Effects of Multi-Directional Seismic Input on Non-Linear Static Analysis of Existing Reinforced Concrete Structures
Abstract
:1. Introduction
2. Case Study Structures and Structural Models
2.1. Case Study Structures
2.2. Structural Models
2.3. Modal Analyses
3. Ground Motion Record Selection
4. Analysis Results and Discussion
4.1. Multi-Directional Nonlinear Static Analyses
4.2. Comparison between Multi-Directional Non-Linear Static and Non-Linear History Analyses
5. Summary and Conclusions
- Step 1: A set of PO analyses are sequentially carried out by applying mass proportional and triangular load patterns at 24 different incident angles θ with 15° increments;
- Step 2: For each θ, the Vb-θ PO curves are obtained in the X and Y directions for CM and two corners;
- Step 3: For each θ, the PO curve (of the two computed at Step 2) that reaches a peak and then softens (and thus is assumed to have reached failure) is selected as the reference PO curve. When both PO curves reach the peak and then soften, the PO curve with the maximum displacement is assumed as the reference PO;
- Step 4: For each load pattern and θ, the structural demand in terms of IDR is computed using the N2 method. The IDR is in the direction of the reference PO curve selected in Step 3.
- It clarifies the methodology that is applied to find the structural demand in multi-directional NSAs;
- It indicates two load patterns (mass proportional and triangular) that can be used to carry out multi-directional NSA and easily compute the relevant participation factors;
- It shows how the structural capacity and demand are affected by the interaction between the buildings’ responses in the X and Y directions for loading angles different from 0° and 90°;
- It validates the proposed approach through multi-directional NSAs on two buildings (one plan regular, the other plan asymmetric obtained by changing the position of the center of mass). The NSA results are compared with those of multi-directional NHAs.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Appendix A. Cross Sections and Reinforcements of the Columns of the Case-Study Buildings
COLUMNS | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|
Story | n. | 1-8-25-32 | 2-7-26-31 | 3-6-27-30 | 4-5-28-29 | 9-16-17-24 | 10-15-18-23 | 11-14-19-22 | 12-13-20-21 | |
5 | Size | 30 × 50 | 30 × 50 | 30 × 50 | 30 × 50 | 30 × 50 | 30 × 50 | 30 × 50 | 30 × 50 | |
AsT | 2ϕ14 | 2ϕ14 | 2ϕ14 | 2ϕ14 | 2ϕ14 | 2ϕ14 | 2ϕ14 | 2ϕ14 | ||
AsP | 1ϕ14 | 1ϕ14 | 1ϕ14 | 1ϕ14 | 1ϕ14 | 1ϕ14 | 1ϕ14 | 1ϕ14 | ||
AsB | 2ϕ14 | 2ϕ14 | 2ϕ14 | 2ϕ14 | 2ϕ14 | 2ϕ14 | 2ϕ14 | 2ϕ14 | ||
4 | Size | 30 × 55 | 30 × 50 | 30 × 50 | 30 × 55 | 30 × 55 | 30 × 50 | 30 × 50 | 30 × 55 | |
AsT | 2ϕ14 | 2ϕ14 | 2ϕ14 | 2ϕ14 | 2ϕ14 | 2ϕ14 | 2ϕ14 | 2ϕ14 | ||
AsP | 1ϕ14 | 1ϕ14 | 1ϕ14 | 1ϕ14 | 1ϕ14 | 1ϕ14 | 1ϕ14 | 1ϕ14 | ||
AsB | 2ϕ14 | 2ϕ14 | 2ϕ14 | 2ϕ14 | 2ϕ14 | 2ϕ14 | 2ϕ14 | 2ϕ14 | ||
3 | Size | 30 × 55 | 30 × 55 | 30 × 55 | 30 × 55 | 30 × 55 | 30 × 55 | 30 × 55 | 30 × 55 | AsT: top rebars |
AsT | 2ϕ14 | 2ϕ14 | 2ϕ14 | 2ϕ14 | 2ϕ14 | 2ϕ14 | 2ϕ14 | 2ϕ14 | AsP: intermediate rebars | |
AsP | 1ϕ14 | 1ϕ14 | 1ϕ14 | 1ϕ14 | 1ϕ14 | 1ϕ14 | 1ϕ14 | 1ϕ14 | AsB: bottom rebars | |
AsB | 2ϕ14 | 2ϕ14 | 2ϕ14 | 2ϕ14 | 2ϕ14 | 2ϕ14 | 2ϕ14 | 2ϕ14 | ||
2 | Size | 30 × 60 | 30 × 55 | 30 × 55 | 30 × 60 | 30 × 60 | 30 × 55 | 30 × 55 | 30 × 60 | |
AsT | 2ϕ14 | 2ϕ14 | 2ϕ14 | 2ϕ14 | 2ϕ14 | 2ϕ14 | 2ϕ14 | 2ϕ14 | ||
AsP | 1ϕ14 | 1ϕ14 | 1ϕ14 | 1ϕ14 | 1ϕ14 | 2ϕ14 | 2ϕ14 | 1ϕ14 | ||
AsB | 2ϕ14 | 2ϕ14 | 2ϕ14 | 2ϕ14 | 2ϕ14 | 2ϕ14 | 2ϕ14 | 2ϕ14 | ||
1 | Size | 30 × 60 | 30 × 60 | 30 × 60 | 30 × 60 | 30 × 60 | 30 × 60 | 30 × 60 | 30 × 60 | |
AsT | 2ϕ14 | 2ϕ14 | 2ϕ14 | 2ϕ14 | 2ϕ14 | 3ϕ14 | 3ϕ14 | 2ϕ14 | ||
AsP | 1ϕ14 | 1ϕ14 | 1ϕ14 | 1ϕ14 | 2ϕ14 | 2ϕ14 | 2ϕ14 | 2ϕ14 | ||
AsB | 2ϕ14 | 2ϕ14 | 2ϕ14 | 2ϕ14 | 2ϕ14 | 3ϕ14 | 3ϕ14 | 2ϕ14 |
Appendix B. Selected Ground Motion Records
n. | Database | Station ID | Earthquake Name | Date | Time (UTC) | Mw | Epicentral Distance (km) | Site Class | Scale Factor |
---|---|---|---|---|---|---|---|---|---|
1 | ESD | ST20 | Friuli | 06/05/1976 | 20:00:13 | 6.5 | 23 | A | 1.2734 |
2 | ESD | ST54 | Tabas | 16/09/1978 | 15:35:57 | 7.3 | 12 | A | 0.8692 |
3 | ESD | ST98 | Campano Lucano | 23/11/1980 | 18:34:52 | 6.9 | 25 | A | 2.8740 |
4 | ESD | ST161 | Golbasi | 05/05/1986 | 03:35:38 | 6 | 29 | A | 4.1699 |
5 | ESD | ST2486 | South Iceland | 17/06/2000 | 15:40:41 | 6.5 | 5 | A | 0.4186 |
6 | ESD | ST2487 | South Iceland | 17/06/2000 | 15:40:41 | 6.5 | 13 | A | 2.1493 |
7 | ESD | ST2496 | South Iceland (aftershock) | 21/06/2000 | 00:51:48 | 6.4 | 14 | A | 1.3983 |
8 | ESD | ST2486 | South Iceland (aftershock) | 21/06/2000 | 00:51:48 | 6.4 | 22 | A | 3.2431 |
9 | ESD | ST2557 | South Iceland (aftershock) | 21/06/2000 | 00:51:48 | 6.4 | 15 | A | 1.6217 |
10 | ESD | ST2563 | South Iceland (aftershock) | 21/06/2000 | 00:51:48 | 6.4 | 24 | A | 3.5147 |
11 | ESD | ST2497 | South Iceland (aftershock) | 21/06/2000 | 00:51:48 | 6.4 | 20 | A | 2.1600 |
12 | ESD | ST2558 | South Iceland (aftershock) | 21/06/2000 | 00:51:48 | 6.4 | 5 | A | 0.4782 |
13 | ESD | ST539 | Bingol | 01/05/2003 | 00:27:04 | 6.3 | 14 | A | 1.0089 |
14 | ESM | MZ19 | Central Italy | 30/10/2016 | 06:40:18 | 6.5 | 22.6 | A | 0.6537 |
15 | ESM | ULA | Northwestern Balkan Peninsula | 15/04/1979 | 06:19:41 | 6.9 | 19.7 | A | 0.7204 |
16 | ESM | ATH4 | Greece | 07/09/1999 | 11:56:49 | 5.9 | 19.7 | A | 3.6782 |
17 | ESM | CLO | Central Italy | 26/10/2016 | 19:18:06 | 5.9 | 10.8 | A | 1.5432 |
18 | ESM | CLO | Central Italy | 30/10/2016 | 06:40:18 | 6.5 | 7.8 | A | 0.3685 |
19 | ESM | MMO | Central Italy | 26/10/2016 | 19:18:06 | 5.9 | 16.2 | A | 2.4060 |
20 | ESM | T1213 | Central Italy | 30/10/2016 | 06:40:18 | 6.5 | 12 | A | 0.5742 |
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Structure 1 | Structure 2 | ||||||
---|---|---|---|---|---|---|---|
T (s) | Mx(%) | My(%) | Rz(%) | T (s) | Mx(%) | My(%) | Rz(%) |
1.50 | 0.00 | 76.19 | 0.00 | 1.61 | 1.0 | 67.7 | 8.2 |
1.07 | 0.02 | 0.00 | 78.78 | 1.10 | 41.1 | 6.7 | 31.6 |
0.99 | 81.44 | 0.00 | 0.02 | 0.89 | 39.3 | 39.8 | 39.0 |
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Cantagallo, C.; Terrenzi, M.; Spacone, E.; Camata, G. Effects of Multi-Directional Seismic Input on Non-Linear Static Analysis of Existing Reinforced Concrete Structures. Buildings 2023, 13, 1656. https://doi.org/10.3390/buildings13071656
Cantagallo C, Terrenzi M, Spacone E, Camata G. Effects of Multi-Directional Seismic Input on Non-Linear Static Analysis of Existing Reinforced Concrete Structures. Buildings. 2023; 13(7):1656. https://doi.org/10.3390/buildings13071656
Chicago/Turabian StyleCantagallo, Cristina, Marco Terrenzi, Enrico Spacone, and Guido Camata. 2023. "Effects of Multi-Directional Seismic Input on Non-Linear Static Analysis of Existing Reinforced Concrete Structures" Buildings 13, no. 7: 1656. https://doi.org/10.3390/buildings13071656