CHAPTER 6

Execution of the Analytical Program

6.1 Selection of the Set of Concrete Segmental Bridges

The objective of this task was to select a set of segmental bridges to be considered in this project. The selected set represents typical segmental bridges encountered in practice.

The team preselected eight DOTs from the following states to consult: Florida, Massachusetts, Texas, Colorado, California, Alabama, Michigan, and Minnesota. Based on the most recent (2023) data available from the NBI and InfoBridge, statistical analysis of segmental bridges was performed based on available bridge characteristics.

Selected bridge structures include those that are representative of location (chosen states), age, bridge maximum span length, total length, width, curvature, material type, rating method, and consequently, design live load model, traffic volume by ADTT, and condition.

These selection criteria were chosen based on the public domain data availability. Table 6-1 shows 50 preselected representative segmental bridge structures, where 41 bridges were selected from the chosen states, and nine bridges were selected based on the available bridge data from project partners. Of the nine bridges, one is in North Carolina and one is in Tennessee.

The broad spectrum of selected segmental bridges serves as a basis for developing new AASHTO rating procedures.

Statistical analysis of segmental bridges for preselected states was conducted. The filtering criteria for all segmental bridges in chosen states were compared to the selected sample data. Figure 6-1 presents the number of all segmental bridges for chosen states, and the number of selected segmental bridges for every state. The location of the selected segmental bridges is shown on the map (Figure 6-2).

The set of comparisons for all segmental bridges and selected segmental bridges is shown for bridge age, maximum span length, total length, number of approaching spans, number of lanes, ADTT per lane, superstructure condition rating, and operating rating method. Figure 6-3 presents the comparison of parameters along with the percentage of each group for the overall sample for selected and all segmental bridges.

6.2 Data Collection

In this step, the data required to conduct analyses of the selected bridges were collected. These data include information that reflects the current bridge condition (including inspection reports, field surveys, and relevant measurements), design and as-built plans, construction documents (contractor-proposed changes, shop drawings, casting and erection plans, material properties, casting records, construction loads, etc.), maintenance records (including repair and rehabilitation records), and rating reports (inventory and operating ratings).

A DOT survey was conducted to gather essential data for performing the reliability-based analysis of segmental bridges. An important part of data collection is the identification of construction methods (balanced cantilever, span-by-span, etc.) and information about erection procedures (such as cantilever alignment and segment age when erected). Table 6-2 presents the data request, which was sent to DOTs for the 50 selected segmental bridges.

The team also collected information on as-inspected deterioration data and the effect on load rating from examples available from the team’s industrial partners. To incorporate the bridge deterioration into the load rating analysis, the team performed the following steps:

1. Collect bridge deterioration information and data; inspection reports going back multiple cycles were requested from various participating states.
2. Categorize the major/dominant deterioration modes on segmental concrete bridges (e.g., section loss of post-tensioned reinforcement) based on field data and expert opinions.
3. Evaluate how the deterioration modes impact the bridge load rating in terms of specific structural components and limit states.
4. Summarize the findings and possible ways of incorporating deterioration into a detailed load rating analysis.

In addition to the bridge condition ratings from inspections, two types of condition ratings data are available, including NBI component ratings and AASHTO element ratings. The team collected data and investigated whether and how to use these data in the load rating analysis.

Four state DOTs provided the data on the segmental bridges as shown in Table 6-3.

6.3 Selection of Limit States

Based on a review of the rating information and preliminary analysis of the structures identified in Section 6.1, as well as input from segmental bridge experts, including those on the research team and ASBI and state transportation agencies, appropriate limit states were identified for service and strength levels. The following five limiting criteria were considered:

• Service limit state
  • Flexural tensile stress
  • Flexural compressive stress
  • Principal tensile stress (combined flexural, shear, and torsional effects)
• Strength limit state
  • Flexural strength
  • Shear strength (from combined direct shear and torsion)

Table 6-2. DOT data collection for segmental bridges.

Table 6-3. Segmental bridge data collected from state DOTs.

Consideration must be given to joint behavior. Thus, in the longitudinal direction, these limit states were at each joint. Similar checks were conducted in the transverse direction.

The service limit states are consistent with the previous service limit state calibration work conducted under NCHRP Project 12-83. The team identified the stress limits at service limit state for longitudinal and transverse analysis as shown in Table 6-4 [based on FDOT’s New Directions for Florida Post-Tensioned Bridges (Corven Engineering 2004)].

The load rating factors (RFs) were calculated using Eqs. (6-1 through 6-4).

$C-\left({\text{γ}}_{\text{DC}}\right)\left(\text{DC}\right)-\left({\text{γ}}_{\text{DW}}\right)\left(\text{DW}\right)\pm \left({\text{γ}}_{\text{EL}}\right)\left(\text{PS}+\text{EL}\right)-\left({\text{γ}}_{\text{FR}}\right)\left(\text{FR}\right)$

For the strength limit states:

For the service limit states:

where

Unless otherwise noted, the baseline or benchmark case used in the comparative analysis included the following options:

• CEB-FIP (1990) model was used for predicting creep and shrinkage behavior, and concrete compressive strength development with time.

6.4.1.3 Compressive Strength Overstrength Factors

Compressive strength overstrength factors are herein defined as the ratio of expected to specified concrete compressive strength. The use of expected rather than specified concrete compressive strength resulted in higher rating factors through two mechanisms: (1) an increase in the allowable stresses, which are typically expressed as a function of concrete compressive strength, and (2) the impact that the use of a stronger concrete has on the time-dependent structural analysis. Both these aspects were investigated. A total of four overstrength factors were considered: 1.0, 1.1, 1.2, and 1.3. The overstrength factors were applied to the specified concrete compressive strength at 28 days.

6.4.1.4 Models for Predicting Concrete Compressive Strength Development over Time

Since the compressive strength of concrete varies with time, the influence of the selected model for predicting this variation on load rating was investigated. The models considered for predicting the variation of concrete compressive strength with time were (1) ACI 209R-92 (ACI 1992), and (2) fib (2010). The variation of compressive strength with time affects the variation of modulus of elasticity with time, which is predicted using functions expressed in terms of the compressive strength. The time-dependent modulus of elasticity is, on the other hand, used to determine time-dependent transformed-section properties, and the effective modulus is used to account for creep effects.

6.4.1.5 Influence of Various Load Cases on Principal Tensile Stress in the Web and Impact of Assumed Allowable Tensile Stress

Since the load rating of concrete segmental bridges is controlled primarily by the service limit state, the impact that the selected allowable tensile stress has on load rating was investigated by considering various allowable tensile stress values for the principal tensile stress in the web. The considered allowable tensile stresses included (1) Zero tension, (2) $0.0632\sqrt{f_c^{\prime }}$ ksi, (3) $0.0948\sqrt{f_c^{\prime }}$ ksi, (4) $0.126\sqrt{f_c^{\prime }}$ ksi, and (5) $0.158\sqrt{f_c^{\prime }}$ ksi. In addition, the contribution of each load case to the principal tensile stress in the web was quantified. The guidance on selecting a value for the allowable principal tensile stress varies in terms of design and load rating. AASHTO LRFD (2020a) specifies a value of $0.1107\sqrt{f_c^{\prime }}$ ksi and indicates that a factor of 0.8 should be used for live load (Service III). Corven Engineering (2004) recommends a value of $0.0948\sqrt{f_c^{\prime }}$ ksi and a live load factor of 0.8 (Service III) for inventory rating.

6.4.1.6 Influence of Condition Factors on Load Rating

Currently, condition factors are used as a metric to characterize deterioration. In the current formulation, condition factors affect the strength limit states (flexural and shear strength). The report by Corven Engineering (2004) provides guidance for how to determine condition factors for concrete segmental bridges. The recommendations were developed by extending the concepts of “structural condition” given in LRFR to the particulars of concrete segmental bridges.

The selection of condition factors for each limit state should be conducted such that it reflects the current condition of the bridge and with consideration for how that condition affects the limit state of interest. For example, Corven Engineering (2004) reports that if corrosion damage to bonded tendons is localized to one region or to one or more particular cross sections and the rest of the structure is otherwise satisfactory, then the low value (0.85) may be applied to those areas and an appropriately higher value to others. However, caution is advised since damage to an internal tendon at one section may mean that it may be partially effective at other sections.

The influence of condition factors on load rating was quantified by assuming different values for the condition factor and by load rating the bridge based on these assumptions.

6.4.1.7 Transformed versus Gross-Section Properties

The sequential nature of construction in concrete segmental bridges includes forces that are applied to the net concrete cross section, such as when post-tensioning is applied, and forces that are applied to the transformed concrete cross section, such as those created by loads applied after the grouting process in the ducts is completed for bridges that feature internally bonded tendons. The impact of the selection of gross- versus transformed-section properties was investigated by conducting load rating computations for each case. The use of transformed versus gross-section properties is typically left to the discretion of the engineer. Maguire et al. (2015) used uncracked, transformed-section properties, including tendons, mild reinforcement, barrier rails, and full flange width for their beamline elements in their beamline longitudinal model. In this investigation, the presence of barrier rails was ignored in the definition of the cross section and the calculation of the section properties. Transformed-section properties included the presence of tendons, whereas gross-section properties were based solely on the concrete segmental cross section.

6.4.1.8 When the Load Rating Was Conducted

To quantify the impact that the time the bridge was rated has on the outcome of the rating, three cases were considered in terms of when the bridge was load rated. The baseline case used in all analyses was 10,000 days after the completion of construction and the opening of the bridge to traffic. The concrete segmental bridge constructed with the balanced cantilever method was load rated two more times at 5,000 days and 15,000 days after the completion of construction and the opening of the bridge to traffic.

6.4.1.9 Influence of Multiple Trucks

The evaluation of the presence of multiple trucks is conducted in two ways. First, the influence of lane configuration on load rating is determined for the concrete segmental bridge constructed with the balanced cantilever method. This is addressed in Section 6.4.5.10. The considered lane configurations include one based on design lanes (three lanes in this case) and another based on striped lanes (two in this case). For each case, the bridge is rated in the longitudinal and transverse directions. While the number of lanes was based on either design or striped lanes, the position of live load in the transverse direction was determined such that it created the worst-case effects based on the limitations provided in AASHTO MBE (2020). Second, the impact of multiple trucks within a given lane configuration was evaluated by considering the results obtained from the three load rating examples that addressed bridges constructed with the span-by-span, balanced cantilever, and incremental launching method. This situation is addressed in Section 6.4.6.

6.4.1.10 Influence of Analysis Technique on Live Load Effects in the Transverse Direction

Computed live load induced strains in the top slab in the transverse direction based on a 2D frame model and influence surfaces as well as on 3D finite element analysis were compared with those measured during a live load test for the Seabreeze Bridge, in Daytona, Florida. The goal of this comparison is to determine the level of conservatism used in the traditional frame analysis and to make recommendations for load rating.

6.4.1.11 Influence of Erection Time

The influence of erection time on load rating factors is investigated for a three-span concrete segmental bridge constructed with the span-by-span method. A comparison of rating factors is conducted assuming two erection scenarios. In the first scenario, it is assumed that two spans are erected each week. In the second scenario, it is assumed that one span is erected each week.

A study of the influence of erection on the balanced cantilever bridge is not included in this report. Such a study would include considering two different erection schedules while maintaining the same production date of the precast segments. In this scenario, the slower erection schedule would lead to the erection of older segments, which would then experience lower time-dependent stress changes, albeit with them having slightly higher stiffness as a function of increased age. In general, for the three-span bridge of Example 2, at some bridge age where time-dependent behavior has ceased, the load ratings of the more slowly erected bridge would be higher at midspan (positive bending) and lower at the piers (negative bending) than those of the bridge erected faster.

6.4.1.12 Influence of the Resal Effect

The influence of the Resal effect on load rating was investigated for the bridge constructed with the balanced cantilever method. The investigated limit state was vertical shear at the ultimate load level. Rating factors for this limit state were computed once by ignoring the Resal effect, and another time by considering it. The percentage change in rating factors was quantified. Taking account of the Resal effect may improve ratings related to principal tension in the webs.

6.4.2 Numerical Modeling Protocol and Load Rating Analysis

The bridges constructed with the span-by-span, balanced cantilever, and incremental launching methods and discussed in the load rating examples were load rated in the longitudinal and transverse directions.

Longitudinal Direction

In the longitudinal direction, the time-dependent structural analysis was conducted in Midas Civil 2023. The analysis results were exported to an Excel file, which in turn served as an input file for load rating calculations in Mathcad 15. For every segment, at the i-joint (the beginning of the segment) and j-joint (the end of the segment), load demand in terms of axial force, bending moment, shear, and torsion were exported to the Excel file. In addition, for every segment at the i-joint and j-joint, sectional capacities in terms of flexural strength and shear strength, computed in Midas Civil 2023, were exported to the Excel file. These flexural and shear capacities were verified with independent manual calculations based on AASHTO LRFD (2020a) as explained in the load rating examples (Appendix C of the Guideline). Similarly, for every segment at the i-joint and j-joint, the section properties in terms of area, moment of inertia, centroidal axis, first moment of area, area enclosed by shear flow path (including any areas of holes therein), and length of median of web measured on slope from mid-depth of top slab to mid-depth of bottom slab were exported to the Excel file. Once this information was exported to Excel, the load rating factors were calculated for each joint, each limit state, and each load combination. These load rating factors were then plotted as a function of segment number to illustrate their variation and to identify controlling segments and locations. An algorithm was created in Mathcad to compute the load rating factors for each of the cases mentioned at each joint.

Temperature gradient was based on solar radiation zone 3. Stresses created due to temperature gradient (self-equilibrating and secondary axial force and bending moment stresses) were obtained from Midas Civil 2023, although independent manual calculations based on free, restrained, and self-equilibrating stresses were conducted to validate the accuracy of the results. This situation is discussed further in the validation section. The uniform temperature change load case (TU) did not create any stress effects in the bridge constructed with the span-by-span method because the superstructure was free to axially contract or expand. In the bridge constructed by the balanced cantilever method, stresses created due to TU were considered because the superstructure and pier were rigidly connected.

The analytical model used to conduct the time-dependent structural analysis in the longitudinal direction was a 3D model featuring beam finite elements for the concrete segments. Timoshenko beam elements were used for the concrete segments. Each beam element featured a total of six degrees of freedom per node, three translational and three rotational. The use of Timoshenko beam elements rather than Euler-Bernoulli beam elements allowed the consideration of shear deformations. Prestressing effects were simulated using the equivalent load concept based on specified tendon coordinates. The stiffness of the tendons was reflected in the computation of transformed-section properties. The tensile stresses in the tendons, which were used to calculate the equivalent loads, were based on the prestress losses at every construction stage caused by various factors such as creep and shrinkage of concrete, relaxation of prestressing strands, friction losses, anchorage seating losses, and elastic losses or gains. While prismatic concrete segments were used for the bridge constructed by span-by-span method, linearly varying segments were considered for the bridge constructed by balanced cantilever method to capture the variable stiffness of the segments. The variation of depth within a segment was considered to be linear. The pier elements for the bridge constructed with the balanced cantilever method were prismatic elements. The analytical model is capable of capturing (1) staged construction; (2) time-dependent effects; and (3) prestress losses due to creep, shrinkage, relaxation, friction, anchorage set, and elastic loss or gain. Both short-term and long-term prestress losses were considered. Short-term losses included (1) elastic shortening losses (or elastic elongations gains), which were captured through strain compatibility by the analytical model as the structure deforms; (2) anchorage set losses, which were calculated based on specified anchorage set, friction, and wobble factors; and (3) friction losses, calculated based on selected code formula, tendon geometry, and friction and wobble factors. Long-term losses included (1) creep and shrinkage, which were calculated together based on strain compatibility for each construction stage, and (2) relaxation losses which were calculated based on Eq. (6-5) (Magura et al. 1964). The calculation of the relaxation loss was based on an assumed variation of the initial prestressing force at each time step. Eq. (6-5) is similar to the AASHTO LRFD (2020a) Eq. 5.9.3.4.2c-1.

A node located at mid-width of the segment and at the top of the segment was used as the reference node to define the superstructure for the bridge constructed with the span-by-span method as shown in Figure 6-4(a). The selection of the top of the segment as the reference node predefines an offset between the reference point and the centroid of the section. Alternatively, the reference point may be selected at the centroid of the segmental cross section. Although, this creates difficulties when modeling non-prismatic elements for the superstructure because the location of the centroid varies along the span. Tendon coordinates are entered based on the reference node, and tendon eccentricities with respect to the section centroid are calculated based on the predefined offset between the reference node and the centroid of the section. The grouping effect of the tendons, that is, “z” offsets as specified in AASHTO LRFD (2020a) Figure C5.9.1.6-1, should be considered. In some cases, the box sections used in concrete segmental bridges are too deep for this to have a significant effect in the analysis. However, this grouping effect might be impactful in shallower cross sections. Rigid links were used to connect the supports to the reference node for the bridge constructed with the span-by-span method as shown in Figure 6-4(a). In addition, for this bridge, the boundary conditions featured pin-roller-roller-roller conditions, which allowed the superstructure to axially expand and contract. For the support defined as pin, translations in x, y, and z directions were restrained. For the supports defined as rollers, only the translations in y and z directions were restrained. This was done by defining two support points as shown in Figure 6-4(a). In the first support, translations in

Secondary prestressing effects and prestresses losses were considered. Secondary moments due to creep and shrinkage were considered; however, they were found to be too small to make an impact. Only one time step was considered to account for time-dependent effects, which was from completion of construction and opening of the bridge to traffic to 10,000 days. Temperature gradient effects were not included in the transverse analysis. Unlike the load rating analysis in the longitudinal direction, which to a certain extent was automated through the use of an algorithm created in Mathcad, load rating analysis in the transverse direction was conducted manually, when it came to the computation of stresses at service and the verification of shear and moment capacities for the top slab obtained from Midas Civil 2023.

6.4.3 Validation of Numerical Modeling Protocol in the Longitudinal Direction

The numerical modeling protocol used in the longitudinal direction was validated by investigating the capability of Midas Civil 2023 to accurately simulate creep, shrinkage, and temperature effects based on a given input. The concrete segmental cross section shown in Figure 6-7 was used to conduct a comparison between theoretical and computed results. The section properties for this concrete segmental cross section are given in Table 6-7. The comparison was conducted between computed and predicted results. Predicted results were based on linear elastic engineering mechanics, and when creep effects were considered, they were based on viscoelastic analysis. Comparison with field data is presented in Section 6.4.7 with respect to live load induced strains in the transverse direction. Since long-term field data in the longitudinal direction included the combined effects of creep, shrinkage, uniform temperature, and temperature gradients, the validation of numerical loading protocol was conducted at the fundamental level between computed and predicted results for each effect independently.

6.4.3.1 Temperature Gradient

The concrete segmental cross section shown in Figure 6-7 was subjected to the positive temperature gradient specified for solar radiation zone 3 in AASHTO LRFD (2020a) as illustrated in Figure 6-8. Cross-sectional stresses calculated based on engineering mechanics were compared

Final stresses in the cross section are calculated by superimposing the free stresses with the stresses created by the axial force and bending moment previously mentioned using the formula. This is illustrated in Figure 6-10. The stresses created due to the integrated axial force and bending moment were obtained using the formula P/A + My/I. It should be noted that the net stresses are self-equilibrating in nature, in the sense that if the net stress diagram were to be integrated along the segmental cross section, the net axial force and bending moment would be zero, since there are no externally applied forces. This check can be used to ensure that the calculations are conducted correctly. However, it should be noted that this check applies to simply supported configurations, where restrained axial forces and bending moments arising due to the statical

${\text{Δ}}_0=\frac{P{L}^3}{48EI}$

Since the simply supported concrete segmental beam considered in this example was assumed to be composed of only concrete (i.e., no tendons) the additional creep deflection may be calculated using Eq. (6-11) and is directly proportional to the creep coefficient. It should be noted that this equation is only valid for plain concrete and assumes that compressive creep is equal to tensile creep (a common assumption in time-dependent structural analysis).

Creep strain can be further calculated as described in the Eq. (6-12), where ε_cc(t, t₀) is the creep strain at time t due to the load applied at t₀; ϕ(t, t₀) is the creep coefficient at time t due to the load applied at t₀; and E_c is the modulus of elasticity at 28 days, which needs to be determined based on the formula given in the relevant code (not the one defined under material properties in Midas Civil 2023).

In the CEB-FIP (1990) code, the modulus of elasticity of the concrete at 28 days was calculated based on the Eq. (6-13) where f_c′ is the concrete compressive strength at 28 days, where f_c′ and E_c are in MPa.

Midas Civil 2023 does not use the E_c value provided under material properties (4,770 ksi) but uses Eq. (6-13) for the calculation of the creep strain, and hence creep deformations. Immediate deflections were calculated based on the E_c value provided under material properties. Using the CEB-FIP (1990) code and assuming f_c′ = 7 ksi concrete, the E_c value was calculated as follows.

In this example, the creep deformation was calculated as follows:

From t₀ = 28 days to t₁ = 228 days, the creep coefficient ϕ_(228,28) was calculated as 0.998 as shown in Eq. (6-15). The creep deformation at the age of 228 days was expected to be 0.164 in. as shown in Eq. (6-16). This calculated creep strain from 28 days to 228 days was compared to that obtained from Midas Civil 2023. Figure 6-16 suggests that the calculated and computed creep deformations for this time step are identical. It should be noted that these deformations are those induced by creep only and do not include elastic deformations.

${\text{Δ}}_{\text{cr}1}={\text{Δ}}_0\frac{E_{c_{\text{provided}}}}{E_{c_{\text{CEB-FIB}1990}}}{\varphi }_{\left(228,28\right)}$

The total creep deflection between 228 days and 10,200 days can be calculated as shown in Eq. (6-17). This predicted creep deformation was compared with that obtained from Midas Civil 2023. Figure 6-17 suggests that the results are rather similar (0.262 in. calculated versus 0.258 in. computed, i.e., 1.5% error). Again, these deformations are those induced by creep only and do not include elastic deformations.

${\text{Δ}}_{\text{cr}2}={\text{Δ}}_0\frac{E_{c_{\text{provided}}}}{E_{c_{\text{CEB-FIB}1990}}}\left[{\varphi }_{\left(10200,28\right)}-{\varphi }_{\left(228,28\right)}\right]+{\text{Δ}}_1\frac{E_{c_{\text{provided}}}}{E_{c_{\text{CEB-FIB}1990}}}\left[{\varphi }_{\left(10200,28\right)}\right]$

When the total creep deformations were considered, the calculated total creep deformation was equal to 0.426 in. as shown in Figure 6-18. The computed total creep deformation obtained from Midas Civil was equal to 0.422 in. (0.9% error).

${\text{Δ}}_{\text{cr}}={\text{Δ}}_{\text{cr}1}+{\text{Δ}}_{\text{cr}2}$

The total calculated and computed deflections (immediate plus creep deflections) were compared in Table 6-10 for the three times considered in this example. Here, the deflections at 228 and 10,200 days were total deflections and included elastic as well as creep deflections. The ratio of computed to calculated deflections was 1.0 and the V was 0.4%, which suggests that Midas Civil 2023 is capable of predicting accurately creep effects.

6.4.3.3 Shrinkage

The simply supported concrete segmental beam mentioned previously was used to conduct a comparison between calculated and computed axial deformations due to a specified shrinkage strain. Since the beam was simply supported (i.e., pin supported on one end and roller supported at the other) it was subjected only to axial deformations and no stresses when subjected to uniform shrinkage. The specified shrinkage was based on CEB-FIP (1990). The ability of Midas Civil to predict shrinkage strains based on this model is illustrated in Figure 6-19. It was assumed that the beam was moist-cured for 28 days. The shrinkage strain at 10,200 days was calculated as −301 µε.

Considering that the beam length is 100 ft, the shrinkage-induced axial deformation at 10,200 days is 0.36 in. An identical axial deformation was computed by Midas Civil 2023 as shown in Figure 6-20.

${\text{Δ}}_1=L_{\text{o}}\ast \text{ε}\left(10200,28\right)$

6.4.3.4 Uniform Temperature Changes

The simply supported concrete segmental bridge mentioned previously was subjected to a uniform temperature change ∆T = +70 °F. The coefficient of thermal expansion was assumed

While these suggestions are presented in terms of additional posting mitigation considerations for longitudinal tension in epoxy joints caused by any load case, tension created by temperature gradients presents an example of when this avenue may be mobilized.

To further illustrate the impact that temperature gradient can have on stresses at service, the stresses caused by each load case on the top fiber are illustrated in Figure 6-28(b). In this case, the load combination considered included a positive temperature gradient, which created compression on the top. It is worth noting the compressive stress caused by temperature gradient is higher than that caused by dead loads. Since compressive stresses are typically not an issue, this is not a concern; it was illustrated here to highlight the potential of TG as a load case in terms of creating significant compressive and tensile stresses at service. When negative temperature gradients were considered, significant tensile stresses were created in the top fiber [Figure 6-28(d)], which may be more vulnerable to deterioration compared to the bottom fiber. However, these spikes in tensile stress apply only to a limited depth, which as noted previously, depends largely on the cross-sectional shape, and are temporary.

6.4.4.4 Influence of Compressive Strength Overstrength Factors on Load Rating

Figure 6-29 shows how the selection of a particular overstrength factor affects load rating. The rating factors in Figure 6-29(a) show the controlling factors for all limit states considered in the longitudinal direction (flexural stress at service, principal tensile stress in the web, flexural strength, and shear strength). A 30% increase in the overstrength factor results in up to a 15% increase in the controlling rating factor [Figure 6-29(b)]. Overstrength factors were applied to the compressive strength of concrete only at 28 days and their influence was considered in the structural analysis as well as in the capacity side. Overstrength strength factors were most impactful when considered in the capacity side at the service limit state since an increase in the specified concrete compressive strength resulted in an increase in the allowable flexural and principal tensile stress. Their influence on time-dependent structural analysis is illustrated in Figure 6-29(c–f) in terms of the top and fiber stress magnitude. The use of overstrength factors resulted in stronger concrete, which creeps less, and results in lower creep-induced prestress losses. This resulted in higher primary and secondary prestressing forces, which resulted in higher stresses. However, this increase was negligible [smaller than 2%, see Figure 6-29(e–f)]. The use of overstrength factors also resulted in smaller stresses caused by secondary creep effects with stronger concretes resulting in lower creep-induced stresses. However, the reduction in top and bottom fiber stresses caused by secondary creep effects was smaller than 6%.

6.4.4.5 Influence of Concrete Strength Development on Load Rating

Figure 6-30(a–c) shows the influence of the predicted variation of compressive strength with time on load rating. Two models were used to predict the variation of compressive strength with time: the CEB-FIP 1990/fib 2010 model and the ACI 209R.92 (ACI 1992) model. For the ACI 209R.92 (ACI 1992) model the parameters (a) for cement type and (b) for curing method were taken as equal to 4 and 0.85, respectively. The CEB-FIP 1990 and fib 2010 models are identical provided that the aggregate factor is assumed to be 1.0 as was done in this case. The functions used to determine the variation of compressive strength with time were used to predict the variation of modulus of elasticity with time. The time-dependent modulus of elasticity was used to determine the effective modulus, which accounted for creep effects. While there was some variation in the predicted strength with time between the two models, this difference diminished after 15 days. The selection of one model or the other was inconsequential when it came to load rating, as the difference in load rating factors was negligible (i.e., smaller than 1%) [Figure 6-30(b–c)].

6.4.4.6 Influence of Various Load Cases on Principal Web Tensile Stress and Impact of Assumed Allowable Tensile Stress

In the analysis, the principal tensile stress check was conducted at all joints in the longitudinal direction. Along the depth of the segmental cross section, the principal tensile stress check was conducted at the centroidal axis. The evaluation of principal tensile stress at the centroidal axis was conducted because at this location shear stresses are highest. However, if the centroidal axis falls in the thickened portion of the web, then the check should be conducted at the critical elevation considering the coexistence of normal stresses. Similarly, if the centroidal axis (or critical elevation) falls within one duct diameter of the top or bottom of an internal, grouted duct, the web width for calculating stresses should be reduced by half the duct diameter (Corven Engineering 2004). When conducting the principal tensile stress check, concurrent vertical normal tensile stresses caused by transverse bending were ignored. Similarly, normal stresses caused by the temperature gradient were ignored.

Figure 6-31(a) shows the influence of each load case on the principal tensile stress calculated at the centroidal axis of a segment located over the interior support. Since the direction of principal tensile stresses caused by each load case was different, these stresses were not added algebraically to calculate a total principal tensile stress. Rather, an allowable shear stress was

6.4.4.7 Influence of Condition Factors on Load Rating

A sensitivity analysis was conducted to determine how the selection of various condition factors affects load rating. The results are shown in Figure 6-32. A condition factor of 1.0 was selected to establish a baseline for comparisons. Two additional condition factors were considered: 0.85 and 1.10. The controlling rating factor pertains to flexural service stress at the 27th element, which is located at the midspan of the second span. Flexural service stress is a limit state not influenced by the selection of condition factors in the current formulation as it pertained to the service limit state (RF = 1.04). The lowest rating factors for flexural and shear strength in the longitudinal direction were 4.07 and 1.30, respectively.

Figure 6-32 suggests that condition factors have a strong influence on load rating; a 15% decrease in the condition factor caused up to a 42% decrease in the rating factors. Similarly, a 10% increase in the condition factors caused up to a 17% increase in the rating factors. For this example, the selection of various condition factors did not result in a change in the controlling limit state when flexural strength in the longitudinal direction is considered (i.e., even if a condition factor of 0.85 was chosen, the bridge still passes the load rating for longitudinal flexural strength with the lowest rating factor being 3.1), while the controlling load rating factor for service

6.4.5 Comparative Analysis for a Concrete Segmental Bridge Constructed with the Balanced Cantilever Method

6.4.5.1 Description of the Bridge

The concrete segmental bridge used in the load rating example and constructed with the balanced cantilever method was used to conduct a comparative analysis. The focus of the comparative analysis is to understand how the selection of certain parameters affects the load rating of the bridge in the longitudinal direction. The goal of the analysis is to identify parameters that have a strong impact on load rating and those that do not. The elevation of the bridge and its cross section are shown in Figure 6-34. Detailed information about this bridge can be found in Appendix C of the Guideline.

6.4.5.2 Influence of Creep and Shrinkage Model on Load Rating

The influence of the creep and shrinkage models on load rating was investigated using various creep and shrinkage models. The considered models include (1) AASHTO LRFD (2020a), (2) fib 2010, (3) CEB-FIP 1990, (4) CEB-FIP 1978, and (5) ACI 209R.92. The load rating of the bridge

A similar evaluation was conducted for stresses at service to determine the impact of creep and shrinkage model selection on concrete segmental bridge design. Figure 6-39 shows the influence on service flexural stresses. Figure 6-39(a) (left) shows the variation of the top fiber stress as a function of location along the span and as a function of the selected creep and shrinkage model. Top fiber stresses are calculated at every joint along the span. Figure 6-39(a) (right) shows the percent difference in top fiber stress as a function of various creep and shrinkage models. Figure 6-39(b) (left) shows the variation of the bottom fiber stress as a function of location along the span, and Figure 6-39(b) (right) shows the percent difference in bottom fiber stress as a function of various creep and shrinkage models. The percent difference graphs are prepared by considering the CEB-FIP 1990 model as a benchmark model. Tensile stresses are positive and compressive stresses are negative. Some tension exists at the beginning and the end of the bridge near the abutments.

Service I/III load combinations are used such that if the live load created tension, the live load factor is taken as 0.80, otherwise the live load factor is taken as 1.0. There are a total of four load combinations for each fiber (top and bottom) due to the positive and negative uniform temperature changes and temperature gradient. The envelope values are presented in these figures. Figure 6-39(a) (right) suggests that there seems to be a maximum 30.7% difference in top fiber stresses when the CEB-FIP 1978 model is used as a benchmark. However, when the stress values are used as a metric for comparison, it can be seen that differences in service flexural stresses are small, that is, 0.026 ksi of tension for the CEB-FIP 1990 model and 0.018 ksi of tension for the CEB-FIP 1978 model (8 psi difference in tensile stresses). The high differences in terms of percent change are driven by the small benchmark value. Figure 6-39(b) (right) suggests that the maximum difference in terms of percent change in service flexural stresses at the bottom fiber is 19.1%. When a direct comparison of stress values is conducted, the maximum difference is determined when the CEB-FIP 1990 results in a flexural compressive stress of −0.968 ksi and the CEB-FIP 1978 model results in a flexural compressive stress of −0.783 ksi. In this case, the difference in service compressive stresses is higher, and it is equal to 185 psi. It is concluded that for this particular bridge, the impact of the selection of various creep and shrinkage models on service tensile stresses is small and limited to 8 psi, whereas the impact on service compressive stresses is higher and equal to 185 psi. Overall, considering the magnitude of allowable stresses at service the impact of the selected creep and shrinkage models in service flexural stresses

6.4.5.4 Influence of Compressive Strength Overstrength Factors on Load Rating

The influence of the compressive strength overstrength (OS) factor, which herein is defined as the ratio of measured concrete compressive strength to the specified concrete compressive strength, on load rating is examined. The results are shown in Figure 6-41 for all limit states considered in the longitudinal direction (flexural stress at service, principal tensile stress in the web, flexural strength, and shear strength). As was done for the span-by-span bridge example, the overstrength factors were applied to the compressive strength of concrete only at 28 days and their influence was considered on the demand side (i.e., forces obtained from structural analysis) as well as on the capacity side. Overstrength strength factors were most impactful when considered on the capacity side at the service limit state since an increase in the specified concrete compressive strength results in an increase in the allowable flexural and principal tensile stress. A 30% increase in the overstrength factor results in up to a 45% increase in the controlling rating factor, which pertains to the limit state of flexural tensile stress at service [Figure 6-41(b)]. In addition, the influence overstrength factor on time-dependent structural analysis is illustrated in Figure 6-41(c-f) in terms of the top and bottom fiber stress magnitude. The use of overstrength factors results in stronger concrete, which creeps less, and results in lower creep-induced prestress losses. This results in higher primary and secondary prestressing forces, which result in higher stresses. However, this increase is negligible, that is, smaller than 12 psi. The use of overstrength factors also results in smaller stresses caused by secondary creep effects with stronger concretes resulting in lower creep-induced stresses. However, here again, the reduction in top and bottom fiber stresses caused by secondary creep effects is smaller than 4 psi.

6.4.5.5 Influence of Concrete Strength Development on Load Rating

The influence of the model that predicts the development of compressive strength with time on load rating was examined. The interest in this evaluation is the impact that the variation of compressive strength with time has on the variation of modulus of elasticity with time. The variation of modulus of elasticity with time is expressed using functions that depended on the variation of compressive strength with time. The variation of modulus of elasticity with time affected the calculation of transformed-section properties and the effective modulus, which captures creep effects. Two models were considered: (1) the CEB-FIP 1990/fib 2010 model, and (2) the ACI 209R-92 (ACI 1992) model. For the ACI 209R-92 (ACI 1992) model the parameters a for cement type and b for curing method were taken as equal to 4 and 0.85, respectively. The CEB-FIP 1990 and fib 2010 models are identical provided that the aggregate factor is 1.0. as was done in this case. Figure 6-42(a) shows the concrete compressive strength variation with time based on these two models. While there was some variation in the predicted strength with time between the two models, this difference diminishes after 15 days [Figure 6-42(a)]. The rating analysis results are shown in Figure 6-42(b) where all four limit states in the longitudinal directions are considered. The percent difference in the rating factor when the CEB-FIP 1990/fib 2010 model is considered as the benchmark is shown in Figure 6-42(c). As can be seen, the selection of one model or the other is inconsequential, as the difference in load rating factors is negligible (i.e., smaller than 2%.). Therefore, either model, ACI 209R-92 (ACI 1992) or the CEB-FIP 1990/fib 2010, may be used in the load rating of concrete segmental bridges to predict the variation of concrete compressive strength with time.

6.4.5.6 Influence of Various Load Cases on Principal Web Tensile Stress and Impact of Assumed Allowable Tensile Stress

The influence of load cases as well as allowable web tensile stresses was investigated for the concrete segmental bridge constructed with balanced cantilever method. The study was conducted for the controlling segment for principal web tension, which is the segment at

It can be concluded that the impact of the time when the bridge is rated depends on the time when the rating is conducted, the selection of the creep and shrinkage models, and the location of the section or joint that is being rated. The service flexure limit state is affected the most by the rating time followed by the principal tensile stress limit state. Ultimate strength limit states are barely influenced by the rating time for the cases considered in this study. Since general tendency is toward smaller rating factors as the bridge gets older, rating the bridge at initial and final ages when reviewing permit loads appears sufficient.

6.4.5.9 Influence of Gross- versus Transformed-Section Properties on Load Rating in Longitudinal Direction

The influence of the use of gross- versus transformed-section properties on load rating was investigated. In internally bonded concrete segmental bridge construction, initially, the self-weight of the segments and post-tensioning forces create stresses in the net cross section since the ducts are not yet grouted. After the grouting of the ducts, the application of subsequent loads, such as overlay, barriers, live loads, secondary effects (to a certain degree) causes stresses in the transformed cross section. In addition, the sequential nature of construction creates circumstances in which stresses are created in a partially grouted (i.e., partially transformed) cross section. The presence of these circumstances raises the question as to which cross-sectional properties would be appropriate for use in load rating. The concrete segmental bridge constructed with the balanced cantilever method was load rated one time using gross-section properties, and another time using transformed-section properties. When either gross or transformed-section properties were used, they were used for all load cases. The use of transformed-section properties included the transformation of reinforcement area into an equivalent concrete area. Other components, such as overlay and barrier were not included in this transformation and were considered only as loads.

The investigation was conducted for all limit states applicable in the longitudinal direction. The results are shown in Figure 6-46. The change in rating factors for service limit states is within 6.5%, and the change in rating factors for the strength limit state is limited to 1.5%. The limit state that was affected the most is service flexure, followed by principal web tension. The 1.5% change in the rating factors at the strength limit state is attributed to changes in the relative flexural stiffness of the different elements that compose the structure and the impact that flexural stiffness has on load distribution. The 6.5% difference in load rating factors may be capitalized on by the load rater when the bridge is on the verge of passing rating. The use of transformed-section properties should be reserved for load cases that justify their use (i.e., loads and deformations imposed after the grouting of the tendons).

6.4.5.10 Influence of Lane Configuration on Load Rating

The influence of lane configuration and multiple trucks was investigated by considering the concrete segmental cross section used in the balanced cantilever bridge load rating example. The configuration of the bridge used in the load rating example is shown in Figure 6-47. To investigate the influence of the number of lanes on load rating, the median barrier was removed, and the lane configuration was recreated such that the bridge features two lanes in Configuration 1 and three lanes in Configuration 2. For each configuration, the bridge was load rated multiple times to determine the controlling scenarios (i.e., single versus multiple lanes loaded) in the longitudinal and transverse directions. MPFs based on AASHTO LRFD (2020a) and AASHTO MBE (2018) were used when conducting this comparison. All ratings were conducted at the inventory level. Configuration 1 may be assumed to represent a scenario in which the bridge is load rated based on the number of striped lanes, and Configuration 2 may be assumed to represent a scenario in which the bridge is load rated based on the number of design lanes. It should be noted that when conducting the comparative analysis in the transverse direction, the notional live load was approached as close to the barrier as allowed by AASHTO MBE (2018) for both Configurations 1 and 2.

6.4.5.10.1 Comparative Analysis in the Longitudinal Direction

The results of the comparative analysis for Configurations 1 and 2 are shown in Table 6-11, Figure 6-48, Table 6-12, and Figure 6-49. Table 6-11 shows the summary of the comparative analysis in the longitudinal direction. Figure 6-48 shows the same information in a graphic format. Table 6-12 shows the ratio of Configuration 2 to Configuration 1 controlling rating factors. Figure 6-49 shows the variation of rating factors as a function of segment number in the longitudinal direction. The rating factors are shown for each limit state. In addition, Figure 6-49 shows the percent change in loading factor from Configuration 1 to Configuration 2. There is a consistent decrease of 22% in the rating factors when the lane configuration changes from Configuration 1 to Configuration 2 (i.e., from two lanes to three lanes). If we assume that Configuration 1 represents a striped lane scenario, and Configuration 2 represents a design lane scenario, there is a notable 22% decrease in the rating factors when the design lanes are

The vertical component of the inclined compressive force in the bottom flange may be calculated as shown in Eqs. (6-21 through 6-23), where V_Resal is the additional shear resistance provided by the Resal effect; M is the unfactored negative moment at the section in question when maximum shear is obtained; α is the angle of inclination of the bottom flange with respect to the longitudinal axis; d_v is the effective shear depth taken as the distance, measured perpendicular to the neutral axis, between the resultants of the tensile and compressive forces due to flexure [based on AASHTO LRFD (2020a) Article 5.7.2.8]; M_n is the nominal moment capacity of the section in question; d_e is the effective depth for bending (equal to d_p in this case, because there is no non-prestressed reinforcement where d_p is the effective depth of the prestressed strands); h is the section depth; A_s and f_y are the area and yield strength of non-prestressed reinforcement (0 in this case because there is no non-prestressed reinforcement); A_ps and f_ps are the area of the strand and strand stress at ultimate, respectively. The method presented previously is an approximation for calculating the Resal effect. In this approach, V_M is a function of M where a concentric prestressing force will also induce V_M in the bottom flange. This effect is ignored. In addition, the neutral axis may fall in the web rather than in the bottom flange when the section is subjected to negative moment. Since the inclination of the flange and that of the web is different, an angle different from α may need to be calculated if a higher level of accuracy is desired. This can be accomplished by considering the stress field for an infinitesimal element and determining the resultant compressive force together with its orientation.

To demonstrate the influence of the Resal effect on load rating for the shear strength limit state, the first span of the concrete segmental bridge constructed with balanced cantilever method is selected. When the bridge was modeled, a second-degree polynomial was used to describe the variation of the section depth along the span. The tapering starts after the I end of the 10th segment, as shown in Figure 6-52(a), meaning that the segment depths for elements No. 1 to 10 are the same. Considering the top of the I end of the 10th segment as the origin, the equation of the centroid of the bottom chord of the segments can be derived by using the known segment depths at the beginning and at the end of the span as follows where both y and x are in inches:

The first derivative of this function with respect to x provides the slope [or inclination: tan(α)] of the centroid of the bottom chord.

Since there is no slope for elements No. 1 and 10, the tan(α) = 0. It should also be noted that the x value provided in these equations should be based on the origin shown in Figure 6-52(a). When calculating the effective shear depth, d_v, the necessary data were imported from Midas Civil 2023 at each joint, such as M_n, d_p, A_ps, and f_ps. Then, the d_v values were calculated at each joint in Microsoft Excel. Similarly, the corresponding moment values in a segment caused by several load components when the shear was maximum were obtained from Midas Civil 2023. Since the load components caused by uniform and non-uniform temperature loads are not considered for the calculation of shear demand for the load rating calculation for the shear strength limit state, these are also not considered when calculating the total corresponding moment. In addition, no load factors were used when obtaining moment for each load case. After the locations of each joint with respect to the origin were determined, the vertical component of the inclined compression force at the bottom flange is calculated. The magnitude of this vertical component (i.e., the contribution of the Resal effect to shear strength) as a function of element number is illustrated in Figure 6-52(b). As expected, the segments that featured a bottom flange with zero slope with respect to the longitudinal axis are unaffected by the Resal effect. Resal effect becomes more pronounced toward the support as the slope of the bottom flange increases.

Having determined the shear force caused by the Resal effect, the load rating analysis for the shear strength limit state is repeated and the obtained rating factors are compared with those previously obtained by ignoring the Resal effect. The results are shown in Figure 6-53. As can be seen, while there is no change in the rating factor for elements No. 1-10, as evinced by the overlapping curves, the Resal effect becomes evident especially for elements No. 17-21, which feature higher rating factors when the Resal effect is included. The increase in rating factor is up to 11.4%. While for this particular bridge, the limit state of vertical shear at the ultimate load level was not the controlling limit state, the inclusion of the Resal effect may be used to benefit rating as an additional posting mitigation consideration tool for bridges controlled by this limit state. On the other hand, negative Resal effects must be included. This scenario is present in constant depth boxes with variable thickness in the bottom flange.

6.4.6 Impact of Multiple Trucks

The impact of multiple trucks on load rating of concrete segmental bridges was investigated by summarizing the results of the three load rating examples, which address bridges constructed with (1) the span-by-span method, (2) balanced cantilever method, and (3) incremental launching method. The goal was to determine which notional live load configuration controlled the rating of these bridges in the longitudinal and transverse directions. All three bridges feature two lanes. The summary of the load rating analysis for these three bridges is shown in Table 6-15. This summary includes the rating factors for each limit state in the longitudinal and transverse directions, the controlling segment or location, the controlling lane configuration, and the controlling live load configuration.

With respect to load rating in the longitudinal direction, a fully loaded bridge (i.e., two-lane loaded in these cases) controlled over a one-lane loaded bridge. While the one-lane loading case creates torsion in all three bridges, the two-lane loaded case with no torsion controlled. In addition, the combination of truck plus lane controlled over the combination of tandem plus lane.

With respect to load rating in the transverse direction, for the bridges constructed with the balanced cantilever method and incremental launching, the one-lane loaded configuration with tandem as the notional live load controlled over the two-lane loaded configuration. The controlling location for these two bridges was always the root of the cantilever for the service and ultimate limit states. For the bridge constructed with the span-by-span method, two-lane loaded configuration with the tandem as the notional live load controlled over the one-lane loaded configuration for the service limit state. The controlling location was the midspan of the top slab. For the ultimate limit state, for this bridge, the one-lane loaded configuration with truck as the notional live load controlled over the two-lane loaded configuration with the root of the cantilever being the controlling location. Generally, for the considered bridges, it was the one-lane loaded configuration that controlled the rating with the tandem as the notional live load and the root of the cantilever as the controlling location.

6.4.7 Comparative Analysis in the Transverse Direction

6.4.7.1 Introduction

A comparative analysis for the live load effects in the transverse direction between various analytical techniques was conducted for the Seabreeze Bridge located in Daytona, Florida. The live load effect in the transverse direction was quantified via live load testing in the field by Maguire et al. (2015). The measured strains due to live load were compared with those obtained using Homberg charts and a 2D frame model as well as those predicted by a 3D shell finite element

The following assumptions were made when creating the 3D model:

1. A second order polynomial function was used to create the non-prismatic cross section.
2. The thickness of the bottom flange varies along the span length. The cross sections between the midspan and pier were divided into six segments, and separate bottom flange thicknesses were assigned to each segment.
3. Similarly, the thickness of the top flange varies in the transverse direction. Various finite elements were used in the transverse direction and each element was assigned an average thickness.
4. Boundary conditions were modeled as roller-pin-roller.
5. A 150-mm- (5.9-in.-) mesh size was used for the locations where the strain gauges were positioned (Sections A and C). For all other locations, a 1,000-mm- (39-in.-) mesh size was selected as shown in Figure 6-58.
6. A linear elastic analysis was conducted.
7. The truck wheel loads were applied as concentrated point loads.

6.4.7.5 Influence of Section Length to Width Ratio on Transverse Analysis

In the previous section, it was noted that while the bridge features 10 spans, only two spans were modeled because the inclusion of additional spans was not deemed necessary because live load effects extend only a certain distance in the longitudinal direction. It is natural to ask, what