Collapse Analyses of Pre- and Low-Code Italian RC Building Types
Abstract
1. Introduction
2. Literature Review
3. Methodology
3.1. Selection of Building Types
3.2. Design and Modeling
3.3. Incremental Dynamic Analyses
4. Results
4.1. Inter-Storey Drift Ratio at Collapse
- IDR values decrease as the number of storeys increases for both GLD and ERD types. Specifically, the minimum mean values for GLD are approximately 3.5%, 2.8%, and 1.9% for 2s, 4s, and 6s types, respectively, while they become 4.4%, 2.9%, and 2.4% for ERD. To understand the observed trend, it is important to note that the collapse mechanism for each type generally involves the bottom storeys, as illustrated in Figure 8, which illustrates the IDR profiles related to the minimum values along the X and Y directions. Since cross-section dimensions of columns and the related reinforcement details do not change significantly across the storeys, the displacement capacity reduces with the number of storeys (i.e., as axial forces increase). This aspect can be better acknowledged in Table 1, where the plastic rotation values (at capping) for the columns of the first storey are reported for all types.
- The minimum IDR values among the two in-plane directions detected for ERD are higher compared to GLD types, with increments of about 25% for 2s and 6s and about 5% for 4s. A different trend is observed between the two in-plane directions. For GLD, the X direction exhibits lower IDR values compared to the Y direction, whereas the opposite is found for the ERD types, with notable differences between the X and Y directions. For this purpose, it is worth noting that, in GLD, the cross-section dimensions and reinforcements details of the columns are quite similar for both in-plane directions. Therefore, the greater lateral displacement capacity along the Y direction mainly depends on the contribution of stairs and infills (which have no openings along the Y direction). On the contrary, lateral forces considered for ERD types significantly increase the lateral displacement capacity of the frames along the X direction compared to those along the Y direction. Indeed, as previously described, the lateral resisting scheme of the considered prototypes has a greater number of frames along the X direction compared to those along the Y direction, which are placed only on the exterior sides. Furthermore, the columns’ response along the Y direction exhibits a greater number of brittle failures compared to the X direction. Finally, note that, according to the common practice of the period, the contribution of the staircase sub-structure is the same as in GLD, since it has been designed only for vertical loads.
- As for dispersion, the σln values associated with the minimum IDR range from 0.35 to 0.49 for GLD, while lower values (0.22–0.35) are observed for ERD. Although simple schemes have been adopted, the interior force analyses carried out for EDR types generally reduce the variability of the response at collapse with respect to GLD, whose structural members have mainly been designed by adopting the minimum requirements of codes.
4.2. Fragility Curves at Collapse
5. Conclusions
- Ground motion intensities at collapse evaluated for ERD types are generally higher than those for GLD, as expected, with larger differences for 4s and 6s types;
- In GLD, the Y direction is stronger than the X direction. On the contrary, in ERD types, lateral load design increases the lateral capacity of frames along the X direction more than along the Y direction, mainly due to the number of frames along the two in-plane directions, which affects the distribution of lateral loads, and the higher occurrence of brittle failures;
- IDR values at collapse decrease as the number of storeys increases, with ERD types exhibiting higher values compared to GLD ones. More specifically, the minimum mean IDR values for GLD are approximately 3.5%, 2.8%, and 1.9% for 2s, 4s, and 6s types, respectively, while for ERD types, the values are 4.4%, 2.9%, and 2.4%. The same trend previously described for ground motion intensities in the two in-plane directions is also found for IDR results.
- As for dispersion, the values range from 0.35 to 0.49 for GLD types, while lower values (0.22–0.35) are found for ERD.
- As expected, for all IMs, ERD types exhibit higher median values compared to GLD ones, with more significant differences observed for 4s and 6s types (in the range of about 20–80%). Lower differences are found for 2s types (in the range of about 5–10%).
- The median values for 2s are higher than those for 4s and 6s, which have similar values. The differences between 2s and 4–6s types are about 40% for GLD and 25% for ERD for all IMs, except for Sa(T1) and AI, which exhibit greater differences (in the range of about 43–66%).
- For GLD types, the median values in the X direction are always higher than those in the Y direction across all the considered IMs, whereas ERD types exhibit the opposite trend.
- The lowest dispersion values are found for HI (0.15–0.22) and Sa,avg (0.16–0.22), revealing greater efficiency compared to the other IMs such as Sa(T1) and AI, whose values are in the range 0.47–0.69 and 0.53–0.72, respectively.
- In general, the dispersion values slightly increase as the number of storeys increases without any significant differences between GLD and ERD types.
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A
Signal | Mw | Repi [km] | VS30 [m/s] | PGA [g] | PGV [cm/s] | HI [m] | Sa (T1 = 0.25 s) [g] | Sa (T1 = 0.5 s) [g] | Sa (T1 = 0.75 s) [g] | Sa,avg [g] | AI [m/s] |
---|---|---|---|---|---|---|---|---|---|---|---|
#1 | 6.4 | 21.37 | na | 0.11 | 6.12 | 0.26 | 0.37 | 0.16 | 0.11 | 0.06 | 0.14 |
#2 | 5.7 | 18.73 | 408 | 0.12 | 8.44 | 0.23 | 0.32 | 0.10 | 0.05 | 0.06 | 0.08 |
#3 | 5.6 | 5.9 | 378 | 0.13 | 10.40 | 0.29 | 0.28 | 0.21 | 0.12 | 0.07 | 0.12 |
#4 | 5.9 | 27.77 | 363 | 0.10 | 4.46 | 0.22 | 0.12 | 0.08 | 0.07 | 0.05 | 0.11 |
#5 | 6.9 | 23.77 | 1149 | 0.06 | 5.06 | 0.20 | 0.13 | 0.11 | 0.06 | 0.05 | 0.06 |
#6 | 6 | 17.53 | na | 0.12 | 9.60 | 0.29 | 0.26 | 0.18 | 0.11 | 0.07 | 0.10 |
#7 | 5.6 | 10.33 | 626 | 0.14 | 6.65 | 0.22 | 0.30 | 0.19 | 0.08 | 0.05 | 0.10 |
#8 | 5.6 | 9.35 | 717 | 0.08 | 4.74 | 0.20 | 0.20 | 0.13 | 0.07 | 0.05 | 0.07 |
#9 | 5.5 | 15.81 | 452 | 0.09 | 5.60 | 0.17 | 0.27 | 0.09 | 0.05 | 0.04 | 0.07 |
#10 | 6.5 | 20.1 | na | 0.09 | 5.84 | 0.17 | 0.08 | 0.07 | 0.05 | 0.04 | 0.09 |
#11 | 6.4 | 20.83 | 852 | 0.10 | 9.09 | 0.28 | 0.21 | 0.27 | 0.12 | 0.07 | 0.09 |
#12 | 5.4 | 16.16 | 717 | 0.05 | 4.14 | 0.19 | 0.07 | 0.07 | 0.07 | 0.04 | 0.02 |
#13 | 6.4 | 30 | na | 0.12 | 8.39 | 0.32 | 0.33 | 0.21 | 0.08 | 0.08 | 0.14 |
#14 | 5.7 | 25.39 | 409 | 0.07 | 4.42 | 0.16 | 0.13 | 0.13 | 0.08 | 0.04 | 0.04 |
#15 | 5.9 | 10.04 | 901 | 0.13 | 6.34 | 0.18 | 0.27 | 0.11 | 0.11 | 0.04 | 0.16 |
#16 | 5.6 | 25.24 | 412 | 0.12 | 4.20 | 0.19 | 0.31 | 0.06 | 0.05 | 0.05 | 0.08 |
#17 | 6.1 | 29.53 | 403 | 0.11 | 4.24 | 0.16 | 0.24 | 0.10 | 0.11 | 0.04 | 0.14 |
#18 | 5 | 7.84 | 529 | 0.10 | 5.54 | 0.17 | 0.23 | 0.15 | 0.08 | 0.04 | 0.05 |
#19 | 5.9 | 23.85 | 601 | 0.08 | 6.73 | 0.16 | 0.13 | 0.13 | 0.09 | 0.04 | 0.05 |
#20 | 5.4 | 12.29 | 685 | 0.07 | 5.17 | 0.17 | 0.13 | 0.12 | 0.10 | 0.04 | 0.03 |
Appendix B. Derivation of Fragility Curves from IDA Results
Appendix C
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Type | ρl_X [%] | ρl_Y [%] | ρw_Y [%] | ρw_Y [%] | Mcap_X [kNm] | Mcap_Y [kNm] | θcap_X [-] | θcap_Y [-] | T1 [s] |
---|---|---|---|---|---|---|---|---|---|
2s-GLD | 0.28 | 0.28 | 0.11 | 0.11 | 68.2 | 68.2 | 0.0235 | 0.0245 | 0.25 |
4s-GLD | 0.25 | 0.29 | 0.11 | 0.10 | 101.2 | 88.3 | 0.0181 | 0.0131 | 0.49 |
6s-GLD | 0.24 | 0.31 | 0.10 | 0.08 | 145.1 | 117.0 | 0.0106 | 0.0100 | 0.77 |
2s-ERD | 0.50 | 0.31 | 0.09 | 0.09 | 114.3 | 102.2 | 0.0113 | 0.0135 | 0.23 |
4s-ERD | 0.56 | 0.30 | 0.10 | 0.08 | 216.4 | 108.4 | 0.0165 | 0.0121 | 0.49 |
6s-ERD | 0.53 | 0.27 | 0.07 | 0.07 | 320.3 | 195.2 | 0.0082 | 0.0082 | 0.70 |
GLD | ERD | ||||||
---|---|---|---|---|---|---|---|
2s | 4s | 6s | 2s | 4s | 6s | ||
IDR dirX | µ (16th–84th) [%] | 3.52 (2.19–4.82) | 2.76 (1.50–3.99) | 1.93 (1.28–2.57) | 7.38 (5.02–9.72) | 5.37 (2.87–7.80) | 6.31 (3.18–9.33) |
σln | 0.40 | 0.49 | 0.35 | 0.33 | 0.50 | 0.54 | |
IDR dirY | µ (16th–84th) [%] | 4.81 (3.03–6.57) | 3.56 (2.29–4.82) | 2.53 (1.82–3.24) | 4.43 (3.22–5.64) | 2.89 (1.93–3.84) | 2.40 (1.87–2.93) |
σln | 0.39 | 0.37 | 0.29 | 0.28 | 0.35 | 0.22 |
Type | In-Plane Direction | PGA | PGV | HI | Sa(T1) | Sa,avg | AI | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
eµ [g] | β [-] | eµ [cm/s] | β [-] | eµ [m] | β [-] | eµ [g] | β [-] | eµ [g] | β [-] | eµ [m/s] | β [-] | ||
2s-GLD | Dir-X | 1.38 | 0.32 | 86.01 | 0.28 | 2.95 | 0.15 | 2.84 | 0.51 | 0.71 | 0.16 | 15.99 | 0.55 |
Dir-Y | 1.41 | 0.31 | 88.22 | 0.25 | 3.02 | 0.13 | 3.12 | 0.46 | 0.73 | 0.14 | 16.82 | 0.53 | |
4s-GLD | Dir-X | 0.81 | 0.34 | 50.86 | 0.31 | 1.74 | 0.20 | 1.04 | 0.73 | 0.42 | 0.20 | 5.59 | 0.53 |
Dir-Y | 0.93 | 0.35 | 57.99 | 0.32 | 1.99 | 0.24 | 1.02 | 0.69 | 0.48 | 0.23 | 7.27 | 0.60 | |
6s-GLD | Dir-X | 0.81 | 0.39 | 50.80 | 0.30 | 1.74 | 0.22 | 0.68 | 0.47 | 0.42 | 0.21 | 5.58 | 0.69 |
Dir-Y | 0.84 | 0.34 | 52.28 | 0.24 | 1.79 | 0.16 | 0.72 | 0.56 | 0.43 | 0.15 | 5.91 | 0.63 | |
2s-ERD | Dir-X | 1.69 | 0.28 | 105.7 | 0.21 | 3.62 | 0.11 | 3.49 | 0.46 | 0.87 | 0.12 | 24.18 | 0.49 |
Dir-Y | 1.45 | 0.29 | 90.39 | 0.26 | 3.10 | 0.18 | 3.20 | 0.47 | 0.74 | 0.19 | 17.66 | 0.53 | |
4s-ERD | Dir-X | 1.29 | 0.32 | 79.02 | 0.30 | 2.77 | 0.22 | 1.61 | 0.41 | 0.65 | 0.22 | 14.14 | 0.53 |
Dir-Y | 1.09 | 0.40 | 68.22 | 0.31 | 2.34 | 0.21 | 1.09 | 0.68 | 0.56 | 0.21 | 10.06 | 0.72 | |
6s-ERD | Dir-X | 1.26 | 0.38 | 80.87 | 0.34 | 2.71 | 0.21 | 1.08 | 0.43 | 0.67 | 0.23 | 13.50 | 0.63 |
Dir-Y | 0.98 | 0.34 | 61.46 | 0.31 | 2.10 | 0.20 | 0.94 | 0.56 | 0.51 | 0.20 | 8.16 | 0.57 |
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Manfredi, V. Collapse Analyses of Pre- and Low-Code Italian RC Building Types. Buildings 2025, 15, 1263. https://doi.org/10.3390/buildings15081263
Manfredi V. Collapse Analyses of Pre- and Low-Code Italian RC Building Types. Buildings. 2025; 15(8):1263. https://doi.org/10.3390/buildings15081263
Chicago/Turabian StyleManfredi, Vincenzo. 2025. "Collapse Analyses of Pre- and Low-Code Italian RC Building Types" Buildings 15, no. 8: 1263. https://doi.org/10.3390/buildings15081263
APA StyleManfredi, V. (2025). Collapse Analyses of Pre- and Low-Code Italian RC Building Types. Buildings, 15(8), 1263. https://doi.org/10.3390/buildings15081263