An analytical method that determines the short and long-term response of prestressed and non-prestressed concrete beam-columns reinforced with any combination of FRP bars or/and plates, steel rebars, bonded and/or unbonded prestressed tendons is proposed. Beams and columns encased with FRP fabrics and FRP tubes filled with concrete are covered with the proposed model. The effects of tension stiffening, creep and shrinkage of the concrete, and the relaxation of the prestressed steel reinforcement are considered. The models proposed by Vecchio and Collins [1] and by Popovics [2, 3] for the stress-strain relationships of the concrete in tension and compression are adopted, respectively. The strain-stress relationships of the steel and FRP reinforcements are modeled using multiple straight lines (polygonal lines). The method of the fibers (modified) is used to calculate the moment-curvature diagrams at different levels of the applied axial load (i.e., the M-P-phi curves), and the Gauss method of integration (for the sum of the contributions of the fibers parallel to the neutral axis) to calculate the lateral rotations and deflections along the span of the beam-column. The validity of the proposed model and corresponding equations were tested against experimental data available in the technical literature (see part II of this publication).
