## 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.