Armadura de tração em seções retangulares submetidas à flexão pura: simplificação de cálculo para armadura simples

Abstract

The present work makes a bibliographic review of the recommendations of ABNT NBR 6118: 2014 regarding the calculation of longitudinal reinforcement for a rectangular section due to pure flexion with simple reinforcement for concretes of group I (C20-C50) and group II (C55-C90). The calculation marches are presented for the determination of the tensile reinforcement for three situations presented in the stress strain diagram in the compressed region of the cross section: 1) the complete parabola-rectangle stress diagram for maximum compression strain εc = εcu; 2) the parabola-partial rectangle stress diagram for maximum compression strain in the interval εc2 < εc < εcu; 3) the parabolic stress diagram for the compression strain εc < εc2. The verification is made with respect to the minimum tensile reinforcement, corresponding to the minimum bending moment in pure flexion, respecting the minimum recommended reinforcement rate. A spreadsheet is implemented, generating a table to assist the teaching-learning process of the subject. With the table in place, several rectangular cross sections (bw x h) were analyzed for steel (CA-50 and CA-60) and concrete (Groups I and II) and a linear behavior was observed for the relation of bending moment and tensile reinforcement for the situations in which εc2 <= εc <= εcu with simple reinforcement (bending moment less than or equal to the limit moment, corresponding to the limit of the relative position of the neutral line, kx). Regarding the minimum bending moment / minimum reinforcement pair, it was noted that this point on the Md x As graph occurs for εc <εc2. In addition to the available spreadsheet, which proves to be an efficient instrument for the study of the subject, the work proposes a linear approximation for the Md x As relation, with immediate determination of the minimum moment (corresponding to the minimum reinforcement) and the value of the reinforcement for any bending moment belonging to the minimum moment - limit moment interval.