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=ASIA6AP2G7AKEBO3RRYE%2F20260126%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20260126T111851Z&X-Amz-Expires=3600&X-Amz-Security-Token=IQoJb3JpZ2luX2VjEG8aDGV1LWNlbnRyYWwtMSJHMEUCIQCIsNKRUZ6qSaHyCRo8j8neiUlJCXaCfReSx4SHH6BymAIgfHtlLtjB%2BYC6sX%2BazOnzGJPG6hfsm0fovzK8L4fbHUgqvQUIOBACGgw5NjMxMzQyODk5NDAiDAEWkxo6xOf9hVW8pSqaBXyZ6csIyCc1ntKdcvRpPlM8TBjzGSCAEssLGqfp1RSCJm1N1%2BoHZAKTGfp425oqOEQUDAwdYdPhebJqHKB8YODRhcFZ%2Be0jChXd8YUJV9BhZoRc0r5y%2Fdv4B%2FeABMBUEbo6uPpSs8jp8C2f5%2B0vi85n3VuzXShNEhSxWnJMJDw32P%2BBepfZNX5pcEYX98GD9dY1QVNixA%2FG6XkJ3RPl3RRPd62SiwYoig7uF%2BaR2uOZoRRwwo5EPRCXyji4QYgxbtkJMzeQbqxrSGh5%2Fx8tWZ4ySn%2BQewNR2kTSGFgmZE5InXAR0g5F9Up7F4sWppXLQ%2BL711CKyKBztMpEfHWy9n%2FUWxavpWJLyIKxz5Tn54wI0sxhjkdk1RYpfP6t%2B4suRz7yQmKz88xs5fAKLJKCHC4LdzMpddljUt%2FvWNRT3YlhNNP6uiwuo7azMIDBj%2F1oC%2Ff4mRF3%2FZK9b1RdLr%2F28KlLB6QaJ1doucIAPzLRWxJUeqeWenkUeJIX5SxAa8rs3xuD3YepmV0MTJL4NR93b%2BfraG4Ixr3WUqnCaj9%2FZmEM7iHIv1c9kMj%2BehacS9lu0TgXkOZfpaIxQHynV9Ek6y%2Bm4xuC1srDrRapm62%2F68r1WZG0%2F2TU129i5Jw%2Fy6bz94DpKxDuS8DQX2m9AAk5%2F%2Bvt6YydAFU%2FD6ehGl43exC4q6cyoJN7xX1oHLcOE8PoqpbyQc%2B4odIVcLllC5PSS%2BmxRLgFCYlMxoSbXpiExEAcmyL9P2NiuLXroJEr0avJ9MpfrB4Cs6u5%2BG7xuvA9dwynpa9zgoW4EOog%2BIO1bwi7BwKBQVG4Ij7gAZqTkSWwHxWDRgB%2B8EgkXfpvMen33w6ottDKnYTKTafrMU5RudiIXqr4E5BTZa0%2B7TCWpdzLBjqxASz21wNNSl4faurIC67w4BlU7Gj%2BPEh5ouc%2FxEw6wGQJfPnGhLnS6s0xOYGWr2vpLmZtd1Wc2wX%2FPGUAwXY0joM11R6zL5lvlTQJwA3EuxopkXFt48y8HHus57LxftNN5bgYWyonFuoGTXmdZxpRi7llpR1h0jGeMBaIVNA%2FPJGLI1kacaW6dSs0pMHvo9f5xsI9pk%2BWXRqPnfhLKqLJInnUXeaKlU2XrKVacwyqWEsIsQ%3D%3D&X-Amz-Signature=71f5f32ff9f08fc00158d4ed283e29df2300c5f3d3abebebd3f51c7759277097&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=ASIA6AP2G7AKEBO3RRYE%2F20260126%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20260126T111851Z&X-Amz-Expires=3600&X-Amz-Security-Token=IQoJb3JpZ2luX2VjEG8aDGV1LWNlbnRyYWwtMSJHMEUCIQCIsNKRUZ6qSaHyCRo8j8neiUlJCXaCfReSx4SHH6BymAIgfHtlLtjB%2BYC6sX%2BazOnzGJPG6hfsm0fovzK8L4fbHUgqvQUIOBACGgw5NjMxMzQyODk5NDAiDAEWkxo6xOf9hVW8pSqaBXyZ6csIyCc1ntKdcvRpPlM8TBjzGSCAEssLGqfp1RSCJm1N1%2BoHZAKTGfp425oqOEQUDAwdYdPhebJqHKB8YODRhcFZ%2Be0jChXd8YUJV9BhZoRc0r5y%2Fdv4B%2FeABMBUEbo6uPpSs8jp8C2f5%2B0vi85n3VuzXShNEhSxWnJMJDw32P%2BBepfZNX5pcEYX98GD9dY1QVNixA%2FG6XkJ3RPl3RRPd62SiwYoig7uF%2BaR2uOZoRRwwo5EPRCXyji4QYgxbtkJMzeQbqxrSGh5%2Fx8tWZ4ySn%2BQewNR2kTSGFgmZE5InXAR0g5F9Up7F4sWppXLQ%2BL711CKyKBztMpEfHWy9n%2FUWxavpWJLyIKxz5Tn54wI0sxhjkdk1RYpfP6t%2B4suRz7yQmKz88xs5fAKLJKCHC4LdzMpddljUt%2FvWNRT3YlhNNP6uiwuo7azMIDBj%2F1oC%2Ff4mRF3%2FZK9b1RdLr%2F28KlLB6QaJ1doucIAPzLRWxJUeqeWenkUeJIX5SxAa8rs3xuD3YepmV0MTJL4NR93b%2BfraG4Ixr3WUqnCaj9%2FZmEM7iHIv1c9kMj%2BehacS9lu0TgXkOZfpaIxQHynV9Ek6y%2Bm4xuC1srDrRapm62%2F68r1WZG0%2F2TU129i5Jw%2Fy6bz94DpKxDuS8DQX2m9AAk5%2F%2Bvt6YydAFU%2FD6ehGl43exC4q6cyoJN7xX1oHLcOE8PoqpbyQc%2B4odIVcLllC5PSS%2BmxRLgFCYlMxoSbXpiExEAcmyL9P2NiuLXroJEr0avJ9MpfrB4Cs6u5%2BG7xuvA9dwynpa9zgoW4EOog%2BIO1bwi7BwKBQVG4Ij7gAZqTkSWwHxWDRgB%2B8EgkXfpvMen33w6ottDKnYTKTafrMU5RudiIXqr4E5BTZa0%2B7TCWpdzLBjqxASz21wNNSl4faurIC67w4BlU7Gj%2BPEh5ouc%2FxEw6wGQJfPnGhLnS6s0xOYGWr2vpLmZtd1Wc2wX%2FPGUAwXY0joM11R6zL5lvlTQJwA3EuxopkXFt48y8HHus57LxftNN5bgYWyonFuoGTXmdZxpRi7llpR1h0jGeMBaIVNA%2FPJGLI1kacaW6dSs0pMHvo9f5xsI9pk%2BWXRqPnfhLKqLJInnUXeaKlU2XrKVacwyqWEsIsQ%3D%3D&X-Amz-Signature=f6dfdd2d48c1706a1dbf4c3f12db40a67f14f07d958d2409787e4dc4c0392ff1&X-Amz-SignedHeaders=host&x-amz-checksum-mode=ENABLED&x-id=GetObject)
Figure 4
Figure 5
Figure 6
Figure 7
Figure 8
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) |