Abstract
Abstract The reinforcement design of concrete cross-sections with the parabola-rectangle diagram is a well-established model. A global limit analysis, considering geometrical and material nonlinear behavior, demands a constitutive relationship that better describes concrete behavior. The Sargin curve from the CEB-FIP model code, which is defined from the modulus of elasticity at the origin and the peak point, represents the descending branch of the stress-strain relationship. This research presents a numerical method for the reinforcement design of concrete cross-sections based on the arc length process. This method is numerically efficient in the descending branch of the Sargin curve, where other processes present convergence problems. The examples discuss the reinforcement design of concrete sections based on the parabola-rectangle diagram and the Sargin curve using the design parameters of the local and global models, respectively.
Highlights
Different constitutive relations have been used for the reinforcement design of concrete beams and columns
This study presents a numerical method for the reinforcement design of concrete sections under combined bending and normal forces that is suitable for the Sargin curve
The reinforcement design of concrete sections based on the parabola-rectangle diagram is a practical and well-established model
Summary
Different constitutive relations have been used for the reinforcement design of concrete beams and columns. CEN Eurocode 2: 2004 [8], FIB Model Code 2010 [9], and ABNT NBR 6118: 2014 [10] all use the parabola-rectangle diagram Such simplified stress diagrams require limiting strain states for reinforcing steel and concrete to ensure valid results under combined axial and bending effects. The Sargin curve presented in the CEB-FIP Model Code 1990 [12] is defined by the initial modulus of elasticity, minimum compression stress, and critical strain This curve represents the descending branch of the stress-strain relationship. This study presents a numerical method for the reinforcement design of concrete sections under combined bending and normal forces that is suitable for the Sargin curve It is based on the arc-length technique, which is stable for negative derivatives of the stress-strain diagram. The influence of the type of aggregate is not discussed in the present investigation
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