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dc.contributor.authorGoodnight, Jason Chad
dc.contributor.authorFeng, Yuhao
dc.contributor.authorKowalsky, Mervyn J.
dc.contributor.authorNau, James M.
dc.date.accessioned2019-06-11T00:40:23Z
dc.date.available2019-06-11T00:40:23Z
dc.date.issued2015-01
dc.identifier.urihttp://hdl.handle.net/11122/10378
dc.description.abstractThis report discusses a research program aimed at defining accurate limit state displacements which relate to specific levels of damage in reinforced concrete bridge columns subjected to seismic hazards. Bridge columns are designed as ductile elements which form plastic hinges to dissipate energy in a seismic event. To satisfy the aims of performance based design, levels of damage which interrupt the serviceability of the structure or require more invasive repair techniques must be related to engineering criteria. For reinforced concrete flexural members such as bridge columns, concrete compressive and steel tensile strain limits are very good indicators of damage. Serviceability limit states such as concrete cover crushing or residual crack widths exceeding 1mm may occur during smaller, more frequent earthquakes. While the serviceability limit states do not pose a safety concern, the hinge regions must be repaired to prevent corrosion of internal reinforcing steel. At higher ductility demands produced by larger less frequent earthquakes, reinforcing bar buckling may lead to permanent elongation in the transverse steel, which diminishes its effectiveness in confining the concrete core. Bar buckling and significant damage to the core concrete represent the damage control limit states, which when exceeded lead to significant repair costs. Furthermore, rupture of previously buckled bars during subsequent cycles of loading leads to rapid strength loss. The life safety or collapse prevention limit state is characterized by fracture of previously buckled bars. The goal of the experimental program is to investigate the impact of load history and other design variables on the relationship between strain and displacement, performance strain limits, and the spread of plasticity. The main variables for the thirty circular bridge column tests included: lateral displacement history, axial load, longitudinal steel content, aspect ratio, and transverse steel detailing. A key feature of the experiments is the high fidelity strain data obtained through the use of an optical 3D position measurement system.Column curvature distributions and fixed-end rotations attributable to strain penetration of reinforcement into the footing were quantified. The following sequence of damage was observed in all of the cyclically loaded experiments: concrete cracking, longitudinal steel yielding, cover concrete crushing, confinement steel yielding, longitudinal bar buckling, and fracture of previously buckled reinforcement. The first significant loss in strength occurred when previously buckled reinforcement fractured. The measured data was used to refine strain limit recommendations. Particular attention was paid to the limit state of longitudinal bar buckling, since it limited the deformation capacity of all of the cyclically loaded specimens. Empirical expression were developed to predict the compressive strain at cover crushing, the compressive strain at spiral yielding, and the peak tensile strain prior to visible buckling after reversal of loading. In design, limit state curvatures are converted to target displacements using an equivalent curvature distribution. The Modified Plastic Hinge Method was developed to improve the accuracy of strain-displacement predictions. Key aspects of the proposed model which differentiate it from the current method include: (1) a decoupling of column flexure and strain penetration deformation components, (2) a linear plastic curvature distribution which emulates the measured curvature profiles, and (3) separate plastic hinge lengths for tensile and compressive strain-displacement predictions. In the experiments, the measured extent of plasticity was found to increase due to the combined effects of moment gradient and tension shift. The proposed tension hinge length was calibrated to match the upper bound of the measured spread of palsticity. The proposed compressive hinge length only contains a term related to the moment gradient effect. Expressions which describe the additional column deformation due to strain penetration of reinforcement into the adjoining member were developed. When compared to the current technique, the Modified Plastic Hinge Method improved the accuracy of both tensile and compressive strain-displacement predictions. Abstract for Volume 3: This report presents the numerical portion of the research project on the impacts of loading history on the behavior of reinforced concrete bridge columns. In well-detailed reinforced concrete structures, reinforcing bar buckling and subsequent bar rupture serve as common failure mechanisms under extreme seismic events. Engineers often use a strain limit state which is associated with bar buckling as the ultimate limit state, but the relationship between the strain demand and resultant bar buckling is not well understood. Past research has indicated large impact of the cyclic loading history on the strain demand to achieve reinforcing bar buckling. On the other hand, sectional analysis is widely implemented by engineers to relate strain to displacement. However, the cyclic load history also has potential impact on the relationship between strain limits and displacement limits. As a result, it is important to study the seismic load history effect on the strain limit state of reinforcing bar buckling and on the relationship between local strain and structural displacement. In addition, Performance-Based Earthquake Engineering (PBEE) strongly depends on an accurate strain limit definition, so a design methodology needs to be developed to identify the strain limit for reinforcing bar buckling including the seismic load history effect. Two independent finite element methods were utilized to accomplish the goal of this research work. First, fiber-based analysis was utilized which employed the Open System for Earthquake Engineering Simulation (OpenSees). The fiber-based method was selected because of its accuracy in predicting strains and its computational efficiency in performing nonlinear time history analysis (NTHA). The uniaxial material models in fiber-based sections were calibrated with data from material tests. In addition, strain data and force-deformation response from large scale testing assists selection of element types and integration schemes to ensure accuracy. The advanced beam-column elements and material models in OpenSees resulted in a very accurate prediction of strain at local sections as well as global dynamic response of structures. A number of nonlinear time history analyses with 40 earthquake ground motions were conducted to investigate the effect of seismic load history on relationship between structural displacement and strain of extreme fiber bars at the critical section. The second finite element model was established with solid elements to predict bar buckling. The model included a segment of reinforcing bar and its surrounding elements, such as spiral turns and concrete. This model separates itself from previous bar buckling research by utilizing actual sectional detailing boundary conditions and plastic material models instead of the simplified bar-spring model. The strain history is considered as the demand on this model. A series of strain histories from the experimental tests and fiber-based analyses were applied to the finite element model to study their impacts on the strain limit for reinforcing bar buckling. Initial analytical investigations have shown significant impact of load history on the strain demand to lead to reinforcing bar buckling in the plastic hinge region. This is also confirmed in the experimental observation which only included a limited number of load histories. The parametric study extended the range of load history types and also studied the effect of reinforcement detailing on bar buckling. On the other hand, analyses with fiber-based models showed that the load history rarely impacts the relationship between local strain and structural displacement. A design approach was developed to include the load history effect on the strain limit state of bar buckling.en_US
dc.description.tableofcontentsVolume I: LIST OF TABLES __________________________________________________ xv LIST OF SELECTED NOTATIONS _________________________________ xxxii Chapter 1: Introduction _______________________________________________ 1 1.1 Background – Performance Limit States ______________________ 1 1.2 The Need for Research ___________________________________ 3 1.3 Research Goals and Scope _________________________________ 5 Chapter 2: Test Setup, Instrumentation, Construction, and Text Matrix ______ 6 2.1 Test Setup _____________________________________________ 6 2.2 Test Matrix ____________________________________________ 13 2.3 Instrumentation ________________________________________ 16 2.4 Construction Process ____________________________________ 22 2.4.1 Construction Sequence ______________________________________ 23 2.4.2 Optotrak Target Marker Application Method _____________________ 39 Chapter 3: Experimental Observations _________________________________ 41 3.1 Contents of Report Volume 2 _____________________________ 41 Chapter 4: The Effect of Load History on Column Performance ____________ 43 4.1 Introduction ___________________________________________ 43 4.1.1 Test Setup ________________________________________________ 46 4.1.2 Instrumentation ____________________________________________ 50 4.1.3 Loading Protocol ___________________________________________ 51 4.2 Experimental Results ____________________________________ 55 4.2.1 Damage Observations _______________________________________ 55 4.2.2 Test 11 – Response to the Kobe 1995 Earthquake _________________ 55 4.2.3 The Effect of Load History on Reinforcement Bar Buckling _________ 58 4.3 Spread of Plasticity _____________________________________ 63 4.3.1 Test 16 – Deformation Components Three Cycle Set Load History with #3 Spiral at 1.5” (38mm) _______________________________________ 63 4.3.2 Measured Spread of Plasticity _________________________________ 69 4.4 Conclusions ___________________________________________ 70 Chapter 5: Impact of Steel Content, Aspect Ratio, and Axial Load Ratio on Column Performance ________________________________________________ 72 5.1 Test Setup and Instrumentation ____________________________ 73 5.2 Symmetric Three-Cycle-Set Loading Protocol ________________ 75 5.3 Gradual Bar Buckling Mechanism with Inelastic Transverse Steel Restraint ______________________________________________ 78 5.3.1 North Reinforcement ________________________________________ 79 5.3.2 South Reinforcement ________________________________________ 81 5.4 Transverse Steel Detailing Variable Experiments ______________ 85 5.5 Aspect Ratio Variable Experiments _________________________ 90 5.6 Longitudinal Steel Content Variable Experiments _____________ 92 5.7 Axial Load Ratio Variable Experiments _____________________ 95 5.8 Equivalent Viscous Damping _____________________________ 98 5.9 Conclusions __________________________________________ 102 Chapter 6: Bridge Column Response Prediction Techniques ______________ 104 6.1 Background and Motivation _____________________________ 104 6.1.1 Experimental Program ______________________________________ 104 6.2 Measured Deformation Components _______________________ 107 6.3 Response Prediction Methods ____________________________ 111 6.3.1 Sectional Response Prediction _______________________________ 112 6.3.2 Member Response Prediction ________________________________ 113 6.3.3 Motivation for a New Equivalent Curvature Distribution ___________ 116 Chapter 7: Modified Plastic Hinge Method _____________________________ 118 7.1 Goals for the Modified Plastic Hinge Method ________________ 118 7.2 Deformation due to Strain Penetration of Reinforcement into Adjoining Members ____________________________________ 120 7.3 Tensile and Compressive Plastic Hinge Lengths _____________ 128 7.4 Tensile Strain-Displacement Predictions using the Modified Plastic Hinge Method ________________________________________ 149 7.5 Compressive Strain-Displacement Predictions using the Modified Plastic Hinge Method __________________________________ 152 7.6 Elastic Force-Deformation Predictions using the Modified Plastic Hinge Method ________________________________________ 157 7.7 Conclusion ___________________________________________ 160 Chapter 8: Performance Strain Limits for Circular Bridge Columns _______ 183 8.1 Background __________________________________________ 183 8.2 Experimental Program __________________________________ 186 8.2.1 Loading Protocol __________________________________________ 188 8.3 Observed Damage Sequence _____________________________ 189 8.4 Equation to Predict Peak Tension Strain Prior to Bar Buckling Upon Reversal of Load ______________________________________ 193 8.5 Column Deformation at Peak Tensile Strain Prior to Bar Buckling ____________________________________________________ 197 8.6 Berry (2006) Statistical Drift-Based Bar Buckling Model for Circular Bridge Columns _______________________________________ 200 8.7 Berry (2006) Bar Buckling Model Applied to the Goodnight et al. Dataset ______________________________________________ 202 8.8 Evaluation of Strain Based Bar Buckling Predictions for the Berry (2006) Dataset ________________________________________ 204 8.9 Drift Based Approach Considering Combined Berry (2006) and Goodnight et al. Datasets ________________________________ 208 8.10 Feng (2013) Bar Buckling Strain Limit Expressions from Finite Element Analysis ______________________________________ 211 8.11 Bar Buckling Predictions for the Combined Berry (2006) and Goodnight et al. Dataset ________________________________ 221 8.12 Evaluation for Full Scale Column Experiments by Cheok and Stone (1989) _______________________________________________ 223 8.13 Compressive Strain at Cover Concrete Crushing _____________ 226 8.14 Compressive Strain at Spiral Yielding in Confinement Regions of the Column ______________________________________________ 227 8.15 Residual Crack Widths _________________________________ 232 8.16 Conclusion ___________________________________________ 234 Chapter 9: Design Recommendations for Limit State Displacements ________ 238 9.1 Performance Strain Limits _______________________________ 238 9.1.1 Serviceability Limit States __________________________________ 239 9.1.2 Intermediate Compressive Limit State _________________________ 239 9.1.3 Damage Control Limit States ________________________________ 240 9.2 Modified Plastic Hinge Method ___________________________ 244 9.2.1 Strain Penetration Length and Tension/Comp. Plastic Hinge Lengths _ 248 9.2.2 Elastic Displacements for a Column in Single Bending ____________ 249 9.2.3 Elastic Displacements for a Column in Double Bending ___________ 249 9.2.4 Inelastic Displacements for a Column in Single Bending ___________ 250 9.2.5 Inelastic Displacements for a Column in Double Bending __________ 250 Chapter 10: Future Research on the Effects of Seismic Load Path __________ 251 10.1 Problem Statement _____________________________________ 251 10.2 Background __________________________________________ 251 10.3 Brief Load Path Literature Review ________________________ 260 10.3.1 Yuk-Lung Wong, T. Paulay, and M. J. Nigel Priestley (1993). “Response of Circular Reinforced Concrete Columns to Multi-Directional Seismic Attack” __________________________________________________ 260 10.3.2 E. Osorio, J.M. Bairán, and A.R. Marí (2012). “Effects of Biaxial Shear Loading on the Seismic Response of RC Columns” _______________ 261 10.3.3 Kazuhiro Tsuno and Robert Park (2004). “Experimental Study of Reinforced Concrete Bridge Piers Subjected to Bi-Directional Quasi-Static Loading” ________________________________________________ 263 10.3.4 Stathis N. Bousias, Guido Verzeletti, Michael N. Fardis, Eugenio Gutierrez (1995). “Load Path Effects in Column Biaxial Bending with Axial Force” 266 10.4 Study Objectives ______________________________________ 268 10.5 Research Plan _________________________________________ 268 10.5.1 Task One: Detailed Literature Review _________________________ 268 10.5.2 Task Two: Load Path Analysis _______________________________ 269 10.5.3 Task Three: Experimental Studies on Columns __________________ 269 10.5.4 Task Four: Analysis of Data and Model Calibration _______________ 274 10.5.5 Task Five: Recommendations ________________________________ 274 REFERENCES ____________________________________________________ 275 Volume 2: LIST OF TABLES ___________________________________________________ x LIST OF SELECTED NOTATIONS __________________________________ xiv Chapter 1: Experimental Observations __________________________________ 1 1.1 Load History Variable Tests 8-12 ___________________________ 1 1.1.1 Test 9 – Symmetric Three Cycle Set Load History __________________ 6 1.1.2 Tests 8 and 8b – Chile 2010 Earthquake and Cyclic Aftershock LH ___ 35 1.1.3 Tests 10 and 10b – Chichi Earthquake and Cyclic Aftershock LH _____ 61 1.1.4 Test 11 – Kobe 1995 Earthquake Load History ___________________ 89 1.1.5 Test 12 – Japan 2011 Earthquake Load History __________________ 108 1.2 Load History and Transverse Steel Variable Tests 13-18 _______ 131 1.2.1 Test 13 –Three Cycle Set Load History with #4 Spiral at 2.75” (1.3%) 135 1.2.2 Test 14 –Three Cycle Set Load History with #3 Spiral at 4” (0.5%) __ 160 1.2.3 Test 15 – Three Cycle Set Load History with #3 Spiral at 2.75” (0.7%) 187 1.2.4 Test 16 – Three Cycle Set Load History with #3 Spiral at 1.5” (1.3%) 215 1.2.5 Test 17 – Chile 1985 Earthquake LH with #3 Spiral at 1.5” (1.3%) ___ 241 1.2.6 Test 18 – Darfield NZ 2010 EQ LH with #3 Spiral at 1.5” (1.3%) ____ 274 1.3 Aspect Ratio and Axial Load Variable Tests 19-24 ___________ 304 1.3.1 Test 19 – Aspect Ratio of 5.33 and 10% Axial Load ______________ 308 1.3.2 Test 20 – Aspect Ratio of 5.33 and 5% Axial Load _______________ 336 1.3.3 Test 21 – Aspect Ratio of 7.33 and 5% Axial Load _______________ 365 1.3.4 Test 22 – Aspect Ratio of 7.33 and 10% Axial Load ______________ 395 1.3.5 Test 23 – Aspect Ratio of 8.67 and 5% Axial Load _______________ 425 1.3.6 Test 24 – Aspect Ratio of 8.67 and 10% Axial Load ______________ 455 1.4 Steel Content and Axial Load Variable Tests 25-30 ___________ 488 1.4.1 Test 25 – 24” Dia. Column with 2.1% Long. Steel and 5% Axial Load 492 1.4.2 Test 26 – 24” Dia. Column with 2.1% Long. Steel and 10% Axial Load 525 1.4.3 Test 27 – 24” Dia. Column with 1.6% Long. Steel and 10% Axial Load 561 1.4.4 Test 28 – 18” Dia. Column with 1.7% Long. Steel and 15% Axial Load 598 1.4.5 Test 29 – 18” Dia. Column with 1.7% Long. Steel and 20% Axial Load 635 1.4.6 Test 30 – 18” Dia. Column with 3.1% Long. Steel and 15% Axial Load 671 Chapter 2: Weldability of A706 Reinforcing Steel _______________________ 707 2.1 Test 7 and Weldability of A706 Reinforcing Steel ____________ 707 2.2 A706 Steel Properties and Weldability for Tests 1-6 and 7-12 ___ 712 2.3 Conclusion ___________________________________________ 713 Chapter 3: Summary of Column Tests 1-6 ______________________________ 717 3.1 Test Setup and Instrumentation for Specimens 1-6 ____________ 717 3.2 Test 1: Pushover Load History ___________________________ 720 3.3 Test 2: Three-Cycle-Set with Full Cover Concrete ____________ 722 3.4 Test 3: Three-Cycle-Set with Cover Blockouts _______________ 727 3.5 Test 4: 1940 El Centro Earthquake Load History _____________ 731 3.6 Test 5: 1978 Tabas Earthquake Load History ________________ 737 3.7 Test 6: 1978 Tabas Earthquake Load History ________________ 744 REFERENCES ____________________________________________________ 748 Volume 3: Chapter 1: Introduction ____________________________________________________ 1 1.1 Background and Scope ___________________________________________ 1 1.2 Layout of Report ________________________________________________ 2 Chapter 2: Literature Review _______________________________________________ 3 2.1 General Discussion ______________________________________________ 3 2.2 Relevant Articles on Numerical Simulation ___________________________ 3 2.2.1 Fiber-Based Modeling of Reinforced Concrete Members ____________ 3 2.2.2 Finite Element Method for Reinforcing Bar Buckling _______________ 8 2.3 Chapter Summery _______________________________________________ 9 Chapter 3: Fiber-Based Modeling of Circular Reinforced Concrete Bridge Columns 10 3.1 Introduction and Background _____________________________________ 10 3.2 Theory of Fiber-Based Modeling __________________________________ 12 3.3 Proposed methods for simulating RC bridge columns __________________ 18 3.3.1 Experimental Observation ____________________________________ 18 3.3.2 Proposed Method to Predict Strain Gradient ______________________ 22 3.3.3 Method to Include Strain Penetration ___________________________ 26 3.3.4 Benchmark Method to Capture Nonlinearity in RC Member with Fiber-Based Model 29 3.4 Calibration and Application of the Fiber Model _______________________ 30 3.4.1 Calibration on Material Constitutive Models _____________________ 31 3.4.2 Prediction on Force and Strain from Static Tests __________________ 32 3.4.3 Prediction on Response of Shake Table Tests _____________________ 42 3.5 Chapter Conclusions ____________________________________________ 44 Chapter 4: Load History Effect on Relationship between Strain and Displacement __ 45 4.1 General Discussion _____________________________________________ 45 4.2 Ground Motion Selection ________________________________________ 45 4.3 Parametric Study _______________________________________________ 51 4.3.1 Strain Comparison for Column #1______________________________ 54 4.3.2 Strain Comparison for Column #2______________________________ 56 4.3.3 Strain Comparison for Column #3______________________________ 57 4.3.4 Strain Comparison for Column #4______________________________ 58 4.3.5 Strain Comparison for Column #5______________________________ 59 4.3.6 Strain Comparison for Column #6______________________________ 60 4.3.7 Strain Comparison for Column #7______________________________ 61 4.3.8 Strain Comparison for Column #8______________________________ 62 4.4 Chapter Summary ______________________________________________ 63 Chapter 5: Development of Finite Element Model for Bar Buckling ______________ 64 5.1 Introduction ___________________________________________________ 64 5.2 Research Objective _____________________________________________ 66 5.3 Experimental Observation on Inelastic Bar Buckling upon Reversal of Loading 67 5.4 Theoretical Inelastic Column Buckling upon Reversal of Loading ________ 69 5.5 Theoretical Case Study on Inelastic Bar Buckling _____________________ 69 5.6 Fiber-Based Modeling of Reinforced Concrete Structures _______________ 73 5.7 Proposed Finite Element Bar Buckling Model (Strain-Based) ____________ 77 5.7.1 Goal of Simulation__________________________________________ 77 5.7.2 Geometric Detailing and Boundary Conditions ___________________ 77 5.7.3 Material Models ____________________________________________ 80 5.7.4 Interactions _______________________________________________ 83 5.7.5 Loading Method ___________________________________________ 83 5.8 Model Validation ______________________________________________ 87 5.8.1 Introduction of Test Results __________________________________ 87 5.8.2 Comparison between Model Prediction and Observation of North Bar from Test B 90 5.8.3 Comparison between Model Prediction and Observation of South Bar from Test B 97 5.8.4 Comparison between Model Prediction and Observation of North Bar from Test A 101 5.9 Summary of Findings __________________________________________ 109 5.10 Chapter Conclusions ___________________________________________ 111 Chapter 6: Deformation Limit States for Longitudinal Bar Buckling ____________ 113 6.1 Introduction __________________________________________________ 113 6.2 Finite Element Model to Capture Bar Buckling ______________________ 114 6.3 Selection of Ground Motions ____________________________________ 115 6.4 Impact of Load History on Buckling Mechanism _____________________ 119 6.4.1 Load History Analysis Results _______________________________ 120 6.4.2 Key Findings from Load History Analysis Results ________________ 126 6.5 Parametric Study on Bar Buckling ________________________________ 130 6.6 Proposed Equations for Bar Buckling Strain Limit State _______________ 135 6.6.1 Comparison of Proposed Model to Tests Conducted at NCSU _______ 137 6.7 Application of the Design Equation _______________________________ 143 6.8 Comparison to Structural Performance Database _____________________ 148 6.9 Chapter Conclusions ___________________________________________ 150 Chapter 7: Conclusions __________________________________________________ 152 7.1 General Discussion ____________________________________________ 152 7.2 Load History Effect on Relationship between Strain and Displacement ___ 154 7.3 Load History Effect on the Strain Limit for Bar Buckling ______________ 155 REFERENCES _________________________________________________________ 156 APPENDICES __________________________________________________________ 162en_US
dc.language.isoen_USen_US
dc.subjectSeismicen_US
dc.subjectreinforced concreteen_US
dc.subjectstrain limitsen_US
dc.subjectbucklingen_US
dc.subjectperformance-based designen_US
dc.subjectbridge designen_US
dc.subjectplastic hinge lengthsen_US
dc.titleThe Effects of Load History and Design Variables on Performance Limit States of Circular Bridge Columnsen_US
dc.typeTechnical Reporten_US
refterms.dateFOA2020-01-25T02:18:00Z


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