# SLENDER COLUMNS MODELING THROUGH INFINITE NUMERICAL SERIES CONVERGENCE

## Palavras-chave:

Slender, Columns, Analysis, Series## Resumo

A numerical series is defined as the sum of terms in a numerical sequence. If the

quantity of terms of the series is known, it is denominated as a finite series, and, the referring sum can

be obtained from the elementary algebra. In the unlike case the series is classified as an infinite series,

and, the employment of elementary algebra is no longer enough, requiring the use of a convergence

analysis procedure. The series used to approach, as a satisfactory numerical quality, a set of values of

given function in a certain work domain, must be of the infinite mode because, in such cases, the

quantity of terms that the series needs to attend such demand, is unpredictable. There are cases

wherein the solution of engineering problems that may be aided, directly, by the modeling based on

approach for infinite numerical series, as the slender columns performance analysis. The slender

columns analysis cast by elastic and ductile material has been based on the concept of critical load, or

Euler’s load. Such modeling version is not enough at all, for specimens cast of weak rupture pattern

material, as the reinforced concrete, but even thus, there are concepts involved in such a formulation

that can be used as a classificatory reference. The Mechanics of the Materials uses the physical

modeling capabilities in deriving the equations object of approach on the featured theme. The aim of

this work is the slender columns mechanical performance modeling through infinite numerical series

convergence concept.