elastic shortening, and anchor set), and account for material properties of concrete and prestressing steel.

Live load effect/distribution for segmental bridges is expected to be different from typical girder bridges. In concrete segmental bridges, live loads produce a smaller stress increment compared to that for a girder bridge, because the load is distributed to the entire bridge cross section, and segmental bridges (particularly long spans) exhibit much greater dead-to-live load ratios than girder bridges.

Of particular interest is the determination of stresses at service since this typically controls the rating factor. These stresses, especially those at the joints, can be determined using internal forces obtained from the 2D planar frame capable of simulating staged construction and conducting time-dependent analysis. An average allowable stress threshold can be determined for inventory and operating ratings. The determination of this threshold depends on the type of joints, such as Type “A” joints with bonded reinforcement, Type A epoxy joints with discontinuous reinforcement, and Type “B” dry joints.

The suitability of an alternative simplified analysis approach proposed by Corven Engineering (2004) was also investigated, as this method was reported to provide reasonable rating results for joints. For the operating rating considering Type A cast-in-place joints with minimum bonded reinforcement, the number of striped rather than design lanes for load effect was considered, and the allowable tensile stress was increased to $0.237\sqrt{f_c^{\prime }}$ (ksi units) from the $0.0948\sqrt{f_c^{\prime }}$ that is currently specified by AASHTO. For Type A epoxy joints with discontinuous reinforcement, the number of striped rather than design lanes were considered for operating rating, although the service-level tensile stress specified in the MBE was unaltered (limited to zero) for both inventory and operating ratings.

When conducting 2D planar frame analysis, torsional effects may be computed separately and included in the results of the 2D analysis (Corven Engineering 2004). The total stress in the joint can be obtained by superimposing the effects of dead and live loads as well as those caused by time-dependent and temperature effects. The influence of each load effect on the total stress magnitude was investigated. These results were then synthesized with those presented in the literature to determine each load effect’s importance and impact.

The importance of properly accounting for creep to determine an accurate load rating of the structure must be thoroughly investigated. This is despite the fact that the current commentary in AASHTO LRFD (2020a) (Article 5.12.5.2.3) states that the creep coefficient appears to have little impact on the magnitude of final stresses and that the selection of the model has a greater impact on final stresses than the value of the creep coefficient. The commentary appears to imply that the shape of the creep curve has a larger importance on the development of final stresses compared to the impact of the ultimate creep coefficient. However, a reference to a creep coefficient suggests that a single creep curve was used throughout the entire analysis, from initial construction to the final time considered. In segmentally constructed bridges, each segment is loaded at a specific time. To accurately account for time-dependent effects, separate creep curves should be invoked for each segment since the creep curve is a function of the loading time. The selection of a separate as opposed to a singular creep curve affects the calculation of the stress history and deflections. An accurate estimation of the former is paramount for an accurate load rating of the bridge for service loads. Thus, as part of this project, the assumption and validation made during the referenced creep study (AASHTO 1999) were investigated since there are various ways to account for creep effects such as the use of an age-adjusted effective modulus (Bažant 1972) versus effective modulus, and the use of a single versus multiple creep curves.

The influence of creep and shrinkage models allowed by AASHTO LRFD (2020a) was similarly investigated by selecting representative bridges (e.g., span-by-span, balanced cantilever) and

by computing stresses at service based on selected creep and shrinkage models. The creep and shrinkage models that were considered include (1) AASHTO LRFD (2020a) and (2) CEB90 and/or latest updated model (i.e., CEB90-99 and fib 2010). The results of these analyses were used to (1) provide a range for how much stresses at services are expected to vary as a function of the selected creep and shrinkage model, and (2) how the magnitude of these stresses compares to those created by permanent and transient loads. The quantification of stress variation at service as a function of the selected creep and shrinkage model is important as there is currently no consensus in the engineering community as to which creep and shrinkage model best predicts creep effects at the material level (ACI 209R-92).

The influence of the erection procedure on the magnitude of stresses at service was evaluated by fixing the analytical method to account for creep effects, fixing the creep and shrinkage model, and varying the segment age at the time of loading for these selected representative bridges. Loading age is a critical parameter when quantifying creep-induced strain.

4.2.2 Transverse Direction

One of the approaches considered is the use of 2D planar frame modeling of a unit-length section of the transverse bridge superstructure cross section for permanent load effects and those induced due to creep, shrinkage, and temperature changes. This approach has been recommended by many designers and researchers (Moreton 1998; Tassin 1998; Barker 1978; Libby 1976; Kurian and Menon 2005, Kurian 2006; Kurian 2008) and includes the use of pin and roller supports at the web-to-bottom slab connection. When using this approach, live load effects were considered using influence surfaces. Moments created due to live loads were then combined with those obtained from planar frame analysis of the transverse cross section. Common approaches used to develop influence surfaces include those developed by Pucher (1977) for slabs of constant thickness and those developed by Homberg (1968) for selected variable-thickness slabs. In some cases, it has been reported that Pucher influence surfaces result in more accurate predictions even though the component geometry is simplified (Maguire et al. 2015).

Live load tests have shown a more efficient spreading of transverse moment and a more accentuated 3D behavior than that predicted using influence surfaces, thus validating the concept of using a 3D approach to obtain more accurate predictions (Maguire et al. 2015). These influence surfaces are developed based on the assumption that the transverse edges are perfectly fixed and infinitely long. They provide peak values of moment on a per-foot basis. Results obtained from 2D planar frames and influence surfaces were compared with those obtained from 3D FE models for bridges that feature a cross section with constant depth as well as those that feature variable depth cross sections. Previous research has shown that while planar frame approaches are typically considered sufficiently accurate for design, in some cases, transverse bridge response is significantly lower in magnitude than that estimated by the 2D frame analysis using influence surfaces for load scaling (Maguire et al. 2015). This finding indicates that 2D analysis neglects important aspects of behavior even though it typically results in conservative predictions. The quantification of this conservatism is critical when load rating segmental bridges using this method to avoid premature bridge posting and was thoroughly investigated in this project.

The calculation of total stresses includes those caused by time-dependent and temperature effects. Existing procedures for how to include these effects were reviewed together with the assumptions made to predict time-dependent behavior. Total stresses and the consequent rating factors were calculated using each method of analysis so that the impact of each factor could be quantified. Although it is impossible to distinguish creep, shrinkage, and temperature effects in the field, the conditions under which the data were obtained were modeled as accurately as possible such that the main variation quantified is that due to the set of assumptions made in each analysis technique.