# Seismic Acceleration and Displacement Demand Profiles of Non-Structural Elements in Hospital Buildings

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Case-Study Hospital Building

_{c}) equal to 20 MPa, while the longitudinal and transverse steel reinforcement have a yield strength (f

_{y}) equal to 320 MPa. According to the design practice at the time, the structural elements were not designed assuming a frame configuration; the columns were designed considering their area of influence, while the beams were designed following a continuous beam static scheme. The columns were only designed for compression, consequently reduced amounts of vertical and transverse reinforcement were used (in specific, the transverse reinforcement is characterized by 6mm-diameter rebars with a spacing of 250 mm). Since the size and the reinforcement layout of the columns vary in plane and along the height of the building, for the sake of brevity, they are not reported here. Moreover, as the hospital building was built before the introduction of modern seismic codes, the structural detailing does not comply with the minimum requirements that presently are applied to design newly built structures subjected to seismic-induced actions, such as the minimum amount of longitudinal, transverse, and shear reinforcement in both beams and columns, strengthening of beam-column joints and application of capacity design principles.

## 3. Numerical Modeling

^{3}, (ii) a permanent load of 5.4 kN/m

^{2}, and (iii) a live load equal to 3 kN/m

^{2}. The total mass of the hospital building, considering the masses corresponding to the aforementioned loads, is estimated to be 6000 tons.

## 4. Hazard Modeling and Ground Motion Record Selection

_{a}(T*), at a conditioning period (T*) was chosen. Concerning the choice of a suitable conditional period, FEMA P58 [39] recommends using a T* deduced from the arithmetic mean of the two orthogonal modal periods. The selected case-study structure has the first two fundamental periods equal to T

_{1}= 2.306 s and T

_{2}= 1.387 s, with an arithmetic mean of T

_{mean}= 1.85 s. Based on these results, the conditioning period was chosen, as a reasonable approximation of T

_{mean}, as T* = 2 s. It is also important to underline that in this study, a hazard consistent record selection was performed; hence, the discrepancy in T* and the first period of vibration can be deemed as a valid approach in case of a risk-based assessment, as pointed out in Lin et al. [40].

## 5. Structural Response Results

^{2}and 1.3 m/s

^{2}, respectively, for the X and Y directions; maxima around 2 m/s

^{2}were predicted, again for both directions, although the variability among the record set is more pronounced in the longitudinal direction, with more scattered acceleration peak profiles over the structure height. As far as RP = 200 years is considered, an increase of approximately 25% is observed in terms of median peak roof accelerations in both building directions with respect to the OLS counterparts (see Figure 5b vs. Figure 4b), thus confirming a nearly linear variation and a nearly elastic building response for both serviceability limit states.

## 6. Discussion of Results and Comparison with Simplified Approaches

_{a}, between 0.6 s and 1.2 s. This range of non-structural periods can typically correspond to many typologies of NSEs [9]. The floor response spectra predicted by NTC 2018 and EC8 are close to each other while higher spectral accelerations are predicted by ASCE 7-16, which may come from the fact that the formulation provided by ASCE 7-16 does not account for the ratio between the fundamental period of the supporting structure and the fundamental period of the NSE. For this reason, the floor spectral acceleration assumes the same value regardless of T

_{a}.

## 7. Conclusions

- Despite the unfavorable characteristics, related to the design for gravity loads only, the case-study hospital building responded in the elastic range for both considered seismic intensities;
- The identified higher modes significantly affected the floor response spectra, particularly due to the high deformability of the structure and to the observed record-to-record variability, even for the low investigated RPs. In this regard, only a few simplified formulations can approximately consider such aspect, while current codes neglect them. It is, therefore, deemed necessary to adapt the simplified approaches to account for this effect, as demonstrated by the presented set of dynamic analysis results;
- For the specific case-study hospital building analyzed, the seismic demand on the NSEs was not successfully predicted by any of the considered code formulations hence more accurate, yet simplified, methodologies are required to support the seismic design of NSEs.

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**Illustration of the main hospital building geometrical configuration; (

**a**) front view in XZ (section A-A), (

**b**) side view in YZ (section B-B), and (

**c**) plan-view in XY.

**Figure 2.**Side view of the 3D numerical model of the hospital building, elements, and fiber sections discretization.

**Figure 3.**(

**a**) Site hazard curve at the conditioning period T* = 2.0 s; and (

**b**) ground motion records selected for 140-year return period.

**Figure 4.**Drift and acceleration peak profiles in longitudinal and transverse directions for RP = 140 years: (

**a**) peak storey drifts in X and Y directions; (

**b**) peak floor accelerations in X and Y directions.

**Figure 5.**Drift and acceleration peak profiles in longitudinal and transverse directions for RP = 200 years: (

**a**) peak storey drifts in X and Y directions; (

**b**) peak floor accelerations in X and Y directions.

**Figure 6.**Individual and statistical acceleration floor spectra for RP = 140 years—First floor, mid-height and roof: (

**a**) longitudinal, X direction; (

**b**) transverse, Y direction.

**Figure 7.**Individual and statistical displacement floor spectra for RP = 140 years—First floor, mid-height and roof: (

**a**) longitudinal, X direction; (

**b**) transverse, Y direction.

**Figure 8.**Acceleration floor spectra for RP = 200 years—First floor, mid-height and roof: (

**a**) longitudinal, X direction; (

**b**) transverse, Y direction.

**Figure 9.**Displacement floor spectra for RP = 200 years—First floor, mid-height and roof: (

**a**) longitudinal, X direction; (

**b**) transverse, Y direction.

**Figure 10.**PFA-normalized maximum spectral accelerations over the structure height: (

**a**) RP = 140 years, X direction; (

**b**) RP = 140 years, Y direction; (

**c**) RP = 200 years, X direction; (

**d**) RP = 200 years, Y direction.

**Figure 11.**Comparison between absolute acceleration top floor response spectra obtained from nonlinear time–history analyses and code formulations: (

**a**) RP = 140 years, X direction; (

**b**) RP = 140 years, Y direction; (

**c**) RP = 200 years, X direction; (

**d**) RP = 200 years, Y direction.

Mode | Period (s) | Type |
---|---|---|

1st | 2.306 | Translation—Y direction |

2nd | 1.387 | Torsional |

3rd | 1.006 | Translation—X direction |

4th | 0.69 | Translation—Y direction |

Height | S_{a} (g) | Direction X or Y | Direction X | Direction Y |
---|---|---|---|---|

T = 0 s | T = 1.0 s | T = 2.3 s | ||

First floor | Median spectrum | 0.0794 | 0.1290 | 0.0360 |

Median spectrum + σ | 0.1008 | 0.1645 | 0.0446 | |

Mid-height | Median spectrum | 0.1122 | 0.5672 | 0.1562 |

Median spectrum + σ | 0.1345 | 0.7379 | 0.2016 | |

Roof | Median spectrum | 0.1689 | 0.8458 | 0.2601 |

Median spectrum + σ | 0.2052 | 1.1020 | 0.3359 |

Height | S_{d} (m) | Direction X or Y | Direction X | Direction Y |
---|---|---|---|---|

T = 0 s | T = 1.0 s | T = 2.3 s | ||

First floor | Median spectrum | 0.0 | 0.0315 | 0.0470 |

Median spectrum + σ | 0.0402 | 0.0582 | ||

Mid-height | Median spectrum | 0.1388 | 0.2040 | |

Median spectrum + σ | 0.1807 | 0.2633 | ||

Roof | Median spectrum | 0.2070 | 0.3375 | |

Median spectrum + σ | 0.2699 | 0.4364 |

Height | S_{a} (g) | Direction X or Y | Direction X | Direction Y |
---|---|---|---|---|

T = 0 s | T = 1.0 s | T = 2.3 s | ||

First floor | Median spectrum | 0.0974 | 0.1584 | 0.0403 |

Median spectrum + σ | 0.1193 | 0.2082 | 0.0520 | |

Mid-height | Median spectrum | 0.1420 | 0.7029 | 0.1659 |

Median spectrum + σ | 0.1724 | 0.9335 | 0.2254 | |

Roof | Median spectrum | 0.2155 | 1.0675 | 0.2810 |

Median spectrum + σ | 0.2674 | 1.4074 | 0.3823 |

Height | S_{d} (m) | Direction X or Y | Direction X | Direction Y |
---|---|---|---|---|

T = 0 s | T = 1.0 s | T = 2.3 s | ||

First floor | Median spectrum | 0.0 | 0.0390 | 0.0524 |

Median spectrum + σ | 0.0512 | 0.0676 | ||

Mid-height | Median spectrum | 0.1713 | 0.2153 | |

Median spectrum + σ | 0.2278 | 0.2929 | ||

Roof | Median spectrum | 0.2600 | 0.3646 | |

Median spectrum + σ | 0.3432 | 0.4968 |

S_{a} (g) | Direction X or Y | Direction X | Direction Y |
---|---|---|---|

T = 0 s | T = 1.0 s | T = 2.3 s | |

Mean NLTH | 0.169 | 0.846 | 0.260 |

NTC 18 | 0.160 | 0.400 | 0.400 |

EC8 | 0.200 | 0.440 | 0.440 |

ASCE 7-16 | 0.600 | 0.600 | 0.600 |

S_{a} (g) | Direction X or Y | Direction X | Direction Y |
---|---|---|---|

T = 0 s | T = 1.0 s | T = 2.3 s | |

Mean NLTH | 0.216 | 1.068 | 0.281 |

NTC 18 | 0.200 | 0.500 | 0.500 |

EC8 | 0.250 | 0.550 | 0.550 |

ASCE 7-16 | 0.750 | 0.750 | 0.750 |

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**MDPI and ACS Style**

Gabbianelli, G.; Perrone, D.; Brunesi, E.; Monteiro, R.
Seismic Acceleration and Displacement Demand Profiles of Non-Structural Elements in Hospital Buildings. *Buildings* **2020**, *10*, 243.
https://doi.org/10.3390/buildings10120243

**AMA Style**

Gabbianelli G, Perrone D, Brunesi E, Monteiro R.
Seismic Acceleration and Displacement Demand Profiles of Non-Structural Elements in Hospital Buildings. *Buildings*. 2020; 10(12):243.
https://doi.org/10.3390/buildings10120243

**Chicago/Turabian Style**

Gabbianelli, Giammaria, Daniele Perrone, Emanuele Brunesi, and Ricardo Monteiro.
2020. "Seismic Acceleration and Displacement Demand Profiles of Non-Structural Elements in Hospital Buildings" *Buildings* 10, no. 12: 243.
https://doi.org/10.3390/buildings10120243