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Article

Methodology and Monitoring of the Strengthening and Upgrading of a Four-Story Building with an Open Ground Floor in a Seismic Region

Department of Civil Engineering, Ariel University, Ariel 40700, Israel
*
Author to whom correspondence should be addressed.
Appl. Sci. 2024, 14(17), 7581; https://doi.org/10.3390/app14177581
Submission received: 15 July 2024 / Revised: 19 August 2024 / Accepted: 20 August 2024 / Published: 27 August 2024

Abstract

:
Many buildings around the world fail to meet current earthquake resistance requirements and have significant potential to be a risk to human life and property. Therefore, a seismic upgrade of such buildings is quite necessary. Over the past decades, hundreds of buildings have been strengthened and upgraded to improve their seismic resistance, and thousands more are planned for years to come. In Israel, this was followed by National Outline Plan No. 38, which provides a basis for retrofitting and adding new areas to existing buildings. It should be noted that adding new floors to existing buildings increases seismic forces. Moreover, structure material properties change over a building’s lifetime, which should be also considered for strengthening. The proposed research investigates and validates the existing practice for strengthening and upgrading buildings in seismic regions and suggests ways of improving their efficiency. Experiments and numerical analysis were performed on a real existing residential building that requires strengthening and upgrading. A corresponding methodology was proposed for monitoring the strengthening and upgrading processes, including selecting measurement devices and their real use. Using sensors with the highest sensitivity enabled measurements of micro-vibrations and investigations of the recorded signal to obtain the building’s natural vibration frequencies. Experimental measurements allowed us to distinguish different frequencies of the building at all strengthening and upgrading stages. The measured dynamic parameters of the building allowed a more accurate calculation of seismic forces for all of these stages and consequently made the design more effective. Therefore, we recommended monitoring buildings in each stage of seismic strengthening and upgrading.

1. Introduction

The seismic strengthening of existing buildings is presently based on concepts of modern design codes and provisions [1,2,3,4] that mostly cover the seismic resistance of structures with additional rigid elements. However, these normative documents do not deal with the influence of additional floors or new parts of buildings constructed to upgrade the existing ones. Following these codes, the earthquake resistance design of old and upgraded buildings is usually performed using basic dynamic parameters that are calculated according to empirical dependencies. The real material properties of existing buildings change over time, and it is logical to consider these changes in design after evaluating them using non-destructive methods.
In the first stage of this research, an experimental and analytical investigation of the dynamic properties of a real residential four-story reinforced concrete (RC) building with an open ground floor (before strengthening) and its upgrading was performed [5]. The present study is a logical extension of that investigation and includes an experimental and analytical evaluation of the building’s dynamic parameters during all stages of its strengthening and upgrading.
Most of the known strengthening methods are aimed at limiting a building’s displacements [6]. New members are designed to ensure a significant increase in structural stiffness and load capacity, including the loads due to additional floors. It is known that the seismic performance of a building can be improved by decreasing the earthquake demand on the structure or increasing its energy dissipation capacity. The first method is achieved by globally strengthening the structure. One of the most popular strengthening methods is the addition of an RC infill. RC infill walls, as a role, greatly improve lateral load capacity and the stiffness of the structure [6,7]. RC walls are usually placed in strengthened structures in a manner that prevents causing torsional effects and irregularities in the structure. Shear walls require demolition and construction in the existing structure, using external shear walls to minimize such difficulties [8].
The second method involves enhancing the elements’ deformation capacities through local strengthening techniques. For example, columns subjected to brittle damage can be jacketed to increase their resistance to shear loads. Recently, the use of fiber-reinforced polymer became widespread in strengthening. It improves the bending, shear, and axial capacities of columns and beams [8]. However, in the authors’ opinion, there is not enough experimental data on the long-term performance of such strengthening techniques. The structural seismic response can also be involved by strengthening a beam’s critical zone [9]. In our opinion, the further strengthening of RC elements should be focused on elements with elastic–plastic deformations (including plastic hinge) under seismic loads, as this problem has not been investigated enough.
The seismic evaluation of an existing RC-framed building located in a high seismic-risk area in Calabria was performed [10]. Experimental research was carried out to assess the present condition of the building and its quality. Non-linear static pushover analysis was performed on bare frame and infilled frame models. However, further experimental validation of the building’s strengthening efficiency is still necessary, as it is important to prove that the desired building’s seismic capacity is achieved.
The structural dynamic behavior of a four-story RC hotel building with a basement level in Greece was investigated before and after strengthening [11]. The structural strengthening included the cast in situ walls, strengthening the columns using plates connected with epoxy, expanding wrapping with RC walls, and strengthening the beams by casting RC sheathing and adding sheets of carbon fiber composite materials connected with epoxy glue to improve the ceiling’s bearing capacity. However, no experimental validation was carried out to check that such strengthening methods were indeed effective. In our opinion, it is necessary to develop experimental methods that allow engineers to determine a building’s dynamic parameters before and after strengthening.
Other examples of seismic resistance evaluation, strengthening, and upgrading are the old Yokufu-en building in Japan, which was constructed in Tokyo about 100 years ago [12], Bnai Zion Hospital in Haifa, Israel [13], a retrofitted church in Slovenia [14], etc.
Presently, seismic strength planning is based on the numerical analysis of a building, aimed at finding the optimal strengthening and upgrading options from technical and economic feasibility viewpoints. In some cases, the main question is to prove the benefit of strengthening and upgrading an existing structure compared with the construction of a new building [15]. However, the real state of the existing as well as the strengthened structure can be obtained experimentally. Therefore, we propose measuring structural dynamic parameters before deciding whether strengthening or upgrading is required, as well as at all stages of strengthening and upgrading. As described below, for the building investigated in the frame of the present study, 11 stages are included.
The response of a real 11-story RC building to seismic-type loadings was investigated experimentally and numerically under dynamic horizontal loads applied by a vibration machine placed on the roof of the building [16]. Preliminarily, a three-story fragment of this building was tested by free vibration, created by an initial force equal to the expected horizontal seismic load [17]. Damages and cracks in structural elements were inspected, and the natural vibration period of the structure was obtained. Following the preliminary design, braces were added in the short direction of the building. Experiments were carried out on a fragment without braces to prove that the bracing was really required. It was concluded that X-shaped braces in this direction are effective and should be used.
An experimental program was carried out to investigate the seismic behavior of structural and nonstructural elements [18]. The research included shake table testing of a full-scale five-story reinforced concrete building with nonstructural components (NSCs). The building was subjected to earthquake motions with increasing intensity. The major components of the structure, its NSCs, and the monitoring systems were described. The response and damage to the structure were presented. Damage observed in various NSCs and its correlation with the structure’s response was discussed.
Numerical values of structural dynamic parameters do not always correspond to experimental values [19]. It was demonstrated that for a 10-story building, slab flexibility should be considered, and for a 12-story building, masonry infill walls should be taken into consideration in dynamic analyses. This supports our idea that the dynamic parameters of a strengthened or upgraded building should be measured and not only calculated. It will allow us to verify if a building’s strengthening and upgrading is indeed effective and corresponds to the design of the building.

2. Research Aims, Scope, and Novelty

The present research is focused on examining the behavior of existing buildings before and after each strengthening stage from the viewpoint of earthquake resistance and upgrading, including adding new parts (floors and/or wings). With this aim, numerical analyses and experiments are carried out on a full-size real building. An additional aim is to develop methods for validating the correspondence of building strengthening and upgrading with the modern standards’ requirements. The proposed method advances the existing engineering knowledge in the field, confirms the existing techniques in engineering practice, and suggests effective ways of improvement.
The novelty of this research is that for the first time, complex investigations are carried out for the entire process of building after each stage of strengthening and upgrading. This process includes experimental and analytical evaluation of a building’s state before strengthening as well as during the strengthening and upgrading phases.
Known approaches for monitoring buildings include updating numerical models to obtain higher accuracy of modeling. The proposed method is aimed at developing a simple procedure that is more convenient for designers. Following this procedure, the dynamic characteristics of the building are updated, and the strengthening and upgrading are carried out using the corresponding design spectrum [5]. This yields a more effective and easy design that makes the procedure less time-consuming. To verify the efficiency of strengthening, the dynamic parameters are monitored at each stage.
The application of the research outcomes is focused on the building’s strengthening by adding RC stiffening walls, columns, cores, etc. The research results allow for the correction of dynamic parameters that correspondingly enable the use of ordinary elastic analyses to obtain more accurate and reliable results, which represent the building’s response to seismic forces.

3. Description of the Investigated Building

A typical residential RC building, constructed in the late 1970s, was chosen [5] (Figure 1). The building has four floors and a non-occupied ground floor.
The existing building is an RC frame system with infill brick walls on the residential floors. The ground floor column section was 40 cm × 40 cm, and the typical floors vary from 40 cm × 20 cm to 30 cm × 20 cm. On the ground floor, there are 40 cm thick RC walls.
The building was designed for strengthening and upgrading by adding wings that include stiff cores and balconies in each apartment. Three additional floors were planned, including a partial floor at the top (Figure 2). The building strengthening for earthquake resistance was planned by adding the following stiffening elements: four stiff cores on each floor, stiff walls along the building’s perimeter, column thickening on the open ground floor, steel columns in the stairwell, proper strengthening of foundations, etc.

4. Research Methodology

ETABS and STRAP software [20,21] were used to perform numerical analyses of the real building and to calculate its dynamic parameters like mode shapes, modal frequencies, damping ratio, etc., according to modern design codes [1,3]. The experimental part of this research is based on measuring the dynamic behavior of the real building in order to obtain the above-mentioned parameters.
The analytical and experimental evaluation of the building’s dynamic parameters was performed for 11 different stages corresponding to the phases of the building’s strengthening and upgrading (Table 1). The analytical and experimental results obtained for each of the phases were compared in order to validate the desired strengthening effect for improving the design procedure.
The analysis of the existing building and evaluation of its seismic resistance were performed using the material strength values of the existing structure that were obtained by non-destructive testing methods [5]. For the analysis of the strengthened and upgraded building, the mechanical properties of the existing building parts and the strengthening components in their current state were used. The properties were obtained by both non-destructive and destructive testing. With this aim, samples of concrete were taken from the existing building before strengthening [5].
The building analysis process included the following steps:
-
Initial 3D linear elastic analysis under vertical static loads only;
-
Modal analysis according to the modern seismic design code requirements [1,3];
-
Comparing the results obtained by ETABS [20] and STRAP [21].
The building’s dynamic behavior was measured using a system of acceleration and velocity sensors, connected to a computer for data logging and processing. The building’s dynamic behavior was recorded under such loads as wind, traffic in the building’s vicinity, etc. The dynamic parameters of the investigated building were obtained experimentally after each strengthening or upgrading stage when the concrete full load-bearing capacity was achieved. The formwork was removed before measurements to avoid the effect on the dynamic parameters of the structure.
It should be mentioned that the dynamic response of a building in the event of a strong earthquake is significantly different quantitatively and qualitatively from that of moderate wind, traffic-induced, and other similar forces. This is because under a strong earthquake, the response of a building is non-linear, which leads to crack formation and corresponding changes in the building’s dynamic parameters. However, the design of strengthening is based on the spectrum, corresponding to the elastic stage of the building before the earthquake (as is). Hence, the dynamic parameters obtained from records of the building’s response to traffic and wind loads correspond to the above-mentioned elastic stage (as is) and may be used for design purposes.

5. Measurement Equipment and Testing Setup

5.1. Four-Dimensional Sensor

The 4D device [22] is based on a multi-sensor technology with the main purpose of monitoring active earthquake areas. In the sensor panel, there are three built-in acceleration sensors that allow for the measurement of medium or strong earthquakes in the X, Y, and Z directions. A velocity sensor enables the measurement of high-sensitivity vibrations in the Z direction only to obtain micro-seismic data.
The device is universal and capable of measuring both strong and micro-seismic vibrations. It enables measuring the dynamic behavior of buildings by switching between sensor signals to monitor vibrations with relatively high amplitudes or micro-vibrations in the Z direction only. This is a disadvantage of the device and the reason for using additionally the 3D one.

5.2. 3D Sensor

The Raspberry Shake 3D device [23] is used for measuring high-quality seismic data in the X, Y, and Z directions. Its main purpose is monitoring local seismic vibrations of any magnitude, including strong earthquakes and micro-seismic ones. Velocity sensors connected to the board allow for the measurement of high-sensitivity vibrations in all directions. The quality of the recorded signals allows for the investigation of damped vibration in the building, high-quality detection of vibration frequencies, effective noise filtering, and performing required mathematical operations.

5.3. Software for Dynamic Data Processing

For dynamic data processing, SWARM [24] and WINQWAKE [25] software packages were used. SWARM software allows for seismic wave analysis and monitoring. It was used to analyze seismic waves in real time. The software was used to view the recorded signals, perform the Fourier transform without noise filtering, create the frequency spectrum, etc. The WINQWAKE package was used to analyze files that were recorded and processed by SWARM. It was used to perform the data Fourier transform (Fast Fourier transform (FFT) or Discrete Fourier transform (DFT)) using digital filters of FFT low-pass, high-pass, notch frequencies, band-pass, etc.

5.4. Analysis of Sensor Efficiency

Seismologists use 4D sensors to sample the seismic wavefield [26]. The sensors were tested at the Albuquerque Seismological Laboratory. It was reported that the devices have sensitivities within 4% of nominal, but they have relatively high self-noise levels, compared with the typically used ones. Therefore, it was concluded that the 4D sensors were suitable for local and regional events.
Experiments carried out for different building types showed that for buildings with slight vibrations without strong environmental noises, like residential buildings, there is a preference for using the Raspberry Shake D3 device, as it has high sensitivity to vibrations [27]. It was concluded that the D3 device has the potential to be used in advanced scientific research.

5.5. Sensor Location in the Building

Before strengthening, the soil was examined, and in the beginning, the foundations were strengthened, and one sensor was located on the ground. Before beginning the construction works related to the building strengthening and upgrading, 4D and 3D sensors were installed. The sensors were placed on the roof and ground floors of the existing building as well as on the ground outside the building (Figure 3). As the upgrading works progressed, the sensors were located on the top floor after completing the ceiling of each floor.
At each stage of the building strengthening and upgrading, the building’s velocities were recorded for 7 days. After analyzing the recorded data, it was decided to use mainly the 3D sensors since their sensitivity was higher by about 3 orders of magnitude. This allowed for measuring micro-vibrations due to traffic loading and investigating the measured signal.

6. Experimental and Numerical Evaluation of the Building’s Dynamic Characteristics in Each Stage of Its Strengthening and Upgrading

6.1. The Building Strengthening and Upgrading Stages

The building strengthening and upgrading process was divided into the following 11 stages:
-
Stage 0—the existing building before beginning the work at the site: the building was modeled according to its state (as is) following the guidelines of the modern code [1];
-
Stage 1—after completing the excavation for strengthening the foundations: the model was similar to that in stage 0, considering the excavation work required for strengthening the foundation that opened the ground floor columns by about 1 m (see Figure 2b);
-
Stage 2—after completing the ground floor columns, walls, and ceilings: the model was based on that used in stage 1, when walls and stiffening cores were added on the ground floor of the building;
-
Stages 3–9—after completing the columns, walls, and ceiling of the first to seventh floors, respectively;
-
Stage 10—structure in the service condition after completing all non-structural elements (the model based on that used in step 9 and full-service loads).
The view of the building in stage 0 is shown in Figure 2. Stages 1–10 are shown in Figure 4.

6.2. Comparing and Discussing the Dynamic Characteristics of the Building at Each Strengthening/Upgrading Stage (1–10)

As mentioned above, the dynamic parameters of the building were obtained both numerically and experimentally at each strengthening/upgrading stage. As the building was designed according to the requirements of the modern code [1] that is based on the linear elastic response spectrum, a linear elastic numerical model was used for numerical analysis. The following design parameters of the building were used according to [1]:
-
Peak ground acceleration (PGA), Z = 0.06;
-
Horizontal spectral acceleration coefficient for the low natural vibration period, Ss = 0.14;
-
Horizontal spectral acceleration coefficient for the natural vibration period of 1 s, S1 = 0.04;
-
Site soil class—type D;
-
Site coefficient for short vibration periods, Fa = 1.6;
-
Site coefficient for long vibration periods, Fv = 2.4;
-
Seismic force reduction coefficient that considers nonlinear deformations in the building, K = 1.5;
-
Importance coefficient of the building, I = 1.
Following the above-mentioned design parameters of the building, the design spectrum of the code [1] was updated similarly to the procedure described in [5], and the design spectrum was obtained, as shown in Figure 5.
Numerical values of the building’s natural vibration periods corresponding to the first 10 eigen modes are presented in Table 2. The table shows that the numerical values (Table 2) of the dominant natural vibration period for all eigen modes increase from stage 0 to stage 1 and decrease from stage 1 to stage 5 (when the stiffness of the building increases), which corresponds to the building strengthening stages without adding floors. In those stages, the contribution of additional stiffness is dominant relative to the mass of the walls. In stage 6, the dominant natural vibration period remains practically without significant change. Starting in stage 7, when new floors are added, the tendency changes, and the dominant natural vibration period begins to increase. The numerical value of the dominant vibration period after completing the work (stage 10, T = 0.432 s) is lower compared with that of the building before strengthening and upgrading (stage 0, T = 0.574 s), which means that the building was strengthened. However, the experimental values of the dominant vibration period decrease with the progress of strengthening (T = 0.315 s in stage 0 to T = 0.279 s in stage 5), which proves that the building was strengthened. Starting in stage 6, the dominant vibration period slightly increases (from T = 0.299 s in stage 6 to T = 0.399 s in stage 10). This increase is caused by the upgrading, as the mass of the building significantly increases because of the addition of three new floors.
Experimental values of the building natural vibration periods corresponding to the first four eigen modes are presented in Table 3. As mentioned above (Section 4), the eigen modes were obtained by the FFT of the recorded building’s vibrations under the natural combination of different dynamic loads, like traffic, wind, etc. The dynamic loading vector is random and constantly changes its direction. In this case, the building response in the main direction corresponds to forced vibration under the external loading.
Table 3 shows that experimental values of natural vibration periods are lower compared with the calculated ones (Table 2). This can be explained by the fact that the original building was constructed at a period when there was no seismic design code. There is no detailed design documentation of the building that would allow for the calculation of its exact stiffness. The stiffness of the structural elements was estimated according to modern codes. This means that the real stiffness may be higher (as it follows from the experimental data). Therefore, the numerical values of the building’s dynamic parameters can be interpreted just as the qualitative ones, compared with experimental results. Correspondingly, the building’s strengthening design as well as its upgrading should be based on experimental data.
At the same time, based on the experimental results, the dominant natural vibration period increases in stage 1, compared with stage 0, and decreases from stage 1 to stage 5. After that, the dominant vibration period values increase, i.e., like in the case of numerical values, the tendencies are similar. This demonstrates the qualitative correspondence of the experimental and numerical results.
A comparison of numerical and experimental values of the natural vibration periods is presented in Figure 6 and Figure 7. As expected, the lowest values in the dominant natural vibration periods correspond to stage 5, representing the building with the highest stiffness. The tendencies in varying natural vibration periods are similar for numerical and experimental data. Moreover, after completing the strengthening and upgrading, the experimental and numerical values of the dominant vibration period are similar (0.399 s and 0.432 s, respectively). The difference between the experimental and numerical results is about 7%, which is indeed satisfactory.

7. Conclusions

The research aimed to investigate a real multistory reinforced concrete residential building experimentally during its seismic strengthening and upgrading in order to validate the existing design practice and improve its efficiency. The existing building had one open floor and four residential ones, and after strengthening, three residential floors were added.
An original methodology was proposed for monitoring the strengthening and upgrading processes. It included selecting measurement devices and sensors with the highest sensitivity to enable the measurement of the real building’s vibrations during all stages of its strengthening and upgrading processes.
The recorded signals were processed in order to obtain the building’s natural vibration periods. Experimental measurements allowed the identification of four vibration modes of the building in all strengthening and upgrading stages.
Known monitoring methods usually include updating numerical models to increase the accuracy of analysis. The results of this study demonstrated the efficiency of the proposed method and its simplicity for design purposes. Updating the dynamic parameters of the building based on the experimental data allowed for an effective and easy design.
The measured dynamic parameters of the building for the first time allowed for a more accurate calculation of seismic forces for all strengthening and upgrading stages and, consequently, made the design more effective for seismic zones. Although the present study was carried out for a typical RC residential building, the proposed method is feasible for other types of structures because it is based on experimental data, thus obtaining the required dynamic characteristics for all types of buildings and structures. Therefore, we recommend monitoring buildings in each stage of seismic strengthening and upgrading.

Author Contributions

Conceptualization, I.I. and Y.R.; methodology, I.I. and Y.R.; software, S.Y.; validation, I.I., S.Y. and Y.R.; formal analysis, S.Y.; investigation, I.I., S.Y. and Y.R.; resources, I.I. and Y.R.; data curation, S.Y.; writing—original draft preparation, I.I., S.Y. and Y.R.; writing—review and editing, I.I. and Y.R.; visualization, S.Y.; supervision, I.I. and Y.R.; project administration, I.I. and Y.R.; funding acquisition, I.I. and Y.R. All authors have read and agreed to the published version of the manuscript.

Funding

This research received no external funding.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The original contributions presented in this study are included in this article.

Conflicts of Interest

The authors declare no conflicts of interest.

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Figure 1. The views [5] (a,b), original plan (c), and section (d) of the investigated building before strengthening and upgrading.
Figure 1. The views [5] (a,b), original plan (c), and section (d) of the investigated building before strengthening and upgrading.
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Figure 2. Strengthening and upgrading of the building: black—existing part, blue—new part, following [5]. (a) Plan, (b) foundations before strengthening, and (c) section view.
Figure 2. Strengthening and upgrading of the building: black—existing part, blue—new part, following [5]. (a) Plan, (b) foundations before strengthening, and (c) section view.
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Figure 3. Location of sensors inside and outside the building. Sensor 1—on the ground, 10 m from the building, sensor 2—on the ground floor, sensor 3—on the top floor.
Figure 3. Location of sensors inside and outside the building. Sensor 1—on the ground, 10 m from the building, sensor 2—on the ground floor, sensor 3—on the top floor.
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Figure 4. The investigated building’s views and corresponding models for each strengthening/upgrading stage.
Figure 4. The investigated building’s views and corresponding models for each strengthening/upgrading stage.
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Figure 5. Design spectrum for the investigated building [1].
Figure 5. Design spectrum for the investigated building [1].
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Figure 6. Numerical values of natural vibration periods [s].
Figure 6. Numerical values of natural vibration periods [s].
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Figure 7. Experimental values of natural vibration periods [s].
Figure 7. Experimental values of natural vibration periods [s].
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Table 1. Building strengthening and upgrading phases.
Table 1. Building strengthening and upgrading phases.
Phase No.Phase Name
0The existing building before strengthening
1After excavation for casting the building raft
2After strengthening the existing and casting new ground floor columns, walls, and floor diaphragms
3Same as phase 2 on the 1st floor
4Same as phase 2 on the 2nd floor
5Same as phase 2 on the 3rd floor
6Same as phase 2 on the 4th floor (roof of the existing building and upgrading the upper horizontal diaphragm)
7Casting columns, walls, and floor diaphragms on the 5th floor (new floor)
8Same as phase 7 on the 6th floor
9Same as phase 7 on the 7th floor (roof of the strengthened and upgraded building)
10The strengthened and upgraded building
Table 2. Numerical values of natural vibration periods of the building, Tnum [s].
Table 2. Numerical values of natural vibration periods of the building, Tnum [s].
StageMode
12345678910
00.5740.5690.3620.1670.1620.1150.0920.0890.0680.067
10.5820.5800.3660.1690.1630.1160.0930.0900.0690.068
20.5210.4980.3460.1590.1540.1130.0890.0860.0680.067
30.3960.3800.2710.1220.1180.0890.0720.0700.0560.051
40.2810.2680.1970.0990.0930.0740.0700.0660.0540.028
50.2040.1820.1370.0990.0950.0750.0390.0350.0280.022
60.2160.1860.1330.0540.0490.0370.0270.0250.0200.020
70.2790.2400.1670.0690.0600.0450.0340.0310.0240.024
80.3410.2920.2050.0870.0750.0570.0430.0380.0290.028
90.3810.3260.2270.1010.0870.0650.0510.0440.0350.034
100.4320.3690.2520.1090.0940.0700.0550.0480.0380.037
Table 3. Experimental values of natural vibration periods of the building, Texp [s].
Table 3. Experimental values of natural vibration periods of the building, Texp [s].
StageMode
1234
00.3150.2600.1670.123
10.3830.2890.1610.120
20.3600.2610.1840.124
30.3300.2300.1620.108
40.2980.2210.1710.101
50.2790.2080.1620.100
60.2990.2190.1500.104
70.3290.2690.1530.068
80.3630.2950.1680.073
90.3920.3210.1760.097
100.3990.3380.1930.088
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Iskhakov, I.; Yehuda, S.; Ribakov, Y. Methodology and Monitoring of the Strengthening and Upgrading of a Four-Story Building with an Open Ground Floor in a Seismic Region. Appl. Sci. 2024, 14, 7581. https://doi.org/10.3390/app14177581

AMA Style

Iskhakov I, Yehuda S, Ribakov Y. Methodology and Monitoring of the Strengthening and Upgrading of a Four-Story Building with an Open Ground Floor in a Seismic Region. Applied Sciences. 2024; 14(17):7581. https://doi.org/10.3390/app14177581

Chicago/Turabian Style

Iskhakov, Iakov, Sharon Yehuda, and Yuri Ribakov. 2024. "Methodology and Monitoring of the Strengthening and Upgrading of a Four-Story Building with an Open Ground Floor in a Seismic Region" Applied Sciences 14, no. 17: 7581. https://doi.org/10.3390/app14177581

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