M - P -ϕ Diagrams for Reinforced, Partially, and Fully Prestressed Concrete Sections under Biaxial Bending and Axial Load

Abstract

An analytical model that determines the M-P-f diagrams including the inelastic structural re- sponse, ultimate strength, and failure mode of reinforced concrete, partially prestressed concrete, and fully prestressed concrete sections of any cross shape under combined biaxial bending and axial load is presented. The proposed method uses (1) a nonlinear stress-strain relationship for the concrete; (2) a multilinear elastic- plastic relationship for the conventional reinforcement; (3) a modified Ramberg-Osgood function for the pre- stressed steel; and (4) Gauss's integral method for equilibrium at the sectional level. The proposed method can be utilized to study the effects of creep, confinement, and tension-stiffening of the concrete and relaxation of the prestressed steel on the behavior, strength, ductility, and failure mode of reinforced concrete, partially pre- stressed concrete, and fully prestressed concrete sections under biaxial bending and axial load. The biaxial bending behavior, ultimate strength, failure mode, and M-P-f diagrams of any concrete section can be obtained using a minicomputer, and as expected, they depend on (1) cross-sectional characteristics and reinforcement layout; (2) the constitutive stress-strain characteristics of the concrete and reinforcements; and (3) the type and intensity of applied loads. Two numerical examples are presented in detail to verify and show the effectiveness of the proposed method.