A Methodology for Platform Collapse Analysis Based on Linear Superposition
Authors: Stewart G. , van de Graaf J.W. 
Published: October 2008

ABSTRACT
A simple and efficient modular simulation system is presented that enables conventional linear structural analysis programs to be used to model the collapse behavior of braced frames. With this tool and the availability of a linear structural model, accurate collapse analyses of complex structures can be performed in a few days. A foundation screening capability, based on the simulation concept, is also discussed - this is suitable for assessing rapidly the ultimate overturning resistance of piled foundations and can provide valuable information prior to performing a full system collapse analysis.
These techniques, which are presently used within Shell in an operational environment, will enable practicing engineers to perform routinely in-house redundancy/overload checks on new structures, or collapse integrity assessments of existing structures, using standard linear structural analysis procedures.

INTRODUCTION
The majority of fixed offshore steel structures are designed and re-assessed using linear structural analysis programs, with acceptance criteria based on providing an adequate margin of safety against first member (or component) failure. In certain circumstances, however, one may wish to evaluate the collapse resistance (ultimate strength) of the structure - for example, to check the robustness of a new platform design or to re-assess the fitness for purpose of an existing structure that no longer complies with present design code recommended practice. These collapse assessments are usually carried out using cumbersome and complex non-linear analysis programs which require substantial expertise to use. In addition, these programs are generally not suited to routine applications.
In this paper, a simple and efficient modular simulation system is presented that enables conventional linear structural analysis programs (SESAM, STRUDL, MARCS, SACS, etc.) to be used to model accurately the collapse behavior of frames in which the collapse mode is dominated by axial brace failure (buckling or yielding) or axial pile failure (pull-out or punch-through). Analysis experience has shown that for many braced steel frames, only these non-linearity's are important.
The simulation technique is a modified form of the 'virtual distortion method' developed by Holnicki-Szulc & Gierlinski [1]. It is based on linear superposition and provides a phenomenological non-linear capability (i.e. the non-linear member data are prescribed by the user). Essentially the non-linear problem is reduced to finding a set of member end forces, Which, when combined with the applied loading, constrain the linear system to follow the behavior of the non-linear system. The set of constraining forces is usually quite small since, even for large structures, very few members (typically around ten) contribute to the collapse mechanism. This approach has several advantages over more complex non-linear analysis programs. Its major strength is that with the availability of a linear structural model and a suitable linear analysis program, a full collapse analysis of a complex structure can be performed within a few days. This contrasts with the several months required to regenerate the model and perform the analysis using a more complex non-linear analysis capability.