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siwalan committed Jul 28, 2022
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# BenchmarkControlProblems

This is OpenSees implementation of Ohtori et al Nonlinear Benchmark Control Problem (https://ascelibrary.org/doi/10.1061/%28ASCE%290733-9399%282004%29130%3A4%28366%29). The model has been checked and found to have a similar eigenvalues number with Ohtori simulation (and previous simulation). However, it must be noted that the OpenSees model may have little bit smaller stifness due to the usage of Fiber Section. To reduce the amount of DOFs on the system, in the model.tcl file for each building, splice is not modeled. However, in case you really need the extra accuracy, a model with splice is also included. The frequency of model with splice is little bit closer to Ohtori's Eigenvalues.
This is OpenSees implementation of Ohtori et al Nonlinear Benchmark Control Problem (https://ascelibrary.org/doi/10.1061/%28ASCE%290733-9399%282004%29130%3A4%28366%29). The model has been checked and found to have a similar eigenvalues number with Ohtori simulation (and previous simulation). However, it must be noted that the OpenSees model may have little bit smaller stifness due to the usage of Fiber Section. To reduce the amount of DOFs on the system, in the model.tcl file for each building, splice is not modeled.

Ohtori Nonlinear Benchmark Control Problem are based on SAC Phase II Building Design.

## 3 Story Building Eigenvalues
From Ohtori Paper, the first 3 Natural Period is : 0.99, 3.06, and 5.83 Hz

OpenSees Eigenvalues:
| Mode | Period (s) | Frequency (Hz) | Frequency (rounded, Hz) | Ohtori Frequency (rounded, Hz) |
|------| -------|-----------| ----| -- |
|1 |1.0097077067198548 | 0.9903856267955097| 0.99 | 0.99 |
|2 |0.32667497129029194 | 3.0611466683542576| 3.061| 3.056 |
|3 | 0.17080331473344545| 5.854687314239736 | 5.855 | 5.827 |
|4 | 0.14030860249371874| 7.1271467481458775 | 7.127 | 7.230 |
|5 | 0.09941529284564488 | 10.058814608660155 | 10.059| 9.974 |
|6 | 0.09053790203823787 | 11.045097991973117| 11.045 | 10.961 |


## 9 Story Building Eigenvalues
From Ohtori Paper, the first 6 Natural Period is 0.443, 1.18, 2.05, 3.09, and 4.27 Hz.

OpenSees Eigenvalues:
| Mode | Period (s) | Frequency (Hz) | Frequency (rounded, Hz) | Ohtori Frequency (rounded, Hz) |
|------| -------|-----------| ---- | --- |
|1 |2.308495285624674 | 0.433182604368803| 0.433 | 0.443 |
|2 |0.8663962990169478 | 1.154206223104421| 1.154 | 1.178 |
|3 | 0.5003944305086168| 1.9984235215878967 | 1.998 | 2.047 |
|4 | 0.33122636480423545| 3.1271467481458775 | 3.127 | 3.095 |
|5 | 0.238455860283037 | 4.058814608660155 | 4.059 | 4.274 |
|7 | 0.208440378354854 | 4.7975349492869155| 4.693 | 4.73 |
|8 | 0.20047370144783241 | 4.988185446659305| 4.798 | 4.873|
|9 | 0.1921842060521685s | 5.20334121383809| 5.203 | 5.03 |


## 20 Story Building Eigenvalues

| Mode | Period (s) | Frequency (Hz) | Frequency (rounded, Hz) | Ohtori Frequency (rounded, Hz) |
|------| -------|-----------| --- | --- |
|1 |3.760731682904276 | 0.26590570248493156| 0.266 | 0.2610 |
|2 |1.312985451850604 | 0.761623061847744| 0.762 | 0.7530 |
|3 | 0.7599609135879114| 1.3158571475456824 | 1.316 | 1.2990 |
|4 | 0.5398783375579737| 1.8522691696119704 | 1.852 | 1.8270 |
|5 | 0.4101396081818257 | 2.4381941662085804 | 2.438 | 2.3980 |
|6 | 0.390398422766829 | 2.561485758351192| 2.561 | 2.4420 |
|7 | 0.32997567778392145 | 3.030526391265818| 3.031 | 2.9230 |
|8 | 0.3269631749829076 | 3.0584484018797387| 3.058 | 3.0060 |
|9 | 0.2698124823956028 | 3.706277749351072| 3.706 | 3.6320 |
|10 | 0.26438009130509105 | 3.782433068479478| 3.782 | 3.6830 |
|11 | 0.22420690266397214 | 4.460165981146174| 4.46 | 4.3310 |
|12 | 0.22095274813268914 | 4.525854547866806| 4.526 | 4.4470 |

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