The Idea of a “Loop Fragment” of the Finite Element Force Method in the Loop Resultant Method for Static Structural Analysis

In this paper, a novel technique called a “loop fragment” (LF) is developed for structural analysis. A simple method is sufficient for establishing the loop system of framed structures using an original idea, the LF of the loop resultant method, and two conversion rules are necessary to find the structure (or equivalent) flexibility matrix of the rod system. This LF is generated by splitting the given structure into indeterminate basic loops. Instead of the conventional approach of treating the redundant forces in the whole structure, the current approach allows for the calculation to be simplified, thanks to the loop compatibility conditions and by dealing with the primary unknowns for each basic loop. Some numerical examples are considered for the structural frame subjected to temperature loads.