Complexity and robustness of frame structures

In structural engineering, the word “complex” is often employed to define something that is difficult to understand or to solve. Anyhow, even if the concept is extensively employed in the practice, any proper definition has not been formulated yet. Taking one’s cue from other scientific disciplines, a metric for complexity based on the performance of the load paths through the structural scheme is proposed. Referring to frames, characterized by large interaction between the beams, an analysis based on graph theory is proposed. A beam importance factor is then deduced and preliminary robustness properties are discussed. Three examples are proposed in order to examine the capabilities of the complexity indices and the beam importance factor. The structural robustness is then worked-out. Load redistribution, which represents an important aspect in structural behavior, should act in the structure in such a way that a damage would not cause collapse. The effects of a prescribed damage on a frame are analyzed and commented.