1.0 Introduction
1.1 General
As
the population of
In
the early days of curved bridge design and construction, bridge superstructures
supporting curved roadway alignment were comprised of short straight girders
linked together at the supports. This
resulted in inefficient use of very short spans between support piers. As the technology for designing and fabricating
curved girders became available, it became possible to design curved bridges
with much greater distances between supports.
Today,
curved girders are widely used in bridge superstructures. The designer has many choices including
material (concrete vs. steel), cross-section shape (tub girder vs. I-beam),
etc. Furthermore, the past three decades
have resulted in advances in optimizing curved bridge design, resulting in
innovative, aesthetically pleasing structures.
However, due to the simple addition of curvature, the design and
construction of bridges becomes immensely more complicated than that of
straight bridges. While the girders,
stringers, and floor beams of straight bridges can be designed by systematically
isolating each member and applying standard loads, curved bridges must be
designed with careful consideration to system-wide behavior. In essence, the addition of curvature adds
torsion to the system that results in significant warping and distortional
stresses within the member cross-sections.
Furthermore, “secondary members” such as cross frames and diaphragms
that provide stability in straight bridges become primary load carrying members
in curved bridges.
Although
the design of curved bridges is much more complex than that of straight
bridges, there are no requirements specific to the design of curved bridges
integrated into the American Association of State Highway Transportation
Officials (AASHTO) Standard Specifications for Highway Bridges (AASHTO 1992). There is, however, the “Guide Specifications
for Horizontally Curved Highway Bridges,” which was first adopted in 1981
(AASHTO 1993). This “guide” is widely
recognized to be outdated, disjointed, and difficult to use. Several significant research projects have
been conducted over the past few years including the Federal Highway
Administration (FHWA) “Curved Steel Bridge Research Project (CSBRP)” and the
National Cooperative Highway Research Program (NCHRP) Project 12-38, “Improved
Design Specifications for Horizontally Curved Steel Girder Highway
Bridges.” Currently, NCHRP Project
12-52, “LRFD Specifications for Horizontally Curved Steel Girder Highway
Bridges,” is being conducted by Modjeski & Masters to prepare
specifications for the design and construction of horizontally curved steel
girder bridges (for both I- and box girders) in a calibrated load and
resistance factor design (LRFD) format that can be recommended to AASHTO for
adoption (www.modjeski.com).
Furthermore, many states have recently conducted or supported research
on curved bridge design and construction.
The only other bridge design document in the world that specifically
addresses curved bridge design is the Japanese “Guidelines for the Design of
Horizontally Curved Girder Bridges” by the Hanshin Expressway Public
Corporation (Hanshin 1988). Several
researchers, including the primary author of this report (Davidson), have demonstrated
disparity in the strength formulations between the Japanese and American curved
bridge design guides, which further emphasizes the need for additional
research.
In
addition to improving design equations for curved bridges, another area that
has been widely recognized for further research is that of lifting and
transporting curved girders during construction. By far, the most frequent problems are
encountered during construction. The
problems are typically more severe and more common than those encountered
during the construction of straight bridges.
During the construction of straight bridges, girders and stringers are easily
erected by one crane using one or two pick-up points, or by two cranes using
one pick-up point each. The individual
straight girders can simply be set in place with little concern for
instability. Lifting and setting
presents little difficulty for straight beams where the center of gravity is
coincident with the centroidal axis of the beam cross-section. But for horizontally curved girders, the
center of gravity is non-coincident with the cross-section centroid. Depending
on the lifting/support mechanism used, significant torsional stresses and
minor-axis bending stresses may be induced.
The handling and erection of horizontally curved girders requires
engineering expertise beyond that needed for the construction of straight
bridges. Engineers not experienced in
the design of curved bridge systems often make the mistake of assuming that
behavior and design is the same as that for straight bridges. Instability during construction can easily
translate into unsafe conditions for construction workers, not to mention
unforeseen additional costs.
Because
of the increasing demand for curved bridges combined with challenges of design
and construction, there is need to investigate and synthesize state-of-the-art
practice for the efficient design and construction of curved bridges. This report summarizes the activities and
accomplishments of a first phase project aimed at establishing a curved steel
bridge research program within The University of Alabama system. A follow-on project, UTCA Project 03228, “Stability
of Curved Bridges during Construction,” is currently underway using the
contacts, literature survey, and research needs synthesis of this project. Technical results of the effort will be
disseminated through conference presentations and proceedings, journal
publications, student theses and dissertations, and the final report of UTCA
Project 03228.
1.2 Objectives
The
overall objectives of this project were to investigate and synthesize
state-of-the-art practice for the efficient design and construction of curved
bridges and to identify research needs regarding strength and stability of
curved bridges. Additional goals of the
project included:
·
Develop relationships with
Alabama Department of Transportation (ALDOT) bridge engineers, FHWA program managers,
prominent curved bridge researchers, and industry leaders;
·
Identify research needs and
topics suitable for graduate research;
·
Identify technology transfer
and continuing education needs of ALDOT and the bridge design industry of the
region;
·
Contribute to bridge
stability research needs through graduate student research;
·
Identify potential sources of
future support;
·
Transfer project results to
stakeholders.
1.3 Scope and Project Description
1.3.1 Tasks
The
four tasks of the project work plan and a synopsis of the accomplishments
associated with each are described below.
The work was accomplished over a 16-month period beginning
TASK 1. Synthesis of current practice
The
data-gathering effort involved investigating the current state-of-the-art
curved bridge design and construction practice around the country. The usual avenues of collecting information
such as publication database searches and Web-based searches were used. However, the synthesis largely depended upon
direct contacts by the investigators.
Many states have conducted investigations to improve the design and
construction of curved bridges and the resulting reports of such projects often
do not show up in the typical library or journal database search. Investigators at the
TASK 2. Identification of research needs
This
task involved reviewing recent literature and meeting with research authorities
and industry leaders. The objective was to identify needs specific to
A
meeting with ALDOT bridge engineers helped to identify how university expertise
can help with their needs. The
investigators also contacted design firms, manufacturers, and construction
companies in the region to establish relationships and to understand their
issues regarding curved bridge design and construction. A local curved I-girder bridge project was
studied to gain a better understanding of practical challenges associated with
fabrication, transportation, and erection.
The
investigators met with FHWA researchers and engineers involved in the FHWA
Curved Steel Bridge Research Project at the Turner-Fairbanks Highway Research
Laboratory to identify areas of national need and to explore the possibility of
future sponsorship. The investigators
also met with prominent curved bridge researchers from several universities and
companies. The “research needs” effort identified
topics suitable for Masters and PhD students with interest in curved bridge stability.
It also provided an understanding of potential sources of support for
continuing curved bridge research.
TASK 3. Student-oriented analytical research
The
“synthesis” and “research needs” aspects of this project identified suitable
Masters and PhD topics. The analytical
research effort involved graduate students who investigated curved bridge
research topics that may lead to improvements in bridge design specifications
or improvements in construction practice.
The graduate student research topics involve steel composite
construction, since that is where the primary focus of current research is
directed. Both I- and box-girder cross
sections were considered. The investigations
were analytical in nature, rather than dependent upon laboratory testing. An MS project report and several publications
were produced. Two PhD students and a
MSCE student continue to work on their topics.
TASK 4. Technology transfer
Ultimately,
success of the project depends on the dissemination of the results to
stakeholders. Interaction with ALDOT,
other researchers, and industry identified the need for guide documents and
continuing education courses. The input
from these stakeholders was used to outline a plan for future activities. Transfer of all findings to stakeholders will
be facilitated through conference presentations and proceedings, journal
publications, student theses and dissertations, and the final report of UTCA
Project 03228.
1.3.2 Project Team
The
research was directed by Dr. Jim Davidson, an Associate Professor in the
Department of Civil and Environmental Engineering at the
Dr.
Davidson was assisted by four civil engineering graduate students: (1) Ramy Abdalla (PhD student), (2) Mahendra
Madhavan (PhD student), (3) Lance Osborne (MSCE student), and (4) Toby Leamon
(MSCE student). Mr. Osborne completed
his MSCE requirements May 2002. Abdalla,
Madhavan, and Leamon continue to work on their degree requirements. A brief description of their stability topics
and accomplishments to-date is presented in Chapter 2.
1.4 Report Content and
Organization
This
report provides a summary of the accomplishments of the research team and is
organized into the following chapters: Chapter 1, “Introduction,” presents a
general introduction, followed by a summary of the main objectives of the
project. The scope of the research and
project description is discussed. Chapter
2, “Accomplishments,” provides a summary of the accomplishments of the project
and findings regarding research needs. Chapter
3, “Conclusions and Recommendations,” summarizes the main conclusions of this
study and provides recommendations for future work.
2.0 ACCOMPLISHMENTS
2.1 Overview
This project has
resulted in progress towards establishing a curved bridge stability research
program within the
2.2 Stability
Research Accomplishments
2.2.1 Design and Construction of
Curved Box Girder Bridges
The “closed” box- or tub-girder cross section
resists curvature induced torsion far more efficiently than the “open” I-girder
cross section. Economic benefits of
using box girder superstructures over I-girder cross sections may be
substantial for sharp curvatures (radius < 1000 ft). An illustration of cross sections commonly
used in curved bridge superstructures is provided in Figure 2-1.
Federally sponsored or coordinated research on
box girder stability is very limited.
The original scope of the FHWA Curved Steel Bridge Research Project
included fundamental research on the behavior of both steel I-girder and
box-girder bridges. However, soon after
the initiation of the project in 1992, investigators and FHWA program managers
realized that there would not be enough resources to address both I- and box-girder
research. All of the box girder research
tasks were subsequently eliminated. There
is still a void in the understanding of curved box-girder behavior and a need
to improve currently used design and construction processes. It is anticipated that a nationally
sponsored large-scale project will occur in the future, after the FHWA Curved
Steel Bridge Research Project is finalized.
Figure 2-1. Cross sections
commonly used in curved bridge superstructures
Box girder construction practices were investigated
and research needs identified.
Information was collected on construction projects that involved curved
box girders toward the goal of understanding the engineering and economic
advantages to using closed cross section girders for curved bridges. Prominent researchers and practitioners were
contacted. An understanding of
construction procedures and stability issues was developed. Box girder designs were collected from other
state DOTs and will be reviewed and used in analytical case studies as part of
student research projects.
There are two overall aims of the box girder
aspects of this project:
(1) Curved box girder bridges have not been
used in
(2) Curved box girders were eliminated from the
FHWA Curved Steel Bridge Research Project and federally organized and sponsored
research projects will likely arise in the future. Therefore the second aim is to conduct
preliminary work needed to be recognized as a leading research program in this
area and perhaps open the door towards participation in future federally
sponsored research.
Analytical stability research was initiated in
this area, with a focus on the effects of distortion on the strength of curved
box girders and lateral bracing requirements.
Finite element models were developed.
Theory-based formulations and analytical models are being developed to
resolve issues associated with construction using curved box girders. The analytical research will culminate in a
PhD dissertation that will address stability issues that are encountered with
curved box-shaped plate girders. An
ultimate goal is to develop and recommend guidelines and design criteria.
2.2.2 Stability of Curved I-Girders during Construction
Students involved in I-girder aspects of the
project are developing theory-based formulations and analytical models to
resolve issues associated with design and construction using curved
I-girders. For example, methods used to
lift single curved girders onto supports may induce significant distortion,
warping, and minor axis bending stresses that were not considered in the
design. It may be necessary to lift two
girders temporarily braced with cross frames to provide stability during
erection. Therefore, strength equations
are needed for various lifting scenarios.
Also, the cross frames can be subjected to significant forces during the
construction of curved I-girder bridges that are not encountered in straight
bridges. Engineers need design
methodology for predicting bracing member forces. Transverse and longitudinal stiffeners may be
required to prevent unacceptable levels of distortion, and design guidance is
needed.
Current focus is on the stability of curved
I-girders during construction. Curved
I-girders, in particular, can be unstable during lifting and transporting
unless adequately braced. Problems are
common yet rarely documented. However,
there are no comprehensive guidelines or recommendations on construction
practices, nor is there a published survey or summary of problems encountered
by DOTs during construction of curved bridges.
Discussions with prominent researchers and FHWA program managers during
this project indicated that this is an issue that warrants additional
research.
Analytical studies have been focused on the
effects of curvature-induced warping on the local buckling of curved I-girder
flanges. Papers entitled “Elastic
Buckling of Plates Subjected to Linearly Varying Edge Load” and “Elastic
Buckling of I-Girder Flanges with a Linearly Varying Stress Distribution,” were
developed. A related paper entitled
“Elastic Local Buckling of Curved I-Girder Flanges” was accepted for
presentation at the 2003 North American Steel Construction/Structural Stability
Research Council (SSRC) Conference and will be included in the SSRC conference
proceedings. A PhD dissertation is
anticipated to thoroughly address stability issues that are encountered with
curved I-shaped plate girders. Advanced
theory and finite element methods are being used. The analytical research will culminate with improved
criteria suggested for curved bridge design and construction.
2.2.3 Analysis of Single I-girders during Erection
Closed-form equations are being developed to
predict maximum stresses that occur under various lifting mechanisms used
during erection of curved I-girders.
Support conditions that are being considered in lifting studies are illustrated
in Figure 2-2. The initial phase of this
research is focused on the development of equations based on small displacement
torsion of thin-walled structures that represent idealized support conditions
for lifting of curved I-girders. Later
phases of the research will involve the use of finite element analyses to
adjust the theory-based equations for deflection amplification and local stress
effects.
Figure 2-2. Support
conditions considered in lifting studies
2.2.4
Case Study of the I-459 Flyover
A local curved bridge construction project, the Galleria I-459 flyover
in Hoover, Alabama (Figures 2-3 and 2-4), was studied from inception and
preliminary design through placement of the girders and concrete deck. This study provided a better understanding of
the curved I-girder bridge design and construction process. The close proximity of the project to the
Figure 2-3. Construction
site of the Galleria Flyover
Figure 2-4. Erection of
girders at the Galleria Flyover construction site
2.2.5 Papers, Presentations, and Reports
An important goal of the project was to
disseminate the results. The following describes papers, presentations, and
reports that were developed as part of this project.
Published
or presented:
“Stability of Curved I-girder Web
Panels” presented at the April 2002 North American Steel Constructors
Conference and published in the proceedings of the 2002 Structural Stability
Research Council meeting.
“Construction of Curved I-girder
Bridges: Case Study of the I-459 Flyover,” Lance Osborne, MSCE student report
and project presentation, April 2002.
“Effects of Distortion on the Strength
of Curved I-Shaped Bridge Girders” presented at the 2003 TRB Annual Meeting,
TRB Committee A2C02 - Steel Bridges, and published in the 2003 Journal of the Transportation Research Board.
“Distortion Effects on the Stability of
Curved I-Shaped Bridge Girders” presented at the 2003 North American Steel
Construction/Structural Stability Research Council (SSRC) Conference and published
in the 2003 SSRC conference proceedings.
“Elastic Local Buckling of Curved
I-Girder Flanges” presented at the 2003 North American Steel Construction/Structural
Stability Research Council Conference and published in the 2003 SSRC conference
proceedings.
Manuscript
completed
“Elastic Buckling of Plates Subjected to
Linearly Varying Edge Load” Mahendrakumar Madhavan and James S. Davidson;
submitted to the International Journal of Thin-walled Structures.
“Elastic Buckling of I-Girder Flanges
with a Linearly Varying Stress Distribution,” Mahendrakumar Madhavan and James
S. Davidson; to be submitted.
“Compactness Requirements for Flanges of
Horizontally Curved I-Girder Bridges,” Mahendrakumar Madhavan and James S.
Davidson; to be submitted.
2.3 Outreach and
Interaction
The project
facilitated valuable interaction with prominent researchers and industry
leaders. The investigators met with
researchers from the University of Houston, Pennsylvania State University, the
2.3.1
Conferences and Meetings
The following summarizes participation
in conferences and meetings facilitated by the project:
·
Developed and submitted white paper
proposal to Dr. Bill Wright, FHWA Research Engineer, at the Turner-Fairbanks
Highway Research Laboratory entitled “Guidelines for the Stability of Curved
Steel Girders during Erection” (September 2001). It is essentially an offer to tackle some of
the construction issues and lead an effort to develop guidelines for
transporting and erecting curved steel bridges.
The hope is that the white paper will initiate dialogue with Mr. Wright
regarding how Dr. Davidson can assist the FHWA in this area of national
need. The subject was identified as of
great importance and an area that UAB could potentially contribute to in an
earlier meeting with Mr. Wright.
·
Participated in the Research Council for Curved Bridges (RCCB) meeting at the
·
Participated in the North
American Steel Constructors Conference (NASCC) and Structural Stability
Research Council (SSRC) meeting, April 23 through 27, 2002. This included a presentation at the NASCC by
Davidson entitled “Stability of Curved I-girder Web Panels.” This also included participation in other
meetings such as SSRC Task Group 27 “Plate and Box Girders” and Davidson’s
leadership role as the chairman of SSRC Task Group 14, “Horizontally Curved
Girders.” The conference and meetings
facilitated valuable interaction with prominent bridge stability researchers
from around the world.
·
Met with Dr. Bill
Wright, Senior Research Engineer, of the FHWA Turner-Fairbanks Research
Laboratory
·
Participated in the
Transportation Research Board (TRB) Annual Meeting,
2.3.2 Curved Bridge
Research Interests of the Alabama Department of Transportation
The
transfer of new technologies to
The Team met
with ALDOT bridge engineers to discuss their interests and needs regarding
curved bridge education and research.
The following summarizes the outcome of the meeting:
Outreach and
Education Needs: ALDOT expressed interest in seminars on LRFD
bridge design (not specific to curved bridge design). ALDOT will have an interest in curved bridge
design education as the current curved bridge research is integrated into the
standard LRFD bridge specification.
Box Girder
Research Interests: There are currently no box girder bridges in
use or under construction in
Stability
During Construction: ALDOT recognizes that problems commonly occur
during the construction of curved I-girder bridges. However, in
2.4 Stability
Research Topics
Based upon the review of literature and
interaction with industry leaders and prominent curved bridge researchers, the
following were identified as discrete stability research topics in need of
further investigation.
·
Effects of curvature on curved I-girder
flange stability, including elastic behavior, post-buckling behavior, and
ultimate strength.
·
Prediction of distortion induced web
stresses that result from curvature for use in fatigue calculations.
·
Effects of curvature on the
lateral-torsional elastic buckling behavior of curved I-girders in the braced
frame superstructure.
·
Guidelines for deck placement sequencing
to minimize construction stresses, fit-up problems, and erection stability
problems for curved I-girders.
·
Maximum stress predictor equations and
guidelines for transporting and lifting single curved I-girders during construction.
·
Simplified ultimate strength predictors
for transition into LRFD format specifications.
·
Requirements for transverse and
longitudinal stiffener spacing and rigidity for curved plate girders based upon
curvature induced distortion.
·
Plate girder web panel slenderness
requirements for regions of pure shear and combined bending and shear.
·
Internal and external cross frame,
diaphragm, and lateral bracing spacing and rigidity requirements for curved box
girders, during construction and in load bearing configurations.
·
Guidelines for deck placement sequencing
to minimize construction stresses, fit-up problems, and stability problems for
curved box girders.
·
Guidelines for temporary shoring to
minimize stresses, fit-up problems, and stability problems for curved box
girders.
·
Guidelines for transporting and erecting
curved box girders.
·
Equations to predict effects of
distortion on the strength of curved box girders.
·
Ultimate strength behavior of curved box
girders.
3.0 CONCLUSIONS AND RECOMMENDATIONS
This project resulted in progress towards
establishing a curved steel bridge stability research program within The
University of Alabama system. Four
students were involved and produced several papers and presentations. This includes two students enrolled in the
recently formed joint UAB-UAH PhD program.
Papers and reports were collected that will facilitate continued
research efforts. The project also
facilitated interaction with prominent curved bridge researchers, state and
federal government division and program managers, and industry leaders. The planning, design, fabrication, and
construction of a local curved I-girder bridge flyover was studied in-depth to
gain a better understanding of practical challenges associated with curved
bridge design and construction. The
background research and interaction with industry leaders resulted in the
identification of stability research topics, and a meeting with ALDOT bridge
engineers provided insight into the research and education needs and interests
of
The analytical research components of the
effort can be categorized into two parts:
(1) stability of curved I-girders during construction and (2) behavior
and design of box girder bridges. From a
national perspective, the design, fabrication, and construction of curved
I-girder bridges is more mature than that of curved box girder bridges. However, significant research challenges
remain for curved I-girders. The “Guide
Specifications for Horizontally Curved Highway Bridges” is widely recognized to
be outdated, disjointed, and difficult to use, so strength and stability
research is needed to improve design formulations. Due primarily to weak torsional rigidity and
a very complex distribution of stresses over the cross section, problems
associated with fabricating, transporting, and erecting curved girders are more
prevalent in curved I-girder construction than in straight bridge
construction. Engineers not experienced
in the design of curved bridge systems often make the mistake of assuming that
behavior and design is the same as that for straight bridges. Instability during construction can easily
translate into unsafe conditions for construction workers, not to mention
unforeseen additional costs. Even though
problems are common, there are no comprehensive guidelines specific to the
construction of curved bridges.
The design, fabrication, and erection of curved
box girders share many of the curvature-induced complications of curved
I-girders. Construction using box
girders often requires heavy equipment and expertise that is not locally
available. However, the use of box
girders for highly curved bridges offers significant cost savings, and a more attractive
appearance.
There is need for research that involves
partnerships of federal, state, academic, and industry to solve problems
associated with the design and construction of curved bridges. Through interaction with industry leaders and
leading researchers, this project identified many areas of stability research
need. However, funding opportunities are
limited. The Federal Highway
Administration Curved Steel Bridge Project (FHWA-CSBRP) being conducted at the
Turner-Fairbanks Highway Research Laboratory in McClean, Virginia, has been
ongoing since 1992 and is the only large-scale federally sponsored and
coordinated curved bridge project today.
Currently, FHWA is wrapping up this program and synthesizing the
results. After the FHWA-CSBRP is
finalized, there may be a shift in interest towards curved box girder bridge
research that will offer the opportunity for researchers who are not currently
sponsored. There may be other avenues
for stability funding such as through the American Iron and Steel Institute (AISI),
the Steel Bridge Alliance, AISC, and others.
Funding from agencies such as the National Science Foundation is not
likely due to the applied nature of the research.
ALDOT has not yet taken advantage of enhanced
torsional resistance provided by box girders and depends on contractors to do
the construction engineering of curved I-girder bridges. No severe problems have been encountered with
the construction of curved bridges in
The following recommendations resulted:
·
Investigate other potential
sources for bridge stability research sponsorship, including AISI, the Steel
Bridge Alliance, and AISC.
·
Increase efforts to find
graduate fellowship opportunities that can be used for stability research.
·
Continue to interact with
FHWA research program managers and participate in meetings of the Research
Council for Curved Bridges.
·
Continue to interact with
ALDOT bridge engineers and to look for opportunities to assist with
construction and erection studies on upcoming curved bridge construction projects.
·
Continue to develop high
impact papers and presentations.
4.0 REFERENCES
http://www.modjeski.com/projects/servproj/horiz.htm,
accessed
AASHTO. Standard
Specifications for Highway Bridges, ASD and LFD - 15th ed., American
Association of State Highway and Transportation Officials, Washington, D.C.,
1992.
AASHTO. Guide Specifications
for Horizontally Curved Highway Bridges, as revised in 1981, 1982, 1984,
1985, 1986, 1990, and 1992. American Association of