OTH 92 365

A REVIEW OF THE ULTIMATESTRENGTH OF TUBULAR

FRAMED STRUCTURES

Authors

H M Bolt, C J Billington and J K Ward

Billington Osborne-Moss Engineering LimitedLedger House, Forest Green Road

MaidenheadBerkshire SL6 2NR

HSE BOOKS

Health and Safety Executive OffshoreTechnology Report

Crown copyright 1996Applications for reproduction should be made to HMSO

First published

ISBN 0-71 76-1040-3

All rights reserved. No part of this publicationmay be reproduced, stored in a retrieval system,or transmitted in any form or by any means(electronic, mechanical, photocopying, recording, or otherwise) without priorwritten permission of the copyright owner.

Thisreport is published by the Health andSafety Executive as part of a series of reports of work which has been supported by fundsprovided by the Executive. Neither theExecutive,or the contractors concernedassume any liabilityfor the report nordo they necessarilyreflect the views or policy of the Executive.

Results, including detailed evaluation and, where relevant,stemming from their research projectsare

published in the series of reports.

Backgroundinformationand from these researchprojectsare published in the seriesof reports.

CONTENTS

SUMMARY

Page

1. INTRODUCTION1 . 1 Background1.2 Objectives and Scope of the Review1.3 Development of the Review

2. DEFINITIONS AND PRACTICAL CONSIDERATIONS2.1 Reserve Strength 2.2 Design Procedures 2.3 Redundancy2.4 Residual Strength 2.5 Ductile Versus Brittle Responses2.6 Reliability Based Versus Deterministic Approaches2.7 Pushover Analysis and Cyclic Loading2.8 Treatment of Loads and Safety Margins in Reserve Strength Assessment2.9 Conclusion

3. EXPERIMENTAL INVESTIGATIONS3.1 Background to Test Programmes3.2 Comparison of Results3.2.1 Single versus two-bay plane frames3.2.2 Role of redundant members 3.2.3 K versus X bracing3.2.4 Effective length factors 3.2.5 Joint versus member failures3.2.63.2.7 Initial imperfections and the effects of scale3.2.8 Comparison with jacket structures3.2.9 Materials3.2.10 Conclusion

4. FOR PUSHOVER ANALYSIS 4.1 Analysis Methods 4.1 Member removal 4.1.2 Member replacement 4.1.3 Linear superposition - strain based4.1.4 Linear superposition - load based 4.1.5 Limit equilibrium analysis 4.1.6 Nonlinear collapse analysis software4.1.7 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 analyses5.1.2 Idealised 3D jacket analyses 5.1.3 Structural jacket analytical investigations 5.1.4 Jacket loading investigations5.1.5 Jacket hindcasting calculations 5.1.6 Reliability analyses5.2 Comparison of Results5.2.1 Quantification of RSR5.2.2 Bracing configuration5.2.3 Joint behaviour 5.2.45.2.5 Foundation modelling5.2.6 The role of comparative analysis

6. DISCUSSION6.1 Summary of Review6.1.1 Experimental results6.1.2 Numerical results6.2 Reserve Strength of Frames6.2.1 Background to evaluating reserve strength6.2.2 Redundancy beyond first member failure6.2.3 Alternative loadpaths and sources of reserve6.2.4 Relation between 2D and 3D structures 6.3 Reserve Strength Considerations for Offshore Jacket Structures6.3.1 Complexity of 3D jacket structures6.3.2 Modelling of jacket loads

Influences on RSR6.3.4 Role of tubular joint failures 6.3.5 Role of foundation failure 6.3.6 Cyclic loading effects 6.3.7 Accounting for damage6.3.8 Target system reserve 6.4 Calculation of Reserve Strength 6.4.1 Analytical tools for pushover analysis6.4.2 Validation

7. CONCLUSIONS AND RECOMMENDATIONS7.1 Conclusions7.2 Recommendations

REFERENCES

APPENDIX A REVIEW UPDATE AUGUST 1993 - MAY 1995Al IntroductionA2 Developments in Reserve Strength TechnologyA3 API RP 2A Section 17.0

- Acceptance and Interpretation of System Reserve StrengthA4 the Use of Ultimate Strength Analysis Techniques A5 Conclusions

A REVIEW OF THE ULTIMATE STRENGTHOF TUBULAR FRAMED STRUCTURES

SUMMARY

This review of the ultimate strength of tubular framed structures has been prepared for theHealth 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 isnow being applied to assure the continued integrity of installations beyond the design event in circumstances of extreme environmental loading or damage. A recent investigationhasconfirmed that an extreme event static pushover analysis generally suffices to demonstratea structure's resistance to the cyclic loading of the full storm.

This report draws together the results from published investigations and identifies keyfactors contributing to system reserve. It is shown that bracing configurations and relativemember properties are important influences. From the work presented, it is demonstrated that many jacket analyses embody simplifying assumptions, and features such as loadingasymmetry, joint nonlinearity, foundation interactions, global deflection criteria etc, areneglected. 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 indrawing comparisons between structures. Nevertheless, jacket examples are cited wherefirst failure precipitates global collapse. Other structures are sufficiently redundant tosustain loads well in excess of the design value, with collapse occurring only after asequence 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 reviewin 1995 a number of important developments have taken place in relation to both theunderstanding 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 ofactions 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 resistancesides of this equation so characteristic values are derived from the available data. Furthermore, safety factors are introduced explicitly to ensure that an 'adequate' safetymargin 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 andredistribute loads is neglected, giving an inherent 'reserve' capacity beyond the design event (typically the year return period storm wave). The risk of exceptional loading beyondthe 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 November1993 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. Atthe 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 theminimum criteria specified, component limit states less onerous than ultimate strength andoverdesign for non-structural requirements, may be considered as implicit sources ofreserve. 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.

Lloyd and (1984) present a discussion of these various sources of reserve andresidual strength but the focus of this review is on the important contribution of framebehaviour. 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 onthe 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 loadswhich cannot be economically designed for on an elastic basis (eg. seismic or accidentalloads). The risks of these are not negligibleand whilst traditional elastic design approaches might preclude economic structural solutions for all conceivable loads, it is essential todemonstrate that extreme events can be sustained without endangering human life or theenvironment.

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 extremeoverloading of the structure as a whole or from localised damage (eg. from impact). Ifalternative 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 individualcomponent failure capacities, in order to demonstrate integrity in the event of such extremeloading 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 ormay 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 thenonlinear 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 orin combination in jacket structures. The presence of alternative load paths within a panelensures 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 slendernessof the braces and redundancy throughout the structure. The hybrid structure (c) is nottherefore considered satisfactory in API RP 2A whereas for (e) failure of one member could be tolerated without structural collapse. Furthermore, the structural reserve depends on alternative load paths through other panels within the frame, (Figure aswell 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 loadin the horizontals between the panels. However, in the event of damage (diagonal bracesremoved), 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 determinethe minimum structural weight to achieve a desired residual capacity beyond primarymember failure. A simple linear programming technique was adopted. Elastic analysis again showed the face frame horizontals and diagonal plan framing in A to be redundantfor the applied loading regime, but in the event of a brace 'failure' these members provideimportant alternative load paths to distribute the forces efficiently down through the structure.

Since the 1970s experimental programmes have been implemented to provide data on thecollapse behaviour of frames (see Section 3). In addition to revealing the responsecharacteristics, the results enable reserve strength to be quantifiedand provide physical dataagainst 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; inothers, a simplified approach in which 'damaged' members are removed has been taken toevaluate 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 willbe useful in both the design of new structures and requalificationand assessment of existinginstallations.

It is on this basis that the Health Safety Executive commissioned BillingtonMoss 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 BillingtonOsborne-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 onlarge 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 testresults 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 toreserve strength. The information is largely deterministic, based on collapse tests or staticpushover 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 inenvironmental 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 wasexpanded 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 RPWSD 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 relationto industry's understanding of ultimate system strength and its application of the technology in the intervening period.

DETERMINATE

WEAKLY REDUNDANTSTRONGLY REDUNDANT

STRONGLY REDUNDANT

Figure 1Principal bracing configurations-adoptedin offshore jacket structures

'NO LOAD INTHESE MEMBERS

figure 1.2Alternative load paths through bracing

figure 1.3Alternative plan bracing to distribute loads in

2. DEFINITIONS AND PRACTICALCONSIDERATIONS

In assessing the ability of a structure to withstand loads in excess of the design load or tosustain 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 sustainloads in excess of the design value. Care should be taken in comparing alternative structural configurations with respect to the design basis safety factors andthe reserve strength definition adopted (see also Section 2.2). For example, in workingstress design (WSD) the ultimate platform resistance should exceed the design load by amargin equivalent to the required safety factor and reserve strength should perhaps only betaken 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 statisticaldata, 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 forfactors 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 isadequate 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:

Ultimate Platform ResistanceRSR = Eqn 2.2

Design Load

This is comparable to the Reserve Resistance Factor (REF) defined by Lloyd and(1984) as:

Environmental Load at Collapse (undamaged)REF = 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 platformbase 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 instancesthe 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 ensurethat the most critical case is identified.

Figure 2.1 illustrates the reserve strength of a test structure. The ratio of the peak loadsustained by the intact structure compared with the design load is the reservestrength.

2.2 DESIGN PROCEDURES

Concepts of reserve strength as noted above are inextricably linked to design criteria andit 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 ayear 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 bycomponent basis (ie. the utilisations are less than unity) the structure may be deemedadequate. Typical guidelines therefore address how the elements of a structure should beproportioned, 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 ofdamage 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 USwaters. The RP 2A commentary relates to the proportioning of members (and joints) toprovide 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 pickup substantial compressive loads to prevent the structure from "unzipping" maindiagonals 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 althoughthese 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 WSDacceptance criteria for components may be given by the following inequality:

Eqn 2.4

where R = characteristic ultimate resistance or strengthD = stillwater loads E = environmental loading due to wave, wind and current in the event of storm

conditionsF = factor of safety which varies with component and loading mode. (In

storm conditions given by E, a overstress is generallyallowed. 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 tothe 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 riskfor extensive damage to or collapse of the structure. Because these loads are large andtheir 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 loadswithout further collapse. The only quantified guidance given is that:

"Where a large characteristic resistance is unfavourable with respect to the safety, thecharacteristic capacity should be based on the 95% rather than the 5% fractile.The design resistance shall be with the material coefficient, set to 1.0, and,for the design of shells, a structural in accordance with Section 3.1.3.

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) makes reference in this context to papers by Lloyd and Moses (1982). 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 isattributable to the 'redundancy' of the system but it is demonstrated below that carefuldefinition of the term is required.

In conventional deterministic structural engineering, redundancy is generally equated to thedegree 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 notsatisfactory for evaluating the ability of a structure to withstand overloads in the intact ordamaged 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 strengthwas developed. They present the hierarchy reproduced in Table 2.1 to demonstrate thegradation 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 2.1Member redundancy hierarchy for indeterminate structures given by Lloyd and

MemberRedundancy

LevelMember 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 liveweight load conditions.

A member whose failure leads to progressive collapse for a limited set of load conditionsthat include dead and live loads in combination with some fraction of the designenvironmental load.

A member whose failure leads to progressive collapse for a limited set of load conditionsthat include dead and live loads in combination with some multiple of the designenvironmental load.

A member whose failure has effect on the design strength, but whose presenceenhances 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. amember.

In 1979 Marshal1 proposed two alternative measures of redundancy. For simple systemswith a number of identical parallel load carrying elements a redundancy factor (RF)was defined as:

Values of RF less than unity therefore imply a high likelihood that initial failure will leadto 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

For more complex structures where is not directly available, the effect of damage isestablished by comparing the results of structural analyses for the intact and damagedstructures. This will be illustrated in examples presented in Section 5.

In later work by et al (1988) another definition of redundancy, again denoted RF,is defined as:

Ultimate structure resistance RF = 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 betweenredundancy and system reserve. Use of this measure of redundancy, RF, will bedemonstrated in the presentation of specific results which follows. Caution in determiningfirst 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 extremefibre conditions, or otherwise might be linked to buckling and a loss of a componentcapacity. Recent use of the term 'System Redundancy Factor' (SRF) hasreferred to first major member failure, to avoid reference to early failure of a secondarycomponent which plays no part in the overall system response. It should be noted that insome instances first component failure may not necessarily be related to a member andtubular joints and foundations may need to be considered.

In the jacket study by Nordal et al (1988) probabilistic measures were introduced andadditional consideration of these is given in Section 2.6. Taking and respectively,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-path to the most-likely-to-fail-first-member which is easier to obtain thanthe combined probabilities.

On the basis of the various redundancy measures proposed to date it is difficult to drawgeneralised 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 outof 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 thereviews that follow.

2.4 RESIDUAL STRENGTH

The concept of residual strength is particularly important in assessing the capacity of astructure which has been damaged, be it due to accidental loading, fatigue, fracture orextreme environmental loads. Lloyd and (1984) define residual strength in termsof a Residual Resistance Factor (RIF) given by:

Load Collapse= Load

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 teststructure. The remaining capacity once a component has failed compared with the peakload 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.

The term robustness is also used by to compare the post-ultimate andultimate system strengths as a measure of resilience or a structure's ability to dissipateenergy 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) andperforming a new analysis. If adequate data are available the latter approach is to bepreferred 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 alocal 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 ofloading, component failure and redistribution, as removing members and repeating the analysis from the unloaded state may not yield the same load distributionand hence ultimate response.

2.5 DUCTILE VERSUS BRITTLE RESPONSES

In the context of overall structural performance, the terms 'ductile' and 'brittle' are usedto identify the stiffness characteristics of the responses. If the global capacity is maintainedor 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 reduced residual capacity is described as semi-brittle. Marshal1 and Bea forexample, use the terms further in the descriptions of 'brittle-redundant' andredundant' structures and responses.

Concepts of ductility and brittleness lead on to considerations of reliability, ie. if twosystems 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 andtension members are denoted C and T, the applied load is Q and the member load F. Iffailure occurs in a K brace the load path through the panel is lost - the tension andcompression 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 carriedthrough the panel via the tension brace. So long as the stiffness of the tension braceexceeds the rate of unloading from the compression brace, the panel as a whole can takeincreasing 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 compared with (an order of magnitude lower) for the X bracing. It may also beconcluded 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 orimpact. Ductility is an important property for consideration of energy absorption. Aductility ratio is used to characterise plastic deformation capability and is the ratio of totalavailable deformation to initial peak elastic deformation (see Figure 2.5). Energyabsorbtion capacity is equivalent to the area under the curve for thestructure 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 staticpushover analysis, using specific nonlinear software, to evaluate the peak and post-ultimatecapacities 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 asvariables with known or assumed distributions. Simplified structural assessments areperformed to identify 'important' sequences of component failures, ie. sequences which have a high probability of occurrence. The results are generally presented in terms of either the probability of occurrence, P, or the safety index, The two measures may beconsidered 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. Thereason 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 thedesign 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 themodels and the real situation needs to be reviewed. For an extreme storm the environmental loading is cyclic, imposed on an underlying dominant direction. Themaximum 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 needsto be considered. Low cycle-high stress fatigue from either the same or different events is the subject of work at SINTEF et al, 1991) where the effects of shakedown were initially studied using nonlinear FE analysis. Results published in 1993, based on studiesof North Sea jackets, suggest that an extreme event static analysis generally suffices todemonstrate 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 ofsystem capacity. Without this work significant questions regarding the applicability ofultimate 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 models developed for nonlinear collapse analysis program USFOS are covered 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 beconsidered 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. Thesequence 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 thestorm, thereby ignoring short term effects. Were these taken into account, it is shown thatthe second and subsequent waves in the storm would be smaller than those given by thepseudo-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 staticpushover 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 inthe absence of wind. et al report the ratio between reverse and forward loads to bein 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 lowcycle fatigue does not necessarily trigger global instability, although this may followfurther cyclic loading. Incremental collapse occurs as loading cycles impose significant overloads, continuously exceeding the elastic recovery until the excessive deformations lead tostructural collapse (FigureShakedown imparts a linear (desirable) characteristic to the subsequent response of thestructure. It is associated with moderate overloads whereby the structure yields less and less with each loading cycle (Figure until the elastic state is achieved. This 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. thedivide 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 therepeated action of extreme waves, or whether shakedown can satisfactorily occur. Basedon 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 RESERVESTRENGTH 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 reservestrength. 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 maybe considered illustrative:

a. An existing jacket structure, for which, for various reasons, some existing components fail to meet current code criteria for the year design condition.

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 maybe 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 thecomponents changes and the effect will vary with water depth, platform geometry andbracing 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 betaken and Edwards, 1992). Alternatively, all loads could be increased by aconstant 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. Norwegian Petroleum Directorate limit state criteria require a load factor of 1.3 with

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,pushover analysis should be undertaken with stillwater loads factored by 1.15 andenvironmental loading increased to a factor beyond 1.5 (ie. = 1.15 1.3).

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 yearwave giving a notional failure probability of et al, 1993).

A further consideration in reserve strength analysis is the confidence level in the accuracyof 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 littleopportunity for benchmarking of different software packages against representative testresults 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 tothis 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 factorthe design wave. Instead a meaningful prediction of the loads is required which may forexample 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 besignificant 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 andminimum 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 safetycombination) and type of analysis (screening, design level or ultimate strength).

The importance of dynamic transient loading effects on the ultimate response of offshorejacket structures can be demonstrated by deriving an appropriate modification factor. Beaand Young (1993) separate imposed 'loadings' and 'loading effects' which are determined by performance characteristics of the structure-foundation system. Based on comparativeresults 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 separateconsideration of the dynamic load and effects.

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 mechanismsof load shedding and redistribution to be modelled analytically. In practice however, if theenvironmental 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 complexand 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 beconsidered. 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 orequipment 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 CONCLUSIONIn this section some key considerations in evaluating the reserve strength of jacket structures have been introduced. Their simple definition has been shown to be complicatedby 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 adoptedwherever possible.

Reserve strength ratioultimate load at collapse

RSR =design load

Redundancy factorultimate capacity RF =

capacity at first member failure

Residual resistance factordamaged structure capacity RIF =

ultimate capacity

Eqn 2.12

Eqn 2.13

Eqn 2.14

Responses are described as brittle when the overall load deflection curve for the structureexhibits 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 toinvestigations 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

8 CAPACITY OF OAMAGEO FRAME

FRAME DESIGN LOAD

Measured response

GLOBAL FRAME DISPLACEMENT

Figure 2.1Definitions of reserve and residual strength

FIG.FRAME CONFIGURATIONS NOT MEETINGGUIDELINES

CONFIGURATIONS GUIDELINES

2.2API guidelines for ductile configurations

MAX.CAPY.

I IDEALLY DUCTILETENSION MEMBER

YIELD

BRITTLE FAILURE

AXIAL STRAIN

Figure 2.3Ductile and failure modes (taken from and Bea)

F

K-BRACE

X-BRACE

X-BRACE

TENSIONMEMBER

COMPRESSIONMEMBER

DISPLACEMENT(NOT TO SCALE FOR

Figure 2.4Series and parallel K- and X-bracing analyses and illustration of X-bracing reserve

(due to and

DUCTILITY RATIO

IID 20 3.0

(INCHES)

Figure 2.5Ductility ratio quantifying plastic deformation capacity based on Gates et

100-year loading Extreme storm loading 100-year loading(or storm loading)

Figure 2.6Environmental load history for cyclic assessment due to and Tromans

Load Low cycle fatigue fracture

yield global

a) Low cyde fatigue

Load ,Single wave

yield deformations

Deck displacement

b) collapse

Load

Initialyield

Shake down state (elastic)

displacement

c) Shakedown

Figure 2.7Failure and survival modes under cyclic loads et

3. EXPERIMENTAL INVESTIGATIONS

A number of experimental programmes have provided physical data on the reserve andresidual strength of tubular frames representative of offshore jacket structures. Not all the tests reported here were undertaken for this specific purpose, nevertheless relevant data (forexample 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 bya comparison and discussion in Section 3.2.

In evaluating the reserve strength of test specimens, the allowable loading for ato 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 teststructures but differs from the evaluation of offshore jackets. These are designed for arange of loading scenarios and components are sized to give elastic utilisations less thanunity in all cases.

Furthermore, test investigations generally identify exact member properties in terms ofdiameter, wall thickness and material yield stress based on tensile coupon test results. Inthe 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, testspecimens are loaded slowly and the results from static tensile coupon tests are morerelevant than from conventional dynamic testing. Material grades at the scale of testingmay differ and the associated distribution of yield stresses may not be the same. SimilarlyERW pipe is often adopted but is annealed after delivery, the minimum specification wouldtherefore not be an appropriate reference.

Caution should therefore be exercised when comparing ultimate strength evaluations for teststructures (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 presentationof the experimental programmes begins with the simplest, single bay two-dimensional (2D) frame and continues, generally with increasing complexity, to the three-dimensional (3D) test results.

The scope of the various experimental programmes completed to date, and their order ofpresentation here, is summarised in Table 3.1.

3.1Experimental frame test programmes

Principal Reference

Briggs and Maison (1978)

Ogawa et (1987)

Grenda et (1988)

BOMEL 992)

Popov et (1980)

SCI (1990)

BOMEL (1 992)

Paik and Shin (1990)

Inoue et (1984)

Soreide et (1987)

Test Frame Configuration

single-bay, X-braced

1 bay trusses (3 trusses)

single bay, K-braced

single bay, K-braced

single bay, X-braced

two bay, X-braced

2D, two bay, X-braced

two bay, K-braced

two bay, X-braced

single bay, X-braced

- member failure (4 frames)

- joint failure (4 frames)

- member failure (2 frames)

- member failure (2 frames)- failure (2 frames)

-joint failure (2 frames)

member failure dented member failure

- member failures frames)- not tubular connections

fracture failuredented 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 wasbraced (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 testresults 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 carryingcapacity. 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 ofthe 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 sustainedload at the yield plateau. The legs acquired the load shed by the compression brace andenabled 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 weldshrinkage may have precipitated the tensile yield prior to compression buckling isdiscussed.

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 oftension 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 etCyclic tests were carried out on planar tubular trusses as shown in Figure 3.2 withdiameter 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 allcases, 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 overlappingjoints in A-3 contrasted with the gap joints in A-l . Member buckling was the cause offailure 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 bylocalised 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 compressionbrace 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 respectsidentical and the overall load-deflection responses may be contrasted as yielding of thetension 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 precipitatinga 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 thecapacities of the otherwise similar specimen A-l .

Table 3.2 compares the maximum load sustained with the load at which the critical bracebuckled.

Table 3.2Comparison of reserve strength for different

Failure Mode

Brace 3 buckling

Brace BucklingLoad

119.6

133.9

131.0

142.3

182.4

Specimen

A-l

A-2

A-3

B-l

B-2

C-l

Brace 3 buckling

MaximumLoad

127.5

137.3

145.1

168.7

197.6

-83.8

Brace 3 buckling

Brace 2 yielding

Brace 3 bucklingBrace 2 yielding

Brace 2 buckling

It can be seen that the stockier members in the shallower B series trusses ensure that thestructural response is more ductile. There is additional reserve beyond first member failurebefore 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, K-braced, 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.

In all four tests the ultimate frame load (given in Table was governed by compressionmember 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, thelateral 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 deformedfar enough to mobilise the portal strength of the legs which gave a residual strength some two thirds of the peak value.

Table 3.3K-braced frame configurations and capacities

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 onK 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 andthus the overall capacity of the test frames, were calculated from the measured curvaturesof the member. Details of the compression member responses are given in Table 3.4.

Maximum appliedframe load

170

168

157

175

Testnumber

1

2

3

4

Table 3.4K bracing behaviour in test frames

Overlap K jointconfiguration

0.156" Can

0.432" Can

0.432" Can

Can

I-- Measured axial capacities - K brace compressiondiagonal

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

Frametest

1234

Brace yieldstress

54525251

Out of planek-value (5)

.63

.61

.57

.81

.77

.72

.67

Peak braceload (ksi)

112116112116

Peak brace

.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 thecompression members, appeared from the curvature measurements to be nearly fixed at thebrace to leg joint and between fixed and pinned at the K node. Hence the measuredeffective 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 hadbuckled. 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 fewpercent 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 bynominal 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 ERWtubulars used for the test frame. These precipitate earlier failure in response to appliedloads and invalidate the comparison with the API RP 2A design provisions which implicitlyassume steels of typical offshore grades and characteristics.

BOMELWithin 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 tocollapse. 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 displacementcontrol at the top of the frames and the supports were pinned at the base. Frame isshown prior to testing in Figure 3.6.

Table 3.5Details of BOMEL's single bay K-braced test frames

Frame Critical JointP

= diameters= chord

Test Objective

Critical gap K joint to investigate capacity variation between isolated and frame mounted joint failures. K joint failure to compare with previous critical X jointframe tests.

Critical gap K joint with lesser to compare withresponse of Frame VII.

Critical lap K joint to compare ultimate frame responsewith gap failure.

Critical gap K joint with wider gap to compare with response of Frame and complete investigation oftypical K-braced frame configurations.

= diameter == brace-chord angle

The global responses for the K-braced frames are presented together in Figure 3.7. It canbe 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 critical joints calculated allowing a overstress, with the peak brace loads transmitted inthe 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 'componentRSR' of 2.89. On the basis of this 'reserve' implicit within the component design, it isexpected that the load sustained by the frame in the test would exceed the design value as a result.

Table 3.6Comparison of component and frame capacity reserves

Joint Frame Frame

For the bracing and vertical legs of the K-framed tests, simplified assessment of axialloads equates the design frame load to the design load for the component. On that basisthe Frame design load to API RP 2A is also whereas in the test the peak frameload was giving an RSR of 3.25, exceeding the component value. However, as 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 theultimate frame response an alternative assessment is proposed. It is the frame RSR beyondthe component conservatism which reflects the frame contribution and in percentage terms this is given by

VIII

IX

X

Frame RSR - Component 'RSR'Frame RSR

API RSRJoint Frame

For Frame the percentage frame contribution is therefore (3.25 - 2.89) 10013.25 =11.1% as shown in the final column of Table 3.6.

%ageFrameContribution

144 202

192 210

298 318

105 185

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 bayK 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) andthe HSE Guidance Notes (1990). These arise due to factors such as different source databases, the chosen lower bound or characteristic philosophies and definitions of firstcrack 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 4.28would become 2.06 and 2.43 if HSE Guidance were the base. This difference isattributable 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 robustmeasure of system reserve.

416 468

375 425

562 621

381 449

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 theportal action is utilised in the regime to enhance the overall capacity.

I

2.89 3.25

1.95 2.21

1.89 2.08

3.63 4.28

11.1

11.9

9.1

15.2

By contrast, the overlapping joint in Frame IX failed in an unexpected mode, with localbuckling of the brace wall at the compression intersection (Figure 3.10). The jointremained 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 theimportance of a proper understanding of tubular joint behaviour within the confines of aframe for structural collapse predictions.

Popov etThe 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; Popov et 1980; Zayas et al, 1982; Popov et al, 1985). Two tests (Frames 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 sectionbecause of the uncertain influence of the development of plasticity on the peak load.Nevertheless the influence of component slenderness on the response characteristics isinstructive. Table 3.7 presents the yield stress values based on tensile coupon tests andsection sizes from which the relative slenderness of Frame I compared with Frame isevident. In the tests this was manifested in earlier and more severe local buckling andtearing failures in Frame I whereas Frame was able to maintain its capacity for a greaternumber of cycles and attain a larger lateral displacement thereby absorbing more energy as required under seismic loading.

Table 3.7Tubulars used in frames tested under loads at University of Berkeley

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 loadapplication 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.

Member

Top bay X-bracing and

Bottom bay X-bracing

X-joint cans

Legs

SCIThe 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 hinged. Frames I and were designed for member failure. The horizontal brace was 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 thecompression 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.

Frame I

D (mm) T (mm)

2 48

114 5 42

150 3 48

320 7 45

Frame

D T (mm)

3 33

130 3 24

150 5 33

320 9 34

Yield

250

250

250

320

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 testedby Grenda et al. Stub column tests confirmed that the annealed tubulars gave a distinctyield 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 3.8Details of SCI two-bay X-braced test frames

Frame I

Critical Components

Critical member18.7,

Critical X joint1.0

Critical member18.7,

Critical X joint

Test Objective

To investigate load shedding and redistribution in X bracingassociated with compressionbrace buckling.

To investigate load shedding and redistribution associated withcompressionX joint failure.

As Frame I but without mid-height horizontal to investigate therole of redundancy.

As Frame but with fatigue cracks at chord-sidesaddle of Xjoint to quantify influence on frame response.

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 thecritical 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 ofsubsequent 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 reducedwith the onset of tensile yielding. This can be seen from the forces recorded by theintegral 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-inpre-tension from fabrication (see also Briggs and 1978).

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 thein-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 thedamaged 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 damageor overload.

The comparisons between the design 'storm' loads that it is calculated the component andframe 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. In fact, for the 1.0 X joints in Frames and IV the API and HSE provisions give almost identical capacities. However, for the general situation it should be noted that theRSR calculated depends on the validity of the base formulation for predicting component capacities.

peak in joint response + see text for discussion

Table 3.9Comparison of component and frame capacity reserves from SCI tests

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. Anyincrease 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 inconjunction with the BOMEL K-braced frame test results.

Frame

I

IV

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 andtensile 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 whichcompression buckling occurs. In this case it is not therefore appropriate to evaluate theframe contribution with respect to this 'apparent' component capacity.

This may not be representative of offshore structures where the welds, degree of constraintand therefore shrinkage differ from scaled test structures. However, understanding this influence, the contribution of X bracing action can be revealed. First yield occurs betweenScans 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 peakload to the frame load at first failure Scan 8 is 1.10, giving a measure of the redundancy factor et al, 1988) due to the frame action.

Frame

API design loadCriticalComponent Frame

409 579

195 276

395 559

200 284

Frame was the first frame in which a joint was the critical component. The top bay Xjoint can was of similar thickness to the brace but had a higher yield stress. In all otherrespects 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 notapparent 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 1 1. 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.

Peak Load

Component Frame

693 922

1080

514 782

952

RSR

Component Frame

1.69 1.59

2.03 3.91

1.30 1.40

1.95 3.35

%ageframecontribution

+NIA

48.1

7.1

41.8

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 ofthe 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 ofload 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 demonstratesthe 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. Bothcompression joint failure and tensile yield are ductile modes of failure without rapidreductions 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 newstiff 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 thebraces. 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-bracedframes (BOMEL) in which first member failure triggers frame collapse. It should be notedthat 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) andmight be omitted in practice to reduce structural weight. The implications of reducedredundancy 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. Withthe 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 baytension member began to yield and the bottom bay compression member buckled withincreasing displacement at Scan 1 1 . Figure 3.22, looking down the top bay compressionbrace, 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 thebottom bay, reduced the residual frame capacity below the design storm load. Figure 3.23compares the Frame I and Frame results. Larger imperfections and compressivein 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 thedifference 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 becamevisible, there being relative displacement between the fatigue crack faces as the brace-sidecrack face slid under the chord side. The X joint response is shown in Figure 3.25 fromwhich 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 (Figure3.26).

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 betweenthe 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. Hadthe crack been oriented differently the effect may have been for fracture to occur earlier with a rapid reduction in capacity and with less action having been mobilised tocontribute to residual capacity.

BOMELIn 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 3.10Details of BOMEL two bay X-braced test frames

Critical Joint Test Objective

Repeat of Frame to investigate unexpected behaviour andcapacity of compression X joint in that test.

Frame V with reserved X joint to investigateultimate frameresponse 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 amultiple of 3.1 on the design load. The global response was ductile again indicating thatthe 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-deflectionresponse 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 tensionloaded 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 thetension path through the joint softened, and this contributed to the yielding and gross plasticdeformation 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 frameaction on redundancy in comparison with the K-braced frame responses in Figure 3.7. Asthe 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 1.0tension 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 intension, 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.

Peak load based on deformation limit and capacity for locked-in

1Comparison of component and frame capacity reserves

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 differences between API and for tension joints and these are manifested in RSRs of 6.58 compared with 3.72. However, isolating frame action by comparing the global andcomponent RSRs in both cases, reveals a consistent contribution of some 20%.

Code

API RP

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

Design storm load Joint Frame

85.9 120

152.3 212

The influence of damage within plane and space frames of K-braced configuration wasinvestigated 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 bracemembers are 60mm OD by WT tubulars with OD by WT tubularlegs. The respective yields are 319 and 286Nlmm2. The K joints were stiffened "by rigidbody" rectangular box sections to protect against local joint failure.

Three plane frame tests were undertaken and the results, in comparison with the ISUManalytical predictions, are shown in the top part of Figure 3.33, where:

Peak Load Joint* Frame

455 789

455 789

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.

RSRJoint Frame

5.30 6.58

2.99 3.72

P-RC Frame with member completely removed (assumed to be the member damaged in P-DC above).

%ageframecontribution

19.5

19.7

The tests were run under displacement control applied at per second. Nodescription of the tests is provided (Paik and Shin, 1990) although the load-deflectionresponse 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 thedamage 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 onethird 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 upwhich cannot be defined but may invalidate reference to API RP 2A provisions. For thisreason the calculated are not reported in the summary tables at the end of Section 3 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 givinga gradual softening characteristic although no description is given in the paper. In thespace frame, with greater redundancy than the plane frame, the removed member hasrelatively less influenceand despite contributing to a reduction in overall stiffness the S-RCanalysis gives a reasonable representation of the performance of the damaged structure.

lnoue etThe effect of a horizontal brace on the performance of X-braced tubular frames was studiedin 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 nottube-to-tube welded connections as used offshore; instead brace members were welded togusset plates attached to the chord. This method of attachment gives fixed end conditionsin 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 thefirst half cycles are of relevance here.

The two dimensional frames were loaded in-plane, whereas the space frame was loadedacross 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 thecompression 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 dominatedlargely 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 theoverall load-deflection response. Nevertheless in the absence of horizontals the peak loadwas about 10%less than in the fully braced case. Direct comparison with the 2D tests isnot possible because of the re-orientation.

Tests (Soreide et all

Two X-braced three dimensional frames were tested by SINTEF to ultimate load as shownin Figure 3.35 a and b. Load was applied along the axis of member EF whose wallthickness was increased accordingly to obviate buckling. The frames, denoted S1 and S2,had different ratios and brace slendernesses and in both cases the joint cans werethickened to ensure member failure dominated.

Soreide et al (1986) presented USFOS (analytical) predictions for the frame responses inadvance 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 testprogrammes 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 appliedload of about At that point member IF, which was at yield, fractured, due to lackof 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 inmember JG at joint J precipitating another abrupt decrease in load bearing capacity. At thispoint 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 bucklingoccurred first in member EI. A small local dent (about 2mm deep) had been introducedin this member during transportation which, given its ratio of 63, was vulnerable to 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 ofstiffness 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 5.23it appears that the frame sustained a load around (slightly higher than predicted for the perfect structure), giving an apparent RSR of 3.3. However, it is likely that theSoreide predictions were based on nominal material properties and dimensions whereas other tests have been interpreted on the basis of actual properties. Furthermore the basisof 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 range are similar in both initial analytical prediction (Figure 5.23) and test.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 indicated a peak load of achieved at around 40mm deflection, whereas in the presence of the dent the ultimate load was associated with a deflection of someIt 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 acceptabledeformations to be associated with the RSR. Figure shows the comparison betweenthe '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 theinformation given in particular references. Comparisons are made in the sub-sectionswhich follow.

Single versus two-bay plane framesSingle bay test structures enable the reserve strength due to portal action in the legs andalternative 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 roleof 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 theultimate 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 membersin the Grenda and BOMEL tests been larger, the reserve capacity would have beengreater. For this reason comparison between different frame test programmes inquantitative, 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). Inthe two-bay structures the impact of load redistribution on other parts of the frame isdemonstrated. Both SCI and Inoue tests show that beyond first buckling in acompression 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 intowhich the member frames. In the latter case the load is distributed between K and Tbranches. However, in the absence of a midheight horizontal all load is shed via thecompression 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 memberwhich 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-ultimatecapacity is much greater.

K versus X bracingComparison 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 tothe 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 andtherefore 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 thelength 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.

On this basis direct comparison of for X and K frames is not meaningful. Theimportant point demonstrated is that the X framing offers an additional source of reservestrength over and above K action. This is reflected in the recommended bracing forframing of structures in earthquake regions embodied in API RP 2A (Figure 2.2).

Tab

le3

.13

Sum

mm

rese

rve

stre

ng

th (

Par

t1of

3)

FAIL

UR

E M

OD

E

RE

FER

EN

CE

Bri

ggs

Mai

son

Oga

wa

et

et

BO

ME

L

ofex

per

imen

tal i

nve

stig

atio

ns

of

LO

AD

-DE

FLE

CT

ION

SYST

EM

RE

SER

VE

RSR

%fr

ame a

ctio

n

NO

TE

S

Rel

ativ

ely

larg

e le

gsSi

gnifi

cant

port

alac

tion

Buc

klin

g in

sens

itive

toch

ange

sin

chor

dat

Kjo

int

MO

DE

3.1

3S

um

m

RE

FER

EN

CE

SCI

BO

ME

L*

and

Shin

ofex

per

imen

tal i

nve

stig

atio

ns

ofsy

stem

rese

rve

(Par

t2

of31

LO

AD

-DE

FLE

CT

ION

SYST

EM

RE

SER

VE

RSR

V3.

16.

58A

PI3.

72

%fr

amea

ctio

n

NO

TE

S

Litt

le in

form

atio

n in

pap

er.

Hea

vily

stiff

ened

join

ts.

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 3.14Comparison of measured and code effective length factors and Grenda et

Source

SCISCISCISCI

GrendaGrendaGrendaGrenda

X-braced Frame I X-braced FrameX-braced Frame X-braced Frame K-braced Frame 1K-braced Frame 2K-braced Frame 3K-braced Frame 4

Effective length factor

Measurednode to nodeout-of-plane

API RP 2AK factor

API RP 2A/measured

I ) X joint when member failed giving2) Significant initial imperfection in-plane driving failure 3) In plane value corresponding to dominant failure mode

Aside from the experimental uncertainties noted, a consistent view of measured effectivelength 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 effective length factors have to be specified by the analyst (see Section the importance of good data for reliable structural collapse load predictions is clear. A dependence oncode 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, fracturegenerates 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 maysustain 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 thecompression 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 framecan 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, ensurethat the frames have a high reserve strength when ultimate capacity is compared with design based on brace loading through the joint.

Ductile joint behaviour can be beneficial in terms of system reserve strength, despitecurrent 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 oneload path, load may still be transmitted via the alternate diagonal (as demonstrated byFrame IV of the SCI tests), depending on the degree of damage, for example,associated with tensile cracking.

3.2.6 2D versus 3DThe degree of reserve that can be exhibited in the 2D tests is limited compared with 3Djacket 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 asreserve 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. TheSINTEF 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 boxframe showed how defects can compromise capacity. The presence of the defect may havebeen 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 newoffshore structures where quality control is particularly stringent. However in an overloadsituation a jacket may contain small fatigue cracks due to the service history and these maycompromise the reserve strength in a similar way.

The Briggs and Maison test was unusual in that compression brace buckling was not abruptnor 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 beassociated with a locked-in pre-tension. Such locked-in forces would clearly depend on thefabrication sequence, but from Figure 3.1 it may be postulated that the large frame legs andtop and bottom would be welded prior to introducing the braces. Having laid thebrace-leg welds, cooling and shrinkage would occur, with deformations restrained by thelegs such that a locked-in pre-tension would develop.

A similar fabrication sequence was adopted by the fabricator for the SCI frames (Figure3.12). 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 orcompressive depending on the fabrication sequence), it can be shown that both the failuremode and load may be influenced. However, the root gap in jacket structures may be ofthe order of but in a test structure this cannot be scaled in proportion with the global geometry as a minimum gap is required. It may therefore be concluded thatthe 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 tothe 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 localplasticity 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, andfor the ability to obtain good agreement with analysis, needs to be accounted for.

The tests were fabricated in accordance with AWS D1.l criteria. Inparticular geometric and initial out-of-straightness tolerances were imposed. The initial compression brace failures in Frames I and occurred at significantly different global loads (Figure 3.23) due largely to the initial out-of-straightness in Frame which was onthe 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 and the more gradual mode of failure in Frame is influenced by some initial 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 thatimperfections, which may be present, can have on capacity predictions. In jacketstructures, sensitivity analyses encompassing locked-in member forces in addition to otheraspects of uncertainty such as material properties, foundations, etc., are recommended (BOMEL, 1993). The important point is that the lower bound, largest imperfection for themember may not give the most conservative solution for the structure as a whole, andsensitivity 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 Shinare 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 thetrusses 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 andcapacity that can be accommodated for a reasonable budget. An additional factor is thestress-strain characteristics of the chosen steel in relation to 'typical' offshore materials andthe 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 andBOMEL tests.

Ogawa et (1987)

Soreide et (1987)

Grenda et (1988)

Paik and Shin

BOMEL (1992)

3.15Comparison of steels in test frames

Not given

Not given

API ERW

Not given

BS 3601 ERW annealed at 690°C (braces), API 5L X52 (legs)

BS 3602 ERW annealed at 690°C (braces), API X52 (legs)

Reference

Maison (1978)

Inoue et (1984)

hot rolled seamless ERW: cold formed welded tube - electric resistance welded

Material Type

API 5LB 42/52

Not given

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 stubcolumn tests also showed that girth welds (present in full scale jackets) had no apparenteffect on the response (Bolt et al, 1994).

The results presented by Grenda et al include a correction for the ERWproperties. However, without further evidence for the treatment state of the Briggs andMaison 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, needto be allowed for in the relation of the results to jacket structures. Furthermore inperforming calibration analyses, appropriate stress-strain characteristics need to bemodelled. This section therefore provides a caution to the immediate adoption of testresults 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 coupontesting 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 resultsin the discussion in Section 6.

i

TO GRADESTRENGTHS ARE BASED ON DYNAMIC

TENSILE COUPON TEST RESULTS

LOAD CELLPRESSURE

J0 1.0 2.0 2.5 3.0

FRAME DEFLECTION

INCLUDE SUPPORT AND RIG

Figure 3.1and Maison single bay X-braced test frame

Brace Nos

figure 3.2trusses tested by Ogawa et

Figure 3.3Truss load deflection response (Ogawa et

Figure 3.4Single bay K-braced frames tested by Grenda et

FRAME FRAME

FRAME FRAME X

Figure 3.5Single bay K-braced frames tested by BOMEL

0 20

FRAME LOAD DISPLACEMENT RESPONSE

P

FRAME OVERALL RESPONSE

FRAME RESPONSE FRAME X OVERALL LOAD-DISPLACEMENTRESPONSE

Figure 3.7Global load-deflection responses for BOMEL K-braced frames

F R A M E

Figure 3.11Two bay X-braced frames tested under cyclic loading by Popov et

FRAME DISPLACEMENT(mm)

0 50 100 150 250 300FRAME DISPLACEMENT (mm)

Figure 3.14SCI Frame I global and local member responses

F

FRAME V

LOAD

WX

0mW

IV MODIFIED

FRAME

Figure 3.28Two 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 loadAPI joint failure

50 100Frame Displacement (mm)

Figure 3.29BOMEL Frame global response

TENSION BRACES

COMPRESSIONCHORD

50 150 200 250 300 350 Frame displacement (mm)

UCD LCD UTD LTD Frame

Figure 3.30Frame member forces showing X bracing load distribution and frame action

C

, l

,point

pin .

-: Present Experiment

Present

0.0 10 30 40 SO 60 70displacement

,: Present Theory

a

0.0 20 70 90displacement

Figure 3.33Frames tested with and without damage by Paik and Shin

Oil

Reaction

PC

Oil

Cel l

Figure 3.34X-braced frames and towers tested by lnoue et

--C c c ---*

Figure3D X-braced box frame tested by Frame S1

failure due to buckling and fracture due to lack of fusion

-o

LOAD

LOAD

Figure3D X-braced box frame tested by Frame S2 -

buckling failure initiated by dent in member

4. SOFTWARE FORPUSHOVER ANALYSIS

4.1 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 beconsidered, namely:

Member removal Member replacement Linear superposition - strain based load basedLimit 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 associatedwith 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 andthe 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 replacementIn this method a series of linear structural analyses are performed and as each memberfails, 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 andGrenda, 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 computer time and and van de 1990).

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 thestructure, hence it is known as the Virtual Distortion Method(VDM). In addition to theelastic 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 bydeformations 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 andtheir load based method enables additional constraining loadcases to be defined simply. The method is restricted to axial nonlinear behaviour but can model cases of practicalimportance 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 nonlinearresponses of a component are identified. The difference is accounted for by applying endforce pairs to each nonlinear member. The constraint equations determine the correct deformations and calculate the components of resistance to be derived from the member orthe 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 tofollow the behaviour of the nonlinear system. The set of constraining forces can be quitesmall 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 readilyavailable, a full collapse analysis of a complex structure can be performed within a fewdays, 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 simplifiedanalysis is performed of the principal structural components - deck, legs, jacket andfoundation (see also Bea and 1993). Storm loading profiles of horizontal shear are developed and compared with the horizontal shear capacity of the platform to identifythe '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 correctstatic 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 ofoffshore structures influence the robustness. It is applied with an assessment ofuncertainties 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 columnsfinite element methodpolynomial beam column modelling finite segment methodphysical 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.

Nonlinear analysis can therefore be demanding in of engineering and computer time, nevertheless it offers the only accurate approach to evaluating the reserve strength of jacketstructures. A number of specific programs for the collapse analysis of jacket structureshave 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 topredict the reserve strength of jacket structures. Full nonlinear analysis is demanding interms both of requirements and computing capacity. However, simplified methods necessarily introduce approximations in the ultimate and particularly post-ultimateresponses of components. In a redundant nonlinear system the difficulty is that conservatism in modelling a component may not be with respect to the globalcapacity. 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 inscreening configurations so that accurate nonlinear modelling can be devoted to criticalscenarios. 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 levels of assessment. (1992) has suggested that assessment needs to begin byclassifying structures in terms of:

failure consequencesincreasing age - deteriorationdecreasing quality of designoperational 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 - scoring factor analyses Level 2 - simplified limit equilibrium analysesLevel 3 - modified elastic state-of-the-art practice Level 4 - state-of-the-art nonlinear analysis.

It is suggested that a fitness for purpose evaluation should start at Level 1 and need onlyproceed to higher levels if the acceptance criteria cannot be satisfied. As a backdrop to fullnonlinear analysis these approaches may be reviewed in detail.

Level 1 RSR is based on factors that address platform capacity (R) and environmental andoperational 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 4.1Level 1 RSR capacity scoring factor guidelines and Craig,

Guideline

Structure and foundation design and construction criteria (in relation to API RP 2A)- 1959- 1964

1965- 19751976- 1993

Structure condition: corrosion, dentedlbent members, dropped objects, fouling, scour poorgoodexcellent

Score

Table 4.2Level 1 RSR storm and operational loadings scoring factor guidelines

and Craig, 1993)

Structure and foundation modifications developed during installation. operations, orreassessment that result in increases or decreases in capacity

decreasesno changes increases

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)

Loading-capacity effects factor waves

earthquakes

0.5 - 0.91

1.1 - 1.5

1.0- 1.11.2 - 1.31.4 - 1.51.6 - 2.0

1.0 - 1.51.0 - 4.0

Factor

S,

Level 2 is based on the limit equilibrium technique due to Bea and (1993)described in Section At Level 3 linear elastic analysis is used where WSD criteriaare 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 loadredistribution effects. Level 4 encompasses a full nonlinear analysis either within the context of deterministic or reliability based approaches.

Guideline

Storm loadings design criteria (Ref. 1993 API RP 2A)

(Cd,,, (dir. spread, shielding, blockage and current corrections)

S,

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 toevaluating approximate estimates of RSR offer a rational and cost-effective methodology for assessing system reserves.

Score

1.0- 1.51.0- 1.5

Lower equipment deck elevation (not in design wave loading)I

Loading modifications: elements added or removed, marine growth management

1.0 - 1.5

0.5 - 1.5

Operating I gravity loading modifications0.5 - 2.0

Furthermore this sequential analysis is the methodology being proposed for the assessmentof 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, todemonstrate 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 presentationis alphabetical by program name. The coverage of this section, the programs anddevelopment organisations are listed in Table 4.3 below.

Table 4.3Nonlinear software for pushover analysis of offshore structures detailed in this review

Program

EDP

FACTS

INTRA

SAFJAC

USFOS

Full title

Extended Program

Finite Element Analysis and for Complex Three dimensional Systems

Developmentof Tower ResponseAnalysis

Strength of and

Proprietary nonlinear dynamic analysisprogram developmentof INTRA

Ultimate Strength ofStructures

Software development organisation

Digital Structures, USA

Structural Software Development, USA

ISEC, USA

BOMEL, UK

PMB Systems Engineering, USA

SINTEF, Norway

Information on the various programs for ultimate strength analysis listed in Table 4.3 isgiven below. The descriptions of each program have been provided by the associated development or support organisations to the same specification. The specification askedfor 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 formulationsSpring elements Method of solution Load application

creation facilities Offshore code processing facilities

facilitiesOngoing developmentslenhancements relevant to collapse analysis of jacket structuresDate of original development, current status and contact details for furtherinformation.

The organisations were also asked to confirm that the current report provides comprehensive coverage of publications involving the use of the software. These areincluded 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 thesame 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 suchas fixed and compliant offshore platforms.

Element formulations

The EDP element library consists of many formulations for modelling thenonlinear response of offshore platforms, including linear and

beams, struts, plates, shells, solids, pipes, quadrilaterals, loading and matrixelements. 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 tocombined axial force and bending moment interaction for primary bending members. Thestrut element is a multipurpose phenomenological element to represent buckling and tensionyield in primary braces or large deformation cable tension response. Special compositetubular 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 andlateral stiffness nonlinearity are modelled using a hysteretic soil element that includesdegradation and Spring elements also model impact, uplift and friction.

Method of solution

EDP contains features which minimise the potential for numerical instability in static anddynamic analyses. Constant stiffness and Newton Raphson iteration schemes are used forboth 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 thencontinues with this revised state and thus simulates progressive collapse situations to thepoint of ultimate instability. When considering such alternate load paths for redundant structures, the failure criteria for brittle and ductile members may be defined by forcelimits, 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 andcomplicated loading sequence experienced by the system. Static loads are applied in a prescribed manner by the user or automatically by the program inincrements. Dynamic loads can be time varying forces (nodal or element), displacement functions, wave loads or ground acceleration time histories. Multiple support excitation andphased 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, evenduring seismic time history analyses. AISC code checks are available for other sections.

facilities

EDP has an integrated comprehensive graphics capability to facilitate interpretation anddocumentation 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 othernonlinear programs. EDP versions exist for a range of computers from throughmainframes.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: 510549 1565, + 1 510 549 1600.

FACTS"FACTS is an integrated library of programs for the linear and nonlinear elementAnalysis of Systems under static and dynamic loads.

Element

The FACTS library includes both general purpose and application specific element typesand internal modelling features including:

3D linear: truss beamstraight and curved pipe3-9 node membrane element 3-9 node shell element8-20 node solid

3D nonlinear: truss cablebeam-column, lumped plasticitybeam-column, distributed plasticity degrading stiffness beam-column, lumped plasticitystraight pipe curved pipe with effects8 node shell 8-20 node solid gap friction shear degrading link free-field soilnear-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 iteration scheme. Component modes for linear substructures.

Response spectrum dynamic analysis. Modal superposition time history dynamic analysis.

static solution Ability to include linear as well as nonlinear elements and to specify that certain substructures remain linear analysis).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 orwithout 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 areinput 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 madeof 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

Tubular Joint Analysis - - Automatic modelling of complex tubular joints inoffshore 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 tosubstructures 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 topredict fatigue life and long term statistics. Performs stress determination, memberchecking 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 Shattuck Avenue, Berkeley, California 94704, USA, Tel 510 849 3458.

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 orstructural integrity of a variety of onshore structures (bridges, overpasses, high-risebuildings, 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 scaleand 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 systems may be performed using a state of the art shifted eigensolver. Theprogram can handle material (steel, concrete, reinforced concrete, soil) as well as geometricnonlinearities. 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 RP 19th Edition approach for tubulars. Joint checks are performed using the AWS Alpha approach for joint classifications. Non-tubular member checks are performed using the AISC recommendations. It also includes the interface to the 3Dgeneral purpose visualisation and 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. Conventional fixed format input or key word oriented input structure. 2. Input data echo and extensive data checking capability. 3. Automated generation of inelastic properties for truss and beam element types.4. Profile minimiser to optimise storage and computations.5. Flexible boundary conditions handling through or multipoint constraints.

6. A generalised damping formulation to allow user specified damping ratios in as manymodes 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).

Karma can be executed on workstations such as the Sun Micro Systems andminicomputers 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,San Francisco, CA 94111 USA, +1 4 421 1692.

SAFJAC - A program for the Strength Analysis of Frames and

SAFJAC is a nonlinear analysis program for determining the reserve and residual strengthand the progressive collapse behaviour of offshore structures. The program is based onconventional finite element analysis techniques but for purposes of efficiency andfriendliness it incorporates high-order beam-column elements and automatic meshrefinement 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 itmodels large deflection behaviour accurately and sub-divides automatically when plasticityis 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 whilstthe 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 tomodel joint flexibility, pile-soil interaction and The behaviour in tension andcompression 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. Specialfacilities also exist to apply and remove loading due to boat impact allowed byenvironmental 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 furtheroptimisation is required to accommodate the extra nodes and elements generated duringsolution. To overcome convergence problems in the vicinity of the ultimate load, both loadand 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 easeof data entry. Interfaces to IDEAS-FEM and allow the model to be displayedgraphically.

facilities

Interfaces to IDEAS-FEM and allow the results to be displayed and plotted. A post processing program RESULTS allows the user to extract results (displacements, forces, stresses) in a tabulated form suitable for input into PC graphics and plottingprograms.

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 ofplastic 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 andresidual strength of large scale tubular frames. SAFJAC has thus been fully calibratedagainst 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 IzzuddinBillington et al (1991) and Bolt et al (1994).

Further information can be obtained from BOMEL, Ledger House, Forest Green Road, Fifield, Maidenhead, Berkshire, SL6 UK, +44 1628 777877.

Introduction

PMB began its development of state-of-the-art nonlinear analysis software for the oil andgas industry in 1978 with the introduction of the INTRAAnalysis) 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 thestandard for nonlinear dynamic analysis in the oil and gas industry. Additional enhancements included the development of advanced soil-pile modelling capabilities which, in 1983, represented a capability that is still unique within the industry. wascreated 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 usedto analyse a variety of offshore structures, including fixed platforms, compliant towers,

stiff and flexible risers, buoys and cable systems. It has been usedextensively 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 anextensive library of nonlinear finite elements which explicitly model material nonlinearityand large deformations including, for example:

Beam columnbending failure surfaces are either generated automatically using an

extension of Mohr plasticity theory or user-specified.

Substructured beam-columnRepresents material and geometric nonlinearity including explicit modelling of local damage.

Pile-soil interaction Discrete elements to model nonlinear axial and lateral interaction for both staticand dynamic loading including rate of loading effects, cyclic degradation, hysteretic behaviour andProperties 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 modelledusing Airy waves, Stokes fifth order waves, or Stream Function waves. Irregular wavescan be modelled with either a user-defined or Pierson-Moskowitz spectra. Bothunidirectional and multidirectional seas can be modelled.

Ice loads can be applied statically (slowly mooring sheet ice) or dynamically (impacting icefloes), with the nonlinear constitutive properties of the ice modelled explicitly.

Earthquake loading can be defined using either ground motion records or spectra, for usein 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 stepintegration 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 keyfeature (ie. all flooded members, all pinned joints, etc), run analyses, and post-processresults.

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 structureresponding to various loading conditions.

The ability to access multiple types of information is demonstrated in Figures 4.4 through4.6 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 alet al et An-Nashif Dolan et Dolan and

Pawsey Nordal (1991) and Bea et al (1988).

Further information can be obtained from: PMB Engineering Inc, 500 Sansome Street, SanFrancisco, CA 11, USA, Fax: +1 415 986 2699.

USFOSMain 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 residualstrength 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. Theformulation 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 wellas eigenvalue analysis may be performed.

Beam element formulation

The beam column is the basic entity of USFOS (Figure 4.7). A coarse element mesh isused, only one finite element is required per physical member of the structure.

The USFOS beam is valid for large lateral displacementsand moderate strains. An updatedLagrange formulation is used based on Green strains. The axial force influence on bendingis represented by Livesly's stability functions. Nonlinear material behaviour is modelledby 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

The basic formulation is extended with special features for load analysis: 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 normalplane 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 loadcombinations.

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 collision according to requirements.

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 begenerated 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

Graphic post-processor, XFOS, based on a X user interface. Results presented as colour fringes (eg. plastic structural utilisation, temperature distribution) onimages 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 earthquakesElasto-plastic cyclic analysis of jackets structures (incremental collapse vsshakedown)Integrated, progressive collapse of structures exposed to fire (fire development, heat transfer, mechanical response)Models for aluminium behaviour, including creepExplosion 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 etSoreide et al Soreide et al Moan and Taby Moan and Amdahl

Moan et van de Graaf and Tromans (1991). Medenos andLogendra Jacobs and Fyfe (1992). Tromans and van de Graafet al Eberg et al Amdahl and Eberg et alet al (1993) and Eberg et al (1993).

USFOS is marketed by Det Norske Veritas Sesam AS, Head office address: Det NorskeVeritas Sesam AS, Veritasveien l , N-1322 Norway, +47 67 57 72 72.

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 termeffects 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 concernedwith 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 ofsuppressions and constraints. For nonlinear analysis relevant material properties anddefinition 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 combinationsand unity checks can be performed. Forlinear analysis non-proportional load history can be specified.

Two types of structural components available in RASOS: two noded beams and joints. Ofthe 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 andconductors. The linear analysis is formulated upon the engineer's beam theory, whereasin the nonlinear collapse analysis critical members are replaced with a sophisticatednonlinear beam column model. This nonlinear member model makes use of a range of post-limit models, such as conventional plasticity with slopes, brittleor ductile failure and member buckling. Joints can be modelled as rigid or flexible, with flexibility characteristics automatically calculated depending on the joint geometry. Fornonlinear 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 dedicatedmodule. During global collapse analysis member and joint failure modes are combined intoresultant limit surface.

RASOS has the capability to allow the user to use both nodal spring supports and pilesupports 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 bya 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. Thealgorithm 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 andtopsides).

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 UserGroup.

References citing the development and application of the VDM within RASOS areand Gierlinski Gierlinski and Yarimer (1992) and Gierlinski and Shetty

(1993).

For further information please contact: Dr J T Gierlinski, Chairman RASOS User Group,WS Atkins Science and Technology, Grove, Ashley Road, Epsom, Surrey KT18

+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 modelthe collapse response of frames. Table 4.4 presents key references for the programs inwhich 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 benoted that the references cited are examples and other publications of similar studies andresults 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 andinfluence 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 fromconventional structural analysis to be adopted. The fact that each element can embody bothtension and compression member characteristics is a significant advantage, placing lessreliance 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 bedrawn. 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 wellas load redistribution, to be demonstrated and will clearly be a valuable exercise.

Table 4.5Comparative analyses of the same structure using different software

(Furtherdetails are given in 5.1)

Structure

2D frameE Nordal, 1991 (FENRIS, USFOS)

References(Programs)

et al, 1988 (MARC, Ward and 1988 (SAFJAC)

et 1991

Good agreement for NW wave.Discrepancy for for N wave differentloads and sequence of collapse but differentanalysis brief and modelling assumptions.

Comparisons

Global loaddeflection responses show goodcorrelation to peak load. SAFJAC and USFOSalso track post-ultimate curves.

4.4Application of nonlinear collapse analyses software in the literature

Program

ABAQUS

EDP

FACTS

FENRIS

INTRA

INTRA (KARMA)

MARC

SAFJAC

USFOS

DYNAS(dynamic)

ADAPTIC(dynamic)

Paper - Authors

Zettlemoyer (1989)

Piermanei et (1990)

Bouwkampet (1980)

(1991)

Moan et (1991)

Lloyd (1984)

Pike Grenda (1987)

(1988)

et (1988)

Gidwani Renault (1990)

et (1988)

Ueda et (1986)

Ward Izzuddin (1988)

Billington et (1991)

(1991)

Dolan et (1992)

Bea et (1988)

(1991)

Medenos (1991)

Jacobs Fyfe (1992)

Soreide et (1987)

Moan et (1991)

van de Graaf Tromans (1991)

Tromans van de Graaf (1

et (1991)

et (1993)

et (1977)

and Gho (1992)

Analysis

Frame subassemblage - detailed joint model

Goodwyn platform optimisation

Elastic 2D jacket frame with joint flexibility (Program also has nonlinear capability)

Veslefrikk platform

Benchmarking against single bay 3D test

Idealised 3D jacket

Simple structures

3D jacket - bracing study

Plane frame and 3D jacket

Idealised jacket - impact

Plane jacket frame

Idealised frame including joint flexibility

Plane jacket frame - benchmarking against 2D frame test

2D test calibration, including joint nonlinearity

Veslefrikk platform

Maui A seismic reassessment and pushover

Example requalification assessment

Veslefrikk platform

Jacket impact

Jacket bracing study

jacket

against single bay 3D test

3D platform hindcasting

3D platform hindcasting

Cyclic shakedown of plane jacket frame

North Sea jackets - static and cyclic pushover

Benchmarking against cyclic frame tests

Idealised including joint

(Note: example publications are cited - where related papers present results of the same or similar analysis, just one reference is given.)

axial load

(a) (b)pseudo structure

additionalforce inmember caused by

axial deformation

(c) response curve for member "I"

Figure 4.1Basis of linear superposition method and van de

a) P-M Interaction Surface for Plastic Hinge Analysis

GAUSS INTEGRATION POINTS

NODE l

STRESS MONITORINGPOSITIONS AT GAUSS

I

Distributed Plasticity

Two newelements

node

Plastic Hinge.

Elasto-plasticcubic elements

Elastic elements

Distributed Plasticity.

C) Subdivision of Quartic Element

Figure 4.2SAFJAC plastic hinge and cubic elements with automatic subdivision of element

LATERALDISPLACEMENTA

LOAD

Single Element Per Member and Joint Flexibility Included

Upper compression0

EXPERIMENTAL RESULTS

----- ANALYTICAL RESULTS

LATERAL DISPLACEMENT

Comparison of Analytical and Experimental Reponses

Figure 4.3SAFJAC analysis correlation with Frames Project test result

Figure 4.4CAP static pushover analysis

R W...

Figure 4.5CAP dynamic failure analysis

Figure 4.6CAP dynamic toppling analysis

P (Elastic)

Non-linear material Non-linear geometry

Figure 4.7USFOS 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, sorepresentative analyses are described in Section 5.1 before the results are compared in Section 5.2. Analyses performed to calibrate software against experimental data andpresented in Section3 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 inTable 5.1. Work was driven initially by the assessment needs for 3D jacket structures andhence the idealised approaches were adopted (eg. Lloyd, 1982). The move was then to 2Dframes, either as representations of offshore platforms (eg. et al, 1988) or as ameans to elucidate some of the key influences on ultimate response characteristics (eg. Pike and Grenda, 1987). As RSR has begun to play a role in offshore practice soexamples 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 withpushover analysis are now emerging (eg. van de and Tromans, 1991). Indeed as USattention turns increasingly to platform requalification for both earthquake and hurricaneenvironments (API draft, 1993). and North Sea regimes require ongoing reassessment forextreme loads (Sharp et al, the number of papers in the literature has proliferated.

The results presented in the following sections indicate the information about platformreserve strength that can be learned from analysis.

Table 5.1Summary of presentation of analytical work

Authors

Pike Grenda (1987)

Bouwkamp et (1980)

Ueda et (1986)

Elnashai

Connelly Zettlemoyer (1989)

et (1988)

Ward Izzuddin (1988)

et (1991)

Gates et (1977)

Lloyd (1984)

Lloyd (1982)

Paik and Shin

Jacobs Fyfe (1992)

(1988)

et (1988)

Nordal (1991)

et (1990)

Dolan et (1992)

Soreide et (1987)

Moan et

Bea et (1988)

Shinners et (1988)

Tromans van de Graaf (1992)

van de Graaf Tromans (1991)

Edwards et (1985)

Holm et (1988)

Nordal et (1988)

Type of Investigation

2D frames

Demonstrationof buckling algorithm

Elastic influence of joint flexibility

Illustration of importance of nonlinear joint

Influence of joint flexibility on seismic response

Influence of frame on joint behaviour

Comparative analyses

et frame, different program

et frame. different program

Contribution of redundantbracing to reserve

Idealised 3D jacket

Demonstrationof redundancy in different framing

Intact and damaged structure calculations

Alternative plan bracing configurations

Intactldamagedlmemberremoval analyses

Jacket (structure investigation)

Alternative bracing configurations

Alternative bracing configurations

interactions

Comparative analyses using three programs

Optimisation to achieve target RSR

Pushover as part of seismic investigation

versus damage investigations

Jacket pushover and 3D frame

Example requalification assessment

Evaluationof upgrading options

Jacket investigations)

Cyclic loading comparisonswith pushover results

Jacket

Jacket reassessment

Comparison of predicted damage with observations

Reliability

Jacket case study to evaluate techniques

Role of variability

Comparison of 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 RSRincreases for increasing brace slenderness and for lower rates of compression brace load shedding. Allowing for the restraining stiffness of the mid-height horizontal, the memberwas 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 panelto 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 isdemonstrated in the paper although the results do not enable the influence on reservestrength 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 theanalysis 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 witha 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. Theconfiguration determined that brace buckling preceded joint failure so just the effects of linear flexibility compared with rigidity are assessed. Little influence on capacity wastherefore found, although the sequence of failure and ductility were affected, as shown inthe 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 thefailure 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 priorto 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" and60" were considered, both with and overlap configurations. It was found thatrestraints in the frame enabled the joints to sustain substantially higher determined from isolated analysis. The results are presented in Table 5.2.

5.2Comparison of apparent joint capacities within the frame and in

K joint type

concentric overlap I 1.11

of ioint in frameCapacity of joint in isolation

eccentric overlap 1.20

loads than

45" eccentric overlap

It was also that the capacity for the joint at that point in the frame was notstrongly influenced by changes to the frame geometry (eg. leg stiffnesses, etc).

1.26

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 aspectand 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-buckling behaviour. 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 andINTRA 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 applied and held constant whilst lateral loads were incremented. state design requires 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-ultimateresponses are not traced. The structure is also analysed by Ward and (1988) and

et al (1991).

Ward and lzzuddin 988)The plane frame analysed by et al (1988) was subjected to a pushover analysis using SAFJAC. Analysis was performed using elements which automatically sub-divide introducing hinges to model plasticity due to bucklingor 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 littleeffect 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 factor of 1.85 compared with the figure around 1.7 calculated by et al. However,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 onmeasures of applied loads when not all components, ie. dead and environmental are beingfactored together.

Finally, the analysis by Ward and Izzuddin was continued beyond the peak. The residualstrength of the structure is = 0.89 and is well in excess of the design load.

Skallerud, Amdahl and MoanAn analysis of the jacket plane frame, analysed previously by et al (1988) andWard and Izzuddin was performed using USFOS. The static pushover formed part of a study of cyclic loading and shakedown. Dead loading, without partial factors, wasapplied first and environmental loads were then incremented. Damage was simulated byremoval of member 36 and additionally 37. The sequence of failures is not described butthe 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 5.3Load factors at first yield and ultimate load for jacket frame

Use of the redundancy factor with respect to first yield is demonstrated in this analysis butthe analytical definition of a single plastic hinge is straightforward compared with the detection of plasticity in a structure in practice.

Analysis

Intact

36 removed

36 37 removed

The USFOS analysis is in close agreement with the SAFJAC results reported by Ward andIzzuddin under the same loading regime. Ultimate load factors of 1.79 and 1.85 wereachieved respectively, at displacementsof and These values are scaled from 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 tubularsteel 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.

Ultimate load factor

1.79

1

-1.1

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

Load factorat first yield

1.24

0.81

-0.65

1.44

1.96

1.69

element failure criteria is based on energy limits and the failure algorithm removes themember stiffness from the structural model. The deck girders, jacket legs and piles were modelled with tubular beam-column elements which are capable of inelasticdeformations through concentrated plastic hinge formation at the member ends.

Whilst a full earthquake analysis was undertaken by the authors, the DYNAS program wasalso 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 deflectionductility 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 buckledor 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 membersdesigned 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 doubledthe 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 nominalproperties within the criteria of design which indicate that the members carrynegligible 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:

damaged strengthRF =strength loss

andDSR =

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.

Lloyd and 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 devisedfor water depth as shown in Figure 5.12.

A storm loading condition was considered (allowing a one third increase in allowable stress in component design). The design loads were based on a wave height with a 60%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 5.4Modelling of jacket structure with

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 theenvironmental 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.

Members

Legs Piles (PL) Diagonal & X-bracing (XB)Horizontal bracing (HB) Piles below

Element type

Nonlinear beam-columns with plastic hingesStrutsNonlinear truss elementsLinear beams

Table 5.5Comparison of collapse and design loads for and jacket

(b) Grouted Pile Model I

Direction

SSEEW

SW

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 thedesign 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 arenot unreasonable.

(a) Conventional Pile Model

Design load

26302410229023002410

3.504.363.292.933.84

To simulate damage, a series of analyses were performed with members removed. Elastic analyses revealed the redistribution of loading and in particular higher utilisations forhorizontal 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. Thefailure scenarios also reveal the remaining redundancy and the sequence of failures required to cause collapse.

XBI Struts StrutsStrutsStrutsStruts

Table 5.6Residual strength of damaged jacket structure

Collapse load

91507810605056007960

RSR

3.483.242.642.433.30

Member Removed

Criticalmembers

Piles and LegsStrutsStrutsStrutsStruts

Ultimate Resistance (kips) ResidualDamaged Undamaged

Level 2 diagonal brace

Level 2 face frame

Level 2 transverse horiz

Level 2-3 half X brace

4900 6050

5450 6050

9150 9150

8350 9150

0.81

0.90

0.91

Lloyd

The examples in this paper illustrate the role of redundancy in optimising the materialdistribution 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 thestructure from and 0". For the three frames the following redundancy studywas 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 developedby 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 thedesired redundancy at minimum structure weight.

For the intact structure, when the compression to tension strength ratio for members is unity the optimum solution shows that horizontal and framing members areunnecessary. This result is consistent with conventional elastic analysis. However, whenthe 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 bracesmust be stronger than given by the case 1.O. It was shown that framing and horizontalbraces 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 than60 it was necessary to increase the system weight considerably. The quantities presentedin 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.

Paik and Shin 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 propertieswere 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 agross 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.

Structural jacket analytical investigations

Jacobs and FyfeThe authors used USFOS to analyse a series of different structures for impact and pushoverloads 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 theextreme storm loading. The RSR is therefore 2.96. The lateral displacements at variouslevels in the structure are presented in the figure and failure was reported in the X bracing between elevations -71 and

Table 5.7Nonlinear analyses performed by Jacobs and Fyfe

8 leg jacket with topsides damage scenarios members removed

Topsides module - explosion

Integrated deck - dropped object

4 leg X-braced jacket in - Impact and damage scenarios - Intact pushover analysis

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 thatbuckling in the compression brace was preceded by load shedding from another compression member which was redistributed within the redundant structure. Details ofthe 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 wasanalysed with different bracing configurations, as shown in Figure 5.15. Bracing was sizedfrom 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 reportedin 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 notcertain 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 impactzones or may determine that K bracing should be over-designed to force initial failure in X panels.

andThe analysis of a platform is presented to illustrate the value of the reserve strength methodin platform optimisations and requalifications. The four leg platform, in water depth, was analysed for the year design wave. in both the jacket and foundationwere modelled using the element types shown in Table 5.8. The analysis method is not cited but it is believed to be INTRA.

Reason

Buckling anticipated so moments ignored

Controlled by axial loads and bending

Expected to remain elastic

5.8Element selection for jacket

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 thefirst failure cited as loading was shed to the legs which rapidly developed plastic hinges.

Components

Vertical diagonals

legs and piles

Launch trusses

Soil resistance

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 wasdeveloped.

Element Type

Struts

Beam-columns

Elastic beams

Nonlinear springs

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 optimisingstructural 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 Section5.1.1, the program was used for the nonlinear analysis of a Southern North Sea platformto demonstrate the use of the limit state assessment criterion with partial factors. The structure stands in of water with topsides loading of 4700 tonnes and a design baseshear 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 membercapacities was accounted for and bending elements were included in parallel with phenomenological strut elements. A two pass analysis thereby allowed end moment effectscaused 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 thata 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 theredundancy factor (RF), where A,,,, = X, RF.

Table 5.10Results from jacket analyses for different structure and foundation conditions

* Does not meet requirement.X, 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 thatX should exceed 1.5 (ie. 1.15 1.3) for acceptance (NPD, 1990). An approximatemeasure 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 casesit is clear that redundancy gives a factor of 1.3 on the environmental loading beyond firstfailure 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.

Nordal 991Three static pushover analyses of the four leg Veslefrikk jacket in 175m waterdepth arepresented using USFOS, FENRIS and (see Section 4). The structure is shown in 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. Environmental loading was based on 28m wave height, 13.5 second period, yearStoke'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.

Table 5.1 1Alternative modelling of Veslefrikk jacket

Components

Members

Piled foundation

Grouted pile inserts

Wind loading

N wave designbase shear (MN)

NW wave design base shear (MN)

MODELLING COMPARISONS

USFOS

Beams with insertion ofhinges

Equivalentbeam elements* text ambiguous

Equivalent linear beams

Not included

39.2

FENRIS

Beams with ofhinges

Linear springs

Equivalent linear beams

Included

45.7

Braces: struts withprescribedLeg: nonlinear beams

Nonlinear springs

Composite sections

Included

39.6

Furthermore, the analyses were performed at different stages of the structure design anddetails of the member slendernesses differed. The analyses were not commissioned as abenchmarking exercise (ie. not with the same brief) and there was no attempt to reconcilethe different results. The analysis was undertaken first and the USFOS andFENRIS 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 onediagonal of the top bay X bracing, simulated ship impact and at simulated incidence 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 5.13which follow. The reserve strength ratios relate the environmental load at collapse to theenvironmental 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 5.12comparisons for under N wave

Design Base shearin MN (load factor)

Base shear in MN(load factor)

Failure mode

Damaged:

Base shear in MN

Failure Mode

Base shear in MN

Failure mode

Load deflection

Deflected shape

USFOS

NORTH WAVE COMPARISONS

Yield at lower end ofcompression legs (2.2).Global stiffness reducing withextreme yielding incompression legs (2.7). Leg capacity reached atand (3.1).

Yielding and tension in upperpart of jacket. Grouted insert piles prevent failure. Failure involves intact failure mode inlower pan of jacket.

Intact failure mode with additional global torsion.

FENRIS

As for USFOS. Buckling of compressionbraces and yielding oftension braces in upperbay followed byyielding in compressionlegs at

Buckling of compressionbraces in upper bays.

* Damaged at

Figure 5.13

comparisons for under NW wave

Design Base shear in MN(load factor)

Base shear in MN(load factor)

Failure mode

at

Base shear in MN (load factor)

Load deflection

Deflected shape

NORTH WEST WAVE COMPARISONS

USFOS

4s wave initial failure in lowereg sections. Failure in compressionegs (2.0). Tension failure in

legs (2.4).

SeaStar

Leg capacities critical

In addition to the tabulated data, the narrative indicates that the USFOS N wave analysisshows the peak load is achieved with a factor of = 1.4 on the load at first failure.

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 termsof failure mode dominated rather than leg failures) and load factors at collapse (1.8compared 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 stagesat which the analyses were performed and the fact that the basis of foundation modellingwas quite different for the SeaStar analysis. Without resolution of this key factor indetermining 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 differentsoftware can be assessed. The discrepancy between the analyses was large and it isessential that such factors in relation to jacket performance are verified. For jacketstructures 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 ratioof the ultimate platform resistance to the design load, based on base shear or overturningmoment. 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 ExtendedDesign Program (EDP).

Initial 2D analysis of the first four legged jacket structure shown in Figure 5.18 gave RSRsof 1.60 and 1 for linear and nonlinear foundations, respectively, and the worst casewesterly 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, loadredistributed 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 mechanismproceeded 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 anelastic 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 primarilyto demonstrate adequate seismic performance. However, as part of the work a static pushover analysis was undertaken. Sufficient details are not given for comparison withdesign capacities to be made but the load deflection curve and damage sequence shown inFigure 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 bracesshown in Figure 5.21 was analysed using USFOS. The configuration is shown in Figure5.21. 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 failure as shown by the RF values in the table. The distinction between P, and is usefulin distinguishing the partial factor contribution to the RSR.

Table 5.14Progressive collapse analysis results

Intact

Corner leg in splash zone removed

Collision simulationDamaged structure

Dropped object simulationLower horizontal removed

FirstYieldHinge

1.81

1.59

1

P,, = design load with partial safety factors

2.49

P, = ultimate collapse load of intact structure = yield hingeP, = ultimate strength of damaged structure = residual strength factor =

= design load = reserve strength factor =

-

0.87

0.88

0.85

Moan, Engseth and Granli (1985)

An 8-leg jacket for 70m water depth with X-bracing in plan, longitudinal and transverseframing is analysed using USFOS. The structure is shown in Figure 5.22. The yeardesign loads for each of three directions are incremented whilst still water loads remainconstant. 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 theextent 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.

In addition to the analysis of the jacket structure, a 3D box frame of similar configuration to the structure tested by SINTEF (Section 3.1 and Figure 3.35) was analysed usingFENRIS. The member properties and dimensions are detailed in Table 5.16 and differfrom the final test structure.

Table 5.15Reserve strength in X-braced jacket structure

Table 5.163D box frame member properties

Load Case

Diagonal wave

Longitudinal wave

Transverse wave

Member Type

REF

4.39 1.69

3.71 1.49

4.32 1.44

Load factor on 100 year return

System

Legs

Horizontal X brace

Vertical X braces

First Hinge

2.60

2.49

2.99

S2

S2

S2

S1S2

Max. Load

4.39

3.71

4.32

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 toAPI 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 5.17Comparison of reserve strengths for 3D box structure

The analyses were repeated with USFOS and good agreement was achieved. In USFOSone element was adopted per member whereas FENRIS required 108 beam elements and93 nodal points. Comparative computing times were 1 hour and 2 minutes (see Section 6.3for further discussion of analysis efficiency). Subsequent USFOS analyses performed bySoreide 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 forrequalifying offshore installations and demonstrate the application to an example Gulf ofMexico 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 orunconservative predictions. The absence of guidelines or evaluation procedures was notedbut 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,1 centre), fixed drilling platform in water depth which was installed in 1962. The structure was analysed using with inelastic beam-column elements modelling the plastic performance of legs, piles and conductors at their load-carrying limit. Braces weremodelled with 'strut' elements to account for buckling in compression or yielding in tensionand the capacities were modified to account for premature punching or tearing at the leg joint. As the is ungrouted and there are no joint cans this frequently controlled the capacities. The force deformation of the pile and conductor soil interfaces was modelledand 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 neglectedwith 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 1 - platform left as isALT 2 - 'repair' missing braces and cracked joints ALT 3 - repair as 2 and grout legs to pilesALT 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 exhibitof l and 1.25, respectively. The paper proceeds to discuss the relative benefit considerations in upgrading the platform.

System

S1= 97)

S2= 1.95)

Loading

NPL(no initial imperfection)

NPL

NPL + EL

NPL

NPL + EL

Frame LoadsDesign Collapse

44.0 82

44.0 80.4

40.0 88.8

8.0 16.9

8.0 18.9

RSR

1.86

1.83

2.22

2.11

2.36

Shinners, Edwardes, Lloyd and Grill (1988)

In upgrading five Bass Strait platforms, installed in the late 1960s (Figure EssoAustralia recognised that it was not practicable for all components of the platform to satisfylate 1980s design standards and a target RSR philosophy was therefore adopted. In additionto more stringent code criteria, the foundation conditions had been found to be worse andthe 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 structure could meet current code requirements but have an RSR of only 1 Given more exact knowledge of actual materials, and fabrication and installation events, a target RSRof 1.5 was adopted, see also and 1988. Supporting research programmes were undertaken into soil conditions, K-brace behaviour (Grenda et al, tubular joint characteristics and material testing.

To determine RSRs, a nonlinear computer model of the jacket was initially loaded with dead and live loads. Then, increments of the year load were progressively applied as 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 asignificant component of bending loading were modelled with inelastic beam-columnelements. Strut elements were pin ended and account for post-buckling strength degradation in compression and strain hardening in tension. The beam-column elementsallow for bending moments at the member ends and account for buckling strength limitations but do not model post buckling strength degradation. Nonlinear strut andcolumn elements were also developed to model joint behaviour. Elastic elements were usedfor members which were not highly stressed. Special elements were required to model thesliding of the piles within the legs and preserve lateral compatibility. The deck structures were replaced by simplified elastic equivalents to reduce computer time. Linearityassumptions were verified at calculated collapse.

The authors felt that the complexity and multiplicity of failure modes that could occur, aswell as the "judgement required by the analyst", meant that an exact measure of platformstrength 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 andfoundation resistances, and A and B (left of Figure 5.25) to be structurecontrolled.

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 althoughwere shown to be feasible. However, these only became effective when deflections were large and the dependence on foundation failure to mobilise the action was thereforenot acceptable. The explicit consideration of deflections is unusual however in analyses of RSR.

5.1.4 Jacket loading investigations

et (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 beconsidered to be representative of the North Sea jacket population. Structures and A2are subjected to similar environmental conditions, and Al , B1 and B2 are also subject toapproximately the same environment.

Table 5.18Structures analysed in pushoverlcyclic investigation e t

Wellhead

Structure

Water depth

Number of legs

Longitudinal Diagonalbracing

bracing Double X

Foundation 4 legsskirtpiles

Fieldterminal

Internalleg piles, grouted

HotelQuarter

Double X X without Khorizontals

Diagonal1Double X

Compressorstation

X withouthorizontals

4 legsSkinpiles

DiagonalK

Diagonal+ K

Internalleg piles, grouted

Internalleg piles,

notgrouted

Internalleg piles, grouted

Analysis was performed using USFOS by SINTEF and consulting engineers Offshore Design and Aker Engineering Bergen Modelling was as follows:

Soil was represented by linear springs. All primary members were given initial imperfections in the dominantwave 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 tensileyield) 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 theload factors at yield and first member failure are non-dimensionalised with respect to thecollapse load. Within the table the load cases for each structure generating the lowestredundancy factor (RF) beyond first member failure to collapse are highlighted, as are thelowest characteristic load factors. It can be seen that these do not necessarily occur for corresponding loadcases. Nevertheless in all cases the minimum reserve strength (lowestcharacteristic load factor 1 is associated with very little margin between first memberfailure and collapse. This is demonstrated in Table 5.20 where comparison is also madewith the bracing configuration in the transverse plane. The highest margin between firstmember failure and collapse is associated with the only X-braced frame.

Table 5.20Reserve strength and ultimate response characteristics from pushover analyses by et

strength

Structure

A2B1B2B3

Min RSRLoadingDirection

BroadsideBroadside

End-onEnd-onEnd-on

Broadside

The structure exhibited a range of system reserves beyond the design events. This is shownmore clearly in Table 5.21 in which the load factors on the 100 year design load are

RF at min RSR

1 .OO1.021.041.121.061.01

divided by 1.5 (product of partial factors 1.3 and 1.15) to give a measure of the capacity

Bracing intransverse frame

KK

DiagonalXK

beyond the design event. The basis of the original structure designs is not known so it is difficult to dra firm conclusionswith 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 5.21Ranges of reserve strength and redundancy for pushover analyses by et

The characteristic load factor at collapse for W is 2.81 and the load factor at first memberfailure 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 pushoverassessment may not therefore reveal the minimum collapse load factor for the structure asa 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 illustration and further information regarding the original structure design would berequired for firm conclusions to be drawn in the specific case.

Structure

A2B1B2B3

RF Indicative

Max

1.281.031.391.131.361.10

Max

6.042.945.475.272.813.08

Min

1.00111 .O11.061.00

1.691.911.632.252.111.37

Table 5.19Results for structures analysed in pushoverlcyclic investigation

STRUCT

A l

A2

B1

B2+

I-

LOADING PUSHOVER LOAD LEVEL CHAR'CDIRECTION , , FACTOR ON

First Collapse Extrememember LOADS AT

COLLAPSE

E 0.65 0.81 1.00 9.06

Broadside N 0.79 0.96 1.00 0.98

Diagonal NW 0.56 0.86 1.00 2.63 0.98

SE 0.55 0.78 1.00 3.63

S 0.65 0.99 1.00 4.41

Broadside W 0.87 0.98 1.00 0.98

E 0.77 4.17

NW 0.78 1.00 0.98

SE 0.45 0.87 1.00 3.48

Broadside SW 0.57 0.72 1.00 4.90 0.84

NE 0.51 0.73 1.00 8.20

Diagonal N 0.63 0.96 1.00 4.80 0.93

S 0.61 0.98 1.00 7.39

Diagonal W 0.51 0.98 1.00 5.10

E 0.45 1.00 7.90

End-on NW 0.72 0.89 1.00

SE 0.66 0.99 1.00 5.87

End-on N 0.73 0.88 1.00 3.36 0.98

et

LIMIT LOAD

cyclic

Amplitude

* 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%. Howeverthe load factors at which first member failure occurs are in the range 2.34 to 3.00 whichis significantly higher than the 1.3 to 1.5 range anticipated. The expectation is based onthe limit state factors which are required to produce adequate component designs and theadditional 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-bracingin 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 andthe 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 unacceptableand 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 andalthough 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-onloading of and B3, and for one end-on loading direction of A2. This is attributed tothe 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 andcompression members, the drop in load was not as pronounced, and the behaviour wasmore ductile. In all systems, the energy dissipation in the post collapse range depended onthe yield capacity (or the number) of tensile members, the residual capacity of the buckledbraces 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 forcomponents 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 firstyield and subsequent member failure can be found, in that early development of a zone ofplasticity does not necessarily lead rapidly to a mechanism of three hinges to precipitatebuckling. 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 givento 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 onthe year environmental loads.

Under broadside loading the four compression K-braces in the transverse frames at Level3 in structure buckle in rapid succession giving a residual capacity plateau associatedwith portal action in the legs (Figure For end-on loading (Figure sequentialcompressive and tensile failure of the diagonal bracing gives a softening characteristic andeventual decay in capacity to portal action in the legs. The progressive failures for diagonalloading (Figure resemble the end-on characteristic.

Structure with K-braced transverse frames exhibit a more brittle response to broadsideloads (Figure It is approximately linear up to a peak load, followed by a suddencollapse due to extensive brace failure as two compression braces fail over elevation 2 andthe 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 seconddeflected shapes. From this stage, a portal frame mechanism is developed in the legs overtwo elevations (between three horizontal framings) as shown in the third plot.

Longitudinal framing of consists of two diagonal and one X-braced row. The behaviourunder end-on loading is linear up to a peak defined by first member failure. The load thendrops (Figure but to a much higher post-collapse capacity than under transverse loading. A portal frame mechanism develops in the legs, before further brace failure is initiated at other levels of the structure.

Under diagonal loading, structure enters into a predominantly transverse failure mode, 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 wasapplied. 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 representative long term cyclic load history incorporating year and extreme storm 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 witha peak load at 98% of the static collapse value.

Typical results, for structure under broadside loading, are reproduced in Figure 5.30and are described in the authors' words as follows. indicate the cyclic loadhistory, 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'100 year' loading (incoming wave), no members yield under reverse year' loading.Further plasticdeformations occur under initial '10, year' extreme storm cycle, but nomember yield under reverse loading. Under the final year' cycles, some yieldingoccurs the first time the load is reversed. In the final cycles, the response is purely elastic.No members experience repeated yielding, and very little cyclic are observed."

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 acceptablemeasure 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 globaldeformations 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% ofcollapse. 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 structureA2 buckling occurred at 72% of the collapse load and shakedown was obtained 18% abovethis 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 inexacerbating 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 wasperformed. The platform survived Hurricane and the risk of failure under that extreme loading was assessed by hindcasting. The structure's long term reliability was alsostudied by Marshal1 and Bea (1976).

The eight leg platform, stands in water depth. Diagonal bracing sizes range from 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 wasdetermined. No mention is made of gravity loads although it is expected that they wereapplied 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 topof the structure was undermined and essentially sheared over two bays in the end-ondirection. 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 ratioshown 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% ofthe ultimate capacity.

van de Graaf and Tromans (1991A 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 forevaluating 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 waterwith piles penetrating to welded off at the jacket top. The jacket was modelled usingUSFOS (see Section 4) and account was taken of the foundation. Using the nonlinear simulation approach based on linear of constraint loads, due to andvan de (1990) and described in Section 4, the critical wave attack angle, fromend-on, was determined.

The pushover analysis was performed for this direction which in the first case caused lateralfailure in the piles below the but in the second, where lateral failure wassuppressed, a sequence of member failures developed. This is shown in Table 5.22, thefinal 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 5.22Member failure sequence in analysis with lateral foundation failure suppressed

Load Factor Member

Leg B4

Pile B4

Leg

Diagonal - Row 2Level I -

Leg A2

Diagonal Row Bbetween Rows 1&2Level I -

Predictedfailure mode

First yielding due to tension

Pile punch through

Leg global buckling

Member buckling

Leg global buckling

Member buckling

Failureobserved?

Table 5.23 compares the overturning moments at various stages of the analysis with the design loads.

Table 5.23Comparison of jacket capacity with design criteria

Overturning moment

Original design

API RP 2A design

API RP 2A design(8" on diameter for marine growth)

At 1st member failure

At collapse

'Original design

Load factor

In comparison with the original design, the reserve ratio on loads is 3.77 but this is a resultof the low wave height and drag coefficient adopted in the early 1960s. Adopting the API RP 2A criterion for a wave height and C, of 0.6, reduces thereserve to and if the presence of marine growth is accounted for this further reduces to 1.3310.78 =1.71.However, the allowable design capacity is reduced bya factor of about 1.48 when code safety factors and differences in material propertiesbetween 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 atfirst failure, the redundancy factor is 1.23 which is quite low but considered to be 'typical' of such older structures.

5.1.6 Reliability analysesEdwards, Heidweiller, Kerstens and Vrouwenvelder (1985)

This paper presents the results of a case study into the reliability of a typical jacketstructure 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 occurringthan mode The authors demonstrate that Monte Carlo analyses alone are notappropriate, and an approach combining with level reliability analysis is put forward. Load deflection characteristics are presented for only a few unspecified loadings andfailures, 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 initialyielding. Upper and lower bounds with respect to plastic collapse are determined for aspatial 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 influencedepends 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 resultsgiven in terms of the safety index, or probability of occurrence, P. For the basebraced case, failures leading to system collapse all involve the members in the vertical Xbraces 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% abovethat to cause first member failure. The reserve strength factors comparing the ultimate anddesign loads are in good agreement for deterministic and probabilistic assessments of theX-braced structure. The reliability analysis gives values of 3.3 and 3.45 for values ofof 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 givecomparable utilisations to the API code as for the X bracing. As in the base X-bracedcase, system collapse corresponded to the first K bracing failure. From theanalysis 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 Xbracing 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 butthe 'system effect' is larger with a greater difference between the union of first memberfailures 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 environmentis an order of magnitude better than K bracing. In the North Sea environment the measureis 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 thatthe non-uniformity from removing a member, leads to a higher reserve beyond firstmember 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 entirelysymmetric. Indeed, the idealism in the structural configuration and loading is stressed bythe authors, nevertheless the demonstration of the methodology and the insight it affords are instructive.

Table 5.24Comparison of performance of intact X and K-braced structures in different environments

Environment

Gulf of Mexico

Sea

Gulf of Mexico

North Sea

J

Most likely to fail member

Probability

Redundancy

Probability

Redundancy

Redundancy = 0.4 I

3.96 3.71 4.40 4.205.4x106

1.3x105 l . lx104 = 0.12

5.10 4.97 5.98 5.943.0x107 1

1.1x109 3.0x107 = 0.003

Probability

Redundancy

Probability

Table 5.25Comparison of performance of damaged X- and K-braced structures in Gulf of Maxico environment

Union of any1st failure

0.8x103

= 0.7

3.84 3.75 4.09 3.958.8x10J 5.4x106

Most likelyfailure path

Most likely to fail member

Systemfailure

Union of anylst failure

K-braced

X-braced

A: Single damage, no reduction in compression capacity. B: Single damage, reduced compression capacity. C: Two damage members in one X-brace.

1.526.4x101

3.15

2.71

2.26

1.2x102

Probability

AProbability

Probability

CProbability

Most likely failure path

Systemfailure

1

3.11

2.71

2.25

1.645.1x102

3.52

3.42

3.20

1.62

3.50

3.40

3.19

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 RSRis 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 toapply the still water loads and hold these constant (Nordal, 1991; and 1988;Tromans and van de 1992). The design load (eg. year storm load) which maycombine environmental factors such as wave, wind and current, is then applied incrementally up to and beyond the design value until structural collapse occurs. Theloading 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 asnonlinear analysis techniques accurately model component responses in place of lower bound assumptions used traditionally in design. At present approaches differ leading toinherent differences in reserve depending on the philosophy adopted.

A more instructive and informative measure may be the redundancy factor (RF) introducedby 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 indicationof 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 furthercomplication 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 andenvironmental loading, respectively, the criteria may be stated:

and(LRFD)

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 lead to

R 0.88 + 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 apushover analysis as vertical loads are largely held constant as lateral loads are increased.

Tab

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et(F

AC

TS) et

(NO

AM

AS)

Gho

(AD

APT

IC)

LO

AD

-DE

FLE

CT

ION

SYST

EM

RE

SER

VE

RSR

NO

TE

S

depe

nds

onra

teof

load

shed

ding

and

brac

e sl

ende

rnes

ses

Res

erve

dep

ends

on

load

and

rate

of

load

shed

ding

Illu

stra

tion

ofel

astic

join

t

and

rigid

join

tcom

pari

sons

redu

ced

and

grea

ter

som

efl

exib

le c

ases

Seis

mic

ofdu

ctili

tyre

spon

se

Exp

licit

FEm

odel

ling

ofK

Res

erve

der

ived

from

hig

her

join

tcap

acity

infr

ame

than

in

5.26

Su

mm

ary

of

anal

ytic

al in

vest

igat

ion

s of

rese

rve

stre

ng

th

Sim

ple

2Dfr

ames

-2(P

art2

of81

STR

UC

TU

RE

RE

FER

EN

CE

-(A

NA

LY

SIS

ME

TH

OD

)

(MA

RC

,

War

d(S

AFJ

AC

)

et(U

SFO

S)

Gat

eset

(DY

NA

S)

LO

AD

-DE

FLE

CT

ION

SYST

EM

RE

SER

VE

I::

RSR

1.7

Loa

dfa

ctor

1.65 1.8 .43

NO

TE

S

Lim

it st

ate,

loa

dfa

ctor

app

roac

h ad

opte

d

No

still

wat

er lo

adfa

ctor

s.Po

st b

uckl

ing

path

trac

ed

No

still

wat

er lo

adfa

ctor

s

Incr

ease

d si

ze s

econ

dary

bra

cing

aff

ects

gre

ater

post

-ulti

mat

e duc

tility

.

Tab

le5.

26S

um

mar

y o

f an

alyt

ical

inve

stig

atio

ns

ofre

serv

e st

ren

gth

Id

ealis

ed3D

iack

ets

(Par

t 3o

f

STR

UC

TU

RE

RE

FER

EN

CE

(AN

AL

YSI

SM

ET

HO

D)

(Sim

plifi

ed h

and

anal

ysis

)

Lloy

d

Lloy

d(L

inea

r

LO

AD

-DE

FLE

CT

ION

SYST

EM

RE

SER

VE

RSR

NO

TE

S

Res

idua

l cap

acity

qua

ntif

ied

inev

ento

fda

mag

e

Ana

lyse

swith

rem

oved

mem

bers

gav

e se

quen

ce

offa

ilure

san

dR

F-1

.5

Mem

bers

rem

oved

and

targ

et r

esid

ual c

apac

ity

achi

eved

fora

dif

fere

nt p

lan

brac

ing

and

3lo

addi

rect

ions

byin

crea

sing

mem

ber s

izes

. C

little

cap

acity

for

redi

stri

butio

n

Tab

le5.2

6S

um

mar

y o

f an

alyt

ical

inve

stig

atio

ns

of

rese

rve

stre

ng

th -J

acke

tst

ruct

ure

inve

stig

atio

ns

(Par

t4o

f

STR

UC

TU

RE

RE

FER

EN

CE

-(A

NA

LY

SIS

ME

TH

OD

)

Jaco

bsFy

fe(U

SFO

S)

FEN

RIS

,

LO

AD

-DE

FLE

CT

ION

SYST

EM

RE

SER

VE

RSR

NO

TE

S

Res

erve

depe

nds o

n lo

adec

cent

rici

tyan

d ra

te o

fpo

st-b

uckl

ing

load

she

ddin

g

Illus

tratio

nof

elas

tic jo

int f

lexi

bilit

y

Flex

ible

and

rigid

join

t com

pari

sons

indi

catin

gre

duce

d ca

paci

ty a

ndgr

eate

r def

lect

ions

inso

me

flexi

ble

case

s

Seis

mic

inve

stig

atio

n of

duct

ility

ass

ocia

ted

with

elas

ticpl

astic

join

t res

pons

e

Tab

le5

.26

Su

mm

ary

of

anal

ytic

al in

vest

igat

ion

s o

fre

serv

e

STR

UC

TU

RE

RE

FER

EN

CE

(AN

AL

YSI

SM

ET

HO

D) et

et(S

EA

STA

R)

Sore

ide

et

(USF

OS)

Moa

net

(USF

OS)

LO

AD

-DE

FLE

CT

ION

SYST

EM

RE

SER

VE

RSR

W2.

0SW

2.2

N2.

0

W2.

3S

2.0 2.49

diag

.4.

394.

32lo

ng.

3.71

Jack

etst

ruct

ure

inve

stig

atio

ns

NO

TE

S

Des

ign

anal

yses

toac

hiev

e ta

rget

in

both

inta

ctan

dda

mag

ed c

ondi

tions

.

Firs

t mem

ber f

ailu

re tr

igge

rs c

olla

pse d

ueto

load

dire

ctio

nan

dst

ruct

ural

con

figu

ratio

n.

Inta

ct r

eser

ve s

tren

gth

Cas

es 2

-4si

mul

ate

dam

age

with

mem

bers

rem

oved

.

Inta

ctre

serv

e st

reng

th C

ases

2-4

sim

ulat

eda

mag

ew

ithm

embe

rsre

mov

ed.

inve

stig

atio

ns

ofre

serv

e

STR

UC

TU

RE

RE

FER

EN

CE

-(A

NA

LY

SIS

ME

TH

OD

)

Bea

et(S

EA

STA

R)

et

LO

AD

-DE

FLE

CT

ION

SYST

EM

RE

SER

VE

N

OT

ES

RSR

Exa

mpl

e re

qual

ific

atio

n an

alys

is to

illus

trat

ero

leof

ultim

ate

capa

city

ana

lysi

s in

ass

essm

ent

insp

ectio

nan

dm

aint

enan

ce.

1-

Plat

form

asis

2-

Rep

air d

amag

e 3

-R

epai

ran

dgr

out l

egs

4-

Rep

air

and

rais

e de

ck

Rea

sses

smen

tto

com

pare

upg

rade

sch

eme

for

exis

ting

inst

alla

tions

faci

ng o

verl

oad.

Tab

le5.

26S

umm

ary

ofan

alyt

ical

inve

stig

atio

nsof

rese

rve

stre

ngth

-Ja

cket

hind

cast

ing

and

relia

bilit

y(P

art8

of

STR

UC

TU

RE

RE

FER

EN

CE

(AN

AL

YSI

SM

ET

HO

D)

Tro

man

s(U

SFO

S)

Tro

man

s(U

SFO

S)

RE

LIA

BIL

ITY

et

Hol

m e

t et

relia

bilit

y)

LO

AD

-DE

FLE

CT

ION

SYST

EM

RE

SER

VE

RSR

3.77

(Ori

gina

lde

sign

load

) 2.

22(A

PI)

NO

TE

S

Firs

t mem

ber b

uckl

ing

sequ

ence

offa

ilure

and

colla

pse

With

pile

fai

lure

max

imum

load

fac

tor=

1.0

Dem

onst

rate

sMon

teC

arlo

ana

lysi

s alo

nem

ayno

tre

veal

corr

ect p

roba

bilit

ies f

or d

iffe

rent

fa

ilure

mod

es.

Com

bina

tiono

fL

evel

relia

bilit

yan

alys

is p

ropo

sed.

Sens

itivi

tyw

ithre

spec

t to

resi

stan

ce e

valu

ated

fo

r di

ffer

ent m

embe

rs

Rel

iabi

lity

asse

ssm

ento

ffa

ilure

for

inta

ctan

dda

mag

ed st

ruct

ures

. G

reat

er s

usce

ptib

iiity

for

K-b

raci

ngsh

own.

brac

ing

utili

satio

n due

en

tirel

yto

shea

r.A

lso

grea

ter c

onse

rvat

ism

inX

brac

ing

effe

ctiv

e le

ngth

s.

Wherever possible, Table 5.26 presents the load factors X on the storm loads as theIn limit state assessment a minimum 1.5 factor would be required to meet 'design' criteriagiving an RSR arguably of the values given.

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-bracedpanels 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 numericaltechniques.

The analyses have been based on both idealised structures (eg. Lloyd and and realstructures, either for design optimisation (Piermattei et al) or evaluations (van deGraaf 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 beinherent 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 analysedby et al exhibit little additional capacity beyond first member failure.

In evaluations it should be noted that more realistic loading may be adopted thanwhen 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 onmembers to reducing capacity. Specific aspects of system reserve may be identified as follows.

5.2.2 Bracing configuration

The simplified assessment by Marshal1and the comparisons of configurations by andand 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,Jacobs and Fyfe, and Nordal, Piermattei et al, and et al etc) generally offer great ductility. The diagonal bracing in the transverse frames of the platformanalysed by Dolan et al gave no reserve beyond first member failure as the load path waseffectively destroyed. Diagonal bracing in the face frames of jacket structures were alsocritical when the framing direction was identical around the platform (Tromans and van deGraaf). 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 reservestrength, compared with fully X-braced panels (Jacobs and Fyfe, Pike and Grenda etc).Lloyd demonstrated significant weight penalties if primary bracing were to be toachieve 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 ofinformation published, quantitative conclusions are difficult to draw beyond the qualitative discussion presented above. This point was emphasised by et al who showed thatin 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 inreserve strength are calculated. and report an increase in RSR from 1.7 to 2.3

as bracing is changed from K to fully braced X. The increase in structural weight to givesuch 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 newjacket 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 member failure is synonymous with structural collapse (Dolan et al, et al, Tromansand van de Graaf). These instances are directly attributable to the bracing configurations (non redundant cross-diagonal bracing in transverse framing and diagonal bracing in onedirection in transverse frames). This emphasises that in addition to the level of RSR animportant 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 behaviourTable 5.27 identifies whether particular types of analyses have been performed. The firstaspect 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 exceedthose 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 beenconsidered to investigate aspects of jacket performance (eg. Piermattei et al, Jacobs andFyfe). In the first example, 3D analyses were undertaken subsequently, but in the work presented elements had been between the two analyses such that direct comparison cannot be made. The best example is therefore given by the simple frame analyses by Pikeand 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 adequateplan bracing to transmit the loads. This was also demonstrated by Lloyd. If sufficientbracing 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 baseloads related to directional sea states may be more meaningful, together with correlationto elastic component (eg. Tromans and van de Graaf, et al, etc).

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 behaviour et al) indicates that the sequence of failure and global structural 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 jacketstructures, appropriate modelling of soil-structureand pile-structure interactions also needsto be undertaken.

Tab

le5.

27A

spec

ts o

f co

llaps

e be

havi

our

mod

elle

d in

rese

rve

stre

ng

th a

naly

ses

RE

FER

EN

CE

SIM

PLE

2DFRAMES

Bou

wka

mp

etal

Ued

aet

Gho

etW

ard

etG

ates

et

IDE

AL

IZE

D3D

JAC

KE

T

Llo

ydL

loyd

JAC

KE

T S

TR

UC

TU

RE

S Ja

cobs

Fyfe

et

etet

Sore

ide

etM

oan

etet

etet

van

de

ASP

EC

TS

OF

CO

LL

APS

E B

EH

AV

IOU

R M

OD

EL

LE

DFO

UN

DA

TIO

NFA

ILU

RE

DA

MA

GE

DM

EM

BE

R

flex

ibili

ty

plas

tic jo

ints

-sho

win

gin

flue

nce

onfr

ame

uctil

ityin

sei

smic

des

ign.

mod

elle

d ex

plic

itly

usin

g FE

.X X X

offr

ame

capa

city

in n

onre

dund

ant

with

wea

kK

ioin

ts.

Invo

lved

infa

ilure

sce

nari

o

van

de G

raaf

etal

Hol

met

al

Nor

dale

t

Not

incl

uded

Infl

uenc

eof

grou

ted

leg

pile

son

jack

etre

spon

sein

clud

edN

otin

clud

ed

X

Bra

ceca

paci

tiesm

odif

ied

sim

ulat

ion

elem

ents

X X X X X X

Not

incl

uded

.N

onlin

ears

prin

gsbe

twee

npi

lesa

nd s

oil.

Inst

ance

sof

failu

re w

here

com

pres

sive

skin

fric

tion

exce

eded

,

With

nonl

inea

r fou

ndat

ion

inta

ctst

ruct

ure

failu

re

mea

nsno

rin

clud

edin

invo

lved

foun

datio

n.

Mod

elle

dbu

tstr

uctu

ral f

ailu

res.

So

il re

sist

ance

mod

elle

d bu

t fai

lure

inja

cket

.N

ot in

clud

ed

No

foun

datio

n fa

ilure

Fo

unda

tion

late

ral

failu

re s

uppr

esse

dat

pile

-soi

lint

erfa

ce.

slip

inle

gs m

odel

led

spri

ngs

Pie

failu

resu

ppre

ssed

bas

ed o

nco

rrel

atio

nw

ithda

mag

e

X X Xcr

itica

lcr

itica

l) b

race

s re

mov

edX=

1.6

(1X

Mem

bers

rem

oved

toev

alua

te r

edun

danc

y in

flue

nce

Mem

bers

rem

oved

-as

ymm

etry

Mem

bers

rem

oved

and

wei

ght

toac

hiev

e

Mem

bers

rem

oved

.X

Mem

bers

rem

oved

Mem

bers

rem

oved

Mem

bers

rem

oved

Mem

bers

rem

oved

Mem

bers

rem

oved

mod

elle

dX X X X X X X

Rel

iabi

lity

for

dam

aged

stat

e

The role of comparative analysis

The analyses presented in Section 5 have revealed important aspects of jacket reservecapacity. However discrepancies between base design criteria the availability of keydetails have limited the comparisons that can be made. In contrast the few comparativeanalyses that have been presented (see Table 4.5) have been most instructive.

Such comparisons enable not only the performance of different software packages to beassessed but also provide unique opportunities to validate different approaches to modellingand 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 reliance that is being placed on the calculation of by the offshore industry. Aprincipal 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 29.00036

C

0.8P,. ofP, F, Area

-014

DESIGN TRADE-OFFOPTIONlI HORIZONTAL BRACE

21 HORIZONTALBRACE

1.00 1.05 1.10 1.20 1.00 1.05 1.15 1.20.... . . . SHEAR. LOAD.

SHEAR V,.

Figure 5.1Two bay X-braced frame analysed by Pike and Grenda

NOTE:

FRAME l

0 -2 -4 -6 -8 -BRACE UNLOADING RATIO

Figure 5.2Parallel K-braced frames showing influence of eccentric loading and rate of brace unloading p on

reserve strength (Pike and Grenda)

JOINT 1

SECTIONSl

JOINT 2

Figure 5.3jacket frame analysed by et to illustrate joint flexibility effects

SHEAR FAILURE (BRACE)

FAILURE (BRACE)

R I G I DFLEXIBLE JOINTS

Figure 5.4of joint capacity on response identified by Ueda et

: hinge

Flexible Frame

-0 .5 0.0 0 . 5

(m)

Figure 5.5Analysis of a jacket frame with flexible and rigid joints by Elnashai and Gho

Figure 5.6Frame models analysed by and showing differences in joint capacity and

post-ultimate axial-moment interaction both within the frame and in isolation

tU

REFERENCE

IS

I

6 ELEMENTS- ELEMENT

0 20 0 3% 0 0 4% 0 0

DISPLACEMENT (m)

Figure 5.7Jacket frame analysed by et using MARC and

TOTAL X LOAOTOTAL Y

ISTONNES

LATERAL LOAO

a . INTACT.

0 . 0 , . , . , . , . , .

Figure 5.8Analyses of jacket frame by Ward and lzzuddin and et

- MARCINTRASAFJACSAFJAC

0 0.5 l

LATERAL LOAD

Figure 5.9Comparison of jacket frame analyses by et IMARC, INTRA),

Ward and lzzuddin (SAFJAC) and et

MEMBER INELASTICITY

STRUT

@m-@

STRUCTURE FORCE-DEFLECTION PLOT.

Figure 5.10Comparison of energy absorption ductility for 2D jacket frame analysed by Gates et

BROADSIDE LOADS

INTERNAL 2.3 .69 e l a s t i cTRUSS 3.0 .79 p l a s t i c

1 .2 e l a s t i cTRUSS 3.8 .79

END-ON 2 .6 .72LOADS 5.8 .85 p las t i c

Figure 5.11Redundancy calculations for Gulf of Mexico structure due to

ROW l A

Figure 5.12and X-braced jacket

I

RESIDUAL STRENGTH

CASE A----CASE B--------- CASE C

Figure 5.13Four-legged jacket used in redundancy study by Lloyd

V EL. -V EL. -

;-- EL. - 41

,

30

o , I I

o 40 80 o

h

Figure 5.14Intact jackets pushover analysis by Jacobs and Fyfe

Figure 5.15Brace configuration study covering X, K and diagonal bracing (Jacobs and Fyfe)

LINEAR FOUNDATION MODEL

l

LINEAR FOUNDATIONMODEL

Figure 5.16Jacket analysed by et

Figure 5.17Analyses of Veslefrikk jacket report by Nordal

FRAME 1 FRAME G

01 02 0.3 0 7 08 09

Lateral Displocernent (meters)

Figure 5.18Nonlinear analysis of four-legged Goodwyn concept et

Lateral Displacement (meters)

Figure 5.19Nonlinear analysis of eight legged Goodwyn concept et

Figure 5.20Failure sequence for the A platform et

Finite model of Collapse mode

2.5

of intact

Figure 5.21Analysis of 3D jacket structure et

Figure 5.22Eight leg jacket analysis by Moan et

Figure 5.233D box frame analysed by Sordde et

Figure 5.24Capacity consequence evaluation due to Bea et

Figure 5.25Load displacement curves for example jacket for AIM alternatives et

AUSTRALIA

LOCALITY

OTHER PLATFORMS - PIPELINES

SOUTH EAST ELEVATION

Figure 5.26Esso Australia platforms for upgrading using RSR approach et all

Structure

Figure 5.27Structures analysed in investigation, to scale et

Lading

Lading (C) (West)

Figure 5.28Pushover responses for structure analysed by et

Figure 5.29Pushover responses for structure analysed by et showing deflected shape

""m*!

Load

Figure 5.30Cyclic analysis of structure under broadside loading et

Figure 5.31Cyclic analysis of structure A2 under broadside loading et

A m

End-on failure mechanism

tStructure failure surface

Load factor: lateraldeck deflection,end-on wave direction

Figure 5.32South Pass SP62-B jacket and van de Graaf)

Row A 1 h3

Elevationviews of

Environmentalbad

Load lateral

C

0.2 0.4 0.6 0.8 1 12(m)

Load deck

Figure 5.33Gulf of Mexico platform used for hindcarting analysis (van de and

(leg)

displ.

Figure 5.34Failure modes in reliability analyses by Edwards et

Figure 5.35Influence of yield on system behaviour demonstratedby Holm et

5 0

Y

3.0

to

17, WAVE :

stressbar 223

Compression yield

\ of bar 244X

240 120 60

FORCE

SEMI - BRITTLE

DEFORMATION

Figure 5.36Ductilelbrittlelsemi-brittle response of member considered by Nordal et

MEMBERGROUP DIA. THICK.

KB2

LG2

LG4

Figure 5.37K-braced variant of Figure 5.12 adopted by Nordal et

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 andBOMEL 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 beof 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 dominatedby plasticity in the legs. These factors reduce their value in relation to assessing offshorestructures where tubular joints are used and bracing failures are more likely. The andShin 3D tests had no mid-height plan bracing and all had boxed face frame joints but gavea 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 availableanalysis 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 relatelargely to the unexpected performance of tubular joints in a frame and the low values aredriven 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.Analysis of idealised jacket structures, such as the study by Lloyd and offeredfundamental into reserve strength. The simple frame analyses by Pike and Grendarevealed the significance of post-buckling member characteristics and system symmetry. Similarly Connelly and Zettlemoyer were able to reveal the important influences of tubularjoint 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 ofresponses which emerge, but the difficultly is in making comparisons on an equal footing. Piermattei et al and Bea provide background to the selection of target from bothintact and damaged structures and and for example, illustratedthe contributionof different bracing types to system reserve. This revealed how changes to bracingconfigurations 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 ultimate capacity (Dolan et Trornans and van de even in real offshore structures. The limitation that foundations can present to system reserve was brought out byet 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 RSRpredictions 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 inpractice 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 notaccounted for in accepted elastic design procedures. In assessing the safety of offshoreinstallations, it is now recognised that the risks of damage from vessel impact and droppedobjects or abnormal environmental loading (eg. hurricanes, typhoons, earthquakes) are notnegligible. 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. Tothat 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:

Ultimate structure resistance (ie load at collapse)RSR =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 onloading and resistance are adopted. These factors, accommodating uncertainty, conservatism and safety, in the original design, mean that an RSR well in excess of unityis 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 forjackets, 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 RSRcompared 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

Ultimate structure resistance RF = Structure resistance at first member failure

Analytically it is important to distinguish between first yield in a compression member andthe 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 againstenvironmental loading, damage to the critical member could cause immediate structuralcollapse. The reserve strength review has identified analyses of existing installations where initial failure triggers immediate structural collapse (Dolan et al, et al, Tromans andvan de Graaf). By virtue of the framing arrangements and relative member sizes, other structures have been shown to have substantial sources of reserve and Jacobsand 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 loadeven after a compression brace buckles, provided members are not too slender and thesupports do not precipitate rapid unloading from the compression member. Similarly,diagonal bracing where members are inclined alternately offers an alternative tension loadpath to counter load-shedding from a buckling compression member. Examples in which the primary X joint has yielded reveal the potential for deformation and redistributionsuchthat the full capacity of both load paths through the brace can combine to give considerable reserve capacity Conversely K bracing offers no alternative load paths 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 theevent of extreme environmental load (Jacobs and Fyfe). A fractional increase in structuralweight 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 fullstructure 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 ofthe 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 threedimensional representations are not presented in the literature. Such investigations wouldoffer significant additional insight into the performance of jacket structures.

6.3 RESERVE STRENGTH CONSIDERATIONSFOR OFFSHOREJACKETSTRUCTURES

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 tobe 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-planestiffness as well as the associated load contributions. For some structures this isstraightforward, but in other instances the translation from 3D to 2D is complicated,requiring experienced engineering judgement. Warning or guidance on this is not generallygiven 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 revealthis.

6.3.2 Modelling of jacket loads

The components of extreme environmental loads (wind, wave and current), as well as thedistribution down the structure, vary with the return period considered. Forevaluations it may therefore be necessary to determine the critical loading state and applyfractions of this loading until collapse occurs. This differs from the usual approach whereby the environmental loading for the year design storm is incremented tocollapse. 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 thesame 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 membercapacity. 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 relativemeasure or reserve this may not be of major importance, however, for evaluationsor accurate predictions, the full loading should be considered. Factored nodal loads maybe applied to give an equivalent influence, or for phenomenological models a reducedcharacteristic 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 furtherconsideration in nonlinear analysis where, because of plasticity, instability and load re-distribution, the ultimate load can be significantly affected by the loading history, see Section 6.3.6 for further discussion.

Influences on RSRFor jacket structures, measures of RSR are often presented in terms of base shear oroverturning moments. This needs qualification as the same storm loading from different directions will generate different base shears and overturning moments. Again, as arelative 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 ultimateRSR 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 anycomponent may be found. In incrementing the loading to collapse, the structure may havesignificant capacity for redistribution beyond first failure giving a high RSR. Subject toloading 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.

Analysis for a rosette of environmental loads (eg. van de and Tromans, 1991) is tobe recommended but may be considered too costly or time consuming. However, if areduced analysis approach is to be followed, it is clear that it needs to be established on afirm 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 olderstructures 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 beapproached 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 loadsachieved in isolated tests and are not related to the limit of linear behaviour or restrainingeffects of chord fixity or continuity.

The platforms analysed by Bea et and Shinners et (1988) were older structureswithout 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 developingspecific nonlinear strut and beam-column elements in the second. Since 1988 however, thepublished 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 thepeak load. It is therefore certain that at the ultimate load levels being predicted for jacketstructures, nonlinear joint behaviour will have commenced. The implications from ignoring this may be significant. As demonstrated in the SCI and BOMEL tests, softening in theresponse of a joint would limit incoming brace loads and so protect the membersthemselves 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 thebehaviour 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 allanalysis 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 jacket and considering it as a component of the system be adequate when consideringboat impact scenarios, for example. In other instances foundation failure is suppressed andlinear interactions are imposed. et al, for example, indicate that for structuresdesigned 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 Nordalmay be largely attributed to foundation modelling assumptions.

To establish a relative measure of structural performance, explicit modelling may not berequired. However, the absolute RSR for the system may be governed by foundationcharacteristics. Furthermore, the global deformations can be far greater when nonlinearfoundations are accounted for and serviceability limit states such as deflection criteria forrisers 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 theliterature, 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 conditions within the need to be considered. The loading will be cyclic but abouta high mean load and so differs from earthquake scenarios where repeated load reversalsmay 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 somepost-buckling capacity is retained, with subsequent reductions and increases in load,fracture from local crimping may be precipitated. Alternatively a structure may survivean 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-cycleperformance of members and joints are sparse.

Recent work by SINTEF and Shell Research et al) has made a significantcontribution 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 froman extreme storm without failure are likely to survive the entire storm indicating thatpushover analysis generally suffices to demonstrate a structure's integrity. However, notall structures were able to achieve shakedown near the static collapse load for each stormscenario. 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 investigated more fully. This work is within the SINTEF programme 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 loadlevel 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 thedisplacements necessary to mobilise alternative loadpaths, significant plastic deformation may or may not occur. This degree of plastic deformation could be assessed at the stageof performing the static pushover. Furthermore, if first member failure and ultimatecollapse are almost simultaneous, it may be concluded without further analysis that thecyclic 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 onidealised 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 redundantsystem plastic deformation of the critical member might take place as loads were redistributed until the ultimate strength was reached at a higher load factor. Figure6. la illustrates the cases.

Both structures may be expected to achieve shakedown around the first member failureload, 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, thismay be of less concern. Any capacity beyond the initial failure load level is a bonuswith respect to the first design which would undergo a static collapse if the load wereexceeded.

2. Reassessment of older structures

A potentially greater concern may be in reassessment of structuresdesigned to outdatedcodes 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 staticcapacity 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 thesame 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 failto meet current component based criteria and this is a practical case in which pushoveranalysis may be used to demonstrate system adequacy. However, it is here that cyclicconsiderations may be important. If the second structure relies on large plasticdeformations to achieve the peak load, it may be that shakedown could only beachieved 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 responsecould 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 componentbased 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 shownwould be equally satisfactory, despite the concerns from a cyclic loading viewpoint expressed for the second case under item 2 above. By having a correspondingcomponent based criterion the second structure would only be acceptable if first failurewere achieved at a higher load level than that shown, thereby potentially increasing thesystem 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 theapplication of these techniques and the development of a philosophy for structural evaluation.

Beyond the high stress low cycle plasticity effects which are being modelled, futureconsideration also needs to be given to low stress high cycle fatigue which may result atpoints of stress concentration associated with component failures, fracture potential andtubular joint performance under cyclic loads.

The need for more data extends also to the assessment of inertia and near failure dynamicsand strain rate effects which may modify the calculated. This is an aspectrequiring further investigation if the realistic performance can be accurately modelled.

6.3.7 Accounting for damageThis also relates to the ultimate strength assessment of damaged structures. Theprogression 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 introducingoverload in others.

Hindcasting analyses can be calibrated against recorded evidence from examples wherestructures 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 inrelation 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 aprobabilistic inspection plan. Conversely, where a component, susceptible to impact orfatigue, 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 thereliance 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 repeatedlyin the literature and may be compared with a baseline factor of around 1.5 which may beanticipated 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. Thiswill inevitably be linked to the purpose of the analysis and the procedure adopted but mustextend beyond a target RSR value. Based on the discussion through Section 6.3, it maybe 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. minorvessel 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 thecontinued integrity and safety of the structure and operations. To that end it is clear thatcombined 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 inoptimising a structural configuration to maximise the RSR envelope without incurring aweight (cost) penalty (eg. and 1988). The value of such analysis, for assuring 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 extremelycomplex. Although nonlinear analysis tools have introduced the facility to model thebehaviour, 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 sothat phenomenological elements are used appropriately at different locations within the structure.

The structural unit method enables one element to be adopted per member in themodel so that conventional elastic analysis models can be readily translated for collapseanalysis. Furthermore in early stages of the collapse analysis, when the structure is responding elastically, solution is rapid. High order polynomial element formulations, forexample, capture both material and geometric nonlinearities. Automatic subdivision onoccurrence 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 andinterpretation of results are important requirements of collapse analysis programs. Formost features, developments are but it will be some years before comprehensiveand validated tools are available.

6.4.2 ValidationValidation 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 sameprogram which offers any opportunity for validating the complex nonlinear redistribution, failure sequences and modelling approaches for 3D jacket structures. However in manycases 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 forcalibration. A further phase of Frames Project is planned (Bolt et al, 1994) toencompass 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 LoadFactor Factor

First Member Failure

First Member Failure

Global Deflection Global Deflection

LoadFactor

ILoadFactor

Global Deflection Global Deflection

Figure 6.1Comparisonof 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 considerableimportance 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 besynonymous with structural collapse. It is this reserve strength which must be utilised todemonstrate that loads beyond the original design scenarios can be sustained safely.

This recognition of the importance of reserve strength technology has been met by thedevelopment 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 tosufficient accuracy. Despite calibration at the component level, benchmarking against the available test data identified in this review is recommended. Furthermore, without 3D testdata for direct comparison, recourse should be made to comparative analyses so that byresolving 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 environmentalloads are factored - the factor on the design load at the peak determines the RSR. Indiscussion, this review has suggested that although providing a relative measure of systemreserve, the RSR has little physical relevance and more meaningful assessment strategiesare proposed, where appropriate. Furthermore, the ability of a structure to withstandextreme loads needs to be assessed not only in relation to capacity but in terms of deflectioncriteria, 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 andevaluating structural reserve should be devised and verified against a series of comparativecases 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 arefollowed 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 isdemonstrated 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 andchord 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 mechanismsunderlying 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,FACTS, INTRA, KARMA, RASOS, SAFJAC, USFOS) based on variations 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 loadsfor 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. Theconclusion 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 removingmembers which may or may not be conservative for the global system response.

Collapse analysis is generally performed by holding stillwater loads constant andincrementing 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 notnecessarily correspond to maximum utilisation.

Selectionof loading strategy. Maintaining loads and factoring environmentalloads changes the loadpattern and more rational distribution, based on uncertainty of

loading scenarios and structural action may be more The sequenceof loads is also important.

Appropriatemodelling. Conservative component responses may not yield lower boundRSR 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 togetherwith 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 steelweight and cost.

Data requirements. Aspects of jacket behaviour have been which may beimportant in the ultimate response of jacket structures but for which 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 jacketstructures are required in the areas listed above. Evidence from the tests and analysesreported is that foundationsand tubular joints are particularly significantand urgentlyrequire consideration given the configuration of older and foundationconditions.

Analysis. Information and criteria on which to select appropriate analysis tools forspecific situations are required. Benchmarking against test data will be a valuable first step. Comparative analyses of the same structure using different programmes and theapproach of different analysts will follow. In test data for jacket typeframe structures and joints should be generated to provide a rigorous test for

Greater confidence in the analytical capability and accuracy will lead toreduced RSR requirements and greater economy.

methods. Current approaches to load application are simplified giving anindicative measure of reserve strength but without modelling all aspects of loading

regime. A more rational methodology for incrementing loads to collapse should bedevised and validated, including for example guidance on the treatment of lateralmember loads, the use of mean (or characteristic) component capacities, selection oforientation, the need for sensitivity studies, etc.

Acceptance criteria. Linked to analysis methods is the need to define target inrelation to bothWSD and designs. criteria should reflect the purpose of theanalysis and should extend beyond the RSR tothe consequences of overload, deflection criteria, vulnerability of key components to other risks etc, so that the continued safe operation of the beyond the extreme loading event may be considered. Acceptancecriteria need to be laid down and in conjunction with the formalisation ofanalysis 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 beingmodelled.

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APPENDIX A

REVIEW UPDATEAUGUST 1993 - MAY 1995

INTRODUCTION

The main text of this Review was completed by February 1993. The document wasexpanded 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 forthe 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 relationto industry's understanding of ultimate system strength and its application of the technology in the intervening period.

Hurricane passed through some 3,000 offshore structures in the Gulf of Mexicoin August 1992 and provided the opportunity for analyses to be performed to 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 bothcollectively and in relation to individual structural performances in Section A2.

This body of Hurricane information also enabled the API Task Group, TGdrafting 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 thatthe 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 encompassingtrial applications of the procedure and a benchmark ultimate strength analysis of a specificplatform. 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 inSections 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 newinformation either illustrating or helping to resolve some of the problems faced. For thisreport 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 inSection 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 hasbeen 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.

A2.1Summary of key references 1993 - May 1995

Reference

et (1994)

Botelho et

et (1994)

et (1994)

et (1994)

van de Graaf (1993.4)

van Langen et (1995)

et (1994)

Bea et Bea (1995)

Key issues

Sensitivity of RSR to assumed imperfections. Relation between ultimate strength analysis and elastic design.

following Hurricane Andrew. Importance of jointmodelling capability.

Use of experimental data and numerical analysis to Hurricaneforces and structural damage.

Redundancy in 1950s Wave in deck loads significance.

Consolidated based on Hurricane hindcasts. Importance ofjoint and foundation modelling.

Dependenceof RSR on environmentand 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 theultimate strength of a platform. Elastic design analysis, on the other hand, is intentionallyconservative 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% to30% 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 theengineer working with both approaches the sources of conservatism may not be readily apparent yet meaningful interpretation of ultimate strength analyses may rely on thisunderstanding. The authors therefore set out to bring the approaches together, firstly bycalibrating nonlinear element formulations to an acceptable design level and secondly byremoving 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 (Popov et al, 1980; et 1982)see Figure 3.11.A planar jacket frame

et al, 1988; Ward and 1988; et 1991)see Figures 5.7, 5.8 and 5.9.A 3D jacket structure

et 1993)see Figure 5.27, Structure A2.

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 butotherwise checked against NPD requirements;nonlinear analysis with the USFOS nonlinear element formulation and failuredefined by the of three hinges;

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 theredundancy factor, RF, which is the ratio of the ultimate strength to the load at which the first component fails.

Table A2.2Comparison of load factors at first member failure predictions and at system collapse

First member failure prediction

Linear analyses NonlinearPushover

Structure K = 0.8 Analysis

Plane frame2D jacketNorth Sea Jacket

broadside 2.90 3.28end-on 2.18 2.35

The conservatism attributable to the K factor can be seen clearly by comparing the first andsecond results columns. By comparing the second and third columns it can be seen thatappropriate selection of effective length factors can give a more meaningful representationof member failure.

The effects are studied more extensively in the paper and two further conclusions may becited. 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 maximummoment occurs near as this coincides with the simplifying assumption of hinges forming only at member ends in USFOS (see USFOS description in Section 4). For conditions of double curvature the largest discrepancy (21%) was found.

Completing the investigation, the effects of initial imperfection on first member failure andsystem collapse loads are reported. Table A2.3 shows the influence of a 0.5%imperfection.

Table A2.3Percentage reduction in collapse loads for a 0.5% imperfection

First member failure System collapse load

It can be seen that for these X-braced structures, where system failure is governed by morethan 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 istherefore 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.

5.21.4

4.38.7

I

Plane frame2D JacketNorth Sea Jacket

broadsideend-on

7.810.9

6.811.2

Botelho, Petrauskas, and Kan

This paper is the first of several in this Appendix dealing with analyses undertakenfollowing the passage of Hurricane through some 3000 offshore structures in theGulf of Mexico in August 1992. Ten major platforms were toppled directly by thehurricane 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.

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 orsurvival, and collectively to provide a basis for future risk management of the manystructures in this hurricane prone region (see et al, 1994 reviewed below).

This specific structure, ST was an 8 pile platform installed in a water depth in 1958 having been designed to the then standard 25 year criteria. However, the deck hadbeen raised in 1991 (Figure A2.1) in anticipationof significant loads should waves encroachthe deck in extreme weather. Nevertheless the platform was completely toppled byHurricane .Pushover analyses were performed by the authors using CAP (Section 4) and some detailsof 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 begoverned 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 maysever 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.

PushoverLoad

Direction

Broadside

Diagonal

End-on

FirstNonlinear

PileEvent

1,550

1,800

1,550

Table A2.4Pushover analysis results for 130 "A"

FirstNonlinearBrace* orJoint **

Event (kips)

Pile HingeslBraces

Buckledl

FailureLoad

2,450

3,000

Failuremechanism

Joint failure1Pile Hingesl

BracesBuckledl

Leg MembersYielded

Joint failure1HingeslBraces

BuckledlLeg Members

Yielded

Median Maximum Base Shear

COV = 0.25

2,150

COV = 0 .0

1.850

The load deflection response for broadside loading in Figure A2.1 also reveals a ductilesoftening 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 Technology Conference (Botelho et al, photographs were shown of platformsrecovered after Hurricane with complete severance across the gap region of Kjoints. Figure A2.2 shows the line of frame action driving shear failure in the gap K jointsin frame tests (Bolt, 1995). This mode of failure was somewhat unexpected inthe frame tests but the complete severance across joints in Hurricane confirmedthe value of the tests in highlighting frame action and potential failure modes.

The table indicates redundancy factors (failure nonlinear event) of 1.7, 2.3 and1.6 for ST in the three directions. These are substantial values which may not beachieved 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.With a COV of 0.25 the probability of failure for ST under the diagonal wave wassome 54%. However, whilst this tied in with the load at failure of the platform, it should be noted that ST located in the same area survived without damage 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 inreserve 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 LightThe South Timbalier 161A platform was one of those damaged by Hurricane Andrew. Theeight 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 priorto the introduction of API guidelines. The maximum hurricane loads corresponded to thebroadside 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 evidenceof 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 testprogramme 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 byBotelho et al tubular joint characteristics were ascribed to members in place of aseparate joint modelling facility. However, with reference to the ductile response of thetest 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 complete platform failure would have been associated with a wave.

A number of other factors relating to the ultimate strength prediction of jacket structurescan 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 Amocoprocedures.Hindcasting demonstrated that K brace effective lengths were less than 0.64 andtherefore 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 theinterpretation 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 analysedusing 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 environmentalconditions and the hydrodynamic loading recipe according to API RP 2A 20th Edition.

The redundancy factors (ultimate failure) are quite considerable (1.3 to 1.5)compared with typical values (1.2 - 1.3) for modem 8 leg jacket designs et al,1994) are clearly attributable to the structural configuration. Detailed results in thepaper 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 deepscour bowl caused by the 1969 blow-out. The uncertainty in foundation characteristics wasaddressed with sensitivity studies to upper and lower bound assumptions as advocated inSection 7.

Table A2.5Reserve strength and redundancy for a 1950s vintage 46 leg shallow water platform

Base Shear for Wave Direction (kips) 1

25 year storm I 1470 1355 It

50 year storm I 1220 1615 I 1650 I

End-on

I I I

First yield 1235 1550 1915

IDiagonal

year storm 1335 1845

Ultimate capacity I I 2910

Broadside

2060

RSR 1.20 I 1.11 I I

The reserve strength ratios, in the range 1.1. to 1.4, are presented with respect to presentday year criteria. These values low in absolute terms but may be considered to besubstantial 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 the100 year storm.

The paper demonstrates the versatility of reserve strength technology to encompass a widerange of offshore structural forms and evaluate structural safety. Calculations of theprobability 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 JIPreported in this paper. Comparison was made between survival, damage and failurepredictions, 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 tomaximise 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 theplatforms had survived, three were damaged and four failed during Andrew. Failure ofmultiple K joints was reported in all four of the failed cases and two in which damage wasreported.

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-ultimateresponses. Furthermore the platform failure mechanisms generally involved some aspects of foundation failure, again underlining the importance of appropriate modelling which wasoften 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. Inaddition to the description of failure modes, it can be seen that the ultimate capacity compared with the loads for the hurricane ranged from 0.73 to 2.80, with reservestrength ratios (in comparison with the year load) in the range 0.58 to 2.28. Additional 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.

Uncertaintywas 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 directjacket 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 FigureA2.3 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 areasonably 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 notbe 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 factorsreflecting 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 strengthevaluations 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 code into key areas (Lloyd and 1984) for a range of Shell structures worldwide. 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 attackdirections or load conditions - 1.26 to 2.39;actual material yield strength and strain rate effects - 1.2 on 36 ksi steel and 1.15on 50 ksi;system redundancy, ie. ratio of ultimate capacity to first component failure - 1.0to 1.3.

The system redundancy factors are also presented individuallyin Table A2.6 together withcorresponding 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 inSi Boon et al (1993). The of the Tern North Sea platform using LRFD principles is described in van de Graaf et al (1994).

Table A2.6Contribution of system redundancy to the reserve strength of some platforms worldwide

Structure

SCS BNDP-B broadside

SCS BNDP-B diagonal

SP62-B

SNS Inde-K

NNS Tern end-on

NNS Tern broadside

NNS Tern diagonal

RSR

This table demonstrateshow first member failure may be synonymouswith system collapsewhilst 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 differentmodelling or analysis strategy adopted (eg. in relation to material properties) there wouldbe a direct influence on the level of RSR calculated.

An important factor is the dependence of RSR on the original design basis. This washighlighted 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 attackdirection. It is demonstrated that RSR is related to the proportions of dead (P,) andenvironmental (P,) loads for WSD and LRFD by the expressions.

RSR, = 1 + 0.52 Eqn (A2.1)

van Langen, Swee, Efthymiou and Overy

It was noted in the main review (Section 6) that many published analyses focused solely onthe ultimate capacity of structures without consideration of the foundation components of the system. The importance of appropriate foundation modelling was emphasised.

RSR,, = 1.83 + 0.49 Eqn (A2.2)

For dead to environmental load ratios in the range 1.6 to 0.4, these expressions 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.

Van de (1994) focuses on the Gulf of Mexico SP62-B, Southern North Sea Inde-Kand Northern North Sea Tern structures for this comparison. The best estimate yearloads 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 loadingwith 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 significantlydifferent probabilities of failure as indicated in Table A2.7. Conversely for a consistentsafety 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 A2.7Relation between reserve strength, probability of failure and environment

The considerations are highlighted further by the analyses reported in this paper of a sixleg tower-type jacket structure supported by 32 piles in 143m water depth. The potentialinteraction between structure and foundation at collapse was recognised. In addition it wasconsidered 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 environmentalload. Integration of these model and physical uncertainties is shown not to be meaningfulin terms of absolute measures of structural reliability. Instead uncertainties are quantified through an expression of the confidence in predicted probabilities of failure, leading to aclearer interpretation of structural reliability. The method demonstrates the need forimproved information on foundation behaviour, particularly in relation to large deformation behaviour in ultimate strength analysis.

Structure

SP62-BInde-KTern

Together these papers demonstrate by example the care that needs to be taken ininterpreting 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.

0.631.091.86

RSR

2.382.471.91

12.693.55

Failure rateper year

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 forassessment is given by Kallaby et al (1994).

Vannan, Thompson, Griffin and Bea (1995); Bea, Mortazavi, Lochand Young

et al (1994) put forward a design approach to simplify the modelling of ultimatesystem strength. Similarly Vannan et al (1994) have proposed so called "simplifiedultimate 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 areevaluated 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 motivationfor 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 thereforebe considered.

A 3 API RP SECTION 17.0 - ACCEPTANCE AND INTERPRETATIONOF SYSTEM RESERVE STRENGTH

As noted in the main report and this Appendix, the draft Section 17.0 to API RP 2A-WSDadmitted the use of ultimate strength analysis as part of the assessment of existing platforms. The draft was subject to wide industry consultation and 1993) and validation et al, 1995) and following four revisions was prepared as an API whitedraft 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 late1995. 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 assessmentprocess. If fitness for purpose can be demonstrated on the basis of a design level analysisor an elastic analysis with sources of conservatism removed, nonlinear analysis need not be performed. However, the sources of reserve strength within the system revealed byrigorous nonlinear analysis may be exploited in the assessment of existing platforms. Theapproach 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 the Task Group, 92-5, which drafted Section 17.0. These papers et al; Kallaby et al; Petrauskas et al; and Turner et al; Kallaby and 1994) and the related BOSS paper et al, 1994) present essential background to the user of 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 tothese aspects of Section 17.0 is presented here, together with the results of backgroundanalyses providing insight to representative jacket responses. The basis of acceptance criteria is given and procedures for determining appropriate criteria outside US waters aredocumented.

Definitions et al, 1994)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 topresent day design loads, ie:

Ultimate Strength LoadAPI 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 tothe 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 thenonlinear 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 thecase in US waters for which Section 17.0 was initially developed.

Ultimate to Linear ratio (ULR)

Ultimate strength loadglobal load giving unity check of 1.0 Eqn (A3.3)

As identified in discussion of work by van de et al (1993, 1994) in Section A2above, the sources of system reserve (ie. ULR in Section 17.0 parlance) can be clearlydefined. 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 findings of et al (1993). However, in other regions the contribution from the different factors may vary, demanding that ULR be carefully defined at an appropriatelevel.

It is then the combination of LRF and ULR (Equations A3.1 and A3.3) which leads to thecalculation 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 ofLRF 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 newdesign (Cornell, 1995). By introducing consequence based criteria and consideringadequate performance to date, the cost and risk of strengthening or maybe shown to be unnecessary. Indeed a consideration in drafting Section 17.0 was thatcriteria 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 A3.1Classification levels

Level

L1

Gulf of Mexico criteria

Description

High consequence permanently manned

L2

L3

Platforms in the Gulf of Mexico are evacuated when there is a threat of hurricanes, soenvironmental impact drives the most critical category. Level 1. Based on experience, all47 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.This and the minimum ULR index of 1.6-1.8 presented above, give a targetRSR 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.

Manned but evacuated in extreme events, low consequence

low consequence

For other classification levels the same principles of setting acceptance criteria with respectto 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 thesignificant experience base on which to draw). In applying the assessment criteria it madesense to translate the for different classification levels to environmental parameters 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 respectto new design (ie. to the present day 20th Edition of API RP 2A) et al, 1994).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 day year environmental loading profile should be incremented to a factor of 1.6 todemonstrate 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 17.0criteria 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 'otherUS' 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 shearto 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 informationregarding the potential for wave loading to impactthe deck. As noted in the Hurricane experiences (Imm et 1994; Petruska et 1994) the structural response may be sensitive to these loads which can contributesignificantly to the global base shear, albeit with considerableuncertainty 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 17.0provides significant acceptance of the technology. However the definition of RSR inSection 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 profileImportance of realistic joint and foundation characteristics Dependence of meaningful reserve strength evaluations on environmental anddesign code basisUncertainty 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 inrepresentative structures are evaluated to give appropriate In addition the acceptance criteria relative to new design (the LRF) must be revisited. Finally a rigorousevaluation of risks with the consistency and methodology put forward by De (1995).drawing on regional environmental criteria and base shear statistics is an essential pre-requisite to the international application of 'Section 17.0' guidelines (Billington and Bolt,

A 4 THE USE OF ULTIMATE STRENGTH ANALYSISTECHNIQUES

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 andSafety 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 application of Section 17.0 with a benchmark analysis of a specified Gulfof 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 andpotential 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 onlyby 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 packagegiving the frame geometries, loading and support conditions, section sizes andmeasured 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 andlocked-in stresses which had been identified as influencing the actual test results. Thestructural responses of the various test cases (see Section 3) were:

Test Case 1 - Compression brace bucklingTest Case 2 - X joint failure followed by compression brace buckling with

significant portal action in frame legsTest 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 thateach 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 solelyon 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 ofinconsistency.

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 verysensitive to effective length selections. Information on the post-buckling capacity ofmembers is sparse (eg. Pike and Grenda, and is influenced by many factorsincluding member slenderness, local buckling, out-of-plane deformations and materialmodelling assumptions. It would appear from the results that the prediction ofbuckling behaviour was a principal source of discrepancy.

However, it should be noted that the frame simplicity particularly highlights suchdiscrepancies. 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 remainsimportant to ensure that loads are redistributed giving the correct sequence of subsequentcomponent 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 jointin Frame compressed to the extent that both braces came into contact across the joint asshown 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-bucklingmember capacities. Where the post-bucklingcapacity 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 3predictions 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 testresults and the predictive capability of software and users can begin to be explained. Itappears there may be only a few key features underlying the divergence in results. Firmconclusions on the industry capability must await detailed investigation and quantificationof these effects by the analysts in open forum.

Puskar, lrick and KriegerThe MMS project encompassed two aspects, namely:

a 'trial' application of Section 17.0 from screening through to ultimate strength analysisA '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), theBay of Campeche (Mexico) and North Sea (UK), the present authors contributing the last two. The platforms were installed in water depths ranging from 37ft to and hadbeen 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 Section17.0. 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 in1970 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 ofthe 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 majorityof participants (10) attributed failure to inadequate soil axial compression capacity for thisload 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 representationdemanded 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 ultimatestrength analysis.

All the results from the study have been shared by participants in order that individualpractices 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) remainvalid 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 continuingemphasis on simplified approaches to provide insight to the probable mechanisms ofsystem reserve et al, 1994; et al, 1994; Bea, 1995). It is thereforeimportant that industry knowledge and experience continues to develop and becomes embodied in best practice guidelines such that the appropriate expertise leads tomeaningful results.

Benchmarking against test data (HSE, 1994) and comparative analyses et al,1995) provide an important vehicle to advance understanding of the technology butdepend on openness and cooperation between organisations for any benefits to bederived.

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 andimplementation of ultimate strength criteria to account for the potential variability due to software differences and user selections or interpretations. Best practices should beidentified 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 bothreserve 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 deflectionserviceability limit states and sensitivity of ultimate strength predictions depending onfailure mode. With the progression of Section 17.0 to the basis of an standard this 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 meanwhilerational account must be taken of the modelling uncertainties.

Figure A2.4The relation between reserve strength, environment and probability of failure

, - Experimental. - 1

I - 2

00 0.05 0.1 0.15 0.2 0.25 0 3

Lateral displacement (m)

0 I0 0.05 0.1 0.15 0.2 0.25 0.3

Lateral displacement (m)

Lateral displacement (m)

Figure A3.1Classification of HSE benchmarking results against Frames Project data et

I

Figure A3.2Benchmark jacket structure et al, 1995)

Figure A3.3Load displacement predictions for the benchmark platform et 1995)

Printed and published by the Health and Safety Executive

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