Ring Frame Design in Orthogonally Stiffened Cylindrical Structures
Authors: Morandi A.C. , Das P.K. , Faulkner D. 
Published: October 2008

ABSTRACT
Ring frame design is the aspect least well treated in the available design codes for orthogonally stiffened cylinders, particularly where axial load is dominant. Recent advances in this particular area are reviewed, together with the relevant theory and experiments. Detailed Finite Element analyses of a typical TLP column, as well as of its redesigned version, are presented and the results are compared with present prediction methods.

INTRODUCTION
With the advent of semi-submersible drilling rigs for worldwide operation, large diameter stiffened cylinders were used for their columns and pontoons. As first design approaches were very conservative. efficient strength models for orthogonally stiffened cylindrical shells had to be developed, mainly for designing the shell plating and the stringers1.2.
However, the design of ring frames in orthogonally stiffened cylinders under axial compression and under combined loading remained an elusive aspect.
Where axial load is dominant the main task of the ring frames is to support the stringers. which in turn stabilise the shell plating. The spacing of the ring frames is not generally critical insofar as the structural weight of the longitudinal structure is concerned. but the size of the ring frames is important. This is the feature least well treated in existing design rules and codes.
A short study was commissioned by Conoco from the last named senior author aimed at addressing the problem. and improved methods for checking required frame area and inertia were proposed as a result3.4. Such requirements are a function of the stringer area and the axial design stress and include the effects of combined loading in a simplified way. These were applied to three designs ofcolumns as proposed for TLPs. and large weight savings were achieved 4
The authors are now involved in a continuation of such work. funded by the UK Engineering and Physical Sciences Research Council and aimed at refining and verifying over wider geometric ranges such improved requirements. In this paper the relevant theory and experimental results are reviewed and results from Finite Element (FE) analyses are presented for the design case given in the second column of Table 1. This case was considered in [3,4] and is representative of an axially dominated loading condition. Having been validated and successfully used in a related research programme concerning reliability-based design of submersibles5, the program ABAQUS6 was chosen for the FE analyses.

BUCKLING DESIGN SOME MAJOR ASPECTS
The design of cylindrical shells under applied stresses of a predominantly compressive nature, as those arising from axial compression and external pressure, tends to be dominated by buckling considerations. The relevant buckling modes for orthogonally stiffened cylinders are shown in Fig. 1:
Local Shell Buckling, Fig. la: involves predominantly shell deflections with little deflection of rings and stringers. To be prevented it needs an adequate choice of shell thickness, ring spacing and stringer spacing.
Bay Instability, Fig. lb: involves both shell and stringer deflection as a column with little ring deflection. To be prevented it needs an adequate choice of stringer dimensions as well as ring and stringer spacings.