effects of skewed abutments on curved bridge …

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 6.7: Ratio of Maximum Vertical Deflections for Bridge 1 ............................................... 35



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 A.1: Bridge 1 Framing Plan............................................................................................... 56




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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.

4

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

13

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


12

34

Radial

AbutmentSkewed

AbutmentRadial

AbutmentSkewed

Abutment


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.

17

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

18

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

19

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


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


Abutment

165' @ CL 165' @ CL

135' @ CL Pour

G1G2

G3G4

Abutment


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.

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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


4 Skew 20º CW

5 Skew 20º CCW

6 Skew 40º CW

7 Skew 40º CCW

8

6.9 (22.5)

Radial



11 Skew 20º CW

12 Skew 20º CCW

13 Skew 40º CW

14 Skew 40º CCW

15

304.8 (1000)

4.6 (15)

Radial



18 Skew 20º CW

19 Skew 20º CCW

20 Skew 40º CW

21 Skew 40º CCW

22

6.9 (22.5)

Radial



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


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


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


31


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


32


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


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


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


37


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


38


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


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


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


44


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


45


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


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

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Appendix A

(Linzell et al. 2010)

Bridge 1:

Figure A.1: Bridge 1 Framing Plan

57

Bridge 2:


58

Bridge 3:


59

Bridge 4:


60

ACADEMIC VITA

Tyler D. Goodman

412-335-6059

362 Cobblestone Circle McKees Rocks, PA 15136

[email protected]

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

effects of skewed abutments on curved bridge …

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