Load Rating of Prestressed Concrete Girder Bridges: A Comparative ...
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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
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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.
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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.
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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.
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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.
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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
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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
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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) …………………………….....…………..
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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 ……………………………………………………..
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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
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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
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(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.
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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)
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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)
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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
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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
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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)
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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.
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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
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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
Bridge 7390: LFR, LRFR Strength I and LRFR Strength II input files
Bridge 7171: LFR, LRFR Strength I and LRFR Strength II input files
Bridge 8852: LFR, LRFR Strength I and LRFR Strength II input files
Bridge 7195: 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
STIRRUP-SCHEDULE 1,2,3,119,1
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
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
76
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
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 1,1,18,15.875,7.5
STIRRUP-SCHEDULE 1,1,13,23.375,5.4167
STIRRUP-SCHEDULE 1,1,12,28.7917,2
STIRRUP-SCHEDULE 1,1,10,30.7917,7.5
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
PS-BEAM-OVERHANG 1,6,6
COMMENT
DEAD-LOAD 1,.960,.155
COMMENT
LIVE-LOAD 3,1.773
TRUCK-CODE1 HS20T
COMMENT
DESIGN 3,1
INVENTORY
OPERATING
POINT-OF-INTEREST 100.949
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
POINT-OF-INTEREST T,ON,ON
ANALYSIS-SPECIAL 1,36
DIST-CONTROL-GIRDER 2
DIST-CONTROL-DL TA,UD
DIST-CONTROL-LL K, ,30, ,YES
DIST-LL-APPLICATION AP
MAP-LIMIT-STATE ST,1,I,Y,N
MAP-LIMIT-STATE ST,2,O,N,Y
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
DECK-GEOMETRY 5,117,7.5625,3*12,3*12,.3125,DC
DECK-TRAVEL-WAY 18,522
DECK-MATL-PROPERTIES .15,.15,.015
DECK-LOAD-DESCR 1,DC,2,BARRIERS-2
DECK-LOAD-UNIFORM 1,.1,0,1*12
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
CONC-SHEAR-CONSTANTS 1
COMMENT STIRRUPS ARE #4 DOUBLE LEG
STIRRUP-GROUP 1,.4
STIRRUP-SCHEDULE 1,1,10,5.5,90
STIRRUP-SCHEDULE 1,1,12,95.5,24
STIRRUP-SCHEDULE 1,1,13,119.5,65
80
STIRRUP-SCHEDULE 1,1,18,184.5,90
STIRRUP-SCHEDULE 1,1,13,274.5,65
STIRRUP-SCHEDULE 1,1,12,339.5,24
STIRRUP-SCHEDULE 1,1,10,363.5,90
PRESTRESS-MATERIALS 4.5,7
PRESTRESS-CONTINUITY AP
PS-BEAM-OVERHANG 1,6,6
LOSS-AASHTO-PRETEN 1,.5,
STRAND-MATL-PRETEN 1,.115,SR, , , , , , , ,.4375
STRAND-GENERAL 1,1,1,6,1
STRAND-STRAIGHT 1,1,34,N,0,0
STRAND-GENERAL 1,2,1,4,1
STRAND-STRAIGHT 1,2,32,N,0,0
STRAND-GENERAL 1,3,1,2,1
STRAND-STRAIGHT 1,3,30,N,1,2
STRAND-GENERAL 1,5,1,2,1
STRAND-HARPED 1,5,4,26,4,13.708*12,24.542*12,1,2,2
STRAND-DEV-LENGTH 1,ALL,
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
SUPPORT-FIXITY 1,R,R,F
SUPPORT-FIXITY 2,F,R,F
LOAD-LIVE-CONTROL B,D
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
POINT-OF-INTEREST T,ON,ON
ANALYSIS-SPECIAL 1,36
DIST-CONTROL-GIRDER 2
DIST-CONTROL-DL TA,UD
DIST-CONTROL-LL K, ,30, ,YES
DIST-LL-APPLICATION AP
MAP-LIMIT-STATE ST,1,I,Y,N
MAP-LIMIT-STATE ST,2,O,N,Y
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
DECK-GEOMETRY 5,117,7.5625,3*12,3*12,.3125,DC
DECK-TRAVEL-WAY 18,522
DECK-MATL-PROPERTIES .15,.15,.015
DECK-LOAD-DESCR 1,DC,2,BARRIERS-2
DECK-LOAD-UNIFORM 1,.1,0,1*12
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, , ,2.5,27.898
CONC-SHEAR 100.784,4, , ,.4,10,90, , ,2.5,27.898
CONC-SHEAR-CONSTANTS 1
COMMENT STIRRUPS ARE #4 DOUBLE LEG
STIRRUP-GROUP 1,.4
STIRRUP-SCHEDULE 1,1,10,5.5,90
STIRRUP-SCHEDULE 1,1,12,95.5,24
STIRRUP-SCHEDULE 1,1,13,119.5,65
82
STIRRUP-SCHEDULE 1,1,18,184.5,90
STIRRUP-SCHEDULE 1,1,13,274.5,65
STIRRUP-SCHEDULE 1,1,12,339.5,24
STIRRUP-SCHEDULE 1,1,10,363.5,90
PRESTRESS-MATERIALS 4.5,7
PRESTRESS-CONTINUITY AP
PS-BEAM-OVERHANG 1,6,6
LOSS-AASHTO-PRETEN 1,.5,
STRAND-MATL-PRETEN 1,.115,SR, , , , , , , ,.4375
STRAND-GENERAL 1,1,1,6,1
STRAND-STRAIGHT 1,1,34,N,0,0
STRAND-GENERAL 1,2,1,4,1
STRAND-STRAIGHT 1,2,32,N,0,0
STRAND-GENERAL 1,3,1,2,1
STRAND-STRAIGHT 1,3,30,N,1,2
STRAND-GENERAL 1,5,1,2,1
STRAND-HARPED 1,5,4,26,4,13.708*12,24.542*12,1,2,2
STRAND-DEV-LENGTH 1,ALL,
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
SUPPORT-FIXITY 1,R,R,F
SUPPORT-FIXITY 2,F,R,F
LOAD-LIVE-CONTROL B,D
83
Bridge 7390 (LFR)
TITLE 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
COMMENT STIRRUPS-#4 DOUBLE LEG
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
COMMENT STIRRUP SCHEDULE IS TAKEN FROM BEAM END
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 1,1,8,1,8
STIRRUP-SCHEDULE 1,1,10,9,10.833
STIRRUP-SCHEDULE 1,1,15,19.833,5
STIRRUP-SCHEDULE 1,1,18,24.833,4.5
STIRRUP-SCHEDULE 1,1,13,29.333,1.083
STIRRUP-SCHEDULE 1,1,18,30.416,4.5
STIRRUP-SCHEDULE 1,1,15,34.916,5
STIRRUP-SCHEDULE 1,1,10,39.916,10.833
STIRRUP-SCHEDULE 1,1,8,50.750,8
STIRRUP-SCHEDULE 1,1,7,58.750,.583
STIRRUP-SCHEDULE 1,1,3,59.333,.25
STIRRUP-SCHEDULE 1,2,2,59.583,.167
COMMENT
PROPERTIES-PC1 150,5,3, , ,4.5
PROPERTIES-PC2 40,40, ,0,AASHTO
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
PS-BEAM-OVERHANG 1,6,6
COMMENT
DEAD-LOAD 1,.937,.148
COMMENT
LIVE-LOAD 3,1.652
TRUCK-CODE1 HS20T
COMMENT
DESIGN 3,1
INVENTORY
OPERATING
POINT-OF-INTEREST 100.376
85
Bridge 7390 (LRFR-Strength I)
TITLE BRIDGE 7390 (LRFR) Strength I
COMMENT PRESTRESSED CONCRETE GIRDER BRIDGE WITH 59.75 FT SPAN (58.75+TWO 6"
OVERHANGS), SPAN 2
COMMENT
ANALYSIS B,3,RAT,S
POINT-OF-INTEREST T,ON,ON
ANALYSIS-SPECIAL 1,45
DIST-CONTROL-GIRDER 2
DIST-CONTROL-DL TA,UD
DIST-CONTROL-LL K, ,19.919, ,YES
DIST-LL-APPLICATION AP
MAP-LIMIT-STATE ST,1,I,Y,N
MAP-LIMIT-STATE ST,2,O,N,Y
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
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-MATL-PROPERTIES .15,.15,.015
DECK-LOAD-DESCR 1,DC,2,BARRIERS-2
DECK-LOAD-UNIFORM 1,.12,0,1*12
DECK-STAGE 1, , ,2
CONC-MATERIALS .150,5,40,40,7, , , , ,NO,
CONC-STD-SECTION 1,AASHTO-III
COMMENT REFINED CRITICAL SECTION IS 42.437 INCHES OR 100.602
CONC-SHEAR 100.602,4, , ,.4,8,90, , ,2.482,28.315
CONC-SHEAR 100.638,4, , ,.4,8,90, , ,2.482,28.315
CONC-SHEAR-CONSTANTS 1
COMMENT STIRRUPS-#4 DOUBLE LEG
STIRRUP-GROUP 1,.4
STIRRUP-SCHEDULE 1,1,6,0,6
STIRRUP-SCHEDULE 1,1,8,6,96
86
STIRRUP-SCHEDULE 1,1,10,102,130
STIRRUP-SCHEDULE 1,1,15,232,60
STIRRUP-SCHEDULE 1,1,18,292,54
STIRRUP-SCHEDULE 1,1,13,346,13
STIRRUP-SCHEDULE 1,1,18,359,54
STIRRUP-SCHEDULE 1,1,15,413,60
STIRRUP-SCHEDULE 1,1,10,473,130
STIRRUP-SCHEDULE 1,1,8,603,96
STIRRUP-SCHEDULE 1,1,6,699,6
PRESTRESS-MATERIALS 4.5,7
PRESTRESS-CONTINUITY AP
PS-BEAM-OVERHANG 1,6,6
LOSS-AASHTO-PRETEN 1,.5,
STRAND-MATL-PRETEN 1,.153,SR, , , , , , , ,.5
STRAND-GENERAL 1,1,1,8,1
STRAND-STRAIGHT 1,1,43,N,1,2
STRAND-GENERAL 1,3,1,2,1
STRAND-HARPED 1,3,4,43,4,21.042*12,37.708*12,1,2,2
STRAND-DEV-LENGTH 1,ALL,
COMPOSITE-MATERIALS 3,40,9
COMPOSITE-SLAB 1,109,8,0
SPAN-STD-XSECT 1,58.75*12
SPAN-SECTION 1,1,58.75*12,1
SUPPORT-FIXITY 1,R,R,F
SUPPORT-FIXITY 2,F,R,F
LOAD-LIVE-CONTROL B,D
87
Bridge 7390 (LRFR-Strength II)
TITLE BRIDGE 7390 (LRFR) Strength II
COMMENT PRESTRESSED CONCRETE GIRDER BRIDGE WITH 59.75 FT SPAN (58.75+TWO 6"
OVERHANGS), SPAN 2
COMMENT
ANALYSIS B,3,RAT,S
POINT-OF-INTEREST T,ON,ON
ANALYSIS-SPECIAL 1,45
DIST-CONTROL-GIRDER 2
DIST-CONTROL-DL TA,UD
DIST-CONTROL-LL K, ,19.919, ,YES
DIST-LL-APPLICATION AP
MAP-LIMIT-STATE ST,1,I,Y,N
MAP-LIMIT-STATE ST,2,O,N,Y
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
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-MATL-PROPERTIES .15,.15,.015
DECK-LOAD-DESCR 1,DC,2,BARRIERS-2
DECK-LOAD-UNIFORM 1,.12,0,1*12
DECK-STAGE 1, , ,2
CONC-MATERIALS .150,5,40,40,7, , , , ,NO,
CONC-STD-SECTION 1,AASHTO-III
COMMENT REFINED CRITICAL SECTION IS 49.074 INCHES OR 100.696
CONC-SHEAR 100.696,4, , ,.4,8,90, , ,2.969,23.483
CONC-SHEAR 100.638,4, , ,.4,8,90, , ,2.969,23.483
CONC-SHEAR-CONSTANTS 1
COMMENT STIRRUPS-#4 DOUBLE LEG
STIRRUP-GROUP 1,.4
STIRRUP-SCHEDULE 1,1,6,0,6
STIRRUP-SCHEDULE 1,1,8,6,96
88
STIRRUP-SCHEDULE 1,1,10,102,130
STIRRUP-SCHEDULE 1,1,15,232,60
STIRRUP-SCHEDULE 1,1,18,292,54
STIRRUP-SCHEDULE 1,1,13,346,13
STIRRUP-SCHEDULE 1,1,18,359,54
STIRRUP-SCHEDULE 1,1,15,413,60
STIRRUP-SCHEDULE 1,1,10,473,130
STIRRUP-SCHEDULE 1,1,8,603,96
STIRRUP-SCHEDULE 1,1,6,699,6
PRESTRESS-MATERIALS 4.5,7
PRESTRESS-CONTINUITY AP
PS-BEAM-OVERHANG 1,6,6
LOSS-AASHTO-PRETEN 1,.5,
STRAND-MATL-PRETEN 1,.153,SR, , , , , , , ,.5
STRAND-GENERAL 1,1,1,8,1
STRAND-STRAIGHT 1,1,43,N,1,2
STRAND-GENERAL 1,3,1,2,1
STRAND-HARPED 1,3,4,43,4,21.042*12,37.708*12,1,2,2
STRAND-DEV-LENGTH 1,ALL,
COMPOSITE-MATERIALS 3,40,9
COMPOSITE-SLAB 1,109,8,0
SPAN-STD-XSECT 1,58.75*12
SPAN-SECTION 1,1,58.75*12,1
SUPPORT-FIXITY 1,R,R,F
SUPPORT-FIXITY 2,F,R,F
LOAD-LIVE-CONTROL B,D
89
Bridge 7171 (LFR)
TITLE 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
COMMENT STIRRUPS-#4 DOUBLE LEG
STIRRUP-GROUP 1,.4
COMMENT STIRRUPS-#6 DOUBLE LEG
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
COMMENT STIRRUP SCHEDULE IS TAKEN FROM BEAM END
STIRRUP-SCHEDULE 1,2,4,0,.5,100, , , ,0,0
STIRRUP-SCHEDULE 1,1,15.25,.5,16.375
STIRRUP-SCHEDULE 1,1,17.375,16.875,1.448
STIRRUP-SCHEDULE 1,1,19.5,18.323,3.25
STIRRUP-SCHEDULE 1,1,20.25,21.573,1.687
STIRRUP-SCHEDULE 1,1,21,23.620,35
STIRRUP-SCHEDULE 1,1,20.25,58.260,1.687
STIRRUP-SCHEDULE 1,1,19.5,59.947,3.250
STIRRUP-SCHEDULE 1,1,17.375,63.197,1.448
STIRRUP-SCHEDULE 1,1,15.25,64.645,16.375
STIRRUP-SCHEDULE 1,2,4,81.020,.5
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
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
PS-BEAM-OVERHANG 1,6,6
COMMENT
DEAD-LOAD 1,.5625,.116
COMMENT
LIVE-LOAD 3,1.212
TRUCK-CODE1 HS20T
COMMENT
DESIGN 3,1
INVENTORY
OPERATING
POINT-OF-INTEREST 100.265
91
Bridge 7171 (LRFR-Strength I)
TITLE BRIDGE 7171 (LRFR) Strength I
COMMENT PRESTRESSED CONCRETE GIRDER BRIDGE WITH 81'6.25" SPAN (80'6.25" SPAN
W/ 6" OVERHANG)
COMMENT
ANALYSIS B,3,RAT,S
POINT-OF-INTEREST T,ON,ON
ANALYSIS-SPECIAL 1,45
DIST-CONTROL-GIRDER 2
DIST-CONTROL-DL TA,UD
DIST-CONTROL-LL K, ,20, ,YES
DIST-LL-APPLICATION AP
MAP-LIMIT-STATE ST,1,I,Y,N
MAP-LIMIT-STATE ST,2,O,N,Y
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
DECK-GEOMETRY 7,80,6.4375,2.5*12,2.5*12,.3125,DC
DECK-TRAVEL-WAY 18,522
DECK-MATL-PROPERTIES .15,.15,.015
DECK-LOAD-DESCR 1,DC,2,BARRIERS-2
DECK-LOAD-UNIFORM 1,.14,0,1*12
DECK-STAGE 1, , ,2
CONC-MATERIALS .150,5,40,40,7, , , , ,NO,
CONC-STD-SECTION 1,AASHTO-III
COMMENT REFINED CRITICAL SECTION IS 42.009 INCHES OR 100.435
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
CONC-SHEAR-CONSTANTS 1
COMMENT STIRRUPS-#4 DOUBLE LEG
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 1,1,20.25,252.875,20.25
STIRRUP-SCHEDULE 1,1,21,273.125,35*12
STIRRUP-SCHEDULE 1,1,20.25,693.125,20.25
STIRRUP-SCHEDULE 1,1,19.5,713.375,3.25*12
STIRRUP-SCHEDULE 1,1,17.375,752.375,17.375
STIRRUP-SCHEDULE 1,1,15.25,769.75,16.375*12
PRESTRESS-MATERIALS 4.5,7
PRESTRESS-CONTINUITY AP
PS-BEAM-OVERHANG 1,6,6
LOSS-AASHTO-PRETEN 1,.5,
STRAND-MATL-PRETEN 1,.115,SR, , , , , , , ,.4375
STRAND-GENERAL 1,1,1,8,1
STRAND-STRAIGHT 1,1,43,N,2,2
STRAND-GENERAL 1,4,1,6,1
STRAND-STRAIGHT 1,4,37,N,0,0
STRAND-GENERAL 1,5,1,2,1
STRAND-HARPED 1,5,8,43,8,343.125,623.125,3,2,2
STRAND-DEV-LENGTH 1,ALL,
COMPOSITE-MATERIALS 3,40,9
COMPOSITE-SLAB 1,80,6.4375,0
SPAN-STD-XSECT 1,966.25
SPAN-SECTION 1,1,966.25,1
SUPPORT-FIXITY 1,R,R,F
SUPPORT-FIXITY 2,F,R,F
LOAD-LIVE-CONTROL B,D
93
Bridge 7171 (LRFR-Strength II)
TITLE BRIDGE 7171 (LRFR) Strength II
COMMENT PRESTRESSED CONCRETE GIRDER BRIDGE WITH 81'6.25" SPAN (80'6.25"
SPAN W/ 6" OVERHANG)
COMMENT
ANALYSIS B,3,RAT,S
POINT-OF-INTEREST T,ON,ON
ANALYSIS-SPECIAL 1,45
DIST-CONTROL-GIRDER 2
DIST-CONTROL-DL TA,UD
DIST-CONTROL-LL K, ,20, ,YES
DIST-LL-APPLICATION AP
MAP-LIMIT-STATE ST,1,I,Y,N
MAP-LIMIT-STATE ST,2,O,N,Y
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
DECK-GEOMETRY 7,80,6.4375,2.5*12,2.5*12,.3125,DC
DECK-TRAVEL-WAY 18,522
DECK-MATL-PROPERTIES .15,.15,.015
DECK-LOAD-DESCR 1,DC,2,BARRIERS-2
DECK-LOAD-UNIFORM 1,.14,0,1*12
DECK-STAGE 1, , ,2
CONC-MATERIALS .150,5,40,40,7, , , , ,NO,
CONC-STD-SECTION 1,AASHTO-III
COMMENT REFINED CRITICAL SECTION IS 46.080 INCHES OR 100.477
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
CONC-SHEAR-CONSTANTS 1
COMMENT STIRRUPS-#4 DOUBLE LEG
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
94
STIRRUP-SCHEDULE 1,1,20.25,252.875,20.25
STIRRUP-SCHEDULE 1,1,21,273.125,35*12
STIRRUP-SCHEDULE 1,1,20.25,693.125,20.25
STIRRUP-SCHEDULE 1,1,19.5,713.375,3.25*12
STIRRUP-SCHEDULE 1,1,17.375,752.375,17.375
STIRRUP-SCHEDULE 1,1,15.25,769.75,16.375*12
PRESTRESS-MATERIALS 4.5,7
PRESTRESS-CONTINUITY AP
PS-BEAM-OVERHANG 1,6,6
LOSS-AASHTO-PRETEN 1,.5,
STRAND-MATL-PRETEN 1,.115,SR, , , , , , , ,.4375
STRAND-GENERAL 1,1,1,8,1
STRAND-STRAIGHT 1,1,43,N,2,2
STRAND-GENERAL 1,4,1,6,1
STRAND-STRAIGHT 1,4,37,N,0,0
STRAND-GENERAL 1,5,1,2,1
STRAND-HARPED 1,5,8,43,8,343.125,623.125,3,2,2
STRAND-DEV-LENGTH 1,ALL,
COMPOSITE-MATERIALS 3,40,9
COMPOSITE-SLAB 1,80,6.4375,0
SPAN-STD-XSECT 1,966.25
SPAN-SECTION 1,1,966.25,1
SUPPORT-FIXITY 1,R,R,F
SUPPORT-FIXITY 2,F,R,F
LOAD-LIVE-CONTROL B,D
95
Bridge 8852 (LFR)
TITLE 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
COMMENT STIRRUPS-#4 DOUBLE LEG
STIRRUP-GROUP 1,.4
COMMENT
SPAN-A 1,97,5
SPAN-C 1,97,1,1
FIXITY 1,1,0,0,1,0
COMMENT STIRRUP SCHEDULE IS TAKEN FROM BEAM END
STIRRUP-SCHEDULE 1,1,2,0,.167,100, , , ,0,0
STIRRUP-SCHEDULE 1,1,4,.167,8
STIRRUP-SCHEDULE 1,1,6,8.167,3
STIRRUP-SCHEDULE 1,1,9,11.167,7.5
STIRRUP-SCHEDULE 1,1,12,18.667,10
STIRRUP-SCHEDULE 1,1,19,28.667,3.167
STIRRUP-SCHEDULE 1,1,17,31.833,1.417
STIRRUP-SCHEDULE 1,1,21,33.25,31.5
STIRRUP-SCHEDULE 1,1,17,64.75,1.417
STIRRUP-SCHEDULE 1,1,19,66.167,3.167
STIRRUP-SCHEDULE 1,1,12,69.333,10
STIRRUP-SCHEDULE 1,1,9,79.333,7.5
STIRRUP-SCHEDULE 1,1,6,86.8333,3
STIRRUP-SCHEDULE 1,1,4,89.833,8
STIRRUP-SCHEDULE 1,1,2,97.833,.167
COMMENT
PROPERTIES-PC1 150,5.5,3, , ,4.75
PROPERTIES-PC2 60,40, ,0,AASHTO
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
POINT-OF-INTEREST 100.464
97
Bridge 8852 (LRFR-Strength I)
TITLE BRIDGE 8852 (LRFR) Strength I
COMMENT PRESTRESSED CONCRETE GIRDER BRIDGE WITH 98' SPAN (97' W/ 6" OVERHANG)
COMMENT
ANALYSIS B,3,RAT,S
POINT-OF-INTEREST T,ON,ON
ANALYSIS-SPECIAL 1,54
DIST-CONTROL-GIRDER 2
DIST-CONTROL-DL TA,UD
DIST-CONTROL-LL K, ,19.267, ,YES
DIST-LL-APPLICATION AP
MAP-LIMIT-STATE ST,1,I,Y,N
MAP-LIMIT-STATE ST,2,O,N,Y
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
DECK-GEOMETRY 6,84,8,36,36,0,DC
DECK-TRAVEL-WAY 18,474
DECK-MATL-PROPERTIES .15,.15,.030
DECK-LOAD-DESCR 1,DC,2,BARRIERS-2
DECK-LOAD-UNIFORM 1,.650,0,1*12
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
CONC-SHEAR-CONSTANTS 1
COMMENT STIRRUPS-#4 DOUBLE LEG BARS
STIRRUP-GROUP 1,.4
STIRRUP-SCHEDULE 1,1,4,0,92
STIRRUP-SCHEDULE 1,1,6,92,3*12
STIRRUP-SCHEDULE 1,1,9,128,7.5*12
STIRRUP-SCHEDULE 1,1,12,218,10*12
98
STIRRUP-SCHEDULE 1,1,19,338,38
STIRRUP-SCHEDULE 1,1,17,376,17
STIRRUP-SCHEDULE 1,1,21,393,378
STIRRUP-SCHEDULE 1,1,17,771,17
STIRRUP-SCHEDULE 1,1,19,788,38
STIRRUP-SCHEDULE 1,1,12,826,10*12
STIRRUP-SCHEDULE 1,1,9,946,7.5*12
STIRRUP-SCHEDULE 1,1,6,1036,3*12
STIRRUP-SCHEDULE 1,1,4,1072,92
PRESTRESS-MATERIALS 4.75,7
PRESTRESS-CONTINUITY AP
PS-BEAM-OVERHANG 1,6,6
LOSS-AASHTO-PRETEN 1,.5,
STRAND-MATL-PRETEN 1,.153,LR, , , , , , , ,.5
STRAND-GENERAL 1,1,1,6,1
STRAND-STRAIGHT 1,1,52,N,0,0
STRAND-GENERAL 1,2,1,10,1
STRAND-STRAIGHT 1,2,50,N,1,2
STRAND-GENERAL 1,4,1,8,1
STRAND-STRAIGHT 1,4,46,N,0,0
STRAND-GENERAL 1,5,1,2,1
STRAND-HARPED 1,5,10,52,10,412,752,4,2,2,2
STRAND-DEV-LENGTH 1,ALL,
COMPOSITE-MATERIALS 3,60,9
COMPOSITE-SLAB 1,84,8,0
SPAN-STD-XSECT 1,97*12
SPAN-SECTION 1,1,97*12,1
SUPPORT-FIXITY 1,R,R,F
SUPPORT-FIXITY 2,F,R,F
LOAD-LIVE-CONTROL B,D
99
Bridge 8852 (LRFR-Strength II)
TITLE BRIDGE 8852 (LRFR) Strength II
COMMENT PRESTRESSED CONCRETE GIRDER BRIDGE WITH 98' SPAN (97' W/ 6" OVERHANG)
COMMENT
ANALYSIS B,3,RAT,S
POINT-OF-INTEREST T,ON,ON
ANALYSIS-SPECIAL 1,54
DIST-CONTROL-GIRDER 2
DIST-CONTROL-DL TA,UD
DIST-CONTROL-LL K, ,19.267, ,YES
DIST-LL-APPLICATION AP
MAP-LIMIT-STATE ST,1,I,Y,N
MAP-LIMIT-STATE ST,2,O,N,Y
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
DECK-GEOMETRY 6,84,8,36,36,0,DC
DECK-TRAVEL-WAY 18,474
DECK-MATL-PROPERTIES .15,.15,.030
DECK-LOAD-DESCR 1,DC,2,BARRIERS-2
DECK-LOAD-UNIFORM 1,.650,0,1*12
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
CONC-SHEAR-CONSTANTS 1
COMMENT STIRRUPS-#4 DOUBLE LEG BARS
STIRRUP-GROUP 1,.4
STIRRUP-SCHEDULE 1,1,4,0,92
STIRRUP-SCHEDULE 1,1,6,92,3*12
STIRRUP-SCHEDULE 1,1,9,128,7.5*12
STIRRUP-SCHEDULE 1,1,12,218,10*12
STIRRUP-SCHEDULE 1,1,19,338,38
100
STIRRUP-SCHEDULE 1,1,17,376,17
STIRRUP-SCHEDULE 1,1,21,393,378
STIRRUP-SCHEDULE 1,1,17,771,17
STIRRUP-SCHEDULE 1,1,19,788,38
STIRRUP-SCHEDULE 1,1,12,826,10*12
STIRRUP-SCHEDULE 1,1,9,946,7.5*12
STIRRUP-SCHEDULE 1,1,6,1036,3*12
STIRRUP-SCHEDULE 1,1,4,1072,92
PRESTRESS-MATERIALS 4.75,7
PRESTRESS-CONTINUITY AP
PS-BEAM-OVERHANG 1,6,6
LOSS-AASHTO-PRETEN 1,.5,
STRAND-MATL-PRETEN 1,.153,LR, , , , , , , ,.5
STRAND-GENERAL 1,1,1,6,1
STRAND-STRAIGHT 1,1,52,N,0,0
STRAND-GENERAL 1,2,1,10,1
STRAND-STRAIGHT 1,2,50,N,1,2
STRAND-GENERAL 1,4,1,8,1
STRAND-STRAIGHT 1,4,46,N,0,0
STRAND-GENERAL 1,5,1,2,1
STRAND-HARPED 1,5,10,52,10,412,752,4,2,2,2
STRAND-DEV-LENGTH 1,ALL,
COMPOSITE-MATERIALS 3,60,9
COMPOSITE-SLAB 1,84,8,0
SPAN-STD-XSECT 1,97*12
SPAN-SECTION 1,1,97*12,1
SUPPORT-FIXITY 1,R,R,F
SUPPORT-FIXITY 2,F,R,F
LOAD-LIVE-CONTROL B,D
101
Bridge 7195 (LFR)
TITLE 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
COMMENT STIRRUPS-#4 DOUBLE LEG
STIRRUP-GROUP 1,.4
COMMENT
SPAN-A 1,107,5
SPAN-C 1,107,1,1
FIXITY 1,1,0,0,1,0
COMMENT STIRRUP SCHEDULE IS TAKEN FROM BEAM END
STIRRUP-SCHEDULE 1,1,9,0,.75,100, , , ,0,0
STIRRUP-SCHEDULE 1,1,11,.75,34
STIRRUP-SCHEDULE 1,1,1.25,34.75,3.75
STIRRUP-SCHEDULE 1,1,1.667,38.5,30
STIRRUP-SCHEDULE 1,1,1.25,68.5,3.75
STIRRUP-SCHEDULE 1,1,11,72.25,34
STIRRUP-SCHEDULE 1,1,9,106.25,.75
COMMENT
PROPERTIES-PC1 150,5,3, , ,4.5
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
PS-BEAM-OVERHANG 1,6,6
COMMENT
DEAD-LOAD 1,.868,.164
COMMENT
LIVE-LOAD 3,1.742
TRUCK-CODE1 HS20T
COMMENT
DESIGN 3,1
INVENTORY
OPERATING
POINT-OF-INTEREST 100.27
103
Bridge 7195 (LRFR-Strength I)
TITLE BRIDGE 7195 (LRFR) Strength I
COMMENT PRESTRESSED CONCRETE GIRDER BRIDGE WITH 108 FT SPAN
COMMENT
ANALYSIS B,3,RAT,S
POINT-OF-INTEREST T,ON,ON
ANALYSIS-SPECIAL 1,63
DIST-CONTROL-GIRDER 2
DIST-CONTROL-DL TA,UD
DIST-CONTROL-LL K, ,21.259, ,YES
DIST-LL-APPLICATION AP
MAP-LIMIT-STATE ST,1,I,Y,N
MAP-LIMIT-STATE ST,2,O,N,Y
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
DECK-GEOMETRY 5,115,7.25,40.859,39.375,0,DC
DECK-TRAVEL-WAY 18,522
DECK-MATL-PROPERTIES .15,.15,.015
DECK-LOAD-DESCR 1,DC,2,BARRIERS-2
DECK-LOAD-UNIFORM 1,.1,0,1*12
DECK-STAGE 1, , ,2
CONC-MATERIALS .150,5,40,40,7, , , , ,NO,
CONC-STD-SECTION 1,AASHTO-V
COMMENT REFINED CRITICAL SECTION IS 53.810 INCHES OR 100.419
CONC-SHEAR 100.419,4, , ,.4,11,90, , ,2.545,25.173
CONC-SHEAR 100.5,4, , ,.4,11,90, , ,2.545,25.173
CONC-SHEAR-CONSTANTS 1
COMMENT STIRRUPS ARE DEFINED AS GROUP 1
STIRRUP-GROUP 1,.4
STIRRUP-SCHEDULE 1,1,11,10,
PRESTRESS-MATERIALS 4.5,7,25
PRESTRESS-CONTINUITY AP
PS-BEAM-OVERHANG 1,6,6
104
LOSS-AASHTO-PRETEN 1,.5,
STRAND-MATL-PRETEN 1,.115,SR, , , , , , , ,.4375
STRAND-GENERAL 1,1,1,10,1
STRAND-STRAIGHT 1,1,61,N,2,2
STRAND-GENERAL 1,4,1,8,1
STRAND-STRAIGHT 1,4,55,N,0,0
STRAND-GENERAL 1,5,1,6,1
STRAND-STRAIGHT 1,5,53,N,0,0
STRAND-GENERAL 1,6,1,3,1
STRAND-HARPED 1,6,12,61,12,38.7*12,68.3*12,5,2,2
STRAND-DEV-LENGTH 1,ALL,
COMPOSITE-MATERIALS 3,40,9
COMPOSITE-SLAB 1,115,7.25,0
SPAN-STD-XSECT 1,107*12
SPAN-SECTION 1,1,107*12,1
SUPPORT-FIXITY 1,R,R,F
SUPPORT-FIXITY 2,F,R,F
LOAD-LIVE-CONTROL B,D
105
Bridge 7195 (LRFR-Strength II)
TITLE BRIDGE 7195 (LRFR) Strength II
COMMENT PRESTRESSED CONCRETE GIRDER BRIDGE WITH 108 FT SPAN
COMMENT
ANALYSIS B,3,RAT,S
POINT-OF-INTEREST T,ON,ON
ANALYSIS-SPECIAL 1,63
DIST-CONTROL-GIRDER 2
DIST-CONTROL-DL TA,UD
DIST-CONTROL-LL K, ,21.259, ,YES
DIST-LL-APPLICATION AP
MAP-LIMIT-STATE ST,1,I,Y,N
MAP-LIMIT-STATE ST,2,O,N,Y
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
DECK-GEOMETRY 5,115,7.25,40.859,39.375,0,DC
DECK-TRAVEL-WAY 18,522
DECK-MATL-PROPERTIES .15,.15,.015
DECK-LOAD-DESCR 1,DC,2,BARRIERS-2
DECK-LOAD-UNIFORM 1,.1,0,1*12
DECK-STAGE 1, , ,2
CONC-MATERIALS .150,5,40,40,7, , , , ,NO,
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
CONC-SHEAR-CONSTANTS 1
COMMENT STIRRUPS ARE DEFINED AS GROUP 1
STIRRUP-GROUP 1,.4
STIRRUP-SCHEDULE 1,1,11,10,
PRESTRESS-MATERIALS 4.5,7,25
PRESTRESS-CONTINUITY AP
PS-BEAM-OVERHANG 1,6,6
106
LOSS-AASHTO-PRETEN 1,.5,
STRAND-MATL-PRETEN 1,.115,SR, , , , , , , ,.4375
STRAND-GENERAL 1,1,1,10,1
STRAND-STRAIGHT 1,1,61,N,2,2
STRAND-GENERAL 1,4,1,8,1
STRAND-STRAIGHT 1,4,55,N,0,0
STRAND-GENERAL 1,5,1,6,1
STRAND-STRAIGHT 1,5,53,N,0,0
STRAND-GENERAL 1,6,1,3,1
STRAND-HARPED 1,6,12,61,12,38.7*12,68.3*12,5,2,2
STRAND-DEV-LENGTH 1,ALL,
COMPOSITE-MATERIALS 3,40,9
COMPOSITE-SLAB 1,115,7.25,0
SPAN-STD-XSECT 1,107*12
SPAN-SECTION 1,1,107*12,1
SUPPORT-FIXITY 1,R,R,F
SUPPORT-FIXITY 2,F,R,F
LOAD-LIVE-CONTROL B,D
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
110 N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A
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
100 N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A
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
110 N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A
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).
Strength I Strength II
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).
Strength I Strength II
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).
Strength I Strength II
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
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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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