# Beams non Linear Analysis from Envelope Concept

## Palavras-chave:

numerical simulation, finite elements, reinforced concrete, continuous beams, envelope## Resumo

The heterogeneous nature of the Portland cement concrete promotes its irregular mechanical

behavior. Due to the shrinkage deformations, the mass of concrete presents cracks, even before loading. Such

material exhibit non linear performance since the stress level around 30% of its compressive strength, and, in this

way, some researchers developed mathematical models designed to describe that kind of mechanical

phenomenon. A model proposed by Branson, is especially useful to analyze reinforced concrete beams from

beam finite elements resulting, consequently, computational effort economy. It is known that, in some cases, it

may be suitable to carry out continuous beam analysis considering several loading arrangement, culminating

over a bend moments envelope. Preliminary comparative studies made over continuous beam, considering the

bend moments due to full load and bend moments envelope drafted from different load arrangement alternatives

show remarkable differences between these two kinds of analyses versions. The purpose of this work is to report

the nonlinear mechanical performance limit analysis of reinforced concrete continuous beams considering,

include, the bend moments envelope. To accomplish such a subject, a computational code was developed, based

on the finite element approach, applied upon the Branson’s formulation.