EFFECTS OF SKEWED ABUTMENTS ON CURVED BRIDGE CONSTRUCTION RESPONSE. Tyler Goodman. Spring 2013

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1 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

2 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. ii

3 Table of Contents List of Figures... v List of Tables...Error! Bookmark not defined. 1. Introduction Background Problem Statement Objectives Scope Tasks Literature Review Research Related to Construction Loading on Curved and Skewed Bridges Horizontally Curved Steel Bridges with Skewed Supports Summary Representative Bridges Bridge Description and Selection Bridge Design Introduction of Skew to Designed Bridges Summary Finite Element Modeling Overview Boundary Conditions Girders Bridge Deck iii

4 4.5 Cross Frames Deck Placement and Loading Summary Parametric Study Overview Parameter Ranges Approach Summary Results Overview Radial Deflections Vertical Deflections Girder Rotations Conclusions Summary Future Work References Appendix A (Linzell et al. 2010) Bridge 1: iv

5 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) Figure 3.2: Representative Skew Orientation CW & CCW Figure 3.3: Representative Skew Orientation CW Figure 3.4: Representative Skew Orientation CCW Figure 3.5: Staggered Cross Frames at Skewed Abutment Figure 4.1: Girder deformation directions (Nevling 2008) Figure 4.2: Deck Placement Stage Figure 4.3: Deck Placement Stage Figure 4.4: Deck Placemen Stage Figure 6.1: Orientation of Radial Direction Figure 6.2: Stage 1 of Deck Pour Figure 6.2: Ratio of Maximum Radial Deflections for Bridge Figure 6.4: Ratio of Maximum Radial Deflections Bridge Figure 6.5: Ratio of Maximum Radial Deflections for Bridge Figure 6.6: Ratio of Maximum Radial Deflections for Bridge Figure 6.7: Ratio of Maximum Vertical Deflections for Bridge Figure 6.8: Ratio of Maximum Vertical Deflections for Bridge Figure 6.9: Ratio of Maximum Vertical Deflections for Bridge Figure 6.10: Ratio of Maximum Vertical Deflections for Bridge Figure 6.11: Orientation of Girder Rotations v

6 Figure 6.12: Ratio of Maximum Girder Rotation Bridge Figure 6.13: Ratio of Maximum Girder Rotation Bridge Figure 6.14: Ratio of Maximum Girder Rotation Bridge Figure 6.15: Ratio of Maximum Girder Rotation Bridge Figure A.1: Bridge 1 Framing Plan Figure A.2: Bridge 2 Framing Plan Figure A.3: Bridge 3 Framing Plan Figure A.4: Bridge 4 Framing Plan vi

7 List of Tables Table 1.1: Parametric study bridges (Linzell et al. 2010) Table 5.1: Parametric Study Cases vii

8 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) 1

9 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 2

10 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. 3

11 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 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. 4

12 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 Bridge (300) 4.6 (15) 3 (10) 2 Bridge (300) 6.9 (22.5) 3 (10) 2 Bridge 3 Bridge (1000) 4.6 (15) 3 (10) (1000) 6.9 (22.5) 3 (10) 2 Span Lengths, m (ft.) Number of Girder ( ) ( ) ( ) ( ) 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. 5

13 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 6

14 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 simplysupported 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. Obtuse Corner Acute Corner 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) 7

15 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 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 8

16 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 9

17 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. 10

18 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 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 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. 11

19 Figure 3.1: Typical cross section (Linzell et al. 2010). 3.2 Bridge Design The bridges were designed by Linzell et al 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 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 12

20 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. Splice 1 Bent Splice 2 Skewed Abutment Skewed Abutment Radial Abutment Radial Abutment Figure 3.2: Representative Skew Orientation CW & CCW 13

21 Splice 1 Bent Splice 2 Skewed Abutment Radial Abutment Radial Abutment Skewed Abutment Figure 3.3: Representative Skew Orientation CW Splice 1 Bent Splice 2 Skewed Abutment Skewed Abutment Radial Abutment Radial Abutment Figure 3.4: Representative Skew Orientation CCW 14

22 Skewed Abutment 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 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. 15

23 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 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. 16

24 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 17

25 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 18

26 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. CL Pour Splice 1 Bent Splice 2 Abutment G1 G2 G3 G4 CL CL Abutment Figure 4.2: Deck Placement Stage 1 19

27 Splice 1 Bent Splice 2 CL Pour Abutment G1 G2 G3 G4 CL CL Abutment Figure 4.3: Deck Placement Stage 2 CL Pour Splice 1 Bent Splice 2 Abutment G1 G2 G3 G4 CL CL CL Abutment 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 20

28 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. 21

29 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 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 m (300 ft.) b m (1000 ft.) 22

30 2. Cross Frame Spacing a. 4.6 m (15 ft.) b 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. 23

31 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 Radial 2 Skew 20º CW & CCW 3 Skew 40º CW & CCW (15) Skew 20º CW 5 Skew 20º CCW 6 Skew 40º CW Skew 40º CCW 8 (300) Radial 9 Skew 20º CW & CCW 10 Skew 40º CW & CCW Skew 20º CW (22.5) 12 Skew 20º CCW 13 Skew 40º CW Skew 40º CCW Two Span 15 ( ) Radial 16 Skew 20º CW & CCW 17 Skew 40º CW & CCW (15) Skew 20º CW 19 Skew 20º CCW 20 Skew 40º CW Skew 40º CCW 22 (1000) Radial 23 Skew 20º CW & CCW 24 Skew 40º CW & CCW (22.5) Skew 20º CW 26 Skew 20º CCW 27 Skew 40º CW 28 Skew 40º CCW 24

32 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 horizontally 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 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. 25

33 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 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 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: 26

34 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. Splice 1 Bent Splice 2 Abutment Abutment G1 G2 G3 G4 Radial Direction 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. 27

35 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. CL Pour Splice 1 Bent Splice 2 Abutment G1 G2 G3 G4 CL CL Abutment Figure 6.2: Stage 1 of Deck Pour 28

36 Ratio of Maximum Radial Deflections G1 G2 G3 G4 No Skew Skewed CW & CCW Skewed CW & CCW Skewed CW Skewed CCW Skewed CW Skewed CCW Figure 6.2: Ratio of Maximum Radial Deflections for Bridge 1 29

37 Ratio of Maximum Radial Deflections G1 G2 G3 G4 No Skew Skewed CW & CCW Skewed CW & CCW Skewed CW Skewed CCW Skewed CW Skewed CCW Figure 6.4: Ratio of Maximum Radial Deflections Bridge 2 30

38 Ratio of Maximum Radial Deflections G1 G2 G3 G4 No Skew Skewed CW & CCW Skewed CW & CCW Skewed CW Skewed CCW Skewed CW Skewed CCW Figure 6.5: Ratio of Maximum Radial Deflections for Bridge 3 31

39 Ratio of Maximum Radial Deflections G1 G2 G3 G4 No Skew Skewed CW & CCW Skewed CW & CCW Skewed CW Skewed CCW Skewed CW Skewed CCW Figure 6.6: Ratio of Maximum Radial Deflections for Bridge 4 32

40 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 33

41 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. 34

42 Ratio of Maximum Vertical Deflections G1 G2 G3 G4 No Skew Skewed CW & CCW Skewed CW & CCW Skewed CW Skewed CCW Skewed CW Skewed CCW Figure 6.7: Ratio of Maximum Vertical Deflections for Bridge 1 35

43 Ratio of Maximum Vertical Deflections G1 G2 G3 G4 No Skew Skewed CW & CCW Skewed CW & CCW Skewed CW Skewed CCW Skewed CW Skewed CCW Figure 6.8: Ratio of Maximum Vertical Deflections for Bridge 2 36

44 Ratio of Maximum Vertical Deflections G1 G2 G3 G4 No Skew Skewed CW & CCW Skewed CW & CCW Skewed CW Skewed CCW Skewed CW Skewed CCW Figure 6.9: Ratio of Maximum Vertical Deflections for Bridge 3 37

45 Ratio of Maximum Vertical Deflections G1 G2 G3 G4 No Skew Skewed CW & CCW Skewed CW & CCW Skewed CW Skewed CCW Skewed CW Skewed CCW Figure 6.10: Ratio of Maximum Vertical Deflections for Bridge 4 38

46 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, 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 39

47 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.? Web Plumb Girder Angle Rotated Gider Center of Curvature 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 40

48 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. 41

49 Ratio of Maximum Girder Rotation G1 G2 G3 G4 No Skew Skewed CW & CCW Skewed CW & CCW Skewed CW Skewed CCW Skewed CW Skewed CCW Figure 6.12: Ratio of Maximum Girder Rotation Bridge 1 42

50 Ratio of Maximum Girder Rotation G1 G2 G3 G4 No Skew Skewed CW & CCW Skewed CW & CCW Skewed CW Skewed CCW Skewed CW Skewed CCW Figure 6.13: Ratio of Maximum Girder Rotation Bridge 2 43

51 Ratio of Maximum Girder Rotation G1 G2 G3 G4 No Skew Skewed CW & CCW Skewed CW & CCW Skewed CW Skewed CCW Skewed CW Skewed CCW Figure 6.14: Ratio of Maximum Girder Rotation Bridge 3 44

52 Ratio of Maximum Girder Rotation G1 G2 G3 G4 No Skew Skewed CW & CCW Skewed CW & CCW Skewed CW Skewed CCW Skewed CW Skewed CCW Figure 6.15: Ratio of Maximum Girder Rotation Bridge 4 45

53 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. 46