
I
= 0.4
Table 5.25
Comparison of performance of damaged X- and K-braced structures in Gulf of Maxico environment
Most likely
to fail member
K-braced
Probability
A
X-braced
1.52
6.4x10 1
1
Most likely
failure path
System
failure
1.64
5.1x10 2
1.62
3.15
3.11
3.52
3.50
2.71
2.71
3.42
3.40
2.26
1.2x10 2
2.25
3.20
3.19
Probability
Probability
C
A:
Union of any
lst failure
Probability
Single damage, no reduction in compression capacity.
B: Single damage, reduced compression capacity.
C: Two damage members in one X-brace.
5.2
COMPARISON OF RESULTS
5.2.1 Quantification of RSR
The analytical investigation of frame and jacket reserve strengths are summarised in Table
5.26 in the order of introduction in Section 5.1. Measures of system reserve are given, as
best derived from the information presented. Some consideration of the appropriate
comparison of measures of system reserve needs to be given.
The alternative load paths through structural systems contribute to the global reserve
strength ratio (RSR) enabling loads in excess of the design value to be sustained. The RSR
is a measure of the ratio of the ultimate load to the design value.
The typical approach analytically in determining the RSR of an offshore structure is to
and
1988;
apply the still water loads and hold these constant (Nordal, 1991;
Tromans and van de
1992). The design load (eg.
year storm load) which may
combine environmental factors such as wave, wind and current, is then applied
incrementally up to and beyond the design value until structural collapse occurs. The
loading profile is not changed to reflect different combinations of components within the
extreme environmental state. Reserve strength is therefore a relative measure of structural
performance and is not necessarily related to absolute environmental conditions.
However, reserve strength is also derived from the conservatism in the design of individual
components and for a real structure it is therefore expected that the RSR will at least
exceed the contribution from explicit safety factors, ie. an RSR greater than unity is
implicit within conventional design codes. Lloyd and
(1984) demonstrated the
change in RSR when elastic component utilisations are changed. The RSR could therefore
be misleading if comparisons are drawn too widely between different structural forms.
When evaluating ultimate capacity it may be argued that it is more appropriate to adopt
mean values for material properties (eg. rather than minimum specified yields) just as
nonlinear analysis techniques accurately model component responses in place of lower
bound assumptions used traditionally in design. At present approaches differ leading to
inherent differences in reserve depending on the philosophy adopted.
A more instructive and informative measure may be the redundancy factor (RF) introduced
by
et al
which relates the load at collapse to the load at which first member
failure occurs. This quantifies the system contribution to the global response. It also gives
an immediate indication of whether the system is brittle (RF = 1.O) and overall capacity loss
is synonymous with first member failure, or whether ductile redistribution takes place
(RF 1.0).
In fact, both the relative magnitude of the peak load the structure can sustain, and the
characteristic of the response as failure is approached, are important. A further
complication is that some pushover analyses are conducted for comparison with working
stress designs. Others are approached from a limit state basis.
If R is the ultimate component resistance and D and E are stillwater loads and
environmental loading, respectively, the criteria may be stated:
(LRFD)
and
where
are partial factors to account for variations in loading,
are partial factors to account for variations in structure and foundation
resistance,
F is safety factor on capacity of different components.
Values proposed by
R
0.88
lead to
+ 1.5 E
with
where F varies between 1.25 and 1.44 depending on the component. Direct correlation
therefore depends on the proportion of 'dead' to 'live' load which in itself varies in a
pushover analysis as vertical loads are largely held constant as lateral loads are increased.
STRUCTURE
Gho
(ADAPTIC)
of ductility
response
Explicit FE modelling of
K
Reserve derived from higher
joint capacity in frame than in
Seismic
and rigid joint comparisons
reduced
and greater
some flexible cases
et
(NOAMAS)
and rate
depends on rate of
load
brace slendernesses
shedding and
NOTES
Illustration of elastic joint
RSR
SYSTEM RESERVE
Bouwkamp et
(FACTS)
LOAD-DEFLECTION
Reserve depends on load
of
load shedding
Grenda
MR
-
investigations of reserve strength Simple 2D frames 1 (Part 1 of
P i e Grenda
(MR algorithm)
Pie
REFERENCE (ANALYSIS
METHOD)
Table 5.26 Summary of
STRUCTURE
Increased size secondary bracing affects greater
post-ultimate ductility.
.43
Gates et
(DYNAS)
No still water load factors.
Post buckling path traced
Limit state, load factor approach adopted
NOTES
No still water load factors
1.65
1.7
Load factor
RSR
SYSTEM RESERVE
1.8
I::
LOAD-DEFLECTION
et
(USFOS)
Ward
(SAFJAC)
(MARC,
REFERENCE (ANALYSIS
METHOD)
5.26 Summary of analytical investigations of reserve strength Simple 2D frames - 2 (Part 2 of 81
STRUCTURE
Members removed and target residual capacity
achieved for a different plan bracing and 3 load
directions by increasing member sizes.
C little capacity for redistribution
-
Residual capacity quantified in event of damage
NOTES
Lloyd
(Linear
RSR
SYSTEM RESERVE
Analyses with removed members gave sequence
of failures and RF 1.5
LOAD-DEFLECTION
Lloyd
(Simplified hand
analysis)
REFERENCE
(ANALYSIS
METHOD)
Table 5.26 Summary of analytical investigations of reserve strength Idealised 3D iackets (Part 3 of
STRUCTURE
-
FENRIS,
Jacobs Fyfe
(USFOS)
REFERENCE (ANALYSIS
METHOD)
LOAD-DEFLECTION
RSR
SYSTEM RESERVE
NOTES
Seismic investigation of ductility associated with
elastic plastic joint response
Flexible and rigid joint comparisons indicating
reduced capacity and greater deflections in some
flexible cases
Illustration of elastic joint flexibility
Reserve depends on load eccentricity and rate of
post-buckling load shedding
Table 5.26 Summary of analytical investigations of reserve strength Jacket structure investigations (Part 4 of
STRUCTURE
Moan et
(USFOS)
Soreide et
(USFOS)
et
(SEASTAR)
et
REFERENCE
(ANALYSIS
METHOD)
LOAD-DEFLECTION
Table 5.26 Summary of analytical investigations of reserve
2.49
2.3
2.0
diag. 4.39
4.32
long. 3.71
W
S
W 2.0
SW 2.2
N 2.0
RSR
SYSTEM RESERVE
Jacket structure investigations
in both
Intact reserve strength Cases 2-4 simulate
damage with members removed.
Intact reserve strength Cases 2-4 simulate
damage with members removed.
First member failure triggers collapse due to
load direction and structural configuration.
Design analyses to achieve target
intact and damaged conditions.
NOTES
STRUCTURE
et
Bea et
(SEASTAR)
REFERENCE (ANALYSIS
METHOD)
LOAD-DEFLECTION
investigations of reserve
RSR
SYSTEM RESERVE
Reassessment to compare upgrade scheme for
existing installations facing overload.
Example requalification analysis to illustrate
role of ultimate capacity analysis in assessment
inspection and maintenance.
1 - Platform as is
2 - Repair damage
3 - Repair and grout legs
4 - Repair and raise deck
NOTES
STRUCTURE
reliability)
et
Holm et
RELIABILITY
et
Tromans
(USFOS)
Tromans
(USFOS)
REFERENCE
(ANALYSIS
METHOD)
LOAD-DEFLECTION
3.77 (Original
design load)
2.22 (API)
RSR
SYSTEM RESERVE
NOTES
sequenceof
Reliability assessmentof failure for intact and
damaged structures. Greater susceptibiiity for
bracing utilisation due
K-bracing shown.
entirely to shear. Also greater conservatism in
X bracing effective lengths.
Sensitivity with respect to resistance evaluated
for different members
DemonstratesMonte Carlo analysis alone may
not reveal correct probabilities for different
failure modes. Combinationof Level
reliability analysis proposed.
With pile failure maximum load factor = 1.0
First member buckling
failure and collapse
Table 5.26 Summary of analytical investigations of reserve strength - J a c k e t hindcasting and reliability (Part 8 of
Wherever possible, Table 5.26 presents the load factors X on the storm loads as the
In limit state assessment a minimum 1.5 factor would be required to meet 'design' criteria
of the values given.
giving an RSR arguably
Having detailed the problems in cross-correlating reserve strength measures for different
structures, general conclusions can be drawn.
The structures in the literature have exhibited a range of structural reserves. Many of the
tests are necessarily simple such that a series of component failures prior to collapse would
not be expected. Nevertheless the relative redundancy associated with X over K-braced
panels is demonstrated. Furthermore the contributions of alternative load paths in the post
ultimate regime are revealed. Analytical work includes simple structures (Pike and Grenda)
which support the experimental findings. In addition, jacket analyses demonstrate the
behaviour of more complex structures as well as the efficacy of the various numerical
techniques.
The analyses have been based on both idealised structures (eg. Lloyd and
and real
structures, either for design optimisation (Piermattei et al) or
evaluations (van de
Graaf and Tromans). The simplified analyses have been instructive enabling parametric
variations in sea states and configurations to be revealed. However, the in-built symmetry
is found to precipitate more rapid failure and less system redistribution than would be
inherent in real jacket structures designed to satisfy multiple temporary, as well as in-place,
conditions. However, the few real structures presented in the literature reveal instances
where first member failure triggers an immediate sequence of failures of structural collapse
due to the pattern of diagonal bracing (Dolan et al) and the six North Sea jackets analysed
by
et al exhibit little additional capacity beyond first member failure.
In
evaluations it should be noted that more realistic loading may be adopted than
when relative idealised assessments are being undertaken. If the load factor is so high as
to imply loading in the deck, the wave force distribution may be changed (Tromans and van
de Graaf). Similarly, account may be taken of the contribution of direct loading on
members to reducing capacity. Specific aspects of system reserve may be identified as
follows.
5.2.2 Bracing configuration
The simplified assessment by Marshal1 and the comparisons of configurations by
and
and Jacobs and Fyfe and
et al, all illustrate the 'brittleness' of the structural
response for K-braced framing. Structures with X-braced panel framing (Gates et al,
and
Nordal, Piermattei et al, and
et al etc) generally
Jacobs and Fyfe,
offer great ductility. The diagonal bracing in the transverse frames of the platform
analysed by Dolan et al gave no reserve beyond first member failure as the load path was
effectively destroyed. Diagonal bracing in the face frames of jacket structures were also
critical when the framing direction was identical around the platform (Tromans and van de
Graaf). Balanced bracing with tension diagonals oriented to balance compression members,
ensures that a more gradual progression of failures precedes collapse.
Diamond bracing (X-bracing without horizontals) is shown to compromise the reserve
strength, compared with fully X-braced panels (Jacobs and Fyfe, Pike and Grenda etc).
to
Lloyd demonstrated significant weight penalties if primary bracing were to be
achieve target reserve capacities.
The influence of bracing configuration depends on the relative slenderness of different
members within the panels and the legs and for this reason, based on the level of
information published, quantitative conclusions are difficult to draw beyond the qualitative
et al who showed that
discussion presented above. This point was emphasised by
in certain circumstances, despite favourable bracing patterns, inadequate section properties
meant the expected reserves were not exhibited.
The most meaningful comparisons of reserve strength associated with different bracing
schemes are derived from specific configuration studies (eg
and
Nordal et al,
Das and Garside). In these a number of parameters are kept constant and changes in
and
report an increase in RSR from 1.7 to 2.3
reserve strength are calculated.
as bracing is changed from K to fully braced X. The increase in structural weight to give
such a significant benefit in RSR is relatively small, underlying the value of such sensitivity
assessments to ensure that adequate system reserve and robustness is introduced in new
jacket designs. Nordal et al identify an order of magnitude increase in the reliability of
braced framing over K-bracing in an idealised jacket structure.
An important conclusion for real jacket structures is that examples exist in which first
et al, Tromans
member failure is synonymous with structural collapse (Dolan et al,
and van de Graaf). These instances are directly attributable to the bracing configurations
(non redundant cross-diagonal bracing in transverse framing and diagonal bracing in one
direction in transverse frames). This emphasises that in addition to the level of RSR an
important consideration must be the mode and consequences of failure. In this regard
'ductile' responses are to be preferred to 'brittle' behaviour where load shedding is rapid
and no warning of failure is observed.
5.2.3 Joint behaviour
Table 5.27 identifies whether particular types of analyses have been performed. The first
aspect is joint behaviour and it can be seen that very few references take account of joint
flexibility and only simple investigations have incorporated models of nonlinear collapse
behaviour. For this reason even elastic and simplified analyses are included in the review.
Current API RP 2A requirements specify that design capacities for joints should exceed
those for members. However, many older platforms contain critical nodes. Comparative
analyses with and without account of joint modelling would be instructive but none are
presented in the open literature.
5.2.4 2D versus 3D
A number of pushover analyses have been undertaken in which plane frames have been
considered to investigate aspects of jacket performance (eg. Piermattei et al, Jacobs and
Fyfe). In the first example, 3D analyses were undertaken subsequently, but in the work
between the two analyses such that direct comparison
presented elements had been
cannot be made. The best example is therefore given by the simple frame analyses by Pike
and Grenda where eccentric loading was redistributed into the alternative bracing plane as
failure in the first was precipitated. Whereas in 2D analysis first failure dictated ultimate
load, 3D redistribution enabled frame reserves of more than 30% to be exploited. This
illustrates the principal of 3D frame action within a jacket and the dependence on adequate
plan bracing to transmit the loads. This was also demonstrated by Lloyd. If sufficient
bracing is not provided, the ultimate response may still be governed by first member
failure.
3D action depends also on the direction of incident loads. In practice, the direction with
the lowest RSR generally forms the focus for descriptions of failure and investigations of
redundancy (Piermattei et al). A systematic investigation for a loading rosette with base
loads related to directional sea states may be more meaningful, together with correlation
(eg. Tromans and van de Graaf,
et al, etc).
to elastic component
5.2.5 Foundation modelling
The numerical investigations of reserve strength also reveal the practical relevance of the
nonlinear interaction between structure and foundation. Many analyses adopt linear
approximations or idealisations (eg. Jacobs and Fyfe) whereas accounting for the nonlinear
et al) indicates that the sequence of failure and global structural
behaviour
deformation can be strongly influenced. The purpose of the present study is to review the
reserve strength within the structural form, However, for the collapse analysis of jacket
structures, appropriate modelling of soil-structure and pile-structure interactions also needs
to be undertaken.
et
nor included in
et al
Holm et al
Nordal et
means
X
X
X
van de
van de Graaf
Brace capacities modified
simulation elements
X
X
X
X
flexibility
of
frame capacity in non redundant
with weak K ioints.
plastic joints-showing influence on frame
uctility in seismic design.
modelled explicitly using FE.
X
X
X
et
Soreide et
Moan et
et
et
et
et
JACKET STRUCTURES
Jacobs Fyfe
Lloyd
Lloyd
et
Gates et
IDEALIZED 3D JACKET
Ward
et
Gho
SIMPLE 2D FRAMES
Bouwkampet al
Ueda et
REFERENCE
critical
X
critical) braces removed X= 1.6 (1
X
X
X
DAMAGED MEMBER
Members removed
With nonlinear foundation intact structure failure
involved foundation.
Modelled but structural failures.
Soil resistance modelled but failure in jacket.
Not included
No foundation failure
Foundationlateral failure suppressed
at pile-soil interface.
slip in legs modelled
springs
P i e failure suppressed based on correlation with damage
X
X
X
X
X
X
X
modelled
X
Reliability for damaged state
Members removed
Members removed
Members removed
Members removed
Members removed.
Not included.
Nonlinear springs between piles and soil. Instances of
failure where compressive skin friction exceeded,
Members removed to evaluate redundancy influence
Not included
Influence of grouted leg piles on jacket response included Members removed - asymmetry
Members removed and weight
to achieve
Not included
Involved in failure scenario
ASPECTS OF COLLAPSE BEHAVIOUR MODELLED
FOUNDATION FAILURE
Table 5.27 Aspects of collapse behaviour modelled in reserve strength analyses
The role of comparative analysis
The analyses presented in Section 5 have revealed important aspects of jacket reserve
the availability of key
capacity. However discrepancies between base design criteria
details have limited the comparisons that can be made. In contrast the few comparative
analyses that have been presented (see Table 4.5) have been most instructive.
Such comparisons enable not only the performance of different software packages to be
assessed but also provide unique opportunities to validate different approaches to modelling
and analysis. This is particularly important given the current absence of physical data for
complex 3D structures against which software can be benchmarked, and the increasing
by the offshore industry. A
reliance that is being placed on the calculation of
principal recommendations from this review (see Section 7.2) is that further comparative
analyses should be undertaken and published as a means to develop the education process
in this important state-of-the-art technology area.
ASSUMPTIONS
E
29.000
36
C
P.,
P,
F,
-014
0.8
of
Area
DESIGN TRADE-OFF
HORIZONTAL BRACE
OPTION lI
21
HORIZONTALBRACE
1.00
1.05
...
1.20
1.10
.
.
1.00
1.05
1.15
..
.
SHEAR LOAD .
SHEAR
V,.
Figure 5.1
Two bay X-braced frame analysed by Pike and Grenda
1.20
NOTE:
FRAME l
0
-2
-4
-6
BRACE UNLOADING RATIO
-
-8
Figure 5.2
Parallel K-braced frames showing influence of eccentric loading and rate of brace unloading p on
reserve strength (Pike and Grenda)
JOINT 1
SECTIONS
l
JOINT
jacket frame analysed by
2
Figure 5.3
et to illustrate joint flexibility effects
SHEAR FAILURE (BRACE)
FAILURE (BRACE)
RIGID
FLEXIBLE JOINTS
of joint capacity on
Figure 5.4
response identified by Ueda et
:
hinge
Flexible Frame
-0.5
0.0
0.5
(m)
Figure 5.5
Analysis of a jacket frame with flexible and rigid joints by Elnashai and Gho
Figure 5.6
Frame models analysed by
and
showing differences in joint capacity and
post-ultimate axial-moment interaction both within the frame and in isolation
t
U
REFERENCE
IS
I
0 20
0
3%
E LE M ENTS
ELEMENT
6
0
0 4%
0
DISPLACEMENT (m)
Jacket frame analysed by
Figure 5.7
et
using MARC and
0
LATERAL LOAO
IS
TOTAL X LOAO
TOTAL Y
TONNES
a
.
INTACT
.
0.0,
. , . , . , . , .
Figure 5.8
Analyses of jacket frame by Ward and lzzuddin and
0
MARC
INTRA
SAFJAC
SAFJAC
0.5
LATERAL LOAD
Figure 5.9
Comparison of jacket frame analyses by
Ward and lzzuddin (SAFJAC) and
et
l
et
et
IMARC, INTRA),
MEMBER INELASTICITY
STRUT
@m-
@
STRUCTURE FORCE-DEFLECTION PLOT.
Figure 5.10
Comparison of energy absorption ductility for 2D jacket frame analysed by Gates et
BROADSIDE LOADS
INTERNAL
TRUSS
2.3
3.0
.69
.79
TRUSS
1.2
3.8
.79
END-ON
LOADS
2.6
5.8
.72
.85
Figure 5.11
Redundancy calculations for Gulf of Mexico structure due to
ROW l
A
and
Figure 5.12
X-braced jacket
elastic
plastic
elastic
plastic
CASE A
---- CASE B
--------- CASE C
I
RESIDUAL STRENGTH
Figure 5.1 3
Four-legged jacket used in redundancy study by Lloyd
V EL.
V EL.
,
;--
EL.
-
- 41
30
o
,
o
I
I
40
80
o
h
Figure 5.14
Intact jackets pushover analysis by Jacobs and Fyfe
Figure 5.15
Brace configuration study covering X, K and diagonal bracing (Jacobs and Fyfe)
l
LINEAR FOUNDATIONMODEL
Figure 5.16
Jacket analysed by
LINEAR FOUNDATIONMODEL
et
Figure 5.17
Analyses of Veslefrikk jacket report by Nordal
FRAME 1
01
02 0.3
07
FRAME G
08 09
Lateral Displocernent (meters)
Figure 5.18
Nonlinear analysis of four-legged Goodwyn concept
et
Lateral Displacement (meters)
Figure 5.19
Nonlinear analysis of eight legged Goodwyn concept
et
Figure 5.20
Failure sequence for the
A platform
Finite
model of
et
Collapse mode of intact
2.5
Figure 5.21
Analysis of 3D jacket structure
et
Figure 5.22
Eight leg jacket analysis by Moan et
Figure 5.23
3D box frame analysed by Sordde et
Figure 5.24
Capacity consequence evaluation due to Bea et
Figure 5.25
Load displacement curves for example jacket for AIM alternatives
et
AUSTRALIA
LOCALITY
-
OTHER PLATFORMS
PIPELINES
SOUTH
Figure 5.26
Esso Australia platforms for upgrading using RSR approach
EAST ELEVATION
et all
Structure
Structures analysed in
Figure 5.27
investigation, to scale
et
Lading
Lading
(West)
(C)
Figure 5.28
Pushover responses for structure
analysed by
Pushover responses for structure
Figure 5.29
analysed by
et
et
showing deflected shape
""m*!
Load
Figure 5.30
under broadside loading
et
Figure 5.31
Cyclic analysis of structure A 2 under broadside loading
et
Cyclic analysis of structure
A
m
End-on failure mechanism
t
Structure failure surface
Load factor:
end-on wave
lateral deck deflection,
direction
Figure 5.32
South Pass SP62-B jacket
and van de Graaf)
Row A
Environmentalbad
1 h3
Elevation views of
Load
lateral
C
0.2
0.4
0.6
0.8
1
12
(m)
Load
deck
Figure 5.33
Gulf of Mexico platform used for hindcarting analysis (van de
and
(leg)
displ.
Figure 5.34
Failure modes in reliability analyses by Edwards et
50
Y
3.0
17, WAVE
:
stress
bar 2 2 3
to
\
240
120
Compression yield
of bar 244
X
60
Figure 5.35
Influence of yield on system behaviour demonstrated by Holm et
FORCE
SEMI
- BRITTLE
DEFORMATION
Figure 5.36
Ductilelbrittlelsemi-brittle response of member considered by Nordal et
MEMBER
GROUP
DIA.
KB2
LG2
LG4
Figure 5.37
K-braced variant of Figure 5.12 adopted by Nordal et
THICK.
6 . DISCUSSION
6.1
SUMMARY OF REVIEW
6.1
Experimental results
In the review of experimental work (see Table 3.13) the BOMEL, SCI, Grenda et al and
BOMEL tests provide a series of results exhibiting joint and member failures within both
X- and K-braced frames. However, in no instance was failure at the intersection with the
main legs investigated. The SINTEF tests offer some insight to 3D behaviour, but will be
of principal use as numerical facilities to model cracking and denting are developed, given
the initial imperfections present in the specimens.
The Inoue specimens had gusset plate connections and failure in the 3D tests was dominated
by plasticity in the legs. These factors reduce their value in relation to assessing offshore
structures where tubular joints are used and bracing failures are more likely. The
and
Shin 3D tests had no mid-height plan bracing and all had boxed face frame joints but gave
a useful demonstration of the relative influence of damage and member buckling on 2D and
3D frame behaviour. The Ogawa trusses are not typical of offshore construction but
demonstrated the importance of relative brace slendernesses on the collapse response
characteristics.
It may therefore be concluded that the experimental database is relatively sparse and it is
important that wherever possible use be made of the results for benchmarking the available
analysis tools. This helps, not only in validating software, but in identifying features such
as locked-in stresses (Briggs and Maison) which may need to be considered within
sensitivity studies for assessing offshore structures.
Variations in RSR from the test programmes are significant ( l .4-3.9) but high values relate
largely to the unexpected performance of tubular joints in a frame and the low values are
driven by the simplicity of the frames in which first component failure dictates peak load
1.0).
6.1.2 Numerical results
Table 5.26 summarises the results from analytical investigations of reserve strength.
offered
Analysis of idealised jacket structures, such as the study by Lloyd and
into reserve strength. The simple frame analyses by Pike and Grenda
fundamental
revealed the significance of post-buckling member characteristics and system symmetry.
Similarly Connelly and Zettlemoyer were able to reveal the important influences of tubular
joint behaviour on system response underlining the need for appropriate modelling.
et al, Ward and
and
et al provide unique and valuable comparison (albeit
of a simple 2D jacket frame) using different software.
From the publication of specific jacket analyses, the striking finding is the range of
responses which emerge, but the difficultly is in making comparisons on an equal footing.
from both
Piermattei et al and Bea provide background to the selection of target
and
for example, illustratedthe contribution
intact and damaged structures and
of different bracing types to system reserve. This revealed how changes to bracing
configurations with only minor increases in structural weight could significantly improve
the reserve strength capacities.
Qualitatively it is important to note that first member failure can be synonymous with
Trornans and van de
even in real offshore structures.
ultimate capacity (Dolan et
The limitation that foundations can present to system reserve was brought out by
et al and again by Nordal, who presented divergent results ostensibly from different
software programs but which on further investigation were found to have utilised different
foundation models. Finally, the value of hindcasting and correlation with inspection is
illustrated by van de Graaf and Tromans, who also discuss the sensitivity of RSR
predictions to input parameters and the need for data.
In a reliability sense the references are preliminary. In the proceedings of the 1992
workshop on reliability of offshore operations it was concluded that the state of the art in
practice for the assessment of steel jackets is "the use of a deterministic, static pushover
analysis to establish an ultimate system capacity". However, the summary of the state of
practice states that "first generation structural-mechanicaland structural reliability tools are
available, but there is no broad consensus on how to use them in decision making".
In the section below, detailed issues surrounding the use of the reserve strength technology
arising from this review are discussed with a view to more rational application.
Conclusions and recommendations are listed in Section 7.
6.2
RESERVE STRENGTH OF FRAMES
6.2.1 Background to evaluating reserve strength
Reserve strength within jacket structures is required to resist extreme loads which are not
accounted for in accepted elastic design procedures. In assessing the safety of offshore
installations, it is now recognised that the risks of damage from vessel impact and dropped
objects or abnormal environmental loading (eg. hurricanes, typhoons, earthquakes) are not
negligible. There is therefore a requirement to demonstrate that structures can resist these
loads without catastrophic collapse. The magnitude of the loading determines that elastic
resistance cannot reasonably be provided and plastic redistribution must be exploited. To
that end experimental programmes have been undertaken and specialised nonlinear software
has been developed to model the collapse behaviour of tubular frames. Through this work,
sources of reserve strength and the role of frame behaviour have been identified.
For offshore structures the operator is concerned to quantify the load the structure can
sustain in excess of the design value. On that basis the following definition of the reserve
strength ratio (RSR) is often adopted:
RSR =
Ultimate structure resistance (ie load at collapse)
Design load (eg
year storm)
However, in designing the structure to resist the original design load (eg. 100 year storm),
safety factors and characteristic values are adopted. In limit state design partial factors on
loading and resistance are adopted. These factors, accommodating uncertainty,
conservatism and safety, in the original design, mean that an RSR well in excess of unity
is to be expected even before failure should occur anywhere within the structure.
et al give a value of 1.48, for example, but the exact correlation depends on the design
philosophy (working stress or limit state), ratio of stillwater to environmental loading etc.
In interpreting both test results from simple structures, and analytical predictions for
jackets, differences in the measures of reserve should be noted. Offshore structures are
designed to withstand specific loading criteria and for no condition shall the elastic
utilisation exceed unity. Test structures are designed for a particular sequence of failure
and, although the capacity of the critical member can be related to the frame load which
would give an interaction ratio of one, the level of implicit reserve is inevitably different.
The interpretation of test results in this way therefore gives a lower bound on RSR
compared with jacket evaluations.
Redundancy beyond first member failure
As conventional design is against first member failure, it may be that the system reserve
should be considered as the margin beyond first member failure that collapse occurs. This
measure of redundancy within the structure is denoted RF, where
RF =
Ultimate structure resistance
Structure resistance at first member failure
Analytically it is important to distinguish between first yield in a compression member and
the occurrence of the three hinges required for buckling to limit the member capacity.
High values of both RSR and RF are desirable to ensure the integrity of a jacket structure.
RSR gives a measure of the overload it can sustain, whilst RF demonstrates the availability
of alternative load paths. If RF were unity, even if there were a high RSR against
environmental loading, damage to the critical member could cause immediate structural
collapse. The reserve strength review has identified analyses of existing installations where
et al, Tromans and
initial failure triggers immediate structural collapse (Dolan et al,
van de Graaf). By virtue of the framing arrangements and relative member sizes, other
and
Jacobs
structures have been shown to have substantial sources of reserve
and Fyfe).
6.2.3 Alternative loadpaths and sources of reserve
Test data and analytical results have demonstrated that X-braced panels offer an alternative
load path to resist loads (eg. Figure 2.2). The panel may therefore sustain increasing load
even after a compression brace buckles, provided members are not too slender and the
supports do not precipitate rapid unloading from the compression member. Similarly,
diagonal bracing where members are inclined alternately offers an alternative tension load
path to counter load-shedding from a buckling compression member. Examples in which
the primary X joint has yielded reveal the potential for deformation and redistribution such
that the full capacity of both load paths through the brace can combine to give considerable
Conversely K bracing offers no alternative load paths
reserve capacity
through the panel once a member (or joint) fails.
Beyond panel failure, reliance is placed on the surrounding structure and the relative
capacity of the legs and adjacent panels. Members which are lightly loaded under fully
elastic conditions can also play an important role in redistributing loads, and examples have
been given where their omission (eg. to save weight) can lead to progressive collapse in the
event of extreme environmental load (Jacobs and Fyfe). A fractional increase in structural
weight can preserve structural integrity and increase the global capacity.
Similarly assessment of simple 3D structures (Pike and Grenda, Soreide et al) has
demonstrated the role of plan bracing in transferring loads between frames so that the full
structure can be utilised. In-plane loading of idealised structures does not reveal this effect,
whereas jacket structures are inherently asymmetric.
It must be emphasised that redistribution depends on the relative strength and stiffness of
the alternative load paths as well as the configuration.
6.2.4 Relation between 2D and 3D structures
It is demonstrated that 2D analyses can give valuable insight into the relative performance
of different structures. However, systematic comparison between two and three
dimensional representations are not presented in the literature. Such investigations would
offer significant additional insight into the performance of jacket structures.
6.3
RESERVE STRENGTH CONSIDERATIONSFOR OFFSHOREJACKET
STRUCTURES
Complexity of
jacket structures
The reserve strength of jacket structures may be evaluated either in the course of
requalification for existing installations or in the design phase to assist in
structural configurations. In the latter case, RSR can be a useful relative measure and
progression from 2D to 3D analyses can be informative and efficient. However, offshore
structures, as opposed to simple tubular frames, have inherent complexities which need to
be addressed.
In modelling a
frame from a 3D structure, it is not sufficient to adopt solely the plane
frame geometry. For a meaningful evaluation it is necessary to account for out-of-plane
stiffness as well as the associated load contributions. For some structures this is
straightforward, but in other instances the translation from 3D to 2D is complicated,
requiring experienced engineering judgement. Warning or guidance on this is not generally
given in the literature, where idealised 2D plane frames are often presented.
The asymmetry in loading arising from appurtenances and secondary structures, should be
considered. It has been shown that this, and the asymmetry in the structure itself,
facilitates the redistribution of loads. Again, 2D idealisation of structures will not reveal
this.
6.3.2
Modelling of jacket loads
The components of extreme environmental loads (wind, wave and current), as well as the
distribution down the structure, vary with the return period considered. For
evaluations it may therefore be necessary to determine the critical loading state and apply
fractions of this loading until collapse occurs. This differs from the usual approach
year design storm is incremented to
whereby the environmental loading for the
collapse. In that case, the applied loading at the peak load may not correspond to a real
environmental condition, rather the RSR gives a relative measure of capacity.
In monotonically increasing environmental loads whilst holding still water loads constant,
it should be recognised that depending on the bracing patterns and batter of the legs, the
proportion of still water to environmental loadings resisted by members will not be the
same and so will influence the RSR based solely on the environmental factor.
Although the current approach is relatively straightforward, more rational procedures could
be devised depending on the purpose of the analysis (ie. reassessment, design comparisons
etc). Proportionate increase in different loads could be related to their quantifiable
uncertainty leading to more realistic scenarios. Otherwise it is important to consider the
interpretation of the RSR values.
An additional complication is the influence of hydrodynamic loading on the member
capacity. Wave loading is generally converted to equivalent nodal forces but this will
overlook the influence of lateral brace loading on the individual member. For a relative
evaluations
measure or reserve this may not be of major importance, however, for
or accurate predictions, the full loading should be considered. Factored nodal loads may
be applied to give an equivalent influence, or for phenomenological models a reduced
characteristic may be adopted to take some account of the direct member loads.
The sequence in which different load components are applied and incremented is a further
consideration in nonlinear analysis where, because of plasticity, instability and load redistribution, the ultimate load can be significantly affected by the loading history, see
Section 6.3.6 for further discussion.
Influences on
RSR
For jacket structures, measures of RSR are often presented in terms of base shear or
overturning moments. This needs qualification as the same storm loading from different
directions will generate different base shears and overturning moments. Again, as a
relative measure, the approach may be satisfactory but in absolute terms results should be
interpreted with caution.
The importance of loading direction and correlation between elastic utilisation and ultimate
RSR is not explored in the literature. However, it is particularly important in the
assessment of jacket structures. Based on elastic analyses for a rosette of wave loadings,
the critical direction and corresponding wave height giving the greatest utilisation in any
component may be found. In incrementing the loading to collapse, the structure may have
significant capacity for redistribution beyond first failure giving a high RSR. Subject to
loading from a different direction, first failure may be at a higher load factor (ie. the
critical component has a lower elastic utilisation), but this may trigger a rapid sequence of
failures such that only a low RSR exists. The peak capacity may also be less. Clearly the
critical load case under elastic design criteria, does not necessarily correspond to the worst
case in terms of reserve strength. Demonstration of this fact is required in the open
literature to ensure that adequate analyses are performed for jacket assessments.
and Tromans, 1991) is to
Analysis for a rosette of environmental loads (eg. van de
be recommended but may be considered too costly or time consuming. However, if a
reduced analysis approach is to be followed, it is clear that it needs to be established on a
firm and rational basis.
6.3.4 Role of tubular joint failures
Most test data are for specimens where members have been the critical components.
Almost all the analytical predictions of reserve strength for jacket structures have
considered critical members and rigid joints have been assumed. In fact, many older
structures were constructed without joint cans so that the tubular joints are highly utilised
and in some cases are 'critical' components. Even where cans are present, once storm
loads are factored in the determination of RSR, the capacity of these joints may be
approached and significant nonlinearity in the local response is to be expected. Joint
checking criteria and modelling capabilities within pushover analysis programs are therefore
required. It should be emphasised that tubular joint criteria are based on the peak loads
achieved in isolated tests and are not related to the limit of linear behaviour or restraining
effects of chord fixity or continuity.
and Shinners et (1988) were older structures
The platforms analysed by Bea et
without joint cans and due to limitations of the available software these authors simulated
tubular joint failure by modifying brace capacities in the first case, and by developing
specific nonlinear strut and beam-column elements in the second. Since 1988 however, the
published results have generally focused on limiting member behaviour and advances in
modelling tubular joint failures are not generally reported.
Depending on the joint configuration, nonlinear behaviour may be exhibited at 40% of the
peak load. It is therefore certain that at the ultimate load levels being predicted for jacket
structures, nonlinear joint behaviour will have commenced. The implications from ignoring
this may be significant. As demonstrated in the SCI and BOMEL tests, softening in the
response of a joint would limit incoming brace loads and so protect the members
themselves from failure. Loads shed to alternative loads paths may generate failures
elsewhere. It is clear therefore, that nonlinear joint behaviour may not only alter the
capacity of a structure but may also affect the sequence and mode of failure predicted.
Indeed, an ultimate strength analysis needs to incorporate all nonlinear aspects of the
behaviour if reliable predictions are to be made.
A problem with joint behaviour is the lack of information on ultimate response
characteristics, in addition to capacity predictions, from the available database. Not all
analysis programs have the explicit facility to model joint behaviour althcugh modifications
to phenomenological strut models may be made to give an effective response characteristic.
Other programs (eg. SAFJAC) enable force-deflectionand moment-rotation characteristics
to be defined, but these need to be specified for each configuration.
A detailed evaluation of the potential influence of joint behaviour on the reserve strength
of jackets needs to be made, both to ensure that confidence can be placed in predictions,
and to determine whether additional information beyond that currently available is required,
eg. for multiplanar joints. Consideration of the influences of thickened joint cans on the
effective buckling lengths of incoming members may be required in some instances.
6.3.5 Role of foundation failure
Similarly to the treatment of joints, the interaction between structure and foundation is often
not included in ultimate strength modelling of jacket structures. Further, isolating the
be adequate when considering
jacket and considering it as a component of the system
boat impact scenarios, for example. In other instances foundation failure is suppressed and
et al, for example, indicate that for structures
linear interactions are imposed.
designed to API, it may be the foundations and not the structure that will determine the
ultimate response and furthermore the discrepancies between analyses reported by Nordal
may be largely attributed to foundation modelling assumptions.
To establish a relative measure of structural performance, explicit modelling may not be
required. However, the absolute RSR for the system may be governed by foundation
characteristics. Furthermore, the global deformations can be far greater when nonlinear
foundations are accounted for and serviceability limit states such as deflection criteria for
risers or topside toppling may be invoked. As in the case of joints, it may be that
additional data are required. Nevertheless, systematic investigations are required first, to
determine the importance of foundations to the global RSR.
With regard to deflection criteria or limit states, no consideration is given to these in the
literature, yet it is clear that appropriate limits need to be evaluated for the results of
pushover analysis to be meaningfully interpreted.
6.3.6 Cyclic loading effects
Having established the capacity of a structure to withstand an extreme storm load, the
need to be considered. The loading will be cyclic but about
conditions within the
a high mean load and so differs from earthquake scenarios where repeated load reversals
may be anticipated. Much of the experimental data have been generated to simulate
earthquake scenarios so data for calibrating storm analyses are therefore inadequate.
Although a compression brace may buckle giving a rapid fall off in load, albeit that some
post-buckling capacity is retained, with subsequent reductions and increases in load,
fracture from local crimping may be precipitated. Alternatively a structure may survive
an extreme event but develop extensive yielding. The resistance of the components in a
subsequent event needs to be quantified. However, data on the high stress low-cycle
performance of members and joints are sparse.
et al) has made a significant
Recent work by SINTEF and Shell Research
contribution to the understanding of cyclic loading effects relevant to offshore structures.
Their conclusion, from a series of comparative pushover and cyclic analyses of six North
Sea jacket structures, is that structures that survive the passage of one large rare wave from
an extreme storm without failure are likely to survive the entire storm indicating that
pushover analysis generally suffices to demonstrate a structure's integrity. However, not
all structures were able to achieve shakedown near the static collapse load for each storm
scenario. Cyclic degradation of system strength was governed by the extent of plastic
deformation imposed on critical members during the initial extreme cycle as well as the
degree of reversal in the pattern of cyclic loading. Whilst the results generally support the
use of pushover analysis it is important that cases subject to cyclic degradation are
within the SINTEF programme
investigated more fully. This work is
et al) but some preliminary remarks on the potential significance can be made.
A key factor is that the degree of plastic deformation in a failed component, not the load
level at which failure occurs, is significant. A member may fail at a load well below the
ultimate structural capacity, but depending on its location in the structure and the
displacements necessary to mobilise alternative loadpaths, significant plastic deformation
may or may not occur. This degree of plastic deformation could be assessed at the stage
of performing the static pushover. Furthermore, if first member failure and ultimate
collapse are almost simultaneous, it may be concluded without further analysis that the
cyclic capacity of the structure would be similar to the static pushover load.
For more complex situations a few practical examples illustrate the pertinent points:
Consider two structures designed to the same code with the critical member in each
having the same utilisation. Under extreme loading it may be anticipated (based on
idealised assumptions) that these members would fail at the same global load factor.
If the first structure were non-redundant the system capacity would fall. In a redundant
system plastic deformation of the critical member might take place as loads were
redistributed until the ultimate strength was reached at a higher load factor. Figure
6. l a illustrates the cases.
Both structures may be expected to achieve shakedown around the first member failure
load, and therefore perform satisfactorily at the same absolute load level. Although the
subsequent plastic deformation in the second structure may cast doubt on the validity
of the ultimate capacity because of the potential inability to achieve shakedown, this
may be of less concern. Any capacity beyond the initial failure load level is a bonus
with respect to the first design which would undergo a static collapse if the load were
exceeded.
2. Reassessment of older structures
A potentially greater concern may be in reassessment of structuresdesigned to outdated
codes with varying levels of safety factor and different relative component capacities.
Figure 6. l b gives two examples where the structures exhibit the same ultimate static
capacity but the first behaves in a brittle manner without the redundancy and
redistribution of the second. It is supposed that both structures are now subject to the
same design storm and, as shown, both can achieve the same global load factor.
In the second case the level of first member failure suggests the structure would fail
to meet current component based criteria and this is a practical case in which pushover
analysis may be used to demonstrate system adequacy. However, it is here that cyclic
considerations may be important. If the second structure relies on large plastic
deformations to achieve the peak load, it may be that shakedown could only be
achieved at a lesser load. In this case the pushover load alone could be misleading and
give an unconservative measure of system performance. The more brittle response
could perhaps be accepted more readily without further cyclic investigation.
3. Design based on global resistance
The responses in Figure 6. can also be used to illustrate the need for both component
based and system based considerations in design. Were two new structures to be
designed on the basis of a system pushover load factor alone, the two responses shown
would be equally satisfactory, despite the concerns from a cyclic loading viewpoint
expressed for the second case under item 2 above. By having a corresponding
component based criterion the second structure would only be acceptable if first failure
were achieved at a higher load level than that shown, thereby potentially increasing the
system load at which shakedown could occur.
The above examples are simplistic, nevertheless they serve to illustrate the interaction
between cyclic and static pushover behaviours which need to be considered in the
application of these techniques and the development of a philosophy for structural
evaluation.
Beyond the high stress low cycle plasticity effects which are being modelled, future
consideration also needs to be given to low stress high cycle fatigue which may result at
points of stress concentration associated with component failures, fracture potential and
tubular joint performance under cyclic loads.
The need for more data extends also to the assessment of inertia and near failure dynamics
calculated. This is an aspect
and strain rate effects which may modify the
requiring further investigation if the realistic performance can be accurately modelled.
6.3.7 Accounting for damage
This also relates to the ultimate strength assessment of damaged structures. The
progression of fracture and the modified response of dented members require explicit
modelling. Member removal gives an indication of residual strength but the complete loss
of stiffness may falsely protect some load paths whilst introducing overload in others.
Hindcasting analyses can be calibrated against recorded evidence from examples where
structures have survived despite local failures. Furthermore, this may assist in locating
overload elsewhere in a structure where limited inspection has been able to reveal damage
in a particular locality.
Similarly, key components in an overload collapse scenario may need to be assessed in
relation to their vulnerability from other extreme events. Where a primary component
plays a key role in maintaining platform integrity, it is given special consideration in a
probabilistic inspection plan. Conversely, where a component, susceptible to impact or
fatigue, plays a key role in a collapse scenario, it may be necessary to review the target
RSR. Alternatively, a rating scheme for loadpaths may be devised. This may limit the
reliance that could be placed on components given the combined probability of damage and
overload.
6.3.8 Target system reserve
Emerging from the literature is the perception of a target RSR of around 2.0 (eg. Piermattei
et al). This needs qualification in terms of the purpose of the assessment and possibly the
future plans for the installation (eg. 5 year requalification versus new design verification).
It must also relate to the realism of the load combination adopted and the variation of
environmental loads with return period. Nevertheless the figure of 2.0 is used repeatedly
in the literature and may be compared with a baseline factor of around 1.5 which may be
anticipated on the basis of elastic design conservatism before any account of system reserve
is taken. These figures should be viewed with caution however, as so many factors such
as the WSD versus LSD basis of the design, the type of component which is critical, the
accuracy of the analysis method and the modelling scheme adopted, determine the exact
values.
Beyond quantifying RSR there is a need to determine the target evaluation criteria. This
will inevitably be linked to the purpose of the analysis and the procedure adopted but must
extend beyond a target RSR value. Based on the discussion through Section 6.3, it may
be concluded that appropriate performance criteria should be related to:
RSR - resistance beyond base design requirements
RF - margin beyond first member failure
Ductility and limiting deflections
Mode and consequences of failure
Inspectability of component failures
Sensitivity of RSR to changes to key component from other scenarios, eg. minor
vessel impact causing significant reduction in strength to primary load path.
The aim is to assess the ability of structures to support loads in excess of their original
design value. That ability relates not only to the ultimate capacity but must relate to the
continued integrity and safety of the structure and operations. To that end it is clear that
combined criteria need to be evolved. The concept is not new - for tubular joints ultimate
capacity under tension is derated by API to the first crack level, reflecting the catastrophic
mode of failure with which tension is associated. Similarly more comprehensive assessment
of system reserve will be derived.
An important demonstration from the literature is the role of pushover analysis in
optimising a structural configuration to maximise the RSR envelope without incurring a
and
1988). The value of such analysis, for assuring
weight (cost) penalty (eg.
the long term safety and integrity at the design stage of a new platform, cannot be
underestimated.
It is clear from this review that the nonlinear response of jacket structures is extremely
complex. Although nonlinear analysis tools have introduced the facility to model the
behaviour, the contributing factors are complex and cannot generally be assessed by
inspection of the platform configuration and some quantitative assessment is required.
6.4
CALCULATION OF RESERVE STRENGTH
Analytical tools for pushover analysis
Advanced nonlinear analysis tools are now available to calculate the reserve strength of
structures. The three approaches most commonly adopted are:
finite elements
phenomenological models
structural unit method.
General purpose finite element approaches require multiple elements per member for large
deflection as well as material
to be accounted for. These require specific
structural modelling and, because of the model size, can be time consuming to run.
Phenomenological models are more efficient to analyse but require expertise from the user
in specifying correct member properties to reflect the likely response of each component,
given its position in the structure. It is also necessary to postulate the mode of failure so
that phenomenological elements are used appropriately at different locations within the
structure.
The structural unit method enables one element to be adopted per member in the
model so that conventional elastic analysis models can be readily translated for collapse
analysis. Furthermore in early stages of the collapse analysis, when the structure is
responding elastically, solution is rapid. High order polynomial element formulations, for
example, capture both material and geometric nonlinearities. Automatic subdivision on
occurrence of plasticity, be it due to tension or compression in combination with bending,
diminishes the reliance on the user.
Facilities to model nonlinear joint behaviour, soil-structure interaction, fracture,
cyclic loading and so on, as well as pre- and post-processing to enable ready modelling and
interpretation of results are important requirements of collapse analysis programs. For
but it will be some years before comprehensive
most features, developments are
and validated tools are available.
6.4.2 Validation
Validation is a prime concern in the application of nonlinear software to jacket structures.
Closed form solutions are available for calibration on a component basis. Two 2D test
results
are available for benchmarking purposes (HSE, 1993). It is only
comparison between analyses using different programs and by different users of the same
program which offers any opportunity for validating the complex nonlinear redistribution,
failure sequences and modelling approaches for 3D jacket structures. However in many
cases the analyses are sensitive to input assumptions and there is a clear need for data on
component characteristics to be available as well as controlled tests for
calibration. A further phase of
Frames Project is planned (Bolt et al, 1994) to
encompass representative collapse tests of a 3D structure to provide a basis for more
rigorous benchmarking.
Whilst this uncertainty remains, it must be necessary to impose a partial factor on the
predictions. This will result in a higher requirement for the target RSR than will be
required as development in modelling ability and experience improve 'confidence'.
Load
Factor
Load
Factor
First Member Failure
First Member Failure
Global Deflection
Load
Factor
Load
Factor
I
Global Deflection
Comparisonof
Global Deflection
Global Deflection
Figure 6.1
and ductile responses for consideration of cyclic effects on achievablecapacity
7. CONCLUSIONS AND RECOMMENDATIONS
The ability to predict the reserve strength of jacket structures is now of considerable
importance to the offshore industry. There is a requirement to extend platform operating
life despite more onerous loadings and more stringent code requirements than at the original
design stage. Furthermore, risks of extreme events which cannot reasonably be resisted
elastically, have been identified and adequate system reserve is therefore a necessary
consideration in configuring new jackets. Redundant structures have an inherent ability to
redistribute loads as plasticity occurs such that first component failure need not be
synonymous with structural collapse. It is this reserve strength which must be utilised to
demonstrate that loads beyond the original design scenarios can be sustained safely.
This recognition of the importance of reserve strength technology has been met by the
development or adaptation of a range of nonlinear software to perform the collapse analysis
of jacket structures. These embody different approximations and numerical devices with
a view to ensuring that the complex nonlinear problems can be analysed efficiently and to
sufficient accuracy. Despite calibration at the component level, benchmarking against the
available test data identified in this review is recommended. Furthermore, without 3D test
data for direct comparison, recourse should be made to comparative analyses so that by
resolving discrepancies, more may be understood about the complexities of nonlinear
responses.
Beyond the variability in software capabilities, is the methodology for performing analysis
and evaluating reserve strength (RSR). The review has indicated that a simple approach
is generally adopted, whereby stillwater loads are maintained constant and environmental
loads are factored - the factor on the design load at the peak determines the RSR. In
discussion, this review has suggested that although providing a relative measure of system
reserve, the RSR has little physical relevance and more meaningful assessment strategies
are proposed, where appropriate. Furthermore, the ability of a structure to withstand
extreme loads needs to be assessed not only in relation to capacity but in terms of deflection
criteria, the condition of the structure once the loads have abated and the subsequent
structural performance.
This discussion is relatively new and many of the issues raised remain to be resolved. The
principal recommendation from this report is therefore that a procedure for modelling and
evaluating structural reserve should be devised and verified against a series of comparative
cases so that it may form the basis of agreement with industry.
This review has focused on reserve strength and the lessons from static pushover analysis
that can be applied to the assessment of the performance of jacket structures. Specific
conclusions from the present review are detailed in the following subsections and are
followed by recommendations in Section 7.2.
7.1
CONCLUSIONS
Test data
0
Test data are available demonstrating various combinations of member and tubular joint
failures for 2D and 3D structures. Four key programmes relate to offshore structures,
namely Popov, SCI, Grenda et and BOMEL.
As the data pass into the public domain, they provide a valuable and essential basis for
benchmarking software.
The reserve strength from the alternative load paths through X-braced panelling is
demonstrated in contrast with the lack of redundancy in K-bracing (or single diagonal)
bracing.
Member failures have correlated well with predictions and have provided valuable
evidence for effective lengths.
Ductile tubular joint failures have protected load paths affording considerable ductility
to the global response and enabling significant system reserves to be developed.
Differences from tubular joint responses predicted from isolated tests have been
observed in the frames due to boundary conditions and the combinations of brace and
chord loading which occur associated with frame action.
3D test data are inadequate as the available data relate to non-offshore configurations
and structures with initial
Numerical data
Simple models have been shown to be valuable in elucidating the mechanisms
underlying nonlinear system responses.
Comparative analyses for different bracing configurations can readily identify efficient
material distribution to improve structural system reserve and illustrate the significance
of relative member properties and redundant members in the process of redistribution.
A wide variety of software programs are adopted by industry (eg. ABAQUS, EDP,
USFOS) based on variations
FACTS, INTRA, KARMA, RASOS, SAFJAC,
of four methods
- the finite element method
- phenomenological models
- polynomial beam column modelling
- structural unit method.
Descriptions on a common basis are not readily available and the review has
reproduced descriptions provided by the software developers.
Comparative analyses have been presented revealing different failure modes and loads
for the same problem. Initial concern is allayed by differences in foundation
modelling, but this reinforces the need for comparative analyses where benchmarking
for jacket analyses is not possible.
In specific cases, jacket analyses identify the importance of foundation characteristics
and the application of realistic load redistributions. However, no systematic assessment
or sensitivity studies are presented.
Few analysis cases are presented where tubular joint failures play a part. The
conclusion is that this reflects the modelling complexity and paucity of data (as for
foundations) and not the known situation amongst older offshore structures.
The pushover analyses presented represent a range of purposes such as design
optimisation, achieving target RSR at the design stage, RSR evaluation as part of
earthquake requalification, hindcasting etc.
In the absence of data and for simplicity, damage is generally modelled by removing
members which may or may not be conservative for the global system response.
Collapse analysis is generally performed by holding stillwater loads constant and
incrementing environmental loads.
Magnitude of RSRs
Comparison of reported RSRs is difficult because the basis of design loads and the use
of WSD or LRFD approaches are a source of confusion.
Target RSRs of 2.0 are reported for intact structures compared with an implicit reserve
for the design process of around 1.5. The above reservations apply.
In many instancesa significant reserve exists beyond first member failure but in several
of the platform analyses presented first member failures triggered collapse.
Considerations for jacket assessment
Selection of load direction for performing reserve strength analysis. RSR does not
necessarily correspond to maximum utilisation.
Selectionof loading strategy. Maintaining
loads and factoring environmental
loads changes the loadpattern and more rational distribution, based on uncertainty of
loading scenarios and structural action may be more
The sequence
of loads is also important.
Appropriatemodelling. Conservative component responses may not yield lower bound
RSR predictions as load paths are protected.
- Tubular joint failures can be significantand if neglected the wrong load and mode
of failure may be predicted.
- Foundation response may
the capacity of the structural system and similarly
affect the load and mode of failure.
Sensitivity studies may be required to reveal possible scenarios for a real
(imperfect)structure.
Assessment criteria. Appropriate and meaningful target
need to be set together
with criteria relating to the continued
beyond the storm loading
event based on deflection criteria, cyclic loading effects, the sequence of failures,
vulnerabilityof the load path to other sources of damage, the
of key components.
Structural optimisation. Pushover analysis is an appropriate tool to ensure favourable
reserve strength characteristics are exhibited by new structures. Configurations studies
can enable
to be improved
for negligible penalty in terms of steel
weight and cost.
Data requirements. Aspects of jacket behaviour have been
which may be
the ultimate response of jacket structures but for which
important in
inadequate data are available:
- member post-buckling characteristics
- post-ultimate tubular joint behaviour
- high-stress low cycle degradation and inertia effects near failure
- multiplanar joinr behaviour
- modelling damage eg. cracks and dents
- magnitude of locked-in member forces
variability for full-size structure components
- the effect of distributed loading on members
- modelling of wave slam on members and in deck
- local buckling
- hydrostatic collapse
- reduction in strength due to shear loads.
7.2 RECOMMENDATIONS
On the basis of the above conclusions, the following key recommendations can be made:
Data. Additional data on key factors contributing to the nonlinear response of jacket
structures are required in the areas listed above. Evidence from the tests and analyses
reported is that foundations and tubular joints are particularly significantand urgently
and foundation
require consideration given the configuration of older
conditions.
Analysis. Information and criteria on which to select appropriate analysis tools for
specific situations are required. Benchmarking against test data will be a valuable first
step. Comparative analyses of the same structure using different programmes and the
approach of different analysts will follow. In
test data for jacket type
joints should be generated to provide a rigorous test for
frame structures and
Greater confidence in the analytical capability and accuracy will lead to
reduced RSR requirements and greater economy.
methods. Current approaches to load application are simplified giving an
indicative measure of reserve strength but without modelling all aspects of loading
regime. A more rational methodology for incrementing loads to collapse should be
devised and validated, including for example guidance on the treatment of lateral
member loads, the use of mean (or characteristic) component capacities, selection of
orientation, the need for sensitivity studies, etc.
Acceptance criteria. Linked to analysis methods is the need to define target
in
designs.
criteria should reflect the purpose of the
relation to both WSD and
and should extend beyond the RSR to
analysis
the consequences of overload, deflection criteria,
vulnerability of key components to other risks etc, so that the continued safe operation
beyond the extreme loading event may be considered. Acceptance
of the
in conjunction with the formalisation of
criteria need to be laid down and
analysis methods noted above.
This report has reviewed the current state of practice embodied within the literature
regarding reserve strength technology. Tools are now readily available to perform collapse
analyses but the complexities of nonlinear analysis demand that the results be investigated
and explored to ensure that meaningful and accurate predictions of the ultimate response
of structures underlie the numbers generated. Furthermore for many packages,
development is ongoing reflecting the complexity of the nonlinear situation that is being
modelled.
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APPENDIX A
REVIEW UPDATE
AUGUST 1993 - MAY 1995
INTRODUCTION
The main text of this Review was completed by February 1993. The document was
expanded in August 1993 specifically to include a series of four papers
et al;
and Tromans;
et al; Eberg et
1993) examining the validity of static
pushover analyses to evaluate ultimate structural response characteristics in a cyclic storm
loading environment. In reformatting the review in anticipation of publication in January
1994, reference was included to the first draft of a Section 17.0 to API RP 2A-WSD for
the assessment of existing platforms which was first published in December 1993. This
appendix has been added in May 1995 to describe the principal developments in relation
to industry's understanding of ultimate system strength and its application of the technology
in the intervening period.
passed through some 3,000 offshore structures in the Gulf of Mexico
Hurricane
analyses to be performed to
in August 1992 and provided the opportunity for
evaluate loading and resistance models against the failurelsurvival experiences. It was not
until 1994 that the findings could be consolidated and these recent results are discussed both
collectively and in relation to individual structural performances in Section A2.
information also enabled the API Task Group, TG
This body of Hurricane
drafting Section 17.0, to develop experience based criteria for the future assessment
of existing platforms in the region. Recognition is given in Section 17.0 to the value of
ultimate strength analysis and a reserve strength ratio (RSR). However it is important that
the basis of the US provisions are understood so that appropriate criteria can be derived for
the acceptance of RSR elsewhere. Section A3 of this Appendix sets down the background
to the definition and use of RSR in Section 17.0, and details the anticipated timescale for
adoption in API RP 2A and the
standard.
To validate the approach to assessment in Section 17.0, MMS initiated a JIP encompassing
trial applications of the procedure and a benchmark ultimate strength analysis of a specific
platform. The findings give some insight to the confidence that can be placed in the
application of the reserve strength technology. These and the results from the HSE
benchmark against the Frames Project test data are reviewed in Section A4.
Finally Section A5 revisits the discussion, conclusions and recommendations presented in
Sections 6 and 7 of the main report. Several of the key areas identified have been
addressed but others remain unresolved and the conclusions in this Appendix underlie these
considerations for the future safe application of the reserve strength technology.
A2
DEVELOPMENTS IN RESERVE STRENGTH TECHNOLOGY
The discussion in Section 6 of this Reserve Strength Review identified key issues related
to the evaluation of system capacity and the appropriate exploitation of the reserve strength
technology. Between 1993 and May 1995 a number of papers have provided new
information either illustrating or helping to resolve some of the problems faced. For this
report to reflect the state-of-the-art at the time of publication, a selection of these papers
is reviewed.
Most of the work has been based on the use of numerical analysis techniques (discussed in
Section 4) for individual platform investigations, in the manner of results already presented
in Section 5. However, in some cases important links have been made to the experimental
database, presented in Section 3. Furthermore the accumulating industry experience has
been consolidated in a number of important references where direct comparison of reserve
strength is made on a common basis across a range of structures. All these areas are
covered in the reviews which follow. Table A2.1 cites the references in order of the
reviews and identifies the key contributions in relation to this review of reserve strength
technology.
A2.1
Summary of key references 1993
Reference
- May 1995
Key issues
et
(1994)
Sensitivity of RSR to assumed imperfections. Relation between ultimate
strength analysis and elastic design.
Botelho et
following Hurricane Andrew. Importance of joint
modelling capability.
et
(1994)
et
et
(1994)
(1994)
van de Graaf (1993.4)
van Langen et
et
Bea et
Hurricane
Use of experimental data and numerical analysis to
forces and structural damage.
(1995)
(1994)
Bea (1995)
Redundancy in 1950s
Wave in deck loads significance.
based on Hurricane
Consolidated
joint and foundation modelling.
hindcasts. Importance of
Dependenceof RSR on environment and design code basis.
Foundation modelling and system reliability.
Role of a simplified assessment method. Joint modelling limitations.
Developmentand verification of a simplified method.
Moan and Drange
Nonlinear pushover analysis is generally undertaken to determine a best estimate of the
ultimate strength of a platform. Elastic design analysis, on the other hand, is intentionally
conservative and simplified to enable safe structures to be designed speedily. The result
is that nonlinear pushover analyses show system failure to occur at loads typically 1 % to
30% above the load causing first member failure
et
but that in turn is
some 50 to 100% above allowable loads in present day elastic design practices. For the
engineer working with both approaches the sources of conservatism may not be readily
apparent yet meaningful interpretation of ultimate strength analyses may rely on this
understanding. The authors therefore set out to bring the approaches together, firstly by
calibrating nonlinear element formulations to an acceptable design level and secondly by
removing the conservatism in linear analysis.
The focus of the work is on member stability and effective buckling lengths and the
findings are quantified using three X-braced structures covered in earlier sections of this
review, namely:
A two-bay plane frame
et
1982)
(Popov et al, 1980;
see Figure 3.11.
A planar jacket frame
et al, 1988; Ward and
see Figures 5.7, 5.8 and 5.9.
A 3D jacket structure
et
1993)
see Figure 5.27, Structure A2.
1988;
et
1991)
Three principal analyses were performed using SESAM and USFOS:
elastic analysis with a design buckling length, K = 0.8, and checked to satisfy
NPD requirements;
elastic analysis with effective buckling lengths based on refined analysis but
otherwise checked against NPD requirements;
nonlinear analysis with the USFOS nonlinear element formulation and failure
of three hinges;
defined by the
Table A2.2 compares the results and, by comparison with the system collapse strengths
gives insight to the capacity beyond first member failure. This is quantified by the
redundancy factor, RF, which is the ratio of the ultimate strength to the load at which the
first component fails.
Table A2.2
Comparison of load factors at first member failure predictions and at system collapse
First member failure prediction
Linear analyses
Structure
Nonlinear
Pushover
Analysis
K = 0.8
Plane frame
2D jacket
North Sea Jacket
broadside
end-on
2.90
2.18
3.28
2.35
The conservatism attributable to the K factor can be seen clearly by comparing the first and
second results columns. By comparing the second and third columns it can be seen that
appropriate selection of effective length factors can give a more meaningful representation
of member failure.
The effects are studied more extensively in the paper and two further conclusions may be
cited. Firstly, the load level at first member failure in these structures is little influenced
by the potential for plasticity to develop elsewhere in the structures. Secondly, the
representation of member collapse by a refined K factor is satisfactory when the maximum
as this coincides with the simplifying assumption of hinges
moment occurs near
in USFOS (see USFOS description in Section
forming only at member ends
4). For conditions of double curvature the largest discrepancy (21 %) was found.
Completing the investigation, the effects of initial imperfection on first member failure and
system collapse loads are reported. Table A2.3 shows the influence of a 0.5%
imperfection.
Table A2.3
Percentage reduction in collapse loads for a 0.5% imperfection
First member failure
System collapse load
7.8
10.9
5.2
1.4
6.8
11.2
4.3
8.7
I
Plane frame
2D Jacket
North Sea Jacket
broadside
end-on
It can be seen that for these X-braced structures, where system failure is governed by more
than one member, that there is relatively less influence of imperfections on collapse strength
than individual member failure. For end-on loading of the jacket structure two compression
braces shed load onto one tension brace and the influence on system collapse load is
therefore more significant.
This paper demonstrates the value in developing a wider appreciation across the divide
between linear elastic design analysis and nonlinear pushover analyses. Furthermore it
highlights the potential significance of imperfections on both component and system strength
depending on the structural configurations and redundancy.
and Kan
This paper is the first of several in this Appendix dealing with analyses undertaken
through some 3000 offshore structures in the
following the passage of Hurricane
Gulf of Mexico in August 1992. Ten major platforms were toppled directly by the
hurricane which involved sustained winds of 140 miles per hour. Twenty-five satellite
installations (including caissons) were also toppled with significant damage incurred by a
further 26 major and 140 satellite platforms.
Botelho, Petrauskas,
This event provided an important opportunity to validate the use of the ultimate strength
analysis techniques both at the individual platform level, hindcasting collapse, damage or
survival, and collectively to provide a basis for future risk management of the many
et al, 1994 reviewed below).
structures in this hurricane prone region (see
was an 8 pile platform installed in a
water depth
This specific structure, ST
in 1958 having been designed to the then standard 25 year criteria. However, the deck had
been raised in 1991 (Figure A2.1) in anticipationof significant loads should waves encroach
the deck in extreme weather. Nevertheless the platform was completely toppled by
Hurricane
.
Pushover analyses were performed by the authors using CAP (Section 4) and some details
of the modelling approach are presented. Effective length factors (k) were set at 0.65,
except for X braces which were modelled as two diagonal struts, eliminating the X joint,
with k equal to 0.325. For face frame K nodes the panel capacity was deemed to be
governed by joint failure and the member characteristics were chosen to simulate the initial
failure characteristics. The authors point out the shortcomings of this approach in that
redistribution of member loads cannot take place in the event of joint failure which may
sever the brace-chord intersections. Furthermore the analyst must determine whether joint
or member behaviour will dominate for a particular wave direction analysis.
The importance of this can be seen in the results in Table A2.4 which identifies the
significance of joint failure for all three wave attack directions.
Table A2.4
Pushover analysis results for
Pushover
Load
Direction
First
Nonlinear
Pile
Event
First
Nonlinear
Brace* or
Joint **
Event (kips)
Failure
Load
130 "A"
Failure
mechanism
Broadside
1,550
2,450
Joint failure1
Pile Hingesl
Braces
Buckledl
Leg Members
Yielded
Diagonal
1,800
3,000
Joint failure1
Hingesl
Braces
Buckledl
Leg Members
Yielded
End-on
1,550
Pile Hingesl
Braces
Buckledl
Median Maximum
Base Shear
COV = 0.25
COV = 0 . 0
2,150
1.850
The load deflection response for broadside loading in Figure A2.1 also reveals a ductile
softening characteristic, whereas evidence from the BOMEL frame tests (Section 3 and
Bolt, 1995) indicates that gap K joint failure may precipitate rapid load shedding requiring
redistribution of forces throughout the structure. In presentation at the Offshore
photographs were shown of platforms
Technology Conference (Botelho et al,
with complete severance across the gap region of K
recovered after Hurricane
joints. Figure A2.2 shows the line of frame action driving shear failure in the gap K joints
frame tests (Bolt, 1995). This mode of failure was somewhat unexpected in
in
confirmed
the frame tests but the complete severance across joints in Hurricane
the value of the tests in highlighting frame action and potential failure modes.
nonlinear event) of 1.7, 2.3 and
The table indicates redundancy factors (failure
1.6 for ST
in the three directions. These are substantial values which may not be
achieved were it possible for post-ultimate response of the K joints to be modelled.
Comparison of the
base shears from the Hurricane in the final two columns of
Table A2.4 shows the need for the uncertainty in various parameters to be accounted for.
under the diagonal wave was
With a COV of 0.25 the probability of failure for ST
load at failure of the platform,
some 54%. However, whilst this tied in with the
located in the same area survived without damage
it should be noted that ST
despite a very high probability of failure calculated on a similar basis (Petrauskas et al,
1994).
The paper highlights the considerable importance of a rigorous joint modelling capability
if the mechanisms of failure and load redistribution are to be accurately reproduced in
reserve strength analyses. In addition, the benefits of hindcasting to benchmark both
deterministic and probabilistic evaluations of reserve strength are confirmed and will be
further examined in the review of Puskar et al. 1994.
Imrn,
and Light
The South Timbalier 161A platform was one of those damaged by Hurricane Andrew. The
eight leg jacket has diagonal bracing on the longitudinal frames and vertical K bracing in
the four transverse planes. It was installed in
water depth in 1964, five years prior
to the introduction of API guidelines. The maximum hurricane loads corresponded to the
broadside wave attack direction and the main damage was associated with concentric
overlapping K joints 10 feet above the water line. The joints were intact with no evidence
of structural cracking, but local buckling had taken place in the intersection region as seen
in the BOMEL Frames Project, Frame IX, Figure 3.10 (Bolt, 1995).
This failure mode is not recognised in design codes yet the correlation between the test
programme findings and the extent of damage throughout the ST 161A platform enabled
the authors to estimate the maximum load experienced. This was achieved with an USFOS
(Section 4) ultimate strength analysis of the platform where, as in the work undertaken by
Botelho et al
tubular joint characteristics were ascribed to members in place of a
separate joint modelling facility. However, with reference to the ductile response of the
test structure (Frame IX) associated with this mode of overlapping joint failure depicted in
Figure 3.7, this simplification may be reasonably valid.
This
evaluation correlated well with the evidence from wave inundation of the deck
that a maximum wave height of 18m was experienced. The pushover analysis indicated that
wave.
complete platform failure would have been associated with a
A number of other factors relating to the ultimate strength prediction of jacket structures
can be drawn from this paper:
Material samples taken from ST 161A indicated yield stress levels of 400 N/rnm2
(58 ksi) some 60% above the minimum 248
(36 ksi) specification.
Hindcasting analyses (as in the work of Botelho,
Puskar et al, 1994; etc)
were based on incrementing the lateral load profile of the maximum
load from
evaluations.
The results were found to be sensitive to the load
underlining the
importance of realistic load profile evaluation, particularly where the deck is
inundated.
Wave in deck loads were significant, contributing about 20% to the overall
Hurricane
base shear. Deck loads were calculated using in-house Amoco
procedures.
Hindcasting demonstrated that K brace effective lengths were less than 0.64 and
therefore significantly less than 0.8 design values.
The overlapping joint configurations deformed in a ductile manner enabling loads
to be redistributed and the platform to survive intact. Local failures at leg
connections occurred at around 20% of the maximum jacket capacity, with first
failure at one of the four overlapping K joints commencing at around 70% of the
overall capacity illustrating the ductility and redundancy in the configuration.
This paper illustrates the realistic insight that test programmes can bring to the
interpretation of jacket performance. The benefits of hindcasting are underlined but the
paper presents cautionary lessons given the complexity of loading and resistance particularly
in relation to older platforms.
Petruska, Berek. Ingersoll. Valdivieso and Day
Vermilion 46-A is an unusual platform by modem standards, comprising two 20 pile (5x4)
jackets with one deck, installed end to end (giving 10 legs 4) in 1956 in 32 feet of water.
Six further legs were added following a blow-out in 1969. The structure was analysed
using KARMA (Section 4) as part of the Hurricane
survivallfailure investigation
(Puskar et al, 1994).
Table A2.5 presents the results for three principal wave directions based on environmental
conditions and the hydrodynamic loading recipe according to API RP 2A 20th Edition.
failure) are quite considerable (1.3 to 1.5)
The redundancy factors (ultimate
compared with typical values (1.2 - 1.3) for modem 8 leg jacket designs
et al,
are clearly attributable to the structural configuration. Detailed results in the
1994)
paper present the sequences of failure largely in the lower bay bracing and piles. The
foundation modelling was complicated by the oyster shell used to
the 60 feet deep
scour bowl caused by the 1969 blow-out. The uncertainty in foundation characteristics was
addressed with sensitivity studies to upper and lower bound assumptions as advocated in
Section 7.
Table A2.5
Reserve strength and redundancy for a 1950s vintage 46 leg shallow water platform
1
Base Shear for Wave Direction (kips)
25 year storm
50 year storm
t
I
I
year storm
I
First yield
End-on
1220
1335
RSR
1.20
Broadside
1470
1355
1615
I
1845
I
1235
Ultimate capacity
Diagonal
I
2060
I
1550
I
I
1650
II
1.11
1915
I
I
2910
I
The reserve strength ratios, in the range 1.1. to 1.4, are presented with respect to present
day
year criteria. These values low in absolute terms but may be considered to be
substantial when the original 25 year design premise is considered. The basis of comparing
must be re-emphasised here, as definitions are often used with respect to the original
design values (see Section 2).
Corresponding with the findings of
et
the authors note that waves impacting
the deck were found to contribute as much as 30% of the total platform loading under the
100 year storm.
The paper demonstrates the versatility of reserve strength technology to encompass a wide
range of offshore structural forms and evaluate structural safety. Calculations of the
probability of failure were demonstrated to be in line with the proposed requirements of
API RP 2A (draft 1993) for fitness for purpose.
Puskar, Aggarwal,
Moses and Petrauskas (1994)
The foregoing review of platform analyses in Section A2, formed part of the
JIP
reported in this paper. Comparison was made between survival, damage and failure
predictions, based on hindcasting and nonlinear ultimate strength analysis, and the actual
of 13 platforms.
The results were used to calibrate a bias factor to provide a general indication of the
accuracy in wave force and ultimate capacity procedures. Platforms were selected to
maximise the information about any bias. Those that survived but were predicted to fail
(or vice versa) provided more information than those that behaved as predicted. Overall
the database encompassed platforms installed between 1958 and 1991 in water depths from
61 feet to 468 feet. Jackets had 4 to 8 legs, with K, X and diagonal framing. Six of the
platforms had survived, three were damaged and four failed during Andrew. Failure of
multiple K joints was reported in all four of the failed cases and two in which damage was
reported.
Figure A2.2 illustrates the gap K joint failures observed in the BOMEL frames project tests
(Section 3; Bolt, 1995) and the above observation regarding in-service K joint failures
confirms the importance of understanding and modelling the ultimate and post-ultimate
responses. Furthermore the platform failure mechanisms generally involved some aspects
of foundation failure, again underlining the importance of appropriate modelling which was
often neglected in early pushover analyses (see discussion, in Section 6).
The results for all 13 platforms are reproduced from Puskar et al as Figure A2.3. In
addition to the description of failure modes, it can be seen that the ultimate capacity
loads for the hurricane ranged from 0.73 to 2.80, with reserve
compared with the
year load) in the range 0.58 to 2.28. Additional
strength ratios (in comparison with the
results given for one of the 8-leg platforms in the paper indicate a redundancy factor of
around 1.5 beyond first K joint failure to attainment of the peak load with hinging in the
piles.
Uncertainty was accounted for in relation to significant wave height, current and base shear
computations by designating a COV. In the latter case a greater COV (0.25) was taken for
the case of wave loads in the deck to reflect the greater uncertainty compared with direct
jacket loading (COV = 0.20). A log normal distribution for ultimate capacity was assumed
with a COV of 0.15. Probabilities of failure were thus calculated and the values in Figure
A2.3 relate to the case with no bias, b = 1.O.
Bayesian updating of the prior assumptions lead to a posterior bias distribution for all 13
platforms in the range 1 to 1.2 with a COV of 0.1. This may be taken to imply a
reasonably good, slightly conservative, industry capability in evaluating the hurricane wave
forces and ultimate structural capacities. Indeed the figures were used to justify the
acceptance of ultimate strength analysis within the procedures for platform assessment (API
draft, 1993).
Importantly, the authors point out that the database is small and the bias factors may not
be appropriate to any specific structure under investigation. It is postulated that multiple
analyses for many platforms with similar failure modes may lead to different bias factors
reflecting the uncertainty in specific aspects of ultimate strength evaluation.
Nevertheless the paper presents an important milestone drawing on the Hurricane
experience to validate the application of reserve strength technology.
van de Graaf, Efthymiou and Tromans
993 and 1994)
In these papers the authors bring together the results of a number of reserve strength
evaluations performed on the same basis for platforms in different environments. This
provides important insight to the dependence of RSR on the original design code and
platform location, as discussed in Section 6.
Tromans et al (1993) break down the sources of reserve strength beyond the original design
1984) for a range of Shell structures worldwide.
code into key areas (Lloyd and
The factors and their range of values for eight cases are:
explicit code safety factors - 1.25 to 1.42 on the effect of buckling lengths;
implicit safety in codes derived from lower bound interpretationof component data
- 1
to 1.3;
engineering practice, eg. non optimisation of members in some cases - values of
1.2 and 1.3 given;
other design requirements, eg. critical components designed by other wave attack
directions or load conditions - 1.26 to 2.39;
actual material yield strength and strain rate effects - 1.2 on 36 ksi steel and 1.15
on 50 ksi;
system redundancy, ie. ratio of ultimate capacity to first component failure - 1.0
to 1.3.
The system redundancy factors are also presented individuallyin Table A2.6 together with
corresponding reserve strength ratios for the five platforms.
The two Gulf of Mexico structures SP62-B ad SS274-A were reviewed in Section 5
(Figures 5.32 and 5.33, respectively). Platform SCS BNDP-B is located in the South
China Sea. Information on the analysis of Inde K in the South North Sea can be found in
Si Boon et al (1993). The
of the Tern North Sea platform using LRFD principles
is described in van de Graaf et al (1994).
Table A2.6
Contribution of system redundancy to the reserve strength of some platforms worldwide
Structure
RSR
SCS BNDP-B broadside
SCS BNDP-B diagonal
SP62-B
SNS Inde-K
NNS Tern end-on
NNS Tern broadside
NNS Tern diagonal
This table demonstrateshow first member failure may be synonymous with system collapse
whilst alternatively there may be significant potential for load redistribution
within the framing. The range of contributing factors means that reserve strength ratios
with respect to the original design basis vary from 1.91 to 3.78. Were a different
modelling or analysis strategy adopted (eg. in relation to material properties) there would
be a direct influence on the level of RSR calculated.
An important factor is the dependence of RSR on the original design basis. This was
highlighted in the original discussion (Section 6) and is illustrated in the paper for the Tern
structure. Different dead and environmental load factors in LRFD practice contrast with
a constant margin of safety in WSD. The authors compare the situations for loading in a
compression leg which governs the platform response for the diagonal wave attack
direction. It is demonstrated that RSR is related to the proportions of dead (P,) and
environmental (P,) loads for WSD and LRFD by the expressions.
RSR,
=1
+ 0.52
Eqn (A2.1)
RSR,,
= 1.83
+ 0.49
Eqn (A2.2)
in the range 1.6 to 0.4, these expressions
For dead to environmental load ratios
imply greater RSRs for an LRFD design by 11 to 17 over WSD levels.
In examining Table A2.6, the RSRs with respect to the original base shear design loads
are instructive but meaningful interpretation depends on an evaluation of failure
probabilities or some relation with the associated return period.
(1994) focuses on the Gulf of Mexico SP62-B, Southern North Sea Inde-K
Van de
and Northern North Sea Tern structures for this comparison. The best estimate
year
loads are denoted L,, and the ratio of the ultimate strength compared with 100 year loads
is therefore given by RSR
Table A2.7 presents the values of
for each of the platform locations together with
governing RSRs from Table A2.6. These lead to a much wider spread in reserve strength
ratios evaluated against present day 100 year criteria. Figure A2.4 presents these values
against the long term environmental statistics which demonstrate a lesser increase in loading
with the limited fetch of the Southern North Sea compared with the hurricane environment
in the Gulf of Mexico. These measures of reserve strength therefore imply significantly
different probabilities of failure as indicated in Table A2.7. Conversely for a consistent
safety margin (probability of failure) the required RSR in the Southern North Sea is less
than for the Gulf of Mexico (Efthymiou et al, 1994)
Table A2.7
Relation between reserve strength, probability of failure and environment
SP62-B
Inde-K
Tern
Failure rate
per year
RSR
Structure
0.63
1.09
1.86
2.38
2.47
1.91
1
2.69
3.55
Together these papers demonstrate by example the care that needs to be taken in
interpreting reserve strength ratios. The values may be dependent on the underlying design
code and basic assumptions in the ultimate strength analysis. Furthermore the interpretation
of RSR in terms of safety depends on the environmental and long term, loading statistics.
van Langen, Swee, Efthymiou and Overy
It was noted in the main review (Section 6) that many published analyses focused solely on
the ultimate capacity of structures without consideration of the foundation components of
the system. The importance of appropriate foundation modelling was emphasised.
The considerations are highlighted further by the analyses reported in this paper of a six
leg tower-type jacket structure supported by 32 piles in 143m water depth. The potential
interaction between structure and foundation at collapse was recognised. In addition it was
considered that uncertainty about the validity of the foundation model and values of the soil
parameters may be of the same order of magnitude as the uncertainty in environmental
load. Integration of these model and physical uncertainties is shown not to be meaningful
in terms of absolute measures of structural reliability. Instead uncertainties are quantified
through an expression of the confidence in predicted probabilities of failure, leading to a
clearer interpretation of structural reliability. The method demonstrates the need for
improved information on foundation behaviour, particularly in relation to large deformation
behaviour in ultimate strength analysis.
The paper therefore serves to underline the importance of foundation consideration in
reserve strength analysis.
Further discussion of the difficulties in determining appropriate soil parameters for
assessment is given by Kallaby et al (1994).
Vannan, Thompson, Griffin and
and Young
Bea (1995); Bea, Mortazavi, Loch
et al (1994) put forward a design approach to simplify the modelling of ultimate
system strength. Similarly Vannan et al (1994) have proposed so called "simplified
ultimate strength" analysis using an equivalent linear approach. Bea (1995) and workers
(Bea et al, 1995) continue to develop their simplified method which is now embodied in
software ULSLEA - Ultimate Limit
This method does account
for nonlinearity by applying the concept of plastic hinge theory and the principle of virtual
work to probable failure mechanisms. The lateral shear capacities of individual bays are
evaluated and compared with reference loadings.
In all cases the experience required of analysts to ensure meaningful reserve strength
predictions are obtained from nonlinear ultimate strength analyses are cited as motivation
for developing "simplified" methods. All agree that an accurate evaluation of system
capacity can only be derived from rigorous nonlinear analysis. However, the role of
simplified or rather 'alternative' approaches may be in providing insight regarding likely
failure mechanisms and a reference against which the validity of nonlinear reserve strength
predictions can be assessed. The benefits and limitations of these methods should therefore
be considered.
A3
API RP
SECTION 17.0 - ACCEPTANCE AND INTERPRETATION
OF SYSTEM RESERVE STRENGTH
As noted in the main report and this Appendix, the draft Section 17.0 to API RP 2A-WSD
admitted the use of ultimate strength analysis as part of the assessment of existing
and
1993) and
platforms. The draft was subject to wide industry consultation
et al, 1995) and following four revisions was prepared as an API white
validation
draft for comment (1995). However in April 1995 it was decided that the provisions could
be submitted for postal ballot without a formal draft issue and it is therefore anticipated that
the provisions of Section 17.0 (Section R in LRFD) will become part of API RP 2A in late
1995. Indeed, the Minerals Management Service have permitted its use in advance of
formal API balloting (Dyhrkopp, 1995).
Within Section 17.0 ultimate strength analysis forms just one part of the assessment
process. If fitness for purpose can be demonstrated on the basis of a design level analysis
or an elastic analysis with sources of conservatism removed, nonlinear analysis need not
be performed. However, the sources of reserve strength within the system revealed by
rigorous nonlinear analysis may be exploited in the assessment of existing platforms. The
approach is a significant departure from design practice embodied in API RP 2A to date
and the many difficult issues raised have been documented in a series of OTC papers by
et al; Kallaby
the Task Group, 92-5, which drafted Section 17.0. These papers
and
Turner et al; Kallaby and
1994) and
et al; Petrauskas et al;
et al, 1994) present essential background to the user of
the related BOSS paper
Section 17.0.
Of relevance to this review of reserve strength technology are the criteria for evaluating and
accepting ultimate strength assessments. They are particularly important because of the
definition of RSR employed and the specific loading regime adopted. The background to
these aspects of Section 17.0 is presented here, together with the results of background
analyses providing insight to representative jacket responses. The basis of acceptance
criteria is given and procedures for determining appropriate criteria outside US waters are
documented.
et al, 1994)
Definitions
Reserve Strength Ratio in API RP 2A Section 17.0 is intended to provide a measure of
platform reliability in a given environmental region. It is therefore defined in relation to
present day design loads, ie:
Ultimate Strength Load
API RP 2A 20th Edition
year design load
Eqn (A3.1)
In many earlier references covered in this review (see also Section 2), RSR was related to
the original design load and this important distinction should be noted.
Underlying Section 17.0 is the recognition that RSR comprises two distinct elements:
1. The change in design resistance and loads from the original design to the 20th Edition.
2. The system strength reserve beyond the maximum design elastic utilisation to the
nonlinear ultimate capacity.
These elements are quantified as follows:
Load Reduction Factor (LRF)
lobal load giving unity check of l to RP 2A 20th Edition
API RP
20th Edition 100 year design load
Note:
changes in design criteria need not result in a reduction, although this is the
case in US waters for which Section 17.0 was initially developed.
Ultimate to Linear ratio (ULR)
Ultimate strength load
global load giving unity check of 1.0
Eqn (A3.3)
et al (1993, 1994) in Section A2
As identified in discussion of work by van de
above, the sources of system reserve (ie. ULR in Section 17.0 parlance) can be clearly
defined. The factors and ranges of values embodied in Section 17.0 are as follows:
code safety factors ( l .2-1.3)
mean to nominal yield strengths (1.2 for mild steel)
system redundancy (1.O-1.3)
designer's prerogatives (unspecified)
strength provided for other criteria (unspecified).
These lead to minimum values for ULR in the range 1.6 to 1.8 and tie in with the
et al (1993). However, in other regions the contribution from the
findings of
different factors may vary, demanding that ULR be carefully defined at an appropriate
level.
It is then the combination of LRF and ULR (Equations A3.1 and A3.3) which leads to the
calculation of RSR:
RSR = LRF
ULR
Eqn (A3.4)
This procedure is clearly distinct from the definition of an RSR value per se.
Basis of Section 17.0 criteria
The approach to defining RSR, the criteria for ultimate strength evaluation, in terms of
LRF and ULR components only becomes apparent when the philosophy of assessing
existing structures in Section 17.0 is understood. The underlying premise is that an
installation may be fit for purpose even though it does not fulfil current standards for new
design (Cornell, 1995). By introducing consequence based criteria and considering
may
adequate performance to date, the cost and risk of strengthening or
be shown to be unnecessary. Indeed a consideration in drafting Section 17.0 was that
criteria should be experience-based and work underlying seismic requalification criteria
(Iwan et al, 1992) set an accepted US precedent.
On that basis the following examples for the Gulf of Mexico and other US areas illustrate
the derivation of specific RSR criteria.
Platform Classification
The process begins with identifying the risk level for an installation based on considerations
of life safety and potential (environmental) consequences of failure. Considerations of
platform economics and global risk management are left to the individual operator (Craig
and Miller, 1995). Table A3.1 illustrates the classification 'levels' in Section 17.0.
Table A3.1
Classification levels
Level
Description
L1
High consequence
L2
Manned but evacuated in extreme events, low consequence
L3
permanently manned
low consequence
Gulf of Mexico criteria
Platforms in the Gulf of Mexico are evacuated when there is a threat of hurricanes, so
environmental impact drives the most critical category. Level 1. Based on experience, all
47 platforms to have collapsed in hurricane conditions were designed to 25 year criteria
whereas structures designed to the 9th Edition of RP
where the 100 year hurricane
criterion was introduced, and beyond had survived. It was decided that acceptance of
existing installations should be measured against the satisfactory performance of these
platforms. In going back from the new environmental loading recipe in the 20th Edition
of API RP 2A to the 9th-19th Edition loads, a Load Reduction Factor of 0.65 resulted.
and the minimum ULR index of 1.6-1.8 presented above, give a target
This
RSR in the range 1.O-1.2 (eg.
1.2). Based on failure survival data from
Hurricane
(Puskar et al, 1994) the Task Group adopted a value of 1.2. Thus the
derivation of RSR is largely experienced based.
For other classification levels the same principles of setting acceptance criteria with respect
to present day (20th Edition) design practice and working through to an RSR (based on an
appropriate ULR for the platforms under consideration) were followed.
The RSR criteria were not based on calculated target probabilities of failure, although
subsequent evaluations confirmed that the reliability was consistent with expectations.
A final consideration in the derivation of Gulf of Mexico criteria was the large number
(some 3,800) of platforms in a small area. (Indeed the justification for the criteria was the
significant experience base on which to draw). In applying the assessment criteria it made
for different classification levels to environmental parameters
sense to translate the
corresponding to a
with respect to the target RSR. In less densely populated areas
assessment criteria are more appropriately specified as target values such as RSR.
Criteria for other US areas
This is illustrated in Section 17.0 for other US areas where the basic premise (in line with
US onshore codes) is to relax the target probability of failure by a factor of 2 with respect
et al, 1994).
to new design (ie. to the present day 20th Edition of API RP 2A)
De (1995) presents full details of the risk evaluation procedures which enable consistent
criteria to be developed. For permanently manned Level 1 structures in US areas outside
the Gulf of Mexico, the factor of 2 translates to an LRF of 0.85. Combined with a ULR
of 1.8, this gave a recommended RSR of 1.6.
It is important to note that ultimate strength analysis in Section 17.0 is intended to provide
an unbiased estimate of the ultimate response. It is not therefore intended that the present
year environmental loading profile should be incremented to a factor of 1.6 to
day
demonstrate that the RSR requirement is met. Instead the base shear corresponding to 1.6
times the 100 year base shear should be calculated and the corresponding realistic
combinations of wave height, wave period, current and windspeed determined (Petrauskas
et al,
Generalisation of RSR criteria
The relation between RSR, return period and environmental conditions in Section 17.0
criteria underlines the fact, as discussed in Section 6 and the review of work by van de
et al above, that a target RSR value cannot be applied in another environmental
region with the same implied reliability (Fisher, 1994 presents a mis-application of 'other
US' criteria to the Southern North Sea). The procedures given by De (1995) take account
of the relation between environmental parameters and return period and relate base shear
to a power of the wave height (hu) calculated for the region.
An additional benefit of evaluating specific environmental criteria to assess the ultimate
system response is the direct information regarding the potential for wave loading to impact
experiences (Imm et
1994; Petruska et
the deck. As noted in the Hurricane
1994) the structural response may be sensitive to these loads which can contribute
significantly to the global base shear, albeit with considerable uncertainty in the calculation.
The commentary in Section 17.0 presents a methodology for calculating lateral deck loads,
but for plated decks the vertical forces may be significant, requiring alternative calculation
methods.
Summary
In relation to reserve strength, the subject of this review, it is clear that Section 17.0
provides significant acceptance of the technology. However the definition of RSR in
Section 17.0 differs from that generally used in the literature to date. The inherent reserve
strength of a platform beyond its original design is more closely reflected by the ULR
(Ultimate to Linear Ratio) in Section 17.0.
Many of the key areas identified in Section 6 of this report have been addressed to some
extent by Section 17.0, for example:
Application of realistic loading profile
Importance of realistic joint and foundation characteristics
Dependence of meaningful reserve strength evaluations on environmental and
design code basis
Uncertainty and importance of wave in deck load calculations.
However the user of Section 17.0 must recognise the US basis of the original provisions.
For application outside US waters it is essential that sources of system reserve in
representative structures are evaluated to give appropriate
In addition the
acceptance criteria relative to new design (the LRF) must be revisited. Finally a rigorous
evaluation of risks with the consistency and methodology put forward by De (1995).
drawing on regional environmental criteria and base shear statistics is an essential prerequisite to the international application of 'Section 17.0' guidelines (Billington and Bolt,
A4
THE USE OF ULTIMATE STRENGTH ANALYSIS
TECHNIQUES
Two significant benchmark studies have been conducted since the recommendation was
made in Section 7 of this review. The first has been undertaken by the UK Health and
Safety Executive (HSE, 1993 and 1994; Nichols et al, 1994) against the SCI frame test data
(Section 3). The second, commissioned by the US Minerals Management Service (MMS),
combined the trial applicationof Section 17.0 with a benchmark analysis of a specified Gulf
of Mexico structure. The scope and findings of these studies are reviewed in this section.
HSE
993,
Nichols, Sharp and Kam
994)
In preparing this review (see also Billington et
1993; Bolt et al, 1993) the need and
potential value of providing to industry the opportunity to benchmark available techniques
for reserve strength analysis against the SCI Frames Project test data (Bolt, 1994) was
identified. HSE managed the benchmarking exercise with external support provided only
by the Marine Technology Support Unit (MaTSU). Together HSE and MaTSU assimilated
and interpreted the results, presenting their findings in late 1994 (Nichols et al).
Eleven organisations participated in the exercise. Each was provided with a data package
and
giving the frame geometries, loading and support conditions, section sizes
measured material yield stresses. Three base cases corresponded to Frames I, and
(see Figure 3.12 to 3.23). A fourth case specificed initial out-of-straightnessof braces and
locked-in stresses which had been identified as influencing the actual test results. The
structural responses of the various test cases (see Section 3) were:
Test Case 1 Test Case 2 -
Compression brace buckling
X joint failure followed by compression brace buckling with
significant portal action in frame legs
Test Cases 3 4 - Sequence of top bay compression brace buckling, load
redistribution and compression brace buckling in bottom bay.
In assimilating the results,
grouped the predictions into three response types:
Type 1 - Poor agreement missing key features of the physical response.
Type 2 - Moderate agreement - key response characteristic captured but inaccurate
replication of load redistribution.
Type 3 - Good agreement - key response characteristics and load redistribution
captured.
With this categorisation the graphs in Figure A3.1 bracket the results obtained, noting that
each line may represent a set of similar predictions. At first sight the predictions appear
to be inconsistent, however it is important to investigate and understand the sources of
difference. This cycle in learning and benefitting from the benchmark exercise has not yet
taken place and the following comments are made by the authors of this review based solely
on the published results in Figure A3.1 and without sight of the individual analysis results.
Nevertheless the following observations are made to help explain the sources of
inconsistency.
Test Case
As noted in Section 3, the yield capacity of the chord and buckling capacity of the
compression brace were similar in the test frames making the response characteristic very
sensitive to effective length selections. Information on the post-buckling capacity of
members is sparse (eg. Pike and Grenda,
and is influenced by many factors
including member slenderness, local buckling, out-of-plane deformations and material
modelling assumptions. It would appear from the results that the prediction of
buckling behaviour was a principal source of discrepancy.
However, it should be noted that the frame simplicity particularly highlights such
discrepancies. The frame test data therefore provide a valuable opportunity to explore these
influences and improve modelling practices. Whilst the load shedding characteristics are
less apparent in the overall response of a jacket structure, accurate modelling remains
important to ensure that loads are redistributed giving the correct sequence of subsequent
component failures.
Test Case 2
Response Types 1 and 2 merely indicate the absence of joint modelling in the analyses.
Code checks to API (1993) or HSE (1990) guidelines would have indicated the high
utilisation of a primary X joint. The conclusion is that the potential for tubular joint
failures must be considered in preparing structural analyses, given the potential significance
it may have on the global response characteristics.
By contrast, the achievement in obtaining results of Type 3 should be noted. The X joint
in Frame compressed to the extent that both braces came into contact across the joint as
shown in Figure 3.17. This enabled the pick up in load and subsequent buckling indicated
in the experimental and Type 3 responses. Isolated test data only reveal the initial yield
characteristic of the X joint but the benchmarking illustrates the need for careful monitoring
of component deformations in predicting the response of framed structures.
Test Case 3
Discrepancies between the results again reflect the different modelling of post-buckling
member capacities. Where the post-buckling capacity remains high insufficient loads are
transmitted into the bottom bay to precipitate the sequence of buckling.
The different load levels and deformations associated with the buckling in the Type 3
predictions compared with experiment, are attributed to the locked-in stresses and initial
imperfections in the test frame.
On the basis of this discussion of the responses in Figure A3.1, the differences between test
results and the predictive capability of software and users can begin to be explained. It
appears there may be only a few key features underlying the divergence in results. Firm
conclusions on the industry capability must await detailed investigation and quantification
of these effects by the analysts in open forum.
Puskar, lrick and Krieger
The MMS project encompassed two aspects, namely:
a 'trial' application of Section 17.0 from screening through to ultimate strength
analysis
A 'benchmark' ultimate strength analyses for a Gulf of Mexico platform.
Twenty-one organisations participated in the 'trial' and thirteen in the 'benchmark'.
BOMEL participated in both activities.
The trials encompassed 16 platforms in the Gulf of Mexico, two offshore Southern
California, and one in each of the Cook Inlet, Offshore Cameroon (West of Africa), the
North Sea (UK), the present authors contributing the
Bay of Campeche (Mexico) and
last two. The platforms were installed in water depths ranging from 37ft to
and had
been designed between 1957 to 1982. The number of legs ranged from 4 through to 36
with K, diagonal and X bracing in different cases.
Results presented in the paper supported the sequence of reducing conservatism through the
various stages of the assessment process and so endorsed the adoption of Section 17.0. The
trial results remain confidential to participants (PMB, 1994) and cannot be reproduced here.
Nevertheless, it is important to note that the analyses were used to verify the assumptions
regarding
(see Section A3) used in developing ultimate strength criteria in Section
17.0. In doing so any errors in modelling, or in software application were implicitly
embodied.
The benchmark platform was an existing 4 leg, 4 pile structure with 4 wells installed in
1970 in
water depth in the US Gulf of Mexico (Figure A3.2). The soil comprised
a soft to very stiff grey clay above a very dense silty sand layer below
Details of
the deck and equipment were provided as the wave crest reached the deck.
In relation to the resistance calculations, the average variation for the critical diagonal wave
attack direction was 23 % . The results are presented together in Figure A3.3. The majority
of participants (10) attributed failure to inadequate soil axial compression capacity for this
load case. The highest result, J, in the figure may be excluded as a linear representation
of the foundation was adopted. Similarly the lowest two curves are not being compared
on the same basis, the analysts having retained some simplified nominal values in place of
the mean capacity representation demanded in Section 17.0. With or without these results
included, the mean capacity prediction remains at 2100
although the COV drops from
23 to 16%. Note this latter variance corresponds with assumptions made in the derivation
of the assessment criteria (Puskar et al, 1994; De. 1995).
Potential sources of remaining discrepancy were indicated by analysts including:
use of static versus cyclic P-Y curves,
modelling of well conductors contributing to foundation capacity,
differences in modelling conductor support at the
These emphasise the need for consistent best practice in the performance of ultimate
strength analysis.
All the results from the study have been shared by participants in order that individual
practices may benefit from the programme. The results however remain confidential
(PMB, 1994) and cannot be reproduced here.
A5
CONCLUSIONS
The discussion and conclusions presented in the main review (Sections 6 and 7) remain
valid and may be read in conjunction with this Appendix. A number of additional points
may be made in relation to the developing application of the reserve strength technology.
Practitioners in operating companies and development organisations alike recognise the
complexities in performing ultimate strength analysis, as witnessed by the continuing
emphasis on simplified approaches to provide insight to the probable mechanisms of
et al, 1994;
et al, 1994; Bea, 1995). It is therefore
system reserve
important that industry knowledge and experience continues to develop and becomes
embodied in best practice guidelines such that the appropriate expertise leads to
meaningful results.
et al,
Benchmarking against test data (HSE, 1994) and comparative analyses
1995) provide an important vehicle to advance understanding of the technology but
depend on openness and cooperation between organisations for any benefits to be
derived.
Discrepancies between ultimate strength predictions should not be used to discredit the
technologies, but should underline the skill and capabilities required of software,
analysts and engineers both in interpreting results and in commissioning ultimate
strength evaluations. Furthmore due allowance should be made in the setting and
implementation of ultimate strength criteria to account for the potential variability due
to software differences and user selections or interpretations. Best practices should be
identified and carried forward and inadequate methods rejected on the basis of industry
experience and consensus.
Whilst Section 17.0 provides a framework for ultimate strength analysis in the process
of platform assessment, it is essential that the regional dependence, in terms of both
reserve strength and environmental loading, be recognised and efforts made to develop
criteria for the safe application of the technology worldwide.
Section 17.0 quantifies ultimate system responses in terms of a single deterministic
capacity measure, the Reserve Strength Ratio. The main review questioned the
sufficiency of RSR given, for example, the potential importance of deflection
serviceability limit states and sensitivity of ultimate strength predictions depending on
standard this
failure mode. With the progression of Section 17.0 to the basis of an
point should be re-emphasised and some account taken of the inadequacy of RSR as a
lone assessment criterion.
Reserve strength predictions for offshore structures depend on accurate data for
member, joint, foundation and fluid load parameters not only at the point of failure but
into the post-ultimate regime. Efforts must continue to obtain data representative of
the large deflection conditions within the constraints of the system and meanwhile
rational account must be taken of the modelling uncertainties.
Figure A2.4
The relation between reserve strength, environment and probability of failure
, --
.
I
Experimental
1
-2
0
0
0
0.05
0.1
0.15
0.2
0.25
Lateral displacement (m)
0
0.05
0.1
0.15
0.2
0.25
Lateral displacement (m)
03
I
0.3
Lateral displacement (m)
Figure A3.1
Classification of HSE benchmarking results against Frames Project data
et
I
Figure A3.2
Benchmark jacket structure
et al, 1995)
Figure A3.3
Load displacement predictions for the benchmark platform
et
1995)
Printed and published by the Health and Safety Executive
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6/96