A Simple and Effective Method to Evaluate Seismic Maximum Floor Velocities for Steel-Framed Structures with Supplementary Dampers
<p>Inelastic velocity ratio for two strong ground motions and <span class="html-italic">q</span> = 4.</p> "> Figure 2
<p>Examples of planar steel frames examined here.</p> "> Figure 3
<p>Bilinear elastoplastic hysteretic model.</p> "> Figure 4
<p><span class="html-italic">P</span>-<span class="html-italic">M</span> interaction diagram (Carr, [<a href="#B32-applmech-04-00057" class="html-bibr">32</a>]).</p> "> Figure 5
<p>Inherent damping ratio as a function of the number of stories for the steel moment-resisting frames under consideration.</p> "> Figure 6
<p>Viscous damper’s model (adapted from [<a href="#B32-applmech-04-00057" class="html-bibr">32</a>]).</p> "> Figure 7
<p>Accelerogram spectra, mean spectrum, and design spectrum EC8 [<a href="#B1-applmech-04-00057" class="html-bibr">1</a>].</p> "> Figure 8
<p>Profiles of inter-story velocities for a 3-story building for <span class="html-italic">ξ<sub>eq.</sub></span> = 5% (<b>left</b>) and 30% (<b>right</b>).</p> "> Figure 9
<p>Profiles of inter-story velocities for 9-story building for <span class="html-italic">ξ<sub>eq.</sub></span> = 5% (<b>left</b>) and 30% (<b>right</b>).</p> "> Figure 10
<p>Predicted vs. ’exact’ maximum story velocities: <span class="html-italic">V<sub>PR</sub></span>/<span class="html-italic">V<sub>NTHA</sub></span> ratio.</p> ">
Abstract
:1. Introduction
2. Steel Structures: Description and Analysis
3. Seismic Input
4. Proposed Methodology
- STEP 1:
- STEP2:
- STEP 3:
- STEP 4:
5. Verification and Applications
6. Conclusions
- It seems impermissible and inaccurate to assume that the inelastic velocity ratio is equal to unity, i.e., that the inelastic velocities are equal to the corresponding elastic ones.
- The proposed research study is simple and straightforward, without increased computational cost.
- Numerous inelastic time-history analyses were carried out and a comprehensive nonlinear regression analysis was carried out to provide simple empirical expressions for the inelastic velocity ratio. The influence of the fundamental period of vibration and the equivalent viscous damping ratio is taken into account.
- This method appears to be useful both for traditional steel frames and for steel frames with supplementary dampers.
- Comparing the proposed method with dynamic inelastic time history analyses, it is found that the proposed study appears to be reliable and accurate.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Frame | ns | nb | Standard Sections (HEB for Columns—IPE for Beams) |
---|---|---|---|
1 | 3 | 2 | 240-360(1-3) |
2 | 3 | 4 | 240-360(1-3) |
3 | 6 | 2 | 280-360(1-4) + 260-360(5-6) |
4 | 6 | 4 | 280-360(1-4) + 260-360(5-6) |
5 | 9 | 2 | 340-360(1-5) + 320-360(6-7) + 300-330(8-9) |
6 | 9 | 4 | 340-360(1-5) + 320-360(6-7) + 300-330(8-9) |
7 | 12 | 2 | 400-400(1-5) + 360-400(6-7) + 340-400(8-9) + 340-360(10) + 340-330(11-12) |
8 | 12 | 4 | 400-400(1-5) + 360-400(6-7) + 340-400(8-9) + 340-360(10) + 340-330(11-12) |
9 | 15 | 2 | 500-450(1-5) + 450-400(6-7) + 400-400(8-12) + 400-360-(13-14) + 400-330(15) |
10 | 15 | 4 | 500-450(1-5) + 450-400(6-7) + 400-400(8-12) + 400-360-(13-14) + 400-330(15) |
11 | 20 | 2 | 600-450(1-5) + 550-450(6-10) + 500-450(11-13) + 500-400(14-16) + 450-400(17) + 450-360(18-19) + 450-330(20) |
12 | 20 | 4 | 600-450(1-5) + 550-450(6-10) + 500-450(11-13) + 500-400(14-16) + 450-400(17) + 450-360(18-19) + 450-330(20) |
No. | Date | Record Name | Comp. | Station Name | PGA (g) |
---|---|---|---|---|---|
1 | 20 September 1999 | Chi-Chi, Taiwan | NS | NST | 0.388 |
2 | 20 September 1999 | Chi-Chi, Taiwan | EW | NST | 0.309 |
3 | 2 May 1983 | Coalinga | EW | 36227 Parkfield | 0.147 |
4 | 2 May 1983 | Coalinga | NS | 36227 Parkfield | 0.131 |
5 | 12 November 1999 | Duzce, Turkey | NS | Bolu | 0.728 |
6 | 12 November 1999 | Duzce, Turkey | EW | Bolu | 0.822 |
7 | 15 October 1979 | Imperial Valley | N015 | 6622 Compuertas | 0.186 |
8 | 15 October 1979 | Imperial Valley | N285 | 6622 Compuertas | 0.147 |
9 | 15 October 1979 | Imperial Valley | N012 | 6621 Chihuahua | 0.270 |
10 | 15 October 1979 | Imperial Valley | N282 | 6621 Chihuahua | 0.284 |
11 | 17 August 1999 | Kocaeli, Turkey | NS | Atakoy | 0.105 |
12 | 17 August 1999 | Kocaeli, Turkey | EW | Atakoy | 0.164 |
13 | 18 October 1989 | Loma Prieta | NS | 1028 Hollister City Hall | 0.247 |
14 | 18 October 1989 | Loma Prieta | EW | 1028 Hollister City Hall | 0.215 |
15 | 24 April 1984 | Morgan Hill | NS | 57382 Gilroy Array #4 | 0.224 |
16 | 24 April 1984 | Morgan Hill | EW | 57382 Gilroy Array #4 | 0.348 |
17 | 17 January 1994 | Northridge | NS | 90057 Canyon Country | 0.482 |
18 | 17 January 1994 | Northridge | EW | 90057 Canyon Country | 0.410 |
19 | 9 February 1971 | San Fernando | EW | 135 LA—Hollywood | 0.210 |
20 | 9 February 1971 | San Fernando | NS | 135 LA—Hollywood | 0.174 |
21 | 26 April 1981 | Westmorland | NS | 5169 Westmorland Fire Sta | 0.368 |
22 | 26 April 1981 | Westmorland | EW | 5169 Westmorland Fire Sta | 0.496 |
23 | 24 November 1987 | Superst. Hills (B) | NS | 01335 El Centro Imp. Co. Cent | 0.258 |
24 | 24 November 1987 | Superst. Hills (B) | EW | 01335 El Centro Imp. Co. Cent | 0.358 |
25 | 27 January 1980 | Livermore | EW | 57187 San Ramon | 0.301 |
Parameter | a | b | c |
---|---|---|---|
ξeq = 5% | 0.35069 | −1.43800 | 1.23579 |
ξeq = 10% | 0.45772 | −1.23279 | 1.08484 |
ξeq = 20% | 0.54494 | −0.87169 | 0.77337 |
ξeq = 30% | 0.55136 | −0.69468 | 0.61634 |
ξeq = 40% | 0.60285 | −0.55529 | 0.49353 |
ξeq = 50% | 0.59042 | −0.49497 | 0.44038 |
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Kosmidou, A.; Konstandakopoulou, F.; Pnevmatikos, N.; Asteris, P.G.; Hatzigeorgiou, G. A Simple and Effective Method to Evaluate Seismic Maximum Floor Velocities for Steel-Framed Structures with Supplementary Dampers. Appl. Mech. 2023, 4, 1114-1126. https://doi.org/10.3390/applmech4040057
Kosmidou A, Konstandakopoulou F, Pnevmatikos N, Asteris PG, Hatzigeorgiou G. A Simple and Effective Method to Evaluate Seismic Maximum Floor Velocities for Steel-Framed Structures with Supplementary Dampers. Applied Mechanics. 2023; 4(4):1114-1126. https://doi.org/10.3390/applmech4040057
Chicago/Turabian StyleKosmidou, Alexia, Foteini Konstandakopoulou, Nikos Pnevmatikos, Panagiotis G. Asteris, and George Hatzigeorgiou. 2023. "A Simple and Effective Method to Evaluate Seismic Maximum Floor Velocities for Steel-Framed Structures with Supplementary Dampers" Applied Mechanics 4, no. 4: 1114-1126. https://doi.org/10.3390/applmech4040057