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 Title:
 Comparison between the standard AASHTO bridge design specifications and the AASHTO LRFD bridge design specifications for buried concrete structures
 Creator:
 Miller, Larry James
 Publication Date:
 2006
 Language:
 English
 Physical Description:
 xv, 205 leaves : ; 28 cm
Subjects
 Subjects / Keywords:
 AASHTO LRFD bridge construction specifications ( lcsh )
Underground construction ( lcsh ) Concrete construction ( lcsh ) Bridges  Design and construction ( lcsh ) Bridges  Design and construction ( fast ) Concrete construction ( fast ) Underground construction ( fast )
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 bibliography ( marcgt )
theses ( marcgt ) nonfiction ( marcgt )
Notes
 Bibliography:
 Includes bibliographical references (leaves 203205).
 Statement of Responsibility:
 by Larry James Miller.
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 University of Colorado Denver
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 Auraria Library
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 All applicable rights reserved by the source institution and holding location.
 Resource Identifier:
 123128151 ( OCLC )
ocn123128151
 Classification:
 LD1193.E53 2006m M54 ( lcc )

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COMPARISON BETWEEN THE STANDARD AASHTO BRIDGE DESIGN
SPECIFICATIONS AND THE AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS FOR BURIED CONCRETE STRUCTURES
by
Larry James Miller
B.S.C.E., University of Colorado at Denver, 1998
A thesis submitted to the University of Colorado at Denver in partial fulfillment of the requirements for the degree of Master of Science Civil Engineering
2006
This thesis for the Master of Science
degree by Larry James Miller has been approved by
Stephan A. Durham
Bruce Janson
\\Tjo 
Date
Miller, Larry James (MSCE, Department of Civil Engineering)
Comparison Between the Standard AASHTO Bridge Design Specifications and the AASHTO LRFD Bridge Design Specifications for Buried Concrete Structures Thesis Directed by Assistant Professor Stephan A. Durham
ABSTRACT
For the past thirty years it has been common practice to use the American Association of State Highway and Transportation Officials (AASHTO) Standard Design Specifications for underground precast concrete structures. Today, the bridge engineering profession is transitioning from the Standard AASHTO Bridge Design Specifications (Load Factor Design, LFD) to the Load and Resistance Factor Design Specifications (LRFD). The Federal Highway Administration (FHWA) has mandated that all concrete bridges designed after October 2007 must be designed using the AASHTO LRFD Bridge Design Specifications if federal funding is to be provided. This extends to buried precast concrete structures as these types of structures are included in the LRFD Specifications. The new LRFD Design Specifications utilize stateoftheart analysis and design methodologies, and make use of load and resistance factors based on the known variability of applied loads and material properties. Structures designed with the LRFD specifications have a more uniform
level of safety. Consequently, designs utilizing the LRFD Specifications will have superior serviceability and longterm maintainability. This thesis examines the current LRFD Design Specifications and the Standard AASHTO Specifications used in designing underground concrete structures such as underground utility structures, drainage inlets, threesided structures, and box culverts. Although many of the provisions of these two codes are the same, there are important differences that can have a significant impact on the amount of reinforcement, member geometry, and cost to produce buried reinforced concrete structures. This thesis compares related provisions from both design specifications. Many of the AASHTO LRFD Code provisions that differ from the Standard Specifications include terminology, load factors, implementation of load modifiers, load combinations, multiple presence factors, design vehicle live loads, distribution of live load to slabs and earth fill, live load impact, live load surcharge, and the concrete design methodology for fatigue, shear strength, and crack control. The addition of the distributed lane load required in the LRFD Specifications significantly increases the service moment. The maximum increase in live load as a result of the impact factor is 21% at a fill depth of 3 ft. The intent of this thesis is to act as a reference on how to apply the current provisions from the LRFD Design Specifications to underground precast concrete structures.
This research shows there is greater reliability and a more uniform factor of safety when utilizing the LRFD Specifications. The provisions in the LRFD Specifications
are more concise and more beneficial to design engineers with the addition of the commentary. Therefore, the code is simpler to apply than the Standard Specifications.
This abstract accurately represents the content of the candidateâ€™s thesis. I recommend its publication.
Signed
Stephan A. Durham
ACKNOWLEDGEMENT
I would like to express my deepest appreciation to Dr. Stephan Durham for his patience over the past year. Thanks for hanging in there with me and giving me words of encouragement. I would like to thank Dr. Kevin Rens and Dr. Bruce Janson for participating on my thesis committee.
Thanks to my colleges Ray Rhees, Clint Brookhart, and Jim Baker for giving me the opportunity to pursue this degree. I appreciate the support and all of the wonderful advice you have given me.
I would like to thank my mom and dad who probably think I am crazy for going back to school, and spending countless nights in front of my computer. Itâ€™s finally over! I want to especially thank my beloved wife, Julie Miller for putting up with me while working on this project. I know it has not been easy, thanks for hanging in there. I would also like to acknowledge by beautiful daughter, Abigail Marie Miller in hopes that she will pursue her dreams as well. I love you all.
TABLE OF CONTENTS
Figures............................................................x
Tables...........................................................xiv
CHAPTER
1. INTRODUCTION................................................1
Historical Development of LRFD Specifications........2
Problem Statement and Research Significance..........9
2. LITERATURE REVIEW......................................... 11
Comparison of Standard Specifications and LRFD
Specifications......................................11
American Concrete Pipe Association Study............13
Flexural Crack Control in Concrete Bridges..........13
National Cooperative Highway Research Program
(NCHRP), Project 15 29..............................14
Design Live Loads on Box Culverts, University
of Florida..........................................16
3. AASHTO LFD STANDARD SPECIFICATIONS.........................23
Load Factors and Load Combinations..................23
AASHTO Standard Vehicular Design Live Loads.........29
Earth Fill and Vertical Earth Pressure Loading......35
vi
Distribution of Live Loads for Depths of Fill
Greater Than 2 ft.......................................38
Case 1  Distribution of Wheel Loads that do not
Overlap..........................................40
Case 2  Distribution of Wheel Load from a Single
Axle Overlap.....................................41
Case 3  Full Distribution of Wheel Loads from
Multiple Axles...................................42
Distribution of Live Loads for Depths of Fill Less
Than 2 ft...............................................47
Impact Factor...........................................50
Lateral Live Load Surcharge.............................51
4. LRFD STANDARD DESIGN SPECIFICATIONS...........................53
Load Factors and Load Combinations......................53
Load Modifiers..........................................59
AASHTO Standard Vehicular Design Live Loads.............62
Earth Fill and Vertical Earth Pressure Loading..........64
Multiple Presence Factors...............................66
Case 1  Depth of Fill is equal to or Greater
Than 2 ft........................................66
vii
Case 2  Depth of fill is less than 2 ft, and the direction
of traffic is parallel to span.....................67
Case 3  Depth of fill is less than 2 ft, and the direction
of traffic is perpendicular to span................67
Distribution of Live Loads for Depths of Fill Greater
Than 2 ft.................................................68
Case 1  Distribution of Wheel Loads that
do not Overlap.....................................71
Case 2  Distribution of Wheel Loads from a
Single Axle Overlap................................72
Case 3  Full Distribution of Wheel Loads
from Multiple Axles Overlap........................73
Case 4  Distribution of Wheel Loads from
Passing Vehicles...................................74
Distribution of Live Loads for Depths of Fill Less
Than 2 ft............................................... 76
Dynamic Load Allowance, Impact (IM).......................78
Lateral Live Load Surcharge...............................79
5. COMPARISONS BETWEEN LFD AND LRFD.................................82
Design Vehicular Live Loads...............................82
viii
Multiple Presence Factor
84
Dynamic Load Allowance, Impact...................... 82
Lateral Live Load Surcharge..........................88
Distribution of Wheel Loads through Earth
Fills for Depths of Fill Greater Than 2 ft...........90
Distribution of Live Loads for Depths of Fill
Less than 2 ft.......................................96
Load Factors and Load Combinations...................98
6. DESIGN EXAMPLES............................................103
Design Example #1...................................103
Design Parameters............................103
Standard AASHTO Specifications...............104
Standard LRFD Specifications.................126
Design Example #2...................................153
Standard AASHTO Specifications...............153
Standard LRFD Specifications.................174
7. SUMMARY AND CONCLUSIONS....................................199
REFERENCES..............................................................202
ix
LIST OF FIGURES
Figure
2.1 Boussinesq Point Load........................................................18
3.1 AASHO 1935 Truck Train Loading...............................................29
3.2 Characteristics of the AASHTO Design Truck...................................31
3.3 Characteristics of Alternative Military Loading..............................33
3.4 Tire Contact Area............................................................34
3.5 Earth Fill Depth and Vertical Earth Pressure Loading.........................36
3.6 LFD Wheel Load Distribution through Earth Fill...............................39
3.7 Overlapping Wheel Load Distribution through Earth Fill.......................39
3.8 Case 1, Wheel Load Distribution through Earth Fill...........................40
3.9 Case 2  Overlapping Wheel Load Distribution through Earth Fill..............41
3.10 Case 3  Overlapping Wheel and Axle load Distribution through Earth Fill...43
3.11 LFD Live Load Pressures through Earth Fill.................................44
3.12 LFD Live Load Spread For 3 ft Overburden..................................45
3.13 LFD Live Load Service Moments vs. Increasing Design Spans..................46
3.14 LFD Distribution Width, E for a Single Wheel Load..........................48
3.15 Effective Distribution Widths on Slabs......................................48
3.16 Reduced Distribution Widths on Slabs........................................49
x
3.17 LFD Equivalent Height.......................................................52
3.18 Live Load Surcharge Pressure................................................52
4.1 Characteristics of LRFD Design Truck and Wheel Footprint....................62
4.2 Characteristics of the Design Tandem........................................63
4.3 Earth Fill Depth and Vertical Earth Pressure Loading........................65
4.4 LRFD Wheel Load Distribution through Earth Fill.............................69
4.5 Overlapping Wheel Load Distribution through Earth Fill......................70
4.6 Wheel Load Distribution through Earth Fill..................................71
4.7 Overlapping Wheel Load Distribution through Earth Fill...,..................72
4.8 Overlapping Wheel and Axle Load Distribution through Earth Fill.............74
4.9 Overlapping Wheel Load Distribution by Passing Vehicles.....................75
4.10 Overlapping Axle Load Distribution by Passing Vehicles.....................75
4.12 Dynamic Load Allowance vs. Burial Depth....................................79
4.13 Wall Height for Live Load Surcharge Pressures..............................81
5.1 Alternative Military Loading vs. Design Tandem Loading......................83
5.2 Increase of Force Effects due to Design Track vs. Design Track + Lane Load..85
5.3 Dynamic Load Allowance vs. Impact...........................................87
5.4 Percent Increase in Dynamic Load Allowance LRFD vs. LFD.....................87
5.5 Live Load Surcharge Equivalent Heights, heq..................................89
5.6 Live Load Distribution Areas for a Single Wheel..............................92
xi
5.7 Overlapping Wheel Load Distribution by Passing Vehicles...................93
5.8 Overlapping Axle Load Distribution by Passing Vehicles....................93
5.9 Distributed Service Live Load Values through Earth Fill with Impact.......95
5.10 Distributed Factored Live Load Values through Earth Fill with Impact.....95
5.11 Service Moment  LRFD vs. LFD Design Live Loads (Multiple presence
factor and impact neglected)............................................98
5.12 Service Moment  LRFD vs. LFD Design Live Loads (Multiple presence
factor and impact included).............................................99
5.13 Loads on a ThreeSided Culvert...........................................101
6.1 Design Example #1, Geometry...............................................105
6.2 LFD Vertical and Lateral Earth Pressures..................................106
6.3 LFD Live Load Surcharge Pressure..........................................107
6.4 HS20 Distribution through Earth Fill.....................................108
6.5 Alternative Military Distribution through Earth Fill......................109
6.6 LFD Service Loading Configuration, Cases 13..............................112
6.7 Critical Locations for Stresses...........................................113
6.8 LFD Reinforcement Placement for Design Example #1.........................126
6.9 LRFD Vertical and Lateral Earth Pressures.................................127
6.10 LRFD Wall Height, Example #1.............................................128
6.11 LRFD Live Load Surcharge Pressure........................................129
xii
6.12 Distribution area for Design Truck.......................................131
6.13 Distribution area for two adjacent design vehicles.......................132
6.14 Distribution area for Design Tandem......................................132
6.15 Design Example #1, LRFD Service Loading Configuration, Cases 1  3.......136
6.16 Critical Locations for Stresses.........................................137
6.17 LRFD Reinforcement Placement for Design Example #1......................153
6.18 LFD Vertical and Lateral Earth Pressures................................155
6.19 LFD Live Load Surcharge Pressure........................................156
6.20 LFD Service Loading Configuration, Cases 13............................159
6.21 LFD Critical Locations for Stresses.....................................160
6.22 LFD Reinforcement Placement for Design Example #2.......................173
6.23 LRFD Vertical and Lateral Earth Pressures...............................175
6.24 LRFD Wall Height.........................................................176
6.25 LRFD Live Load Surcharge Pressure.......................................177
6.26 Loading Configuration, Cases 13........................................182
6.27 Locations of Critical Stresses...........................................183
6.28 LRFD Reinforcement Placement for Design Example #2......................197
xiii
TABLES
Table
3.1 AASHTO Group Loading Coefficients and Load Factors.......................26
3.2 AASHTO Earth Pressure and Dead Load Coefficients........................27
3.3 AASHTO Resistance Factors for Underground Concrete Structures...........29
3.4 AASHTO Standard HS Design Truck Classes.................................30
3.5 Case 1..................................................................40
3.6 Case 2..................................................................41
3.7 Case 3..................................................................42
3.8 Service Moments from HS20, HS25, and Alternative Military Loads.......46
3.9 Impact Factor...........................................................50
4.1 Load Combinations and Load Factors.......................................57
4.2 Load Factors for Permanent Loads, yp....................................59
4.3 Multiple Presence Factors...............................................67
4.4 Case 1..................................................................71
4.5 Case 2..................................................................72
4.6 Case 3..................................................................73
4.7 Equivalent Heights......................................................80
5.1 Load Factors for LRFD and LFD Specifications............................100
6.1 LFD  Structural Analysis Results per Foot Width, Example 1.............113
xiv
6.2 LRFD  Structural Analysis Results per Foot Width, Example 1.............138
6.3 Area of Steel comparison...................................................152
6.4 Impact Factor..............................................................156
6.5 LFD  Structural Analysis Results per Foot Width, Example 2................161
6.6 LRFD  Structural Analysis Results per Foot Width, Example 2.........'...183
6.7 Area of Steel comparison...................................................152
xv
Chapter 1 Introduction
Historically, much of the design methodology and design loads for underground concrete structures such as pipe and box culvert came from the American Association of State Highway and Transportation Officials (AASHTO). In the 1930's AASHTO began publishing the Standard Specifications for Highway Bridges. The standard practice at the time was to use one factor of safety. This methodology is commonly known as allowable stress design (ASD). In the 1970s, AASHTO began varying the factor of safety for each load in relation to the engineer's ability to predict the corresponding load. This corresponding bridge design methodology was referred to as load factor design (LFD). The change from ASD to LFD was made in the form of interim revisions by AASHTO. In fact, the Standard Specifications have never been completely revised and still include provisions from both the LFD and ASD methodologies (â€LRFD: State Departmentâ€ 2006).
AASHTO introduced the Load and Resistance Factor Design (LRFD) Bridge Design Specification in 1994, with the intent of replacing the Standard Specifications for Highway bridges with this reliability based code that provides a more uniform safety for all elements of bridges. The AASHTO LRFD Highway Bridge Design Specifications were developed with the intent of implementing a more rational approach for the design of highway structures. The LRFD Specifications utilize load
1
and resistance factors based on the known variability of applied loads and material properties. The load and resistance factors were calibrated from actual bridge statistics ensuring a more uniform level of safety (â€œLRFD: State Departmentâ€ 2006).
1.1 Historical Development of LRFD Specifications
In the late 1970â€™s the Ontario Ministry of Transportation and Communication, now known as the Ministry of Transportation, developed its own bridge design specifications, rather than continue to use the AASHTO Standard Specifications for Highway Bridges. The Ontario Ministry of Transportation and Communication required that the new design specifications be based on probabilistic limit states. As a result, the first edition of the Ontario Highway Bridge Design Code (OHBDC) was released in 1979 to the design community as North Americas first calibrated, reliabilitybased limit state specification (NCHRP 1998). The OHBDC is currently in its third edition after being updated in 1983 and 1993. In addition, the OHBDC included a companion volume of commentary in which the AASHTO Standard Specifications did not. Over time, more and more U.S. engineers became familiar with the OHBDC. They recognized certain logic in the calibrated limit states design. Many American engineers began to question the Standard AASHTO Specifications and whether it should be based on comparable philosophy.
2
The National Cooperative Highway Research Program (NCHRP), National Science Foundation (NSF), and various states completed numerous research projects. These organizations were collecting new information on bridge design faster than it could be critically reviewed and were appropriately adopted to form the AASHTO Standard Specifications. Later research revealed that many of the revisions that have occurred to the Standard AASHTO Specifications since its inception had resulted in numerous inconsistencies and it made the document appear patchwork.
In the spring of 1986, a group of state bridge engineers or their representatives met in Denver and drafted a letter to the AASHTO Highway Subcommittee on Bridges and Structures (HSCOBS) indicating their concern that the AASHTO Standard Specifications must be revised. They also raised concerns that the Technical Committee Structure, operating under the HSCOBS, was not able to keep up with emerging technologies. As a result, this group of state bridge engineers began the process leading to the development of the LRFD Specifications. A group of state bridge engineers met with the staff of the NCHRP in July of 1986 to consider whether a project could be developed to explore the concerns raised in the letter submitted at the meeting in Denver. This led to the NCHRP project 1228(7) â€œDevelopment of Comprehensive Bridge Specifications and Commentary.â€ A pilot study was conducted by Modjeski and Masters, Inc. with Dr. John M Kulicki as Principle
3
Investigator. The list of tasks for this project and the brief outcome are listed below (NCHRP 1998).
â€¢ Task 1  Review other specifications, and the philosophy of safety and coverage provided. Information collected from various sources around the world indicated that most of the First World Countries appeared to be moving in the direction of a calibrated, reliabilitybased, limit states specification.
â€¢ Task 2  Other than the Standard Specifications, review other AASHTO documents for their inclusion into a revised standard specification. This can be best described as a search for gaps and inconsistencies in the 13th edition of the AASHTO Standard Specifications for Highway Bridges. â€œGapsâ€ were areas where coverage was missing; â€œInconsistenciesâ€ were internal conflicts, or contradictions of wording or philosophy. Numerous gaps and inconsistencies were found in the Standard Specifications.
â€¢ Task 3  Assess the feasibility of a probabilitybased specification.
The design philosophy used in a variety of specifications was reviewed. They were the ASD, LFD, and the Reliability Based
4
Design. It was generally agreed upon that the probabilitybased specification was more suitable.
â€¢ Task 4  Prepare an outline for a revised AASHTO Specification for Highway Bridge Design and commentary, and present a proposed organizational process for completing such a document.
The findings of NCHRP Project 1228(7) were presented to the AASHTO HSCOBS in May of 1987. There were 7 options that were available:
â€¢ Option 1  Keep the Status Quo
â€¢ Option 2  Table Consideration of LRFD for the Short Term
â€¢ Option 3  Immediate Adoption of the OHBDC
â€¢ Option 4  Replace Current with LRFD Immediately
â€¢ Option 5  Replace Current LFD with LRFD in the Near Term
â€¢ Option 6  Develop LRFD for Evaluation Only, or
â€¢ Option 7  Develop LRFD as a Guide Specification
A recommendation was made to develop a probabilitybased limit states specification, revise as many of the gaps and inconsistencies as possible, and develop a commentary specification. Thus NCHRP Project 1233, entitled â€œDevelopment of Comprehensive Specification and Commentary,â€ began in July of 1988. The primary objective was to develop a recommended LRFDbased bridge design specifications
5
and commentary for consideration by the AASHTO Subcommittee on Bridges and Structures. Thirteen task groups were responsible for developing the recommended specifications. The task groups were: general features, loads, analysis and evaluation, deck systems, concrete structures, metal structures, timber structures, joints, bearings, and accessories; foundations; soilstructure interaction systems, moveable bridges, bridge rail, and specification calibration. The project consisted of four contractors and 47 consultants employed to assist with the development of the specification and commentary. In addition, more than 20 state, federal, and industry engineers worked on the project volunteering their time (Project 1233 2006). The project was completed on December 31, 1993. The LRFD specifications were adopted by AASHTO and published as the AASHTO LRFD Bridge Design Specifications. The 1994 edition was the first version, with both SI unit and customary U.S. unit specifications available. Currently, the 2006 interim revision edition is the third edition of the AASHTO LRFD Bridge Design Specifications.
Today, the Federal Highway Administration (FHWA) and State Departments of Transportation have established as a goal that the LRFD Standard Specifications be used on all new bridge designs after 2007. In fact, AASHTO in concurrence with FHWA has set a deadline of October 1st, 2007 for full implementation by all states. States must design all new bridges according to the LRFD Specifications. At least 46 states have fully or partially implemented the LRFD Specifications to date, or are
6
working with the FHWA to develop a plan for implementation. A 2004 AASHTO Oversight Committee survey found that 12 states have fully implemented the specifications. Another 34 states have partially implemented the LRFD Specifications or are currently in the stage of developing implementation plans and designing pilot projects (â€œLRFD: Achieving Greater Reliabilityâ€ 2004). The FHWA is providing assistance to states in transition by providing a number of resources that include a team of structural, geotechnical, and research engineers who can meet with individual states and provide guidance in developing a StateSpecific LRFD implementation plan, training courses, and LRFD Design Workshops. In fact, the FHWA lists tips for successful implementation on the following website, http://www.fhwa.dot.gov/BRIDGE/lrfd/tips.cfm. Tips on the website include:
â€¢ Staff: Dedicate staff for LRFD planning and design (and studies if necessary) and train the initial design and study squad in LRFD. Utilize FHWA and other State Departments of Transportation assistance.
â€¢ Design Transition Strategy: Set a target date for full LRFD implementation on all new and replacement bridges and on all inhouse and consultant projects. Perform inhouse trial LRFD design of LFD projects (or have pilot LRFD projects) to develop questions and
7
resolutions. These trials also help to gain familiarity with the LRFD Specifications. After the completion of the trial/pilot projects, utilize the LRFD design in increments up to the target date or have a onestep conversion to LRFD. The latter should help you minimize the problem of maintaining two separate design specifications and manuals. The pilot projects should be selected carefully to represent low priority, routinely designed bridges.
â€¢ Software: Acquire a computer program that utilizes LRFD. There are many state and private LRFD software programs available for steel and concrete bridge superstructures and concrete substructures
â€¢ Training: Sponsor inhouse training courses for all designers (by inhouse instructors, local universities instructors, industry, or by FHWA). Acquire LRFD design examples and software for handson training. Require that consultants attend LRFD training before they perform LRFD designs in a particular state.
â€¢ Technical Support: Develop a technical support group that is readily available to answer questions pertaining to the LRFD Specifications. Utilize LRFD support teams, states, industry, universities, and FHWA resources. In addition, retaining a firm experienced in LRFD for questions may prove to be beneficial.
8
â€¢ Documentation Support: Update standards, manuals, and guidance to coordinate with the LRFD Specifications. Develop predesigned LRFD decks and barriers to shorten the design process if standardized designs are not available. Contract services to update existing design materials to LRFD.
â€¢ FineTune Documentations: After the completion of the pilot project and/or full LRFD conversion, finetune the LRFD standards, manuals, and guidance if and when needed.
1.2 Problem Statement and Research Significance
This thesis examines the current LRFD Design Specifications and the Standard AASHTO Specifications used in designing underground concrete structures such as underground utility structures, drainage inlets, threesided structures, and box culverts. Many of the AASHTO LRFD Code provisions that differ from the Standard Specifications include terminology, load factors, implementation of load modifiers, load combinations, multiple presence factors, design vehicle live loads, distribution of live load to slabs and earth fill, live load impact, live load surcharge, and the concrete design methodology for fatigue, shear strength, and crack control. The October 1st, 2007 deadline that AASHTO in concurrence with the Federal Highway Administration has set for all states to be completely converted to the AASHTO
9
LRFD Bridge Design Specifications is soon approaching. Although there are many training tools available to utilize the LRFD Specifications on highway bridges, there are very little resources available for designing underground precast concrete. This thesis addresses how to transition from the Standard Specifications to the LRFD Specifications when designing underground precast concrete. This thesis includes:
â€¢ A comprehensive literature review of existing and current studies associated with the Standard LFD and LRFD Specifications.
â€¢ A detailed summary of the variables and design methodology for buried precast concrete structures using the AASHTO LFD Standard Specifications.
â€¢ A detailed summary of the variables and design methodology for buried precast concrete structures using the AASHTO LRFD Bridge Design Specifications.
â€¢ A thorough comparison between the LRFD and LFD specifications.
â€¢ Two design examples illustrating the use of both specifications. The examples are of a buried threeside precast concrete structure.
â€¢ A summary of this thesis document.
10
Chapter 2 Literature Review
Currently, bridge designers are transitioning from the Standard AASHTO Bridge Design Specifications to the Load and Resistance Factor Design Specifications. The LRFD Bridge Design Specifications were developed in 1994; however, bridge designers were given the option of using either specification. The new specifications utilize stateoftheart analysis and design methodologies. In addition, the LRFD Specifications make use of load and resistance factors based on the known variability of applied loads and material properties. Differences between the two specifications include terminology, load factors, implementation of load modifiers, load combinations, multiple presence factors, design vehicle loads, distribution of live load to slabs and earth fill, live load impact, live load surcharge, and the concrete design methodology for fatigue, shear strength, and control of cracking. There has been very little research comparing all of the provisions from both specifications when designing underground concrete structures. However, there has been research completed comparing specific topics from both specifications and impact the LRFD Specification has had on the engineering community.
2.1 Comparison of Standard Specifications and LRFD Specifications
Rund and McGrath (2000) compared all of the provisions from AASHTO Standard Specifications and the LRFD Specifications for precast concrete box
11
culverts. The research analyzed several combinations of box culvert sizes and fill depths utilizing both specifications. Typically, the provisions from the LRFD Specifications yielded greater design loads and therefore required more area of steel reinforcement. The differences in reinforcement areas were the most pronounced for fill depths less than 2 ft. This was primarily the result of the differences in distributing the live load to the top slab into equivalent strip widths. The equivalent strip width is the effective width of slab that resists the applied load. In addition, for culvert spans up to 10 ft, the LRFD Specifications required shear reinforcement. Analysis utilizing the Standard AASHTO Specifications also show required shear reinforcement for a similar range of spans, but provisions permit the shear effects to be neglected. For depths of fill between 2 and 3 feet, the differences in reinforcement areas were due to fatigue requirements. The provisions in the Standard Specifications for fatigue were not present in the LRFD Specifications. For depths of overburden greater than 3 ft, the differences in the reinforcing areas decreased slightly. However, with increasing depth, the LRFD Specifications required greater required area of steel reinforcement. This was primarily due to the distribution of live load through earth fill. The provisions in the LRFD Specifications often yield higher design forces from wheel loads than the Standard Specification. It is important to note that the research utilized the first edition of the LRFD Specifications, which has since been revised and
12
is in its 3rd edition. Many of the provisions from this research have been modified slightly.
2.2 American Concrete Pipe Association Study
The American Concrete Pipe Association wrote a short article comparing the live loads on concrete pipe from both specifications (ACPA 2001). The primary objective of this research was to compare the live load model and distribution methods used in both specifications. The article included four design examples illustrating the design steps that are required to be taken when designing reinforced concrete pipe using the Standard LRFD Specifications. Similar to the article written by Rund, and McGrath (2000), the paper concluded that the LRFD Specifications typically produced greater design forces than the Standard Specification.
2.3 Flexural Crack Control in Concrete Bridges
Several States have found that crack control requirements tend to govern the design of flexural steel in concrete structures more frequently with the provisions of the 1994 LRFD Specifications than under the Standard AASHTO Specifications (DeStefano, Evans, Tadros, and Sun 2004). At the time it was believed that this was primarily due to the higher loads specified in the LRFD Specifications. In the 1994 AASHTO LRFD Specifications, flexural crack control requirements were based on the Z factor method developed by Gergely and Lutz in 1968 (DeStefano, Evans,
13
Tadros, and Sun 2004). Research completed by DeStefano et al. (2004) suggested a new equation be adopted in the LRFD Specifications. Their recommendation for a new equation was for the development of a simple, straight forward equation that accounts for the differences between bridge and building structures. The proposed revised crack control requirements identified a number of short comings identified with the Z factor method. Example designs were included on box culverts to compare the allowable stresses in the existing Z factor method and the proposed crack control method. The results indicated reasonable increases in allowable stresses, thus permitting more economical designs without sacrificing long term durability. The proposed equation developed in this research has been adopted in the current edition of the LRFD Specifications.
2.4 National Cooperative Highway Research Program, Project 15  29
The NCHRP funded a project that examined the distribution of live load through earth fill (Project 1529 2006). This research compared provisions form both specifications regarding distribution of live load through earth fill. The design and evaluation of buried structures requires an understanding of how vertical earth loads and vehicular live loads are transmitted through earth fills. When the depth of overburden is equal to or greater than 2 ft, both the Standard AASHTO Specifications and the LRFD Specifications allow for the wheel load to be distributed throughout the
14
earth fill. Both specifications utilize approximate methods for estimating the distribution of vehicular live loads through earth fill. The Standard LRFD Specifications takes into account the contact area between the footprint of the tire and ground surface. The distribution area is equal to the tire footprint, with the footprint dimensions increased by either 1.15 times the earth fill depth for select granular backfill, or 1.0 for other types of backfill. The Standard AASHTO Specifications does not account for the dimensions of the tire. Instead the wheel load is considered to be a concentrated point load. The wheel load is distributed over a square equal to 1.75 times the depth of fill, regardless of the type of backfill. One major difference between the two specifications is the AASHTO LRFD Bridge Design Specification uses different approximate methods that significantly increase live load pressures on buried structures when compared to the Standard Specifications. In addition, the basis for the methodology in which the live load is distributed through soil is not well documented or understood. As a result the NCHRP developed project 1529, Design Specifications for Live Load Distribution to Buried Structures. Administered by the Transportation Research Board (TRB) and sponsored by the member departments (i.e., individual state departments of transportation) of the American Association of State Highway and Transportation Officials, in cooperation with the FHWA, the NCHRP was created in 1962 as a means to conduct research in acute problem areas that affect highway planning, design, construction, operation, and maintenance
15
nationwide. The objective of Project 1529 is to develop recommended revisions to the AASHTO LRFD Bridge Design Specifications relating to the distribution of live load to buried structures. The project completion date is scheduled for October 20lh, 2007. The status of the project is unknown at this time.
2.5 Design Live Loads on Box Culverts, University of Florida
Other research that has been completed with regards to the distribution of live load through earth fill was performed by Bloomquist and Gutz (2002) at the University of Florida. The research was sponsored by the Florida Department of Transportation and prepared in cooperation with the Federal Highway Administration. The Florida Department of Transportation adopted the Standard LRFD Specifications as the design standard for all structures beginning in 1998. The research report discusses the development of equations to calculate the distribution of live loads through earth fill for the design of precast concrete box culverts. The objective of the research was to develop a new method and establish a single design equation for distributing live loads to the tops of precast concrete box culverts. The existing LRFD methodology is considered to be a rigorous design procedure that is extremely difficult to apply and too conservative when compared to the Standard AASHTO Specifications. A significant amount of design time can be shortened by simplifying this process. Also, the work was aimed at producing a simplified design
16
equation that would be thorough but not overly conservative. The approach of the research was to use theoretical methods to calculate the distribution of live loads through varying earth fill depths and compare them with the current LRFD provisions. The first method that was reviewed was developed by Boussinesq in 1855 (Bloomquist and Gutz 2002). His method considers the stress increase based on a point load at the surface of a semiinfinite, homogenous, isotropic, weightless, elastic halfspace, shown in Figure 2.1. The value of the vertical stress can be calculated using Equation 2.1.
P(3z3) Equation 2.1
Â°z = + z2)5/2
Where:
P= Point load
Z = Depth from ground surface to where oz is desired r = Horizontal distance from point load to where cz is desired
17
F
â€™
Figure 2.1  Boussinesq Point Load
Natural soil deposits do not approach ideal conditions that the Boussinesq equation was based upon. Many soil deposits consist of layered strata of fine and course materials or alternating layers of clay and sand. In 1938, Westergaard proposed a solution that was applicable for these types of deposits (Bloomquist and Gutz 2002). Using the Westergaard theory, the vertical stress can be calculated using Equation 2.2.
1 + 2
'r'2
i3/2
\Zj
Equation 2.2
Both the Boussinesq and Westergaard theory assume the loading acts as a point load. The provisions in the Standard LRFD Specifications require the
18
dimensions of the tire be utilized. Newmark integrated the Boussinesq solution over an area to calculate the distribution of a patch load through soil in 1935. This lead to the development of Equation 2.3, and is known as the superposition method.
Equation 2.3
+ arctan *
Where:
qo = Contact stress at the surface m = x/z n = y/z
x,y = Length and width of the uniformly loaded area z = Depth of surface point where stress increase is desired
Another method that was reviewed was the buried pipe method. The buried
pipe method is also based of the Boussinesq solution. The equation for the buried
pipe method is shown in Equation 2.4
Wsd =CspF'Bc
Equation 2.4
19
Where:
Wsd = Load on pipe in lb/unit length P = Intensity of distributed load (psf)
Fâ€™ = Impact Factor Bc = Diameter of pipe (ft)
Cs = Load coefficient which is a function of D/(2H) and M/(2H), where D and M are the width and length, respectively, of the area over which the distributed load acts.
The last method to be reviewed and one of the simplest methods to calculate the distribution of load with depth is known as the 2:1 method calculated in Equation 2.5.
a. 
i
Load
(B + ZXL+Z)
Equation 2.5
Where:
oz = Live load stress Z = Depth of fill
B, L = Width and length, respectively, of the loaded area at the surface
20
The 2:1 method is an empirical approach that assumes the area over which the load acts increases in a systematic way with depth. The methodology in the Standard LRFD Specifications is based on a variation of this method.
Each of the methods described above were used to calculate the live load pressure through earth fill and compared to the current LRFD Specifications. The objective was to compare methods of live load distribution and determine suitable alternatives. The Design Truck and Design Tandem vehicles were used when examining the methods. The findings suggest that the superposition method be used in place of the provisions in the Standard LRFD Specifications. Once the different methods to distribute live load were compared, the next step was to develop a simplified equation that would produce the same force effects as the current LRFD Specifications. Based on the superposition method, shears and moments acting on the top slab of box culverts were calculated for varying design spans and earth fill depths. An equivalent uniform load model was developed by statistical modeling and curve fitting to produce the same moments and shears. The research developed Equation
2.6 for determining the equivalent uniformly distributed load:
o
Z
2300
Z
Equation 2.6
21
Where:
Gz = Equivalent Load (plf)
Z = Depth of fill (ft)
The researchers recommend that Equation 2.6 only be used for box culverts with span lengths that were in the scope of the research. Further refinement of the equation may be accomplished with a more rigorous statistical analysis.
22
Chapter 3
AASHTO LFD Standard Specifications
3.1 Load Factors and Load Combinations
All structures must be designed to withstand multiple loads acting simultaneously at once. Vehicle live loads may act on a structure at the same time as lateral earth pressure. The design engineer is responsible for ensuring the design is sized and reinforced properly to safely resist combinations of loads. To account for this the Standard AASHTO Specifications contain load combinations, subdivided into groups, which represent a combination of simultaneous loadings on the structure.
The general equation used to define a group load is given by Equation 3.1 (AASHTO
2002).
Group(N) = y[PDD + pL (L +1) + pcCF + peE + PbB + PsSF + PwW + PwlWL + Pllf+pr(r + s+t)
+ PeqEQ + Pice ICE]
Equation 3.1
Where:
N = group number y = load factor from Table 3.1 P = coefficient from Table 3.1 D = dead load
23
L = live load
I = impact factor
E = earth pressure
B = buoyancy
W = wind load on structure
WL = wind load on live load
LF = longitudinal force from live load
CF = centrifugal force
R = rib shortening
S = shrinkage
T = temperature
EQ = earthquake
SF = stream flow pressure
ICE = ice pressure
Table 3.1 lists values for both y and (3. These values are based on the service load and load factor design. The coefficient (3 varies based on the type of load. The load factor y is the same for service loads; however, it varies for different load factor design groupings. The (3 coefficients for both dead load and earth pressure vary depending on the load group and design method shown in Table 3.1. This variation
24
results from different values being applied for different types of elements or components. A description of the dissimilar results is illustrated in Table 3.2.
The Standard AASHTO Specifications incorporates two principle design methods:
â€¢ Service Load Design (Allowable Stress Design or Working Stress Design)
â€¢ Strength Design (Load Factor Design or Ultimate Strength Design) The service load design method is an approach in which the structural
members are designed so that the unit stresses do not exceed predefined allowable stresses. The allowable stress is defined by the material strength reduced by a factor of safety. In other words the total stress caused by the load effects must not exceed this allowable stress. This is further expressed in Equation 3.2.
factual ~ f allowable
Equation 3.2
25
Table 3.1  AASHTO Group Loading Coefficients and Load Factors
Col No. 1 2 3 3A 4 5 6 7 8 9 10 11 12 13 14
p FACTORS
GROUP 1 D (L+I)n (L+I)p CF E B SF W WL LF R+S+T EQ ICE %
i 1.0 1 1 0 1 h 1 1 0 0 0 0 0 0 100
IA 1.0 1 2 0 0 0 0 0 0 0 0 0 0 0 150
IB 1.0 1 0 1 1 Pe 1 1 0 0 0 0 0 0 **
II 1.0 1 0 0 0 1 1 1 1 0 0 0 0 0 125
o < o III 1.0 1 1 0 1 Pe 1 1 0.3 1 1 0 0 0 125
_l LU O > IV 1.0 1 1 0 1 Pe 1 1 0 0 0 1 0 0 125
V 1.0 1 0 0 0 1 1 1 1 0 0 1 0 0 140
cc LU cn VI 1.0 1 1 0 1 Pe 1 1 0.3 1 1 1 0 0 140
VII 1.0 1 0 0 0 1 1 1 0 0 0 0 1 0 133
VIII 1.0 1 1 0 1 1 1 1 0 0 0 0 0 1 140
IX 1.0 1 0 0 0 1 1 1 1 0 0 0 0 1 150
X 1.0 1 1 0 0 Pe 0 0 0 0 0 0 0 0 100
1 1.3 Pâ€ž 1.67 0 1 PE 1 1 0 0 0 0 0 0
IA 1.3 PD 2.20 0 0 0 0 0 0 0 0 0 0 0
IB 1.3 P0 0 1 1 PE 1 1 0 0 0 0 0 0
2 0 II 1.3 Pâ€ž 0 0 0 PE 1 1 1 0 0 0 0 0 LU _J
0 LU III 1.3 Pd 1 0 1 PE 1 1 .3 1 1 0 0 0 CD < o _J Q_
CC n IV 1.3 PD 1 0 1 Pe 1 1 0 0 0 1 0 0
i o V 1.25 PD 0 0 0 Pe 1 1 1 0 0 1 0 0 CL <
< Li. Q VI 1.25 Pd 1 0 1 Pe 1 1 .3 1 1 1 0 0 o z
< o VII 1.3 Pd 0 0 0 Pe 1 1 0 0 0 0 1 0
VIII 1.3 Pd 1 0 1 Pe 1 1 0 0 0 0 0 1
IX 1.2 Pd 0 0 0 Pe 1 1 1 0 0 0 0 1
X 1.3 1 1.67 0 0 Pe 0 0 0 0 0 0 0 0
26
Table 3.2  AASHTO Earth Pressure and Dead Load Coefficients
p Load Value Element
Pf Earth Pressure 1.0 Vertical and lateral loads on all other structures
Pf Earth Pressure 1.0 and 0.5 Lateral loads on rigid frames (check both loadings to see which one governs)
PF Earth Pressure 1.3 Lateral earth pressure for retaining walls and rigid frames excluding rigid culverts
[L Earth Pressure 0.5 Lateral earth pressure when checking positive moments in rigid frames
Pf Earth Pressure 1.0 Rigid culverts
Pf Earth Pressure 1.5 Flexible culverts
Pd Dead Load 0.75 Columns, when checking member for minimum axial load and maximum moment or maximum eccentricity
Pd Dead Load 1.0 Columns, when checking member for maximum axial load and minimum moment
Pd Dead Load 1.0 Flexural and tension members
Bridge substructures such as foundations and abutments have traditionally been designed using the Service Load Design methodology. Underground precast concrete box culverts and threesided structures are designed by the load factor design, thus this thesis focuses solely on the load factor design methodology. In this methodology, the general relationship is defined utilizing Equation 3.3.
X TiQi ^
Equation 3.3
27
Where:
Yi = Load factors Qi = Force effects <(> = Resistance factors Rn = Nominal resistance Rr = Factored resistance
The nominal resistance of a member, Rn, is calculated utilizing procedures given in the current AASHTO Specifications. A resistance factor, (j), is used to obtain the factored resistance Rr. The appropriate resistance factors are determined for specific conditions of design and construction process. Typical values for underground concrete structures are listed in Table 3.3. The force effects, Qi, that should be considered when designing underground concrete structures are live load, impact, live load surcharge pressures, self weight, and vertical and horizontal earth pressures. Loads considered important for other types of structures such as wind, temperature, and vehicle breaking are insignificant compared to the force effects previously mentioned for buried concrete structures. The following sections will examine these critical force effects when designing underground concrete structures, specifically reinforced precast concrete box culverts and threesided concrete structures, using the Standard AASHTO Specifications.
28
Table 3.3  AASHTO Resistance Factors for Underground Concrete Structures
Structure Type Flexure Shear Radial Tension
Load Factor Design of Precast 1.0 0.90 0.90
Reinforced Concrete Pipe, type 1 installations 0.90 0.82 0.82
Reinforced Concrete Arch, Cast InPlace 0.90 0.85 NA
Reinforced Concrete Box Culverts, Cast InPlace 0.90 0.85 NA
Reinforced Concrete Box Culverts, Precast 1.0 0.90 NA
Precast Reinforced Concrete ThreeSided Structures 0.95 0.90 NA
3.2 AASHTO Standard Vehicular Design Live Loads
The American Association of State and Highway Transportation Officials, founded in 1914 as American Association of State Highway Officials, created a truck train configuration in 1935 based on the railroads industry standards as shown in Figure 3.1.
Figure 3.1  AASHO 1935 Truck Train Loading (Tonias, 1995).
29
Historically, many structures, mainly bridges began to show evidence of overstressing in structural components as a result of increased truck traffic and heavier truck loading (Tonias 1995). This led to the introduction of five hypothetical trucks designated as H and HS class trucks in 1944. The design truck designations and gross vehicle weights are listed in Table 3.4.
Table 3.4  AASHTO Standard HS Design Truck Classes
Design Truck Gross Weight
H10  44 20,000 LB  9072 KG
H15  44 30,000 LB  13,608 KG
H20  44 40.000 LB  18,144 KG
HS1544 54,000 LB  24.494 KG
HS20 44 80.000 LB  32,659 KG
Currently all design truck classes are included in the AASHTO Standard Specifications with the exception of the HI044. The policy of affixing the year to the loading to identify the design truck class was instituted in the 1994 AASHTO edition. Figure 3.2 illustrates these design trucks and their associated geometries.
30
14 FT 14 FT  30 FT
HS2544 10.000 lbs. +0.000 lbs. +0.000 lbs.
HS2044 8.000 lbs. 32.000 lbs. 32,000 lbs.
HS154+ 6,000 lbs. 24,000 lbs. 24,000 lbs.
H2044 8.000 lbs. 32,000 lbs.
H1544  6,000 lbs.24,000 lbs.
Figure 3.2  Characteristics of the AASHTO Design Truck (AASHTO, 2002).
31
The H15 and H20 truck loading is represented by a twoaxle single unit truck. The â€œSâ€ in the HS1544 and HS2044 designates a semitrailer combination with an additional third axle. The H15 44 truck configuration has a gross weight of 30,000 lb. with 6,000 lb. on its steering axle and 24,000 lbs. on its drive axle. Similarly, the HS 1544 weighs 56,000 lb. with an additional 24,000 lb. on its semi trailer axle. The H20  44 has a gross weight of 40,000 lb. with 8,000 lb. on its steering axle and 32,000 lb. on its drive axle. A HS2044 truck weighs 72,000 lb. with an additional 32,000 lb. on its semi trailer axle. Although not a provision in the current AASHTO Standard Specifications some states have began using a HS25 design truck with a gross vehicle weight of 90,000 lb., as shown in Figure 3.2. Some states have developed additional live load configurations known as permit design loadings in order to provide for future overweight trucks. The primary design truck used in designing underground structures is the HS2044 truck loading.
Another form of live loading to represent heavy military vehicles was developed in 1956 by the Federal Highway Administration (Tonias 1995). This loading configuration is known as the Alternative Military Loading as shown in Figure 3.3. This loading consists of two axles weighing 24,000 lb. spaced 4 ft. apart. A comparison of the force affects from both the design truck and the alternative military loading configuration should be considered. The final design of the structure will depend on which loading configuration creates the largest stress.
32
Typically, the depth of overburden and the span of the member will govern the design vehicle configuration. This will be further illustrated in subsequent sections including the design examples in Chapter 6.
60 
12 KIPS
12 KIPS
Direction
of Travel
4â€™â€”0â€
12 KIPS
12 KIPS â€”
Figure 3.3  Characteristics of Alternative Military Loading.
The tire contact area for both the Alternative Military Loading and the HS Design Truck is assumed as a rectangle with the length in the direction of traffic equal to 10 in, and a width of 20 in. The width is double the length based on the assumption of a dual tire as illustrated in Figure 3.4. For other design vehicles, such as customer specified live loads the Standard AASHTO Specifications allow the practicing engineer to determine the dimensions. The Standard AASHTO Specifications only allows the dimensions of the tire to be used when the earth fill
33
depth is less than 2 ft. To simplify the design calculations it is acceptable to neglect the contact area of the tire, and assume the tire acts as a point load.
HS20
(
icr
L
20â€™
Figure 3.4  Tire Contact Area
For design purposes, procedures for applying and distributing the Alternative Military Loading and the HS design truck to a structure is dependent upon the depth of fill. Two cases are examined,
â€¢ When the earth fill depth is less than 2 ft.
â€¢ When the earth fill depth is equal to or greater than 2 ft.
In both cases, the Alternative Military Loading and the HS Design Truck are examined as wheel line loads.
34
3.3 Earth Fill and Vertical Earth Pressure Loading
Initially when designing underground concrete structures the earth fill depth or depth of overburden on the structure must be determined. The earth fill depth dictates load combinations, impact, allowable shear, concrete cover, live load surcharge, and particularly live load application. The earth fill is the backfill or fill placed on the top slab. Earth fill depth is defined as the distance between the top of the top slab to the top of earth fill or roadway surface. Typical unit weights, ys, of earth fill are 110 pcf.  130 pcf, and are typically governed by the geotechnical report. The vertical earth pressure values from the earth fill can be calculated using Equation 3.4. The depth of fill and vertical earth pressure are illustrated in Figure 3.5.
WuSL = ys * z Equation 3.4
Where:
WuSL = Constant vertical earth pressure (psf) ys = Unit weight of soil (pcf) z = Earth Fill Depth (ft)
35
Figure 3.5  Earth Fill Depth and Vertical Earth Pressure Loading
Buried structures are placed in three basic methods; trench excavation, embankment filling, and tunneling. Each method effects the soilstructure interaction based on the earth fill depth, side compaction, and bedding characteristics (Sanford 2006). Therefore the effects of soilstructure interaction must be taken into account. The Standard AASHTO Specification requires that the vertical earth pressure values from Equation 3.4 must be multiplied by a soilstructure interaction factor, Fe, when designing reinforced concrete box culverts. The soilstructure interaction factor depends the on type of installation. For embankment installations, Fc is calculated using Equation 3.5, for trench installations use equation 3.6. The Standard AASHTO Specifications do not require the soilstructure interaction factor to be applied to threesided concrete structures. It is important to note that the soilstructure interaction factor for reinforced concrete pipe differs from Equations 3.5  3.6. The soilstructure interaction factor for reinforced concrete pipe is beyond the scope of this thesis and is not discussed.
36
Equation 3.5
Fâ€ž, =1+0.20â€”
Bc
Where:
Fei = Soilstructure interaction for embankment installations
< 1.15 for installations with compacted fill at the sides
< 1.4 for installations with uncompacted fill at the sides H = Earth fill depth, ft.
Bc = Outtoout horizontal span of pipe or box, ft.
r _cdBd2
e2 HBC Equation 3.6
Where:
Fe2 = Soilstructure interaction for trench installations
H = Earth fill depth, ft.
Bc = Outtoout horizontal span of pipe or box, ft.
Cd = Load coefficient for trench installations, Figure 3.6.
37
3.4 Distribution of Live Loads for Depths of Fill Greater Than 2 ft.
When the depth of fill is equal to or greater than 2 ft., the Standard AASHTO Specifications allows for the wheel load to be distributed over a square equal to 1.75 times the depth of fill. Figure 3.6 illustrates that the Standard AASHTO Specifications does not account for the dimensions of the tire, instead the wheel load is considered as a concentrated point load. The distributed live load value, WuLL for a single wheel load is calculated using Equation 3.7. When the dimension of the load area exceeds the design span, only the portion of the distributed load on the span is considered in the design.
WuLL = Wheel Load / (1.75 * H)2 Equation 3.7
Where:
H = Earth Fill Depth (ft)
38
WHEEL LOAD
H
\
/
Iâ€”1.75 * H^
Figure 3.6  LFD Wheel Load Distribution through Earth Fill
Due to the increased depth of overburden, the areas from several concentrated wheel loads may overlap. The total load should be distributed over the area defined by the outside limits of the individual areas as shown in Figure 3.7.
Figure 3.7  Overlapping Wheel Load Distribution through Earth Fill
39
As the earth fill depth increases, distributed wheel load areas created by adjacent wheels or axles begin to overlap. This complicates the distributed live load area and load value calculation. There are 3 cases that are considered:
3.4.1 Case 1  Distribution of Wheel Loads that do not Overlap
Case 1 occurs when the distribution of wheel loads do not overlap. The distributed live loads are calculated using Table 3.5. The depth of overburden, H, in the table is the maximum earth fill depth allowed. Both the parallel and perpendicular load distribution widths for a single design vehicle are shown in Figure 3.8.
Table 3.5  Case 1
H Spread, S WuLL
Design Vehicle (ft) Wheel Load (lb) (ft2) (lb/ft2)
HS20 Truck H < 3.43 16.000 (1.75 * H)2 16,000/(1.75 * H)2
HS25 Truck H < 3.43 20,000 (1.75 * H)2 20.000/(1.75 * H)2
Alternative Military Load H < 2.29 12.000 (1.75 * H)2 12,000/(1.75 * H)2
Figure 3.8  Case 1, Wheel Load Distribution through Earth Fill
40
3.4.2 Case 2  Distribution of Wheel Loads from a Single Axle Overlap.
Case 2 occurs when both wheels from a single axle overlap for the HS Truck configuration. The wheels from separate axles overlap for the Alternative Military truck configuration. This is due to an axle spacing of 4 ft. compared to the wheel spacing of 6 ft. The distributed live loads are calculated using Table 3.6. Both the Alternative Military Truck and HS Design Truck configurations are illustrated in Figure 3.9.
Table 3.6  Case 2
H Wheel Load Spread, S WuLL
Design Vehicle (ft) (lb) (ft2) (lb/ft2)
HS20 Truck 3.43 < H > 8.00 16.000 S = (1.75 * H) * (1.75 * H + 6) 32.000 / S
HS25 Truck 3.43 < H > 8.00 20.000 S = (1.75 * H) * (1.75 * H + 6) 40,000/S
Alternative Military Load 2.29 < H > 3.43 12.000 S = (1.75 * H) * (1.75 * H + 4) 24.000 / S
HS DESIGN TRUCK
DIRECTION OF TRAFFIC
"igure 3.9  Case 2, Overlapping Wheel Load Distribution through Earth Fil
41
3.4.3 Case 3  Full Distribution of Wheel Loads from Multiple Axles.
When the wheel loads from all axles overlap, the distributed live load is calculated using Table 3.7. Full distribution occurs for the HS Design Truck at an earth fill depth of 8 feet as shown in Figure 3.10. The live load may be neglected as stated in the Standard AASHTO Specifications when the earth fill depth is greater than 8 feet, and exceeds the effective span length. For multiple spans, it may be neglected when the depth of overburden exceeds the distance between faces of end supports or abutments. As a result, Case 3 will typically govern for the Alternative
Military Load based on full distribution at a fill depth of approximately 3.43 ft.
Table 3.7  Case 3
H Wheel Load Spread, S WuLL
Design Vehicle (ft) (lb) (ft2) (lb/ft2)
HS20 Truck 8.00
HS25 Truck 8.00
Alternative Military Load 3.43 < H 12.000 S = (1.75 * H + 4) * (1.75 * H + 6) 48.000 / S
42
HS DESIGN TRUCK
Figure 3.10  Case 3, Overlapping Wheel and Axle Load Distribution
Through Earth Fill
As detailed in Section 3.2, a comparison of force effects from both the HS2044 Design Truck and the Alternative Military Loading configuration should be made. The loading configuration that creates the largest stress should then be selected in the design. Both the earth fill depth and the span of the member must be considered in the design. Wheel load pressure versus depth of fill is plotted in Figure 3.11 for both the HS2044 Design Truck and Alternative Military Loading. The HS2044 Truck Loading produces higher wheel load pressures for shallow depths between 2 ft.  4.5
43
ft., while the Alternative Military Loading produces larger wheel load pressures for depths between 5 ft  15 ft. For earth fill depths greater than 15 ft, the HS2044 Truck Loading produces higher wheel load pressures.
Figure 3.11 LFD Live Load Pressures through Earth Fill
The design vehicle that produces the greatest live load pressure with regards to earth fill depth will not necessarily control the design. The critical live load pressure used will depend not only on the earth fill depth but the member span. This is attributed to the area in which the load is spread. For example, for a depth of fill of 3.0 ft an HS20 truck produces a service live load pressure of 0.581 ksf. An Alternative Military vehicle produces a service live load pressure of 0.494 ksf.
44
However the Alternative Military vehicle has a larger load spread as illustrated in Figure 3.12, which may induce larger service moments for various spans.
Figure 3.12 LFD Live Load Spread for 3 ft Overburden
In Figure 3.13 the service moment produced by the HS 2044, HS 2544, and the Alternative Military live loads for an earth fill depth of 3 ft are plotted versus design spans. The corresponding service pressure values and load lengths are illustrated in Table 3.8. Although the HS2544 Design Truck produces higher load pressures than the Alternative Military Loading, the Alternative Military loading produces a higher service moment for spans in excess of 15 feet.
45
3.00 6.00 9.00 12.00 15.00 18.00 21.00 24.00
Design Span (FT)
Figure 3.13 LFD Live Load Service Moments vs. Increasing Design Spans
Table 3.8  Moments from HS20, HS25, and Alternative Military Loads
Live Load Model WsLL (klf) Load Length (ft)
HS20 .581 5.25
HS25 .725 5.25
Alternative Military .494 9.25
46
3.5 Distribution of Live Loads for Depths of Fill Less Than 2 ft.
For depths of overburden less than 2 ft the Standard AASHTO Specifications simplify the design procedures by providing a single equation for distributing the live load to the top slabs of buried concrete structures. The live load is divided into equivalent strip widths, which is the effective width of slab that resists the applied load. The live load is modeled as a concentrated wheel load distributed over a distribution width, E. The distribution width is calculated using Equation 3.8.
E = 4 + .06 * S < 7 ft. For H < 2 ft. Equation 3.8
Where:
E = Width of slab over which a wheel load is distributed (ft)
S = Effective span length (ft)
H = Cover depth from top of structure to top of Pavement (ft)
Concrete slabs are analyzed as a beam with the equivalent concentrated live load divided by the distribution width, E, see Figure 3.14. The distribution width applies to all design spans for both positive and negative bending, and shear force effects.
47
Wheel Load
Figure 3.14 LFD Distribution Width, E for a Single Wheel Load
The Standard AASHTO Specifications does not allow any load transfer between adjacent structures. The distribution widths must be limited to the unit width of the structure. Figure 3.15 illustrates two cases. The distribution width exceeds the width of the member in Case 1. The effective distribution width will be limited to the member width of the structure. In Case 2 the distribution width is less than the unit width of the member. Therefore design calculations consider the full distribution width.
Figure 3.15 Effective Distribution Widths on Slabs
48
The tire is assumed to act in the center of the member, as shown in Figure 3.15. One provision that is unclear in the Standard AASHTO Specifications is when the tire is placed at the edge of a member as illustrated in Figure 3.16, Case 3. Case 3 is not addressed in the current Standard AASHTO Specifications; however it is a common practice to assume a reduced distribution width. This new distribution width is calculated using Equation 3.9.
Er = (4 + .06 * S) / 2 + WT / 2 Equation 3.9
Where:
Er = reduced distribution width (ft)
S = effective span length (ft)
WT = width of tire contact area parallel to span, as specified in section 3.2 (ft)
Case 3
Figure 3.16 Reduced Distribution Widths on Slabs
49
3.6 Impact Factor (IM)
To account for the dynamic load affects of moving vehicles, the AASHTO Standard Specifications applies an impact factor to the live load for varying burial depths. The impact factor is applied to both the Design Truck and Alternative Military Load as a multiplier. The Impact factor varies with the depth of overburden as shown in Table 3.9.
Table 3.9  Impact Factor
Overburden Impact
0â€™0â€  roâ€ 30%
p fN 1 20%
2â€™ 1â€  2â€™ 11â€ 10%
>2â€™11â€ 0%
The dynamic force effects applied to the live load as a result of moving vehicles can be attributed to the hammering effect of the wheel assembly riding on surface discontinuities such as deck joints, cracks, potholes, and undulations in the roadway pavement caused by settlement of fill (AASHTO 2005). The decrease in impact with the depth of overburden is due to the damping effect of soil when the wheel is in contact with the ground.
50
3.7 Lateral Live Load Surcharge
The Standard AASHTO Specifications require a lateral live load surcharge pressure be applied when highway traffic comes within a horizontal distance from the top of the structure equal to onehalf its height. Additional lateral earth pressure is produced on soil retaining walls as a result of surcharge loads. The Standard AASHTO Specifications require that the live load surcharge pressure be equal to or greater than 2 ft. of additional earth cover, applied to the exterior walls. There are two methods to apply the lateral live load surcharge pressure. Both methods yield the same results. The first is by assuming an equivalent height of additional earth cover on the outside walls, typically 2 ft., as shown in Figure 3.17. The second is by designating the live load surcharge pressure as a separate load as shown in Figure 3.18. The second method is preferred due to the ease of computer programming. The magnitude of the lateral live load surcharge is determined using Equation 3.10:
LLS = k * ys * Heq Equation 3.10
Where:
LLS = Constant horizontal earth pressure due to live load surcharge (psf) k = coefficient of lateral earth pressure ys = unit weight of soil (pcf)
Heq = equivalent height of soil, typically 2 ft.
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LIVE LOAD SURCHARGE
Figure 3.17  LFD Equivalent Height
PRESSURE
Figure 3.18  Live Load Surcharge Pressure
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Chapter 4
AASHTO LRFD Bridge Design Specifications
4.1 Load Factors and Load Combinations
In LRFD, the design framework consists of satisfying what are called limit states. All limit states shall satisfy Equation 4.1.
rji = Load modifier Yi = Load factors Qi = Force effects (j> = Resistance factors Rn = Nominal resistance Rr = Factored resistance
Selection of the load factors to be used is a function of the type of load and limit state being evaluated. To obtain an understanding of this concept, it is helpful to refer to the actual definition of "limit state" contained in the LRFD Specifications. A Limit State is a condition beyond which the bridge or component ceases to satisfy the provisions for which it was designed. There are four limit states prescribed by the
Equation 4.1
Where:
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LRFD Specifications (AASHTO 2005). Each of the four limit states are described
below:
â€¢ STRENGTH  Requires the strength and stability be adequate for specified load combinations.
â€¢ EXTREME EVENT  Relates to events with extremely long periods of return (earthquakes, ice loads, vehicle collision, and vessel collision).
â€¢ SERVICE  Relates to stresses, deformations, and cracking.
â€¢ FATIGUE  Places restrictions on stress ranges in reinforcement from application of a single design truck under service load conditions.
When designing underground concrete structures, the LRFD Specifications require that all applicable limit states be evaluated. The load for each limit state should be modified by the appropriate load factor, y, and the factored loads for each limit state combined in a prescribed manner. The limit states, load factors and load combinations from the AASHTO LRFD Specifications are listed in Table 4.1 and Table 4.2. Based on applicable load combinations the limit states are further subdivided as follows (AASHTO 2005):
â€¢ STRENGTH I  Basic load combination related to normal vehicular use of the bridge without wind.
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â€¢ STRENGTH II  Load combination relating to the use of the bridge by owner specified special design vehicles and/or evaluation permit vehicles without wind.
â€¢ STRENGTH III  Load combination relating to the bridge exposed to wind velocity exceeding 55 mph without live load.
â€¢ STRENGTH IV  Load combinations relating to very high dead load to live load force effect ratios.
â€¢ STRENGTH V  Load combinations relating to normal vehicular use of the bridge with wind velocity of 55 mph.
â€¢ EXTREME EVENT I  Load combinations including earthquake and flood.
â€¢ EXTREME EVENT II  Load combination relating to ice load or collision by vessels and vehicles.
â€¢ SERVICE I  Load combination relating to the normal operational use of the bridge with 55 mph winds and all the loads taken at their nominal values.
â€¢ SERVICE II  Load combinations intended to control yielding of steel structures and slipcritical connections due to vehicular live load.
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â€¢ SERVICE III  Load combination for longitudinal analysis relating to tension in prestressed concrete superstructures.
â€¢ SERVICE IV  Load combinations relating only to tension in prestressed concrete substructures with the objective of crack control.
â€¢ FATIGUE  Fatigue and fracture load combinations relating to the repetitive gravitational vehicular live load and dynamic responses under a single design truck.
A majority of the loads and loading combinations specified in the Standard AASHTO Specifications are eliminated for buried structures. Buried structures are sheltered by earth cover which reduces much of the concern. Buried structures need to be designed to resist the force effects resulting from horizontal and vertical earth pressures, pavement load, vehicular live load and impact, and surcharge loads. Wind, temperature, vehicle breaking, and centrifugal forces typically have little effect due to earth protection.
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Table 4.1 Load Combination and Load Factors
Load Combination DC DD DW EH EV ES EL LL IM CE BR PL LS 7U CR SH Use one of These at a Time
Limit State WA ws WL FR TG SE EQ IC CT cv
STRENGIHI (unless noted) Yp 1.75 1.00 . . 1.00 0.50/1.20 Ytg Yse . . . .
STRENGTHII Yp 1.35 1.00  1.00 0.50/1.20 Ytg Yse  â€¢  
STRENGTHIII Yp 1.00 1.40 1.00 0.50/1.20 ytg Yse    
STRENGTHIV EH, EV, ES, DW DC ONLY YP 1.50 1.00 1.00 0.50/1.20
STRENGTHV Yp 1.35 1.00 0.40 1.00 1.00 0.50/1.20 Ytg Yse  
EXTREME EVENT1 Yp y 1 eq 1.00 .  1.00  .  1.00 . . .
EXTREME EVENTII Yp 0.50 1.00  1.00     1.00 1.00 1.00
SERVICEI 1.00 1.00 1.00 0.30 1.00 1.00 1.00/1.20 Ytg Yse   
SERVICEII 1.00 1.30 1.00   1.00 1.00/1.20      â€¢
SERVICE111 1.00 0.80 1.00  1.00 1.00/1.20 Ytg Yse   
SERVICEIV 1.00  1.00 0.7  1.00 1.00/1.20  1  
FATIGUELL.IM & CE ONLY  0.75 .  . . . . . . . . .
The service limit state required by the AASHTO LRFD Specifications for buried structures is Service Load Combination I. The required Strength Limit State required is Strength Load Combinations I and II. The Extreme limit states do not govern unless the structure crosses an active fault. Load factors for permanent loads labeled as yp in Table 4.1, are presented in Table 4.2 as maximum and minimum values. Criteria for their application require that:
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â€¢ For each combination, load factors should be selected to produce the total extreme factored force effect. Both maximum and minimum extremes should be investigated.
â€¢ Maximum and minimum load factors are utilized for load combinations where one force effect decreases the effect of another force. The minimum value shall be applied to the load that reduces the force effect.
â€¢ The load factor which produces the more critical combination for permanent force effects should be selected from Table 4.2.
â€¢ If a permanent load increases the stability or load carrying capacity of a structure component, the minimum value for that permanent load should also be investigated.
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Table 4.2  Load Factors for permanent Loads, yp
Load actor
Type of Load Maximum Minimum
DC: Component and Attachments 1.25 0.90
DD: Downdrag 1.80 0.45
DW: Wearing Surfaces and Utilities 1.50 0.65
EH: Horizontal Earth Pressure
 Active 1.50 0.90
 AtRest 1.35 0.90
EL: Locked in Erection Stresses 1.0 1.0
EV: Vehicle Earth Pressure i i
 Overall Stability 1.00 N/A
 Retaining Walls and Abutments 1.35 1.0
 Rigid Buried Sturcture 1.30 0.90
Rigid Frames 1.35 0.90
Flexible Buried Structures other than 1.95 0.90
Metal Box Culverts i 1
Flexible Metal Box Culverts 1.50 0.90
ES: Earth Surcharge 1.50 1.50
4.2 Load Modifiers
In the LRFD Specification, each factored load is adjusted by a load modifier, rj. The load modifiers account for combined effects of redundancy, rR, ductility, rD, and operational importance, rji. Loads in which a maximum load factor is appropriate, the load modifier can be calculated using Equation 4.2. For minimum value load factors the load modifier can be calculated using Equations 4.3.
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Tii = nD *nR *ni ^Â°95
Equation 4.2
ri =>1.05
0d *nR *ni
Where:
qi = Load modifier Td = factor for ductility % = factor for redundancy ri = factor for importance
Equation 4.3
The values for the ductility, redundancy, and importance factor are listed below:
â€¢ Ductility, Td
> 1.05 for nonductile components and connections = 1.00 for conventional designs and details
> 0.95 for components and connections for which additional ductility enhancing measures are required
For all other limit states: qo = L00
â€¢ Redundancy, qR
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> 1.05 for nonredundant components and connections = 1.00 for conventional levels of redundancy
> 0.95 for exceptional levels of redundancy For all other limit states: % = 1.00
â€¢ Importance, ri
> 1.05 for important structures = 1.00 for typical structures
> 0.95 for relatively less important structures For all other limit states: ri = 1.00
When designing at the Service Limit State, r)D = rR = r\\ = 1.00 Typically the ductility of buried structures is 1.00. Buried structures are considered nonredundant under earth fill, and redundant under live load and dynamic load allowance. The importance is determined on an evaluation of necessity for continued function and safety.
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4.3 AASHTO Standard Vehicular Design Live loads
The AASHTO LRFD Specifications require an HL93 live load. This load includes two types of vehicular deign loads. The HL93 Design live loads consist of a combination of the
â€¢ Design Truck or Design Tandem
â€¢ Design Lane Load
The Design Truck used in the AASHTO LRFD Specifications has the same configuration as the HS20 Design Truck in the Standard Specifications discussed in Chapter 3. The design truck weights and spacing of axles and wheels are specified in Figure 4.1.
14 FT I 14 FT  30 FT
HS20......8,000 lbs..... ...32,000 lbs...................32,000 lbs.
HS20
Figure 4.1 Characteristics of the Design Truck (AASHTO, 2005)
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The LRFD Specifications utilize the Design Tandem load configuration consisting of a pair of 25.0kip axles spaced 4.0 ft apart. The transverse spacing of wheels is taken as 6.0 feet as shown in Figure 4.2.
A
12,5 KIPS
Direction of Traffic 4â€”0
6â€™  0â€
i
12,5 KIPS
Figure 4.2 Characteristics of the Design Tandem
The loads from both the Design Truck and the Design Tandem are assumed to be distributed transversely within a 10.0 ft. design lane. A rectangular tire contact area shown in Figure 4.1, consisting of a 20.0 in. width and a 10.0 in length, is used in the design. A dynamic load allowance defined in a later section is applied to both the
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Design Truck and Design Tandem. Both the Design Truck and Design Tandem loading configuration are used in conjunction with the Design Lane Load to determine the worst case force effects on the structure. This will primarily depend on the depth of overburden and/or the span of the structure. The Design Lane Load consists of a load of 0.64 klf, uniformly distributed in the longitudinal direction. Transversely, the Design Lane Load is assumed to be uniformly distributed over a 10.0 ft. design lane width. This lane load converts to an additional live load of .064 ksf, applied to the top of the structure for any depth of burial less than 8 ft. The force effects from the Design Lane Load are not subject to a dynamic load allowance.
4.4 Earth Fill and Vertical Earth Pressure Loading
Similar to the Standard AASHTO Specifications, when designing underground concrete structures the earth fill depth or depth of overburden on the structure must be determined. The earth fill depth dictates load combinations, impact, allowable shear, concrete cover, live load surcharge, and particularly live load application. The earth fill is the backfill or fill placed on the top slab. Earth fill depth is defined as the distance between the top of the top slab to the top of earth fill or roadway surface. Typical unit weights, ys, of earth fill are 110 pcf.  130 pcf, and are generally governed by the geotechnical report. The vertical earth pressure values from the earth
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fill are calculated using Equation 4.4. Figure 4.3 demonstrates depth of fill and the vertical earth pressure applied to the top slab. Therefore the effects of soilstructure interaction must be taken into account. The LRFD Specification requires that the vertical earth pressure values from Equation 4.4 must be multiplied by a soilstructure interaction factor, Fe, when designing reinforced concrete box culverts. This is similar to the AASHTO Standard Specifications specified in Section 3.3.
WuSL = ys * z Equation 4.4
Where:
WuSL = Constant vertical earth pressure (pcf) ys = Unit weight of soil (pcf) z = Earth Fill Depth (ft)
Figure 4,3  Earth Fill Depth and Vertical Earth Pressure Loading
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4.5 Multiple Presence Factors
The LRFD Specifications require the use of multiple presence factors, Table 4.3, to account for the effects of multiple lanes on a bridge. Multiple presence factors are based on the number of loaded lanes. The table provides factors for the cases of one lane, two lanes, three lanes, and three or more loaded lanes. For underground concrete structures, there are three cases that must be examined.
4.5.1 Case 1  Depth of fill is equal to or greater than 2 ft.
Case 1 occurs for depths of fill equal to or greater than 2 ft. The Standard LRFD Specifications require two checks.
â€¢ A check to determine the force effects from multiple truck axles positioned 4 ft side by side with a multiple presence factor of 1.00.
â€¢ A check to determine the force effects from a single design vehicle with a multiple presence factor of 1.20.
The loading combination with the worst case force effects on the structure will control the design. This will typically depend on the overburden depth and/or the span of the structure. This is further discussed in Section 4.6.
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4.5.2 Case 2  Depth of fill is less than 2 ft, and direction of traffic is parallel to
span.
When the traffic travels parallel to the design span, the structure is analyzed using a single loaded lane. The Standard LRFD Specifications distribute a single loaded lane into strip widths. This strip width is the effective width of the slab that resists the applied load. Therefore, the multiple presence factor is 1.20
4.5.3 Case 3  Depth of fill is less than 2 ft, and direction of traffic is perpendicular to span.
When the depth of fill is less than 2 ft and the direction of traffic is perpendicular to the span, the appropriate multiple presence factors must be chosen from Table 4.3. The number of loaded lanes is a function of span length.
Table 4.3 Multiple Presence Factors
Number of Loaded Lanes Multiple Presence Factors "m"
1 1.2
2 1.00
3 0.85
>3 0.65
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4.6 Distribution of Live Loads for Depths of Fill Greater Than 2 ft.
When the depth of overburden is equal to or greater than 2 ft, the Standard LRFD Specifications allows for the wheel load to be distributed throughout the earth fill.
The Standard LRFD Specifications use an approach similar to the 2:1 method. The 2:1 method is an empirical approach that assumes the total applied load on the surface of soil is distributed over an area of the same shape as the loaded area on the surface. The dimensions of the loaded area are increased by the amount equal to the depth below the surface. The AASHTO LRFD method is a variation of this method. The distribution area is equal to the tire footprint, with the footprint dimensions increased by either 1.15 times the earth fill depth for select granular backfill, or 1.0 for other types of backfill, shown in Figure 4.4. The distributed live load value, WuLL for a single wheel load can be calculated using Equation 4.5.
WuLL = Wheel Load / (LLDF*H + WT) * (LLDF*H + LT) Equation 4.5
Where:
WuLL = Uniform Distributed Live Load (psf) H = Earth fill depth (ft)
Wt = Tire Width (in)
Lx = Tire Length (in)
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LLDF = factor for distributing the live load through earth fill 1.15 for select granular backfill 1.00 for all other backfill
Figure 4.4 LRFD Wheel Load Distribution through Earth Fill
69
As noted with the Standard AASHTO Specification, the distributed live load area and load value calculations are complicated as a result of distributed area overlap as the earth fill depth is increased (United States FHA 2001). The overlapping is the result of adjacent wheels and axles, and varying live load design vehicles. The total load should be distributed over the area defined by the outside limits of the individual areas illustrated in Figure 4.5.
Figure 4.5  Overlapping Wheel Load Distribution through Earth Fill
Unlike the Standard AASHTO Specifications there are 5 cases which must be examined:
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4.6.1 Case 1  Distribution of Wheel Loads that do not Overlap
Case 1 occurs when no wheel loads overlap. The distributed live loads are calculated using Table 4.4. In this case, the depth of overburden, H is the maximum allowable earth fill depth. Both the parallel and perpendicular load distribution widths for a single design vehicle are shown in Figure 4.6
Table 4.4  Case 1
Sleet Granular Fill.
Wheel Load Spread B Spread A WuLL
Design Vehicle H (ft) (lbs) (ft) (ft) (psf)
HS20 Truck H < 3.77 16,000 (1.15 *H + 0.83) (1.15 * H + 1.67) 16,000/(A * B)
HS25 Truck H < 3.77 20.000 (1.15 * H +0.83) (1.15 *H + 1.67) 20,000 / (A * B)
Tandem H < 2.75 12.500 (1.15 * H + 0.83) (1.15 * H + 1.67) 12,500/(A * B)
Other Fill
Wheel Load Spread B Spread A WuLL
Design Vehicle H (ft) (lbs) (ft) (ft) (psf)
HS20 Truck H < 4.33 16.000 (1.00 *H + 0.83) (1.00* H + 1.67) 16,000 /(A * B)
HS25 Truck H < 4.33 20.000 (1.00 *H+ 0.83) (1.00* H+ 1.67) 20.000/(A * B)
Tandem H < 3.17 12.500 (1.00 *H +0.83) (1.00* H+ 1.67) 12,500 / (A * B)
SPREAD ASPREAD A
SPREAD Bâ€”I Iâ€”SPREAD Bâ€”I
Figure 4.6 Wheel Load Distribution through Earth Fill
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4.6.2 Case 2  Distribution of Wheel Loads from a Single Axle Overlap.
Case 2 occurs when both wheels from a single axle overlap. The distributed live loads are calculated using Table 4.5. It is important to note that a single wheel load from separate axles overlap in the Tandem Loading. This is a result of the 4 ft.
axle spacing, compared to the 6 ft. wheel spacing Figure 4.7.
Table 4.5  Case 2
Sleet Granular Fill
Design Vehicle H (ft) Wheel Load (lb) Spread B (ft) Spread A (ft) WuLL (psf)
HS20 Truck < H < 11.44 16.000 (1.15 * H + 0.83 + 6) (1.15 *H +1.67 + 6) 32,000/(A * B)
HS25 Truck 3.77
Tandem 2.75 < H < 3.77 12,500 (1.15 * H+ 1.67 + 6) (1.15 *H+ 0.83+ 4) 25.000 / (A * B)
Other Fill
Design Vehicle H (ft) Wheel Load (lb) Spread B (ft) Spread A (ft) WuLL (psf)
HS20 Truck 3.77
HS25 Truck < H < 11.44 20,000 <1.00 H + 0.83 6i (1.00* H + 1.67 + 6) 40.000/ (A *B)
Tandem 3.17 < H <4.33 12,500 (1.00 * H + 1.67 + 6) (1.00 *H+ 0.83+ 4) 25.000/(A * B)
Figure 4.7  Overlapping Wheel Load Distribution through Earth Fill
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4.6.3 Case 3  Full Distribution of Wheel Loads from Multiple Axles Overlap.
In this case the wheel loads from all axles overlap resulting in full distribution. The distributed live loads are calculated using Table 4.6. For the HS Design Truck, full distribution occurs at an earth fill depth of 11.44 ft as shown in Figure 4.8. The AASHTO LRFD Specifications does allow for the live load to be neglected when the earth fill depth is greater than 8 ft. and exceeds the effective span length. The live load for multiple spans is neglected when the depth of overburden exceeds the distance between the outer face of the end supports or abutments. Due to this provision, Case 3 typically governs when the Alternative Military Load is examined. The Alternative Military load is based on full distribution at a fill depth of 3.77 ft.
Table 4.6  Case 3
Select Granular Backfill
Design Vehicle H (ft) Wheel Load (lb) Spread B (ft) Spread A (ft) WuLL (psf)
HS20 Truck H> 11.44 16,000 (1.15 *H +0.83 + 6) (1.15 * H + 1.67 + 6) 64,000/(A * B)
HS25 Truck H > 11.45 20.000 (1.15 *H+0.83+ 6) (1.15 * H + 1.67 + 6) 80.000/(A * B)
Tandem H > 3.77 12.500 (1.15 * H + 1.67 + 6) (1.15 * H+ 0.83+ 4) 50.000/(A * B)
Other Fill
Design Vehicle H (ft) Wheel Load (lb) Spread B (ft) Spread A (ft) WuLL (psf)
HS20 Truck H> 11.44 16,000 (1.00* H + 0.83 + 6) (1.00* H+ 1.67 + 6) 64.000 / (A * B)
HS25 Truck H > 11.45 20,000 (1.00 *H+ 0.83+ 6) (1.00* H + 1.67 + 6) 80,000/(A * B)
Tandem H > 3.77 12,500 (1.00* H + 1.67 + 6) (1.00 *H+ 0.83+ 4) 50,000/(A * B)
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Figure 4.8 Overlapping Wheel and Axle Load Distribution through Earth Fill
4.6.4 Case 4  Distribution of Wheel Loads from Passing Vehicles
Cases 1  3 are for a single design vehicle. For Cases 4  5, the Standard LRFD Specifications require a check to determine if the distributed live load area from multiple truck axles positioned side by side overlap. Case 4 is when two wheels from separate axles overlap illustrated in Figure 4.9. The total load from the two wheels is distributed over the area illustrated. Case 5 occurs when both axles from each design truck overlap. The total load from both axles is distributed within the boundaries of the two axles shown in Figure 4.10.
74
ISPREAD AJ
Figure 4.9  Overlapping Wheel Load Distribution by Passing Vehicles
Figure 4.10  Overlapping Axle Load Distribution by Passing Vehicles
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4.7 Distribution of Live Loads for Depths of Fill Less Than 2 ft.
For depths of overburden less than 2 ft, the Standard LRFD Specifications and the Standard AASHTO Specifications are similar with respect to the design procedures. The Standard LRFD Specifications distribute the live load into equivalent strip widths. The equivalent strip width is the effective width of the slab that resists the applied load. Equivalent strip widths are used to simplify the analysis of the threedimensional response to live loads. There are two cases that apply:
â€¢ Case 1  When the traffic travels parallel to the design span.
â€¢ Case 2  When the traffic travels perpendicular to the design span.
This thesis focuses on Case 1. When the traffic travels parallel to the design
span, the structure is analyzed using a single loaded lane with the appropriate multiple presence factors specified in Section 4.5. The axle of the design vehicle is distributed over a distribution width E. This distribution width is perpendicular to the design span. Equation 4.6 is used to calculate the distribution width, E
E = 8 + 1.2 * S for H < 2 ft. Equation 4.6
Where:
E = width of slab over which an axle load is distributed (ft)
S = effective span length (ft)
H = cover depth from top of structure to top of Pavement (ft)
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The Standard LRFD Specifications also take into account the length of the
load due to the tire contact area and the parallel distribution length of the tire through earth fill, Figure 4.11. The load length, Espan is determined using Equation 4.7.
Espan= Lt + LLDF * (H) Equation 4.7
Where:
Espan= equivalent distribution length parallel to span, load length (ft)
Lt = length of tire contact area parallel to span, specified in section 4.6 (ft)
LLDF = factor for distributing factor through earth fdl, specified in Section 4.6
H = earth fill depth from top of structure to top of Pavement (ft)
The concrete slabs are analyzed as a 1.00 ft wide beam with an equivalent axle load divided by the distribution width, E, and a load length Espan shown in Figure 4.11. The distribution width is applied to all design spans for both positive and negative bending, and shear force effects.
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4.8 Dynamic Load Allowance, Impact (IM)
To account for the dynamic load affects of moving vehicles, the AASHTO LRFD Specifications includes an Impact Factor or Dynamic Load Allowance, to the live load for varying burial depths. The impact is only applied to the Design Truck or Tandem Load, and not the Lane Load. The Dynamic Load Allowance varies linearly from a 33% increase at 0 ft. of fill to a 0% increase at 8 ft. of fill, as shown in Figure 4.12. The Dynamic Load Allowance in the LRFD Specifications is calculated using Equation 4.8
IM = 33(10.125DE) / 0% Equation 4.8
Where:
De = the minimum depth of earth cover above the structure (ft)
Similar to the Standard Specifications the dynamic force effects applied to moving vehicles is attributed to the hammering effect of the wheel assembly traveling across surface discontinuities such as deck joints, cracks, potholes, and undulations in the roadway pavement caused by settlement of fill (AASHTO 2005).
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Dynamic Load Allowance, IM
Figure 4.12 Dynamic Load Allowance vs. Burial Depth
4.9 Lateral Live Load Surcharge
The AASHTO LRFD Specifications require a live load surcharge to be applied where vehicular load is expected to act on the surface of the backfill within a distance equal to the wall height behind the back face of the wall. Surcharge loads produce a lateral pressure component on soil retaining walls in addition to lateral earth loads. Similar to the Standard AASHTO specifications there are two methods to apply the lateral live load surcharge pressure to the structure. This was discussed in Section 3.5. The increase in horizontal pressure due to the live load surcharge is estimated by Equation 4.9:
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LLS = k * ys * Heq
Equation 4.9
Where:
LLS = Constant horizontal earth pressure due to live load surcharge (psf)
k = Coefficient of lateral earth pressure
Ys = Unit weight of soil (pcf)
heq = Equivalent height of soil for a vehicle load (ft)
The equivalent height of soil, heq, specified by the LRFD Specifications for highway loading as a function of the wall height is extrapolated from Table 4.7. Linear interpolation should be used for intermediate wall heights. The wall height is considered to be the distance between the top surface of backfill and the footing bottom. Figure 4.13 illustrates the wall height used for live load surcharge pressures.
Table 4.7  Equivalent Heights
Abutment Height (FT) heq (FT)
5.0 4.0
10.0 3.0
1 20.0 2.0
80
I
Abutment Height
Figure 4.13  Wall Height for Live Load Surcharge Pressures
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Chapter 5
Comparison Between LFD AND LRFD Specifications
5.1 Design Vehicular Live Loads
The most significant change introduced in the Standard LRFD Specifications is the new vehicular live load model. In the Standard AASHTO Specifications, the vehicular design live load is considered to be either the HS Design Truck Loading or an Alternate Military Loading. The design includes the configuration that produces the critical conditions. The LRFD Specifications include three components of the live load:
â€¢ Design Truck
â€¢ Design Tandem
â€¢ Design Lane Load
A combination of the Design Truck or Design Tandem plus the Lane Load is used as the vehicular live load in the LRFD Specifications. The force effects from both the Design Truck and the Design Tandem must be compared. The LRFD design truck is identical to the axle load portion of the HS20 truck of the Standard AASHTO Specifications. However, the LRFD design truck is not scaleable like the HS20 truck. For example, there is no HS15 or HS25 equivalent under the Standard LRFD
82
Specifications. The Design Tandem has the same tire and axle spacing as the Alternative Military loading, but the load is slightly heavier, see Figure 5.1.
r f o â€œ1 r 60 1
12 KIPS 12 KIPS â€” 12.5 KIPS 12.5 KIPS
i,
Direction
of Travel
4â€™â€”0â€
Direction
of Travel
4'â€”0â€
12 KIPS 12 KIPS 12,5 KIPS 12.5 KIPS
Alternative Military Loading
Design Tandem
Figure 5.1  Alternative Military Loading vs. Design Tandem Loading
As previously noted, another change with regards to the live load from the Standard Specifications is the addition of the Design Lane Load. In the Standard LRFD Specifications a Design Lane Load which consists of a distributed load of 0.64 klf is added to the Design Truck or Design Tandem load, to produce the worst case force effects. Furthermore, the design lane load is also assumed to be uniformly distributed over a 10.0 ft design lane width. Therefore, the lane load converts to an additional distributed live load of 0.064 ksf. The force effects from the Lane Load
83
directly correlate with the design span, as the span increases the force effects increases, and vise versa. The increase of the force effects from the Lane Load is shown in Figure 5.2. The percent increase in service moment due to the Lane Load plus Design Truck for various depths of fill and increasing span lengths are shown. For short spans of approximately 4 ft., the increase in service moment is approximately 4%, depending on the earth fill. The increase in the service moment approaches 18% with the addition of the Lane Load for a span of 16 ft..
5.2 Multiple Presence Factor
The LRFD Specifications require the use of multiple presence factors to account for the effects of multiple loaded lanes on a bridge, Table 4.3. Multiple presence factors are provided for the cases of one, two, three, and three or more loaded lanes. For a single loaded lane the multiple presence factor is 1.2, whereas 1.00 for 2 loaded lanes.
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Full Text 
PAGE 1
COMPARISON BETWEEN THE STANDARD AASHTO BRIDGE DESIGN SPECIFICATIONS AND THE AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS FOR BURIED CONCRETE STRUCTURES by Larry James Miller B.S.C.E., University of Colorado at Denver , 1998 A thesi ubmitted to the University of Colorado at Denver in partial fulfillment of the requirement for the degree of Ma ter of Science Civil Engineering 2006
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This thesis for the Master of Science degree by Larry James Miller has been approved by Stephan A. Durham Bruce Janson Date
PAGE 3
Miller, Larry James (MSCE, Department of Civil Engineering) Comparison Between the Standard AASHTO Bridge Design Specifications and the AASHTO LRFD Bridge Design Specifications for Buried Concrete Structures Thesis Directed by Assistant Professor Stephan A. Durham ABSTRACT For the past thirty years it has been common practice to use the American Association of State Highway and Transportation Officials (AASHTO) Standard Design Specifications for underground precast concrete structures. Today, the bridge engineering profession is transitioning from the Standard AASHTO Bridge Design Specifications (Load Factor Design, LFD) to the Load and Resistance Factor Design Specifications (LRFD). The Federal Highway Administration (FHW A) has mandated that all concrete bridges designed after October 2007 must be designed using the AASHTO LRFD Bridge Design Specifications if federal funding is to be provided. This extends to buried precast concrete structures as these types of structures are included in the LRFD Specifications. The new LRFD Design Specifications utilize stateoftheart analysis and design methodologies, and make use of load and resistance factors based on the known variability of applied loads and material properties. Structures designed with the LRFD specifications have a more uniform
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level of safety. Consequently, designs utilizing the LRFD Specifications will have superior serviceability and longterm maintainability. This thesis examines the current LRFD Design Specifications and the Standard AASHTO Specifications used in designing underground concrete structures such as underground utility structures, drainage inlets, threesided structures, and box culvens. Although many of the provisions of these two codes are the same, there are important differences that can have a significant impact on the amount of reinforcement, member geometry, and cost to produce buried reinforced concrete structures. This thesis compares related provisions from both design specifications. Many of the AASHTO LRFD Code provisions that differ from the Standard Specifications include terminology, load factors, implementation of load modifiers, load combinations, multiple presence factors, design vehicle live loads, distribution of live load to slabs and earth fill, live load impact, live load surcharge, and the concrete design methodology for fatigue, shear strength, and crack control. The addition of the distributed lane load required in the LRFD Specifications significantly increases the service moment. The maximum increase in live load as a result of the impact factor is 21% at a fill depth of 3ft. The intent of this thesis is to act as a reference on how to apply the current provisions from the LRFD Design Specifications to underground precast concrete structures. This research shows there is greater reliability and a more uniform factor of safety when utilizing the LRFD Specifications. The provisions in the LRFD Specifications
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are more concise and more beneficial to design engineers with the addition of the commentary. Therefore, the code is simpler to apply than the Standard Specifications. This abstract accurately represents the content of the candidate's thesis. I recommend its publication. Sign Stephan A. Durham
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ACKNOWLEDGEMENT I would like to express my deepest appreciation to Dr. Stephan Durham for his patience over the past year. Thanks for hanging in there with me and giving me words of encouragement. I would like to thank Dr. Kevin Rens and Dr. Bruce Janson for participating on my thesis committee. Thanks to my colleges Ray Rhees , Clint Brookhart , and Jim Baker for giving me the opportunity to pursue this degree. I appreciate the support and all of the wonderful advice you have given me. I would like to thank my mom and dad who probably think I am crazy for going back to school, and spending countless nights in front of my computer. It's finally over! I want to especially thank my beloved wife, Julie Miller for putting up with me while working on this project. I know it has not been easy, thanks for hanging in there. I would also like to acknowledge by beautiful daughter, Abigail Marie Miller in hopes that she will pursue her dreams as well. I love you all.
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TABLE OF CONTENTS Figures ........................................................ . ...................... ...... x Tables .............................. . .. . . ................................................ xiv CHAPTER 1. INTRODUCTION ..................................... . ... ....................... 1 Historical Developme nt of LRFD Speci ficatio n s ................. 2 Problem Statement and Re searc h Significance .................... 9 2. LITERATURE REVIEW ............................................ . .... .. . 11 Comparison of Standard Specifications and LRFD Specifications ....... .. . . . ............................................. 11 American Concrete Pipe Association Study ...................... 13 Flexural Crack Control in Concrete Brid ges ............ ......... 13 National Cooperative Highway Research Program (NCHR P ), Project 15 29 ............................................. 14 Des ign Live Loads on Box Culverts, University ofFlorida ..................................................... .. . . .. ... 16 3. AASHTO LFD STANDARD SPECIFICATIONS ........... ............ 23 Load Factors and Load Combination s .......................... ... 23 AASHTO Standard Vehicular Design Live Loads ........ . ..... 29 Earth Fill and Vertical Earth Press ure Loading ........ ... ........ 35 Vl
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Di s tribution o f Live Loa d s f or Depth s o f Fill Gre a ter Than 2 ft. ..... . . ... . . . .. .. .......... . . ... . . ... ... ... ...... .... 38 Cas e 1 Dis tribution of Wheel Load s tha t do not Overl a p ................................ .. ...... . ............... 40 Cas e 2 Dis tribution of Wheel Load from a Sin g le Axle O v erl a p . .. . ....... ................ . ..................... 41 Cas e 3 Full Di s tribution of Wh ee l Loa d s fr om Multiple Axle s . . .. ....... . ........... . .. ................. .... 4 2 Di s tribution of Liv e Loa d s f or Depths o f Fill Le ss Than 2 ft .......... ... . ... ......................... ... . .. ............... 47 Impact Factor ... ......................................... ... ....... ... 50 Lateral Live Load Surchar g e ........ . . ... ........... . .. .. . ......... 51 4. LRFD STANDARD DESIGN SPECIFICATIONS ...................... 53 Load Factor s and Load Combination s ........ ..................... 53 Load Modifier s .......... .......... . . ........................ ....... .. . 59 AASHTO Standard Veh i cular Design Live Load s .. . ............ 62 Earth Fill and Vertical Earth Pre s sure Loading .. .. .............. 64 Multiple Pre s enc e Factor s .............. . ......... ................... 66 Case 1 Depth of Fill i s equal to or Greater Th a n 2ft. ............................... .. . .. ................. 66 Vll
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Case 2 Depth of fill is less than 2 ft, and the direction of traffic is parallel to span ................................ 67 Case 3 Depth of fill is less than 2 ft, and the direction of traffic is perpendicular to span .... ....... ........... ... 67 Di s tribution of Live Load s for Depth s of Fill Great er Than 2ft. . .. . . . .. . .................................. . ....... ... . . . ..... 68 Case 1 Distribution of Wheel Loads that do not Overlap ............. .. . . .................... . .. . .. .. .. 71 Case 2 Distribution of Wheel Loads from a Single Axle Overl ap ............................. ............ 72 Case 3 Full Di stribution of Wheel Loads from Multiple Axles Overlap .............. ..... ........... 73 Case 4Distribution of Wheel Loads from Pas sing Vehicles .......................................... .. 74 Di tribution of Live Loads for Depth s of Fill Less Than 2ft. .. .............. . ................................. ............. 76 Dynamic Load Allowance , Impact (IM) ......... ............ ..... 78 Lateral Live Load Surcharge ....................................... 79 5. COMPARISONS BETWEEN LFD AND LRFD .... ......... . ........... 82 Design Vehicular Live Load s ................................ . . .... 82 Vlll
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Multiple Pre sence Factor. .. .. .................................. .... . 84 Dynamic Load Allowance , Impact. ....................... ......... 82 Lateral Live Load Surcharge ............................. . ......... . 88 Di stribution of Wheel Load s through Earth Fills for Depth s of Fill Greater Than 2 ft.. ..................... . . 90 Di strib ution of Live Load s for Depth s of Fill Less than 2 ft. ........................................................ 96 Load Factors and Load Combinations ................. . . .. .. .. . . . 98 6. DESIGN EXAMPLES . . ................................ .......... ... . ....... 103 De sign Example # 1 ..................... ................. ...... . .. . . 1 03 Design Parameter s ....... . ................. ..... ...................... 103 Standard AASHTO Specifications ... . ........... ....... 104 Standard LRFD Specification s ................... .... ......... 126 De sign Example #2 .. ..................................... ... .... . .. 153 Standard AASHTO Specifications ...................... 153 Standard LRFD Specifications .......................... 174 7. SUMMARY AND CONCLUSIONS ..................................... 199 REFERENCES ......... . ... .. ... .............................................................. 202 IX
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LIST O F FIGURES Figure 2.1 Bou ssinesq Point Load ................. . ... ............... . ... ............................. 18 3.1 AASHO 1935 Truck Train Loading . .................................................... 29 3.2 Characteristics of AASHTO De sig n Truck .................................... .... 31 3.3 Characteristics of Alternative Military Loading .................... . . .............. .... 33 3.4 Tire Contact Area .. ........... . ....................................... ............. .......................... ... ... 34 3.5 Earth Fill Depth and Vertical Earth Pres s ure Loading ................................ 36 3.6 LFD Wheel Load Di strib ution through Earth Fill... ..................... . ....................... 39 3.7 Overlapping Wheel Load Di stribut ion through Earth Fill.. .......... . ................ . .. .... 39 3.8 Case 1, Wheel Load Distribution through Earth Fill ................................. .40 3.9 Case 2Overlapping Wheel Load Di stti bution through Earth Fill. .............. . .41 3.10 Case 3Overlapping Wheel and Axle load Distribution through Earth Fill.. . . .43 3.11 LFD Live Load Pre ss ure s through Earth Fill.. .. ... ............ ...................... .44 3.12 LFD Live Load Spread For 3ft O verburden ................. .. .................... .45 3 .13 LFD Live Load Service Moments vs. Increasing Design Spans ........... ....... .46 3.14 LFD Di stri bution Width, E for a Single Wheel Load ............................... .48 3.15 Effective Distribution Widths on Slabs .............................. ........... ...... .48 3 .16 Reduced Distribution Widths on Slab s ................... ...... . . .................... .49 X
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3.17 LFD Equivalent Height. ..... .... ............... . ......................................... 52 3.18 Live Load Surcharge Pressure .......................................................... 52 4.1 Characteristics of LRFD De sign Truck and Wheel Footprint. .................. . .... 62 4.2 Characteristics of the Design Tandem .. ......................................... ... .... . 63 4.3 Earth Fill Depth and Vertical Earth Pressure Loading .. .. .. ...................... .... 65 4.4 LRFD Wheel Load Distribution through Earth Fill .................................... 69 4.5 Overlapping Wheel Load Distribution through Earth Fill .................. .......... 70 4.6 Wheel Load Distribution through Earth Fill.. .......................................... 71 4.7 Overl apping Wheel Load Di stribution through Earth Fill .. ._ ........................ 72 4.8 Overl apping Wheel and Axle Load Distribution through Earth Fill .............. .. 74 4.9 Overlapping Wheel Load Di stribution by Passing Vehicles ......................... 75 4.10 Overl apping Axle Load Di stribution by P assing Vehicles ........................ . . 75 4.12 Dynamic Load Allowance vs. Burial Depth .................................... .. ..... 79 4.13 Wall Height for Live Load Surcharge Pressures . .......... .......................... 81 5.1 Alternative Military Loading vs. Design Tandem Loading ........................... 83 5.2 Increase of Force Effects due to Design Truck vs. Design Truck +Lane Load ............. 85 5.3 Dynamic Load Allowance vs. Impact. ........... ................................. ....... 87 5.4 Percent Increase in Dynamic Load Allowance LRFD vs. LFD ...................... 87 5.5 Live Load Surcharge Equivalent Heights, heq ......................................... 89 5.6 Live Load Di stribution Areas for a Single Wheel.. ....... .... ........................ 92 Xl
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5.7 Overl appi n g Wheel Load Di stribution by P assing Vehicle s ............ ........ . . . .. 93 5.8 O verlapping Axle Load Di stributio n by P assing Vehicle s ....... ....... ............. 93 5.9 Di stributed S ervice Live Load Value s through Eart h Fill with Impact.. . .......... 95 5.10 Di s tributed Factored Li ve Lo ad Valu es through Earth Fill wit h Impact.. ........ 95 5.11 Ser vice MomentLRFD vs . LFD D esign Live Loads (Multiple presence factor and impact neglected ) ........... .. . . .. . ... .. ................. ........ ......... 98 5.12 Ser vice MomentLRFD vs. LFD D esign Live Loads ( Multiple pr esence factor and impact included) ...................... ... .. .... . . ...... .................... 99 5 .13 Load s on a ThreeSided Culvert ............... ................... . .. . ................. 1 0 1 6 . 1 D esign Example #1, Geometry ....... ........ ...... .............. . .. ............. ....... 105 6.2 LFD Vertical and Lateral Earth Pre ss ures .. ...................... ..................... 106 6.3 LFD Live Load Surchar ge Pre ss ure ....... . ........................ . ... ....... . .. . . .... 107 6.4 HS20 Dis tribution through Earth Fill ... ...... ... .......... .. . ........................ 108 6 . 5 Alternative Military Di s tribution through Earth Fill. ........... .. . . . .. .............. 109 6 . 6 LFD S ervice Loading Configuration , Ca s e s 1 3 ....... . ..................... .. ..... 112 6 . 7 Critical Locations for Stre sses . ........ .. ...... . . ... ............... . .................... 113 6 . 8 LFD Rein forcement Placement for D esign Examp l e #1 ............. ...... . ................ 126 6.9 LRFD Vertical and Lateral Earth Pressures ......... .................... .. .......... . 127 6.10 LRFD Wall Height , Example #1 .. .. . . .. ... .. ......................... . ...... . .. . ..... 128 6.11 LRFD Live Load Surcharge Pr ess ur e .................... ......... .. .. : ...... .. ...... 129 xu
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6.12 Di s tribution area for De sig n Truck ............ ....... .. .. ....... . ..................... 131 6.13 Di strib ution area for two adjacent de sig n vehicles ............... ................... 132 6.14 Di s tribution area for De sig n Tand e m ................................................. 132 6 .15 De sig n Example #1, LRFD Se rvice Lo a din g Configuration , Ca ses 13 ....... 136 6.16 Critical Locations for Stre sses ........ ........... . . ...... .............................. 137 6 .17 LRFD R ei n forceme nt Pl acement for D es ign Example # 1 ............ ............. . 153 6.18 LFD Vertical and Lateral Earth Pre ss ure s ........................................... 155 6 .19 LFD Live Load Surcharge Pre ssure . ............ ........ .............................. 156 6 . 2 0 LFD Service Loading Con fig ur atio n , Cases 13 ................................... 159 6 .21 LFD Critical Locations for Stre es .. .. ............................................... 160 6.22 LFD Reinforcement Placement for De s ign Example # 2 . .......................... 173 6. 23 LRFD V ertica1 and Lateral Earth Pre ss ure s .......................................... 1 7 5 6.24 LRFD Wall Heigh t.. . .................. .................. . ............................ ... 176 6.25 LRFD Live Load Surcharge Pre s ur e ................................................. 177 6.26 Loadin g Configur a tion , C ases 13 ................................................... 182 6.27 Location s of Critical Str esses ............................ . ...... ........................ 183 6.28 LRFD Reinforcement Pl acement fo r De s ign Example #2 .......................... 197 Xlll
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TABLES Table 3.1 AASHTO Group Loading Coefficients and Load Factor s .......................... . 26 3.2 AASHTO Earth Pre s ure and Dead Load Coefficients ................................ 27 3.3 AASHTO Re istance Factors for Underground Concrete Structures .. .............. 29 3.4 AASHTO Standard HS De s ign Truck Classes ......................................... 30 3.5 Case 1 .. ................ . ... . .......... ............................................... ..... . ... 40 3 . 6 Case 2 ....................... ..................... ... .............................. .. . ........ 41 3 . 7 Ca s e 3 .............. . .. . ... . .. ............................................ . .. . .. . . .. .. ........ 42 3 . 8 Service Moments from HS20, HS25, and Alternative Military Load s ............ 46 3.9 Impact Factor. ...................... ..................... .. . . . .. .. . . ................ ..... .... 50 4.1 Load Combinations and Load Factors ................................................... 57 4.2 Load Factors for Permanent Load , yp .................................... ........ ...... 59 4.3 Multiple Presence Factor .. ............................. ................................. . 67 4 .4Case 1 ................................................... ... ....... ........................... 71 4.5 Case 2 ............................................. ... ........................... . ............. 72 4.6 Case 3 .............................. . ....................................... ... .. . . ............ 73 4.7 Equivalent Heights ............... . .................. . ............... . . ... .......... ........ 80 5.1 Load Factors for LRFD and LFD Specification s .............................. ........ 100 6.1 LFDStructural Analysis Result per Foot Width, Example 1 .................... 113 XIV
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6.2 LRFDStructural Analysis Re sults per Foot Width , Example 1. .. .............. . 138 6.3 Area of Steel compari on ............................. . . ....... ...................... .. ... 152 6.4 Impact Factor. ....................................... ....................... . . ... .......... 156 6.5 LFDStructural Analysis Result s per Foot Width , Example 2 ................ . .. . 161 6.6 LRFDStructural Analysis Re sults per Foot Width , Example 2 .............. : . . . 183 6.7 Area of Steel comparison ................. .. .. ..... ......... ... . .......................... 152 XV
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Chapter 1 Introduction Historically, much of the design methodology and de s ign load s for underground concrete structures such as pipe and box culvert came from the American A s ociation o f State Highw ay and Tran s portation Officials ( AASHTO ) . In the 1930's AASHTO began publi s hing the Standard Specification s for Highway Bridges. The sta ndard practice at the time was to u se one factor of safety . This methodology is commonly known a allowable stress de sig n (ASD). In the 1970s, AASHTO b egan vary ing the factor of afety for each load in relation to the engineer's a bility to predict the corresponding load. This corresponding bridge design methodology was referred to as load fact or design ( LFD ) . The change from ASD to LFD was made in the form of interim revisions by AASHTO. In fact, the Standard Specification s have never been completely revised and still include provision s from both the LFD and ASD methodologie s (" LRFD: State Department " 2006). AASHTO introduced the Load and Resistance Factor De s ign ( LRFD ) Bridge Design Specification in 1994, with the intent of r e placing the Standard Specification s for Highwa y bridges with this reliability base d code that provide s a more uniform safe ty for all e lement s of bridge s . The AASHTO LRFD Highw ay Bridge De s ign Specification s were developed with the intent of implementing a more rational approach for the design of highway st ructures . The LRFD Specification s utilize load 1
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and resistance factots based on the known variability of applied loads and material properties. The load and resistance factors were calibrated from act ual bridge statist ic s ensuring a more uniform level of safety ("L RFD : State Departm ent" 2006). 1.1 Historical Development of LRFD Specifications In the late 1970's the Ontario Ministry of Transportation and Communication, now known as the Ministry of Transportation, developed its own bridge design specifications, rather than continue to use the AASHTO Standard Specifications for Highway Bridges. The Ontario Ministry of Transportation and Communication required that the new design specifications be based on probabilistic limit states. As a result, the first edition of the Ontario Highway Bridge Design Code ( OHBDC ) was released in 1979 to the design community as North Americas first calibrated, reliabilitybased limit state specification (NCHRP 1998). The OHBDC is currently in its third edition after being updated in 1983 and 1993. In addition, the OHBDC included a companion volume of commentary in which the AASHT O Standard Specifications did not. Over time, more and more U.S . engineers became familiar with the OHBDC. They recognized certain logic in the calibrated limit states design . Many American engineers began to question the Standard AASHTO Speci fications and whether it sho uld be based on comparable philosophy. 2
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The National Cooperative Highway Research Program (NCHRP) , National Science Foundation (NSF), and various states completed numerous research projects . These organizations were collecting new information on bridge design faster than it could be critically reviewed and were appropriately adopted to form the AASHTO Standard Specifications. Later research revealed that many of the revision s that have occurred to the Standard AASHTO Specifications since its inception had resulted in numerous inconsistencies and it made the document appear patchwork. In the spring of 1986, a group of state bridge engineers or their representatives met in Denver and drafted a letter to the AASHTO Highway Subcommittee on Bridges and Structures ( HSCOBS) indicating their concern that the AASHTO Standard Specifications must be revised . They also raised concerns that the Technical Committee Structure, operating under the HSCOBS, was not able to keep up with emerging technologies. As a result, this group of state bridge engineers began the process leading to the development of the LRFD Specifications. A group of state bridge engineers met with the staff of the NCHRP in July of 1986 to consider whether a project could be developed to explore the concerns raised in the letter submitted at the meeting in Denver. This led to the NCHRP project 1228(7) "Development of Comprehensive Bridge Specifications and Commentary." A pilot study was conducted by Modjeski and Masters, Inc. with Dr. John M Kulicki as Principle 3
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Investigator. The list of ta s k s for thi s project and the brief outcome are lis ted below ( NCHRP 1998 ) . â€¢ Task 1 Rev iew other s pecifications, and the philo s ophy o f s afety and coverage pro v ided . Information collected from v ariou s s ource s around the world indicated that mo s t of the Fir s t World Countrie s a ppeared to be moving in the direction of a calibrated , reliabilitybased , limit state s specification. â€¢ Tas k 2Other than the Standard Specification s, review other AASHTO document s f or their inclu s ion into a rev i s ed standard specification. Thi s can be best de s cribed as a s earch for gap s and inconsi s tencies in the 131 h edition of the AASHTO Standard Specification s for Highwa y Bridge s . " Gap s" were area s where coverage was missing; " Inconsi s tencie s " were internal conflict s, or contradictions of wording or philosophy. Numerou s gap s and inconsistencies were found in the Standard Specifications. â€¢ Task 3 Ass es s the fea s ibility of a probabilityba s ed specification. The de s ign philosophy used in a variety of specifications wa s reviewed. They wer e the ASD , LFD , and the Reliability Ba s ed 4
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Design. It was generally agreed upon that the probabilitybased specification was more suitable. â€¢ Task 4 Prepare an outline for a revised AASHTO Specification for Highway Bridge De sign and commentary, and present a proposed organizational process for completing suc h a document. The findings of NCHRP Project 1228(7 ) were presented to the AASHTO HSCOBS in May of 1987. There were 7 options that were available: â€¢ Option 1 Keep the Status Quo â€¢ Option 2 Table Consideration of LRFD for the Short Term â€¢ Option 3 Immediate Adoption of the OHBDC â€¢ Option 4 Replace Current with LRFD Immediately â€¢ Option 5 R eplace Current LFD with LRFD in the Near Term â€¢ Option 6Develop LRFD for Evaluation Only, or â€¢ Option 7 Develop LRFD as a Guide Specification A recommendation was made to develop a probabilitybased limit states specification, revise as many of the gaps and incon s istencies as possible, and develop a commentary specification. Thus NCHRP Project 1233, entitled " Development of Comprehensive Specification and Commentary," began in July of 1988. The primary objective was to develop a recommended LRFDbased bridge design specifications 5
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and commentary for consideration by the AASHTO Subcommittee on Bridges and Structures. Thirteen task groups were responsible for developing the recommended specifications. The task groups were: general features, loads, analysis and evaluation, deck systems, concrete struct ure s, metal structures, timber struct ures, joints , bearings, and accessories; foundations; soil structure inter action systems, moveable bridges , bridge rail , and s pecification calibration. The project consisted of four contractors and 47 consultants employed to assi s t with the development of the specification and commentary. In addition , more than 20 state, federal , and industry engineers worked on the project volunteering their time ( Project 1233 2006). The project was completed on December 31, 1993. The LRFD specifications were adopted by AASHTO and published as the AASHTO LRFD Bridge De sign Specifications. The 1994 edition was the first version, with both SI unit and customary U . S . unit specifications availa ble. Currently , the 2006 interim revision edition is the third edition of the AASHTO LRFD Bridge De sig n Specifications. Today , the Federal Highway Administration (FHW A ) and State Departments of Transportation have established as a goal that the LRFD Standard Specification s be used on all new bridge de sig ns after 2007 . In fact, AASHTO in concurrence with FHW A ha s set a deadline of October 151, 2007 for f ull implementation by all states. States must design all new bridges according to the LRFD Specifications . At least 46 states have fully or partially implemented the LRFD Specifications to date , or are 6
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working with the FHW A to develop a plan for implementation . A 2004 AASHT O Oversight Committee survey found that 12 states have fully implemented the specificat ion s . Another 34 states have partially implemented the LRFD Specifications or are currently in the stage of developing implementation plans and designing pilot projects (" LRFD : Achieving Greater R eliability" 2004). The FHW A is providing assistance to states in transition by providing a number of resources that include a team of structural, geotechnical, and research engineers who can meet with individual states and provide guidance in developing a StateSpecific LRFD implementation plan, training courses , and LRFD Design Workshops. In fact, the FHW A list s tips for successful implementation on the following website, http://www.fhwa.dot.gov/BRIDGE/lrfd/tips.cfm. Tips on the website include: â€¢ Staff: Dedicate staff for LRFD planning and design (and studies if necessary ) and train the initial design and study squad in LRFD. Utilize FHW A and other State Departments of Transportation assistance. â€¢ Design Transition Strategy: Set a target date for full LRFD implementation on all new and replacement bridges and on all in house and cons ultant projects. Pe rform inhouse trial LRFD design of LFD projects (or have pilot LRFD projects) to develop questions and 7
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resolutions. These trials also help to gain familiarity with the LRFD Specifications. After the completion of the trial/pilot project , utilize the LRFD de ign in increments up to the target date or hav e a onestep conversion to LRFD . The latter sho uld help you minimize the problem of maintaining two separate design specifications and manuals. The pilot projects should be se lected carefully to represent low priority, routinely de igned bridges. â€¢ Software: Acquire a computer program that utilizes LRFD. There are many state and private LRFD software programs available for steel and concrete bridge s uper str ucture s and concrete s ubstructure s â€¢ Training: Sponsor inhouse training course for all designer s (by in house instructors, local universities instructors, industry, or by FHW A). Acquire LRFD de sign examples and software for handson training. Require that consultants attend LRFD training before they perform LRFD de sig n s in a particular state. â€¢ Technical Support: Develop a technical s upport group that i readily available to answer questions pertaining to the LRFD Specifications. Utilize LRFD support teams, states, industry, universities , and FHW A resources . In addition, retaining a firm experienced in LRFD for questions may prove to be beneficial. 8
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â€¢ Documentation Support: Update standards, manuals, and guidance to coordinate with the LRFD Specifications. Develop predesigned LRFD deck and barriers to shorten the design process if standardized designs are not available. Contract services to update existing design materials to LRFD. â€¢ FineTune Documentations: After the completion of the pilot project and/or full LRFD conversion , finetune the LRFD standards , manuals , and guidance if and when needed. 1.2 Problem Statement and Research Significance This thesis examine s the current LRFD Design Specifications and the Standard AASHTO Specifications used in designing underground concrete structure s uch as underground utility structure , drainage inlets , threesided structures , and box culverts. Many of the AASHTO LRFD Code provisions that differ from the Standard Specifications include terminology, load factor , implementation of load modifiers, load combinations , multiple presence factors , design vehicle live loads, distribution of live load to slabs and earth fill, live load impact, live load surcharge, and the concrete design methodology for fatigue, shear strength, and crack control. The October 1 s t, 2007 deadline that AASHTO in concurrence with the Federal Highway Administration has set for all states to be completely converted to the AASHTO 9
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LRFD Bridge Design Specifications is soon approaching. Although there are many training tools available to utilize the LRFD Specifications on highway bridges, there are very little resources available for designing underground precast concrete. This thesis addresses how to transition from the Standard Specifications to the LRFD Specifications when designing underground precast concrete. This thesis includes: â€¢ A comprehensive literature review of existing and current studies associated with the Standard LFD and LRFD Specifications . â€¢ A detailed summary of the variables and design methodology for buried precast concrete structure s using the AASHTO LFD Standard Specifications. â€¢ A detailed summary of the variables and design methodology for buried precast concrete structures using the AASHTO LRFD Bridge Design Specifications. â€¢ A thorough comparison between the LRFD and LFD specifications. â€¢ Two design examples illustrating the use of both specifications. The examples are of a buried threeside precast concrete structure . â€¢ A summary of this thesis document. 10
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Chapter 2 Literature Review Currently , bridge designers are tran s itioning from the Standard AASHTO Bridge Design Specification s to the Load and Resistance Factor Design Specifications . The LRFD Bridge Design Specifications were developed in 1994; however, bridge designers were given the option of using either specification. The new specifications utilize tateoftheart analysi s and design methodolo gies. In addition, the LRFD Specifications make u e of load and resistance factor ba ed on the known variability of applied loads and material properties. Difference s between the two specifications include terminology , load factors, implementation of load modifiers, load combinations, multiple pre se nce factors, de sign vehicle load , distribution of live load to s labs and earth fill, live load impact , Live load surc harge , and the concrete design methodology for fatigue, shear strength, and control of cracking. There has been very little research comparing all of the provisions from both specifications when de igning underground concrete structures. However , there ha s been research completed comparing specific topics from both specifications and impact the LRFD Specification has had on the engineering community. 2.1 Comparison of Standard Specifications and LRFD Specifications Rund and McGrath (2000) compared all of the provisions from AASHTO Standard Specification and the LRFD Specifications for precast concrete box 11
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culverts. The research analyzed several combinations of box culvert sizes and fill depths utilizing both specifications. Typically, the provisions from the LRFD Specifications yielded greater design loads and therefore required more area of steel reinforcement. The differences in reinforcement areas were the most pronounced for fill depths less than 2 ft. This was primarily the result of the differences in distributing the live load to the top slab into equivalent strip widths. The equivalent strip width is the effective width of slab that resists the applied load. In addition, for culvert spans up to 10 ft, the LRFD Specifications required shear reinforcement. Analysis utilizing the Standard AASHTO Specifications also show required shear reinforcement for a similar range of spans, but provisions permit the shear effects to be neglected. For depths of fill between 2 and 3 feet, the differences in reinforcement areas were due to fatigue requirements. The provisions in the Standard Specifications for fatigue were not present in the LRFD Specifications. For depths of overburden greater than 3ft, the differences in the reinforcing areas decreased slig htly . However, with increasing depth, the LRFD Specifications required greater required area of steel reinforcement. This was primarily due to the distribution of live load through earth fill. The provisions in the LRFD Specifications often yield higher design forces from wheel loads than the Standard Specification. It is important to note that the research utilized the first edition of the LRFD Specifications, which has since been revised and 12
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is in its 3rd edition. Many of the provisions from this research have been modified lightly. 2.2 American Concrete Pipe Association Study The American Concrete Pipe Association wrote a short article comparing the live loads on concrete pipe from both specifications (A CPA 2001). The primary objective of this re earch was to compare the live load model and distr ibution methods used in both specifications. The article included four design examples illustrating the design step that are required to be taken when designing reinforced concrete pipe using the Standard LRFD Specification s . . Similar to the article written by Rund , and McGrath (20 00), the paper concluded that the LRFD Speci ficatio n s typically produced greater design forces than the Standard Specification. 2 . 3 Flexural Crack Control in Concrete Bridges Several State s have found that crack control requirements tend to govern the design of flexural steel in concrete structures more frequently with the provisions of the 1994 LRFD Specification s than under the Standard AASHTO Specification s ( DeStefano , Evans, Tadros , and Sun 2004). At the time it was believed that this was primarily due to the higher loads specified in the LRFD Specifications. In the 1994 AASHTO LRFD Specifications, flexural crack control requirements were based on the Z factor method de velope d by Gergely and Lutz in 1968 ( DeStefano , Evans, 13
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Tadros, and Sun 2004). Research completed by DeStefano et al. (2004 ) suggeste d a new equation be adopted in the LRFD Specifications. Their recommendation for a new equation was for the development of a s imple , straight forward equation that acco unt s for the differences between bridge and building structures. The proposed revised crack control requirements identified a number of short comings identified with the Z factor method. Example de igns were included on box culverts to compare the allowable stresses in the existing Z factor method and the propo se d crack control method. The re ults indicated rea onable increa es in allowable stres e , thus permitting more economical designs without sacrificing long term durability. The proposed equation developed in this research h as been adopted in the current edition of the LRFD Specifications. 2.4 National Cooperative Highway Research Program, Project 15 29 The NCHRP funded a project that examined the distribution of live load through earth fill ( Project 1529 2006). This research compared provisions form both specificat ion s regarding distribution of live load through earth fill. The design and evaluation of buried structures requires an understanding of how vertical earth load s and vehicular live load s are transmitted through earth fills. When the depth of overburden is equal to or greater than 2 ft, both the Standard AASHTO Specifications and the LRFD Specification s allow for the wheel load to be distributed throughout the 14
PAGE 31
earth fill. Both specifications utilize approximate methods for estimating the distribution of vehicular live loads through earth fill. The Standard LRFD Specifications takes into account the contact area between the footprint of the tire and ground surface. The di tribution area is equal to the tire footprint, with the footprint dimensions increased by either 1.15 times the earth fill depth for select granular backfill, or 1.0 for other types of backfill . The Standard AASHTO SpecificaUons does not account for the dimensions of the tire. Instead the wheel load is considered to be a concentrated point load . The wheel load is distributed over a square equal to 1.75 times the depth of fill, regardless of the type of backfill. One major difference between the two specifications is the AASHTO LRFD Bridge Design Specification u es different approximate methods that significantly increase live load pressures on buried structures when compared to the Standard Specifications . In addition, the basis for the methodology in which the live load is distributed through soil i not well documented or understood. As a result the NCHRP developed project 1529 , Design Specifications for Live Load Distribution to Buried Structures. Administered by the Transportation Research Board (TRB ) and sponsored by the member departments (i.e., individual state departments of transportation) of the American AssociaUon of State Highway and Transportation Officials, in cooperation with the FHW A, the NCHRP was created in 1962 a a means to conduct research in acute problem areas that affect highway planning , design, construction , operation, and maintenance 15
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nationwide. The objective of Project 1529 is to develop recommended revi ions to the AASHTO LRFD Brid ge De sign Specification s relating to the distribution of live load to buried tructures. The project completion date is scheduled for October 20t\ 2007. The statu of the project is unknown at thi s time. 2.5 Design Live Loads on Box Culverts, University of Florida Other research that ha been completed with regards to the distribution of li ve load through earth fill was performed by Bloomqui st and Gutz ( 2002) at the University of Florida. The research was sponsored by the Florida Department of Transportation and prepared in cooperation with the Federal Highway Administration. The Florida Department of Transportation adopted the Standard LRFD Specifications as the design stan dard for all st ructure s beginning in 1998. The re earch report di cusses the development of equation to calculate the distribution of live loads through earth fill for the de sig n of preca st concrete box culverts. The objective of the research was to develop a new method and establish a single de sig n equation for di strib uting live loads to the tops of precast concrete box culverts. The existing LRFD methodology i s considered to be a rigorous design procedure that is extremely difficult to apply and too conservative when compared to the Standard AASHTO Specifications. A sig nificant amount of design time can be shortened by simplify ing this process. Al o , the work was aimed at producing a si mplified design 16
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equation that would be thorough but not overly conservative. The approach of the research was to u e theoretical methods to calculate the distribution of live loads through varying earth fill depths and compare them with the current LRFD provisions . The first method that was reviewed was developed by Boussinesq in 1855 (Bloomquist and Gutz 2002) . His method considers the stress increase based on a point load at the surface of a semiinfinite, homogenous, isotropic, weightless, elastic halfspace, shown in Figure 2.1. The value of the vertical stress can be calculated using Equation 2 .1. Equation 2.1 Where: P = Point load Z = Depth from ground surface to where
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p Figure 2.1 Boussinesq Point Load Natural oil deposit do not approach ideal condition that the Bou ine q equation wa ba ed upon. Many soil deposits consist of layered s trata of fine and cour e material s or alternating layer of clay and and. In 1938 , Westergaard proposed a solution that wa applicable for these types of depo s it ( Bloomquist and Gutz 2002) . Using the We tergaard theory, the vertical s tres s can be calculated using Equation 2 .2. Equation 2.2 Both the Boussinesq and Westergaard theory as ume the loading acts a a point load . The provisions in the Standard LRFD Specification s require the 18
PAGE 35
dimension s of the tire be utilized. Newmark integrated the Bou ssi ne s q solution over an area to calculate the distribution of a patch load through soil in 1935. Thi s lead to the development of Equation 2 . 3, and is known as the s uperpo sit ion method. Equation 2.3 Where: qo = Contact stress at the urface m= x/z n = y / z x,y = Length and width of the uniformly loaded area z = Depth of surface point where s tress increa s e i s desired Another method that was reviewed wa s the buried pipe method. The buried pipe method i also ba se d of the Boussinesq s olution. The equation for the buried pipe method is shown in Equation 2.4 Equation 2.4 19
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Where: W s d =Load on pipe in lb/unit length P = Intensity of distributed load (psf) F' = Impact Factor B e = Diameter of pipe (ft) C = Load coefficient which is a function of D/(2H ) and M/(2H), where D and M are the width and length, respectively, of the area over which the di tributed load acts . The last method to be reviewed and one of the implest methods to calculate the distribution of load with depth is known as the 2: 1 method calculated in Equation 2.5. Load (j =z (B + Z)(L+ Z) Equation 2.5 Where: crz =Live load stress Z = Depth of fill B, L =Width and length , respectively, of the loaded area at the surface 20
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The 2:1 method is an empirical approach that a sumes the area over which the load acts increase in a y tematic way with depth. The methodology in the Standard LRFD Specifications i ba ed on a variation of thi method. Each of the method described above were used to calculate the live load pressure through earth fill and compared to the current LRFD Specifications. The objective was to compare methods of live load di tribution and determine uitable alternatives. The De ign Truck and De ign Tandem vehicles were u ed when examining the method . The findings suggest that the superposition method be used in place of the provi ions in the Standard LRFD Specifications. Once the different method to distribute live load were compared, the next tep was to develop a implified equation that would produce the arne force effects as the current LRFD Specifications . Ba ed on the uperposition method, hears and moments acting on the top slab of box culvert were calculated for varying de ign spans and earth fill depths. An equivalent uniform load model was developed by statistical modeling and curve fitting to produce the same moments and hears. The research developed Equation 2.6 for determining the equivalent uniformly di tributed load: 2300 a=z z 21 Equation 2 . 6
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Where:
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Chapter 3 AASHTO LFD Standard Specifications 3.1 Load Factors and Load Combinations All tructures must be designed to withstand multiple loads acting sim ultaneou sly at once. Vehicle live loads may act on a st ructure at the same time as lateral earth pressure. The de ign engineer i responsible for ensuring the design is sized and reinforced properly to safely resist combinations of loads. To acco unt for this the Standard AASHTO Specification contain load combinations, subdivi d ed into groups, which represent a combination of simultaneous loadings on the struct ure. The general eq uation u ed to define a group load is given by Equation 3.1 ( AASHTO 2002). Where: Group (N) = + (L +I)+ + WL + + ( R + S + T) + + N = group number y = load factor from Table 3.1 from Table 3.1 D =dead load 23 Equation 3.1
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L =live load I = impact factor E = earth pre ure B =buoyancy W = wind load on structure WL =wind load on live load LF = longitudinal force from live load CF =centrifugal force R = rib shortening S = shrinkage T = temperature EQ = earthquake SF = stream flow pressure ICE = ice pre ure Table 3.1 lists value for both y and These values are based on the service load and load factor design. The coefficient varie based on the type of load. The load factory i the same for service loads; however, it varies for different load factor design grouping . The coefficients for both dead load and earth pressure vary depending on the load group and design method shown in Table 3.1. This variation 24
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results from different values being applied for different types of elements or component . A description of the di ss imilar res ult s is illustrated in Table 3.2. The Standard AASHTO Specification s incorporates two principle design methods : â€¢ Service Load De s ign (Allowable Stress Design or Working Stress Design ) â€¢ Strength Design (Load Factor De s ign or Ultimate Strength Design ) The serv ice load de sig n method i an approach in which the structural members are designed so that the unit s tre sses do not exceed predefined allowable stresses. The allowable stress is defined by the material trength reduced by a factor of safety. In other word the total stress caused by the load effects must not exceed this allowable stress. This is further expressed in Equation 3.2. fac tual ::; fallowa bl e Equation 3.2 25
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Table 3.1AASHTO Group Loading Coefficients and Load Factors Col No . 1 2 3 3A 4 5 6 7 8 9 10 11 12 13 14 GROUP y D (l+I)N (L+I) p CF E B SF w WL LF R+S +T E Q ICE % I 1 . 0 1 1 0 1 J3E 1 1 0 0 0 0 0 0 100 lA 1.0 1 2 0 0 0 0 0 0 0 0 0 0 0 150 IB 1 .0 1 0 1 1 1 1 0 0 0 0 0 0 .. II 1.0 1 0 0 0 1 1 1 1 0 0 0 0 0 125 0 Ill 1 . 0 1 1 0 1 J3E 1 1 0.3 1 1 0 0 0 125 0 _J w IV (.) 1.0 1 1 0 1 J3E 1 1 0 0 0 1 0 0 125 > v 1.0 1 0 0 0 1 1 1 1 0 0 1 0 0 140 a: w VI 1 .0 1 1 0 1 J3E 1 1 0.3 1 1 1 0 0 140 (fJ VII 1.0 1 0 0 0 1 1 1 0 0 0 0 1 0 133 VIII 1.0 1 1 0 1 1 1 1 0 0 0 0 0 1 140 IX 1 . 0 1 0 0 0 1 1 1 1 0 0 0 0 1 150 X 1 . 0 1 1 0 0 J3E 0 0 0 0 0 0 0 0 100 I 1 . 3 J3o 1.6 7 0 1 J3E 1 1 0 0 0 0 0 0 l A 1 . 3 13o 2 . 20 0 0 0 0 0 0 0 0 0 0 0 IB 1.3 13o 0 1 1 J3E 1 1 0 0 0 0 0 0 z II 1.3 13o 0 0 0 1 1 1 0 0 0 0 0 w (!) _J U5 13o J3E co w Ill 1 . 3 1 0 1 1 1 .3 1 1 0 0 0 0 (.) a: IV 1 . 3 13o 1 0 1 J3E 1 1 0 0 0 1 0 0 :J 0 a_ a_ Iv 13o 0 0 0 J3E 1 1 0 0 1 0 0 (.) 1 . 25 1 ILL. VI 1 .25 13o 1 0 1 J3E 1 1 . 3 1 1 1 0 0 0 0 z 0 VII 1 . 3 0 0 0 1 1 0 0 0 0 1 0 _J VIII 1 . 3 13o 1 0 1 J3E 1 1 0 0 0 0 0 1 IX 1 . 2 0 0 0 1 1 1 0 0 0 0 1 X 1 . 3 1 1 . 6 7 0 0 J3E 0 0 0 0 0 0 0 0 26
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Table 3.2 AASHTO Earth Pressure and Dead Load Coefficients B Load Value Element BE Earth Pressure 1.0 Vertical and lateral loads on all other structures Lateral loads on rigid frames (check both loadings to BE Earth Pressure 1 . 0 and 0.5 see which one governs) Lateral earth pressure for retaining walls and rigid BE Earth Pressure 1 . 3 frames excluding rigid culverts Lateral earth pressure when checking positive BE Earth Pressure 0 . 5 moments in rigid frames BE Earth Pressure 1 . 0 Rigid culverts BE Earth Pressure 1 . 5 Flexible culverts Columns, when checking member for minimum axial Bo Dead Load 0.75 load and maximum moment or maximum eccentricity Columns, when checking member for maximum axial Bo Dead Load 1 . 0 load and minimum moment Bo Dead Load 1 . 0 Flexural and tension members Bridge substructures such as foundations and abutments have traditionally been designed using the Service Load Design methodology. Underground precast concrete box culverts and threeided structures are de sig ned by the load factor de sig n , thu s thi s thesis focuses so lel y on the load factor design methodology . In this methodology , the general relationship i s defined utilizing Equation 3.3. Equation 3.3 27
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Where: 'Yi = Load factors Qi = Force effects <1> = Re istance factors Rn = Nominal resistance RR = Factored resistance The nominal resistance of a member , Rn. i s calculated utilizing procedures given in the current AASHTO Specifications. A resistance factor, , is used to obtain the factored resistance RR. The appropriate resistance factors are determined for specific condition of design and construction process. Typical values for underground concrete structures are listed in Table 3.3 . The force effects, Qi. that should be considered when designing under ground concrete structures are live load, impact, live load surcharge pressures, self weight , and vertical and horizontal earth pressures. Loads considered important for other types of structures s uch as wi nd , temperature, and vehicle breaking are insignificant compared to the force effects previously mentioned for buried concrete structures. The following sections will examine these critical force effects when designing underground concrete structures, specifically reinforced precast concrete box culverts and threesided concrete structures, u s ing the Standard AASHTO Specifications. 28
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Table 3.3 AASHTO Resistance Factors for Underground Concrete Structures Structure Type Flexure Shear Radial Tension Load Factor Design of Precast 1.0 0.90 0 . 90 Reinforced Concrete Pipe , type 1 installations 0.90 0.82 0.82 Reinforced Concrete Arch , Cast InPlace 0.90 0.85 NA Reinforced Concrete Box Culverts , Cast InPlace 0 . 90 0 .85 NA Reinforced Concrete Box Culverts , Precast 1 . 0 0 . 90 NA Precast Reinf orced Concrete ThreeSided Structures 0.95 0.90 NA 3.2 AASHTO Standard Vehicular Design Live Loads The American Association of State and Highway Transportation O fficials, founded in 1914 as American Association of State Highway Official s, created a truck train configuration in 1935 ba sed on the railroads industry standar d s as show n in Figure 3.1. v... i l .:a...... . LOADIJG .... )f r;;;;;J>t.utt: I "0"tJ' Figure 3.1AASHO 1935 Truck Train Loading (Tonias, 1995). 29
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Historically, many structures, mainly bridges began to show evidence of over tressing in structural component as a result of increased truck traffic and heavier truck loading (Tonias 1995). This led to the introduction of five hypothetical trucks designated as H and HS class trucks in 1944. The design truck designations and gross vehicle weight are listed in Table 3.4. Table 3.4 AASHTO Standard HS Design Truck Classes Design Truck Gros s Weight Hl044 20,000 LB 9072 KG H15 44 30,000 LB 13,608 KG H2044 40 000 LB18,144 KG HS15 44 54,000 LB 24,494 KG HS20 44 80,000 LB 32,659 KG Currently all design truck classes are included in the AASHTO Standard Specifications with the exception of the Hl044. The policy of affixing the year to the loading to identify the design truck class was in tituted in the 1994 AASHTO edition. Figure 3.2 illu trates these de ign trucks and their associated geometries. 30
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14 FT , 14 FT 30 FT HS254410.000 lbs.40,000 lbs . 4 0.000 lbs. HS2044 8,000 lbs . 32,000 lbs. 3 2 ,000 lbs. H S 1 5 446,000 lbs. 24,000 lbs. 24,000 lbs . B 0 D u I r 14 FT . H20 448 . 0 00 lbs . 32.000 lbs. H15446,000 lbs. 24,000 lbs . Figure 3.2 Characteristics of the AASHTO Design Truck (AASHTO, 2002). 31
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The H15 and H20 truck loading i s repre se nted by a twoaxle s ingl e unit truck. The " S " in the HS 1544 and HS2044 de s i g nate s a emitrailer combination with an additional third axle. The Hl5 44 truck configuration has a gross weight o f 30,000 lb . with 6 , 000 lb . on its s teering axle and 24, 000 lbs. on its drive axle . Similarly , the HS 1544 weigh 56 , 000 lb. with an a dditional 24,000 lb. on it semi trailer axle. The H2044 ha s a gross weight of 40,000 lb. with 8,000 lb. on it s ste ering axle and 32,000 lb. on it s drive axle . A HS2044 truck weighs 72 , 000 lb. with an additional 32,000 lb. on its se mitrailer axle. Although not a provision in the current AASHTO Standard Specifications some s tates have began u s ing a HS2 5 de s ign truck with a gross vehicle weight of 90 , 000 lb., a s s hown in Figure 3 .2. Some s tates have developed additional live load configurations known as permit de s ign loadings in order to provide for future overweight trucks. The primary de sig n truck u se d in de sig ning underground st ructure s i s the HS2044 truck loading . Another form of live loading to repre se nt heav y military vehicles wa developed in 1956 by the Federal Highway Admini s tration ( Tonia s 1995 ) . Thi s loading configuration i s known as the Alternative Military Loading as s hown in Figure 3.3. Thi s loading consists of two axles weighing 24,000 lb . spaced 4ft. apart. A comparison of the force affects from both the de s ign truck and the alternative military loading configuration should be con s idered . The final design of the s tructure will depend on which loading configuration creates the large s t st re ss. 32
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Typically, the depth of overburden and the span of the member will govern the de ign vehicle configuration. This will be further illustrated in s ub sequent sectio n s including the de ign examples in Chapter 6 . O"c..__ __ ____, l12 KIPSI D irection oF Tro.vel 4' 0" Figure 3.3 Characteristics of Alternative Military Loading. The tire contact area for both the Alternative Military Loading and the HS Design Truck is assumed as a rectangle with the length in the direction of traffic equal to 10 in, and a width of 20 in. The width is double the length ba ed on the assumption of a dual tire as illustrated in Figure 3.4. For other design vehicles, s uch as customer spec ified live load s the Standard AASHTO Specification s allow the practicing engineer to determine the dimensions . The Standard AASHTO Specification s only allows the dimensions of the tire to be u sed when the earth fill 33
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depth i le ss than 2ft. To sim plify the design calculations it i s acceptable to neglect the contact area of the tire, and assume the tire act s as a point load . H S 20 10 " = L2o"_j Figure 3.4 Tire Contact Area For design purposes , procedures for applying and distributing the Alternative Military Loading and the HS design truck to a structure is dependent upon the depth of fill. Two case are examined , â€¢ When the earth fill depth is less than 2 ft. â€¢ When the earth fill depth is equal to or greater than 2 ft. In both cases, the Alternative Military Loading and the HS De ign Truck are examined as wheel line loads. 34
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3.3 Earth Fill and Vertical Earth Pressure Loading Initially when de sig nin g underground concrete structures the earth fill depth or depth of overburden on the structure mus t be determined . Th e earth fill depth dictat es load combinations, imp act, allowable s hear , concrete cover, live load surcharge, and particularly live load application. The earth fill is the backfill or fill placed on the top lab. Earth fill depth i s defined as the di s tance between the top of the top s lab to the top of earth fill or roadway s urface. Typical unit weights, "(5 , of earth fill are 110 pcf. 130 pcf, and are typically governed by the geotechnical report. The vertical earth pressure values from the earth fill can be calculated using Equation 3.4. The depth of fill and vertical earth pre ss ure are illu s trated in Figure 3.5. Where: WuSL = Y s * z WuSL =Consta nt vertical earth pre ss ure ( psf) Y s =Unit weight of soi l ( pcf) z =Earth Fill Depth (ft) 35 Equation 3.4
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. z /IJlJ'SL .. ys l z CPSP l U'Lllllll .. . . . . . Figure 3 . 5 Earth Fill Depth and Vertical Earth Pressure Loading Buried struct ure s are placed in three basic methods; trench excavation , embankment filling, and tunneling. Each method effects the soilstr uctur e interaction based on the earth fill depth , side compaction, and bedding characteristics (Sanford 2006). Therefore the effects of soilstructure interaction must be taken into account. The Standard AASHTO Specification requires that the vertical earth pressure va lue s from Equation 3.4 must be multiplied by a oiltructure interaction factor, F e , when designing reinforced concrete box culverts. The soiltructure interaction factor depend the on type of installation. For embankment installations , F e is calculated u ing Equation 3 . 5, for trench installations u se equation 3.6. The Standard AASHTO Specifications do not require the soil structure interaction factor to be applied to threesided concrete tructures. It is important to note that the soiltructure interaction factor for reinforced concrete pipe differs from Equations 3.5 3.6. The soi lstructure interaction factor for reinforced concrete pipe is beyond the sco p e of this the sis and is not discussed. 36
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Where: Where: H F e ! = 1 + 0.20B c Equation 3.5 F e1 = Soilstructure interaction for embankment in tallations :::; 1.15 for installation with compacted fill at the side :::; 1.4 for installations with uncompacted fill at the s ide s H = Earth fill depth , ft. B e = Outtoout horizontal span of pipe or box, ft. Equation 3.6 F e2 = Soiltructure interaction for trench installations H = Earth fill depth, ft. B e = Out toout horizontal span of pipe or box, ft. C d =Load coefficient for trench installations , Figure 3.6. 37
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3.4 Distribution of Live Loads for Depths of Fill Greater Than 2 ft. When the depth of fill is equal to or greater than 2ft., the Standard AASHTO Specifications allows for the wheel load to be distributed over a square equal to 1.75 times the depth of fill. Figure 3.6 illustrates that the Standard AASHTO Specifications does not account for the dimension of the tire, instead the wheel load is considered as a concentrated point load. The distributed live load value , WuLL for a single wheel load is calculated u sing Equation 3 .7. When the dimension of the load area exceeds the design span, only the portion of the distributed load on the span is considered in the design. WuLL =Wheel Load I (1.75 *H) 2 Equation 3.7 Where: H = Earth Fill Depth (ft) 38
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IJHEEL LOAD Figure 3.6 LFD Wheel Load Distribution through Earth Fill Due to the increa ed depth of overburden , the areas from several concentrated wheel load s may overlap. The total load hould be di s tributed over the area defined by the outside limit of the individual areas a s shown in Figure 3 .7. 1Jt(l LOAD 1JHEL LOAD I H Figure 3.7Overlapping Wheel Load Distribution through Earth Fill 39
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As the earth fill depth increa es, distributed wheel load areas created by adjacent wheels or axles b egin to overlap. Thi s complicates the di s tributed live load area and load v alue calculation. There are 3 ca ses that are con s idered: 3.4.1 Case 1 Distribution of Wheel Loads that do not Overlap Ca se 1 occurs when the distribution of wheel loads do not overlap. The distributed live loads are calculated using Table 3.5. The depth of overburden , H, in the table i s the maximum earth fill depth allowed. Both the parallel and perpendicular load dis tribution width s for a ingle de s ign vehicle are shown in Figure 3.8. Table 3 5Case 1 H Spread, S WuLL Design Vehicle ( ft ) Wheel L o ad (lb) (ft2 ) (lblft2 ) HS20 Truck H < 3.4 3 16, 000 ( 1.75 * H ) 2 1 6 , 000 I ( 1 . 75 * H ) 2 HS25 Truck H < 3 . 43 20,000 (1.75 * H ) 2 20.000 I (1. 75 * H) 2 Alternative Military L oad H < 2 . 29 12, 000 ( 1 . 75 * H ) 2 12, 000 I (1. 75 * H) 2 Figure 3.8 Case 1 , Wheel Load Distribution through Earth Fill 40
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3.4.2 Case 2 Distribution of Wheel Load s from a Single Axle Overlap. Case 2 occurs when both wheels from a sing le axle overlap for the HS Truck config u ration. The wheel from separate ax l es overlap for the Alternative Military truck configuration. Thi s is due to an axle s pacing of 4 ft. compared to the wheel spa cing of 6ft. The distrib ut ed live loads are calculated u sing Tab l e 3 .6 . B oth the Alternative Military Truck and HS Desig n Truck configuration are illustrated in F i gure 3.9. Tabl e 3 6 Case 2 H Wbee!Load Spread, S WuLL Design Vehicle (ft) Ob) (ft2 ) (lblft2 ) HS20 Truck 3.43 < H > 8.00 16 , 000 S = ( 1.75 * H)* (1.75 * H + 6) 32 000 IS HS25 Truck 3.43 < H > 8.00 20.000 S = ( 1.7 5 * H ) * ( 1.75 * H + 6) 40 , 0001 s Alternative Military Load 2.29 < H > 3.43 12, 000 S = ( 1.75 * H)* (1.75 * H +4) 24 , 000 IS H S DESIGN TRUCK l N G DIRECTior.1 OF"" TRAFFIC Figure 3.9 Case 2, Overlapping Wheel Load Distribution through Earth Fill 41
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3.4.3 Case 3 Full Distribution of Wheel Loads from Multiple Axles. When the wheel loads from all axles overlap, the di stri buted live load is calculated u s ing Table 3.7 . Full di s tribution occurs for the HS Des ign Truck at an earth fill depth of 8 feet a s hown in Figure 3 . 10. The live load may be ne g lected as s tated in the Standard AASHTO Specification s when the earth fill depth i s greater than 8 feet, and exceeds the effective s pan length. For multiple s pans , it ma y be neglected when the depth of overburden exceeds the dis tance between faces of end s upport s or ab utm ents. A a re s ult, Case 3 will typically govern for the Alte rna tive Military Load based on f ull di s tribution at a fill depth of approximately 3.43 ft. Table 3 7Case 3 H Whe e l Load Spread , S WuLL Desian Vehicle ( ft ) (I b ) (f t2 ) (lblf t2 ) HS20Truck 8.00 < H 16, 000 S = (1.75 * H + 14) * ( 1.75 * H + 6) 64,000 IS HS25 Truck 8.00 < H 20,000 S = (1.75 * H + 14) * ( 1.75 * H + 6) 64, 000 IS Alternative Military Load 3.43 < H 12, 000 S = (1.75 * H + 4 ) * ( 1.75 * H + 6 ) 48,000 IS 42
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H S DESIGI< TRUCK ALTERNATIV E MILITARY â€¢ VH((L DlRCTWN O i l R AfnC .. Figure 3.10Case 3 , Overlapping Wheel and Axle Load Distribution Through Earth Fill As detailed in Section 3.2, a comparison of force effects from both the HS2044 Design Truck and the Alternative Military Loading configuration s hould be made . The loading config ur ation that creates the largest stress s hould then be selecte d in the design. Both the earth fill depth and the s pan of the member must be considered in the design. Wheel load pre ss ur e versus depth of fill is plotted in Figure 3.11 for both the HS2044 Design Truck and Alternative Military Loading. The HS2044 Truck Loading produce s higher wheel load pressures for s hallow depth s between 2 ft. 4.5 43
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ft., while the Alternative Military Loading produce s larger wheel load pre ss ur es for depth s between 5 ft 15 ft. For earth fill depth s greate r than 15 ft , the HS204 4 Truck Loading produce s higher wheel lo a d pressures . HS20 Design Truck vs . Alternative Military Loading Through Earth Fill 1400 . 00 1 1200 . 00 1000 . 00 ;;::800 . 00 Ul !!:. ....J ....J \ Mi6ta " 600.00 400 . 00 200 . 00 \ "' 0 . 00 0 . 00 2 . 00 4 . 00 6 . 00 6 . 00 10 . 00 12 . 00 14. 00 16.00 16 . 00 20 . 00 Depth Of Fill (It) Figure 3.11 LFD Live Load Pressures through Earth Fill The de s ign vehicle that produces the greatest live load pre ss ure with regard s to earth fill depth will not nece ssari ly control the design. The critical live load pre ss ure u se d will depend not only on the earth fill depth but the member s pan. Thi s is attributed to the area in which the load i s s pread. For example, for a depth of f ill of 3.0 ft an HS20 truck produce s a se rvice live load pres s ure of 0.581 k sf. An Alternative Military ve hicle produces a s ervice live load pre ss ure of 0.494 ksf. 44
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However the Alternative Military vehicle ha s a larger load spread as illustrated in Figure 3.12 , which may induce larger ervice moments for various spans . HS20 Design Truck Alternative Militar y Truck WsLL... 14'0" Axle spacing Figure 3.12 LFD Live Load Spread for 3 ft Overburden 3'0" In Figure 3.13 the service moment produced by the HS 2044 , HS 2544, and the Alternative Military live loads for an earth fill depth of 3 ft are plotted versus design spans . The corresponding service pressure val u es and load l engths are illustrated in Table 3.8. Although the HS2544 Design Truck produces higher load pressures than the Alternative Military Loading, the Alternative Military loading produces a higher service moment for spans in excess of 15 feet. 45
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Depth of Fill = 3.00 FT 25 . 00...., HS20 .MIUTARY HS25 II) ::!: 10 . 00 0 . 00 +,..,,..........l 3 . 00 6 . 00 9 . 00 12 .00 15.00 18. 00 21.00 24 . 00 Design Span (FT) Figure 3.13 LFD Live Load Service Moments vs. Increasing Design Spans Table 3.8 Moments from HS20, HS25, and Alternative Military Loads Live Load Model W s LL (klf) Load Length (ft) HS20 . 581 5.25 HS25 . 725 5.25 Alternative Military .494 9.25 46
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3.5 Distribution of Live Loads for Depths of Fill Less Than 2 ft. For depths of overburden less than 2ft the Standard AASHTO Specifications simplify the design procedures by providing a single equation for distributing the live load to the top slabs of buried concrete structur es. The live load is divided into equivalent strip widths, which is the effective width of slab that resists the applied load. The live load i modeled as a concentrated wheel load distributed over a distribution width, E. The distribution width is calculated using Equation 3.8. Where: E = 4 + . 06 * S <7ft. For H <2ft. Equatio n 3.8 E = Width of slab over which a wheel load is distributed (ft) S =Effective span length (ft) H = Cover depth from top of struct ure to top of Pa vement (ft) Concrete labs are analyzed as a bean1 with the equivalent concentrated live load divided by the distribution width, E, see Figure 3.14. The distribution width applies to all de sign spans for both positive and negative bending , and shear force effects. 47
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Figure 3.14 LFD Distribution Width, E for a Single Wheel Load The Standard AASHTO Specification s does not allow any load transfer between adjacent structure . The distribution widths must be limited to the unit width of the structure. Fig ure 3.15 illustrates two cases. The di tribution width exceed the width of the member in Case 1. The effective distribution width will be limited to the member width of the st ructure . In Case 2 the distrib ution width is les s than the unit width of the member. Therefore de sig n calculations consider the full di stri bution width. Cose 1 i i i I LMember Width_j Figure 3.15 Effective Distribution Widths on Slabs 48
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The tire i s a s sumed to act in the center of the member , a s hown in Figure 3.15. One provi s ion that i unclear in the Sta ndard AASHTO Specification i s when the tire i s pl a ced at the edge of a member a s illu s trated in Figure 3.16 , Cas e 3 . Case 3 i not addr e s ed in the current Standard AASHTO Specification s ; however it i s a common practice to as s ume a r e duced di s tribution width. Thi s new di s tribution width i s calculated using Equation 3.9. E r = ( 4 + . 06 * S ) I 2 + W T I 2 Equation 3 . 9 Where: E r = reduced di tribution width (ft) S =effective s pan len g th (ft ) W T = width of tire contact area parallel to s pan , a s s pecified in Case 3 Effectiv9 istributio Width s ection 3. 2 ( ft ) . .. . ...... ! Joint ! i ' LMember WidthLMember Widlh___j_Memebr Width_j Figure 3.16 Reduced Distribution Widths on Slabs 49 Top S lab
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3 .6 Impa ct Factor (IM) To account for the dynamic load affects of moving vehicles, the AASHTO Standard Specifications applies an impact factor to the live load for varying burial depths . The impact factor is applied to both the Design Truck and Alternative Military Load as a multiplier. The Impact factor varies with the depth of overburden as shown in Table 3.9. Tab l e 3.9 Impact Fact or Overburden Impact 0'0"1 ' 0 " 30 % 1 ' 1" 2' 0 " 20% 2'1"2'11" 10% >2'11" 0 % The dynamic force effects applied to the live load as a result of moving vehicles can be attributed to the hammering effect of the wheel assembly riding on surface discontinuitie such as deck joints , cracks, potholes, and undulations in the roadway pavement caused by settlement of fill (AASHTO 2005). The decrease in impact with the depth of overburden is due to the damping effect of soil when the wheel is in contact with the ground. 50
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3.7 Lateral Live Load Surcharge The Standard AASHTO Specifications require a lateral live load surcharge pressure be applied when highway traffic comes within a horizontal distance from the top of the structure equal to onehalf its height. Additional lateral earth pressure is produced on soil retaining walls as a result of surcharge loads. The Standard AASHTO Specifications require that the live load surcharge pre sure be equal to or greater than 2 ft. of additional earth cover, applied to the exterior walls. There are two methods to apply the lateral live load surcharge pressure. Both methods yield the same results. The first is by assuming an equivalent height of additional earth cover on the outside walls, typically 2ft., as shown in Figure 3.17. The second is by designating the live load surcharge pressure as a separate load as shown in Figure 3.18. The econd method is preferred due to the ease of computer programming. The magnitude of the lateral live load surcharge is determined using Equation 3.10: Where: LLS = k * Y s * H e q Equation 3.10 LLS =Constant horizontal earth pressure due to live load surcharge (psf) k = coefficient of lateral earth pressure Y s = unit weight of soil (pcf) Heq =equivalent height of soil , typically 2 ft. 51
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q ORIZDNTAL EARTH PRESSURE + LIVE LOAD SURCHARGE Figure 3.17 LFD Equivalent Height DRIZDNTAL EARTH PRESSURE .. IVE LOAD SURCHARGE Figure 3.18Live Load Surcharge Pressure 52
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Chapter 4 AASHTO LRFD Bridge Design Specifications 4.1 Load Factors and Load Combinations In LRFD, the design framework consists of atisfying what are called limit tates. All limit states s hall atisfy Equation 4.1. Equation 4.1 Where : lli = Load modifier Yi = Load factors Q i = Force effect <1> = Resistance factors R n = Nominal re istance R r = Factored resistance Selection of the load factors to be used i s a function of the type of load and limit tate being evaluated. To obtain an understanding of this concept, it is helpful to refer to the actual definition of "limit state" contained in the LRFD Specifications. A Limit State i a condition beyond which the bridge or component ceases to satisfy the provisions for which it was designed. There are four limit s tate s prescribed by the 53
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LRFD Specification s (AASHTO 2005). Each of the four limit s tate s are de scr ibed below: â€¢ STRENGTH Require s the s trength and s tability be adequate for s p ec ified load combinations. â€¢ EXTREME EVENT Relate s to e ve nt s with extremely long periods of return (earthquakes, ice load s, vehicle colli s ion , and vessel collision) . â€¢ SERVICERelate s to s tres ses, deformations , and cracking. â€¢ FA TIGUE Pl aces restric tion s on s tre ss ranges in reinforcement from application of a s ingle de s ign truck under service load conditions. When de s igning underground concrete s tructures, the LRFD Specification s require that all applicable limit states be evaluated. The load for each limit state should be modified by the appropriate load factor, y , and the factored load s for each limit state combined in a pr esc ribed manner. The limit s tates, load factors and load combination s from the AASHTO LRFD Specification s are list ed in Table 4 . 1 and Table 4.2. Ba ed on applicable load combination s the limit s tate s are further s ubdivided a s follows (AASHTO 2005): â€¢ STRENGTH IBa sic load combination related to normal vehicular u se of the bridge without wind. 54
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â€¢ STRENGTH IILoad combination relating to the use of the bridge by owner pecified special design vehicles and/or evaluation permit vehicle without wind. â€¢ STRENGTH IIILoad combination relating to the bridge expo ed to wind velocity exceeding 55 mph without live load. â€¢ STRENGTH IV Load combinations relating to very high dead load to live load force effect ratio . â€¢ STRENGTH V Load combinations relating to normal vehicular use of the bridge with wind velocity of 55 mph . â€¢ EXTREME EVENT ILoad combinations including earthquake and flood. â€¢ EXTREME EVENT IILoad combination relating to ice load or collision by vessels and vehicles. â€¢ SERVICE ILoad combination relating to the normal operational use of the bridge with 55 mph winds and all the loads taken at their nominal values. â€¢ SERVICE IILoad combinations intended to control yielding of steel structures and slipcritical connections due to vehicular live load. 55
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â€¢ SERVICE IIILoad combination for longitudinal analysis relating to tension in prestressed concrete s uperstructures. â€¢ SERVICE IVLoad combinations relating only to tension in prestressed concrete substructures with the objective of crack control. â€¢ FA TIGUE Fatigue and fracture load combinations relating to the repetitive gravitational vehicular live load and dynamic respon ses under a single design truck . A majority of the load s and loading combinations specified in the Standard AASHTO Specification s are eliminated for buried s tructures. Buried structures are s heltered by earth cover which reduce s much of the concern. Buried structure need to be designed to resist the force effects res ulting from horizontal and vertical earth pressures, pavement load, vehicular live load and impact, and urcharge lo a ds. Wind , temperature, vehicle breaking , and centrifugal force typically have Little effect due to earth protection. 56
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Table 4.1Load Combination and Load Factors Load C omb i nation DC LL TU Us e on e of These at a Time DD IM CR DW CE SH EH BR EV PL ES L S EL EQ IC CT cv Limit S tat e WA WS WL FR TG SE ::iiHt:N\:ilH1 (un l ess not e d ) Y p 1 .75 1 . 00 1 . 00 0 . 50 / 1 .2 0 Y ra Y s E STRENGTHII Y p 1 . 35 1.00 1.00 0 . 50 / 1 .20 Y ra YsE STRENGTHIll Y p 1 . 00 1 .40 1 . 00 0 . 50 / 1 . 20 YTG YsE STRENGTH IV Y p E H , EV , ES , DW DC ONL Y 1 . 50 1 . 00 1 . 00 0 . 50 / 1 . 20 STRENGTHV Y p 1 .35 1 .00 0 .40 1 .00 1 . 00 0 . 50 / 1 .20 Yra YsE EXTREME EVENTI Y p Y o q 1 . 00 1 . 00 1 . 00 EXTREME EV ENTII Y p 0 . 50 1 . 00 1 . 00 1 . 00 1 . 00 1.00 SERVICEI 1.00 1.00 1 . 00 0.30 1.00 1 . 00 1.00/ 1 .20 Yra YsE SERVICEII 1 . 00 1.30 1 . 00 1 . 00 1.00 / 1 .20 S ERVICE Ill 1 . 00 0 . 80 1 . 00 1 . 00 1 . 00/ 1 .20 YTG YsE SERVICEIV 1.00 1 . 00 0 . 7 1 . 00 1 . 00/ 1 .20 1 FATIGUELL,IM & C E ONLY 0.75 The service limit state required by the AASHTO LRFD Specification s for buried structures is Servi ce Load Combination I. The required Strength Limit State required is Strength Load Combinations I and II. The Extreme l imit states do not govern unle ss the st ructure crosses an active fault. Load factors for permanent loads labeled as yp in Table 4.1, are presented in Table 4.2 as maximum and minimum val ues. Criteria for their application require that: 57
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â€¢ For each combination, load factors s hould be selecte d to produce the total extreme factored force effect. Both maximum and minimum extremes sho uld be investigated. â€¢ Maximum and minimum load factors are utilized for load combinations where one force effect decreases the effect of another force. The minimum value shall be applied to the load that reduces the force effect. â€¢ The load factor which produces the more critical combination for permanent force effects should be se lected from Table 4.2. â€¢ If a permanent load increases the stability or load carrying capacity of a structure component , the minimum value for that permanent load sho uld also be investigated. 58
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Table 4.2 Load Factors for permanent Loads, 'YP Load Factor Type of Load Maximum Minimum DC: Component and Attachments 1.25 0.90 DD: Downdrag 1.80 0 .45 DW : Weari ng Surfaces and Utilities 1.50 0.65 EH : Horizontal Earth Pressure Active 1.50 0 .90 AtRest 1.35 0.90 EL: Locked in Erection Stresses 1 . 0 1 . 0 EV: Verticle Earth Pressure ' ' Overall Stability 1.00 N/A Retaining Wails and Abutments 1.35 1.0 Rigid Buried Sturcture 1.30 0.90 Rigid Frames 1.35 0.90 Flexible Buried Structures other than 1.95 0 .90 Metal Box Culverts ' ' Flexible Metal Box Culverts 1.50 0 .90 ES: Earth Surcharge 1.50 1.50 4.2 Load Modifiers In the LRFD Speci ficat ion , each factored load is adjusted by a load modifier, lli The load modifiers account for combined effects of redundancy, llR. ductility, llo , and operational importance, lli Load s in which a maximum load factor is appropriate, the load modifier can be calculated using Equation 4.2. For minimum val u e load factors the load modifier can be calculated u sing Equations 4.3. 59
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Equation 4 . 2 1 111 =2:: 1.05 11o *11R *111 Equation 4.3 Where: Tli = Load modifier T)o = f actor for ductility TlR = factor for redundancy 111 =factor for importance The value s for the ductility, redundancy, and importance factor are listed below: â€¢ Ductility, T)o 1.05 for nonductile components and connection s = 1.00 for conventional designs and details 0.95 for components and connection s for which additional ductility enhancing measures are required For all other limit states: T)o = 1.00 â€¢ Redundancy , TlR 60
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2: 1.05 for nonredundant component s and connection s = 1.00 for conventional le v el s of redundanc y 2: 0.95 for exceptional levels of redundancy For all other limit states : llR = 1.00 â€¢ Importance , llr 2: 1.05 for important s tructure s = 1.00 for typical structure s 2: 0.95 for relatively le ss important s tructure s For all other limit states: llr = 1.00 When designing at the Service Limit State , ll o = llR = 111 = 1.00 Typically the ductility of buried s tructure s i s 1.00. Buried structure s are considered nonredundant under earth fill , and redundant under live load and dynamic load allowance. The importance i s determined on an evaluation of nece s sity for continued function and s afety. 61
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4.3 AASHTO Standard Vehicular Design Live loads The AASHTO LRFD Specifications require an HL93 live load. This load includes two types of vehicular deign loads. The HL93 Design live loads consist of a combination of the â€¢ Design Truck or Design Tandem â€¢ Design Lane Load The Design Truck used in the AASHTO LRFD Specifications has the same configuration as the HS20 Design Truck in the Standard Specifications discussed in Chapter 3. The design truck weights and spacing of axles and wheels are s p e cified in Figure 4.1. H$20 8 ,000 lbs. HS20 ,Q11 't:::;:=J Figure 4.1Characteristics of the Design Truck (AAS HTO, 2005) 62
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The LRFD Specifications utilize the Design Tandem load configuration consisting of a pair of 25.0 kip axles spaced 4.0 ft apart. The transverse spacing of whee l s is taken as 6.0 feet as shown in Figure 4.2. Direction of Traffic 0" 112.5 KIPS 11l 12. 5 KIPS I Figure 4.2Characteristics of the Design Tandem The loads from both the Design Truck and the Design Tandem are assumed to be distributed transversely within a 10.0 ft. design lane. A rectangular tire contact area shown in Figure 4.1 , consisting of a 2 0.0 in . width and a 10.0 in length, is used in the design. A dynamic load allowance defined in a later section is applied to both the 63
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Design Truck and Design Tandem. Both the Design Truck and Design Tandem loading configuration are u ed in conjunction with the Design Lane Load to determine the worst case force effects on the structure. This will primarily depend on the depth of overburden and/or the span of the structure. The De sign Lane Load consists of a load of 0.64 klf, uniformly di s tributed in the longitudinal direction . Tran s versely , the De s ign Lane Load i as umed to be uniformly distributed over a 10.0 ft. de sign lane width . This lane load converts to an additional live load of .064 ksf, applied to the top of the tructure for any depth of burial les s than 8 ft. The force effects from the De sign Lane Load are not subject to a dynamic load allowance . 4.4 Earth Fill and Vertical Earth Pressure Loading Similar to the Standard AASHTO Specifications , when de s igning underground concrete structures the earth fill depth or depth of overburden on the structure must be determined. The earth fill depth dictates load combinations, impact, allowable shear, concrete cover, live load surcharge, and particularly live load application . The earth fill is the backfill or fill placed on the top slab. Earth fill depth is defined as the distance between the top of the top slab to the top of earth fill or roadway surface. Typical unit weights , "(5 , of earth fill are 110 pcf.130 pcf , and are generally governed by the geotechnical report. The vertical earth pressure values from the earth 64
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fill are calculated u sing Equation 4.4. Figure 4.3 demonstrate s depth of fill a nd the vertical earth pressure applied to the top s lab. Therefore the effects of soilst ructure interaction must be taken into account. The LRFD Specification require s that the vertical earth pressure values from Equation 4.4 must be multiplied by a soilstr ucture interaction factor, F e , when de signi n g reinforced co ncrete box culverts. This is simi lar to the AASHTO Standard Specification s s pecified in Section 3.3. WuSL=Ys * z Equation 4.4 Where: WuS L =Constant vertical earth pressure (pcf) Y s = Unit weight of s oil (pcf) z =Earth Fill Depth (ft) De>p"th Of FlU z \1 s _[_ u L = ys " z
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4.5 Multiple Presence Factors The LRFD Specifications require the u se of multiple presence factors, Table 4.3, to account for the effects of multiple lane on a bridge. Multiple presence factor are based on the number of loaded lane . The table provide factor for the cases of one lane , two lanes , three lanes, and three or more loaded lanes. For underground concrete structures, there are three cases that must be examined. 4.5.1 Case 1 Depth of fill is equal to or greater than 2 ft. Case 1 occurs for depth s of fill equal to or greater than 2ft. The Standard LRFD Specification s require two checks. â€¢ A check to determine the force effects from multiple truck axles po s itioned 4ft side by side with a multiple pre se nce factor of 1 . 00. â€¢ A check to determine the force effects from a single design vehicle with a multiple presence factor of 1.20. The loading combination with the worst case force effects on the structure will control the design. Thi s will typically depend on the overburden depth and/or the span of the struct ure. This i s further discussed in Section 4 .6. 66
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4.5.2 Case 2 Depth of fill is less than 2 ft, and direction of traffic is parallel to span. When the traffic travels parallel to the design span, the struct ure i s analyze d using a single loaded lane. The Standard LRFD Specifications distribute a s ingle loaded lane into strip widths. This strip width is the effective widt h of the s lab that resists the applied load. Therefore, the multiple presence factor is 1.20 4.5.3 Case 3 Depth of fill is less than 2 ft , and direction of traffic is perpendicular to span. When the depth of fill is less than 2 ft and the direction of traffic is perpendicular to the span, the appropriate multiple presence factors must be chosen from Table 4.3 . The number of loaded lanes i a function of span length. Table 4.3 Multiple Presence Factors Number of Loaded Multiple Pre sence Lanes Factors "m" 1 1.2 2 1.00 3 0.85 >3 0 . 65 67
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4.6 Distribution of Live Loads for Depths of Fill Greater Than 2 ft. When the depth of overburden is equal to or greater than 2 ft , the Standard LRFD Specifications allows for the wheel load to be distributed throughout the earth fill. The Standard LRFD Specification s use an approach s imilar to the 2:1 method. The 2: 1 method is an empirical approach that assumes the total applied load on the s urface of soil is di stributed over an area of the s ame shape as the loaded area on the surface . The dimension of the loaded area are increased by the amount eq ual to the depth below the surface. The AASHTO LRFD method is a variation of thi method . The distribution area is equal to the tire footprint , with the footprint dimension s increased by either 1.15 times the earth fill depth for e lect granular backfill , or 1.0 for other type s of backfill, s hown in Figure 4.4 . The distributed live load val u e, WuLL for a single wheel load can be calculated using Equation 4.5. Where: WuLL =Wheel Load I (LL DF * H + Wr) * ( LLDF * H + Lr) Equation 4.5 WuLL =Uniform Distributed Live Load (p f) H = Earth fill depth (ft) Wr =Tire Width (in) Lr = Tire Length (in) 68
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LLDF =factor for di tributing the live load through earth fill 1.15 for elect granular backfill 1.00 for all other backfill DISTRIBUTED LOAD AREA Figure 4.4LRFD Wheel Load Distribution through Earth Fill 69
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As noted with the Standard AASHTO Speci fica tion, the distributed live load area and load value calculations are complicated as a result of distributed area overlap as the earth fill depth is increased (United States FHA 2001). The overlapping is the result of adjacent wheels and axles, and varying live load design vehicles. The total load should be distributed over the area defined by the outside limits of the individual areas illustrated in Figure 4.5. DISTRIBUTED LOAD AREA Figure 4.5 Overlapping Wheel Load Distribution through Earth Fill Unlike the Standard AASHTO Specifications there are 5 cases which must be examined: 70
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4.6.1 Case 1 Distribution of Wheel Loads that do not Overlap Case 1 occurs when no wheel load overlap . The distributed live loads are calculated using Table 4.4. In this case, the depth of overburden , H i s the maximum allowable earth fill depth . B oth the parallel and perpendicular load di t ribu tion widths for a sing l e design vehicl e are shown in Figure 4.6 Table 4.4Case 1 Sleet Granular F ill. Wh ee l Load Spr e ad B Spread A WuLL Design Vehicle H ( ft) (lbs) (ft ) (ft ) (psf) HS20 Truck H < 3.77 16, 000 (1.15 * H + 0.83 ) (1.15 * H + 1.67) 16,000 I (A* B ) HS25 Truck H < 3. 77 20,000 ( 1.15 * H + 0.83 ) (1.15 * H + 1.67 ) 20,000 I ( A * B ) Tandem H < 2.7 5 12, 500 (1.15 * H + 0.83 ) (1.15 * H + 1.67) 12 , 500 I ( A * B ) O t her F1ll Whe e l Load Spread B Spread A WuLL De s ign V e hicl e H (ft) (lbs ) (ft) (ft) ( p sf) HS2 0 Truck H < 4.33 16.000 ( 1.00 * H + 0 .83) ( 1.00 * H + 1.67 ) 16 , 000 I (A* B ) HS25 Truck H < 4.33 20,000 ( 1.00 * H + 0 .8 3) ( 1.00 * H + 1.67 ) 20 , 000 I (A* B ) Tandem H <3.17 12,500 ( 1.00 * H + 0.83) ( 1.00 * H + 1.67) 12 , 500 I (A * B ) 'WH EEL LOAD "'HEEL LOAD ISPREAD A1 'WHEEL LOAD \o'HEEL LOAD 1AXL SPACINGI ISPREAD B1 ISPREAD BJ Figure 4.6 Wheel Load Distribution through Earth Fill 71
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4.6.2 Case 2 Distribution of Wheel Loads from a Single Axle Overlap. C ase 2 occ urs w h e n b oth w h ee l s fro m a si n g l e ax l e overlap. Th e di s t r ibu te d li ve l oa d s are calculate d u s in g T a bl e 4. 5 . It i s i mp ortan t to n o t e t h a t a s in g l e w h ee l l oa d f rom se p arate ax l es overla p in th e T a nd e m L oa din g . Thi s i s a r es ult o f t h e 4 ft. ax l e s pacing, co mp a red t o the 6 ft. w h ee l s pacin g Fi g ur e 4. 7 . T ab l e 4.5Case 2 Sle e t Granu l a r Fill Whe e l Load Spr ead A W u LL Design Veh i cle H ( ft ) (I b) Spread B (ft) ( ft ) ( psf) HS20 Truck 3. 77 < H < 11.44 16.000 (1.15 * H + 0 .83 + 6 ) ( 1.15 * H + 1.67 + 6 ) 32,000 I ( A * B ) HS2 5 Truck 3 .77 < H < 11.44 2 0.000 ( 1.15 * H + 0 . 8 3 + 6 ) (l.l5 * H + 1.67 + 6 ) 40.000 I ( A * B ) Tandem 2.75 < H < 3 . 77 12,500 ( 1.15 * H + 1.67 + 6 ) ( 1.15 * H + 0 . 8 3 + 4 ) 25.000 I ( A * B ) O th e r Fill W heel Load Sp r ead A WuLL Design Vehicle H ( ft ) ( l b ) Sp r ead B (fl) ( ft ) ( psf) HS20Truck 3 .77 < H < 11.44 16,000 ( 1.00 * H + 0.83 + 6 ) ( 1.00 * H + 1.6 7 + 6 ) 32 , 000 I ( A * B ) HS25 Truck 3.77 < H < 11.44 20 , 000 ( 1.00 * H + 0 .83 + 6 ) ( 1.00 * H + 1.67 + 6 ) 40. 000 I ( A * B ) Tandem 3 .17 < H < 4.33 12.500 ( 1.00 * H + 1.67 + 6 ) (1.00 * H + 0 . 8 3 + 4 ) 25 . 000 I ( A * B ) Figure 4.7Overlapping Wheel Load Distribution through Earth Fill 7 2
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4.6.3 Case 3 Full Distribution of Wheel Loads from Multiple Axles Overlap. In thi case the wheel load s from all axles overlap resulting in full distribution. The distributed live load are calculated u s ing Table 4 .6. For the HS De sig n Truck , full distribution occurs at an earth fill depth of 11.44 ft a s shown in Figure 4.8. The AASHTO LRFD Specification s does allow for the live load to be neglected when the earth fill depth i s greater than 8ft. and exceeds the effective span length . The live load for multiple spans i s neglected when the depth of overburden exceed s the distance between the outer face of the end suppmts or ab utment s . Due to thi s provi s ion, Case 3 typically governs when the Alternative Military Load i s examined. The Alternative Military load is based on full distribution at a fill depth of 3.77 ft. Table 4.6Case 3 Select Granular Backfill Wh ee l Load Spread A WuLL Des ign Vehicle H ( ft) ( I b ) Spread B ( ft) (ft ) ( p sf) HS20Truck H > 11.44 16,000 (l.l5 * H + 0 .83 + 6 ) (1.15 * H + 1.67 +6) 64,000 I ( A * B ) HS25 Truck H > 11.45 20000 ( 1.15 * H + 0.83 + 6) ( 1.15 * H + 1.67 + 6) 80.000 I ( A * B ) Tandem H > 3.77 12, 500 ( 1.15 * H + l.67 + 6) (1.15*H+0.83+4) 50 , 000 I (A * B ) O ther F1ll Wheel Load Spread A WuLL Des i g n Vehicle H (ft ) (I b) Spread B (ft) (ft ) ( psf) HS20 Tru ck H > 11.44 16, 000 ( 1.00 * H + 0.83 + 6) ( 1.00 * H + 1.67 + 6) 64,000 I ( A * B ) HS25 Truck H> 11.45 20,000 ( 1.00 * H + 0.83 + 6) (1.00 * H + 1.67 + 6) 80 , 000 I (A * B ) Tandem H > 3.77 12, 500 (1. 00 * H + 1.67 + 6) ( 1.00 * H + 0 .83 + 4) 50,000 I (A * B ) 73
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Figure 4.8 Overlapping Wheel and Axle Load Distribution through Earth Fill 4.6.4 Case 4 Distribution of Wheel Loads from Passing Vehicles Cases 1 3 are for a single design vehicle . For Cases 4 5, the Standard LRFD Specifications require a check to determine if the distributed live load area from multiple truck axles positioned side by s ide overlap. Ca se 4 is when two wheels from separate ax le s overlap illustrated in Figure 4.9. The total load from the two wheels is distributed over the area illustrated. Ca s e 5 occurs when both axles from each de s ign truck overlap. The total load from both axle s is dis tributed within the boundaries of the two axles shown in Figure 4.10 . 74
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o'"if'READ A' Figure 4.9Overlapping Wheel Load Distribution by Passing Vehicles Figure 4.10Overlapping Axle Load Distribution by Passing Vehicles 75
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4.7 Distribution of Live Loads for Depths of Fill Less Than 2ft. For depths of overburden less than 2ft, the Standard LRFD Specifications and the Standard AASHTO Specification are simi lar with respect to the design procedures. The Standard LRFD Specifications distribute the live load into equiva len t strip widths. The equivalent strip width is the effective width of the lab that resists the applied load. Equivalent trip widths are used to simplify the analysis of the three dimensional response to live loads. There are two cases that apply: â€¢ Case 1 When the traffic travels parallel to the design span . â€¢ Case 2 When the traffic travels perpendicular to the design span. This thesis focuse on Case 1 . When the traffic travels parallel to the desi g n span, the structure is analyzed u sing a single loaded lane with the appropriate multiple presence factors specified in Section 4.5. The axle of the design ve hicle is distributed over a distribution width E. This distribution width is perpendicular to the design span. Equation 4 . 6 is used to calculate the distribution width , E Where: E = 8 + 1.2 * S for H <2ft. Equation 4.6 E = width of slab over which an axle load is di s tributed (ft) S =effective span length (ft) H = cover depth from top of st ructure to top of P aveme nt (ft) 76
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The Standard LRFD Specifications also take into account the length of the load due to the tire contact area and the parallel distribution length of the tire through earth fill, Figure 4.11. The load length, E p a n is determined using Equation 4 . 7 . Where: E span= LT + LLDF * (H) Equation 4.7 E s pan= equivalent distribution length parallel to span , load length (ft) LT = length of tire contact area parallel to span, specified in section 4.6 (ft) LLDF = factor for distributing factor through earth fill , specified in Section 4.6 H = earth fill depth from top of structure to top of Pavement (ft ) The concrete slabs are analyzed as a 1.00 ft wide beam with an equivalent axle load divided by the distribution width, E, and a load length E pan shown in Figure 4.11. The distribution width is applied to all design spans for both positive and negative bending, and shear force effects. 77
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4.8 Dynamic Load Allowance, Impact (IM) To account for the dynamic load affects of moving vehicles, the AASHTO LRFD Speci ficatio n s include s an Impact Factor or Dynamic Load Allowance, to the live load for varying burial depth s . The impact is only applied to the De sig n Truck or Tandem Load , and not the Lane Load. The D y namic Load Allowance varies linearly from a 33% increase at 0 ft. of fill to a 0% increase at 8 ft. of fill, as shown in Figure 4.12. The Dynamic Load Allowance in the LRFD Specifications is calculated using Equation 4.8 1M= 33(10.125DE) I Oo/o Equation 4.8 Where: D E = the minimum depth of earth cover above the struc ture (ft) Similar to the Standard Specifications the dynamic force effects app lied to moving vehicles i s attributed to the hammering effect of the wheel a sembly traveling across s urface discontinuitie s s uch as deck joints, cracks, potholes, and undulation s in the roadway pavement cau ed by settleme nt of fill (AA SHTO 2005). 78
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Dynamic Load Allowance, IM 35 % 30% 25 % 20 % IM% 15 % 10 % 5 % 0 % 0 2 3 4 5 6 7 8 Burial Depth (ft) Figure 4.12Dynamic Load Allowance vs. Burial Depth 4.9 Lateral Live Load Surcharge The AASHTO LRFD Specifications require a live load surcharge to be applied where vehicular load is expected to act on the surface of the backfill within a distance equal to the wall height behind the back face of the wall. Surcharge loads produce a lateral pressure component on soil retaining walls in addition to lateral earth loads. Similar to the Standard AASHTO specifications there are two methods to apply the lateral live load surcharge pressure to the st ructure. This was discussed in Section 3.5. The increase in horizontal pres sure due to the live load s urch arge is estimated by Equation 4.9: 79
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LLS = k * y s * Heq Equation 4.9 Where: LLS =Constant horizontal earth pressure due to live load surcharge (p f) k = Coefficient of lateral earth pressure Y s = Unit weight of soil (pcf) heq =Equivalent height of soil for a vehicle load (ft) The equivalent height of soil, heq, specified by the LRFD Specifications for highway loading as a function of the wall height is extrapolated from Table 4.7. Linear interpolation should be used for intermediate wall heights. The wall height is considered to be the distance between the top surface of backfill and the footing bottom. Figure 4 .13 illustrates the wall height used for live load surcharge pressures. Table 4.7Equivalent Heights !Abutment Height (FT) heq (FT) I 5.0 4.0 10.0 3.0 J 20.0 2.0 80
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Abutment Height Figure 4.13 Wall Height for Live Load Surcharge Pressures 8 1
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Chapter 5 Comparison Between LFD AND LRFD Specifications 5.1 Design Vehicular Live Loads The mo st sig nificant change introduced in the Standard LRFD Specification s is the new vehicular live load model. In the Standard AASHTO Specifications, the vehicular de ign liv e load i s considered to be either the HS De s ign Truck Loading or an Alternate Military Loading. The design includes the configuration that produces the critical conditions. The LRFD Specification s include three components of the live load: â€¢ Design Truck â€¢ Design Tandem â€¢ De s ign Lane Load A combination of the Design Truck or Design Tandem plus the Lane Load is used as the vehicular live load in the LRFD Specifications. The force effects from both the De sig n Truck and the Design Tandem must be compared. The LRFD de s ign truck is identical to the axle load portion of the HS20 truck of the Standard AASHTO Specifications. However, the LRFD design truck is not scaleable like the HS20 truck. For example, there is no HS 15 or HS25 equivalent under the Standard LRFD 82
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Specifications. The De ign Tandem has the same tire and axle pacing a s the Alternative Military loading, but the load is slightly heavier , see Figure 5.1. 1.{)5' o" . .66'o" . Ell '""";" KIPs I J Bl Tro.vel 4 ' o" BJ Al ternative Military Loading De sign To. ncl e M Figure 5.1 Alternative Military Loading vs. Design Tandem Loading As previously noted , another change with regards to the live load from the Standard Specification s is the addition of the Design Lane Load. In the Standard LRFD Specifications a Design Lane Load which consists of a distributed load of 0.64 klf is added to the De ign Truck or De sign Tandem load, to produce the worst case force effects. Furthermore, the design lane load is also assumed to be uniformly distributed over a 10.0 ft design lane width. Therefore , the lane load converts to an additional distributed live load of 0.064 ksf. The force effects from the Lane Load 83
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directly correlate with the design span, as the span increases the force effects increa es, and vise versa. The increase of the force effects from the Lane Load is shown in Figure 5 .2. The percent increase in service moment due to the Lane Load plus Design Truck for various depths of fill and increasing span lengths are shown . For hort span of approximately 4 ft., the increase in service moment is approximately 4%, depending on the earth fill. The increase in the service moment approaches 18% with the addition of the Lane Load for a span of 16ft.. 5 .2 M ultipl e Pr esen c e F a ct o r The LRFD Specifications require the use of multiple presence factors to account for the effects of multiple loaded lanes on a bridge , Table 4.3 . Multiple presence factors are provided for the cases of one , two, three, and three or more loaded lanes. For a single loaded lane the multiple presence factor i 1 . 2, whereas 1.00 for 2 loaded lanes. 84
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20. 0 % 18 . 0 % 0 0.00 ft. fill â€¢ 0 . 50 ft. fill 16. 0 % 10 1 . 00 ft. fill 14. 0 % 10 1 . 50 ft. fill 1â€¢ 1.99 ft. fill (/) 12. 0 % == 1Q) (/) 10. 0 % 1as I!! (J .E 8 . 0 % 1!!1:::!! 0 6.0 % 11 1 '14 . 0 % 11111 12.0 % I1 III0.0 % 4 . 00 6 . 00 8 . 00 10 . 00 12 .00 14. 00 16.00 Design Span (ft) Fig ure 5.2 Increase of Force Effects due to Design Truck vs. Design Truck + Lane Load 85
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5 . 3 Dynamic L o ad Allowance, Impact Both the Standard AASHTO Specifications and the LRFD Specification require an increase in the live load due to the dynamic load effects of moving vehicle s . The Standard Specifications refers to the dynamic load effect increase as Impact , while the Standard LRFD Specifications refer to it a s the Dynamic Load Allowance . Although the terminology is different the application is the same . Both codes require an increase in the live load with respect to the earth fill depth. The LRFD provisions apply a factor that varies linearly from 33% at 0 ft of fill to 0 % at 8ft. The Standard Specifications decrease in 10% steps , shown in Figure 5 . 3 . In general , the Standard LRFD Specification requirements produce a greater increase in the dynamic load effects when compared to the Standard AAS H 0 Specifications. This is considerably evident for depths of fill equal to and greater than 3 ft. The main difference between both provisions i s the application of the Dynamic Load Allowance for depths up to 8 ft by the Standard LRFD Specifications. The Standard Specifications neglects the Dynamic load allowance for depths greater than 3 ft. The increase in the load effect is demonstrated in Figure 5.4. The maximum increase in live load is 21% which corresponds to an earth fill depth of 3 feet. 86
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Dynamic Load Allowance LRFD vs . LFD 35% ,1 LRFD 'U .. I 2 3 4 5 6 7 8 9 Earth Fill Depth (It) Figure 5.3 Dynamic Load Allowance vs. Impact 25 % Increase in 0 namic Load Allowance LRFD vs. LFD 15 % S! '" u ..: ;fl. 5% 5 6 7 8 5 % Earth Fill Depth (It) Figure 5.4 % Increase in Dynamic Load Allowance LRFD vs. LFD 87
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5.4 Lateral Live Load Surcharge Both the Standard AASHTO Specification s and the LRFD Specifications require a liv e load surc harge pressure. The live load surcharge pre ss ure is an increase of the lateral earth pressure due to the live Joad. The increase in horizontal pressure is calculated by Equation 5.1. Where: LLS = k * Y s * h e q Equation 5.1 LLS =Constant horizontal earth pre ss ure due to live load surcharge (psf) k = Coefficient of lateral earth pressure Y s =Unit weight of soil (pet) heq =Equivalent height of soil for a vehicle load (ft) The equivalent height of soil, heq, s pecified by the Standard Specification s is 2ft. The Standard LRFD Specifications calculate the equivalent height of soil as a function of the wall height ex trapolated from Table 4.7. Linear interpolation s hould be used for intermediate wall heights. The wall height is considered to be the di s tance between the top s urfac e of backfill and the footing bottom. See Figure 4.12. 88
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In general, the Standard LRFD Specification requirement s produce a greater increase in the lateral live load s urcharge pre ss ure when compared to the Standard AASHTO Specification s for abutment heights up to 20ft. The lateral live load s urcharg e pressure i s considerably greater u s in g the LRFD Specification s than the Standard AASHTO Specification for abutment height s le ss than 4 ft. The difference in live load s urcharge height i s s hown in Fi g ure 5.5. The increase in the equivalent height o f soil for various abutment heights for both specifications is also s hown in Figure 5 . 5 . The lower v alue of 2ft for the equivalent live load s urcharge height in the Standard Specification s was originally derived from an HSl044 de s ign truck ( AASHTO 2 005 ) . The values of the equivalent live load s urcharge height in the Standard LRFD Specification s were determined from a HL 93 De s ign Li ve Load. This ex plain t he large di sc repancy between both s pecification . 4 . 5 Live Load Surcharge Height 4 . 0 fCLRFD1 3 . 5 ffâ€¢LFD 3 . 0 ffg 2 . 5 fff1 rI 2 . 0 rr1 . 5 rcr1 . 0 rrf:r0 . 5 r,..._ ff'r0 . 0 0 2 4 6 8 10 12 14 16 18 20 Abutment Height (It) 89
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Figure 5.5 Live Load Surcharge Equivalent Heights, heq. 5.5 Distribution of Wheel Loads through Earth Fills for Depths of Fill Greater Than 2FT. When the depth of overburden is equal to or greater than 2 ft, both the Standard AASHTO Specifications and the LRFD Specifications allow for the wheel load to be distributed throughout the earth fill. The Standard LRFD Specification s takes into account the contact area between the footprint of the tire and ground s urface. The distribution area is equal to the tire footprint, with the footprint dimensions increased by either 1.15 times the earth fill depth for select granular backfill, or 1.0 for other types of backfill. The Standard AASHTO Specification do not account for the dimensions of the tire, instead the wheel load is considered as a concentrated point load. The wheel load is distributed over a square equal to 1.75 times the depth of fill , regardless of the type of backfill. Both distribution areas are illustrated in Figure 5.6. As the earth fill depth increases, distributed wheel load areas created by adjacent wheels or axles begin to overlap. This complicates the distributed live load area and load value calculation. 90
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In the Standard AASHTO Specification there are 3 cases which are considered: â€¢ Ca se 1 Di stri bution of Wheel Loads that do not Overlap â€¢ Ca se 2 Distribution of wheel Loads from a Single Axle Overlap â€¢ Ca se 3 Full Distribution of Wheel Loads from Multiple Axles. The Standard LRFD Specification s require two additional cases , Cases 45. The Standard LRFD Specifications require a check to determine if the distri buted live load pressure from multiple truck axles positioned side by side overlap. In other words, a calculation i required to determine the live load pres s ure from two vehicles traveling sidebyside s paced 4 ft apart. Case 4 is when two wheels from separa te axles overlap as illu s trated in Figure 5.7 . Case 5 occurs when both axles from each de sig n truck overlap as illustrated in Figure 5.8. It i s important to note that for cases 1 3 a multiple presence factor of 1 . 2 must be used, while for cases 4 5 a multiple pre se nce factor of 1.00 applies as specified in Section 4.5. 91
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LFD Di s tribution Width s \./HEE L LOAD H / LRFD Di s tribution Width STRIBUTED LOAD ARE A Figure 5.6 Live Load Distribution Areas for a Single Wheel 9 2
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'SPREAD A' Figure 5.7Overlapping Wheel Load Distribution by Passing Vehicles Figure 5.8Overlapping Axle Load Distribution by Passing Vehicles 93
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The provisions from the LRFD Specification s often yield greater design forces than the Standard AASHTO Specifications, specifically at shal low covers. Figure 5.9 s how s the live load se rvice pre ss ure s for both the LFD and LRFD design ve hicle s at various depth s of fill. The s ingle LRFD De sig n Truck with a multiple presence factor of 1.2 produce s the worst case serv ice live load pre ss ure for depth s of overburden between 0 and 5 ft. For depth of overburden greater than 5 ft , the D esig n Tandem spaced 4 ft apart with a multiple presence factor of 1.00 produce s the lar ges t service live load pre ss ure s. However , thi i s not theca e for factored live l oa d pre ss ures found in Figure 5.10. The s ingle HS20 De s ign Truck s pecified in the Standard AASHTO Specificati o n s produce a hi ghe r live load pressure for an earth fill depth at 2 ft. For depth s greater than 2 ft, the live load pre ss ure s follow a similar path as the serv ice live load pre ss ure s pre vious ly di sc u sse d. The s ingle LRFD De s ign Truck with a multiple pre se nce factor of 1.2 produce s the wor st case factored live load pre ss ure for depth s of overburden b etwee n 0 and 5 ft. For depth s of ove rburden greater than 5 ft the Design Tandem s paced 4 ft apart with a multiple pre se nce factor of 1.00 produc es the largest facto red live load pre ss ures. 94
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Distributed Load Values Through Earth Fill (includes Impact+ MPF) 2000 . 00 1800 . 00 1800 . 00 1400 . 00 1200 .00 ! ::j1000 . 00 800 .00 800.00 400 . 00 200 .00 0 . 00 0 . 00 LFD HS20 Design Truck LFD AHemative MWtary LRFD Design Truck ' LRFD Dual Design Truck _.,._ LRFD Design Tandem ' +LRFD Dual Design Tandem .\\ ' "' 4 . 00 8 . 00 12. 00 16 . 00 Ooplh O t Rll (ft) 20. Figure 5.9Distributed Service Live Load Values through Earth Fill with Impact 3500 . 00 Factored Distributed Load Values Through Earth Fill (includes Impact+ MPF) 3000 . 00 2500.00 .;:2000 . 00 a j i 1500 . 00 1000.00 500.00 0 . 00 0 . 00 . LFD HS20 Design Truck _.,_ LFD AHemative Mititary LRFD D esign Truck _,__ LRFD Dual Design Truck _,._ LRFD Design Tandem ;. \ _.,_.. LRFD Dual Des ign Tandem 4 . 00 8.00 12.00 16.00 llopth ot Rll (ft) 20 .00 Figure 5.10 Distributed Factored Live Load Values through Earth Fill with Impact 95
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5.6 Distribution of Live Load s for Depth s of Fill Less Than 2 Feet. Underground concrete structu re s are typically analyzed as twodimensional frames . For depth s of overburden le ss than 2ft, equivalent strip widths are u ed in both Specification s to simp lify the analysis of the threedimensional response due to live loads. Both s pecification s examine the live load in strip widths . Thi s strip width i s the effective width of s lab that resists t h e applied load. The primary difference s are s ummarized in the following sections: Truck Configuration: The Standard AASHT O Specification breaks the design ve hicl e into a line of wheel load s, whereas the Standard LRFD Speci fica tion s utilize s a full axle on the member. Both codes allow the res pected live load s to then be distributed by a distribution width, E . Distribution Width: The values of the distribution widths from both specifications are identical. However, the di stri bution width in the Standard LRFD Specification s i s twice the distribution width found from the Standard Specifications. This increase is a result of the LRFD Specification s u s ing a full ax l e instea d of a single wheel. â€¢ LFD Specifications: P wheel IE =Wheel Load I (4 + . 06 *Span) â€¢ LRFD Specifications: Paxle I E = Axle Load I (8 + 1.2 * Span ) 96
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Tire Contact Area: Both specifications as ume the tire contact a a rectangle with the length in the direction of traffic equal to 10 in, and a width of 20 in. Lateral Distribution (loa d length): The Standard AASHTO Specifications does not take into account earth fill that is placed on the structure. The wheel load is simply assumed to act as a point load. The Standard LRFD specifications allow the designer to take advantage of earth fill by assuming the axle load to be distributed laterally increasing the load length. As a result of this provision, the Standard LRFD Specifications produces smaller service moments when compared to the Standard AASHTO Specifications for earth fill depths les than 2 ft. This i comparison is shown in Figure 5 .11. The live load service moments for both the LFD (HS20) and LRFD design vehicles at various design spans and an earth fill depth of 1 .00 ft are included in the figure. For each case the service moments caused by the Standard Specifications control the design. This is attributed to the load effect from the Standard LRFD Specifications acting more like di tributed load than a concentrated load. However, it is important to note that when the multiple presence factors and the dynamic load allowance are taken into account the service moments from the Standard LRFD Specifications con trol the design, Figure 5.12. 97
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5. 7 Load Factors and Load Combinations The load factor design methodology in the Standard AASHTO Specifications is s imilar to the lo a d and resistance factor design requ irem e nt s in the Standard LRFD Specification s . Both specification s utilize lo ad factors , strength re ducti on factors , a nd rely o n l oading combination to check for strength and s erviceability requirements. However in the LRFD method , l oad and re s istance factors are determi n ed throug h s tatistical studies of the varia bility o f load s and resi s tance . 20.00 18.00 1 6 .00 14.00 :::: 12.00 :: 10.00 "' ::1: 8 .00 6 .00 4 .00 2 .00 0.00 Servi ce Moment comparison (depth of fill = 1 . 0 It) Neglects Impact+ Multiple presence factor I [J LFD DESIGN T RUCK I â€¢ LRFD DESIGN T RUCK r.frfrrft:_ f''''4 .00 6 .00 8 .00 1 0.00 12.00 14.00 Desi gn Span (It) r, _ '16.00 Figure 5.11 Service Moment LRFD vs. LFD Design Live Loads (Multiple presence factor and impact neglected ) 98
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20.00 18 . 00 16 . 00 14 . 00 ? 12 . 00 10 . 00 .. :::;; 8 . 00 6 . 00 4 . 00 2.00 0 . 00 r..__ 4 . 00 Service Moment comparison (depth of fill = 1 . 0 It) Includes Impact+ Multiple presence factor I D LFD DESIGN TRUCK crI â€¢ LRFD DESIGN TRUCK fr;; f110 111c,.:' ffc., 1 fc1111'II r'"""" ..._ ',''6 . 00 8 . 00 10 .00 12 .00 14. 00 16 . 00 Design Span (It) Figure 5.12 Service Moment LRFD vs. LFD Design Live Loads (Multiple presence factor and impact included) Thi s approach is considered to be more reali s tic than the application of judgment based factors in the LFD Specifications. The goal of the LRFD approac h i s to provide a more rational design ba sis with more uniform reliability. The reliability theory on whic h the LRFD method is created and the calibration of t he lo ad and st rength reduction factors are well documented. When designing underground precast concrete cu l verts and three side d s tmcture s, the Standard AAS HTO Specifications applies one set of load factors to the force effect , whi le Stand ard LRFD Specification s varies the load factors to maximize the load effects. Table 5.1 lists the load factors for both specificatio n s . 99
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Table 5.1 Load Factors for LRFD and LFD Specifications Load D esignation LRFD Load Fa c tor s Standard Load Factor s Self Weight , DC 0.90 and 1.25 1.3 Wearing Surface, DW 0.65 and 1.50 1.3 Horizontal Earth 0 . 90 and 1.50 1.30 Pressure , EH Vertical Earth Pressure, 0.90 and 1.3 1.3 EV Live Loads, LL 1.75 2 .17 Live Load Surchar_g_e, LS 1.75 2 .17 The minimum and maximum load factor values utilized by the Standard LRFD Specifications adjust the load effects such that one design load decrease the effect of another. The minimum load factor is used for the load that decreases the force effect of another load. For example , consider the threesided c ul vert shown in Figure 5.13 . If the va lu e of the maximum positive moment in the deck was to be calculated, the maximum load factors from Table 5 . 1 wo uld be u s ed to determine the vertica l lo ads. Since the force effects from the horizontal loads decrease the force effect on the deck, the minimum load factors are used for the horizontal load s . The corres pondin g load combination would be calculated using Equation 5.2. 1.25 * (DC) + 1.35 * (EV) + 1.50 * (DW) + 0.90 * (E H ) + Equation 5.2 1.75 * (LL + IM) 100
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LL+ IM .J. I I I I I I I I I I I I I EV Fi gu re 5.13 L o a d s on a T hre e S ided C ul v ert The Standard AASHT O Specification s doe s not vary the load factor and hence , the corre s ponding load combination for the culvert in Figure 5.3 would be determined using Equ ation 5.3. 1.30 *( DC) + 1.30 *( EV) + 1.30 *(DW) + Equation 5.3 1 . 30 * (EH ) + 2.17*(LL + IM ) T h e mo s t s ignificant difference between both s pecification s is the live load factors. The Live load factor in the Standard LRFD Specification s has been red u ced from 2 .17 to 1.75 , a decrease of 19.4 % . However , both the magnitude and the effective depth of the live load impact (Dynamic Load Allowance ) have been 101
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increa ed. A multiple presence factor of 1.2 ha also been introduced in the Standard LRFD Specification s for a ingle loaded lane. Therefore, the load factor for a si ngle loaded lane equates to 2.1. Overall the load effect from the LRFD Specifications produces greater live load effects . 102
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Design Example #1 6.1 Problem Statement Chapter 6 Design Examples This example illustrates the design of a threesided precast concrete struct ure. The threesided structure was analyzed utilizin g both the Standard AASHTO Specifications, and the Standard AASHTO LRFD Specifications . After determining the individual load components and assembl ing the design load combinations, the design of the flexural reinforcement is presented. The de s ign example concludes with the shear calculation from both specificat ion s. The inside dimensions of the threesided st ructure are 20ft. x lOft, . The deck thickness is 14in., and the wall thickness is lOin. with a lft. x 1ft. haunch. Earth fill will be placed on top of the precast struct ure to a depth of 5ft. A typical sect ion of the culvert i s show n in Figure 6.1. 6.1.2 Design Parameters Material Properties: Yield Strength, fy = 60,000 psi Compre ssive Strength , f'c = 6000 psi Minimum concrete cover = 2 in 103
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Maximum aggregate size, Ag = 0.75 i n Design Loads: Depth of earth fill = 5 ft Unit weight of concrete , yc=l50 pcf Unit weight of oil, ys = 120 pcf Equiva len t fluid pr essure , EFP = 30 pcf B ackfill Material = Sel ect granular Live load pecified in applicable codes Strength Reduction Factors: Flexure, = 0.95 Sh ear = 0.90 6.1.3 Standard AASHTO Specifications: 6.1.3.1 Vertical and Horizontal Earth Pressures: The de s ign venical earth pressure on t h e top of the culvert is calculated as: WuSL=ys* Z WuSL = ( 120 pet) * (5 ft) = 600 p f 104
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Earth Fill 5._0 , ___________________ ] _________ _ 1o'o" ThreeSided Stru cture Elevatio n 1'2" r... ..
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The lateral earth pressure (EH) o n the culvert i s found using the equivalent fluid method. Section 6.2.1 in the Standard AASHT O Specification s require s a minim um and maximum equivalent fluid pressure of 30 pcf and 60 pcf respectively. At the top of the culvert, the lateral earth pressures are calculate d as: EH =EFP* Z EH MIN = (30 pcf) * ( 5 ft) = 150 psf EHMAX = ( 60 pcf) * ( 5 ft) = 300 psf At the bottom of the culvert, the lateral earth pressure are calculated as: 14 EHMIN = (30 pcf) * (5 ft +ft +10ft)= 485 psf 12 14 EHMAX = ( 60 pcf) * ( 5 ft +ft +10ft) = 970 psf 12 Figure 6.2 illustrates the vertical and the min an d max lateral earth pressures applied to the threesided struct ure. E V = 600pst WII 1_11_1 1_1 I I '.'I I ! .'1 . â€¢ t . â€¢. , â€¢ â€¢ â€¢.â€¢ . . . . : . . EH = 485 r;6f E H = 485 psf E V = 600 pst I II I I I 1 1 1 EH= 9 70r;61 E H = 9 7 0psf Figure 6.2 LFD Vertical and Lateral Earth Pressures 1 06
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6.1.3.2 Live Load Surcharge The live load surcharge (LLS) pressure is calculated utilizing the maximum equivalent fluid pressure. The Standard AASHTO Specifications require an equivalent height of soil, Heq of 2ft. The live load surcharge is calculated as: LLS = EFP * Heq LLS = (60 pcf) *(2ft)= 120 psf Figure 6.3 illustrate the live load s urchar ge pressure applied to the threesided structure. 6.1.3.3 Impact For depths of fill greater than 3 ft no Live Load Impact is considered in the Standard AASHTO Specifications. Therefore no increase in Live Load due to the dynamic load effects is necessary. LLS = 120 psf LLS = 120 psf ... . ... . . . . . .: Figure 6.3 LFD Live Load Surcharge Pressure 107
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6.1.3.4 Design Live Loads The de s ign live load s include the HS20 de s ign Truck and the Alternative Military Truck. For depth s of fill greater than 2 ft. the Standard AASHTO Specification s allow s for the wheel load to be di s tributed through s oil over a quare equal to 1.75 time s the depth of fill. For a HS20 De s ign Truck the distribution width for a wheel i s larger than the dis tance between the cent e r s of the two wheel s in the same axle . Therefore , the di s tribution area s overlap and the total load from both wheel s is a s sumed to be uniformly distributed o yer the area within the outer boundarie s of the overlapped areas. The dis tribution area is illu s trated in Figure 6.4. HS20 Design Truck ThreeSided Structure Ele v ation ThreeSided S t ructure Cross Sect io n Figure 6.4 HS20 Distribution through Earth Fill 108
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The HS20 Des ign Truck prodl}ces a service live load pressure of: WuLL = 2 * (P w) (1.75 * H) * (1.75 * H +Axle Width) WuLL = 2 * (16000 lbs I wheel ) "'"248 sf ( 1. 7 5 * 5 ft) * ( 1. 7 5 * 5 ft + 6 ft) p For the Alternative Military Truck the distribution areas from all four wheels from both sets of axles overlap. Therefore, the total load is distributed over the total area within the boundaries of the four wheel distribution areas . The di stribution area is illustrated in Figure 6 . 5. Alternative Military Truck 112'9"'f ThreeSide d Structure Elevation ThreeSided Structure C ross Section Figure 6.5 Alternative Military Distribution through Earth Fill 109
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The Alternative Military load produces a service live load pre ss ure of: 4 * cPw) WuLL = '"(1. 75 * H +Axle Spacing) * (1.75 * H +Axle Width ) WuLL = 4 * (12000 lbs I wheel) ""255 sf ( 1. 7 5 * 5 ft + 4 ft) * ( 1. 7 5 * 5 ft + 6 ft) p The Alternative Military Truck produces live load intensity slightly higher than that of the HS20 Design Truck. It also has a larger influence ar e a than the HS20 Design Truck. Therefore the Alternative Military load controls the design . Thus , the Alternative Military Truck will be u se d to design for the stre ngth and limit states. 6.1.3.5 Load combinations: For both the strength and service limit stat es, three load cases are considered as shown in Figure 6 .6. The load cases are described in detail below. â€¢ Case 1: Maximum vertical load s on deck, minimum lateral loads on legs. This case produce s maximum stresses in the bottom of the deck. â€¢ Case 2: Maximum vettical and horizontal load on the s tructure. This ca e produce maximum stresses on the corner of the deck , and outside walls. 110
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â€¢ Case 3: Minimum vertical loads on deck, and maximum horizontal load on walls. This case produces maximum stresses on the inside of the leg. The load combinations are as follows : Strength: 1. 2. 3. Service: U = 1.3*DL+l.3*EV +1.3 *EHMJN +2.17*LL U = 1.3 * DL + 1.3 * EV + 1.3 * EHMAX + 1.3 * LLSur c harge + 2 .17 * LL U = 1.3 * DL + 1.3 * EV + 1.3 * EHMAX + 1.3 * LLSurcharge 1. u = 1.0 * (DL + EV + EHMIN + LL) 2. U = 1.0 * (DL + EV + EHMAX + LLSurcharge + LL) 3. U = l.O*(DL+EV +EHMAX +LLsurc harge) A structural analysis was performed utilizing a commercial software package , SAP2000. The structure wa modeled and ana l yzed for a 1 foot wide design strip oriented parallel to the direction of traffic. The structure was modeled assuming a pinpin connection as specified in 16.8.5 of the Standard AASHTO Specifications. The axial forces were neglected to simplify the design calculation s . The location of the live load was positioned to create maximum stresses. The critical locations of the internal forces are illustrated in Figure 6. 7. Table 6.1 lists the critical stresses for each load combination at the critical locations. The values in bold are the maximum stresses that occur between load cases 1 3 for the specified section in Figure 6 . 7 . Both the factored and service values are lis ted per foot width in Table 6.1. 111
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n LL =255ps I { II * { { Jill { { E V = 600 psf IllllllllllliiillllllillH . . . â€¢ I . 1 . Case 1 LL = 255 ps + ' ' 4 4 * ' ' I 4 i * I ' 4 4 E V = 600 psf EH = 485 psf I { t II I { { I t t I t { I I I { { { II I { { LLB = 120 psf EH = 300 psf Case 2 EH = 970 psf E V = 600 psf { t l l l t f I l i i t t I l l t f t I l l t I I i LLB = 1 20 psf ' , : : . , . . EH = 300 psf Case .3 EH = 970 psf Figure 6.6 LFD Service Loading Configuration, Cases 1 3 112
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.. ..________ .,._, ' ' ' ' ' / ' ' ' ' ' ' ' . ' ! Figure 6. 7 Critical Locations for Stresses Table 6.1 LFD Structural Analysis Results per Foot Width, Example 1 Load Case 1. Load Case 2. Load Case 3. ...... .......... (/) Q.l a. ..c (f)6 1 __ +_o._o_or __ __ 2_.9_1+ __ 4_.8_9 __ 2 22.80 4.32 22.24 6.74 15.16 5.96 __ 4 50.20 0.00 46.40 0 . 00 29 . 23 0.00 Location Load Case 1 . Cot=
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6.1.3.6 Reinforcing Design The bottom of the s lab will be designed u ing #5 , Grade 60 , reinforcing bar . . ( rebar diameter ) d =slab thickness clear cover+ 2 d = 14in ( 2 in+ = 11.69in Asreq . = [0.8 5 *fc*b]*[dd2 24 *Mu ] fy
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Check Minimum Reinforcement (LFD 16.8.5.8): A min = 0.002 * b * h A min= 0.002 * 12 in * 14 in A . 0.34 in2 srrun =ft Try #5 ' s @ 3 inche on center: A provided= 12 in * .30 7 in 2 = 1 . 23 in 2 3 Check Crack Control (LFD 16.8.5.7 ) : The crack control equatio n s are checked to ensure the primary reinforcement is well distribut ed . Typically the crack control equations will govern the spacing , and amount of reinforcement. The size of rebar and spacing were already cho en to ensure the crack control requirements are met. Calculate Allowable Stress , fsa: f 98 ksi f ::; sa = === Vdc * A d 1 rebardiam ete r 2 . 0.625in 231. c = c ear cover+ = m + = . m 2 2 115
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A= 2 * dc * b =2* 2.3 1 *12in=13_86 Number of bars , N g 3 f 98 ksi sa = 3 0 .86 ksi :t/2.31 in* 1 3.86 Calculate Actual Stress in Reinforcement: Es 29000000 p s i n == Ec wct.5 * 33 * Jh. n = 2900 0000 p s i = 6 _18 u se 6 ( 150 lb /ft3)t.5 * 33 * p s i ) b * x*(;)=(n* A prov.)*(dx) b * x2 n * A prov. * ( d x ) = 0 2 12in * x2 6 * 1.23 in2 * ( 11.69 inx) = 0 2 x = 3 .22in 116
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' * d d x 1169. 3 22in 1062 . J . In. tn 3 3 fs = M s = 33 32 k f t * 1 2 = 3 0 . 6 2 k i ::> 30.8 6 k s i o k A s * j * d 1.23in*10. 6 2in Next , the reinforcing steel will be des igned for the top of the s lab. Further , #5, Grade 60 , reinforcing bar s will be used for the de s ign. d = 14 in( 2 in+ in) = 11.69 in A s = [0.85 * 6000 psi * 12 in]* [ 11.69 in_ l1. 69 in2 _ 2 4 * 15. 56 * 1000 lb f t ] 60000 psi 0.95 * 0 .85 * 6000 p s i 12 in A 0.28in2 s req. = ftCheck Maximum Reinforcement (LFD 8.16.3): A max=0. 75*(0.85 * 6000psi * 0.75 ) * ( 87000 )*12in * 11.69 in 60000 psi 87000 + 60000 p s i A 3.97 in2 smax=ft 117
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Check Minimum Reinforcement (LFD 16.8.5.8 ) : A smin = 0.002 * 12 i n * 14 in A . . 0 .34in2 srrun =ft Try #5's @ 3 inc h es on center : p A s provided = * . 307 in 2 = 1.23 in 2 3 Check Crack Control (LFD 16.8.5.7 ): Calculate Allowable Stress , fsa: f 98 ksi 1 S ::; sa = :r=== V d c * A d 2 . 0.625 in 2 31' c= m+ = . m 2 A= 2*2.31*12in = 1 3 . 86 12 3 98k i fa= = 30.86ks i V2.31in * 13.86 118
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Calculate Actual Stress in Reinforcement: n = 29 000000p i = 6 .lBuse 6 ( 150 lb/ ft 3 ) 15 * 33 * ( p si) 12in * x2 6 * 1.23in2 * (ll.69inx) =0 2 x=3.22in j * d = d= 11.69 in3 22 in = 10 . 6 2 in 3 3 M s 10.74 kft * 12 fs= = ok As* j * d 1.23in *10.62in The reinforcing pattern for the out s ide walls will now be de sig ned. Once again, #5 , Grade 60 , reinforcing bars will be utilized in the de ign. d =lOin( 2 in+ = 7 .69 in A s reg.= [0.85 * 6000psi *12in] * [7 _ 69 in_ 7 _69 in2 _ 24 * 22.80 * 1000 lbft ] 60000 psi 0.95 * 0 .85 * 6000 psi â€¢12 in A 0.65in2 s reg.= ft 119
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Check Maximum Reinforcement (LFD 8.16.3): A s max= 0.75 *(0.85 * 6000 psi * 0.75 J * ( 87000 J * 12 in* 7.69 in 60000 psi 87000 + 60000 psi A 2 .61in2 smax=ft Check Minimum Reinforcement (LFD 16.8.5.8): A s rnin = 0.002 * 1 2 in * 10 in A . 0 .24in2 sJTIJn =ft Try #5 ' s @ 3 inche on center: d d 1 2 in * 307 2 1 23 2 A s prov1 e = . m = . m 3 120
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Check Crack Control (LFD 16.8.5.7): Calculate Allowable Stress , fsa: f f 98 ksi sa = ;:::=== Vctc*A d 2 . 0.625 in 2 31 . c= m+ = . m 2 A= 2*2.31*12in =13. 86 12 3 fsa = 98 ksi = 30.86 ksi V2.31 in * 13.86 Calculate Actual Stress in Reinforcement: n = 29000000 p s i = 6 .18 u se 6 (150 lb/ft3l5 * 33 * p si) 12 . * 2 m x 6* 1.23in2*(7.69inx)=0 2 x = 2.52in 121
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' *dd x 769' . 2 52in 685' J . to. m 3 3 fs= Ms = 1535kft* l 2 =21.86ks i ok As * j * d 1.23 in * 6.85 in Finally, the inside of the walls will be designed u si ng #4 , Grade 60 , reinforcing bars. d 10 . ( 2 . 0.50inJ 77_ . = mm+ = . )lll 2 As reg . = [0.85 * 6000 psi * 12 in]* [ 7 . 75 in_ 7 . 75 in2 _ 24 * 4.89 * 1000 lbft ] 60000psi 0.95 * 0.85 *6000psiâ€¢12in A 0.13in2 s reg.= ft Check Maximum Reinforcement (LFD 8 . 16.3): A s max= 0.75 *(0 .85 * 6000 psi * 0.75 ] *( 87000 J * 12 in * 7 . 75 in 60000 psi 87000 + 60000 psi A 2.63 in2 smax=ft 122
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Check Minimum Reinforcement (LFD 16.8.5.8 ) : A min= 0 . 002 * 1 2 in * 10 in . 0 .24in2 A srrun =ft Try #4 ' s @ 6 inc h es o n center : A s prov id e d = 12in * .196in2 = 0 .392in2 6 C heck Crack Control ( L F D 16.8.5.7 ) : Calculate Allowable Stress , f s a: f 98 k s i f $ sa = r=== Vdc * A d 2 . 0 .50 i n ? 25 . c= m + =m 2 A= 2 * 2 . 25 * 12 in = 27 12 6 98k i f s a = = 24.9 3 k s i V2 . 2 5 in * 27 123
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Calculate Actual Stress in Reinforcement: n = 29000000p s i = 6 _18 use 6 ( 150 lb/ft3 ) t.s * 33 * psi ) 12 0 * 2 m . x 6*0.39in2 *(7.75inx)=O 2 x = 1.56in . * d d x 7 75 . 1.56 in 7 23 . J . m. m 3 3 Ms 3.76kft*12 fs = = = 16.00 k s i 24 . 93 k s i ok As * j * d 0.39in * 7 . 23in 6.1.3.7 Calculate shear (LF D 8.16.6.2 ): The allowable hear in the threesided structure wa s calculated u ing the simplified equation. Shear in the Deck: eve;;::: Vu Vu = 13.48 kips eve= e * 2 *Fc * b * d eve= i * 12in * 11.69in =19558.91b=19.56kips = 19.56 kips> 13.48 kips OK 124
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Shear in the Walls: Vu Vu = 6.74 kip s eve= e*2*Fc * b * d eve= 0.90 * 2 * psi *12 in* 7.69 in= 12866.4lb = 12.87 kips = 12.87 kips> 6.74 kip s OK 6.1.3.8 Summary Figure 6.8 illustrate the required reinforcement for the inside face and outside face of the s ide walls, top s lab , and bottom slab. Note that the reinforcement s pacing is the same or on increments of one another. Thi s is typical in precast concrete in order to simplify the construction of the cage. There are numerou s combinations of rebar size and s pacing. A s long as a ll requirement s are met the de s igner s hould choose the mo s t economical and practical de s ign. 125
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2" #5 @ 3.0" O.C. 2" #4 @ 6.00" o.c . #4 @ 6.00" O.C. 2" #5 @ 3.00" STEEL S E CTION Figure 6.8 LFD Reinforcement Placement for Design Example #1 6.1.4 Standard LRFD Specifications 6.1.4.1 Vertical and Horizontal Earth Pressures The design vertica l earth pressure on the top of the culvert is calculated as: WuSL=ys* Z WuSL = (120 pcf) * (5 ft) = 600 psf Similar to the Standard AASHTO Specifications , the lateral earth pressure (EH) on the culvert is found usin g the equivalent fluid method. However , the LRFD Specification s does not specify minimum and maximum equivalent fluid pressure. This is taken into account in the load factors, and loading combinations. An 126
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equivalent fluid pressure of 30 pcf is assumed for this example . Typically the l ateral earth pressure i s determined from the geotechnical report. At the top of the culvert , the lateral earth pressure is calculated as : EH=EFP* Z EH = (30 pet) * (5 ft ) = 150 psf At the bottom of the culvert , the lateral earth pressure is calculated as: 14 EH = (30 pet) * (5 ft +ft +10ft) = 485 psf 12 Figure 6.9 illustrates the vertical and lateral earth pressures applied to the threesided structure. EV = 600 psf EH = 150 psf l I ( I I I I I I I I I I l I I EH = 150 psf ... .. . .. . .. . ' . EH = 485 pst EH = 485 psf Figure 6.9 LRFD Vertical and Lateral Earth Pressures 6.1.4.2 Live Load Surcharge The live load surcharge pressure is calculated utilizing an equivalent height of soil, Heq . The equivalent height of soil, Heq, is determined as a function of the wall 127
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height in Table 4.4. The wall height is considered to be the distance between the top urface of backfill and the footing bottom. A 1 ft thick footing was assumed for this examp le. Figure 6.10 illustrates the wall height u sed in this example. After linear interpolation the equivalent height of soil was determined to be 2.28 ft. . . . 17'2" I .. Figure 6.10LRFD Wall Height, Example #1 The live Load Surchar ge is calculated as: LLS = EFP * Heq LLS = ( 30 pcf) * (2.28 ft) = 68.4 psf Figure 6.11 illustrate the Live Load Surcharge pressure applied to the threeided struct ure. 128
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LLS = 68.4 psf LLS = 68 . 4 psf ..... Figure 6.11 LRFD Live Load Surcharge Pressure 6.1.4.3 Dynamic Load Allowance: The increase in the Live Load due to the dynamic load effect s changes for varying burial depths. The Dynamic Load Allowance i s only applied to the Design Truck a nd Tandem Load, and not the Lane Load . The D ynamic Load Allowance for a fill depth of 5 ft i s calculated as: IM=33*(10.125 *DE) 0 % IM = 33 * ( 10 . 125 * 5 ft) = 12.375 % 6.1.4.4 Design Live Loads: The de s ign live load s include the HL93 De s ign Truck , Design Tandem , and Lane Loads. Similar to the Standard AASHT O Specifications , the Standard LRFD Specifications allows for the wheel load to be dis tributed through soi l when the earth fill exceeds 2 ft. The distribution area is equa l to the tire footprint, with the footpri n t dimensions increased by 1.15 time s the eart h fill depth for select gran ul ar backfill. 129
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To determine the live load that s hould be carried into the st ructural analysis, the u se of multiple pre sence factor mus t be taken into account. The multiple presence factor for a single loaded lane for strength and service limjt s tate s is 1.20 . For two lanes loaded use 1.00 . For a si ngle HL93 De sig n Truck the distrib ution width for a wheel is larger than the distance between the center s of the two wheels in the same axle. Therefore, the di st ribution area s overlap and the total load from both wheels is assumed to be uniformly distributed over the area within the outer boundarie s of the overlapped areas. The dis tribution area i s illustrated in Figure 6.12. A s ingle HL93 Design Truck axle produce s a serv ice live load pre ssure of: 2 * (P w)*MPF WuLL = (LLDF * H + LT) * (LLDF * H + W T +Axle Width) WuLL = 2 * ( 16000 lbs I wheel) * 1.2 ""434. 75 sf ( 1.15 * 5 ft + 0 . 83 ft) * ( 1.15 * 5 ft + 1.67 ft + 6 ft) p 130
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Design T r uck t"6' 0"j WuLL ThreeS ided Structure Elevation ThreeSided Structure C r oss Sectio n Figure 6.12 Distribution area for Design Truck The AASHTO LRFD Specifications also require that the force effects for two de s ign vehicle s positioned 4ft. apart be evaluated . In this example the di s tribution width of both axles for two trucks positioned sidebyside overlap. The total load from the two axles was then distributed over the area within the boundarie s of the two axles. The distribution width i s shown in Figure 6.13. Two HL93 Design Truck axle s adjacent to each other (4ft apart) produces a service live load pressure of: 4*(Pw) * MPF WuLL = ________ ___:_.:.:...;_ _________ _ ( LLDF * H + LT) * (LLDF * H + W T +Axle Width+ 4ft) WuLL = 4 * (16000 lbs I wheel)* 1.0 ""415 .15 p s f (1.15 * 5 ft+0.83ft) * (1.15 * 5ft+ 1.67 ft +6ft+ 4ft+ 6ft) 131
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2 Design Vehicles WuLL ThreeSided Structure Elev a i o n Figure 6.13 Distribution area for two adjacent de s ign vehicles For a s ing l e HL93 D esign Tandem the distribution area s from all four whee l s overla p from both sets of ax l es overlap. Therefore, the total load is distributed over the total area with in the boundaries of the four wheel di tribution areas. The distribution area is illustrated in Figure 6 . 14 . 5'0' c iY 5.__J fhreeSl ded S truc t ure E levation Thr ee Sided S tructure Cross Section Figure 6.14Distribution area for Design Tandem 132
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A single HL93 Design Tandem Truck produce s a service live load pressure of: 4 * (Pw) * MPF ( LLDF * H + L T +Axle Spacing)* ( LLDF * H + W T +Axle Width ) WuLL = 4 * (12500 lb s I wheel) * 1.2 ""422 _ 56 psf ( 1.15 * 5 ft + 0.83 ft +4ft) * ( 1 .15 * 5 ft + 1.67 ft +6ft) The force affect s for two HL93 De sign Tandem Truck s adjacent to each other (4ft apart) produce s a service live load pressure of: 8 * ( P w) * MPF WuLL = ""( LLDF * H + LT) * ( LLDF * H + W T +Axle Width+ 4ft) WuLL = 8 * (12500 lbs I wheel)* 1.0 = 403.45 sf (1.15*5ft+0.83ft+4ft)*(l.15 *5ft+l.67ft+6ft+4ft6ft) p The dis tribution width for the lane load i s ass umed con sta nt and equal to the width at the s urface of the backfill for ease of calculations . The effect of the lane load on the threesided s tructure is relatively s mall compared to the load affects fro m the design vehicle . It s hould also be noted that the u se of multiple pre s ence factors with regards to the lane load i s not addressed in the AASHTO LRFD Bridge De sig n 133
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Specification s. However thi example a sumes the lane load does get multiplied by the appropriate multiple presence factor. The Lane Load produce s a service live load pressure of: WuLL = 640 plf * MPF = 64psf * MPF 10ft The Single Design Truck produce s the ma x imum live load intensity ; however the Single Design Tandem ha s a larger influeqce area. After analysis it wa s determined the Single Design Tandem with a multipl e presence factor of 1.2 controlled the design . Therefore the Lane Load produces a live load pressure of: 640 plf * 1.2 WuLL = = 64 psf * 1.2 = 76.8 psf 10ft 6 . 1 . 4.5 L o a d c o m bi nations: Similar to the LFD Specifications , for both the st rength and se rvice limit sta tes , three load configurations are considered as ill u strated in Figure 6.15 . The load cases correspond to: 134
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â€¢ Case 1: Maximum vertical loads on deck, minimum lateral loads on legs. Thi case produce s maximum tresse s in the bottom of the deck. â€¢ Case 2: Maximum vertical and horizontal loads on the tructure. The case produces maximum tresses on the corner of the deck, and out ide walls. â€¢ Case 3: Minimum vertical loads on deck , and maximum horizontal load on walls. This case produces maximum stre es on the in ide of the leg. The load combination are as follows: Strength: 1. U = 1.25 *DC+ 1.30 * EV +0.90* EH + 1.75 * (LL + IM) 2. U = 1.25 *DC+ 1.30 * EV + 1.50*EH + 1.75 * LS + 1.75 * (LL + IM) 3. U = 0.90 *DC+0.90*EV +1.50*EH+l.75* LS Ser vice: 1. U = 1.00 * (DC+ EV + EH + ( LL + IM)) 2. U = l.OO*(DC+EV + EH + LS + (LL+IM)) 3. U=l.OO*(DC+EV+EH+LS) 135
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I l '1 LL = 422 . 6 psf LL = 76. 8 psf â€¢â€¢ t t t t 4 4 4 4 4 4 4 l I I t t t t t t t t l 4 4 = 600 psf . :r.: . .. .. . . â€¢ . â€¢ EH =150pst Case 1 EH = 485 psf rt LL = 42 2 . 6 pst too on n n n LL=? 6 .8psf H H H H H H H H J J t H 01ft=6oopst ' + o o o o n n n n + + o o t1LLs = 68.4 psf EH = 150psl C a se 2 EH = 485 psi E V = 600 psf 1 1 o o o o n n n n + + o o OLLs = 68.4 psf EH = 150psl Case 3 EH = 485 psi Figure 6.15 Design Example #1, LRFD Service Loading Configuration, Cases 1 3 136
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Similar to the St a ndard AASHTO Specific a tion s the st ructure was mode l ed ass uming a pinpin connection as s pe cified ection in 12 . 14.5 of the LRFD Specifications. The l ocatio n s of the critical s tre s es and the val ue s are illustrated in Figure 6.16 , and Table 6.2 . Both the factored and serv ice values are li ted per foot width in T ab l e 6.2. ,... .... __ , I I I I I I t t I I I I I I I I I I I I I I I I I I I I I I I I I I l i I I I I I I I I I I I I I I I I I I I I I I I I I I Figure 6.16 Critical Locations for Stresses 137
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Table 6.2 LRFD Structural Anal y sis Results per Foot Width , Example 1 Location Load Case 1 . Load Case 2. Load Case 3 . ................ ...... .......... ...... .......... c ...... ...... .......... c................ c.:::: ...... .......... Q) ....... (/)
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. ( rebar diameter ) d =slab th1ckness clear cover+ 2 d = 14in ( 2in + = 11.56in As req. = [0.85 * fc * b ] * [d _ d2 __ 2_4_*_M_u_] fy
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Check Minimum Reinforcement (LRFD 12.14.5.8): A min = 0 . 002 * b * h A s min = 0.002 * 12 in * 14 in A . 0.34in2 smm = ft Check Crack Control (LRFD 12.14.5.7): Calculate minimum allowable spacing to satisfy cracking (LRFD 5. 7.3.4): 700*ye 2 * d c B s * fs d 2 . 0.875in 2 44. c= m+ = . m 2 B = 1 + de = 1 + 2.44 in = 1.30 s 0.7 *(hdc) 0.7 *(14in2.44in) ye =exposure factor= 1.00 140
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Calculate actual stress in reinforcement: n = 29000000p i = 6 .18 use6 (150 lb/ft3 ) t.s * 33 * psi) 12. * 2 m x 6 * 1.20 in 2 * (11.56 inx) = 0 2 x=3.17in j * d =d = 11.56in3 17 in= 10.50in 3 3 f = Ms = 41.47kft*12 =39.4Sksi As* j * d 1.20 in 2 * 10.50 in 700 * 1.00 s::; 2*2.44in=8.76in 1.30* 39.48 ksi Actual Spacing= 6.0in:::; 8.76in OK Calculate Maximum Spacing of Reinforcing (LRFD 5.10.3.2) max = 1.5 * h :::; 18in smax = 1.5 * 14in = 21 in therefore u se 18 in Actual Spacing = 6.0 in :::; 18 in OK 141
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Calculate Minimum Spacing of Reinforcing (LRFD 5.10.3.1) min;;::: db= . 625 in 1.33 * Ag = 1.33 * 0.75 in= 1.0 in 1.0 in Actual spacing = 6 in OK Next the reinforcement for the top of the s lab will be designed with #4 , Grade 60, reinforcing bars. d = 14in ( 2in + = 11.75 in A =[0. 85 *6000psi*12in]* [ 11.75in11.75 in2 ] 60000psi 0.95:;<0.85 *6000pstâ€¢12m 0.27 in2 A req.=ft Try #4 ' s @ 3 inches on center: A provided =12in*O.l96in2=0.78in2 3 142
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Check Maximum Reinforcement Ratio (LRFD 5.7.3.3): c 00 78 in 2 * 60000 psi = = 0.09 0.42 ok d 0085 * 6000 p s i * 12 in* 0075 * 11.75 in Check Minimum Reinforcement (LRFD 12.14.5.8 ) : Asrrtin = 0 0 002 * 12 in * 14 in A 0 0034in2 smm=ft Check Crack Control (LRFD 12.14.5.7 ) : Calculate minimum allowable spacing to satisfy cracking (LRFD 5.7.3.4): 2 * dc d 2 0 0050 in 2 25 0 c= m+ = 0 m 2 = 1 + de = 1 + 2.25 in = 1.27 s Oo7*(hdc ) Oo7*(14in2025in) ye = expos ur e factor= 1000 143
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Calculate actual stress in reinforcement: n = 29000000 psi = 6 .18 u s e 6 (150 lb/ft3 ) '5 * 33 * p s i ) 12. * 2 10 x 6* 0.78in2*(11.75inx)=O 2 x=2.66in 2 66 in =10.86in 3 3 = 9 .87kft*12 =13.98k i 0.78 in 2 * 10.86 in 700 * 1.00 2*2.25in=34.93in 1.27 * 13.98 ksi Actual Spacing= 3.0 34.93 in OK Calculate Maximum Spacing of Reinforcing (LRFD 5.10.3.2) s max = 1.5 * h 18in smax = 1.5 * 14in = 21 in therefore use 18 in Actual OK 144
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Calculate Minimum Spacing of Reinforcing (LRFD 5.10.3.1 ) s db=. 625in 1.33 * Ag = 1.33 * 0.75 in = 1.0 in 1.0 in Actual spacing = 3 in OK The outside reinforcement for the walls will include #4, Grad e 60, reinforcing bars. d =lOin( 2in + = 7.75 in As= [0. 85 * 6000 p si * 12 in] * [ 7 . 75 in_ 7 . 75 in2 _ 24 * 27.04* lOOOlbft ] 60000psi 0.95 * 0 .85*6000psiâ€¢l2in A 0.77in2 sreq.=ft Try #4' s @ 3 inches on center: As provided= 12 in *0.196in2 = 0 .78in2 3 Check Maximum Reinforcement Ratio (LRFD 5.7.3.3): c 0 . 78 in2* 60000 psi = = 0.13 0 .42 d 0.85 * 6000 psi * 12 in* 0 . 75 * 7.75 in 145
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Check Minimum Reinforcement (LRFD 12.14.5.8): Asmin = 0.002 * 12 in * 10 in A . 0.24in2 srrun =ft Check Crack Control ( LRFD 12.14.5.7): Calculate minimum allowable spacing to satisfy cracking (LRFD 5.7.3.4): 700* s :::; y e 2 * d e P s *fs d 2 . 0.50 in 2 25 . c= m+ = . m 2 p = 1 + de = 1 + 2.25 in = 1.41 s 0.7 *(hdc) 0.7*(10in2.25in) ye = exposure factor = 1.00 146
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Calculate actual stress in reinforcement: n = 29000000 p s i = 6 .18 u se 6 (150 lb/ft3 ) 1.s * 33 * p si) 12 in * x 2 6 * 0.78in2 *(7.75inx)=0 2 x = 2.10in * d d x 7 75 2 1 0 in 7 05 J . m. m 3 3 fs= Ms = 18.58kft*12 = 40 . 54 ksi As * j * d 0.78in2 * 7.05in 700 * 1.00 2 *2.25in=7.74in 1.41 * 40.54k s i Actual Spacing= 3.00 7.74in OK Calculate Maximum Spacing of Reinforcing (LRFD 5.10.3.2) s max= 1.5* h 18in s max = 1.5 * 14in = 21 in therefore u se 18 in Actual Spacing= 6 . 0 18 in OK 147
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Calculate Minimum Spacing of Reinforcing (LRFD 5.10.3.1) smin db= .625in 1.33 * Ag = 1.33 * 0.75 in= 1.0 in 1.0 in Actual spacing = 6 in 0 K The reinforcement on the inside of the walls will be designed u s ing #4, Grade 60, reinforcing bar s . d =lOin( 2in + = 7.75 in As= [0.85 * 6000psi * 12 in]* [ 7 .75 in_ 7 . 75 in2 _ 24 * 2.55 * 1000 lbft ] 60000 psi 0.95 * 0 .85 * 6000 psi 12 in A 0 . 07 in2 s req.= ft Try #4's @ 12 inches on center: Asprovided= 12 in * 0.196in2 =0.196in2 12 148
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Check Maximum Reinforcement Ratio (LRFD 5.7.3.3): c 0 .196in2 * 60000 psi = = 0.03 0.42 d 0.85 * 6000 psi * 12 in * 0 . 75 * 7.75 in Check Minimum Reinforcement (LRFD 12.14.5.8): Asmin = 0 . 002 * 12 in* I 0 in A . 0.24 in2 smJn =ft Check Crack Control (LRFD 12.14.5.7 ) : Calculate minimum allowable spacing to satisfy cracking (LRFD 5. 7.3.4): 700* s $; Y e 2 * de *fs d 2 . 0.50 in 2 25 . c= m+ = . m 2 = 1 + de = 1 + 2.25 in = 1.41 s 0.7 *(hdc) 0.7*(10in2.25in) ye = exposure factor= 1.00 149
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Calculate actual stress in reinforcement: 0 = 29000000 psi = 6 .18 use 6 (150 lb/ft3)1.5 * 33 * psi) 12. * 2 10 x 6* 0.196in2*(7.75inx)=O 2 x = 1.14in ' *dd _l.l4in 737 J. m . m 3 3 Ms 0.52 k ft * 12 fs = = = 4.32 ks i As* j * d 0.196in2 *7 .37in s 700 * l.OO 2 * 2.25 in= 110.42 in 1.41 * 4.32 ksi Actual Spacing = 6.0 in 110.42 in OK Calculate Maximum Spacing of Reinforcing (LRFD 5.10.3.2) s max = 1.5 * h 18in smax = 1.5 * 14in = 21 in therefore use 18 in Actual Spacing= 6.0 18 in OK 150
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Calculate Minimum Spacing of Reinforcing (LRFD 5.10.3.1) s min 2:: db= .625 in 1.33 * Ag = 1.33 * 0 . 75 in= 1.0 in 1.0 in Actual spacing = 9 in 0 K 6.1.4.7 Calculate shear (LRFD 5.8.3.3): The allowable s hear in the threes ided s tructure i s calculated u s ing the simplified equation. Shear in the Deck: Vu Vu=16.16kips * b *dv dv = maximum vulue of 0.9 * d or 0.72 * h 0.9 *de= 0 . 9 * 11.56 = 10.40 0 . 72 * h = 0 . 72 * 14 = 10 . 08 eve= 0 . 90 * 2 * p s i * 12 in* 10.40 in= 17400.5lb = 17.40 kip s =17.40kip s>16. 16kip OK 151
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Shear in the Walls: Vu Vu = 5.57 kip s eve= e * p * .Jh * b * dv dv = maximum vulue of 0.9 * d or 0.72 * h 0.9 * de=0.9 * 7.75 = 6.98in 0.72 * h =0.72 * 10 = 7.2in P=2 ev c = 0.90 * 2 * p si * 12 in * 7.2 in= 6023.3lb = 6.02 kip s = 6.02 kips> 5.57 kips OK 6.1.4.8 Summary Figure 6.17 illustrates the required reinforcement for the inside face and outside face of the side walls, top slab, and bottom slab. Similar to the LFD design there are numerous combinations of rebar size and spacing . As long as all requirements are met the designer should choose the most economical and practical design. A comparison between both designs with regards to the area of steel required is presented in Table 6.3. Table 6.3 Area of Steel comparison Location :_1 ___ _ :2._ 3 ___ 4LFD _______ _ i ___ o.13 ___ i ___ o _ _ 65_ _ _ LRFo:o.a?ra _77152
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2" 2" #7 @ 6 . 0 .. D.C. 14@ 12.00" Q.C. 14@ 1 2.00" Q.C. #4 @ STEEL SECT! ON Figure 6.17LRFD Reinforcement Placement for Design Example #1 Design Example #2 6.2 Problem Statement This example is a continuation of design example #1, but with a 1 ft depth of overburden. The threesided struct ure is once again analyzed utilizing both the Standard AASHTO Specifications, and the Standard AASHTO LRFD Specification s . 6.2.1 Standard AASHTO Specifications: 153
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6.2.1.1 Vertical and Horizontal Earth Pressures: The design vertical earth pressure on the top of the culvert is calculated as: WuSL = ys * Z WuSL = (120 pcf) *(LOft)= 120 psf The lateral earth pressure (EH) on the culvert is found using the equivalent fluid method. Section 6.2.1 in the Standard AASRTO Spe cifications require s a minimum and maximum equivalent fluid pressure of 30 pcf and 60 pcf respectively. At the top of the culvert, the lateral earth pressures are calculated as: ER=EFP* Z ERMIN = (30 pcf) * (1.0 ft) = 30 psf ERMAX = (6 0 pcf) * (1.0 ft) = 60 psf At the bottom of the culvert, the lateral earth pressures are calculated as: 14 ERMIN = (30 pcf) * (1.0 ft +ft +10ft)= 365 psf 12 14 ERMAX = (60 pcf) * (1.0 ft +ft +10ft)= 730 psf 12 Figure 6.18 illu strates the vertical and the min and max lateral earth pressures applied to the threesided struct ure. 154
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EV â€¢ 120 psf EH = 30 psf 4 ! J ! J J J J ! J ! ! J I l J ! J ! ! ! J ! { l l EH = 30 p s f EH = 365psf r EH = 365 psf EVz 120 psf EH = 60 psf EH = 60 p s f rf? I t EH = 730 psf 1 EH = 730psf Figure 6.18 LFD Vertical and Lateral Earth Pressures 6.2.1.2 Live Load Surcharge The Live Load Surcharge pressure is calculated utilizing the maximum equivalent fluid pressure. The Standard AASHTO Specifications require an equiva lent height of soil, Heq of 2ft. The live Load Surcharge is calculated as: LLS = EFP * Heq LLS = ( 60 pet) * (2ft ) = 120 psf Figure 6.19 illu s trates the Live Load Surcharge pres s ure applied to the threesided structure. 155
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LLS= 120 psf LLS = 1 2 0 psf . ... Figure 6.19 LFD Live Load Surcharge Pressure 6.2.1.3 Impact The increase .in the Live Load due to the dynamic load effects varie s for varying burial depth s as illustrated in Table 6.4. The impact factor is applied to both the De s ign Truck and Alternative Military Load as a multiplier. The live loa d impact fac tor for 1.0 ft of fill i s 30 % . T b l 6 4 I a e . mpac tF t ac or Overburden Impact 0'0"1 ' 0 " 30 % 1 ' 1 " 2'0" 20% 2'1"2'11" 10% >2 '11" 0 % 156
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6.2.1.4 Design Live Loads The design live loads include the HS20 design Truck and the Alternative Military Truck. For depths of fill l ess than 2ft., the Standard AASHTO Specifications allows for the wheel load to be divided into strip widths. Determine the Equivalent Strip Width Deck span beteewn centerline of walls= 20ft+ 0.83 ft = 20.83 ft Ewidth = 4+.06*Span:::;; 7.0ft Ewidth = 4 + (.06 * 20.83)=5.25 ft The HS20 De sign Truck produces a service live load value of: PLL = 16000 lbs!Wheel = 3047.6lbs I (ftwidth) 5 .25 ft PuLL= 2.17 * 1.3 * 3047 .6lbs I (ftwidth) = 8597 .3lbs I (ftwidth) spaced 14ft apart The Alternative Military De s ign Truck produces a service live load value of: PLL = 12000 lbs /Wheel = 2285.7lbs I (ftwidth) 5.25 ft PuLL= 2.17 * 1.3 * 2285.7 lbs I (ftwidth)= 6448.0 lb s I (ftwidt h) spaced 4 feet apart A single axle from the HS20 design truck produces live load intensity higher than the Alternative Military Load. Howe ver the axles of the Alternative Military are only 4.00 ft apart, producing 2 concentrated loads. After analysis it was determined 157
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that the Alternative Military load control s the design. Use the Alternative Military to design for the s trength and limit states . 6.2.1.5 Load combinations: For both the strength and s ervice limit s tate s, three lo ad ca ses are considered. The load cases are as follows. The loading configuration s are illu s trated in Figure 6.20. The load cases correspond to: â€¢ Case 1: Maximum vertica l loads on deck, minimum lateral loads on leg s . Thi s case produces maximum s tre ss es in the bottom of the deck. â€¢ Case 2 : Maximum vertical and horizontal load s on the s tructure. The case produce s maximum s tresse s on the corner of the deck , and outside walls . â€¢ Cas e 3 : Minimum vertical load s on deck , and maximum horizontal load s on walls. Thi s ca se produces maximum stresses on the in s ide of the leg. The load combination s are as follows: Strength : 1. u = 1.3 * DL + 1.3 * EV + 1.3 * EHMlN + 2.17 * (LL + IM) 2 . u = 1.3 * DL+ 1.3* EV + 1 . 3 * EHMAX + 2.17 * (LL+ IM) 3 . u = 1.3 * DL+ 1.3 * EV + 1.3 * EHMAX 158
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= 2285.71b I E V = 120 p sf 'tJJtt44tt4Jl+J4t+4tt+4lO C ase 1 EH = 365 psf = 2285 .71b I J E V = 1 2 0 p s f U 4 t 0 4 0 4 J t 0 t t 0 t tJ 4 t 0 L L S = 120 p s f ... â€¢ . â€¢ "'" â€¢ â€¢ . â€¢ â€¢ _s::i:r;' . .â€¢ E H=60ps f Case 2 E H = 730 p s f E V = 120 psf ' 4 J t t 4 4 t + 4 4 t + J t t + 4 t t 4 4 t t 4 t L LS = 120 p s f E H = 60 psf C
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Service : 1. u = 1.0 * ( DL + EV + EH MIN + LL) 2. u = 1.0 * ( DL + EV + EH MAX + LL) 3. u = 1.0* (DL+ EV + EHMAX) The critical location of the internal forces are illustrated in Figure 6.21. Table 6.4 lists the factored and se rvice stresses for each load combination at the critical locations. Once again the axial forces where neglected in to simplify the design calculations . I I : I t I o I I o I : ! I o ' ' ' ' ' ' ' ' ' ' ' ' ! i : ! ' ' I : ' ' ' ' : : ' ' ' ' I : ' I Figure 6.21 LFD Critical Locations for Stresses 160
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Table 6.5 LFD Structural Analysis Results per Foot Width, Example 2 Load Case 1 . Load Case 2 . Load Case 3 . c..... _ c..... _ C,::= ..... _ Q)l (J) Q) .... (J) Q) I (J) Eo. Q)Q. Q) 0. E o. Q) 0. ..c ..c ..c Location 0 Cf)2 0 Cf)6 0 Cf)6 1 0.00 0.10 1.01 2.45 5.29 3.29 2 20.22 3.32 19.89 5.07 5.66 3.49 3 12.43 14.23 15.19 14.23 6.37 3.45 4 50.20 4.84 47.45 4.84 9 . 16 0 . 00 Location Load Case 1 . Load Case 2. Load Case 3. c..... _ c..... _ c .. ..... _ IDI (J) IDI (J) Q) .... (J) E o. Q) 0. E o. Q)Q. E Q) 0. ..c ..c ..c 0 Cf)2 0 Cf)2 0 Cf)2 1 0.00 0.34 1.95 2.14 4.07 2.53 2 11.17 2.07 1 0 .91 3.41 4.36 2 .69 3 6.84 7.62 8.96 7.62 4.90 2.66 4 26.79 2.23 24.67 2.23 7.05 0.00 161
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6.2.1.6 Rein forcing Design The bottom reinforcement for the slab will be de s igned with #5 , Grade 60 , reinforcing bars. . ( rebar diameter ) d =slab thicknes s clear cover+ 2 d = 14in ( 2in + = 11.69in A sreq.=[0.85*fc*b]*[dd2 24 * Mu ] fy * 0.85 * f c . b As req. = [0.85 * 6000 psi * 12 in]* [ 11.69 in_ 11_ 69 in2 _ 24 * 50.20 * 1000 lbft ] 60000 p s i 0.95 * 0.85 * 6000 p s i â€¢12 in A 0.94in2 s req.= ft 162
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Check Maximum Reinforcement (LFD 8.16.3): A 87000 ]*b * d fy 87000+fy Asmax=0.75*(0.85 * 6000psi * 0.75J*( . 87000 ]*12in * 11.69in 60000 psi 87000 + 60000 psi A 3.97in2 smax=ft Check Minimum Reinforcement (LF D 16.8.5.8 ) : As min = 0.002 * b * h Asmin = 0.002 * 12 in * 14 in A . 0.34in2 siTlln = ft Try #S's @ 3.5 inches on center: As provided = 12 in * .307 in 2 = 1.05 in 2 3.5 163
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Check Crack Control (LFD 16. 8 . 5.7): Calculate Allowable Stress, fsa: c < f 98 ksi 1 s _ sa = c== Vdc* A d I rebar diameter 2 . 0 .625 in 2 3 1 . c = c ear cover+ = m + = . m 2 2 A = 2 * de * b = 2 * 2.31 * 1 2 in = 16.17 Number of bars , N 12 3 . 5 fsa = 98 ksi = 29.31 ksi V2.31in * 16.17 Calculate actual stress in reinforcement: Es 29000000 p si n === Ecwcl.5 * 33 *Fc n = 29000000psi = 6 .18 u se 6 (150 lb/ft3 )1.5 * 33 * p s i ) 164
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b * x * ( ; ) = ( n * A s pro v.)*(dx) b * X 2 n *As prov . * ( dx) = 0 2 12. * 2 tn x 6* 1.05 in2 *(ll.69inx) = 0 2 x = 3.02 in j * d = d= 11.69 in3 02 in = 10.68 in 3 3 fs = Ms = 26 79 kft * 12 = 28.67 k s i $ 30.86 k s i ok As* j * d 1.05 in 2 * 10. 68 in The top reinforcement in the deck is designed u sing #4 , Grade 60, reinforcing bars . d = 14in ( 2in + = 11.75in A =[0.85* 6000psi *12in]*[ll.7Sinll.7Sin2 24*15 . 15.19 *1000lbft] 60000 psi 0 .95 * 0 .85 * 6000 p i â€¢12 in A 0.28in2 s req . = ft 165
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Check Maximum Reinforcement (LFD 8.16.3 ) : A s max= 0 .75 *[0.85 * 6000 psi * 0.75 ] * [ 87000 J * 12 in * 11.75 in 60000 p si 87000 + 60000 p s i A 3.99i . n2 smax=ft Check Minimum Reinforcement (LFD 16.8.5.8) : A srnin = 0 . 002 * 12 in* 14 in A . 0.34in2 smm=ft Try #4's @ 3.5 inches on center: A s provided= 12 in * .196 in 2 = 0.67 in 2 3.5 Check Crack Control (LFD 16.8.5.7): Calculate Allowable Stress , fsa: f f 98 ksi sa=:;:::== 'Vctc*A d 2 . 0.50 in 2 25 . c= m+ = . m 2 1 166
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A= 2*2025 * 12i n = 15 75 12 3 0 5 fsa = 98 ksi = 29 0 84 ks in* 15075 Calculate actual stress in reinforcement: n = 29000000 psi = 6 0 18 use 6 (150 lb/ft3 )1.5 * 33 * p s i ) 12 in* x 2 6 * 0067 in 2 * (11.75 in x) = 0 2 x = 2o50in o*d d x 0 2o50in 10 92 0 J = =11.75m= 0 m 3 3 M s fs=A s* j * d 8096 k ft *12 2 = 140 69 ksi $ 29084 ksi ok 0067 in * I 0092 in 167
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The outside reinforcement in the walls is designed using #4, Grade 60, reinforcing bar. d I 0 . . ( 2 . 0 . 50 in) 7 75 . = mm+= . m 2 Asreq .=[0.85* 6000 psi*l2in]* [ 7 .75in7 .75in2 24 * 20.22 *10001bft l 60000 psi 0 .95 * 0.85 * 6000 p s i â€¢12 in A 0.57in2 s req.= ft Check Maximum Reinforcement (LFD 8.16.3 ) : A max= 0 .75*(0.85* 6000p i * 0.75)*( 87000 )*12 i n * 7 .75 in 60000 p i 87000 + 60000 psi A 2 . 63i n2 smax=ft Check Minimum Reinforcement (LFD 16.8.5.8 ) : Asmin = 0.002 * 12 in * 10 in A . 0.24in2 SITilll =ft Try #4's @ 3.5 inches on ce nt er : As provided= 12 in* .196 in 2 = 0 .67 in 2 3.5 168
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Check Crack Control (LFD 16.8.5.7): Calculate Allowable Stress, fsa: fs fsa = 98 k s i 'Vctc* A d 2 . 0 .50 in 2 25 . c= rn+ = . m 2 A= 2*2.25 * 1 2 in =15 . 75 12 3.5 fsa = 98 ksi = 29 . 84 ksi 'V2.25 in* 15.75 Calculate actual stress in reinforcement: n = 29000000 p si = 6 . lS use 6 (150 lb/ft3)1.5 * 33 * p s i ) 12. * 2 10 x 6* 0.67in2*(7.75inx)=O 2 x = 1.97 in 169
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* d d x 7 75 1.97 in 7 12 J . Jn. tn 3 3 Ms 11.17 kft *12 fs = . = 2 = 28 . 09 ksi 29.84 k s i ok As*J * d 0.67in * 7 .12in The inside reinforcement in the walls will be designed u sing #4 , Grade 60 , reinforcing bar . d =lOin( 2 in+ = 7.75in As req. = [0.85 * 6000 psi * 12in] *[7 .75 in_ 7 .75 in2 _ 24 * 5.29 * 1000 lbft ] 60000p i 0.95 * 0.85 * 6000p i * 12in A 0.15 in2 s req.= ft Check Maximum Reinforcement (LFD 8.16.3): As max= 0.75 * ( 0.85 * 6000 psi * 0.75 ] * ( 87000 J * 12 in* 7.75 in 60000 psi 87000 + 60000 psi A 2 . 63in2 smax=ft 170
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Check Minimum Reinforcement (LFD 16.8.5.8 ) : A min = 0.002 * 12 in * 10 in 0 ?4' 2 A . m min=ft Try #4's @ 7 inc h es on center : Asprovided= 12 i n *. 196in2 =0.34in2 7 Check Crack Control ( L F D 16.8.5.7 ) : Cal c ulate A llowabl e S tress, f sa: f < f 98 ksi s _ sa= 'Vdc*A d 2 . 0.50 in 2 ?5. c = ill+ = tn 2 A= 2*2.25 *12in = 31.50 12 7 fsa = 98 ksi = 23.68 ksi V2.25 in * 31. 5o 171
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Calculate actual stress in reinforcement: n = 29000000p i = 6 _18use 6 (150lb/ft3l5 l2in*x2 2 x = 1.46in 6 *0.34in2 *(7 .75inx)=O . . d d x 7 75 . 1.46 in 7 26. J'i' = = . m= . m 3 3 fs= Ms = 4 07kft* l 2 ok As * j * d 0.34in2*7.26in 6.2.1.7 Calculate shear (LF D 8.16.6.2 ) The allowable hear in the threesided structure i s calculated using the simplified equation . Shear in the Deck: Vu Vu = 14.23 kip eve= e * 2 * Fc * b * d eve= 0.90 * 2 * p i * 12 in * 11.75 in= 19659.261b = 19.65 kips = 19.65 kips> 1 4.23 kips OK 172
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Shear in the Walls: Vu Vu = 5.07 kips eVc=e* 2 *Fc* b * d eve= 0 . 90 * 2 * psi * 12 in * 7.75 in= 12966.7lb =12.97 kips = 12.97 kips> 5.07 kip s OK 6.2.1.8 Summary Figure 6 . 22 illustrates the required reinforcement for the inside face and outside face of the side walls , top s lab , and bottom slab. 2" #5 @ 3.0" O.C. # 4 @ 6.00" O.C . # 4 @ 6 . 00" o.c. #5 @ 3.00" STEEL S ECTION Figure 6.22 LFD Reinforcement Placement for Design Example #2 173
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6.2.2 Standard LRFD Specifications 6.2.2.1 Vertical and Horizontal Earth Pressures: The design vert ical earth pressure on the top of the culvert is calculated as: WuSL = ys* Z WuSL = (120 pet)* (1. 0 ft) = 120 psf Similar to the Standard AASHTO Specifications, the lateral earth pressure (E H ) on the cul vert i s found using the equivalent fluid method. However , the LRFD Specification s does no t pecify minimum a nd maximum equi va lent fluid press ure. This is taken into account in the load factors, a n d loading combinatio ns. An equivalent fluid pressure of 30 pcf is as umed. At the top of the c ul vert, the latera l earth pressure is calc ul ate d as: EH = EFP* Z EH = (30 pet) * ( 1 ft) = 30 psf At the bottom of the cu l vert, the lateral earth pressure is calc ul ated as: 14 EH = (30 pet) * (1ft+ft +10ft) = 365 p sf 12 Figure 6.23 illustrate s the vertical and lateral earth pre ss ures a ppli ed to the threesided struc ture. 174
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EV = 120 psf EH = 30 psf ! t t t t I I I I l I I I I I I I l t I I I II I t EH = 30 psf I 1 ' ! I ! I r â€¢â€¢ â€¢ I I I 1 f ! : 1 ! i f I : L . I EH = 365 psf EH = 365 psf Figure 6.23 LRFD Vertical and Lateral Earth Pressures 6.2.2.2 Live Load Surcharge The Live Load Surcharge pres s ure i s calculated utilizing an equivalent height of s oil, Heq. The equivalent height of soi l , Heq , is determined as a function of the wall height in Table 4.4. The wall height is con s idered to be the distance between the top surface of backfill and the footing bottom . Figure 6.24 illustrates the wall height used in this example . After linear interpolation the equivalent height of s oil was determined to be 2.68 ft. 175
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1 3' 2 " I â€¢ .. I I â€¢ I Figure 6.24 LRFD Wall Height The live Load Surcharge is calculated as: LLS = EFP * Heq LLS = (30 pcf) * (2.68 ft) = 80.4 psf Figure 6.25 illustrates the Live Load Surcharge pre s ure applied to the threesided structure . 176
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LLS = 80.4 psf LLS = 80.4 psf Figure 6.25 LRFD Live Load Surcharge Pressure 6.2.2.3 Dynamic Load Allowance: The increase in the Live Load due to the dynarrlic load effects varies for varying burial depths. The Dynamic Load Allowance is only applied to the Design Truck and Tandem Load , and not the Lane Load . The Dynarrlic Load Allowance for a fill depth of 1.0 ft is calculated as: IM=33* (10.125 *DE) 0 % IM = 33 * (10.125 *1ft)= 28.875 % 6.2.2.4 Design Live Loads: The design live loads include the HL93 Design Truck, Design Tandem, and Lane Loads. 177
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Similar to the Standard AASHTO Specifications , the Standard LRFD Specification allows for the live load to be divided into s trip widths . However the LRFD Specifications require that the axle is distributed over a distribution width E in instead of a line of wheels. Determine the Equivalent Strip Width: Deck span betewwn centerline of walls= 20ft+ 0.83 ft = 20.83 ft Ewidth = 8 + 0.12 * Span Ewidth = 8 + (0.12 * 20.83 )= 10. 5 ft The Design Truck produces a live load va lu e of: PLL = 32000 lbsl Axle = 3047 .6lbs I (ftwidth) 10.5 ft PuLL= 1.75 * 1.29 * 3047.6lb I (ftwidth) = 6880 lb s I (ftwidth) The Standard LRFD Specifications also take into account the tire contact area and the distribution of the tire through any earth fill. The load can then be converted from a point load to a patch load. The length of the patch load is calculated as: Espan = Lt + LLDF *(H) Espan = 0 . 83FT + 1.15 *LOft<== 2.0ft 178
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The Design Truck produce s a live load pre sure of: Wull =PuLL E pan Wull = 6880lb I (ftwidth) = 3440 psf 2ft The Design Tandem produces a live load value of: PLL = 25000 lb /Axle= 2381.0 lbs I (ftwidth ) 10.5 ft PuLL= 1.75 * 1.29 * 2381lb I (ftwidth) = 5375 . 0 lbs I (ftwidth) The Design Tandem produce s a live load pressure of: Wull =PuLL Epan Wull = 5375 . 0 lb I (ftwidth)= 2687 . 5 psf 2ft The Lane Load produce a live load pressure of: WuLL = 640 plf * MPF = 64psf * MPF 10ft The Single De ign Truck produce the maximum live load intensity; however the Single Design Tandem has a larger influence area. After analysis it was 179
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determined the Single Design Tandem controlled the design . Therefore the Lane Load produces a live load pressure of: WuLL = 640 plf * 1.2 = 64 psf * 1.2 = 76.8 psf 10ft 6.2.2.5 Load combinations: For both the strength and service limit states , three load cases are considered. The load cases are as follows. The loading configurations are illustrated in Figure 6.26. The load cases correspond to: â€¢ Case 1: Maximum vertical loads on deck, minimum lateral loads on legs. This case produces maximum stresses in the bottom of the deck. â€¢ Case 2: Maximum vertical and horizontal loads on the str ucture. The case produces maximum stresses on the comer of the deck, and outside walls. â€¢ Case 3: Minimum vertical loads on deck, and maximum horizontal loads on walls. This case produces maximum stresses on the inside of the leg. The load combinations are as follows: Strength: 1. U = 1.25 *DC+ 1.30* EV + 0.90 * EH + 1.75 * (LL+ IM) 2. U = 1.25 *DC+ 1.30 * EV + 1.50 * EH + 1.75 *LS + 1.75 * (LL+ IM) 3. U = 0.90* DC+ 0 . 90* EV + 1.50 * EH + 1.75 * LS 180
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Service: 1. U = 1.00* (DC+ EV + EH + (LL+ IM )) 2. U = 1.00 *(DC+ EV + EH + LS + (LL + IM ) ) 3. U=l.OO*(DC+EY+EH+LS) Similar to the Sta ndard AASHTO Specifications the structure wa modeled assuming a pinpin connection specified in section 12.14.5 of the LRFD Specifications. Table 6.5 li t the critical tre s e for each load combination at the critical locations. The locations of the critical tre s es are shown in Figure 6.26. 181
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r l! 1 LL = 422 . 6 psf t j j j j j j j j t t j L L = 76 . 8 psf oonnnnJIOoooon t II t i i i i i 4 4 4 I I t t I t II i i = 600 pst ,.;..,. .. . . EH = 150psf Case 1 EH = 485 psf rt L L = 422. 6 p s f o o I o n n n o psf + J t llll + + I i i i i i i i i J I t t t t n E = 600 pst ! J t t t t t t t I i 4 4 4 4 i 4 4 J J I t t I tiLLS= 68.4 psf EH = 15 0psf ...... Case 2 EH = 485 psf EV= 600 p sf + 1 o o o o n n n o 1 1 o o ULLs = 68.4 psf .. . !( . . Cas e 3 E H = 150 psf E H = 485 psf Figure 6.26 Loading Configuration, Cases 1 3 1 82
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___ , I 1 I I I I I 1 I I I I I I I I I I I I I : ill Figure 6.27 Locations of Critical Stresses I I I I I I I I I I I I I I Table 6.7LRFDStructural Analysis Results per Foot Width, Example 2 t1) u t1) C/) ... 1 2 3 4 Location 1 2 3 4 Load Case 1. C,t: "...... a> I co (/) E c.. Q)Q. .s= 0 cn6 :26 0.00 0 . 00 21.84 3.18 12.36 14.54 53.82 3.54 Load Case 1 . .......... c"....... wj co (/) Ea. Q)Q. .s= 0 cn6 :26 0 . 00 0.00 13.73 2 . 36 8.11 9.03 32.98 2.02 Load Case 2. Load Case 3 . c .... "...... c"....... wco (/) wco (/) Q) c.. E Q) c.. .s= .s= 0 cn6 0 cn6 :26 :26 0.32 0.66 3.37 2.09 21.58 4.31 3.89 2 . 34 14.14 14.54 4.28 2.39 52.05 3.54 6.47 0 . 00 Load Case 2. Load Case 3 . .......... .......... C,t: "....... c,_ ....... a> I co (/) wco (/) Ea. Q) c.. E Q) 0. .s= .s= 0 cn6 0 cn6 :26 :26 0 . 00 0.41 1.47 1.12 13 .61 2.72 4.49 1.71 8.67 9.03 3.35 2.65 32.42 2.02 8.60 0 . 00 183
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6.2.2.6 Reinforcing Design The bottom reinforcement for the deck will be designed u sing #7 , Grad e 60, reinforcing bars. . ( rebar diameter ) d =slab thicknessc lear cover+ 2 d = 14 in( 2 in+ in) = 11.56 in A req.= [ 0.85 *fc*b]*[dd2 _ 24*Mu ] fy q>* 0 .85* f c * b A s req. = [0.85* 6000 p i *12 in ]*[11.56 in_ 11.56 in 2 _ 24 * 53.82 * 1000 ft. ] 60000 psi 0.95 * 0.85 * 6000 psi* 12m 1.03 in 2 A req.=ft Try #7's @ 7 inches on center: A s provided= 12 in * 0.60in 2 = 1.03in 2 7 184
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Check Maximum Reinforcement Ratio (LRFD 5.7.3.3 ) : c A max =::; 0.42 d c = A s pro v * fy ::; 0.4 2 d 0.85 * f c * b * d c 1.03 in 2 * 60000 psi = = 0.12$ 0 .42ok d 0.85 * 6000 psi * 12 in* 0. 75 * 11.56 in Check Minimum Reinforcement (LRFD 12.14.5.8 ) : A min = 0.002 * b * h Asmin = 0.002 * 12 in* 14 in A . 0.34in2 smm =ft 185
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Check Crack Control (LRFD 12.14.5.7): Calculate minimum allowable spacing to satisfy cracking (LRFD 5. 7.3.4): 700 * y s :5; e 2 * de d 2 . 0.875 in 2 44 . c= m+ = . m 2 = 1 + de = 1 + 2.44 in = 1.30 s 0.7 *(hdc) 0.7 *(14in2.44in) ye =expo ure factor = 1.00 Calculate actual stress in reinforcement: n = 29000000 p i = 6.18 u s e 6 (150 lb/ft3)I.5 * 33 * psi ) 12. * 2 m x 6* 1.03in2*(11.56inx)=O 2 x = 2.98in 186
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0 * d d x 11 56 2 098 in I 0 57 J 0 m. m 3 3 f s = M s = 32098 kft * 12 = 36035 k s i A s* j * d 1.03in2* 10057in 700 * 1.00 2 * 2.44 in = 9 . 93 in 1030 * 36 . 35 ksi Actual Spacing= 7.0 in 9093 in OK Calculate Maximum Spacing of Reinforcing (LRFD 5.10.3.2 ) s rriax = 1.5 * h 18in smax = 1.5 * 14in = 21 in therefore u s e 18 in Actual Spacing= 700 18 in OK Calculate Minimum Spacing of Reinforcing (LRFD 5.10.3.1 ) s db= .6 25 in 1.33 * Ag = 1.33 * 0 .75 in= 1.0 in 1.0 in Actual spaci ng= 6 in OK 187
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The top reinforce m ent in the deck will be designed u sing #4, Grade 60, reinforcing bars. d 14. (2. 0 .50 in) 11 75. = mtn+= . In 2 As=[0.85* 6000psi *l2in]*[ll.7Sinl1. 7 Si n2 _ 24 *14.14* 1000lbft l 60000psi 0.95 * 0 .85*6000 p i â€¢ 12in A 0.26in2 req . ft Try #4's @ 3.5 inches on center: As provided = 12 in * 0 . 196 in 2 = 0 .67 in 2 3.5 Check Maximum Reinforcement Ratio (LRFD 5.7.3.3): c 0.67 in 2 * 60000 p i 0 .07 0.42 ok d 0.85 * 6000psi*12in*0.75*11.75in Check Minimum Reinforcement (LRFD 12.14.5.8): Asrnin = 0.002 * 12 in * 14 in A . 0 .34 in2 ffiln = ft 188
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Check Crack Control (LRFD 12.14.5.7): Calculate minimum allowable spacing to satisfy cracking (LRFD 5. 7.3.4): 700 * r . s $ e 2 :rdc d 2 . 0.50 in 2 25 . c= m + = . m 2 = 1 + de = 1 + 2.25 in = 1.27 s 0.7 * (hde ) 0.7 *(14 in2.25 in) ye = exposure factor = 1.00 Calculate actual stress in reinforcement: n = 29000000p i = 6.18u se6 (150lb/ft3)1.5 12. * 2 m . x 6 * 0.67 in 2 * (11.75 inx ) = 0 2 x = 2.50in 2.SOin =10.92in 3 3 f s = M = 8 .67kft*l2 =14.22ks i As* j * d 0.67 in 2 * 10.92 i n 189
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700* 1.00 s 2 * 2 . 25 in = 34.32 in 1.27 * 14.22 ksi Actual Spacing= 3.5 34 . 32 in OK Calculate Maximum Spacing of Reinforcing (L RFD 5.10.3.2 ) max= 1.5 * h 18in smax = 1.5 * 14in = 21in therefore u e18in Actua l Spacing= 3 .. 5 18 in OK Calcu lat e Minimum Spacing of Reinforcing (L RFD 5.10.3.1 ) s min;:::: db= .625 in 1.33 * Ag = 1.33 * 0.75 in = 1.0 in 1.0 in Actual spacing= 3.5 in OK The outside reinforcement in the walls will be de igned using #4 , Grade 60, reinfo r cing bars. d 10. ( 2 . 0 . 50 in) 7 75. = mm+2 . = . m As=[0.85* 6000psi *l2in]*[7 .75in7 _75in2 24*21.84*10001bft l 60000psi 0 .95* 0.85*6000p i â€¢l2in A 0 . 62in2 sreq.= ft 19 0
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Try #4's @ 3.5 inche s on center : A " d d 12 in 0 196 ? 0 6 ? provt e = "' . m = . 7 m 3.5 Check Maximum Reinforcement Ratio (LRFD 5.7.3.3): c 0.67 in 2 * 60000 psi = = 0.11 0 . 42 d 0 .85* 6000 p s i *12 in * 0.75 * 7 .75 in Check Minimum Reinforcement (LRFD 12.14.5.8): Asmin = 0.002 * 12 in * 10 in A . 0.24in2 Tnln =ft Check Crack Control (LRFD 12.14.5.7): Calculate minimum allowable spacing to satisfy cracking (LRFD 5.7.3.4): 700* s ::5: Y e 2 *de * fs d 2 . 0.50 in 2 25 . c= m+ = . m 2 = 1 + de = 1 + 2.25 in = 1.41 s 0.7 *(hdc) 0.7 *(10in2.25in) ye =exposure factor= 1.00 191
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Calculate actual stress in reinforcement: n = 29000000 psi = 6 .18 u e 6 (150 lb/ft3 ) 1.s * 33 * p s i ) 12 . * 2 m x 6* 0 .67in2*(7.75inx)=0 2 x = 1.97 in j * d = d= 7.75 in1.97 in = 7.09 in 3 3 fs= M = 13.73kft*l2 = 34 . 68k i As * j*d 0.67in2 *7.09in 700* 1.00 s $ 2 * 2.25 in = 9.81 in 1.41 * 34.68 ksi Actual Spacing= 3.5 in$ 9.81 in OK Calculate Maximum Spacing of Reinforcing (LRFD 5.10.3.2) s max = 1.5 * h $ 18in smax = 1.5 * 14in = 21 in therefore use 18 in Actual Spacing= 6 . 0 in $18 in OK 192
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Calculate Minimum Spacing of Reinforcing (LRFD 5.10.3.1) s db= .625in 1.33 * Ag = 1.33 * 0.75 in = 1.0 in 1.0 in Actual spacing= 3.5 in OK Th e inside reinforcement will be de s igned usin g #5 , Grade 60 , reinforcing bar s . d 10. (2. 0 . 625 in) 7 69. mm + . m 2 As=[0.85* 6000p s i * 1 2in]* [ ? .69in7 _69in2 _ 24* 3 .37* 100 0Ibft l 60000 p s i 0 .95 * 0.85 * 600 0 p s i * 12 i n A 0 .09i n2 req.=f t Try #5's @ 14.00 inche s on center : As provided= 12 in * 0.306 in 2 = 0.262 in 2 14.00 Check Maximum Reinforcement Ratio (LRFD 5.7.3.3): c = 0.262 in 2 * 60000 psi = 0.0 4 0.4 2 d 0.85 * 6000 psi * 12 in * 0.75 * 7.69 in 193
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Check Minimum Reinforcement (LRFD 12.14.5.8): A min= 0.002 * 12 in* 10 in A . 0.24in2 smm=ft Check Crack Control (LRFD 12.14.5.7): Calculate minimum allowable spacing to satisfy cracking (LRFD 5.7.3.4) : 700 * y e 2*d s c * fs d 2 . 0.625 in 2 3 1 . c= m+ = . m 2 = 1 + de = 1 + 2 . 3 1 in = 1.43 5 0.7 * (hdc) 0.7 * (10i n2.3lin) ye =expos ur e factor= 1.00 194
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Calculate actual stress in reinforcement: n = 29000000 psi = 6 . 18 use 6 (150 lb/ft3 / 5 * 33 * psi ) 12 in * x 2 6 * 0.262 in 2 * (7.69 inx) = 0 2 x = 1.30in * d d x 7 69 1.30 in 7 26 J " = = . 10= . 10 3 3 M 1.47kft* 12 fs = = 2 = 9.27 k i A * j * d 0.262 in * 7.26 in 700 * 1.00 2*2.31in=48.16in 1.43 * 9 .27ksi ActualSpacing = 14.00in 48.16 in OK Calculate Maximum Spacing of Reinforcing ( LRFD 5.10.3.2 ) smax=l.5*14in=2lin therefore u el8in Actual Spacing= 14.00 18 in OK 195
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Calculate Minimum Spacing of Reinforcing (LRFD 5.10.3.1 ) db= .625in 1.33 * Ag = 1.33 * 0 . 75 in = 1.0 in l .Oin Actual spaci ng= 14.00 in OK 6.2.2.7 Calculate shear (LRFD 5.8.3.3): The allowable s he ar in the threeside d st ructur e i calculated using the simplified equ ation. Shear in the Deck: eve Vu = 14 .54 kip eve =e * b * dv dv = maximum vulue of 0 .9*d or 0 .72*h 0.9 * de = 0.9 * 11.75 = 10.58 0.72 * h = 0.72 * 14 = 10.08 eve= 0 . 90 * 2 * p i * 12 in * 10.58 in= 17701.7lb = 17.70 kip = 17.70 kips> 14.54 kips OK 196
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Shear in the Walls: Vu Vu = 4.31 kip s * b *dv dv = maximum v ulue of 0.9 * d or 0.72 * h 0.9 *de= 0.9 * 7 .75 = 6.98in 0.72*h =0.72 *10=7.2in eve= 0.90 * 2 * psi * 12 in* 7.2 in= 6023.3lb = 6.02 kips = 6 . 02 kips> 4 .31 kips OK 6.2.2.8 Summary Figure 6 . 28 illustrates the required reinforcement for the inside face and outside face of the side walls, top sla b , and bottom lab. . A comparison between both de signs with regard s to the area of steel required is pre sente d in Table 6 . 3. Table ().8 Area of Steel compari s on Location 1 : 2 3 4 LFD 0.15 : 0.57 0.28 0 . 94 LRFD 0 . 09 : 0.62 0.26 1 . 03 197
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2" 2" # 7 @ 7.0" O .C. #4 @ 12.00" o.c. #5 @ 14.00" o.c. #4 @ 3 . 50 " STEEL S E C TION Figure 6.28 LRFD Reinforcement Placement for Design Example #2 198
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Chapter 7 Summary and Conclusions The objective of this thesis wa to examine and compare the current LRFD Desig n Speci fications and the Standard AASHTO Specification s used in de igning underground preca st concrete structures s uch as underground utility structures, drainage inlets, threesided st ructure s, and box culverts. This thesis compares relevant provisions from both specificatio ns. Provisions discussed within this document include: terminology, load factors, implementation of load modifiers, load combination , multiple presence factors, design vehicle live loads, distribution of live load to s labs , and through earth fill, live l oad impact, and live load s urcharge. A brief summary of each a major provision and its impact on design i s as follow : â€¢ De sign Vehicular Live LoadsThe de s ign truck, and application i s identical in both specifications . However, the LRFD provi ions require an additional distributed load of 0.64 klf be added to the live load model. In addition, the Design Tandem Truck , whic h replaced the Alternative Military Loading from the Standard Specifications , is 4% heavier. â€¢ The LRFD Specifications introduced the use of a multiple presence factor. For a single loaded lane the multiple presence factor is 1.2. The multiple presence factor is similar to the load reduction factor in the 199
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Standard Specification s . The load reduction factor for a sing le loaded lane is 1.0. Thus, comparing the two factors result in an increase from 1.0 to 1.2 for one loaded lane. This balance s the reduction in the live load factor. The Standard Specifications require a live load factor of 2.17, while the LRFD Specification s require 1.75 . With the introduction of the multiple pre sence factor, the live load fac tor in the LRFD Specifications converts to 2.1. â€¢ Dynamic Load Allowance (Impact) Both specifications require an increase in the live load with respect to the earth fill depth. The LRFD Specification s require an impact factor be applied up to a fill depth of 8 ft. The Standard Specification s neglects the effects of impact for depth greater than 3 ft. In general, the requirements in the Standard LRFD Speciation produce a greater load effect than does the Standard Specifications . â€¢ Lateral Live Load SurchargeBoth specifications require an increase in the lateral earth pre ss ure due to the live load. The Standard AASHTO Specification s require a live load s urcharge pre s ure of 2ft, regardless of structure type and geometry. The Standard LRFD Specifications calculates the live load surcharge height as a function of the structure's wall height. The lateral live load surcharge pressure is 200
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significantly greater in the Standard LRFD Specification than the Standard AASHTO Specifications. â€¢ Distribution of Wheel Loads Through Earth Fill Both specifications allow for the live load to be distributed through earth fill. The LRFD Specifications allow the dimension s of the tire to be utilized. However the LRFD Specifications generally produce greater load effects. The live load distribution areas are complicated; particularly when multiple loads from several vehicles overlap. There is continuing research being performed by the FHW A in order to simplify the calculations. â€¢ Load Factors and Load Combinations Both specifications utilize load factors and strength reduction factors. However, the load and resistance factors are determined through statistical studies and are more accurate in the Standard LRFD Specification. There is greater reliability and a more uniform factor of safety when utilizing the LRFD Specifications. The provisions in the LRFD Specifications are more concise and more beneficial to design engineers with the addition of the commentary. Therefore, the code is simpler to apply than the Standard Specifications . There is still a great amount of research that must be performed, especially when examining the distribution of live load through earth fill. Design engineers proficient with the 201
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Standard AASHTO Specifications should ha ve little trouble converting to LRFD Specifications as some level of familiarity and comfort is attained. 202
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References American Association of State Highway and Transportation Officials (AASHT O). Standard Specifications for Highway Bridges. 17th ed. Washington: GPO, 2002 . LRFD Bridge Design Specifications. 3rd ed. Washington: GPO, 2005. American Concrete Pipe Association (AC PA). Highway Live Loads on Concrete Pipe . Irving , TX: ACPA, 2001. Bloomquist, D. G., and Gutz, A. J. Evaluation of Precast B ox Culvert S vste ms Design Live Loads on Box Culverts. Gainesville , FL: Univer s ity of Florida , 2002. DeStef ano, R. J., Evans , J., Tadros , M. K., and Sun, C. "Flexural Crack Control in Concrete Bridge Structure s." Florida Dep artme nt of T . ransportation.2004. 1 May .2006 "LRFD: Achieving Greater Reliability and Service for Bridges." Focus . July 2004. U.S. Department of Transportation Federal Highway Division. 10 May.2006 < http://www.tfhrc.gov/focus/july04/0l.htm>. "LRFD: S tate Departm ent of Transp01tation LRFD Implementation Plan Initial Draft. " Bridg e Technology. 15 Apr. 2006 . U.S . Departme nt of Transportation 203
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Federal H ighway Div i s i on . 1 6 Apr. 2006 . National Cooperative Highway Re s earch Program (NCHRP ) . "Development of Comprehensive Bridge Specification s and Commentary ." Research Result s Digest 198 (1998 ) . " Project 1529: Design Specifications for Live Load Distribution to Buried Structures. " N a tional Cooperative High way Research Program. 6 Apr. 2006. Tran s portation Research Board. 6 Apr. 2006 . " Project 1 233: Development of a Comprehen s ive Bridge Specification and C o mmentary. " National Cooperative Highway Re s earch Program. 2 4 May. 2006. Transportation Research Board. 26 May 2006 . Rund , R. E., and McGrath , T . J . " Comparison of AASHTO Standard and LRFD Code Provi s ions for Buried Concrete Box Culverts. " Concrete Pipe for the New Millennium: ASTM STP 1368 . Ed. I. I. Ka s par and J. I. Enyart. Wes t Conshohocken , PA: American Society for Testing and Material s, 2000 . 45 60. 204
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Sanford, T. C. "SoilStructure interaction of buried Structure s . " Transportation Re earch Board . 2000. 2 Apr 2 006 . . Tonias, D . E. Bridge Engineering. United Stat es of Ametica: McGrawHill , 1995 . United St ates. Federal Highway Administration (FHA). Load and Re sistance Factor Design (LRFD) for Highway Btidge Substructures: NHI Course No. J 32 068. HI98032 . Washington: GPO, 2001. 205

