## 1 Introduction
It is a continuous process of softening, internal damage, and debonding, eventually leading to a geometrical discontinuity [8]. Hence, to correctly consider the effects of cracking, the material must be modeled in a way that describes the actual phenomena and that considers the contributions of the concrete between cracks to the overall stiffness of the member. This tensile action of the concrete between cracks is called tension stiffening [9]. According to [PERSON] et al. [9], the tension stiffening effect can be reduced by creep and cyclic loading. American Concrete Institute (ACI) Committee 224R-01 [10] states that long-term or repetitive loading extends the magnitude of cracking by up to 200%. Although the coupled hygral and structural analysis approaches are more suitable for capturing the above-mentioned factors simultaneously, they are considerably complicated and computationally expensive. In addition, most commercial software is not capable of performing such an analysis; thus, one must develop a custom-made code adapted for that specific analysis. In addition to the above-mentioned factors, discrepancies in design estimations of time-dependent deflections can arise from an oversimplified structural analysis model [4]. In the structural analysis of a design calculation, PSC girders are often simplified as one-dimensional (1D) beams. However, such a simplification cannot account for the differences in the drying rates of the slab and girder resulting from the different thicknesses of the members and environmental exposures, and/or the shear lag effect. The shear lag effect is a nonuniform stress distribution along the flanges of slender flexural members, such as box girders. The large shear force transferred from the vertical webs to the horizontal flanges of the box girder induces an in-plane shear deformation resulting in a higher longitudinal deflection at the flanges near the web [11]. In summary, the current design calculations significantly underestimate the long-term deflection, especially for large-span bridges built using a segmental construction method [2,9]. For a more realistic calculation of the long-term deflection, the PSC bridge superstructure should be analyzed using a three-dimensional (3D) model that considers the effects of non-uniform shrinkage and cracking, as well as creep and uniform shrinkage. With this background, this study proposes a simplified approach for capturing the additional effects of nonuniform shrinkage in a 3D structural analysis simultaneously with those concrete creep, uniform shrinkage, and cracking models, based on commercial software. In this approach, the structural and moisture transport analyses are conducted using two 3D finite element (FE) models. The moisture transport analysis is performed independently from the structural analysis. The curvature owing to the nonuniform shrinkage is calculated from the moisture transport analysis, converted to an equivalent load at every time step, and applied to the nonlinear structural analysis model. In the nonlinear structural analysis, the combined effects of creep, uniform shrinkage, and cracking are analyzed by superimposing the equivalent load on other permanent loads such as the self-weight, prestressing force, and/or weight of the track or pavement.