The Idealized Structural Unit Method on Concrete Structures
Authors: Soreide T.H. , Amdahl F. , Brodtkorb B. 
Published: October 2008

ABSTRACT
The paper presents an extension of the Idealized Structural Unit Method into the collapse analysis of concrete structures. The technique is especially aimed at progressive collapse analysis of concrete offshore structures for arctic conditions.
A short description is given of the basic theory behind a computer program, indicating the process of handling large deflections. Special attention is given to the formulation for nonlinear material behaviour of concrete using interaction curves and flow theory of plasticity. The concrete capacity is expressed by stress resultants instead of Cauchy stresses.
Examples are given on the analysis of concrete structures in different collapse modes including structural stability. Emphasis is given on the comparison with conventional finite element formulation and the efficiency of the Idealized Structural Unit Method is demonstrated. Finally, examples are given on practical design of concrete offshore structures in ultimate limited state.
The redistribution of stresses during loading is demonstrated by graphics of interaction curves for stress resultants together with load deformation curves.

INTRODUCTION
The Idealized Structural Unit Method (Ueda and Rashed - 1974, Rashed -1980) has been widely used in the ultimate strength analysis of transverse ship frames and tubular frame structures. Refinements of the technique have been carried out in the formulation for large deflections and solution strategy (Aanhold - 1983, Aanhold - 1983, S0reide - 1986) as well as for modeling damaged structural members.
The result of the study is a computer program USFOS (Ultimate Strength of Framed Offshore Structures) aimed for the analysis of steel offshore platforms in the progressive limit state. The latest version (Soreide, Amdahl, Astrup 1987) also includes structural elements in the deck modeled as plate girders.
The program system USFOS has widely been used in accidental load analysis of fixed and floating steel offshore structures (Soreide, Amdahl,' Granli, Astrup - 1986). Modifications of the program are still going on including temperature effects on material behaviour as well as crack criteria in tubular joints.
Effort is also being made to modify USFOS into ultimate load analysis of concrete platforms. The same basic solution strategy is used as for steel structures, the only extension being in the specification of interaction curves of cross sections.

BASIC THEORY
The main philosophy behind the Idealized Structural Unit Method is twofold.
First stress resultants are used for capacity control over cross sections instead of conventional Cauchy stresses. Capacity curves for the cross sections are given as input. Alternatively, appropriate interaction curves may be chosen among predefined curves in the program.
Second, large displacement, small strain theory is implemented. A formulation is chosen so that nodal point coordinates referred to the global reference system are updated by displacement increments. The element stiffness's include nonlinear strain-displacement terms in order to minimize the number of elements in the model. Thus, large deflection effects are handled both on global level and on local element level. In most cases of frame analysis it is sufficient to use one numerical element per physical element in the structure