## 1 Introduction  
Urban development through accelerated expansion of large cities, correlated with the appearance of rather daring architectural concepts, requires the use in structural design, of increasingly complex calculations, and modeling procedures. The majority of practitioners performing in the civil engineering domain are familiar with the concept of the response spectrum method (RSM) to evaluate the structural response of the commonly designed structures. For nearly 60 years, the RSM was used to produce a maximum peak value for one force or one displacement at an unspecified point in time [1]. Consequently, in order to take into account the actual behavior, the structural response is reduced by specific factors that are correlated with well-defined geometrical and ductility requirements imposed by the design code prescriptions. The technology evolution and its current availability oblige the structural engineers to move forward and to consider more advanced analysis methods, which take into account the full nonlinear dynamic behavior of the structural elements as well as more accurate models in terms of seismic excitation. In this respect, a simple, accurate, and fast procedure to obtain the nonlinear dynamic structural response is one of the challenges and is still being a hot topic in this domain. Among the methods available to determine the nonlinear dynamic structural response [2], the force analogy method (FAM) has proved to be both accurate and numerical efficient [3]. The key idea in FAM is to retain the initial stiffness matrix and to modify the displacement vector such that the same level of restoring forces are produced. Consequently, the displacement vector is decomposed in its elastic and inelastic components. The inelastic component of the displacement is moved to the right-hand side of the equation of motion and regarded as some perturbation forces. Coupling FAM with an explicit solver to integrate the equation of motion has proved to be both accurate and numerically efficient not only for regular problems of obtaining the nonlinear structural response of isolated structures [4] but also in the more complex case of structural bounding due to earthquake action [5]. In recent papers, [PERSON] et al. [6] studied the accuracy of the FAM for nonlinear static analysis. They concluded that the results are in good agreement with those obtained by other analysis techniques commonly used for seismic performance assessment of structures. [PERSON] et al. [7] concluded that FAM is effective and accurate to estimate the plastic energy dissipation of multi-story and high-rise structures. They conducted several numerical simulations on different types of structures in order to compare the plastic energy dissipation of MDOF systems and their equivalent SDOF systems. Using the force analogy method, [PERSON] et al. [8] investigated the seismic performances of two plane portal frames, one modeled with Timoshenko and one using Bernoulli beam finite element. They showed that the resulting differences in structural response are not significant for engineering purposes. Moreover, [PERSON] et al. [9] used the FAM to investigate the effects of location and intensity of single-floor mass irregularity, on seismic response of mid-rise moment-resisting steel frames. A major breakdown of the FAM has been achieved when the concept of FAM 3D was introduced [10]. The 3D case of FAM was addressed in [11] for the analysis of structural models subjected to long-duration time-histories of wind loads and for the assessment of the structural damage state. The concept of axial force-bending moment interaction surface, coupled with an efficient return mapping algorithm was used [12]. Although the main features of the FAM 3D modeling technique were introduced in [10], there are several topics that were not fully addressed. An obvious issue in [10] is that the usage of material bilinear model is arguable for modeling cyclic behavior of reinforced concrete (RC) elements.