## 1 Introduction
The procedure calculates the distance of a given arbitrary wall which coincides with the center of mass and the modal center of rigidity. NTHA of the case study shows that the lowest roof rotation is indeed achieved when the center of mass and rigidity are aligned on an axis. However, NTHA produces a base shear demand that exceeds the strength due to the higher-mode responses. The paper does not address the effect of the center of mass variation along the height or strength assignment for fixed positions of the walls and frames. [PERSON] et al. [24] developed a displacement-based procedure for plan asymmetric multi-story buildings. It decouples the translational and torsional deformations using an approximate technique formulated by [PERSON] and [PERSON] [25]. The method is found to be accurate for linear systems. On the other hand, NTHA of a nonlinear (elastic-perfectly plastic) system showed that it is conservative in achieving the allowable story drift; hence, it needed further refinement. The P-\(\Delta\) effect is checked after the design is completed. If the stability coefficient is greater than 0.1, redesign is necessary. To incorporate torsional responses in DDBD's framework, [PERSON] [26] derived semi-empirical equations for estimating twist-induced displacements of plan-asymmetric wall buildings. These equations are limited for use in the seismic design of torsionally restrained regular-asymmetric systems. [PERSON] et al. [27] applied the semi-empirical equations to two asymmetric RC frame buildings having the same geometry but different lateral strength distribution along the plan. The case studies did not account for the effects of P-\(\Delta\) and center of mass variation along the height. The mean NTHA story displacements are low compared to the design displacements for both cases. The NTHA confirmed that design for different strength assignment (zero strength eccentricity) resulted in lower floor rotation than design for equal strength. The mean NTHA drifts have exceeded the allowable first-story drifts for some frames even though the difference is only about 5 percent. The plastic hinge rotations of the members were also not discussed. Many researchers have attempted to incorporate higher-mode effects in DDBD's framework. [PERSON] et al. [28] formulated parametric equations of story displacements for application in DDBD of RC frames. [PERSON] and [PERSON] [29] modified the equations to include drift amplification due to higher modes. The case studies range from two to 20-story vertically regular tube frames, thus not representative of typical frames with longer beam spans where gravity load action may dominate. The P-\(\Delta\) effect is also not considered. [PERSON] [30] discussed that the P-\(\Delta\), building height, number of stories, and ground motion intensity are the major factors affecting the story displacement equations. Hence, he suggested that the equations be a function of the aforementioned factors. Though DDBD concluded that the maximum drift occurs in the first story, the study showed this is not the case. [PERSON] and [PERSON] [31] found that for cantilever wall buildings ranging from two to 20 stories, reducing the elastic modal force effects by the behavior factor (force-reduction factor) and produces an unsafe design. Thus, they recommended using Modified Modal Superposition (MMS). MMS combines DDBD-obtained inelastic first-mode and elastic higher-mode force effects by the Square Root of Sum Squares (SRSS) method. It gives a satisfactory result for shorter walls (four- to eight-story cases), while it is slightly conservative for taller walls (12- and 20-story cases). [PERSON] [32] showed that MMS should not be applied for RC frames since yielding causes a significant increase in higher-mode periods compared to walls. Higher-mode periods tend to slide down the constant velocity slope of the response spectrum. Consequently, design by MMS results in conservative responses when checked by NTHA.