Perturbation analysis of frames with semi-rigid joints

Résumé du projet

The global and the local response of structures, such as their internal distributions of forces, static displacements, critical or failure loads, for instance, are significantly influenced by the stiffness of the connections. Nevertheless, for the sake of simplicity in the analysis of such structures, the joints are traditionally assumed to be either perfectly flexible, either perfectly rigid in rotation. These hypotheses are considered licit provided the modification of the response which is due to the idealization of the connections is limited.

Over time, this discrepancy has been quantified by means of analytical studies in single-bay single-storey steel frames. Numerical and experimental campaigns have then been conducted as soon as the structures included connections characterized by different stiffnesses, distributed among several bays and/or several storeys. Classification criteria have thus been defined in accordance with these observations, but the current framework suffers from obvious limitations. Indeed, as it is based on parametric analysis, it should not be used outside of the parameter space that has been employed to set the rules up.

Therefore, the aim of this research project is to extend the analytical approach for structures that contain more than a single-bay and a single-storey, in order to provide an accurate estimation of the influence that the small flexibility of almost rigid joints (or the small stiffness of almost hinged joints) has on the structural response of realistic frames.

Since the problem involves small numbers, the perturbation theory can be invoked. It has already appeared in the asymptotic case that the linear elastic displacement of a structure with very stiff joints can be approximated by analyzing the structure with infinitely rigid joints and by modeling their actual small deformability by means of equivalent loads.

We believe that it shall open new perspectives for the derivation of classification criteria with a broader domain of applicability, once the same method has been applied for critical and failure loads.

Publications

Nouvelle approche de la classification par rigidité des assemblages poutre-colonne en construction métallique, 2018, mémoire de licence/master