The localization of buckle patterns in elastic structures is reviewed from three complementary viewpoints: ( a ) from a modal perspective, ( b ) from a formulation which allows the amplitude to modulate in an asymptotically defined ‘slow’ space and ( c ) from a dynamical analogy in phase space suggested by the form of the underlying differential equation. A simple strut on an (asymmetric) nonlinear foundation provides a typical illustrative example. The three approaches emphasize different features of the localization phenomenon. The modal view illustrates the distinctive effects of boundary conditions, the modulated approach generates a convenient second-order differential equation in the amplitude function and the dynamical phase-space analogy suggests a useful interpretation of localization as a homoclinic connection. Comparisons are also made with nonlinear numerical solutions. As the strut length approaches infinity it is shown that the fully localized solution represents the unstable post-buckled state with the lowest energy, allowing evaluation of the minimum energy barrier relevant to dynamical impact studies. Attention is drawn to the possibility of spatial chaos, becoming manifest as a randomly spaced sequence of localizations caused by a regular sinusoidal spatial imperfection.

This paper waa selected for presentation by the OTC Program Committee following review of Information contained in an abstract submitted by the author(s). Contents of the paper, as presented, have not been reviewed by the Offshore Technology Conference and are subject to Correction by the author(s). T'ho material, w presWtOd, d~s nOt n@@*~ilY reffeã ny position of the Offshore Technology Conference or its officers. Permission to coPy [s restricted to an abstract of not more than w words, Iifustrations may not be copied.~e abatract should contain mnsplcuous acknowledgment of where and by whom the paper Is presented, ABSTRACT Phase II of the JIP Frames Project included four large scale collapse tests of K-braced frames in which both gap and overlap Kjoints were thecriticai components. Theresu/ts are presented inthispaper.?helocal failure modes differed from typical isolated component tests, yet were representative of sbuctural damage observed following Hum'cane Andrew. lhe frame test results therefore provide important insight to the ultimate response of offshore jacket structures.

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The Frames Project was established to provide large scaie test data on the collapse performance of frames representative of offshore jacket structures. Four two-bay X-braced frames were tested in Phase / and the results were re/eased from confidentiality in late 1993. With a variety of configurations, the frames exhibited different sequences of member and joint failure providing important insight into potential jacket responses. A relatively weak X joint typical of an older structure, was shown to impart significant ductility, mobilizing alternative Ioadpaths and giving a high frame capacity albeit at large global deformation. Members with low utilisation under moderate frame loads, were shown to play an essential role in redistributing internal forces once other components failed, offering lessons for modem jacket weight reduction strategies. Material tests indicated an appropriate correlation between the minimum specified and actual yield properties and the rate of tensile coupon tests and stub column performance. In addition to the testing, a comprehensive and efficient program for nonlinear structural collapse analysis was developed and validated and now provides a powerful tool for jacket assessment. As the work continues with K-braced frame tests and a new 3D test programme, the additional benefit of the results from benchmarking other pushover analysis software packages, on which the industry is becoming increasingly reliant is demonstrated. INTRODUCTION Design of a steel offshore jacket has traditionally been based on an elastic skeletal frame analysis to determine the distribution of forces through the structure when subject to specified design environmental loads. Checks are then performed on a component basis to ensure that no element of the jacket fails to meet the governing criteria, Advancement of knowledge leading to revisions of these codified loading and resistance criteria, changes to topsides loading or structural deterioration, may mean that older installations fail to satisfy current design requirements. However the potential for nonlinear structural interaction between components through plastic deformation and load redistribution, means that jackets may in fact exhibit reserve strengths beyond the required design resistance. In addition, altering the bracing configuration and disposition of steel within a frame can significantly influence the ultimate resistance and failure mode. Indeed, it has been shown (1) that, without incurring a weight penalty, a structure can be designed not only to meet the governing elastic design criteria but also to provide a reserve strength beyond the design requirement as insurance should extreme events or unforeseen operational changes arise in the course of the platform life, The need to understand and predict the ultimate response of jacket structures is therefore of considerable importance for the economic exploitation of hydrocarbon reserves from both new and existing installations. The Frames Project was initiated in 1987 specifically to address this need by generating data representative of offshore jacket structures from collapse tests on large scale tubular frames.