A new form of the Active Moments Method

Abstract

The paper desires to pay a tribute to Professors A. Şesan and N. Orlovschi, which professed last century at the Faculty of Civil Engineering and Installations from Iasi.
These professors imagined a calculation procedure for frames, named active moment method, as a response to the displacement (deformation) method.
The structure calculation by displacement methods is conducted on a base system, obtained by introducing fictive connections which deters the possible displacement of the nodes – revolutions and translations.
The elements in question in the displacement method are the nodes real
displacements (written Zi). Under the exterior forces action and displacements, on the elements in question direction, in the complementary connections appear reactions. Total reactions from complementary connections must be equal to zero. This way it can be obtained the condition equations.
Despite the active moments method, the basic system is similar to that in the displacements method, but the element in question are “active moments†of nodes Mi and displacement (kinematic chains), MA.
The active moment is defined as the moment which by its action on the base system, on the node “i†or in the degree of freedom “aâ€, creates the real displacement of the node “iâ€, and the real displacement of the nodes which are part of the kinematic chain “aâ€.
The condition equations from the active moments method expresses the structure static equilibrium and has two types: nodes equilibrium equations and kinematic chains equilibrium equations. Must be mentioned the fact that none of the papers written by the authors didn’t demonstrated the way in which the equilibrium equations have been obtained.
In the present paper have been obtained the equilibrium equations by active moments method by using the girder, node and nodes and beams chain equilibrium conditions with the help of the methodology "Gh. Em. Filipescu". This way has been obtained calculation relations for the extremity moments more general than the ones used in the displacements method, relations (4.6.) and (4.19.).