Figure 1
![Base shear versus roof displacement relationship [5, 22].](https://sciendo-parsed.s3.eu-central-1.amazonaws.com/64737a264e662f30ba53f8cb/j_sgem-2022-0028_fig_001.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Content-Sha256=UNSIGNED-PAYLOAD&X-Amz-Credential=AKIA6AP2G7AKOUXAVR44%2F20251206%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20251206T190128Z&X-Amz-Expires=3600&X-Amz-Signature=296e1d78f21bb6f8b08a33f4a382b19878b14adabb642cf8ac0d5263bf30b7b5&X-Amz-SignedHeaders=host&x-amz-checksum-mode=ENABLED&x-id=GetObject)
Figure 2
Figure 3
![Plastic hinges of a cross section [32].](https://sciendo-parsed.s3.eu-central-1.amazonaws.com/64737a264e662f30ba53f8cb/j_sgem-2022-0028_fig_003.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Content-Sha256=UNSIGNED-PAYLOAD&X-Amz-Credential=AKIA6AP2G7AKOUXAVR44%2F20251206%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20251206T190128Z&X-Amz-Expires=3600&X-Amz-Signature=e95641f8d8776b7c4d5ef8aee1e08312b9b897e65ff859ff08ff7f442678831b&X-Amz-SignedHeaders=host&x-amz-checksum-mode=ENABLED&x-id=GetObject)
Figure 4
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Figure 9
Modal periods and mass ratios of the analyzed XBF steel structures_
| Storey number | λi | T1 (s) | T2 (s) | T3 (s) | M*1 | M*2 | M*3 | Vd/W |
|---|---|---|---|---|---|---|---|---|
| Three stories | λ1 = 1.93 | 0.41 | 0.14 | 0.09 | 0.86 | 0.11 | 0.02 | 0.22 |
| λ2 = 1.56 | 0.36 | 0.13 | 0.08 | 0.87 | 0.10 | 0.02 | 0.23 | |
| λ3 = 1.30 | 0.32 | 0.11 | 0.07 | 0.85 | 0.12 | 0.02 | 0.23 | |
| Six stories | λ1 = 1.93 | 0.83 | 0.28 | 0.16 | 0.78 | 0.15 | 0.03 | 0.13 |
| λ2 = 1.56 | 0.75 | 0.25 | 0.14 | 0.79 | 0.15 | 0.03 | 0.14 | |
| λ3 = 1.30 | 0.68 | 0.22 | 0.12 | 0.77 | 0.16 | 0.04 | 0.16 | |
| Nine stories | λ1 = 1.93 | 1.37 | 0.44 | 0.24 | 0.75 | 0.17 | 0.04 | 0.08 |
| λ2 = 1.56 | 1.24 | 0.40 | 0.22 | 0.76 | 0.17 | 0.04 | 0.09 | |
| λ3 = 1.30 | 1.10 | 0.34 | 0.19 | 0.75 | 0.19 | 0.04 | 0.10 |
XBF steel structures considered in parametric studies_
| Storey number | λi | Columns: HEB (N° of storey) | Braces: TUBO (N° of storey) |
|---|---|---|---|
| Three stories | λ1 = 1.93 | 220 (1–3) | 127X4 (1) + 108X3.6 (2) + 101.6X3.6 (3) |
| λ2 = 1.56 | 240 (1–3) | 152.4X4 (1) + 133X4 (2) + 127X4 (3) | |
| λ3 = 1.30 | 260 (1–3) | 193.7X4.5 (1) + 159X4 (2) + 139.7X4 (3) | |
| Six stories | λ1 = 1.93 | 240 (1–2) + 220 (3–4) + 200 (5–6) | 127X4 (1–3) + 108X3.6 (4) + 101.6X3.6 (5) + 82.5X3.2 (6) |
| λ2 = 1.56 | 260 (1–2) + 240 (3–4) + 220 (5–6) | 152.4X4 (1–2) + 139.7X4 (3) + 133X4 (4) + 127X4(5) + 101.6X3.6 (6) | |
| λ3 = 1.30 | 280 (1–2) + 260 (3–4) + 240 (5–6) | 193.7X4.5 (1–2) + 168.3X4 (3) + 159X4 (4) + 139.7X4(5) + 127X4 (6) | |
| Nine stories | λ1 = 1.93 | 260 (1–3) + 240 (4–6) + 220 (7–9) | 127X4 (1–4) + 108X3.6 (5–6) + 101.6X3.6 (7) + 88.9X3.2 (8) + 76.1X3.2 (9) |
| λ2 = 1.56 | 280 (1–3) + 260 (4–6) + 240 (7–9) | 152.4X4 (1–3) + 139.7X4 (4) + 133X4 (5) + 127X4 (6–7) + 108X3.6 (8) + 88.9X3.2 (9) | |
| λ3 = 1.30 | 320 (1–3) + 300 (4–6) + 280 (7–9) | 193.7X4.5 (1–4) + 159X4 (5) + 152.4X4 (6) + 139.7X4 (7) + 127X4 (8) + 108X3.6 (9) |