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DEVELOPMENT OF GUIDELINES FOR ERECTION PROCEDURES FOR HORIZONTALLY CURVED STEEL I-GIRDER BRIDGES THROUGH ANALYSIS OF A PARAMETRIC GROUP OF BRIDGES
ABSTRACT
A three dimensional finite element modeling technique was compared to field test results obtained from a horizontally curved steel I-girder bridge during construction. The three-dimensional finite element modeling technique was utilized to examine construction methods for 30 parametric bridges. The 30 parametric bridges were designed for use in the current study. The number of bridges to be analyzed was determined from prevailing parameters that were selected. The following parameters were investigated for this study: 1) varying radii; 2) single span structures; 3) two span structures (balanced spans); 4) two span structures (unbalanced spans); 5) 4 and 5 girder cross sections; 6) varying radius to unbraced length (R/L) ratios; 7) single girder erection; 8) paired girder erection; and 9) erection sequence (inner girder to outer girder vs. outer girder to inner girder). After designing the parametric bridges, three-dimensional finite element models were created for each bridge. The models were analyzed using 4 methods of construction for each bridge (paired outer, paired inner, single outer, and single inner). The deflection results were analyzed using ANOVA to determine which parameters were influencing the deflection results. The statistical model results were used to determine general trends in the radial, tangential, and vertical deflection results for the parametric bridges. The statistical results examine the influence of the study parameters on the radial, tangential, and vertical deflection. Recommendations are made for selecting an erection procedure for each bridge that minimizes radial, tangential, and vertical deflections. Recommendations are also made for determining which construction method should not be used for each of the parametric bridges.
TABLE OF CONTENTS
LIST OF FIGURES ………………………………………………………………………………………..vii
LIST OF TABLES………………………………………………………………………………………….xvii
ACKNOWLEDGEMENTS……………………………………………………………………………..xxviii
Chapter 1 Introduction……………………………………………………………………………………1
1.1 Background………………………………………………………………………………………..1
1.2 Problem Statement………………………………………………………………………………2
1.3 Objectives ………………………………………………………………………………………….3
1.4 Scope and Tasks …………………………………………………………………………………4
Chapter 2 Literature Review……………………………………………………………………………7
2.1 Introduction………………………………………………………………………………………..7
2.2 Curved Girder Analysis Studies ……………………………………………………………7
2.3 Field Studies ………………………………………………………………………………………11
Chapter 3 Finite Element Model Verification ……………………………………………………19
3.1 Introduction………………………………………………………………………………………..19
3.2 Description of Bridge ………………………………………………………………………….20
3.3 Instrumentation Plan……………………………………………………………………………22
3.4 Field Data Processing………………………………………………………………………….23
3.4.1 Strain Calculations……………………………………………………………………..24
3.4.2 Stress Calculations……………………………………………………………………..24
3.4.3 Girder Moment Calculations……………………………………………………….25
3.4.4 Deflection Calculations ………………………………………………………………26
3.5 Finite Element Model Benchmarking…………………………………………………….26
3.5.1 Benchmark Model Geometry………………………………………………………27
3.5.2 Benchmark Model Analysis Steps………………………………………………..36
3.5.3 Benchmark Model Vertical Bending Moment Distribution Results….39
3.5.4 Benchmark Model Lateral Bending Moment Distribution Results……46
3.5.5 Benchmark Model Stress Results During Slab Pour……………………….48
3.5.6 Deflection Results During Slab Placement ……………………………………55
3.5.7 Curved Beam Results Comparisons……………………………………………..60
3.5.8 Slab Placement Comparisons ………………………………………………………65
3.5.9 Flange Offset Results …………………………………………………………………70
3.5.10 Flange Shell Results…………………………………………………………………72
3.6 Summary……………………………………………………………………………………………78 Chapter 4 Parametric Study Development…………………………………………………………80
4.1 Introduction………………………………………………………………………………………..80
4.2 Selection of Parameters ……………………………………………………………………….80
4.3 Base Model Design……………………………………………………………………………..85
4.3.1 Single Span Bridge Designs………………………………………………………..86
4.3.2 Two Equal Span Bridge Designs………………………………………………….92
4.3.3 Two Unequal Span Bridge Designs ……………………………………………..97
4.4 Three Dimensional Finite Element Models of Parametric Bridges…………….103
4.4.1 Single Span Three Dimensional Finite Element Models …………………104
4.4.2 Two Equal Span Three Dimensional Finite Element Models…………..108
4.4.3 Two Unequal Spans Three Dimensional Finite Element Models ……..113
Chapter 5 Parametric Study Statistical Analysis ………………………………………………..117
5.1 Introduction………………………………………………………………………………………..117
5.2 Parametric Bridge Deflection Results ……………………………………………………119
5.3 Statistical Analysis of Deflection Results……………………………………………….130
5.3.1 Vertical Deflection …………………………………………………………………….133
5.3.2 Radial Deflection……………………………………………………………………….149
5.3.3 Tangential Deflection…………………………………………………………………165
5.4 Summary……………………………………………………………………………………………179
Chapter 6 Construction Method Deflection Results for Parametric Bridges…………..182
6.1 Introduction………………………………………………………………………………………..182
6.2 Construction Method Recommendations ……………………………………………….182
6.3 Single Span Bridges…………………………………………………………………………….183
6.3.1 Single Span 4 Girder Bridges………………………………………………………183
6.3.2 Single Span 5 Girder Bridges………………………………………………………185
6.4 Two Equal Span Bridges ……………………………………………………………………..188
6.4.1 Two Equal Span 4 Girder Bridges………………………………………………..188
6.4.2 Two Equal Span 5 Girder Bridges………………………………………………..189
6.5 Two Unequal Span Bridges………………………………………………………………….192
6.5.1 Two Unequal Span 4 Girder Bridges ……………………………………………192
6.5.2 Two Unequal Span 5 Girder Bridges ……………………………………………193
Chapter 7 Conclusions……………………………………………………………………………………196
7.1 Summary……………………………………………………………………………………………196
7.2 Conclusions………………………………………………………………………………………..197
7.3 Future Research ………………………………………………………………………………….204
Bibliography ………………………………………………………………………………………………….206
Chapter 1
Introduction
1.1 Background
Alignment restrictions and environmental demands often necessitate the use of horizontally curved steel I-girder brides instead of straight girder bridges. Insufficient or inaccurate analysis of horizontally curved steel girder bridges during the erection process can lead to excessive displacements, stresses and instabilities in the structure during construction. In Pennsylvania, bridges of this type have experienced major problems during the construction process leading to unanticipated delays and litigation (Earls and Chavel, 1999; Bell, 2004). Excessive deflections and deformations of the curved girders under self- weight can lead to fit-up problems during the erection procedure. Horizontally curved steel I-girder bridges are erected using a number of different techniques. The construction method is generally selected by the contractor erecting the structure. Commonly used erection methods involve placing the girders individually or in pairs, and either placing the exterior girder first or the interior girder first, and then placing the subsequent girder sequentially. This study investigates different erection procedures for a number of horizontally curved steel I-girder bridges to determine the preferred erection procedure for a range of parameters. The preferred erection method is considered to be the most economical method that induces the least amount of stresses and displacements in the structure during erection and the placement of the concrete deck.
1.2 Problem Statement
Currently there is no specification in the United States that specifies erection procedures and/or construction techniques for horizontally curved steel I-girder bridges. The AASHTO LRFD Bridge Design Specifications (2008) states that “constructability issues should include, but not be limited to, consideration of deflection, strength of steel and concrete, and stability during critical stages of construction”. The AASHTO LRFD Bridge Design Specifications (2008) also state that for horizontally curved steel I-girder bridges the cross frames should be designed as primary load carrying members. The AASHTO LRFD Bridge Design Specifications (2008) does not provide any quantitative specifications that assist the bridge designer in selecting an appropriate erection method for horizontally curved steel I-girder bridges. The AASHTO Guide Specifications for Horizontally Curved Steel Girder Highway Bridges (2003) provides limited information on recommended erection procedures for horizontally curved steel I-girder bridges. This specification merely states procedures that may be used during construction of bridges of this type, but ultimately states that the steel superstructure should not exceed limit states, allowable flexural stresses, shear stresses and deflection during construction. No specific construction method or erection procedure recommendations are made for bridges based on radius, length, number of girders, span ratio, etc. The AASHTO/NSBA Steel Bridge Collaboration Guidelines for Design for Constructability (2003) also provides no specific guidelines for construction procedures for horizontally curved steel I-girder bridges. It only states that if phased construction is required, deflection due to dead load can be significant and “that the design must detail deflections anticipated and provide guidance to the contractor for deck forming, reinforcement displacements, and concrete placements sequence to avoid damage.” All of these guidelines are lacking quantitative information explaining when specific girder procedures (e.g. single girder versus paired girder erection) are preferred. These guidelines also do not specify when the use of temporary shoring is important. There are also no recommendations clarifying whether girder erection should be completed by placing the girders from the exterior girder to the interior girder or whether the bridge should be constructed by placing the interior girder first. These are just a few examples of possibly beneficial information that has not been provided to the design engineer and construction contractor.
There is a need for a specification that details preferred construction and erection procedures for horizontally curved steel I-girder bridges. The current study computationally examines thirty representative horizontally curved steel I-girder bridges with varying parameters (number of girders, radius, R/L ratio, number of spans, etc.) throughout construction to determine the preferred construction and erection procedures. Results of this study were used to assist with the development of guidelines for erecting and constructing horizontally curved steel I-girder bridges.
The current study utilizes a three dimensional finite element procedure to analyze the thirty representative horizontally curved steel I-girder bridges. The three-dimensional finite element models of the horizontally curved steel I-girder bridges are utilized to investigate whether second order geometric effects need to be included during analysis and also to confirm if additional steps need to be included in the finite element model to represent the stage of construction when the concrete is placed, but has no stiffness. A nonlinear geometric analysis may be required due to the horizontal curvature of the girders. The nonlinear geometric analysis uses a large rotation and large displacement based analysis compared to the linear geometric analysis which uses a small strain and small displacement based analysis. The stage of construction were the slab is placed, but has no stiffness could result in excessive deflections of the horizontally curved steel structure. Both the issues of using a nonlinear geometric analysis technique and including additional step in the finite element model to represent the stage of construction where the concrete is placed, but has no stiffness are investigated in this study.
1.3 Objectives
The objectives of this research study are:
- To develop a finite element procedure (level of discretization, element types, etc.) that accurately predicts stresses and deflections observed during the erection of a horizontally curved steel I-girder bridge,
- To confirm whether second order effects need to be included during analyses of the erection of horizontally curved steel I-girder bridges selected for this study,
- To confirm whether additional steps need to be included in the finite element model to represent the stage of construction when the concrete is placed but has no stiffness,
- To develop initial construction guidelines for erecting horizontally curved steel I-girder bridges based on radius, number of girders in a cross section, L/R ratio.
1.4 Scope and Tasks
The main point of the study is to determine the preferred erection procedure (lowest deflections) for the thirty horizontally curved bridges that were designed for this study. The scope of this study is limited to the following:
- A single field study was used to validate the finite element procedure used in this study.
- Thirty base bridges were examined.
- The bridges are single span, two equal span, and two unequal span.
- The bridges have either a 4 or 5 girder cross section.
- The bridges have one of three radii (91 m (300 ft.), 198 m (650 ft.), and 305 m (1000 ft.)).
- The unbraced lengths of the bridges are 4.6 m (15.0 ft.), 5.3 m (17.33 ft.), 6.9 m (22.5 ft.), and 8.6 m (28.1 ft.).
- The girders for all thirty base bridges were spaced at 2.4 m (8.0 ft.).
- All cross frames were designed as x-braced members.
- Upper and lower lateral bracing was not included in any of the bridges.
The following tasks were completed for this project:
- A finite element model was created of a horizontally curved steel I-girder bridge, PennDOT Bridge 207, during construction. Based upon a search of the available literature, the finite element model was meshed to optimize its ability to predict the behavior of the bridge in the field during construction. The finite element model was developed using appropriate element types recommended from the literature for different components of the bridge. The results of the finite element model were compared to field test results for Bridge 207 during construction.
- The differences between finite element model results and field testing results were analyzed. The following items were investigated to determine if they could increase the model’s ability to replicate the field test results: a.) flange element type; b.) flange offset from web; and c.) slab placement technique. The final modeling approach for Bridge 207 was used as the basis for the rest of the study.
- Bridge component sizes and erection plans were determined for thirty base bridges following AASHTO LRFD Bridge Design Specifications (2008) criteria that represent the parameters selected for this study.
- Finite element models of all 30 base bridges were created using techniques determined during the benchmarking phase.
- The 30 base models under self weight were analyzed while investigating the following three different construction parameters selected for this study: 1.) inner to outer girder erection vs. outer to inner girder erection; 2.) single girder erection vs. paired girder erection.
- Locations of maximum displacement were determined for each of the models.
- Lists of the preferred construction practices for certain types of horizontally curved steel I-girder bridges were developed.
- Lists of the least preferred construction practices for certain types of horizontally curved steel I-girder bridges were developed. This table lists the construction processes that resulted in the largest deflections and most instabilities for a given bridge type.
DEVELOPMENT OF GUIDELINES FOR ERECTION PROCEDURES FOR HORIZONTALLY CURVED STEEL I-GIRDER BRIDGES THROUGH ANALYSIS OF A PARAMETRIC GROUP OF BRIDGES
