Instability Of Plane And Curved Concrete Walls In The Design Of Gravity Offshore Platforms
Authors: Furnes Olav 
Published: December 2007

Abstract
This paper deals with structural instability analysis of offshore concrete structures. Design methods are presented which can be applicable for designers and authorities responsible for safe design of such structures.
As a basis for the methods reviewed a general outline of structural instability problems is presented. The simplified methods which are discussed to some extent frequently appear to be adequate tools for the design engineers in performing checks of the structural safety. Emphasis is put on the tangent modulus approach which appears well suited for this purpose.
Some computer programs frequently used by DnV are briefly mentioned, revealing their most important capabilities with respect to non-linear analysis as regards structural instability.
The tangent modulus method is demonstrated for a number of concrete slab and shell test specimens. Emphasis is put on the handling and importance of initial geometric imperfections. In general this rather simple method yields results that contain fairly well with the test results reported.
In summary there still seems to be an appreciable need for further tests on structural instability of reinforced concrete members, to provide a more broad basis for the design methods which so far are being developed. It is pointed out that the simplified methods should be used with care and sound engineering judgement. Preferably they should be checked against relevant test results before being used for practical design purposes. In particular, effects of tension cracking, creep and long term load durations on saturated concrete members need further study comprising tests with structural reinforced concrete models.

Introduction
Modern design of reinforced and prestressed concrete structures is based on limit state methods of analysis. The load-carrying capacity of the structures is analysed in the ultimate limit state (ULS), in which the critical modes of failure are investigated by use of load and material strength parameters which are factorizied by appropriate partial safety factors.
Instability modes of failure will thus be analysed in the ULS, ensuring sufficient load-carrying resistance when considering the structure in an allowable deformed state.
For slender, linear-elastic structures carrying large in-plane compressive forces, failures caused by instability (buckling) are characterized by a sudden growth of lateral deformations. This may lead to an almost immediate failure with practically no prior warning. In case the postbuckling resistance should increase as a function of the deformations, then a failure induced by instability could be associated with unacceptable states of deformations. Hence, instability failures are characterized by large and sudden deformations which may or may not stabilize.
It follows, that analysis of structural instability must take due account of the current deformations of the structure. This calls for a non-linear analysis which can allow for the change of geometry in a proper manner.
Reinforced concrete exhibits non-linear material (structural) properties, mainly due to the effects of cracking, creep and non-linear stress-strain relationship. Structural instability analysis of concrete structures must therefore include such non-linear effects together with the deformations. Broadly speaking, such an analysis is rather complex to carry out in full detail.
Generally, it can be stated that reinforced and prestressed concrete has a modest sensivity with respect prestressed concrete has a modest sensivity with respect to buckling. However, vital parts of gravity offshore platforms, such as caisson storage cell members, are platforms, such as caisson storage cell members, are frequently subject to large in-plane compressive forces caused by external water pressure. This has neccessitated close investigations of structural instability to be made for such concrete members. As the amount of experimental data is quite small, reliable methods are needed for safe buckling design of concrete members frequently encountered in offshore gravity platforms.
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