Citation
Comparison between the standard AASHTO bridge design specifications and the AASHTO LRFD bridge design specifications for buried concrete structures

Material Information

Title:
Comparison between the standard AASHTO bridge design specifications and the AASHTO LRFD bridge design specifications for buried concrete structures
Creator:
Miller, Larry james
Place of Publication:
Denver, CO
Publisher:
University of Colorado Denver
Publication Date:
Language:
English

Thesis/Dissertation Information

Degree:
Master's ( Master of science)
Degree Grantor:
University of Colorado Denver
Degree Divisions:
Department of Civil Engineering, CU Denver
Degree Disciplines:
Civil engineering
Committee Chair:
Durham, Stephan A.
Committee Members:
Rens, Kevin L.
Janson, Bruce

Record Information

Source Institution:
University of Colorado Denver
Holding Location:
Auraria Library
Rights Management:
Copyright Larry James Miller. Permission granted to University of Colorado Denver to digitize and display this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.

Downloads

This item has the following downloads:


Full Text
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
W-'Vo -
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 state-of-the-art 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 long-term 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, three-sided 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 candidate’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. 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.


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 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 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 Three-Sided 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 HS-20 Distribution through Earth Fill.....................................108
6.5 Alternative Military Distribution through Earth Fill......................109
6.6 LFD Service Loading Configuration, Cases 1-3..............................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 1-3............................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 1-3........................................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 HS-20, HS-25, 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 (”LRFD: State Department” 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 (“LRFD: State Department” 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, reliability-based 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 12-28(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


Investigator. The list of tasks for this project and the brief outcome are listed below (NCHRP 1998).
• 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, reliability-based, limit states specification.
• 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. “Gaps” were areas where coverage was missing; “Inconsistencies” were internal conflicts, or contradictions of wording or philosophy. Numerous gaps and inconsistencies were found in the Standard Specifications.
• Task 3 - Assess the feasibility of a probability-based 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 probability-based specification was more suitable.
• 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 12-28(7) were presented to the AASHTO HSCOBS in May of 1987. There were 7 options that were available:
• Option 1 - Keep the Status Quo
• Option 2 - Table Consideration of LRFD for the Short Term
• Option 3 - Immediate Adoption of the OHBDC
• Option 4 - Replace Current with LRFD Immediately
• Option 5 - Replace Current LFD with LRFD in the Near Term
• Option 6 - Develop LRFD for Evaluation Only, or
• Option 7 - Develop LRFD as a Guide Specification
A recommendation was made to develop a probability-based limit states specification, revise as many of the gaps and inconsistencies as possible, and develop a commentary specification. Thus NCHRP Project 12-33, entitled “Development of Comprehensive Specification and Commentary,” began in July of 1988. The primary objective was to develop a recommended LRFD-based 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; soil-structure 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 12-33 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 (“LRFD: Achieving Greater Reliability” 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 State-Specific 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:
• 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.
• Design Transition Strategy: Set a target date for full LRFD implementation on all new and replacement bridges and on all in-house and consultant projects. Perform in-house 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 one-step 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.
• 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
• Training: Sponsor in-house training courses for all designers (by in-house instructors, local universities instructors, industry, or by FHWA). Acquire LRFD design examples and software for hands-on training. Require that consultants attend LRFD training before they perform LRFD designs in a particular state.
• 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


• Documentation Support: Update standards, manuals, and guidance to coordinate with the LRFD Specifications. Develop pre-designed LRFD decks and barriers to shorten the design process if standardized designs are not available. Contract services to update existing design materials to LRFD.
• Fine-Tune Documentations: After the completion of the pilot project and/or full LRFD conversion, fine-tune 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, three-sided 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:
• A comprehensive literature review of existing and current studies associated with the Standard LFD and LRFD Specifications.
• A detailed summary of the variables and design methodology for buried precast concrete structures using the AASHTO LFD Standard Specifications.
• A detailed summary of the variables and design methodology for buried precast concrete structures using the AASHTO LRFD Bridge Design Specifications.
• A thorough comparison between the LRFD and LFD specifications.
• Two design examples illustrating the use of both specifications. The examples are of a buried three-side precast concrete structure.
• 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 state-of-the-art 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 AASFITO 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 15-29 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 15-29, 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 15-29 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 20th, 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 semi-infinite, homogenous, isotropic, weightless, elastic half-space, shown in Figure 2.1. The value of the vertical stress can be calculated using Equation 2.1.
P(3Z3) Equation 2.1
°I = 2^(r2+z2)5'2
Where:
P = Point load
Z = Depth from ground surface to where Gz is desired r = Horizontal distance from point load to where <57 is desired
17


p
'

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.

z~o
1 + 2

n3/2
\Z)
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 = CsPFBc
Equation 2.4
19


Where:
Wsd = Load on pipe in lb/unit length P = Intensity of distributed load (psf)
F’ = 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.
o. =
£
Load
(B + Z)(L + Z)
Equation 2.5
Where:
az = 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:
2300
^ Equation 2.6
21


Where:
Oz = 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)
+ P EQ EQ + P ICE 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:
• Service Load Design (Allowable Stress Design or Working Stress Design)
• 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
fi FACTORS
GROUP y D (L+I)n (L+')p CF E B SF W WL LF R+S+T EQ ICE %
1 1.0 1 1 0 1 Pe 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
Q < 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
GC 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 Pd 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 Pd 0 1 1 Pe 1 1 0 0 0 0 0 0
z o II 1.3 Pd 0 0 0 Pe 1 1 1 0 0 0 0 0 LU _J
CO LU III 1.3 Pd 1 0 1 Pe 1 1 .3 1 1 0 0 0 CD < o _l Q-
cc o IV 1.3 Pd 1 0 1 Pe 1 1 0 0 0 1 0 0
h- o V 1.25 Pd 0 0 0 Pe 1 1 1 0 0 1 0 0 Q_ <
< LL Q VI 1.25 fio 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
Pe 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)
Pe Earth Pressure 1.3 Lateral earth pressure for retaining walls and rigid frames excluding rigid culverts
Pf Earth Pressure 0.5 Lateral earth pressure when checking positive moments in rigid frames
Pf Earth Pressure 1.0 Rigid culverts
Pe 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 three-sided 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 Y,Q, ^ 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, 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 In-Place 0.90 0.85 NA
Reinforced Concrete Box Culverts, Cast In-Place 0.90 0.85 NA
Reinforced Concrete Box Culverts, Precast 1.0 0.90 NA
Precast Reinforced Concrete Three-Sided 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.
H-20-35 LOADING
H-15-35 10A0INC
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
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 HI0-44. 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


HS20-44 8,000 lbs. 32,000 lbs. 32,000 lbs.
HS15-44 6,000 lbs. 24,000 lbs. 24,000 lbs.
H20-44 8,000 lbs. 32,000 lbs.
H15-44 6,000 lbs. 24,000 lbs.
MB
Figure 3.2 - Characteristics of the AASHTO Design Truck (AASHTO, 2002).
31


The H-15 and H-20 truck loading is represented by a two-axle single unit truck. The “S” in the HS15-44 and HS20-44 designates a semi-trailer 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 15-44 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 HS20-44 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 HS-25 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 HS20-44 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.
-6-0“
12 KIPS
12 KIPS
Direction
of Travel
4’—0"
12 KIPS
12 KIPS —
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.
HS-20
icr
L
-20’
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,
• When the earth fill depth is less than 2 ft.
• 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 soil-structure interaction based on the earth fill depth, side compaction, and bedding characteristics (Sanford 2006). Therefore the effects of soil-structure 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 soil-structure interaction factor, Fe, when designing reinforced concrete box culverts. The soil-structure interaction factor depends the on type of installation. For embankment installations, Fe is calculated using Equation 3.5, for trench installations use equation 3.6. The Standard AASHTO Specifications do not require the soil-structure interaction factor to be applied to three-sided concrete structures. It is important to note that the soil-structure interaction factor for reinforced concrete pipe differs from Equations 3.5 - 3.6. The soil-structure interaction factor for reinforced concrete pipe is beyond the scope of this thesis and is not discussed.
36


H
Fel =1 + 0.20
B,
Where:
Equation 3.5
Fei = Soil-structure interaction for embankment installations
< 1.15 for installations with compacted fill at the sides
< 1.4 for installations with un-compacted fill at the sides H = Earth fill depth, ft.
Bc = Out-to-out horizontal span of pipe or box, ft.
F, = W1
ez HBC Equation 3.6
Where:
Fe2 = Soil-structure interaction for trench installations
H = Earth fill depth, ft.
Bc = Out-to-out horizontal span of pipe or box, ft.
Ca = 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 LDAD
\ WuLL
i
I—------1.75 * H-----—I
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)
HS-20 Truck H < 3.43 16.000 (1.75 * H)2 16.000/(1.75 * H)2
HS-25 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)
HS-20 Truck 3.43 < H > 8.00 16.000 S = (1.75 * H) * (1.75 * H + 6) 32.000 / S
HS-25 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 OR TRAFFIC
figure 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)
HS-20 Truck 8.00 HS-25 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
DIRECTION Dr TRAFFIC
ALTERNATIVE MILITARY
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 HS20-44 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 HS20-44 Design Truck and Alternative Military Loading. The HS20-44 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 HS20-44 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 HS-20 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 20-44, HS 25-44, 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 HS25-44 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 HS-20, HS-25, 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 Looct
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.
>
77^
— —Member Width —— Effective ^-doint —— Memebr Width— J
Width — Member 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 + Wj / 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
o’o”- ro” 30%
1 to o 20%
2’i”-2’H” 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 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 one-half 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.
51


LIVE LDAD SURCHARGE
Figure 3.17 - LFD Equivalent Height
PRESSURE
Figure 3.18 - Live Load Surcharge Pressure
52


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.
r|i = Load modifier Yi = Load factors Qi = Force effects = 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:
53


LRFD Specifications (AASHTO 2005). Each of the four limit states are described below:
• STRENGTH - Requires the strength and stability be adequate for specified load combinations.
• EXTREME EVENT - Relates to events with extremely long periods of return (earthquakes, ice loads, vehicle collision, and vessel collision).
• SERVICE - Relates to stresses, deformations, and cracking.
• 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):
• STRENGTH I - Basic load combination related to normal vehicular use of the bridge without wind.
54


• STRENGTH II - Load combination relating to the use of the bridge by owner specified special design vehicles and/or evaluation permit vehicles without wind.
• STRENGTH III - Load combination relating to the bridge exposed to wind velocity exceeding 55 mph without live load.
• STRENGTH IV - Load combinations relating to very high dead load to live load force effect ratios.
• STRENGTH V - Load combinations relating to normal vehicular use of the bridge with wind velocity of 55 mph.
• EXTREME EVENT I - Load combinations including earthquake and flood.
• EXTREME EVENT II - Load combination relating to ice load or collision by vessels and vehicles.
• 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.
• SERVICE II - Load combinations intended to control yielding of steel structures and slip-critical connections due to vehicular live load.
55


• SERVICE III - Load combination for longitudinal analysis relating to tension in prestressed concrete superstructures.
• SERVICE IV - Load combinations relating only to tension in prestressed concrete substructures with the objective of crack control.
• 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.
56


Table 4.1- Load Combination and Load Factors
Load Combination DC DD DW EH EV ES EL LL IM CE BR PL LS TU CR SH Use one of Ttiese at a Time
Limit State WA ws WL FR TG SE EQ IC CT cv
STRENGTHS" (unless noted) Yp 1.75 1.00 . . 1.00 0.50/1.20 Ytg Yse . . . .
STRENGTH-II Yp 1.35 1.00 - - 1.00 0.50/1.20 Ytg Yse - - - -
STRENGTH-III Yp • 1.00 1.40 - 1.00 0.50/1.20 Ytg Yse - - - -
STRENGTH-IV EH, EV, ES, DW DC ONLY Yp 1.50 1.00 1.00 0.50/1.20
STRENGTH-V Yp 1.35 1.00 0.40 1.00 1.00 0.50/1.20 Ytg Yse - -
EXTREME EVENT-1 Yp Y.p 1.00 . . 1.00 . . . 1.00 . -
EXTREME EVENT-II Yp 0.50 1.00 - - 1.00 - - - - 1.00 1.00 1.00
SERVICE-I 1.00 1.00 1.00 0.30 1.00 1.00 1.00/1.20 Ytg Yse - - - -
SERVICE-II 1.00 1.30 1.00 - - 1.00 1.00/1.20 - - - -
SERVICE-IH 1.00 0.80 1.00 • • 1.00 1.00/1.20 Ytg Yse ■ - - -
SERVICE-IV 1.00 - 1.00 0.7 - 1.00 1.00/1.20 - 1 - - -
FATIGUE-LUM & 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:
57


• For each combination, load factors should be selected to produce the total extreme factored force effect. Both maximum and minimum extremes should be investigated.
• 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.
• The load factor which produces the more critical combination for permanent force effects should be selected from Table 4.2.
• 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.
58


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: Wearing Surfaces and Utilities 1.50 0.65
EH: Horizontal Earth Pressure
- Active 1.50 0.90
- At-Rest 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
-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, r)i. The load modifiers account for combined effects of redundancy, T|r, ductility, r)D, and operational importance, r)i. 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.
59


“Hi = "Hd *r\R *Tli ^°-95
Equation 4.2
- ~ ” -1 -05 Equation 4.3
Where:
rji = Load modifier r|D = factor for ductility % = factor for redundancy rji = factor for importance
The values for the ductility, redundancy, and importance factor are listed below:
• Ductility, r|D
> 1.05 for non-ductile 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: r)D = 1.00
• Redundancy, r|R
60


> 1.05 for non-redundant components and connections = 1.00 for conventional levels of redundancy
> 0.95 for exceptional levels of redundancy For all other limit states: % = 1.00
• Importance, rji
> 1.05 for important structures = 1.00 for typical structures
> 0.95 for relatively less important structures For all other limit states: rp = 1.00
When designing at the Service Limit State, T|d = % = T|i = 1-00 Typically the ductility of buried structures is 1.00. Buried structures are considered non-redundant 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.
61


4.3 AASHTO Standard Vehicular Design Live loads
The AASHTO LRFD Specifications require an HL-93 live load. This load includes two types of vehicular deign loads. The HL-93 Design live loads consist of a combination of the
• Design Truck or Design Tandem
• Design Lane Load
The Design Truck used in the AASHTO LRFD Specifications has the same configuration as the HS-20 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.
Km ■**»'
0"—J—4’-cf—L—6'—0”—J
HS-20
Figure 4.1- Characteristics of the Design Truck (AASHTO, 2005)
62


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 wheels is taken as 6.0 feet as shown in Figure 4.2.
Direction of Traffic
4’ - 0’
-6’ - 0”-
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
63


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
64


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 soil-structure 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 soil-structure 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
65


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.
• 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.
• 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.
66


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
67


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)
68


LLDF = factor for distributing the live load through earth fill 1.15 for select granular backfill 1.00 for all other backfill
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:
70


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)
HS-20 Truck H < 3.77 16.000 (1.15 * H + 0.83) (1.15 * H + 1.67) 16,000 / (A * B)
HS-25 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)
HS-20 Truck H < 4.33 16.000 (1.00 *H+ 0.83) (1.00 * H + 1.67) 16,000/(A *B)
HS-25 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 A-------^-l-^-----SPREAD A-------
-SPREAD B--------—I I—-------SPREAD B
Figure 4.6 Wheel Load Distribution through Earth Fill
71


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)
HS-20 Truck 3.77 < H < 11.44 16.000 (1.15 * H + 0.83 + 6) (1.15 *H +1.67 + 6) 32.000/(A * B)
HS-25 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)
HS-20 Truck 3.77 < H < 11.44 16,000 (1.00 * H + 0.83 + 6) (1.00* H+ 1.67 + 6) 32.000/(A * B)
HS-25 Truck 3.77 < H < 11.44 20,000 (1.00 *H + 0.83 + 6) (1.00* H + 1.67 + 6) 40.000/(A * B)
Tandem 3.17 Figure 4.7 - Overlapping Wheel Load Distribution through Earth Fill
72


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)
HS-20 Truck H > 11.44 16,000 (1.15 *H +0.83 + 6) (1.15 *H+1.67 + 6) 64,000 / (A * B)
HS-25 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)
HS-20 Truck H > 11.44 16,000 (1.00 *H+ 0.83+ 6) (1.00 * H + 1.67 + 6) 64,000/(A *B)
HS-25 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 (LOO* H + 1.67 + 6) (1.00 *H+ 0.83+4) 50,000/(A * B)
73


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


/ \ / \ / \ / \
rrrm â–  /TTTTTfTTV â–  i/i , i N
SPREAD A
Figure 4.9 - Overlapping Wheel Load Distribution by Passing Vehicles
Figure 4.10 - Overlapping Axle Load Distribution by Passing Vehicles
75


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 three-dimensional response to live loads. There are two cases that apply:
• Case 1 - When the traffic travels parallel to the design span.
• 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)
76


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 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 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.
77


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( 1 -0. 125De) / 0% Equation 4.8
Where:
Df. = 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).
78


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:
79


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) beq (FT)
5.0 4.0
10.0 3.0
I 20.0 2.0
80


Figure 4.13 - Wall Height for Live Load Surcharge Pressures
81


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:
• Design Truck
• Design Tandem
• 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 6-0 1 r 6’—0
12 KIPS 12 KIPS — 12.5 KIPS 12.5 KIPS

i
Direction
of
Travel
4’—0”
Direction
of Travel
4’-0”
12 KIPS 12 KIPS 12.5 KIPS 12.5 KIPS
Alternative Military Loading
Design Tanden
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.
84


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., Univer ity of Colorado at Denver , 1998 ' A thesis submitted to the University of Colorado at Denver in partial fulfillment of the requirement for the degree of Ma ter of Science Civil Engineering 2006

PAGE 2

Thi 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 Specification 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 A sociation of State Highway and Transportation Officials (AASHTO) Standard Design Specifications for underground precast concrete structures. Today, the bridge engineering profes ion i 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 state-of-the-art analysis and design methodologies, and make use of load and resistance factors based on the known variability of applied loads and material properties. Structures de igned with the LRFD specifications have a more uniform

PAGE 4

level of safety. Consequently, designs utilizing the LRFD Specifications will have superior serviceability and long-term maintainability. This thesis examines the current LRFD Design Specifications and the Standard AASHTO Specifications used in de igning underground concrete structures such a underground utility structures, drainage inlets, three-sided 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 co t to produce buried reinforced concrete structure . This the is compare 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 slab and earth fill, live load impact, live load surcharge, and the concrete de ign methodology for fatigue, shear strength, and crack control. The addition of the distributed Jane 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

PAGE 5

are more concise and more beneficial to design engineer with the addition of the commentary. Therefore, the code is simpler to apply than the Standard Specifications. Thi abstract accurately represents the content of the candidate's thesis. I recommend its publication . Stephan A. Durham

PAGE 6

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 Rhee , Clint Brookhart, and Jim Baker for giving me the opportunity to pursue this d egree . 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 spendi ng countless nights in front of my computer. It's finally over! I want to especially thank my beloved wife, Juli e Miller for putting up with me while working on this project. 1 know it has not been easy, thanks for hanging in there. I would also like to acknowledge by beauti ful daughter, Abigail Marie Miller in hopes that she will pursue her dreams as well. I love you all.

PAGE 7

TABLE OF CONTENTS Figure s ............................... . .. . .. . ...... . . . . . ........ . . .. . . ...................... x Tables ....... . ...................... . ............. ......... .............. . . .............. xi v CHAPTER 1. INTRODUCTION ........................... .... ................................. 1 Hi s torical Development o f LRFD Specification s ...... . . ......... 2 Problem Statement and Research Significance ...... .. . . . ......... 9 2. LITERATURE REVIEW ............................... ........ . ............ 11 Comparison of Standard Specification s and LRFD Specifications .... . ....... .. .. .. ...... . ................................ 11 American Concrete Pipe A s sociation Stud y ...................... 13 Flexural Crack Control in Concrete Bridges ..................... 13 National Cooperative Highway Research Program (NCHRP), Project 15 29 ............................................. 14 Des ign Live Loads on Box Culverts, University ofFlorida . . . .. . .. .. . ................................................... 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

PAGE 8

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 O verlap ................................................ .41 Case 3 -Full Di stribution of Wheel Loads from Multiple Axles ............................................... 42 Distribution of Live Loads for Depth s of Fill Less Than 2ft. ........................................................... ... 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 Pre sence Factors ........................................... 66 Case 1 -Depth of Fill is equal to or Greater Than 2 ft .. ........ . ................ ... ... ..................... 66 Vll

PAGE 9

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 Gre ater Than 2ft. .. .. .. . .. .. .. ............. ..... ..... .......... .... . . . ......... 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 Di strib ution of Wheel Loads from Multiple Axles Overlap .............................. 73 Case 4 -Distribution of Wheel Loads from Pa ssing Vehicles ............................ ........ ...... .. 74 Distribution 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 Loads .................... . . ... ... . . ... ..... 82 Vlll

PAGE 10

Multiple Pre s ence Factor. ....... . .. .. . ............ .. . . .............. 84 Dynamic Load Allowance , Impact. . . ................ . ......... .... 82 Lateral Live Load Surcharge .................................. ...... 88 Di s tribution of Wheel Load s through Earth Fill s for Depths of Fill Greater Than 2 ft.. ....................... 90 Di s tribution of Live Load s for Depth s of Fill Less than 2 ft. .................... .................................... 96 Load Factors and Load Combinations .. .......................... 98 6 . DESIGN EXAMPLES .. ..................................................... l03 Design Example #1 .................................... . .. .. ........ 103 De s ign Parameter s .............................................. . ..... 103 Standard AASHTO Specification s .. .................... 104 Standard LRFD Specifications .............. .................. 126 De s ign Example #2 ..... .......... .................................. 153 Standard AASHTO Specifications ...................... 153 Standard LRFD Specifications .......................... 174 7. SUMMARY AND CONCLUSIONS . .................................... 199 REFERENCES ................... . .................................................... . ....... 202 I X

PAGE 11

LIST O F FIGURES Figure 2.1 Bou ssines q Point Load . ......................... ... . ... . .. . . ........................ ....... 18 3 . 1 AASHO 1935 Truck Train Loading ..................................................... 29 3 . 2 Characteri s tic s of AASHTO De sig n Truck ........................................ 31 3.3 Characteristics of Alternative Military Loadin g ... .. ... . ............................... 33 3.4 Tire Contact Area .................................................................................................. 34 3.5 Earth Fill Depth and Vertical Earth Pre ss ure Loading ................................ 36 3.6 LFD Wheel Lo ad Di s tribution through Earth Fill.. ................ .............. ................ 39 3.7 Overlapping Wheel Load Di stri bution through Earth Fill. ...................... ...... ....... 39 3.8 Case 1, Wheel Load Distribution through Earth Fill .................................. 40 3 . 9 Ca se 2-Overlapping Wheel Load Di s tribution thro ugh Earth Fill. ................ 41 3.10 Case 3-O verlapping Wheel and Axle load Dist ribution thro u gh 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. Increa sing Design Spans ................... 46 3.14 LFD Distribution Width , E for a Single Wheel Load ........... . ... ........ . . ...... .48 3 .15 Effective Di stribution Width s on Slab s ... . ......... .................. . .. . ........ .... .48 3.16 R educed D istribution Width s on Slab s ....... . . .. .............................. ...... .49 X

PAGE 12

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 De s ign Tandem .. . . ............................................... 63 4.3 Earth Fill Depth and Vertical Earth Pre ss ure 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 Pa ssi ng Vehicle s .......................... 75 4.12 Dynamic Load Allowance vs. Burial Depth . .............. . . ...................... .... 79 4 .13 Wall Height for Live Load Surcharge Pressure s ........................... .. ........ 81 5 . 1 Alternative Military Loading vs. De sig n Tandem Loading ....... .............. ..... . 83 5.2 Increase of Force Effects due to De sig n 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 Distribution Areas for a Single Wheel.. ................................... 92 Xl

PAGE 13

5.7 Overlapping Wheel Load Distribution by Pa ss ing Vehicle s . .. . ............ . .. ...... 93 5 . 8 Overlapping Axle Load Distribution by P assing Vehicle s .. . .............. .. ....... . 93 5 . 9 Distributed Service Live Load Value s through Earth Fill with Impact. ............ 95 5.10 Distributed Factored Live Load Value s through Earth Fill with Impact.. ........ 95 5 .11 Service MomentLRFD vs. LFD De sign Live Loads (Multiple presence factor and impact neglected ) ...... . .. . .. . . .. . ..... . . ............................ . . ... 98 5 .12 Ser vice Moment-LRFD vs. LFD De s ign Live Loads ( Multiple pre se nce factor and impact included) ... . .. .......... .................. ... .. .. .................. 99 5.13 Load s on a Three-Sided Cul ve rt ....... .. ....... ... .............. .. .................... 101 6 . 1 Design Example #1, Geometry .. .. .. .................................................... 105 6.2 LFD Vertical and Lateral Earth Pre ss ures .. . . ....... . . ... .................... .. . ...... 106 6.3 LFD Live Load Surcharge Pre ss ure ................... ............................ ..... 107 6.4 HS-20 Di s tribution through Earth Fill ... . .. . . ...... . ........ . ........ .. ............... 108 6.5 Alternative Military Di s tribution through Earth Fill ...................... . .......... 109 6 . 6 LFD Service Loading Configuration, Ca s e s 1-3 ... .. . ........ .. ................. . . . 112 6.7 Critical Locations for Stresses .......... ... ...... . ... ...... . ... . ........... ...... .. .. ... 113 6.8 LFD Reinforcement Placement for De s ign Example #1 . ... ............ ................... . 126 6.9 LRFD Vertical and Lateral Earth Pressures ....... ... .......... .. .................... 127 6.10 LRFD Wall Height , Example #1. ............... ... . ...................... ..... . . .... . 128 6 .11 LRFD Liv e Load Surcharge Pressure ................................. : .. ............ 129 Xll

PAGE 14

6.12 Distribution area for De sig n Truck ................................................. .. . 131 6.13 Distribution area for two adjacent design vehicles .................................. 132 6 . 14 Di stributio n area for Design Tandem .. ............................................... 132 6 .15 De sign Example #1, LRFD Service Loading Configuration , Cases 13 ....... 136 6.16 Critical Locations for Stresses ........ ............ .. .............. ..................... 137 6.17 LRFD R einforcement Placement for D esign Example #1 .......................... 153 6.18 LFD Vertical and Lateral Earth Pressures ........................................... 155 6 .19 LFD Live Load Sur charge Pre ssure ................................................... 156 6 . 20 LFD Service Loading Configuration, Cases 1 3 ................................... 159 6.21 LFD Critical Locations for Stre sses .. ................................................. 160 6 .22 LFD Reinforcement Placement for De sign Example #2 ........................... 173 6.23 LRFD Vertical and Lateral Earth Pre ssures .......................................... 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 Reinforcem ent Placement for De sign Example #2 .......................... 197 Xlll

PAGE 15

TABLES Table 3.1 AASHTO Group Loading Coefficient s and Lo a d Factor s .............. . . . . . . . . . .. .. 26 3.2 AASHTO Earth Pre ss ure and Dead Load Coefficient s ................. ...... ......... 2 7 3.3 AASHTO Re s i s tan c e Factors for Underground Concrete Structure s ................ 29 3 .4 AASHTO Standard HS De s ign Truck Cl asses ........................ ................ . 30 3.5 Case 1 .. ............... . . . .............. .. .. . . .............. .. . .......................... . . .... 40 3.6 Ca s e 2 . .. .. ........................................ .. ......... . ............. . . .. . ......... . ... 41 3.7 Case 3 ... ............... ... . .. ............ . .. . .............. .. .. . . .. .. ................... .. ... 42 3.8 Service Moments from HS-20 , HS-25 , and Alternative Military Load s ............ 46 3.9 linpact Factor. ........................................................ .. . .. . .. . . . . . ..... ..... 50 4.1 Load Combination s a nd Load Factor s ................................................... 57 4 . 2 Load Factor s for Permanent Load s, yp . . . . ... . .. ................ ........... . . . ... .. ..... 59 4. 3 Multiple Pr es ence Factor s ...... . ........................ .. . ........ . .. .................... 67 4.4 Case 1 ... . .. ............ .. . ... ....................................... . ... . .......... . ......... 71 4.5 Ca s e 2 .................. ... . .. . .. . . ..................................... .. ....... . ............. 72 4.6 Ca s e 3 ...................... .. ................... .. ........................ .. . ... .............. 7 3 4.7 Equivalent Heights ........... . ............... . .. ........ ........................... ... ..... 80 5.1 Load Factor s for LRFD and LFD Speci f ication s ...................................... 100 6 . 1 LFD Structural An a ly s i s Result s per Foot Width , Example 1 .................... 113 X I V

PAGE 16

6.2 LRFD-Structural Analy sis Result s per Foot Width , Example 1. ..... .. . ......... 138 6.3 Area of Steel compari son . ............ ... . ... . . . . ........................ . . .......... .. ... 152 6 .4 Impact Factor. .. . . . .................... ............. ............. .. ........................ 156 6.5 LFD-Structural Analy s i s Re sults per Foot Width , Example 2 .. . .. ........... . ... 161 6.6 LRFD-Structural Analysis Result s per Foot Width , Example 2 .............. : ... 183 6.7 Area of Steel compari s on ............................... .................................. 152 XV

PAGE 17

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 Specification for Highwa y Bridges. The standard practice at the time was to u se one factor of safety. This methodology i s 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 corre pending bridge design methodology was referred to a load factor 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 revi se d and till include provi sio n s from both the LFD and ASD methodologie s ("LRFD: State Department " 2006) . AASHTO introduced the Load and Resistance Factor De sign ( LRFD ) Bridge Design Specification in 1994 , with the intent of replacing the Standard Specifications for Highway bridges with this reliability ba ed code that provide s a more uniform safe ty for all e lements of bridges. The AASHTO LRFD Highway Bridge Design Specification s were developed with the intent of implementing a more rational approach for the design of highway s tructures. The LRFD Specifications utilize load 1

PAGE 18

and resistance factots 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 ("LRFD: State Department " 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, reliability-based 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

PAGE 19

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 12-28(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

PAGE 20

Investigator. The list of ta s k for this project and the brief outcome are li ted below (NCHRP 1998). • 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 , reliability-based , limit states specification . • Task 2Other than the Standard Specification , review other AASHTO document s for their inclusion into a revised standard specification. This can be be st de sc ribed as a search for gaps and inconsistencies in the 13th edition of the AASHTO Standard Specification for Highwa y Bridge s . " Gap s" were areas where coverage was missing; " Inconsistencie s" were internal conflicts, or contradictions of wording or philosophy. Numerous gaps and inconsistencies were found in the Standard Specification s . • Task 3 -As ess the feasibility of a probability-ba se d specification. The de sign philosophy u ed in a variety of specifications wa reviewed. They were the ASD, LFD , and the Reliability Based 4

PAGE 21

Design . It wa generally agreed upon that the probability-b a ed specification was more suitable. • Task 4 -Prepare an outline for a revi ed AASHTO Specification for Highway Bridge De sig n and commentary, and present a propo se d organizational process for completing s uch a document. The findings of NCHRP Project 12 -2 8(7 ) were presented to the AASHTO HSCOBS in May of 1987 . There were 7 option s that were available: • Option 1 Keep the Statu Quo • Option 2 -Table Consideration of LRFD for the Short Term • Option 3 Immediate Adoption of the OHBDC • Option 4 -Replace Current with LRFD Immediately • Option 5 Replace Current LFD with LRFD in the Near Term • Option 6-Develop LRFD for Evaluation Only , or • Option 7 -Develop LRFD as a Guide Specification A recommendation was made to develop a probability-ba se d limit s tate s s pecification , revise as many of the gaps and inconsi s tencies as possible, and develop a commentary s pecification. Thu s NCHRP Project 1 2-33, entitled " Development of Comprehensive Specification and Commentary ," began in July of 1988. The primary objective was to develop a recommended LRFD-b a ed bridge de sig n s pecifications 5

PAGE 22

and commentary for consideration by the AASHTO Subcommittee on Bridges and Structures. Thirteen task groups were responsible for developing the recommended s pecification s . The task groups were : general features , loads, analysis and evaluation, deck systems, concrete structures, metal structures, timber structures, joints , bearings , and acces s ories; foundations ; soil-structure interaction systems, moveable bridges, bridge rail, and specification calibration . The project con s isted of four contractors and 47 con s ultants 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 12-33 2006). The project was completed on December 31, 1993. The LRFD specifications were adopted by AASHTO and published a s the AASHTO LRFD Bridge Design Specifications. The 1994 edition wa s 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 FHW A has set a deadline of October 1 s r , 2007 for full implementation by all states. State s 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

PAGE 23

working with the FHW A to develop a plan for implementation. A 2004 AASHTO Over s ight Committee survey found that 12 states have fully implemented the specif ications. Another 34 states have partially implemented the LRFD Specification s or are currently in the stage of developing implementation plans and de s igning pilot projects ("L RFD: Achieving Greater Reliability " 2004). The FHW A is providing assistance to states in transition by providing a number of resources that include a team of st ructural , geotechnical, and research engineers who can meet with individual state and provide guidance in developing a State-Specific LRFD implementation plan , training courses, and LRFD Design Workshops. In fact, the FHW A lists tips for successful implementation on the following website, http://www.fhwa.dot.gov/BRIDGE/lrfd/tips.cfm. Tips on the website include: • Staff: Dedicate staff for LRFD planning and de sign (an d studie if necessary) and train the initial design and study squad in LRFD. Utilize FHW A and other State Departments of Transportation ass i stance. • Design Transition Strategy: Set a target date for full LRFD implementation on all new and replacement bridges and on all in house and consultant projects. Perform in-house trial LRFD de s ign of LFD projects (or have pilot LRFD projects) to develop questions and 7

PAGE 24

resolution . These trials also help to gain familiarity with the LRFD Specifications. After the completion of the triaVpilot project , utilize the LRFD design in increments up to the target date or have a one-step conversion to LRFD . The latter sho uld help you minimize the problem of maintaining two separate design specifications and manuals. The pilot projects hould be se lected carefully to represent low priority, routinely designed bridges. • Software: Acquire a computer program that utilize s LRFD . There are many state and private LRFD software programs available for steel and concrete bridge superstructures and concrete substructures • Training: Sponsor in-house training courses for all designer s ( by in hou se instructors, local univer sities in tructors, industry, or by FHW A ) . Acquire LRFD design examples and software for hands-on training. Require that consultants attend LRFD training before they perform LRFD designs in a particular s tate. • Technical Support: Develop a technical support group that is readily available to answer question s 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 question s may prove to be beneficial. 8

PAGE 25

• Documentation Support: Update standards, manuals , and guidance to coordinate with the LRFD Specifications. Develop pre-designed LRFD decks and barriers to shorten the design process if standardized designs are not available. Contract services to update existing design materials to LRFD. • FineTune Documentations: After the completion of the pilot project and/or full LRFD conversion, fine-tune 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 struct ure s such as underground utility structures, drainage inlets, three-sided 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 151, 2007 deadline that AASHTO in concurrence with the Federal Highway Administration has set for all states to be completely converted to the AASHTO 9

PAGE 26

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 de s igning underground precast concrete. Thi s thesi s include s : • A comprehensive literature review of existing and current studies associated with the Standard LFD and LRFD Specifications. • A detailed summary of the variables and design methodology for buried precast concrete structures using the AASHTO LFD Standard Specifications . • A detailed summary of the variables and design methodology for buried precast concrete stmctures using the AASHTO LRFD Bridge Design Specifications. • A thorough comparison between the LRFD and LFD specifications . • Two design examples illustrating the u e of both specifications. The examples are of a buried three-side precast concrete stmcture . • A summary of this thesis document. 10

PAGE 27

C h a p ter 2 Literatu r e R ev i ew Currently , b1idge de igners are transitioning from the Standard AASHTO Bridge De s ign 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 u s ing either pecification. The new specifications utilize state-of-the-art analysis and design methodologies. In addition, the LRFD Specifications make u se of load and resistance factors based on the known variability of applied load s and material properties. Difference 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 s urcharge, and the concrete design methodology for fatig u e, shear strength, and control of cracking. There has been very little research comparing all of the provisions from both specifications when de s igning 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 C ompari s on of Standard S pecifications a nd LRFD S pecification s R und and McGrath (2 000) compared all of the provisions from AASHTO Standard Specifications and the L RFD Specifications for preca s t concrete box 11

PAGE 28

culverts . The research analyzed several combination s of box culvert sizes and fill depths utilizing both s pecifications . Typically , the provi s ion s from the LRFD Specifications yielded greater de s ign load s and therefore required more area of s teel reinforcement. The differences in reinforcement areas were the most pronounced for fill depth s less than 2 ft. Thi s was primarily the re s ult of the difference s in distributing the liv e load to the top sla b into equivalent strip widths . The equivalent strip width i s the effective width of s lab that resists the applied load. In addition, for culvert s pan s up to 10ft, the LRFD Specification s required s hear reinforcement. Analysi s utilizing the Standard AASHTO Specification s also s how required s hear reinforcement for a s imilar range of s pans , but provisions permit the s hear effect s to be neglected. For depth s of fill between 2 and 3 feet , the difference s in reinforcement areas were due to fatigue requirements. The provi s ions in the Standard Specification s for fatigue were not pre s ent in the LRFD Specifications. For depth s of o ve rburden greater than 3ft, the differences in t he reinforcing areas decrea se d s lightly . However , with increasing depth , the LRFD Specifications required greater required area of s teel reinforcement. Thi s was primarily due to the di s tribution 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 ha s since been revised and 12

PAGE 29

is in its 3rd edition. Many of the provision s 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 di stri bution methods used in both specificat ions. 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 (2 000) , 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 requirement s tend to govern the design of flexural steel in concrete st.mctures 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

PAGE 30

Tadro s, and Sun 2004). Re earch completed by DeStefano et al. (2004 ) s ugge ste d 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 difference s between bridge and building structures. The proposed revised crack control requirements identified a number of short coming s identified with the Z factor method. Example de igns were included on box culvert s to compare the allowable st res ses in the existing Z factor method and the propo s ed crack control method. The res ult s indicated rea s onable increases in a llowable stresses, thu s permitting more economical de s igns without sa crificing long t er m durability. The proposed equation developed in thi s re sear ch ha s 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 15-29 2006). Thi s re sear ch compared provi s ion s form both s pecification s regarding disuibution of live load through earth fill . The d esig n and evaluation of buried structures require s an und erstanding of how vertical earth load s and vehicular live load s are transmitted through earth fill . When the depth of overburden i equal to or greater than 2 ft, both the Standard AASHTO Specification s and the LRFD Specification s allow for the wheel load to be dis tributed 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 Specification takes into account the contact area between the footprint of the tire and ground surface. The distribution area i s 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 s does not account for the dimensions of the tire. Instead the wheel load i s 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 specification is the AASHTO LRFD Bridge Design Specification uses different approximate methods that ignificantly increase live load pressures on buried structures when compared to the Standard Specifications . In addition , the ba s i for the methodology in which the live l oad is distributed through soi l is not well documented or understood. As a result the NCHRP developed project 15-29 , 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 tran portation ) of the American As socia tion of State Highway and Transportation O fficials, in cooperation with the FHW A , 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

PAGE 32

nationwide. The objective of Project 15-29 i s to develop recommended revi s ion s 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 20th' 2007. The stat u s of the project is unkno wn 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 live load through earth fill was performed by Bloomquist and Gutz (2 002) 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 a the de ign standard for all structures beginning in 1998 . The research report discusse s the development of equations to calculate the di st ribution of live loads through earth fill for the design of precast concrete box culverts. The objective of there earch 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 Specification . A ignificant amount of design time can be shortened by simplify ing this process. Also, the work was aimed at producing a simplified design 16

PAGE 33

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 semi-infinite, homogenous, isotropic, weightless, elastic half-space, 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
PAGE 34

p l 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. 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

PAGE 35

dimension of the tire be utilized. Newmark integrated the Bous inesq 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 Where: qo = Contact stress at the surface m=xlz 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 Equation 2.4 19

PAGE 36

Where: W d = Load on pipe in lb/unit length P = Intensity of di tributed 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 Mare the width and len gth, respectively, of the area over which the di tributed load acts. The last method to be reviewed and one of the s implest method s to calculate the di tribution of load with depth is known a the 2:1 method calculated in Equation 2 .5. Where: Load a _=-----( B + Z)(L+ Z) crz = Live load stress Z = Depth of fill Equation 2.5 B , L =Width and l e ngth , respectively, of the loaded area at the surface 20

PAGE 37

The 2:1 method i an empirical approach that assumes the area over which the load acts increase s in a sy tematic way with depth . The methodology in the Standard LRFD Specification s i s ba ed on a variation of thi s method. Each of the method s de sc ribed above were u se d to calculate the live load pressure through earth fill and compared to the current LRFD Specification s . The objective was to compare methods of live load distribution and determine s uitable alternative s . The Design Truck and De s ign Tandem vehicles were used when examining the methods. The findings sugge t that the superposition method be u s ed in place of the provi s ion s in the Standard LRFD Specifications. Once the different method s to di tribute live load were compared , the next step was to develop a si mplified equation that would produce the arne force effects as the current LRFD Specifications. Base d on the s uperpo s ition method , s hear s and moments acting on the top s lab of box culverts were calculated for varying de s ign spans and earth f ill depths. An equivalent uniform load model was de ve loped b y statistical modelin g and curve fitting to produce the same moments and shears . The research developed Equation 2.6 for determining the equivalent uniformly di s tributed load: 2300 a=z z 21 Equation 2.6

PAGE 38

Where: crz =Equivalent Load (plf) Z = Depth of fill (ft) The researcher recommend that Equation 2.6 only be used for box culverts with pan lengths that were in the cope of the re earch. Further refinement of the equation may be accomplished with a more rigorou tati tical analysis . 22

PAGE 39

Chapter 3 AASHTO LFD Standard Specifications 3.1 Load Factors and Load Combinations All structures must be designed to withstand multiple loads acting sim ultaneou sly at once. Vehicle liv e loads may act on a struct ure at the same time as lateral earth pressure. The de ign engineer is responsible for ensuri ng the de ign is ized and reinforced properly to safely resist combination of loads. To account for this the Standard AASHTO Sp ec ific at ion s contain load combinations, s ubdi vided into groups, which represent a combination of sim ultaneou s loadings o n the struct ure . The general equat ion used to define a gro up load is given by Equation 3.1 (AA SHTO 2002). Where: Group (N) = + (L + D + + W WL + L LF + R ( R + s + T ) + ICE] N =group number y = load factor from Table 3.1 from Table 3.1 D =dead load 23 Equation 3.1

PAGE 40

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 pre sure ICE = ice pressure Table 3 .1lists values for both y and p . These values are based on the serv i ce load and load factor design. The coefficient p varie ba ed on the type of load . The load factory is the arne for ervice loads; however, it varies for different load factor design groupings. The p coefficients for both dead load and earth pre sure vary depending on the load group and design method shown in Table 3.1. This variation 24

PAGE 41

results from different values being applied for different types of elements or components . A de cription of the dissimilar results is illustrated in Table 3.2 . The Standard AASHTO Specification incorporates two principle de ign methods: • Service Load De ign (Allowable Stres Design or Working Stre s D esign) • 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 Eq uation 3.2 . f ac tual :s; !allow abl e Equation 3.2 25

PAGE 42

Ta bl e 3.1 AASHT O G r o up Loa din g Coefficie n ts and Loa d Factors Col No . 1 2 3 3A 4 5 6 7 8 9 10 11 12 13 14 p FACTORS GROUP y 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 PE 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 BE 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 P E 1 1 0.3 1 1 0 0 0 125 0 ....J w IV u 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 a: UJ VI 1 . 0 1 1 0 1 BE 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 BE 0 0 0 0 0 0 0 0 100 I 1 . 3 P o 1.67 0 1 P E 1 1 0 0 0 0 0 0 lA 1 . 3 B o 2 . 20 0 0 0 0 0 0 0 0 0 0 0 IB 1 . 3 P o 0 1 1 P E 1 1 0 0 0 0 0 0 z II 1 . 3 P o 0 0 0 PE 1 1 1 0 0 0 0 0 UJ (!) ....J ii5 13o BE CD UJ Ill 1 . 3 1 0 1 1 1 .3 1 1 0 0 0 <( 0 u a: IV 1 . 3 P o 1 0 1 BE 1 1 0 0 0 1 0 0 ::J 0 a... a... 1v 1 . 25 P o 0 0 0 PE 1 1 1 0 0 1 0 0 <( u 1<( lL VI 1 . 25 B o 1 0 1 13E 1 1 .3 1 1 1 0 0 0 0 z <( 13o B E 0 V I I 1 . 3 0 0 0 1 1 0 0 0 0 1 0 ....J VIII 1 .3 P o 1 0 1 PE 1 1 0 0 0 0 0 1 IX 1 . 2 B o 0 0 0 BE 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

PAGE 43

Table 3.2 AASHTO Earth Pressure and Dead Load Coefficients 13 Load Value Element 13E Earth Pressure 1 . 0 Vertical and lateral loads on all other structures Lateral loads on rigid frames (check both loadings to 13E Earth Pressure 1 . 0 and 0 . 5 see which one governs) Lateral earth pressure for retaining walls and rigid 13E Earth Pressure 1 . 3 frames excluding r i gid culverts Lateral earth pressure when checking pos iti ve 13E Earth Pressure 0 . 5 moments in rigid frames 13E Earth Pressure 1 . 0 Rig i d culverts 13E Earth Pressure 1.5 F l exible culverts Columns , when checking member for minimum axial Dead Load 0 . 75 load and maximum moment or maximum eccentricity Columns , when checking member for max imum axial Dead Load 1 . 0 load and minimum moment 13o Dead Load 1 . 0 Flexural and tens ion members Bridg e s ub s tructur es s uch as foundations and a butment s h ave traditionally been de s igned u si ng the Se rvi ce Load De s ign methodology. Underground pr ecas t concrete box culverts and three ided str uctur es are de s igned by the load fac tor de s i g n , thu s this the sis focuses so lel y on the load factor de sig n methodology. In this methodology , the general relation s hip i s de f ined utilizing Equation 3.3 . Equation 3.3 27

PAGE 44

Where: 'Yi = Load factors Qi = Force effects <1> = Re s i stance factors Rn =Nominal re s i sta nce RR = Factored resistance The nominal re istance of a member , Rn, is calculated utilizing procedure s given in the current AASHTO Specifications . A resis tance factor , , is u se d to obtain the factored resistance RR. The appropriate re sistance factors are determined for specific conditions of design and construction process. Typical values for underground concrete structures are lis ted in Table 3.3. The force effects, Qi, that should be considered when designing underground concrete str uctures 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 wind, temperature, and vehicle breaking are insig nificant compared to the force effects previously mentioned for buried concrete structures. The following sections will examine the se critical force effects when designing underground concrete structures, specifically reinforced preca s t concrete box culverts and three-sided concrete structures, u s ing the Standard AASHTO Specifications. 28

PAGE 45

Table 3.3AASHTO 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 In-Place 0 . 90 0.85 NA Reinforced Concrete Box Culverts , Cast In-Place 0 . 90 0.85 NA Reinforced Concrete Box Culverts , Precast 1 . 0 0 .90 NA Precast Reinforced Concrete Three-Sided Structures 0.95 0.90 NA 3.2 AASHTO Standard Vehicular Design Live Loads The American Association of State and Highway Transportation Official s, founded in 1914 as American A ss ociation of State Highway Official s, created a truck train configuration in 1935 ba s ed on the railroads industry standards as shown in Figure 3.1. '"I ""' mi til s 4 : .:.... ______ n_ ______ ____...,,___.!:l _ _ IHS.lS t.OADIItG Figure 3.1AASHO 1935 Truck Train Loading (Tonias, 1995). 29

PAGE 46

Hi torically, many s tructure s, mainly bridge s began to s how evidence of overstressing in structural components as a res ult of increased truck traffic and heavier truck loading (Toni as 1995). Thi led to the introduction of five hypothetical trucks designated a H and HS class truck s 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 De sig n Truck Gross Weight H1044 20,000 LB 9072 KG H15 -44 30,000 LB -13, 608 KG H20-44 40 , 000 LB-18,144 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 Specification s with the exception of the Hl0-44. 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 truck s and their associated geometries. 30

PAGE 47

0 I • I 1 4 FT I 1 4 FT 30 FT HS25-44 ---10 .000 lbs.-----40.000 lbs. ---------40.000 lbs. HS20-44 ---8,000 lbs. ---------32,000 lbs. ---------32,000 lbs. HS15-44-6,000 lbs. ----24,000 lbs. ------------2 4,00 0 lbs . d 0 D l lr l I 14-FT ! H20-44--8 . 000 lbs.------------------32.000 lbs. H15-44 ---6,000 lbs .----------------------------24,000 lbs . Figure 3.2 Characteristics of the AASHTO Design Truck (AA SHTO , 2002). 31

PAGE 48

The H-15 and H-20 truck loading is represented by a two-axle single unit truck. The " S " in the HS 15-44 and HS20-44 designates a semi-trailer combination with an additional third axle. The H15 44 truck configuration ha s a gross weight of 30,000 lb. with 6 , 000 lb . on it s steering axle and 24,000 lbs. on it s drive axle. Similarly, the HS 15-44 weighs 56,000 lb. with an additional 24,000 lb. on it s em1 trailer axle. The H2044 ha a gross weight of 40,000 lb . with 8,000 lb . on its steering axle and 32,000 lb. on it s drive axle. A HS20-44 truck weighs 72,000 lb. with an additional 32,000 lb. on it s se mitrailer axle. Although not a provision in the current AASHTO Standard Specification s some s tate s have began u s ing a HS-25 design truck with a gross veh icl e weight of 90,000 lb., as shown in Figure 3.2. Some states have developed a dditional live load configurations known as permit des ign loading s in order to provide for future overweight truck s . The primary de s ign truck used in designing underground s tructure is the HS20-44 truck loading . Another form of live loading to represent heavy military vehicles was developed in 1956 by the Federal Highwa y Admini s tration ( Tonia s 1995). Thi s loading configuration i s known as the Alternative Military Loading as shown in Figure 3.3. Thi loading consists of two axles weighing 24,000 lb . s paced 4ft. apart. A comparison of the force affects from both the de s ign 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

PAGE 49

Typically, the depth of overburden and the pan of the member will govern the design veh icl e configuration . This will be further illustrated in subsequent sections including the design examples in Chapter 6. 1 4 6'-0" l12 K IPSI l12 KIPS I D irection i oF TrClvel 4'-o" 112 K IPSI 112 KIPS I 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 2 0 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 pecified 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

PAGE 50

depth is less than 2ft. To simplify the design calculations it i acceptable to neglect the contact area of the tire, and assume the tire acts as a point load. H S -20 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 , • When the earth fill depth is less than 2 ft. • 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

PAGE 51

3.3 Earth Fill and Vertical Earth Pressure Loading Initially when designing underground concrete structure s the earth fill depth or depth of overburden on the s tructure mus t be determined. The earth fill depth dictate s load combinations, impact , allowable s hear, concrete cover, live load surcharge, and particularly live load application. The earth fill i s the backfill or fill placed on the top slab . Earth fill depth i s defined a s the dis 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 pres s ure value s 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 . Where: WuSL = Y s * z W uSL = Constant vertical earth pre s sure ( p sf) Y s =Unit weight of soil (pcf) z =Earth Fill Depth (ft) 35 Equation 3.4

PAGE 52

Ilepth O f r IU, :: /'w'uSL : ys + z CF!:r> l l l l l l I l II .. . 4 4 .. 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 soil-structure interaction based on the earth fill depth, side compaction, and bedding characteristics (Sanford 2006). Therefore the effects of soil-structure interaction must be taken into account. The Standard AASHTO Specification requires that the vertical earth pre sure values from Equation 3.4 mu st be multiplied by a soil-structure interaction factor, Fe, when designing reinforced concrete box culverts. The soiltructure interaction factor depends the on type of installation. For embankment installations, F e is calculated using Equation 3.5, for trench installations use equation 3.6. The Standard AASHTO Specifications do not require the soil-structure interaction factor to be applied to three-sided concrete structures . It is important to note that the soil-structure interaction factor for reinforced concrete pipe differs from Equations 3.5-3.6. The soil-structure interaction factor for reinforced concrete pipe i beyond the scope of this thesis and is not discussed. 36

PAGE 53

Where: Where: H F e l = 1 +0.20B c Equation 3.5 F e1 = Soil-structure interaction for embankment installations :::; 1.15 for in tallations with compacted fill at the side :::; 1.4 for installations with un-compacted fill at the ide s H = Earth fill depth, ft. B e = Out -to-out horizontal span of pipe or box, ft. Equation 3.6 F e2 = Soil-structure interaction for trench installations H = Earth fill depth, ft. B e = Out-to-out horizontal span of pipe or box , ft. Cct =Load coefficient for trench installations, Figure 3.6 . 37

PAGE 54

3.4 Distribution of Live Loads for Depths of Fill Greater Than 2 ft. When the depth of fill i s equal to or greater than 2ft., the Standard AASHTO Specifications allows for the wheel load to be distributed over a s quare equal to 1.75 times the depth of fill. Figure 3.6 ill u strates that the Standard AASHTO Specification does not account for the dimen sions of the tire, instead the wheel load is considered as a concentrated point load. The distributed live load value, WuLL for a sing l e wheel load i s 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 spa n is considered in the design. WuLL =Wheel Load I (1.75 *H) 2 Equation 3.7 Where: H =Earth Fill Depth (ft) 38

PAGE 55

I./HEEL LOAD 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 hould be distributed over the area defined by the outside limits of the individual area as hown in Figure 3 .7. \JHE:EL LOAD IJHEEL LOAD Figure 3. 7 Overlapping Wheel Load Distribution through Earth Fill 39

PAGE 56

As the earth fill depth increa s es, 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 dist1ibution widths for a single design vehicle are shown in Figure 3.8. Table 3 5Case 1 H Spread, S WuLL Design Vehicle (ft ) Wheel Load (lb) (ft 2 ) (lblft2 ) HS-20 Truck H < 3.43 16,000 (1.75 * H ) 2 1 6 , 000 I (1.75 * H) 2 HS-25 Truck H < 3.43 20,000 ( l.75 * H )2 20.000 I (1.75 * H) 2 Alternative Military Load H < 2 . 29 12, 000 (1.7 5 * H ) 2 12.000 I (1 .75 * H) 2 Figure 3.8 Case 1, Wheel Load Distribution through Earth Fill 40

PAGE 57

3.4.2 Case 2 Distribution of Wheel Loads from a Single Axle Overlap. Case 2 occ ur s w h e n both wheels from a si n g l e axl e overlap for the HS Truck co nfi g u ration. The wheel from separate ax l es overlap for the Alternative Military truck co nfi g u ration. Thi s is due to an ax l e pacing of 4 ft. compared to the whee l s pacing of 6ft. The distributed live loads are calculat e d using Tab l e 3.6. B ot h the Alternat i ve Military Truck and HS Desig n Truck configuration are illustrated in Figure 3.9 . H Desig n Vehicle (ft) HS-20 Truck 3.43 < H > 8.00 HS-25 Truck 3.43 < H > 8.00 A lt e rnativ e Mjlitary Load 2.29 < H > 3.43 H S DESIGN TRUCK Table 3 6-Case 2 Wheel Load Spread , S (!b ) (ft2 ) 16 , 000 S = (1.75 * H)* (1.75 * H + 6) 20 , 000 S = (1.75 * H)* ( 1.75 * H + 6) 12,000 S = ( 1.75 * H)* (1.75 * H +4) D IRECTION OF"' TRAF" FT C W uLL (lblft2 ) 32 , 000 IS 40,000 IS 24 , 000 IS 6 VHEEL Figure 3.9 -Case 2 , Overlapping Wheel Load Distribution through Earth Fill 41

PAGE 58

3.4.3 Case 3 -Full Distribution of Wheel Loads from Multiple Axles. When the wheel load s from all axles overlap , the dis tributed live load i s calculated u ing Table 3.7. Full distribution occur s for the HS De s i g n Truck at an earth fill dep th of 8 feet as s hown in Figure 3.10. The live load may be n eglecte d as state d in the Standard AASHTO Specification s when the earth fill depth is greater tha n 8 feet , and excee d s the effective s pan len g th. For multiple s p a n s, it may b e neglected when the depth of overburden exceeds the dista nce between faces of end s upport s or ab utments. A a re s ult , Case 3 will typically govern for the Alternative Military Lo a d ba se d on full dis tribution at a fill depth of approximately 3.43 ft. Table 3 7-Cas e 3 H Wheel Load Spread, S WuLL D esilm V e hicl e (ft) (I b ) (ft2 ) (lblf t1 ) HS-20 Truck 8.00 < H 16,000 S = (1.75 * H + 14) * (1.75 * H + 6) 64,000 IS H S-25 Truck 8.00< H 20, 000 S = (1.75 * H + 14) * (1.75 * H + 6) 64.000 IS Alternative MiJhary Loa d 3.43 < H 12.000 S = (1.75 * H + 4 ) * (1.75 * H + 6) 48.000 IS 42

PAGE 59

H S DESIGN TRUCK • 'W'HC:tl DJRCtmN o r tRArnc .. 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 De sign Truck and the Alternative Military Loading configuration should be made. The loading configuration that creates the large st 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 pre ss ure versus depth of fill is plotted in Figure 3.11 for both the HS20-44 De sign Truck and Alternative Military Loading. The HS20-44 Truck Loading produces higher wheel load pressures for sha llow depths between 2 ft. 4.5 43

PAGE 60

ft. , while the Alternative Military Loading produce s larger whe e l load pre s sure s for depths between 5 ft-15ft. For earth fill depth s greater than 15ft, the HS20-44 Truck Loading produce s higher wheel load pre ss ure s . HS20 Design Truck vs . Alternative Military Loading Through Earth Fill 1400 . 00 i 1200 . 00 1000 . 00 iL 800 . 00 Vl e:. ..J ..J " 600 . 00 ;= 400 . 00 200 . 00 \ HS-20v I ...._ Mil ilafY I \ 0 . 00 0 .00 2 .00 4 . 00 6 . 00 8 . 00 10 . 00 12 . 00 14. 00 16. 00 18 . 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 pressure with regard s to earth fill depth will not nece ss arily control the de s ign. The critical live load pres s ure u s ed 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 fill of 3.0 ft an HS-20 truck produce s a service live load pres s ure of 0 . 581 ksf. An Alternative Military vehicle produce s a s ervice live load pre ss ure of 0.494 k sf. 44

PAGE 61

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. HS-20 Design Truck Alternative Military Truck WsLL----... 1 4 ' -0" Axl e spacing Figure 3.12 -LFD Live Load Spread for 3 ft Overburden 3"-o" In Figure 3 .13 the ervice moment produced by the HS 20-44, HS 25-44, 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 HS25-44 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

PAGE 62

Depth of Fill = 3.00 FT 25 . 00.,...-----------------------, I 1/) -HS20 __..._IV.IUTARY -HS25 ::!: 10.00 +-----------#---7'"'-------------j 0 . 00 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 HS-20, HS-25, 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

PAGE 63

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 structure . The live load is divided into equivalent strip widths, which is the effective width of slab that resi s ts the applied load . The live load is modeled as a concentrated wheel load distributed over a di tribution width, E . The distribution width is calculated using Equation 3.8 . Where: E = 4 + .06 * S <7ft. For H <2ft. Equation 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 structure to top of Pavement (ft) Concrete slabs are analyzed a 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

PAGE 64

Figure 3.14 -LFD Distribution Width, E for a Single Wheet Load The Standard AASHTO Specification s doe s not allow any load tran sfer between adjacent tructure s. The distribution widths must be limited to the unit width of the struct ure. Figure 3.15 illu strates two cases. The di stri bution width exceeds the width of the member in Case 1. The effective di s tribution width will be limited to the member width of the structure. In C ase 2 the di stri bution width is less than the unit width of the member. Therefore de sig n calculations consider the full di s tribution width . Case I r--1 ' -' Top Slob i L .. WidthFigure 3.15 -Effective Distribution Widths on Slabs 48

PAGE 65

The tire is ass um ed 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 Stand ard AASHTO Specifications; however it is a common practice to assume a reduced distribution width. Thi new distribution width i calculated using Equation 3.9. 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 Case 3 section 3.2 (ft) ! Joint i i L----Member Widlh--_L----Member Widlh---_L---Memebr Width--Figure 3.16 -Reduced Distribution Widths on Slabs 49 Top S lob

PAGE 66

3 .6 Impact Factor (IM) To account for the dynamic load affects of moving vehicles , the AASHTO Standard Specification s applies an impact factor to the live load for varying burial depths . The impact factor i s applied to both the De sig n 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 O verb urden 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 veh icle can be attrib uted to the hammering effect of the wheel assem bly riding on s urface discontinuities suc h as deck joints , cracks, potholes, and undulation s in the roadway pavement caused by settlement of fill (AA SHTO 2005). The decrease in impact with the depth of overburden i s due to the damping effect of soi l when the wheel is in contact with the ground . 50

PAGE 67

3.7 Lateral Live Load Surcharge The Standard AASHTO Specification require a lateral live load surcharge pre s sure be applied when highway traffic comes within a horizontal distance from the top of the structure equal to one-half its height. Additional lateral eatth pressure is produced on soil retaining wall s a s a result of s urcharge 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 result s . The first i by a suming 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 a a s eparate load a 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: Where: LLS = k * Y s * Heq 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) H e q =equivalent height of soil , typically 2 ft. 51

PAGE 68

.. ORIZDNTAL EARTH PRESSURE + LIVE LOAD SURCHARGE Figure 3.17 LFD Equivalent Height ORIZDNTAL EARTH PRESSURE I V E LOAD SURCHARGE Figure 3.18 Live Load Surcharge Pressure 52

PAGE 69

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. Equation 4.1 Where: Tli =Load modifier Yi = Load factors Q i = Force effects


PAGE 70

LRFD Specifications (AASHTO 2005). Each of the four limit states are described below: • STRENGTH-Requires the strength and stability be adequate for specified load combinations. • EXTREME EVENT Relates to events with extremely long periods of return (earthquakes, ice loads, vehicle collision, and vessel collision). • SERVICE-Relates to stresses, deformations, and cracking. • FA TIGUE Places restrictions on stre 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 Specification 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): • STRENGTH I-Basic load combination related to normal vehicular use of the bridge without wind. 54

PAGE 71

• STRENGTH II-Load combination relating to the use of the bridge by owner specified special design vehicles and/or evaluation permit vehicles without wind. • STRENGTH III-Load combination relating to the bridge exposed to wind velocity exceeding 55 mph without live load. • STRENGTH IV -Load combinations relating to very high dead load to live load force effect ratios. • STRENGTH V Load combinations relating to normal vehicular use of the bridge with wind velocity of 55 mph . • EXTREME EVENT I-Load combinations including earthquake and flood. • EXTREME EVENT II Load combination relating to ice load or collision by vessels and vehicles. • 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 value . • SERVICE II-Load combinations intended to control yielding of steel structures and slip-critical connections due to vehicular live load. 55

PAGE 72

• SERVICE lliLoad combination for longitudinal analysis relating to tension in pre tressed concrete superstructures. • SERVICE IV-Load combinations relating only to tension in prestressed concrete substructures with the objective of crack control. • FA TIGUE -Fatigue and fracture load combinations relating to the repetitive gravitational vehicular live load and dynamic respon es under a single design truck. A majority of the loads and loading combination 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 ve1tical 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. 56

PAGE 73

Tab l e 4.1-Loa d Com b i n ation and Load Factors Load Combi nation DC LL TU Use one of These at a Time DD IM CR ow CE SH EH BR EV PL ES LS EL EO I C C T CV Limi t State WA WS W L FR TG SE ::; I HI::N(j IH-1 ( unless noted ) Y p 1.75 1 . 00 1 . 00 0 .50/ 1 .20 Yra YsE STRENGTH-II Y p 1 . 35 1.00 1 . 00 0 .50/ 1 .20 Y m YsE STRENGTH Ill Y p 1 . 00 1.40 1 . 00 0 .50/ 1 .20 Y m YsE STRENGTH-IV Y p EH , EV , ES, OW D C ONLY 1 .50 1.00 1 . 00 0.50 / 1.2 0 STRENGTH V Yp 1.35 1. 00 0 . 40 1 . 00 1 . 00 0 .5 0 / 1 .20 Yra YsE EXTREME EVENT-I Y p Yeq 1 . 00 1.00 1 . 00 EXTRE ME E VENT-II Y p 0 . 50 1 . 00 1 . 00 1 . 00 1.00 1 . 00 SERVICE I 1 .00 1 . 00 1.00 0 . 30 1.00 1.00 1.00 / 1 .20 Y m YsE SERVICE-II 1.00 1.30 1 . 00 1 . 00 1 .00/ 1 .20 SERVIGE-111 1 . 00 0.80 1 . 00 1.00 1 .00/ 1 .20 Y m YsE SERVI<.;E-IV 1 . 00 1.00 0 .7 1 . 0 0 1 .00/1.20 1 FATIGUE LL ,IM & CE ONLY 0 . 75 The service limit state required by the AASHTO LRFD Specifications for buried structures is Service Load Combination L The required Strength Limit State required is Strength Load Combinations I and II. The Extreme limit s tate s do not govern unless the structure cro s ses 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: 57

PAGE 74

• For each combination , load factors should be selected to produce the total extreme factored force effect. Both maximum and minimum extremes should be investigated. • 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. • The load factor which produces the more critical combination for permanent force effects should be selected from Table 4 .2. • 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 . 58

PAGE 75

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: Wearing Surfaces and Utilities 1 .50 0.65 EH : Horizontal Earth Pressure -Active 1.50 0 .90 -At-Rest 1.35 0 .90 EL : Locked in Erection Stresses 1.0 1.0 EV: Verticle Earth Pressure I I 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 I I -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, Tli The load modifiers account for combined effects of redundancy , 11R, ductility, Tlo, an d operational importance, 111 . 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. 59

PAGE 76

Equation 4.2 Equation 4.3 Where: Tli =Load modifier Tlo =factor for ductility TlR = factor for redundancy Tlr =factor for importance The values for the ductility, redundancy, and importance factor are listed below: • Ductility, Tlo ::::: 1.05 for non-ductile 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: Tlo = 1.00 • Redundancy, TlR 60

PAGE 77

1.05 for non-redundant component and connection = 1 . 00 for conventional level of redundancy 0.95 for exceptional level of redundancy For all other limit states: 11R = 1.00 • Importance , 111 1 . 05 for important structures = 1.00 for typical tructure s 0 . 95 for relatively les s important tructures For all other limit states: 111 = 1.00 When de s igning at the Service Limit State, 11o = 11R = 111 = 1.00 Typically the ductility of buried structure i 1.00. Buried tructure s are con idered non-redundant 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 afety. 61

PAGE 78

4.3 AASHTO Standard Vehicular Design Live loads The AASHTO LRF D Specific ations require an HL-93live load. Thi s load incl ud es two type s of vehicular d eign loads. The HL93 D esign live load s consist of a combination of the • D esig n Truck or D esign Tandem • D esig n Lane Load The Design Truck u se d in the AASHTO LRFD Specification s has the s ame configuration as the HS-20 D es i g n Truck in the Standard Specifications di s cussed in Chapter 3. The de i g n truck we i g ht s and s pacing of ax l es and whee l s are spec ified in Figure 4 .1. H S20 8. 000 lbs. HS-20 ,fTI '--t;;:=j Figure 4.1-Characteristics of the Design Truck (AA SHTO , 2005 ) 62

PAGE 79

The LRFD Specification s utilize th e De sig n Tandem load configuration consisting of a pair of 25.0-kip axles s paced 4 .0 ft a part. The transverse spaci n g of wheels is taken as 6.0 feet as s hown in Fi g ure 4.2. Direction of Traffic 4 ' 0 " 112. 5 KIPS 12 5 KIPS I ------6 , 0 Figure 4.2-Characteristics of the Design Tandem The loads from both the Design Truck and the Design Tand e m are as umed to be di s tributed tran sve r sely within a 10.0 ft. de s ign lane. A rectangular tire contact area s hown in Figure 4 .1, con s isting of a 20 .0 in. width and a 10.0 in length , is u s ed in the de s ign. A dynamic load allowance defined in a later section is applied to both the 63

PAGE 80

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 Design Lane Load consists of a load of 0.64 klf, uniformly di tributed in the longitudinal direction. Transversely , the Design Lane Load i 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 8ft. 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 lab. 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

PAGE 81

fill are calculated u s ing Equation 4.4. Figure 4.3 demonstrates depth of fill and the vertica l earth pressure applied to the top s lab. Therefore the effects of soil-struct ure interaction must be taken into account. The LRFD Specification requires that the vert ical earth pressure values from Equation 4.4 must be multiplied by a soil-structure interaction factor, F e , when designing reinforced concrete box culverts. This is similar to the AASHTO Standard Specifications specifie d in Section 3.3. Where: WuSL = 'Ys * z WuS L =Constant vertical earth pressure (pcf) 'Ys = Unit weight of soil (pcf) z =Earth Fill Depth (ft) • ! • Equation 4.4 Figure 4.3 Earth Fill Depth and Vertical Earth Pressure Loading 65

PAGE 82

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 lanes on a brid ge. 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 lo aded lanes. For underground concrete st ructure s, 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 occur s for depth s of fill equal to or grea ter than 2 ft. The Stand ard LRFD Specification s require two checks. • A check to determine the force effects from multiple truck axles positioned 4 ft s ide by side with a multiple pre sence factor of 1.00. • A check to determine the force effects from a sing le de sign vehicle with a multiple presence factor of 1.20. The loading combination with the worst case force effects on the struct ure will control the design . Thi s will typically depend on the overburden depth and/or the s pan of the structure. Thi s i s further disc ussed in Section 4.6 . 66

PAGE 83

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 parall e l to t he de sign pan, the struct ur e is analyzed using a single loaded l ane . The Standard LRFD Spe cificat ion s distribute a sing le loaded lan e into strip widt h s . This strip w idth is t h e effe cti ve widt h of the slab that resists t he applied load. Therefore, the multiple presence factor is 1.20 4.5.3 Case 3 Depth of flU is less than 2ft, and direction of traffic is perpendicular to span. When the depth of fill is less th an 2 ft and the dir ect ion of traffic is perp e ndicular to the span, the appropriate multiple pre ence factors must be cho en from Table 4.3 . The number of loaded l a ne s is a function of s pan length. Table 4 . 3 Multiple Presence Factors N umber of Loaded Multiple Pre sence Lane s Factor "m" 1 1.2 2 1.00 3 0 .85 >3 0 .65 67

PAGE 84

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 simi lar 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 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 dimension s increased by either 1.15 times the earth fill depth for select gran ular 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. Where: WuLL =Wheel Load I (LLDF * H + WT) * (LLDF*H + LT) Equation 4.5 WuLL =Uniform Distributed Live Load (psf) H = Earth fill depth (ft) WT =Tire Width (in) LT = Tire Length (in) 68

PAGE 85

LLDF =factor for distributing the live load through earth fill 1.15 for select granular backfill 1.00 for all other backfill D ISTRIBUTED LOAD AREA Figure 4.4-LRFD Wheel Load Distribution through Earth Fill 69

PAGE 86

As noted with the Standard AASHTO Specification , the distributed live load area and load va lue calculations are complicated as a result of distributed area overlap as the earth fill depth is increased (United State s FHA 2001) . The overlapping i s 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 illu s trated 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

PAGE 87

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 de sign vehicle are show n in Figure 4.6 Table 4.4-Case 1 Sleet Granular Fill Whee l Load Spread B Spread A WuLL Design Vehicle H (ft) (lbs) (ft) (ft) (psf) HS-20 Tru ck H < 3.77 16, 000 ( 1.15 * H + 0.83) (1.15 * H + 1.67) 16 ,000 I (A* B ) HS-25 Truck H < 3.77 20,000 (1.15 * H + 0.83 ) (1.15 * H + 1.67 ) 20,000 I (A* B) Tandem H < 2.75 12, 500 (1.15 * H + 0 . 83) (1.15 * H + 1.67) 12, 500 I ( A * B ) Other F1ll Wheel Load Spread B Spread A WuLL Design Vehicle H (ft) (lbs) (ft ) (ft) ( p sf) HS-2 0 Truck H <4.33 16.000 ( 1.00 * H + 0.83) ( 1.00 * H + 1.67) 16 , 000 I (A* B) HS-25 Truck H < 4.33 20,000 (1.00 * H + 0 .83) ( 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) I----SPREAD \.'HEEL LOAD I--------AXLE SPACING--------I I----SPREAD B---l I----SPREAD B'---1 Figure 4.6 Wheel Load Distribution through Earth Fill 71

PAGE 88

4.6.2 Case 2 Distribution of Wheel Loads from a Single Axle Overlap. C ase 2 occ ur s when both w he els from a si ngle axle overlap . The distributed live load s are calculated u si ng Table 4.5 . It i s important to note that a single wheel load from eparate axle overlap in the Tandem Loading. This is a re s ult of the 4 ft. ax l e spacing, compared to the 6ft. whee l s p acing Fig ur e 4 .7. T able 4 . 5 -Case 2 Sleet Granular F ill Wheel Load Spr e ad A WuLL Design Vehicle H ( ft ) (I b ) Spre ad B (ft) ( ft ) ( psf) HS-20 Truck 3 . 7 7 < H < I 1.44 16.000 ( 1.15 * H + 0 . 83 + 6 ) ( 1.15 * H + 1.67 + 6 ) 3 2 , 000 I ( A * B ) HS-25 Truck 3 . 77 < H < 1 1.44 20,000 ( 1.15 * H + 0 . 83 + 6 ) (1.15 * 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 . 83 + 4 ) 25.000 I ( A * B ) Other Ftll Whee l Load Spread A WuLL Design Vehicle H (ft) (I b ) Spread B (ft ) (ft) ( psf) HS-20 Truck 3 .77 < H < 11.44 16,000 ( 1.00 * H + 0 . 83 + 6 ) (1.00 * H + 1.67 + 6) 32,000 I ( A * B ) HS-25 Truck 3 . 77 < H < 11.44 20,000 ( 1.00 * H + 0.8 3 + 6 ) ( 1.00 * H + 1.67 + 6) 40. 000 I ( A * B ) Tandem 3.17 < H < 4. 33 12.500 ( 1.00 * H + 1.6 7 + 6) (1.00 * H + 0 . 83 + 4 ) 25.000 I ( A * B ) Figure 4. 7 Overlapping Wheel Load Distribution through Earth Fill 72

PAGE 89

4.6.3 Case 3 Full Distribution of Wheel Loads from Multiple Axles Overlap. In this case the wheel load s from all ax le s overlap resulting in full distribution. The distributed live load s are calculated using Table 4.6. For the HS De sign Truck, full distribution occurs at an earth fill depth of 11.44 ft as s hown in Figure 4 .8. The AASHTO LRFD Specifications does allow for the live load to be neglected when the earth fill depth i s greater than 8ft. and exceeds the effective spa n length. The live load for multiple spans is neglected when the depth of overburden exceeds the distance between the outer face of the end s upport s 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 Backfil l Wh ee l Load Spread A WuLL De s ign V e hicl e H (ft) (I b ) Spr ea d B (ft) (ft) ( psf) HS-20 Tru ck H > 11.44 16,000 (l.l5 * H + 0.83 + 6 ) ( 1.15 * H + 1.67 + 6) 64,000 I (A* B) HS-25 Truck H > 11.45 20,000 (1.15 * H + 0.83 + 6) ( 1.15 * H + 1.67 + 6) 80, 000 I ( A * B ) T a ndem H > 3.77 12 , 500 (1.15 * H + 1.67 + 6 ) ( 1.15 * H + 0.83 + 4) 50 , 000 I (A * B ) Ot her F1ll Whe e l Load Spread A WuLL Des ign Vehicle H (ft) ( lb ) Spread B (ft) (ft ) ( psf) HS-20Truck H>ll.44 16,000 ( 1.00 * H + 0.8 3 + 6) ( 1.00 * H + 1 .67 + 6 ) 64,00 0 I (A * B ) HS-25 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

PAGE 90

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 sin g l e design ve hicle. For Case s 4 5, the Standard LRFD Spe cificat ion s require a c h eck to determine if the distributed live load area from m ultip le truck axle po s itioned side by s id e overlap. C ase 4 is when two wheels from se parate ax le s overlap illustrated in Figure 4.9 . The total load from the two wheels is distributed over the area illustrated. Ca se 5 occurs when both axles from each de ign truck overlap . The total load from both ax l es is distri buted within the boundaries of the t wo axles s hown in Figure 4.1 0. 74

PAGE 91

Figure 4.9 Overlapping Wheel Load Distribution by Passing Vehicles Figure 4.10Overlapping Axle Load Distribution by Passing Vehicles 75

PAGE 92

4. 7 Distribution of Live Loads for Depths of Fill Less Than 2 ft. For depths of overburden less than 2ft, 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 st rip 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 three dimensional response to live loads. There are two cases that apply: • Case 1 When the traffic travels parallel to the design span. • Case 2 When the traffic travels perpendicular to the design s pan. This thesis focuses on Case 1. When the traffic travels parallel to the desig n 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 s pan. Equation 4.6 is used to calculate the di s tribution width, E Where: E = 8 + 1.2 * S for H <2ft. Equation 4.6 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) 76

PAGE 93

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 s p a n is determined using Equation 4. 7. Where : E span= LT + LLDF * (H) Equation 4.7 E span= 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 span shown in Figure 4.11. The distribution width i s applied to all design spans for both positive and negative bending, and shear force effects . 77

PAGE 94

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 i s only applied to the Design Truck or Tandem Load, and not the Lane Load. The D ynamic Load Allowance varie s linearly from a 33% incre as e at 0 ft. of fill to a 0 % increase at 8ft. of fill, a s shown in Figure 4.12 . The D ynamic Load Allowance in the LRFD Specification s i s calculated u sing Equation 4.8 1M= 33(1-0.125DE) I 0 % Equation 4 . 8 Where: D E = the minimum depth of earth cover above the structure (ft) Similar to the Standard Specification s the dynamic force effects applied to moving vehicles is attributed to the hammering effect of the wheel assembly traveling across s urface discontinuities s uch as deck joints, cracks, pothole s, and undulations in the roadway pavement cau s ed by settlement of fill (AA SHTO 2005) . 78

PAGE 95

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 4.12-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 ve hicul ar load is expected to act on the s u rface of t h e backfill wit hin a distance equal to the wall height behind the back face of the wall. Surch arge loads produce a lateral pressure component on oil retaining walls in addition to lateral earth lo ads. Similar to the Standard AASHT O specifications there are two met hod s to apply the lateral live load surc har ge pressure to the s tructure. This was discussed in Section 3.5. The increase in horizontal pressure due to the live load surcharge i s estimated by Equat ion 4.9: 79

PAGE 96

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 Y s =Unit weight of soil (pcf) heq =Equivalent height of soil for a vehicle load (ft) The equivalei).t 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) I heq (FT) 4.0 3.0 2 . 0 80

PAGE 97

Abutment Height Figure 4.13-Wall Height for Live Load Surcharge Pressures 81

PAGE 98

Chapter 5 Comparison Between LFD AND LRFD Specifications 5.1 Design Vehicular Live Loads The most significant change introduced in the Standard LRFD Specification s i the new vehicular live load model. In the Standard AASHTO Specifications, the vehicular de s ign liv e load i s considered to be either the HS Design Truck Loading or an Alternate Military Loading . The de sig n include s the configuration that produces the critical conditions. The LRFD Specification s include three component of the live load: • Design Truck • Design Tandem • Design Lane Load A combination of the De sign Truck or D esign Tandem plus the Lane Load i s used as the vehic ular 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 sig n truck is identical to the axle load portion of the HS20 truck of the Standard AASHTO Specification s . However, the LRFD design truck is not scaleable like the HS20 truck. For example, there is no HS 15 or HS25 equivalent unde r the Standard LRFD 82

PAGE 99

Specifications. The De sign Tandem has the same tire and axle spacing as the Alternative Military loading , but the load is slightly heavier, see Figure 5 .1. 8l Trm; 12 KIP s I J T r o. vel 4-' o" Al-terno-tive Loodlng Design T o.ncleM 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 De sign 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 sign 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

PAGE 100

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 16ft.. 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. 84

PAGE 101

20. 0 % 18 . 0 % f-0 0.00 ft. fill • 0.50 ft. fill 16. 0 % f-0 1 . 00 ft. fill 14.0 % f-0 1.50 ft. fill -• 1.99 ft. fill IIJ 12.0 % :::!: f--c: Q) IIJ 10.0% ff--., Ill u -= 8 . 0 % -ff--:::!! 0 6 . 0 % f--ff--4 . 0 % 1---'--ff--2 . 0 % f-ff0 . 0 % 4.00 6 . 00 8 . 00 10 . 00 12. 00 14. 00 16 . 00 Design Span (ft) Figure 5.2-Increase of Force Effects due to Design Truck vs. Design Truck + Lane Load 85

PAGE 102

5 . 3 Dynamic Loa d Allowance, Impact Both the Standard AASHTO Specification s and the LRFD Specification s require an increase in the live lo ad due to the dynamic load effects of moving vehicles. The Standard Specification s refers to the d y namic load effect increa se as Impact , while the Standard LRFD Specifications refer to it as the Dynamic Load Allowance . Although the terminology is different the application is the same . Both codes require an increa se in the live load with re spect to the earth fill depth . The LRFD provisions apply a factor that varies linearly from 33% at 0 ft of fill to 0 % at 8 ft. The Standard Specifications decrease in 10 % steps, s hown 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 con s iderably evident for depths of fill equal to and greater than 3ft. 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 Specification neglects the Dynamic load allowance for depth s greater than 3 ft. The increase in the load effect i s demonstrated in Figure 5.4. The maximum increase in live load is 21% which corre ponds to an earth fill depth of 3 feet. 86

PAGE 103

35 % 30 % 25 % 20 % ti .. . 15 % 10% 5 % 0 % 0 25% 20"/o 1 5"/o 5: .. 1 0"/o u .: 5"/o O"'o 5 % 2 Dynamic Load Allowance LRFD vs . LFD 3 4 5 Earth Fill Depth (It) 6 7 8 9 Figure 5.3 -D ynamic Load Allowance vs. Impact Increase in D namic Load Allowance LRFD vs. LFD 5 6 7 8 Earth Fill Depth (It) Figure 5.4 % Increase in Dynamic Load Allowance LRFD vs. LFD 87

PAGE 104

5.4 Latera l Live Loa d Surcharge Both the Standard AASHTO Specification s and the LRFD Specification s require a live load surcharge press ure. The live load s ur charge pre ss ure is an increa se of the lateral earth pres ure due to the live load . The increase in horizontal pressure is calculated by Equation 5 .1. Where: LLS = k * Y s * heq Equation 5.1 LLS = Con s tant horizontal earth pressure due to live load s urcharge ( p sf) k = Coefficient of lateral earth pre ure Y s =Unit weight of s oil (pcf) heq =Equivalent height of soil for a vehicle load (ft) The equivalent height of soil, heq , specified by the Standard Specification s i s 2ft. The Standard LRFD Specifications calculate the equivalent height of s oil as a function of the wall height extrapolated from Table 4 .7. Linear interpolation s hould be used for intermediate wall height s . The wall height i s considered to be the distance between the top surface of backfill and the footing bottom . See Figure 4.12 . 88

PAGE 105

In general, the Standard LRFD Specific ation requirements produce a greater increase in the lateral live load surc harge pre ss ure when compared to the Standard AASHTO Specifications for abutment heights up to 20 ft. The lateral live load s urcharge pressure is considerably greater using the LRFD Specifications than the Standard AASHTO Specifications for abutment heights less than 4 ft. The difference in live load s urch arge height is shown in Figure 5.5. The increase in the equivalent height of soi l for various abutment heights for both specifications is also show n in Figure 5.5. The lower value of 2ft for the equivalent live load surcharge height in the Standard Specifications was originally derived from an HSl0-44 design truck (AA SHTO 2005). The values of the equivalent live load s urcharge height in the Standard LRFD Specifications were determined from a HL-9 3 Design Live Load. This explains the large discrepancy between both specifications. Live Load Surcharge Height 4 . 5 4 . 0 J c LRFDl 3 . 5 -1.LFD 3 . 0 -1 -g 2 . 5 -1-1-I 2 . 0 ,.,.-r--rr--1 . 5 1 -rr--r-r--, _ -r--1 . 0 rrr--r-r--f' -, _ r--0 . 5 1 -rr--r-r----, _ r--0 . 0 0 2 4 6 8 10 12 14 16 18 20 Abutrrent Height (It) 89

PAGE 106

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 Spe cifications takes into acco unt the contact area between the footprint of the tire and ground s urfa ce . The distribution area is equal to the tire footprint, with the footprint dimensions increased by either 1.15 times the earth fill depth for se lect granular backfill, or 1.0 for other types of backfill. The Standard AASHTO Specification s do not account for the dimensions of the tire, instead the wheel load i s considered as a concentrated point load. The wheel load is distributed over a sq uar e 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. Thi s complicates the distributed live load area and lo a d value calculation. 90

PAGE 107

In the Standard AASHTO Specifications there are 3 cases which are considered: • Ca e 1 Di tribution of Wheel Loads that do not Overlap • Case 2 -Distribution of wheel Load from a Single Axle Overlap • Case 3 -Full Distribution of Wheel Loads from Multiple Axles. The Standard LRFD Specifications require two additional cases, Cases 4-5. The Standard LRFD Specifications require a check to determine if the distributed live load pressure from multiple truck axles positioned side by side overlap. In other words, a calculation is required to determine the live load pressure from two vehicles traveling side-by-side spaced 4 ft apart. Case 4 is when two wheels from separate axles overlap as illustrated in Figure 5.7. Case 5 occurs when both axles from each design truck overlap as illustrated in Figure 5.8 . It i important to note that for cases 1-3 a multiple presence factor of 1.2 must be used, while for ca es 4-5 a multiple presence factor of 1.00 applies as specified in Section 4 . 5. 91

PAGE 108

LFD Di stri bution Width s IJHEEL LOA D H LRFD Di stri bution Width DISTRIBUTED LOAD AREA Figure 5.6 Live Load Distribution Areas for a Single Wheel 92

PAGE 109

Figure 5.7-Overlapping Wheel Load Distribution by Passing Vehicles Figure 5.8-Overlapping Axle Load Distribution by Passing Vehicles 93

PAGE 110

The provi s ion s from the LRFD Specification s often yield greater design forces than the Standard AASHTO Specification s, specifically at s hallow covers. Figure 5.9 s how the li ve load se rvice pre s ures for both the LFD and LRFD de s ign vehjcles at various depth s of fill . The s ingle LRFD Desig n Truck with a multiple pre se nce factor of 1.2 produces the worst case service live load pressure for depths of overburden between 0 and 5 ft. For depth s of overburden greater than 5 ft , the De sign Tandem spaced 4 ft apart with a multiple presence factor of 1.00 produces the large s t service live load pre ss ure s . Howe ver, thj is not theca e for factored live load pre ss ures found in Figure 5 .10. The single HS20 Design Truck specified in the Standard AASHTO Specification s produce a higher live load pre ss ure for an earth fill depth at 2ft. For depths greater than 2ft, the live load pre ss ure s follow a sirru lar path as the service live load pres ure pre v iou s ly discus se d . The single LRFD Design Truck with a multiple presence factor of 1.2 produce s the worst case factored live load pressure for depths of overburden between 0 and 5 ft. For depths of overburden greater than 5 ft the Design Tandem spaced 4ft apart with a multiple presence factor of 1.00 produces the largest factored live load pressure s . 94

PAGE 111

Distr i buted Load Values Through Earth Fill (includes Impact+ MPF ) 2000 .00 1800 .00 1600 .00 1400.00 1200.00 ! j1000. 00 800. 00 600 . 00 400 . 00 200 . 00 0 . 00 0 . 00 -+LFD HS20 D esign T ruck ..-LFD AHemat ive Military LRFD Design Truck LRFD Dual D esign Truck _,._ LRFD Design Tandem __._ LRFD Dual Desig n Tande m I % ' ,, 4 . 00 8 . 00 12 . 00 16 .00 Dep th Of All (It) 20 . Figure 5.9 Distributed 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. ; i 1500 . 00 1000 . 00 500.00 0 . 00 0 . 00 . I d , -+LFD H S 2 0 Design Truck _.._ LFD Mema tive Military LRFD Design Truck _,. LRFD Dual Des i gn T ruck \ -+LRFD D esi gn Tande m \ __._ LRFD Dual D esi g n Tande m \ .. 4 .00 8 . 00 12. 00 16 .0 0 Dopth or All (Ill 20 . 00 Figure 5.10 -Distributed Factored Live Load Values through Earth Fill with Impact 95

PAGE 112

5.6 Distribution of Live Loads for Depths of Fill Less Than 2 Feet. Underground concrete struct ure s are typically analyzed as two-dimensional frames. For depths of overburden less than 2ft, equivalent strip widths are used in both Specifications to simplify the analysis of the three-dimensional respon e due to live loads. Both specificatio n s examine the liv e load in str ip widths. This strip width is the effective width of slab that resists the applied load . The primary differences are summarized in the following sections : Truck Configuration: The Standard AASHTO Specification breaks the design vehicle into a line of wheel loads, whereas the Standard LRFD Specifications utilizes a full axle on the member. Both codes allow the re spected live loads 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 strib ution width in the Standard LRFD Specification s is twice the distribution width found from the Standard Specifications. This increase i a result of the LRFD Specification u ing a full axle instead of a single wheel. • LFD Specifications: Pwheel IE =Wheel Load I (4 + .06 *Span) • LRFD Specifications: Paxle IE = Axle Load I (8 + 1.2 * Span ) 96

PAGE 113

Tire Contact Area: Both specifications a s sume the tire contact a s a rectangle with the length in the direction of traffic equal to 10 in , and a width of 2 0 in. Lateral Distribution (load length): The Standard AASHTO Specification s doe s not take into account earth fill that i s placed on the s tructure. The wheel load i s s imply as s umed to act a s a point load. The Standard LRFD s pecifications allow the de s igner to take advanta g e of earth fill by as s uming the axle load to be di tributed laterally increa s ing the load length. As a re s ult of thi s provision, the Standard LRFD Specifications produce s s maller service moment s when compared to the Standard AASHTO Specification s for earth fill depth s less than 2 ft. Thi s i s compari s on i s hown in Figure 5 .11. The live load s ervice moments for both the LFD ( HS-20 ) and LRFD de s ign vehicle s at variou s de s ign span s and an earth fill depth of 1.00 ft are included in the figure. For each cas e the service moments cau s ed by the Standard Speci f ication s control the de s ign. Thi s i s attributed to the load effect from the Standard LRFD Specifications acting more like distributed load than a concentrated load. However , it i s 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 Specification s control the design, Figure 5.12. 97

PAGE 114

5. 7 Load Factors and Load Combinations The load factor design methodology in the Standard AASHT O Specification s is simi lar to the l oa d and resistance factor design requirements in the Standard LRF D Specification s . Both specifications utilize load factors, s treng th reduction factors, and rely on loading co mbin ations to check for strength a nd se rviceability requirements. However in the LRFD met hod , load and resistance fac tor s are determined through s tatistical studies of the variability of load s and resistances. 20.00 18.00 16.00 14.00 E' 12.00 ;! 10.00 .. :::E 8.00 6 .00 4 .00 2 .00 0.00 Service Moment comparison (depth offill = 1 . 0 ft) Neglects Impact+ Multiple presence f actor I 0 LFD DESIGN TRUCK I • LRFD DESIGN TRUCK J --;; -..... _H r-f--, _ [l:_ I ' , J f---, _ '--.__ '--4 .00 6 .00 8 .00 10.00 12.00 14.00 Design Span (ft) f-f--f--f-f--'--r--16.00 Figure 5.11 Service Moment LRFD vs. LFD Design Live Loads ( Multiple presence factor and impact neglected) 98

PAGE 115

20 . 00 18 . 00 1 6 . 00 14. 00 12 . 00 g 10 . 00 rn :::; 8.00 6 . 00 4 . 00 2 . 00 0 . 00 1-r-1-t-L.. 4 . 00 Service Moment comparison (depth of fill= 1 . 0 ft) Includes Impact + Multiple presence factor 1---I [] LFD DESIGN TRUCK f--.--1 -I • LRFD DESIGN TRUCK 1-r-f.--1---.--1-1-1-1-r-f.--1-f.--1---r-f.-f.--1 -r--1-,---1-1-1-1-1-r--11-1-t-1---1 -1-1 -L.. L.,_ L.,_ ._ L--L-L.. L 6 . 00 8 . 00 10 . 00 1 2 . 00 14. 00 16 . 00 Design Span (It) Figure 5.12 Service Moment LRFD vs. LFD Design Live Loads (M ultiple presence factor and impact included ) This approac h i s considered to be more realistic than the application of judgment-based factors in the LFD Specifications. The goal of the LRFD approach i s to provi de a more rational design ba s i s wit h more uniform r eliability. The reliability theory on which the LRFD method is created and the calibration of the load and strengt h reduction factors are well do c umented . When designing underground preca s t concrete culverts and t hr ee sided tructures, the Standard AASHT O Specification s applies one set of load factors to the force effect, while Standard LRFD Specification varies th e load factors to maximize the load effects . Table 5.1 lists the load factors for b oth specifications. 99

PAGE 116

Table 5.1 Load Factors for LRFD and LFD Specifications Load Designation LRFD Lo ad Factors Standard Load Factors 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 Pre ssure, EH Vertical Earth Pre ssure, 0.90 and 1.3 1.3 EV Live Load s, LL 1.75 2.17 Live Load Surcharge, LS 1.75 2.17 The minimum and maximum load factor val ue s util ized by the Standard LRFD Specific atio n s adjust the load effects s uch that one de sign load decreases the effect of another. The minimum load factor i s used for the load that decrea ses the force effect of another load . For example, consider the three-sided culvert s hown in Figure 5.13. If the val ue of the maximum po sitive moment in the deck was to be calculated, the maximum load factors from Table 5.1 would be used to determine the verti cal loads. 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 corresponding load combination would be calculated using Equation 5.2. 1.25*(DC) + 1.35 *( EV) + 1.50*(DW) + 0.90 *(EH) + Equation 5.2 1.75*(LL + IM) 100

PAGE 117

L L + IM .J. ! I l I I I I I I LL+ IM ow I I l I I I I I I EV 1-o c ' Figure 5.13 Loads on a Three-Sided Culvert The Standard AASHTO Specifications does not vary the load factors and hence , the corre s ponding load combination for the culvert in Figure 5 . 3 would be determined using Equation 5.3. 1.30 *( DC) + 1.30 * (EV) + 1.30 *( DW ) + Equation 5.3 1.30 * (EH ) + 2 .17*(LL + IM ) The mo s t s ignificant difference between both s pecification s is the live load factors. The Live load factor in the Standard LRFD Specifications has been reduced from 2.17 to 1.75 , a decrease of 19.4 % . Howe v er, both the m a gnitude and the effective depth of the live load impact (Dynamic Load Allowance ) have been 101

PAGE 118

increased. A multiple presence factor of 1.2 has also been introduced in the Standard LRFD Specifications for a single loaded lane. Therefore, the load factor for a single loaded lane equates to 2.1. Overall the load effect from the LRFD Specifications produces greater live load effects. 102

PAGE 119

Design Example #1 6.1 Problem Statement Chapter 6 Design Examples This example illustrates the design of a three-sided precast concrete str u ct ure . The three-sided tructure was analyzed utilizing both the Standard AASHTO Specifications, a nd the Standard AASHTO LRFD Specifications. After determining the individual load components and assembling the design load combinations, the design of the flexural reinforcement is presented. The design example conclude with the shear calculations from both s pecifications. The inside dimen ion s of the three-sided structure are 20ft . x lOft,. The deck thickness is 14in., and the wall thickness is lOin. with a 1ft. x 1ft. haunch . Earth fill will be placed on top of the precast structure to a depth of 5ft. A typical section of the culvert is shown in Figure 6.1. 6.1.2 Design Parameters Material Properties: Yield Strength, fy = 60,000 psi Compressive Strength, f ' c = 6000 psi Minimum concrete cover = 2 in 103

PAGE 120

Maximum aggregate ize, Ag = 0 .75 in Design Loads: Depth of earth fill = 5 ft Unit weight of concrete, yc=150 pcf Unit weight of s oil , ys = 120 pcf Equivalent fluid pressure , EFP = 30 pcf Backfill Material= Select granular Live load specified in applicable code s Strength Reduction Factors: Flexure,


PAGE 121

Earth Fill ____________________ ] __________ _ 1 o'-o" Three-Si ded Stru cture E le vatio n 1'-2" r---ot •• •. • L. . A . 4 . , . ' 4 . -4 X 1 ' ... . . . ... . . f-----------------'20 ' -0 "'----------------f.-+'1 0. Three-Sided Structure Cross Section Figure 6.1 Design Example #1, Geometry 105

PAGE 122

The lateral earth pressure (EH) on the culvert is found usi n g the equivalent fluid method. Section 6.2 . 1 in the Standard AASHT O Specification s require a minimum and maximum equivalent fluid pres ure of 30 pcf and 60 pcf re spectively . At the top of the culvert, the lateral earth pre ss u res are calculated as : EH =EFP* Z EH MIN = (30 pcf) * ( 5 ft) = 150 psf EHMAX = ( 60 pcf) * ( 5 ft) = 300 psf At the bottom of the c u lvert, the lateral earth pressures are calc ul ated as: 14 EHMIN = ( 30 pcf) * (5 ft +-ft +10ft)= 485 psf 12 14 E H MAX = ( 60 pcf) * (5 ft +-ft +10ft) = 970 psf 12 Figure 6.2 illustr ates the vertical and the min and max lateral earth pressures applied to the threesi ded struct ur e . EV: 600pst I _ I . 1 _ _ 1 :' 1.1 I I ' I I I I _1 11 . . : . /!J • • . EH : 4 85 pst EH : 485 psf EV: 600pst rll II II I I I I I I I I t EH: EH: 970 pst EH: 970 psf Figure 6.2 LFD Vertical and Lateral Earth Pressures 106

PAGE 123

6.1.3.2 Live Load Surcharge The live load surcharge (LLS) pressure is calculated utilizing the maximum equivalent fluid pres s ure. The Standard AASHTO Specification s require an equivalent height of soil , Heq of 2ft. The live load s urcharge is calculated as: LLS = EFP * Heq LLS = (60 pcf) *(2ft) = 120 psf Figure 6.3 illu strates the live load s urchar ge pressure applied to the threeside d structure. 6.1.3.3 Impact For depth s of fill greater than 3 ft no Live Load Impact is considered in the Standard AASHTO Specification s . Therefore no increase in Live Load due to the dynamic load effects i s necessary. LLS = 120 psf LLS = 120 psf . ' . Figure 6.3 -LFD Live Load Surcharge Pressure 107

PAGE 124

6.1.3.4 Design Live Loads The design live load s include the HS-20 design Truck and the Alternative Military Truck. For depth s of fill greater than 2 ft. the Standard AASHTO Specifications allows for the wheel load to be dist ributed through soil over a s quare equal to 1.75 times the depth of fill. For a HS-20 Design Truck the distribution width for a wheel is larger than the distance between the centers of the two wheels in the sa me axle. Therefore , the di stri bution area overlap and the total load from both wheels is assumed to be uniformly distributed oyer the area within the out er boundaries of the overlapped areas. The dis tribution area is illu s trated in Figure 6.4. HS-20 Design Truck WuLL Three Sided Structure E levation Three Sided Structure Cross Section Figure 6.4 HS-20 Distribution through Earth Fill 108

PAGE 125

The HS-20 De sign Truck prodl}ce s a service live load pressure of: WuLL= 2 * (Pw) (1.7 5 * H)* ( 1.75 * H +Axle Width ) WuLL = 2 * (16000 lb I wheel) ""248 sf ( 1.75 *5ft)*(l.75 *5ft+6ft) p For the Alternativ e Military Truck the di str ibution areas from all four wheels fro m both se t s of axles overlap . Therefore , the total load i s dis tributed over the total area wit hin the bound aries of the four whee l di st ribution area s . The distribution area is illustrated in Figure 6.5. Alternative Military Truck f----12"-9"'------1 Three Sided Structure Elevation Three-Si ded St ructure Cross Sec tion Figure 6.5 -Alternative Military Distribution through Earth Fill 109

PAGE 126

The Alternative Military load produces a service live load pressure of: 4*(Pw) WuLL = _________ ____;c_ _______ _ ( 1.75 * H +Axle Spacing) * ( 1.75 * H +Axle Width ) WuLL = 4 * (12000 lbs I wheel) "" 255 sf (1.75 * 5 ft +4ft)* (1.75 * 5 ft +6ft) p The Alternative Military Truck produce s live load intensity s lightl y higher than that of the HS-20 Design Truck. It also has a larger influence ar e a than the HS20 De sign Truck. Therefore the Alternative Military load controls the design. Thus , the Alternative Military Truck will be used to design for the strength and limit states. 6.1.3.5 Load combinations: For both the st rength and service limit states, three load cases are considered as s hown in Figure 6.6. The load cases are described in detail below. • Case 1: Maximum vertical loads on deck , minimum lateral loads on legs. This case produces maximum stresses in the bottom of the deck. • Case 2 : Maximum vertical and horizontal loads on the struct ure. This case produces maximum stresses on the corner of the and outside walls. 110

PAGE 127

• 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 = 1.3 * DL + 1.3 * EV + 1.3 * EHMIN + 2.17 * LL 2. U = 1.3 * DL + 1.3 * EV + 1.3 * EHMAX + 1.3 * LLSurcharge + 2.17 * LL 3 . U = 1.3 * DL + 1.3 * EV + 1.3 * EHMAX + 1.3 * LLSurcharge Service: 1. u = 1.0 * (DL + EV + EHM[N + LL) 2. U = 1.0 * (DL + EV + EHMAX + LLsurcharge + LL) 3. U = 1.0 * (DL + EV + EHMAX + LLsurcharge) A structural analysis was performed utilizing a commercial software package , SAP2000. The structure was modeled and analyzed for a 1 foot wide design strip oriented parallel to the direction of traffic. The structure was modeled assuming a pin-pin connection as specified in 16.8.5 of the Standard AASHTO Specifications. The axial forces were neglected to simplify the design calculations . 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 locatio n s . 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 listed per foot width in Table 6.1. Ill

PAGE 128

Case 1 --.-L-f-":::\l . . . I I . , I l , 1 ; r:xl LL= 255 ps + o n * l l l n o o + Ev-6oo psf E H = 485 psf t } + ' ' + i i + } I + + + } } I + + + } } u.s = 120 psf EH = 300 psf .... . . Case 2 E H = 970 psf EV = 600 psf t t J J J * f f J i * f + J J * + + + J J * + + u.s = 120 psf . ; .. . . . . . EH = 300 psf Case .3 E H = 9 7 0 psf Figure 6.6 LFD Service Loading Configuration, Cases 1 -3 112

PAGE 129

@) .----------------------------------------------------------------------, l ! ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ! ! ' ' ' ' ' ' ' ' ' ' ' ' ' i Figure 6.7-Critical Locations for Stresses Table 6.1 LFD Structural Analysis Results per Foot Width , E x ample 1 Load Case 1. Load Case 2. Load Case 3 . ..... .--. Cd en Q)Q.. ..c (j)C 1 __ __ __ 2_.9_1-+ __ 4_.8_9 __ 2 -22.80 4.32 -22 . 24 6.74 -15 . 16 5.96 3 11.76 13.48 -15.56 13.48 -11.58 9.07 4 50.20 0.00 46.40 0.00 29.23 0 . 00 Location Load Case 1. Load Case 2 . Load Case 3 . ... .--. ... .--. ... .--. c.:= ..... .--. c.:= ..... .--. c.:= ..... .--. a> I Cd en a> I Cd en a> I Cd en E c.. Q) c.. Ea. Q)Q.. E c.. Q)Q.. ..c -..c -..c -0 -(j)c 0 -(j)c 0 -(j)c .::: ::::22 ::::22 ::::22 1 0 . 00 0.00 2.90 2.46 3.76 2.80 2 -15.35 3.08 -14.93 4.94 -11.66 4.58 3 -7.82 9.01 -10.74 9 .01 -8.91 6 . 98 4 33.32 0.00 30.4 0.00 22.48 0 . 00 113

PAGE 130

6.1.3.6 Reinforcing Design The bottom of the slab will be designed using #5 , Grade 60 , reinforcing bar . . ( rebar diameter ) d =slab thicknessclear cover+ 2 d = 14in -( 2in + = 11.69in Asreq.=[0.85*fc*b]*[d-d2 -24 *Mu ] fy q> * 0.85 * f c. b Asreq.=[0.85* 6000p i *l2in]*[ll.69in-ll.69in2 24 * 50.20 * 1000lb-ft ] 60000 psi 0.95 * 0 .85 * 6000 psi •12 in A 0 . 94in2 s req. = ft Check Maximum Reinforcement ( LFD 8.16.3): 87000 ]*b* d fy 87000+fy As max= 0.75 *[0.85 * 6000 p i * 0.75]*[ 87000 ]* 12 in* 11.69 in 60000p i 87000+60000psi A 3.97in 2 smax=--ft 114

PAGE 131

Check Minimum Reinforcement (LFD 16.8.5.8): As min = 0.002 * b * h As min= 0.002 * 12 in* 14 in A . 0.34in2 s!Tiln =---ft Try #5's @ 3 inches on center: As provided= 12 in * .307 in2 = 1.23 in2 3 Check Crack Control (LFD 16.8.5.7): The crack control equations are checked to ensure the primary reinforcement is well distributed. Typically the crack control equations will govern the spacing , and amount of reinforcement. The size of rebar and spaci ng were already chosen to ensure the crack control requirements are met. Calculate Allowable Stress, fsa: f f 98 ksi s $: sa = --=== 'Vdc* A d I rebar diameter 2 . 0.625 in 2 31. c=c earcover+ = m + = . m 2 2 115

PAGE 132

2*dc* b 2 *2.31* 12in A= _N_u_m_b-er_o_f_b-ar_s _ , = 12 = 1 3 .86 3 98 k i . fsa = =30.86k 1 V2.31 in* 13.86 Calculate Actual Stress in Reinforcement: E 29000000 psi Ec wcl.5 *33*Fc n = 290000 00 psi = 6 .18 u se 6 (150 lb/ft3l5 * 33 * psi ) b * x * (%) = (n *As prov. ) * (d-x) b * x2 ---n * A prov. * (d-x) = 0 2 1 2in* x2 ----6 * l.23in2 * (11.69in-x ) =0 2 x=3. 22in 116

PAGE 133

"*d-d x-1169" 3 22in_l062" J ----. m---. In 3 3 fs = Ms = 33 32 k-ft * 12 = 30.62 k s i $ 30 . 86 ksi ok As* j * d 1.23in * 10.62in Next , the reinforcing steel will be designed for the top of the slab. Further , #5, Grade 60, reinforcing bars will be u sed for the design. d = 14in ( 2in + = 11.69in As= [0.85 * 6000 psi* 12 in] * [ 11.69 in_ 11.69 in2 _ 24 * 15. 56*1000 lb-ft ] 60000 psi 0.95 * 0.85 * 6000 psi •12 in A 0.28 in2 s req . = --ft-Check Maximum Reinforcement (LFD 8.16.3): As max= 0.75 *(0.85 * 6000 psi * 0.75) * ( 87000 ) * 12 in* 11.69 in 60000 psi 87000 + 60000 psi A 3 . 97 in2 smax=---ft 117

PAGE 134

Check Minimum Reinforcement (LFD 16.8.5.8 ) : Asrni n = 0.002 * 12in * 14 in A . 0.34in2 srrun =---ft Try #5' s @ 3 inches on center : p A s provided = m * .307 in 2 = 1 . 23 in 2 3 Check Crack Control ( LFD 16.8.5.7 ) : Calculate Allowable Stress , fsa: f < f 98 ksi s _ sa = -:-;:::::== V d c * A d 2 . 0.625 in 2 31. c= m+ = . m 2 A= 2 * 2 .31*12in =l3.86 12 3 fsa = 98 ksi = 30 . 86 ksi V2.31in * 13.86 118

PAGE 135

Calculate Actual Stress in Reinforcement: n = 29000000 psi = 6 _18 use 6 ( 150 lb/ft 3 ) 1.s * 33 * ( psi) 12. * 2 10 x 6 * 1.23 in 2 * (11.6 9 in-x) = 0 2 x = 3 . 22in 3 22in =10.62in 3 3 M s 10.74k-ft*12 fs = = = 9 . 86 ksi 30 .86 ksi ok As* j * d 1.23in * 10.62in The reinforcing pattern for the outside walls will now be designed . Once again, #5 , Grade 60, reinforcing bars will be utilized in the design . d =lOin-( 2 in+ = 7 . 69 in A s req. = [0.85 * 6000psi * 12 in]* [ 7 .69 in_ 7 _ 69 in2 _ 24 * 22.80 * 1000 lb-ft ] 60000 psi 0.95 * 0.85 * 6000 p s i • 12 in A 0.65in2 sreq.= ft 119

PAGE 136

Check Maximum Reinforcement (LFD 8.16.3): As max= 0.75 *(0.85 * 6000 psi * 0.75 ) * ( 87000 ) * 12 in * 7.69 in 60000 psi 87000 + 60000 psi A 2.61in2 smax=---ft Check Minimum Reinforcement (LFD 16.8.5.8): Asmin = 0.002 * 12 in* 10 in A . 0 . 24 in2 siTIJn =---ft Try #5 ' s @ 3 inches on center: As provided = 12 in * .307 in 2 = 1.23 in 2 3 120

PAGE 137

Check Crack Control (LFD 16.8.5.7): Calculate Allowable Stress, fsa: f < f 98 ksi s _ 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 k s i V2.31 in * 13.86 Calculate Actual Stress in Reinforcement: n = 2 9000000p si = 6 .18 u se 6 ( 150 lb/ft3l5 * 33 * ( 6000 p si) 12 . * 2 m x -6*1.23in2*(7.69in-x)=0 2 x = 2.52in 121

PAGE 138

* d d x 7 69 2 52 in 6 85 J . = --= . lll= . lll 3 3 f s = Ms = 1535 k-ft * 12 = 21.86 ksi 30.86 ksi ok As * j * d 1.23in * 6.85in Finally , the inside of the walls will be designed using #4 , Grade 60, reinforcing bars. d =lOin-( 2in + = 7.75 in As req. = [0.85 * 6000 psi * 12 in]* [ 7 . 75 in_ 7 . 75 in2 _ 24 * 4.89 * 1000 lb-ft ] 60000 psi 0.95 * 0.85 * 6000 psi • 12 in A 0.13in2 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 122

PAGE 139

Check Minimum Reinforcement (LFD 16.8.5.8): Asmin = 0.002 * 12 in* 10 in A . 0.24in2 smm=--ft Try #4 ' s @ 6 inches on center : "d d 12 in 96 2 0 392 2 A s prov1 e = -.1 m = . m 6 Check Crack Control (LFD 16.8.5.7): Calculate Allowable Stress, fsa: f f 98 ksi s :::; sa = -:r=== Vctc* A d 2 . 0 . 50 in 2 25 . c = m+ = . m 2 A= 2 * 2.25 * 12in =27 12 6 98ks i f s a = = 24.93 ksi V2.25in *27 123

PAGE 140

Calculate Actual Stress in Reinforcement: n = 29000000p s i = 6 .18 use 6 (150 lb/ft 3 ) t.s * 33 * ( psi ) 12. * 2 m x -6* 0 .39in2*(7.75in-x)=O 2 x = 1.56in j * d = d = 7. 7 5 in -1.56 in = 7.23 in 3 3 M s 3.76 k-ft * 12 fs = = = 16.00 ksi::; 24.93 ksi ok As * j * d 0.39in * 7.23in 6.1.3.7 Calculate shear (LF D 8.16.6.2 ): The allowable shear in the three-sided structure was calculated using the simplified equation. Shear in the Deck: Vu = 13.48 kips eve eve= 0.90 * 2 * psi *12 in * 11.69 in= 19558.9lb = 19.56 kips = 19.56 kips> 13.48 kips OK 124

PAGE 141

Shear in the Walls: Vu Vu = 6.74 kips 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 kips OK 6.1.3.8 Summar y Figure 6.8 illustrates the required reinforcement for the inside face and outside face of the side walls, top slab, and bottom slab . Note that the reinforcement spacing is the same or on increments of one another. This is typical in precast concrete in order to simplify the construction of the cage. There are numerous combinations of rebar s ize and spacing. As long as all requirements are met the designer should choose the most economical and practical design. 125

PAGE 142

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 vertical earth pressure on the top of the culvert is calculated as: WuSL= ys*Z WuSL = (120 pet)* (5 ft) = 600 psf Similar to the Standard AASHTO Specifications , the lateral earth pressure (EH) on the culvert is found using the equivalent fluid method. However, the LRFD Specifications does not specify minimum and maximum equi v alent fluid pressure. This is taken into account in the load factors , and loading combinations. An 126

PAGE 143

equivalent fluid pressure of 30 pcf is assumed for this example. Typically the lateral earth pressure is 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 three-sided structure. EV = 600 psf EH = 150 psf I I I I I I I I I I I I I I I I I l EH = 150 psf o,. " . .. . .. . . . . . EH = 485 psf EH = 485 psf Figure 6.9 -LRFD Vertical and Lateral Earth Pressures 6.1.4.2 Live Load Surcharge The live load s urcharge 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

PAGE 144

height in Table 4.4. The wall height is considered to be the distance betw een the top urface of backfill and the footing bottom . A 1 ft thick footing was assumed for this example. Figure 6.10 illustrates the wall height u se d in thi s example. After linear interpolation the equivalent height of soi l was determined to be 2 . 28 ft. _ __:_____,_ __ _._____;:__---;. 17'-2" • I L .. Figure 6.10LRFD Wall Height, Example #1 The live Load Surchar ge i s calculated as: LLS = EFP * Heq LLS = (30 pcf) * (2.28 ft) = 68.4 psf Figure 6.11 illu s trate s the Live Load Surchar ge pre ss ure applied to the three-sided s tructure. 128

PAGE 145

LLS = 68 . 4 psf LLS = 68.4 psf . . ... 4 . ' . ..... 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 effects changes for varying burial depths. The Dynamic Load Allowance i s only applied to the Design Truck and Tandem Load , a nd not the L a ne Load. The Dynamic Load Allowance for a fill depth of 5 ft i s calculated as: IM=33*(1-0.125*DE) 0 % IM = 33 * (1-0 . 125 * 5 ft) = 12.375 % 6.1.4.4 Design Live Loads: The de s ign live loads include the HL-93 De s ign Truck , Design Tandem , and Lane Loads. Similar to the Standard AASHTO Specifications , the Standard LRFD Specification s allows for the wheel load to be distributed through soi l when the earth fill exceeds 2 ft. The dis tribution area is equal to the tire footpr i nt, with the footprint dimension s increased b y 1.15 time s the earth fill depth for selec t granular backfill. 129

PAGE 146

To d ete rmine the live load tha t s hould be carried into the s tructur a l a n a lysi s, the use of multiple presence factors mus t be taken into account. The multiple pre s ence factor for a single loaded lane for s tren g th and se rvice limit states is 1 . 20 . For two lane s loaded use 1 . 00 . For a single HL-93 De s ign Truck the distribution width for a wheel i s larger than the dis t a nce between the center s of th e two wheels in the sa me axle. Therefore, the distribution areas overlap and the total load from both wheels i s assumed to be uniformly di stri buted over the area w ithin the outer boundarie s of the overl a pped areas. The dis tribution area i s illustrated in Figure 6 .12. A s ingle HL93 Des ign Truck axle produce s a serv ice liv e load pre ss ure of: WuLL = 2 * cPw) *MPF ( LLDF * H + LT) * (LLDF * H + W T +Axle Width ) WuLL = 2 * (16000 lbs I wheel)* 1.2 :::; 434 . 75 psf ( 1.15 * 5 ft + 0.83 ft) * (1.15 * 5 ft + 1 . 67 ft +6ft) 130

PAGE 147

Design T ruck WuLL Three-Sided S t r ucture Elevation Three-Sided Structure Cross Section Figure 6.12 -Distribution area for Design Truck The AASHTO LRFD Specification s also require that the force effects for two design vehicles positioned 4ft. apart be evaluated. In this example the distribution width of both axles for two trucks positioned side-by-si de overlap. The total load from the two axles was then distributed over the area within the boundaries of the two axles. The distribution width is shown in Figure 6.13. Two HL93 Design Truck axles adjacent to each other (4ft apart) produces a service live load pressure of: 4 * cPw)* MPF WuLL = ________ __:_....:..:....:.. _________ _ ( LLDF * H + LT) * (LL DF * H + W T +Axle Width+ 4ft) WuLL = 4 * (16000 lbs I wheel)* 1.0 ""415 _15 psf ( 1. 15 * 5 ft + 0 . 8 3 ft) * ( 1.15 * 5 ft + 1. 6 7 ft + 6 ft + 4 ft + 6 ft) 131

PAGE 148

2 Desig n Vehicles Three-Sided Structure Ele vation Figure 6.13 Distribution area for two adjacent design vehicles For a sing le HL-93 D es ign Tandem the distribution area s fro m all fo ur wheels overlap from both sets of axles overlap. There fore, the total load is distributed over the total area within the boundarie s of the four w heel di tribution areas. The di s tribution area i s illustrated in Figure 6 .14. sc Three-Sided Structure Elevation Three-Sided Structure Cross Section Figure 6.14-Distribution area for Design Tandem 132

PAGE 149

A single HL93 Design Tandem Truck produces a service live load pressure of: 4*(Pw) *MPF (LLDF * H + LT +Axle Spacing)* (LLDF* H + WT +Axle Width) WuLL = 4 * (12500 lbs I wheel) * 1.2 ""422 . 56 sf (1.15 * 5ft +0.83ft +4ft)* (1.15 * 5 ft+ 1.67 ft +6ft) p The force affects for two HL93 Design Tandem Trucks adjacent to each other ( 4 ft apart) produces a service live load pressure of: 8*(Pw)*MPF WuLL = -------------_:___::c._:__ ________________ _ (LLDF* H + LT) * (LLDF* H + WT +Axle Width+ 4ft) WuLL = 8 * (12500 lbs I wheel)* 1.0 ""403.45 sf (1.15 * 5 ft + 0.83 ft +4ft)* (1.15 * 5 ft + 1.67 ft +6ft+ 4ft 6ft) p The distribution width for the lane load is assumed constant and equal to the width at the surface of the backfill for ease of calculations. The effect of the lane load on the three-sided structure is relatively small compared to the load affects from the design vehicles. It should also be noted that the use of multiple presence factors with regards to the lane load is not addressed in the AASHTO LRFD Bridge Design 133

PAGE 150

Specifications. However this example assumes the lane load does get multiplied by the appropriate multiple presence factor. The Lane Load produces a service live load pressure of: WuLL = 640 plf * MPF = 64psf * MPF 10ft The Single Design Truck produce s the maximum live load intensity; however the Single Design Tandem has a larger influeqce area. After analysis it wa s determined the Single Design Tandem with a multiple presence factor of 1.2 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 lOft 6.1.4.5 Load combinations: Similar to the LFD Specifications, for both the strengt h and service limit states, three load configuration s are considered as illustrated in Figure 6.15. The load cases correspond to: 134

PAGE 151

• Case 1: Maximum vertical load on deck, minimum lateral loads on legs. This case produces maximum s tresses in the bottom of the deck. • Case 2 : Maximum vertical and horizontal loads on the s tructure. The case produces maximum stresses on the comer of the deck, and outside walls. • 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 combination s 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 Service : 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

PAGE 152

Case 1 EH = 485 psf rlf-----J LL= 422.6psf 1 ' ' ' ' * ' ' 1 1 11 1 n Llo..:J6.8 psf ! H H t H H H H H J ! 0 H nfY. = 600 pst ' + o o o o n n n o + + o o t1LLs = 684 psf . • EH=150psf Case 2 EH = 4 85 psf E V = 600 psf ' + o o o o n n n n + + o o OLLs = 684 pst EH = 150psf . . . . t Case 3 EH = 4 85 psf Figure 6.15 Design Example #1, LRFD Service Loading Configuration , Cases 1 -3 136

PAGE 153

Sirrtilar to the Standard AASHTO Spe cificat ion s the structure was modeled as urrting a pin-pin connection as specified section in 12.14.5 of the LRFD Specification . The locations of the critical stres es and the value are illustrated in Figure 6.16, and Table 6 .2. Both the factore d and service values are listed per foot width in T able 6.2. @ ---+---------------------------------------------------------------------, I I I I I I t t I I I I I I I I I I I I I I l Figure 6.16-Critical Locations for Stresses 137 I I I I I I I I I I I :

PAGE 154

Table 6.2 -LRFD Structural Analysis Results per Foot Width, Example 1 Location Load Case 1 . Load Case 2. Load Case 3 . ....... _ ....... _ ....... _ C.t:: ..... _ C.t:: ..... _ c ...... ..... _ a> I ctl (/) a> I ctl (/) Q)-ctl (/) E c.. Q) c.. E c.. Q) c.. E 6_ Q) c.. ..c -..c -..c -0 -Cf)6 0 -Cf)6 0 1 0.00 0.00 0.07 0.38 2.55 2.03 2 -27.04 4.24 -26.72 5.57 -10.56 3.77 3 -12.88 16.16 -14.96 16.16 -7.46 6.28 4 61.67 0.00 59.60 0.00 20.79 0.00 Load Case 1 . Load Case 2. Load Case 3 . ....... _ ....... _ ....... _ C.t:: ..... _ c ...... ..... _ c ...... ..... _ a> I ctl (/) Q)-ctl (/) Q)-ctl (/) Ea. Q) c.. E 6_ Q)Q. E6_ Q)Q. ..c ..c -..c -0 -0 -Cf)6 0 Location 1 0.00 0.00 0.00 0.11 0.52 0.75 2 -18.58 3.44 -18.49 3.73 -11 .99 3.01 3 -9.41 11.07 -9.87 11.07 -6.44 6.98 4 41.47 0.00 41.01 0 . 00 24.95 0.00 6.1.4.6 Reinforcing Design The reinforcement for the bottom of the deck will be designed. Further , #7 , Grade 60 , reinforcing bars will be used in the design. 138

PAGE 155

. ( rebar diameter) d =slab thickness clear cover+ 2 d = 14in ( 2in + in) = 11.56in Asreq.=[0.85*fc*b]*[d-d2 -24 *Mu ] fy


PAGE 156

Check Minimum Reinforcement (LRFD 12.14.5.8): A s min = 0 . 002 * b * h A min= 0.002 * 12 in * 14 in A . 0 .34 in2 rrun =---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 * de A * f tJ s s d 2 . 0.875in 244. c= m+ = . m 2 = 1 + de = 1 + 2.44 in = 1.30 0. 7 * (h -de) 0. 7 * (14 in-2.44 in ) ye = ex po s ure factor = 1.00 140

PAGE 157

Calculate actual stress in reinforcement: n = 29000000 psi = 6 _18 use 6 ( 150lb/ft3)t.5 12 * 2 m x -6* 1.20in2 *(11.56in-x) =O 2 x = 3.17in in =10.50in 3 3 fs= Ms = 41.47k-ft*12 =39.4Sksi As* j * d 1.20in 2 * 10.50in 700 * 1.00 -2*2.44in=8.76in 1.30 * 39.48 ksi Actual Spacing= 6.0 8.76 in OK Calculate Maximum Spacing of Reinforcing (LRF D 5.10.3.2 ) s max= l.S * h 18in smax = 1.5 * 14in = 21 in therefore use 18 in Actual Spacing= 6.0 18 in OK 141

PAGE 158

Calcu late Minimum Spacing of Reinforcing (LRF D 5.10.3.1) -db= .625in -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 lab will be designed with #4, Grade 60, reinforcing bar . d 14in -( 2in + 11.75in A = [0.85 * 6000 psi * 12 in]* [11. 75 in_ 11.75 in2 _ 24 * 14.96 * 1000 lb-ft ] 60000 psi 0.95 * 0.85 * 6000 psi • 12 in A 0.27 in2 s req.= ft Try #4 ' s @ 3 inches on center : . d 12 in * 0 196. 2 0 78. 2 As provtde = --. m = . m 3 142

PAGE 159

Check Maximum Reinforcement Ratio ( LRFD 5.7.3.3 ) : c 0.78 in2 * 60000 psi = = 0.09 $ 0.42 ok d 0.85 * 6000 psi* 12 in* 0.75 * 11.75 in Check Minimum Reinforcement (LRFD 12.14.5.8 ) : A min= 0.002 * 12 in* 14 in A . 0.34 in2 srrun =---ft Check Crack Control (LRFD 12.14.5.7): Calculate minimum allowable spacing to satisfy cracking (LRFD 5. 7.3.4 ) : 700* 'Y e s $ 2*dc d 2 . 0.50 in 2 25 . c= m+ = . m 2 = 1 + de = 1 + 2.25 in = 1.27 s 0.7 *(h-dc) 0.7 *(14in-2.25in) ye = exposure factor= 1.00 143

PAGE 160

Calculate actual stress in reinforcement: n = 29000000 psi = 6 _18 u s e 6 (150lb/ft3)1.5 i ) 12 . :1< 2 m . x -6*0.78in2 *(11.75in-x)=O 2 x = 2.66in * d x 1 75 2 66 in 0 86 J =d--=1 . m-=1. m 3 3 fs = M = 9 . 87 k 2 -ft * 12 = 13.98 ksi As * j * d 0.78in *10.86in 700 * 1.00 s:s; 2 * 2 .25in =34.93in 1.27 * 13.98 ksi Actual Spacing = 3.0 in ::;; 34.93 in OK Calculate Maximum Spacing of Reinforcing (LRFD 5.10.3.2) s max = 1.5 * h ::;; 18in max= 1.5 * 14in = 21 in therefore use 18 in Actual Spacing= 3.0 in ::;; 18 in OK 144

PAGE 161

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 s pacing = 3 in OK The outside reinforcement for the walls will include #4, Grade 60, reinforcing bars. d =JOin-( 2in + = 7.75in As= [0.85 * 6000ps i * 12 in]* [ 7 _ 75 in_ 7 _ 75 in2 _ 24 * 27. 04 * 1000 lb-ft ] 60000psi 0.95*0.85*6000psi •12in A 0.77 in2 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 = O.l3 $0.42 d 0.85 * 6000 psi * 12 in* 0.75 * 7.75 in 145

PAGE 162

Check Minimum Reinforcement (LRFD 12.14.5.8 ) : Asmin = 0.002 * 12 in* 10 in 0 ?4. 2 A . -Jn srrun =---ft Check Crack Control ( LRFD 12.14.5.7): Calculate minimum allowable spacing to satisfy cracking (LRFD 5.7.3.4): 700*y S e -2 * de * f d 2 . 0.50 in 2 25 . c= m+ = . m 2 s = 1 + de = 1 + . 2 .. 25 in . = 1.41 0.7 * (h -de) 0.7 *(10m2.25 m) ye = exposure factor = 1.00 146

PAGE 163

Calculate actual stress in reinforcement: n = 29000000p i = 6 .18 use 6 (150 lb/ft 3 ) 1.s * 33 * ( .J6000 p s i ) 12in*x2 6 * 0 .78in2 *(7.75in-x)=O 2 x = 2.10in * d -d x 7 75 2 1 0 in -7 05 J ----. m-. m 3 3 fs= M = 18.58k-ft*12 =40. 54 ksi As * j * d 0.78in2 * 7.05in 700 * 1.00 2*2.25in=7.74in 1.41 * 40.54 ksi Actual Spacing= 3.00 in 7.74 in OK Calculate Maximum Spacing of Reinforcing (LRFD 5.10.3.2 ) s max= 1.5 * h 18in max= 1.5 * 14in = 21 in therefore u e 18 in Actual Spacing= 6.0in 18in OK 147

PAGE 164

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 OK The reinforcement on the inside of the walls will be de s i g ned u s ing #4 , Gr a de 60 , rein f orcin g bar s . d =JOin( 2in + = 7.75 in As= [0.85 * 6000ps i * 12 in] * [7 . 75 in_ 7 . 75 in2 _ 24 * 2. 55 * 1000 lb-ft ] 60000p i 0.95 * 0.85 * 6000ps i • 12in A 0 .07in2 sreq.= ft Try #4's @ 12 inches on center : A s provided= 12 in * 0.196 in 2 = 0.196 in 2 12 148

PAGE 165

Check Maximum Reinforcement Ratio (LRFD 5.7.3.3): e 0.196in2 * 60000 psi = = 0.03 :5 0.42 d 0.85 * 6000 p s i * 12 in* 0 .75 * 7.75 in Check Minimum Reinforcement (LRFD 12.14.5.8): A sntin = 0.002 * 12 in* 10 in 0 ? 4 . 2 A . -In snun=---ft Check Crack Control (LRFD 12.14.5.7 ) : Calculate minimum allowable spacing to satisfy cracking (LRFD 5. 7.3.4): 700 * y S $; e 2 * de d 2 . 0.50 in 2 25. e= m+ = . m 2 =1+ de =1+ 2.25in =1.41 s 0.7 *(h-de) 0.7 *(10in-2.25in) ye = exposure factor = 1.00 149

PAGE 166

Calculate actual stress in reinforcement: n = 29000000 p s i = 6 .18 u s e 6 (150 lb/ft3)1.5 * 33 * psi ) 12. * 2 m x -6* 0.196in2*(7.75in-x)=0 2 x=l.14in * d -d x -7 75 1.14 in -7 37 J ----. m . m 3 3 Ms 0.52k-ft*l2 f s = = = 4.3 2 k s i As * j * d 0.196in2*7.37in s 700 *l.OO -2* 2.25in = 110.42in 1.41 * 4 .32 ksi Actual Spacing = 6.0 in II 0.42 in OK Calculate Maximum Spacing of Reinforcing (LRFD 5.10.3.2) max = 1.5 * h 18in smax = 1.5 * 14in = 21 in therefore use 18 in Actual Spacing= 6.0 18 in OK 150

PAGE 167

Calculate Minimum Spacing of Reinforcing (LRFD 5.10.3.1 ) -db= .6 25 in -1.33 * Ag = 1.33 * 0.75 in= 1.0 in -1.0 in Actual spaci n g = 9 in 0 K 6.1.4.7 Calculate shear (LRFD 5.8.3.3 ) : The allowable hear in the three-sided struct ure i calculated using t h e implified equation. Shear in the Deck: Vu = 16.16 kips eve= e * p *Fc * b * dv dv = maximum v ulu e 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 .51b = 17.40 kip =17.40kips>16.16k.ip OK 151

PAGE 168

Shear in the Walls: eVc:2:: Vu Vu = 5.57 ldps ev c = e * p * .Jh * 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 P=2 eve= 0.90 * 2 * p s i * 12 in* 7.2 in= 6023.3Ib = 6.02ldps = 6.02ldps > 5 .57 ldps OK 6.1.4.8 Summary Figure 6.17 illu trates the required reinforcement for the inside face and outside face of the si de walls, top slab, and bottom s lab . 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 de sign s with regards to the area of stee l required is presented in Table 6.3. Table 6.3 -Area of Steel comparison Location -----------------------------------------------------------1 : 2 3 4 -LFo ________ -a.-13--:---
PAGE 169

. . #7 @ D.C. I+ @ 1 2.00M o.c. I+ @ 12.00M o.c. #4 @ 3.00" STEEL SECTION Figure 6.17 LRFD Reinforcement Placement for Design Example #1 Design Example #2 6.2 Problem Statement Thi s example i a continuation of de ign example# 1 , but with a 1 ft depth of overb urden . The threeided s tructure is once again analyzed utilizing both the Standard AASHTO Specifications , and the Standard AASHTO LRFD Specific atio ns. 6.2.1 Standard AASHTO Specifications: 153

PAGE 170

6.2.1.1 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) * (1.0 ft) = 120 psf The lateral earth pressure (EH) on the culvert is found using the equivalent fluid method. Section 6.2.1 in the Standard AASHTO Specifications 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: EH = EFP*Z EHMJN = (30 pcf) * ( 1.0 ft) = 30 psf EHMAX = (60 pcf) * (1.0 ft) = 60 psf At the bottom of the culvert, the l atera l earth pressures are calc ulated as : 14 EHMIN = (30 pcf) * (1.0 ft + 12 ft +10ft) = 365 psf 14 EHMAX = (6 0 pcf) * (1.0 ft +-ft +10ft)= 730 psf 12 Figure 6.18 illustrates the vertical and the min and max lateral earth pressures applied to the three-sided structure . 154

PAGE 171

EVz 120psf EH = 30 psf j t t t l l t t I l t t l t l t I l t l t I I t l t EH = 30 psf 1 r 1 EH = 365 psf EH = 365 psf EV= 120psf EH=60psf I I 0 0 0 tl 0 I I 0 lit 0 II O t EH=60psr 1 r EH = 730 psf EH = 730 psf Figure 6.18 -LFD Vertical and Lateral Earth Pressures 6.2.1.2 Live Load Surcharge The Live Load Surcharge pre ss ure i s calculated utilizing the maximum equivalent fluid pres s ure . The Standard AASHTO Specification s require an equivalent height of soil, Heq of 2ft. The live Load Surcharge is calculated as: LLS = EFP * Heq LLS = (60 pet)* (2ft) = 12 0 psf Figure 6.19 illu s trate s the Live Load Surcharge pre ss ure applied to the three-sided st ructure . 155

PAGE 172

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 varies for varying burial depths as illustrated in Table 6.4. The impact factor is applied to both the Design Truck and Alternative Military Load as a multiplier. The live load impact factor for 1.0 ft of fill is 30 % . T bl 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

PAGE 173

6.2.1.4 Des ign Live Loads The de ign live loads include the HS-20 design Truck and the Alternative Military Truck. For depth of fill less than 2ft., the Standard AASHT O Specification s 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 HS-20 De sign Truck produces a serv ice live load val u e of: PLL = 16000 lb !Wheel= 3047.6lbs I (ft-width) 5.25 ft PuLL= 2.17 * 1.3 * 3047 .6lb s I (ft-wi dth)= 8597 .3lbs I (ft-wid th ) s paced 14ft apart The Alternative Military De sign Truck prod uc es a se r v ice live load value of: PLL = 12000 lbs/Wheel = 2285.7lbs I (ft-width) 5.25 ft PuLL= 2.17 * 1.3 * 2285 . 7 lbs I (ft -width)= 6448.0 lb s I (ft-widt h ) spaced 4 feet apart A single axl e from the HS-20 design truck produces live load int ensity hig h er than the Alternative Military Load. However the axle of the Alternative Military are only 4.00 ft apart, producing 2 concentrated loads. After analysis it was determined 157

PAGE 174

that the Alternative Military load controls the design. Use the Alternative Military to design for the strength and limit states . 6.2.1.5 Load combinations: For both the strength and service limit states, three load cases are con s idered. The load cases are as follows. The loadin g configurations are illustrated in Figure 6.20 . The load cases correspond to: • Case 1: Maximum vertical loads on deck, minimum lateral loads on legs. This case produces maximum stresses in the bottom of the deck. • Case 2: Maximum vertica l and horizontal loads on the structure. The case produce s maximum stresses on the corner of the deck , and outside walls. • Case 3: Minimum vertical loads on deck, and maximum horizontal loads on walls. This ca e produces maximum stres es on the inside of the leg. The load combinations are as follows: Strength: 1. u = 1.3 * DL + 1.3 * EV + 1.3 *ERMIN+ 2.17 * (LL + IM) 2 . U = 1.3*DL+l.3* EV +1.3 *EHMAX +2.17*(LL+IM) 3. u = 1.3 * DL+ 1.3* EV + 1.3 * EHMAX 158

PAGE 175

= 2285.71b I EV= 120 psf ',.I' 'I J ''I J '*J J t+I t t+I t 0 Case 1 EH = 365 psf = 2285.7 1 b I J EV= 120psf 0 I t 0 0 U J 0 I t 0 J t 0 I t 0 l L LS = 120 psf ., . • ::i:q ..... -EH=60psf Case 2 EH = 730 p s f E V = 120 psf 0 I t 0 I t u J 0 0 0 J t 0 I t t n L L S = 120 p s f . ' ",. . . : ' . . . EH=60psf Case 3 EH = 730 psf Figure 6.20 LFD Service Loading Configuration, Cases 1 -3 159

PAGE 176

Service: 1. u = 1.0 * (DL + EV + EH MIN + LL) 2. U = l.O*(DL+ EV +EHMAX + LL) 3. u = 1.0* (DL+ EV + EHMAX) The critical locations of the internal forces are illustrated in Figure 6.21. Table 6.4 lists the factored and service stresses for each load combination at the critical locations. Once again the axial forces where neglected in to simplify the design calculations . ..----------------------------------------------------------------., ' ' ' ' ' ' :I : ! ! 'Figure 6.21 -LFD Critical Locations for Stresses 160

PAGE 177

Table 6.5 LFD Structural Analysis Results per Foot Width , Example 2 Load Case 1 . Load Case 2 . Load Case 3. ----c..... _ c..... _ C.t:: ..... _ Q)-ctl (/) Q)-ctl (/) Q) I ctl (/) Q)Q. Q) Cl. E o. Q)Q. ..c ..c ..c Location 0 -({)6 0 -({)6 0 -({)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 ...... ....._ Q)-ctl (/) Q)-ctl (/) IDI ctl (/) E Q)Q. E Q)Q. E o. Q) Cl. ..c -..c -..c -0 -({)6 0 -({)6 0 -({)6 1 0.00 0.34 1.95 2 . 14 4.07 2.53 2 -11.17 2.07 -10 .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

PAGE 178

6.2.1.6 R einforcing De ign The bottom reinforcement for the slab will be designed with #5 , Grade 60 , reinforcing bars. . ( rebar diameter ) d = lab th1ckne s-clear cover+ 2 d = 14in ( 2in + in)= I 1.69in A sreq.=[0.85*fc*b]* [d-d2 -24 *Mu ] fy


PAGE 179

Check Maximum Reinforcement (LFD 8.16.3): A max=0.75*pb* b * d b=0.75*(0 85* fc*P1)*( 87000 )*b * d fy 87000+ fy Asmax=0.75*(0.85* 6000psi * 0 .75)*( . 87000 )*12in * 11.69in 60000 psi 87000 + 60000 p s i A 3.97in2 smax=---ft Check Minimum Reinforcement (LFD 16.8.5.8 ) : As min = 0.002 * b * h Asmin = 0 . 002 * 12 in * 14 in A . 0 .34in2 srrun =---ft Try #S's @ 3.5 inches on center: As provided= 12 in * .307 in 2 = 1.05 in 2 3.5 163

PAGE 180

Check Crack Control (LFD 16.8.5.7): Calculate Allowable Stress, fsa: f f 98 ksi s:::; sa=--=== Vdc* A d 1 rebar diameter 2 . 0.625 in 2 31. c = c ear cover + = m + = . m 2 2 A= 2 *dc* b =2* 2.31*12in=l6 .17 Number of bars , N 12 3 . 5 fsa = 98 ksi = 29.31 ksi V2.31in * l6.17 Calculate actual stress in reinforcement: Es 29000000psi n ---___ ____;:;...___ -Ec-wcl.5 *33*Fc n= 29000000psi = 6 .18 use 6 (150 lb/ft3 )1.5 * 33 * psi ) 164

PAGE 181

b * x *(; ) = ( n * A s pro v.)*( d -x) b * X 2 ---n * A s prov. *(d-x) = 0 2 1 2in* x2 2 x = 3 .02 in 6 * 1.05 in2 *( 11.69 in-x) = 0 3 0 2in =10.68in 3 3 M s 26 .79k-ft* 1 2 f s = As* J .* d = 2 = 28 . 67 k s i 30.8 6ksi ok 1.05 in * 10.68 in Th e top reinforcement in the deck i s de s igned u sing #4 , Grade 60, reinforcing bar s . d = 14in ( 2in + = 11.75in A s = [0.85 * 6000psi * 1 2 in]* [ 11.75 in_ 11.75 in2 _ 24 * 15.15 .19* lb] 60000p s i 0.95 * 0.85 *6000ps1*12m A 0 . 28in2 s req.= ft 165

PAGE 182

Check Maximum Reinforcement (LFD 8.16.3 ) : As max = 0 .75 * (0.85 * 6000 psi * 0.75 ] * ( 87000 J * 12 in* 11.75 in 60000 p si 87000 + 60000 psi A 3.99in2 smax=---ft Check Minimum Reinforcement (LFD 16.8.5.8 ) : A min = 0. 002 * 12 in * 14 in A . 0.34in2 smm= ft Try #4's @ 3.5 inches on center: A 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 s_ sa=-::r:::.== Vctc* A d 2 . 0.50 in 2 25. c = m + = . In 2 166

PAGE 183

A= 2 * 2.2 1 5 2 *12 in = 15.75 3.5 fsa = 98 ksi = 29.84 ks V2. 25i n *15.75 Calculate actual stress in reinforcement: n = 29000000 psi = 6.18 u se 6 (150 lb/ft3l5 * 33 * p si) 12in*x2 -6* 0 . 67in2 *(11.75in-x)=O 2 x = 2.50in .* d d x . 2.50in 10 92. J = --=11.75tn---= . tn 3 3 f s = Ms = ok As* j * d 0 . 67in *10. 92in 167

PAGE 184

The outside reinforcement in the walls is designed using #4 , Grade 60, reinforcing bars. d 10 . ( 2 . 0 . 50in ) 7 7 5 . = InIn+--= . 10 2 Asreq .=[0.85* 6000p s i * l 2in]* [ 7 .75in7 _75in2 _ 2 4 * 20.22 * 10001b-ft l 60000p s i 0.95 * 0.85 * 6000p s i • l2in A 0 .57 in2 s req.= f t Check Maximum Reinforcement ( LFD 8.16.3 ) : A s max =0.75*(0 .85* 6000p s i * 0 .75)* ( 87000 ) * 12in * 7.75in 60000 p s i 87000 + 60000 p s i A 2 . 6 3in2 smax=---ft Check Minimum Reinforcement ( LFD 16.8.5.8 ) : Asmin = 0.002 * 12 in* 10 in A . 0.24in2 smm=---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

PAGE 185

Check Crack Control (LFD 16 . 8.5.7): Calculate Allowable Stress, fsa: f < f 98 k i s _ sa=-=== 'J./dc* A d 2 . 0 . 50 in 2 25 . c= m+ = . m 2 A= 2*2.25* 12in =]5 _ 75 12 3.5 fsa = 98 ksi = 29.84 ksi 'J./2.25 in* 15.75 Calculate actual stress in reinforcement: n = 29000000 psi = 6 _18 use 6 (150 lb/ft3)1.5 * 33 * p i ) 12in*x2 -6* 0.67in2*(7.75in-x)=O 2 x = 1.97 in 169

PAGE 186

* d -d x -7 7 5 1.9 7 in 7 12 J ----. In---. In 3 3 M s fs=---As*j * d 11.17k-f t * l 2 2 = 28. 0 9 ksi 29.8 4 k s i o k 0 .67 in * 7 . 1 2 in The inside reinforcement in the wall s will be des i g ned using #4 , Grade 60 , rein f orcing bar s . d = 10 in-( 2 in+ = 7.75 in A s req. = [0.85 * 6000 p s i * 12 in]* [ 7 .75 in_ 7 .75 in2 _ 24 * 5 .29 * 1 000 lb -f t ] 60000 p s i 0.95 * 0.85 * 6000 p s i * 12 in A 0.15in2 sreq.=--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 p s i 87000 + 60000 p s i A 2 . 63in2 smax=---ft 170

PAGE 187

Check Minimum Reinforcement (LFD 16.8.5.8): A min = 0. 002 * 12 in * 10 in 0 ?4. 2 A . -In min=---ft Try #4's @ 7 inches on center: A provided= 12in *.196in2 =0.34in2 7 Check Crack Control (LF D 16.8.5.7): Calculate Allowable Stress, fsa: f fsa = 98 k i 'Vdc* A d 2 . 0 . 50 in 2 25 . c= m+ = . m 2 A= 2*2.25*12in = 31.50 l2 7 f a= 98 ksi = 23 . 68 ksi V2.25 in * 3I.5o 171

PAGE 188

Calculate actual stress in reinforcement: n = 29000000 p s i = 6 .18 u se 6 ( 1501b/ft3l5 12. * 2 m x -6*0.34in2 *(7.75in-x)=O 2 x = 1.46 in * d -d 7 75 -l.46 in -7 26 J---. m . m 3 3 fs= Ms = 4 0 7k-ft* l 2 ok As * j * d 0 .34 in 2 * 7.26 in 6.2.1.7 Calculate shear ( LFD 8.16.6.2) The allowable hear in the three-sided structure i s calculated using the simplified equation. Shear in the Deck: Vu Vu = 14. 23 kip eve= e * 2 * Jfc, * b * d eve= 0.90 * 2 * p i * 12 in * 11.75 in= 19659.26lb = 19.65 kips = 19.65 kips> 14.23 kip OK 172

PAGE 189

Shear in the Walls: Vu = 5.07 kip s eve= e * 2 *Fc * b * d eve= 0.90 * 2 * psi * 12 in * 7.75 in= 12966 .7lb = 12.97 kip s = 12. 97 kip > 5.07 kip s OK 6.2.1.8 Summary Fig ure 6.22 illu s trate s the required rein f orcement for the ins ide f ac e and out s ide face of the side walls , top s lab , and bottom s lab. 2 " # 5 @ 3.0" o.c. 2" #4 @ 6.00" O.C. # 4 @ 6 .00" O .C. STEEL S ECTION Figure 6.22 -LFD Reinforcement Placement for Design Example #2 173

PAGE 190

6.2.2 Standard LRFD Specifications 6.2.2.1 Vertical and Horizontal Earth Pressures : The design vertical earth pressure on the top of the culvert is calculated as: WuSL = ys* Z WuSL = (12 0 pcf) * (1.0 ft) = 120 psf Similar to the Standard AASHTO Speci f ications, the lateral earth pressure (E H) on the culvert i found using the equivalent fluid method . However, the LRFD Specifications doe s not pecify minimum and maximum equivalent fluid pressure. This i s taken into account in the load factors, and loading combinatio ns. An equivalent fluid pressure of 30 pcf is assumed . At the top of the culvert, the lateral earth pressure is calculated as: EH =EFP* Z EH = (30 pcf) * (1ft ) = 30 psf At the bottom of the culvert , the lat eral earth pressure is calculated as: 14 EH = (3 0 pcf) *(1ft+-ft +10ft)= 365 psf 12 Figure 6.23 illu trates the vertical and l atera l earth pre ss ures applied to the three-sided s tructure. 174

PAGE 191

EV = 120 psf EH = 30 psf l l l l I I I I l I I I I I I l I I I l I I I Il EH = 30 psf EH = 365 psf . : EH = 365 psf Figure 6.23 LRFD Vertica l and Lateral Earth Pressures 6.2.2.2 Live Load Surcharge The Live Load Surcharge pressure is calculated utilizing a n equivalent height of 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 considered to be the distance between the top s urfac e of backfill and the footing bottom. Figure 6.24 illu s trates the wall height u sed in this example. After linear interpolation the equivalent height of soil was determined to be 2.68 ft. 175

PAGE 192

1 3' 2" I • .. I r Figure 6.24 -LRFD Wall Height The live Load Surcharge is calculated as: LLS = EFP * Heq LLS = (30 pcf) * (2.68 ft) = 80.4 p f Figure 6.25 illustrate the Live Load Surcharge pressure applied to the threesided structure. 176

PAGE 193

LLS = 80.4 psf LLS = 80.4 psf .... ... . I e1 43 4 .a • 1 i . 1 . t ' I 1 l l I , I I I 1 . I I I • I i I . I I . I " I I I I I I I , I i I I I Figure 6.25 LRFD Live Load Surcharge Pressure 6.2.2.3 Dynamic Load Allowance: The increa e in the Live Load due to the dynamic load effect vane for varying burial depth s . The Dynamic Load Allowance i s onl y applied to the Design Truck and Tandem Load , and not the Lane Load . The Dynamic Load Allowance for a fill depth of 1 . 0 ft is calculated as: 1M =33 * ( 10.125 0 % 1M= 33 * ( 10.125 * 1ft ) = 2 8 . 875 % 6.2.2.4 Design Live Loads: The design live loads include the HL-93 Design Truck , Design Tandem , and Lane Loads. 177

PAGE 194

Similar to the Standard AASHTO Speci fications, the Standard LRFD Specification s allows for the live load to be divided into str ip widths. However the LRFD Specification s 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 value of: PLL = 32000 lbsiAxle = 3047.6lbs I (ft-width) 10.5 ft PuLL= 1.75 * 1.29 * 3047.6lb I (ft-width)= 6880 lbs I (ft-width) 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 * l.Oft z 2.0ft 178

PAGE 195

The Design Truck produces a live load pressure of: Wull = PuLL Espan Wull = 6880lb I (ft-width) = 3440 psf 2ft The Design Tandem produces a liv e load value of: PLL = 25000 lb I Axle = 2381.0 lbs I (ft-width ) 10 . 5 ft PuLL= 1.75 * 1.29 * 2381lbs I (ft-width)= 5375.0 lbs I (ft-width) The Design Tandem produces a live load pressure of: Wull =PuLL Epan Wull = 5375.0 lb I (ft-width) = 2687 . 5 p f 2ft The Lane Load produce s a live load pressure of: WuLL = 640 plf * MPF = 64psf * MPF 10ft The Single Design Truck produces the maximum live load intensity; however the Single De ign Tandem has a larger influence area. After analysis it was 179

PAGE 196

determined the Single Design Tandem controlled the design. Therefore the Lane Load produce 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 follow . The loading configurations are illu s trated in Figure 6 . 26. The load cases correspond to: • Case 1: Maximum vertical loads on deck, minimum lateral load s on legs . Thi case produces maximum stresses in the bottom of the deck. • Case 2: Maximum vertical and horizontal loads on the structure. The case produces maximum stresses on the comer of the deck, and outside walls. • 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 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+l.30 * EV +1.50*EH+l.75*LS+l.75*(LL+IM) 3. U = 0.90 * DC+ 0.90 * EV + 1.50 * EH + 1.75 *LS 180

PAGE 197

Service: 1. U=l.OO*(DC+EV+EH+(LL+IM)) 2. U = 1.00 *(DC+ EV + EH + LS + (LL + IM ) ) 3. U = 1.00 *(DC+ EV + EH + LS ) Similar to the Standard AASHTO Specifications the s tructure wa modeled assuming a pin-pin connection s pecified in ection 12.14.5 of the LRFD Specification s . Table 6.5 U ts the critical tre es for each load combination at the critical locations. The location of the critical tresses are shown in Figure 6.26. 181

PAGE 198

I • ll 1 L L = 422 . 6 psf t t + + + + + + + 4 4 t t + 4 LL = 76_ 8 psf oonnnnJIOOOOOH t t t t 4 4 4 4 4 4 I I t t t t t t t t 4 4 4 t E v = 600 psf . • . . . . . • . • E H = 150psf Ca s e 1 E H = 4 85 psf rt L L = 422 . 6 psf o too n n no + + + + l l l l l l • • l • • • • • f f + + l + ntt = 600 psf ! 1 4 ' + ' ' ' ' + 4 4 4 4 4 4 4 4 1 1 t ' ' + nLLs = 68.4 psf E H = 150psf . . . Case 2 EH = 485 psf EV = EDO psf 4 1 o o o o n n n o 1 1 o o ULL s = 68.4 psf :t.-.. . t/ Case 3 E H = 1 5 0 psf EH = 485 psf Figure 6.26 Loading Configuration , Cases 1 -3 182

PAGE 199

----. -----------------------------------------------------------------, Figure 6.27 Locations of Critical Stresses I I I I t(2) I I I I I I I I I I I I I !CD I I I I I I I I I I I I I ! Table 6. 7 LRFD Structural Analysis Results per Foot Width, Example 2 Load Case 1. Load Case 2. Load Case 3. ---------c..-,_--c..-,_--c..-,_--Q)-ctl (/) Q)-ctl (/) Q)-ctl (/) E 6_ Q) c.. E6_ Q) c.. E6_ Q) c.. ..c -..c -..c -0 -Cf)6 0 -Cf)6 0 -Cf)6 '-< 1 0.00 0 . 00 0.32 0 . 66 3.37 2.09 2 -21.84 3 .18 -21.58 4.31 -3.89 2.34 3 -12.36 14.54 -14.14 14.54 -4.28 2 . 39 4 53.82 3.54 52.05 3.54 6.47 0 . 00 Location Load Case 1. Load Case 2. Load Case 3 . ---------c..-,_-C.t:: ,_-c..-,_-Q)-ctl (/) Q) I ctl (/) Q)j" ctl (/) E 6_ Q) c.. E c.. Q) c.. E c.. Q) c.. ..c -..c -..c -0 -Cf)6 0 -Cf)6 0 -Cf)6 1 0.00 0.00 0.00 0.41 1.47 1.12 2 -13.73 2 . 36 -13 .61 2.72 -4.49 1.71 3 -8.11 9.03 -8.67 9.03 -3 . 35 2 . 65 4 32.98 2.02 32.42 2.02 8 . 60 0.00 183

PAGE 200

6.2.2.6 Reinforcing Design The bottom reinforcement for the deck will be designed using #7 , Grade 60, reinforcing bars. . ( rebar diameter] d =slab thtckness-clear cover+ 2 d = 14 in-( 2 in + in)= 11.56 in A req.=[0.85*fc*b]*[d-d2 _ 24* Mu l fy


PAGE 201

Check Maximum Reinforcement Ratio (LRFD 5.7.3.3): c As max =0.42 d c A prov *fy = :5; 0.42 d 0.85 *f C * b d c 1.03 in 2 * 60000 psi = = 0.12:5 0.42ok d 0.85 * 6000 psi * 12 in * 0.75 * 11.56 in Check Minimum Reinforcement (LRFD 12.14.5.8): As min = 0.002 * b * h Asrnin = 0 . 002 * 12 in* 14 in . 0.34 in2 Asmm=--ft 185

PAGE 202

Check Crack Control (LRFD 12.14 . 5.7): Calculate minimum allowable spacing to satisfy cracking (LRFD 5. 7.3.4): 700 * y s e -2 *de *fs d 2 . 0.875in 244. c= m+ = . m 2 = 1 + de = 1 + 2.44 in = 1.30 s 0.7 *(h-dc) 0.7*(14in-2.44in) ye =exposure factor= 1.00 Calculate actual stress in reinforcement: n = 29000000psi = 6 .lSu e 6 (150 lb/ft3)1.s * 33 * psi ) 12. * 2 m x -6* 1.03in2*(11.56in-x)=O 2 x = 2.98in 186

PAGE 203

j * d = d = 1 1.56 in 2 98 in = 1 0 . 57 in 3 3 M s 32.98 k -ft * 12 fs = = = 36 . 35 k s i As* j * d 1.03 in2 * 10.57 in 700* 1.00 $ -2 * 2.44 in = 9.93 in 1.30 * 36.35 ksi Actual Spacing= 7.0in $ 9.93in 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 = 7.0 in $ 18 in OK Calculate Minimum Spacing of Reinforcing (LRFD 5.10.3.1) s db= .625 in 1.33 * Ag = 1.33 * 0.75 in= 1.0 in 1.0 in Actual spacing = 6 in OK 187

PAGE 204

T h e top reinforcement in t h e deck will b e designed using #4, Grade 6 0 , reinforc i ng b ars . d 14. ( 2 . 0.50 in) 11 75. = m m+--= . m 2 As=[0.85 * 6000psi * 12in]*[l1.? 5inll.?5 i0 2 _ 24* 14.14*10001b-ft l 60000psi 0 . 95 * 0.85 * 6000ps i • 1 2 in A 0 .26in 2 s req.= ft Try #4's @ 3 . 5 inc h e on cen t er: A provided= 12 i n * 0 . 196 i n 2 = 0 . 67 i n 2 3 . 5 Check Maximum Reinforcement Ratio (LRFD 5.7.3.3 ) : Check Minimum Reinforcement ( LRFD 12.14.5.8 ) : A s min = 0 . 00 2 * 12 in* 14 i n A . 0.34 in2 smm=---ft 188

PAGE 205

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 s = 1 + de = 1 + 2?5 in . = 1.27 0.7 *(h-dc) 0.7*(14m-2.25m) ye = exposure factor = 1.00 Calculate actual stress in reinforcement: n = 29 000000 psi = 6 _18 u e 6 (1501b/ft3)J.5 12. * 2 m x -6* 0.67in2 * (11.75in -x) = 0 2 x = 2.50in j * d = d= 11.75 in2 50 in = l 0 . 92 in 3 3 fs= Ms = 8.67k-ft*12 =l4 . 22 ksi As* j * d 0 .67 in 2 * 10.92 in 189

PAGE 206

700* 1.00 s :::; -2 * 2.25 i n = 34.32 in 1.27 * 14.22 ksi Actu al Spacing= 3 . 5 in:::; 34.32 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 u s e 18 in Actual Spacing= 3 .. 5 in:::; 18 in OK Calculate Minimum Spacing of Reinforcing (L RFD 5.10.3.1 ) s min 2:: db= .625 in 1.33 * Ag = 1.33 * 0.75 in = 1.0 in 1.0 i n Actual spacing= 3.5 in O K The outside reinforcement in the walls will be des igned using #4, Grade 60, reinforcing bars. d 10. ( 2 . 0 . 50 in) 7 75. = mm+--= . m 2 . As= [0.85 * 6000psi *12in]* [ 7 .75 in_ 7 .75 in 2 _ 2 4 *2 1.84 * 1000lb-ft l 60000 p s i 0 .95 * 0 .85 * 6000 p s i • 1 2 in A 0 . 62in2 s req. = ft 190

PAGE 207

Try #4's @ 3.5 inches on center: A s 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 psi = = 0 .11 $ 0.42 d 0.85 * 6000 psi *12 in * 0.75 * 7.75 in Check Minimum Reinforcement ( LRFD 12.14.5.8 ) : A min= 0.002 * 12 in* 10 in A . 0.24in2 srru n =---ft Check Crack Control (LRFD 12.14.5.7 ) : Calculate minimum allowable spacing to satisfy cracking (LRFD 5.7.3.4 ): 700* y s e -2 *de d 2 . 0.50 in 2 2 5 . c= m+ = . m 2 = 1 + d e = 1 + 2.25 in = 1.41 s 0.7 * (h-de) 0.7 * (10 in-2.25 in) ye =exposure factor= 1.00 191

PAGE 208

Calculate actual stress in reinforcement: n = 29000000 p s i = 6 _18 u se 6 (150 lb/ft3 ) 1.s * 33 * p s i ) 1 2 . * 2 10 x -6* 0 .67in2*(7 .75in-x)=O 2 x = 1.97 in j * d = d= 7.75 in-1.97 in = 7.09 in 3 3 f s = M = 13.73k-ft*12 = 34 _ 68 k s i As* j * d 0.67in2 * 7.09in 700 * 1.00 s -2 * 2.25 in = 9.8 Lin 1.41 * 34.68 k s i OK Calculate Maximum Spacing of Reinforcing (LRFD 5.10.3.2) max= 1.5 * h 18in smax = 1 . 5 * 14in = 21 in therefore use 18 in Actual Spacing= 6.0 18 in OK 192

PAGE 209

Calculate Minimum Spacing of Reinforcing (LRFD 5.10.3.1) s db= . 625 in 1.33 * Ag = 1.33 * 0.75 in = 1.0 in 1.0 in Actual spacing= 3.5 in OK The inside reinforcement will be designed u sing #5, Grade 60, reinforcing bars. d = lOin-( 2in + in) = 7.69 in A s=[0.85* 6000psi *l2in]*[?.69in-7 .69i112 _ 24* 3.37 *1000lb-ft l 60000 psi 0.95 * 0.85 * 6000 psi * 12 in A 0 . 09in2 sreq.=--ft Try #5's @ 14.00 inches 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 = = 0.04 0 . 42 d 0.85 * 6000psi *12in * 0.75 *7 .69in 193

PAGE 210

Check Minimum Reinforcement (LRFD 12.14.5.8): Asmin = 00002 * 12 in* 10 in A 0 Oo24in2 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 *de * fs d 2 0 00625 in 2 31 0 c= m+ = 0 m 2 = 1 + de = 1 + 2031 in = 1.43 5 007*(h-dc) 007*(10in-2o3lin) ye =exposure factor= 1000 194

PAGE 211

Calculate actual stress in reinforcement: n = 29000000 p i = 6.18 use 6 (150 lb/ft3l5 * 33 * p s i ) 12 in* x 2 6 * 0.262 in 2 * (7 .69 in-x ) = 0 2 x = 1.30in j * d = d = 7.69 in1.30in = 7.26 in 3 3 Ms 1.47 k-ft*12 fs= = 2 =9.27ks i A * j * d 0.262 in * 7 . 26 in 700 * 1.00 s 2 * 2.31 in = 48.16 in 1.43 * 9.27 k i Actual Spacing = 14. 00 in 48.16 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 u s e 18 in Actual Spacing = 14. 00 in 18 in OK 195

PAGE 212

Calculate Minimum Spacing of Reinforcing (LRF D 5.10.3.1 ) s db= .625 in 1 .33 * Ag = 1.33 * 0.75 in = 1.0 in l.Oin Actual spacing= 14. 00 in OK 6.2.2.7 Calculate shear (LRFD 5.8.3.3): The allowable shear in the three-sided structure i calculated using the simplified equation. Shear in the Deck: Vu = 14.54 kip * 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 * psi * 12 in * 10.58 in= 17701.7lb = 17.70 kips = 17.70 kips> 14. 54 kip s OK 196

PAGE 213

Shear in the Walls: Vu Vu = 4 .31 kips eVe=e* p *Fc"* 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 eve= 0.90 * 2 * psi * 12 in* 7.2 in= 6023.31b = 6.02 kip s = 6.02ldp > 4 . 3 1 kip s OK 6.2.2.8 Summary Figure 6.28 illustrates the req u ire d rein force ment for the inside face an d out s ide face of t h e side walls , top lab, and bottom s lab. . A comparison between both des igns with regard s to the area of steel required i s pre ented in Table 6.3. Table ().8 -Area of Steel comparison Location ---------------r----------,-------------------------------: 1 : 2 3 4 ---------------------LFD : 0.15 : 0.57 0.28 0.94 -------------------LRFD : 0.09 : 0 .62 0.26 1.03 197

PAGE 214

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

PAGE 215

Chapter 7 Summary and Conclusions The objective of this thesi s was to examine and compare the current LRFD Desig n Specification s and the Standard AASHTO Specifications used in de s igning underground precast concrete structures such as underground utility structures, drainage inlets, threeside d structures , and box culverts. Thi s thesis compare s relevant provi ions from both specifications. Provisions discu ss ed within this document include: terminology, lo a d factors, implementation of load modifiers, load combinations , multipl e pre se nce factors, design ve hicle live loads, distribution of live load to s la bs , and through earth fill, live load impact, and live load surcharge. A brief summary of each as major provision and its impact on design is as follows: • Design Vehicular Live Loads-The design truck, and application is identical in both specifications. However, the LRFD provisions require an additional distributed load of 0.64 kif be added to the live load model. In addition, the Design Tandem Truck, which replaced the Alternative Military Loading from the Standard Specifications, i s 4 % heavier . • 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 pre se nce factor is similar to the load reduction factor in the 199

PAGE 216

Standard Specifications. The load reduction factor for a single 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 balances the reduction in the live load factor. The Standard Specifications require a live load factor of 2.17, while the LRFD Specifications require 1.75. With the introduction of the multiple presence factor, the live load factor in the LRFD Specifications converts to 2.1. • Dynamic Load Allowance (Impact) -Both specifications require an increase in the live load with respect to the earth fill depth . The LRFD Specifications 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. • Lateral Live Load Surcharge-Both specifications require an increase in the lateral earth pressure due to the live load . The Standard AASHTO Specifications require a live load surcharge pressure 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

PAGE 217

significantly greater in the Standard LRFD Specification than the Standard AASHTO Specifications. • Distribution of Wheel Loads Through Earth Fill -Both specif ication s allow for the live load to be distributed through earth fill. The LRFD Speci ficat ion s allow the dimensions of the tire to be utili zed. Howe ver the LRFD Specification s generally produce greater load effects . The live load distr ibution areas are complicated; particularly when multiple load from several vehicles overlap. There is continuing research being performed by the FHW A in order to simplify the calculations. • Load Factors and Load Combinations -Both specif ication s utilize load factors and strength reduction factors. However, the load and resistance factors are determined through statistical studie and are more acc urate in the Standard LRFD Specification. There is greater reliability and a more uniform factor of safety when utilizing the LRFD Specificat ions. The provisions in the LRFD Specifications are more concise and more bene ficial to design engineers with the addition of the commentary . Therefore, the code i simpler to apply than the Standard Specification s . There i s still a great amount of research that must be performed, especially when examining the distribution of live load through earth fill. De sign engineers proficient with the 201

PAGE 218

Standard AASHTO Specifications should have little trouble converting to LRFD Specifications as some level of familiarity and comfort is attained. 202

PAGE 219

References American A ss ociation of State Highwa y and Tr a n s portation Official s ( AASHTO ) . St a ndard Specifi ca tion s f or Highway Bridg es. 17th ed . W as hingt on: GPO , 200 2 . LRFD Bridge Design Specific a t io n s . 3rd e d . Was hington : GPO , 2005 . American Concrete P i p e A ss ociation ( ACPA ) . Highway Li ve Lo a d s on C o n c r e t e P i p e . Irving , TX: A CP A, 2 001. Bloomqui s t , D. G., and Gutz , A. 1 . Evaluation of Precast B ox Culve1t Svstem s Design Live Loads on Bo x Culverts. G aine svi lle , FL: Univer s ity of Flmida , 2002. D e Stef a no , R. 1., E va ns, J., Tadro s, M . K. , and Sun , C . " Fle x ur a l Crack C o ntrol in Concrete Brid g e Structur es . " Florid a Dep art ment of T_ra n s port a tion. 2 004. 1 M ay . 2 006 " LRF D : Achievi n g Greater Reliability and Service for Bridge ."Focus. July 2004 . U . S. D epartment of Transportatio n Federal Highway Division . 10 May .200 6 . " LRFD: State Dep artment of Tran s pmtatio n LRFD Implementatio n P lan Initial Draft. " B1idge Techno l ogy. 15 Apr. 2006. U.S . Department of Transportation 2 03

PAGE 220

Federal Highw ay Divi sion. 16 Apr. 2006 . National Cooperative Highway Re sea rch Pro gram ( NCHRP ) . " Development of Comprehen sive Bridge Specification s and Commentary. " Research Re s ults Dige st 198 (1998 ) . " Project 15-29: Design Specifications for Live Load Distribution to Buried Structures ." National Cooper ative High way Research Program. 6 Apr. 2006. Tr a nsportation Re earch Board . 6 Apr. 2006 . " Project 12-33: Development of a Comprehen s ive Bridge Specification and Commentary ." National Cooperative Highway R esearch Program. 24 May. 2006. Transport a tion Research Board . 26 May 2006 . Rund, R. E., and McGrath , T. J. " Comparison of AASHTO Standard and LRFD Code Provisions for Buried Concrete Bo x Culverts. " Concrete Pipe for the New Millennium : ASTM STP 1368. Ed. I. I. Kaspar and J. I. Enyart. Wes t Conshohocken , PA: American Society for Testing and Material s, 2000 . 45 60. 204

PAGE 221

Sanford , T. C. " Soil-Structure interaction of buried Structure s." Transportation Research Board. 2000. 2 Apr 2006. . Tonias, D. E. B ridge Engineering. United States of America: McGr aw-Hill, 1995 . Un it ed States. Federal Highway Administration (FHA). Lo ad and Re sista nce Factor Design (LRFD) for High way Bridge Substruct u res: NHJ Co ur se No. J 32068. HI-98-032. Washington: GPO, 2001. 205