Short- and long-term deflections in reinforced, prestressed, and composite concrete beams

A model that calculates both short- and long-term deflections (i.e., transverse deflections and section rotations) in reinforced, prestressed (or posttensioned) and composite concrete beams with generalized end conditions subjected to bending about any transverse axis proposed. The effects of creep, shrinkage, and tension stiffening in the concrete and flexural rotational restraints at the beam extremes are included in the proposed model. The model is limited to beams in which torsional moments or deformations along the member are not induced by the externally applied loads or by the prestressing or posttensioning. The moment-curvature (M-phi) diagrams are first determined at each section in order to calculate both the transverse deflections and section rotations. The concrete stress-strain curve is modeled by: (1) a hyperbola for high-strength concrete (HSC) for the zone under compression and (2) a straight line combined with a hyperbola for the zone under tension. The stress-strain curves of the reinforcements are modeled using a modified Ramberg-Osgood function for the prestressed steel (bonded or unbonded) and a multilinear function for regular rebars and composites (like fiber-reinforced polymers (FRP) and carbon fiber-reinforced polymers (CFRP)). Five examples are included that show the effectiveness of the proposed method to predict the load-deflection behavior of reinforced, prestressed (or posttensioned), composite HSC beams, and steel-concrete composite beams.