Geometric Non-Linear Approach to Stiffness State of Semi–Rigid Structures

Abstract

Present contribution intends to emphasize the contribution of geometric non-linearity to the stiffness state of semi-rigid multi–storey steel structures. Though semi-rigidity of beam – column connections involves a nonlinearity at constitutive bending momentrelative rotation level, the geometric nonlinearity associated to deformed conFigure uration at element level is less referred to. The main objective of the study is to express the stiffness state of geometric non-linear elements semi-rigidly connected at its ends. Stiffness state is, in its term, expressed by element level stiffness matrix considering the six degrees of freedom of the planar element. Regarding the reference system, both local and global systems are employed allowing a simple and direct transition from element level vectorial relations to their structural level forms. The three fundamental vectorial relations (static equilibrium, kinematic compatibility, material constitutivity) emphasize that the principle of virtual work holds in the case of semi-rigidly connected skeletal structures as well.