Load Rating of Segmental Bridges (2024)
Chapter: 2 Literature Review
CHAPTER 2
Literature Review
The literature review forms the foundation of the research, encompassing a review of relevant domestic and international research and guidelines, including the historical development of load rating specifications, research conducted under the SHRP2 R19B, Modjeski and Masters, Inc. et al. (2015), FHWA, and other national, state, and pooled-fund sponsored research, existing guidelines, and owner and industry experience. The following key documents have been identified:
- AASHTO LRFD Bridge Design Specifications, 9th ed. (AASHTO 2020a).
- AASHTO’s The Manual for Bridge Evaluation, 3rd ed. (MBE) (AASHTO 2020b).
- NCHRP Report 406: Redundancy in Highway Bridge Superstructures (Ghosn and Moses 1998).
- NCHRP Report 454: Calibration of Load Factors for LRFR Bridge Evaluation (Moses 2001).
- NCHRP Report 368: Calibration of LRFD Bridge Design Code (Nowak 1999).
- NCHRP Web-Only Document 201: Calibration of AASHTO LRFD Concrete Bridge Design Specifications for Serviceability (Wassef et al. 2014).
- Florida Department of Transportation’s (FDOT’s) Bridge Load Rating, Permitting and Posting Manual (2017).
- FHWA’s Post-Tensioned Box Girder Design Manual (Corven Engineering 2016).
- FDOT’s New Directions for Florida Post-Tensioned Bridges—Volume 10A: Load Rating Post-tensioned Concrete Segmental Bridges (Corven Engineering 2004).
The key documents are summarized in the following sections.
2.1 AASHTO’s The Manual for Bridge Evaluation
AASHTO’s The Manual for Bridge Evaluation, 3rd ed. (MBE) is reviewed to reflect the current provisions in the inspection and the load rating of segmental bridges (AASHTO 2020b). In the inspection of prestressed segmental bridges, MBE Section 4.3.6.5 emphasizes several points to be examined, such as localized sags or humps, corrosion of prestressing tendons due to moisture existing in tendon ducts, keys in the girder stems, slabs with cracks, and deck soffits with cracks and spalls. In the evaluation of segmental bridges, temperature gradient (TG) may be considered (C6A.2.3.6). In the rating of segmental concrete bridges, Section 6A.5.11 presents several requirements such as the live load factor for one loaded lane and the limit states to be checked. According to MBE Section 6A.5.11.2, “The load rating capacity of post-tensioned concrete segmental bridges shall be checked in the longitudinal and transverse directions.” Commentary mentions that transverse effects might govern a capacity of the load rating for a bridge; therefore, it is necessary for a complete load rating. For the transverse operating load ratings, Section 6A.5.11.3 states that the factor of 1.20 specified in LRFD Design Table 3.6.1.1.2-1 for one loaded lane for the application of vehicular live load shall be limited to the maximum
of 1.00. The reason is explained in the Commentary. Axle loads govern the transverse design of the slab for such bridges, and the amplification of individual axle load is not suitable for the single-lane condition. Also, in the design load rating, the Strength I and both the Service I and Service III limit states shall be checked (Section 6A.5.11.4). Similarly, both the Service I and Service III limit states are mandatory for legal and permit load rating (Section 6A.5.11.5.1 and 6A.5.11.5.2). At service limit state, the number of striped lanes might be used as the number of live load lanes for the operating rating of design load to calibrate the service limit states and differentiate the operating rating from the inventory rating; however, loads shall be applied in such a way as to create the maximum effects. Also, principal tensile check of LRFD Design Article 5.9.2.3.3 shall be performed at the Service III limit state to verify the adequacy of webs of segmental box girder bridges for longitudinal shear and torsion.
MBE Section 6A.5.11.6 provides Table 6A.5.11.6-1 (see Table 2-1) for the system factors for post-tensioned segmental concrete box girder bridges. In the commentary, it is stated that “the system factor must account for a few significant and important aspects different than other types of bridges.” These aspects include longitudinally continuous versus simply supported spans, inherent integrity afforded by the closed continuum of box section, multiple-tendon load paths, number of webs per box, and the type of details and their post-tensioning. The system factors for segmental concrete bridges in MBE are based on the findings of NCHRP Report 406 (Ghosn and Moses 1998) and FDOT’s New Directions for Post-Tensioned Bridges—Volume 10A: Load Rating Post-Tensioned Concrete Segmental Bridges. The system factor shall be taken as 1.0 for the longitudinal shear and torsion, transverse flexure, and punching shear of segmental concrete box girder bridges. The longitudinal shear and torsion capacity shall be evaluated for design load, legal load, and permit load rating for post-tensioned segmental bridges.
AASHTO LRFD Section 4.6.2.9 provides a section related to the analysis of segmental concrete bridges (AASHTO 2020a). For instance, influence surface or other elastic analysis procedures (Articles 4.6.2.1 and 4.6.3.2) may be used in the evaluation of live load plus impact moment effects in the top flange of the box section. Effective flange width may be determined by provisions of Article 4.6.2.6.2. In Section 3.4.1, load factor and load combination are presented to be investigated. For instance, in concrete segmental structures creep (CR) and shrinkage (SH) are factored by γp for dead load (DC) due to nonlinear time-dependent effects in segmental bridges. Also, Section 9.7.6 provides a few details for the deck slabs in segmental construction.
Table 2-1. MBE Table 6A.5.11.6-1—system factors for post-tensioned segmental bridges.
| Bridge Type | Span Type | # of Hinges to Failure | System Factors (φs) | |||
|---|---|---|---|---|---|---|
| No. of Tendons per Web | ||||||
| 1/Web | 2/Web | 3/Web | 4/Web | |||
| Precast Balanced Cantilever Type A Joints |
Interior Span | 3 | 0.90 | 1.05 | 1.15 | 1.20 |
| End or Hinge Span | 2 | 0.85 | 1.00 | 1.10 | 1.15 | |
| Statically Determinate | 1 | n/a | 0.90 | 1.00 | 1.10 | |
| Precast Span-by-Span Type A Joints |
Interior Span | 3 | n/a | 1.00 | 1.10 | 1.20 |
| End or Hinge Span | 2 | n/a | 0.95 | 1.05 | 1.15 | |
| Statically Determinate | 1 | n/a | n/a | 1.00 | 1.10 | |
| Precast Span-by-Span Type B Joints |
Interior Span | 3 | n/a | 1.00 | 1.10 | 1.20 |
| End or Hinge Span | 2 | n/a | 0.95 | 1.05 | 1.15 | |
| Statically Determinate | 1 | n/a | n/a | 1.00 | 1.10 | |
| Cast-in-Place Balanced Cantilever |
Interior Span | 3 | 0.90 | 1.05 | 1.15 | 1.20 |
| End or Hinge Span | 2 | 0.85 | 1.00 | 1.10 | 1.15 | |
| Statically Determinate | 1 | n/a | 0.90 | 1.00 | 1.10 | |
2.2 Calibration of LRFD Concrete Bridge Design Specifications for Serviceability
As of the year that NCHRP Project 12-83 was initiated (2014), the service limit state in the AASHTO LRFD was not yet statistically calibrated owing to the lack of clear consequences of exceeding the service limit state. Therefore, the panel called for a need to perform the calibration of the service limit state related to concrete bridges in AASHTO LRFD. The study, coupling the literature review with the available datasets, calibrated the service limit state in terms of (1) cracking of reinforced concrete components under Service I limit state and (2) tension in prestressed concrete beams under Service III limit state. The cracking control under Service I limit state was calibrated based on concrete deck, and based on the Standard Specifications for Highway Bridges (AASHTO 2002), the crack width is limited to be 0.017 in. and 0.01275 in. for Class 1 and Class 2 exposure conditions, respectively. For Service III limit state, three different limit state functions were investigated: (1) decompression limit state, (2) stress limit state, and (3) crack width limit state. The study evaluated both the existing prestressed bridge and the new bridges that are designed based on AASHTO LRFD. The details of the calibration procedures are presented in Appendix A.
For both Service I and Service III limit states, the calibration procedures were generally subdivided into the following procedures:
- Construct criteria that determine whether the limit state is exceeded (i.e., limit state function).
- Collect statistical parameters for the variables used in the limit state function.
- Develop a statistical live load model for service limit state incorporating a large set of national weigh-in-motion (WIM) data.
- Determine the target reliability index (βT).
- Perform calibration to determine the load and resistance factors for design that lead to the uniform reliability indices (β).
2.3 Deterioration of Segmental Bridges
2.3.1 Types of Segmental Bridge Deterioration
Deterioration for segmental and post-tensioned bridges in history have been mostly related to the corrosion of tendons, cracks due to temperature gradients, or early age failure of tendons (Roberts 1993; Trejo et al. 2009). Various researchers indicated that the major reason for concrete deterioration is reinforcement corrosion (e.g., Virmani 2003; Roelfstra et al. 2004). Similarly, post-tensioning tendon corrosion has been seen in several bridges in Florida (West et al. 2002). The Durability Survey of Segmental Concrete Bridges conducted by the American Segmental Bridge Institute (ASBI) presents a suite of structurally deficient segmental bridges and illustrates the examination results (Pielstick and Offredi 2012).
In prestressed concrete, the presence of high stresses in tendons alters the corrosion process, which is characterized by the coupling between the conventional corrosion and steel microcracking (induced by high stress level and hydrogen embrittlement) (Coronelli et al. 2009). The reasons for post-tensioning corrosion might be voids and moisture between strands and between wires; water bleeding from grout; grout segregation; water penetration from anchorage pocket, joints, or cracks; water penetration due to floods, chloride-contaminated grout, soft grout, or high corrosive ion concentration; and dissimilar grouts in the same tendon (Haixue and Whitmore 2013). Grouting protects strands from harsh environmental conditions, such as rainwater, seawater, salt-fog, and deicing salt, and enhances the compatible strain between concrete and strand. In prestressed concrete precast post-tensioned segmental bridge decks, the voids and the water that often exist in the ducts result in local rusting of tendons (Kamaitis 2002). Corrosion of
tendons at joints might be crucial because it is a long-term problem that can cause a sudden failure. Examples include the collapse of the Bickton Meadows Bridge in the United Kingdom (Poston and Wouters 1998) and the collapse of the Ynys-y-Gwas Bridge. It is also supposed that dune sand had been included in the mortar filling the transverse joints (Woodward 1989). According to Poston and Wouters (1998), in the United States, the post-tensioned Walnut Lane Bridge had corrosion problems due to improper grouting and detailing. Powers et al. (2002) conducted a study about the failure of the Niles Channel Bridge and Mid-Bay Bridge in Florida due to corrosion distress and post-tensioned tendon failure. It has been stated that grout voids and grout bleed water initiated the corrosion. Another case is the failure of the Malle Bridge in Belgium due to corrosion of post-tensioning through the hinged joint of the end tie-down member (Youn and Kim 2006).
2.3.2 Deterioration Protections and Impacts
The effect of strand corrosion on structural behavior has been investigated by researchers through experimental testing and analytical models. Zhang et al. (2017) evaluated the behavior of locally ungrouted post-tensioned concrete beams after the corrosion of strands by performing a corroded strand test for constitutive law development and a beam test for the flexural behavior investigation. It was observed that the effect of corrosion loss on the yield strength and elastic modulus is less than that on the ultimate strain of strand.
Salas et al. (2008) investigated the corrosion protection of internal tendons at segmental joints by using the testing method based on ASTM G109. They fabricated beam specimens to observe the effects of post-tensioning and crack width on corrosion protection of internal tendons. Severe duct destruction and pitting were observed in most of the specimens with metal ducts. Haixue and Whitmore (2013) listed the methods for post-tensioning evaluation as visual inspection/test pits; post-tensioning (PT) corrosion evaluation by moisture testing; chloride analysis of PT grout; pH and chemical testing; petrographic analysis; scanning electron microscopy examination; and cable break detection. Trejo et al. (2009) performed a 1-year long strand corrosion test program to identify and quantify the factors affecting corrosion and tendon capacity of PT strands. The authors considered grout class, moisture content, chloride concentration, void type, and stress level. The results showed that the most severe corrosion existed at or near the grout-air-strand interface. Also, orthogonal, inclined, and bleedwater void conditions were more corrosive than parallel and no-void conditions. Salas et al. (2002) conducted research related to corrosion protection for bonded internal tendons in precast segmental construction. The researchers evaluated the effect of different parameters such as joint type, duct type, joint precompression, and grout type. Based on the experimental results, it was seen that the most significant effect is the joint type. The highest strand corrosion ratings, so that of the largest deterioration, were observed on dry joint specimens with normal grout and low-to-medium precompression. The epoxy joint specimen with the same grout type, duct, and precompression force had strand corrosion ratings on the order of 8 to 10 times smaller. Also, steel ducts showed a much higher corrosion rating than plastic ducts. Jeon et al. (2019) investigated corrosion of external tendons of two segmental bridges located on urban arterial roads. The location of the corrosion was mostly inside the duct having voids not filled by grout. Rafols et al. (2013) identify areas of anticipated corrosion susceptibility as the tendon high points, grout void locations, and other locations with grout deficiencies.
2.3.3 Corrosion Rate versus Time
Lee and Zielske (2014) conducted a 6-month accelerated corrosion testing program to determine chloride threshold(s) of post-tensioning strands exposed to chloride-contaminated
grout. Chloride threshold values of 0.4% and 0.8% by weight of cement were obtained for corrosion initiation and corrosion propagation, respectively. It was seen that the corrosion rate over time for the single wires in pH 13.6 solutions was lower than 0.05 mil/year at chloride concentration up to 0.6%. In another study conducted by FHWA, the relation of time to initial fracture/failure and mean corrosion rate is obtained from an experimental grout study of four standard deviation of corrosion rate/mean corrosion rate ratios [σ(CRE)/µ(CRE)] (see Figure 2-1) (Hartt and Lee 2016). Mean and standard deviation of corrosion rates are given as the function of chloride concentration in physically sound grout, and time to failure (Tf) is given as the function of mean corrosion rate for four different σ(CRE)/µ(CRE) ratios.
In addition, the deterioration models and the numerical expressions of corrosion progress in tendons are also reviewed and documented in Appendix A.
2.4 Condition Factors in Load Rating
The idea of the condition factor, φc, is to capture the increased uncertainties of the structure resistance variabilities when the structure experiences deterioration. MBE Table 4.2.3-1 prescribes the condition factor. The improved inspection helps reduce the resistance variability, and in such cases, the condition factor may be increased by 0.05 (φc ≤ 1.0).
The original idea of the condition factor was first introduced in NCHRP Project 12-28(1) and was documented in NCHRP Report 301: Load Capacity Evaluation of Existing Bridges (Moses and Verma 1987). The calibration was done based on the steel girder bridge data only. The other bridge types were not investigated due to lack of sufficient data.
The test specimen is categorized into three groups: (1) good condition, (2) slight corrosion, and (3) severe corrosion. For each condition, Eq. (2-1) was deployed to establish the condition factor (American Institute of Steel Construction 1986), among which BR is the bias factor of the resistance, β is the target reliability index (i.e., 2.5), and VR is the coefficient of variation (V) of the resistance.
| (2-1) |
The resistance bias factor and V account for the uncertainties caused by material yield, fabrication, and accuracy of strength prediction theories. The NCHRP Project 12-28 provided estimates and derived the resistance statistical parameter that resulted from the effects of sheltering and salt usage.
For the deteriorated member, the study obtained the test data from ASTM and many other private and public agencies over a long period at sites all over the world. The authors have accounted for three main effects that contribute to the corrosion: (1) initial climate, (2) sheltering, and (3) salt. A detailed illustration is in Appendix A.
Moses (2001) followed the same recommendations derived in NCHRP Report 301 (Moses and Verma 1987). However, the author revisited the procedures and clarified that the initial study applied double penalties for decreased capacity of the deteriorated members and the increased resistance variability. In contrast, these two parameters should be considered independently. The calibration results have remained the same ever since.
For post-tensioning concrete segmental bridges, the condition factor (φc) represents the degree of damage or concrete/post-tensioning section loss due to corrosion, accidental damage, and so forth, Corven Engineering 2004). The FDOT (2002) conducted a study to recommend some improvements in the load rating of post-tensioned concrete segmental bridges. Based on Volume 10A of that study, the condition factor for the bridges built in accordance with the FDOT’s New Directions for Florida Post-Tensioned Bridges, a condition factor of 1.10 might be used. However, the team is not recommending using a condition factor higher than 1.0. The final recommendations are provided in Section 6.5.10. Corven Engineering (2004) also presents illustrative examples for φc, as tabulated in Appendix A. It is proposed that the low value (0.85) might be applied to local corroded cross section(s) and a higher value to other satisfactory areas.
2.5 System Redundancy
Redundancy refers to the ability of a structure to support loads beyond first member failure. In other words, the structural system has capacity beyond the resistance of its highest-strength single member. For bridge structures, several commonly recognized forms of redundancy include internal redundancy, where the failure of a single component does not cause additional component failures; structural redundancy, due to the continuity of a given load path; and load path redundancy, due to the existence of multiple supporting components (Ghosn et al. 2014).
The AASHTO’s Standard Specifications for Highway Bridges (2002) required consideration of redundancy in some cases but provided little guidance on how to quantify or implement this requirement. Later, AASHTO LRFD (2020a) introduced the load modifier η, a product of
three factors to account for ductility, redundancy, and operational classification, where each factor is given a range from 0.95 to 1.05, depending on the bridge characteristics. However, how these factors are defined and implemented is somewhat subjective and open to some interpretation by the designer. The MBE (2019) provides a set of system factors for post-tension segmental construction when considering longitudinal flexure in Table 6A.5.11.6, based on the results of Corven Engineering (2004).
In NCHRP Report 406, Ghosn and Moses (1998) proposed a less subjective, quantitative approach to determine system redundancy factors for girder bridges. Four generalized limit states were considered: component failure, ultimate system failure, functionality, and a damaged condition evaluation. Ultimate system failure was defined as the development of a collapse mechanism or when the bridge is damaged to the extent that it is no longer operational. The functionality limit was taken as a deflection exceeding a hundredth of the span length, while the damaged condition considered ultimate system capacity once a single member is damaged and nonfunctional. To evaluate these limit states, simplified (grillage) finite element (FE) models of typical girder bridges were constructed and loaded with dead load and two side-by-side HS20 truck configurations, while the load factor (LF) on the trucks was increased until each limit state was exceeded, resulting in limiting load factors for a single component (LF1), the bridge system (LFu), functionality (LFf), and the damaged system (LFd). It was found that average load factor ratios were as follows: LFu/LF1 = 1.3; LFf/LF1 = 1.1; and LFd/LF1 = 0.50. Based on these results, it was proposed that the system redundancy factor for a particular bridge be taken as the minimum of three ratios, which are computed as each of the ratios specified previously but computed for a particular bridge, to the numerical value specified previously. As an alternative to bridge-specific analysis, a table of results is given for typical girder bridge geometries. In terms of reliability, it was found that the average difference between reliability index for the system and component was 0.85, 0.25, and −2.70 for the ultimate, functionality, and damaged limit states, respectively. The report notes that unique bridges are best analyzed for redundancy individually rather than using the general, average factors provided.
Expanding on NCHRP Report 406 (Ghosn and Moses 1998), Ghosn et al. (2014), in NCHRP Report 776: Bridge System Safety and Redundancy, present methods for developing system factors for bridges under lateral and vertical loads. The study determined system factors that would provide the increase in reliability index recommended in NCHRP Report 406 but as a function of beam dead load to resistance ratio, for different bridge geometries and conditions. An objective of this study was to expand the range of bridges considered from minimally designed structures as in NCHRP Report 406, to bridges with over- as well as under-designed members. It should be emphasized that NCHRP Report 406 and NCHRP Report 776 both focused on girder bridges.
Corven Engineering (2004) produced a report for FDOT specifically addressing system factors for segmental bridges. Here, system factors accounted for redundancy with regard to longitudinal continuity; the continuum behavior of a closed box girder; and multiple post-tensioning tendon paths. The proposed system factors for longitudinal flexure ranged from 0.82 to 1.30 and are given as a function of different types of segmental construction; the expected degree of continuity; the number of girder webs in the section; and the number of prestress tendons per web. Values were based on structural and statistical analyses (information given in NCHRP Report 406), performance of existing bridges, and judgment. For longitudinal flexure, the system effect was determined like that proposed in NCHRP Report 406 for continuous structures, where the number of plastic hinges required for a failure mechanism was considered (Ghosn and Moses 1998). Considering closed box girder behavior, it was noted that, in terms of redundancy, the number of box girder webs is not equivalent to the number of beams on a girder bridge because of the different load-carrying mechanisms of the webs. For example, in torsion, only exterior webs are primarily active, while in shear, more force is carried by a center web, if present; and in
flexure, all webs are significantly active. Multiple post-tensioning tendons were also considered as a form of internal redundancy, where additional tension load-carrying paths may increase system factor.
2.6 Analysis in the Longitudinal Direction
The following describes the approach typically followed when conducting structural analysis of concrete segmental bridges in the longitudinal direction.
2.6.1 General Approach
AASHTO LRFD (Article 4.6.2.9.5) requires that longitudinal analysis of segmental concrete bridges consider a specific construction method and schedule as well as time-related effects of concrete creep, shrinkage, and prestress loss (AASHTO 2020a). The effects of secondary moments due to prestressing are required to be included in the stress calculations at the service limit state. At the strength limit state, the secondary force effects induced by prestressing, with a load factor of 1.0, are required to be added algebraically to other applicable factored loads.
The requirement for time-dependent analysis is due to changes in the statical system during erection as spans are made continuous in the span-by-span construction method, or as cantilevered portions are made continuous through closure joints in the balanced cantilever method of construction. Information regarding segment casting date, segment installation time, and the time when changes in the statical system take place is required. In addition, a method to account for the time-dependent properties of concrete must be established. Such a method is specifically required for spans more than 250 ft, for which AASHTO LRFD Article 4.6.2.9.1 requires that specific consideration be given to variations in the modulus of elasticity of concrete, variations in concrete creep and shrinkage properties, and the impact of variations in the construction schedule on these and other design parameters (AASHTO 2020a). The time-dependent properties of concrete are typically a function of environmental humidity, cross-sectional dimensions, concrete composition, rate of hardening, and ambient temperature. Section properties are determined for each section, considering the effects of shear lag in top and bottom flanges as discussed in the subsequent sections.
The analyst must possess an analytical tool that is capable of simulating staged construction so that stresses at service are calculated in a way that reflects the sequence of construction for the bridge. Among the many programs developed for this purpose, several are in the public domain and may be purchased for a nominal amount (e.g., Ketchum 1986; Shushkewich 1986; Danon and Gamble 1977) (AASHTO LRFD 2020a).
Since longitudinal analysis typically focuses on global bending, shear, torsion, and time-dependent effects, the modeling approach for determining load effects includes the use of 2D frames featuring beams (segmental superstructure) and columns (segmental or non-segmental piers). The purpose of longitudinal analysis, as it relates to load rating, is the determination of internal forces and stresses due to various load effects so that this information can be used to load rate the bridge. Beam and column elements may be divided into segments or sections to simulate the installation of the segmental bridge superstructure and the introduction of post-tensioning at various stages. The stiffness of each segment should be determined based on its length and superstructure cross section, an accurate estimation of which has a profound effect on analysis results. Beam elements should capture three degrees of freedom at each node to determine vertical and axial displacements and in-plane rotation. The selected analysis tools should be investigated for their ability to conduct time-dependent analysis; consider step-by-step
construction sequences; account for locked-in erection forces; capture the redistribution of forces due to creep and shrinkage effects from casting to the current day in the life of the bridge; account for post-tensioning effects (primary, secondary, and losses such as due to friction, wobble, elastic shortening, anchor set, creep, shrinkage, and relaxation); and account for material properties of concrete and prestressing steel.
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.
2.6.2 Erection Procedure
To be able to conduct a time-dependent analysis, information regarding segment casting date, segment installation time, and the time when changes in the statical system take place must be known. Casting dates are a function of an assumed number of casting cells and the time required to cast each segment. To estimate these dates, Chen and Duan (2014) recommend that the segment production rate is assumed to be one segment per day per casting cell and one pier/expansion joint segment per week per casting cell. In addition, it is recommended that segments not be erected earlier than 1 month after casting. Corven Engineering (2004) states that when the exact dates of key activities are not available, it is recommended that the model follow the general sequence of construction and that missing dates be approximated. For example, in Florida, if no casting or erection dates are available, conservative assumptions about time are made as follows:
- Precast Concrete Balanced Cantilever Construction
- Assume the age of segments at erection is 28 days.
- Assume two segments are placed at both ends of cantilever each day.
- Assume continuity between spans takes 1 week.
- Cast-in-Place Concrete Balanced Cantilever Construction
- Assume it takes 5 to 7 days to construct a segment.
- Precast Concrete Span-by-Span Construction
- Assume the age of segments at erection is 28 days.
- Assume two spans are erected each week.
2.6.3 Live Load Effect
Live load effect/distribution for segmental bridges is expected to be different from typical girder bridges. Compared with inventory rating, a heavy vehicle used in operating rating or permit rating typically produces less load increment in a segmental bridge than that in a girder bridge, since the load will distribute to the entire bridge cross section, and segmental bridges (particularly long spans) exhibit much greater dead-to-live load ratios than girder bridges. However, one challenge, for load rating concrete segmental bridges that were designed based on AASHTO’s Standard Specifications for Highway Bridges, is the change in the notional live load model. This change represents an increase in the live load demand and is one of the reasons some concrete segmental bridges do not meet target ratings. To provide an avenue to incorporate reduced reliability at operating conditions, Corven Engineering (2004) recommends the use of striped lanes rather than design lanes when calculating rating factors. In addition to the suggestion made by Corven Engineering (2004), AASHTO MBE Section 6A.5.11.4 also suggests that “for operating rating of the design load at the service limit state, the number of live load lanes may be taken as the number of striped lanes.” The updated provisions are illustrated in Section 6.5.3.
2.6.4 Shear Lag in Slender Flanges
One challenge when conducting longitudinal analysis is accounting for the nonlinear strain distribution in slender flanges known as shear lag, which is typically handled using the effective flange width approach. The AASHTO’s Guide Specifications for Design and Construction of Segmental Concrete Bridges, 1st ed., adopted shear lag provisions of DIN 1075 (German Concrete Code), which uses a linear transition of effective flanges (AASHTO 1989a). However, in the second edition, shear lag provisions changed to a step-wise function between support and span regions. Conversely, AASHTO LRFD (2020a) provide shear lag provisions that are similar to DIN 1075 as outlined in Article 4.6.2.6.2. The difference between the two methods is insignificant, but the AASHTO LRFD (2020a) shear lag provisions are considered to be more accurate (Chen and Duan 2014).
Chen and Duan (2014) report that when determining section properties, it is commonly assumed that shear lag effects are considered when calculating the moment of inertia and neutral axis location. However, the cross-sectional area is based on the full gross cross section, with the purpose of not overestimating the “P/A” component of post-tensioning induced stresses, where P = effective post-tensioning force and A = gross cross-sectional area. Shear lag is a function of the structural system at the time of interest. If the analytical tool permits, section properties may be changed in the analytical model to approximate true statical conditions at all intermediate steps. This additional accuracy may not be warranted for all designs but could be evaluated on a case-by-case basis (Chen and Duan 2014).
2.6.5 Temperature Effects
Two types of temperature effects—those caused by uniform temperature changes and those caused by temperature gradients—are described in AASHTO LRFD (2020a). Uniform temperature changes (TU) are intended to represent seasonal temperature changes and apply to the entire segment cross section. Temperature gradients (TG) represent daily variations in temperature, which are characterized by a nonlinear temperature distribution along the depth of a segment (thus the name temperature gradient). This nonlinear distribution of temperatures tends to cause a nonlinear distribution of thermal strains, typically referred to as free strains, which can be calculated by multiplying the temperature at a given fiber by the coefficient of thermal expansion. Since plane sections before bending tend to remain plane after bending, this nonlinear distribution of strains cannot be realized, giving rise to restrained stresses. The free stresses and restrained stresses are then combined to calculate the final self-equilibrating stress distribution in the segmental cross section. It should be noted that these self-equilibrating stresses develop at the cross-sectional level and are present regardless of whether the bridge superstructure is simply supported or continuous. Detailed analysis procedures for calculating temperature gradient-induced stresses are provided in Gilbert and Ranzi (2011).
Chen and Duan (2014) report that AASHTO LRFD (Article 3.12.3) (2020a) adopted a temperature gradient profile that differs from that used by AASHTO’s Guide Specifications for Thermal Effects in Concrete Bridge Superstructures (AASHTO 1989b), which is an abridged version of NCHRP Report 276: Thermal Effects in Concrete Bridge Superstructures (Imbsen et al. 1985). One challenge that is encountered when load rating concrete segmental bridges is that AASHTO’s Standard Specifications for Highway Bridges did not include a requirement for temperature gradient analysis. Therefore, segmental concrete bridges rated based on a consideration of temperature gradient effects may not meet target rating levels. In addition, the distribution of self-equilibrating stresses caused by temperature gradients is such that tensile stresses apply only to a limited depth. These considerations have raised questions regarding the necessity to include temperature gradient as a load case when rating concrete segmental bridges.
Both uniform temperature and temperature gradient are included in service limit state load combinations. Temperature gradient is allowed to be reduced by 50% if the live load is considered to account for the reduced likelihood of maximum permissible live load occurring with maximum thermal gradient effects (Corven Engineering 2004). For concrete segmental bridges, a special load combination (LRFD Equation 3.4.1-2) for service is required to be checked. This load combination has no live load; therefore, 100% of the temperature gradient is included. In general, this load combination controls for concrete segmental bridges where live load force effects are small (Chen and Duan 2014). According to Chen and Duan (2014), temperature gradient effects are not required to be included in strength limit state load combinations, whereas uniform temperature effects are required to be included. Corven Engineering (2004) reports that “In most cases, longitudinal expansion and contraction of concrete bridges is accommodated by sliding or flexible bearings, with little effect in the superstructure. Forces induced by thermal expansion and contraction (TU) should be considered where superstructures are rigidly restrained to substructures. These forces should only be included at the Service Limit State for Inventory Ratings.”
When conducting inventory ratings, temperature gradient effects are considered as described for service limit states. For operating ratings, the effects of temperature gradients are not included for either service or strength limit states (Corven Engineering 2004).
2.6.6 Time-Dependent Effects
Concrete structures that are characterized by significant nonhomogeneities or those that are constructed in a sequential manner (such as segmental concrete bridges) are sensitive to time-dependent effects (Chiorino 2018). There are two challenges when it comes to quantifying the structural effects of creep and shrinkage. The first is related to predicting creep and shrinkage behavior at the material level (i.e., a materials problem). This issue continues to be characterized by a pending debate in the engineering community especially when it comes to predicting long-term creep effects. The second is related to the structural analysis methodology that is used to link creep and shrinkage behavior at the material level to that at the cross-section, element, or structure level (i.e., a structural analysis problem). Both issues are discussed as follows.
Modulus of Elasticity, Creep, and Shrinkage of Concrete
An accurate prediction of the modulus of elasticity of concrete is paramount especially when it comes to the calculation of time-dependent deflections as it represents the stiffness of the material. While long-term deflections do not affect the rating of concrete segmental bridges, the variation of modulus of elasticity with time is of interest as it affects the flexural stiffness of each segment and the redistribution of forces due to time-dependent effects. Modulus of elasticity of concrete is a time-dependent property and is typically calculated as a function of compressive strength, which also varies with time. Various models exist to predict the variation of compressive strength and modulus of elasticity with time such as those presented in American Concrete Institute (ACI) 209.2R-92 (ACI Committee 209) and fib (2010). These models are typically expressed as a function of the modulus of elasticity at discrete times such as at 28 days. Another set of models exists to predict modulus of elasticity at such discrete times, such as those presented in AASHTO LRFD (2020a), ACI 318-19 [ACI Committee 318 (2019)], ACI 363R-10 [ACI Committee 363 (2010)], and fib 2010. Other models include those presented in AASHTO LRFD (2020a) and fib 2010 model. Factors affecting the shrinkage and creep of hardened concrete are discussed in ACI 209.1R (ACI 2005).
Similarly, various models exist to predict concrete creep and shrinkage behavior at the material level. Some of these are discussed in ACI 209.2R-08 [ACI Committee 209 (2008)]. Appendix A in ACI 209.2R-08 provides a full description of four models: ACI 209R-92 [ACI Committee 209
(1992)], CEB-MC90-99 (CEB MC 1999), Bažant and Baweja B3 model (Bažant and Baweja 1995), and Gardner and Lockman (GL) (2000) model. Other models include that presented in AASHTO LRFD (2020a), fib 2010 model code, and so forth.
Chen and Duan (2014) report that although AASHTO LRFD allows creep and shrinkage effects to be evaluated using the provisions of CEB-FIP Model Code or ACI 209, for concrete segmental bridges, the CEB-FIP Model Code provisions are commonly used. Huang and Hu (2020) confirm this and state that the CEB-FIP Model Code has been generally used by the concrete segmental bridge community for the past 30 years. Similarly, Corven Engineering (2004) states that the majority of concrete segmental bridges in Florida were designed in accordance with the creep and shrinkage models presented in Appendix E of CEB-FIP (1978). The 1983 revision of CEB-FIP presented mathematical expressions to facilitate the calculation of creep and shrinkage parameters, which in the 1978 version were presented in a tabular form. The creep and shrinkage models presented in the 1990 edition of CEB-FIP were slightly different from those presented in the 1983 edition. For example, Corven Engineering (2004) reports that the formulations provided in the 1990 edition compared to the 1983 edition, underestimate creep by approximately 16% to 18% and shrinkage by 10% to 13%. Since one effect of concrete creep and shrinkage is the reduction of the post-tensioning force, it remained customary and conservative practice within certain sectors of industry, particularly segmental bridges, to continue using the 1983 CEB-FIP (Corven Engineering 2004). This practice continued because no significant casting curve or erection elevation problems had arisen (Corven Engineering 2004). On the other hand, the publication of the 1990 edition of CEB-FIP brought pressure from some owners to use it based on it being more recent and presumably “better” (Corven Engineering 2004). The subject of which creep and shrinkage model best predicts creep and shrinkage behavior at the material level continues to be debated. Because of the lack of consensus, technical committees such as ACI 209 have taken the approach to present various models without endorsing a particular model. A similar approach is taken in AASHTO LRFD (2020a) where various creep and shrinkage models are presented as allowable options.
A sensitivity analysis was conducted for one segmental concrete bridge superstructure by Ketchum (AASHTO 1989a) and considered the effect of two creep models on final stresses. The considered models were ACI 209 and CEB-FIP. For each model the ultimate creep coefficient was taken equal to 1, 2, and 3 with an assumed loading age of 7 days, and its effect on final stresses was quantified. It was concluded that when using the ACI 209 model, final stresses remained essentially unchanged regardless of the value of the creep coefficient. When the CEB-FIP model was used, a higher variation in final stresses as a function of creep coefficient was observed. However, considering the change in the creep coefficient, the variation in final stresses was considered to be small (AASHTO 2020a). It was concluded that the selection of one model versus the other had a higher impact on final stress magnitude compared to the variation of creep coefficient. Article C5.12.5.2.3 of AASHTO LRFD (2020a) states that it is doubtful that the full range of stresses reflected in the six analyses described would be of practical significance with respect to the performance of the structure.
Relaxation of Steel
Steel relaxation results in a change in force in a prestressing steel strand under constant length and temperature over time. It is common practice to use low relaxation strand to prevent excessive losses in the prestressing force. Various models exist to predict the relaxation of steel as a function of time. One such model is presented in AASHTO LRFD (2020a).
Time-Dependent Structural Analysis
Creep strains and prestress losses that occur after closure of the structure cause a redistribution of force effects (AASHTO 2020a). Various methods exist to account for creep effects when
conducting time-dependent structural analysis. These methods have been incorporated into various computer programs and analytical procedures to determine creep and shrinkage effects in segmental concrete bridges. Common approaches include the use of either the effective modulus method or age-adjusted effective modulus (Trost 1967; Bažant 1972). Article C5.14.2.3.6 of AASHTO LRFD (2020a) states that for permanent loads, the behavior of segmental bridges after closure may be approximated by use of an effective modulus of elasticity, which may be calculated as shown in Eq. (2-2).
In this approach, the modulus of elasticity is reduced to account for creep effects.
| (2-2) |
where
| Eeff = | Effective modulus of elasticity of concrete. |
| Ec = | Modulus of elasticity of concrete. |
| φ(t, ti) = | Creep coefficient at time t, for a concrete loaded at time ti. |
When predicting creep effects for concrete loaded at different ages, various approaches can be taken. Two of these approaches are described in Gilbert and Ranzi (2011) as the rate of creep method and step-by-step method (see Figure 2-2). The RCM originally developed by Glanville (1930), further developed by Whitney (1932), and first applied to the analysis of concrete structures by Dischinger (1937) is based on the assumption that the rate of change of creep with time is independent of the age of loading. This means that creep curves for concrete loaded at different times are assumed to be parallel even though the initial stiffness of the curve for a given loading age will be different. This theoretically is a distortion of actual creep behavior but is an attractive approach because only a single creep curve is required to calculate creep strains due to any stress history. A more accurate method would involve the generation of distinct creep curves for every loading event (i.e., not only is the initial slope a function of loading age but so is the rate of creep that occurs after loading).
In most analytical approaches, it is assumed that compressive creep is equal to tensile creep and flexural creep. Although Gilbert and Ranzi (2011) report that the ratio between tensile and compressive creep varies from 1 to 3. However, for most practical purposes, especially for concrete segmental bridges, which are designed to be primarily in a state of compression, this assumption is believed to be reasonable. Also, while the creep models presented in ACI 209.2R-08 are intended
Figure 2-2. Illustration of (a) the rate of creep method and (b) step-by-step method.
for hardened concrete subject to compressive forces, it is stated that it may be assumed that predictions apply to concrete under tension and shear [ACI Committee 209 (2008)].
Most commercially available computer programs capable of conducting time-dependent staged analysis use beam elements in the longitudinal direction. The advantages and disadvantages of using such elements are discussed by Giaccu et al. (2021), Malm and Sundquist (2010), and Bažant et al. (2008). One limitation of such beam models is the stress distribution in a segmental bridge cross section varies and because creep strains are a function of the applied stress, this tends to create a nonlinear distribution of strains in the cross section. However, for most practical purposes beam elements are appropriate due to the large number of segments, number of construction stages, and tendon configurations, which make the use of more sophisticated 3D models impractical.
One objective when conducting time-dependent structural analysis is the determination of secondary forces due to creep which affect the calculation of stresses at service. Many computer programs capable of conducting staged analysis allow the calculation of such secondary forces. Simplified methods suitable for preliminary design and hand calculations also exist, such as Dischinger’s method, which is illustrated in Eq. (2-3) (Huang and Hu 2020).
| (2-3) |
where
| MDt(x) = | Final dead load moment at time t in the final structural system. |
| MD1(x) = | Initial moment due to dead load in first stage structure. |
| MD2(x) = | Moment due to dead load in second stage structure. |
| τ0 = | Initial loading time. |
| τ = | Time at which the first stage structural system is changing into the second stage. |
| t = | Final time. |
| φ = | Creep coefficient. |
Final dead load moments on the completed structure may also be computed using Eq. (2-4), which is a simpler version of Eq. (2-3) and is based on the results of numerous analytical studies (Huang and Hu 2020).
| (2-4) |
where
| MDf(x) = | Final dead load moment in completed structure. |
| MDca(x) = | Dead load moment in cantilevered structure. |
| MDco(x) = | Dead load moment in the completed structure. |
Eq. (2-4) applies to concrete segmental bridges constructed using the cantilever method in two stages and assumes that all segments have the same casting time. Eq. (2-5) can also be used to estimate creep moments due to post-tensioning forces. While these moments vary with time, they can be approximated by considering the post-tensioning force before creep losses as a constant, and by calculating the secondary moments due to the post-tensioning force using an average effective force (Huang and Hu 2020). The final creep moment due to post-tensioning forces can be estimated as:
| (2.5) |
where
| MPt(x) = | Final moment due to post-tensioning forces in the final structural system. |
| MP1(x) = | Initial moment due to post-tensioning forces in first stage structure. |
| m1(x) = | Moment in primary structure due to X1Pt = 1. |
| X1Pt = | Secondary moment caused by post-tensioning forces before creep loss in second stage structure. |
| C = | Pe/Po. |
| Pe = | Average final post-tensioning force after creep. |
| Po = | Average post-tensioning force before creep. |
The final combined moment due to both dead load and post-tensioning forces may be estimated using Eq. (2-6) and may be used to estimate creep effects in bridges constructed with the span-by-span and balanced cantilever methods (Huang and Hu 2020).
| (2-6) |
Shrinkage effects are typically simulated using an equivalent temperature change that is applied uniformly in the segmental cross section. When beam elements are used in the time-dependent structural analysis, shrinkage effects may be simulated using nodal loads in the load vector. If there are no axial restraints in the longitudinal direction of the bridge, no secondary forces will be developed due to shrinkage, and the superstructure will be free to contract.
2.6.7 Secondary Forces
Secondary forces are internal forces generated as a result of applied deformations or imposed loads to statically indeterminate systems. Such secondary forces may be generated due to the following:
- Post-tensioning
- Locked-in forces created during construction
- Creep and shrinkage effects
- Temperature effects (uniform temperature changes and temperature gradients)
- Support settlement
All these secondary forces are included in service limit state load combinations. However, the inclusion of different types of secondary forces in strength limit state load combinations may differ from code to code (Chen and Duan 2014).
In AASHTO LRFD (2020a), the locked-in forces (EL) are separated from prestressing secondary forces (PS), which is unlike the editions before 2012 (such as the 6th edition). For strength limit state load combinations, both EL and PS have a load factor of 1.0, while dead loads (DC) have a load factor of 0.9 (minimum) and 1.25 (maximum). In most segmental bridge software, dead loads are not distinguished from locked-in forces. The sequential nature of construction in concrete segmental bridges leads to the creation of multiple sets of dead loads and locked-in forces. Chen and Duan (2014) report that attempting to separate the effects of these load cases creates a complex bookkeeping process that serves little benefit to end results. The question is which load factor should be applied in the chosen computer programs provided that dead loads and locked-in forces are combined. Chen and Duan (2014) recommend that the load factor for EL be the same as that specified for dead loads.
Secondary forces due to temperature gradient are not included in strength limit state load combinations, while support settlement secondary forces are to be considered on a project-specific
basis (Chen and Duan 2014). Uniform temperature secondary forces, including creep and shrinkage effects, are included in strength limit state load combinations with a load factor of 0.5 (Chen and Duan 2014).
2.6.8 Service Flexural Stress Check
Demand
In general, the use of an accurate analytical tool that considers the phenomena discussed in the previous sections is paramount as the chosen analytical approach determines the magnitude of stresses at service. In general, in the longitudinal direction, the analytical approach is established in the concrete segmental bridge engineering community and follows the guidelines presented in the previous sections. This analytical approach is incorporated in commercially available software, and stresses at service can be readily obtained for various load cases, including time-dependent and temperature effects.
Concrete segmental bridges are typically designed for Service I and Service III load combinations as well as a special load case appropriate for these bridges. In the Service III load combination, flexural tensile stresses are allowed to be evaluated using a 0.8 live load factor, while the Service I load combination is used to check compressive stresses with a 1.0 live load factor. For Service I and III load combinations, which consider the full live load, AASHTO LRFD (2020a) specifies a factor of 0.5 for the temperature gradient. Conversely, for the special load case that applies to concrete segmental bridges, the load factor for temperature gradient is 1.0, since live load is not included. While the special load case may not control at locations where large amounts of post-tensioning are present, it may govern at locations where live load effects are small or at locations outside the precompressed tensile zone. Such locations may include tension in the top of closure pours and compression in the top of the box at pier locations (Chen and Duan 2014).
Additionally, Corven Engineering (2004) recommends the use of striped lanes rather than design lanes when calculating rating factors at the operating level.
Capacity
Article 5.9.4.2 in AASHTO LRFD (2020a) provides guidance regarding the appropriate allowable stresses at service limit state after losses for segmental and non-segmental concrete bridges. For load rating, Corven Engineering (2004) provides a set of allowable stresses for inventory and operating rating drawn from the criteria provided in AASHTO LRFD (2020a), AASHTO’s Guide Specifications for Design and Construction of Segmental Concrete Bridges (AASHTO 1999), and FDOT LRFR rating criteria (2021). The following guidance is provided with respect to longitudinal tension in joints.
Type “A” Joints with Minimum Bonded Reinforcement.
The service-level flexural tensile stress is limited to , where is in ksi for cast-in-place joints with continuous longitudinal mild steel reinforcement for both inventory and operating ratings (Corven Engineering 2004), in compliance with AASHTO LRFD (2020a) and AASHTO’s Guide Specifications for Design and Construction of Segmental Concrete Bridges (AASHTO 1999). For operating ratings, an allowable tensile stress of , where in ksi is recommended. This increased allowable stress together with a reduction in live load demand by using the number of striped lanes rather than design lanes results in reduced reliability, which is considered appropriate for operating conditions.
Type “A” Epoxy Joints with Discontinuous Reinforcement.
In this case, the service-level allowable flexural tensile stress is limited to zero for both inventory and operating ratings
(Corven Engineering 2004). This limit is in compliance with AASHTO LRFD (2020a) and AASHTO’s Guide Specifications for Design and Construction of Segmental Concrete Bridges (AASHTO 1999). While there is no distinction between inventory and operating conditions when it comes to allowable stresses, reduced reliability is obtained by using the number of striped lanes as outlined previously.
Type “B” Dry Joints.
Early precast segmental bridges with external tendons and non-epoxy-filled Type “B” (dry) joints were designed for no tension in the longitudinal direction. In 1989, a requirement for 0.2 ksi residual compression was introduced with the first edition of AASHTO’s Guide Specifications for Design and Construction of Segmental Concrete Bridges (AASHTO 1989a). This was subsequently revised in 1999 to 0.1 ksi compression (Corven Engineering 2004). Corven Engineering (2004) recommends that service-level inventory ratings be based on a residual compression of 0.1 ksi for dry joints and that operating ratings be based on a zero tensile stress at the joints. These criteria are based on AASHTO’s Guide Specifications for Design and Construction of Segmental Concrete Bridges (AASHTO 1999) and AASHTO LRFD (2020a). Additional reduced reliability at the operating level may be obtained by using the number of striped lanes as indicated previously.
2.6.9 Service Principal Tensile Stress Check
Demand
AASHTO’s Standard Specifications for Highway Bridges did not include a requirement to conduct a principal stress check when designing concrete segmental bridges. The inclusion of this requirement in the AASHTO LRFD presents a challenge when load rating concrete segmental bridges that were designed based on AASHTO’s Standard Specifications for Highway Bridges because some of these bridges may not meet target load ratings. The principal stress check was introduced to verify the adequacy of webs of segmental concrete bridges for longitudinal shear and torsion (AASHTO 2020a).
Principal tensile stresses may be calculated using Mohr’s circle. As maximum principal tension may not occur at the centroidal axis, various locations along the height of the web should be checked. Since principal stress is a function of longitudinal, vertical, and shear stress, it is necessary to determine concurrent moments for the maximum live load shear. It should be noted that high principal stresses commonly occur at interior pier locations, and the HL-93 live load moment corresponding to shear should only use one truck, rather than two back-to-back design trucks, as used when calculating the negative moment at interior piers (Chen and Duan 2014). The live load factor is 0.8, similar to the Service III limit state. If the full live load is used, Chen and Duan (2014) report that it would be practically impossible to satisfy principal stresses while the extreme fiber is in tension.
Finally, it is important to note that AASHTO LRFD (2012) Article 5.8.5 states that “Local transverse flexural stress due to out-of-plane flexure of the web itself at the critical section may be neglected in computing the principal tension in webs.” This allows the principal stress check to be conducted using only results from analysis in the longitudinal direction.
Capacity
AASHTO LRFD (2020a) limits the principal tension stresses to a maximum value of (ksi) at service loads (Article 5.9.2.3.3) and (ksi) during construction (Table 5.12.5.3.3-1) for segmental bridges. In situations when the principal tensile stress exceeds the allowable limit, vertical post-tensioning in the web may be specified, the thickness of the web could be increased, or the amount of longitudinal prestressing may be increased. Of course, when load rating a bridge none of these options represent a convenient or practical solution.
2.6.10 Flexural Strength Check
The flexural capacity of concrete segmental bridges in the longitudinal direction may be calculated based on AASHTO LRFD (2020a), including the use of strain compatibility approaches when appropriate. Segmental bridges often combine the use of bonded and unbonded tendons in the same member (Corven Engineering 2004), and accurately predicting the stress in the prestressing tendons at ultimate (strength) limit states is crucial for accurate flexural resistance. In addition to the use of the strain compatibility approach mentioned in AASHTO (2020b) under the Detailed Analysis (Article 5.6.3.1.3a), Article 5.6.3.1.3b Simplified Analysis is also allowed in lieu of the Detailed Analysis. Article 5.6.3.1.3b states that when computing the nominal flexural resistance of a component with both bonded and unbonded tendons, the average stress in the prestressing tendons shall be taken as the weighted average of the stress in the bonded and unbonded prestressing tendons. To calculate the stresses in each of the tendons, Article 5.6.3.1.3b in AASHTO (2020b) proposes that the stress in the unbonded tendons may be conservatively taken as the effective stress in the prestressing tendons after losses, fpe, and for the bonded tendons it shall be computed using Eqs. (5.6.3.1.1-1) through (5.6.3.1.1-4) with the term Apsfpu in Eqs. (5.6.3.1.1-3) and (5.6.3.1.1-4) replaced with the term Apsbfpu + Apsufpe. For load rating, capacity should be determined based on actual rather than nominal material properties, if available. Data on concrete strengths may be found from construction records or verified by suitable tests (Corven Engineering 2004). If such data are unavailable, one approach is to scale the specified properties based on established overstrength factors that relate specified to measured compressive strength. Examples of such relationships can be found in Rizkalla et al. (2011) and Rosa et al. (2007).
2.6.11 Shear and Torsional Strength Check
AASHTO LRFD (2020a) provides several options for determining the shear and torsional strength of prestressed concrete members. One option is to use the provisions of Article 5.7.3 (Sectional Design Model). Another option, appropriate for concrete segmental bridges, is to use the provisions of Article 5.12.5.3.8 (Alternative Shear Design Procedure). When the provisions of Article 5.7.3 are used, a parameter that accounts for the presence of ducts is introduced in AASHTO LRFD (2020a) when calculating the contribution of shear reinforcement to the overall shear strength of the member as shown in Eq. (5.7.3.3-4) and Eq. (5.7.3.3-5). For ungrouted ducts, λduct is 1.0, and the web or flange width is reduced to account for the presence of ducts. For grouted ducts, no adjustment is made in the web or flange width, and the presence of ducts is accounted for through Eq. (5.7.3.3-5). The shear strength reduction factor λduct is based on research that included full-scale tests of post-tensioned concrete girder bridges (Moore et al. 2015). Spliced girders that featured plastic and metal ducts were examined. If the λduct factor is used in determining the shear capacity of post-tensioned girders containing ducts in the web, no reduction in effective web thickness is required (i.e., be = bw).
| (5.7.3.3-4) |
| (5.7.3.3-5) |
where
| Vs = | shear resistance provided by transverse reinforcement (kips). |
| Av = | area of transverse reinforcement within distance s (in.2). |
| fy = | specified minimum yield strength of reinforcement (ksi). |
| dv = | 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 (in.). |
| θ = | angle of inclination of diagonal compressive stresses (degrees). |
| α = | angle of inclination of transverse reinforcement to longitudinal axis (degrees). |
| s = | spacing of transverse reinforcement measured in a direction parallel to the longitudinal reinforcement (in.). |
| λduct = | Shear strength reduction factor accounting for the reduction in the shear resistance provided by transverse reinforcement due to the presence of grouted post-tensioning duct. Taken as 1.0 for ungrouted post-tensioning ducts with a reduced web or flange width to account for the presence of ungrouted duct. |
| δ = | Duct diameter correction factor, taken as 2.0 for grouted ducts. |
| ϕduct = | Diameter of post-tensioning duct present in the girder web within depth dv (in.). |
| bw = | Gross width of web, not reduced for the presence of post-tensioning ducts (in.). |
If the shear strength is determined based on Article 5.12.5.3.8, the contribution of shear reinforcement to the overall strength of the member is calculated using Eq. (5.12.5.3.8c-4).
| (5.12.5.3.8c-4) |
In this case, the effective web width is calculated as follows:
| bv = | Effective web width taken as the minimum web width, measured parallel to the neutral axis, between the resultants of the tensile and compressive forces due to flexure, or for circular sections, the diameter of the section, modified for the presence of ducts where applicable (in.). For grouted ducts, no modification is necessary. For ungrouted ducts, reduce bv by the diameter of the duct. |
Corven Engineering (2004) states that the modified compression field theory (MCFT) of LRFD may be used as an alternative but only for structures with continuously bonded reinforcement such as those used in large cast-in-place concrete boxes in cantilevered construction or on false-work. In other words, if a continuous tension tie does not exist [such as in Type “A” epoxy joints, Type “B” dry joints, and potentially in cast-in-place joints (Type “A” joints with minimum bonded reinforcement)] to satisfy the requirement set forth in the MCFT as presented in AASHTO LRFD (2020a), the alternative shear design procedure presented in Article 5.12.5.3.8 should be used.
2.7 Analysis in the Transverse Direction
The 2D planar frame modeling approach is commonly used for transverse bridge analysis. It involves modeling a unit-length section of the bridge superstructure cross section to account for permanent loads and those induced by creep, shrinkage, and temperature changes. Live load effects are determined using influence surfaces such as those presented by Pucher (1977) and Homberg (1968).
Live load tests have shown that a 3D approach provides more accurate predictions than using influence surfaces because this approach considers the more efficient spreading of transverse moments and accentuated 3D behavior. The influence surfaces assume perfectly fixed and infinitely long transverse edges, leading to peak moment values per foot. However, 2D frame analysis with influence surfaces can sometimes overestimate the transverse bridge response, neglecting crucial aspects of behavior despite being typically conservative in predictions. More details are in Section 4.2.2.
An alternative approach is the use of 3D analysis in which a longitudinal section of the bridge is selected for conducting analysis in the transverse direction. Challenges associated with this approach include selection of a reasonable section length in the longitudinal direction and applying appropriate boundary conditions. For example, Huang and Hu (2020) suggest that a section that is twice the deck width be considered. However, transverse moments in the deck vary along the longitudinal direction of the bridge, so, a related challenge is selecting the appropriate location of the 3D section to model. According to Huang and Hu (2020), analytical results show that the maximum transverse moments occur in the end portion of the bridge within a distance of about two times the length of the cantilever slab from the ends of the support if there is no edge beam or thickened cantilever slab provided at the end of the girder. However, Huang and Hu (2020) report that as an edge beam is generally provided at the end of the box girder to resist a large cantilever moment, the transverse moments of the slab in the end portion of the girder will generally be smaller than those in the center. Thus, the transverse moments at the midspan determined by the finite element method can be safely used for the bridge transverse design (Huang and Hu 2020).
Corven Engineering (2004) reports that while the use of 3D finite element analysis is an acceptable alternative to the use of influence surfaces, the use of 3D finite element analysis that considers the entire structure may only be used as a means to enhance rating as an additional posting mitigation method. In addition, it has been reported that to size web reinforcement, bending moments obtained from transverse analysis are combined with shear and torsion obtained from analysis in the longitudinal direction; sizing web reinforcement need not be done for load rating unless there is evidence of distress in the structure. In such a case, an explanation for the observed behavior should be sought, and an appropriate evaluation of capacity should be made (Corven Engineering 2004).
In terms of allowable stresses, for transversely prestressed decks, the allowable stress is taken as (ksi) and (ksi) for inventory and operating ratings, respectively, based on AASHTO’s Guide Specifications for Design and Construction of Segmental Concrete Bridges (AASHTO 1999) Article 9.2.2.3 and AASHTO LRFD Table 5.9.2.3.2b-1 (AASHTO 2020a).
2.8 Inventory versus Operating Load Rating Procedures
Inventory versus operating rating procedures are an integral part of a comprehensive rating package and are to be calculated at service and strength limiting states (Corven Engineering 2003). Inventory and operating ratings vary in the type of loading that is considered. Inventory rating is defined by the FDOT as the “unlimited application of live loads at this level (which) will not damage the bridge. This is the lowest rating. Permissible stressing is minimized.” Operating rating is defined as the “unlimited application of live loads at this level (which) may shorten the life of the bridge. This is the highest rating” (FDOT 2021). Furthermore, strength limit states are evaluated at flexure, shear, and compression zones, whereas service limit states are evaluated at tension zones.
FDOT (2021) specifies prescriptive load factors for inventory and operating ratings at strength and service limits for post-tensioned I-girder bridges as shown in Table 2-2.
However, the following cautionary guidance for segmental bridges is offered:
“The evaluation of segmental post-tension structures is unusually complex. Before performing load rating analysis, as part of the scope development, peruse bridge inspection reports, gather as-built data, and review this section. Identify any local details (i.e., diaphragms, anchorage zones, blisters, and deviation saddles) exhibiting distress, and add their evaluation to the scope. For expanded guidance on segmental post-tension bridge evaluation, see New Directions for
Table 2-2. Inventory and operating rating factors for Strength I and Service III limit states.
| Live Load Inventory | Live Load Operating | |
| Strength I | 1.75 | 1.35 |
| Service III | 0.8 | 0.8 |
Florida Post-Tensioning Segmental Bridges, Volume 10A, Load Rating Post-Tensioned Concrete Segmental Bridges, FDOT, and Corven Engineering (2004).” [FDOT Bridge Load Rating Manual (2017), section 6A.5.11—Rating of Segmental Concrete Bridges].
Referencing New Directions for Florida Post-Tensioning Segmental Bridges, Volume 10A, Load Rating Post-Tensioned Concrete Segmental Bridges, FDOT, and Corven Engineering, October 2004, Corven Engineering states, “As a result of recent findings of corrosion of prestressing steel in post-tensioned bridges, the Florida Department of Transportation has changed policies and procedures to ensure the long-term durability of post-tensioned tendons.” (Preface, Corven Engineering 2004). And continuing, “Load rating post-tensioned concrete segmental bridges has historically presented difficulties for Owners and Engineers. These bridges are designed at service load limits. Precast segmental bridges are post-tensioned to keep joints closed under the design service load limits. Difficulties in load rating segmental bridges (especially precast segmental bridges) arise because, regardless of whether the bridge is being load rated at inventory or operating level, serviceability requirements typically govern.” (Chapter 1, Introduction, Corven Engineering 2004).
Corven Engineering (2003) also indicates that “if allowable service stress (tension) is zero, ratings for Inventory and Operating condition are the same” (ASBI20, Load Rating of Segmental Concrete Bridges Consistent with LRFR Requirements, Corven 2003).
Historically, a target reliability index (β) for inventory rating of bridges in general was specified as 3.5, and conversely, for operating rating as 2.5. The reliability index is a measure of the expectation of a system to perform as intended throughout the inspection interval or the design life. The reliability index is inversely related to the system’s risk of failure. Reliability is a function of known variability or uncertainty of the system variables, and the index is used directly in the determination of appropriate load and resistance factors. The indicated reliability indices of 3.5 and 2.5 for inventory and operating ratings, respectively, correspond to the load factors indicated in Table 2-2.
Calculation of inventory and operating load ratings for segmental bridges has proven difficult because serviceability generally controls the design and load rating. Other difficulties arise relating to redundancy or lack thereof, wherein segmental bridges are typically constructed of monolithic box girder cross sections.
