## 1 Introduction  
A considerable number of problems related to building analysis and design procedures have been studied for many years. For steel building structures subjected to strong earthquakes, modeling the stiffness (\(K\)), damping (\(C\)), and stiffness (\(K\)) matrices has not been the exception. The appropriate modeling of such matrices is a crucial step toward an accurate estimation of the seismic response. One of the most widely used structural systems in steel buildings is that based on moment-resisting frames (MRFs), where the prismatic framed-type members are represented by beam and beam-column members. It is essential to properly represent the aforementioned matrices, at both local and global levels, for this structural system.  
The most common and simplest procedure to define the inertial properties of a building is to consider the mass as a concentrated type at the translational degrees of freedoms (DOFs) defined in the structure; it will result in a matrix (\(M_{L}\)) with non-zero numbers in the diagonal corresponding to such DOFs. It is possible, however, to derive a kinematically equivalent mass matrix called the consistent mass matrix (\(M_{C}\)) so inertia forces are also obtained for the rotational DOFs. It will give a matrix with values out of the diagonal, with the same band wide as the \(K\) matrix. Because of the better representation of the rotational inertia, it is expected that \(M_{C}\) will give more accurate results than \(M_{L}\). It is also important to mention that in seismic analyses of steel MRFs, the \(M\) and \(K\) matrices are usually formulated by considering only one element to represent each structural member [1; 2; 3], which may introduce inaccuracy in the results.  
Energy dissipation should also be properly estimated to correctly simulate the structural behavior. Since it can be generated from many sources, it is more important for steel structures. Due to its inherent complexity, this parameter is considered in building codes [4; 5; 6] by a linear viscous damper with equivalent damping of 5% of the critical (\(\zeta=5\%\)), implying in general that the variation with the type of material or with the type of source is not explicitly identified. A significant number of investigations exist where energy dissipation produced by inelastic behavior of the material is represented by using a linear damper [7; 8; 9; 10; 11].  
A more reasonable approach adopted in steel structures consists in modeling the dissipation of energy for small or moderated deformations (occurring within the elastic limit and termed as viscous energy) by a viscous damper, while that occurring at large deformations (termed as plastic energy) is considered by the constitutive law of the material. The traditional approach to consider the viscous energy has been through the Rayleigh Damping, which consists of expressing the matrix \(C\) as a combination of the \(M\) and \(K\) matrices. In this regard, two special cases of \(K\) need to be identified: the elastic (or initial) stiffness matrix (\(K_{o}\)) corresponding to small or moderate levels of deformations and the tangent stiffness matrix (\(K_{l}\)) corresponding to inelastic behavior.  
In the analysis of MRFs under the action of large earthquakes, particular aspects as the second-order effects and the dissipation of energy at plastic hinges need to be captured in \(K_{l}\). These issues are broadly discussed in the literature [2; 12], particularly for prismatic members with straight axes, such as those used in the models of this study.  
The effect of modeling the three abovementioned fundamental matrices has been broadly studied; however, as further discussed below, many problems require additional investigation. The primary objective of this research is to evaluate the responses of steel MRFs, considering different alternatives for the \(M\) matrix, as well as to evaluate the accuracy of considering one element to represent each beam.