The influence of the reinforced concrete deformability in the design of slender columns. (15th October 2021) - Pissinatti, Celso; Poncetti, Bernardo L.; Buchaim, Roberto; Vanderlei, Romel D.
Highlights: The deformability of reinforced concrete and the design of slender columns. Secant flexural rigidity correspondent to the reinforcement. Applicability of the parabolic law for concrete deformability. Abstract: This work aims to evaluate the influence of the main parameters related to the deformability of reinforced concrete columns in the design of pin-ended rectangular slender columns, under combined bending and axial force. For this, the objective is to analyse the influence of the elasticity modulus of the concrete and the type of coarse aggregate on the deformability of slender columns and consequent dimensioning, and to propose an adaptation of the parabolic law, inserting the influences of the coarse aggregate and the initial tangent modulus of elasticity in this equation, being able to use it to evaluate the local second order effects. Concrete characteristic strengths in the range 20–50 MPa (Group I) and 55–90 MPa (Group II) and CA-50 steel ( f y k = 500 M P a ) and their respective constitutive laws are considered. Geometric non-linearity is defined from the exact solution of the second-order differential equation for two simultaneous loading cases: geometric imperfection of the column axis and equal moments applied at its extremities. Physical non-linearity is defined from the moment–curvature diagram of the cross-section under the action of the compression force. The constitutive laws used in this diagram are: the bilinear law with horizontal threshold for steel, and for concrete in compression, the parabola-rectangle diagram on the dimensioning of the cross-section at the ultimate limit state under combined bending and axial force, and the law given in MC-90, MC-2010 [13], EC2-2010 [17] and in the Brazilian Bridge Standard ABNT NBR 7187 [20] . It is also examined the parabola of degree n, corrected for the local physical non-linearity consideration (i.e. of the column's length). These laws explicitly or implicitly include the modulus of elasticity of concrete and the type of aggregate in it, through the factor α e defined in ABNT NBR 6118 [14] . The concrete strength in tension is disregarded in this work, that is, the tension-stiffening effect for the cracked column is taken equal to zero, which is on the safe side in case of slender columns, as its cracking moment increases with increasing axial compression force. Besides, this strength depends also on the height of the cross-section, frequently considered in prestressed beams. Another important parameter, besides the concrete characteristic strength, is the geometric ratio of the total reinforcement. Thus, it is possible to determine more precisely and securely the second order effect of the slender column, and the consequent variation in reinforcement in relation to the basic case in which α e = 1 . The results showed that the influence of the type of aggregate can be considered irrelevant for the determination of reinforcement of columns with low slenderness. However, for columns with high slenderness and high strength concrete, the type of aggregate had a significant influence on the design of these columns, where the column with aggregate α e = 0, 7 required twice the reinforcement compared to the column with aggregate α e = 1 . In addition, a parabolic law adapted to analyse the second order effects of slender columns is proposed with the replacement of f c k b y ∝ 0 ∙ α e ∙ f c d 0 .