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.

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.

A step-by-step procedure is used for computing the state of stress in a prestressed concrete cylinder pipe accounting for the effects of creep and shrinkage of concrete core and mortar coating and of wire relaxation. The procedure is applied to an embedded-cylinder pipe subjected to the outdoor environment and to that of a buried pipe with varying humidity conditions. The results show that for pipe exposed to the outdoor environment, the prestress in the inner and the outer cores of embedded-cylinder pipe are significantly different. However, the change in the environment resulting from burial of the pipe and filling it with water reduces the losses, and the difference in the prestress of the inner and the outer core of embedded-cylinder pipe.

SP-129 With today's powerful computers and sophisticated testing methods, new formulation for predicting the structural response of concrete structures to creep and shrinkage of concrete are emerging. Actual structural behavior can now be predicted by mathematical modeling of material behavior. This special publication provides the means for better understanding the important creep and shrinkage characteristics of concrete. Ten papers cover a variety of topics including the theoretical and experimental parts of the long-term behavior of a railway bridge, results for creep in reinforced and prestressed concrete columns, long-term behavior of prestressed concrete beams, evaluation of creep and shrinkage deflection of reinforced concrete members, the rational and approximate methods for time-dependent deflection of prestressed concrete members, predicting and testing for creep and shrinkage, computing stress and strain, and time-dependent analysis for partially prestressed composite members.

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.