Numerically Modeling Structural Behavior of Precast Three-Sided Arch Bridges for 
Analysis and Design 
 
by 
 
Timothy Jared Jensen 
 
 
 
 
A thesis submitted to the Graduate Faculty of 
Auburn University 
in partial fulfillment of the 
requirements for the Degree of 
Master of Science 
 
Auburn, Alabama 
August 4, 2012 
 
 
 
 
Keywords: numerical modeling, precast three-sided arch bridge 
 
Copyright 2012 by Timothy Jared Jensen 
 
 
Approved by 
 
Justin D. Marshall, Chair, Assistant Professor of Civil Engineering 
Jeremy Brian Anderson, Co-chair, Associate Professor of Civil Engineering 
Robert Barnes, James J. Mallett Associate Professor of Civil Engineering 
 
ii 
 
Abstract 
 
 
 Foley Products contracted with Auburn University to perform laboratory testing 
and design validation of three-sided bottomless precast concrete structures being 
produced. Tests performed included a field test on an active construction project, a 
laboratory test of a 20 ft clear span structure, and a laboratory test of a 36 ft clear span 
structure. The field test was performed in Midland, North Carolina on a 42 ft clear span 
arch structure. The field test was a service load level test performed by backfilling around 
the structure and driving a truck with a known weight over the bridge and stopping at 
various locations. The 20 ft clear span and 36 ft clear span laboratory tests were 
performed in the Auburn University Structural Research Laboratory. Gauges were 
installed in these structures prior to casting so data could be collected during testing. In 
both laboratory tests the structures were loaded to failure using hydraulic loading 
actuators. 
 Following testing, the computer program SAP2000 was used to develop two 
structural models. SAP2000 structural models of the 20 ft clear span structure as well as 
the 36 ft clear span structure was developed to correlate results between the structural 
analysis performed in SAP2000 and the data and results found during laboratory testing. 
Nonlinear behavior was accounted for in analysis. Moment hinges were incorporated in 
the structural model to correlate deflection magnitude in analysis to deflection 
measurements in the laboratory testing.   
 
iii 
 
Once the SAP2000 structural models were developed and correlated well with the 
laboratory test results, an evaluation of the design methodology in use by the designers of 
the Foley Arch was carried out. A structural computer model was developed in RISA 3-D 
by the designers and used in design of the structure to predict the point of maximum 
moment. The RISA 3-D model used in design of the Foley Arch was compared to the 
model developed in SAP2000 to evaluate how well the structure corresponded to the 
behavior the designers expected. 
 It was found that the strength of the structures was adequate and that the design 
methodology being used was reasonable and safe.  
iv 
 
Acknowledgments 
 I would like to thank Foley Products, Dr. Justin Marshall, Dr. Brian Anderson, 
and Dr. Robert Barnes who have all been a source of knowledge and guidance throughout 
this project and I thank them for giving me the opportunity to contribute to the research. 
My research partner, Luke Meadows, has been a pleasure to work with and I wish him all 
the best in his future pursuits. The entire Civil Engineering staff has provided me with 
invaluable experience throughout the duration of my education; I respect and appreciate 
the hard work and commitment to progress I have seen in the department.   
 I would also like to thank my parents. Since I was young, they have been 
dedicated to raising me to appreciate the importance of my spirituality, setting priorities, 
being disciplined, and remaining well rounded and balanced as I matured into an adult. 
Their persistent efforts to instill these qualities in me coupled with their tremendous 
example have given me an excellent model to follow as I live my life. Without their 
support I would not have been able to accomplish what I have at Auburn University.  
Finally, I extend my deepest appreciation to my loving wife, Meredith. She has 
supported me in all that I have endeavored to accomplish and has been a tremendous 
source of encouragement and support throughout my time at Auburn University. 
Academic obligations and responsibilities have been a source of tremendous stress on 
many occasions, but she has always been right by my side, ready and willing to support 
me in any way. I love her and will forever appreciate all her love, support, and devotion. 
 v 
 
 
 
 
 
Table of Contents 
 
 
Abstract ............................................................................................................................... ii 
Acknowledgments ............................................................................................................. iv 
List of Tables ................................................................................................................... viii 
List of Figures .................................................................................................................... ix 
Chapter 1 ? Introduction and Background   .........................................................................1 
 1.1 - Background   ....................................................................................................1 
 1.2 ? Project Objective   ...........................................................................................1 
 1.3 ? Project Scope   ................................................................................................1 
 1.3.1 ? Field Test   .......................................................................................2 
 1.3.2 ? Laboratory Tests   ............................................................................3 
 1.3.3 ? Computer Modeling and Design Methodology   .............................5 
 1.4 ? Outline of Thesis   ...........................................................................................5 
Chapter 2 ? Literature Review   ...........................................................................................8 
2.1 ? Precast Arch Structures   .................................................................................8 
2.2 ? McGrath and Mastroianni   .............................................................................9 
2.3 ? Zoghi and Farhey   ........................................................................................11 
2.4 ? Zoghi and Hastings   .....................................................................................12 
2.5 ? McGrath, Selig, and Beach   .........................................................................13 
2.6 ? Beach  ...........................................................................................................14 
 vi 
2.7 ? Summary   .....................................................................................................15 
Chapter 3 ? Experimental Testing   ...................................................................................16 
3.1 ? Introduction   .................................................................................................16 
3.2 ? Field Test   ....................................................................................................16 
3.2.1 ? Field Test Gauges   ........................................................................16 
3.2.2 ? Field Test Loading   .......................................................................18 
3.2.3 ? Field Test Results and Behavior   ..................................................19 
3.3 ? Laboratory Tests   .........................................................................................19 
3.3.1 ? Laboratory Test Gauges   ...............................................................20 
3.3.2 ? Laboratory Test Loading Configuration   ......................................26 
3.3.3 ? Lateral Soil Pressure Considerations   ...........................................27 
3.3.4 ? Test Results and Behavior   ...........................................................32 
3.4 ? Conclusions   .................................................................................................36 
Chapter 4 ? Computer Modeling   .....................................................................................37 
4.1 ? Introduction   .................................................................................................37 
4.2 ? Geometric Properties   ..................................................................................37 
4.3 ? Cross Sectional Element and Material Properties   .......................................38 
4.4 ? Loading Configuration   ................................................................................41 
4.5 ? Nonlinear Analysis  ......................................................................................42 
4.5.1 ? User-Defined M3 Hinges   .............................................................42 
4.5.2 ? Nonlinear Load Case  ....................................................................50 
4.6 ? Model Analysis Results   ..............................................................................54 
4.7 ? Conclusions   .................................................................................................65 
 vii 
Chapter 5 ? Design Methodology   ....................................................................................66 
5.1 ? Introduction   .................................................................................................66 
5.2 ? General Methodology   .................................................................................67 
5.3 ? Analysis and Modeling   ...............................................................................67 
5.4 ? Experimental Results versus Design   ...........................................................78 
5.5 ? Conclusions   .................................................................................................81 
Chapter 6 ? Summary, Conclusions, and Recommendations   ..........................................82 
6.1 ? Summary   .....................................................................................................82 
6.2 ? Conclusions   .................................................................................................83 
6.3 ? Future Research   ..........................................................................................84 
References   ........................................................................................................................86 
 
 
 
 
 viii 
List of Tables 
 
 
Table 4-1: Cross Sectional Properties Used in Hinge Parameter Calculations  ................44 
Table 4-2: Displacement Control Parameters of Hinges ? 20 ft Clear Span Model  .........45 
Table 4-3: Displacement Control Parameters of Hinges ? 36 ft Clear Span Model  .........46 
Table 4-4: I3 Property Modifiers  ......................................................................................54 
Table 4-5: 20 ft Clear Span SAP2000 Structural Model Results ......................................55 
Table 4-6: 36 ft Clear Span SAP2000 Structural Model Results ......................................56 
Table 5-1: Design Calculation Properties  .........................................................................73 
Table 5-2: Comparison of RISA Model Moment to SAP2000 Model Moments  .............77 
Table 5-3: Test/Model Structure Midspan Properties  .......................................................79 
Table 5-4: Ratio of Design Properties to Test/Model Specimen Properties  .....................80 
 
ix 
 
List of Figures 
 
 
Figure 1-1: Midland, NC Field Test Site Conceptual View  ...............................................2 
Figure 1-2: Midland, NC Field Test Section  ......................................................................3 
Figure 1-3: Laboratory Test ? 20 ft Span Section ...............................................................4 
Figure 1-4: Laboratory Test ? 36 ft Span Section ...............................................................4 
Figure 3-2: Field Test Earth Pressure Cell and Wire Pot Layouts  ....................................17 
Figure 3-3: Field Testing ? Three Axle Dump Truck at Midspan  ....................................18 
Figure 3-4: Laboratory Test Specimen ? 20 ft Clear Span Section  ..................................19 
Figure 3-5: Laboratory Test Specimen ? 36 ft Clear Span Section  ..................................20 
Figure 3-6: Gauge Layout ? 20 ft Clear Span Test Specimen  ..........................................21 
Figure 3-7: Gauge Layout ? 36 ft Clear Span Test Specimen  ..........................................22 
Figure 3-8: Reinforcing Cage of Precast Section Prior To Casting  ..................................23 
Figure 3-9: Securing Wires of Strain Gauged Reinforcing Bar  ........................................23 
Figure 3-10: Midspan Wire Pot Deflection Gauge Installed  ............................................25 
Figure 3-11: Wire Pot Installed on Lateral Restrain Frame  ..............................................25 
Figure 3-12: Loading Actuator Configuration  ..................................................................27 
Figure 3-13: Horizontal Earth Pressure Distribution at Various Fill Depths ....................29 
Figure 3-14: Structure with Lateral Restrain System Installed  .........................................31 
Figure 3-15: Detailed View of Laterally Restraining HSS Sections Installed ..................32 
Figure 3-16: Internal Moments in 20 ft Clear Span Laboratory Test  ...............................33
x 
 
Figure 3-17: Displacements in 20 ft Clear Span Laboratory Test .....................................34 
Figure 3-18: Corner Moments in 36 ft Clear Span Laboratory Test ..................................35 
Figure 3-19: Displacements in 36 ft Clear Span Laboratory Test .....................................35 
Figure 4-1: 20 ft Clear Span ? SAP2000 Elements ...........................................................39 
Figure 4-2: 36 ft Clear Span ? SAP2000 Elements ...........................................................39 
Figure 4-3: Concrete Cylinder Test ...................................................................................41 
Figure 4-4: SAP2000 Hinge Property Definition Points ...................................................44 
Figure 4-5: Displacement Control Parameters of Hinges ? 20 ft Clear Span Model ........45 
Figure 4-6: Displacement Control Parameters of Hinges ? 36 ft Clear Span Model ........46 
Figure 4-7: Hinge Locations and Labels ? 20 ft Clear Span Model ..................................48 
Figure 4-8: Hinge Locations and Labels ? 36 ft Clear Span Model ..................................48 
Figure 4-9: Alternative Load Application for 20 ft Clear Span Test Specimen ................51 
Figure 4-10: Model versus Laboratory Specimen ? 20 ft Span Midspan Moment ...........57 
Figure 4-11: Model versus Laboratory Specimen ? 20 ft Span Displacement ..................58 
Figure 4-12: Model versus Laboratory Specimen ? 20 ft Span Corner Moment ..............58 
Figure 4-13: Model versus Laboratory Specimen ? 20 ft Span Corner Displacement ......59 
Figure 4-14: Model versus Laboratory Specimen ? 36 ft Span Midspan Moment ...........61 
Figure 4-15: Model versus Laboratory Specimen ? 36 ft Span Midspan Displacement ...61 
Figure 4-16: Model versus Laboratory Specimen ? 36 ft Span Corner Moment ..............62 
Figure 4-17: Model versus Laboratory Specimen ? 36 ft Span Corner Displacement ......62 
Figure 4-18: Model versus Laboratory Specimen ? 36 ft Span Corner Moment ..............63 
Figure 5-1: Extruded View ? 20 ft Span RISA Model ......................................................68 
Figure 5-2: Factored Loads ? 20 ft Span RISA Model ......................................................69 
xi 
 
Figure 5-3: Moment Diagram ? 20 ft Span RISA Model ..................................................69 
Figure 5-4: Beam Elements ? 36 ft Span RISA Model .....................................................70 
Figure 5-5: Dead Load ? 36 ft Span RISA Model .............................................................71 
Figure 5-6: Live Load + Impact ? 36 ft Span RISA Model ...............................................71 
Figure 5-7: Moment Diagram ? 36 ft Span RISA Model ..................................................71 
Figure 5-8: Equivalent Factored Design Loads on 20 ft SAP2000 Model ........................74 
Figure 5-9: Moment Diagram of Factored Design Loads on 20 ft SAP2000 Model ........75 
Figure 5-10: Equivalent Factored Design Loads on 36 ft SAP2000 Model ......................76 
Figure 5-11: Moment Diagram of Factored Design Loads on 36 ft SAP2000 Model ......76 
 
1 
 
Chapter 1: Introduction and Background 
1.1 ? Background 
Foley Products contracted Auburn University to perform third party analytical and 
experimental validation of the performance, design, and analysis methods currently in use 
for three-sided bottomless arch bridges being produced. The project included one field 
test and two laboratory tests of arches. A structural computer model was developed to 
correlate to the results of the laboratory tests. The design methodology was evaluated to 
determine what improvements could be made. 
 
1.2 ? Project Objective 
The ultimate goal of the project was to validate all aspects of the Foley Arch 
bottomless bridge. Data from the laboratory tests were used to develop analytical 
computer models. The models were developed to the point that the analytical results 
correlated to the results of the laboratory test. The tests and structural computer models 
could then be used to validate the design methodology used for the arches. 
 
1.3 ? Project Scope 
The experimental validation of the three sided bottomless arch bridges included 
one service load level test in a field test and two ultimate load level tests in the 
laboratory. The two laboratory tests were conducted on a 20 ft clear span structure and a 
2 
 
 
36 ft clear span structure. Correlation to the results of the laboratory testing was achieved 
using a structural computer model developed within SAP2000. The design methodology 
used in the design calculations provided by Foley Products was reviewed and evaluated 
to determine the effectiveness. 
1.3.1 ? Field Test 
The first test performed was a field test. This test was performed during construction of a 
precast arch bridge in Midland, North Carolina. This field test was performed on a 42 ft 
span bridge with a vertical rise of 14 ft. The field test site concept and the test specimen 
cross section is shown in Figure 1-1 and Figure 1-2, respectively. This field test was 
utilized to evaluate precast arch bridge sections under a known truck load by installing 
instrumentation to measure strains. Deflection and earth pressure transducers were 
installed on-site prior to backfilling and loading the bridge. 
 
 
 
Figure 1-1: Midland, NC Field Test Site Conceptual View 
3 
 
 
Figure 1-2: Midland, NC Field Test Section 
 
 
1.3.2 ? Laboratory Tests 
In addition to a field test, two laboratory tests were performed to evaluate bridge 
behavior up to ultimate loading conditions. The first laboratory test section was a 20ft 
span bridge with an 8ft vertical rise. This laboratory test specimen is shown in Figure 1-3. 
The second laboratory test section was a 36 ft span bridge with a 9 ft vertical rise. This 
test specimen is shown in Figure 1-4. Strain gauges were installed on reinforcing bars 
that were added to the reinforcing cage of the bridge prior to casting of the section. The 
two tested sections were meant to be on the bottom and top of the design range spectrum 
4 
 
of the precast sections available for production. Therefore, the range of behavior could be 
effectively evaluated by testing the two different sections. 
 Figure 1-3: Laboratory Test ? 20 ft Span Section 
 
 
Figure 1-4: Laboratory Test ? 36 ft Span Section 
5 
 
1.3.3 ? Computer Modeling and Design Methodology 
Following the field and laboratory testing, a computer model of the Foley Arch 
structure was created in SAP2000 to correlate the results of the laboratory testing to the 
analysis results of the computer model. This was used to determine if any economic or 
serviceability improvements could be reasonably recommended and/or implemented in 
the design or production of the structures. The design methodology was investigated by 
evaluation of the design calculations provided by Foley products.  
 
1.4 ? Outline of Thesis 
This paper describes the testing performed in the field and laboratory tests; 
however, primary focus is placed on details of the analytical computer models that 
were developed based on the structures tested. Also discussed is the correlation of 
these models to test results and an evaluation of the design methodology used in 
design calculations provided by Foley Products for review.  
Chapter 2 discusses the literature review that was conducted to understand and 
benefit from the work previously done related to testing and modeling of precast arch 
bridge structures. This assisted in planning for instrumentation needed. It also helped 
in developing how to effectively carry out and improve upon past experiments related 
to field testing. This in turn gave insight into what would be effective and useful in 
the laboratory testing. Work previously performed related to analytical modeling of 
precast arch structures was also reviewed to understand effective methods used in the 
past for modeling purposes. 
6 
 
In Chapter 3 the experimental tests are discussed. The field and laboratory testing 
procedure is reviewed and illustrated. This includes installation of gauges prior to 
casting of the test specimen and installation of other instrumentation prior to testing 
of the specimen. The field test loading was done by stopping a truck with a known 
weight at various locations. The laboratory testing allowed a more controlled 
environment and setup for test monitoring. Hydraulic loading actuators were used at 
three locations for testing in the laboratory. It was necessary to design various steel 
members to create a system that would allow loading of the structure. These designs 
are summarized and explained. During the two laboratory tests the specimens were 
loaded to failure.  The loading progression of the specimen during testing provided 
numerous points of comparison to develop an analytical model that correlated to 
actual behavior. Those points of comparison and critical moments measured in the 
specimen are outlined and then discussed with the modeling summary.  
The typical application of a three-sided arch bridge culvert consists of backfilling 
around and above the structure. Therefore, lateral restraints were designed for use 
during the first laboratory test to simulate the lateral earth pressure of the soil around 
the specimen. These designs and considerations in design are discussed in detail.  
Chapter 4 explains in detail the analytical computer models developed in the 
program SAP2000 version 14 of the test specimens. The goal was to correlate the 
model analysis and results to the laboratory testing results. As with any structural 
analytical model, an appropriate level of detail needed to be achieved to produce 
appropriately accurate and reliable results. However, this is also balanced with 
computation and analysis time. One of the test specimens was on lower end of the 
7 
 
range of spans typically produced and the other test specimen was on the higher end 
of the range of spans typically produced. The model was generated using the 
properties attained by examining the construction documents produced for the test 
section as well as physical inspection and measurements taken before and after 
casting.  
Since the test specimens were loaded to ultimate failure in the laboratory setting, 
it was essential to include nonlinear material behavior in the computer modeling of 
the structure. Therefore, research on the manner in which SAP2000 V14 analyzes 
nonlinear behavior was performed in order to decide the most appropriate way in 
which to model the structure using that software. Concrete sections were assigned 
within SAP and a combination of prismatic and non-prismatic frame elements were 
used. Various changes throughout the modeling process are discussed as adjustments 
were made to better correlate to the actual behavior of the structure.  
When the modeling was complete, the objective was to have good correlation to 
test results and be able to constructively review the design methodology. The design 
methodology and modeling used by the designer was reviewed to determine whether 
the design was effective. This review and assessment of the design methodology is 
discussed in Chapter 5. Recommendations were made regarding any changes deemed 
necessary or appropriate based on the testing and modeling performed.   
To conclude, a summary of the paper is provided, conclusions made are 
discussed, and recommendations for further research are provided. 
8 
 
 Chapter 2: Literature Review 
 
2.1? Precast Arch Structures 
Precast concrete members are increasingly used as a result of their time and cost 
efficiency. Ensuring a safe, but efficient, design with such a streamlined production and 
broad application becomes ever more important to companies utilizing this procedure. To 
ensure safe designs, controlled tests have been and continue to be performed on precast 
members. The precast arch bridge discussed herein is one such precast structure that has 
seen increased implementation on projects in the United States. 
Companies including, but not limited to, Foley Products, CON/SPAN, and Con 
Arch are businesses that have utilized the arch bridge system for overpasses or 
underpasses, culverts, vaults, or combinations thereof. The result of widening interest in 
the precast arch bridge market has led to broader and creative applications of this time 
and cost effective product. This industry has also seen a considerable amount of 
investments in research and testing to better understand the performance, serviceability, 
and safety of arch structures. This chapter will review a number of such research projects, 
the objectives of those projects, and conclusions of the research.  
 
 
9 
 
2.2 ? McGrath and Mastroianni (McGrath and Mastoianni 2002) 
This project was related to the field testing and subsequent development of 
computer models for two 28 ft span reinforced concrete arch culverts. The field test data 
included arch deflections, pressures at the interface of the structure and backfill material, 
concrete strain, and reinforcing bar strain. The structure was cast and backfilled with the 
native material excavated from the site. Two types of loading were simulated for the field 
testing procedure, tandem-axle load conditions and HS20 load conditions. Both arch 
designs under consideration carried the maximum load that the equipment being used 
could apply. In both tests, loading was terminated due to bearing failure under the load 
plates. No failure or yielding of the reinforcement occurred up to the point of highest 
loading. No significant cracking had occurred in either of the structures until well beyond 
the ultimate factored HS20 load was achieved. The performance of both of the designs 
was found to be excellent during the field tests. Each structure carried a live load in 
excess of 240 kips without failing. The factored design load for the HS20 truck was 87 
kips. When comparing the live load carried by the structure with no failure, it was 
apparent the structure had more than adequate strength capacity. Cores were cut from the 
tested structure and it was determined that the reinforcement at the crown of the structure 
had not yielded at the maximum load applied during the test.  
A two dimensional structural model was developed using the computer program 
CANDE (Katona and Smith 1976) after completing the field tests. This software was a 
finite-element soil structure interaction program that incorporated nonlinear soil 
properties as well as nonlinear concrete behavior. A three dimensional structural model 
was developed using the computer program ABAQUS (ABAQUS 2006). ABAQUS is a 
 
10 
 
general purpose finite-element program with nonlinear capabilities. The same in-plane 
mesh was used for both the two and three dimensional models. The three dimensional 
model was an extrusion of the two dimensional cross section to a total length of 70 ft. 
Results of the testing and modeling indicated that deflections and strains were often 
underestimated in the three dimensional computer model. Adjustments were made to the 
model to decrease the tensile strength limit which accounted for various parameters such 
as sustained loads, losses in concrete strength over time, and material variability in the 
concrete. Changing the concrete model parameters had a significant effect on the ability 
of the model to accurately predict structure behavior to correlate to testing results. The 
researchers concluded that internal forces could be well predicted even if the concrete 
modulus or cracking characteristics were not fully known. The three dimensional model 
developed within ABAQUS accurately predicted design forces but deflection and 
deformations were only correlated with test results by altering the concrete properties 
within the model. The two dimensional model developed within CANDE exaggerated the 
predicted deflection and deformation.  
After testing, McGrath and Mastroianni concluded that ?the performance of the 
standard and special test structures met AASHTO criteria for performance, 3-D analysis 
provided good predictions of the culvert performance and should be a useful design tool, 
and modifications or further study should be undertaken to correct the prediction of 2-D 
analysis to make them suitable for design for live loads? (McGrath and Mastroianni 
2002). 
 
 
11 
 
2.3 ? Zoghi and Farhey(Zoghi and Farhey 2006) 
 This project involved a field test of a 36 ft span bridge. During the field test, 
backfill up to 3 ft of cover was placed over the bridge. Load was applied in 20 kip 
increments, and data was collected at each increment. After applying the full capacity of 
the jack, 200 kips, there was only 1.5 in of vertical deflection and no yielding or damage 
to the structure. There was no lateral displacement at the bottom of the legs. Idealizing 
the structure to be pin supported at the bridge foundation was reasonable. Measured 
deflections at the top of the legs were around ? in. at most.  
 A two dimensional structural model of the bridge was developed in the computer 
program CANDE. The material properties of the concrete, reinforcing steel, and soil from 
the field testing were incorporated in the model.  
 The model results were compared to that of the field tests. It was found that the 
soil pressures at the top of the vertical legs of the structure correlated well. The soil 
pressures at the bottom of the vertical legs correlated well up to the ultimate design load 
of 57 kips. However, beyond this design load, the finite element model over predicted 
earth pressures. The vertical displacement predicted by the model correlated well up to 
the same design load of 57 kips; beyond the design load the model was sufficiently 
accurate but not as good as the lower range of loading. The horizontal displacements 
predicted by the model correlated well to the field test up to the design load of 57 kips, 
beyond which the deviation between the model and field test grew but was reasonably 
sufficient. 
 
12 
 
 Some of the conclusions drawn from the research were that ?the reliability of the 
analysis is highly dependent on the accuracy of the soil models and properties that are 
used for the given site conditions, the contribution of earth pressures is relatively small 
under normal operating loads, an extreme overload capacity can be developed by 
mobilizing the passive earth pressures along the side walls without concern for local 
failures, very small deflections were recorded at both design and factored loads,? and the 
ultimate load capacity of the bridge was not achieved (Zoghi and Farhey 2006).  
2.4 ? Zoghi and Hastings (Zoghi and Hastings 2000) 
 On a project prior to this one, discussed in Section 2.3, testing of full scale live 
load testing had been carried out on a 36 ft precast reinforced concrete arch culvert but 
the ultimate capacity could not be achieved due to the load exceeding the capability of 
the hydraulic jack during the test.  
?The objectives of this second phase of the research project were two fold. First, 
the failure mode of the test culvert was investigated utilizing a more rigorous 
analysis based on the modified CANDE finite-element computer program.  
Second, the soil-structure interaction characteristics of long-span precast concrete 
arch culverts were analyzed under a wide variety of site conditions using the 
previous full scale load test results as a benchmark? (Zoghi and Hastings 2000). 
 In the previous testing of a 36 ft span, the vertical and horizontal deflections, 
crack widths, and surrounding earth pressures were monitored as the structure was loaded 
in 10 kip increments. The findings of that test verified the structure performed 
satisfactorily and exceeded required design load specifications. The same project verified 
 
13 
 
a CANDE model developed correlated very well with actual deflections and soil pressure 
readings collected during testing.  
 The failure mode could not be established from this previous testing since the 
hydraulic jack reached its limit. Therefore, part of the second phase of this project was to 
identify the structure?s failure mechanism using a modified CANDE finite-element 
computer program. Beam-column elements were used to model the culvert structure 
behavior and quadrilateral or triangular elements were used for the surrounding soil. A 
step by step procedure of analysis was used, with backfill incrementally being added into 
the model and monitoring the behavior with this increasing backfill. Laboratory tests 
were used to determine at what point the steel was expected to yield and the point at 
which the concrete was expected to crush. Using this information, CANDE runs were 
performed to find the applied loads corresponding to the steel yielding and concrete 
crushing points. The yielding of steel was found to occur at a total load of approximately 
235 kips. The concrete was found to begin crushing at approximately 250 kips.  ?The 
point, at which sudden change of structural response took place, was considered to be the 
ultimate failure. Based on this methodology and the concept of soil-structure interaction, 
the ultimate load that arch culvert structure can withstand is approximately 340 kips [at a 
deflection of 7 in]. This is an impressive 13 times greater than the design load of 26 kips? 
(Zoghi and Hastings 2000). 
2.5 McGrath, Selig, and Beach (McGrath, Selig, and Beach 1996) 
 This research was related to a field test of a 36 ft span arch bridge. Using 1 ft of 
cover, a live load test was performed by driving a three-axle truck over the bridge and 
 
14 
 
stopping at certain locations. The load on the truck was intended to represent an HS-
25+30% AASHTO specified load truck. After this initial load test, 3 ft of cover was put 
on the bridge and measurements were taken. Additional deflection measurements were 
taken 6, 12, 18, and 24 months after the completion of the test. It was found that the 
structure reacted proportionally very little to the live loading. The maximum vertical 
deflection under the live load was 0.1 in. When the 2 ft of additional cover was added on 
top of the system, the reaction was larger than the live load, but all the displacement and 
pressure values were relatively small.  
 The computer analysis program CANDE was used for analysis. An attempt was 
made to match the measured properties of the actual soil in the computer model. 
Researchers found that the analysis agreed generally well with the test results; however, 
the actual live load deflections were lower than that predicted by the model. This 
relationship was true of the soil pressures as well. 
2.6 ? Beach (1988) 
 This research was related to load testing of a 19 ft span bridge. A cover depth of 1 
ft was used for the test. Load was applied in increments of 6.2 kips. The ultimate load of 
the bridge was reached at a load of 133.4 kips. At this point in the loading, the structure 
began to deflect a considerable amount without increasing the resisted load. The midspan 
deflection increased to approximately 2.75 in before the unit failed at midspan. Near the 
corners and at midspan the tension steel yielded and snapped with the concrete never 
crushing in compression. The structure maintained a load carrying capacity of 133.5 kips 
 
15 
 
after failure, assumed to have been due to the backfill pressure supporting the legs. Also 
noted was the appropriateness of treating the legs as pin supported at their base. 
 The software analysis program CANDE was used to correlate a model to the test 
results. The model analysis gave good correlation to measured deflections, though the 
theoretically predicted values were higher. The CANDE model was run without any 
backfill or cover and it was found that ?its load-deformation curve was nearly identical 
until the loading reached 4.5 times the service load, at which time the effects of the 
support from the backfill were realized.? The researchers concluded that ?because of the 
relatively high stiffness of the culvert, the predominant effect in this test was the 
structural behavior of the precast unit? and they speculated that the soil-structure 
interaction would have more effect on longer spans and higher fills.  
2.7 ? Summary 
 The projects discussed in this chapter highlight important research related directly 
to the research and testing done in the Foley Arch project discussed throughout the rest of 
this thesis. This previous work allowed insight into issues faced in the past with testing 
arch structures, such as not reaching the ultimate load of the structure due to limitations 
of the loading devices and difficulty in correlating computer model analysis results to 
testing results. Regarding modeling, considerations and assumptions of previous research 
allowed a more thorough and confident approach to modeling the Foley Arch. This 
previous work allowed an overall more educated and effective approach to various 
aspects of the project. As a result the project goals were more successfully met. 
 
16 
 
Chapter 3: Experimental Testing 
3.1 ? Introduction 
 Three experimental tests were performed to evaluate the Foley Arch structure. A 
field test was performed at an actual construction project to evaluate the behavior of the 
structure under service loads. A laboratory test was performed on a 20 ft clear span Foley 
Arch. Laboratory test loading continued up to failure of the structure. A second 
laboratory test was performed on a 36 ft clear span Foley Arch. This laboratory test 
loading also continued up to failure of the structure. The purpose of the discussion in this 
chapter is to give enough detail to reasonably convey what tests were performed in order 
to develop a computer model that correlated to the results of the laboratory tests. 
Meadows (2012) has supplied more detail on test procedure and results.  
3.2 ? Field Test 
The first experimental test performed was a field test at an active project in 
Midland, NC. The sections being installed on site had a clear span of 42ft. The objective 
of this field testing was to evaluate the behavior of a structure under service level loads. 
3.2.1 ? Field Test Gauges 
Vibrating wire strain gauges were installed on the inside face of three individual 
arch cross sections. Two of the three sections had five gauges installed on their inside 
face. One of the three sections had the same five gauges installed on the inside face as
17 
 
well as six additional gauges on the exterior face. The locations where the strain gauges 
were installed are shown in Figure 3-1. The section with the additional gauges on the 
exterior face also had earth pressure cells installed on the vertical walls of the section. 
The same section with additional gauges also had two displacement wire potentiometers; 
one was placed at midspan to measure vertical displacement and the other on a vertical 
wall to measure horizontal displacement. These were installed on the interior face of the 
section. The placement and layout of the earth pressure cells and displacement wire pots 
can be seen in Figure 3-2. 
 
 
Figure 3-1: Field Test Strain Gauge Layout 
 
 
Figure 3-2: Field Test Earth Pressure Cell and Wire Pot Layouts 
 
18 
 
3.2.2 ? Field Test Loading 
The load test was performed by using a loaded three axle dump truck with a gross 
vehicle weight of 56,280 lbs. The truck was incrementally driven across the bridge after 
backfill had been place and compacted around and on top of the bridge. The trucks axles 
were positioned and held over specific points on the bridge in order to allow the gauges 
to record several measurements. The highest strains were recorded when the centerline of 
the rear axles was placed over the midspan of the bridge. A photo of the truck used to 
load the bridge at various locations is shown in Figure 3-3. Its position in Figure 3-3, 
midspan, was the location that induced the greatest measured response. 
 
 
Figure 3-3: Field Testing ? Three Axle Dump Truck at Midspan 
 
19 
 
3.2.3 ? Field Test Results and Behavior 
The behavior of the bridge was similar to what was expected. Negative moments 
developed at the corners of the legs and positive moments developed at midspan. The 
lateral earth pressure measured near the top of the wall confirmed the arch deflected away 
from the centerline of the bridge. The lateral pressure was relatively zero at the bottom of 
the wall, as the bottom was restrained from moving laterally.  
 
3.3 ? Laboratory Tests 
Two laboratory tests on Foley Arch specimens were performed at the Auburn 
University Structural Research Laboratory (SRL). The first laboratory test specimen was 
a 4 ft wide 20 ft clear span precast arch section as shown in Figure 3-4. The vertical rise 
of the 20 ft span section, at its tallest point, was 8ft clear. 
  
Figure 3-4: Laboratory Test Specimen ? 20 ft Clear Span Section 
20 
 
The second laboratory test specimen was a 4 ft wide 36 ft clear span precast arch 
section as shown in Figure 3-5. The vertical rise of the 36 ft span section, at its tallest 
point was 9 ft clear. The arch bridge sections to be tested were cast at Foley Products? 
casting yard in Winder, GA. 
 
Figure 3-5: Laboratory Test Specimen ? 36 ft Clear Span Section 
3.3.1 ? Laboratory Test Gauges 
Prior to the casting date strain gauges were installed on multiple reinforcing bars. 
This was done by grinding the deformations of the reinforcing bar off, completely 
smoothing the surface of the bar, and installing gauges with adhesive and protective 
coverings. These gauged bars were taken to the casting yard and installed on the 
reinforcing cage of the structure. The bars were placed at locations of anticipated critical 
stress. A schematic diagram is shown in Figure 3-6 of the approximate location of the 
reinforcing bar mounted strain gauges. On the 20 ft span test specimen, the corner gauges 
were an average of 55 in from the edge of the wall, the midspan gauges were placed as 
close as possible to midspan, and the gauges placed in the legs of the structure were an 
21 
 
average of 45 in from the base of the legs. The specific layout of the gauges on the 20 ft 
clear span test specimen is shown in Figure 3-6. 
 
 
Figure 3-6: Gauge Layout ? 20 ft Clear Span Test Specimen 
 
 On the 36 ft span there were two sets of gauges placed near the corners; one set 
of corner gauges was approximately 22 in from the edge of the wall, and the second set 
was approximately 75 in from the edge of the wall. As with the 20 ft span, the midspan 
gauges on the 36 ft span were placed as close as reasonably possible to the midspan point 
of the arch and the gauges installed in the legs of the structure were approximately 20 in 
from the base of the legs. The specific layout of the gauges on the 36 ft clear span test 
specimen is shown in Figure 3-7. 
 
22 
 
 
Figure 3-7: Gauge Layout ? 36 ft Clear Span Test Specimen 
 
There were three bars/gauges placed across the width of the section at each 
critical location of interest on the 20 ft clear span test specimen and at the midspan 
location of the 36 ft clear span test specimen. There were two bars/gauges placed across 
the width of the section at all locations but midspan of the 36 ft clear span test specimen. 
A set of gauges was placed on each vertical wall of the structure just prior to the arch 
forming on the interior face. A set of gauges was placed on the arch portion of the section 
approximately where a constant thickness of the arch was reached; this was done at both 
ends of the arch. One additional set of gauges was placed near the quarter span point of 
the 36 ft clear span specimen. A set of gauges was placed in the arch directly at midspan 
of the structure.  The installation of the reinforcing bar mounted strain gauges to the 
reinforcing cage of the structure can be seen in Figure 3-8 and Figure 3-9.  
 
 
 
 
 
23 
 
 
Figure 3-8: Reinforcing Cage of Precast Section Prior To Casting 
 
 
 
Figure 3-9: Securing Wires of Strain Gauged Reinforcing Bar 
 
24 
 
Concrete strain gauges were also installed on the face of the concrete after 
delivery of the test specimen to the laboratory. These were placed at the same stress 
locations as the strain-gauged rebar. A set of two gauges were placed on the compression 
side of the concrete surface at each location of interest. A set of gauges was placed on the 
interior face of each vertical wall of the structure just prior to where the arch formed. A 
set of gauges was placed on the interior surface of the arch portion of the section 
approximately where a constant thickness of the arch was reached; this was done on both 
ends of the arch. A set of gauges was placed on the arch directly at midspan on the 
exterior face of the concrete. The diagrams of Figure 3-6 and Figure 3-7 shows the 
approximate locations where the concrete strain gauges were mounted on the 
compression face of the specimen.  
During the 20 ft clear span test, three wire potentiometer deflection measurement 
devices were used during testing. One measured vertical deflection at midspan and was 
mounted to a platform that was constructed for that purpose. This midspan wire pot can 
be seen in Figure 3-10. The other two wire pots were installed on the lateral restraint 
frames constructed and placed on each end of the structure to measure horizontal 
displacement. The discussion in this section is limited solely to instrumentation of the 
structure, see Section 3.3.3 for a discussion of the lateral forces and restraints designed 
for testing. A wire pot installed on the lateral restraint frame is shown in Figure 3-11. 
25 
 
 
Figure 3-10: Midspan Wire Pot Deflection Gauge Installed 
 
 
Figure 3-11: Wire Pot Installed on Lateral Restraint Frame 
26 
 
3.3.2 ? Laboratory Test Loading Configuration 
Three hydraulic actuators were used for the laboratory testing. One was placed at 
midspan. The two other loading actuators were offset from the middle actuator by 4 ft on 
either side. A preliminary estimate of ultimate capacity of the structure, including a 
margin of safety on the estimate, enabled an initial analysis of forces expected at multiple 
locations. Therefore, appropriately conservative design of the steel members used in the 
loading configuration was possible. The design of the loading system allowed loading of 
the structure to be applied from above while having the loading actuators anchored to the 
floor below the specimen. The loading configuration setup used on the 20ft span structure 
is shown in Figure 3-12. The loading actuators were anchored to the strong floor of the 
Auburn University SRL using three-quarter inch thick steel plates. The actuators were in 
tension as they attached and pulled down on an I-beam that spanned a distance greater 
than the width of the bridge which in turn was attached to another I-beam placed on top 
of the bridge. I-beams on top of the bridge had neoprene padding placed between the 
steel and the concrete section to avoid bearing directly on the concrete. The two outer I-
beams, at approximately third points of the structure, also had roller type supports 
between the neoprene padding and the I-beam to achieve a loading condition 
approximately vertical from the actuators.  
27 
 
 
Figure 3-12: Loading Actuator Configuration 
3.3.3 ? Lateral Soil Pressure Considerations 
Three-sided bottomless arch bridge culverts are typically loaded both vertically 
and laterally due to backfill material. These lateral forces occur due to the pressure from 
the soil against the structure?s vertical legs. Lateral pressure develops as the structure 
experiences heavy vertical loading and lateral deflection at either end occurs. This 
pressure was calculated for typical conditions given the amount of backfill and the 
dimensions of the structure. To reasonably approximate the behavior of the structure with 
the presence of this confining pressure on the bridge, a lateral restraining system was 
designed to be used during the laboratory testing of the 20 ft clear span specimen. The 
system, after exploring multiple options, involved an angle mounted to the base plate 
under each leg of the structure, to restrain any lateral movement outwards at the bottom 
28 
 
of the legs. This was appropriate as the typical installation calls for a key in the 
foundation for the bridge leg to be placed in to restrict lateral motion at the base of the 
leg.  
The range of fill depth considered on the 20 ft test section was 2 ft to 10 ft. An 
approximate soil unit weight of 100 pcf and a lateral earth pressure coefficient (Ko) of 0.3 
was used in calculations. The range of lateral earth pressure at the top of the 
approximately 6 ft vertical walls of the bridge was calculated to be 60 psf to 300 psf. The 
range of pressures at the bottom of the vertical walls was calculated to be 246 psf to 486 
psf. The minimum of the range of pressures is based on 2 ft of fill over the structure and 
the maximum of the range of pressures is based upon 10 ft of fill over the structure. 
To observe the influence of lateral earth pressure during service loads, a design 
was developed to place lateral restraints on the exterior faces of the 20 ft clear span 
section to apply confining pressure. This system induced behavior similar to that 
produced by passive pressure of the soil backfill in typical application. Two HSS 6x6x1/2 
sections were used to apply lateral confinement/load to the section. One HSS was placed 
at the top of each vertical leg of the structure. The other HSS section was placed at 
approximately mid-height of the vertical leg of the structure.  
A set of threaded steel rods on both sides of the wall spanned the length of the 
section and attached the HSS sections to each other. These rods were spliced at two 
locations to allow the insertion of a shorter section of threaded steel rod that was 
instrumented with a strain gauge. Having a gauged rod on each set of threaded rods 
allowed adjustment of the tension in each span of rods to the desired amount. The amount 
of tension to place in the bar was a function of the anticipated horizontal soil pressure 
29 
 
experienced by the bridge at a given fill depth. The minimum pressures calculated were 
for the minimum fill depth of 2 ft and the maximum pressures calculated were for the 
maximum fill depth of 10 ft. Intermediate fill depths were used to calculate pressures at 
given points. The calculated earth pressure distribution at various fill depths on the 
vertical walls of the 20 ft clear span section is shown in Figure 3-13.  
 
 
Figure 3-13: Horizontal Earth Pressure Distribution at Various Fill Depths 
  
To calculate the force required in each bar to reach an equivalent loading and 
behavior as the horizontal earth pressure in application, the relationship between axial 
force and strain gauge reading had to be determined for each of the threaded rods that had 
strain gauges placed on them. This was accomplished by using a testing machine to apply 
0 
1 
2 
3 
4 
5 
6 
7 
0 100 200 300 400 500 600 
Wal
l Hei
gh
t - 
ft 
Earth Pressure - psf 
Earth Pressure - 2ft Fill 
Earth Pressure - 10ft Fill 
Earth Pressure - 5 ft Fill 
Earth Pressure - 8ft Fill 
30 
 
tensile load and take readings on the strain measured by the gauge on the threaded rod at 
small increments. Multiple tests were performed for each of the gauged bars to produce 
an average axial load to strain gauge reading relationship 
A general view of the entire structure with the laterally restraining system in place 
is shown in Figure 3-14. Figure 3-15 shows a closer view of the HSS sections as they 
were placed on the wall of the structure. The force required in the threaded rods to create 
the laterally restrained condition was based on calculations for an approximately median 
fill depth of 5 ft. With 5 ft of fill on the 20 ft clear span test specimen, the calculated 
lateral earth pressure at the top of the wall was 150 psf. The pressure calculated at the 
bottom of the vertical wall of the structure was 336 psf. Using the assumption that the 
pressure distribution along the wall is approximately linear, the average of the pressures 
at the bottom and top of the wall provide the pressure at the middle of the wall as 243 psf. 
The HSS sections were placed approximately at the top and middle of the vertical walls 
of the test specimen during testing. To calculate the required force in the rods that were 
spanning between the HSS sections on either end of the structure a tributary area for the 
top and middle HSS section was used. The HSS at the top of the wall was assumed to 
account for the pressure on the top quarter of the wall, approximately 1.5 ft. Accounting 
for the linearly increasing pressure along the wall?s depth by averaging the pressure 
across the tributary depth, the top HSS should apply a distributed load of 260 lb/ft across 
the width of the section. With a threaded rod on each end of the HSS to provide this 
confining force, the axial force required in each of the rods on the top HSS was 
approximately 520 lbs. The middle HSS was assumed to account for pressure on the 
middle half of the wall, approximately 3 ft. Again accounting for the linearly increasing 
31 
 
pressure along the wall?s depth by averaging the pressure across the tributary depth, the 
middle HSS should apply a distributed load of 730 lb/ft across the width of the section. 
With a threaded rod on each end of the middle HSS to provide this confining force, the 
axial force required in each of the rods on the middle HSS was approximately 1,460 lbs.  
 
 
Figure 3-14: Structure with Lateral Restraint System Installed 
32 
 
 
Figure 3-15: Detailed View of Laterally Restraining HSS Sections Installed 
3.3.4 ?Test Results and Behavior 
While the field test provided useful information related to service-level load 
behavior, it was not used directly for correlation with the computer model developed after 
testing. Meadows (2012) has provided a detailed discussion of field testing results. 
The test structures behaved very much as anticipated throughout the service load 
range and higher load conditions. The maximum moments were seen at midspan and at 
the corners of the arches. The maximum vertical deflections were seen at midspan of the 
structure. The maximum lateral deflection was seen in the corners of the structure. While 
the magnitude of values varied significantly between the two, the general behavior of the 
20 ft clear span test specimen and the 36 ft clear span test specimen was similar. While 
the failure mode is of interest and was recorded in each of the test specimens, this subject 
was not the focus of this paper; Meadows (2012) discusses the failure modes observed 
33 
 
during testing. The focus of this work was to monitor the ultimate capacity of the 
structure and to then correlate a structural model constructed in SAP2000 to those test 
results. Therefore, the remaining portions of this chapter discuss the results of the lab test 
critical to correlation of the SAP2000 structural model. Meadows (2012) discusses the 
laboratory testing results in detail. 
Using the strain data from gauges installed on the 20 ft clear span arch prior to 
casting, the internal moments were calculated at critical locations. The moments 
calculated in the 20 ft clear span arch at midspan and at both ends of the arch are plotted 
against total load in Figure 3-16. In addition, displacements were monitored using wire 
pots at midspan and approximately 56 in from the edge (corners) of the 20 ft clear span 
arch. These displacements are plotted against total load in Figure 3-17. 
 
Figure 3-16: Internal Moments in 20 ft Clear Span Laboratory Test 
  
0 
50 
100 
150 
200 
250 
300 
350 
400 
450 
500 
0 25 50 75 100 125 150 175 200 
Mo
me
nt 
(k-
ft)
 
Total Load (k) 
Corner 
Midspan 
34 
 
 
Figure 3-17: Displacements in 20 ft Clear Span Laboratory Test 
Similar to the 20 ft span, the strain data readings in the 36 ft span were used to 
calculate the moments at various locations along the structure. The moments were 
calculated in the 36 ft clear span arch at midspan, approximately 75 in from the edge of 
the wall (corner) up the arch, and approximately 22 in from the edge of the wall (thick 
corner) up the arch. These moments are plotted against total load in Figure 3-18. In 
addition to moments being calculated using the monitored strain gauges measurements, 
vertical displacements were monitored using wire pots at midspan and lateral 
displacement was monitored at the corners of the 36 ft clear span arch. These 
displacements are plotted against total load in Figure 3-19. 
 
0 
0.25 
0.5 
0.75 
1 
1.25 
1.5 
1.75 
2 
2.25 
2.5 
0 25 50 75 100 125 150 175 200 
Disp
lac
em
en
t (i
n) 
Total Load (k) 
Corner 
Midspan 
Corner 
35 
 
 
Figure 3-18: Corner Moments in 36 ft Clear Span Laboratory Test 
 
 
Figure 3-19: Displacements in 36 ft Clear Span Laboratory Test 
0 
50 
100 
150 
200 
250 
300 
350 
400 
450 
500 
550 
600 
0 20 40 60 80 100 120 140 160 
Mo
me
nt 
(k-
ft)
 
Total Load (k) 
Thick Corner 
Corner At Arch 
Midspan 
Corner At Arch 
Thick Corner 
0 
1 
2 
3 
4 
5 
6 
7 
0 20 40 60 80 100 120 140 160 
Disp
lac
em
en
t (i
n) 
Total Load (k) 
Corner 
Midspan 
Corner 
36 
 
3.4 ? Conclusions 
The laboratory test yielded results that were conceptually compatible with the 
anticipated behavior. The highest moments being developed at midspan and at the corner 
of the arch section along with the highest deflections being measured at midspan were all 
logical. The data collected and analyzed provided a solid comparison point to move 
forward with the project in developing a structural computer model in SAP2000. This 
process will be discussed in the following chapter. 
37 
 
Chapter 4: Computer Modeling 
4.1 ? Introduction 
The objective in creating a structural computer model was to correlate the results 
of the model to those found during the laboratory testing described in Chapter 3. The 
computer software program used for development of the structural model was SAP2000. 
Since the structure was loaded to failure during the laboratory tests, the range of behavior 
the model needed to correlate to included nonlinear behavior of the structure. Therefore, 
SAP2000?s (SAP2000) nonlinear analysis capabilities were of particular importance in 
choosing it to develop the structural model. SAP2000 was chosen in place of other 
programs that offered more soil-structure interaction capabilities because it was 
determined that the soil pressure had a minimal effect on the behavior of the bridge at its 
ultimate capacity. SAP2000?s ability to model reinforced concrete was easier to 
implement and researchers on the project had previous experience with SAP2000.  
4.2 ? Geometric Properties 
 Geometric dimensions based on the construction documents and physical 
measurements provided a reference point for which to construct the structural model. A 
barrel shell element was created from the new model templates within SAP2000. This 
allowed for creation of the geometric arch portion of the structure. The appropriate 
length, roll down angle, radius, axial divisions, and angular divisions were input. The  
 
38 
 
barrel shell created was a three dimensional object. However, the model of the arch was 
to be a 2-D frame element. Therefore, all objects aside from the end cross section of the 
barrel shape were deleted and the grid lines and points of the one cross section of the 
barrel shape were used to create the arch shape of the Foley Arch being modeled. 
Once the basic arch shape was created, the legs of the arch were manually drawn 
in. Grid lines and grid points were added at the appropriate locations below the arch to  
allow the legs of the arch to be drawn in. The desired number of divisions of the legs 
dictated the location of the grid lines and points used to draw in the vertical legs. The 
number of divisions was based on various parameters including how much and at what 
rate the geometry of the cross section of the laboratory test specimens changed when 
approaching the corner of the arch. All elements were located along the geometric 
centerline of the structure. 
4.3 ? Cross Sectional Element and Material Properties 
Using the concrete frame section generator within SAP2000, the cross sectional 
dimensions and reinforcing details were assigned to the frame elements.   While a 
majority of the frame element could appropriately be assigned as uniform prismatic 
rectangular sections throughout the length of the element, the corner sections of the 
structure were in reality much stiffer due to a non uniform section throughout their 
length. To represent this in the model, non-prismatic frame sections were assigned to 
these corner elements. The geometric properties of these elements linearly change 
throughout their length to two distinctly defined cross sections assigned at each end of the 
element. The prismatic and non-prismatic sections used in the 20 ft clear span model are 
 
39 
 
conceptually shown in Figure 4-1. The prismatic and non-prismatic sections used in the 
36 ft clear span model are conceptually shown in Figure 4-2. 
 
 
Figure 4-1: 20 ft Clear Span ? SAP2000 Elements 
 
 
 
Figure 4-2: 36 ft Clear Span ? SAP2000 Elements 
 
 
40 
 
 The material properties used in the SAP2000 model were a combination of default 
material properties built into the software and appropriate adjustments to these default 
properties based on tests performed using material samples taken from the structures 
tested. Concrete cylinders made from the same batch of concrete used for each of the two 
arches tested in the Auburn University laboratory were used for modulus of elasticity and 
compressive strength tests. Reinforcing bar samples were taken from the 36 ft clear span 
structure for testing. The expected yield strength and ultimate strength of the reinforcing 
bar were found using these tests.  
 The tests for modulus of elasticity performed on the concrete cylinders were in 
accord with ASTM C 469-02 (ASTM). The modulus of elasticity of the concrete used in 
the 20 ft clear span structure at the time of testing was 5,950 ksi. The compressive 
strength of the concrete used in the 20 ft clear span structure at the time of testing was 
12,500 psi. The modulus of elasticity of the concrete used in the 36 ft span at the time of 
testing was 4,100 ksi. The compressive strength of the concrete used in the 36 ft clear 
span structure at the time of testing was 7,040 psi. These concrete material properties 
were incorporated in the models for the respective 20 ft clear span and 36 ft clear span 
models. These properties were manually defined within SAP2000. Figure 4-3 shows one 
of the concrete cylinders in the testing machine after having been tested for ultimate 
compressive strength.  
 
41 
 
 
Figure 4-3: Concrete Cylinder Test 
 Tests were performed on reinforcing bar samples from the 36 ft clear span 
structure for use in the computer model of both the 20 ft clear span and 36 ft clear span. 
The yield strength of the reinforcing steel was 65 ksi. The rupture strength of the 
reinforcing steel was 80 ksi. These material properties were manually incorporated into 
the default material settings for A615Gr 60 steel within SAP2000.  
 
4.4 ? Loading Configuration 
 To simulate the behavior in the laboratory testing within the SAP2000 model of 
the 20 ft clear span structure and the 36 ft clear span structure, the loading configuration 
was setup to be the same. Therefore, the point loading configuration used in the SAP2000 
 
42 
 
structural computer model geometrically matched that of the laboratory testing load 
setup.  
 Three point loads on the 20 ft and 36 ft clear span SAP2000 structural models 
were set up at locations imitating those used in the laboratory tests. The load cases 
incrementally increased the magnitude of each of these three point loads by 10 kips, a 30 
kip total increase per load case. The lowest magnitude load case in both models was 20 
kips per point load, 60 kips total load. The highest magnitude load case for the 20 ft clear 
span model was 64 kips per point load, 192 kips total load. The lowest magnitude load 
case in the 36 ft model was 20 kips per point load, 60 kips total load. The highest 
magnitude load case in the 36 ft model was 51 kips per point load, 153 kips total load. 
 
4.5 ? Nonlinear Analysis 
 As the laboratory testing carried out loading up to ultimate capacity of the 
structure, it was necessary to include nonlinear effects in the computer analysis model. 
This was accomplished in SAP2000 through the use of M3 hinges assigned to various 
frame elements throughout the structure in conjunction with nonlinear load cases.  
 
4.5.1 ?User Defined M3 Hinges 
 User defined M3 type hinges were decided upon after considering the benefits and 
data comparison of various models with different types of potential hinges within 
SAP2000. M3 hinges are dependent on moments at the assigned hinge location. Fiber 
 
43 
 
hinges were experimented with to account for axial load effects. However, axial forces 
ended up being negligible. Therefore, flexural behavior, or M3 forces, was the dominant 
contributing factor to increased deformation. User defined M3 hinges accounted for these 
forces well and produced results with the best correlation those of the actual results in the 
laboratory. As the cross sectional properties of the structures were very well known from 
the construction documents, reinforcing detail specifications, and physical measurements 
taken in the laboratory, it was possible to perform detailed cross sectional analysis 
calculations for critical cross sections to define the needed range of data points necessary 
to utilize user defined M3 hinge properties, as opposed to automatically generated M3 
hinge properties. The cross sectional properties used in calculating hinge parameters are 
shown in Table 4-1. The cracking, yielding, and nominal moment capacities and 
corresponding curvatures were calculated for three different cross sections corresponding 
to the desired hinge locations. A limiting steel stress of 78 ksi was imposed when 
calculating the ultimate moment capacity of the cross sections. This was based on the 
data collected from running tensile tests on reinforcing bar samples from the test 
specimens. A moment-curvature type property definition was used in defining the hinge 
properties. The frame hinge property data form for the various M3 hinges allows for 
definition of five distinct displacement control parameters using a user defined value for 
moment and a value for curvature. These points are conceptually illustrated in Figure 4-
4.These points are labeled A through E. Point A corresponded to the unstressed origin 
point. Point B was setup to correspond to the calculated cracking moment with a 
curvature of zero. Point C corresponded to the yield moment and yield curvature. Point D 
and E corresponded to the ultimate moment capacity and ultimate curvature. These 
 
44 
 
displacement control parameters for the hinges of the 20 ft and 36 ft clear span SAP2000 
structural models are shown in Table 4-2 and Table 4-3, respectively. Figure 4-5 and 
Figure 4-6 are graphical representations of the hinge definition point values given in 
Table 4-2 and Table 4-3, respectively. 
Table 4-1: Cross Sectional Properties Used In Hinge Parameter Calculations 
Span 
Span 
Location 
Cross Sectional Property 
b (in.) h (in.) d (in.) As (in2) d? (in.) A?s (in2) 
20 ft 
Mid 48 10 8.04 8.02 2.18 1.26 
Quarter 48 10 7.82 2.52 1.68 1.26 
Corner 48 22 19.82 2.52 13.68 1.26 
36 ft 
Mid 48 12 10.62 5.34 2.13 1.27 
Quarter 48 12 9.64 4.60 1.20 3.04 
Corner 48 28 25.64 4.60 8.15 4.30 
 
Figure 4-4: SAP2000 Hinge Property Definition Points 
 
45 
 
Table 4-2: Displacement Control Parameters of Hinges ? 20 ft Clear Span Model 
Hinge 
Definition 
Point 
Hinge Location 
Midspan Quarter Span Corner 
M (k-ft) ? (in-1) M (k-ft) ? (in-1) M (k-ft) ? (in-1) 
A 0 0 0 0 0 0 
B 62 0 58 0 277 0 
C 308 0.000428 99 0.000367 299 0.000134 
D 388 0.001555 135 0.003375 430 0.003375 
E 388 0.001555 135 0.003375 430 0.003375 
  
 
Figure 4-5: Displacement Control Parameters of Hinges ? 20 ft Clear Span Model 
0 
50 
100 
150 
200 
250 
300 
350 
400 
450 
500 
0 0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004 
Mo
me
nt 
(k-
ft)
 
? (in-1) 
Midspan 
Quarter Span 
Corner 
 
46 
 
Table 4-3: Displacement Control Parameters of Hinges ? 36 ft Clear Span Model 
Hinge 
Definition 
Point 
Hinge Location 
Midspan Quarter Span Corner 
M (k-ft) ? (in-1) M (k-ft) ? (in-1) M (k-ft) ? (in-1) 
A 0 0 0 0 0 0 
B 68 0 66 0 346 0 
C 276 0.000299 217 0.000321 614 0.000109 
D 343 0.001439 269 0.001978 924 0.000867 
E 343 0.001439 269 0.001978 924 0.000867 
 
 
Figure 4-6: Displacement Control Parameters of Hinges ? 36 ft Clear Span Model 
0 
100 
200 
300 
400 
500 
600 
700 
800 
900 
1000 
0 0.0005 0.001 0.0015 0.002 0.0025 
Mo
me
nt 
 (k
-ft
) 
?  (in-1) 
Midspan 
Quarter Span 
Corner 
 
47 
 
As can be seen primarily in the moment capacity defined in the hinge property definition, 
the additional size/thickness of the concrete cross section at the corners of the structure 
resulted in larger moments at cracking, yielding, and ultimate loading conditions. This 
was appropriate as the corner sections were physically thicker and stiffer. Therefore, 
stiffer hinges were needed in the model at those corner locations. An isotropic hysteresis 
type was used for the hinge definition. The moments and curvatures values calculated and 
used in the definition of points A through E were used directly; therefore a scaling factor 
of 1.0 for moment and curvature was defined. 
The location of the hinges in the SAP2000 model matched the highest 
concentration of observed cracking and rotation during the laboratory testing of both the 
20 ft clear span and 36 ft clear span structures. The location of the hinges in the 20 ft 
clear span and the 36 ft clear span SAP200 structural model were (a) the corners of the 
structure, (b) approximately quarter span of the structure, and (c) midspan of the 
structure. Since the midspan location of the structure was at the intersection of two 
individual elements, a hinge was assigned to both elements at the extreme end of each of 
those two elements. This assured continuity and symmetric behavior at this location. 
Therefore, a total of six user defined M3 hinges were assigned in the 20 ft clear span 
SAP2000 structural model. The hinges and their locations in the 20 ft clear span model 
and the 36 ft clear span model are shown in Figure 4-7 and Figure 4-8, respectively. 
 
 
48 
 
 
Figure 4-7: Hinge Locations and Labels ? 20 ft Clear Span Model 
 
 
Figure 4-8: Hinge Locations and Labels ? 36 ft Clear Span Model 
 Failure modes are not predicted by SAP2000. However, the ?failure point? of the 
structure was assumed to have occurred when a drastic, unrealistic increase in deflection 
occurred in the model analysis. For the 20 ft clear span model, this drastic increase in 
displacement occurred around 65 kips per loading location, 195 kips total load. This was 
very close to the ultimate total load in testing of the 20 ft clear span of 185 kips. The 
deflection in the 20 ft clear span SAP2000 model increased from 1.839 in. at midspan 
 
49 
 
with 192 kips total load to thousands of inches at midspan with 195 kips total load. The 
hinges near the quarter span point were closest to their rotational capacity at the 192 kips 
total load case than either the midspan hinges or the corner hinges. This indicates that 
theoretical failure that occurs slightly above a total load of 192 kips; the exact location of 
the hinge closest to its rotational capacity is not necessarily a reliable prediction of where 
failure will occur since the hinge properties are all user defined based on cross sectional 
analysis; even though in the case of the 20 ft clear span the highest hinge rotation did 
correspond to the laboratory specimen?s failure location. However, the ultimate load 
capacity of the structure could be reasonably predicted based on the comparison of the 20 
ft model capacity to laboratory specimen capacity. 
 For the 36 ft clear span model, the drastic increase in displacement occurred at 
approximately 52 kips per loading location, or a total load of 156 kips. This was very 
close to the ultimate total load in testing of the 36 ft clear span of approximately 150 kips. 
The deflection in the 36 ft clear span SAP2000 model drastically increased from 3.501 in. 
at a total load of 156 kips to thousands of inches around a total load of 156 kips. The 
hinges at midspan were closer to their rotational capacity than the hinges at the quarter 
span points or the corners. However, similar to the 20 ft clear span case, the exact 
location of the hinge closest to its rotational capacity is not necessarily a reliable 
prediction of where failure will occur since the hinge properties are all user defined based 
on cross sectional analysis; this unreliability was evident in the 36 ft clear span test where 
failure occurred near the quarter span point and not at midspan. However, the ultimate 
load capacity of the structure was reasonably predicted based on a comparison of the 36 
ft model capacity to the laboratory specimen capacity.   
 
50 
 
4.5.2 ?Nonlinear Load Case 
 SAP2000 allows the incorporation of multiple load cases for desired loading 
conditions and settings for each individual load case. The load cases used in the 20 ft 
clear span structural model were all nonlinear static load cases beginning from an 
unstressed state. Load patterns were assigned to the load cases. These load patterns 
corresponded to the magnitude of load application being considered in each load case. 
Six load patterns were assigned. All assigned loads were live loads with a self weight 
multiplier of zero. The loads were assigned to joints corresponding closest to the actual 
load location used in the laboratory testing. The smallest load intensity included three 
point loads with a 20 kip magnitude; a total load of 60 kips. The load intensity increased 
by 10 kips per load location up to 60 kips per load location; a total load of 180 kips. The 
final stable load pattern in the 20 ft clear span model was 64 kips per load location; a total 
load of 192 kips.  
During testing of the 20 ft clear span structure it was necessary to use two steel 
angles, one directly on either side of the middle actuator to reach the ultimate loading 
capacity of the bridge. A photo of this configuration is shown in Figure 4-9. 
 
51 
 
 
Figure 4-9: Alternative Load Application for 20 ft Clear Span Test Specimen 
The hydraulic actuators reached their maximum capacity before the ultimate load was 
reached. This slightly different loading configuration was also incorporated into the 
SAP2000 model of the 20 ft clear span structure. However, this alternative load 
application configuration made essentially no difference in the moment diagram or other 
results as compared to a load case with just three point loads. Therefore, all final results 
for the 20 ft clear span model reported herein correspond to a load case utilizing three 
load application points.  
 
52 
 
The load application control was typically set up to apply the full load, or force 
controlled analysis, with a monitored displacement in the vertical direction at the joint 
corresponding to midspan. However, at various stages of model development it was 
advantageous to run a displacement controlled analysis to better observe the behavior of 
the model structure at various loading increments. This displacement controlled analysis 
proved useful in identifying potential improvements to details, especially hinge 
properties, of the model and overall progression of the model in developing good 
correlation to laboratory results.  
It was necessary to save multiple states of the analysis results in order to view 
detailed results of the hinge behavior throughout load application during analysis. Once 
the model was in the later stages of development, the final stages of the analysis were of 
more interest than incremental stages and therefore the analysis was set to include only 
the final state of analysis.  
The default nonlinear parameters and settings incorporated in SAP2000 were 
primarily used, as opposed to user defined nonlinear settings. The hinge unloading 
method was to unload the entire structure. The solution control default values were all 
adequate for the analysis performed. 
The structure under consideration was composed of reinforced concrete. As is true 
of most concrete structures, loading resulted in flexural cracking of the concrete. Cracked 
sections have a decreased moment of inertia which directly decreases the stiffness of the 
overall structure. Prior to this cracking, the moment of inertia of a given cross section is 
often represented simply by the gross moment of inertia of the section. However, after 
 
53 
 
cracking has occurred, it becomes necessary to adjust the moment of inertia to an 
effective moment of inertia for cross sectional analysis purposes since part of the section 
is cracked and therefore not contributing to the stiffness of the section. It was necessary 
to account for this change in section stiffness in the SAP2000 structural models by the 
use of an I3 property modifier. Calculating this property modifier was done by 
calculating the effective moment of inertia as discussed in Section 9-4, particularly 
Equation 9-10b, of Wight and MacGregor?s ?Reinforced Concrete ? Mechanics and 
Design.?   
Ie=Icr+(Ig - Icr)*(Mcr/Ma)3 
The I3 multipliers to be incorporated into the SAP2000 model were found by dividing the 
effective moment of inertia by the gross section moment of inertia. Property modifiers 
were calculated for and assigned to two different sections of elements. A middle portion 
of elements and the quarter span portion of elements. The middle portion of elements 
included four total elements, two on either side of midspan. The quarter span portion of 
elements included the rest of the elements making up the arch section of the structure 
except for the most exterior element in the corner on each end of the arch. Since the 
effective moment of inertia is a function of the actual moment at a cross section under the 
applied loading, each load case had a different I3 property modifier. The I3 property 
modifiers used in the 20 ft clear span model and 36 ft clear span model are shown in 
Table 4-4. 
 
 
54 
 
Table 4-4: I3 Property Modifiers 
Total Load 
SAP2000 Model 
I3 Property Modifier ? 20 ft I3 Property Modifier ? 36 ft 
Middle Section Quarter Section Middle Section Quarter Section 
0 1.0 1.0 1.0 1.0 
60 0.45 0.43 0.43 0.44 
90 0.36 0.27 0.36 0.30 
120 0.34 0.26 0.35 0.27 
150 0.34 0.26 0.34 0.26 
180 0.34 0.26 N/A N/A 
195 0.34 0.26 N/A N/A 
 
4.6 Model Analysis Results 
 The objective of developing a SAP2000 structural model was to correlate the 
results of the model with those of the laboratory testing. The primary means of 
comparison used to evaluate how well the model correlated to the laboratory results and 
to further develop the model were moment diagrams and deflections. 
 The moments and deflections were recorded at locations of interest after running 
each of the load cases. Table 4-5 shows the SAP2000 20 ft clear span model results. 
Table 4-5 shows the SAP2000 36 ft clear span model results.  
 
 
 
55 
 
Table 4-5: 20 ft Clear Span SAP2000 Structural Model Results 
Load 
Case 
Total 
Load 
(kips) 
Midspan 
Moment   
(k-ft) 
Corner Moment 
(Interior of 2nd 
Element From Corner) 
(k-ft) 
Lateral 
Deflection 
(in) 
Midspan 
Deflection 
(in) 
0 0 0 0 0 0 
20 60 97 58 0.06 0.29 
30 90 146 84 0.12 0.57 
40 120 203 105 0.16 0.82 
50 150 267 120 0.22 1.11 
60 180 331 132 0.32 1.54 
64 192 376 123 0.37 1.84 
 
 
 
 
 
 
 
 
 
 
56 
 
Table 4-6: 36 ft Clear Span SAP2000 Structural Model Results 
Load 
Case 
Total 
Load 
(kips) 
Midspan 
Moment   
(k-ft) 
Corner At 
Arch 
Moment 
(Middle of 2nd 
Element From 
Corner) (k-ft) 
Thick 
Corner 
Moment 
(Middle of 1st 
Element At 
Corner)      
(k-ft) 
Lateral 
Deflection 
(in) 
Midspan 
Deflection 
(in) 
0 0 0 0 0 0 0 
20 60 123 133 172 0.14 0.83 
30 90 193 193 252 0.25 1.59 
40 120 253 253 333 0.36 2.26 
50 150 315 315 416 0.52 3.38 
53 159 339 321 424 0.54 3.50 
 
 The moment diagrams and displacements were found for each load case of the 20 
ft clear span model and the 36 ft clear span model in order to compare the results to those 
recorded during the laboratory testing. Figure 4-10 shows a plot of the midspan moment 
versus the total load for the 20 ft clear span SAP2000 model compared to the midspan 
moment versus the total load for the 20 ft clear span test specimen. Figure 4-11 shows a 
plot of the midspan vertical deflection versus total load for the 20 ft clear span SAP2000 
model compared to midspan deflection measured during the laboratory testing of the 20 ft 
clear span test specimen. Figure 4-12 shows a plot of the corner moment versus total load 
for the 20 ft clear span SAP2000 model compared to the corner moment measured during 
 
57 
 
testing of the 20 ft clear span test specimen. Figure 4-13 shows a plot of the lateral 
deflections at the corners of the arch versus total load for the SAP2000 model analysis 
compared to the laboratory testing of the 20 ft clear span.  
 
 
Figure 4-10: Model versus Laboratory Specimen ? 20 ft Span Midspan Moment 
  
0 
50 
100 
150 
200 
250 
300 
350 
400 
450 
500 
0 25 50 75 100 125 150 175 200 
Mo
me
nt 
(k-
ft)
 
Total Load (k) 
Midspan 
SAP Model - 
Midspan 
 
58 
 
 
Figure 4-11: Model versus Laboratory Specimen ? 20 ft Span Midspan 
Displacement 
 
Figure 4-12: Model versus Laboratory Specimen ? 20 ft Span Corner Moment 
0 
0.25 
0.5 
0.75 
1 
1.25 
1.5 
1.75 
2 
2.25 
2.5 
0 25 50 75 100 125 150 175 200 
Displ
ace
men
t (i
n) 
Total Load (k) 
WP 2 - Midspan 
SAP Model - 
Midspan 
0 
20 
40 
60 
80 
100 
120 
140 
0 25 50 75 100 125 150 175 200 
Mo
me
nt 
(k-
ft)
 
Total Load (k) 
Corner 
SAP Model - 
Corner 
 
59 
 
 
Figure 4-13: Model versus Laboratory Specimen ? 20 ft Span Corner Displacement 
The midspan moment versus total load plot for the 20 ft clear span SAP2000 
model has less than 20 percent difference than the laboratory throughout the range of 
loading. The SAP2000 model midspan moment was slightly lower than the 20 ft clear 
span laboratory test midspan moment throughout the range of testing.  
The midspan displacement versus total load plot for the 20 ft clear span SAP2000 
model is approximately 10 percent lower than the laboratory throughout the range of 
loading. The SAP2000 model midspan displacement was slightly lower than the 20 ft 
clear span laboratory test test midspan displacement throughout the range of testing. 
The corner moment versus total load plot for the 20 ft clear span SAP2000 model 
is significantly higher than the laboratory throughout the range of loading. Of the 
0 
0.25 
0.5 
0.75 
1 
1.25 
0 25 50 75 100 125 150 175 200 
Disp
lac
em
en
t (i
n) 
Total Load (k) 
WP 1 - Corner 
WP 3 - Corner 
SAP Model - Lateral 
 
60 
 
properties recorded for comparison between the SAP2000 model and laboratory 
specimen, this is the only parameter that was overestimated in the 20 ft SAP2000 model 
compared to the laboratory testing. 
The corner displacement of the 20 ft clear span test specimen was slightly 
different for the two corners. The 20 ft clear span SAP2000 model was approximately 20 
to 30 percent lower than the 20 ft clear span laboratory test specimen corner deflection.    
Figure 4-14 shows a plot of the midspan moment versus total load for the 36 ft 
clear span SAP2000 model compared to the midspan moment versus total load for the 36 
ft clear span test specimen. Figure 4-15 shows a plot of the midspan vertical deflection 
versus total load for the 36 ft clear span SAP2000 model compared to midspan deflection 
measured during the laboratory testing of the 36 ft clear span test specimen. Figure 4-16 
shows a plot of the quarter span moment versus total load for the 36 ft clear span 
SAP2000 model compared to the quarter span moment measured during testing of the 36 
ft clear span test specimen. Figure 4-17 shows a plot of the lateral deflections at the 
corners of the arch versus total load for the SAP2000 model analysis compared to the 
lateral deflections measured during laboratory testing of the 36 ft clear span. Figure 4-18 
shows a plot of the corner moment versus total load for the 36 ft clear span SAP2000 
model compared to the laboratory test data. 
 
61 
 
 
Figure 4-14: Model versus Laboratory Specimen ? 36 ft Span Midspan Moment 
 
Figure 4-15: Model versus Laboratory Specimen ? 36 ft Span Midspan 
Displacement 
0 
50 
100 
150 
200 
250 
300 
350 
400 
450 
500 
550 
600 
0 20 40 60 80 100 120 140 160 
Mo
me
nt 
(k-
ft)
 
Total Load (k) 
Midspan 
SAP Model - 
Midspan 
0 
1 
2 
3 
4 
5 
6 
7 
0 20 40 60 80 100 120 140 160 
Disp
lac
em
en
t (i
n) 
Total Load (k) 
WP 2 - Midspan 
SAP Model - 
Midspan 
 
62 
 
 
Figure 4-16: Model versus Laboratory Specimen ? 36 ft Span Corner Moment 
 
Figure 4-17: Model versus Laboratory Specimen ? 36 ft Span Corner Displacement 
0 
50 
100 
150 
200 
250 
300 
350 
400 
0 20 40 60 80 100 120 140 160 
Mo
me
nt 
(k-
ft)
 
Total Load (k) 
Corner At Arch 
Corner At Arch 
SAP Model - Corner At 
Arch 
0 
0.1 
0.2 
0.3 
0.4 
0.5 
0.6 
0.7 
0.8 
0.9 
1 
0 20 40 60 80 100 120 140 160 
Disp
lac
em
en
t (i
n) 
Total Load (k) 
WP 1 - Corner 
WP 3 - Corner 
SAP Model - 
Lateral 
 
63 
 
 
Figure 4-18: Model versus Laboratory Specimen ? 36 ft Span Corner Moment 
 The midspan moment generated by the 36 ft clear span SAP2000 model was less 
than 5 percent different than the laboratory specimen data throughout the first 40 percent 
of the load range. After the first 40 percent of the load range, the 36 ft clear span 
SAP2000 model gradually increased in its underestimate of the midspan moment. At the 
ultimate load the 36 ft clear span SAP2000 model was approximately 40 percent less than 
the midspan moment of the 36 ft clear span test specimen. The average difference 
between the SAP2000 model and the laboratory test specimen was approximately 25 
percent. 
 The midspan displacement generated by the 36 ft clear span SAP2000 model was 
approximately 5 percent different than the laboratory specimen data throughout the first 
70 percent of the load range. For the final 30 percent of the load range, the 36 ft clear 
0 
50 
100 
150 
200 
250 
300 
350 
400 
450 
500 
550 
600 
0 20 40 60 80 100 120 140 160 
Mo
me
nt 
(k-
ft)
 
Total Load (k) 
Thick Corner 
Thick Corner 
SAP Model - Thick 
Corner 
 
64 
 
span SAP2000 model gradually increased its underestimate of the midspan displacement. 
At the ultimate load the 36 ft clear span SAP2000 model was approximately 30 percent 
less than the laboratory test specimen midspan displacement. The average difference 
between the 36 ft clear span SAP2000 model and36 ft clear span laboratory test specimen 
for the final 30 percent of the load range was approximately 15 percent. 
The two corner at arch moments measured in on the 36 ft clear span test specimen 
were different by approximately 30 to 40 percent. The corner arch moment generated in 
the 36 ft clear SAP2000 model fell, in between the two different corner at arch moments 
measured in the laboratory. Therefore, the SAP2000 model was approximately equal to 
the average of the two laboratory measured corner at arch moments throughout the load 
range. 
The two corner displacements measured in on the 36 ft clear span test specimen 
were different by approximately 20 to 25 percent. The corner displacement generated in 
the 36 ft clear span SAP model fell, on average, right in line with the lower of the two 
measured laboratory test specimen corner displacements. Therefore, the SAP2000 model 
was approximately equal to the lower of the two measured corner displacements in the 
laboratory and 20 to 25 percent less than the higher of the two laboratory measured 
corner displacements throughout the load range. 
 The two thick corner moments measured in on the 36 ft clear span test specimen 
were different by less than 5 percent throughout the range of loading. The thick corner 
moment generated in the 36 ft clear SAP2000 model fell within approximately 5 to 10 
percent of the two different thick corner moments measured in the laboratory for the first 
 
65 
 
75 percent of loading. For the last 25 percent of the loading range, the 36 ft clear span 
SAP2000 model underestimated the thick corner moment by an average of approximately 
15 to 20 percent  
4.7 - Conclusions 
For the various load combinations, the SAP2000 structural models provided good 
correlation of the moments and deflections seen during the laboratory testing. This was 
especially true throughout the first three quarters of the loading range. Near the ultimate 
capacity of the arches the model underpredicted, with the exception of the model 
overpredicting the corner moment of the 20 ft clear span arch, the moments and 
deflection by 15 to 20 percent.  Based on the results, the SAP2000 structural models 
provided a reasonable starting point for assessment of the design and performance of the 
arches which will be discussed in the following chapter. 
66 
 
Chapter 5: Design Methodology 
5.1 ? Introduction 
Foley Products provided the design methodology and calculations used by the 
engineer of record to evaluate the effectiveness of the arch structures? design. The 
designs were evaluated based upon laboratory testing results described in Chapter 3 and 
the detailed SAP2000 model described in Chapter 4.  
The same methodology was used in design of both the 20 ft clear span structure and 
the 36 ft clear span structure. The computer program RISA 3-D (RISA Technologies) 
was used to evaluate various load combinations. The RISA model analysis indicated the 
highest moment in the structure was at midspan. In the design calculations provided, this 
midspan moment was used to perform standard reinforced concrete design to specify the 
required reinforcing. 
The effectiveness of the design methodology is discussed in this chapter. Details of 
the design methodology are provided. The RISA model used in design is compared to the 
SAP2000 model that correlated to laboratory results. An overall evaluation of the design 
is provided based on a comparison to laboratory testing and the corresponding SAP 
model. The ratio of demand to capacity at specific arch sections, namely midspan, was 
used to determine the effectiveness of the design.  
67 
 
5.2 ? General Methodology 
The expected loads on the structure were calculated to begin design. Dead load, 
live load, and lateral loads were calculated. The dead load was a function of the 
anticipated depth of fill. Live loads were calculated based on the 17th Edition of the 
American Association of State Highway and Transportation Officials Standard 
Specification for Highway Bridges HS20 design truck (AASHTO). Allowance was made 
for impact loading as well as its distribution through a given depth of soil medium based 
on AASHTO provisions. Lateral loads, or pressures, were calculated based on the depth 
of fill above the point of interest. The vertical walls of the structure were the main 
location of interest in calculating the lateral soil pressure. This lateral pressure was 
calculated based on the unit weight of the soil being approximated at 120 pcf. The lateral 
pressure is based on the active case with a coefficient of lateral earth pressure equal to 
0.3. 
 The analysis program RISA was used to create a structural model to determine the 
demand forces. The gravity and lateral loads were incorporated in the model. The 
controlling moment from the load cases, including load factors, considered in RISA was 
used to perform cross sectional analysis in designing the section. Details of the RISA 
model and cross sectional analysis are discussed in Section 5.3.  
5.3 ? Analysis and Modeling 
 The RISA structural model used in the design of the Foley Arch was a two 
dimensional model that was based on common assumptions and practice in structural 
engineering. The 20 ft clear span RISA model was composed of 34 frame elements. All 
68 
 
these elements were rectangular and prismatic beam frame elements. The concrete 
material defined in the 20 ft clear span RISA model was 5000 psi compressive strength. 
The reinforcing steel yield strength was 60 ksi. Support conditions in the model consisted 
of pin supports, no moment resistance, at the base of the vertical structure legs. The 
extruded view of the members is shown in Figure 5-1. The loads shown in Figure 5-2 are 
after a load factor of 1.3 was applied to the vertical distributed load, the active lateral 
load, and the live load within RISA. As can be seen in Figure 5-2, springs with 
appropriate spring constants, not specified in the design calculations, were used to 
simulate soil passive pressures as the bridge deflected into the soil. The computer 
analysis was then run and the moment diagram shown in Figure 5-3 was output by RISA.  
 
Figure 5-1: Extruded View ? 20 ft Span RISA Model 
 
 
69 
 
 
Figure 5-2: Factored Loads ? 20 ft Span RISA Model 
 
 
Figure 5-3: Moment Diagram ? 20 ft Span RISA Model 
The maximum moment used in the cross sectional analysis and design provided was 
taken at midspan of the structure in Figure 5-3. The moment at this location in the 20 ft 
span location is 65 k-ft per foot of arch width. All calculations related to reinforced 
concrete design were in accordance with Section 8.16 of the 17th Edition AASHTO 
70 
 
Standard Specification for Highway Bridges provisions. Based on the demand of 65 kip-
ft, the required area of steel for a representative 1 ft wide strip was calculated to achieve 
the needed capacity. The design calculations were performed for a 1 ft width strip and 
therefore, to make comparisons with the test structures, they were multiplied by 4 since 
the bridge tested in the laboratory and modeled in SAP2000 was a 4 ft wide section.  
 Similar properties and methodology were used in the design of the 36 ft clear span 
structure. A two dimensional RISA structural model was developed for design purposes. 
The 36 ft clear span structure RISA model was composed of 42 frame elements. All these 
elements were rectangular prismatic beam frame elements. The concrete material defined 
in the 36 ft clear span RISA model was 6000 psi compressive strength. The reinforcing 
steel yield strength was 60 ksi. A view of the 36 ft span members and the schematic 
division of beam elements is shown in Figure 5-4. The 36 ft span loads in the RISA 
model shown in Figure 5-5 are dead loads and the loads shown in Figure 5-6 are live 
loads plus impact loading. The moment diagram shown in Figure 5-7 is for the 
controlling factored load combination; this moment diagram was generated within RISA 
after having run the analysis.  
 
Figure 5-4: Beam Elements ? 36 ft Span RISA Model 
71 
 
 
 
Figure 5-5: Dead Load ? 36 ft Span RISA Model 
 
 
Figure 5-6: Live Load + Impact ? 36 ft Span RISA Model 
 
 
Figure 5-7: Moment Diagram ? 36 ft Span RISA Model 
72 
 
The maximum moment used in the cross sectional analysis and design provided was 
taken at midspan of the structure in, Figure 5-7. The moment at this location in the 36 ft 
RISA model is 48.7 k-ft per foot of arch width. As was the case with the 20 ft clear span 
design calculations, all calculations for the 36 ft clear span related to reinforced concrete 
design were in accordance with Section 8.16 of the 17th Edition AASHTO Standard 
Specification. Based on the demand of 48.7 kip-ft, the required area of steel for a 
representative 1 ft wide strip was calculated to achieve the needed capacity. The design 
calculations were performed for a 1 ft width strip and therefore, to make comparisons 
with the test structures, they were multiplied by 4 since the bridge tested in the laboratory 
and modeled in SAP2000 was a 4 ft wide section.  
The design calculations were used to collect and record various properties of the 
Foley Arch as it was designed and modeled in RISA. The required flexural steel area at 
the midspan cross section was examined; the amount provided in construction of the 
structure fluctuated slightly with the steel area of actual reinforcing bars. A typical 
compressive strength of the concrete was designed for. The standard reinforcing bar yield 
strength was used. These properties were used in standard specified analysis procedures 
to calculate the nominal flexural moment capacity of the cross section under 
consideration. These properties are shown in Table 5-1 and are from the design 
calculations provided by Foley Arch. 
 
 
 
73 
 
Table 5-1: Design Calculation Properties 
Structure 
Clear 
Span 
Design Calculations  
1 ft Width 
Flexural 
Steel 
Area, As 
(in2) 
Equivalent 
4 ft Width 
Steel Area, 
As (in2) 
Compressive 
Strength, f?c 
(psi) 
Steel 
Yield 
Strength, 
fy (ksi) 
1 ft Width 
Nominal 
Moment 
Capacity, 
Mn     (k-ft) 
Equivalent 
4 ft Width 
Nominal 
Moment 
Capacity, 
Mn     (k-ft) 
20 ft 2.40 9.6 6,000 60 76.7 307 
36 ft 1.22 4.88 6,000 60 54.4 218 
 
The design moment capacity for the midspan section of the 20 ft clear span structure was 
307 k-ft. The design moment capacity for the midspan section of the 36 ft clear span 
structure was 218 k-ft. One of the reasons for the high design moment capacity of the 20 
ft clear span structure is the fact that it was designed for 10 ft of fill. The 36 ft clear span 
structure was designed for half the fill of the 20 ft structure, 5 ft. Depending on the depth 
of fill being designed for, the dead load can easily be, and often is, the largest 
contributing factor to the demand load on the structure. In the two structures under 
consideration herein, the design loads due to the soil fill were substantially greater than 
the live loads resulting from AASHTO specified bridge loading requirements. Therefore, 
the design is heavily dependent on the depth of fill being designed for.  
 A moment distribution comparison between the RISA models and the SAP2000 
models was made. The factored design loads put on the structure in the RISA model were 
74 
 
for a 1 ft wide strip of the bridge. Therefore, the values from the 1 ft wide strip 
calculations and modeling could be multiplied by the width of the desired section. Since 
the test structures were 4 ft wide, the factored loads form the RISA models were 
multiplied by 4 to get the equivalent loads to put into the SAP2000 model for 
comparison. There were three sections of load magnitudes to consider. These were the 
horizontal loads applied on the vertical legs of the structure simulating lateral earth 
pressure, vertical loads on the exterior ends of the arch simulating primarily dead load of 
the soil on the structure, and the loads on the middle portion of the arch simulating a 
combination of both dead load of the soil on the structure as well as the required live 
load. The factored design loads input to the SAP2000 20 ft clear span model are shown in 
Figure 5-8. The resulting moment diagram for this load case on the 20 ft clear span in 
SAP2000 is shown in Figure 5-9. Figure 5-8 and Figure 5-9 are of half the structure for 
clarity. The moment diagram is symmetric about the midspan point of the structure.  
 
Figure 5-8: Equivalent Factored Design Loads on 20 ft SAP2000 Model 
75 
 
 
Figure 5-9: Moment Diagram of Factored Design Loads on 20 ft SAP2000 Model 
The moment at midspan of the SAP2000 model under the factored design loads was 
approximately 90 k-ft. The moment at the corners of the arch of the SAP2000 model 
under the factored design loads was approximately 222 k-ft.  
The equivalent factored design loads input to the 36 ft clear span SAP2000 model 
are shown in Figure 5-10. The resulting moment diagram for this load case on the 36 ft 
clear span in SAP2000 is shown in Figure 5-11. Figure 5-10 and Figure 5-11 are of half 
the structure for clarity. The moment diagram is symmetric about the midspan point of 
the structure. 
76 
 
 
Figure 5-10: Equivalent Factored Design Loads on 36 ft SAP2000 Model 
 
Figure 5-11: Moment Diagram of Factored Design Loads on 36 ft SAP2000 Model 
The moment at midspan of the 36 ft SAP2000 model under the factored design loads was 
approximately 130 k-ft. The moment at the corners of the 36 ft SAP2000 model under the 
factored design loads was approximately 312 k-ft. 
77 
 
A comparison was made between the moment diagrams output by RISA and by 
SAP2000 with the same design loading configuration applied. The moment diagram of 
the RISA model of the 20 ft clear span with the factored design loads applied was shown 
in Figure 5-3. This can be compared to the moment diagram of the SAP2000 model of 
the 20 ft clear span with the factored design loads applied in Figure 5-9. The moment 
diagram of the RISA model of the 36 ft clear span with the factored design loads applied 
was shown in Figure 5-7. This can be compared to the moment diagram of the SAP2000 
model of the 36 ft clear span with the factored design loads applied in Figure 5-11. A 
summary of the comparison between moment magnitudes of the RISA model to the 
moment magnitudes of the SAP2000 models is shown in Table 5-2. 
Table 5-2: Comparison of RISA Model Moments to SAP2000 Model Moments 
Location 
RISA Model ? Equivalent 4 ft 
Wide Section 
SAP2000 Model 
20 ft Clear 
Span Moment 
(k-ft) 
36 ft Clear 
Span Moment 
(k-ft) 
20 ft Clear 
Span Moment 
(k-ft) 
36 ft Clear 
Span Moment 
(k-ft) 
Midspan 260 196 90 130 
Corner 68 130 222 312 
 
The moments from the RISA model and the SAP2000 model do not correlate well. In the 
RISA model the midspan moment was the maximum. However, in the SAP2000 model 
the corner moments were the maximum. One reason this could be the case is that the 
78 
 
corner section members in the SAP2000 model are slightly more massive than those in 
the RISA model, therefore increasing the stiffness and moment flow to those areas. 
Another possible source of difference is the incorporation of various springs by the 
designers in the RISA 3-D models. The SAP2000 model also made use of non prismatic 
elements at the corner sections while the RISA model used all prismatic elements 
assigned along a slight different centerline than the SAP2000 non prismatic frame 
elements. Both nonlinear and linear analyses were performed in SAP2000. Under the 
design loads being considered, the moment diagrams in both the linear and nonlinear case 
were the same magnitude. This indicates that nonlinear effects did not have a significant 
impact in the distribution of moments throughout the range of loading. 
5.4 ? Experimental Results versus Design 
Midspan cross sectional analysis was the only cross sectional analysis provided in 
the design calculations and therefore the midspan will be used for comparison to the 
laboratory testing and SAP2000 model. This comparison provides a means of evaluating 
the overall effectiveness, see Section 5.5, of the design methodology currently used for 
the Foley Arch. 
Table 5-3 shows an approximate average between the laboratory test results and 
the SAP2000 model results for the 20 ft and 36 ft clear span structures. The average 
ultimate moment shown in the last column of Table 5-3 can be seen in Figure 4-10 and 
Figure 4-14 for the 20 ft and 36 ft clear span structure, respectively. It shows the cross 
sectional flexural steel area in the lab specimens, the compressive strength of the concrete 
specimen samples, and the yield strength of the flexural steel used in the 20 ft clear span 
79 
 
structure and the 36 ft clear span structures tested in the laboratory and modeled in 
SAP2000.  
Table 5-3: Test Structure Midspan Properties 
Structure 
Clear Span 
Test/Model Structure 
Flexural 
Steel, As 
(in2) 
Compressive 
Strength, f?c (psi) 
Steel Yield 
Strength, fy 
(ksi) 
Ultimate Midspan 
Moment Capacity, 
Mu (kip-ft) 
20 ft 8.02 12,506 65 448 
36 ft 5.34 7,044 65 550 
 
Of particular interest from Table 5-3, is the compressive strength of the concrete in the 20 
ft clear span test specimen. It was significantly higher that the design strength of 6000 psi 
as shown in Table 5-1. This may raise some concerns related to directly comparing the 
design calculations and associated moment capacity to the test specimens and 
corresponding SAP2000 model results. 
 A comparison between the structure as it was designed and analyzed in RISA to 
the structure tested in the laboratory and the SAP2000 model was of primary interest at 
this stage of the project. As was discussed earlier in this section, the midspan cross 
sectional properties and capacity was the critical location shown in detail in the design 
calculations provided. For comparison, a ratio of test properties to design properties was 
used as shown in Table 5-4. The test properties used in the ratio is an average between 
the laboratory test specimen and SAP2000 model. The design properties, as shown in 
80 
 
Table 5-1, are based on the details contained in the design calculations provided by 
Foley. 
Table 5-4: Ratio of Design Properties to Test/Model Specimen Properties 
Structure Clear Span ??,?????
?,??????
 ?
??,????
???,?????? 
??,????
??,?????? 
??,????
??,?????? 
20 ft 0.835 2.08 1.08 1.46 
36 ft 1.09 1.17 1.08 2.52 
 
 The 20ft clear span structure and the 36ft clear span structure exceeded the 
required design strength. The structures are safe as designed under the test conditions. It 
appears that the 20 ft clear span test specimen had slightly less steel than called for in the 
reinforcement details reviewed in the design calculations. At the time of testing the 20 ft 
clear span concrete had reached a much higher compressive strength than was designed 
for. The effect the small reduction in cross sectional steel had on the structure was 
explored using the 20 ft clear span SAP2000 structural model. It was found that the 
difference in ultimate capacity was small enough that it could be neglected for the 
purpose of evaluating the design methodology. The effect the increased compressive 
strength of concrete had on the structure was also explored using the SAP2000 model. 
Similarly, it was found that the difference in ultimate capacity was small enough that this 
difference was not a source of concern. Based on the ratio of an average between the 
laboratory test and the model results to the design calculations, the 20ft clear span 
specimen had a 30 percent higher moment capacity at midspan than the design 
calculations for the same structure indicated. Based on the ratio of an average between 
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the laboratory test and the model results to the design calculations, the 36ft clear span 
specimen had an 84 percent higher moment capacity at midspan than the design 
calculations. Both designs, the 20 ft clear span and 36 ft clear span, were reasonably 
effective. The 36 ft clear span is slightly higher than an ideal overstrength, but not to an 
exorbitant or overly uneconomical point. 
5.5 ? Conclusions 
It was concluded from evaluation of the 20 ft clear span structure and the 36 ft 
clear span structure that the designs were effective and the design methodology was 
reasonably well representative of actual behavior of the structure when tested. The 
designs are safe but not exceedingly overdesigned. It was also concluded that the SAP200 
models and the RISA models did not have the same maximum moment locations under 
the factored design loads in the design calculations provided by Foley due to a 
combination of thicker corner sections in the SAP2000 models as well as springs 
incorporated into the RISA model that were not in the SAP2000 models. While there 
were slight differences in the RISA and SAP2000 models when analyzed under 
approximately equivalent loads, this did not impact the determination of the overall 
capacity of the structure. It was concluded that the way the design methodology is carried 
out is safe and effective.  
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 Chapter 6: Summary, Conclusions, and Recommendations 
6.1 ? Summary 
Foley Products contracted Auburn University to perform third party analytical and 
experimental validation of the performance, design, and analysis methods. The goal of 
the project was to validate all aspects of the Foley Arch bottomless bridge. The 
experimental validation of the three sided bottomless arch bridge included one 
serviceability field test during an existing project?s construction and two laboratory tests 
which included loading the structure to its ultimate capacity. The two laboratory tests 
were conducted on a 20 ft clear span structure and a 36 ft clear span structure. Correlation 
to the results of the laboratory testing was achieved using a structural computer model 
developed within SAP2000. The design methodology used in the design packages 
provided by Foley Products was reviewed and evaluated to determine its effectiveness. 
This field test was utilized to evaluate precast arch bridge sections under a known truck  
load by installing instrumentation to measure reinforcing bar and concrete strains. 
Deflection and earth pressure transducers were installed on-site prior to backfilling the 
bridge. This test was during construction of a precast arch bridge project in Carrabus 
County, North Carolina.  
In addition to a field test, two laboratory tests were performed to evaluate bridge 
behavior up to ultimate loading conditions. The first laboratory test section was a 20ft
 
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span bridge with an 8ft vertical rise. The second laboratory test section was a 36ft span 
bridge with a 9ft vertical rise. 
Following the field and laboratory testing, a computer model of the Foley Arch 
structure was created in SAP2000 to correlate the results of the laboratory testing to the 
analysis and results of the computer model. This was used to determine if any economic 
or serviceability improvements could be reasonably recommended and/or implemented in 
the design or production of the structures. 
6.2 ? Conclusions 
The conclusions reached based on the research performed were: 
- The laboratory testing results were conceptually compatible with the 
anticipated behavior.  
- The highest moments were developed at midspan and at the corner of the arch 
section along with the highest deflections being measured at midspan.  
- The data collected and analyzed provided a solid comparison point to move 
forward with the project in developing a structural computer model in 
SAP2000. 
- The SAP2000 structural models provided good correlation of the moments 
and deflections seen during the laboratory testing. This was especially true 
throughout the first three quarters of the loading range.  
- Near the ultimate capacity of the arches the model under predicted, with the 
exception of the model over predicting the corner moment of the 20 ft clear 
span arch, the moments and deflection by 15 to 20 percent.   
 
84 
 
- The designs were effective and the design methodology was reasonably well 
representative of actual behavior of the structure when tested.  
- The designs are safe but not exceedingly over designed.  
- The SAP2000 models and the RISA models did not have the same maximum 
moment locations under the factored design loads in the design package 
provided by Foley.  
- The difference between the SAP2000 models and RISA models did not 
require a change in the design methodology. 
6.3 ? Future Research 
 While the service load range test performed in the field and the ultimate loading 
behavior test performed in the laboratory both provided a solid basis for analysis of the 
behavior and design of the Foley Arch structure, there are some additional considerations 
that could result in an even better understanding of the structures behavior. A full scale 
test set up under fill material that is typically used in construction would allow a better 
understanding of how exactly the fully distributed lateral pressure effects the initial 
condition of the structure. If a full scale field test were performed all the way to ultimate 
loading conditions, it would be possible to trace this active pressure influence and any 
developing passive pressures as the structure deflects.  
The structural computer models developed using SAP2000 well represented the 
behavior of the structure in the laboratory. However, if the above full scale field test were 
performed up to ultimate loading conditions, a structural model that incorporates detailed 
 
85 
 
soil properties and soil structure interaction would be even more representative of true 
behavior of the structure in its application.  
86 
 
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