• The Effects of Load History and Design Variables on Performance Limit States of Circular Bridge Columns

      Goodnight, Jason Chad; Feng, Yuhao; Kowalsky, Mervyn J.; Nau, James M. (2015-01)
      This 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.