A Generalized Solution for Time-Dependent Response and Strength of Noncomposite and Composite Prestressed Concrete Beams

A computer program is developed for the analysis of initial and time-dependent responses and strength in simple bending of partially of fully prestressed concrete members. The program is capable of analyzing members of any cross-sectional shape having one axis of symmetry, noncomposite or composite, subjected to various sequences of loading and construction. It accounts for the effects of nonlinearity of stress-strain responses of materials, variations with time of strength, creep, and shrinkage of concrete, and relaxation of bonded prestressing steel in different parts of cross-sections. The linearity of rotational and translational supports can also be accounted for in the analysis.

A step-by-step method divides the time interval of interest into several smaller time increments in which the responses are determined as if they are independent of time as a part of the time-dependent response analysis. An iterative procedure where structures are modeled using a discrete element method is used to analyze instantaneous responses.

The changes in strength and shrinkage of concrete are considered to be functions of time only. Creep of concrete is considered proportional to applied strains and is a function of time and age of concrete when strains are applied. Relaxation of prestressing steel is a function of time and stress level. Both the rate of creep method and the superposition method are used in predicting creep strains of concrete under variable stresses. A method equivalent to the rate of creep method is used in estimating relaxation stresses of prestressing steel under variable stresses.

The program is capable of analyzing instantaneous load-deflection response up to failure of a prestressed concrete beam in addition to time-dependent response analysis. The beam may be pre-tensioned or post-tensioned providing that the prestressing tendons are perfectly bonded to the surrounding materials. The program may be used equally well in analyzing beams of other materials.

Five example problems are presented to demonstrate the validity and the application of the program. The solutions are compared with field and laboratory measurements and previous analytical results, if available.