The extensive node: a way to solve a common error in programs of matritial analysis of bar structures written for the project of reinforced concrete structures

Abstract

Seeing the deep errors that result on the use of the matritial analysis programs in structures where the bars center lines do not converve in one unique point on the nodes, - that's always the case in reinforced concrete structures, but is also usual in steel structures -, the author proposes to leave the idea that the bars that connect on a node have thier ends on a commont point. Using conventional ends geometrically correct for each of that's bars, all that has to be done is to refer to another unique point, that represents the node, in a rigourous manner, all the analysis of it's equilibrium and movement, clearing in that way all the possibilities for that kind of errors. This article shows that the use of a new form of the transformation matrix of the axis is all that is needed to solve that problem in a natural and definitive manner.