# Integrated Cost-Analysis Approach for Seismic and Thermal Improvement of Masonry Building Façades

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Integrated Approach at the Mesoscale Level

#### 2.1. Procedure

- Acquisition of the structural and thermal parameters needed for the analysis (mechanical parameters, such as tensile strength, shear strength, etc. and thermal parameters, such as thermal conductivity, thicknesses, etc.)
- Definition of a set of integrated interventions, namely retrofitting strategies that have positive effects on either the seismic response, or the thermal performance or both of them.
- Identification of a performance indicator at mesoscale level: as for the structural behavior, the variation of base shear capacity $\mathsf{\Delta}V$ and the corresponding variation of ductility capacity $\mathsf{\Delta}\mu $ are considered, defined by well-known methods (non-linear static analysis); as for the thermal side, the variation of thermal transmittance $\mathsf{\Delta}U$ is taken into account.
- Economic and environmental iso-cost curves representing the relationships between the thermal capacity indicator ($\mathsf{\Delta}U$) and the structural capacity indicators ($\mathsf{\Delta}V$ or $\mathsf{\Delta}\mu )$. For each integrated intervention, after an economic budget (investment) or an environmental impact in terms of CO
_{2eq}are fixed, one can calculate, as explained in Section 2.2 and Section 2.3, the corresponding pair of capacity indicators. That represents a single point in the graphs $\mathsf{\Delta}U$−$\mathsf{\Delta}V$ or $\mathsf{\Delta}U$−$\mathsf{\Delta}\mu $. By varying the economic budget or the environmental impact, several points are obtained. Finally, the curves fitting these points can be regarded as iso-cost curves. Moreover, the iso-performance curves, that will be the subject of future work, will express, for the same seismic or energetic performance, the economic investment needed or the environmental impact caused by each integrated intervention. - Definition of dimensionless parameters ${c}_{U}$ and ${c}_{R}$, defined in [28], to identify the demand for thermal and seismic performances respectively, with the expressions:$${c}_{U}=\frac{D{D}_{i}}{D{D}_{max}};{c}_{R}=\frac{PG{A}_{i}}{PG{A}_{max}},$$
- The hypothesis of a correlation between energy efficiency demand and seismic demand, through demand curves identified by these analytical expressions:$$\mathsf{\Delta}U=\alpha \frac{{c}_{U}}{{c}_{R}}\mathsf{\Delta}V;\mathsf{\Delta}U=\alpha \frac{{c}_{U}}{{c}_{R}}\mathsf{\Delta}\mu .$$

#### 2.2. Thermal Performance Indicator

- ${R}_{si}$ is the thermal resistance of the internal surface,$\left[{\mathrm{m}}^{2}\mathrm{K}/\mathrm{W}\right];$
- $\frac{{s}_{i}}{{\lambda}_{i}}$ is the resistance of the i-th layer,$\left[{\mathrm{m}}^{2}\mathrm{K}/\mathrm{W}\right]$, where ${\mathrm{s}}_{\mathrm{i}}$ is the thickness of the i-th wall layer $\left[\mathrm{m}\right]$;
- ${R}_{se}$ is the resistance of the external surface,$\left[{\mathrm{m}}^{2}\mathrm{K}/\mathrm{W}\right]$.

- ${A}_{g}$ is the glass area [${\mathrm{m}}^{2}$];
- ${U}_{g}$ is the glass heat transmission [$\mathrm{W}/{\mathrm{m}}^{2}\mathrm{K}$];
- ${A}_{t}$ is the area of the support [${\mathrm{m}}^{2}$];
- ${U}_{t}$ is the support heat transmission [$\mathrm{W}/{\mathrm{m}}^{2}\mathrm{K}$];
- ${l}_{g}$ is the glass perimeter [$\mathrm{m}$];
- ${\mathsf{\Psi}}_{g}$ is the spacer heat transmission [$\mathrm{W}/\mathrm{mK}$].

- (a)
- select the thermal characteristics of the frame support ${U}_{f}$;
- (b)
- select the thermal characteristics of the glass ${U}_{g}$;
- (c)
- cross the values of ${U}_{f}$ and ${U}_{g}$ by selecting the percentage of the support with respect to the entire opening and find the value of ${U}_{w}$ of the opening with the chosen characteristics.

- ${A}_{m}$ is the area of the masonry element [${\mathrm{m}}^{2}$];
- ${U}_{m}$ is the thermal transmittance of the masonry portion [$\mathrm{W}/{\mathrm{m}}^{2}\mathrm{K}$];
- ${A}_{w}$ is the area of the window [${\mathrm{m}}^{2}$];
- ${U}_{w}$ is the thermal transmittance of the window [$\mathrm{W}/{\mathrm{m}}^{2}\mathrm{K}$];
- $l$ is the perimeter of the wall [$\mathrm{m}$];
- $\mathsf{\Psi}$ is the linear thermal transmittance [$\mathrm{W}/\mathrm{mK}$].

#### 2.3. Structural Performance Indicators

## 3. Application of the Integrated Approach at Mesoscale Level

#### 3.1. Case of Study

#### 3.2. Assumptions on the Integrated Interventions

#### 3.3. The Procedure of Estimation of the Varied Mechanical and Thermal Properties

- $s$ is the wall thickness;
- ${A}_{h},{A}_{v}$ are the reinforcement area placed in horizontal and vertical direction per unit of length;
- ${p}_{h},{p}_{v}$ are the spacings between horizontal or vertical strips.

- ${V}_{R,max}=0.3\xb7{f}_{k}\xb7s\xb7b$.

**.**, the values of the thermal transmittance are analogously calculated (Table 3 and Table 4). All the interventions cause a reduction of the thermal transmission; the best improvement is obtained with the polystyrene panel. The corresponding base shear capacity and ductility values are reported in Table 5, Table 6, Table 7 and Table 8.

#### 3.4. Cost Analysis

#### 3.4.1. Economic Cost Analysis

#### 3.4.2. Environmental Cost Analysis

_{2eq}emissions that are normally produced when retrofitting interventions are made. The CO

_{2eq}emission is one of the main indicators chosen to measure building sustainability.

_{2eq}emissions related to the phase of production of the materials for intervention are considered. Although this analysis can be extended to the entire life of the building, this paper neglects that aspect, which will be considered in future works. The assumed parameter of CO

_{2eq}emission varies from 5 kgCO

_{2eq}/m

^{3}to 35 kgCO

_{2eq}/m

^{3}. The specific environmental costs for each material are reported in Table 12.

_{0}and α

_{1}are reported in Table 13 and in Table 14, whilst Figure 6 shows the environmental regression curves for $\mathsf{\Delta}$U$-\mathsf{\Delta}\mu $ ($\mathsf{\Delta}$U$-\mathsf{\Delta}V$).

## 4. Definition of Demand Curves and Discussion of Results

_{2}). The optimal point for each location is given by the intersection of the lines with the hyperboles. The decision-makers can act through two aspects: which hyperbole should be considered (i.e., which level of economic or environmental cost) and which “tuning parameter” α has to be assumed (i.e., the slope of the line graphs) to give more importance to the thermal or to the seismic aspect, provided that the location influences the inclination of the line through the coefficients of Equation (1).

^{2}one should expect in Rocchetta di Vara an increase of base shear strength by 7%, of ductility by 10% and of thermal transmittance by 8%, whereas with a budget of 300 €/m

^{2}the expected increase of base shear and thermal transmittance are respectively by 14% and 17%. It should be noticed that the information gathered by this procedure is able to give an overall look at the improvement obtained by integrated approaches. An alternative way to proceed is to define the capacity curves by keeping constant the type of intervention and tuning its thickness, or coupling two interventions, one with more impact on the structural performance, and the other more effective from a thermal point of view. This procedure, which will be investigated in the future, will allow us to refine the decisional practice about the intervention to adopt.

^{2}stands between that obtained for 100 €/m

^{2}and that for 300 €/m

^{2}(Figure 8). This aspect is due to the fact that for the FRP interventions, beyond a threshold value, the increase of the cost (and therefore of the entity of the intervention) does not imply an increment of ductility, but instead a decrement of it. In other words, a greater thickness of FRP strips worsens the structural performance. This influence is stronger with respect to the other interventions and therefore the fitted curves do not follow a monotonic trend. A way to avoid this apparently counter-intuitive response is, as mentioned above, to plot the fitted curves for interventions with similar and monotonic effects.

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 2.**Disposition of the most common linear thermal bridging (Figure 1, paragraph 5.4 UNI EN ISO 14683).

**Figure 3.**Façade selected as a case study for the integrated meso-scale approach (

**a**); macro-element model of the façade (units in m) (

**b**).

**Figure 4.**Types of integrated interventions assumed in the case study: polystyrene panel (

**a**), polystyrene panel and diatons (

**b**); ferro-cement (

**c**); CFRP (

**d**) and GFRP (

**e**) stripes; GFRP net (

**f**).

**Figure 5.**Iso-cost $\mathsf{\Delta}U-\mathsf{\Delta}V$ (

**a**) and $\mathsf{\Delta}U-\mathsf{\Delta}\mu $ (

**b**) regression curves.

**Figure 6.**Environmental iso-cost $\mathsf{\Delta}U-\mathsf{\Delta}V$ (

**a**) and $\mathsf{\Delta}U-\mathsf{\Delta}\mu $ (

**b**) regression curves.

**Figure 7.**Economic performance curves for planes $\mathsf{\Delta}U-\mathsf{\Delta}V$ (

**a**) and $\mathsf{\Delta}U-\mathsf{\Delta}\mu $ (

**b**).

**Figure 8.**Environmental performance curves for planes $\mathsf{\Delta}U-\mathsf{\Delta}V$ (

**a**) and $\mathsf{\Delta}U-\mathsf{\Delta}\mu $ (

**b**).

R | Connections Between External Elements | Corners Between Vertical Walls and Roof |

B | Corners between vertical walls and projecting elements | |

C | Corners between vertical walls | |

GF | Corner between vertical walls and floors | |

IF | Corners between external vertical walls and intermediate floors | |

IW | Corners between inner vertical walls and external elements | |

P | Presence of external columns | |

W | Presence of doors and windows |

**Table 2.**Masonry parameters: f

_{m,k}average compression strength, τ

_{0}: shear strength in absence of normal stress, E: elastic modulus, G: tangential elastic modulus, w: specific weight, λ: thermal conductivity.

f_{m,k} | τ_{0} | E | G | w | λ |
---|---|---|---|---|---|

[N/mm^{2}] | [N/mm^{2}] | [N/mm^{2}] | [N/mm^{2}] | [kN/m^{3}] | [W/mK] |

3.20 | 0.065 | 1740.00 | 580.00 | 21.00 | 2.30 |

**Table 3.**Thermal transmittance $U$ of the entire façade with the different integrated interventions—economic analysis.

Type of Intervention | Investment | |||||
---|---|---|---|---|---|---|

100 €/m^{2} | 150 €/m^{2} | 200 €/m^{2} | 250 €/m^{2} | 300 €/m^{2} | 350 €/m^{2} | |

Polystyrene panel | 1.753 | 1.660 | 1.608 | 1.574 | 1.551 | 1.534 |

Polystyrene panel + diatons | 2.305 | 1.854 | 1.708 | 1.636 | 1.593 | 1.564 |

Ferro-cement | 2.845 | 2.802 | 2.762 | 2.725 | 2.689 | 2.656 |

CFRP strips | 2.845 | 2.845 | 2.845 | 2.845 | 2.835 | 2.832 |

GFRP strips | 2.845 | 2.845 | 2.779 | 2.757 | 2.730 | 2.718 |

GFRP net | 2.839 | 2.794 | 2.753 | 2.713 | 2.676 | 2.641 |

**Table 4.**Thermal transmittance $U$ of the entire façade with the different integrated interventions—environmental analysis.

Type of Intervention | Emissions | |||||
---|---|---|---|---|---|---|

10 kgCO_{2eq}/m^{2} | 15 kgCO_{2eq}/m^{2} | 20 kgCO_{2eq}/m^{2} | 25 kgCO_{2eq}/m^{2} | 30 kgCO_{2eq}/m^{2} | 35 kgCO_{2eq}/m^{2} | |

Polystyrene panel | 1.933 | 1.729 | 1.642 | 1.593 | 1.562 | 1.540 |

Polystyrene panel + diatons | 1.950 | 1.735 | 1.645 | 1.595 | 1.563 | 1.541 |

Ferro-cement | 2.915 | 2.893 | 2.872 | 2.851 | 2.831 | 2.812 |

CFRP strips | 2.845 | 2.845 | 2.845 | 2.845 | 2.834 | 2.832 |

GFRP strips | 2.845 | 2.845 | 2.766 | 2.741 | 2.730 | 2.718 |

GFRP net | 2.848 | 2.808 | 2.769 | 2.733 | 2.699 | 2.666 |

**Table 5.**Base shear capacity V [kN] of the entire façade with the different integrated interventions—economic analysis.

Type of Intervention | Investment | |||||
---|---|---|---|---|---|---|

100 €/m^{2} | 150 €/m^{2} | 200 €/m^{2} | 250 €/m^{2} | 300 €/m^{2} | 350 €/m^{2} | |

Polystyrene panel | 446.803 | 446.803 | 446.803 | 446.803 | 446.803 | 446.803 |

Polystyrene panel + diatons | 458.259 | 458.259 | 458.259 | 458.259 | 458.259 | 458.259 |

Ferro-cement | 469.716 | 469.716 | 469.716 | 469.716 | 469.716 | 469.716 |

CFRP strips | 572.824 | 653.019 | 712.169 | 736.157 | 759.093 | 793.436 |

GFRP strips | 561.367 | 707.326 | 715.263 | 781.991 | 838.286 | 838.286 |

GFRP net | 504.085 | 562.998 | 561.367 | 584.280 | 595.737 | 607.193 |

**Table 6.**Base shear capacity V [kN] of the entire façade with the different integrated interventions—environmental analysis.

Type of Intervention | Emissions | |||||
---|---|---|---|---|---|---|

10 kgCO_{2}/m^{2} | 15 kgCO_{2}/m^{2} | 20 kgCO_{2}/m^{2} | 25 kgCO_{2}/m^{2} | 30 kgCO_{2}/m^{2} | 35 kgCO_{2}/m^{2} | |

Polystyrene panel | 446.803 | 446.803 | 446.803 | 446.803 | 446.803 | 446.803 |

Polystyrene panel + diatons | 458.259 | 458.259 | 458.259 | 458.259 | 458.259 | 458.259 |

Ferro-cement | 469.716 | 469.716 | 469.716 | 469.716 | 469.716 | 469.716 |

CFRP strips | 607.193 | 690.176 | 715.270 | 736.182 | 770.554 | 793.436 |

GFRP strips | 687.389 | 726.755 | 759.086 | 816.354 | 838.286 | 838.286 |

GFRP net | 504.085 | 515.541 | 561.367 | 572.000 | 595.737 | 607.193 |

**Table 7.**Ductility capacity µ of the entire façade with the different integrated interventions—economic analysis.

Type of Intervention | Investment | |||||
---|---|---|---|---|---|---|

100 €/m^{2} | 150 €/m^{2} | 200 €/m^{2} | 250 €/m^{2} | 300 €/m^{2} | 350 €/m^{2} | |

Polystyrene panel | 2.633 | 2.633 | 2.633 | 2.633 | 2.633 | 2.633 |

Polystyrene panel + diatons | 2.811 | 2.811 | 2.811 | 2.811 | 2.811 | 2.811 |

Ferro-cement | 3.220 | 3.220 | 3.220 | 3.220 | 3.220 | 3.220 |

CFRP strips | 3.338 | 3.201 | 3.104 | 2.915 | 2.866 | 2.727 |

GFRP strips | 3.235 | 3.163 | 3.006 | 2.808 | 2.563 | 2.563 |

GFRP net | 2.477 | 2.566 | 2.911 | 3.258 | 3.260 | 3.302 |

**Table 8.**Ductility capacity µ of the entire façade with the different integrated interventions—environmental analysis.

Type of Intervention | Emissions | |||||
---|---|---|---|---|---|---|

10 kgCO_{2}/m^{2} | 15 kgCO_{2}/m^{2} | 20 kgCO_{2}/m^{2} | 25 kgCO_{2}/m^{2} | 30 kgCO_{2}/m^{2} | 35 kgCO_{2}/m^{2} | |

Polystyrene panel | 2.633 | 2.633 | 2.633 | 2.633 | 2.633 | 2.633 |

Polystyrene panel + diatons | 2.811 | 2.811 | 2.811 | 2.811 | 2.811 | 2.811 |

Ferro-cement | 3.220 | 3.220 | 3.220 | 3.220 | 3.220 | 3.220 |

CFRP strips | 2.914 | 3.253 | 3.002 | 2.947 | 2.802 | 2.727 |

GFRP strips | 2.812 | 2.969 | 2.875 | 2.738 | 2.563 | 2.563 |

GFRP net | 2.603 | 2.690 | 2.911 | 2.923 | 3.260 | 3.285 |

Material | Cost |
---|---|

Polystyrene panel | 1517 €/m^{3} |

Diatons | 80 €/m^{2} |

Ferro-cement | 2080 €/m^{3} |

CFRP stripes | 2160 €/m^{3} |

GFRP stripes | 1723 €/m^{3} |

GFRP nets | 4667 €/m^{3} |

**Table 10.**Economic cost regression coefficients for $\mathsf{\Delta}U-\mathsf{\Delta}V$ regression curves.

Economic Investment | α_{0} | α_{1} |
---|---|---|

100 €/m^{2} | 0.0079 | 0.0166 |

150 €/m^{2} | 0.0162 | 0.0305 |

200 €/m^{2} | 0.0209 | 0.0376 |

250 €/m^{2} | 0.0240 | 0.0421 |

300 €/m^{2} | 0.0267 | 0.0460 |

350 €/m^{2} | 0.0291 | 0.0497 |

**Table 11.**Economic cost regression coefficients for $\mathsf{\Delta}U-\mathsf{\Delta}\mu $ regression curves.

Economic Investment | α_{0} | α_{1} |
---|---|---|

100 €/m^{2} | 0.0121 | 0.0258 |

150 €/m^{2} | 0.0165 | 0.0353 |

200 €/m^{2} | 0.0287 | 0.0519 |

250 €/m^{2} | 0.0265 | 0.0482 |

300 €/m^{2} | 0.0231 | 0.0465 |

350 €/m^{2} | 0.0160 | 0.0319 |

Material | Emissions of CO_{2eq} |
---|---|

Polystyrene panel | 138 kgCO_{2eq}/m^{3} |

Diatons | 0.25 kgCO_{2eq}/m2 |

Ferro-cement | 450 kgCO_{2eq}/m^{3} |

CFRP stripes | 87,140 kgCO_{2eq}/m^{3} |

GFRP stripes | 15,062 kgCO_{2eq}/m^{3} |

GFRP nets | 520 kgCO_{2eq}/m^{3} |

**Table 13.**Environmental cost regression coefficients for $\mathsf{\Delta}U-\mathsf{\Delta}V$ regression curves.

Environmental Impact | α_{0} | α_{1} |
---|---|---|

5 kgCO_{2eq}/m^{2} | 0.0128 | 0.0301 |

10 kgCO_{2eq}/m^{2} | 0.0166 | 0.0325 |

20 kgC kgCO_{2eq}/m^{2} | 0.0199 | 0.0364 |

30 kgCO_{2eq}/m^{2} | 0.0216 | 0.0381 |

40 kgCO_{2eq}/m^{2} | 0.0232 | 0.0401 |

50 kgCO_{2eq}/m^{2} | 0.0245 | 0.0417 |

**Table 14.**Environmental cost regression coefficients for $\mathsf{\Delta}U-\mathsf{\Delta}\mu $ regression curves.

Environmental Impact | α_{0} | α_{1} |
---|---|---|

5 kgCO_{2eq}/m^{2} | 0.0155 | 0.0377 |

10 kgCO_{2eq}/m^{2} | 0.0182 | 0.0434 |

20 kgCO_{2eq}/m^{2} | 0.0246 | 0.0460 |

30 kgCO_{2eq}/m^{2} | 0.0206 | 0.0392 |

40 kgCO_{2eq}/m^{2} | 0.0185 | 0.0367 |

50 kgCO_{2eq}/m^{2} | 0.0142 | 0.0279 |

Site | PGA_{i} | c_{R} | DD_{i} | c_{U} |
---|---|---|---|---|

Rocchetta di Vara | 0.120 | 0.436 | 1934 | 0.374 |

Torino | 0.060 | 0.218 | 2617 | 0.507 |

L’Aquila | 0.250 | 0.909 | 2514 | 0.487 |

Catania | 0.215 | 0.782 | 833 | 0.161 |

Cagliari | 0.050 | 0.182 | 990 | 0.192 |

© 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**

Giresini, L.; Paone, S.; Sassu, M.
Integrated Cost-Analysis Approach for Seismic and Thermal Improvement of Masonry Building Façades. *Buildings* **2020**, *10*, 143.
https://doi.org/10.3390/buildings10080143

**AMA Style**

Giresini L, Paone S, Sassu M.
Integrated Cost-Analysis Approach for Seismic and Thermal Improvement of Masonry Building Façades. *Buildings*. 2020; 10(8):143.
https://doi.org/10.3390/buildings10080143

**Chicago/Turabian Style**

Giresini, Linda, Simona Paone, and Mauro Sassu.
2020. "Integrated Cost-Analysis Approach for Seismic and Thermal Improvement of Masonry Building Façades" *Buildings* 10, no. 8: 143.
https://doi.org/10.3390/buildings10080143