Re-Qualification of Aged Reinforced Concrete T … - Requalification of...Re-Qualification of Aged Reinforced Concrete T-Beam Bridges in Pennsylvania Executive Summary Submitted to:

Re-Qualification of Aged Reinforced

Concrete T-Beam Bridges in

Pennsylvania

Executive Summary

Submitted to:

Pennsylvania Department of Transportation

Bridge Quality Assurance Division

&

Federal Highway Administration

Submitted by: F. N. Catbas, S. K. Ciloglu, O. Hasancebi, J. S. Popovics, A. E. Aktan

Drexel Intelligent Infrastructure Institute Drexel University

January 2003

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PROBLEM STATEMENT

Initiation of the project

PADOT Chief Engineer Mr. Hoffman presented Drexel researchers a number of research needs in a

letter dated 12 May 1998. The challenge with the highest priority was: “What is the load capacity of

reinforced concrete T-beam bridges in Pennsylvania?” This question provided Di3 researchers

with the opportunity to demonstrate the concept of evaluating and managing bridge populations as

“fleets” as opposed to every bridge as a distinct “individual” structure. RC T-beam bridges as well

as many other bridge structural types such as RC deck on steel girder, RC deck on PC I-girder, etc.,

comprise large populations within the state bridge inventories. 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 fleets may be governed by only a limited

number of independent parameters. It should be possible to classify bridge populations into fleets 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, bridge managers may take advantage of fleet strategies to

manage bridges more effectively.

Di3 developed a research proposal to study the RC T-beam bridges in PA and submitted the first

draft of the proposal to PADOT on August 24, 1998. After several meetings between DI3 and

PADOT engineers, the proposal took its final form and a notice to proceed for the project was given

by PADOT on August 10, 2000.

Problem Statement

The total T-beam bridge population in the US is 38,170 based on the NBI (2001). With 2,440 T-

beam bridges, Pennsylvania has the third largest reinforced concrete (RC) T-beam population after

California and Kentucky. However, Pennsylvania has the greatest number of structurally deficient

and functionally obsolete T-beam bridges in the Nation (NBI, 2001). The total number of single

span T-beam bridges in PA is 1,899 and approximately 60% of this population is older than 60

years, with a maximum age of 101 years. Given the number, advanced age and condition of the T-

beam population, their objective condition evaluation for management decisions has become a

primary concern for PADOT.

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 low

condition ratings may imply. However, there has not been a scientifically proven method to

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confidently evaluate the impacts of accumulated deterioration and damage on the safe load capacity

of a bridge. The principal objective of this research effort is therefore to determine the load capacity

of the RC T-beam bridges in Pennsylvania , recognizing that the challenge posed by the Chief

Engineer has at least two components:

1) What is the actual load capacity of RC T-beam bridges in Pennsylvania that can be

determined using state -of-the-art scientific measurement and analysis techniques for

highway bridges?

2) What is the highest utilizable load capacity of RC T-beam bridges in Pennsylvania that

PADOT can implement into its current load rating procedure for management purposes

in conformance with the current AASHTO provisions?

Relation between Load Capacity Rating and Bridge Management

PADOT led the nation by developing its Bridge Management System (BMS) before PONTIS was

developed by AASHTO. BMS incorporates the Bridge Management Subsystem (BMTS) and the

Bridge Rehabilitation Replacement Subsystem (BRRS). The parameters that provide a basis for

prioritizing maintenance in BMTS fall under “Bridge Maintenance Activity” (structural stability and

failure modes), and “Bridge Adequacy” (load capacity and condition rating). BRRS prioritizes

rehabilitation and replacement based on “Total Deficiency Rating (TDR)”, also a function of load

capacity and condition rating. It follows that the reliability of PADOT’s BMS depends on the

reliability of data on both bridge condition and bridge load capacity ratings. PA is one of only two

states that have established a rigorous quality assurance review program for ascertaining the

consistency of visual inspections and bridge condition ratings. It is therefore important to ensure the

reliability of the other critical input, i.e. load capacity rating, as this highly impacts the bridge

maintenance or replacement decisions based on BMS.

PADOT and FHWA Input throughout the Research

The first technical meeting was held on 24 January 2001 to review the scope of the work and future

studies based on the initial findings. Participants at the meeting included engineers from FHWA

Turner-Fairbanks, FHWA Mid-Atlantic Region and FHWA PA District, PADOT Bridge Quality

Assurance Division and several District engineers. At this meeting the proposed research direction

was approved in general with a request to take full advantage of PADOT’s rigorous visual

inspection quality program.

Following the partial completion of the work-plan and reporting of the results at the end of the first

year of the research, PADOT engineers requested the remaining research efforts to be redirected. A

step-by-step procedure to evaluate the load rating of T-beam bridges in conjunction with the

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conservatism that is implicit in the AASHTO load rating recommendations based on analyses of

idealized simple-beam modeling and effective lateral live load distribution factors was requested.

The researchers developed an analytical study plan for microscopic 3D FE modeling and analysis of

40 representative T-beam bridges that represented the geometry and detailing of the T-beam bridge

population with a fine resolution. However, these analytical models deliberately excluded any

secondary elements or mechanisms such as diaphragms, parapets, sidewalks or support restraints.

The load rating of the bridges obtained by using AASHTO and FEM-based analysis methods are

compared and the resulting load ratings are presented along with the equivalent lateral live load

distribution factors for flexure as well as for shear for BAR7 analysis. PADOT engineers indicated

that the study will be presented to AASHTO and following approval, would be used by PADOT for

load rating of T-beam bridges.

It is important to add that an effective communication and free exchange of ideas and observations

between PADOT, FHWA and Di3 research engineers was maintained in the spirit of a government-

academe partnership throughout the research. This was beneficial to reach research results and

products that potentially offer value to practice and may impact the manner we have managed

highway bridges since the 1970’s. The researchers are grateful to the federal and state government

engineers who have greatly contributed to the research by their participation and input. It is hoped

that the relevance of the fleet strategy demonstration and the importance of the findings regarding

the T-beam bridge population will exemplify the importance of effective partnership between

government and academic engineers and researchers for more effective management of our

infrastructure.

INTRODUCTION: CRITICAL ISSUES GOVERNING THE STUDY

Identification of Actual Condition: Challenges and Requirements

A three-dimensional (3D) Finite Element (FE) model of a bridge can be analyzed to determine the

load capacity, expressed in terms of load capacity rating or simply load rating (LR). A 3D FE

model, when properly constructed, calibrated by field data and validated, completely and accurately

simulates the geometry, boundary conditions and actual distribution of material properties within a

bridge. Live load demand envelopes due to various trucks and their loading configurations can be

simulated. The critical load demands for a bridge and the corresponding capacity at the initiation of

yielding can be computed. Use of FE modeling permits to compute the load rating more accurately

than the analysis of idealized lumped models such as a simple-beam or a grillage model. The latter

do not explicitly represent all of the load distribution and capacity mechanisms, and although they

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generally lead to over-conservative estimates of load rating, there is no assurance that these load

ratings do consistently correlate to actual reliability even for the same bridge population.

On the other hand, finite element models have to be calibrated with a sufficient amount and variety

of properly measured test data so that a 3D FE model is validated to be free of errors and that it does

represent the as-is actual condition of a bridge as closely as possible. Calibrated models developed

by experts may simulate any actually existing damage, deterioration, the variations in material

properties, all of the existing structural or nonstructural elements and the existing bearing and

support conditions of a specific bridge. However, the development and calibration of 3D FE models

is not practical for all bridges. Further, there is evidence that if FE modeling and analysis of a bridge

is carried out without proper training and expertise, and without properly calibrating a FE model by

reliable experimental data, the confidence in the resulting load rating may be actually less than the

corresponding estimate provided by an idealized simple beam free-body representation used in

practice.

State DOTs follow AASHTO recommendations and procedures that incorporate the spirit of these

recommendations for the load rating process. Although AASHTO does not rule out using load tests

and/or the use of FE models for bridge rating, the conditions, assumptions and the level of

conservatism intrinsic in the related AASHTO recommendations may fall into conflict with the

results obtained from field calibrated FE models. An example is when a FE model is calibrated

including all of the secondary (non-structural) elements and possibly additional mechanisms such as

support fixity that may be temporary and that are excluded from the AASHTO practice. Therefore,

although field-calibrated FE models can reliably answer the currently existing load capacity rating

of an actual bridge, this result may need further qualification before it may be adopted for

management purposes.

In this research project the researchers conducted extensive field investigations and experiments

leading to field calibrated FE models of a statistical sample of RC T-beam bridges. Analyses of

field-calibrated models in conjunction with the researchers’ past experiences with different types of

bridges, related work reported by other researchers, and the experiences of the District Engineers

indicate that the current flexural load capacity rating of a T-beam bridge in PADOT’s inventory is

expected to be at least as much as twice higher than its current load rating based on AASHTO

recommendations, provided that any undesirable failure modes such as due to shear as a result of

deterioration and damage are eliminated.

At the same time, in order to determine the highest utilizable load capacity rating that PADOT can

implement for management decisions and in conjunction with the intrinsic conservatism of the

AASHTO provisions, it became clear that secondary elements such as the parapets and transverse

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diaphragm beams should be ignored and the boundary conditions for the T-beams should be

idealized as simple pin-and-roller in the FE models. The researchers conducted extensive parametric

analytical studies with 3D FE models as well as with idealized simple beam models, and concluded

that even after ignoring all of the secondary elements such as the diaphragm beams and

mechanisms such as the actually restrained boundary conditions that enhance load distribution,

and by 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 in PA by 10%-55% depending on

the geometry of the bridge. This is because of the conservatively imprecise nature of the lateral live-

load distribution factors that have been recommended in the AASHTO specifications and that are

now being re-investigated in a current NCHRP study (NCHRP, 2002).

Evaluation of Large Bridge Populations: Technical and Socio-Technical Issues

A critical consideration in bridge condition assessment and load rating for management is the total

number of bridges in the inventory of a jurisdic tion with similar structural and material

characteristics. Determining the load capacity distribution of an entire population of bridges is a far

greater challenge than determining the load capacity of a single bridge. Today, if proper analytical

and experimental technologies are integrated in an investigation that is properly designed and

executed by experienced engineers, the condition evaluation and load capacity rating of any small-

span bridge can be achieved with excellent reliability and with a thorough understanding of how the

actual bridge elements and mechanisms are contributing to the load capacity rating. Naturally,

destructive load testing of a sufficient number of decommissioned bridges would be critical for

understanding the effects of deterioration and damage on failure mode, as even the best nonlinear

FE analysis may not be reliable in simulating failure modes and capacity at failure (Shahrooz et al,

1994, Huria et al, 1994).

However, when a large population of bridges is concerned, the problem becomes daunting and

requires a clear understanding of the interconnected nature of both the structural engineering and

socio-technical aspects. For example, the limitations and conservatism implicit in the application of

greatly idealized models such as those incorporated in BAR7, and the reliability in the manner we

take advantage of subjective and qualitative condition evaluation based on visual inspections have

been discussed by many researchers and engineers. State DOT’s often do not have sufficient

resources to objectively evaluate the condition of a large population of bridges by means of

objective field experiments such as load tests, NDE applications or FE modeling.

The development and implementation of new approaches for condition evaluation is a multi-layer

process requiring the participation of researchers, practicing engineers, DOT’s and ultimately the

AASHTO committees. As a result, the most recent recommendations, methods or tools may not be

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immediately available to DOT engineers. In the meantime, DOT engineers often rely on the over-

conservatism implicit in the AASHTO specifications to assure safety due to deterioration that cannot

be quantitatively evaluated due to a lack of objective condition assessment. At the same time there is

a great need to understand whether the conservatism that is implicit in various AASHTO

specifications mitigates potential problems for some bridges while a larger portion of the population

is unjustifiably under-rated.

As a consequence of insufficient load rating of a large segment of bridge population, as is the case

with PA’s T-beam bridges, considerable amounts of funding may have to be diverted or

programmed for their rehabilitation or replacement. If the actual load ratings are consistently and

considerably higher, this may not be the most judicious use of the funds given the urgent and

possibly more deserving needs of many other components of the transportation infrastructure within

a jurisdiction. Additionally, work on some other bridges that may indeed urgently require

rehabilitation or retrofit for example due to their fatigue-sensitive and fracture-critical characteristics

may have to be delayed. Clearly, more effective and reliable strategies for load rating of a bridge

population are necessary, requiring the integration of engineering research with a clear

understanding of the socio-technical implications in how the conclusions are reached and how the

results are implemented.

Research Approach

Research approach included the application of three critical concepts, and the related studies

requiring integration of different sets of analytical, experimental and information technology tools

for establishing the actual load capacity rating of the T-beam bridge population in PA:

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 statistical population that reliably

represents the critical relevant characteristics of the entire population, 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.

For example, more than 1.1 million children were missed during the 2000 census, and the

Census Bureau figures had to be adjusted using statistical sampling for federal purposes

such as for redrawing political districts (NY Times, 2002).

2) Observations and experiments with the bridges in the statistical sample, and analytical

studies with field calibrated 3D FE models. These studies helped determine the most critical

condition and structural parameters governing the condition, health and performance of the

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T-beam bridges and helped establish the actual condition of the T-beam bridge population in

terms of objective parameters 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 is identified. Effective load

distribution factors were formulated for PADOT engineers to be able to compute the highest

utilizable capacity of any T-beam bridge. The effective load distribution formulations

developed for the RC T-beam bridges should be of considerable value for all state DOT’s

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 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 would not lead to undesirable failure modes.

This report therefore presents the efforts and findings to ultimately address the question posed by the

PADOT Chief Engineer: “What is the load capacity of reinforced concrete (RC) T-beam bridges

in Pennsylvania?”

OBJECTIVE AND SCOPE

The objective of the project is to identify the (a) current actual; and, (b) the highest utilizable load

capacity of Pennsylvania’s RC T-beam bridges by integrating observation, experience and objective

experiments in the field, integrated with analytical and information technologies. Results are

presented in such a manner that PADOT and other states can take advantage of the different levels

of data and information to increase the load rating of their T-beam bridges without conflicting with

the inherent conservatism in the current AASHTO specifications for management decisions. In

addition, knowledge of the actual reliable load capacity rating would help in special permit cases for

individual bridges.

The scope of the project incorporated four distinct areas of investigation:

1) Fleet strategy and statistical sampling for the management of T-beam bridge population

2) Analytical modeling and parameter studies in conjunction with field evaluations

3) Extensive field experiments for field-calibrated 3D FE modeling of the test bridges and

simulations by these models for a study of the mechanisms affecting their load rating

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4) Analytical modeling and parameter sensitivity study for 40 representative T-beam bridges

followed by a formulation for modified load distribution factors

WORKPLAN

1) Bridge Management Practice and Fleet Health Monitoring Concept: First, the status of the

nation’s bridge populations and bridge management practice are reviewed. Research needs for

improvements to the current practice especially by taking advantage of the health monitoring

concept and its application to bridge populations are presented.

2) Identification of PA’s T-beam Bridges from the National Bridge Inventory (NBI): The data

from NBI is used for the statistical analysis of the bridge characteristics. The NBI information is

regenerated in a database so that specific data could be easily queried and linked with GIS maps.

3) Evaluation of the T-beam Bridge Database Using Geographic Information Systems (GIS): GIS

is used for the visualization and conceptualization of the geographical distribution of T-beam

bridges within PA. Pertinent information such as the density of distribution, strategic importance of

a location, District jur isdiction, climate and environmental conditions, and visualizing the selections

are facilitated by software such as ArcVIEW and Street Map.

4) Parameter Sensitivity Analysis of the Bridge Database: The Load Capacity Rating and the most

critical structural, location and condition parameters that affect the LCR are correlated. Parameters

that are most likely to affect the actual load capacity rating are presented in this section. The most

critical parameters that are evaluated are as follows:

Nominal Structural Parameters Condition Parameters Info from PADOT Districts

• Materials

• Geometry

• Detailing

• Substructure

• Boundary Conditions

• Age

• Climate

• Location

• Maintenance

• Deterioration

• Damage

• Condition Rating

• PADOT documentation

• List of most critical bridges

• District engineers feedback

A correlation study between different parameters is conducted to determine the interdependence of

the parameters. As a result of the parameter sensitivity study, the critical independent parameters are

identified for subsequent analyses.

5) Identification of a Representative Statistical Sample for the Population: Analyses to determine

the statistical characteristics of the entire population in terms of the independent parameters are

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conducted. The identified parameters are evaluated in terms of their distribution within the entire

population. A representative sample population is determined for further analysis and field studies.

Bridges identified as the most critical and/or most deteriorated by the District engineers are also

included in the statistical sample.

6) Preliminary Analytical Studies and Field Evaluations:

a) Finite Element Modeling of a Typical Bridge: The most critical structural parameters that

govern the load rating are identified from preliminary analytical studies. A bridge

representing an average geometry and condition is selected for FE modeling and analysis.

Issues in constructing and using the results from 3D FE models, and especially, the

requirements and procedures for the validation of any FE model are described. Analysis

results helped to determine the contribution of different structural parameters (elements and

mechanisms) to load rating. Different levels of deterioration and damage are simulated to

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 far more comprehensively than in a typical biennial inspection.

b) Field Evaluations of 27 Bridges based on FE model studies: In-depth field investigations

including detailed deterioration and damage mapping, imaging, coring, and additional

condition documentation of 27 bridges are conducted with a focus on the critical areas,

elements and mechanisms such as the boundary restraints that affect load rating. This is

what could be accomplished during the first year and corresponded to approximately one-

half of the initial statistical sample. Inspection results made available by PADOT are

incorporated during the field evaluations as an additional source for identifying damage and

deterioration patterns and sampling the material properties. A data -base is constructed for

managing the information.

7) In-Depth Field Testing of Four Sample Bridges: In-depth field tests included extensive

instrumentation and proof-level truck load tests, impact modal testing using an impact-hammer and

Falling Weight Deflectometer testing. 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 frequency and mode shapes,

critical concrete and steel strains and maximum deflections under various levels and configurations

of live load. These results are used for FE model calibration as described next.

We note that in-depth field tests of only four sample bridges is considerably less than testing of the

twelve that was initially planned had the original work-plan was completed. Due to the change in

scope and work-plan in the second half of the project, additional field tests could not be executed.

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However, field inspections of 27 bridges in conjunction with in -depth testing and field -calibrated

modeling of only four bridges were still sufficient for concluding that the current actual flexural

load capacity rating of the entire T-beam population, in conjunction with all the appropriate load,

materials and capacity reduction factors, should be at least twice that of the rating that is presently

recorded for any T-beam bridge in PA for which data is available.

8) Finite Element Model Calibration by Field Test Data and Related Studies

a) Discussion of Construction and Calibration of FE Models: Calibrated 3D FE models may

simulate the actual geometry and as-is material, continuity and boundary conditions of a

structure. Such models may provide a much more reliable estimate to the actual load

capacity 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 deserves discussion. The

related issues are described illustrating how discrepancies between the various sets of

experimentally measured results and the simulated model responses are minimized by

calibration.

b) Sensitivity Study by Calibrated FE Model: The sensitivity of load capacity rating due to

possible bounds in the variation of structural parameters and in the level and distribution of

deterioration and damage is evaluated.

c) Field Calibrated Modeling of Four Test Bridges: Based on the statistical study, 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 using the field inspection, NDE, material test results and structural

load test results. The field-calibrated models are then load rated by simulating two side-by-

side HS20-44 trucks separately positioned for maximum moment and shear, respectively.

The results are compared with those obtained by using BAR7 analysis.

9) Analytical Study of FE Models of 40 Bridges for Modified Load Distribution Factors

a) FE Modeling of 40 Bridges for Live Load Distribution Study: 40 T-beam bridge FE

models, which provide a fine resolution of the geometry and structural design details, are

constructed based on the nominal values of the structural and material parameters, pin-roller

boundary conditions and without any of the secondary elements. A statistical analysis is

conducted to determine the relationship of the 40 bridges to the entire population. The

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currently recommended equivalent live load distribution factors for bridges are presented

and discussed.

b) FE Analysis Results: All of the 3D FE models with are analyzed under two HS20-44 trucks

for critical moment and shear, separately. Effective live load distributions and load capacity

rating for flexure and shear are calculated. In addition, the same bridges are load rated using

load distribution recommended by AASHTO, and BAR7 analysis of simple beam models.

The results are tabulated for a comparative analysis.

c) Developing Live Load Distribution Factors for RC T-Beam Bridges: The maximum live

load demands from the FE analyses are employed to compute the effective load distribution

factors for T-beam bridges in order to modify the live load demands for flexure and shear

obtained from an idealized simple beam model. Closed-form expressions are developed to

easily compute the load distribution factors.

SUMMARY OF THE RESEARCH RESULTS

Fleet Strategy for Managing Bridge Populations

The statistical study included 1,651 bridges out of the entire population of 1,899 single span RC T-

beam bridges in Pennsylvania because complete information was not available for the entire bridge

population in NBI. The findings may be useful for making the decisions regarding the entire

population as long as the limitations are clearly recognized. The load capacity of the RC T-beam

bridge population is considered to be a function of a small number of “nominal structural,” and “as-

is condition” parameters. Establishing the load capacity distribution throughout the entire bridge

population is therefore possible by studying a smaller, statistically representative set of those

bridges, selected based on the governing independent structural and condition parameters.

The governing independent structural parameters are established as only the span length and skew

angle, as the bridges were constructed from one set of typical plans. Therefore, all other parameters

such as proportioning and reinforcement detailing were dependent on the length and skew. The

governing independent condition parameters are established as the location of a bridge, age, current

condition rating and input from District Engineers regarding the most deteriorated bridges that they

are concerned with. These parameters that are used for the statistical identification incorporate

population density, the geographic/climate distribution and any related socio-technical factors such

as the personnel resources of the District. Geographic distribution of the statistically representative

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.

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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 7

38%

> 55 ft 0%

16 ft to 32 ft64%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 7

38%

> 55 ft 0%


22%

41 ft to 55 ft14%

Span Skew Angle(deg)> 50

1%

8 to 2219%

23 to 3722%

38 to 5020% 0 to 7

38%

Skew Angle(deg)> 50

1%

8 to 2219%

23 to 3722%

38 to 5020% 0 to 7

38%

> 55 ft 0%


22%

41 ft to 55 ft14%

Span

> 55 ft 0%


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 1: Single Span T-beam Population and the Locations of Statistically Representative 60Bridges

Figure 2: Critical Parameters of the Entire Single Span T-beam Bridge Population and theStatistically Representative 60 Bridges

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In-depth field inspections and material sampling are carried out to assess the condition of 27 of these

bridges, and four of them were used as test-specimens for further rigorous experimental study and

structural identification. These studies were conclusive in identifying that the actual load capacity of

any of the existing 1,651 T-beam bridges would be more than twice greater than their current load

capacity rating calculated by PADOT engineers using BAR7 analysis. However, the actual load

capacity ratings that are actually proposed for adoption are 10-50% higher than the results obtained

by BAR7 analysis. The 10%-50% increase in load rating is achieved only by refining the lateral live

load distribution factors by rigorous analysis of forty 3D microscopic FE models representing PA’s

T-beam bridge population with fine resolution.

Results from FE Model Studies and Field Evaluations

The structural mechanisms that are incorporated in the rating calculations based on AASHTO

standards do not incorporate all of the actual structural mechanisms of T-beam bridges that are

simulated by field calibrated 3D FE models. Contributions of the most critical structural

mechanisms that affect load capacity rating of actual bridges and that lead to the conservatism in the

current practice are described and presented in this Executive Summary. Two of the test bridges,

named as the Swan Road Bridge and the Manoa Road Bridge serve as examples in the Executive

Summary. The photographs in Figures 3 and 4 illustrate these bridges. Close-up photographs in

Figures 3 and 4 show the condit ions and any damage at critical areas. Swan Road Bridge was

constructed in 1937, is 26 ft long, has no skew and is 26 ft wide supported on 6 T-beams. The

condition rating of its superstructure is 6.

The Manoa Road Bridge is 32 ft long with a 15 degree skew, was constructed in 1929 and its

superstructure condition rating is 4. While the geometry of the Swan Road Bridge may be

considered typical, the Manoa Road Bridge geometry represents a case with a larger width. The

latter bridge is 53 ft wide and is supported by 11 T-beams while both bridges feature just two traffic

lanes. 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) for a complete and accurate modeling of the

geometry, detailing and material properties are illustrated in the example in Figure 5. 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 any existing deterioration or damage.

15

Figure 3: Swan Road Bridge: General and Close-up Views

Figure 4: Manoa Road Bridge: General and Close-up Views

16

Cross Section of the Model

16.85”

15.5”

15.75”

8.5”

Reinforcement

Statistics of The Model:Number of DOF =108243Number of Solid Elements = 22940Number of Frame Elements = 7636

T-Beams

Parapet

End Diaphragm

Structural Details & Boundary Condition

3.375”

3.375”12”

3.375”

3.375”12”

Typical Solid ElementDimensions

Pin End

Roller End

axial thrust

Figure 5: 3D Finite Element Modeling of the T-Beam Bridges using Solid and Frame Elements

17

Snapshots from load testing of the two bridges are shown in Figures 6 and 7 followed by the

relevant experimental results. Figures 6 and 7 include the instrumentation plan for the static and

crawl speed load tests. Linear Variable Direct Current (LVDT) sensors are used to measure

displacements. Weldable strain gages which are microdot welded to rebars 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 dynamic

characteristics, deflections and strains under static loads before and after calibrating the 3D FE

models are presented in Figures 8-9.

The instrumentation details and the procedures followed during the experiments, as well as the FE

modeling and model calibration procedures are described in detail in the body of the Report. We

note that the most significant modification that was required for calibrating the FE models regarded

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 exerted on the bridge by the pavement proved to be an additional mechanism at

the boundaries (Figure 5).

18

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 6: Swan Road Bridge Field Testing and Instrumentation Plan

KJIEDCBA HGF

Weldable Gage (5)

Displacement Gage (4)

Clip Gage (7)Instrumentation Plan

Figure 7: Manoa Road Bridge Field Testing and Instrumentation Plan

19

Bridge Road

Name

Truck Load

Applieda

(Kip)

Max.

Deflection

(in)

L/800

(in)

Max.

Rebar Stress

(psi)

Max.

Concrete Stress (psi)

Manoa 106 0.032 0.040 1237 222

Swan 98 0.015 0.032 886 120

Modal Frequencies (Hz) Flexibility Coefficients (in/kip x 10-3)

Bridge Road Name Mode 1 Mode 2 Mode 3 Load Test Impact Test FWD

Manoa 16.62 19.77 23.75 0.462 0.479 0.444

Swan 22.36 41.38 55.40 0.409 0.415 0.525

Swan Road Bridge Manoa Road Bridge

Mode Field Test (Hz)

Nominal FE

(Hz)

Calib. FE (Hz)

Field Test (Hz)

Nominal FE

(Hz)

Calib. FE

(Hz) 1 22.38 14.64 25.83 16.60 10.22 19.01 2 41.26 27.31 35.69 19.74 12.13 20.53 3 55.40 34.19 39.43 23.71 16.77 22.12

Table 1: Summary of Swan and Manoa Bridge Dynamic Test Results

Table 2: Summary of Swan and Manoa Bridge Load Test Results

Table 3: Modal Frequencies obtained from Field Tests, Nominal FEM and Calibrated FEM

20

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

Displacement Sensor Location

A B C D E F G H J K L

1

2

3B-B

A-A

K K

K = 1000 kip/in

K K

K = 1000 kip/in

Superstructure

F3 F2 F1

Def

lect

ion

(in

)

-0.010

-0.020

-0.030

0

-0.040

-0.050

-0.060

-0.070

-0.080

-0.090-0.100

Section A-A

C2D2E2F2G2H20

0.010.02

0.03

0.040.050.06

0.070.080.090.10

Def

lect

ion

(in

)

J2

Section B-B

Truck and Sensor Locations: Boundary Condition Idealization of Different Models:

Figure 8: Step by step calibration of Swan Bridge FE Model to match test data

Figure 9: Step by step calibration of Manoa Bridge FE Model to match test data

21

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 two example

bridges are then qualitatively generalized to the broader population.

For each one of the two bridges, seven analyses are performed using their calibrated 3D FE models,

and these are repeated by using the nominal FE models with and without the contribution of various

mechanisms. The results are displayed in Table 4, and also summarized schematically in Figure 11.

Figures 12 and 13 illustrate details of normal and shear stress distributions of the bridges under live

loads positioned for critical flexure and shear demands, together with the critical dead and live load

demands and the corresponding capacities. These figures illustrate the detailed output that is

available from a microscopic 3D FE model and the stress gradients that are associated with critical

live load positions.Table 4 is organized into two parts:

1) In Table 4a the following results are presented:

a) Load ratings for flexure and shear from BAR7 analyses of idealized models that are

currently in the PADOT’s inventory, as obtained from District 6.

b) Load rating for flexure and shear from analyses of field calibrated 3D FE models of the

Swan and Manoa Bridges representing the current as-is conditions of these two bridges.

c) Load ratings corresponding to a hypothetical deterioration extreme for the bridges, obtained

by analysis of the calibrated FE models after removing about 40% of the depth of the beams

to simulate cracking, spalling and deterioration throughout their length. The areas of the first

and second layers of tension steel are also reduced by 50% and 20%; respectively for

simulating rebar corrosion and loss of bond as illustrated in Figure 10. Consequently, the

flexural and shear capacities are decreased accordingly as a result of the concrete loss and

corroded rebars. These analyses are assumed to provide estimates for extreme probable

lower bounds of load ratings that may occur in the next 5-10 years if ongoing deterioration

is not mitigated.

22

BAR7 Model Calibrated FE Models

Bridge Geometry Simple beam model using

LFD Distribution

Factors (1)

As-is Condition

w/ All Elements, End Restraints &

Pin-Pin Supports

(2)

Projected Extreme Possible

Deterioration in 5-10 years

(3)

Swan Road Bridge

L=26’ Skew=0 Width=27’

RFM=1.27

RFV=1.80

RFM=3.18 (150% higher than BAR7)

RFV=2.69

(50% higher than BAR7)

RFM=2.11 (66% higher than

BAR7)

RFV=2.30 (28% higher than

BAR7)

Manoa Road Bridge


RFM=0.96

RFV=1.10

RFM=3.27 (240% higher than BAR7)

RFV=2.64


RFM=2.27 (136% higher than

BAR7)

RFV=1.96 (78% higher than

BAR7)

Notes :

Current Inventory Rating using AASHTO

Actual Load Rating Based on Field Measurements.

Actual LR w/ Added Deterioration.

BAR7 Model Nominal Parameters with and without Secondary Elements

Bridge Geometry Simple beam model using

LFD Distribution

Factors (1)

Pin-pin Parapets

Diaphragms (2)

Pin-roller Parapets

Diaphragms (3)

Pin-roller Parapets

w/o Diaphragms

(4)

Pin-roller w/o Parapets

w/o Diaphragms

(5)

Pin-roller w/o Parapets

w/o Diaphragms w/ Extreme

Possible Deterioration

(6)

Swan Road Bridge


RFM=1.27

RFV=1.80

RFM=3.05 (140% higher than BAR7) RFV=3.54








RFM=0.88 (31% less than

BAR7) RFV=1.97


Manoa Road Bridge


RFM=0.96

RFV=1.10











Notes :

Current Inventory Rating using AASHTO

Investigation of Elements and Mechanisms relative to BAR7 analysis that Provide Additional Redundancy and Load Rating

Investigation of the effects of Deterioration on Case (5).

Table 4a: Comparison of the BAR7 Results with FE Models for As-is and ExtremeDeterioration Cases

Table 4b: Comparison of the BAR7 Results with FE Models with Different Mechanisms

23

As-is Condition with All Elements, End Restraints, Pin-pin Supports (using calibrated FEM)

Swan Road Bridge; RFM=3.18, RFV=2.69Manoa Road Bridge; RFM=3.27, RFV=2.64

Projected Extreme Deterioration (using calibrated FEM)


BAR7 AnalysisSwan Road Bridge; RFM=1.27, RFV=1.80Manoa Road Bridge; RFM=0.96, RFV=1.10

Pin-roller Supports with Parapets and Diaphragms (Nominal FEM) w/o pavement thrust


Pin-pin Supports with Parapets and Diaphragms (Nominal FEM) w/o pavement thrust


Pin-roller Supports without Parapets and Diaphragms (Nominal FEM) w/o pavement thrust


Pin-roller Supports with Parapets and without Diaphragms (Nominal FEM) w/o pavement thrust

Swan Road Bridge; RFM=1.88, RFV=3.10 Manoa Road Bridge; RFM=1.67, RFV=2.77

Pin-roller Supports without Parapets and without Diaphragms (Nominal FEM) and with Extreme Deterioration w/o pavement thrust


BAR7 AnalysisSwan Road Bridge; RFM=1.27, RFV=1.80Manoa Road Bridge; RFM=0.96, RFV=1.10

x DF

x DF

Figure 11: Summary of the Rating Factor Analysis for the Swan and Manoa Road Bridges

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 10: Extreme Deterioration/Damage Simulation

24

Model Normal Stress Distribution (ksi) due to the Most Critical Live Load

Configuration (Moment values are kip-in)

Shear Stress (ksi) Distribution due to the Most Critical Live Load Configuration

(Shear values are in kips)

As-is Condition w/All Elements, End Restraints & Pin-pin supports

MD= 364 ML= 553 MU= 454

VD= 11.02 VL = 13.53 VU= 117.06

110 (ksi) 0 -110 -220 0 36 72 (ksi) 36 72

Model Normal Stress (ksi) Distribution due to the Most Critical Live Load

Configuration (Moment values are kip-in)

Shear Stress (ksi) Distribution due to the Most Critical Live Load Configuration

(Shear values are in kips)

As-is Condition w/All Elements, End Restraints & Pin-pin supports

MD= 539 ML= 718 MU= 611

VD= 12.80 VL = 15.82 VU= 134.35

0 160 (ksi) 320 0 44 88 (ksi) -44 -88

Figure 12: Swan Road Bridge Stress Distributions for Moment and Shear

Figure 13: Manoa Road Bridge Stress Distributions for Moment and Shear

25

2) In Table 4b it is possible to see the effects of structural mechanisms that are not taken into

account when idealized models using the BAR7 software are analyzed for demand calculations.

Four 3D FE models are generated for each bridge using the nominal parameters for materials, and

by representing different possibilities for the boundary conditions and the existence of secondary

elements such as the diaphragm beams and parapets. The load rating results corresponding to the

following mechanisms are investigated:

a) Actually identified pin-pin boundary conditions, and the reinforced concrete parapets and

diaphragms beams are included in the model. Note that any lateral thrust is not included.

b) Pin-roller as opposed to pin-pin boundary conditions are incorporated while RC parapets

and diaphragms beams are retained in the model.

c) Pin-roller boundary conditions and parapets are included in the model but the diaphragm

beams are excluded,

d) Pin-roller boundary conditions are maintained but both the RC parapets and diaphragms

beams are ignored. Note that this model incorporates all of the implicit assumptions in a

rating approach based on the AASHTO recommendations. However, rather than

representing the bridge by an idealized simple beam and using lateral live-load distribution

factors, all of the beams and the entire slab is incorporated as the critical demands are

calculated under the total weight of two loaded trucks.

e) Finally, a simulated extreme deterioration case using the model in Case 5 is studied by

eliminating 35%-40% of concrete along the depth from all of the beams, and the areas of the

first and second layers of tension steel in the beams are reduced by 50% and 20%,

respectively.

Flexural Load Rating Results

1) Table 4a indicates that the BAR7 analyses of the Swan Road and Manoa Road Bridges yield

rating factors of 1.27 and 0.96 for flexure, respectively for the two bridges, and these are indeed

the current load ratings for these bridges in District 6 records.

2) The load ratings for flexure based on the field calibrated 3D FE models are 3.18 (150% higher

than the BAR7 load rating) for the Swan Road Bridge and 3.27 (240% higher) for the Manoa

Road Bridge, respectively. 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

26

load rating results based on BAR7, although the latter do not incorporate any deterioration. The

reasons will be discussed in the following.

3) The stress distributions corresponding to the critical live load for flexure are illustrated in

Figures 11 and 12. The output from the 3D solid elements used for FE modeling provides the

stresses at element nodal points; these are then integrated to compute the resulting moment and

shear demands from each girder. The stress distributions in Figures 12 and 13 reveal that there is

significant capacity for redistribution of stresses as the maximum stresses are associated with

very high gradients.

4) In the event of possible extreme deterioration, simulated by reducing the concrete and steel of

the beams in the field-calibrated models, the load ratings are reduced to 2.11 for the Swan Road

Bridge and 2.27 for the Manoa Road Bridge. These values are still 66% and 136% higher,

respectively, than their counterparts 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.

5) The results presented in Table 4b 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) and 1.79 (compare to 2.91 for pin-pin

boundary conditions) for the Swan and Manoa Road Bridges, respectively. These load ratings,

however, are still 57% and 87% higher than the BAR7 ratings mainly due to the lateral load

distribution due to the slab and contributions of the secondary elements (diaphragms and

parapets).

6) 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. In Case 4 in Table 4b where diaphragms are excluded

from these models, the load ratings for the bridges slightly decrease as compared to Case 3 of

Table 4b. However, the load ratings are still 48% and 74% higher than the BAR7 load ratings

for the Swan Road and Manoa Road Bridges, respectively.

27

7) Using the 3D FE models for calculating the demands for these bridges after neglecting the

restraints at the boundaries, and the contributions of the diaphragms and parapets results in

rating factors of 1.44 and 1.60 for the Swan Road and Manoa Road Bridges, respectively. These

are still 13% and 67% higher than their BAR7 rating counterparts. These increases in load

ratings are due to correctly simulating the distribution of stresses in the transverse direction due

to the slab in the 3D FE model. Another conclusion is that the parapets contribute less to load

rating when a bridge is wider, as the reduction in load rating of Manoa Road Bridge when

parapets are removed is less than the reduction in load rating of the Swan Road Bridge.

8) Table 4b reveals that when the 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 and 1.07 for Manoa Road Bridge). We

also note that when extreme deterioration is simulated, the flexural capacities are reduced by as

much as 35%. At the same time, the critical dead load demand for either case is reduced by 19%

and live load demand is reduced by 3-7% due to redistribution as shown in Figure 12 and 13.

The reduction due to redistribution would be expected to increase if a non-linear model is used

for concrete.

Shear Load Rating Results

1) BAR7 analyses yield rating factors of 1.80 and 1.10 for shear for the Swan Road and Manoa

Road Bridges, respectively.

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 ratings for

Swan Road and Manoa Road Bridges obtained from 3D FE analysis, respectively, are 2.69 and

2.64, which are 50% and 140% higher than the corresponding ratings by BAR7 analysis.

3) Shear rating factors obtained by 3D FE analysis decrease to 2.30 and 1.96 for the Swan Road

and Manoa Road Bridges, respectively, when extreme probable deterioration is simulated. The

dead load and live load demands are obtained from the FE models in which deterioration is

simulated. In addition, shear capacity computations include the reductions of concrete, stirrups

and bent longitudinal reinforcing bars; as a result, the section capacities are decreased

accordingly. However, shear load ratings are still 28% and 78% higher than the corresponding

shear ratings from BAR7 analyses.

28

4) Using nominal parameters, pin-pin boundary conditions and including the secondary elements,

the shear ratings are 3.54 for the Swan Road Bridge, and to 2.94 for the Manoa 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 condit ions are changed to pin-roller for the Swan Road and Manoa Road

Bridges, the corresponding rating factors for shear become 3.90 and 3.06, respectively. The

increase in load rating is as a result of the reduced shear demand at the critical locations when

boundary restraints are released.

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 and 2.50 for the Swan Road and Manoa Road Bridges, respectively. These are still 46%

and 127% higher than the corresponding shear load rating by BAR7 analysis. We note that the

3D FE models used in this case conform to the same assumptions in BAR7 analyses as the

secondary elements and boundary restraint are excluded.

6) When extreme future probable deterioration is simulated in the nominal 3D FE models, the

shear rating factors decrease to 1.97 for the Swan Road and 1.83 for the Manoa Road. This is a

consequence of the reduced shear capacities and shear load distributions as shown in the shear

in Figure 12 and 13. The shear ratings are 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.

The Implications of Relative Values of Shear and Flexure Rating Factors

A critical factor in evaluating the load rating of T-beam bridges is to determine the probable failure

mode and not just a number for load rating. We note that the material limit states that are considered

for flexural and shear rating are fundamentally different in terms of the safety they provide against

undesirable failure modes. Therefore, the relative ratio of load rating for shear to that for flexure is

as important as these two load rating factors individually even if they both exceed unity. Given the

uncertainty in the failure modes due to aging, deterioration and damage, it is critical to ensure that

shear failure will not occur before flexural yielding. This is especially a concern for short, single

29

span bridges. The writers have experienced such an undesirable failure mode while testing a RC slab

bridge to failure (Aktan et al, 1993).

Therefore when evaluating the possible failure modes of the Swan and Manoa Road Bridges from

Table 4, it is important to determine the governing load rating type and the relative change in

flexural and shear rating depending on the analysis method and the assumptions for capacity

calculation:

1) BAR7 Model Results: The BAR7 load rating results indicate that flexure governs the load

rating of both bridges. Since the BAR7 model does not consider any secondary mechanisms,

the fact that flexure governs the load rating should be confirmed.

2) Calibrated FE Model Results: When the calibrated FE models are used for load rating

(Table 4a), the results indicate that shear governs both Swan and Manoa Road Bridges

although their flexural ratings are greatly improved relative to BAR7 analysis. When

extreme deterioration is simulated, shear rating governs load rating of the Manoa Road

Bridge, whereas flexure governs load rating of the Swan Road Bridge. It follows that the

impact of deterioration on load rating and possible failure mode may vary depending on the

bridge as well as the extent of any deterioration and damage.

3) Nominal FE Models Results with and without Secondary Elements: Table 4b illustrates that

in every one of the cases studied by nominal models, flexure remains as the governing

mechanism for load rating.

Since the expected failure mode is often as important as the individual load rating factors for flexure

and for shear, the conservatism of the simple beam modeling and analysis for load rating may

become questionable if this erroneously points to a flexural mode of failure and not reveal that shear

may be the more probable failure mode. The rating results for field-calibrated models from Table 4a

indicate that shear may become the governing failure mode for many bridges currently operating

daily under traffic as a result of deterioration. We also note that the load rating factor is as much

dependent on the assumptions made for capacity as for demand computations.

For example, PADOT engineers compute the shear capacity of T-beams by including the capacity

due to the effective concrete section, the stirrups and the longitudinal reinforcing bars bent at the

high shear regions. If the capacity of any one of these contributors is reduced due to deterioration,

the shear load rating is directly affected. On the other hand, it is also possible to consider that shear

failure of a T-beam bridge with diaphragms would have to involve both diagonal web-shear and

punching shear mechanisms. These two mechanisms should occur together or one after the other for

any possible shear failure. Consequently, the maximum shear demand should in reality exceed the

30

sum of diagonal web-shear capacity and the punching shear capacity of the structure for shear to

govern rating.

It follows that shear load rating of deteriorated bridges is a very complicated problem governed by

extensive uncertainty, far exceeding the uncertainty that prevails in the computation of the flexural

load rating. As a result, special emphasis on boundary conditions should be given during inspections

and the analysis method should carefully incorporate any deterioration identified from the field

evaluations. Finally, it is very important that the analytical simulation of the impacts of deterioration

for shear load rating is confirmed by properly designed and executed destructive testing of some T-

beam bridges.

Demand Mechanisms That Contribute To Higher Load Rating by FE Analysis

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 models, it is still possible to increase the load rating 13% for the Swan Road

Bridge and 66% for the Manoa 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:

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. Since the pin-pin boundary conditions provide the largest

increase in the simulated load capacity rating factors, it is recommended that the boundaries

at the super-and-substructures are carefully inspected and any movement is reported during

biannual inspections.

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.

31

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.

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.

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) 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 effectively reducing the demands and leading to a higher load rating (Shahrooz et

al. 1994; Huria et al, 1994).

Capacity Mechanisms That Contribute To Higher Load Rating

Throughout this study and in deriving the load capacity rating factors in Table 4, 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

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

32

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:

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 offsets the tensile forces in steel and considerably enhances 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.

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, 1999). For example, tests on tensile yield strength of Grade 60 rebars with nominal

yield strength of 60 ksi 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.

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.

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 either 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

33

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).

Analytical Studies of 40 Bridge FE models for Modified Load Distribution Factors

We may rationalize ignoring many of the mechanisms that provide actually higher load capacity

rating of RC T-beam bridges for a need to be conservative. Analytical sensitivity studies clearly

indicate that given a single-span RC T-beam bridge, the actual lateral load distribution 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) as illustrated in Figure 14. Based on the very

same observation, PADOT District engineers do not use LRFD methods for T-beam bridges. The

experience of the PADOT District engineers is that the T-beam bridges are capable of carrying

higher loads than what is obtained using AASHTO LFD and LRFD methods. As a result of this,

they implement the AASHTO Working Stress method for permit evaluation of T-beam bridges since

the Working Stress method leads to a slightly higher load rating.

Therefore, it makes sense to examine and derive again 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 microscopic

3D FE models that represent the geometric characteristics of the population with a fine discritization

are needed for improved precision. For example, when we analyze the Manoa Road Bridge using a

3D FE model constructed by using 2D shell elements as opposed to 3D solid elements. The flexural

and shear load capacity ratings obtained using the shell-element based model were 1.91 and 2.66,

respectively , as opposed to 1.60 and 2.50 that are obtained from the solid model. The discrepancy in

these load capacity rating values is only due to the load demands obtained from the two different

types of FE models. For example, the live load demand obtained from the solid model is 1408 kip-in

whereas, the live load demand obtained from the shell model is 1195 kip-in. The 15% discrepancy

in live load demand leads to discrepancy in load capacity rating obtained from the two models. This

example illustrates that 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.

Therefore, forty 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 microscopic 3D FE models. These models were constructed and analyzed under

34

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 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 (Table 5) and

presented in detail in the report.

35

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

utio

n Fa

ctor

s

LFD Moment Distribution FactorOne Lane LRFD Moment Distribution Factor for 90 deg SkewTwo Lane LRFD Moment Distribution Factor for 90 deg SkewFEM Moment Distribution Factor for 90 deg SkewDF from Formulations

LFD Distribution Factors from AASHTO Standard Specifications for Highway Bridges (1996)LRFD Distribution Factors from AASHTO LRFD Bridge Design Specifications (1994)

Figure 14: Distribution Factor for Moment as a Function of Span Length for Bridges with No Skew

36

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

[ ]

−∗+∗+∗= −

152

502.0103347606.36 5 θLg

Equations Derived for Single Span T-Beam Population

[ ]

−∗++∗∗−∗= − 1

452

022.018664.2103.91455.124 52 θLLg

[ ]

−∗+∗+∗= − 1

452

032.01030315744 5 θLg

g=distribution factorL=clear span as given in PA Standards for Old Bridgesθ=skew angle

Table 5: Distribution Factor Equations Derived for PA R.C. T-beam Bridges

37

CONCLUSIONS AND RECOMMENDATIONS

1) This study demonstrated that statistical sampling in conjunction with a “fleet strategy” may

serve as an effective approach for condition assessment and management of large bridge

populations with common structural and condition parameters. The fleet strategy requires a

determination of the critical nominal and as-is condition parameters that govern the load

capacity of a “fleet” of bridges.

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 or “fleet” 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 is documented is summarized in the

Report. Executive Summary contains results of in-depth analyses by field-calibrated 3D FE

models for two of the test bridges. These analysis results describe and quantify the mechanisms

that affect both the demand side and the capacity side of the load rating equation. The studies

reported in the Report 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 twice and up to almost four 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 reasons for

such high level of conservatism in the load rating of highly redundant cast-in-place RC bridges

have been described earlier. 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

improve the load rating of the population by between 10% and 55% due to only the enhanced

lateral 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. The corresponding

equations and findings are expected to impact the management of T-beam bridges after their

review and approval by PADOT and AASHTO.

5) The bridge management consequences of the conclusion reached in this study are not

insignificant. Currently, Pennsylvania has the most structurally deficient and functionally

38

obsolete bridges T-beam bridges in the US. 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 may exceed

$Billions. 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.

6) 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 safety associated with

a flexure-governed load rating is much greater than the corresponding safety if shear governs

load capacity.

7) In an attempt to be conservative and conform to AASHTO specifications, it is possible to

exclude the secondary mechanisms as in the case BAR7 results. However, in reality the

secondary mechanisms do exist and they change the load demands within the structure and this

may lead to shear 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, our experiments were conducted under proof load

levels (upper threshold of operating loads). Unless testing is conducted at damage levels, we

may not assure that a desired margin of safety will remain 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.

8) 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. 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

39

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.

9) The Falling Weight Deflectometer (FWD) tests indicate that these tests may be used as an

effective, objective experiment for accompanying visual inspection. The FWD results may be

processed to provide a close measure of the static flexibility of a bridge. This is an excellent

indicator of the structural health of a bridge as any increases of 15% of higher in flexibility have

been shown to correlate with damage (Catbas and Aktan, 2002).

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., 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.

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, Vol. 123, No. 12, pp: 1674-1684, December.

Aktan, A. E., Catbas, F.N., Turer, A. and Zhang, Z., (1998), "Structural Identification: Analytical

Arts", Journal of Structural Engineering, ASCE, Vol.124, No.7, July, 1997, p.817- 829.

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.

ArcVIEW Software (2001), Environmental Systems Research Institute, Inc.

Catbas, F.N. and Aktan, A.E. (2002) “Condition and Damage Assessment: Issues and Some

Promising Indices”, J. of Structural Eng., ASCE, 2002, Vol.128, No. 8, pp.1026-1036.

40

Federal Highway Administration (FHWA) (2002), U.S. Department of Transportation, Federal

Highway Administration, http://www.fhwa.dot.gov

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.

MacGregor, J. G. (1988) “Reinforced Concrete-Mechanics and Design,” Prentice Hall.

NBI, (1998), National Bridge Inventory Data (NBID).Rep.No.FHWA-PD-96-001, Washington

D.C., 1998.

NCHRP (2002) "Simplified Live-Load Distribution-Factor Equations," National Cooperative

Highway Research Program- Pending Project, Project 12-62.

New York Times (2002), National Briefing in Washington, December 7, 2002

Park, T. and Gamble, W., (2000) “Reinforced Concrete Slabs”, John Wiley and Sons, 2nd Edition.

SAP2000 (2002), Integrated Software for Structural Analysis and Design, Version 8.0, Computers

and Structures, Inc., Berkeley, CA.

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 Analysis of

Reinforced Concrete T-girder Bridges,” Engineering Structures, Vol. 24, pp-151-162.

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