# Advanced Seismic Retrofit of a Mixed R/C-Steel Structure

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Case Study School Building

^{2}. The total area of the three floors is about 2100 m

^{2}and the total volume of the building is 8300 m

^{3}. As highlighted by the cross sections in Figure 2 and Figure 3, storey heights are equal to 3.30 m (ground storey) and 3.75 m (upper storeys). According to the nomenclature in Figure 1, and as illustrated in Figure 4, R/C beams T

_{1,RC}have cross section of (250 × 740) mm

^{2}and are reinforced by ϕ12 circular bars and square bars (indicated by a square symbol in the drawing) with sides of 10 mm, and 8 mm square stirrups; R/C beams T

_{2,RC}have section of (250 × 740) mm

^{2}, with 18 mm square bars and 8.5 mm square stirrups. R/C columns have section of (400 × 400) mm

^{2}, with 18 mm square bars and 8 mm square stirrups; R/C walls S

_{1,RC}have section of (5900 × 200) mm

^{2}with ϕ12 vertical bars and ϕ8 transversal bars. The floors are of R/C “Predalles” type on the ground floor, and constituted by prefab joists on the upper floors. The foundation is made of grade beams at the base of the R/C columns and two slabs situated below the stairwell R/C walls. The second and third floor plans are shown in Figure 5 and Figure 6. The seven different types of reticular steel beams numbered in these drawings are displayed in Figure 7. A single type of reticular steel column is present, detailed in Figure 8. The roof is made of light prefab R/C purlins supported by Mohnié-type steel trusses.

## 3. On-Site Testing Campaign

^{2}; yield stress of reinforcing steel equal to 421 MPa; yield stress of the steel members equal to 235 MPa.

## 4. Assessment Analysis in Current Conditions

#### 4.1. Modal Analysis

#### 4.2. Time-History Verification and Performance Assessment Analysis

_{R}); serviceability design earthquake (SDE, with 50%/V

_{R}probability); basic design earthquake (BDE, with 10%/V

_{R}probability); and maximum considered earthquake (MCE, with 5%/V

_{R}probability). The V

_{R}period was fixed at 75 years, which was obtained by multiplying the nominal structural life V

_{N}of 50 years by a coefficient of use C

_{u}equal to 1.5, imposed to the design of school buildings or the assessment analysis of existing ones. By referring to topographic category T1 (flat surface), and B-type soil, the resulting peak ground accelerations for the four seismic levels for the city of Florence are as follows: 0.065 g (FDE), 0.078 g (SDE), 0.181 g (BDE), and 0.227 g (MCE). For the development of the time-history analyses, two families of seven accelerograms were generated by SIMQKE-II software [39] from the pseudo-acceleration elastic response spectra for Florence, plotted in Figure 13. In each time-history analysis the accelerograms were applied in groups of two simultaneous components, with the first one selected from the first generated family of seven motions, and the second one selected from the second family.

_{max}, and maximum stress states in the structural members.

_{max}envelopes obtained for the four seismic levels, plotted in Figure 14 for the weakest direction Y, were below the immediate occupancy level-related threshold ID

_{IO}, equal to 0.5% [36,37], for the FDE and SDE limit states. ID

_{IO}was slightly exceeded at the BDE, where ID

_{max}reached 0.54% on the first storey, and more appreciably at the MCE, with a ID

_{max}value of 0.66% on the same storey.

## 5. Retrofit Solution

#### 5.1. Mechanical Characteristics of the FV Dampers

_{0}= static pre-load; k

_{1}, k

_{2}= stiffness of the response branches situated below and beyond F

_{0}; and x(t) = displacement.

#### 5.2. Sizing Design Procedure of FV Dampers and Performance Verification Analysis in Retrofitted Conditions

_{s}, of the most critical response parameters in current conditions, which are set as equal to the maximum non-safety factors determined by the preliminary assessment analysis. Simple formulas relating the α

_{s}factors to the equivalent viscous damping ratio of the dampers, ξ

_{eq}, allow the calculation of the ξ

_{eq}values that guarantee the achievement of the target α

_{s}values. Finally, the energy dissipation capacity of the devices is deduced from ξ

_{eq}, finalizing their sizing process.

_{s}must be computed by considering also the possible axial instability of the profiles composing the reticular steel members. Hence, said ${M}_{j}^{a}$ the maximum moment calculated from the analysis in current conditions for the most stressed R/C member and ${N}_{j}^{a}$ the maximum axial force in a reticular steel member profile belonging to the j-th storey, and ${M}^{R},{N}^{cr}$the corresponding limit resistance moment and axial force buckling limit, the α

_{s}ratio is given by:

_{e}= elastic storey shear limit, and ID

_{e}= elastic inter-storey drift limit, the energy dissipation capacity of the FV dampers, E

_{D}, can be estimated, and then the devices with the nearest mechanical characteristics, can be selected, as identified from the manufacturer’s catalogue [42].

^{S}= 390.2 kN), and ${M}_{GS,X}^{R}$ = 128.2 kNm (N

^{S}= 403.6 kN). The most critical conditions on the first storey were checked in the diagonal trusses of column 1C, with maximum calculated axial force values ${N}_{IS,Y}^{a}$ = 73.9 kN along Y and ${N}_{IS,X}^{a}$ = 51.6 kN along X, and a corresponding axial force buckling limit, ${N}_{diag}^{cr}$, of 33.3 kN. Concerning the second storey, the most demanding axial force conditions were surveyed in the vertical profiles of column 1C, equal to ${N}_{IIS,X}^{a}=$ 450.6 kN in X and ${N}_{IIS,Y}^{a}=$ 399.1 kN in Y, in comparison to the axial force buckling limit ${N}_{vert}^{cr}=279.6$kN.

_{s}were computed for the three storeys and the two directions in the plan: α

_{s,GSM,X}= 2.53, α

_{s,GSM}

_{,Y}= 2.26 (ground storey); α

_{s,ISN,X}= 2.22, α

_{s,ISM}

_{,Y}= 1.55 (first storey); and α

_{s,IISN}

_{,X}= 1.6, α

_{s,IISN,Y}= 1.42 (second storey). The corresponding equivalent viscous damping ratios of the sets of FV spring-dampers to be installed on the three levels, calculated by means of Equation (4), were: ξ

_{eq,GS,X}= 0.38, ξ

_{eq,GS,Y}= 0.35, ξ

_{eq}

_{,IS,X}= 0.35, ξ

_{eq,IS,Y}= 0.23, ξ

_{eq,IIS,X}= 0.24, and ξ

_{eq}

_{,IIS,Y}= 0.3. The E

_{D}energy dissipation capacities of the spring-dampers were consequently computed by Equation (5), for the following values of the elastic shear limit of the j-th storey (given by the sum of the elastic limit shear forces of all columns belonging to the same storey) in X, F

_{ej,X}, and Y, F

_{ej,Y}: F

_{eGS,Y}= 3502 kN, F

_{eGS,Y}= 4098 kN, F

_{eIS,X}= F

_{eIS,Y}= F

_{eIIS,X}= F

_{eIIS,Y}= 4288 kN, and the corresponding elastic drift limits: ID

_{eSG}= 16 mm; ID

_{eSI}= ID

_{eSII}= 19 mm. Therefore, the following tentative E

_{D}values were estimated: E

_{DGS,X}= 395 kJ, E

_{DGS,Y}= 278 kJ, E

_{DIS,X}= 397 kJ, E

_{DIS,Y}= 182 kJ, E

_{DIIS,X}= 409 kJ, E

_{DIIS,Y}= 196 kJ.

_{Dtot,X}= E

_{DGS,X}+ E

_{DIS,X}+ E

_{DIIS,X}= 1201 kJ, E

_{Dtot,Y}= E

_{DGS,Y}+ E

_{DIS,Y}+ E

_{DIIS,Y}= 656 kJ. By dividing these values by the number of devices placed in X and Y, equal to 48 and 28, respectively, the maximum energy dissipation capacity E

_{Ddev,X,max}, E

_{Ddev,Y,max}that should be assigned to each one of them to reach the target performance at the MCE was as follows: E

_{Ddev,X,max}= 24.8 kJ, E

_{Ddev,Y,max}= 23 kJ. Assuming these two similar energy values as sizing limits, the spring-damper type with the nearest nominal energy dissipation capacity E

_{n}to E

_{Ddev,X,dmax}, E

_{Ddev,Y,dmax}has the following mechanical properties, as drawn from the manufacturer’s catalogue [42]: E

_{n}= 24 kJ; stroke s

_{max}= ±50 mm; damping coefficient c = 38 kN(s/mm)

^{γ}, with γ = 0.15; F

_{0}= 60 kN; and k

_{2}= 1.55 kN/mm.

_{IO}limit of 0.5% for all storeys. Moreover, it can be noted that all drifts also fell below the limit assumed by Italian Standards for the Operational performance level, ID

_{OP}, equal to 0.33%, which guarantees a completely undamaged response of non-structural elements, in addition to structural members, up to the MCE.

_{i}), FV-dissipated (E

_{d}) and modal (E

_{m}) energy time-histories deriving from the analyses carried out with the most severe SDE, BDE, and MCE-scaled input accelerograms are plotted in Figure 18. These curves assess that the FV spring-dampers were already activated at the SDE, and their contribution ranged from 90% (SDE) to 85% (MDE) of the total input energy.

^{2}, i.e., about the same as that computed for buildings with different structural characteristics examined in previous steps of this research [30,31,33,35]. At the same time, the cost is approximately 30% lower than the typical cost of a conventional rehabilitation intervention carried out on public buildings with R/C or steel frame skeleton, located in a site of comparable seismicity to the case study one. The duration of the structural works is about nine months, which translates to one school-year of interruption of usage only, including any working uncertainties.

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**First floor plan with alphanumerical alignment identification and reinforced concrete (R/C) beam numbering.

**Figure 2.**Transversal section (denoted as A–A in Figure 1).

**Figure 3.**Longitudinal section (denoted as B–B in Figure 1).

**Figure 4.**T

_{1,RC}, (

**a**,

**b**) and T

_{2,RC}(

**c**,

**d**) beam sections at half-span (

**a**–

**c**) and at the ends (

**b**–

**d**); P

_{RC}column section (

**e**); S

_{1,RC}wall section (

**f**).

**Figure 8.**Reticular steel columns: cross section (

**a**), lateral view (

**b**), and constituting profiles (

**c**).

**Figure 9.**Positions in plan and type of tests carried out on the ground (

**a**), first (

**b**), and second storeys (

**c**).

**Figure 10.**Tests on the R/C members: placement of the core drill on a ground storey column (

**a**); a concrete core after extraction (

**b**); a pacometer used in the tests (

**c**); resulting bar and stirrup positions traced out on a column (

**d**).

**Figure 11.**Tests on the reinforcing steel bars: a microdurometer used in the tests (

**a**); a steel bar of a ground storey wall before the extraction of a portion, highlighted in red (

**b**).

**Figure 12.**View of the finite element model of the structure and detail of a steel beam-to-column joint.

**Figure 15.**Portion of a perimeter column containing the profiles in buckling-related unsafe conditions at the Basic Design Earthquake level, highlighted in red.

**Figure 16.**Finite element model of the structure, including the dissipative bracing system and installation details of the latter.

**Figure 17.**Maximum inter-storey drift ratio envelopes for the Maximum Considered Earthquake level in retrofitted conditions, and comparison with the corresponding graph in current state.

**Figure 18.**Energy time-histories obtained from the most demanding Serviceability Design Earthquake (

**a**), Basic Design Earthquake (

**b**), and Maximum Considered Earthquake (

**c**) scaled groups of input accelerograms.

© 2019 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**

Terenzi, G.; Bazzani, C.; Costoli, I.; Sorace, S.; Spinelli, P.
Advanced Seismic Retrofit of a Mixed R/C-Steel Structure. *Buildings* **2019**, *9*, 241.
https://doi.org/10.3390/buildings9120241

**AMA Style**

Terenzi G, Bazzani C, Costoli I, Sorace S, Spinelli P.
Advanced Seismic Retrofit of a Mixed R/C-Steel Structure. *Buildings*. 2019; 9(12):241.
https://doi.org/10.3390/buildings9120241

**Chicago/Turabian Style**

Terenzi, Gloria, Caterina Bazzani, Iacopo Costoli, Stefano Sorace, and Paolo Spinelli.
2019. "Advanced Seismic Retrofit of a Mixed R/C-Steel Structure" *Buildings* 9, no. 12: 241.
https://doi.org/10.3390/buildings9120241