This paper presents a general strategy to select the numerical values of the coefficients defining an uniaxial tensioned concrete equivalent constitutive relationship to simulate, under serviceability conditions, the instantaneous and time-dependent flexural behavior of reinforced and prestressed concrete members. Such values are determined by a least-squares algorithm aiming to minimize the differences between the moment-curvature diagrams obtained with two fiber models: The first one uses the proposed stress-strain law and the second one follows suggestions from the Comité Euro-International du Béton. To obtain general conclusions, a numerical parametric analysis is performed on a number of reinforced and prestressed concrete rectangular and T beams undergoing bending moments and axial compressive forces. Closed-form solutions providing the sought values of the coefficients are given for reinforced concrete rectangular cross sections. These analyses yield a better understanding of the influence of the main considered parameters in the tension-stiffening effect. The proposed equivalent constitutive law is suitable to be incorporated into global models of concrete structures. Some examples on multistory plane frames are shown to highlight this capability. As well, various benchmark tests have been satisfactorily simulated.