Analysis of reinforced concrete beams by the equivalent section method

Abstract

This research investigates the analysis of reinforced concrete beams subjected to combined axial load, bending moment and shear force. Cross-sections of general shape are divided, along the height, into plane elements. The biaxial behavior is represented according to the smeared rotating crack approach. Using traditionally accepted hypotheses for beams, the shear flow is determined by applying the Jouravski formula to an "equivalent section", which takes into account the nonlinear material behavior. The "Equivalent Section Method", originally proposed by Diaz (1980) and Diaz and Schulz (1981), is improved and simplified. The formulation is implemented applying the bidimensional constitutive model A, proposed by Vecchio and Collins (1993). The tension-stiffening effect is considered as adopted by Polak and Vecchio (1993). Shear slip at crack surfaces, Poisson's ratio and other secondary effects are not considered. Validation is undertaken by comparison with experimental results obtained by other researchers. The examples include reinforced and prestressed concrete beams, for normal and high strength concrete. The formulation satisfactorily predicts the ultimate capacity under different load combinations. The whole set of equilibrium, compatibility and constitutive equations are satisfied, the stiffness derivatives are explicitly calculated and the algorithms show good convergence.