LONG-TERM DEFLECTION OF PRESTRESSED CONCRETE BEAMS

Abstract

A study of long-term deflection of statically determinate prestressed concrete beams under service loads is described. Concrete tensile strength and tensile strain softening are accommodated. Creep and shrinkage effects are determined by adopting the BP and BP2 models proposed by Bazant and Panula. An accurate implementation of the BP and BP-2 creep and shrinkage models is carried out using a step-by-step numerical time-integration scheme, originally developed for reinforced concrete beams and extended for prestressed concrete beams during the course of this study. The analysis involves discretizing the beam length into a number or segment and each segment into layers. Each finite element of concrete is assumed to be subjected to a constant uni-axial stress, which is determined by the equilibrium condition of the segment and a linear distribution of the total strain across the depth of the beam (Bernoulli-Navier hypothesis). The total strain is taken as the algebraic sum or three components namely the instantaneous elastic strain, the creep strain and the shrinkage strain. The steel behavior is assumed to be linearly elastic without bond-slip. An approximate linear moment-curvature isochrone is also presented in this study. The moment-curvature isochrone, defined as the locus of the moment-curvature points along a beam segment subjected to a constant load fur a given duration, provides a direct method of determining strain and curvature without intensive computation.

Available published experiment results in the literature are compared with computed deflection, strain and prestress force predictions by the aforementioned methods. The step-by-step time-integration methods based on the BP model had produced better results when compared with the method based on the BP-2 model. The approximate linear moment-curvature isochrone method gives reasonable predictions, and shows that this simplified method of calculation is capable of providing accurate estimates.