# A Novel Contribution for Resilient Buildings. Theoretical Fragility Curves: Interaction between Energy and Structural Behavior for Reinforced Concrete Buildings

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. A Brief Review of the Seismic Fragility Curves

_{f}is the failure probability for a specific damage state, S

_{d}and S

_{c}are respectively the structural demand and structural capacity. It should be noted that Equation (1) merely defines values for the probability, under a certain seismic load, because the structural demand (S

_{d}) depends by the intensity of the earthquake ground motion.

_{d}and S

_{c}are described by a lognormal probability distribution. Hence, fragility P

_{f}may be expressed as a standard normal distribution reported in Equation (2).

_{c}is the mean value of the structural capacity, defined for the damage state; β

_{c}is the lognormal standard deviation of the structural capacity; S

_{d}is the mean value of seismic structural demand, in terms of a chosen ground motion intensity parameter; β

_{d}is the lognormal standard deviation of the structural seismic demand. There are many methodologies for obtaining the structural demand, and thus the elastic response spectral analysis, nonlinear static analysis and nonlinear time history analysis.

## 3. Innovative Integrated Approach for Energetic and Structural Fragility Curves

#### 3.1. The Building Stock Classification

_{IE}) as defined by [33] that describe the dynamic behavior of the building envelope during the summer. The effects on the indoor environment (in terms of heat stress) due to the climate overheating have been recently investigated by Rajapaksha [34] with reference to office buildings located at the tropics.

#### 3.2. Intensity Measure Selection

#### 3.3. The Performance Levels

## 4. Residential Reinforced Concrete Building Stock

#### 4.1. Reference Building Stock

- detached or semi-detached house: on one or two floors, without or with bordering buildings;
- terraced house: one of a row of similar houses (one or two floors) joined together by their sidewalls;
- multi-dwelling units: several housing units inside one building or multiple buildings within a unique complex;
- apartment blocks: high-rise buildings, multi-storey, with a large number of flats.

^{2}[47]. For this reason, the proposed methodology has been applied, as a case study, to a multi-family unit.

^{2}for flat 5 at the ground floor and 128 m

^{2}for flat 4. The number of stories can vary from 2 to 6 but the internal distribution is the same shown in Figure 2a.

^{2}K) (warmer cities) to 0.28 W/(m

^{2}K) (colder cities), for the roof and the slab on the ground the values are respectively 0.33 W/m

^{2}K and 0.38 W/m

^{2}K, otherwise for the windows, the thermal transmittance has to be lower than 2.2 W/m

^{2}K. Moreover, in the matter of thermal inertia, for the vertical opaque envelope, on all sides except north, north-east and north-west, the surface mass (M

_{s}) has to be higher than 230 kg/m

^{2}and/or the periodic thermal transmittance (Y

_{IE}) must be lower than 0.10 W/m

^{2}K. Instead for horizontal envelope Y

_{IE}must be lower than 0.18 W/m

^{2}K.

#### 4.2. Intensity Measures

#### 4.3. Performance Levels

- EP
_{H}: primary energy for heating; - EP
_{S}: threshold level for heating consumptions; - ${\mathsf{\mu}}_{\mathrm{HDD}}$: mean of the HDD of a climatic zone, for which the building reaches the consumption threshold;
- $\mathsf{\beta}$: standard deviation of the natural logarithm of heating degree days of the consumption threshold;
- Φ: normal cumulative distribution function.

_{H}is calculated by means of simulation software for the considered heating period in each city. It is the heating energy demand that characterizes the simulated constructive configuration. The equation allows calculating the probability to have a value of EP

_{H}higher than the threshold level, when the HDD is fixed.

_{S}. One of the possible choices consists of the consideration of the energy consumptions of the building stock. More in detail, the simulated consumptions can be compared with the reference energy demand of the building stock for evaluating what is the most critical solution. In other words, it is possible to evaluate what kind of envelope solution determines energy performance too much different compared to the national average. If the probability is high, it means that this type of building has the need of refurbishment interventions more than other building typologies. With reference to the proposed case study, it has been used the specific heating consumption by age and by type of dwellings proposed by ENTRANZE Project [47]. Before the last energy efficiency regulation in building sector (2015), three main thermal regulations were implemented since the 1970s (1976, 1991 and 2005). These standards can be associated to level of energy performance required for the new and refurbished building. performance required. According to this evolution, the theoretical maximum consumptions are considered as threshold values. These are the adopted categories:

- SC 100 if EP
_{H}> 100 kWh/m^{2}y; - SC 95 if EP
_{H}> 95 kWh/m^{2}y; - SC 85 if EP
_{H}> 85 kWh/m^{2}y; - SC 70 if EP
_{H}> 70 kWh/m^{2}y.

## 5. The Energy Modeling of the Case Study

#### 5.1. Input Data for the Dynamic Energy Model

^{2}K. In order to define reliable thermal loads, four typologies of thermal zones have been created (see Table 1) in each flat according to classifications and requirements provided by the Italian standard UNI 10339 [57]. The Air Change Rate (ACH or vol/h) has been fixed to 0.5 h

^{−1}, in order to guarantee the required comfort conditions, as identified by the standard UNI EN 15251 [58].

#### 5.2. Energy Simulation Results

^{2}), it is confirmed that the energy heating demand does not steadily increase or decrease with the theoretical heating degree days and the behavior of the building–plants system is more complex.

^{2}y) to 289 (kWh/m

^{2}y) in case of Fucino; it ranges between 275 (kWh/m

^{2}y) and 414 (kWh/m

^{2}y) in case of Monte Cimone; and between 270 (kWh/m

^{2}y) and 400 (kWh/m

^{2}y) when the weather file of Paganella is used. These values indicate that the consumptions are more different than those associated with other areas. This behavior could depend by several causes. First of all, it is possible that the adopted envelope solutions are not representative of the constructive sector in these cities; indeed, also if these localities falling within the climatic zone E (Fucino) and F (Paganella and Monte Cimone), the latitude and the particular geomorphologic configuration have caused the adoption of different solutions. Another motivation could be the wrong estimation of the climatic condition; indeed, the weather file could be defined starting from old data, or data monitored in the not representative area (e.g., rural area rather than city center).

^{2}value. Thus, it can be concluded that an in-depth analysis of the highlighted cities is necessary for two main reasons:

- the degree days may be not aligned with respect to a calculation using dynamic energy simulation because they are based on a stationary method which involves the use of an average monthly external reference temperature;
- the envelope types associated with the available data are not really representative of the reference stock.

## 6. Structural and Energetic Fragility Curves for the Proposed Buildings Stock

#### 6.1. Structural Fragility Curves

#### 6.2. Energetic Fragility Curves

^{2}y) is zero.

^{2}y), this probability is 18% for 1821 (K day), it becomes 33% at 2087 (K day) and 60% when the HDDs are higher than 2561 (K day). More in general, the analysis suggests that all cities characterized by heating degree days greater than 2300 (K day) could benefit from insulation intervention on the building envelope.

^{2}y) is not null and, for instance, it is around 4% for 1034 (K day) (Napoli, South Italy). The variation from the climatic zone D to E determines a rapid rise in the probability that goes from 21% (1464 K day) to 53% (2087 K day). The curve related to 85 kWh/ (m

^{2}y) differs from the other two, more than in the previous case. The critical point is 1195 (K day) for which the probability to exceed the reference consumption is 1.7%; it becomes 50% at 2312 (K day) and 80% at 2964 (K day). For the other two thresholds, the distribution indicates that the limit is passed starting from 1350 (K day) (Termoli, south Italy) and it has the greatest variation from 1821 (K day) (Florence, central Itlay) and 2087 (K day) (Forlì, central Italy); indeed, in the case of 100 kWh/(m

^{2}y) the probability passes from 18% to 33%. Additionally in this case, for the climatic zone F and the great part of E the curves coincide with a probability near the unitary value. Herein, it is very important to improve the insulation building level.

^{2}y), the probability is 3% at 899 (K day) (Crotone, south Italy). The climatic zones D to E correspond to a probability of 22% to 56%, respectively. The curves of 85 kWh/(m

^{2}y) and 95 kWh/(m

^{2}y) are comparable and the probability to exceed the thresholds regards all cities with more than 1000 (K day). In case of 95 kWh/(m

^{2}y), the probability is 22% at 1550 (K day) and it becomes 60% at 2255 (K day). For the 2-storey building, the most different trend is found with 100 kWh/(m

^{2}y). Until 1100 (K day) the probability is null and it is low for climatic condition characterized by HDDs near 1800 (K day); starting from 2087 (K day), the probability rises up 40%. As in the previous cases for zones F and E, the curves are quite similar.

#### 6.3. Example of Combined Application

^{2}y). Thus, an integrated refurbishment campaign could improve at the same time the structural and energetic performances, with higher advantages in terms of costs because the intervention on the structure surely requires removing and restoring a part of the envelope.

_{1}and W

_{2}. These values represent the importance that each aspect assumes for the decision-makers. The equation is proposed in the following:

## 7. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Hosseinzadeh, S.; Galal, K. Seismic Fragility Assessment and Resilience of Reinforced Masonry Flanged Wall Systems. J. Perform. Constr. Facil.
**2020**, 34, 04019109. [Google Scholar] [CrossRef] - Iddon, C.; Mills, T.; Giridharan, R.; Lomas, K. The influence of hospital ward design on resilience to heat waves: An exploration using distributed lag models. Energy Build.
**2015**, 86, 573–588. [Google Scholar] [CrossRef] [Green Version] - Quaglia, C.; Yu, N.; Thrall, A.P.; Paolucci, S. Balancing energy efficiency and structural performance through multi-objective shape optimization: Case study of a rapidly deployable origami-inspired shelter. Energy Build.
**2014**, 82, 733–745. [Google Scholar] [CrossRef] - Longo, F.; Lassandro, P.; Moshiri, A.; Phatak, T.; Aiello, M.A.; Krakowiak, K.J. Lightweight geopolymer-based mortars for the structural and energy retrofit of buildings. Energy Build.
**2020**, 225, 110–352. [Google Scholar] [CrossRef] - Pohoryles, D.; Maduta, C.; Bournas, D.; Kouris, L. Energy performance of existing residential buildings in Europe: A novel approach combining energy with seismic retrofitting. Energy Build.
**2020**, 223, 110024. [Google Scholar] [CrossRef] - Manfredi, V.; Masi, A. Seismic Strengthening and Energy Efficiency: Towards an Integrated Approach for the Rehabilitation of Existing RC Buildings. Buildings
**2018**, 8, 36. [Google Scholar] [CrossRef] [Green Version] - Hamzeh, L.; Ashour, A.; Galal, K. Development of Fragility Curves for Reinforced-Masonry Structural Walls with Boundary Elements. J. Perform. Constr. Facil.
**2018**, 32, 04018034. [Google Scholar] [CrossRef] - Rota, M.; Penna, A.; Strobbia, C. Processing Italian damage data to derive typological fragility curves. Soil Dyn. Earthq. Eng.
**2008**, 28, 933–947. [Google Scholar] [CrossRef] - Golparvar-Fard, M.; Ham, Y. Automated Diagnostics and Visualization of Potential Energy Performance Problems in Existing Buildings Using Energy Performance Augmented Reality Models. J. Comput. Civ. Eng.
**2014**, 28, 17–29. [Google Scholar] [CrossRef] - Masi, A.; Vona, M.; Digrisolo, A. Costruzione di Curve di Fragilità di Alcune Tipologie Strutturali Rappresentative di Edifici Esistenti in c.a. Mediante Analisi Dinamiche non Lineari; ANIDIS—XIII Convegno ANIDIS: Bologna, Italy, 2009. (In Italian) [Google Scholar]
- Borzi, B.; Pinho, R.; Crowley, H. Simplified pushover-based vulnerability analysis for large-scale assessment of RC buildings. Eng. Struct.
**2008**, 30, 804–820. [Google Scholar] [CrossRef] - Lagomarsino, S.; Cattari, S. Seismic Vulnerability of Existing Buildings. In Seismic Vulnerability of Structures; Wiley: Hoboken, NJ, USA, 2013; pp. 1–62. [Google Scholar]
- Shirazi, R.S.; Pekcan, G.; Itani, A. Analytical Fragility Curves for a Class of Horizontally Curved Box-Girder Bridges. J. Earthq. Eng.
**2017**, 22, 881–901. [Google Scholar] [CrossRef] - Perdomo, C.; Monteiro, R.; Sucuoğlu, H. Development of Fragility Curves for Single-Column RC Italian Bridges Using Nonlinear Static Analysis. J. Earthq. Eng.
**2020**, 1–25. [Google Scholar] [CrossRef] - Rossetto, T.; Ioannou, I.; Grant, D.N. Existing Empirical Fragility and Vulnerability Relationships: Compendium and Guide for Selection; GEM technical report 2013-X; GEM Foundation: Pavia, Italy, 2013; p. 62. [Google Scholar]
- Zuccaro, G.; Cacace, F. Seismic vulnerability assessment based on typological characteristics. The first level procedure “SAVE”. Soil Dyn. Earthq. Eng.
**2015**, 69, 262–269. [Google Scholar] [CrossRef] - Lagomarsino, S.; Giovinazzi, S. Macroseismic and mechanical models for the vulnerability and damage assessment of current buildings. Bull. Earthq. Eng.
**2006**, 4, 415–443. [Google Scholar] [CrossRef] - Braga, F.; Dolce, M.; Liberatore, D. A statistical study on damaged buildings and an ensuing review of the MSK-76 scale. In Proceedings of the 7th European Conference on Earthquake Engineering, Athens, Greece, 20 September 1982; pp. 431–450. [Google Scholar]
- Sabetta, F.; Goretti, A.; Lucantoni, A. Empirical fragility curves from damage surveys and estimated strong ground motion. In Proceedings of the11th European Conference on Earthquake Engineering, Paris, France, 6–11 September 1998. [Google Scholar]
- Karababa, F.S.; Pomonis, A. Damage data analysis and vulnerability estimation following the August 14, 2003 Lefkada Island, Greece, Earthquake. Bull. Earthq. Eng.
**2010**, 9, 1015–1046. [Google Scholar] [CrossRef] - Liel, A.B.; Lynch, K.P. Vulnerability of Reinforced-Concrete-Frame Buildings and Their Occupants in the 2009 L’Aquila, Italy, Earthquake. Nat. Hazards Rev.
**2012**, 13, 11–23. [Google Scholar] [CrossRef] - Del Gaudio, C.; De Martino, G.; Di Ludovico, M.; Manfredi, G.; Prota, A.; Ricci, P.; Verderame, G.M. Empirical fragility curves from damage data on RC buildings after the 2009 L’Aquila earthquake. Bull. Earthq. Eng.
**2016**, 15, 1425–1450. [Google Scholar] [CrossRef] - Paez-Ramirez, J.; Lizarazo-Marriaga, J.; Medina, S.; Estrada, M.; Mas, E.; Koshimura, S. A comparative study of empirical and analytical fragility functions for the assessment of tsunami building damage in Tumaco, Colombia. Coast. Eng. J.
**2020**, 62, 362–372. [Google Scholar] [CrossRef] - Kappos, A.J.; Panagopoulos, G.; Panagiotopoulos, C.; Penelis, G. A hybrid method for the vulnerability assessment of R/C and URM buildings. Bull. Earthq. Eng.
**2006**, 4, 391–413. [Google Scholar] [CrossRef] - Kappos, A.J. An overview of the development of the hybrid method for seismic vulnerability assessment of buildings. Struct. Infrastruct. Eng.
**2016**, 12, 1573–1584. [Google Scholar] [CrossRef] - Nägeli, C.; Jakob, M.; Catenazzi, G.; Ostermeyer, Y. Towards agent-based building stock modeling: Bottom-up modeling of long-term stock dynamics affecting the energy and climate impact of building stocks. Energy Build.
**2020**, 211, 109–763. [Google Scholar] [CrossRef] - Österbring, M.; Mata, E.; Thuvander, L.; Mangold, M.; Johnsson, F.; Wallbaum, H. A differentiated description of building-stocks for a georeferenced urban bottom-up building-stock model. Energy Build.
**2016**, 120, 78–84. [Google Scholar] [CrossRef] [Green Version] - Oberegger, U.F.; Pernetti, R.; Lollini, R.; Ulrich, F.O.; Roberta, P.; Roberto, L. Bottom-up building stock retrofit based on levelized cost of saved energy. Energy Build.
**2020**, 210, 109–757. [Google Scholar] [CrossRef] - Dall’O’, G.; Galante, A.; Torri, M. A methodology for the energy performance classification of residential building stock on an urban scale. Energy Build.
**2012**, 48, 211–219. [Google Scholar] [CrossRef] - Ali, U.; Shamsi, M.H.; Hoare, C.; Mangina, E.; O’Donnell, J. A data-driven approach for multi-scale building archetypes development. Energy Build.
**2019**, 202, 109–364. [Google Scholar] [CrossRef] - Westermann, P.; Evins, R. Surrogate modelling for sustainable building design—A review. Energy Build.
**2019**, 198, 170–186. [Google Scholar] [CrossRef] - ISO. Building Components and Building Elements—Thermal Resistance and Thermal Transmittance—Calculation Method; International Organization of Standardization: Geneva, Switzerland, 2008. [Google Scholar]
- ISO. Thermal Performance of Building Components—Dynamic Thermal Characteristics—Calculation Methods; International Organization of Standardization: Geneva, Switzerland, 2007. [Google Scholar]
- Rajapaksha, U. Environmental Heat Stress on Indoor Environments in Shallow, Deep and Covered Atrium Plan Form Office Buildings in Tropics. Climate
**2020**, 8, 36. [Google Scholar] [CrossRef] [Green Version] - Dolce, M.; Zuccaro, G.; Kappos, A.; Coburn, A.W. Report of the EAEE working group 3: Vulnerability and risk analysis. In Proceedings of the 10th European Conference on Earthquake Engineering, Vienna, Austria, 28 August–2 September 1994; Volume 4, pp. 3049–3077. [Google Scholar]
- Rossetto, T. Vulnerability Curves for the Seismic Assessment of Reinforced Concrete Structure Populations. Ph.D. Thesis, Imperial College, London, UK, 2004. [Google Scholar]
- Singhal, A.; Kiremidjian, A.S. Method for Probabilistic Evaluation of Seismic Structural Damage. J. Struct. Eng.
**1996**, 122, 1459–1467. [Google Scholar] [CrossRef] - Spence, R.J.S.; Coburn, A.W.; Pomonis, A. Correlation of ground motion with building damage: The definition of a new damage-based seismic intensity scale. In Proceedings of the 10th World Conference on Earthquake Engineering, Madrid, Spain, 19–24 July 1992. [Google Scholar]
- Webb, A.L. Energy retrofits in historic and traditional buildings: A review of problems and methods. Renew. Sustain. Energy Rev.
**2017**, 77, 748–759. [Google Scholar] [CrossRef] - Rouleau, J.; Gosselin, L.; Blanchet, P. Understanding energy consumption in high-performance social housing buildings: A case study from Canada. Energy
**2018**, 145, 677–690. [Google Scholar] [CrossRef] - Ascione, F.; Bianco, N.; De Masi, R.F.; Mastellone, M.; Mauro, G.M.; Vanoli, G.P. The role of the occupant behavior in affecting the feasibility of energy refurbishment of residential buildings: Typical effective retrofits compromised by typical wrong habits. Energy Build.
**2020**, 223, 110–217. [Google Scholar] [CrossRef] - BPIE. Europe’s Buildings under the Microscope. Available online: http://bpie.eu/wp-content/uploads/2015/10/HR_EU_B_under_microscope_study.pdf (accessed on 10 October 2020).
- Eurostat Database—Eurostat. Available online: https://ec.europa.eu/eurostat/data/database (accessed on 10 October 2020).
- Composition of the Load-Bearing Structure of Residential Buildings in Italy between 2018 and 2019, by Material. Available online: https://www.statista.com/statistics/1090304/material-composition-residential-buildings-italy/ (accessed on 10 October 2020).
- Rossetto, T.; Elnashai, A. Derivation of vulnerability functions for European-type RC structures based on observational data. Eng. Struct.
**2003**, 25, 1241–1263. [Google Scholar] [CrossRef] - Eurostat Housing Statistics, Data Extracted in May 2020. Available online: https://ec.europa.eu/eurostat/statistics-explained/index.php/Housing_statistics#Type_of_dwelling (accessed on 10 October 2020).
- ENTRANZE. The Challenges, Dynamics and Activities in the Building Sector and Its Energy Demand in Italy. Available online: https://www.entranze.eu/files/downloads/D2_1/D2_1_Short_country_summary_report_-final-Italy.pdf (accessed on 10 October 2020).
- Di Pasquale, G.; Orsini, G.; Romeo, R.W. New Developments in Seismic Risk Assessment in Italy. Bull. Earthq. Eng.
**2005**, 3, 101–128. [Google Scholar] [CrossRef] - Corrado, V.; Ballarini, I.; Paolo Cognati, S.P. Building Typology Brochure-Italy, Fascicolo Sulla Tipologia Edilizia Italiana. 2014. Available online: https://episcope.eu/fileadmin/tabula/public/docs/brochure/IT_TABULA_TypologyBrochure_POLITO.pdf (accessed on 10 October 2020).
- UNI—Italian Unification Body UNI/TS 11300-1: Energy Performance of Buildings—Part 1: Evaluation of Energy Need for Space Heating and Cooling. 2014. (In Italian). Available online: http://store.uni.com/catalogo/catalogsearch/advanced/ (accessed on 10 October 2020).
- Italian Government. Decreto Requisiti Minimi; Ministerial Decree of 26 June 2015; Italian Government: Rome, Italy, 2015.
- Working Group. Redazione Della Mappa di Pericolosità Sismica Prevista dall’Ordinanza PCM 3274 del 20 Marzo 2003; Dipartimento della Protezione Civile: Milano-Roma, Italy, 2004; 65p. (In Italian)
- Italian D.P.R. 26 Agosto 1993, n. 412: Regolamento Recante Norme per la Progettazione, l’installazione, l’esercizio e la Manutenzione Degli Impianti Termici Degli Edifici ai Fini del Contenimento dei Consumi di Energia, in Attuazione dell’art. 4, Comma 4, Della Legge 9 Gennaio 1991, n. 10 (In Italian). Available online: https://www.gazzettaufficiale.it/eli/id/1993/10/14/093G0451/sg (accessed on 10 October 2020).
- UNI—Italian Unification Body. UNI 10349-3: Heating and Cooling of Buildings—Climatic Data—Part 3: Accumulated Temperature Differences (Degree-Days) and Other Indices (in Italian). 2016. Available online: http://store.uni.com/catalogo/catalogsearch/advanced/ (accessed on 10 October 2020).
- DesignBuilder v.6.1. Available online: http://www.designbuilder.co.uk/ (accessed on 20 October 2020).
- EnergyPlus. Available online: https://energyplus.net/ (accessed on 10 October 2020).
- UNI—Italian Unification Body. UNI 10339: Air-Conditioning Systems for Thermal Comfort in Buildings. General, Classification and Requirements. Offer, Order and Supply Specifications (In Italian). 1995. Available online: http://store.uni.com/catalogo/catalogsearch/advanced/ (accessed on 10 October 2020).
- UNI—Italian Unification Body. UNI EN 15251: Indoor Environmental Input Parameters for Design and Assessment of Energy Performance of Buildings Addressing Indoor Air Quality, Thermal Environment, Lighting and Acoustics (In Italian). 2008. Available online: http://store.uni.com/catalogo/catalogsearch/advanced/ (accessed on 10 October 2020).
- Grunthal, G. European Macroseismic Scale 1998 (EMS 1998); Cahiers du Centre Europeen de Geodynamique et de Sismologie: Luxembourg, 1998; p. 15. [Google Scholar]
- Ballarini, I.; Corrado, V.; Madonna, F.; Paduos, S.; Ravasio, F. Energy refurbishment of the Italian residential building stock: Energy and cost analysis through the application of the building typology. Energy Policy
**2017**, 105, 148–160. [Google Scholar] [CrossRef] - Bonakdar, F.; Kalagasidis, A.S.; Mahapatra, K. The Implications of Climate Zones on the Cost-Optimal Level and Cost-Effectiveness of Building Envelope Energy Renovation and Space Heat Demand Reduction. Buildings
**2017**, 7, 39. [Google Scholar] [CrossRef]

**Figure 8.**Structural fragility curves for building with 1–3-storeys: (

**a**) seismic design; (

**b**) no seismic design; (

**c**) no seismic design 4-storey.

Appliance | Lighting | |
---|---|---|

Kitchen | 30 W/m^{2} | 3.5 W/m^{2} |

Dining room | 3.1 W/m^{2} | 3.5 W/m^{2} |

Bathroom | 2.0 W/m^{2} | 3.5 W/m^{2} |

Bedroom | 3.6 W/m^{2} | 3.5 W/m^{2} |

Winter | Summer | |||||
---|---|---|---|---|---|---|

Climatic Zone | Months (All Days) | Hours | Months (All Days) | Hours | ||

A | 1/12–15/03 | 05:00 | 08:00 | 15/05–01/10 | 11:00 | 15:00 |

20:00 | 23:00 | 17:00 | 21:00 | |||

B | 01/12–31/03 | 05:00 | 08:00 | 15/05–01/10 | 11:00 | 15:00 |

18:00 | 23:00 | 17:00 | 21:00 | |||

C | 15/11–31/03 | 05:00 | 08:00 | 15/05–15/09 | 12:00 | 15:00 |

14:00 | 16:00 | 18:00 | 21:00 | |||

18:00 | 23:00 | |||||

D | 01/11–15/04 | 05:00 | 09:00 | 15/05–15/09 | 12:00 | 15:00 |

14:00 | 16:00 | 18:00 | 21:00 | |||

17:00 | 23:00 | |||||

E | 01/11–15/04 | 04:00 | 09:00 | 15/05–15/09 | 12:00 | 15:00 |

15:00 | 00:00 | 18:00 | 21:00 | |||

F | 01/10–01/05 | 00:00 | 24:00 | 15/06–30/08 | 12:00 | 15:00 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

De Angelis, A.; Ascione, F.; De Masi, R.F.; Pecce, M.R.; Vanoli, G.P.
A Novel Contribution for Resilient Buildings. Theoretical Fragility Curves: Interaction between Energy and Structural Behavior for Reinforced Concrete Buildings. *Buildings* **2020**, *10*, 194.
https://doi.org/10.3390/buildings10110194

**AMA Style**

De Angelis A, Ascione F, De Masi RF, Pecce MR, Vanoli GP.
A Novel Contribution for Resilient Buildings. Theoretical Fragility Curves: Interaction between Energy and Structural Behavior for Reinforced Concrete Buildings. *Buildings*. 2020; 10(11):194.
https://doi.org/10.3390/buildings10110194

**Chicago/Turabian Style**

De Angelis, Alessandra, Fabrizio Ascione, Rosa Francesca De Masi, Maria Rosaria Pecce, and Giuseppe Peter Vanoli.
2020. "A Novel Contribution for Resilient Buildings. Theoretical Fragility Curves: Interaction between Energy and Structural Behavior for Reinforced Concrete Buildings" *Buildings* 10, no. 11: 194.
https://doi.org/10.3390/buildings10110194