DESIGN OF REINFORCED CONCRETE UNDER ECCENTRIC LOADS WITH NEWTON-RAPHSON’S METHOD

Resumo

This article aims to use a numerical algorithm in Matlab for the design of rectangular
reinforced concrete columns under eccentric loads. Usually, both in academic and professional practice,
the design of such columns makes use of dimensionless charts or tables. These charts are subject to
specific restrictions as section shape, reinforcement positioning, covering dimensions, among others, so
that the design is limited to their availability. The alternative described employs Newton-Raphson’s
method to solve the nonlinear system of equations that arises from section equilibrium, keeping the
neutral axis position and reinforcement diameters as variables. The nonlinear constitutive behavior of
both materials involved is considered so that the equilibrium is expressed as a system of two nonlinear
equations for bending normal to a symmetry axis. The concrete stress distribution proposed by Brazilian
standard NBR 6118:2014 was used and a perfect elasto-plastic model was adopted for steel. The
algorithm was validated by comparing the steel area and modes of failures obtained with traditional
design methods, for several columns on different limit states.