## 1 Introduction
This raises a crucial question: can we accurately identify the damage in a structure that is already compromised? This can be achieved by installing a monitoring multi-channel accelerometer network on the damaged structure to detect its dynamic properties through ambient vibrations after the strong post-seismic sequence has ended. According to the \"\(M\) and \(P\)\" technique, the detected in the field fundamental eigenfrequency (Hz) by the monitoring process is inserted into the frequency diagram of the existing structure. This key diagram of the methodology is initially plotted as a function of the roof displacement in the nonlinear area and is then combined with the capacity curve of the structure. This is achieved by conducting a series of pushover analyses with increasing target roof displacement followed by corresponding stepping modal analyses. Using this diagram, the seismic roof displacement of the structure corresponding to the detected (in the field) fundamental eigenfrequency is revealed. All other higher eigenfrequencies of the structure can also be directly found in the previous diagram. Furthermore, the mode shapes of the damaged existing structure can be found by conducting stepping modal analysis at the same inelastic step corresponding to the seismic roof displacement found in the key diagram. Additionally, the stepping lateral stiffness matrix of the damaged structure at the same inelastic step can be found, considering all developed plastic hinges and stiffness degradation of the structural elements (in case of RC structures) in the inelastic region. This matrix provides insights into the localization of damage in the structure and its severity. An accurate damage image of the structure can be obtained by examining the state of developing plastic hinges in the final step of the pushover analysis with target displacement equal to that found in the key diagram. This paper validates the effectiveness of the \"\(M\) and \(P\)\" technique for identifying seismic damage in planar multistory, steel moment-resisting frames that are braced with concentric vertical links. An extensive parametric analysis on ductile frames of this type is conducted. The study focuses on steel frames with multiple spans of varying lengths and multiple stories of different heights, which are braced with X- or V-type concentric braces in single stacks or in split configuration among the spans along the elevation. Multiple concentric braces placed in single-stack or split configuration along the elevation are also considered. The behavior of steel X- or V-braced frames is similar to that of dual-reinforced concrete (RC) frames coupled with walls, where the bracing elements of the steel frame represent the bending subsystem, while the frame elements represent the shear subsystem. In these ductile steel-braced frames, in which the beams are rigidly connected to the columns, severe seismic damage occurs mainly to the braces. In strong seismic motion, the seismic behavior of steel frames braced with concentric vertical braces is characterized in general by the complete failure of the compressed brace due to buckling and the high ductile behavior of the brace in tension. Additionally, the end sections of beams or of some columns of ductile, steel-braced, moment-resisting frames can sustain moderate seismic damage. It is noted that the bracing columns of X-braced steel frames with the braces in single-stack configuration along the elevation can sustain severe seismic damage due to high uplifting/settling axial force. For this reason, various researchers have suggested the use of staggered braces arranged in split-X configurations rather than the conventional single-stack braced frame [34]. A numerical example of a six-story steel frame, braced with two concentric vertical X-braces in single-stack configuration in the first two floors and with staggered braces arranged in split-X configurations in the other floors, is presented in detail in this paper. This frame features four equal spans and a higher ground floor.