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In modern computerized structural analysis, realistic material laws should be used. This research will present a constitutive law and a numerical procedure based on the finite element method for the analysis of a prestressed concrete structure including the time-dependent effects due to the load history, creep, shrinkage, aging of concrete, and relaxation of prestress. A 32.1 meter (105 ft) long U-shaped railway bridge, composed of two precast post-tensioned concrete girders and an in situ cast prestressed young concrete slab, was instrumented to observe its long-term structural behavior and used for the comparisons with numerical analysis. To evaluate and predict the structural behavior of this concrete structure, the related experiments were designed and performed both in the field and laboratory. Some material properties needed for the analysis were obtained through the extensive program carried out in the laboratory with controlled environments. This paper will describe the details of structure, test program, and experimental results.

Tests results from long-term experiments on prestressed and partially prestressed concrete beams are reported. Tests were carried out on 10 rectangular beams spanning 2 m and undergoing sustained loading for five years. After that time, there was no evidence of stabilization of the time-dependent behavior of concrete. Numerical modeling of the deformation of the midspan section explains experimental observations and confirms that the presence of ordinary reinforcing steel in a prestressed concrete section leads to a redistribution of stresses between concrete and steel which should be taken into account in serviceability limit-state computations. Tests to failure of the beams at 5 years yield no significant differences in carrying capacity with tests executed at an early age. It is suggested that the deflection limit state is a major consideration in design and that the degree of prestressing should be chosen in function of ratio of permanent load to total design load (permanent and live).

Continuing the study of long-term behavior of a U-type composite prestressed concrete bridge, this paper presents a constitutive law for structural analysis and a nonlinear diffusion theory for the understanding of internal humidity distribution in a structure. The constitutive law was formulated based on a new rheological concrete element, which is a series coupling of a generalized Kalvin chain unit, a cracking unit, and a unit representing thermal strain or shrinkage. The previously obtained exponential algorithm for cracking, treated as strain softening, is combined with the exponential algorithm for generalized Kelvin chain element. The nonlinear diffusion theory, which considers both the pore humidity and aging effects on the diffusivity, was found to give very good fit to the distribution of internal humidity of concrete. The material parameters needed for the constitutive law and diffusion theory were identified. The numerical results using finite element method show the history of the prestress transfer between a young bridge deck and more matured girders. The calculated strains based on the presented method were found to be in good agreement with field measured data.

The long-term camber prediction under sustained loads is an important part of the design of pretensioned flexural members. Critical members are noncomposite roofs and bridge members which have medium or large span-depth ratios or elements made of lightweight concrete. Currently the most common approximate design method is one that relies on empirical multipliers applied to initial cambers and deflections. When compared to a rational approach, substantial differences in prediction of long-term camber or deflection are noticed. The approximate method appears to overestimate the permanent sag or underestimate the camber. It also does not consider certain creep, shrinkage, and relaxation properties. It is concluded that such methods may be unreliable for critical members and that the rational method is preferred. For preliminary design of longer spans, revised multipliers are suggested for use with the approximate method.

Pressurized water reactor containment building structures in nuclear power plants are designed to withstand internal accident pressure. Prestressed concrete is commonly used to resist such a pressure. The structure must maintain its structural integrity for the service life of the plant; therefore, the design must consider the effect of creep and shrinkage of concrete on the prestressing system. This effect is mainly in the form of prestressing force losses over time. Since creep and shrinkage are time-dependent, their values at any point in time during the service life of the plant must be predicted. The approach utilized in the design of the prestressed containment structure and the required periodic inspection are described. Also addressed is the procedure for establishing predicted changes in the prestressing forces as a result of creep and shrinkage of concrete at any point in time. Comparisons between predicted values and actual measurements of prestressing forces at different time intervals are presented. The comparison includes a number of reactor containment buildings and different concrete proportions.