The University of Akron IdeaExchange@UAkron Honors Research Projects The Dr. Gary B. and Pamela S. Williams Honors College Spring 2015 Parametric Study of Self-Centering Concentrically- Braced Frames in Response to Earthquakes Nicholas F. Roth The University Of Akron, nfr3@zips.uakron.edu Please take a moment to share how this work helps you through this survey. Your feedback will be important as we plan further development of our repository. Follow this and additional works at: http://ideaexchange.uakron.edu/honors_research_projects Part of the Civil Engineering Commons, Dynamics and Dynamical Systems Commons, Other Engineering Commons, and the Structural Engineering Commons Recommended Citation Roth, Nicholas F., "Parametric Study of Self-Centering Concentrically-Braced Frames in Response to Earthquakes" (2015). Honors Research Projects. 64. http://ideaexchange.uakron.edu/honors_research_projects/64 This Honors Research Project is brought to you for free and open access by The Dr. Gary B. and Pamela S. Williams Honors College at IdeaExchange@UAkron, the institutional repository of The University of Akron in Akron, Ohio, USA. It has been accepted for inclusion in Honors Research Projects by an authorized administrator of IdeaExchange@UAkron. For more information, please contact mjon@uakron.edu, uapress@uakron.edu.
Nicholas F. Roth Department of Civil Engineering Honors Research Project Submitted to The Honors College
Abstract: This research project consisted of the use of computer aided numerical software to test the response of an earthquake resistance system within various buildings when exposed to various design-level earthquakes. This research project is an extension of an existing NSF research project. The relevant questions and investigations of this and the greater project surround the performance of an earthquake resistance system with the intentions of better understanding its abilities and limitations. This project has been aided by Dr. David Roke, the faculty sponsor, in order to perform the research and collect, organize, and analyze the data. This research was performed using the software package OpenSees and the data was organized and analyzed using Microsoft Excel. Ultimately, the goal of this project is to aid in the NSF research project in any way possible. Ideally, this project will help with the determination of different design parameters of the earthquake resistance system. Although specific parameters were not established within this project, a few identifiable trends were. Observation of the studied data concludes that decreasing the self-centering concentrically-braced frame s tributary area also decreases, on average, the resultant force responses within the frame. Correspondingly, increasing the structure s (and therefore the frame s) height also produces a decrease in the resultant force responses. Another topic of interest is the location of the maximum brace force within the frame. The investigated data suggests that the maximum brace force will be at or just above the middle of the structure as the structure height increases, so does the location of the maximum force above the structure s center. Not all of the described trends are clearly intuitive. Further research on the topic of the maximum brace force may provide more insight into where the location of the maximum force will occur and why. Also, further study on the relationship of the structure s height to the experienced forces may provide conclusions as to what causes the described phenomenon. 1
Table of Contents: Abstract:...1 List of Figures:...3 List of Tables:...4 Background and Purpose:...5 OpenSees:...7 6-Story Building:...12 10-Story Building:...18 6-Story Reduced Area Building:...23 10-Story Reduced Area Building:...28 Comparisons, Correlations, and Conclusions:...33 References:...37 2
List of Figures: Figure 1: SC-CBF Geometry... 5 Figure 2: Example Output Geometry... 7 Figure 3: Typical Building Cross-Section... 8 Figure 4: 6-Story La01 Normalized Story Drift... 12 Figure 5: 6-Story La01 Normalized Roof Drift... 12 Figure 6: 6-Story La01 PT Bar Axial Force... 13 Figure 7: 6-Story La01 Normalized PT Bar Force... 14 Figure 8: 6-Story La01 Brace Force Results... 15 Figure 9: 6-Story La01 First Story Brace Force Results... 16 Figure 10: 10-Story La01 Normalized Roof Drift... 18 Figure 11: 10-Story La01 PT Bar Axial Force... 19 Figure 12: 10-Story La01 Normalized PT Bar Force... 19 Figure 13: 10-Story La01 Brace Force Results... 20 Figure 14: 10-Story La01 First Story Brace Force Results... 21 Figure 15: 6-Story Reduced Area La01 Normalized Roof Drift... 23 Figure 16: 6-Story Reduced Area La01 Normalized PT Bar Force... 24 Figure 17: 6-Story Reduced Area La01 Brace Force Results... 25 Figure 18: 6-Story Reduced Area La01 First Story Brace Force Results... 26 Figure 19: 10-Story Reduced Area La01 Normalized Roof Drift... 28 Figure 20: 10-Story Reduced Area La01 Normalized PT Bar Force... 29 Figure 21: 10-Story Reduced Area La01 Brace Force Results... 30 Figure 22: 10-Story Reduced Area La01 First Story Brace Force Results... 31 Figure 23: Normalized Roof Drift Comparison... 33 Figure 24: Normalized PT Bar Force Comparison... 34 Figure 25: Normalized Brace Force Comparison... 35 3
List of Tables: Table 1: Example OpenSees Displacement Output (6-Story)... 9 Table 2: Example OpenSees PT Force Output (6-Story)... 10 Table 3: Example OpenSees Brace Force Output (6-Story)... 11 Table 4: 6-Story La01 Normalized Drift Summary... 13 Table 5: 6-Story La01 Brace Force Summary... 14 Table 6: 6-Story Master Data Summary... 17 Table 7: 10-Story La01 Normalized Drift Summary... 18 Table 8: 10-Story La01 Brace Force Summary... 20 Table 9: 10-Story Master Data Summary... 22 Table 10: 6-Story Reduced Area La01 Normalized Drift Summary... 23 Table 11: 6-Story Reduced Area La01 Brace Force Summary... 24 Table 12: 6-Story Reduced Area Master Data Summary... 27 Table 13: 10-Story Reduced Area La01 Normalized Drift Summary... 28 Table 14: 10-Story Reduced Area La01 Brace Force Summary... 29 Table 15: 10-Story Reduced Area Master Data Summary... 32 4
Background and Purpose: Earthquakes can easily destroy and damage buildings. The number one consideration today in earthquake design of structures is, of course, the preservation of human life. Today this goal is achieved mostly through designing buildings to stay standing during and after an earthquake. A building that survives an earthquake is a building that preserves human life. However, one major downfall of the current design method is that the buildings usually suffer a great deal of structural damage that may be beyond repair. Therefore, even if a building survives an earthquake it may have to be torn down afterwards and rebuilt. This process is very expensive and time consuming. The ideal situation would be that buildings are able to survive earthquakes and suffer only minor damage (or none at all). This level of performance would not only preserve human life but also save time and money. The earthquake resistance system being tested here will hopefully allow buildings to achieve such high levels of performance during earthquakes. This system, called a self-centering concentrically-braced frame (SC-CBF) is pictured in Figure 1 (Sause et al. 2010). Figure 1: SC-CBF Geometry (Sause et al. 2010) The general concept of the SC-CBF is that it is a rigid frame that will be placed between certain gravity columns of a building (as noted in Figure 1). The building columns will still act as the gravity supports as they usually do, but the rigid frame will provide lateral support during an earthquake. However, this frame not only provides lateral support but also provides a means by which to dissipate energy through friction. Friction bearing dampers are placed between the SC-CBF columns and the building gravity columns, as depicted in Figure 1. As the building sways back and forth during an earthquake, the resistance frame will rock up and down along the columns of the building, thus dissipating a great deal of energy through friction. This is a critical component of the whole system because removing energy from the system helps to remove motion from the system, the main concern of earthquakes. The less motion the building experiences during an earthquake, the less damage the building accumulates during an earthquake. This thought process is the logic behind the system as a whole. From here, the primary focus shifts to learning exactly how the system performs. 5
As previously stated, this research project focuses on the testing of the system using computer aided numerical software. A few main questions of concern exist: How does the performance of the SC-CBF change as the building height changes? How does the performance of the SC-CBF change as the building mass changes? Do any other noticeable correlations exist between the building and the SC-CBF s performance? In order to address these questions, a few key scenarios were coded and tested. A 6-story building with a total of eight SC-CBFs (four along each building axis) was first tested. Second, the SC-CBFs were tested in a 10-story building. Last, the 6- and 8-story scenarios were both tested again but with the addition of four more SC-CBFs in each structure (two additional SC-CBFs along each building axis). All in all, the answers to these and other questions will help to further establish design parameters of the SC-CBF. These parameters may not be directly established within this specific research project; however, this research should help to move one step closer to those answers. 6
OpenSees: OpenSees is the primary means by which the research has been conducted. OpenSees is an object-oriented framework for finite element analysis (Mazzoni et al. 2000). This program has been designed for the research community as it is a very flexible and versatile framework built on a foundational main code that uses a specific language called Transaction Control Language (TCL). OpenSees allowed for the creation of the coding for the specific cases in which the SC-CBF was tested. Dr. Roke has, mainly, provided those codes for this project. In order to model the SC-CBF, several things had to be considered and included into each program. First, all of the steel member sections, including the materials and section properties, had to be defined and assigned within the program (units of kip, in, s). All of the corresponding dimensions and properties for each section were input into each specific program and connected with each element of each specific type. The corresponding floor masses were also assigned at each floor level. Next, the SC-CBF geometry was input, including the relevant boundary conditions. One significant aspect to note is that of the lean on column (LOC). The LOC is essentially what the SC-CBF and adjacent gravity columns are connected to or lean onto, and represents the mass of the entire building. Figure 2 shows an example of the program geometry output once the program is running. LOC SC-CBF Figure 2: Example Output Geometry (6-Story) The geometry shown is for the 6-story building. In Figure 2, the LOC is to the left of the SC-CBF, though its actual location is arbitrary. For simplicity s and time s sake, symmetry was taken advantage of, and only onequarter of each structure was modelled. Therefore, one frame was modelled with one LOC representing onequarter of the mass of the entire structure. Figure 3 shows a typical floor plan of each building (non-reduced area). 7
Figure 3: Typical Building Cross-Section (Sause, R. et al. 2010) (The square highlights the quarter of the building modelled. The oval indicates the SC-CBF modelled.) The square in Figure 3 shows the quarter of the building that was modelled. All of the mass of the building within the square is represented by the LOC in Figure 2. The oval in Figure 3 highlights the position of the SC-CBF and is identical to the SC-CBF in Figure 2. Note that, in Figure 3, another SC-CBF exists within the square. Since these frames are designed to resist lateral loads within the building, they are placed perpendicular to each other; each frame only resists lateral loads acting parallel to itself. So, only one frame needs to be modelled since the other frame would produce identical results in the perpendicular direction through symmetry. This is the general format in which all of the test cases were set up in OpenSees. In addition to a change in the structure of the different test cases, twenty different design-level earthquakes were used for each case. Each earthquake produces a unique response from the SC-CBF. An average response can then be produced from the compilation of the results from each design earthquake. These averages will better help to compare between the various test cases. OpenSees was able to produce a lot of information about the SC-CBFs, but it must be post-processed for use in this research. The relevant output information that OpenSees gives was pasted into Excel and further organized and interpreted there. The output information that is relevant to this project includes the lateral displacements, the post-tensioning (PT) bar forces, and the brace forces. The PT bars are indicated in Figure 1, and the braces are the diagonal members within the frames in Figures 1 and 2. Table 1 shows the lateral displacement outputs for the first half-second of earthquake response only (since the output file is so large) of the 6-story structure during the first design earthquake (La01) as an example of a typical output. Table 2 shows a typical output of the PT force during La01 of the 6-story structure, and Table 3 shows a typical output of the brace force during La01 of the 6- story structure (only the first segment of the left brace on the first story is shown since the output is so large). All of these outputs have already been pasted into Excel and are presented from there. The specific results of each case can be found in their respective sections. 8
Table 1: Example OpenSees Displacement Output (6-Story) (Only the first half-second is displayed) 9
PT Forces Time Axial i Y Shear i Z Shear i Torsion i My i Mz i Axial j Y Shear j Z Shear j Torsion j My j Mz j 0.00-910.82 0.00 0.00 0.00 0.00 0.00 910.82 0.00 0.00 0.00 0.00 0.00 0.02-964.56 0.00 0.00 0.00 0.00 0.00 964.56 0.00 0.00 0.00 0.00 0.00 0.04-998.46 0.00 0.00 0.00 0.00 0.00 998.46 0.00 0.00 0.00 0.00 0.00 0.06-953.09 0.00 0.00 0.00 0.00 0.00 953.09 0.00 0.00 0.00 0.00 0.00 0.07-955.90 0.00 0.00 0.00 0.00 0.00 955.90 0.00 0.00 0.00 0.00 0.00 0.07-976.97 0.00 0.00 0.00 0.00 0.00 976.97 0.00 0.00 0.00 0.00 0.00 0.07-986.00 0.00 0.00 0.00 0.00 0.00 986.00 0.00 0.00 0.00 0.00 0.00 0.08-989.56 0.00 0.00 0.00 0.00 0.00 989.56 0.00 0.00 0.00 0.00 0.00 0.08-989.46 0.00 0.00 0.00 0.00 0.00 989.46 0.00 0.00 0.00 0.00 0.00 0.08-988.20 0.00 0.00 0.00 0.00 0.00 988.20 0.00 0.00 0.00 0.00 0.00 0.08-982.98 0.00 0.00 0.00 0.00 0.00 982.98 0.00 0.00 0.00 0.00 0.00 0.10-964.03 0.00 0.00 0.00 0.00 0.00 964.03 0.00 0.00 0.00 0.00 0.00 0.12-981.91 0.00 0.00 0.00 0.00 0.00 981.91 0.00 0.00 0.00 0.00 0.00 0.13-978.22 0.00 0.00 0.00 0.00 0.00 978.22 0.00 0.00 0.00 0.00 0.00 0.14-969.51 0.00 0.00 0.00 0.00 0.00 969.51 0.00 0.00 0.00 0.00 0.00 0.16-977.38 0.00 0.00 0.00 0.00 0.00 977.38 0.00 0.00 0.00 0.00 0.00 0.17-977.72 0.00 0.00 0.00 0.00 0.00 977.72 0.00 0.00 0.00 0.00 0.00 0.18-972.81 0.00 0.00 0.00 0.00 0.00 972.81 0.00 0.00 0.00 0.00 0.00 0.20-975.48 0.00 0.00 0.00 0.00 0.00 975.48 0.00 0.00 0.00 0.00 0.00 0.22-974.60 0.00 0.00 0.00 0.00 0.00 974.60 0.00 0.00 0.00 0.00 0.00 0.23-972.47 0.00 0.00 0.00 0.00 0.00 972.47 0.00 0.00 0.00 0.00 0.00 0.23-972.38 0.00 0.00 0.00 0.00 0.00 972.38 0.00 0.00 0.00 0.00 0.00 0.24-973.57 0.00 0.00 0.00 0.00 0.00 973.57 0.00 0.00 0.00 0.00 0.00 0.25-973.35 0.00 0.00 0.00 0.00 0.00 973.35 0.00 0.00 0.00 0.00 0.00 0.25-972.37 0.00 0.00 0.00 0.00 0.00 972.37 0.00 0.00 0.00 0.00 0.00 0.26-970.72 0.00 0.00 0.00 0.00 0.00 970.72 0.00 0.00 0.00 0.00 0.00 0.28-971.07 0.00 0.00 0.00 0.00 0.00 971.07 0.00 0.00 0.00 0.00 0.00 0.30-971.16 0.00 0.00 0.00 0.00 0.00 971.16 0.00 0.00 0.00 0.00 0.00 0.32-972.12 0.00 0.00 0.00 0.00 0.00 972.12 0.00 0.00 0.00 0.00 0.00 0.34-975.71 0.00 0.00 0.00 0.00 0.00 975.71 0.00 0.00 0.00 0.00 0.00 0.36-975.06 0.00 0.00 0.00 0.00 0.00 975.06 0.00 0.00 0.00 0.00 0.00 0.38-974.52 0.00 0.00 0.00 0.00 0.00 974.52 0.00 0.00 0.00 0.00 0.00 0.40-974.98 0.00 0.00 0.00 0.00 0.00 974.98 0.00 0.00 0.00 0.00 0.00 0.42-970.69 0.00 0.00 0.00 0.00 0.00 970.69 0.00 0.00 0.00 0.00 0.00 0.43-971.89 0.00 0.00 0.00 0.00 0.00 971.89 0.00 0.00 0.00 0.00 0.00 0.44-973.59 0.00 0.00 0.00 0.00 0.00 973.59 0.00 0.00 0.00 0.00 0.00 0.46-970.34 0.00 0.00 0.00 0.00 0.00 970.34 0.00 0.00 0.00 0.00 0.00 0.48-972.56 0.00 0.00 0.00 0.00 0.00 972.56 0.00 0.00 0.00 0.00 0.00 0.50-973.10 0.00 0.00 0.00 0.00 0.00 973.10 0.00 0.00 0.00 0.00 0.00 Table 2: Example OpenSees PT Force Output (6-Story) (Only the first half-second is displayed. The Axial j column is the force of interest in this output.) 10
Segment 1 Time Axial i Y Shear i Z Shear i Torsion i My i Mz i Axial j Y Shear j Z Shear j Torsion j My j Mz j 0 98.5433-8.92879 2.01561-20.5764 122.687-1519.92-98.5433 8.92879-2.01561 20.5764 121.418 438.584 0.02 147.683-11.723 3.0546-29.287 186.494-1947.87-147.683 11.723-3.0546 29.287 183.44 528.131 0.04 57.5631-5.42646 1.08365-2.94896 64.0869-897.819-57.5631 5.42646-1.08365 2.94896 67.1508 240.638 0.06 193.536-14.4417 4.07422-42.963 249.969-2407.58-193.536 14.4417-4.07422 42.963 243.447 658.583 0.065 122.907-10.1011 2.43959-16.2949 146.847-1673.12-122.907 10.1011-2.43959 16.2949 148.604 449.797 0.07 137.451-10.727 2.79829-20.334 169.996-1775.85-137.451 10.727-2.79829 20.334 168.897 476.728 0.0725 168.13-9.48781 3.50395-26.5883 214.443-1584.36-168.13 9.48781-3.50395 26.5883 209.911 435.323 0.075 106.215-7.75548 2.13555-12.3822 129.192-1284.6-106.215 7.75548-2.13555 12.3822 129.438 345.359 0.07625 109.82-8.72319 2.22574-13.841 135.029-1442.51-109.82 8.72319-2.22574 13.841 134.523 386.072 0.0775 118.13-8.33486 2.41455-15.3743 146.9-1385.32-118.13 8.33486-2.41455 15.3743 145.52 375.909 0.08 129.536-9.54769 2.66238-20.9412 162.256-1578.62-129.536 9.54769-2.66238 20.9412 160.176 422.329 0.1 200.037-11.6895 4.12146-19.7271 251.181-1950.81-200.037 11.6895-4.12146 19.7271 247.956 535.131 0.12 212.444-11.0209 4.38935-20.4101 267.633-1831.81-212.444 11.0209-4.38935 20.4101 263.948 497.11 0.13 235.094-11.1184 4.8458-15.162 295.223-1868.41-235.094 11.1184-4.8458 15.162 291.637 521.9 0.14 263.548-12.8957 5.44308-25.6097 331.672-2175.45-263.548 12.8957-5.44308 25.6097 327.522 613.695 0.16 250.742-12.2139 5.12357-21.8628 311.155-2067.2-250.742 12.2139-5.12357 21.8628 309.345 588.009 0.17 251.953-12.7507 5.14033-27.9589 312.041-2171.84-251.953 12.7507-5.14033 27.9589 310.489 627.647 0.18 252.663-13.3056 5.11515-31.55 309.717-2258.39-252.663 13.3056-5.11515 31.55 309.763 646.994 0.2 243.072-13.5625 4.89107-33.2828 295.594-2330.24-243.072 13.5625-4.89107 33.2828 296.749 687.727 0.22 250.784-13.9553 5.03638-37.6896 304.159-2404.36-250.784 13.9553-5.03638 37.6896 305.782 714.272 0.225 255.949-14.3648 5.13339-34.5478 309.863-2485.47-255.949 14.3648-5.13339 34.5478 311.827 745.791 0.23 262.977-14.3457 5.28867-39.6636 319.501-2495.42-262.977 14.3457-5.28867 39.6636 320.995 758.06 0.24 268.183-14.7686 5.39606-36.4297 326.007-2563.65-268.183 14.7686-5.39606 36.4297 327.493 775.069 0.245 272.893-14.5305 5.50128-36.1334 332.564-2535.84-272.893 14.5305-5.50128 36.1334 333.68 776.089 0.25 278.317-15.0625 5.61436-37.9432 339.449-2632.63-278.317 15.0625-5.61436 37.9432 340.489 808.46 0.26 289.94-15.3626 5.86506-38.0019 354.884-2687.52-289.94 15.3626-5.86506 38.0019 355.416 826.996 0.28 306.212-16.0592 6.20911-37.8321 375.907-2808.71-306.212 16.0592-6.20911 37.8321 376.059 863.828 0.3 328.593-16.6025 6.66398-40.5112 403.38-2903.82-328.593 16.6025-6.66398 40.5112 403.674 893.138 0.32 348.66-17.1981 7.04735-42.5643 425.989-3001.99-348.66 17.1981-7.04735 42.5643 427.495 919.181 0.34 359.759-17.1495 7.24715-45.3209 437.54-2991.74-359.759 17.1495-7.24715 45.3209 440.141 914.812 0.36 396.806-17.8213 7.99336-45.6741 482.371-3108.22-396.806 17.8213-7.99336 45.6741 485.68 949.932 0.38 417.562-18.1915 8.45237-46.6726 510.755-3163.22-417.562 18.1915-8.45237 46.6726 512.886 960.106 0.4 431.775-18.3305 8.76605-41.9988 530.111-3191.9-431.775 18.3305-8.76605 41.9988 531.519 971.952 0.42 437.604-18.8346 8.92634-44.8609 540.598-3274.52-437.604 18.8346-8.92634 44.8609 540.444 993.517 0.43 408.553-18.3288 8.31012-41.5244 502.935-3200.47-408.553 18.3288-8.31012 41.5244 503.478 980.723 0.44 393.969-17.9844 8.00072-43.7332 484.09-3136.45-393.969 17.9844-8.00072 43.7332 484.852 958.413 0.46 337.347-17.4303 6.78917-45.6686 409.817-3067.03-337.347 17.4303-6.78917 45.6686 412.398 956.091 0.48 284.176-16.2718 5.67306-46.2409 341.766-2864.95-284.176 16.2718-5.67306 46.2409 345.281 894.319 0.5 233.59-15.17 4.63577-43.7982 278.899-2676.19-233.59 15.17-4.63577 43.7982 282.525 838.996 Table 3: Example OpenSees Brace Force Output (6-Story) (Only the first half-second is displayed. Only the first segment of the left brace on the first story is displayed. The Axial j column is the force of interest in this output.) 11
6-Story Building: The 6-story building was the first case to be modelled. The 6-story building is 77.5-ft tall. All in all, this model took around 16.5 hours to run all of the twenty design earthquakes. The first data of interest was the lateral displacement (drift). The displacement that was output was the relative displacement at each floor; however, the displacement of interest is the normalized displacement that is relative to the story beneath. This drift was calculated for each story and graphed. Figure 4 shows this information for La01; the story drifts are all similar because the system s response is essentially a rigid-body rotation about the base. The roof drift was also a point of interest and was calculated with respect to the total building height. Figure 5 shows the normalized roof drift. Figure 4: 6-Story La01 Normalized Story Drift Figure 5: 6-Story La01 Normalized Roof Drift 12
A summary of the maximum and minimum normalized drifts can be seen in Table 4. The absolute maximum drift found was 1.78%. Normalized Drift Max and Min (%) First Story Second Story Third Story Fourth Story Fifth Story Sixth Story Roof Max 1.58 1.72 1.70 1.78 1.77 1.60 1.65 Min -1.51-1.52-1.56-1.58-1.58-1.49-1.49 Table 4: 6-Story La01 Normalized Drift Summary The next type of relevant data is the PT bar forces. The overall design of the SC-CBFs expects that the PT bars will yield around half of the time. In order to easily compare the PT bars with their yield strength of 120-ksi, the PT force output from OpenSees was normalized with respect to the yield strength. Both the axial force output and the normalized force were graphed, as shown in Figures 6 and 7, respectively. A normalized force of 100% or greater signifies yielding; the PT bars experienced no yielding within the first design earthquake, as shown in Figures 6 and 7. The maximum PT force experienced in this record was about 2,213-k (with a yield force of about 2,275-k). Figure 6: 6-Story La01 PT Bar Axial Force 13
Figure 7: 6-Story La01 Normalized PT Bar Force The final category of data is the brace forces. Each floor contains two braces, a right and a left, and each brace is broken down into two segments. OpenSees gave the force output per segment of brace. Therefore, each story has four segments with data. Similar to the PT bars, the brace forces were also collected and normalized; however, the force was normalized with respect to the design force rather than the yield force, to determine the performance of the design procedure. The design force of the braces varied by floor; Table 5 gives a summary of the brace design, actual, and normalized forces for the La01 design earthquake. Figure 8 shows these values visually. As can be seen from Table 5 and Figure 8, the third story brace force response exceeded the design force for the LA01 earthquake. Figure 9 shows the brace force outputs graphically for the first floor. Because of the sheer quantity of outputs, only the first floor graph will be shown in this report. Brace Force Results Story Design (k) Actual (k) Normalized (%) 1st 1978.3 1861.19 94.08027094 2nd 1596.081 1475.25 92.42951955 3rd 615.347 639.389 103.9070638 4th 765.105 723.739 94.59342182 5th 1852.739 1684.19 90.90271215 6th 836.659 559.736 66.90133017 Table 5: 6-Story La01 Brace Force Summary 14
Figure 8: 6-Story La01 Brace Force Results 15
Figure 9: 6-Story La01 First Story Brace Force Results Parametric Study of Self-Centering Concentrically-Braced Frames in Response to Earthquakes 16
All of the above data (Figures 4-9, Tables 1-5) is only for the La01 design earthquake and is similar for the other nineteen earthquakes. The quantity of data is rather large, so the other earthquake response data will not be shown. However, the governing data from each relevant type of data is summarized in Table 6. Further analysis has taken place to produce the statistics for each section shown at the bottom of the table. The COV statistic is the coefficient of variation (standard deviation divided by mean), which measures the relative dispersion of the data. The drift values had the most variability, at around 40%. One interesting statistic is the statistical mode of the story on which the maximum brace force occurred. For this structure, the maximum brace force usually occurred on the third story. The maximum drift reached was 3.09%, the maximum normalized PT force was 1.01, and the maximum normalized brace force was 1.62. 6 Story Normalized Drift PT Force Brace Force DBE Max (%) Max Roof (%) Max (K) Normalized Max Normalized Max <---- Story La01 1.78 1.65 2213 0.97 1.04 3 La02 0.97 0.90 1643 0.72 0.99 4 La03 2.34 2.28 2287 1.01 0.97 3 La04 0.58 0.47 1284 0.56 0.73 4 La05 2.14 2.07 2283 1.00 0.98 3 La06 1.02 0.93 1649 0.72 0.73 3 La07 1.18 1.11 1783 0.78 0.84 3 La08 1.25 1.15 1815 0.80 0.81 3 La09 2.35 2.29 2288 1.01 1.15 3 La10 1.59 1.42 2084 0.92 1.20 3 La11 2.47 2.37 2289 1.01 1.22 3 La12 0.70 0.64 1427 0.63 1.55 4 La13 1.75 1.59 2204 0.97 1.62 3 La14 1.69 1.59 2210 0.97 1.28 1 La15 1.79 1.65 2247 0.99 1.10 3 La16 2.34 2.27 2287 1.01 1.18 4 La17 2.68 2.59 2294 1.01 1.03 3 La18 3.09 2.99 2301 1.01 1.35 3 La19 1.09 0.81 1583 0.70 1.27 4 La20 2.33 2.18 2285 1.00 1.45 4 Statistics Min 0.58 0.47 1284 0.56 0.73 - Max 3.09 2.99 2301 1.01 1.62 - Mode - - - - - 3 Average 1.76 1.65 2023 0.89 1.12 - Std Dev 0.703 0.713 340.633 0.150 0.252 - COV 0.400 0.433 0.168 0.168 0.225 - Table 6: 6-Story Master Data Summary 17
10-Story Building: The second overall case was that of the 10-story structure. The 10-story building is 127.5-ft tall, and took just under fifteen hours to complete the analysis of all twenty design earthquakes. As before, the relevant data is the displacement, PT bar forces, and brace forces. First, the drift data was collected. Since the normalized story and roof drift data are very similar and the normalized roof drift data is the most important, only roof drift will be shown from here on. Thus, Figure 10 shows the normalized roof drift for the La01 design basis earthquake. Figure 10: 10-Story La01 Normalized Roof Drift The summary of maximum normalized drifts can be seen in Table 7. The overall maximum drift was 2.29%. Normalized Drift Max and Min (%) First Story Second Story Third Story Fourth Story Fifth Story Sixth Story Seventh Story Eighth Story Ninth Story Tenth Story Roof Max 1.07 1.04 1.07 1.10 1.17 1.31 1.29 1.26 1.27 1.20 1.12 Min -1.98-2.07-2.11-2.13-2.16-2.29-2.26-2.25-2.28-2.25-2.13 Table 7: 10-Story La01 Normalized Drift Summary Moving on, the PT bar forces were collected next. The yield strength remained at 120-ksi, and the forces were once again normalized. Figure 11 shows the PT bar axial forces for La01, and Figure 12 shows the normalized forces. The maximum PT force experienced was just under 3,848-k. As shown in Figure 12, the PT bars did not yield during this design basis earthquake. 18
Figure 11: 10-Story La01 PT Bar Axial Force Figure 12: 10-Story La01 Normalized PT Bar Force 19
Brace Force Results Story Design (k) Actual (k) Normalized (%) 1st 3226.595 2085.16 64.62416262 2nd 2849.246 1729.16 60.68833649 3rd 2263.791 1105.73 48.84417334 4th 1936.289 930.502 48.05594619 5th 1087.703 765.714 70.39734192 6th 1152.653 780.238 67.69062328 7th 1755.27 1354.91 77.19097347 8th 1775.045 1151.79 64.88793242 9th 2474.705 1910.54 77.2027373 10th 961.757 698.648 72.64288173 Table 8: 10-Story La01 Brace Force Summary The next relevant data type is the brace forces. The force output is very similar to the 6-story building, so it was organized much in the same exact way. Again, because of the magnitude of the data, the graphical data will be limited. Table 8 gives a summary of the brace design, actual, and normalized forces for the La01 design earthquake. Figure 13 shows these values visually. None of the braces exceeded the design forces during this earthquake. Figure 13: 10-Story La01 Brace Force Results The graph of the first story brace forces for the first design earthquake is shown in Figure 14. 20
Figure 14: 10-Story La01 First Story Brace Force Results Parametric Study of Self-Centering Concentrically-Braced Frames in Response to Earthquakes 21
All of the relevant data has been investigated. Table 9 gives the master summary of all of the data from the 10- story analysis. As can be seen, PT bar and brace element yielding did occur during some of the other design basis earthquakes. The maximum drift at any point was 3.5%, and the mode of the location of the maximum brace force was on the seventh story. The maximum overall normalized PT and brace forces were 1.0 and 1.30, respectively. The drift values varied the most, by as much as 40%. 10 Story Normalized Drift PT Force Brace Force DBE Max (%) Max Roof (%) Max (K) Normalized Max (%) Normalized Max (%) <---- Story La01 2.29 2.13 3847.86 0.87 0.77 7 La02 1.31 1.23 3041.30 0.69 0.84 6 La03 3.30 3.18 4414.35 1.00 0.78 9 La04 1.91 1.71 3510.50 0.80 0.96 7 La05 3.61 3.50 4421.76 1.00 0.79 9 La06 1.37 1.31 3089.05 0.70 1.30 5 La07 1.10 1.04 2828.74 0.64 0.74 6 La08 1.64 1.58 3331.70 0.76 0.57 7 La09 2.22 2.05 3803.65 0.86 0.72 6 La10 0.84 0.74 2541.77 0.58 0.61 9 La11 1.95 1.77 3440.42 0.78 0.76 7 La12 0.68 0.59 2378.33 0.54 1.14 6 La13 1.23 1.03 2881.21 0.65 1.23 7 La14 1.75 1.53 3280.17 0.75 0.92 7 La15 1.35 1.13 2779.47 0.63 0.80 7 La16 1.50 1.28 3076.93 0.70 0.77 6 La17 2.21 2.07 3871.96 0.88 0.84 6 La18 1.97 1.64 3349.28 0.76 1.27 6 La19 1.05 0.65 2412.91 0.55 1.11 7 La20 1.58 1.28 2972.27 0.68 1.19 7 Statistics Min 0.68 0.59 2378.33 0.54 0.57 - Max 3.61 3.50 4421.76 1.00 1.30 - Mode - - - - - 7 Average 1.74 1.57 3263.68 0.74 0.91 - Std Dev 0.742 0.754 588.078 0.134 0.222 - COV 0.426 0.480 0.180 0.180 0.245 - Table 9: 10-Story Master Data Summary 22
6-Story Reduced Area Building: The 6-story reduced area structure is significant in that it effectively allows for the comparison of the addition of more SC-CBFs to the structure. By adding more SC-CBFs, the tributary area for each frame decreases by onethird. This action allows for a comparison of the performance of the structure with more frames in it to the performance of the structure with fewer frames and a recommended number of SC-CBFs to potentially be determined. Note that this is a preliminary study of the effect of an additional frame the frame has not been redesigned to accommodate the lower expected force demands. Aside from the addition of SC-CBFs, the geometry is synonymous the height is still 77.5-ft tall. Just as before, similar types of data were collected. Figure 15 shows the normalized roof drift of this structure. Figure 15: 6-Story Reduced Area La01 Normalized Roof Drift Table 10 gives the summary of the maximum and minimum normalized drifts experienced during La01; the governing drift was 1.05%. Normalized Drift Max and Min (%) First Story Second Story Third Story Fourth Story Fifth Story Sixth Story Roof Max 0.97 1.02 1.02 1.05 1.05 0.97 0.98 Min -0.97-0.96-0.97-1.01-1.02-0.90-0.93 Table 10: 6-Story Reduced Area La01 Normalized Drift Summary The PT bar forces were examined next. Since the axial and normalized graphical data are identical, only the normalized data will be presented from this point on. From Figure 16, the maximum normalized PT force was right around 74.5 %. 23
Figure 16: 6-Story Reduced Area La01 Normalized PT Bar Force The final data type is, once again, the brace forces. Table 11 summarizes the brace force data numerically while Figure 17 does so visually. As expected, due to the reduced lateral force demand, none of the braces reached their design force during the earthquake presented here. Brace Force Results Story Design (K) Actual (K) Normalized (%) 1st 1978.3 1293.17 65.36773998 2nd 1596.081 980.576 61.43648098 3rd 615.347 493.188 80.14794904 4th 765.105 535.505 69.99104698 5th 1852.739 1227.24 66.23922744 6th 836.659 455.276 54.4159568 Table 11: 6-Story Reduced Area La01 Brace Force Summary 24
Figure 17: 6-Story Reduced Area La01 Brace Force Results As usual, the brace forces within the first story are presented graphically in the next figure, Figure 18. 25
Figure 18: 6-Story Reduced Area La01 First Story Brace Force Results Parametric Study of Self-Centering Concentrically-Braced Frames in Response to Earthquakes 26
Finally, the overall results are organized in Table 12, the master data summary table for this case. As shown within the Statistics section of Table 12, the maximum normalized drift experienced was 3.01%, the maximum normalized PT force was 1.01, and the maximum normalized brace force was 1.34 some yielding did occur in the PT bars, and some brace forces exceeded the design demands. Also, the maximum brace forces for each design basis earthquake were most often seen within the third story of the structure. The drift values had the most variability, up to 50%. 6 Story Reduced Area Normalized Drift PT Force Brace Force DBE Max (%) Max Roof (%) Max (K) Normalized Max (%) Normalized Max (%) <---- Story La01 1.05 0.98 1693.35 0.74 0.80 3 La02 0.90 0.79 1562.11 0.69 0.74 3 La03 1.33 1.28 1947.05 0.86 0.73 3 La04 0.53 0.48 1293.14 0.57 0.58 3 La05 0.62 0.55 1369.14 0.60 0.50 5 La06 0.52 0.49 1302.31 0.57 0.57 3 La07 0.76 0.72 1488.98 0.65 0.62 3 La08 1.25 1.18 1870.20 0.82 0.73 3 La09 3.01 2.94 2300.85 1.01 0.99 3 La10 1.74 1.67 2255.29 0.99 0.99 3 La11 1.86 1.80 2277.76 1.00 1.07 3 La12 0.81 0.59 1395.80 0.61 1.24 4 La13 1.61 1.48 2080.53 0.91 1.12 3 La14 1.63 1.55 2159.33 0.95 0.97 3 La15 1.79 1.70 2253.65 0.99 1.12 3 La16 2.67 2.62 2294.27 1.01 0.99 3 La17 1.37 1.30 1962.90 0.86 0.81 3 La18 2.47 2.38 2288.92 1.01 1.07 3 La19 1.11 1.02 1730.96 0.76 1.01 4 La20 2.48 2.34 2288.55 1.01 1.34 4 Statistics Min 0.52 0.48 1293.14 0.57 0.50 - Max 3.01 2.94 2300.85 1.01 1.34 - Mode - - - - - 3 Average 1.48 1.39 1890.75 0.83 0.90 - Std Dev 0.738 0.737 379.299 0.167 0.235 - COV 0.500 0.529 0.201 0.201 0.262 - Table 12: 6-Story Reduced Area Master Data Summary 27
10-Story Reduced Area Building: The 10-story building was modified to produce the 10-story reduced area model just as the 6-story model was modified to produce the 6-story reduced area model. So, the geometry of the 10-story building remains constant aside from the fact that the tributary areas of the SC-CBFs within are effectively reduced to two-thirds of their original values. The same data was collected for comparison s sake. Figure 19 graphically shows the normalized roof drift of this case. Figure 19: 10-Story Reduced Area La01 Normalized Roof Drift Table 13 gives the summary of the maximum and minimum normalized roof drift results experienced during La01. The governing value is 1.62%. Normalized Drift Max and Min (%) First Story Second Story Third Story Fourth Story Fifth Story Sixth Story Seventh Story Eighth Story Ninth Story Tenth Story Roof Max 1.43 1.55 1.55 1.58 1.62 1.61 1.62 1.58 1.61 1.59 1.57 Min -1.09-1.15-1.15-1.17-1.21-1.21-1.21-1.18-1.20-1.18-1.16 Table 13: 10-Story Reduced Area La01 Normalized Drift Summary Next the PT bar forces were obtained. As seen in Figure 20, the maximum normalized PT bar force was about 76%. No yielding occurred during this first design earthquake. 28
Figure 20: 10-Story Reduced Area La01 Normalized PT Bar Force Last, the brace forces were investigated. Table 14 summarizes the brace force results for the La01 design basis earthquake; the maximum normalized brace force was only around 54%, so the design force was never exceeded for this earthquake. Figure 21 graphically demonstrates this result. Brace Force Results Story Design (K) Actual (K) Normalized (%) 1st 3226.595 1305.66 40.46556819 2nd 2849.246 1209.27 42.44175477 3rd 2263.791 808.945 35.73408499 4th 1936.289 703.556 36.33527846 5th 1087.703 563.438 51.80072134 6th 1152.653 621.497 53.918829 7th 1755.27 841.158 47.92185818 8th 1775.045 791.481 44.58934844 9th 2474.705 1264.8 51.1091221 10th 961.757 469.217 48.78747958 Table 14: 10-Story Reduced Area La01 Brace Force Summary 29
Figure 21: 10-Story Reduced Area La01 Brace Force Results Once again, the first story brace forces are graphed in Figure 22. 30
Figure 22: 10-Story Reduced Area La01 First Story Brace Force Results Parametric Study of Self-Centering Concentrically-Braced Frames in Response to Earthquakes 31
All in all, the master summary of the results of all of the earthquakes is shown in Table 15. The maximum experienced normalized roof drift was 3.22%, the maximum normalized PT force was 1.0, and the maximum normalized brace force was 1.42. The sixth story is where the brace force was the maximum most of the time. The drift had the highest variability in numbers and varied by as much as 50%. 10 Story Reduced Area Normalized Drift PT Force Brace Force DBE Max (%) Max Roof (%) Max (K) Normalized Max (%) Normalized Max (%) <---- Story La01 1.62 1.57 3332.13 0.76 0.54 6 La02 0.84 0.74 2555.08 0.58 0.64 7 La03 2.89 2.81 4404.77 1.00 0.72 6 La04 0.57 0.51 2300.11 0.52 0.49 7 La05 3.31 3.22 4414.45 1.00 0.75 9 La06 0.54 0.46 2261.74 0.51 1.42 5 La07 1.07 0.99 2781.31 0.63 0.72 6 La08 0.86 0.74 2496.14 0.57 0.49 7 La09 1.47 1.38 3171.76 0.72 0.53 5 La10 0.99 0.92 2705.97 0.61 0.81 6 La11 2.13 1.97 3661.68 0.83 0.75 9 La12 0.67 0.52 2328.16 0.53 0.83 7 La13 1.41 1.33 3116.76 0.71 0.83 6 La14 1.28 1.16 2919.87 0.66 0.85 6 La15 1.03 0.91 2648.23 0.60 0.59 7 La16 1.57 1.43 3229.95 0.73 0.82 7 La17 2.44 2.34 4078.64 0.93 1.35 6 La18 2.20 2.09 3830.03 0.87 0.80 7 La19 0.78 0.62 2447.71 0.56 0.74 1 La20 1.70 1.38 3067.83 0.70 1.12 6 Statistics Min 0.54 0.46 2261.74 0.51 0.49 - Max 3.31 3.22 4414.45 1.00 1.42 - Mode - - - - - 6 Average 1.47 1.35 3087.62 0.70 0.79 - Std Dev 0.780 0.782 681.686 0.155 0.252 - COV 0.531 0.577 0.221 0.221 0.318 - Table 15: 10-Story Reduced Area Master Data Summary Thus concludes all of the individual data for all of the four total test models run. Once again, aside from the master summary tables at the end of each model (Tables 6, 9, 12, and 15), all of the data presented is for the first design earthquake, La01, only. 32
Comparisons, Correlations, and Conclusions: This section seeks to compare the performance of the SC-CBF in each of the four building scenarios. Each model gives a unique perspective on the frame s performance and will hopefully provide a means by which to identify any correlations and conclusions. It is the hope of this project that those conclusions formed will be able to offer any insight into the design parameters of SC-CBFs. The same specific data types that have been of interest from the beginning will be used to compare the data. The first relevant data type was the roof drift. Figure 23 shows the roof drift for all four models and all of the twenty design basis earthquakes. Figure 23: Normalized Roof Drift Comparison Each model is represented by a different shape and color in Figure 23. Each data point within a series is a different design earthquake, and the solid bars represent the average for each series. Between the two 6-story structures, the average drift decreased as the tributary area decreased. The same trend can be seen between the two 10-story models as well; the drift decreases with tributary area, as expected. Next, the average drift of the 6-story 33
structure is slightly higher than that of the 10-story structure. However, the 10-story did have a higher COV value (as shown in Tables 6 and 12). Similarly, the drift of the 6-story reduced area structure was slightly higher than that of the 10-story reduce area structure, however only ever so slightly. Since these average drifts are so similar between the two 6-story buildings in comparison to the two 10-story buildings, it appears that the structure s height has very little connection to the drift of the structure (at least in comparing the studied structures). Moving on, the next major source for comparison is the PT forces between structures. Figure 24 gives a comparison of all of the normalized PT forces for all of the twenty earthquakes for all four structures. Figure 24: Normalized PT Bar Force Comparison Figure 24 is set up just like Figure 23, with the averages shown by the bars. Here, the normalized average PT forces decreased with the decrease in tributary area between both the 6-story and 10-story structures, as expected. However, the magnitude of decrease seemed to drop when comparing the two 10-story structures as opposed to when comparing the two 6-story structures. Based on these results, the shorter the structure is, the greater the impact of reducing the tributary area on the PT forces of the SC-CBF. Also, the PT force seems to be proportional to the tributary area, which is expected. Clearly the PT forces dropped when comparing the 6-story building to the 34
10-story building like with the reduced area buildings. From this trend it appears that PT forces are inversely proportional to building height. Finally, the normalized brace forces are also of interest. Figure 25 gives a comparison of all of the brace forces for each structure for each earthquake. Figure 25: Normalized Brace Force Comparison From Figure 25, the average normalized brace force definitely decreased as the tributary area decreased. Also, the brace force decreased as the building height increased. Once again, though, the magnitude of decrease between the 10-story and 10-story reduced area was less than the magnitude of decrease between the 6-story and 6-story reduced area. So, it appears that reducing the tributary area in a shorter building has a greater effect on the brace forces than reducing the tributary area in a taller building. As shown in Tables 6 and 12, the maximum brace force was most often on the third story, the middle of the 6-story building. So, it appears that the brace force will usually be greatest around the center of the structure s height. However, from Tables 9 and 15, the brace force seemed to be greatest just above the center of the building s height around the sixth or seventh floor. So, it appears that the average maximum brace force may creep up the building from the center as the building height increases. 35
Based on this study with only four different cases, it is difficult to establish many trends that are not obvious. However some of the trends were clear. From a building geometry standpoint, it appears that decreasing the tributary area of a SC-CBF will decrease most of its force responses. Similarly, it appears that increasing the building height will decrease all of the forces (at least in the structures modelled in this project). A decrease in tributary area would be expected to decrease the forces; however, increasing the building height to decrease the forces is not necessarily intuitive. Further research of the relationship of experienced forces to building (and therefore SC-CBF) height may further develop more insights and conclusions to the performance of the SC-CBFs. Similarly, additional research investigating the location of the maximum brace force may also provide more conclusions and explanations of the observed data and possibly lead to establishing corresponding design parameters of the SC-CBF. 36
References: Mazzoni, S., F. McKenna, and G.L. Fenves, (2000). OpenSees Command Language Manual, 10. Sause R., J.M. Ricles, D.A. Roke, N.B. Chancellor, and N.P. Gonner, (2010). Large-Scale Experimental Studies of Damage-Free Self-Centering Concentrically-Braced Frame under Seismic Loading. ASCE. 37