## 2 Introduction  
Building codes and design standards typically require that torsional effects be accounted for when designing structural systems for seismic forces. When static analysis is used to evaluate structural response, torsional effects are accounted for by applying equivalent static forces at a prescribed design eccentricity, \(e_{d}\), from the center of stiffness (\(CS\)). Such eccentric forces generate story twisting moments, shear forces and overturning moments. The prescribed design eccentricity accounts for both inherent and accidental torsion effects. Inherent torsion moment, \(Mt\), is caused by the eccentricity between the locations of the center of mass (\(CM\)) and the center of rigidity, while accidental torsion moment, \(Mta\), accounts for uncertainties in mass or strength distribution assumed in the analysis, and any torsional vibrations that might be induced by base rotational motion. Some standards such as ASCE 7-16 [1] and codes such as Mexico Federal District Code [2] and National Building Code of Canada [3] provide some form of the Equation (1) for design eccentricity, \(e_{d}\), that accounts for both inherent and accidental torsions. \[e_{d}=\alpha e_{s}+\beta b\text{ or }e_{d}=\delta e_{s}-\beta b, \tag{1}\]  
where:  
\(e_{s}=\) static stiffness eccentricity, representing the distance between \(CM\) and \(CS\). \(b=\) building plan dimension, perpendicular to the direction of ground motion. \(\alpha\), \(\beta\), and \(\delta\) are code specified coefficients. The first two terms in Equation (1), \(\alpha e_{s}\) and \(\delta e_{s}\), are intended to account for the effect of lack in building symmetry on inducing coupled lateral and torsional responses. The second term, \(\beta b\), accounts for: (i) accidental eccentricity between \(CM\) and \(CS\), (ii) possible discrepancy between strength distributions assumed during the analysis phase, and the actual distribution at the time of earthquake, (iii) torsional vibrations at upper floors induced by rotational motion at the base of the building, and (iv) other sources of torsion not considered during the analysis/design phase. The present paper focuses on accidental torsion in buildings evaluated using ASC7-16 standard. It is recognized however that different design codes specify different values of the coefficients \(\alpha\), \(\beta\), and \(\delta\). Mexico Federal District Code [2] adopts a value of \(\alpha=1.5\), \(\delta=1\) and \(\beta=0.1\); while National Building Code of Canada [3] uses \(\alpha=1.5\), \(\delta=0.5\) and \(\beta=0.1\). The present study assumes values of \(\alpha=\delta=1\) and \(\beta=0.05\) in accordance with ASCE 7-16 Sections 12.8.4.1 and 12.8.4.2 [1]. It is worthy to note that probabilistic studies by [PERSON] et al. [4] confirmed the appropriateness of ASCE 7 requirements for displacement of center of mass by 5% (\(\beta=0.05\)) to account for accidental torsion in tall buildings. The investigators found that 10% displacement of the center of mass is more suitable for shorter buildings. It is often accepted in practice to assume linear elastic behavior of buildings while considering accidental torsion effects on structural response. The accidental torsion effect can be included in the static analysis of the building by applying lateral static forces, equivalent to the prescribed design seismic forces, at an eccentricity of \(\pm\beta b\) from the \(CM\) on each floor. The eccentric static forces produce larger effects including torsion to be used in design of lateral forces resisting system. Alternatively, the effects of accidental torsion on structural response can be considered through dynamic analysis of the building after notional shifting of the \(CM\) of each floor by a distance equal to the accidental eccentricity \(\pm\beta b\) from its nominal position. The two methods of accounting for eccentricity produce different force magnitudes on structural members. Other approaches to account for accidental torsion were proposed in the literature.