## 2 Introduction
When static analysis is used in this article, forces are calculated using the Equivalent Lateral Force (_ELF_) method. The accidental eccentricity has been used by engineers to account for various uncertainties, but also to account for torsional ground motion, although the latter is not indicated in ASCE 7-16 to be part of the eccentricity definition. [PERSON] et al. [5] proposed accountingfor the effect of torsional ground motion through a process in which the translational component is multiplied by a factor that is a function of the accidental eccentricity proposed by the authors. The parameters affecting the torsional response of a building can be classified as parameters, which are function of the stiffness of the lateral resisting system; and parameters which are function of the geometric configuration of the building. The most significant stiffness parameter influencing torsional response of a building is the ratio between fundamental frequencies of uncoupled torsional and lateral vibrations [6; 7; 8]. The ratio between building fundamental frequencies of uncoupled torsional and lateral vibration, \(\Omega\), is defined as ratio between uncoupled angular torsional frequency, \(\omega_{\theta}\), and uncoupled angular translational frequencies, \(\omega_{x}\) and \(\omega_{y}\). The angular frequency in general is proportional to the square root of the mass divided by the stiffness as indicated by Equations (2)-(5) [9]. The ratio of uncoupled torsional and lateral frequency, \(\Omega\), can be calculated by Equation (6). It is worthy to note that the uncoupled frequency is obtained from the structure mode shapes that include both translation and torsional vibrations and are beyond the scope of this article. On the other hand, the uncoupled translation frequency is obtained from a pure translational mode shapes and uncoupled torsional frequency obtained from pure torsional mode shape. \[T_{\theta} =2\pi\sqrt{l_{m}/k_{\theta}}, \tag{2}\] \[\omega_{\theta} =\sqrt{l_{m}/k_{\phi}},\] (3) \[T_{x} =2\pi\sqrt{M/k_{x}}\text{ and }T_{y} =2\pi\sqrt{M/k_{y}},\] (4) \[\omega_{x} =\sqrt{M/k_{x}}\text{ and }\omega_{y} =\sqrt{M/k_{y}},\] (5) \[\Omega_{x} =\
icefrac{{\omega_{\theta}}}{{\omega_{x}}}\text{ and }\Omega_{y} =\
icefrac{{\omega_{\theta}}}{{\omega_{y}}} \tag{6}\]  
where,  
* \(Jm\), is the torsional constant, \(K_{\theta}\) is building torsional stiffness \(K_{x}\) and \(K_{y}\) are building translational stiffness in \(X\) and \(Y\) direction respectively. * \(M\) is building mass \(\Omega_{x}\) or \(\Omega_{y}\) are the ratios of uncoupled torsional and translation frequencies. Several studies showed that accidental torsion increases the structural response of symmetric buildings more than unsymmetrical buildings [6]. Therefore, emphasis in this article is on symmetrical buildings. For symmetric buildings in general; the uncoupled torsional and lateral frequencies \(\omega_{\theta}\), \(\omega_{x}\) and \(\omega_{y}\) can be computed using standard modal analysis procedures such as Eigen value or Ritz methods. For unsymmetrical buildings, which are not addressed in this article, the uncoupled frequencies cannot be obtained from modal analysis directly. Procedures are found in literature to calculate the uncoupled frequencies for unsymmetrical buildings [6]. The most significant geometric parameter influencing torsional response of a building is the ratio of the length of the building in the direction perpendicular to the direction of seismic excitation to building radius of gyration. Radius of gyration is an important parameter needed for checking the regularity in plan as will be discussed later in this article. Mathematically, the radius of gyration is the square root of the ratio of the polar moment of inertia of the floor mass in plan to the floor mass. In the case of the rectangular floor area with plan dimensions \(a\) and \(b\) and with uniformly distributed mass over the floor, the radius of gyration, \(r\), can be expressed by Equation (7).