Load Rating of Prestressed Concrete Girder Bridges: A Comparative

Load Rating of Prestressed Concrete Girder Bridges: A Comparative Analysis of LFR and LRFR Report NM02STR-01 Prepared by: New Mexico State University Bridge Center Las Cruces, New Mexico May 2005 Prepared for: New Mexico Department of Transportation Research Bureau 7500B Pan American Freeway NE Albuquerque, NM 87109 In Cooperation with: The U.S. Department of Transportation Federal Highway Administration

1. Report No.

NM02STR-01 2. Government

Accession No. 3. Recipient’s Catalog No.

5. Report Date May, 2005

4. Title and Subtitle Load Rating of Prestressed Concrete Girder Bridges: A Comparative Analysis of LFR and LRF 6. Performing Organization Code 7. Author (s) Brandy Jo Rogers, David Villegas Jáuregui

8. Performing Organization Report No. 10. Work Unit No.

9. Performing Organization Name and Address New Mexico State University Department of Civil Engineering Hernandez Hall, Box 30001, MS 3CE Las Cruces, NM 88003

11. Contact or Grant No.

13. Type of Report and Period Covered Final Report January 2004 – May 2005

12. Sponsoring Agency Name and Address U.S. DOT Office of Federal Highway Administration 6300 Georgetown Pike McLean, VA 22101-229 14. Sponsoring Agency Code 15. Supplementary Notes 16. Abstract

With the intention of supporting the Federal Highway Administration’s implementation of Load and Resistance Factor Design (LRFD), research efforts were made to facilitate the transition from Load Factor Rating (LFR) to Load and Resistance Factor Rating (LRFR) in the state of New Mexico. Five prestressed concrete girder bridges, courtesy of the NM bridge inventory, were rated using the BRASS-GIRDER and BRASS-GIRDER (LRFD) software. Research objectives include 1.) the evaluation of the BRASS software prior to full implementation by the NM Department of Transportation (DOT), 2.) the identification of the source of dissension between LFR and LRFR rating factors, 3.) the identification of any trends in the rating factors as affected by bridge geometry, 4.) the identification of any questionable bridges within the sample, and 5.) the use of the research findings to provide training of the LRFR method to the NMDOT.

In verifying the BRASS software, all strength-based rating factors were in agreement with hand computations for LFR. The serviceability rating factor, however, differed by 16.7 percent and was therefore considered inadequate. With respect to BRASS-GIRDER (LRFD), potential errors relating to the Modified Compression Field Theory interfered with the computation of beta and theta, thus affecting the shear resistance. However, it was concluded that BRASS-GIRDER (LRFD) produces accurate results under the premise that the shear resistance is determined by means of a user defined beta and theta.

The LRFR method generally yielded lower rating factors for flexure, with the longer span bridges demonstrating a larger deviation between LFR and LRFR. The live load effects were identified as the contributing parameter to the difference in rating methods. The dead load effects and flexural resistance had little impact.

The LRFR rating factors for shear were generally lower than those produced by LFR. The discrepancy in rating factors was linked to the live load effects and shear resistance. The dead load effects contributed little to the variation in LFR and LRFR rating factors for shear.

Overall, the shear ratings controlled over those based on flexure. Finally, a number of bridges proved inadequate for the shear ratings, while the flexure ratings were satisfactory. 17. Keywords Load and Resistance Factor Rating (LRFR) Load Factor Rating (LFR)

18. Distribution Statement No restrictions.

19. Security Classif. (of this report) Unclassified

20. Security Classif. (of this page) Uclassified

21. No. of Pages 98

22. Price

LOAD RATING OF PRESTRESSED CONCRETE GIRDER BRIDGES: A COMPARATIVE ANALYSIS OF LFR AND LRFR

by

Brandy Jo Rogers, M.S. David Villegas Jáuregui, Ph.D.

Bridge Center New Mexico State University

Las Cruces, New Mexico

Report NM02STR-01

A Report on Research Sponsored by: New Mexico Department of Transportation

Research Bureau

in Cooperation with: The U.S. Department of Transportation

Federal Highway Administration

May 2005

New Mexico Department of Transportation Research Bureau

7500B Pan American Freeway NE PO Box 4690

Albuquerque, NM 87199-4690

© New Mexico Department of Transportation

i

PREFACE

This project supports the Federal Highway Administration’s implementation of Load and

Resistance Factor Design (LRFD). The research reported herein aims to further inform the bridge

engineering community of the similarities and differences between Load Factor Rating (LFR)

and Load and Resistance Factor Rating (LRFR). In response to this research objective, five

prestressed concrete girder bridges, courtesy of the new Mexico bridge inventory, were rated

using the Bridge Rating and Analysis of Structural Systems (BRASS) software; a detailed

comparison of LFR and LRFR, as well as the identification of trends based on bridge geometry,

resulted from this research.

NOTICE

DISCLAIMER

The United States Government and the State of New Mexico do not endorse products or manufacturers. Trade or manufacturers’ names appear herein solely because they are considered essential to the object of this report. This information is available in alternative accessible formats. To obtain an alternative format, contract the NMDOT Research Bureau, 7500B Pan American Freeway NE, (PO Box 4690) Albuquerque, NM 87199-4690, or by telephone (505) 841-9145.

This report presents the results of research conducted by the author(s) and dos not necessarily reflect the views of the New Mexico Department of Transportation. This report does not constitute a standard or specification.

ii

ABSTRACT

With the intention of supporting the Federal Highway Administration’s implementation of Load

and Resistance Factor Design (LRFD), research efforts were made to facilitate the transition

from Load Factor Rating (LFR) to Load and Resistance Factor Rating (LRFR) in the state of

New Mexico. Five prestressed concrete girder bridges, courtesy of the NM bridge inventory,

were rated using the BRASS-GIRDER and BRASS-GIRDER (LRFD) software. Research

objectives include 1.) the evaluation of the BRASS software prior to full implementation by the

NM Department of Transportation (DOT), 2.) the identification of the source of dissension

between LFR and LRFR rating factors, 3.) the identification of any trends in the rating factors as

affected by bridge geometry, 4.) the identification of any questionable bridges within the sample,

and 5.) the use of the research findings to provide training of the LRFR method to the NMDOT.

In verifying the BRASS software, all strength-based rating factors were in agreement

with hand computations for LFR. The serviceability rating factor, however, differed by 16.7

percent and was therefore considered inadequate. With respect to BRASS-GIRDER (LRFD),

potential errors relating to the Modified Compression Field Theory interfered with the

computation of beta and theta, thus affecting the shear resistance. However, it was concluded

that BRASS-GIRDER (LRFD) produces accurate results under the premise that the shear

resistance is determined by means of a user defined beta and theta.

The LRFR method generally yielded lower rating factors for flexure, with the longer span

bridges demonstrating a larger deviation between LFR and LRFR. The live load effects were

identified as the contributing parameter to the difference in rating methods. The dead load

effects and flexural resistance had little impact.

iii

The LRFR rating factors for shear were generally lower than those produced by LFR.

The discrepancy in rating factors was linked to the live load effects and shear resistance.

The dead load effects contributed little to the variation in LFR and LRFR rating factors for shear.

Overall, the shear ratings controlled over those based on flexure. Finally, a number of

bridges proved inadequate for the shear ratings, while the flexure ratings were satisfactory.

iv

ACKNOWLEDGEMENTS The authors would like to acknowledge the New Mexico Department of Transportation

(NMDOT) and the Wyoming Department of Transportation (WYDOT) for supplying the NM

bridge plans/other supplementary information and the Bridge Rating and Analysis of Structural

Systems (BRASS) software, respectively.

v

METRIC CONVERSION FACTORS PAGE

APPROXIMATE CONVERSIONS TO SI UNITS

SYMBOL WHEN YOU KNOW MULTIPLY BY TO FIND SYMBOL LENGTH

in inches 25.4 millimeters mm ft feet 0.305 meters m yd yards 0.914 meters m mi miles 1.61 kilometers km

AREA in2 square inches 645.2 square millimeters mm2 ft2 square feet 0.093 square meters m2 yd2 square yard 0.836 square meters m2 ac acres 0.405 hectares ha mi2 square miles 2.59 square kilometers km2

VOLUME fl oz fluid ounces 29.57 milliliters mL gal gallons 3.785 liters L ft3 cubic feet 0.028 cubic meters m3 yd3 cubic yards 0.765 cubic meters m3

NOTE: volumes greater than 1000 L shall be shown in m3 MASS

oz ounces 28.35 grams g lb pounds 0.454 kilograms kg T short tons (2000 lb) 0.907 megagrams (or

"metric ton") Mg (or "t")

TEMPERATURE (exact degrees) oF Fahrenheit 5 (F-32)/9

or (F-32)/1.8 Celsius oC

ILLUMINATION fc foot-candles 10.76 lux lx fl foot-Lamberts 3.426 candela/m2 cd/m2

FORCE and PRESSURE or STRESS lbf poundforce 4.45 newtons N lbf/in2 poundforce per square inch 6.89 kilopascals kPa

vi

TABLE OF CONTENTS

Section

Page

PREFACE i ABSTRACT ii ACKNOWLEDGEMENTS iii METRIC CONVERSION FACTORS PAGE v LIST OF TABLES ……………………………………………………………………… viii LIST OF FIGURES ……………………………………………………………………... ix CHAPTER 1. INTRODUCTION …………………………………………..................... 11.1 Introduction to Load Rating …………………………………………………….. 1

1.1.1 Rating Methods …………………………………………………….......... 41.1.2 Rating Aids …………………………………………………………….... 7

1.2 Previous Research …………………………………………................................. 91.2.1 Comparison of LFR and LRFR for Concrete Bridges …………………... 91.2.2 Manual for Condition Evaluation and Load Rating of Highway Bridges

Using Load and Resistance Factor Philosophy and New AASHTO Guide Manual for Load and Resistance Factor Rating of Highway Bridges …………………………………………………………………... 11

1.3 Objective ….…………………………………………………………………….. 15 CHAPTER 2. DESCRIPTION AND VERIFICATION OF BRASS SOFTWARE ……. 172.1 Software Description ………………………………………………..................... 172.2 Software Verification …………………………………………………………… 20

2.2.1 BRASS-GIRDER ……………………………………………………….. 212.2.2 BRASS-GIRDER (LRFD) ……………………………………………… 25

2.3 Application of Software ………………………………………………………… 35 CHAPTER 3. BRIDGE DESCRIPTION ……………………………………………….. 373.1 Bridge 7169 ……………………………………………………………………... 373.2 Bridge 7390 ………………………………………………………….………….. 383.3 Bridge 7171 ………………………………………………………….………….. 393.4 Bridge 8852 ………………………………………………………….………….. 403.5 Bridge 7195 ………………………………………………………….………….. 403.6 Effects of Skew ……………………………………………………...………….. 41 CHAPTER 4. RESULTS ……………………………………………………………….. 434.1 Discussion of Live Load Effects ………………………………………………... 534.2 Discussion of Dead Load Effects ……………………………………………….. 564.3 Discussion of Effects Related to Resistance ………………………...………….. 564.4 Contribution of Parameters to Rating Factor ………………………..………….. 59

vii

CHAPTER 5. CONCLUSIONS AND RECOMMENDATIONS ……………………… 635.1 Summary ………………………………………………………………………... 635.2 Conclusions ……………………………………………………………………... 635.3 Recommendations …………………………………………………..................... 65 Section

Page

APPENDICES A. SOFTWARE VERIFICATION, PCI EXAMPLES 9.3 AND 9.4 ……………… 69B. BRASS INPUT FILES ………………………………………………………….. 72C. TABULAR RESULTS: BRASS RATINGS ………………………..................... 107 REFERENCES ………………………………………………………………………….. 97

LIST OF TABLES

Table

Page

1.1 Analysis Vehicles ……………………………………………………………….. 1.2 Governing Load Effect (HL-93) ………………………………………………... 2.1 Files Generated by BRASS-GIRDER (LRFD) …………………......................... 2.2 PCI Example 9.3, Comparison of Hand Calculations vs. BRASS Output ………2.3 Shear Resistance, Comparison of Hand Calculations vs. BRASS Output ……… 2.4 PCI Example 9.4, Comparison of Hand Calculations vs. BRASS Output ………4.1 LRFR Shear Parameters ………………………………………………………… 4.2 Critical Sections for Shear …………………………………………...…………..4.3 Distribution Factors, LFR vs. LRFR ………………………………...………….. 4.4 Deviation of LFR and LRFR ………………………………………...…………..A.1 LFR Rating Factor Computations …………………………………...………….. A.2 LRFR Rating Factor Computations ………………………………….…………..C.1 LRFR Rating Factors: Flexure ………………………………………………….. C.2 LRFR Critical Rating Factors: Shear ………………………………..………….. C.3 LFR Rating Factors: Flexure ………………………………………...………….. C.4 LFR Critical Rating Factors: Shear ……………………………….....………….. C.5 LRFR Live Load Effects: Flexure (k-ft.) ……………………………………….. C.6 LRFR Critical Live Load Effects: Shear (kips) ……………………..………….. C.7 LFR Live Load Effects: Flexure (k-ft.) ……………………………...………….. C.8 LFR Critical Live Load Effects: Shear (kips) …………………….....………….. C.9 Dead Load Effects: Flexure (k-ft.) …………………………………..………….. C.10 LRFR Critical Dead Load Effects: Shear (kips) ………………….....………….. C.11 LFR Critical Dead Load Effects: Shear (kips) ………………………………….. C.12 Resistance: Flexure (k-ft.) …………………………………………...………….. C.13 LRFR Critical Resistance: Shear (kips) ……………………………..………….. C.14 LFR Critical Resistance: Shear (kips) …………………………….....…………..

viii

LIST OF FIGURES

Figure

Page

1.1 LRFR Flow Chart ……………………………………………………………….. 2.1 PCI Example Bridge Description ……………………………………………….. 2.2 PCI Example 9.3 (LFR) BRASS Input ……………………………..................... 2.3 Percent Deviation in Rating Factors, Hand Calculations vs. BRASS Output (PCI Example 9.3) …………………………………………................................. 2.4 PCI Example 9.4 (LRFR) BRASS Input …………………………….…………..2.5 Correlation between Shear Resistance and Applied Loading ……….………….. 3.1 Location of Bridge Sample, NM Map …………………………….....………….. 4.1 Critical Rating Factors: Flexure ……………………………………..………….. 4.2 Critical Rating Factors: Shear …………………………………….....………….. 4.3 Critical Live Load Effect: Flexure …………………………………..………….. 4.4 Critical Live Load Effect: Shear ………………………………….....………….. 4.5 Critical Dead Load Effect …………………………………………...………….. 4.6 Critical Resistance: Shear ………………………………………………………..4.7 Critical Resistance: Flexure ……………………………………………………..

1

CHAPTER 1 INTRODUCTION Bridge evaluation is critical to the safety of the nation’s transportation system

considering, for example, that the viaducts within the U.S. highway infrastructure are on average

40 years old with a theoretical design life of 50 years (Friedland and Small, 2003). Based on the

Federal Highway Administration’s 2003 National Bridge Inventory, the vehicle miles of travel

(VMT) in the U.S. have increased 148% in the last 30 years (Key, 2003). Considering this

increase in vehicular traffic and the effects of aging on our nation’s transportation system, the

deterioration of highway bridges is inevitable. As of the year 2003, 27 percent of bridges

nationwide with lengths 20 feet and over, are considered to be either structurally deficient or

obsolete. New Mexico alone contributes 720 bridges to these statistics, 340 of which are

considered functionally obsolete (FHWA, 2004). A structurally deficient bridge is defined as

one showing signs of deterioration, yet yielding safe passage over the structure. A functionally

obsolete bridge, on the other hand, no longer meets current highway design standards (Deficient

Bridges, 2003). These alarming statistics illustrate the importance of bridge evaluation; hence,

maintaining the nation’s transportation infrastructure is vital for the safety of the traveling public.

The Federal Highway Administration (FHWA) through partnerships with the American

Association of State Highway and Transportation Officials (AASHTO), state transportation

agencies, the Transportation Research Board (TRB), and the National Cooperative Highway

Research Program (NCHRP) are supporting research related to bridge design, evaluation,

inspection, and maintenance. Customary bridge design and rating procedures are based on Load

Factor Design (LFD), with the AASHTO Standard Bridge Specifications being the primary

design guide. However, a transition to Load and Resistance Factor Design (LRFD) is in

2

progress, and shall be fully instated by the year 2007 (Friedland and Small, 2003). Although this

target year corresponds to the “design” of bridges, it is anticipated that “rating” bridges in

accordance with LRFD-based guidelines will follow. The LRFD design philosophy ensures a

more uniform level of safety across different bridge types and force effects (i.e. shear, flexure,

etc.) by using calibrated load and resistance factors to account for the variability of applied loads

and material properties. The FHWA is contributing to the transition to LRFD in the following

ways (Friedland and Small, 2003):

Providing planning assistance to the state departments of transportation.

Developing illustrative design examples for steel and concrete bridges.

Deploying technical LRFD training to the state departments of transportation through

courses offered by the National Highway Institute.

Supporting LRFD related research.

With a new limits state design philosophy facing the bridge engineering community, a keen

understanding of the LRFD Bridge Design Specifications is necessary to facilitate the transition

from one design / rating method to the other.

1.1 Introduction to Load Rating Bridge evaluation is of much importance in the determination or prevention of

overstressing a bridge component. Overloading of a structural member may be a result of a

reduction in live load capacity due to deterioration, an increase in dead loads, out-dated designs,

etc., all of which may render a bridge structurally deficient. Rating, as defined by Taly (1998), is

based upon a “structural capacity analysis to determine the reduced loading that a structurally

deficient bridge can safely carry.” A rating is expressed in terms of a rating factor (RF), which

is defined as the ratio of the actual to the required live-load capacity. All components of a bridge

3

(including the deck, superstructure, and substructure) need to be rated. The component with the

smallest rating factor represents the weakest link in the bridge, therefore controlling the rating of

the structure as a whole. In this thesis, attention will be given to the load rating of the

superstructure.

Rating procedures include Design, Legal, and Permit load rating, which are defined as

follows:

Design load rating is a “measure of the performance of existing bridges to new bridge

design standards” (Lichtenstein, 2001); based upon the HL-93 design load per Load

and Resistance Factor Rating (LRFR) and the HS-20 design load per Load Factor

Rating (LFR).

Legal load rating provides information necessary to the posting of loads or the

rehabilitation of the structure (based upon AASHTO legal loads).

Permit load rating allows for the issuance of overload permits.

In terms of function, a rating analysis may allow for overload permits to avoid any

unnecessary detours or restrictive traffic loadings while maintaining a safe and serviceable

structure.

It is important to note that ratings may be performed by either an experimental or

analytical means. However, the scope of this research will be based on analytical ratings only.

Thus, an understanding of the differences in design philosophy among the Load Factor Rating

(LFR) Method and the Load and Resistance Factor Rating (LRFR) Method is essential.

4

1.1.1 Rating Methods

Load Factor Rating (LFR) Method

The Load Factor Rating Method, currently in use by the New Mexico Department of

Transportation and a number of other states, specifies two levels of capacity ratings: inventory

and operating. The inventory rating represents the magnitude of load that a bridge can safely

sustain for an indefinite period of time, whereas the operating rating refers to the absolute

maximum load that may be permitted on a bridge (Taly, 1998). The rating equation used in the

LFR Method is as follows:

where: φRn = the capacity of the member; γD, γL = load factors for dead load (D) and live load (L), respectively; D, L = dead load and live load effects, respectively; and I = impact factor for live load. The live load factors differ between the inventory and operating ratings; γL is 2.17 for inventory

and 1.3 for operating. The dead load factor, γD, is fixed at a value of 1.3 (AASHTO, 1994).

Furthermore, the live load effects are based on the AASHTO HS-20 design load.

Load and Resistance Factor Rating (LRFR) Method

The AASHTO LRFD Bridge Design Specifications, based on a limit states design

philosophy, is calibrated to achieve uniform reliability in bridge design (Minervino et al., 2004).

The same philosophy used in the development of the LRFD Design Specifications was extended

to the evaluation of existing bridges in the AASHTO Guide Specifications for LRFR of Highway

Bridges (Minervino et al., 2004). A major difference is that the design stage is characteristic of

greater uncertainties in the loading, whereas with evaluation, the uncertainties lie within the

resistance. With regards to evaluation, the level of uncertainty can be reduced by obtaining

RF R DLL ILFRn D

L

=−

+φ γγ ( )1

(1.1)

5

improved resistance data, site-specific traffic data, and improved load distribution analyses that

were not available or considered in the design stage (Lichtenstein, 2001). The load rating

equation applicable to LRFR is:

where: φRn = the capacity of the member; φc, φs = condition and system factor, respectively (φcφs ≥ 0.85); γDC, γDW, γL = load factors for structural components and attachments (DC), wearing surfaces and utilities (DW), and live load (L), respectively; DC, DW, LL = dead load effect due to structural components and attachments, dead load effect due to wearing surfaces and utilities, and live load effects, respectively; and IM = dynamic load allowance. A discussion of the LRFR rating approach compared to LFR is provided in the following

paragraphs.

The dead load factors for the LRFR method are divided into two categories: DC (relates

to component loads) and DW (relates to wearing surface loads). The reason for separating the

two loadings is that the load due to the wearing surface has a higher degree of variability than

that of the component loads (Goodrich and Puckett, 2002). Calibrated load factors are applied to

the different dead loads to account for this variability.

The condition factor accounts for the increased uncertainty in the resistance of

deteriorated members and their probability of future deterioration. This factor ranges from 0.85

to 1.0 for members in poor condition to members in satisfactory condition. This factor does not

account for any observed changes in the physical dimensions of the member (Lichtenstein, 2001;

Moses, 1987).

RF R DC DWLL IMLRFR

c s n DC DW

L

=− −

+φ φ φ γ γ

γ ( )1(1.2)

6

The system factor is related to the level of redundancy in a structural system.

Redundancy is defined as the capability of a structure to redistribute loads upon damage or

failure to one or more of the members within the structure. The system factor ranges from 1.0 to

0.85 for redundant multigirder bridges to nonredundant systems; hence, the system factor for

bridges with less redundancy will reduce a member’s capacity resulting in lower rating factors.

Furthermore, a direct redundancy analysis approach as specified in NCHRP Report 406 (2001) is

available for bridge configurations not covered in the guide specifications (Minervino et al.,

2004). It is also important to note that the load modifiers (η) relating to ductility and redundancy

are incorporated into the system factor (Lichtenstein, 2001; Minervino et al., 2004; Liu, 2001).

The factored live load component of the LRFR rating equation generates the highest

degree of variability when compared to the LFR Method. For starters, the LRFR dynamic load

allowance (IM) is a fixed value, whereas the LFR impact factor (I) varies with span length. Also

influencing the live load effects are the distribution factors for moment and shear; the AASHTO

LRFD Bridge Design Specifications introduced new empirical equations that yield more accurate

distribution factors (PCI, 1997). The LRFD empirical equations consider span length, girder

spacing, girder stiffness, and slab thickness, whereas the LFD distribution factors consider only

the girder spacing. For interior girders, the LRFD distribution factors for moment and shear are

considered separately. This is not the case with LFD; only one distribution factor is computed

and is representative of both moment and shear. For exterior beams, the LRFD distribution

factors are determined by either modifying the distribution factors for the interior beam or by

employing the lever rule. The lever rule is applicable to LFD distribution factors for exterior

beams. Finally, the LRFD distribution factors account for skew and rigid intermediate

diaphragms. Another difference in the live load component lies in the type of vehicles used in

7

the analysis; LRFR applies the HL-93 design load, while LFR employs the HS-20. The HL-93

design load considers a HS-20 design truck (with two 32 kip axles and one 8 kip axle), a design

tandem (with two 24 kip axles) and a design lane loading of 0.64 kips per linear foot. The HL-

93 notional load allows for the combination of the truck or tandem load with the lane load, thus

resulting in a heavier loading configuration. Conversely, the LFR method considers the truck

and lane load separately. Yet another parameter is the LRFR live load factor. Based on the

LRFR design loads, the live load factor, γL, is 1.75 for the inventory check and 1.35 for the

operating check. Under legal loads, however, the live load factor ranges from 1.4 to 1.8

depending on the Average Daily Truck Traffic (ADTT) levels (Lichtenstein, 2001; PCI, 1997).

1.1.2 Rating Aids The rating aids listed below provide guidance and support for the previously discussed

load rating methods.

AASHTO LRFD Bridge Design Specifications (1998) and the Manual for Condition

Evaluation and Load Rating of Highway Bridges using Load and Resistance Factor

Philosophy (Lichtenstein, 2001; Minervino et al., 2004).

AASHTO Standard Bridge Design Specifications (1996) and the AASHTO Manual

for Condition Evaluation of Bridges (1994).

Bridge Rating and Analysis of Structural Systems (BRASS) (2002a, 2003).

AASHTO Virtis (2002).

These aids are discussed in detail in the following paragraphs.

The AASHTO Standard Bridge Design Specifications and the Manual for Condition

Evaluation of Bridges are the customary references used to rate bridges. However, with the

adoption of the AASHTO LRFD Bridge Design Specifications in 1994, and its corresponding

8

rating manual, a change in rating method is imminent. The LRFR rating specifications were

developed under the National Cooperative Highway Research Program (NCHRP Project C12-

46) in 2001, and were recently adopted for use in 2002. In general, the LRFR rating

specification is an upgrade of the existing AASHTO Manual for Condition Evaluation of

Bridges; the major revisions made in the manual include (Lichtenstein, 2001):

A new section on load rating bridges based on LRFR.

Procedures to determine site-specific live load factors.

Load factors specific to permit loads.

A new section on fatigue evaluation of steel bridges.

A new section on non-destructive load testing of bridges.

Illustrative load rating examples.

Parallel commentary.

References other than the LRFD Bridge Design Specifications (AASHTO, 1998) used in the

development of the LRFR rating manual include the Guide Specifications for Strength

Evaluation of Existing Steel and Concrete Bridges (AASHTO, 1989) and the Guide

Specifications for Fatigue Evaluation of Existing Steel and Concrete Bridges (AASHTO, 1990).

Other rating aids employ computer software, such as the BRASS and Virtis programs

which were originally developed and currently maintained by the Wyoming Department of

Transportation. Both programs operate in accordance with the AASHTO Standard (LFD) and

LRFD Bridge Design Specifications. Virtis is a database that stores input data such as material

properties, cross-sectional properties, span lengths, and other information pertinent to the bridge

description. The program then relies on external third-party engines to perform the structural

analysis and ratings. Available load rating engines include BRASS-GIRDER (based on LFD)

9

and BRASS-GIRDER (LRFD). Ratings can alternatively be performed by the sole use of

BRASS; however, Virtis has a graphical user interface that facilitates the input of the bridge

data.

1.2 Previous Research

1.2.1 Comparison of LFR and LRFR for Concrete Bridges (Goodrich and Puckett, 2002) Using the AASHTO Virtis load rating software and its associated BRASS analysis

engines, the authors analyzed and rated a set of concrete bridges according to LFR and LRFR

guidelines. A total of 24 reinforced concrete T-beam bridges, both simple-span and continuous,

were rated for flexure and shear under the loading configurations outlined in table 1.1. Findings

from the study showed different rating factors between LFR and LRFR; observations made by

the authors are discussed in the following paragraphs.

Flexure

The design and permit load ratings for flexure were generally lower for LRFR than LFR.

The legal load ratings, on the other hand, were higher for LRFR than LFR. The factored

resistances and dead load effects showed little distinction between the two methods, thus having

little or no effect on the difference in the rating factors. The primary source of the deviation lied

within the live load component, which was affected by the different live load factors, impact

factors, distribution factors, and design load configurations.

Shear

The LRFR rating factors for shear were generally higher for all of the live load groups

(design, legal, and permit). As previously mentioned for the flexure ratings, the factored dead

load effects for shear had negligible differences between the two rating methods. The LRFR

factored resistances were higher than LFR as attributed to the Modified Compression Field

10

Theory (MCFT), which is incorporated in the LRFD specifications. Similar to flexure, other

sources of variation in the shear rating factors were the different live load factors, impact factors,

distribution factors, and design load configurations.

Another observation made by the authors was that the permit load ratings will vary

depending on the live load factors chosen for LRFR. In their study, relatively low factors were

utilized, therefore minimizing the impact. Larger live load factors, however, will decrease the

LRFR ratings.

11

TABLE 1.1 Analysis Vehicles (Goodrich and Puckett, 2002). Live Load Groups Load Types Live Loads

Truck HS-20 Lane

Design Truck Design tandem Design Truck Train Design Lane

Design

HL-93

Fatigue Truck Type 3 Type 3-3

AASHTO Type

Type 3S2

Legal Lane Legal Lane

P7 Cal Trans P-Loads P11

Permit

Lane Permit Lane

1.2.2 Manual for Condition Evaluation and Load Rating of Highway Bridges Using Load and Resistance Factor Philosophy (Lichtenstein, 2001) and

New AASHTO Guide Manual for Load and Resistance Factor Rating of Highway Bridges (Minervino et al., 2004) A research team led by Lichtenstein Consulting Engineers, Inc. completed a study to

extend the LRFD limit states design philosophy to the evaluation end of the spectrum. In March

of 1997, NCHRP Project 12-46 was initiated to develop a new AASHTO rating manual for

highway bridges based on LRFD. The final draft of the manual was completed in March 2000

and was adopted in 2002 by the AASHTO Subcommittee on Bridges and Structures (Minervino

et al., 2004).

A unique feature of the LRFR manual is that the load rating chapter from the 1994

Manual for Condition Evaluation (which is based on the AASHTO Standard Specifications) was

added as an appendix, therefore creating a single source for all load rating approaches

(Minervino et al., 2004). In addition to the development of the LRFR based manual,

Lichtenstein Consulting Engineers outlined the major differences between the LFR and the

12

LRFR rating procedures so as to instill user confidence. Some aspects of the LRFR approach

leading to different results are:

Three load rating procedures: design, legal, permit.

Calibrated load and resistance factors.

Site-specific load factors for rating purposes.

Introduction of the system and condition factors.

Live load models for evaluation.

Live load distribution factors.

Impact factor (dynamic load allowance).

Load factors for overweight permits.

Serviceability checks.

Member resistances.

The LRFR manual is based on a tiered approach for the various live loads used in rating practice,

as illustrated in figure 1.1. The design load rating is the first level of rating and is a “measure of

the performance of existing bridges to new bridge design standards contained in the LRFD

Specifications” (Minervino et al., 2004). Like LFR, the design rating produced by LRFR is a

suitable value to report to the FHWA. However, the difference lies within LRFR’s capability of

providing screening checks for all AASHTO trucks and the State legal exclusion vehicles in the

US; if the inventory rating factor based on the HL-93 design load is greater than one, then the

bridge’s performance is adequate for legal loads. This is not true under LFR, where the lighter

HS-20 design load is applied. If the initial HL-93 check is not satisfied, legal loads may be

applied using the limit states and live load factors indicated in the LRFR based manual.

13

Overweight permit vehicles may also be considered, but are only applicable if the bridge has

adequate strength to support legal loads.

In a pre-final draft of the LRFR manual, fifteen volunteer states (Alabama, California,

Florida, Idaho, Illinois, Iowa, Massachusetts, Minnesota, New Jersey, New York, Pennsylvania,

Tennessee, Texas, Vermont, and Washington) participated in trial ratings for a variety of bridge

types and sizes. A total of 78 bridges were rated: 43 concrete bridges (21 reinforced and 22

prestressed), 31 steel bridges, and 4 timber bridges (Minervino et al., 2004). The rating results

showed that the design load inventory ratings for LRFR and LFR were comparable, while the

design load operating ratings were lower for LRFR. With respect to the LRFR legal load, the

ratings were generally greater than the LFR ratings for inventory and lower for operating. It is

important to note that the prestressed concrete I-girder bridges demonstrated the widest scatter in

results. In addition, the prestressed concrete bridges were characteristic of lower shear ratings,

where shear normally governed over flexure. Table 1.2 illustrates the governing load effect,

flexure or shear, for the strength limit state in the LRFR trial ratings. Within the table, the

governing load effect pertaining to prestressed concrete is highlighted in order to emphasize the

importance of the shear ratings; the shear ratings generally governed for prestressed concrete,

whereas flexure usually governed for the other bridge types. Unlike LFR, the shear rating factor

at the design level has a noticeable impact under LRFR for most structures and therefore needs to

be considered. The reason being that the heavier HL-93 loading results in larger shear force

effects than the HS-20. Also, the LRFR distribution factors for shear are higher than those used

in LFR, which are based solely on girder spacing. Yet another contributing factor to the

difference in shear rating factors is the use of the Modified Compression Field Theory to

compute the LRFR shear resistance (Lichtenstein, 2001).

14

FIGURE 1.1 LRFR Flow Chart (Minervino et al., 2004).

RF<1

RF<1

DESIGN LOAD CHECK HL-93

DESIGN LEVEL RELIABIILITY

SERVICE STRENGTH NO ACTION REQUIRED

RF>1

IDENTIFY VULNERABLE LIMIT STATES FOR FUTURE

INSPECTION/ MAINTENANCE/ LOAD RATING

RF<1

CHECK OPERATING LEVEL RATING

RF<1

RF<1

RF>1*

RF>1

LEGAL LOAD RATING AASHTO & STATE LOADS

(GENERALIZED LOAD FACTORS) OPERATING LEVEL RELIABILITY

SERVICE STRENGTH SEE LRFR MANUAL

GUIDELINES

RF>1

HIGHER LEVEL EVALUATION (OPTIONAL)

• REFINED ANALYSIS • LOAD TESTING • SITE-SPECIFIC LOAD FACTORS • DIRECT SAFETY ASSESSMENT

RF>1

NO RESTRICTIVE POSTING MAY ALLOW PERMIT LOADS

*OK for AASHTO Legal Loads

LOAD POSTING OR STRENGTHING REQUIRED

NO PERMIT VEHICLES

15

TABLE 1.2 Governing Load Effect (HL-93), (Lichtenstein, 2001).

Material Limit Number of Bridges Percentage Flexure 22 81% Steel Shear 5 19%

Flexure 18 90% Reinforced Concrete Shear 2 10%

Flexure 7 41% Prestressed Concrete Shear 10 59%

Flexure 4 100% Timber Shear 0 0%

Flexure 51 75% Total Shear 17 25%

1.3 Objective The objective of this research is to support the FHWA’s implementation of load and

resistance factor design by initiating the transition from LFR to LRFR in New Mexico. New

Mexico has participated in LRFD workshops in 1999 and 2002; two week courses hosted by the

NMDOT bridge section have provided training in the design of steel and prestressed concrete

bridges based on LRFD guidelines. However, the state has yet to offer similar assistance in

rating bridges in accordance with LRFR. To fulfill this task, five prestressed concrete bridges

from New Mexico’s bridge inventory were rated using BRASS-GIRDER and BRASS-GIRDER

(LRFD). Detailed verification models of both BRASS programs were created to provide a guide

to new users. The selected bridges were then rated for flexure and shear based on the strength

limit state and any outlying trends were identified. Specific objectives of the research reported

herein are outlined below:

Evaluate the BRASS software prior to full implementation by the NMDOT so as to

facilitate the use of the program.

Identify any variables leading to the difference in LFR and LRFR rating factors.

16

Identify any trends in the rating factors as affected by bridge geometry, even though

the sample of bridges is limited.

Identify any questionable bridges within the sample.

Use research findings to provide training, relative to the LRFR method, to the NMDOT.

The ultimate goal of this research is to further educate the bridge engineering community, so as

to provide understanding of the LFR and LRFR rating and design methods.

17

CHAPTER 2

DESCRIPTION AND VERIFICATION OF BRASS SOFTWARE Applicable to this research project is the extensive use of the Bridge Rating & Analysis

of Structural Systems (BRASS) software. BRASS is a family of programs that assist in the

design and rating of structural systems. The BRASS family includes: BRASS-GIRDER,

BRASS-PIER, BRASS-CULVERT, BRASS-TRUSS, BRASS-SPLICE, BRASS-PAD, BRASS-

POLE, and BRASS-DIST. Of these programs, special attention was given to BRASS-GIRDER,

which is used to load rate superstructure elements, in particular the bridge girders, according to

both LFD and LRFD. The software based on LFD is current with the 16th edition of the

AASHTO Standard Specifications for Highway Bridges (1996), including the 1997 thru 2000

Interims. The BRASS-GIRDER (LRFD) software is current with the 2nd edition of the

AASHTO LRFD Bridge Design Specifications (1998), including the 2000 Interim (BRASS-

GIRDER, 2002b; BRASS-GIRDER (LRFD), 2002).

2.1 Software Description BRASS-GIRDER is a program that assists in the design and rating of highway bridge

decks and girders according to the AASHTO specifications, with plane frame analysis for LFD

and finite element theory for LRFD being the basis of the structural analysis. The program is

based on a command format. The user creates an ASCII data file by describing the structure

with a series of commands and their corresponding parameters. For example, the properties of a

prestressed concrete girder with γ=150 lbs/ft3, f’c=6.5 ksi, f’c,slab=4.0 ksi, f’ci=5.5 ksi, Ec=4888.0

ksi, and Ec,slab=3834.0 ksi are described using the command “PROPERTIES-PC1” as follows:

PROPERTIES-PC1 150.0, 6.5, 4.0, 4888.0, 3834.0, 5.5

18

For further details related to the BRASS commands, the reader is referred to the user/command

manuals (BRASS-GIRDER, 2002b; BRASS-GIRDER (LRFD), 2002). The manuals are

organized in such a fashion that information pertaining to a specific bridge descriptor is grouped

in chapters. For example, all information supporting a steel cross-section would be located in a

chapter designated for steel only. Within the manual are command descriptions, command

parameters, examples, figures, and any applicable notes. Most of the commands within BRASS-

GIRDER are order-dependent, whereas with BRASS-GIRDER (LRFD) they are not. Generally,

the user manual is organized so that the commands correspond to the correct placement order in

the input file. In entering a command, the data may be a real (including a decimal point), an

exponential (i.e. 12.345e4), an integer (excluding a decimal point), or an alpha character. Alpha

characters are case insensitive; however, a blank space following the command is required. With

most commands, default entries are an option and are employed by leaving the field blank; zero

is not the same as a blank field. Finally, each command has a three-character abbreviation that

may be used in lieu of the full command name.

To facilitate data entry, a Microsoft Windows based Graphical User Interface (GUI) has

been developed. The GUI may be used to view output files with minimal output; however, the

use of a text editor or word processor is more appropriate and is independent of file size. With

regards to BRASS-GIRDER (LRFD), an assortment of files may be generated upon execution of

the input file. A list and description of such files is provided in table 2.1. Likewise, the LFR

software creates three additional output files (TABLE1.TBL, TABLE2.TBL and TABLE3.TBL)

that are used to insert the results into a database (BRASS-GIRDER, 2002b).

19

TABLE 2.1 Files Generated by BRASS-GIRDER (LRFD). (BRASS-GIRDER (LRFD), 2002). Output File: Filename.OUT

This file contains the main output reports generated from the main executable program. This file is generally named the same as the input data file except it is given a different extension. The Output chapter commands control the various output reports that are sent to this file.

Program Error File: Filename.ERR

If an error occurred while running the main program, this file will be created. This file lists the errors and indicates the source of the problem.

X-Y Plot Files: LRFD-TBL.P01 to LRFD-TBL.P03

These files contain unfactored dead load, unfactored live load, and combined force effects produced by the program in the form of x-y data. These files are related tables and may be imported into a spreadsheet program or relational database to produce x-y plots.

AASHTO Specifications Result Files: LRFD-TBL.S01 to LRFD-TBL.S08

These files contain the results of the AASHTO specification checks performed by the program. These files are related tables and may be imported into a relational database to generate queries, forms, and reports.

Mesh Plot File: LRFD-TBL.MSH

This file contains the x- and y-coordinates of the structural analysis mesh.

Drawing File: LRFD-PLT.DXF

This DXF file contains the drawing x- and y-coordinates of the structural analysis mesh.

DL and LL Distribution File: Filename.DST

This file contains intermediate output for dead load distribution and live load distribution factor computations. The OUTPUT-DIST-DL and OUTPUT-DIST-LL commands control the output for this file.

Shear Connector File: Filename.SHR

This file contains detailed intermediate output for shear connector computations. This file is only applicable to steel structures. The OUTPUT-SHEAR-CONN command controls the output for this file.

Prestress File: Filename.PS

This file contains intermediate output for load balancing, prestress loss, prestress action loss, and stress computations. This file is only applicable to prestressed concrete structures. The OUTPUT-PRESTRESS command controls the output for this file.

20

TABLE 2.1 Files Generated by BRASS-GIRDER (LRFD), Continued.

Point of Interest Files: Filename(000.000).OUT

These files contain detailed intermediate output for AASHTO specification checks, and load factoring / load combination computations. These files are designed to contain output for a single point of interest. The file name addition (listed in parentheses) is constructed from the point of interest input by the user; for example, Point of Interest: 104.0 File Name: Filename(104.000).OUT

To gain confidence in the use of this program, verification ratings for both the LFD and

LRFD methods were deemed necessary. To not only execute the BRASS software, but to

understand and know that it is yielding accurate output was considered very important to the

validity of this research.

2.2 Software Verification In verifying the BRASS software, hand computations based on design examples provided

in the Prestressed Concrete Institute (PCI) Bridge Design Manual (1997) were compared to load

ratings generated by BRASS-GIRDER and BRASS-GIRDER (LRFD). The reader is referred to

appendix A and B for rating computations and BRASS Input files. As a documented source, the

PCI examples provide strength to the verification process. The examples, found in sections 9.3

and 9.4 of the PCI Bridge Design Manual (1997), illustrate the design process for a prestressed

concrete girder bridge according to the AASHTO Standard Specifications for Highway Bridges

(1996) and the AASHTO LRFD Bridge Design Specifications (1998). These design examples

demonstrate the design of an interior girder for a 120 ft. single-span bridge. The superstructure

consists of six prestressed concrete bulb-tee (BT-72) girders spaced at 9 ft. on center and are

designed to act compositely with an 8 inch reinforced concrete deck. Pertinent information

21

regarding the design is given in figure 2.1. Based on hand computations, the bridge girders were

rated using design information from the two PCI examples; the ratings were performed in

accordance with the Manual for Condition Evaluation of Bridges (1994) and the Manual for

Condition Evaluation and Load Rating of Highway Bridges using Load and Resistance Factor

Philosophy (Lichtenstein, 2001; Minervino, 2004). A comparative discussion of the BRASS

analysis and the hand computations is provided in sections 2.2.1 and 2.2.2 of this thesis.

2.2.1 BRASS-GIRDER To initiate the verification process, an input file was created in BRASS-GIRDER. As an

aid to the reader, in particular unfamiliar users of the BRASS software, the input file based off of

PCI Example 9.3 is illustrated in figure 2.2. Outlined in red are the descriptions of the data

input. Much of the input is self-explanatory; however, special attention needs to be given to the

XSECT commands. Bulb-tee cross-sections are not in the section library; therefore, the

commands XSECT-A thru XSECT-E are required to describe the dimensions of the section. If

the desired member is in the section library, then the user can employ a command for standard

cross-sections and thus simplify the input process. Note that the section library can be updated

and maintained by the user.

22

FIGURE 2.1 PCI Example Bridge Description.

Bridge Cross-Section Cast-in-place slab: Actual Thickness, ts = 8.0 in. Structural Thickness = 7.5 in. Concrete strength at 28 days, f’c = 4,000 psi Precast beams: AASHTO-PCI BT-72 Concrete strength at release, f’ci = 5,500 psi Concrete strength at 28 days, f’c = 6,500 psi Concrete unit weight = 150 pcf Overall beam length = 121 ft. Design Span = 120 ft. Pretensioning strands: ½ in. diameter, seven wire, low relaxation Area of one strand = 0.153 in.2 Ultimate stress, f’s = 270,000 psi Yield strength, f*y = 0.9f’s = 243,000 psi Initial pretensioning, fsi = 0.75f’s = 202,500 psi Modulus of Elasticity, Es = 28,500 psi Reinforcing bars: Yield strength, fy = 60,000 psi Future wearing surface: additional 2 in. with unit weight = 150 pcf New Jersey-type barrier weight = 300 lbs/ft/side

23

With regards to the BRASS output, composite section properties are calculated with the

exclusion of the haunch. All other beam properties, girder actions, member capacities and rating

factors were repeatable, with the exception of the serviceability rating factor. Comparisons of

the hand calculations versus the BRASS output are presented in table 2.2, with the computer

output being the number in parenthesis and the hand computations residing above that.

The values reported in table 2.2 were evaluated at the critical sections, which are 3.33 ft. from

the end of the beam for shear and midspan for moment. Rating factors, as well as the

components comprising the rating factor equation were evaluated. It is important to note that

within the BRASS output the load and resistance factors are internal in the summary of factored

dead load and live load actions; refer to equation 1.1, as reiterated below.

For illustrative purposes, the dead load effect for the inventory shear rating computed by hand

was A1D = 1.3(114.5) = 148.9 kips. The BRASS output yielded a non-composite dead load

effect of 126.8 kips plus a composite dead load effect of 22.10 kips, totaling a dead load effect of

148.9 kips.

RF C A DA L I

=−

+1

2 1( )

Dead Load Effect

Live Load Effect

FIGURE 2.2 PCI Example 9.3 (LFR) BRASS Input.

24

TABLE 2.2 PCI Example 9.3, Comparison of Hand Calculations vs. BRASS Output. Shear a Moment a

Inventory Operating Inventory Operating ServiceabilityCapacity 315.8

(315.1) 10,660 (10,660)

5,729 (------)

DL Effect 148.9 (148.9)

4,729 (4,729)

3,637 (------)

LL Effect 137.6 (138.2)

82.45 (82.80)

4,019 (4,044)

2,408 (2,421)

1,852 (------)

Rating Factor 1.21 (1.20)

2.02 (2.00)

1.48 (1.46)

2.46 (2.44)

1.13 (0.94)

Note. Hand Calculations/(BRASS Output) a Units: the shear is in kips, the moment is in k-ft and the rating factors are unitless.

To better compare the accuracy of the rating factors, the percent deviation was considered

(see figure 2.3). The serviceability rating factor differed by 16.7 percent and was thus,

considered inaccurate. Extended efforts were made to verify the serviceability rating factor, but

were unsuccessful; the findings will be reported to the Wyoming DOT. The strength based

rating factors were within 1.2 percent. Because the serviceability rating factor could not be

verified, only strength was considered in this research.

25

FIGURE 2.3 Percent Deviation in Rating Factors, Hand Calculations vs. BRASS Output (PCI Example 9.3).

2.2.2 BRASS-GIRDER (LRFD) An input file representative of PCI Example 9.4 was created using BRASS-GIRDER

(LRFD) and is illustrated in figure 2.4. As before, certain parameters have been described to

help the reader better understand the input and its format. Commands and parameters not

discussed can be reviewed in the BRASS-GIRDER (LRFD) user manual (BRASS-GIRDER

(LRFD), 2002).

Special attention is directed to a number of the commands. The first command of special

significance is the command PRESTRESS-CONTINUITY. This required command specifies

the continuity of the structure by coding one of three options: SC = simple or continuous spans

only; CA = simple spans made continuous by composite action and non-prestress reinforcement;

and AP = pretensioned simple spans made continuous by post-tensioning additional strands.

With the bridge under consideration being a simple span, SC seems to be the applicable code.

1.1 1.2 1.0 0.9

16.7

0

2

4

6

8

10

12

14

16

18

Perc

ent

RFv,inv RFv,oper RFm,inv RFm,oper RFm,serv

PCI Example 9.3, Percent DeviationHand Calculations Vs. BRASS Output

26

Upon execution of the file, errors were reported and the analysis was terminated. The errors

implied that the code AP was required when a three-stage construction was specified under the

ANALYSIS command. When revised, the analysis of the input file was successful.

28

TITLE PCI Example 9.4 - LRFD COMMENT Prestressed concrete girder bridge COMMENT ANALYSIS B, 3, RAT, S POINT-OF-INTEREST T, ON, ON ANALYSIS-SPECIAL 1, 72 DIST-CONTROL-GIRDER 2 DIST-CONTROL-DL TA, UD DIST-CONTROL-LL K, , 0, , NO DIST-LL-APPLICATION AP MAP-LIMIT-STATE ST, 1, I, N, N MAP-LIMIT-STATE ST, 2, O, N, N MAP-SPEC-CHECK ST, 1, D, FLX, Y MAP-SPEC-CHECK ST, 1, D, SHR, Y MAP-SPEC-CHECK ST, 2, D, FLX, Y MAP-SPEC-CHECK ST, 2, D, SHR, Y OUTPUT 2, YES DECK-GEOMETRY 6, 9*12, 7.5, 3*12, , 0.5, DC SOFFIT-INTERIOR .5, 21, 21 SOFFIT-LT-EXT .5, 21, 21, .5, 21, 21 SOFFIT-RT-EXT .5, 21, 21, .5, 21, 21 DECK-TRAVEL-WAY 18, 594 DECK-MATL-PROPERTIES 0.15, .15, .025 DECK-LOAD-DESCR 1, DC, 2, BARRIERS-2 DECK-LOAD-UNIFORM 1, .6, 0, 1*12 DECK-STAGE 1, , , 2 CONC-MATERIALS .150, 6.5, 60, 60, 6, 4887.733, , , , NO, .00065 CONC-I-SECTION 1, 42, 3.5, 6, 6, 26, 6 CONC-FILLETS 1, 2, 0, 2, 2, 0, 0, 4.5, 10 CONC-SHEAR 100.5, 4, , , .4, 12, 90, 72, , 2.6, 22 CONC-SHEAR-CONSTANTS 3 COMMENT STIRRUPS ARE DEFINED AS GROUP 1 STIRRUP-GROUP 1, .4 STIRRUP-SCHEDULE 1, 1, 12, 0, PRESTRESS-MATERIALS 5.8, 6, 70, , 4617.053 PRESTRESS-CONTINUITY AP PS-BEAM-OVERHANG 1, 6, 6 LOSS-AASHTO-PRETEN 1, .5, .325, , , STRAND-MATL-PRETEN 1, .153, LR, 270, 243, 28500, .75, , , , .5 STRAND-GENERAL 1, 1, 1, 12, 1 STRAND-STRAIGHT 1, 1, 70, N, 1, 2 STRAND-GENERAL 1, 3, 1, 8, 1 STRAND-STRAIGHT 1, 3, 66, N, 0, 0 STRAND-GENERAL 1, 4, 1, 4, 1 STRAND-STRAIGHT 1, 4, 64, N, 0, 0 STRAND-GENERAL 1, 5, 1, 2, 1 STRAND-HARPED 1, 5, 12.515, 62, 12.515, 48*12, 72*12, 5, 2, 2 STRAND-DEV-LENGTH 1, ALL, COMPOSITE-SLAB 1, 108, 7.5, .5 SPAN-LINEAR 1, 120*12, 62.5, 62.5 SPAN-SECTION 1, 1, 120*12, 1 SUPPORT-FIXITY 1, R, R, F SUPPORT-FIXITY 2, F, R, F LOAD-LIVE-CONTROL B, D

Defines the Effective flange width, slab thickness, and haunch thickness.

Defines γ - deck, γ - curbs & median, and wearing surface weight.

Defines the thickness and tapers (if any) of the haunch. If tapers do not exist, the distance from the centerline of the girder to the beginning and end of the taper is equal to half the girder width.

Defines the # of girders, girder spacing, slab thickness, left and right cantilevers, sacrificial topping thickness, and the type of topping DL.

Defines the left and right edge of the deck’s travel way.

Describes the top flange width and thickness, top and bottom web thickness, and the bottom flange width and thickness.

Defines the POI, shear indicator, stirrup area, stirrup spacing, stirrup angle, shear distance and user defined beta and theta.

Stirrup Group 1, stirrup area, and stirrup spacing.

Defines strand area, strand type, fpu, fpy, and Ep.

Describes the layout of the straight and harped prestressed strands; includes row #, number of strands, distance to centroid, distance to harp points, etc.

Defines f’ci, modular ratio, RH, and Eci.

Defines the span length and the web depth at the right and left ends of the span. Web depth includes the height of the tapers and fillets.

Defines the horizontal, vertical and rotational reactions at the left and right supports.

Defines the density of the concrete, f’c, fy, fys, n, Ec, etc.

Defines the girder of interest, with girder 2 being an interior girder.

FIGURE 2.4 Example 9.4 (LRFR) BRASS Input.

29

The second command of interest is CONC-SHEAR, which is used to control the

calculation of the shear resistance. The second parameter of this command, the shear indicator,

greatly affects the resulting capacity. Four options regarding the type of shear analysis to be

performed are available to the engineer. The options include: 1 = ignore shear; 2 = simplified

procedure; 3 = general procedure; and 4 = user defined beta and theta. The simplified

procedure, in accordance with AASHTO LRFD Article 5.8.3.4.1, uses fixed values of beta (β =

2) and theta (θ = 45o), whereas with the general procedure (AASHTO LRFD Article 5.8.3.4.2)

the values of beta and theta vary along the length of the span1. As noted in the PCI Bridge

Design Manual (1997), the shear design based on the Modified Compression Field Theory

(MCFT) depends on the angle of the compressive stresses (theta) at the particular point of

interest along the girder. Generally, the angle theta ranges from 22o to 30o in areas of high shear

forces and low bending moments; areas with low shear forces and high bending moments yield

larger angles up to a limit of 45o. To conform to PCI Example 9.4 (PCI, 1997), the general

procedure was initially used in the input file. Upon execution of the data file, all values, with the

exception of the shear resistance, correlated well with the hand calculations. The shear

resistance generated by BRASS, at the critical section, deviated from the hand computations by

17.7 percent. Further investigation of the shear resistance resulted in comparable numbers when

the simplified procedure was employed; the percent deviation decreased from 17.7 percent to 5.0

percent. However, the simplified procedure underestimates the shear resistance. For this

example, the shear resistance based on the MCFT was twice as large as that computed with the

simplified procedure. Thus, it is to the engineer’s advantage to make use of the newer

technology. To incorporate the advances in shear design, hand calculated values of beta and 1 Theta = angle of inclination of diagonal compressive stresses (PCI, 1997). Beta = a factor indicating the ability of diagonally cracked concrete to transmit tension (PCI, 1997).

30

theta were entered into BRASS using option four (user defined beta and theta). The results

yielded a 0.3 percent variance between the hand calculations and the BRASS output. Table 2.3

compares the shear resistances obtained from the various computer procedures to that of the hand

calculations for Strength I. Basically, a software error linked to the computation of beta and

theta resulted in a disagreement between the BRASS output and the hand computations; this

oversight will be reported to the Wyoming DOT. Based on these results, a user defined beta and

Table 2.3 Shear Resistance, Comparison of Hand Calculations vs. BRASS Output. Analysis Type Shear Resistance Calculated at:

Simplified Procedure (θ = 45, β = 2)

150.9 kips End of the span

General Procedure (θ, β vary)a

288.9 kips Critical section

BRASS output

User Defined θ, β (θ = 22, β = 2.6)a

352.1 kips Critical section

(θ = 45, β = 2) 158.9 kips End of the span Hand Calculations (θ = 22, β = 2.6)a 351.1 kips Critical section

a Beta and theta are calculated with respect to the Modified Compression Field Theory. theta was utilized for the remainder of this study. The CONC-SHEAR command is only applicable to the point of interest defined in

parameter one; for the PCI Example 9.4 input file, the critical section for shear (100.5) was

defined as the point of interest. If the simplified or general procedures are to be used, the

CONC-SHEAR-CONSTANTS command may be used to define the analysis type at all tenth

points along the span. However, since the general procedure could not be verified due to a

potential bug, user defined values of beta and theta must be input at any desired point of interest

using the command CONC-SHEAR. Since the determination of beta and theta is an iterative

process, only the critical sections were considered for the shear ratings in this study. Research

conducted by Goodrich and Puckett (2002) confirmed that the shear ratings were lowest at the

critical section.

31

Within the philosophy of the MCFT, the shear resistance is dependent upon the applied

loads, as illustrated in figure 2.5. The figure presents a tiered approach that links the ultimate

load effects (Mu, Vu and Nu) to the determination of theta and beta, which in turn affect the shear

resistance (φVn). Given the direct correlation to the applied loads, the shear resistance has two

values (one based on the minimum load factors and the other on the maximum). Applying the

same reasoning, the shear resistance will differ between the Strength I and Strength II limit states

due to the different live load factors. When using a user defined beta and theta, it is important to

keep track of which limit state (Strength I or II) and load factors (maximum or minimum) are

being used. Since the assigned beta and theta are fixed in the BRASS analysis, the values

entered will be applied to all limit states. For example, if the hand calculated values of beta and

theta are based on Strength I with maximum load factors, the shear resistance corresponding to

this limit state will also be used for Strength II. This, however, is incorrect since the live load

factor for Strength I and Strength II differ. Therefore, only the rating factor computed for

Strength I is correct. If a Strength II rating factor is desired, a separate pair of beta and theta

values will have to be defined.

Rating factors, as well as each component in the rating factor equation are reported in

table 2.4, with the BRASS output given in parenthesis. As before, only the critical sections were

evaluated; the critical section for shear was 6 ft. from the end of the beam, whereas for moment,

the midspan was considered. Note that the critical section for shear differs between LFR and

LRFR. In addition, the BRASS results are dependent upon user defined values of beta and theta,

which were found to be 2.6 and 22o, respectively. Since beta and theta were calculated using the

maximum load factors relative to Strength I, this will be the only limit state reported. Finally,

the summary of dead load and live load actions produced by BRASS include the load and

32

resistance factors. As with LFR, Equation 1.2 is restated to illustrate the terms within the

BRASS output; for example, the dead load effect reported by BRASS is (γDCDC + γDWDW).

LRFR reports only one value for the dead load parameter, whereas with LFR, the dead load is

divided into composite and non-composite load effects.

Dead Load Effect

Live Load Effect

RF C DC DWLL IMLRFR

DC DW

L

=− −

+γ γγ ( )1

33

FIGURE 2.5 Correlation between Shear Resistance and Applied Loading. The rating factors (BRASS vs. hand computations) differed by only 3.1 percent for shear

and 0.3 percent for moment. Thus, it is concluded that the BRASS-GIRDER (LRFD) software

generates accurate results under the premise that the shear resistance is determined by means of a

user defined beta and theta. With the complexities of the MCFT, it appears that an internal error

φ φV V V Vn c s p= + +d i

VA f d

ssv y v=

cotθV f b dc c v v= 0 0316. 'β

Determination of θ and β is dependent upon εx and v/f’c .

vV V

A

M d N V A fE A E A

u p

xu v u u ps ps

s s p ps

=−

=+ + −

+≤

φφ

εθ05 05

0 002. . cot

.

Mu, Nu and Vu are load dependent and are therefore affected by the load factors used.

γDC γDW γLL

Max. 1.25 1.50 1.75 Strength I Min. 0.90 0.65 1.75

Max. 1.25 1.50 1.35 Strength II Min. 0.90 0.65 1.35

34

relating to the determination of beta and theta exists in the computer software; this finding will

be reported to the Wyoming DOT.

TABLE 2.4 PCI Example 9.4, Comparison of Hand Calculations vs. BRASS Output.

Shear Moment Strength I Strength I

Capacity 351.1 (352.1)

11,360 (11,360)

DL Effect 138.7 (139.1)

4,637 (4,637)

LL Effect 188.4 (183.3)

4,678 (4,691)

Design Ratio 1.073 (1.090)

1.220 (1.220)

Rating Factor 1.127 (1.162)

1.438 (1.434)

Note. Hand Calculations/(BRASS Output)

It is important to note that BRASS-GIRDER (LRFD) reports a design ratio rather than a rating

factor. The design ratio is the ratio of the resistance to the total load effects and is not equivalent

to a rating factor. The rating factor, however, can easily be determined given the capacity, dead

load effect and live load effect. Comparisons of a design ratio versus a rating factor are

illustrated in the equations below.

35

2.3 Application of Software

With the verification of the BRASS software, these programs will be used as a tool in

rating five prestressed concrete girder bridges located in New Mexico. The ratings will be

performed for both LFR and LRFR so that comparisons can be made. Rating factors, capacities,

dead load effects and live load effects will all be of consideration in identifying any trends and

differences among the two rating methods.

Resistance

Total Load Effects (Dead Load + Live Load)

DR CDC DW LL IMLRFR

DC DW L

=+ + +( ) ( )γ γ γ 1

Dead Load Effect

Live Load Effect

RF C DC DWLL IMLRFR

DC DW

L

=− −

+γ γγ ( )1

36

37

CHAPTER 3

BRIDGE DESCRIPTION Extracted from the NM bridge inventory, five prestressed concrete girder bridges were

selected for the comparative analysis of LFR and LRFR. The choice bridges are located along I-

10 and I-40, as illustrated in figure 3.1. Common characteristics among the five bridges are that

they are all simple spans with pretensioned girders and harped strands. All of the girders, with

the exception of those for Bridge 8852, were designed with a concrete compressive strength of 5

ksi and an initial strength of 4.5 ksi; the girders for Bridge 8852 were designed with a greater

compressive strength of 5.5 ksi and an initial strength of 4.75 ksi. All five bridges encompass a

3 ksi compressive strength for the deck concrete. Finally, the structures were chosen with

varying span lengths ranging from 38 ¼ ft. to 107 ft.; in general, a step size of approximately 20

ft. was used. Detailed descriptions of each individual bridge are provided in the

following paragraphs.

3.1 Bridge 7169

Acting as a vital link on Interstate-10 since 1970, Bridge 7169 provides a means of

transportation over NM highway 359. Span 3 of the eastbound bridge was considered for

analysis. Five AASHTO-II girders, spaced at 9 ¾ ft. on center, provide structure for the 38 ¼ ft.

span viaduct. Six inch overhangs result in a total beam length of 39 ¼ ft. The 45 ft. wide deck

has a nominal thickness of 7 9⁄16 inches with a 5⁄16 inch integral wearing surface. In addition, the

deck geometry consists of a 30o skew. Each girder is comprised of 18 stress-relieved strands, 4

of which are harped; a nominal strand diameter of 7⁄16 in. and a harp length of 14 ft.-2 ½ in. from

the beam’s end were used. Transverse reinforcement consists of #4 double leg stirrups with a

yield stress of 40 ksi. As noted in Chapter 2, the shear analysis will only be conducted at the

38

critical section; hence, a stirrup spacing of ten inches spans the region of interest. Finally, the

deck includes a future wearing surface of 15 lbs/ft2 and type “A” bridge rails.

3.2 Bridge 7390 Designed in 1973, Bridge 7390 carries eastbound traffic on Interstate-10 over Animas

Street, located in the southwest region of New Mexico. The second of three spans has a length

of 58 ¾ ft. with 6 inch left and right overhangs. The superstructure consists of six AASHTO-III,

prestressed concrete girders with an unequal bay spacing. The first four bays are spaced at 9 ft.-

1 in. on center, while the spacing of the fifth bay varies between 8 ft.-1 7⁄16 in. to 8 ft.-11 1⁄8 in.

As a result of the varying bay length, as well as inconsistent overhangs, an unequal deck width is

present. Using the larger spacing for bay five and an average overhang width, an approximate

deck width of 52 ft.-1⁄4 in. was used; note that the larger spacing (8 ft.-11 1⁄8 in) for bay five

contributes to a greater dead load. On the same note, BRASS-GIRDER (LRFD) is capable of

recognizing an unequal bay spacing under the premise that the girders are parallel along the

entire length of the bridge, whereas BRASS-GIRDER is not. Thus, only an interior girder with a

spacing of 9 ft.-1 in. is considered for this analysis. Finally, the deck has a thickness of 8 inches

and an approximate skew of 20o. The prestressing strands were stress relieved with a ½ inch

diameter. Twenty strands, 16 straight and 4 harped, were used along with a harp length of 21 ft.-

6 ½ in. from the beam’s end. Transverse reinforcement consisted of #4 double leg bars spaced at

8 inches in the region of the critical section; a yield stress of 40 ksi was specified. Lastly, type

“A” bridge rails and a future wearing surface of 15 lbs/ft2 were applied.

39

FIGURE 3.1 Location of Bridge Sample, NM Map.

3.3 Bridge 7171 Built in 1970, Bridge 7171 located over the Rio Grande River in southern New Mexico

consists of twelve simple spans, all of which are similar. Each span has a length of 80 ft.-6 ¼ in.

with six inches of overhang on each end of the beam. The superstructure consists of seven

AASHTO-III, prestressed concrete girders spaced at 6 ft.-8 in. on center and are designed to act

Bridge 7169 I-10 MP 136.950

Bridge 7171 I-10 MP 138.060

Bridge 7390 I-10 MP 22.970

Bridge 7195 I-40 MP 277

Bridge 8852 I-40 MP 17.570

40

compositely with the 6 7⁄16 inch deck. In addition, 5⁄16 inch is specified for the integral wearing

surface. The deck is 45 ft. wide with a 20o skew. The prestressing force results from 38 stress-

relieved strands, eight of which are harped. The strands have a diameter of 7⁄16 inch and a harp

length of 29 ft.-1 1⁄8 in. from the end of the beam. Transverse reinforcement consists of #4

double leg stirrups, a yield stress of 40 ksi, and a stirrup spacing of 15.25 inches.

3.4 Bridge 8852

Bridge 8852, designed in 1992, is a one span bridge located on Interstate-40 over West

Yard Arroyo. The 97 ft. span is supported by six AASHTO-IV beams spaced at 7 ft. on center.

The girder concrete has a compressive strength of 5.5 ksi and an initial strength of 4.75 ksi. The

deck has a thickness of 8 inches, a width of 41 ft., and an approximate skew of 19o. The girders

are prestressed with 44 strands, 10 harped and 34 straight. Half inch diameter, low-relaxation

strands are used. Furthermore, a harp length of 34 ft.-10 in. from the beam’s end is specified in

the bridge plans. In addition, #4 double leg stirrups, with a yield stress of 40 ksi, are provided at

a spacing of 4 inches. Finally, the bridge has a future wearing surface of 30 lbs/ft2 and concrete

barriers.

3.5 Bridge 7195 Bridge 7195 completes the junction of Interstate-40 and US-84 in northeastern New

Mexico. Designed in 1970, this three span bridge lends the longest span of 107 ft. to this

research project. The superstructure is comprised of five AASHTO-V girders spaced at 9 ft.-7

in. on center. The deck has a width of 45 ft. and a thickness of 7 ¼ inches. An approximate

skew of 21o is present. The girders contain 62 stress-relieved strands, 18 harped and 44 straight.

A strand diameter of 7⁄16 inch is used. Transverse reinforcement includes #4 double leg bars with

41

a yield stress of 40 ksi. In addition, a stirrup spacing of 11 inches is specified. Finally, a future

wearing surface of 15 lbs/ft2 and type “A” barriers are applied.

3.6 Effects of Skew It is important to observe that all five of the bridges selected for analysis were designed

with a skew. Generally the skew angles were small; however, the skew for Bridge 7169 was

considerable. Thus, it is important to understand the effects of skew and how it is accounted for

under the bridge design specifications. The AASHTO Standard Bridge Specifications consider

only non-skewed bridges, whereas the LRFD Bridge Design Specifications address the issue for

skew angles greater than or equal to 30 degrees (PCI, 1997). Further investigation of the effects

of skew was conducted by Barr et al. (2001). The authors’ research compared the effects of

distribution factors at various skew angles to ones with zero skew; skew angles up to 60o were

considered. Findings showed that skews less than 20o had little effect on the distribution factors.

At larger skew angles, however, a noticeable decrease in live load distribution factors was

observed. In addition, a comparison of the AASHTO LRFD skew factor yielded comparable

distribution factors, therefore concluding that the LRFD approach is a reasonable approximation.

Finally, it is important to note that skew is accounted for in the BRASS-GIRDER (LRFD)

software.

With the exception of Bridge 7169, the effects of skew are negligible. Bridge 7169 was

designed with a skew of 30o and will therefore be accounted for under the LRFR guide

specifications. Note that within the study conducted by Barr et al., a skew of 30o resulted in a

decrease in the distribution factors of approximately 2.5%.

42

43

CHAPTER 4

RESULTS The five bridges described in chapter 3 were rated according to LFR and LRFR for the

purposes of comparing the different guide specifications. The rating factors, as well as the

individual parameters comprising the rating factor equation, are evaluated within this chapter.

Primary factors under consideration are the rating factor, member resistance, dead load effect,

and live load effect. Upon evaluation, differences among the rating methods and any trends

based on bridge geometry are to be considered.

The ratings were computed using the BRASS software. As mentioned in chapter 2,

errors relating to the Modified Compression Field Theory in BRASS-GIRDER (LRFD) required

that user defined values of beta and theta be applied. Since this error solely affected the shear

resistance, the load effects required to compute beta and theta could still be obtained from the

initial output. The load effects and all other necessary information were entered into an excel

spreadsheet, where an iterative process in conjunction with AASHTO (LRFD) table 5.8.3.4.2-1

produced refined values of beta, theta, and the critical section. These values were then re-entered

into the BRASS data file and a final analysis was executed. It is important to note that the shear

analysis was restricted to the critical section due to the iterative process. This complimented the

study by Goodrich and Puckett (2002), where the rating factor was smallest at the critical

section. Thus, the load effects entered into the spreadsheet are representative of this point of

interest. In addition, the load effects vary with respect to the different limit states; thus, the

iterative process for computing beta and theta was conducted for both Strength I and Strength II.

Table 4.1 summarizes the parameters used in the LRFR shear analysis.

44

TABLE 4.1 LRFR Shear Parameters.

Bridge ID Shear Parameters

Limit State 7195 8852 7171 7390 7169

Strength I 2.545

2.940

2.585 2.482 2.039Beta

Strength II

2.623

5.390

2.786 2.969 2.500

Strength I 25.17 21.67 24.14 28.32 33.79Theta Strength

II 23.35 22.94 22.27 23.48 27.90

Strength I 100.42 100.49 100.44 100.60 100.73Critical Section a Strength

II 100.46 100.46 100.48 100.70 100.73

a The critical section is relative to the span length. For instance, the point of interest 101.0 refers to the first tenth point along the span length.

In table 4.1, as well as all tables and figures to follow, the bridges decrease in span length from

left to right. Note that the critical section, relative to the span length, is generally larger for the

shorter spans. The angle of compressive stresses (theta) is governed by the location of the

critical section and generally ranges from 22o near the beam’s end to 45o near the beam’s

centerline. The shorter spans experienced larger angles of theta since the critical section is

further from the support (relative to the span length). In addition, an indirect correlation between

beta and theta yields larger values of beta for smaller angles of theta more often than not.

Smaller angles of theta and larger values of beta result in an increase in shear resistance by

affecting the contribution of the transverse reinforcement and concrete, respectively. The LFR

method constitutes an angle of 45o at all locations along the bridge and does not consider beta.

Upon completion of the data files, the BRASS output was filtered and organized into a

series of figures and tables (See figures 4.1 thru 4.7 and appendix C, tables 1 thru 14).

The figures consider only the critical sections, where the midspan controls the flexure ratings and

45

the critical sections relative to shear are listed in table 4.2. The tables regarding flexure (in

appendix C) contain output at each tenth point along the span.

TABLE 4.2 Critical Sections for Shear.

Bridge ID Method Level / Limit State

7195 8852 7171 7390 7169

LFR Inv. / Oper. 100.27 100.46 100.26 100.38 100.95

Strength I 100.42 100.49 100.44 100.60 100.73 LRFR Strength

II 100.46 100.46 100.48 100.70 100.73

Figures 4.1 and 4.2 illustrate the LFR and LRFR rating factors for flexure and shear,

respectively. Each figure contains two bar graphs, one for Inventory/Strength I and the other for

Operating/Strength II. The graphical comparison shows moderate differences among LFR and

LRFR, with the Operating/Strength II ratings demonstrating the largest deviations. With the

exception of the Inventory/Strength I ratings for Bridge 7169, LRFR yielded lower rating factors

for flexure. Likewise, the shear rating factors were lower for LRFR, not including the outlier,

Bridge 7390. Bridge 7390 resulted in greater LRFR ratings for both Inventory/Strength I and

Operating/Strength II. Note that the inconsistent ratings are relative to the shorter span bridges.

The flexure ratings showed that the bridges were adequate with regards to strength (i.e. RF > 1)

based on LFR and LRFR. A number of the shear ratings, on the other hand, produced rating

factors less than one; the inadequate LFR ratings showed less variance from a rating factor of

one than that of the LRFR rating factors. Finally, the shear based rating factors generally

controlled over flexure. The flexure ratings for Bridge 8852 controlled over shear for

Inventory/Strength I and Operating/Strength II, while the flexure rating for Bridge 7390

dominated the Operating/Strength II limit state.

46

The results indicate a difference in rating factors among LFR and LRFR, but do not

identify the source of the dissension. Thus, the individual parameters comprising the rating

factor equation were studied in detail. Figures 4.3 thru 4.7 compare the live load effects, dead

load effects and resistances computed by LFR and LRFR. Further investigation of these

parameters and their effects on the rating factors are explained in sections 4.1 thru 4.3. Finally,

the contribution of each parameter to the rating factor is analyzed in section 4.4.

47

1.45

1.30

1.98

1.66

1.44

1.241.31 1.29 1.29

1.40

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

1.80

2.00

Rat

ing

Fact

or

7195 8852 7171 7390 7169

Bridge ID

Critical Rating Factors: FlexureInventory/Strength I

LFR LRFR

2.43

1.68

3.31

2.15

2.40

1.61

2.19

1.67

2.16

1.81

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

Rat

ing

Fact

or

7195 8852 7171 7390 7169

Bridge ID

Critical Rating Factor: Flexure Operating/Strength II

LFR LRFR

Figure 4.1 Critical Rating Factors: Flexure.

48

1.03

0.52

2.692.56

1.06

0.57

0.96 1.000.86

0.59

0.00

0.50

1.00

1.50

2.00

2.50

3.00R

atin

g Fa

ctor

7195 8852 7171 7390 7169

Bridge ID

Critical Rating Factors: Shear Inventory/Strength I

LFR LRFR

1.73

0.79

3.89

3.31

1.62

0.85

1.601.74

1.45

1.03

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

Rat

ing

Fact

or

7195 8852 7171 7390 7169Bridge ID

Critical Rating Factors: Shear Operating/Strength II

LFR LRFR

FIGURE 4.2 Critical Rating Factors: Shear.

49

0

500

1000

1500

2000

2500

3000

3500

4000

4500L

L E

ffec

t, k-

ft

7195 8852 7171 7390 7169

Bridge ID

Critical Live Load Effect: FlexureInventory/Strength I

LFR LRFR

0

500

1000

1500

2000

2500

3000

3500

LL

Eff

ect,

k-ft

7195 8852 7171 7390 7169

Bridge ID

Critical Live Load Effect: Flexure Operating/Strength II

LFR LRFR

FIGURE 4.3 Critical Live Load Effect: Flexure.

50

0

20

40

60

80

100

120

140

160

180

200L

L E

ffect

, kip

s

7195 8852 7171 7390 7169

Bridge ID

Critical Live Load Effect: Shear Inventory/Strength I

LFR LRFR

0

20

40

60

80

100

120

140

160

LL

Effe

ct, k

ips

7195 8852 7171 7390 7169

Bridge ID

Critical Live Load Effect: Shear Operating/Strength II

LFR LRFR

FIGURE 4.4 Critical Live Load Effect: Shear.

51

0

500

1000

1500

2000

2500

3000

3500

4000D

ead

Loa

d E

ffec

t, k-

ft

7195 8852 7171 7390 7169

Bridge ID

Critical Dead Load Effect: Flexure

LFR LRFR

0

20

40

60

80

100

120

140

Dea

d L

oad

Effe

ct, k

ips

7195 8852 7171 7390 7169

Bridge ID

Critical Dead Load Effect: Shear

LFR LRFR

FIGURE 4.5 Critical Dead Load Effect.

52

0

50

100

150

200

250

300

350

400

450

500R

esis

tanc

e, k

ips

7195 8852 7171 7390 7169

Bridge ID

Critical Resistance: Shear Inventory/Strength I

LFR LRFR

0

50

100

150

200

250

300

350

400

450

500

Res

istan

ce, k

ips

7195 8852 7171 7390 7169

Bridge ID

Critical Resistance: Shear Operating/Strength II

LFR LRFR

FIGURE 4.6 Critical Resistance: Shear.

53

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000R

esis

tanc

e, k

-ft

7195 8852 7171 7390 7169

Bridge ID

Critical Resistance: Flexure

LFR LRFR

FIGURE 4.7 Critical Resistance: Flexure.

4.1 Discussion of Live Load Effects As illustrated in figures 4.3 and 4.4, the LRFR live load effects are greater than the LFR

effects for both flexure and shear; note that the longer spans demonstrate a greater deviation

between LFR and LRFR. Percentages between the LFR and LRFR live load effects show that

the shear induced effects exhibit greater variance between the two methods. In addition, the

Inventory/Strength I results impart a better correlation between LFR and LRFR when compared

to the Operating/Strength II outcomes. The flexural live load effects produced by bridges 7169

and 7390 (the two shortest bridges) compare well for the Inventory/Strength I limit state.

However, the remaining bridges bear considerable differences in live load for flexure and shear

at both limit states. Attributing factors include the dynamic load allowance or impact factor,

distribution factors, live load factors, design loads, and effects of skew.

54

The LRFR dynamic load allowance (IM) increases the live load effects due to the truck

loads by 33 percent, whereas the LFR impact factor, based on span length, has to be less than or

equal to 30 percent. For the five bridges under consideration, the LFR impact factor ranges from

21.6 percent to 30 percent; the shorter span lengths produce a larger impact factor, therefore

producing effects similar to LRFR.

The effect of the distribution factors is easier explained by comparing the actual values,

as done in table 4.3.

TABLE 4.3 Distribution Factors, LFR vs. LRFR.

Distribution Factor 7195 8852 7171 7390 7169 LFR a 0.871 0.636 0.606 0.826 0.886

LRFR-Shear 0.924 0.743 0.719 0.890 0.935 LRFR-Moment 0.798 0.616 0.620 0.797 0.834

a The LFR distribution factor is representative of both shear and moment.

As shown in the table, the LRFR shear distribution factors are much greater than those based on

LFR. Since the distribution factor and the dynamic load allowance (or impact factor) are

multipliers, it is certain that the LRFR live load effects for shear will be greater than those for

LFR. The LRFR moment distribution factors, on the other hand, are generally lower than the

LFR-based distribution factors. The LRFR live load effect due to flexure may or may not be

greater than the LFR effect depending on the interaction between the distribution factor and the

dynamic load allowance. For example, the live load multipliers2 (with respect to flexure) for

Bridge 7169 are:

LRFR: IM*(DFM) = 1.33(0.834) = 1.11 LFR: I*(DFM) = 1.30(0.886) = 1.15

2 The term, live load multipliers, refers to the product of the distribution factors and impact factors.

55

The LFR multiplier is slightly larger and therefore explains why the LFR live load effect is

greater than LRFR for Inventory/Strength I. Bridge 7195, on the other hand, produces the

opposite effect, with the LRFR and LFR live load multipliers being 1.061 and 1.059,

respectively. Generally, the difference between the LRFR and LFR live load multipliers

discussed above is rather small, ranging from 0.002 to 0.072 for the five bridges. Finally, it is

important to observe that the two shorter span bridges yield distribution factors similar to the

longest span bridge, while the distribution factors for Bridges 8852 and 7171 are much smaller.

An explanation for this erratic trend is the girder spacing (i.e. the only variable in computing the

LFR distribution factors). Bridges 7169, 7390, and 7195 are character of a girder spacing of 9

ft.-9 in., 9 ft.-1 in., and 9 ft.-7 in., respectively. Bridges 8852 and 7171 have a smaller girder

spacing of 7 ft. and 6 ft.-8 in., respectively. A direct correlation shows that an increase in girder

spacing will result in a larger distribution factor. This reasoning may explain the larger live load

effects experienced by the shorter span bridges (See figure 4.4). In addition, the distribution

factors for Bridge 7169 may be slightly less due to the effect of the 30o skew. Note that all of the

girders analyzed were interior girders; exterior girders may have a different impact depending on

the distribution factors.

As mentioned in chapter 1, LRFR employs the heavier HL-93 design load as compared to

the LFR HS-20. Recall that the HL-93 design load considers the HS-20 design truck in

conjunction with the lane load. In LFR, the HS-20 design truck and lane load are considered

separately. The design load configurations have a substantial impact on the LRFR and LFR live

load effects.

The live load factors also contribute to the difference between the LFR and LRFR live

load effects. The LFR live load factors for Inventory and Operating are 2.17 and 1.3,

56

respectively. Likewise, the LRFR live load factors for Strength I and Strength II are 1.75 and

1.35, respectively. The LRFR Strength II live load effects are much larger than the LFR

Operating effects due to the combination of the slightly larger live load factor and the heavier

HL-93 design load. The variance in live load effects based on LRFR Strength I and LFR

Inventory is dependent on the interaction between the load factors and applied loads; for

instance, the LRFR load factor is much smaller, while the applied load of the HL-93 is greater.

In general, the live load effects based on LFR and LRFR are influenced by the dynamic

load allowance/impact factor, distribution factors, live load factors, and the design loads.

4.2 Discussion of Dead Load Effects

The dead load effects, as illustrated in figure 4.5, show little distinction between LFR and

LRFR. Slight differences in dead load are due to the applied load factors. The dead load factors

for LFR and LRFR are 1.3 and (1.25DC + 1.50DW), respectively. Note that these factors are

representative of both Inventory/Strength I and Operating/Strength II. Finally, the shear dead

load effects resulted in a slightly larger variance than those based on flexure. The reason being

that the critical section with respect to shear differed between LFR and LRFR. Consider Bridge

7169. The LFR dead load effect for shear was smaller than the LRFR load effect due to the

location of the critical section; the LFR critical section was farther from the support than that of

the LRFR, therefore resulting in a smaller dead load shear force. However, the impact of the

critical section and the dead load factors is negligible.

4.3 Discussion of Effects Related to Resistance

The shear resistance, as seen in figure 4.6, contributes to the variance in rating factors due

to the difference in design philosophy. The resistance as calculated by LFR and LRFR is

57

dependent upon the contribution of the concrete (Vc), transverse reinforcement (Vs), and vertical

prestressing force (Vp). Although the general procedure is similar, differences lie within the

computation of Vc and Vs. For clarification, the equations for shear resistance are listed below.

Consider the shear resistance due to the concrete; notice that the equations for both LRFR and

LFR are dependent upon f’c. The impact of the concrete strength is quite noticeable in figure

4.6. All of the bridges were designed with a concrete strength of 5 ksi, with the exception of

Bridge 8852 which was designed with a greater strength of 5.5 ksi. As evident in figure 4.6,

Bridge 8852 yielded a much larger shear resistance when compared to the other bridges. Further

comparison of the concrete shear resistance requires a more in-depth analysis than provided

within this thesis. The contribution of shear resistance due to the transverse reinforcement,

however, is much more explainable. The LFR and LRFR equations for Vs have the same format;

the main difference among the two equations is the angle of the compressive stresses. With the

introduction of the Modified Compression Field Theory in LRFR, the angle of compressive

stresses (theta) is no longer constant. Rather, the angle theta ranges from approximately 22o to

45o depending on the location under consideration. As the angle theta deviates from 45o, the

term “cot θ” increases, thus resulting in an increase in shear resistance. The resistance increases

because more stirrups interact with the angle of stresses. Furthermore, the angle theta varies

between the LRFR strength limit states as described earlier in chapter 4 and chapter 2 (section

2.2.2). The stirrup area and yield strength are constant for the entire sample of bridges, therefore

having no effect on the difference in shear resistance. The stirrup spacing, however, varies with

respect to the different bridges; this parameter contributes to differences in shear resistance

among the various bridges, but not with respect to the design process (LFR or LRFR).

58

Shear Resistance-LRFR3:

Shear Resistance-LFR3:

3 Notation (PCI, 1997): β = a factor indicating the ability of diagonally cracked concrete to transmit tension. f’c = concrete strength at 28 days. bv = b’ = effective web width. dv = effective shear depth. Av = stirrup area. fy = yield stress of transverse reinforcement. θ = angle of inclination of diagonal compressive stresses. s = stirrup spacing. Vp = vertical prestressing force. Vc = nominal shear strength provided by the concrete. Vs = nominal shear strength provided by the transverse reinforcement. d = distance from the extreme compressive fiber to the centroid of pretensioned reinforcement. Vi = factored shear force at section due to externally applied loads occurring simultaneously with Mmax. Mmax = maximum factored moment at section due to externally applied loads. Mcr = cracking moment. fpc = compressive stress in concrete at centroid of cross-section resisting externally applied loads.

Vc Vs

cot θ > 1 when θ < 45o

V f b dA f d

sVn LRFR c v v

v y vp, . '

cot= + +0 0316β

θ

Where Vc is the lesser of

V f f b d V

V f b d V V MM

f b d

cw c pc p

ci c di cr

c

= + +

= + + ≥

( . ' . ) '

. ' ' . ' 'max

35 0 3

0 6 17

1

V VA f d

sn LFR cv y

,

cot= +

45

Vs

59

Observing figure 4.6, it is apparent that there are no trends between the LFR and LRFR shear

resistances. Rather, the resistance is dependent on an interaction of variables. For example, the

stirrup spacing (4 inches) and angle of compressive stresses (θ = 21.67o) are rather small for

Bridge 8852, thus resulting in a larger shear resistance. The larger value of f’c for Bridge 8852

also accounts for an increase in concrete shear resistance. Bridge 7171, on the other hand,

produced a smaller resistance with respect to LRFR. A possible explanation may be the

interaction between the large stirrup spacing (15.25 inches) and the relatively small angle theta

(θ = 24.14 o). As mentioned before, the contribution of the concrete to the shear resistance is

equally important in identifying differences in resistance between LFR and LRFR. Finally, the

deviation of the critical section may also lend to the variance in LFR and LRFR based resistance.

The flexural resistance, as illustrated in figure 4.7, compares well between LFR and

LRFR and therefore requires no discussion.

4.4 Contribution of Parameters to Rating Factor

As discussed in the previous sections, the rating factors differ between LFR and LRFR as

a result of the live load effects, dead load effects, and member resistances. However, some of

the parameters had little effect, while others had more of an impact. To better understand which

parameters are affecting the rating factor the most, a series of ratios were considered. A ratio of

the LRFR to LFR rating factors was calculated to illustrate the deviation between the two

methods. A ratio of “one” would indicate that the LFR and LRFR rating factors are identical.

Likewise, ratios greater than one indicate that the LRFR rating factor is greater than that of LFR

and vice versa for ratios less than one. Ratios pertaining to the live load effects, dead load

effects, and member resistances were compared to the rating factor ratios. Since the live load

effects comprise the denominator of the rating factor equation, the ratio was calculated by taking

60

the inverse of LRFR to LFR. The deviation of each parameter is given in table 4.4. In addition,

the deviation of the live load, dead load, and resistance was subtracted from a value of one to aid

in the comparison process; values closer to zero indicate that the parameter being considered had

little or no effect on the difference between the LFR and LRFR rating factors. Finally, the

following check was conducted:

ΔRF + (1 - ΔLL) + (1 - ΔDL) + (1 − ΔRes.) ~ 1.0

For example, if the rating factors for LFR and LRFR were the same, ΔRF = 1 and (1 - ΔLL) =

(1 - ΔDL) = (1 − ΔRes.) = 0 (i.e. the live load effect, dead load effect, and member resistance had

zero variance because the rating factors were identical); the check, ΔRF + (1 - ΔLL) + (1 - ΔDL)

+ (1 − ΔRes.) = 1, would be satisfied.

From table 4.4, consider the flexure based results. Notice how similar the ratios of the

rating factor and live load effects are; for instance, Bridge 7195 yielded ΔRF = 0.894 and ΔLL =

0.875 for Inventory/Strength I. The deviation is almost identical, therefore implying that the

source of the variation lies within the live load effects. This can be confirmed by observing the

deviation of the ratios from a unit ratio. For Bridge 7195 (Inventory/Strength I), the live load

effects show a larger variance than that of the dead load effects and resistance. A sample from

table 4.4 is provided below to aid in the interpretation of the table. The portion below,

corresponding to Bridge 7195, is based on flexure for the Inventory/Strength I limit state.

TABLE 4.4 Deviation of LFR and LRFR.

Flexure ~ Inventory / Strength I Flexure ~ Operating / Strength II

Ratio / Bridge ID 7195 8852 7171 7390 7169 7195 8852 7171 7390 7169

ΔRF (LRFR/LFR) 0.894 0.838 0.982 0.861 1.085 0.691 0.650 0.762 0.670 0.840

ΔLL (LFR/LRFR)

(1−ΔLL)

0.875

(0.125)

0.857

(0.143)

0.971

(0.029)

0.854

(0.146)

1.073

(-0.073)

0.679

(0.321)

0.665

(0.335)

0.753

(0.247)

0.663

(0.337)

0.833

(0.167)

ΔDL (LRFR/LFR)

(1−ΔDL)

0.965

(0.035)

0.951

(0.049)

0.973

(0.027)

0.970

(0.030)

0.972

(0.028)

0.965

(0.035)

0.951

(0.049)

0.973

(0.027)

0.970

(0.030)

0.972

(0.028)

ΔRes. (LRFR/LFR)

(1−ΔRes.)

0.996

(0.004)

0.966

(0.034)

0.999

(0.001)

0.995

(0.005)

0.999

(0.001)

0.996

(0.004)

0.966

(0.034)

0.999

(0.001)

0.995

(0.005)

0.999

(0.001)

ΔRF + (1- ΔLL, ΔDL, ΔRes.) 1.058 1.065 1.040 1.041 1.042 1.051 1.068 1.037 1.041 1.037

Shear ~ Inventory / Strength I Shear ~ Operating / Strength II

Ratio / Bridge ID 7195 8852 7171 7390 7169 7195 8852 7171 7390 7169

ΔRF (LRFR/LFR) 0.506 0.950 1.046 0.538 0.688 0.454 0.851 1.086 0.524 0.711

ΔLL (LFR/LRFR)

(1−ΔLL)

0.797

(0.203)

0.731

(0.269)

0.924

(0.076)

0.771

(0.229)

0.963

(0.037)

0.619

(0.381)

0.567

(0.433)

0.728

(0.272)

0.598

(0.402)

0.754

(0.246)

ΔDL (LRFR/LFR)

(1−ΔDL)

0.936

(0.064)

0.944

(0.056)

0.925

(0.075)

0.936

(0.064)

1.023

(-0.023)

0.928

(0.072)

0.944

(0.056)

0.906

(0.094)

0.936

(0.064)

1.023

(-0.023)

ΔRes. (LRFR/LFR)

(1−ΔRes.)

0.775

(0.225)

1.200

(-0.200)

1.065

(-0.065)

0.785

(0.215)

0.779

(0.221)

0.826

(0.174)

1.329

(-0.329)

1.303

(-0.303)

0.897

(0.103)

0.966

(0.034)

ΔRF + (1- ΔLL, ΔDL, ΔRes.) 0.997 1.075 1.132 1.047 0.924 1.082 1.011 1.149 1.093 0.967

62

With an understanding of the table’s structure, an overall comparison considering the entire

sample of bridges is summarized in the following two paragraphs.

Flexure

The Operating/Strength II ratios pertaining to the rating factors and live loads, in table

4.4, are approximately 22.4% less than those computed for the Inventory/Strength I limit state.

For the different limit states, the rating factors based on flexure differ between LFR and LRFR as

a result of the live load effects. The dead load effects showed little variation while the flexural

resistance had no impact.

Shear

The live load effects and shear resistance were the primary sources leading to the

difference in rating factors. Trends regarding the impact of the above two parameters were not

apparent. The deviation in live load effects and shear resistance were similar for

Inventory/Strength I. With respect to Operating/Strength II, the live load effects generally had a

larger impact than the resistance. Finally, the dead load effects had a minimal impact on the

variation in LFR and LRFR rating factors for shear.

Ratio / Bridge ID 7195

ΔRF (LRFR/LFR) 0.894

ΔLL (LFR/LRFR)

(1−ΔLL)

0.875

(0.125)

ΔDL (LRFR/LFR)

(1−ΔDL)

0.965

(0.035)

ΔRes. (LRFR/LFR)

(1−ΔRes.)

0.996

(0.004)

ΔRF + (1- ΔLL, ΔDL, ΔRes.) 1.058

The dead load effect and resistance between LRFR and LFR shows negligible deviation. Therefore, the flexural resistance and dead load effects do not contribute to the variance in the rating factors.

The live load effect shows a distinctive deviation between LRFR and LFR and is therefore identified as the source of the difference in the rating factors.

63

CHAPTER 5

CONCLUSIONS AND RECOMMENDATIONS

5.1 Summary As a result of an increase in vehicular traffic and the effects of aging on the U.S. highway

infrastructure, 27 percent of bridges nationwide (for spans greater than 20 ft.) are considered to

be either structurally deficient or obsolete (FHWA, 2003). Thus, a greater emphasis needs to be

directed towards bridge evaluation, in particular, bridge rating. This research, intended to

support the FHWA’s implementation of load and resistance factor design, involves the rating

analysis of five prestressed concrete girder bridges courtesy of the NM bridge inventory. The

sample of bridges was rated using the BRASS software for LFR and LRFR so that comparisons

could be made. The analysis focused on flexure and shear for the strength limit state. Rating

factors, live load effects, dead load effects, and member capacities were studied in detail in order

to identify any trends and differences among the two rating methods. Research objectives

included 1.) the evaluation of the BRASS software prior to implementation, 2.) identifying the

variables contributing to the differences in LFR and LRFR rating factors, 3.) distinguishing any

trends relating to bridge geometry, 4.) recognizing questionable bridges within the sample, and

5.) using the research findings to provide training, relative to the LRFR method, to the NMDOT.

5.2 Conclusions

Overall comparisons between the LFR and LRFR method are provided below. In

addition, important findings relative to the BRASS software are reported.

64

Verification of BRASS-GIRDER

All beam properties, girder actions, member capacities, and rating factors were verified,

with the exception of the serviceability rating factor. The serviceability rating factor differed by

16.7 percent between the BRASS output and the hand computations, whereas the strength based

rating factors deviated by only 1.2 percent. Thus, it is concluded that the BRASS software based

on LFR is correct with regards to the strength limit state.

Verification of BRASS-GIRDER (LRFD)

The flexure ratings generated by the BRASS software agreed with the hand

computations, showing only a 0.3 percent difference. However, errors relating to the MCFT

interfere with the computation of beta and theta, thus affecting the shear resistance. The

resistance computed by the BRASS software (based on the general method or MCFT) deviated

17.7 percent from the hand computations. Applying a user defined beta and theta yielded a

better comparison between the BRASS software and hand calculations (0.3 percent difference).

Thus, it is concluded that BRASS-GIRDER (LRFD) produces accurate results under the premise

that the shear resistance is determined by means of a user defined beta and theta.

Comparison of Rating Factors: Flexure

The LRFR method generally yielded lower rating factors for flexure, with the longer span

bridges demonstrating a larger deviation between LFR and LRFR. In addition, the

Operating/Strength II limit state showed greater variance between the two rating methods when

compared to the Inventory/Strength I limit state. The live load effects were identified as the

contributing parameter, while the dead load effects and flexural resistance had little impact.

Finally, all five bridges were deemed structurally adequate with respect to flexure, since the

rating factors were greater than one.

65

Comparison of Rating Factors: Shear

The LRFR rating factors for shear were generally lower than those produced by LFR,

with the Operating/Strength II ratings displaying a more notable difference in rating method.

The discrepancy in rating factors was linked to the live load effects and shear resistance. The

live load effects and member resistance impacted the rating factors equally for

Inventory/Strength I, while the live load effects had a greater influence on the Operating/Strength

II ratings. The dead load effects contributed little to the variation in LFR and LRFR rating

factors for shear. Finally, a number of bridges yielded rating factors less than one; the

inadequate ratings based on LFR showed only a slight deviation from a unit rating factor. The

bridges of concern are: Bridge 7390 (LFR rating for Inventory level), Bridge 7169 (LFR rating

for Inventory level and LRFR rating for Strength I limit state), Bridge 7171 (LRFR rating for the

Strength I and Strength II limit states), and Bridge 7195 (LRFR rating for the Strength I and

Strength II limit states).

General Comparisons The LRFR method generally resulted in lower rating factors for flexure and shear; the

shorter span bridges, however, were often controlled by the LFR method. In addition, the shear

ratings typically controlled over those pertaining to flexure.

5.3 Recommendations The research efforts described within this thesis have contributed to the implementation

of LRFR to the engineering society. However, rating with respect to LRFR still requires further

investigation. Recommendations regarding this research project are provided below.

It is recommended that the Wyoming DOT address the potential errors found in the BRASS software. Further investigation of the serviceability rating factors in BRASS-GIRDER and the computation of beta and theta (errors relating to the MCFT) in BRASS-GIRDER (LRFD) is required.

66

Further investigation of the contribution of the concrete to the shear resistance is

recommended. Only general comparisons were made in this research paper.

Further research relating to LRFR is suggested. Parameters not studied in this research should be considered; for example, the effect of girder material, span continuity, post-tensioned strands, etc. should be evaluated. Larger bridge samples are recommended.

It is recommended that the NMDOT re-evaluate the following bridges with respect to

shear: Bridge 7169 and 7390. Note that the inadequate ratings relative to LRFR are not considered since the state of New Mexico has yet to complete the transition from LFR to LRFR. Upon full implementation of LRFR, it is recommended that Bridges 7169, 7171, and 7195 be reconsidered.

It is recommended that the research findings produced within this thesis be applied to the training of the NMDOT with respect to the LRFR method.

67

APPENDICES

68

69

APPENDIX A

SOFTWARE VERIFICATION PCI EXAMPLES 9.3 AND 9.4 In verifying the BRASS software, girder ratings performed by means of hand

computations based on Examples 9.3 and 9.4 of the Prestressed Concrete Institute (PCI) Bridge

Design Manual (1997) were compared to ratings produced by the structural analysis program.

The ratings were performed in accordance with the Manual for Condition Evaluation of Bridges

(AASHTO, 1994) and the Manual for Condition Evaluation and Load Rating of Highway

Bridges using Load and Resistance Factor Philosophy (Lichtenstein, 2001; Minervino et al.,

2004). Provided within this appendix are the rating computations produced by hand. Note that

the design process illustrated in PCI Examples 9.3 and 9.4 was computed by hand; thus, the

design values used may slightly vary from those in the PCI Bridge Design Manual since the

author’s hand computations were reported.

A.1 Rating Computations Based on LFR The rating computations for LFR are based on PCI Example 9.3. Load ratings for shear

and flexure were calculated for the Inventory and Operating levels. In addition, a serviceability

rating factor was computed for flexure for the Inventory level. Note that the shear and flexure

ratings were performed at the critical section (3.33 ft. from the support) and midspan,

respectively. The rating equation, defined in chapter 1, is reiterated below as an illustration of

the shear computation for the Inventory level. The rating factors pertaining to flexure, as well as

the other rating levels, are calculated in the same manner; hence, the values that were entered

into the rating equation are summarized in table A.1.

70

RF C A DA L IShear Inventory, ( )

. . ( . ). ( . )

.=−

+=

−=1

2 13158 13 114 5

217 63431213

TABLE A.1 LFR Rating Factor Computations. Level C D L(1+I) A1 A2 RF

Inventory

315.8

114.5

63.43

1.3 2.17 1.213 Shear

Operating

315.8

114.5

63.43

1.3 1.3 2.024

Inventory 10,658 3097+360+1

80

1852 1.3 2.17 1.475

Operating 10,658 3097+360+1

80

1852 1.3 1.3 2.463

Mome

nt

Serviceabil

ity

5,729 3097+360+1

80

1852 1.0 1.0 1.129

Note. The units for the shear and flexure effects are kips and k-ft., respectively. The constants A1 and A2, as well as the rating factor are unitless.

A.2 Rating Computations Based on LRFR The rating computations for LRFR were based on PCI Example 9.4. As before, load

ratings were computed for shear and flexure with respect to the Strength I and Strength II limit

states. The shear ratings were analyzed at the critical section (6 ft. from the centerline of the

bearing), while the flexure ratings were calculated at midspan. Only the strength limit state was

considered. The rating factor equation for LRFR, as defined in chapter 1, is provided below as a

sample calculation. Computing the rating factors for flexure, as well as the other limit states

utilizes the same equation with different values; the appropriate values are summarized in table

71

A.2. Note that the dead load factors are fixed at 1.25 for structural components and attachments,

and 1.50 for wearing surfaces and utilities.

RF R DC DWLL IMShear St I

c s n DC DW

L, . ( )

. . ( . ) . ( . ). ( . . )

.− =− −

+=

− −+

=φ φ φ γ γ

γ 13511 125 98 06 150 10 77

175 73 73 33 941127

TABLE A.2 LRFR Rating Factor Computations. Limit

State

φRn DC DW LL(1+IM) γL RF

Strength I

351.1

98.06

10.77 73.73+33.

94

1.75 1.12

7

Shear

Strength II

351.1

98.06

10.77 73.73+33.

94

1.35 1.45

6

Strength I 11,360 3,278 360 1,830+843

.1

1.75 1.43

8

Mome

nt

Strength II 11,360 3,278 360 1,830+843

.1

1.35 1.86

4 Note. The units for the shear and flexure effects are kips and k-ft., respectively. The live load factor and rating factor are unit-less.

72

APPENDIX B

BRASS INPUT FILES

After verifying the BRASS software, five prestressed concrete girder bridges from the

NM bridge inventory were rated based on LFR and LRFR. In verifying BRASS-GIRDER

(LRFD), a potential error relating to the Modified Compression Field Theory was identified. As

a result, user defined values of beta and theta were required. Since, the different strength limit

states yielded different values of beta and theta, two input files were required for the LRFR

analysis (one for Strength I and the other for Strength II). Included in this appendix are the LFR

and LRFR input files (three data files per bridge) for the five bridges that were analyzed. In

addition, input files based on PCI Examples 9.3 and 9.4 are included. Only Strength I was

considered in the LRFR verification model (PCI Example 9.4). A summary of the data files

within this appendix are listed below.

PCI Example 9.3 (LFR)

PCI Example 9.4 (LRFR)

Bridge 7169: LFR, LRFR Strength I and LRFR Strength II input files





73

PCI Example 9.3 (LFR)

TITLE PCI Example 9.3

COMMENT Prestressed concrete girder bridge

COMMENT

ANALYSIS 1,0,7,1,0.000650,4,0

COMMENT

XSECT-A 1

XSECT-B 6,6,26,42,3.5,6

XSECT-C 108,7.5,0.5

XSECT-D 2,0,2,2,0

XSECT-E 4.5,10

COMMENT

STIRRUP-GROUP 1,0.4

COMMENT STIRRUP GROUP 2 IS FOR ANCHORAGE- PAIR OF #5 BARS

STIRRUP-GROUP 2,0.61

COMMENT

SPAN-A 1,120.000,1,62.5,62.5

SPAN-C 1,120.000,1,1

FIXITY 1,1,0,0,1,0

COMMENT

STIRRUP-SCHEDULE 1,2,3,0,1,100, , , ,0,0

STIRRUP-SCHEDULE 1,1,12,1,118


COMMENT

PROPERTIES-PC1 150.0,6.500,4.000,4888.0,3834.0,5.50

PROPERTIES-PC2 60.00,60.00,70.0,0,AASHTO

COMMENT

STRAND-ST1 1,2,1,243.00,270.00,28500.0

STRAND-ST2 0.75, , , , , 2.083

CABLE-S1 1,1,12,0.153,70.0000

CABLE-S2 1,1,

CABLE-S1 1,2,12,0.153,68.0000

CABLE-S2 1,1,

CABLE-S1 1,3,8,0.153,66.0000

CABLE-S2 1,1,

CABLE-S1 1,4,2,0.153,64.0000

74

CABLE-S2 1,1,

CABLE-H1 1,5,2,0.153,10,64

CABLE-H2 10,48,72,1,1

CABLE-H3 4,2,2

COMMENT

TRANSFER 1,3.333,116.667

PS-BEAM-OVERHANG 1,6,6

COMMENT

DEAD-LOAD 1,0.922,0.300

COMMENT

LIVE-LOAD 3,1.63600

TRUCK-CODE1 HS20T

COMMENT

DESIGN 3,1 INVENTORY

OPERATING

POINT-OF-INTEREST 100.28

75

PCI Example 9.4 (LRFR)

TITLE PCI Example 9.4 - LRFD

COMMENT Prestressed concrete girder bridge

COMMENT

ANALYSIS B,3,RAT,S

POINT-OF-INTEREST T,ON,ON

ANALYSIS-SPECIAL 1,72

DIST-CONTROL-GIRDER 2

DIST-CONTROL-DL TA,UD

DIST-CONTROL-LL K, ,0, ,NO

DIST-LL-APPLICATION AP

MAP-LIMIT-STATE ST,1,I,N,N

MAP-LIMIT-STATE ST,2,O,N,N

MAP-SPEC-CHECK ST,1,D,FLX,Y

MAP-SPEC-CHECK ST,1,D,SHR,Y



OUTPUT 2,YES

DECK-GEOMETRY 6,9*12,7.5,3*12, ,0.5,DC

SOFFIT-INTERIOR .5,21,21

SOFFIT-LT-EXT .5,21,21,.5,21,21

SOFFIT-RT-EXT .5,21,21,.5,21,21

DECK-TRAVEL-WAY 18,594

DECK-MATL-PROPERTIES 0.15,.15,.025

DECK-LOAD-DESCR 1,DC,2,BARRIERS-2

DECK-LOAD-UNIFORM 1,.6,0,1*12

DECK-STAGE 1, , ,2

CONC-MATERIALS .150,6.5,60,60,6,4887.733, , , ,NO,.00065

CONC-I-SECTION 1,42,3.5,6,6,26,6

CONC-FILLETS 1,2,0,2,2,0,0,4.5,10

CONC-SHEAR 100.5,4, , ,.4,12,90,72, ,2.6,22

CONC-SHEAR-CONSTANTS 3

COMMENT STIRRUPS ARE DEFINED AS GROUP 1

STIRRUP-GROUP 1,.4

STIRRUP-SCHEDULE 1,1,12,0,

PRESTRESS-MATERIALS 5.8,6,70, ,4617.053

76

PRESTRESS-CONTINUITY AP


LOSS-AASHTO-PRETEN 1,.5,.325, , ,

STRAND-MATL-PRETEN 1,.153,LR,270,243,28500,.75, , , ,.5

STRAND-GENERAL 1,1,1,12,1

STRAND-STRAIGHT 1,1,70,N,1,2






STRAND-HARPED 1,5,12.515,62,12.515,48*12,72*12,5,2,2

STRAND-DEV-LENGTH 1,ALL,

COMPOSITE-SLAB 1,108,7.5,.5

SPAN-LINEAR 1,120*12,62.5,62.5

SPAN-SECTION 1,1,120*12,1

SUPPORT-FIXITY 1,R,R,F

SUPPORT-FIXITY 2,F,R,F

LOAD-LIVE-CONTROL B,D

77

Bridge 7169 (LFR)

TITLE BRIDGE 7169 (LFR)

COMMENT PRESTRESSED CONCRETE GIRDER BRIDGE WITH 39.25 FT SPAN (OR 38.25 FT W/

6 INCH OVERHANG)

COMMENT

ANALYSIS 1,0,7, , ,4,0

COMMENT

XSECT-STD 1,AASHTO-II

XSECT-A 1

XSECT-C 117,7.5625,0

COMMENT STIRRUPS-#4 DOUBLE LEG

STIRRUP-GROUP 1,.4

COMMENT

SPAN-A 1,38.25,5

SPAN-C 1,38.25,1,1

FIXITY 1,1,0,0,1,0

COMMENT STIRRUP SCHEDULE IS TAKEN FROM BEAM END

STIRRUP-SCHEDULE 1,1,11.5,0,.9583,100, , , ,0,0

STIRRUP-SCHEDULE 1,1,10,.9583,7.5

STIRRUP-SCHEDULE 1,1,12,8.4583,2

STIRRUP-SCHEDULE 1,1,13,10.4583,5.4167





STIRRUP-SCHEDULE 1,1,11.5,38.2917,.9583

COMMENT

PROPERTIES-PC1 150,5,3, , ,4.5

PROPERTIES-PC2 40,40, ,0,AASHTO

COMMENT

STRAND-ST1 1,1,1, ,270,28500

STRAND-ST2 .7, , , , ,1.823

CABLE-S1 1,1,6,.115,34

CABLE-S2 1,1

CABLE-S1 1,2,4,.115,32

CABLE-S2 1,1

78

CABLE-S1 1,3,2,.115,30

CABLE-S2 1,1, ,1,2

CABLE-H1 1,5,2,.115,4,26

CABLE-H2 4,13.708,24.542,1,1

CABLE-H3 1,2,2

COMMENT

TRANSFER 1,1.815,36.435


COMMENT

DEAD-LOAD 1,.960,.155

COMMENT

LIVE-LOAD 3,1.773

TRUCK-CODE1 HS20T

COMMENT

DESIGN 3,1

INVENTORY

OPERATING


79

Bridge 7169 (LRFR-Strength I)

TITLE BRIDGE 7169 (LRFR) Strength I

COMMENT PRESTRESSED CONCRETE GIRDER BRIDGE WITH 39.25 FT SPAN (38.25 FT WITH

6 INCH OVERHANG)

COMMENT

ANALYSIS B,3,RAT,S





DIST-CONTROL-LL K, ,30, ,YES


MAP-LIMIT-STATE ST,1,I,Y,N

MAP-LIMIT-STATE ST,2,O,N,Y





OUTPUT 2

DECK-GEOMETRY 5,117,7.5625,3*12,3*12,.3125,DC


DECK-MATL-PROPERTIES .15,.15,.015



DECK-STAGE 1, , ,2

CONC-MATERIALS .150,5,40,40,7, , , , ,NO,

CONC-STD-SECTION 1,AASHTO-II

COMMENT REFINED CRITICAL SECTION IS 33.556 INCHES OR 100.731

CONC-SHEAR 100.731,4, , ,.4,10,90, , ,2.039,33.792

CONC-SHEAR 100.784,4, , ,.4,10,90, , ,2.039,33.792


COMMENT STIRRUPS ARE #4 DOUBLE LEG

STIRRUP-GROUP 1,.4




80





PRESTRESS-MATERIALS 4.5,7



LOSS-AASHTO-PRETEN 1,.5,

STRAND-MATL-PRETEN 1,.115,SR, , , , , , , ,.4375








STRAND-HARPED 1,5,4,26,4,13.708*12,24.542*12,1,2,2


COMPOSITE-MATERIALS 3,40,9

COMPOSITE-SLAB 1,117,7.5625,0

SPAN-STD-XSECT 1,38.25*12

SPAN-SECTION 1,1,38.25*12,1




81

Bridge 7169 (LRFR-Strength II)

TITLE BRIDGE 7169 (LRFR) Strength II

COMMENT PRESTRESSED CONCRETE GIRDER BRIDGE WITH 39.25 FT SPAN (38.25 FT WITH

6 INCH OVERHANG)

COMMENT

ANALYSIS B,3,RAT,S













OUTPUT 2

DECK-GEOMETRY 5,117,7.5625,3*12,3*12,.3125,DC





DECK-STAGE 1, , ,2


CONC-STD-SECTION 1,AASHTO-II


CONC-SHEAR 100.731,4, , ,.4,10,90, , ,2.5,27.898

CONC-SHEAR 100.784,4, , ,.4,10,90, , ,2.5,27.898


COMMENT STIRRUPS ARE #4 DOUBLE LEG

STIRRUP-GROUP 1,.4




82

















STRAND-HARPED 1,5,4,26,4,13.708*12,24.542*12,1,2,2









83

Bridge 7390 (LFR)


COMMENT PRESTRESSED CONCRETE GIRDER BRIDGE WITH 59.75 FT SPAN

COMMENT

ANALYSIS 1,0,7, , ,4,0

COMMENT

XSECT-STD 1,AASHTO-III

XSECT-A 1

XSECT-C 109,8,0


STIRRUP-GROUP 1,.4

COMMENT ANCHORAGE STEEL-#6 DOUBLE LEG

STIRRUP-GROUP 2,.88

COMMENT

SPAN-A 1,58.75,5

SPAN-C 1,58.75,1,1

FIXITY 1,1,0,0,1,0


STIRRUP-SCHEDULE 1,2,2,0,.167,100, , , ,0,0

STIRRUP-SCHEDULE 1,1,3,.167,.25

STIRRUP-SCHEDULE 1,1,7,.416,.583


STIRRUP-SCHEDULE 1,1,10,9,10.833








STIRRUP-SCHEDULE 1,1,7,58.750,.583



COMMENT



84

COMMENT

STRAND-ST1 1,1,1, ,270,28500

STRAND-ST2 .7, , , , ,2.083

CABLE-S1 1,1,8,.153,43

CABLE-S2 1,1, ,1,2

CABLE-H1 1,3,2,.153,4,43

CABLE-H2 4,21.042,37.708,1,1

CABLE-H3 1,2,2

COMMENT

TRANSFER 1,2.208,56.542


COMMENT

DEAD-LOAD 1,.937,.148

COMMENT

LIVE-LOAD 3,1.652

TRUCK-CODE1 HS20T

COMMENT

DESIGN 3,1

INVENTORY

OPERATING


85



COMMENT PRESTRESSED CONCRETE GIRDER BRIDGE WITH 59.75 FT SPAN (58.75+TWO 6"

OVERHANGS), SPAN 2

COMMENT

ANALYSIS B,3,RAT,S





DIST-CONTROL-LL K, ,19.919, ,YES








OUTPUT 2

DECK-GEOMETRY 6,109,8,3.417*12,3.333*12,.25,DC

DECK-VSPACING 5,107.125

DECK-TRAVEL-WAY 15.125,609.125




DECK-STAGE 1, , ,2


CONC-STD-SECTION 1,AASHTO-III


CONC-SHEAR 100.602,4, , ,.4,8,90, , ,2.482,28.315

CONC-SHEAR 100.638,4, , ,.4,8,90, , ,2.482,28.315



STIRRUP-GROUP 1,.4



86


















STRAND-HARPED 1,3,4,43,4,21.042*12,37.708*12,1,2,2



COMPOSITE-SLAB 1,109,8,0






87



COMMENT PRESTRESSED CONCRETE GIRDER BRIDGE WITH 59.75 FT SPAN (58.75+TWO 6"

OVERHANGS), SPAN 2

COMMENT

ANALYSIS B,3,RAT,S













OUTPUT 2

DECK-GEOMETRY 6,109,8,3.417*12,3.333*12,.25,DC

DECK-VSPACING 5,107.125

DECK-TRAVEL-WAY 15.125,609.125




DECK-STAGE 1, , ,2




CONC-SHEAR 100.696,4, , ,.4,8,90, , ,2.969,23.483

CONC-SHEAR 100.638,4, , ,.4,8,90, , ,2.969,23.483



STIRRUP-GROUP 1,.4



88


















STRAND-HARPED 1,3,4,43,4,21.042*12,37.708*12,1,2,2









89

Bridge 7171 (LFR)


COMMENT PRESTRESSED CONCRETE GIRDER BRIDGE WITH 81.5208 FT SPAN (80.5208 FT

W/ 6 INCH OVERHANG)

COMMENT

ANALYSIS 1,0,7, , ,4,0

COMMENT

XSECT-STD 1,AASHTO-III

XSECT-A 1

XSECT-C 80,6.4375,0


STIRRUP-GROUP 1,.4


STIRRUP-GROUP 2,.88

COMMENT

SPAN-A 1,80.5208,5

SPAN-C 1,80.5208,1,1

FIXITY 1,1,0,0,1,0



STIRRUP-SCHEDULE 1,1,15.25,.5,16.375

STIRRUP-SCHEDULE 1,1,17.375,16.875,1.448









COMMENT



COMMENT

STRAND-ST1 1,1,1, ,270,28500

STRAND-ST2 .7, , , , ,1.823

90

CABLE-S1 1,1,8,.115,43

CABLE-S2 1,1,N,2,2

CABLE-S1 1,4,6,.115,37

CABLE-S2 1,1,N,0,0

CABLE-H1 1,5,2,.115,8,43

CABLE-H2 8,28.594,51.927,1,1

CABLE-H3 3,2,2

COMMENT

TRANSFER 1,2.143,78.377


COMMENT

DEAD-LOAD 1,.5625,.116

COMMENT

LIVE-LOAD 3,1.212

TRUCK-CODE1 HS20T

COMMENT

DESIGN 3,1

INVENTORY

OPERATING


91



COMMENT PRESTRESSED CONCRETE GIRDER BRIDGE WITH 81'6.25" SPAN (80'6.25" SPAN

W/ 6" OVERHANG)

COMMENT

ANALYSIS B,3,RAT,S













OUTPUT 2

DECK-GEOMETRY 7,80,6.4375,2.5*12,2.5*12,.3125,DC





DECK-STAGE 1, , ,2




CONC-SHEAR 100.435,4, , ,.4,15.25,90, , ,2.585,24.1438

CONC-SHEAR 100.466,4, , ,.4,15.25,90, , ,2.585,24.1438



STIRRUP-GROUP 1,.4

STIRRUP-SCHEDULE 1,1,15.25,0,16.375*12

STIRRUP-SCHEDULE 1,1,17.375,16.375*12,17.375

STIRRUP-SCHEDULE 1,1,19.5,213.875,3.25*12

92


STIRRUP-SCHEDULE 1,1,21,273.125,35*12















STRAND-HARPED 1,5,8,43,8,343.125,623.125,3,2,2




SPAN-STD-XSECT 1,966.25

SPAN-SECTION 1,1,966.25,1




93



COMMENT PRESTRESSED CONCRETE GIRDER BRIDGE WITH 81'6.25" SPAN (80'6.25"

SPAN W/ 6" OVERHANG)

COMMENT

ANALYSIS B,3,RAT,S













OUTPUT 2

DECK-GEOMETRY 7,80,6.4375,2.5*12,2.5*12,.3125,DC





DECK-STAGE 1, , ,2




CONC-SHEAR 100.477,4, , ,.4,15.25,90, , ,2.786,22.273

CONC-SHEAR 100.466,4, , ,.4,15.25,90, , ,2.786,22.273



STIRRUP-GROUP 1,.4

STIRRUP-SCHEDULE 1,1,15.25,0,16.375*12

STIRRUP-SCHEDULE 1,1,17.375,16.375*12,17.375


94


STIRRUP-SCHEDULE 1,1,21,273.125,35*12















STRAND-HARPED 1,5,8,43,8,343.125,623.125,3,2,2




SPAN-STD-XSECT 1,966.25

SPAN-SECTION 1,1,966.25,1




95

Bridge 8852 (LFR)


COMMENT PRESTRESSED CONCRETE GIRDER BRIDGE WITH 98' SPAN (97' W/ 6" OVERHANG)

COMMENT

ANALYSIS 1,0,7, , ,4,0

COMMENT

XSECT-STD 1,AASHTO-IV

XSECT-A 1

XSECT-C 84,8,1


STIRRUP-GROUP 1,.4

COMMENT

SPAN-A 1,97,5

SPAN-C 1,97,1,1

FIXITY 1,1,0,0,1,0



STIRRUP-SCHEDULE 1,1,4,.167,8














COMMENT

PROPERTIES-PC1 150,5.5,3, , ,4.75


COMMENT

STRAND-ST1 1,2,1, ,270,28500

96

STRAND-ST2 .75, , , , ,2.083

CABLE-S1 1,1,6,.153,52

CABLE-S2 1,1, ,0,0

CABLE-S1 1,2,10,.153,50

CABLE-S2 1,1, ,1,2

CABLE-S1 1,4,8,.153,46

CABLE-S2 1,1, ,0,0

CABLE-H1 1,5,2,.153,10,52

CABLE-H2 10,34.333,62.667,1,1

CABLE-H3 4,2,2

COMMENT

DEAD-LOAD 1,.744,.313

COMMENT

LIVE-LOAD 3,1.273

TRUCK-CODE1 HS20T

COMMENT

DESIGN 3,1

INVENTORY

OPERATING


97




COMMENT

ANALYSIS B,3,RAT,S













OUTPUT 2

DECK-GEOMETRY 6,84,8,36,36,0,DC





DECK-STAGE 1, , ,2

CONC-MATERIALS .15,5.5,60,40,7, , , , ,NO,

CONC-STD-SECTION 1,AASHTO-IV

COMMENT REFINED CRITICAL SECTION IS 57.469 OR 100.494

CONC-SHEAR 100.494,4, , ,.4,4,90, , ,2.94,21.671

CONC-SHEAR 100.464,4, , ,.4,4,90, , ,2.94,21.671


COMMENT STIRRUPS-#4 DOUBLE LEG BARS

STIRRUP-GROUP 1,.4


STIRRUP-SCHEDULE 1,1,6,92,3*12

STIRRUP-SCHEDULE 1,1,9,128,7.5*12


98














STRAND-MATL-PRETEN 1,.153,LR, , , , , , , ,.5








STRAND-HARPED 1,5,10,52,10,412,752,4,2,2,2




SPAN-STD-XSECT 1,97*12





99




COMMENT

ANALYSIS B,3,RAT,S













OUTPUT 2

DECK-GEOMETRY 6,84,8,36,36,0,DC





DECK-STAGE 1, , ,2

CONC-MATERIALS .15,5.5,60,40,7, , , , ,NO,

CONC-STD-SECTION 1,AASHTO-IV

COMMENT REFINED CRITICAL SECTION IS 53.857 or 100.463 ~ 100.464

CONC-SHEAR 100.464,4, , ,.4,4,90, , ,5.390,22.94


COMMENT STIRRUPS-#4 DOUBLE LEG BARS

STIRRUP-GROUP 1,.4






100













STRAND-MATL-PRETEN 1,.153,LR, , , , , , , ,.5








STRAND-HARPED 1,5,10,52,10,412,752,4,2,2,2









101

Bridge 7195 (LFR)


COMMENT PRESTRESSED CONCRETE GIRDER BRIDGE WITH 108 FT SPAN

COMMENT

ANALYSIS 1,0,7, , ,4,0

COMMENT

XSECT-STD 1,AASHTO-V

XSECT-A 1

XSECT-C 115,7.25,0


STIRRUP-GROUP 1,.4

COMMENT

SPAN-A 1,107,5

SPAN-C 1,107,1,1

FIXITY 1,1,0,0,1,0



STIRRUP-SCHEDULE 1,1,11,.75,34


STIRRUP-SCHEDULE 1,1,1.667,38.5,30




COMMENT


PROPERTIES-PC2 40,40,25,0,AASHTO

COMMENT

STRAND-ST1 1,1,1, ,270,28500

STRAND-ST2 .7, , , , ,1.823

CABLE-S1 1,1,10,0.115,61

CABLE-S2 1,1, ,2,2

CABLE-S1 1,4,8,.115,55

CABLE-S2 1,1

CABLE-S1 1,5,6,.115,53

CABLE-S2 1,1

CABLE-H1 1,6,3,.115,12,61

102

CABLE-H2 12,38.2,68.8,1,1

CABLE-H3 5,2,2

COMMENT

TRANSFER 1,2.927,104.073


COMMENT

DEAD-LOAD 1,.868,.164

COMMENT

LIVE-LOAD 3,1.742

TRUCK-CODE1 HS20T

COMMENT

DESIGN 3,1

INVENTORY

OPERATING


103




COMMENT

ANALYSIS B,3,RAT,S













OUTPUT 2

DECK-GEOMETRY 5,115,7.25,40.859,39.375,0,DC





DECK-STAGE 1, , ,2


CONC-STD-SECTION 1,AASHTO-V


CONC-SHEAR 100.419,4, , ,.4,11,90, , ,2.545,25.173

CONC-SHEAR 100.5,4, , ,.4,11,90, , ,2.545,25.173



STIRRUP-GROUP 1,.4


PRESTRESS-MATERIALS 4.5,7,25



104










STRAND-HARPED 1,6,12,61,12,38.7*12,68.3*12,5,2,2









105




COMMENT

ANALYSIS B,3,RAT,S













OUTPUT 2

DECK-GEOMETRY 5,115,7.25,40.859,39.375,0,DC





DECK-STAGE 1, , ,2


CONC-STD-SECTION 1,AASHTO-V

COMMENT REFINED CRITICAL SECTION IS AT 58.582 INCHES OR 100.456

CONC-SHEAR 100.456,4, , ,.4,11,90, , ,2.6225,23.35

CONC-SHEAR 100.5,4, , ,.4,11,90, , ,2.6225,23.35



STIRRUP-GROUP 1,.4


PRESTRESS-MATERIALS 4.5,7,25



106










STRAND-HARPED 1,6,12,61,12,38.7*12,68.3*12,5,2,2









107

APPENDIX C

TABULAR RESULTS: BRASS RATINGS

From the BRASS analysis, the rating factors, live load effects, dead load effects, and

member resistances were tabulated in tables C.1 thru C.14 for both LFR and LRFR. The results

pertaining to flexure were determined at the tenth points along the span, where the midspan

results were studied in detail in chapter 4. The shear effects were only analyzed at the critical

section. It is important to note that the critical section is different for the five bridges being

studied and also varies among the Inventory/Strength I and Operating/Strength II limit states.

109

TABLE C.1 LRFR Rating Factors: Flexure.

Strength I Strength II POI/

Bridge 7195 8852 7390 7171 7169 7195 8852 7171 7390 7169

100 N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A

101 3.94 5.09 3.65 3.44 2.99 5.11 6.60 4.73 4.46 3.87

102 2.09 2.71 1.97 1.95 1.96 2.71 3.51 2.55 2.53 2.54

103 1.58 2.03 1.50 1.51 1.56 2.05 2.63 1.94 1.96 2.02

104 1.38 1.75 1.30 1.33 1.41 1.78 2.27 1.68 1.73 1.83

105 1.30 1.66 1.24 1.29 1.40 1.68 2.15 1.61 1.67 1.81

106 1.38 1.75 1.30 1.33 1.41 1.78 2.27 1.68 1.73 1.83

107 1.58 2.03 1.50 1.51 1.56 2.05 2.63 1.94 1.96 2.02

108 2.09 2.71 1.97 1.95 1.96 2.71 3.51 2.55 2.53 2.54

109 3.94 5.09 3.65 3.44 2.99 5.11 6.60 4.73 4.46 3.87


TABLE C.2 LRFR Critical Rating Factors: Shear.

Strength I Strength II

Bridge 7195 8852 7171 7390 7169 7195 8852 7171 7390 7169

RF 0.52 2.56 0.57 1.00 0.59 0.79 3.31 0.85 1.74 1.03

Section 100.42 100.49 100.44 100.60 100.73 100.46 100.46 100.48 100.70 100.73

TABLE C.3 LFR Rating Factors: Flexure.

Inventory Operating POI/

Bridge 7195 8852 7171 7390 7169 7195 8852 7171 7390 7169


101 4.37 6.03 4.15 3.54 3.07 7.30 10.08 6.93 5.91 5.13

102 2.33 3.22 2.26 1.96 1.76 3.89 5.38 3.77 3.27 2.95

103 1.77 2.43 1.73 1.52 1.41 2.95 4.06 2.89 2.55 2.36

104 1.53 2.08 1.50 1.35 1.30 2.56 3.48 2.50 2.25 2.17

105 1.45 1.98 1.44 1.31 1.29 2.43 3.31 2.40 2.19 2.16

106 1.53 2.09 1.50 1.35 1.29 2.56 3.50 2.52 2.25 2.16

107 1.77 2.41 1.71 1.52 1.41 2.95 4.03 2.86 2.55 2.36

108 2.33 3.20 2.24 1.96 1.78 3.89 5.35 3.75 3.27 2.97

109 4.37 6.00 4.12 3.54 3.09 7.30 10.02 6.89 5.91 5.16


TABLE C.4 LFR Critical Rating Factors: Shear.

Inventory Operating

Bridge 7195 8852 7171 7390 7169 7195 8852 7171 7390 7169

RF 1.03 2.69 1.06 0.96 0.86 1.73 3.89 1.62 1.60 1.45

Section 100.27 100.46 100.26 100.38 100.95 100.27 100.46 100.26 100.38 100.95

91

Table C.5: LRFR Live Load Effects: Flexure (k-ft.).

Strength I Strength II POI/

Bridge 7195 8852 7171 7390 7169 7195 8852 7171 7390 7169

100 0 0 0 0 0 0 0 0 0 0

101 1620 1092 853.0 714.8 408.7 1250 842.2 658.0 551.4 315.3

102 2848 1916 1496 1247 697.5 2197 1478 1154 961.8 538.1

103 3688 2486 1931 1589 874.9 2845 1917 1489 1226 674.9

104 4187 2819 2184 1787 963.2 3230 2174 1685 1378 743.1

105 4329 2906 2245 1823 960.0 3340 2242 1732 1406 740.6

106 4187 2819 2184 1787 963.2 3230 2174 1685 1378 743.1

107 3688 2486 1930 1590 874.9 2845 1917 1489 1226 674.9

108 2848 1916 1496 1247 697.6 2197 1478 1154 961.8 538.1

109 1620 1092 852.7 714.8 408.7 1250 842.1 657.8 551.4 315.3

110 0 0 0 0 0 0 0 0 0 0

Table C.6: LRFR Critical Live Load Effects: Shear (kips).


Bridge 7195 8852 7171 7390 7169 7195 8852 7171 7390 7169

LL 183.7 142.5 130.3 142.6 123.3 141.7 110.0 100.5 108.4 95.1

Section 100.42 100.49 100.44 100.60 100.73 100.46 100.46 100.48 100.70 100.73

92

Table C.7: LFR Live Load Effects: Flexure (k-ft.).

Inventory Operating POI/

Bridge 7195 8852 7171 7390 7169 7195 8852 7171 7390 7169

100 0 0 0 0 0 0 0 0 0 0

101 1440 947.3 740.7 714.1 454.2 862.4 567.2 443.5 427.6 272.0

102 2526 1658 1292 1235 770.4 1513 992.8 773.5 739.7 461.3

103 3258 2132 1653 1563 955.7 1951 1277 989.9 936.1 572.3

104 3687 2425 1876 1750 1035 2208 1452 1123 1048 619.9

105 3787 2490 1918 1769 1030 2268 1491 1148 1059 616.7

106 3687 2412 1865 1750 1043 2208 1444 1117 1048 624.5

107 3258 2148 1666 1563 955.6 1951 1286 997.5 936.1 572.2

108 2526 1669 1300 1235 764.1 1513 999.1 778.6 739.7 457.6

109 1440 952.5 745.0 714.1 451.0 862.4 570.4 446.1 427.6 270.1

110 0 0 0 0 0 0 0 0 0 0

Table C.8: LFR Critical Live Load Effects: Shear (kips).

Inventory Operating

Bridge 7195 8852 7171 7390 7169 7195 8852 7171 7390 7169

LL 146.5 104.1 100.4 131.7 118.7 87.7 62.4 60.1 78.9 71.7

Section 100.27 100.46 100.26 100.38 100.95 100.27 100.46 100.26 100.38 100.95

TABLE C.9 Dead Load Effects: Flexure (k-ft.).

LRFR LFR POI/

Bridge 7195 8852 7171 7390 7169 7195 8852 7171 7390 7169

100 0 0 0 0 0 0 0 0 0 0

101 1349 983.8 464.4 327.8 124.7 1398 1034 478.6 336.9 128.3

102 2399 1749 825.5 582.7 221.7 2485 1839 850.9 598.9 228.2

103 3148 2295 1084 764.8 291.0 3262 2413 1117 786.0 299.4

104 3598 2623 1238 874.0 332.6 3728 2758 1276 898.3 342.2

105 3748 2732 1290 910.4 346.4 3883 2873 1329 935.8 356.5

106 3598 2623 1238 874.0 332.6 3728 2758 1276 898.3 342.2

107 3148 2295 1084 764.7 291.0 3262 2413 1117 786.0 299.5

108 2398 1749 825.5 582.7 221.7 2485 1839 850.9 598.9 228.2

109 1349 983.5 464.4 327.7 124.7 1398 1034 478.6 336.9 128.3

110 0 0 0 0 0 0 0 0 0 0

TABLE C.10 LRFR Critical Dead Load Effects: Shear (kips).


Bridge 7195 8852 7390 7171 7169 7195 8852 7390 7171 7169

DL 128.4 101.5 54.5 58.5 30.9 127.3 101.5 53.4 58.5 30.9

Section 100.42 100.49 100.60 100.44 100.73 100.46 100.46 100.70 100.478 100.73

94

TABLE C.11 LFR Critical Dead Load Effects: Shear (kips).

Inventory Operating

Bridge 7195 8852 7171 7390 7169 7195 8852 7171 7390 7169

DL 137.2 107.5 62.53 58.92 30.20 137.2 107.5 62.53 58.92 30.20

Section 100.27 100.46 100.26 100.38 100.95 100.27 100.46 100.26 100.38 100.95

TABLE C.12 Resistance: Flexure (k-ft.).

LRFR LFR POI/

Bridge 7195 8852 7171 7390 7169 7195 8852 7171 7390 7169

100 1295 1087 620.5 414.4 251.6 1.0E-5 1.0E-5 3291 1.0E-5 1453

101 7730 6545 3575 2785 1346 7701 6754 3553 2866 1524

102 8347 6940 3773 3020 1590 8381 7187 3772 3022 1590

103 8970 7340 3974 3169 1653 9031 7602 3979 3174 1655

104 9357 7557 4073 3256 1690 9396 7822 4092 3261 1692

105 9357 7557 4073 3256 1690 9396 7822 4092 3261 1692

106 9357 7557 4073 3256 1690 9396 7822 4092 3261 1692

107 8970 7340 3974 3169 1653 9031 7602 3979 3174 1655

108 8347 6940 3773 3020 1590 8381 7187 3772 3022 1590

109 7730 6545 3575 2785 1346 7701 6754 3553 2866 1524

110 1295 1087 620.5 414.4 251.6 1.0E-5 1.0E-5 3291 1.0E-5 1453

95

TABLE C.13 LRFR Critical Resistance: Shear (kips).


Bridge 7195 8852 7171 7390 7169 7195 8852 7171 7390 7169

Resistance 224.1 465.8 132.8 197.7 103.9 238.6 465.7 143.8 241.8 128.9

Section 100.42 100.49 100.44 100.60 100.73 100.46 100.46 100.48 100.70 100.73

TABLE C.14 LFR Critical Resistance: Shear (kips).

Inventory Operating

Bridge 7195 8852 7171 7390 7169 7195 8852 7171 7390 7169

Resistance 289.0 388.0 169.1 185.6 133.4 289.0 350.4 160.3 185.6 133.4

Section 100.27 100.46 100.26 100.38 100.95 100.27 100.46 100.26 100.38 100.95

96

REFERENCES American Association of State Highway and Transportation Officials (AASHTO). (1989). Guide Specifications for Strength Evaluation of Existing Steel and Concrete Bridges, Washington, D.C. American Association of State Highway and Transportation Officials (AASHTO). (1990). Guide Specifications for Fatigue Evaluation of Existing Steel and Concrete Bridges, Washington, D.C. American Association of State Highway and Transportation Officials (AASHTO). (1994). Manual for Condition Evaluation of Bridges, Washington, D.C. American Association of State Highway and Transportation Officials (AASHTO). (1996). Standard Specifications for the Design of Highway Bridges, 16th Ed., Washington, DC. American Association of State Highway and Transportation Officials (AASHTO). (1998). LRFD Bridge Design Specifications, 2nd Ed., Washington, DC. American Association of State Highway and Transportation Officials (AASHTO) Virtis. (2002). Computer software, version 4.2.0, Washington, D.C. Barr, P. J., Eberhard, M. O., and J.F. Stanton. (2001). “Live-Load Distribution Factors in Prestressed Concrete Girder Bridges.” J. Bridge Engeering., ASCE, 6(5), 298-306. BRASS-GIRDER (2002a). Bridge Rating & Analysis of Structural Systems computer software; version 5.8, Wyoming Department of Transportation, University of Wyoming, Bridge Tech, Inc., Cheyenne, WY. BRASS-GIRDER (2002b). Bridge Rating & Analysis of Structural Systems user manual; version 5, Wyoming Department of Transportation, WY. BRASS-GIRDER (LRFD) (2002). Bridge Rating & Analysis of Structural Systems command manual; version 1.5.1, Wyoming Department of Transportation, WY. BRASS-GIRDER (LRFD) (2003). Bridge Rating & Analysis of Structural Systems computer software; version 1.5.3, Wyoming Department of Transportation, Bridge Tech, Inc., Cheyenne, WY. “Deficient Bridges.” (2003). <http://www.tripnet.org/DeficientBridges070903.pdf>. “FHWA National Bridge Inventory Data.” (2004). http://www.fhwa.dot.gov/bridge/deficient.htm.

http://www.tripnet.org/DeficientBridges070903.pdf�

Friedland, I. M., and E. P. Small, (2003). “FHWA Bridge Research and Technology Deployment Initiatives.” Proc., 2003 Mid-Continent Transportation Research Symposium, Iowa State University, Ames, Iowa. Goodrich, B. L., and J. A. Puckett, (2002). Comparison of LFR and LRFR for Concrete Bridges. 2002 Concrete Bridge Conference, University of Wyoming, Bridge Tech, Inc., Laramie, WY. Key Facts About America’s Road and Bridge Conditions and Federal Funding.(2003). <http://www.tripnet.org/nationalfactsheet.htm> downloaded Feb. 3, 2004. Lichtenstein Consulting Engineers, Inc. (2001). Manual for Condition Evaluation and Load Rating of Highway Bridges Using Load and Resistance Factor Philosophy. NCHRP Web Document 28 (Proj. C12-46), National Cooperative Highway Research Program, Transportation Research Board, National Research Council, Washington D.C. Liu, D. Redundancy in Highway Bridge Substructures. NCHRP Report No. 406, Journal of the National Cooperative Highway Research Program, National Research Council, Washington, D.C. 2001. Minervino, C., Sivakumar, B., Moses, F., Mertz, D., and W. Edberg. (2004). “New AASHTO Guide Manual for Load and Resistance Factor Rating of Highway Bridges.” Journal of Bridge Engineering. ASCE, 9(1), 43-54. Moses, F. (1987). “Load Capacity Evaluation of Existing Bridges.” NCHRP Rep. 301, National Cooperative Highway Research Program, Washington, D.C. Precast / Prestressed Concrete Institute (PCI). (1997). Bridge Design Manual, 1st Ed., Chicago, IL. Taly, N. (1998). “Inspection, Evaluation, Rehabilitation, and Maintenance of Bridges.” Design of Modern Highway Bridges, the McGraw-Hill Companies, Inc., 1156-

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Load Rating of Prestressed Concrete Girder Bridges: A Comparative