The idealized structural unit method and its application to deep girder structures

An efficient method of analysis of non-linear behavior until collapse of large size redundant structures is presented. The method is named as The “Idealized Structural Unit Method”. In this method the structure is divided into the biggest possible “Structural Units” whose geometric and material nonlinear behavior can be idealized and described in a concise analytical-numerical form. The structure is reassembled and load is applied incrementally until ultimate strength is attained.In this method, modeling is an obvious operation of dividing the structure into its actual structural units. This eliminates the effort required for the choice of type of element or size of mesh as in the finite element method. The number of structural units and overall degrees of freedom required for the analysis of a structure by this method are less in order than the number of elements and overall degrees of freedom required to analyze the same structure by the FEM. Costs of computer and data preparation may be drastically reduced.Application of the method to metal structures built up of deep I girders, such as bridge girders, ships deep girders and grillage structures is considered. The “Girder Structural Unit” is defined and its behavior under increasing loads is idealized based on existing as well as newly developed theoretical and experimental studies. Conditions for web bucking, ultimate strength and full plastic strength are established and expressions for stiffness during various stages are derived. A deep girder structure may then be treated as an assembly of such “Girder Structural Units”. Results of analysis of example structures are presented. The consumed computer time is found to be very short, as expected. Comparisons with results of experimental studies show good agreement.