Parametric Analysis of Moment-Resisting Timber Frames Combined with Cross Laminated Timber Walls and Prediction Models Using Nonlinear Regression and Artificial Neural Networks
Abstract
:1. Introduction
2. Methods
2.1. Structural System
2.2. Parametric Study
2.3. Finite Element Analysis
2.4. Calculation of Wind-Induced Acceleration
- Fundamental basic wind velocity : 10, 15, 20, 25, 30, 35, and 40 m/s.
- Damping ratio ξ: 0.01, 0.015, 0.02, 0.025, and 0.03.
- Cross wind dimension of the building (confer Figure 1): 10, 15, 20, 25, and 30 m.
3. Results and Discussion
3.1. Nonlinear Regression
- Frames with fundamental frequency , where Hz or Hz, were excluded.
- For frames with a number of storeys , , , and were considered.
- For frames with a number of storeys , mm was considered.
- For frames with number of storeys , m was considered.
3.1.1. Fundamental Frequency
3.1.2. Mode Shape
3.1.3. Top Floor Displacement
3.1.4. Inter-Storey Drift
3.1.5. Wind-Induced Acceleration
3.2. Artificial Neural Networks (ANNs)
3.3. Solved Example
3.3.1. Solving the Individual Frames in 2D
3.3.2. Estimating the 3D Properties Based on the 2D Results
4. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Appendix A
- The building is symmetric; see the symmetry line in Figure A1a (i.e., no eccentricity), and diaphragm action is assumed at all floor levels.
- All frames have the same mode shape, i.e., , where is the frame number.
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Parameter | Value | Parameter | Value | Parameter | Value |
---|---|---|---|---|---|
4/6/8/10/12/14 | (kN/m2) | 1.5/3.0 | (mm) | 450/540/630 | |
(m) | 3.0/3.5 | (kN/m) | 1.0 | (mm) | 420/585/765 |
2/3 | (m) | 3.0/4.5/6.0 | (m) | 1.0/2.0/3.0 | |
(m) | 6.0/7.5/9.0 | (mm) | 140/215/430 | , , | 1/2/5/10 |
Parameter | Value |
---|---|
Directional factor | 1.0 |
Seasonal factor | .00 |
Probability factor | |
Orography factor | .00 |
Turbulence factor | .00 |
Terrain category | Urban environment () |
Reference height | 200 |
Reference length | 300 |
Parameter | Frames 1 and 6 | Frames 2 and 5 | Frames 3 and 4 |
---|---|---|---|
8 | |||
(m) | 3.0 | ||
3 | |||
(m) | 9.0 | ||
2 | 2 | 1 | |
(m) | 2.5 | 2.5 | 2.5 |
(m) | 0.585 | 0.585 | 0.585 |
(m) | 0.54 | 0.54 | 0.54 |
(m) a | 0.43 | 0.43 | 0.43 |
1.5 | 1.5 | 1.5 | |
2.5 | 2.5 | 2.5 | |
2.0 | 2.0 | 2.0 | |
(kNm/rad) b | 279,948 | 279,948 | 279,948 |
(kNm/rad) b | 25,906 | 25,906 | 25,906 |
(kNm/rad) b | 6113 | 6113 | 6113 |
(kN/m2) | 2.0 | 2.0 | 2.0 |
(kN/m) | 5.0 | 10.0 | 10.0 |
(kN/m) c | 2.125 | 4.25 | 4.25 |
Method of Calculation | Frames 1 and 6 | Frames 2 and 5 | Frames 3 and 4 | ||||||
---|---|---|---|---|---|---|---|---|---|
(Hz) | (mm) | (mm) | (Hz) | (mm) | (mm) | (Hz) | (mm) | (mm) | |
Analytical expressions | 1.29 | 8.26 | 1.33 | 0.91 | 16.51 | 2.66 | 0.82 | 17.70 | 3.05 |
ANNs | 1.24 | 8.81 | 1.34 | 0.88 | 17.62 | 2.69 | 0.77 | 23.22 | 3.58 |
FEA | 1.27 | 8.69 | 1.27 | 0.89 | 17.37 | 2.55 | 0.76 | 24.10 | 3.85 |
Method of Calculation | (Hz) | (mm) | (mm) |
---|---|---|---|
Analytical expressions | 0.97 | 14.07 | 2.31 |
ANNs | 0.92 | 15.97 | 2.44 |
FEA | 0.96 | 15.20 | 2.24 |
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Hegeir, O.A.; Stamatopoulos, H.; Malo, K.A. Parametric Analysis of Moment-Resisting Timber Frames Combined with Cross Laminated Timber Walls and Prediction Models Using Nonlinear Regression and Artificial Neural Networks. Buildings 2024, 14, 2975. https://doi.org/10.3390/buildings14092975
Hegeir OA, Stamatopoulos H, Malo KA. Parametric Analysis of Moment-Resisting Timber Frames Combined with Cross Laminated Timber Walls and Prediction Models Using Nonlinear Regression and Artificial Neural Networks. Buildings. 2024; 14(9):2975. https://doi.org/10.3390/buildings14092975
Chicago/Turabian StyleHegeir, Osama Abdelfattah, Haris Stamatopoulos, and Kjell Arne Malo. 2024. "Parametric Analysis of Moment-Resisting Timber Frames Combined with Cross Laminated Timber Walls and Prediction Models Using Nonlinear Regression and Artificial Neural Networks" Buildings 14, no. 9: 2975. https://doi.org/10.3390/buildings14092975