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=ASIA6AP2G7AKFSMUWIIF%2F20260318%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20260318T105845Z&X-Amz-Expires=3600&X-Amz-Security-Token=IQoJb3JpZ2luX2VjEDsaDGV1LWNlbnRyYWwtMSJHMEUCID6%2BC4fd%2FM7dFmOsGfZMfE3D4ks34pk1dc9gCjmod%2F0TAiEAx6T2Fg9SGB48Dr%2FNSdjRJssg1buZpfCBYNK0x3Iqfu0quwUIBBACGgw5NjMxMzQyODk5NDAiDK2y4nW7QM6bfbPjAiqYBe0ETDq8Eo3IUkhC3WTiSzBpPdr9m4aeRYU%2FPt9ej1vCoTYUVa2%2FJYmv1HFH66h%2FUBiJ2YvtdfruD%2F4DWBMTStTZgB7cCMvsVKmYVMH%2FsG%2Bvu4iAdHs8IcWudaLG1f3na9RuOu%2FXZDjjzCe6E%2BT9YwcnR59minwllJY0TLIpBPjMLiBmYukoVOe1jHoBfqaUMuXs%2B7fET5g72NDjmgvEqFhQKQDJxDoero5CuKpfG749pVqnIHT9VPWHNZJqPQTlp91URY3QTI%2FpkUPzRI0NMQdDPr5sW3m1yApzJxUP1Ilj3d%2BH1o0HBrp3HhhizaKhxXcRhgga9OCaNyPo45VxThMQQ5%2FTs%2B26%2BFf24r3cmN1Hy4l6h04xxSbRCMIMI8HyT69P1d9h6B5amJzkFNKi59RhX15tlmOa7vXZb0MyjOaRsOeS228iHgNP9Fe9tyt8SGzCw31iHwW5YjX1Cfd69lJWpXM%2Bt7f6naySCci3wrGEmKu11EkTH0%2Fg6yIsrZaacMSKyu8uuWmpHn9g62xGJhbek%2FPAw9KzSWVbWV0PJGxtqJ%2FLgOnK%2FEEyjKiDpoR0pDsOI%2BUWhjzEBF%2FvxAGa9NXnv8vnC7s0I9UDO5AS4%2Fuuitasll4A32S5DhGruFRkXMaGxPHwiUNCIMAiqqKuHc%2FkHeJtfjHscBo1Lzfg%2FIRauFR9%2BELekaLUwxZSlwLPbtcKtrPrbAxhziOqe3RfNes5%2B32DwBIC05WPCZhN2JbFzh6WuhvDJUluXLTQalDU2GujLRFJul6mKmb2v2EHqOrioNwWLVi%2BiUeL7NMhhgRL7%2F10P361AO8KS8nF2YMasDxPYe6oCkk8rXiYTYOuKIHrZ56LggCkzEmrA9DrOj36XPJCFRX85rMwgIDqzQY6sQEBIWIrkwcRhPuqD5vsbJe%2Fj94z4Sebk76tqQsGz4LbxzxK0nXUnM28%2FjwapT6%2Bn4bvuPa%2FOjn%2FqvR%2Bj3nYfo2oXN3tW7ie6VWZNpxAQrx2cSa%2Bg32YuvU9%2B4j96aWV6OE%2Fcf5myJIiAp5h5ZmQAdgpaE2Ir0uqcidYiZ9F1rolsopRAX3oOadC26RR6QpbW1SGoa1ozHcR%2F%2Bin26QrfK7KUfqiAmohhoTcmB9Ofp1eXo4%3D&X-Amz-Signature=2efbb45dac648c0070215052606b1715ea99f6a912b4eab1427d6de4fa1b2c48&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=ASIA6AP2G7AKFSMUWIIF%2F20260318%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20260318T105845Z&X-Amz-Expires=3600&X-Amz-Security-Token=IQoJb3JpZ2luX2VjEDsaDGV1LWNlbnRyYWwtMSJHMEUCID6%2BC4fd%2FM7dFmOsGfZMfE3D4ks34pk1dc9gCjmod%2F0TAiEAx6T2Fg9SGB48Dr%2FNSdjRJssg1buZpfCBYNK0x3Iqfu0quwUIBBACGgw5NjMxMzQyODk5NDAiDK2y4nW7QM6bfbPjAiqYBe0ETDq8Eo3IUkhC3WTiSzBpPdr9m4aeRYU%2FPt9ej1vCoTYUVa2%2FJYmv1HFH66h%2FUBiJ2YvtdfruD%2F4DWBMTStTZgB7cCMvsVKmYVMH%2FsG%2Bvu4iAdHs8IcWudaLG1f3na9RuOu%2FXZDjjzCe6E%2BT9YwcnR59minwllJY0TLIpBPjMLiBmYukoVOe1jHoBfqaUMuXs%2B7fET5g72NDjmgvEqFhQKQDJxDoero5CuKpfG749pVqnIHT9VPWHNZJqPQTlp91URY3QTI%2FpkUPzRI0NMQdDPr5sW3m1yApzJxUP1Ilj3d%2BH1o0HBrp3HhhizaKhxXcRhgga9OCaNyPo45VxThMQQ5%2FTs%2B26%2BFf24r3cmN1Hy4l6h04xxSbRCMIMI8HyT69P1d9h6B5amJzkFNKi59RhX15tlmOa7vXZb0MyjOaRsOeS228iHgNP9Fe9tyt8SGzCw31iHwW5YjX1Cfd69lJWpXM%2Bt7f6naySCci3wrGEmKu11EkTH0%2Fg6yIsrZaacMSKyu8uuWmpHn9g62xGJhbek%2FPAw9KzSWVbWV0PJGxtqJ%2FLgOnK%2FEEyjKiDpoR0pDsOI%2BUWhjzEBF%2FvxAGa9NXnv8vnC7s0I9UDO5AS4%2Fuuitasll4A32S5DhGruFRkXMaGxPHwiUNCIMAiqqKuHc%2FkHeJtfjHscBo1Lzfg%2FIRauFR9%2BELekaLUwxZSlwLPbtcKtrPrbAxhziOqe3RfNes5%2B32DwBIC05WPCZhN2JbFzh6WuhvDJUluXLTQalDU2GujLRFJul6mKmb2v2EHqOrioNwWLVi%2BiUeL7NMhhgRL7%2F10P361AO8KS8nF2YMasDxPYe6oCkk8rXiYTYOuKIHrZ56LggCkzEmrA9DrOj36XPJCFRX85rMwgIDqzQY6sQEBIWIrkwcRhPuqD5vsbJe%2Fj94z4Sebk76tqQsGz4LbxzxK0nXUnM28%2FjwapT6%2Bn4bvuPa%2FOjn%2FqvR%2Bj3nYfo2oXN3tW7ie6VWZNpxAQrx2cSa%2Bg32YuvU9%2B4j96aWV6OE%2Fcf5myJIiAp5h5ZmQAdgpaE2Ir0uqcidYiZ9F1rolsopRAX3oOadC26RR6QpbW1SGoa1ozHcR%2F%2Bin26QrfK7KUfqiAmohhoTcmB9Ofp1eXo4%3D&X-Amz-Signature=1d773ad591eb2b1d5c25168da3262beb456584adc52d37af4605e72db082e147&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) |