effects of skewed abutments on curved bridge …
TRANSCRIPT
THE PENNSYLVANIA STATE UNIVERSITY SCHREYER HONORS COLLEGE
DEPARTMENT OF CIVIL AND ENVIROMENTAL ENGINEERING
EFFECTS OF SKEWED ABUTMENTS ON CURVED BRIDGE
CONSTRUCTION RESPONSE
Tyler Goodman
Spring 2013
A thesis
submitted in partial fulfillment of the requirements
for a baccalaureate degree in Civil Engineering
with honors in Civil Engineering
Reviewed and approved* by the following:
Daniel G. Linzell Associate Professor of Civil Engineering
Thesis Supervisor
Patrick M. Reed Associate Professor of Civil Engineering
Honors Adviser
* Signatures are on file in the Schreyer Honors College
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Abstract
Bridges provide mankind with the opportunity to connect the once disconnected. Bridge
design and construction are often restricted by existing roadways and landscapes that affect the
geometry of bridges. Two popular situations are bridges that require a horizontal curve rather
than a traditional straight bridge and bridges that require skewed abutments rather than
abutments normal to the bridge’s girders. The construction of horizontally curved steel I-girder
bridges and bridges with skewed abutments has historically been a challenge for contractors and
designers. A lack of understanding exists for the effects of curvature and skew on deformations
and deflections. These deformations and deflections are most critical during the placement of
the wet concrete deck when the girders lack the stability added by the stiffness of the hardened
concrete. This study examined the effects of skewed abutments on superstructure response of a
horizontally curved steel I-girder bridge during the placement of the wet concrete deck. For this,
the performance of several two span bridges with varying skewed abutment orientations were
compared to the normal case with abutments oriented radially relative to the radius of curvature.
The main objective of this study is to examine the effects skewed abutments play on girder
deflections and rotations in horizontally curved steel I-girder bridges. Generally skewed
abutments caused reductions in girder deflections and rotations if the skew decreased a girder’s
overall span length and increases were seen if the skew increased a girder’s overall span length.
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Table of Contents
List of Figures................................................................................................................................ v
List of Tables .....................................................................................Error! Bookmark not defined.
1. Introduction ............................................................................................................................... 1
1.1 Background ...................................................................................................................... 1
1.2 Problem Statement ........................................................................................................... 3
1.3 Objectives ......................................................................................................................... 3
1.4 Scope ................................................................................................................................ 4
1.5 Tasks................................................................................................................................. 5
2. Literature Review ..................................................................................................................... 6
2.1 Research Related to Construction Loading on Curved and Skewed Bridges ....................... 6
2.2 Horizontally Curved Steel Bridges with Skewed Supports .................................................. 9
2.3 Summary ............................................................................................................................. 10
3. Representative Bridges ........................................................................................................... 11
3.1 Bridge Description and Selection........................................................................................ 11
3.2 Bridge Design...................................................................................................................... 12
3.3 Introduction of Skew to Designed Bridges ......................................................................... 12
3.4 Summary ............................................................................................................................. 15
4. Finite Element Modeling ........................................................................................................ 16
4.1 Overview ............................................................................................................................. 16
4.2 Boundary Conditions........................................................................................................... 16
4.3 Girders ................................................................................................................................. 17
4.4 Bridge Deck......................................................................................................................... 18
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4.5 Cross Frames ....................................................................................................................... 18
4.6 Deck Placement and Loading.............................................................................................. 18
4.7 Summary ............................................................................................................................. 21
5. Parametric Study .................................................................................................................... 22
5.1 Overview ........................................................................................................................ 22
5.2 Parameter Ranges ........................................................................................................... 22
5.3 Approach ............................................................................................................................. 25
5.4 Summary ............................................................................................................................. 25
6. Results ...................................................................................................................................... 26
6.1 Overview ........................................................................................................................ 26
6.2 Radial Deflections .......................................................................................................... 27
6.3 Vertical Deflections........................................................................................................ 33
6.4 Girder Rotations ............................................................................................................. 39
7. Conclusions .............................................................................................................................. 47
7.1 Summary ........................................................................................................................ 47
7.2 Future Work ................................................................................................................... 48
References .................................................................................................................................... 50
Appendix A (Linzell et al. 2010) Bridge 1: ............................................................................... 56
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List of Figures
Figure 1.1: representative Horizontally Curved, Steel, I-Girder Bridge (FHWA 1997) ................ 1
Figure 2.1 Screed Position for Deck Placement (Choo et al. 2005) ............................................... 7
Figure 3.1: Typical cross section (Linzell et al. 2010). ................................................................ 12
Figure 3.2: Representative Skew Orientation CW & CCW ......................................................... 13
Figure 3.3: Representative Skew Orientation CW........................................................................ 14
Figure 3.4: Representative Skew Orientation CCW ..................................................................... 14
Figure 3.5: Staggered Cross Frames at Skewed Abutment........................................................... 15
Figure 4.1: Girder deformation directions (Nevling 2008)........................................................... 17
Figure 4.2: Deck Placement Stage 1 ............................................................................................. 19
Figure 4.3: Deck Placement Stage 2 ............................................................................................. 20
Figure 4.4: Deck Placemen Stage 3 .............................................................................................. 20
Figure 6.1: Orientation of Radial Direction .................................................................................. 27
Figure 6.2: Stage 1 of Deck Pour .................................................................................................. 28
Figure 6.2: Ratio of Maximum Radial Deflections for Bridge 1 .................................................. 29
Figure 6.4: Ratio of Maximum Radial Deflections Bridge 2........................................................ 30
Figure 6.5: Ratio of Maximum Radial Deflections for Bridge 3 .................................................. 31
Figure 6.6: Ratio of Maximum Radial Deflections for Bridge 4 .................................................. 32
Figure 6.7: Ratio of Maximum Vertical Deflections for Bridge 1 ............................................... 35
Figure 6.8: Ratio of Maximum Vertical Deflections for Bridge 2 ............................................... 36
Figure 6.9: Ratio of Maximum Vertical Deflections for Bridge 3 ............................................... 37
Figure 6.10: Ratio of Maximum Vertical Deflections for Bridge 4 ............................................. 38
Figure 6.11: Orientation of Girder Rotations................................................................................ 40
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Figure 6.12: Ratio of Maximum Girder Rotation Bridge 1 .......................................................... 42
Figure 6.13: Ratio of Maximum Girder Rotation Bridge 2 .......................................................... 43
Figure 6.14: Ratio of Maximum Girder Rotation Bridge 3 .......................................................... 44
Figure 6.15: Ratio of Maximum Girder Rotation Bridge 4 .......................................................... 45
Figure A.1: Bridge 1 Framing Plan............................................................................................... 56
Figure A.2: Bridge 2 Framing Plan............................................................................................... 57
Figure A.3: Bridge 3 Framing Plan............................................................................................... 58
Figure A.4: Bridge 4 Framing Plan............................................................................................... 59
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List of Tables
Table 1.1: Parametric study bridges (Linzell et al. 2010). .............................................................. 5
Table 5.1: Parametric Study Cases ............................................................................................... 24
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1. Introduction
1.1 Background
Bridges are vital components of our transportation system, giving us the opportunity to
connect the once disconnected. Certain restrictive situations and landscapes call for bridges
requiring a horizontal curve rather than traditional straight bridges. Horizontally curved, steel, I-
girder bridges can offer the most efficient solution for design when restrictions require a curved
bridge with little availability for interior piers. The curved geometry of these bridges is often a
challenge for contractors and designers. Most problems arise during construction, particularly
the placement of wet concrete, due to a lack of understanding of girder behavior and
deformations. Due to the geometry of a horizontally curved I-girder, the centerline of the girder
web in each span is not collinear with a cord between the supports. During construction, these
eccentricities induce excessive torsional moments, which may cause large out of plane
deformations and rotations in girder cross sections (Sharafbayani et al. 2012).
Figure 1.1: representative Horizontally Curved, Steel, I-Girder Bridge (FHWA 1997)
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In the past, the design of these bridges typically focused on the stability and strength of
the completed structure during service and under ultimate load conditions and ignored
construction (Grubb 1996). However, with more efficient and precise computer analysis models,
curved bridges continue to become shallower and longer, and in turn less stiff, and more efficient
designs that address movements during construction must be developed. Currently, little
regulation is provided for designers and contractors with respect to curved member’s effects on
fabrication, shipment, erection, and deck placement.
Not understanding the effects of curvature during erection and deck placement can cause
problems during construction. These problems include fit-up problems between the girder and
cross frame members as well as girder fit-up at splice locations (Chavel and Earls 1999). If
either of these problems arises during construction, it can cause delays that cost money and time.
To prevent these problems, a dedicated effort should be placed on understanding the effects of
curved geometry on steel I-girder bridges during construction.
Abutments play a crucial role in the behavior of curved and straight steel I-girder bridges.
Abutments provide vertical support to the bridge superstructure at the bridge ends, connects the
bridge with the approach roadway, and retains the roadway base materials from the bridge spans.
In horizontally curved bridges, abutments are commonly placed in the radial direction normal to
the girder webs. This pattern results in smaller brace spacing for interior girders, which
generally experience smaller deformations and rotations, and larger spacing for exterior girders
which experience larger deformations and rotations. This often leads to the exterior girders
controlling design and a less than optimal design. The addition of necessary skew to the
abutments of horizontally curved steel I-girder bridges could reduce or increase the unbraced
lengths of the outermost girders leading to smaller deformations and rotations. This study
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investigated effects of skewing the abutments on two span horizontally curved, I-girder bridges
and the resulting construction behavior.
1.2 Problem Statement
The construction of horizontally curved steel I-girder bridges has been a challenge for
contractors and erectors. Nationally, one quarter of steel girder bridges erected include a
horizontal curve, so effort must be made to better understand curved girder construction
response. Research has been completed that focused on predicting and modeling girder
deformations during construction and these studies indicated that the critical load case with respect to
girder deformations and rotations was during placement of the wet concrete deck where girders are
forced to support the load without the added stiffness of the hardened deck. The influence of
skewing abutments, when considering the behavior of deflections and rotations in horizontally
curved steel I-girder bridges during placement of the wet concrete deck is largely unknown.
1.3 Objectives
The objectives of this study are:
Determining how skewing abutments affect displacements in curved girders during
construction when compared to a radial arrangement.
Assessing the effects of skewed abutments in varying radii curved bridges with various
pier spacing.
Establishing the most efficient skewed geometry of abutments within the bounds of the
selected parameters and their ranges.
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1.4 Scope
This study investigated the effects of skewing the abutments on 4 two span curved steel I-
girder bridges with average radii of 91.4 m (300 ft.) and 304.8 m (1000 ft.). These bridges were
selected using statistics from a group of curved I-girder bridges located in Maryland, New York,
and Pennsylvania (Linzell et al. 2010). The bridges each have a 4-girder system and have cross
frame spacing of either 4.6 m (15 ft.) or 6.9 m (22.5 ft.). Refer to Table 1.1 for more detail on the
4 bridges. Structural analyses simulating the placement of the wet concrete deck on the
superstructure were conducted using CSI Bridge to examine the girders’ non-composite
response. The skew of the abutments on each bridge was tested at and relative to normal
to the girder web. These parameters were chosen due to a limit adopted from AASHTO LRFD
Bridge Design Specifications (AASHTO 2007). 20 degrees is the AASHTO limit for not
considering skew so this upper limit was tested as well as a limit above 20 degrees where skew
must be considered in design was tested.
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Table 1.1: Parametric study bridges (Linzell et al. 2010).
Bridge
Number
Radius of
Curvature,
m (ft.)
Cross
Frame
Spacing, m
(ft.)
Girder-
Spacing, m
(ft.)
Number
of Spans
Span Lengths, m
(ft.)
Number
of Girder
Bridge 1 91.4 (300) 4.6 (15) 3 (10) 2 68.6 - 68.6 (225 - 225) 4
Bridge 2 91.4 (300) 6.9 (22.5) 3 (10) 2
68.6 - 68.6
(225 - 225) 4
Bridge 3 304.8 (1000) 4.6 (15) 3 (10) 2
68.6 - 68.6 (225 - 225) 4
Bridge 4 304.8 (1000) 6.9 (22.5) 3 (10) 2
68.6 - 68.6 (225 - 225) 4
1.5 Tasks
This study was completed by performing the following tasks:
A review of literature associated with abutments in horizontally curved steel I-girder
bridges, finite element modeling of curved I-girder bridges, design procedures of
abutments in curved bridges, and construction procedures of horizontally curved steel I-
girder bridges.
Modifications to 4 horizontally curved steel I-girder bridges designed by Linzell et al.
(2010) to fit this study’s scope and parameters.
Modeling representative bridges using CSI Bridge following construction deck placement
loading.
Conducting a parametric study to observe the effects of skewing abutments by
monitoring deformations and rotations developed during construction.
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2. Literature Review
This chapter provides a discussion and review of the existing literature on the response of
horizontally curved steel I-girder bridges during construction and the effects of skewed
abutments on superstructure behavior during construction. It will also summarize the relevant
research on the effects of skewing abutments on horizontally curved I-girder bridges.
2.1 Research Related to Construction Loading on Curved and
Skewed Bridges
This section discusses research related to the effects of construction loading on
horizontally curved I-girder bridges and skewed I-girder bridges. Multiple studies have been
conducted using finite-element models as well as field data to examine both horizontally curved
I-girder bridges and skewed bridges under construction loading. Few studies have been
conducted on the construction response of a horizontally curved bridge having skewed
substructure elements.
Skewed bridges present a challenge for design. In normal bridges, the deck is
perpendicular to the supports and loading is transferred in a direct perpendicular line to supports.
On skewed bridges, load transfer to parallel supports is complicated as the skew can cause
transfer distances to vary. In turn, the reactions and deflections in parallel supports can differ
therefore creating torsion in the bridge. Torsion is a twist of the bridges cross section around the
longitudinal axis. This must be taken into account during design, and especially during
construction. During construction of bridges with perpendicular, non-skewed supports, the
screed used to place the wet concrete is aligned perpendicular to the centerline of the
superstructure and, subsequently, concrete is placed perpendicular to the superstructure. When
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pouring the deck this leads to an even sharing of the wet concrete dead load by the supporting
girders. When placing the deck onto a skewed bridge perpendicular to its centerline an uneven
distribution of its dead load results across the superstructure. “The skew in the abutments causes
the weight of the wet concrete placed by the screed near the acute corner to take more of the
load, causing girders near this corner to deflect more than girders near the obtuse corner (L1 >
L2 see Fig 2.1). Differential deflections that result under this dead load cause gross rotation of
the bridge cross section” (Norton et. al 2003). Two studies have investigated the effects of
screed positions perpendicular to the girders and parallel to the abutment skew during placement
of the concrete deck (see Fig. 2.1). Norton et al. (2003) investigated the effects on a simply-
supported steel structure and Choo et al. (2005) investigated the effects on a continuous bridge
with semi-integral abutments. Norton showed that attempts to place the deck parallel to the skew
would provide significantly reduced differential deflections and stresses across the
superstructure, while Choo showed reductions that were relatively small.
Figure 2.1 Screed Position for Deck Placement (Choo et al. 2005)
Horizontally curved I-girder bridge construction behavior has been the subject of several
research projects in attempts to explore procedures that would lessen the likelihood of
construction issues. Prior to the 1960’s, there were no standardized design specifications for
horizontally curved bridges. Due to this, in 1969 the Federal Highway Administration (FHWA)
Obtuse Corner
Acute Corner
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conducted a research project, the Consortium of University Research Teams (CURT) Project.
CURT was a large scale research effort that involved several laboratory experiments and
analytical studies. The objectives of the CURT project were to evaluate all past research,
integrate results from research led by state agencies, perform a multitude of studies to further
knowledge on curved bridges, develop design and analysis methods, and finalize one in-depth
design code (Mozer and Culver 1970: Mozer et al. 1971 and 1973; Brennan 1970, 1971 and
1974; Brennan and Mandel 1979).
A second large scale research project examining the behavior of horizontally curved
bridges during construction was initiated by FHWA in 1993; the Curved Steel Bridge Research
Project (CSBRP). The CSBRP consisted of two major full-scale experimental testing set-ups.
The CSBRP project was conducted in three main phases that studied: (1) the behavior of curved
bridges during erection; (2) the strength of bridge components; and (3) the behavior of a
composite curved bridge. The studies for the first phase examined erection sequencing effects,
and the effects of various shoring setups on girder construction response. Results were largely
published by Linzell (1999), Zureick et al. (2000) and Linzell et al. (2004). Studies have also
been completed to observe the effects of different erection placement on girder induced stresses
and deformations, improve design and construction guidelines, and monitor the capability of
analysis models to closely predict bridge response (Linzell et al. 2004; White and Grubb 2005).
Construction behavior of horizontally curved bridges has been the subject of several
studies recently. Girder erection procedures have been a topic of intense research and have been
investigated by Bell (2004), Nevling (2008) and Linzell and Shura (2010). “Linzell found that
paired girder erection, which involves first placing pairs of girder segments that have the lowest
radius (inner) and interconnected with cross frames on bridge supports, can result in smaller
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displacements and rotations in the completed superstructure than other studied erection schemes”
(Sharafbayani et al. 2012). Other topics of recent research include the effects of temporary
shoring locations during construction on bridge response. Chavel and Earls (2006a) determined
optimum locations to place shoring towers to retain web plumb conditions. Web plumb
conditions are very important during construction of horizontally curved bridges and web out of
plumb occurrences can cause major girder fit up and displacement problems. Chavel and Earls
(2006b) and Howell (2007) discuss the importance of web plumb girders on horizontally curved
bridges. The importance of a web plumb condition in the girders of horizontally curved bridges
during construction was addressed in literature by Chavel and Earls (2006b) and Howell and
Earls (2007). The National Cooperative Highway Research Program (NCHRP) group recently
completed a thorough report for improved guidelines for analysis methods and construction
engineering of curved and skewed steel girder bridges (White et al. 2012). From this study
White et al. were able to find several recommendations for improvements of construction
analysis of curved steel girder bridges. Some of the main recommendations include improving
common dramatic underestimations of I-girder torsional stiffness, using equivalent beam
elements for cross-frames that lead to an inability to model the physical load-deformation
qualities of the sections, a lack of a direct method for calculated flange lateral bending stresses
for a skewed I-girder bridge, a lack of attention to locked-in-forces of cross-frame elements
(White et al. 2012).
2.2 Horizontally Curved Steel Bridges with Skewed Supports
This section discusses the research that has been performed in regards to horizontally
curved steel I-girder bridges with skewed supports. Currently no studies have been completed
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on horizontally curved steel bridges with skewed supports. This displays a general lack of
knowledge on the topic and justifies the reason of this study.
2.3 Summary
This literature review studied construction response of the superstructure for skewed and
horizontally curved steel I-girder bridges. No literature was found that investigated the effects of
using skewed abutments on horizontally curved steel I-girder bridges as a means of decreasing
stresses and deformations of the superstructure under construction loading. This implies that this
research area is limited, and rationalizes the need and practicality of the current study.
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3. Representative Bridges
3.1 Bridge Description and Selection
Four representatives horizontally curved steel I-girder bridges that were part of a
PennDOT research project were used as models for this study (Linzell et al. 2010). The current
study utilized these designed bridges to investigate effects of skewing their abutments on
superstructure construction response. The bridges selected from this study represent a small (300
ft.) radius of curvature bridge with small (15 ft.) and large (22.5 ft.) cross frame spacing and a
large (1000 ft.) radius of curvature bridge with small (15 ft.) and large (22.5 ft.) cross frame
spacing. The concrete deck and steel superstructure designs were completed by Linzell et al.
2010 in compliance with criteria from the AASHTO LRFD Bridge Design Specification
(AASHTO, 2007) and PennDOT Design Manual Part 4 (PennDOT, 2007). The geometries of
the bridges were selected by Linzell et al. (2010) using statistical studies of data from existing
horizontally curved steel I-girder bridges in the states of Maryland, New York, and
Pennsylvania. For this study it was decided this was a good representation of two span curved
bridges to investigate. The nine two span bridges include a large, medium, and small radius of
curvature as well as large, medium, and small cross frame spacing.
All 4 bridges have an 11.6 m (38 ft.) wide deck with four girders spaced at 3 m (10 ft.)
apart. Figure 3.1 presents a typical cross section. The bridges are separated into three groups
having an average radius of curvature of 91.4 m (300 ft.) and 304.8 m (1000 ft.), with differing
cross frame spacing of a constant 4.6 m (15 ft.) or 6.9 m (22.5 ft.). Table 3.1 presents a
breakdown of the differences of the studied bridges.
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Figure 3.1: Typical cross section (Linzell et al. 2010).
3.2 Bridge Design
The bridges were designed by Linzell et al. 2010 to satisfy strength, constructability, and
service limit states. Preliminary and final analyses of these bridges were completed using
SAP2000; structural analysis software often used for the preliminary analysis and design of
horizontally curved I-girder bridges. For the purposes of this study, because a max abutment
skew of 20° will be used, it will be assumed that this skew will not have significant effect on
superstructure stresses. Therefore, the superstructure design including girder sections, cross
frames, and deck will remain the same for the bridges already analyzed and designed to
AASHTO specifications by Linzell et al. 2010 for the radial, 20° skewed, and 10° skewed
abutment cases. This will also allow for a fair analysis of skew effects. Bridge framing plans
and section information can be found in Appendix A.
3.3 Introduction of Skew to Designed Bridges
For this study’s purposes the already designed bridges chosen had to be modified to
include 20° and 40° skew at the abutments. The abutments were arbitrarily skewed for this study
rather than the pier. The angle of skew will be changed to test three different orientations. One
will be with the abutment on the left in plan rotated clockwise and the abutment on the right
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oriented counterclockwise (CW & CCW). This orientation was chosen because it effectively
decreased the overall unbraced length of the outermost girder, which typically experiences the
maximum stresses and controls design. Figure 3.2 displays this orientation of the skewed
abutments vs. the radial abutments for a representative bridge. Two other orientations were
studied with both abutments being skewed clockwise (CW) and both being skewed
counterclockwise (CCW). These orientations were chosen because it is typical in the field for
both abutments to need to be skewed in the same direction. Figures 3.3 and 3.4 display these
orientations. As recommended in AASHTO LRFD Bridge Design Specifications (AASHTO
2007) for the studied bridges, staggered cross frames were used only near the skewed abutments.
The intermediate sections of the girders had cross frames positioned in a continuous pattern.
Figure 3.5 depicts a view of staggered cross frames for a representative bridge at a skewed
abutment.
Figure 3.2: Representative Skew Orientation CW & CCW
Abutment
Splice 1 Bent Splice 2
12
34
Radial
AbutmentSkewed
AbutmentRadial
AbutmentSkewed
14
Figure 3.3: Representative Skew Orientation CW
Figure 3.4: Representative Skew Orientation CCW
Abutment
Splice 1 Bent Splice 2
12
34
Radial
AbutmentSkewed
AbutmentRadial
AbutmentSkewed
Abutment
Splice 1 Bent Splice 2
12
34
Radial
AbutmentSkewed
AbutmentRadial
AbutmentSkewed
15
Figure 3.5: Staggered Cross Frames at Skewed Abutment
3.4 Summary
This study examined 4 horizontally curved steel I-girder bridges designed using
AASHTO (2007) and PennDOT DM4 (2007) provisions by Linzell et al. (2010). The bridges
were comprised of nine two-span bridges with average radius of curvatures of 91.4 m (300 ft.)
and 304.8 m (1000 ft.) and various cross frame spacing. It was assumed that the maximum 40°
skew for this study did not affect design, therefore the superstructure of the models for the radial,
20°, and 40° skew cases were all designed to the specifications found in Appendix A.
12
34
AbutmentSkewed
16
4. Finite Element Modeling
4.1 Overview
The selected bridges for the study were all modeled as three dimensional finite element
models using CSIBridge v.15, the updated bridge modeler of SAP2000 (CSIBridge 2012). All
elements were modeled to true size and steel components of the model were assigned
corresponding nominal material properties from Linzell et al. 2010. The analysis was run using
dead load sequencing to recreate the process of pouring a wet concrete deck for a horizontally
curved bridge. All elements were set to include self-weight.
4.2 Boundary Conditions
Boundary conditions were set to restrain the bottom node of girders at supports to
represent the abutments, piers, and temporary shoring towers at splices. Nodes at abutments
were restrained in the radial, tangential, and vertical directions to represent a pinned support.
Nodes at piers were restrained in the radial and vertical direction. Nodes at temporary shoring
towers were restrained in the vertical direction to represent a roller support. Figure 4.2 illustrates
the radial, tangential, and vertical direction relative to the girders.
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Figure 4.1: Girder deformation directions (Nevling 2008)
4.3 Girders
All bridge girders for this study were modeled as frame objects in CSIBridge. Biaxial
bending, torsion, axial deformation, and biaxial shear are all accounted for in the beam-column
formulation CSIBridge uses to characterize frame behavior. All frame objects were assigned
corresponding dimensions to match the plate girder sections defined by Appendix A. To account
for the girders being nonprismatic members the girders were initially drawn with a constant cross
section, then assigned a tapered section definition. These tapers occurred at splice locations
along the designed bridges. All girder sections were assigned the CSIBridge ASTM A992
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material properties which corresponds to the properties of ASTM A992 the typical material for
steel rolled shapes.
4.4 Bridge Deck
The concrete decks of all bridges were modeled as a shell object in CSIBridge. The deck
of every bridge was modeled according to Figure 3.1 with a 38 ft. total width, two 4 ft.
overhangs, 10 ft. girder spacing, and a slab thickness of 8 in. The decks were all assigned the
4,000 psi concrete material property in CSIBridge which corresponds to the material properties
of a concrete with a 28 day strength exceeding 4,000 pounds per square inch. Modeling the deck
as a shell element was crucial in later loading steps when nonlinear properties were assigned.
4.5 Cross Frames
The cross frames of all bridges were modeled using frame elements in CSIBridge. How
frame behavior is modeled in CSIBridge is discussed in chapter 4.3. All cross frame objects
were modeled to match the X-cross bracing displayed for each bridge in Appendix A including
the 6” offsets from girder flanges. All cross frame objects were assigned the corresponding
angle labeled in Appendix A for each bridge. In CSIBridge the cross frame connections to
girders are modeled as link elements. A link connects two joints and allows the CSIBridge
models to simulate specialized structural behavior degrees of freedom between cross frames and
girders.
4.6 Deck Placement and Loading
This study was intended to imitate superstructure response during the placement and
forming of the wet concrete deck across the superstructure. To create this loading effect and
model the girders in non-composite action this study utilized staged construction in CSI Bridge
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and the property modifiers tool. Staged construction in CSIBridge allows for static modeling
and analysis of construction stages in which structural systems and loads can be added and
evaluated in a certain order. Loads accounted for in the wet concrete deck load include the
weight of wet concrete and rebar as well as forms. A deck placement sequence was created
following typical real-world construction sequences where wet concrete is placed in positive
bending sections of the bridge first and then in negative bending sections. Figure 4.2 through 4.4
detail the deck placement sequence used on representative bridge for this study.
Figure 4.2: Deck Placement Stage 1
Abutment
Splice 1 Bent Splice 2
Abutment
G1G2
G3G4
165' @ CL 165' @ CL
135' @ C
L Pour
20
Figure 4.3: Deck Placement Stage 2
Figure 4.4: Deck Placemen Stage 3
This deck placement sequence was set up in CSIBridge using staged construction load
cases. For the first stage, the pouring in the first positive bending section, the substructure was
added, followed by the superstructure under its own self-weight, then property modifiers were
applied to the deck section of Stage 1 to give the section its full weight and no stiffness. This
modified deck was then added to the superstructure and results were tabulated. Stage 2 and
Abutment
Splice 1 Bent Splice 2
Abutment
165' @ CL 165' @ CL
135' @ CL Pour
G1G2
G3G4
Abutment
Splice 1 Bent Splice 2
Abutment
165' @ CL
120' @ CL165' @ CL
180' @ CL Pour
G1G2
G3G4
21
Stage 3 of the deck placement sequence followed a similar process, however before the new wet
concrete was added to the structure, the previously poured concreted was added with a modifier
for full weight and full (short-term) stiffness. Results were collected for each stage of deck
placement.
4.7 Summary
The representative horizontally curved steel I-girder bridges used for this study were all
modeled using CSIBridge v.15. All bridge elements were modeled true to size and material
properties. Boundary conditions were set to simulate restraints at the supports of the abutments,
piers, and temporary shoring locations at splices. The loading applied followed a nonlinear
staged construction to represent the pouring and forming of a new concrete deck for a
horizontally curved I-girder bridge.
22
5. Parametric Study
5.1 Overview
The parametric study was completed using the models described in Chapter 4 and
running analysis using CSI Bridge v.15. Each bridge was modeled using seven separate
orientations of abutments: radial abutments, abutments with 20º skew relative to the
superstructure arc (CW & CCW), abutments with 40º relative to the superstructure arc (CW &
CCW), abutments with 20º skew clockwise (CW), abutments with 20º counterclockwise (CCW),
abutments with 40º skew clockwise (CW), and abutments with 40º counterclockwise (CCW).
Skew angles of 20º and 40º were chosen because 20º is the AASHTO limit for considering skew
in design so this upper limit was tested as well as a skew greater than this limit. The three
parametric variables include the radius of curvature, cross frame spacing, and most importantly
abutment skew. Parameter ranges resulted in a total of 28 analysis cases. In all, a small (300 ft.)
and a large (1000 ft.) radius of curvature two span bridges with small (15 ft.) and large (22.5 ft.)
cross frame spacing with radial, 20º, and 40º skewed abutments were analyzed.
5.2 Parameter Ranges
Three parameter ranges were selected for this study and based on the statistical analysis
of curved steel girder bridges in Maryland, New York, and Pennsylvania by Linzell et al. 2010.
The two span bridges from Linzell’s study were adopted by this study to include a skewed
abutment parameter. Relevant parameter and ranges include:
1. Radius of Curvature
a. 91.4 m (300 ft.)
b. 304.8 m (1000 ft.)
23
2. Cross Frame Spacing
a. 4.6 m (15 ft.)
b. 22.5 m (22.5 ft.)
3. Abutment Orientation
a. Radial
b. 20º Skew – Clockwise & Counterclockwise (CW & CCW)
c. 40º Skew – Clockwise & Counterclockwise (CW & CCW)
d. 20º Skew – Clockwise (CW)
e. 20º Skew –Counterclockwise (CCW)
f. 40º Skew – Clockwise (CW)
g. 40º Skew – Counterclockwise (CCW)
Table 5.1 displays the 28 total analysis cases with these three parameters.
24
Table 5.1: Parametric Study Cases
Analysis Case
Number Spans Span Length,
m (ft.) Radius, m
(ft.) Cross Frame
Spacing, m (ft.) Abutment Orientation
1
Two Span 68.6 - 68.6 (225 - 225)
91.4 (300)
4.6 (15)
Radial
2 Skew 20º CW & CCW
3 Skew 40º CW & CCW
4 Skew 20º CW
5 Skew 20º CCW
6 Skew 40º CW
7 Skew 40º CCW
8
6.9 (22.5)
Radial
9 Skew 20º CW & CCW
10 Skew 40º CW & CCW
11 Skew 20º CW
12 Skew 20º CCW
13 Skew 40º CW
14 Skew 40º CCW
15
304.8 (1000)
4.6 (15)
Radial
16 Skew 20º CW & CCW
17 Skew 40º CW & CCW
18 Skew 20º CW
19 Skew 20º CCW
20 Skew 40º CW
21 Skew 40º CCW
22
6.9 (22.5)
Radial
23 Skew 20º CW & CCW
24 Skew 40º CW & CCW
25 Skew 20º CW
26 Skew 20º CCW
27 Skew 40º CW
28 Skew 40º CCW
25
5.3 Approach
This study’s approach was to systematically analyze the four bridge models while
modifying the changing parameters for each bridge model. This led to first modeling and
analyzing the small (300 ft.) radius of curvature bridge with small (15 ft.) cross frame spacing
first and changing to run all the abutment orientation parameters. The small radius of curvature
bridge was then modeled with large (22.5 ft.) cross frame spacing and the abutment orientation
parameter was changed to run all the models for this bridge. Then the large (1000 ft.) radius of
curvature bridge was modeled and analyzed in similar fashion to the small radius of curvature
bridge.
5.4 Summary
The focus of this study investigated the effects of skewed abutments on horizonta lly
curved, steel, I-girder bridge response during the placement of wet concrete to form the deck.
This was the focus because it is the worst case of girder deflections, rotations, and stresses during
construction. To complete this study a group of 4 two span bridges designed in a study by
Linzell et al. 2010 were utilized to test the main parameter of abutment orientation. An efficient
approach was used to analyze 28 cases and produce accurate and profound conclusions.
26
6. Results
6.1 Overview
The results from the parametric study described in chapter 5 are presented in this chapter.
The study includes 4 two span bridges that represent a small (300 ft.) radius of curvature bridge
with small (15 ft.) and large (22.5 ft.) cross frame spacing and a large (1000 ft.) radius of
curvature bridge with small (15 ft.) and large (22.5 ft.) cross frame spacing. These bridges were
selected from a study by Linzell et al. 2010 and were chosen as a good representation of two
span horizontally curved steel I-girder bridges. The bridge design was completed by Linzell et
al. 2010 and all bridges used in this study kept the design for each bridge throughout the
changing abutment orientation cases. This was done to ensure a true representation of strictly the
effects of adding skew to the abutments was modeled.
Each finite element model was subjected to the non-composite loading and sequencing
described in chapter 4. The models were then used to find: maximum radial and vertical girder
deflections, as well as maximum girder rotations. Maximum radial deflections were important to
monitor because they effect the overall displacement of the bridge cross section and can be
important in foreseeing and preventing potential girder fit-up and failure problems. Maximum
vertical deflections were important to monitor because during the pouring and forming of wet
concrete excessive vertical deflections can cause an uneven distribution of concrete causing
further vertical deflections and a ponding effect which may cause eventual failure. Girder
rotations can also lead to an uneven distribution of concrete during pouring, so they were
monitored. Every girder of each bridge was compared normalized to the radial abutment
parameter. Nomenclature found in the graph includes:
27
G1 = Exterior Fascia Girder
G2 = Interior Girder 1
G3 = Interior Girder 2
G4 = Interior Fascia Girder
Skewed CW & CCW = Figure 3.2 Skew Orientation
Skewed CW = Figure 3.3 Skew Orientation
Skewed CCW = Figure 3.4 Skew Orientation
6.2 Radial Deflections
Maximum radial deflections and locations of maximum were compared in all bridges
with same radius of curvature and cross frame spacing. Radial deflections are critical because
they affect the overall global displacement of the bridge. Figure 6.1 displays the orientation of
radial deflections relative to one of the curved bridges studied.
Figure 6.1: Orientation of Radial Direction
The deflections were compared for each bridge with changing abutment orientation
parameters to gain an idea of how skewed supports affected radial deflections for each bridge.
Abutment
Splice 1 Bent Splice 2
Abutment
Radial DirectionG1
G2G3
G4
28
Then the 4 separate bridges were compared to investigate how cross frame spacing and radius of
curvature affected the skews outcome on radial deflections. The results focus on stage 1 of 3 of
the deck pour and the girders before Splice 1. This was where maximum increases and decreases
in radial deflection due to skew were found. It can also be said that for the cases where both
abutments are skewed either clockwise or counterclockwise the same decreases and increases
would be seen in stage 2 of the deck pour for the girders after Splice 2 for the opposite case.
Figure 6.2 details stage 1 of the deck pour for a representative bridge. Figures 6.3 to 6.6 detail
the maximum radial deflections for each bridge. The bar graphs display the radial deformations
of each girder and are normalized to the radially oriented abutment parameter.
Figure 6.2: Stage 1 of Deck Pour
Abutment
Splice 1 Bent Splice 2
Abutment
G1G2
G3G4
165' @ CL 165' @ CL
135' @ C
L Pour
29
Figure 6.2: Ratio of Maximum Radial Deflections for Bridge 1
G1 G2 G3 G4
No Skew 1.00 1.00 1.00 1.00
Skewed CW & CCW - 20° 0.88 0.89 0.90 0.91
Skewed CW & CCW - 40° 0.74 0.76 0.79 0.83
Skewed CW - 20° 0.88 0.89 0.90 0.91
Skewed CCW - 20° 0.97 0.96 0.92 0.83
Skewed CW - 40° 0.75 0.77 0.80 0.84
Skewed CCW - 40° 1.01 0.98 0.92 0.76
0.00
0.20
0.40
0.60
0.80
1.00
1.20
Ratio of Maximum Radial Deflections
30
Figure 6.4: Ratio of Maximum Radial Deflections Bridge 2
G1 G2 G3 G4
No Skew 1.00 1.00 1.00 1.00
Skewed CW & CCW - 20° 0.92 0.93 0.73 1.00
Skewed CW & CCW - 40° 0.76 0.80 0.85 0.92
Skewed CW - 20° 0.92 0.93 0.96 0.99
Skewed CCW - 20° 1.02 1.00 0.97 0.89
Skewed CW - 40° 0.76 0.79 0.84 0.90
Skewed CCW - 40° 0.98 0.94 0.87 0.70
0.00
0.20
0.40
0.60
0.80
1.00
1.20
Ratio of Maximum Radial Deflections
31
Figure 6.5: Ratio of Maximum Radial Deflections for Bridge 3
G1 G2 G3 G4
No Skew 1.00 1.00 1.00 1.00
Skewed CW & CCW - 20° 0.91 0.94 0.98 1.03
Skewed CW & CCW - 40° 0.82 0.89 0.98 1.09
Skewed CW - 20° 0.91 0.94 0.98 1.02
Skewed CCW - 20° 1.02 0.99 0.95 0.89
Skewed CW - 40° 0.99 0.92 0.98 1.09
Skewed CCW - 40° 1.07 1.01 0.93 0.94
0.00
0.20
0.40
0.60
0.80
1.00
1.20
Ratio of Maximum Radial Deflections
32
Figure 6.6: Ratio of Maximum Radial Deflections for Bridge 4
G1 G2 G3 G4
No Skew 1.00 1.00 1.00 1.00
Skewed CW & CCW - 20° 0.92 0.96 1.00 1.05
Skewed CW & CCW - 40° 0.80 0.88 0.97 1.09
Skewed CW - 20° 0.92 0.96 1.00 1.05
Skewed CCW - 20° 1.05 1.02 0.98 0.92
Skewed CW - 40° 1.00 0.93 0.97 1.09
Skewed CCW - 40° 1.08 1.01 0.93 0.94
0.00
0.20
0.40
0.60
0.80
1.00
1.20
Ratio of Maximum Radial Deflections
33
The four bridges studied displayed similar trends. These trends were also evident across
all four girders. The 20° and 40° clockwise and counterclockwise skew cases displayed similar
trends of significant decreases in exterior girder G1 radial deflections and increases in those
deflections for interior girder G4. This trend was displayed on all four bridges and seemed to be
independent of radius of curvature as well as cross frame spacing. Both the 20° and 40°
clockwise skew cases displayed similar trends across all four girders for each bridge. Exterior
girder G1 experienced decreases in radial deflection while interior girder G4 experienced
increases. This is due to the decrease in unbraced length of the exterior girder while the interior
girder experiences an increase. The opposite result occurred for the counterclockwise cases.
Exterior girder G1 experience increases in radial deflection while interior girder G4 experienced
decreases. For these cases the smaller radius of curvature bridges experienced greater increases
and decreases than the larger radius of curvature bridges. Cross frame spacing appeared to have
no effect. For each bridge the maximum radial deflection occurred at the same location
regardless of the skew orientation.
6.3 Vertical Deflections
Maximum vertical deflections were compared in all bridges with same radius of
curvature and cross frame spacing. Vertical deflections are critical because they affect the
overall global displacement of the bridge, and excessive vertical deflections during the
placement of wet concrete can cause an uneven distribution of concrete which could in turn lead
to more deflection and eventual failure.
For each analysis case run, the vertical deflections along the whole length of each girder
were measured. The deflections were compared for each bridge with changing abutment
orientation parameters to gain an idea of how skewed supports affected vertical deflections for
34
each bridge. Then the 4 separate bridges were compared to investigate how cross frame spacing
and radius of curvature affected the skews effects on vertical deflections. For vertical deflections
all stages of the deck pour were considered and maximum deflections anywhere along the whole
span of girder lengths were compared. This was done to show that the increases and decreases
for the cases where both abutments are skewed in the same direction are the same in Stage 1 and
Splice 1 girders compared to Stage 2 and Splice 2 Girders. Figures 6.7 to 6.10 detail the
maximum vertical deflections for each bridge. The bar graphs display the vertical deformations
of each girder and are normalized to the radial abutment parameter.
35
Figure 6.7: Ratio of Maximum Vertical Deflections for Bridge 1
G1 G2 G3 G4
No Skew 1.00 1.00 1.00 1.00
Skewed CW & CCW - 20° 0.86 0.89 0.93 1.08
Skewed CW & CCW - 40° 0.69 0.75 0.86 1.21
Skewed CW - 20° 1.10 1.09 1.06 1.08
Skewed CCW - 20° 1.10 1.09 1.07 1.08
Skewed CW - 40° 1.24 1.21 1.16 1.21
Skewed CCW - 40° 1.26 1.23 1.17 1.21
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
Ratio of Maximum Vertical Deflections
36
Figure 6.8: Ratio of Maximum Vertical Deflections for Bridge 2
G1 G2 G3 G4
No Skew 1.00 1.00 1.00 1.00
Skewed CW & CCW - 20° 0.86 0.89 0.98 1.06
Skewed CW & CCW - 40° 0.69 0.75 0.87 1.19
Skewed CW - 20° 1.12 1.10 1.06 1.06
Skewed CCW - 20° 1.12 1.10 1.07 1.06
Skewed CW - 40° 1.24 1.21 1.15 1.19
Skewed CCW - 40° 1.24 1.21 1.16 1.19
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
Ratio of Maximum Vertical Deflections
37
Figure 6.9: Ratio of Maximum Vertical Deflections for Bridge 3
G1 G2 G3 G4
No Skew 1.00 1.00 1.00 1.00
Skewed CW & CCW - 20° 0.86 0.93 1.02 1.15
Skewed CW & CCW - 40° 0.71 0.84 1.05 1.36
Skewed CW - 20° 1.13 1.07 1.02 1.15
Skewed CCW - 20° 1.13 1.07 1.02 1.15
Skewed CW - 40° 1.29 1.16 1.05 1.36
Skewed CCW - 40° 1.29 1.16 1.05 1.36
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
1.60
Ratio of Maximum Vertical Deflections
38
Figure 6.10: Ratio of Maximum Vertical Deflections for Bridge 4
G1 G2 G3 G4
No Skew 1.00 1.00 1.00 1.00
Skewed CW & CCW - 20° 0.86 0.93 1.02 1.15
Skewed CW & CCW - 40° 0.70 0.85 1.05 1.35
Skewed CW - 20° 1.13 1.07 1.01 1.14
Skewed CCW - 20° 1.13 1.06 1.02 1.15
Skewed CW - 40° 1.29 1.16 1.04 1.34
Skewed CCW - 40° 1.28 1.15 1.05 1.35
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
1.60
Ratio of Maximum Vertical Deflections
39
All four bridges used for this study displayed similar results for vertical deflections. On
all four bridges having the 20° and 40° clockwise and counterclockwise skewed abutment cases
the exterior girder, Girder 1; saw the greatest decrease in vertical deflection compared to the
radial abutments case. Working inward from Girder 1 to 2, 3, and 4 reductions decreased and at
some points became increases relative to the radial abutment case. This result could be expected
as skewing the abutments decreased the overall unbraced length of Girder 1 while increasing that
of Girder 4. The reduction in the vertical deflection of the outermost girders is desirable as these
are typically the maximum deflections. When comparing bridges of the same radius with
different cross frame spacing (Bridge 1 to Bridge 2 and Bridge 3 to Bridge 4), they saw very
similar results and it can be reasoned that cross frame spacing does not affect any deviations in
vertical deflections from skewing abutments. The locations of maximum vertical deflections did
see a shift due to skew. For small (300 ft.) radius of curvature bridges the skews offset the
location of the maximum girder deflection one quarter of the cross frame spacing for every 20°
of skew in the directions of the skew. For example Girder 1 of Bridge 1 with 15 ft. cross frame
spacing saw its max vertical deflection at 75 ft. along its centerline for the radial case, 78.75 ft.
along its centerline for any 20° clockwise skew, 82.5 ft. along its centerline for any 40°
clockwise skew. The large radius of curvature bridges saw less of an offset with the deflections
occurring around the same location for the radial and 20° skew cases, and one quarter of the
cross frame spacing offset for 40° skew cases.
6.4 Girder Rotations
Maximum girder out of plane web rotations were measured and compared for all analysis
cases with the same radius and cross frame spacing. In horizontally curved steel I-girder bridges
differential deflections between neighboring and connected girders cause these rotations out of
40
plane. Large girder rotations have been found to cause higher displacements and stresses in
bridge girders and cross frames (Howell and Earls 2007). These rotations are most prominent
during deck placement; therefore this was an important response quantity to measure for this
study. Figure 6.11 displays the orientation of girder rotation as measured for this study.
Figure 6.11: Orientation of Girder Rotations
For each analysis case, the girder rotations along the whole length of each girder were
measured. The rotations were compared for each bridge with changing abutment orientation
parameters to gain an idea of how skewed supports affected girder rotations for each bridge.
Then the 4 separate bridges were compared to investigate how cross frame spacing and radius of
curvature affected the skews effects on girder rotation. The results focus on stage 1 of 3 of the
deck pour and the girders before Splice 1. This was where the max increases and decreases in
girder rotation due to skew were found. It can also be said that for the cases where both are
?
Web Plumb
Girder
Angle
Rotated Gider
Center of Curvature
41
either clockwise or counterclockwise the same decreases and increases would be seen in stage 2
of the deck pour for the girders after Splice 2 for the opposite case. Figures 6.12 to 6.15 detail
the maximum girder rotations for each bridge. The bar graphs display the girder rotations of
each girder and are normalized to the radial abutment parameter.
42
Figure 6.12: Ratio of Maximum Girder Rotation Bridge 1
G1 G2 G3 G4
No Skew 1.00 1.00 1.00 1.00
Skewed CW & CCW - 20° 0.90 0.91 0.92 0.95
Skewed CW & CCW - 40° 0.77 0.78 0.83 0.90
Skewed CW - 20° 0.90 0.91 0.92 0.95
Skewed CCW - 20° 1.06 1.06 1.07 1.09
Skewed CW - 40° 0.77 0.78 0.83 0.90
Skewed CCW - 40° 1.24 1.21 1.14 1.12
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
Ratio of Maximum Girder Rotation
43
Figure 6.13: Ratio of Maximum Girder Rotation Bridge 2
G1 G2 G3 G4
No Skew 1.00 1.00 1.00 1.00
Skewed CW & CCW - 20° 0.92 0.94 0.96 0.99
Skewed CW & CCW - 40° 0.81 0.83 0.86 0.97
Skewed CW - 20° 0.92 0.93 0.93 0.98
Skewed CCW - 20° 1.07 1.08 1.08 1.06
Skewed CW - 40° 0.81 0.83 0.86 0.97
Skewed CCW - 40° 1.23 1.21 1.16 1.12
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
Ratio of Maximum Girder Rotation
44
Figure 6.14: Ratio of Maximum Girder Rotation Bridge 3
G1 G2 G3 G4
No Skew 1.00 1.00 1.00 1.00
Skewed CW & CCW - 20° 0.85 0.89 0.92 0.97
Skewed CW & CCW - 40° 0.70 0.77 0.83 0.93
Skewed CW - 20° 0.85 0.89 0.92 0.97
Skewed CCW - 20° 1.13 1.11 1.08 1.03
Skewed CW - 40° 0.81 0.78 0.83 0.93
Skewed CCW - 40° 1.29 1.24 1.18 1.08
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
Ratio of Maximum Girder Rotation
45
Figure 6.15: Ratio of Maximum Girder Rotation Bridge 4
G1 G2 G3 G4
No Skew 1.00 1.00 1.00 1.00
Skewed CW & CCW - 20° 0.90 0.93 0.96 0.99
Skewed CW & CCW - 40° 0.78 0.83 0.90 0.99
Skewed CW - 20° 0.90 0.93 0.96 0.99
Skewed CCW - 20° 1.09 1.07 1.04 1.01
Skewed CW - 40° 0.78 0.83 0.90 0.99
Skewed CCW - 40° 1.18 1.14 1.09 1.02
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
Ratio of Maximum Girder Rotation
46
All four bridges used for this study displayed similar results for girder out of plane
rotations. The clockwise and counterclockwise skew case saw reductions in girder rotation
across all girders for each bridge. The cases with both abutments skewed in one direction saw an
increase in girder rotations when the skew was clockwise and decreases when the skew was
counterclockwise. This result would be reversed for Stage 2 and the girders after Splice 2. The
location of maximum girder rotation saw no displacement due to skew. For each bridge it
always occurred in the center of the loading being applied during that stage. Reduction in the
girder rotation of the outermost girders is desirable as these are typically the maximum
deflections. When comparing bridges of the same radius with different cross frame spacing
(Bridge 1 to Bridge 3 and Bridge 7 to Bridge 9), they saw very similar results and it can be
reasoned that cross frame spacing does not affect any deviations in girder rotations from skewing
abutments. Also, when comparing bridges of the same cross frame spacing with different radius
of curvatures (Bridge 1 o Bridge 7 and Bridge 3 to Bridge 9), it can be reasoned that radius of
curvature has little effect on any benefit or disadvantage in girder rotation due to adding a
skewed abutment.
47
7. Conclusions
7.1 Summary
The effects of skewed abutments on construction response during the placement of wet
concrete in horizontally curved steel I-girder bridges were investigated employing the parametric
study detailed in Chapter 5. The bridges studied were chosen from a statistical study of curved
bridges in the Maryland, New York, and Pennsylvania done by Linzell et al. 2010 and consisted
of 4 two span bridges with varying radius of curvatures of 91.4 m (300 ft.) and 304.8 m (1000
ft.). The bridges all utilized a 4-girder layout and had varying cross frame spacing of 4.6 m (15
ft. or 6.9 m (22.5 ft.). These 4 bridges were modeled using three dimensional finite element
models created in CSI Bridge. The models were adjusted to fit the parameters and goals of this
study by modeling each bridge with a radial abutment case, a 20° clockwise and
counterclockwise skewed abutment case, a 40° clockwise and counterclockwise skewed
abutment case, a 20° clockwise skewed abutment case, a 20° counterclockwise skewed
abutment, a 40° clockwise skewed abutment case, and a 40° counterclockwise skewed abutment
case. Each model was then subjected to a sequence of loading to simulate the pouring and
forming of wet concrete. The models were then used to find: maximum radial and vertical girder
deflections, as well as maximum girder rotations. Results were analyzed and compared to the
standard radial abutment model to observe the effects skewed abutments had on curved I-girder
bridges as well as the effects varying radius of curvatures and cross frame spacing had on the
effects of skewed abutments. Results from these studies led to the following conclusions:
Skewed abutments showed similar effects for radial deflections on small and large radius
curvature bridges with small and large cross frame spacing when compared to the radially
48
supported case. Generally reductions were seen if the skew decreased a girder’s overall
span length and increases were seen if the skew increased a girder’s overall span length.
Locations of maximum radial deflections saw no change due to adding skew to a
horizontally curved bridge.
Skewed abutments showed similar effects for vertical deflections on small and large
radius curvature bridges with small and large cross frame spacing when compared to the
radial case. Generally reductions were seen if the skew decreased a girder’s overall span
length and increases were seen if the skew increased a girder’s overall span length.
Locations of maximum vertical deflections saw changes that were in the direction of the
skew and related to the degree of skew.
Skewed abutments showed similar effects for girder rotations on small and large radius
curvature bridges with small and large cross frame spacing when compared to the radial
case. Generally reductions were seen if the skew decreased a girder’s overall span length
and increases were seen if the skew increased a girder’s overall span length.
Locations of maximum girder rotations saw no change due to adding skew to a
horizontally curved bridge.
7.2 Future Work
The results of this parametric study show that future investigation may need to be made
on the following areas with respect to construction response of skewed abutments on
horizontally curved steel I-girder bridges:
Examining the effects of larger and smaller spans and more than two spans.
Investigating the effects of greater skew angles than 40°.
49
Studying the effects of different sections and systems, such as number of girders, girder
spacing, and deck size.
Considering the effects of a combination of skewed abutments and skewed cross frames
50
References
American Association of State Highway and Transportation Officials. (2007). LRFD
Design Specifications, Washington, D.C.
AASHTO/NSBA Steel Bridge Collaboration (2003). Guidelines for Design for Constructability.
Washington, D.C.
Bell, B.J. (2004). “Effects of erection procedures on the response of a horizontally curved I-
girder bridge.” Master’s dissertation, Department of Civil and Environmental
Engineering, Pennsylvania State University, University Park, PA.
Brennan, P.J. (1970). “Horizontally curved bridges first annual report: Analysis of horizontally
curved bridges through three-dimensional mathematical model and small scale structural
testing.” Syracuse University, First Annual Rep., Research Project HPR-2(111),
Syracuse, NY.
Brennan, P.J. (1971). “Horizontally curved bridges second annual report: Analysis of Seekonk
River Bridge small scale structure through three-dimensional mathematical model and
small scale structural testing.” Syracuse University, Second Annual Rep., Research
Project HPR-2(111), Syracuse, NY.
Brennan, P.J. (1974). “Analysis and structural testing of a multiple configuration small scale
horizontally curved highway bridge.” Syracuse University, Research Project HPR-
2(111), Syracuse, N.Y.
51
Brennan, P.J., and Mandel, J.A. (1979). “Multiple configuration curved bridge model studies.”
ASCE Journal of Structural Engineering, 105(5), 875-890.
Bradford, M.A. and Pi, U.Y. (2001). “Behavior of Unpropped Composite Girders
Curved in Plan Under Construction Loading,” Engineering Structures, v23, 779-789.
Chang, C.J. (2006). “Construction simulation of curved steel I-girder bridges.” PhD dissertation.
College of Civil and Environmental Engineering, Georgia Institute of Technology,
Atlanta, GA.
Chang, C. J. and White, W. W. (2008). “An assessment of modeling strategies for
composite curved steel I-girder bridges “Engineering Structures, v30, 2991–
3002
Chavel, B.W., Earls, C.J. (2006a). “Construction of a horizontally curved steel I-girder bridge.
Part I: Erection sequence.” ASCE Journal of Bridge Engineering, 11(1), 81-90.
Chavel, B.W., Earls, C.J. (2006b). “Construction of a horizontally curved steel I-girder bridge.
Part II: Inconsistent detailing.” ASCE Journal of Bridge Engineering, 11(1), 91-98.
Choo, T.W., Linzell D.G., Lee J.I., Swanson J.A. (2005). “Response of Continuous, Skewed,
Steel Bridge During Deck Placement.” Journal of Constructional Steel Research, 61(5),
567-586
CSIBridge User’s Manuals; Version 15 (2012). CSI Berkeley, Berkeley, CA.
DeSantiago, E., Mohammadi, J. and Albaijat, H. M. O. (2005) “Analysis of Horizontally
Curved Bridges Using Simple finite-element models.” Practice Periodical on
Structural Design and Construction, 10(1)
52
Earls, C.J. and Chavel, B.W. (1999). “Evaluation of Erection Procedures of the
Horizontally Curved Steel I-Girder Ford City Bridge,” Research Report No.
CE/ST 18, Department of Civil and Environmental Engineering, University of
Pittsburgh.
Federal Highway Administration (1997). “Curved Steel Bridge.” Retrieved March 18, 2013
from http://www.fhwa.dot.gov/publications/transporter/97apr/index.cfm
Howell, T.D., Earls, C. J. (2007). “Curved steel I-girder bridge response during construction
loading: Effects of web plumbness.” ASCE Journal of Bridge Engineering, 12(4), 485-
493.
Linzell, D.G. (1999). “Studies of a full-scale horizontally curved steel I-girder bridge system
under self-weight.” PhD thesis, School of Civil and Environmental Engineering, Georgia
Institute of Technology, Atlanta.
Linzell, D.G., Leon, R.T., Zureick, A. (2004). “Experimental and analytical studies of
horizontally curved steel I girder bridge during erection.” ASCE Journal of Bridge
Engineering, 9(6), 521-530.
Linzell, D.G., Shura, J.F. (2010). “Erection behavior and grillage model accuracy for a large
radius curved bridge.” Journal of Constructional Steel Research, 66 (3), 342-350.
Linzell, D.G., Chen, C.C., Sharafbayani, M., Seo, J., Nevling, D., Jaissa-Ard, T., Ashour,
O. (2010) “Guidelines for Analyzing Curved and Skewed Bridges and Designing
them for Construction.” Prepared for the Pennsylvania Department of
Transportation.
53
Mozer, J., Cook, J., Culver, C. (1973). “Horizontally curved highway bridges–Stability of curved
plate girders.” Carnegie Mellon Univ., Rep. No. P3, Research Project HPR-2(111),
Pittsburgh, PA.
Mozer, J., and Culver, C. (1970). “Horizontally curved highway bridges–Stability of curved plate
girders.” Carnegie Mellon Univ., Rep. No. P1, Research Project HPR-2(111), Pittsburgh,
PA.
Mozer, J., Ohlson, R., and Culver, C. (1971). “Horizontally curved highway bridges–Stability of
curved plate girders.” Carnegie Mellon Univ., Rep. No. P2, Research Project HPR-
2(111), Pittsburgh, PA.
Nevling D. (2008) “Development of Guidelines for Erection Procedure for Horizontally
Curved Steel I-Girder Bridges Through Analysis of A Parametric Group of
Bridges” PhD Dissertation, The Pennsylvania State University, University Park,
PA 16802
Norton, EK. (2003) "Examination of response of a skewed steel bridge superstructure during
deck placement” in DESIGN OF STRUCTURES 2003, (p. 66)
Pennsylvania Department of Transportation Publication 15M (2007) Design Manual
Four, Pennsylvania, USA
Puckett, Jay A., and Barker, Richard M. (1997). Design of Highway Bridges. John Wiley
& Sons, Inc. New York, NY. 736-737.
Schelling, D., Namini, A.H., and Fu, C.C. (1989). “Construction Effects on Bracing on
Curved I-Girders,” ASCE Journal of Structural Engineering, September, v115,
n9, pp. 2145-2165.
54
Schuh, A.C. (2008). “Behavior of horizontally curved steel I-girders during lifting.” Master’s
dissertation, Department of Civil Architectural and Environmental Engineering,
University of Texas at Austin, Austin, TX.
Sharafbayani, M., Linzell D.G. (2012). “Optimizing cross frame plan orientation in a
horizontally curved steel bridge – is it worth it?” Structural Stability Research Council,
Annual Stability Conference, Grapevine, Texas April 18-21, 2012.
Shura, J.F. (2005). “The Effects of Horizontal Curvature on Warping During
Construction of a Steel Plate Girder Bridge with Large Radii,” Thesis in Civil
Engineering, Pennsylvania State University, May 2005.
Stith, J., Schuh, A., Farris, J. F., Petruzzi, B., Helwig, T., Williamson, E., Frank, K., Engelhardt,
M., and Kim, H. J. (2009). “Guidance for erection and construction of curved I-girder
bridges.” Rep. No. FHWA/TX-10/0-5574-1, Center for Transportation Research at the
University of Texas at Austin, Austin, TX.
“USS Highway Structures Design Handbook” (1981), v1, ch12.
White, D.W., and Grubb, A. (2005). “Unified resistance equations for design of curved and
tangent steel bridge I girders.” Transportation Research Record, CD 11-S, 121–128.
White, D.W., Colleti D., Chavel B.W., Sanchez A., Ozgur C., Chong J., Leon R.T. Medlock
R.D., Cisneros R.A., Galambos T.V., Yadlosky J.M., Gatti W.J., Kowatch G.T. (2012).
“Guidelines for Analysis Methods and Construction Engineering of Curved and Skewed
Steel Girder Bridges.” National Cooperative Highway Research Program, Report 725.
Zureick, A., Linzell, D.G., Leon, R.T., and Burrell, J. (2000). “Curved steel I-girder bridges:
Experimental and analytical studies.” Engineering Structures, 22(2), 180-190.
55
Zhang, H., Huang, D., and Wang, T. (2003). “Lateral Load Distribution in Curved Steel
I-Girder Bridges” Journal of Bridge Engineering, 10(3), 2005.
56
Appendix A
(Linzell et al. 2010)
Bridge 1:
Figure A.1: Bridge 1 Framing Plan
57
Bridge 2:
Figure A.2: Bridge 2 Framing Plan
58
Bridge 3:
Figure A.3: Bridge 3 Framing Plan
59
Bridge 4:
Figure A.4: Bridge 4 Framing Plan
60
ACADEMIC VITA
Tyler D. Goodman
412-335-6059
362 Cobblestone Circle McKees Rocks, PA 15136
Education: The Pennsylvania State University, University Park, PA
Bachelor of Science in Civil Engineering – Structures Spring 2013 The Schreyer Honors College
Thesis Title: Effects of Skewing Abutments on Curved Bridge Construction
Response Thesis Supervisor: Dr. Daniel G. Linzell
Experience:
Walsh Construction Pittsburgh, PA Summer 2012 Estimating Intern
Restoration East, LLC. Baltimore, MD Summer 2011
Honors, Activities, Memberships: • Engineer in Training Certified
• Recipient of the H. Thomas and Dorothy Willits Hallowell Scholars Endowment
• Dean’s List every semester enrolled at Penn State
• American Society of Civil Engineers, Member
• Earthquake Engineering Research Institute, Member