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Bond-slip Model to Capture Strain Penetration Effects |
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| Validation of bar stress vs. slip model: |
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The applicability of the material model to describe the bar stress vs. loaded-end slip response under monotonic loading is demonstrated below by comparing experimental data from two bar pull-out tests with the corresponding theoretical curves. The parameters used to define the theoretical curves are included in the figure. A good agreement is seen between the theoretical curves and experimental data, indicating that the model is capable of capturing the strain penetration effects in the analytical simulation of concrete flexural members. Nevertheless, the determination of the model parameters needs further investigation. |
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A bridge tee-joint system (specimen IC1) tested in an inverted position by Sritharan et al. was studied to verify the feasibility of the proposed model for analyzing a structural system. This specimen with a conventional reinforced concrete cap beam evaluated a new design method suitable for bridge cap beam-to-column joints. Under constant axial load of 90 kips, the column was subjected to cyclic lateral loading at a height of 72 in. above the column-to-cap beam interface. The yield lateral displacement for the tee-joint system was reported to be 0.67 in. with the corresponding lateral resistance of 56 kips. The test joint experienced strength deterioration at lateral displacement of 4 in. due to formation of large joint cracks and subsequent joint damage. |
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| Example: bridge Tee-joint system: |
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The simulation model included six fiber-based beam-column elements for the cap beam and four beam-column elements for the column. An additional fiber-based beam-column element with the elastic column section properties modeled the joint. The zero-length section element is located between this elastic element and the adjoining column element.
The analysis, which included the strain penetration effects, produced force-displacement response that closely matched with the measured response in both loading directions. The analysis that did not include the strain penetration effects overestimated both the lateral load resistance and the unloading-reloading stiffness. Furthermore, the analysis that ignored the strain penetration effects overestimated the column end curvature by approximately 90% towards the end of the test, indicating that the bar slip due to strain penetration greatly affects the local response measures that are indicative of damage to the plastic hinge region. A significant improvement to the moment-curvature response prediction was obtained when the analysis included the strain penetration effects.
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| Examples: short rectangular column |
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The short rectangular column (specimen U6) was designed and tested by Saatcioglu and Ozcebe. The testing of this column was part of a study that evaluated the effects of confinement reinforcement specified in ACI 318-83 on the ductility capacity of short columns. The column had a square cross section and a clear height of 40 in. above the footing. The column was modeled using five fiber-based beam-column elements.
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| Examples: circular column |
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The circular column tested by Smith served as the reference column for an investigation on strategic relocation of plastic hinges in bridge columns. This column had a clear height of 144 in. above the column footing. Under constant axial load of 400 kips, the column was loaded cyclically. The failure of the column occurred due to fracture of the longitudinal bars at the column base, after attaining lateral displacement of 13 in. with a lateral resistance of 80 kips. The column model contained five fiber-based beam-column elements.
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| Examples: concrete walls |
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The simulation work is part of a PreNEESR project headed by Dr. Cathy French of the University of Minnesota, Dr. Sri Sritharan of Iowa State University, and Dr. Ricardo Lopez of the University of Puerto Rico – Mayaguez. Details of the tests of the walls can be found here. The lateral displacement due to an applied lateral load can be broken down into the contributions from various components. The flexural deformation of the wall contributes to the displacement, shear deformation contributes some of the displacement. P-Delta effects from the axial load also adds displacement. Additionally, at the wall foundation interface strain penetrating in the foundation causes crushing between the lugs of the reinforcement and localized slip. This slip causes rotation at the base of the wall adding to the displacement. |
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| The walls analyzed were tested by Thomsen and Wallace. The wall is modeled in OpenSees using force based nonlinear beam column elements, for the wall height and a zero-length element to model the interface between the wall and foundation. The model includes the P-Delta effects from the axial load, but not deformation due to shear. In the zero-length interface element the reinforcement fibers are replaced with a strain penetration material that uses the model developed by Zhao and Sritharan. This material relates the stress in the bar to the slip at the wall foundation interface. It is available in the current version of OpenSees. The reinforcement is modeled using a modified Menegotto-Pinto model that includes isotropic strain hardening. The confined concrete is modeled using a Kent-Park model with nonlinear tension softening. The confined concrete properties such as peak stress and strain and ultimate stress and strain were calculated using Mander’s confined concrete model and the transverse reinforcement details. The unconfined concrete was modeled using the same Kent-Park model with nonlinear tension softening, however the peak stress and strain, and ultimate stress and strain were chosen to reflect the behavior of unconfined concrete.  
RW2 was a 48 in long. 4 inch think wall that was 12 feet tall.
TW2 had a 48 inche wide, 4 inch thick flange and a 48 inch long, 4 inch think web. Simulation of the walls tested in UMN-MAST …. |
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