strategies for load rating of infrastructure populations
TRANSCRIPT
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Strategies for Load Rating of Infrastructure Populations: A Case Study on T-beam Bridges
F. N. Catbas1, S. K. Ciloglu2, A. E. Aktan3
ABSTRACT: There is consensus on the importance of objectively and reliably assessing the condition
and load capacity of aged bridges. Although each bridge may be considered as a unique structure, the
behavior of many bridge types may be governed by only a few mechanisms and related parameters,
especially if a population is constructed from standard designs. By identifying these parameters, and their
variation within the population, it is possible to extend findings such as load rating obtained from a
statistical sample to the entire population. Bridge type-specific strategies for load rating and condition
assessment in conjunction with statistical sampling may therefore offer significant advantages for
inspecting and load rating bridges sharing common materials, similar geometry and detailing, and the same
critical behavior mechanisms. In this paper, the writers present their recent work on load rating of the
reinforced concrete T-beam bridge population in Pennsylvania to objectively re-qualify them based on
field-calibrated finite element models.
Keywords: Load rating, distribution, bridge, population, field test, finite element model 1 Assistant Professor, Civil and Environmental Engineering Department, University of Central Florida
P.O. Box 162450, Orlando, FL 32816-2450, Phone: 407-823-3743; e-mail: [email protected] (corresponding author)
2 Ph.D. Student, Drexel Intelligent Infrastructure and Transportation Safety Institute, Drexel University, 3001 Market Street, Suite 50,
Philadelphia, PA 19104
3John Roebling Professor of Civil Infrastructure Studies, Director of Drexel Intelligent Infrastructure and Transportation Safety Institute,
Drexel University, 3001 Market Street, Suite 50, Philadelphia, PA 19104
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1 INTRODUCTION
1.1 Statement of the Problem
It is generally acknowledged that most critical infrastructure systems have been falling short of providing
satisfactory operational performance under everyday demands, and their constructed elements have been
appraised to have poor structural conditions (ASCE 2003, Report Card for America’s Infrastructure).
Highway bridges are critical nodes of the highway transportation network. Nearly 30% of the entire U.S.
bridge population (592,246 bridges) in the National Bridge Inventory (NBI) has been reported as
“structurally deficient or obsolete” based on their “condition rating” and factors such as “posting”
regardless of size or importance (NBI 2003). The bridge population continues to age, and we lack the
funds for immediate rehabilitation or renewal of existing bridges that are deemed as “structurally deficient
or obsolete.” As we defer rehabilitating or replacing posted bridges due to financial constraints, it has
become even more important to be able to objectively evaluate the structural condition and safe load
capacity of bridges and prioritize their replacement in an integrated asset management framework. In the
last decade there has been a great thrust for objective condition assessment, repair and renewal
technologies, and non-destructive evaluation methods. However, it is not a realistic expectation to have
the time and resources for an in-depth evaluation of every single one of over 150,000 bridges deemed
“structurally deficient or functionally obsolete” (Chase 2001).
1.2 Review of Current Practice
The National Bridge Inventory (NBI) contains 116 data fields for each bridge irrespective of the bridge
type, importance and other possible distinctions. There are three data fields containing information for the
structural condition rating, five data fields for the appraisal ratings, and several fields for the general
attributes of a bridge. The structural condition is mainly evaluated through data from the biennial
inspections that are conducted in accordance with the guidelines set forth in the National Bridge
Inspection Standards (NBIS) (NBI 1998, 2003, FHWA 1995).
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Only a limited amount of structural condition information exists in the NBI, consisting of condition
ratings based on visual inspection. The NBI contains three data fields for condition rating which are
described in the Recording and Coding Guide for the Structure Inventory and Appraisal of the Nation’s
Bridges (FHWA 1995). The coding descriptions are very general and subjective. A recent study by Federal
Highway Administration (FHWA, 2001) has indicated that on the average at least 78% of the average
Condition Ratings from visual inspections were incorrect with a 95% probability if FHWA Non-
destructive Validation Center (NDEVC) reference condition ratings are assumed correct (FHWA-
NDEVC, 2004). The variations are a result of factors such as the inspectors’ experience, type of bridge
and condition of the bridge. It should be noted that some states such as Pennsylvania have instituted
additional quality standards for consistency in bridge inspections. In addition, some states, such as
California, have incorporated a more detailed element-level inspection and recording program for their
bridge management (Roberts and Shepard 2001).
In many bridge management programs, condition rating is complemented with load capacity rating, where
the latter is typically obtained as described in the American Association of State Highway and
Transportation Officials (AASHTO) “Manuals” for Condition Evaluation and for Strength Evaluation
(AASHTO 1989, 2000). Most transportation departments utilize software such as BAR7 (PennDOT,
2001) to compute capacity and demand as defined by the “Manuals.” Typically, highly idealized analysis
methods are used, resulting in conservative load rating results. The “Manuals” support various indirect
manners for incorporating inspection results into load rating such as by modifying the impact factor for
demand based on the wearing surface condition evaluation, or by modifying the resistance factors based
on field inspection or maintenance activities. However, even the best practice cannot objectively link “as-
is condition” and “load capacity rating” of a bridge. Such a linkage, however, is possible through
“structural identification” (Aktan et al, 1997, 1998).
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1.3 Evaluation of Large Populations
To restructure the problem of bridge condition assessment and effective maintenance management by
taking advantage of objective experimental data from the field, the concept of statistical sampling offers
great promise. For example, airplane fleet owners take advantage of common symptoms and in-depth
inspections of just a few members of a fleet and effectively extrapolate these to large populations of
similar vehicles sharing a standard design, use-history and age. Many bridge engineers and managers have
viewed every highway bridge as a distinct and unique structure. In spite of considerable variation in
material properties, geometry, structural details and visual appearance, the load resisting
mechanisms and critical failure modes of most bridge populations may be governed by only a limited
number of independent parameters. It should be possible to classify bridge populations by establishing
the critical parameters for load capacity and failure mode by properly designed and executed research. This
would permit the evaluation and management of a large bridge population by selecting and studying a
statistical sample. In this manner, although every individual bridge may still be inspected as a distinct
structure for bridge-specific critical problems, bridge managers may take advantage of information from
statistical samples to manage bridges more effectively.
It should also be noted that the concept of statistical sampling of large bridge populations has been
implemented by other researchers. Livingston and Amde (2000) investigated the causes of micro-cracking
and additional deterioration in concrete due to formation of mineral ettringite by analyzing bridge
populations. Madanat et al. (1997) developed statistical models for infrastructure facility deterioration by
including the presence of persistent facility-specific but unobserved factors such as construction quality.
They then extended the model to investigate the presence of state dependence to develop a model for
bridge-deck deterioration. The data used for their study consisted of 5,700 state-owned bridges in Indiana
and the condition ratings of these bridges were included in the analysis.
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1.4 Re-Qualification of T-beam Bridges in Pennsylvania
The total number of single span T-beam bridges in Pennsylvania is 1,899 and approximately 60% of this
population is older than 60 years, with a maximum age of 101 years. Approximately 90 of these bridges
have been posted. Bridge engineers have intuitively sensed that even after aging and deterioration, cast-in-
place RC T-beam bridges with sound abutments inherently possess a greater load capacity than what their
current BAR7 rating give and their low condition ratings may imply. However, there has not been a
scientifically proven method to confidently evaluate the impacts of accumulated deterioration and damage
on the safe load capacity of a bridge.
1.5 Objectives and Scope
The writers have been exploring how to develop and implement condition assessment and load rating
strategies for recurring types of structures by taking advantage of the statistical sampling concept, which
makes it possible to have a better understanding of the bridge performance and to develop more effective
and practical methods to manage a specific bridge-type. They also anticipate that this concept can be
implemented on different bridge types as well as other infrastructure systems. The main objective of this
paper is to present the statistical sampling approach applied to large populations of recurring bridges and
the use of experimental, analytical and information technologies on the statistical sample for objective
condition assessment of the entire population. An overview of the issues related to this approach is
provided along with the various experimental and analytical technologies. These technologies are
employed as a complement to visual inspection results, providing objectivity to the current practice for
better operation and maintenance management of large populations of structures with similar geometric
and condition parameters. To illustrate the application and implementation on real life structures, the
findings and results from a recent research study to re-qualify the load rating of single span reinforced
concrete T-beam bridges in Pennsylvania are presented. In this context, the scope of the paper is given as
follows: 1) Discuss and provide an example on the statistical sampling strategy for the management of a
T-beam bridge population for objective, quantitative bridge load condition evaluation and capacity
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assessment; 2) Discuss possible methods to determine the contribution of critical structural mechanisms
affecting load condition by means of objective measurements, analytical modeling and parameter
sensitivity studies that can be implemented on statistical populations; 3) Discuss how current visual
inspections and load rating procedures can be complemented and improved using experimental, analytical
technologies and statistical sampling strategies.
2 RESEARCH APPROACH
Research approach included:
1) Statistical evaluation of the entire T-beam bridge population as a fleet analogous to a truck or
an aircraft fleet: By identifying a representative sample that reliably represents the critical
relevant characteristics of the entire population (Ang and Tang, 1975), and by investing in
instrumentation, testing and monitoring of the statistical sample, reliable management decisions
may be reached for the entire fleet. The use of statistical sampling has been common for polling;
the use of this approach has been debated extensively for census, and in fact it was proven as a
more reliable approach than attempting a one-by-one headcount (NY Times, 2002).
2) Observations and experiments on the bridges in the statistical sample, and analytical studies
with field calibrated 3D FE models: These studies helped determine the most critical condition
and nominal structural parameters and helped establish the actual condition of the T-beam bridge
population in terms of objective parameters such as strain and deflection influence coefficients
and their measured values.
3) The socio-technical factors governing the determination and use of the load capacity rating in
bridge management: The highest acceptable load capacity rating that would conform to the
inherent conservatism in the current AASHTO specifications and the uncertainty in the visual
inspections is identified. Effective load distribution factors for use with simple-beam models for
analysis were formulated for Pennsylvania Department of Transportation (PennDOT) engineers to
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be able to compute the highest utilizable load rating of any T-beam bridge without violating
AASHTO specifications. The effective load distribution formulations developed for the RC T-
beam bridges should be of considerable value for all state departments of transportation
following review by AASHTO. However, researchers see a need and anticipate that AASHTO will
agree to further verification by destructive tests of several decommissioned T-beam bridges.
Properly designed and executed destructive tests, accompanied by appropriate nonlinear finite
element (FE) analyses would be needed to confirm that even the extreme levels of deterioration
and any loss in the secondary elements or boundary restraint mechanisms would not affect the
minimum expected level of serviceability, safety and reliability from RC T-beam bridges and
more importantly, would not lead to undesirable failure modes.
3 STATISTICAL SAMPLING OF BRIDGE POPULATIONS
A main objective of this study is to present that structural identification of a statistically representative
sample of a bridge population may be used for objectively and reliably characterizing the entire
population. For example, an authority may classify its ten thousand steel-stringer bridges into various
groups of several thousand each, depending on the statistically independent parameters that govern the
load capacity rating and other concerns that are taken into consideration for bridge management. The
bridges making up a sample may be rigorously inspected and tested by expert bridge engineers, creating a
sufficient amount of data and insight for the management of the entire group for decades to come. In this
manner, it is possible to take maximum advantage of the bridge-type specific heuristics that has been
accumulated, and to integrate this with the advanced technological tools that offer reliable and
measurement-based determination of serviceability and load capacity.
3.1 Statistical sampling of T-beam bridges in Pennsylvania
The writers selected a statistical sample of single span, RC T-beam bridges in Pennsylvania. Although a
large number of the T-beam bridges are aged and deteriorated, anticipated to be nearing the end of their
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service life, it is also realized that the actual load capacities and structural condition of these bridges may
be much greater than the estimates due to the desirable inherent qualities of cast-in-place RC beam-slab
systems. The entire reinforced concrete single span T-beam bridge population in PA consists of
approximately 1,899 RC T-beam bridges and these bridges were constructed mostly between 1900’s and
1960’s. Most of the bridges were constructed using standard set of drawings (Standards, 1983). As most
of these T-beam bridges share geometry and design details, materials and similar cast-in-place
construction, and since recent field experiments on monolithic cast-in-place RC beam-slab behavior
demonstrated excellent reserve capacity (Al-Mahaidi et al. 2000 and Song et al. 2002), this bridge
population was an excellent candidate for implementing statistical evaluation approaches. A statistical
study was conducted on 1,651 bridges with complete information in the NBI out of the entire population
of 1,899 single span RC T-beam bridges in Pennsylvania. We note that the entire population of T-Beam
bridges including multi-span bridges is 2,384 in PA and 37,408 in the USA (NBI, 2003). The findings
from the study are expected to be useful for making decisions on the entire population.
In this study, the writers assume that the load capacity of the RC T-beam bridge population can be
considered to be a function of “nominal structural,” and “as-is condition” parameters.
The governing independent nominal structural parameters are established as the span length and the
skew angle. T-beam bridges were constructed using a standard set of drawings, the majority dating back to
the 1930’s (Standards, 1983). In the standard design drawings, the element dimensions and reinforcement
details are dependent only on the span length and skew of the bridges. For example, when a bridge with
certain plan geometry is selected, the beam sizes, reinforcement and all other details such as parapets,
diaphragms, support details, etc. are automatically established. This “mechanistic” dependency greatly
reduces the number of independent structural parameters.
The governing independent condition parameters are the location of a bridge, its age, its current
condition rating and input from District Engineers regarding the most deteriorated bridges that they are
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concerned with. The challenge was in identifying which of the many possible parameters were dependent
on others, and those that impacted the actual load carrying capacity of a bridge. Different parameters were
analyzed by manipulating the inventory records by the help of GIS software ArcVIEW (2001). Statistics,
histograms, population characteristics and geographic distribution of the bridges within the state of
Pennsylvania were evaluated (Catbas et al, 2002, 2003). The parameters that are used for the statistical
identification incorporate population density, density of bridges within a geographic region, the
geographic/climate distribution and any related socio-technical factors such as the personnel resources of
the District with jurisdiction over a geographic region. Geographic distribution of the selected statistically
representative sample of 60 bridges along with the entire population is shown in Figure 1. Additional
parameters and their distribution with respect to the entire population are presented in Figure 2.
In the course of one year, the writers visited 27 bridges within the T-beam bridge population sample for
in-depth visual inspection, material sampling, non-destructive evaluation (NDE) studies, and to confirm
that the independent parameters that governed load capacity were indeed those that were stipulated in the
sampling process. Of the sample, four bridges were then subjected to in-depth structural testing and field-
calibrated finite element modeling for structural identification so that reliable simulations for sensitivity
studies of load capacity could follow. The results validated the potential of the fleet concept, and were
sufficient for reaching several recommendations that promise significant impact on bridge management.
The entire study was completed in two years.
4 EXPERIMENTAL AND ANALYTICAL STUDIES ON THE BRIDGE POPULATION
4.1 Preliminary Analytical Studies and Field Evaluations
4.1.1 Finite Element Modeling of a Typical Bridge
A bridge representing an average geometry and condition is selected for FE solid modeling and analysis
based on a fine mesh. Analysis results helped to determine the contribution of different structural
elements and mechanisms to load rating. Different levels of deterioration and damage are simulated to
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investigate their impact on load rating. These findings from preliminary analyses of an average bridge are
used to design and conduct field inspections to document the as-is conditions of 27 bridges.
4.1.2 Field Evaluations of Bridges
In-depth field investigations including detailed deterioration and damage mapping, imaging, coring, and
condition documentation with a focus on the critical areas, elements and mechanisms such as the
boundary restraints that affect load rating. Inspection results made available by Pennsylvania Department
of Transportation are used as a guide during the field evaluations. A data-base is constructed for managing
the information corresponding to approximately one-half of the initial sample of 60 bridges. The reduced
sample-size of 27 bridges also included some bridges with the worst condition ratings.
4.2 In-depth Testing of Four Sample Bridges
In-depth field tests included extensive instrumentation and truck load tests, impact modal testing using an
impact-hammer, and Falling Weight Deflectometer (FWD) testing. The dynamic tests were conducted to
verify the global mass and stiffness distribution characteristics. In addition, using FWD and modal tests on
T-beam bridges to extract flexibility coefficients as condition indices were explored on T-beam bridges.
Four T-beam bridges were studied in this manner for objective data to quantify the actual operating
stresses and behavior of the bridges in their as-is conditions. The test results are processed to determine
the bridge dynamic response frequencies and mode shapes, critical concrete and steel strains and
maximum deflections under various levels and configurations of live load. The four bridges covered the
spectrum of geometric and condition parameters.
4.3 Finite Element (FE) Model Calibration by Field Test Data
4.3.1 Construction and Calibration of FE Models
3D FE models are calibrated to simulate the actual geometry and as-is material, continuity and boundary
conditions of a structure. Such models may provide much more reliable estimates of actual load capacity
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rating of a bridge than idealized simple beam models. However, the process of first constructing and then
calibrating a 3D FE model using both dynamic modal analysis and static load test measurements requires
considerable expertise and may not be routinely implemented in practice although feasible in the context
of evaluating a sub-set of the statistical sample.
4.3.2 Field calibrated modeling of four test bridges
Based on the statistical study (Catbas et al, 2003), four bridges in the sample population were selected for
detailed investigations, including 3D FE modeling, field testing and FE model calibration by field test
data. The FE models of the bridges are initially developed using the nominal structural and condition
parameters, and these are then calibrated based on the field inspection, NDE, material test results and
structural load test results. The field-calibrated models are then analyzed for load rating by simulating two
side-by-side HS20-44 trucks positioned for maximum moment and shear, respectively. The results are
compared with those obtained by using BAR7 structural analysis software.
5 RESULTS FROM FE MODEL STUDIES AND FIELD EVALUATIONS
Writers tested and analyzed several bridges. One of the test bridges, the Swan Road Bridge, is selected to
serve as an example, and the results from other bridge tests are also reported later in this paper. One of the
main reasons of selecting Swan Road Bridge is that the geometric and condition characteristics of the
Swan Road Bridge represent an almost population average. Swan Road Bridge was constructed in 1937,
is 26 ft (7.9 m) long, has no skew and is 26 ft (7.9 m) wide supported on 6 T-beams. The condition rating
of its superstructure is 6 (Figure 3). A typical 3D FE model that is constructed using solid elements and
frame elements available in the library of the SAP 2000 V8 software (2002) is illustrated in Figure 4.
Each reinforcing bar and its bond with concrete are explicitly simulated. Such a fine microscopic approach
to 3D geometric-replica analytical modeling is now practical and enables explicitly simulating every
material point of the bridge for an accurate representation of the geometry, the actual behavior
mechanisms and a wide range of possibly existing deterioration or damage.
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An example snapshot illustrating the load testing of the Swan Road Bridge is shown in Figure 5 followed
by the relevant experimental results. Figure 5 includes the instrumentation plan for the static and crawl
speed load tests. Linear Variable Displacement Transducer (LVDT) sensors are used to measure
displacements. Weldable strain gages which are microdot welded to reinforcement are used for rebar
strain measurements and clip gages are used for concrete strain measurements. These sensors are installed
under the bridge and the respective locations of the sensors are shown in the figures. In addition, 12-15
accelerometers are mounted on the deck to measure the dynamic properties of the bridges.
The test results from the impact test, Falling Weight Deflectometer and the load testing are summarized in
Tables 1 and 2. For global calibration of the FE models, the results of the dynamic tests were compared
with the finite element eigenvalue analysis results. The frequencies of the nominal models for both
bridges are lower than the measured frequencies, indicating that the analytical models simulate a greater
flexibility than actual. After calibration, especially of the existing boundary conditions, the errors in
frequencies for the first three global modes of the models were reduced by more than 50% (Table 3). It
should be noted that although a "100% match" between all experimental data and analytical models for
real life structures cannot be expected, an even better correlation than summarized in Table 3 can be
achieved by conducting a parameter study at a microscopic level, such as by modifying the input
properties for various finite elements and each abutment seating separately. However, writers experience
has been that such a microscopic level fine-tuning of the models for correlating strains would not have
any significant impact on the calculated load rating factors. The correlations between the measured and
simulated deflections and strains under static loads before and after calibrating the 3D FE models are
presented in Figure 6.
The most significant modification that was required during the calibration of the FE models was
incorporating the actual restraints at the boundaries, between the stiff diaphragm beams sitting on and
connected by dowels and expansion plates anchored to the sub-structure. The lateral compressive thrust
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exerted on the bridge by the pavement proved to be an additional mechanism at the boundaries (Figure 4)
significantly affecting load rating. When the 27 bridges were visually inspected, the condition of
continuous pavement that provides lateral thrust was observed and documented.
In order to determine the contribution of various mechanisms and to evaluate the impact of extreme
damage (Figure 7), parametric sensitivity analyses were conducted using the 3D FE model. The results are
summarized schematically in Figure 8. The analytical study summarized in the following serves to:
1) Compare the load capacity ratings based on an idealized modeling of the bridges by a simple beam
free-body and analyzed by the BAR7 software with those determined by analyses of field
calibrated 3D FE models.
2) Estimate possible changes in load ratings in the event of possible extremes of unmitigated
deterioration and damage that may occur during, say, the next five to ten years.
3) Evaluate the 3D FE analysis results for deriving conclusions regarding the possible impacts of
critical material properties, structural elements and load distribution mechanisms on the load
capacity ratings of these two bridges. The conclusions derived for the four bridges (one is given as
an example in the paper) are then qualitatively generalized to the broader population.
5.1 Flexural Load Rating Results
1) Figure 9 indicates that the BAR7 analysis of the Swan Road Bridge yields rating factors of 1.27 for
flexure, and this is indeed the current load ratings for these bridges in PennDOT District 6 records.
2) The load ratings for flexure based on the field calibrated 3D FE model is 3.18 (150% higher than the
BAR7 load rating) for the Swan Road Bridge. It is important to note that the calibrated FE models
incorporate a reduced elasticity modulus for concrete and simulate all of the deterioration that was
identified during field inspections. The corresponding load rating values are still much higher than the
load rating results based on BAR7, although the latter do not incorporate any deterioration.
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3) In the event of possible extreme deterioration, simulated by reducing the concrete and steel of the
beams in the field-calibrated models, the load rating is reduced to 2.11 for the Swan Road Bridge.
This value is still 66% higher than its counterpart based on BAR7 analysis. Simulated deterioration
does not affect the demands significantly, and in fact somewhat attenuates the maximum demands
while the reductions around 30% are mainly caused by the reductions in the capacity due to loss of
material.
4) The results presented in Figure 9 indicate that the boundary conditions have the most significant
impact on the load ratings. The field tests revealed that friction and dowels between the stiff lateral
diaphragm beams of the superstructure and the beams on the abutments create a very effective
restraint, prohibiting any slippage and other movements. Lateral soil pressure and pavement thrust
further slightly contribute to the restraint. When these effects are ignored and the boundary conditions
are changed to pin-roller, the resulting load ratings become 1.99 (compare to 3.05 with pin-pin
boundary conditions) for the Swan Road Bridge. This load rating, however, is still 57% higher than
the BAR7 rating mainly due to the lateral load distribution due to the slab and contributions of the
secondary elements (diaphragms and parapets).
5) The diaphragm beams provide effective rotational restraints (and thereby increased bending stiffness)
at the boundaries, which in turn reduce the critical flexural demand at the mid-span. Similarly,
parapets help distribute the flexural stresses from the mid-span towards the edges by creating very stiff
girders at the edges. When diaphragms are excluded from the model, the load ratings for the bridge
slightly decrease. However, the load rating is still 48% higher than the BAR7 load rating for the Swan
Road Bridge. Using the 3D FE models for calculating the demand for this bridge after neglecting the
restraints at the boundaries, and the contributions of the diaphragms and parapets results in rating
factors of 1.44 for the Swan Road Bridge. This is still 13% higher than their BAR7 rating
counterparts. These increases in load rating are due to fully simulating the distribution of stresses in
the transverse direction due to the slab in the 3D FE model. Figure 9 also reveals that when the
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probable future deterioration extremes are simulated for the bridges without including any of the
secondary elements and mechanisms, the load ratings for flexure may fall below one (0.88 for Swan
Road Bridge). However, the reduction in load demand due to redistribution would be expected to
yield a load rating higher than 0.88 if a non-linear model is used for concrete.
5.2 Shear Load Rating Results
1) BAR7 analyses yield rating factors of 1.80 for shear for the Swan Road Bridge.
2) 3D FE models effectively simulate the more effective shear distribution due to the presence of the
deck, an effect that is ignored in shear rating by the BAR7 model. The critical shear demands occur
near the supports of T-beams under load at the obtuse angle side of skew bridges. The shear capacity
mechanisms considered in rating included the effective beam concrete, stirrups and bent rebar
contributions similar to the DOT practice. The shear rating for the Swan Road Bridge obtained from
3D FE analysis is 2.69, which is 50% higher than the corresponding rating by BAR7 analysis.
3) Shear rating factors obtained by 3D FE analysis decrease to 2.30 for the Swan Road Bridge, when
extreme probable deterioration is simulated. The dead load and live load demands are obtained from
the FE model in which deterioration is simulated. In addition, shear capacity computation includes the
reductions of concrete, stirrups and bent longitudinal reinforcing bars; as a result, the section capacity
is decreased accordingly. However, shear load rating is still 28% higher than the corresponding shear
rating from BAR7 analysis.
4) Using nominal parameters, pin-pin boundary conditions and including the secondary elements, the
shear rating is 3.54 for the Swan Road Bridge. Because the boundaries are the most critical sections
for shear, an increased stiffness at the boundaries when pin-pin boundary conditions are simulated
result in higher shear demands. When the boundary conditions are changed to pin-roller for the Swan
Road Bridge, the corresponding rating factors for shear become 3.90. The increase in load rating is as
a result of the reduced shear demand at the critical locations when boundary restraints are released.
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5) Secondary elements in 3D FE models provide an increase in the rating factors by enhancing the
redistribution of stresses and reducing the maximum demand. If both parapets and diaphragms are
ignored and pin-roller boundary conditions are simulated, the shear rating factors become 2.64 for the
Swan Road Bridge. This is still 46% higher than the corresponding shear load rating by BAR7
analysis.
6) When extreme future probable deterioration is simulated in the nominal 3D FE model, the shear
rating factor decreases to 1.97 for the Swan Road Bridge. This is a consequence of the reduced shear
capacity and shear load distribution. The shear rating is still greater than one, and do not govern the
load rating as flexure remains as the critical effect. Shear does not appear to be a concern even when
extreme deterioration is concerned provided that unchecked and hidden deterioration for example due
to alkali-silica reaction is mitigated and the substructures remain in good condition, eliminating
settlements. However, it is important to determine whether shear becomes the prevailing failure mode
due to deterioration, and this is further discussed in the following section.
6 MECHANISMS LEADING TO HIGHER LOAD CAPACITY RATINGS
The analyses presented here for the Swan Road Bridge was repeated for the remaining test bridges which
are shown in Figure 10. The load rating values for the four test bridges obtained by field-calibrated finite
element models and obtained by idealized BAR7 analysis are also compared in the same figure. We
observe that the load rating values based on field-calibrated models range between 3.18 and 5.15, and the
ratio of field-calibrated FE based rating to BAR7 based rating factors vary between 2.50 and 5.10. Based
on these results, it is concluded that the BAR7 approach to load rating of T-beam bridges overestimate the
demand by 2.5 times or larger, and that this conservatism is consistent irrespective of the span, the skew or
condition. During the course of the project it was observed that there is a consistent correlation between
the DOT records of the 27 inspected bridges and their actual condition. The mechanisms that contribute to
higher load rating are summarized in the following.
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6.1 Demand Mechanisms That Contribute to Higher Load Rating by FEM
The load rating results summarized earlier indicate several mechanisms and parameters that contribute to
a decrease in the load demand, thus considerably enhancing the load rating relative to what is obtained
from a BAR7 analysis. Even after eliminating all of the secondary mechanisms and elements in the 3D FE
model, it is still possible to increase the load rating 13% for the Swan Road Bridge. It is possible to
generalize the mechanisms that reduce critical load demands and lead to rating increases that are not
incorporated in BAR7 analyses:
6.1.1 Importance of Boundary Conditions:
The use of pin-pin boundary conditions may not be justified if this is due to mechanisms such as frozen
bearings. However, when boundary restraints are due to permanent mechanisms such as dowels and lateral
confinement provided by the pavement, and, if the lateral restraints persist during load tests that are
conducted at proof load levels, the use of pin-pin boundary conditions for load rating purposes may be
appropriate. Figure 9(b) and (c) show that the pin-pin boundary conditions provide the largest increase
(53%) in the simulated load capacity rating factors, it is recommended that the boundaries at the super-
and-substructures are carefully inspected and any evidence of movement reported during biannual
inspections.
6.1.2 Lateral Restraint due to Earth Pressure and Pavement Thrust:
The individual T-beams are idealized as simply-supported (pin-roller) when analysis programs such as
BAR7 are utilized. However, as observed during visual inspections as well as identified and simulated in
the field-calibrated FE models, there are effective lateral restraints at the ends of the bridges due to earth
pressure and pavement thrust. The lateral restraints create compressive membrane forces and also increase
the flexural beam stiffness at the boundaries. This effect reduces the maximum span moments.
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6.1.3 Reinforced Concrete Parapets:
The parapets serve as stiff edge girders along the traffic direction. The corresponding edge stiffness may
have a major effect on flexural and shear distribution. For narrower bridges, the contribution of the stiff
edge girders is more significant than wider bridges. Parapets’ effect on load rating factor may be
quantified based on parameter sensitivity analyses conducted on Swan Road Bridge. Figures 9(d) and (e)
indicate that the load rating factor increased 30% due to the parapets.
6.1.4 Diaphragm Beams:
Lateral and longitudinal movements of actual bridges are restrained due to the dowels and the friction
between the superstructure and substructure at both ends as observed from the field inspections and
indicated by experimental measurements under loads. The lateral diaphragm beams also provide effective
rotational restraints to the superstructure, further reducing the flexural demands at the mid-span. In
addition, the diaphragm beams distribute the reactions along the super-sub structure interface thereby
reducing the shear demand.
6.1.5 Lateral Load Distribution:
In the current load capacity rating practice, an individual beam is taken out as a free-body, idealized as
simply-supported, and the continuity of the bridge in the transverse direction is indirectly accounted for by
means of axle-load distribution factors. This approach is found to significantly underestimate the deck
slab’s contributions to lateral load distribution for many bridge geometries. This contribution is properly
simulated when a properly constructed, geometric replica 3D FE model is used for analysis.
6.1.6 Effective Force Redistribution Due To Cracking:
In general, although the load capacity rating is based on the initiation of yielding in the reinforcement, we
ignore the effects of concrete cracking that occur in advance of yielding. Cracking of concrete is a
mechanism that provides a very effective redistribution of stresses within a T-beam bridge, and therefore
19
effectively reducing the demands and leading to a higher load rating (Shahrooz et al. 1994; Huria et al.
1994).
6.2 Capacity Mechanisms That Contribute to Higher Load Rating
Throughout this study and in deriving the load capacity rating factors in Figure 8, capacity of the T-beam
bridges are computed by strictly following the AASHTO Load Factor Design procedures. The capacity of
each T-beam is calculated as an element separated from the bridge system, and by assuming that flexural
capacity is reached when the first layer of reinforcing steel reaches the nominal yield strain. Shear capacity
is attained when either the stirrups or the bent-bars reach their nominal yield strain. This approach for
computing capacity is well known to underestimate the actual available capacity. Just as many
mechanisms not considered in rating reduce actual internal force demands, there are also many other
mechanisms that are not incorporated in rating but that are known to lead to an increase in capacity. The
actual capacity of T-beam bridges can be better estimated by means of properly conducted non-linear
analysis of 3D FE models, calibrated based on destructive load test data. However, even without
destructive testing or nonlinear FE analysis of an entire bridge, we note the following mechanisms which
are not included in load rating that may considerably increase the actual attainable capacity:
6.2.1 Axial Restraints at the Boundaries:
The axial restraints at the boundaries due to lateral earth pressure and pavement thrust lead to compressive
membrane forces in bridges that induce a multi-axial state of compression in the beam and slab concrete.
Additionally, pin-pin boundary conditions also lead to axial compression in the beams and the slab upon
the deflection of a bridge, termed as the membrane effect. Multi-axial compression due to the lateral
thrust and membrane effect is known to delay the formation of cracking and bond slip, offsetting the
tensile forces in steel, and considerably enhance the compressive strength of concrete relative to what is
obtained from a cylinder test. Therefore, the axial restraints at the boundaries not only reduce demands but
also increase the capacity.
20
6.2.2 Higher Yield Strength and Strain Hardening of Steel:
It is well known that actual reinforcing steel bars have about 25% or greater yield strength than the
nominal strength (ACI 1998). For example, tests on tensile yield strength of Grade 60 rebars with nominal
yield strength of 60 ksi (414 MPa) indicate 133% higher yield strength for about 10% of the test
specimens (MacGregor 1988). Further, steel stress-strain behavior is idealized in load rating as elastic-
plastic. However, at the ultimate, steel stress may be about 40 % higher than at yield due to strain-
hardening. These increases in steel yield stress and maximum strength lead to an increase in the attainable
flexural capacity of an under-reinforced beam by a similar ratio.
6.2.3 Multiple Rebar Layers:
Capacity of the T-beams is computed based on the assumption that the capacity would be attained when
the first layer of rebar reaches the yield strain. When there are additional rebar layers, the yielding of the
rebar layers will be achieved sequentially, and this phenomenon provides redistribution of strains within a
cross-section between different beams. Considerable additional flexural capacity as compared to what is
calculated based on the current assumption that capacity is reached when the rebars at the lowermost layer
yield is attained with multiple rebar layers.
6.2.4 Slab Contribution:
The capacity of beam-slab systems are known to be significantly higher than what is obtained by summing
up the capacity of isolated T-beams. The actual modes of failure observed during laboratory testing of
beam-slab systems have been through a flexural collapse mechanism typically after significant overloads
and excessive deformations are reached following the formation of yield lines (Park and Gamble 2000). In
addition, the shear capacity of T-beam bridges are significantly greater than code values as observed from
destructive testing of T-beam bridges due to the redundancy provided by beam flexural-shear and slab
punching-shear mechanisms that are both present (Al-Mahaidi et al. 2000, Song et al. 2002).
21
7 PRACTICAL EVALUATION OF THE T-BEAM POPULATION
We may rationalize ignoring many of the mechanisms that provide higher load capacity rating of RC T-
beam bridges for a need to be conservative. However, analytical sensitivity studies clearly indicate that the
actual lateral load distribution in a single-span RC T-beam bridge between various beams due to a truck
positioned on the deck may be considerably more effective than what is obtained by using the AASHTO
distribution factors. In addition, the distribution factors for RC T-beam bridges computed using LRFD
(AASHTO 1994) are determined to be more conservative than the LFD based distribution factors
(AASHTO 1989) shown in Table 4 and as illustrated in Figure 11. PennDOT bridge and district engineers
are favorable to incorporating the accurate extent of the live load distribution mechanism into load rating.
Therefore, it makes sense to examine and derive the equivalent distribution factors more accurately by
taking into account the actual geometry and detailing of the T-beam bridges. Although the AASHTO load
distribution factors were derived using FE analysis, it is clear that detailed 3D FE solid models that
represent the geometric characteristics of the population with a fine discretization are needed for
improved precision (Catbas et al, 2003). The distribution factors derived from analyses of geometric
replica 3D FE models that precisely represent PA’s T-beam bridge population will help improve load the
rating of these bridges while still strictly conforming to the AASHTO standards and provisions. The
equations that were derived for the Pennsylvania single span T-beam bridges are given in Table 5.
Therefore, 40 T-beam bridges representing the entire geometry and design spectrum of the RC T-beam
population in Pennsylvania were identified for deriving the lateral distribution factors more accurately
using 3D FE models. These models were constructed and analyzed under critical positions of two
simultaneous rating trucks. The diaphragm beams, parapets and boundary restraints were ignored in the
analyses as all beams were assumed to be simply-supported, permitting axial movement. The maximum
flexural and shear demands from FE analysis were compared to the corresponding demands obtained from
BAR7 analyses of the same bridge conducted by applying one-half of a truck as live load. The ratio of the
22
maximum demands from 3D FE analysis and BAR7 analysis for the same bridge provided an equivalent
lateral load distribution factor for that bridge.
These studies indicate that by using the distribution factors obtained from 3D microscopic FE models that
precisely represent the geometry of T-beam bridges, and by strictly complying with all of the capacity and
demand calculation requirements of AASHTO, it is still possible to increase the load rating of RC T-beam
bridges by 10%-55% depending on the geometry of the bridge. The distribution factors are expressed in
terms of simple equations in closed form and can be very easily implemented in load rating procedures.
23
8 CONCLUSIONS AND RECOMMENDATIONS
1) This study demonstrated that the statistical sampling strategy may serve as an effective approach for
condition assessment and management of large bridge populations that share common structural and
condition parameters. This strategy requires a determination of the critical nominal and as-is
condition parameters that govern the load capacity of a bridge population that will be evaluated by
statistical sampling.
2) This study took advantage of FE modeling and load testing in the context of structural identification
of a statistically representative sample of a bridge family to characterize the entire population. This
approach makes it possible to take maximum advantage of the bridge-type specific heuristics that has
been accumulated by experienced District engineers, and integrate this with the advanced
technological tools that offer reliable and measurement-based determination of serviceability and load
capacity.
3) Data on 27 RC T-beam bridges that were inspected and documented and the four bridges that were
subjected to controlled tests and structural-identification is summarized in a Report (Catbas et al.
2003). Results of in-depth analyses by field-calibrated 3D FE models for four of the test bridges
were adequate to describe and quantify the mechanisms that affect both the demand side and the
capacity side of the load rating equation. The studies revealed that load capacity rating of the RC T-
beam bridges by field-calibrated 3D FE models indicate rating factors that exceed the corresponding
factors obtained by BAR7 analysis by at least 2.5 times and up to five times. The actual load capacity
rating factors that would have been observed if the bridges were loaded to damage levels in the field
would in fact be much higher than even what is estimated by the FE analysis. The mechanisms that
lead to higher rating are consistent throughout the population, these are not temporary mechanisms,
and the reliability of their current existence has been verified by in-depth inspections of the 27 bridges.
4) Even if all of the mechanisms that are not typically included in the idealized modeling and analysis of
bridges by BAR7 are excluded, 3D FE models still indicate that it is possible to increase the load
24
rating of the population by between 10% and 55% due to only the enhanced live load distribution in
short single-span RC T-beam bridges. Alternative load distribution factors for RC T-beam Bridges in
Pennsylvania are developed for PADOT using 40 FE models that represent the entire population
geometry and design spectrum with a fine resolution. The corresponding equations and findings are
expected to impact the management of T-beam bridges after their review and approval by PADOT and
AASHTO. However, before we may take advantage of the more favorable distribution factors that
have been derived for PA’s single-span T-Beam population, it is recommended to perform carefully
designed field experiments on various decommissioned T-Beam bridges under controlled load levels
leading to damage and failure.
5) Whether shear or flexure governs the load capacity rating is one remaining very important issue since
this relates to the failure mode that should be expected in the case of overloading or the loss of
capacity due to continued deterioration and damage. The inherent deformability and resiliency
associated with a flexure-governed load rating is much greater than the corresponding attributes if
shear governs load capacity.
6) In an attempt to be conservative and to conform to AASHTO specifications, it is possible to exclude
the secondary mechanisms as in the case of BAR7 results. However, in reality the secondary
mechanisms do exist and they change the load demands within the structure and this may lead to a
shear failure mechanism governing the load rating. This study clearly illustrated that shear load rating
may govern due to existence of mechanisms that are ignored in an idealized simple-beam modeling.
Consequently, in spite of the apparent conservatism of the AASHTO provisions, shear may in fact
become the governing failure mode for many bridges operating daily under traffic as a result of
deterioration. The field studies, experiments and analyses here have indicated that the contributions
due to the secondary elements and mechanisms that enhanced load-rating were always greater than any
negative contributions due to existing deterioration and damage that reduce load rating. However, the
experiments were conducted under proof load levels (upper threshold of operating loads). Unless
25
testing is conducted at damage levels, a desired margin of safety may not be assured against
undesirable failure modes past the initiation of yielding, especially if extreme cases of deterioration
and damage are present. Tests should be conducted at higher load levels and up to failure to reveal the
extent of any adverse effects of existing deterioration and damage on load distribution, and help to
verify that the load distribution coefficients remain valid at higher load levels up to failure.
7) Therefore, it is recommended as prudent to evaluate the actual load capacity and failure modes of
several decommissioned T-Beam bridges by destructive testing. It is possible to conduct destructive
tests under loading by actuators reacting against rock-anchors, and with loading blocks that properly
simulate load distribution under a tandem-axle (Aktan et al, 1993). In addition, destructive testing
should be accompanied by nonlinear finite element analysis in order to derive maximum benefit from
them. A safe and meaningful design of the destructive testing in conjunction with nonlinear analysis
may permit the results to be generalized to the entire population and this may serve for validation of
the findings for the highest actual and the highest utilizable load rating of T-beam bridges.
8) The bridge management consequences of the conclusion reached in this study are not insignificant.
Currently, Pennsylvania has the third largest RC T-beam population after CA and KY and has the
most structurally deficient and functionally obsolete bridges T-beam bridges in the US (NBI, 2003).
Without a rational approach for taking advantage of their inherent capacity, greater numbers of these
bridges will soon have be posted and replaced. The financial impact of deferring the replacement of
the posted bridges for a decade is expected to be large amount of public funds. However, with the
promise of statistical sampling strategies integrated with objective measurements and advanced
analytical technologies, it would be possible to develop more effective inspection procedures, to
obtain a better estimate of the load rating of the bridge which will enable us to better evaluate, operate
and maintain infrastructure populations.
26
9 ACKNOWLEDGMENTS
The Pennsylvania Department of Transportation and the Federal Highway Administration have sponsored
the research reported here. The authors are grateful to Mr. Gary Hoffman, Mr. Scott Christie and Ms. Patti
Kiehl (PennDOT), and Drs. Steve Chase, Hamid Ghasemi and Mr. William Williams (FHWA) for their
support in making this project possible. Also, assistance and coordination of PennDOT District 6
engineers, especially Mr. Larry Ward during the conduct of the tests and field visits is appreciated. We
acknowledge the contributions of Messers. Grimmelsman, Barrish, von Haza Radlitz and Drs. Hasancebi
and Pervizpour (Drexel Infrastructure Institute) at different stages of the project. Especially, Dr. Oguzhan
Hasancebi’s invaluable contributions in developing and analyzing the finite element models are greatly
appreciated.
The contents of this paper reflect the views of the authors. The contents do not necessarily reflect the
official view or policies of the Commonwealth of Pennsylvania.
27
10 REFERENCES
AASHTO (1989), “Guide Specifications for Strength Evaluation of Existing Steel and Concrete Bridge,”
Washington D.C. 2001.
AASHTO (1994), “LRFD Bridge Design Specifications”, Washington D.C.
AASHTO (2000), “Manual for condition evaluation of bridges.” American Association of State Highway
and Transportation Officials, Washington D.C.
ACI (1998) Building Code Requirements for Structural Concrete, American Concrete Institute
Committee 318.
Aktan, A.E., Catbas, F.N., Grimmelsman, K.A. and Pervizpour, M. (2002), “Development of a Model
Health Monitoring Guide for Major Bridges”, Report, submitted to FHWA Research and
Development.
Aktan A.E., Catbas F. N., Turer A., Zhang Z.F. (1998), “Structural identification: Analytical aspects.”
Journal of Structural Engineering, ASCE, 124(7), 817-829.
Aktan A.E., Farhey D. N., Helmicki, A.J., Brown, D.L., Hunt, V.J., Lee, K.L., and Levi, A. (1997),
“Structural identification for condition assessment: experimental arts” Journal of Structural
Engineering, ASCE, 123(12), 1674-1684.
Aktan, A.E., Zwick, M.J., Miller, R.A. and Shahrooz, B.M., (1993) “Nondestructive and Destructive
Testing of a Decommissioned RC Slab Highway Bridge and Associated Analytical Studies,” paper
presented at TRB 92 and published in Transportation Research Record (TRR) 1371, pp:142-153;
National Academy Press, Washington, D.C. 1993.
28
Al-Mahaidi, R., Taplin, G. and Giufre, A. (2000) “Load Distribution and Shear Strength Evaluation of an
Old Concrete T-beam Bridge,” Transportation Research Record - Journal of the Transportation
Research Board 1696, Vol.1, pp.52-61.
Ang, A. A-S. and Tang, W. H., (1975) “Probability Concepts in Engineering Planning and Design,
Volume I - Basic Principles,” John Wiley & Sons, New York, 1975.
ArcVIEW Software (2001), Environmental Systems Research Institute, Inc.
ASCE (2003) Report Card for America’s Infrastructure, http://www.asce.org/reportcard/
Catbas, F.N., Ciloglu, S.K. Hasancebi, O. and Aktan, A.E. (2002) "Fleet Strategies for Condition
Assessment and Its Application for Re-qualification of Pennsylvania's Aged T-beam Bridges", Paper
No.02-3890, presented at the 81th Annual Meeting of Transportation Research Board and
submitted for publication in TRR, Washington DC, 2002.
Catbas, F. N., Hasancebi, O., Ciloglu, S. K., and Aktan, A.E. (2003) “Re-qualification of Aged
Reinforced Concrete T-beam Bridges in Pennsylvania,” Project Report Submitted to Pennsylvania
Department of Transportation Bureau of Design, Bridge Quality Assurance Division by Drexel
Intelligent Infrastructure and Transportation Safety Institute, Drexel University.
Chase, S.B (2001) “Hi-tech Inspection,” Civil Engineering Magazine, ASCE, pp.62-65, September.
FHWA (1995), Recording and Coding Guide for the Structure Inventory an Appraisal of the Nation’s
Bridges, U.S. Department of Transportation, Federal Highway Administration, Report Number
FHWA-PD-96-001, Washington D.C., December 1995.
FHWA (2001), “Reliability of Visual Inspection for Highway Bridges," FHWA Report Nos. FHWA-
RD-01-020 and FHWA-RD-01-021, 2001.
29
FHWA (2004), Non-Destructive Evaluation Validation Center,
http://www.tfhrc.gov/hnr20/nde/home.htm, 2004
Huria, V., Lee, K.L. and Aktan, A.E. (1994),”Different Approaches to Rating Slab Bridges”, Technical
Note, Journal of Structural Engineering, ASCE, October 1994.
Livingston, R.A. and Amde, A.M. (2000), "Nondestructive Test Field Survey for Assessing the Extent of
Ettringite-Related Damage in Concrete Bridges," presented in International Symposium on the
Nondestructive Characterization of Materials, Karuizawa, Japan.
MacGregor, J.G. (1998) “Reinforced Concrete-Mechanics and Design”, Prentice Hall.
Madanat, S.M., Karlaftis, M.G. and McCarthy, P.S. (1997), “Probabilistic Infrastructure Deterioration
Models with Panel Data” ASCE J. of Infrastructure Systems, Vol. 3, No. 1, pp.4-9.
New York Times (2002), National Briefing in Washington, December 7, 2002.
NBI, (1998), National Bridge Inventory Data (NBID).Rep.No.FHWA-PD-96-001, Washington D.C.,
1998.
NBI, (2003), National Bridge Inventory Data (NBID). http://www.fhwa.dot.gov/bridge/britab.htm,
Washington D.C.
Park, T. and Gamble, W., (2000) “Reinforced Concrete Slabs”, John Wiley and Sons, 2nd Edition.
PennDOT (2001), Bridge Analysis and Rating Program - BAR7, V7.10, PennDOT Bureau of Information
Systems Application Development Division.
Roberts, J. and Shepard, R. (2001), "Bridge Management for the 21st Century", Proceedings of the SPIE's
6th International Symposium on NDE and Health Monitoring and Diagnostics, Vol. 4337, pp.48-59,
Newport Beach, CA.
30
Shahrooz, B., Ho, I.K., Lee, K.-L., Aktan, A.E., de Borst, R., Blaauwendraad, J., van der Veen, C., Iding,
R. H., Miller, R. A. (1994), “Nonlinear Finite Element Analysis of Deteriorated RC Slab Bridge,”
Journal of Structural Engineering, Vol. 120, No. 2, pp. 422-440, ASCE.
Song, H.W., You, D.W., Byun, K.J. and Maekawa, K. (2002) “Finite Element Failure Analysis of
Reinforced Concrete T-girder Bridges,” Engineering Structures Vol.24, pp.151-162.
"Standards For Old Bridges" (1983) Commonwealth of Pennsylvania, Department of Transportation,
Bureau of Highway Design Bridge Division (from 1931 to 1940) Volumes 1-2, May 1983.
31
11 LIST OF FIGURES
Figure 1: Single Span T-Beam Population (grey squares) and the Locations of Statistically Representative
sample of 60 Bridges (dark squares).
Figure 2: Critical Parameters of the Entire Single Span T-Beam Bridge Population and the Statistically
Representative sample of 60 Bridges
Figure 3: Swan Road Bridge: General and Close-up Views
Figure 4: 3D Finite Element Modeling Of the T-Beam Bridges Using Solid and Frame Elements
Figure 5: Swan Road Bridge Field Testing and Instrumentation Plan
Figure 6: Step-By-Step Calibration of the Swan Bridge FE Model to Match Test Data
Figure 7: Extreme Deterioration/Damage Simulation
Figure 8.a: Swan Road Bridge Calibrated FEM Load Rating. b: Swan Road Bridge Damage Simulation
Load Rating
Figure 9: Swan Road Bridge Rating Factor Parameter Sensitivity Study.
Figure 10: Tested Bridges.
Figure 11: Live Load Moment Distribution Factors as a Function of Span Length for Bridges with No
Skew
12 LIST OF TABLES
Table 1: Summary of Load Test Results
Table 2: Summary of Dynamic Test and FWD Results
Table 3: Correlation of Modal Frequencies for Swan Road Bridge
Table 4: Current AASHTO Equations for T-beam Bridges
Table 5: Equations Derived for Single Span Bridge Population
32
Table 1: Summary of Load Test Results
Truck Load Applied
(2)
Max. Deflection
(3)
L/800
(4)
Max. Rebar Stress
(5)
Max. Concrete Stress
(6) Bridge Name
(1) (kip) (in) (in) (psi) (psi)
Swan 98 0.015 0.032 886 120
1 kip=4.45 kNt; 1 in=2.54 cm; 1 psi=6.89 kPa
33
Table 2: Summary of Dynamic Test and FWD Results
Modal Frequencies (Hz) (2)
Flexibility Coefficients (in/kip x 10-3) (3) Bridge Name
(1) Mode 1 Mode 2 Mode 3 Load Test Impact Test FWD
Swan 22.38 41.26 55.40 0.409 0.415 0.525
1 kip=4.45 kNt; 1 in=2.54 cm
34
Table 3: Correlation of Modal Frequencies for Swan Road Bridge
Mode No (1)
Test (Hz) (2)
Preliminary (Hz) (3)
Calibrated Model (Hz) (4)
1 22.38 14.64 25.83
2 41.26 27.31 35.69
3 55.40 34.19 39.43
35
Table 4: Current AASHTO Equations for T-beam Bridges
S (beam spacing), L (span of beam), Kg (long. Stiffness parameter), ts (slab thickess)
(See AASHTO LRFD Specs for details)
AASHTO LRFD Bridge Design Specs.
if θ <30 then c1=0.0if θ >60 then θ =60
AASHTO Standard Specs for Highway Bridges (LFD)
If S exceeds 10 ft: Assume flooring between stringers acts as a simple beam with the load on each stringer being the wheel load reaction
Moment DF for Two Design Lane Loaded
Range
AASHTO LRFD Bridge Design Specs.
if θ <30 then c1=0.0if θ >60 then θ =60
AASHTO Standard Specs for Highway Bridges (LFD)
If S exceeds 10 ft: Assume flooring between stringers acts as a simple beam with the load on each stringer being the wheel load reaction
Moment DF for Two Design Lane Loaded
Range
( )[ ]5.113
2.06.0
tan10.125.9
075.0 θcLt
K
LSS
gs
g −
+=
424020125.4165.3
≥≤≤≤≤≤≤
b
s
NLtS
AASHTO LRFD Bridge Design Specs.
AASHTO Standard Specs for Highway Bridges (LFD)For T-beams S < 6 ft
Shear DF for Two Design Lane LoadedRange
AASHTO LRFD Bridge Design Specs.
AASHTO Standard Specs for Highway Bridges (LFD)For T-beams S < 6 ft
Shear DF for Two Design Lane LoadedRange
+
−
+= θtan
0.1220.01
35122.0
3.032
g
s
KLtSS
g
600
710
4
24020
125.4165.3
≤≤
≤≤≥
≤≤≤≤≤≤
θ
MKK
N
L
tS
g
b
s
621 S
g ∗=
−
+∗=S
Sg
41
21
=
5.025.0
31 1225.0
LS
Lt
Kc
s
g
36
Table 5: Equations Derived for Single Span Bridge Population
g=distribution factor, L=clear span as given in PA Standards for Old Bridges, θ=skew angle
32’-42’θ=30-45
24’-32’θ=30-45
32’-42’θ=0-30
24’-32’θ=0-30
Moment DF for Two Design Lane Loaded (for PA T-beams given in Standards for Old Bridges)
Range
32’-42’θ=30-45
24’-32’θ=30-45
32’-42’θ=0-30
24’-32’θ=0-30
Moment DF for Two Design Lane Loaded (for PA T-beams given in Standards for Old Bridges)
Range
32’-42’θ=0-45
24’-32’θ=0-45
Shear DF for Two Design Lane Loaded (for PA T-beams given in Standards for Old Bridges)
Range
32’-42’θ=0-45
24’-32’θ=0-45
Shear DF for Two Design Lane Loaded (for PA T-beams given in Standards for Old Bridges)
Range
[ ]
−∗++∗∗−∗= −
15101.0185.1106170115 52 θ
LLg
[ ]
−∗+∗+∗−= −
151013.0104007888.62 5 θ
Lg
[ ]
−∗++∗∗−∗= −
152
5021.0009.110506745.94 52 θLLg
[ ]
−∗+∗+∗= −
152502.0103347606.36 5 θLg
[ ]
−∗++∗∗−∗= − 1
452
022.018664.2103.91455.124 52 θLLg
[ ]
−∗+∗+∗= − 1
452
032.01030315744 5 θLg
Figure 1: Single Span T-Beam Population And The Locations Of Statistically Representative 60 Bridges
Entire Population Sample Population
Figure 2: Critical Parameters Of The Entire Single Span T-Beam Bridge Population And The Statistically Representative 60 Bridges
Condition Rating
5
36%
623%
7 to 818% 4
20%
33%
Age
1929 to 1938
34%
< 192924%
>1948
24%
1939 to 1948
18%
Skew Angle(deg)> 50
1%
8 to 2219%
23 to 3722%
38 to 5020%
0 to 738%
> 55 ft 0%
16 ft to 32 ft
64%33ft to 40 ft
22%
41 ft to 55 ft14%
Span
Entire T-Beam Bridge Population
> 500%
0 to 7
43%8 to 22
18%
23 to 3722%
38 to 50
17%
Skew Angle(deg)
Skew Angle
(degrees)
> 55 ft 0%
16 ft to 32 ft
62%33ft to 40ft18%
41 ft to 55 ft
20%
Span
< 1929
30%
1929 to 1938
30%
1939 to 194817%
> 1948
23%
Age
3
7%7 to 8
15%6
17%
4
27%
5
34%
Condition Rating
Statistical Representative 60 T-Beam Bridges
Condition Rating
5
36%
623%
7 to 818% 4
20%
33%
Age
1929 to 1938
34%
< 192924%
>1948
24%
1939 to 1948
18%
Condition Rating
5
36%
623%
7 to 818% 4
20%
33%
Condition Rating
5
36%
623%
7 to 818% 4
20%
33%
Age
1929 to 1938
34%
< 192924%
>1948
24%
1939 to 1948
18%
Age
1929 to 1938
34%
< 192924%
>1948
24%
1939 to 1948
18%
Skew Angle(deg)> 50
1%
8 to 2219%
23 to 3722%
38 to 5020%
0 to 738%
> 55 ft 0%
16 ft to 32 ft
64%33ft to 40 ft
22%
41 ft to 55 ft14%
Span Skew Angle(deg)> 50
1%
8 to 2219%
23 to 3722%
38 to 5020%
0 to 738%
Skew Angle(deg)> 50
1%
8 to 2219%
23 to 3722%
38 to 5020%
0 to 738%
> 55 ft 0%
16 ft to 32 ft
64%33ft to 40 ft
22%
41 ft to 55 ft14%
Span
> 55 ft 0%
16 ft to 32 ft
64%33ft to 40 ft
22%
41 ft to 55 ft14%
Span
Entire T-Beam Bridge Population
> 500%
0 to 7
43%8 to 22
18%
23 to 3722%
38 to 50
17%
Skew Angle(deg)
Skew Angle
(degrees)
> 55 ft 0%
16 ft to 32 ft
62%33ft to 40ft18%
41 ft to 55 ft
20%
Span> 50
0%
0 to 7
43%8 to 22
18%
23 to 3722%
38 to 50
17%
Skew Angle(deg)> 50
0%
0 to 7
43%8 to 22
18%
23 to 3722%
38 to 50
17%
Skew Angle(deg)
Skew Angle
(degrees)
> 55 ft 0%
16 ft to 32 ft
62%33ft to 40ft18%
41 ft to 55 ft
20%
Span
Skew Angle
(degrees)
> 55 ft 0%
16 ft to 32 ft
62%33ft to 40ft18%
41 ft to 55 ft
20%
Span
< 1929
30%
1929 to 1938
30%
1939 to 194817%
> 1948
23%
Age
3
7%7 to 8
15%6
17%
4
27%
5
34%
Condition Rating
< 1929
30%
1929 to 1938
30%
1939 to 194817%
> 1948
23%
Age
< 1929
30%
1929 to 1938
30%
1939 to 194817%
> 1948
23%
Age
3
7%7 to 8
15%6
17%
4
27%
5
34%
Condition Rating
3
7%7 to 8
15%6
17%
4
27%
5
34%
Condition Rating
Statistical Representative 60 T-Beam Bridges
Figure 3: Swan Road Bridge: General And Close-Up Views
Cross Section of the Model
16.85”
15.5”
15.75”8.5”
T-Beams
Parapet
End Diaphragm
Rebar Layout Structural Details and Boundary Conditions
Statistics of The ModelNumber of DOF =108243Number of Solid Elements = 22940Number of Frame Elements = 7636
3.375”
12”3.375”
Figure 4: 3D Finite Element Modeling Of The T-Beam Bridges Using Solid And Frame Elements
1 in=2.54 cm
Displacement Sensor Location
Steel Strain Sensor Location Concrete Strain Gauge Location
A-A
A B C D E F
3
2
1
CL
CL
B-B
Truck and Sensor Locations:
Figure 5: Swan Road Bridge Field Testing And Instrumentation Plan
Figure 6: Step By Step Calibration Of The Swan Bridge FE Model To Match Test Data
b) Local Calibration and Correlation
Transverse Centerline Deflection of the Superstructure (Test vs. Models)
Def
lect
ion
(in
)
-0.010
-0.020
-0.030
0
-0.040
-0.050
-0.060
-0.070
Section A-A
A2 B2 C2 D2 E2 F2
-0.010
-0.020
-0.030
0
Def
lect
ion
(in)
-0.040
-0.050
-0.060
-0.070
Deflection of the T-Beam "C" (Test vs. Models)
Superstructure
C3 C2 C1
Section B-BLoad Test Truck
51.5 kips 48.0 kips
a) Regional Calibration and Correlation
Ste
el S
tres
s (p
si)
300
900
0
1200
1500
1800
2100
2500
600
Transverse Centerline Steel Rebar Stresses (Test vs. Models)
Co
ncr
ete
Str
ess
(psi
)
0
40
80
120
160
200 Concrete Stressesalong T-beam "C" (Test vs. Models)
A2 B2 C2 D2 E2 C2C3 C1
Models for Calibration –from Nominal to Calibrated
1 in=2.54 cm1 psi = 6.9 kPa
Assumed Damage: 40% concrete spalling at all beams. 50% rebar corrosion at lower layer and stirrups and 20% at upper layer rebars
Deterioration/Damage Simulation
d=24'' (Swan)d=28.5'' (Manoa)
40% of the entire depth
8.5"
~3.4"~2.6"
Figure 7: Extreme Deterioration/Damage Simulation
As-is Condition with All Elements, End RestraintsPin-pin Supports (using calibrated FEM)
Swan Road Bridge; RFM = 3.18 RFV = 2.69
(b)
Figure 8: Swan Road Bridge a) Calibrated FEM Load Rating, b) Damage Simulation Load Rating
As-is Condition with All Elements, End RestraintsPin-pin Supports (using calibrated FEM)Projected Extreme DeteriorationSwan Road Bridge; RFM = 2.11 RFV = 2.30
(a)
Pin-roller Supports w/ Parapetsw/o Diaphragmsw/o Pavement Thrust
RFM = 1.88 RFV = 3.10
x DF
Pin-roller Supports w/o Parapetsw/o Diaphragmsw/o Pavement Thrust
RFM = 1.44 RFV = 2.64
Pin-roller Supports w/o Parapetsw/o Diaphragmsw/o Pavement Thrustw/ Extreme Deterioration
RFM = 0.88 RFV = 1.97
Pin-Pin Supports w/ Parapetsw/ Diaphragmsw/o Pavement Thrust
RFM = 3.05 RFV = 3.54
Pin-Roller Supports w/ Parapetsw/ Diaphragmsw/o Pavement Thrust
RFM = 1.99 RFV = 3.90
BAR7 AnalysisRFM = 1.27 RFV = 1.80
Figure 9(a)-(f): Swan Road Bridge Rating Factor Parameter Sensitivity Study
(a) (b) (c)
(d) (e) (f)
Ratio (FEM/AASHTO) = 5.10
BAR7 Rating = 1.01Field Calibrated FEM = 5.15
Ratio (FEM/AASHTO) = 2.75
BAR7 Rating = 1.22Field Calibrated FEM = 3.35
Ratio (FEM/AASHTO) = 2.50
BAR7 Rating = 1.27Field Calibrated FEM = 3.18
Ratio (FEM/AASHTO) = 3.46
BAR7 Rating = 0.92Field Calibrated FEM = 3.18
Figure 10: Tested Bridges
Live Load Moment Distribution Factors for 90 deg Skewed Bridges
0.200
0.300
0.400
0.500
0.600
0.700
0.800
22 24 26 28 30 32 34 36 38 40 42 44
Span Length (ft)
Dis
trib
uti
on
Fac
tors
Drexel FEM Moment Distribution Factor for 90 deg SkewCurve Fit and Closed Form DF Formulation for Two Lanes
AASHTO LFD Moment Distribution FactorAASHTO LRFD One Lane Moment Distribution Factor for 90 deg Skew
AASHTO LRFD Two Lane Moment Distribution Factor for 90 deg Skew
Figure 11: Live Load Moment Distribution Factors As A Function Of Span Length For Bridges With No Skew
1 ft=0.305 m