Influence of a small flexibility of connections on the elastic structural response of frames

This paper addresses the analysis of planar frames with stiff semirigid joints. If they are stiff enough, a concept which is discussed with respect to the local stiffness of the neighboring beams and columns as well as the global flexibility of the whole structure, the joints can be modeled as fully rigid. This makes the structural analysis easier for practitioners who sometimes are reluctant to perform a structural analysis accounting for the semirigidity of the joints. If joints cannot be classified as fully rigid, a more sophisticated structural analysis is required, according to current practices and standards. This paper developed an asymptotic analysis of the static structural response of frames with stiff (but not infinitely rigid) joints. It was demonstrated that the small deformability of the joints in rotation can be taken into account by analyzing the structural response of the fully rigid frame as the sum of two load cases: (1) the actual loading on the considered structure, and (2) an additional virtual loading which takes the (small) flexibility of the joints into account and which is expressed as a function of the response of the structure to the actual loading. The proposed method therefore avoids the consideration of the semirigidity of the joints in a structure when they are not perfectly rigid. It is similar to other practices in the field of structural engineering such as the use of equivalent loads to account for small initial imperfections or to deal with a second-order analysis. The method was derived formally and validated with several examples with increasing complexity. The method offers new perspectives on the classification of joints in a very simple and general way; it also might inspire similar approaches for structural stability analysis of structures with almost rigid or almost hinged connections.