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Continuing the development of the equations in Transfer of Inherent Torsion, lets consider the affect of accidental eccentricity ae, in which the center of loading is arbitrarily shifted by that amount in each direction. Assuming the shift is in the same direction on both levels, the torsion on the lower level now becomes
TL = FU ( CLU + ae – CRL) + FL ( CLL + ae - CRL )
= FU CLU + FL CLL + (FU + FL ) (ae - CRL)
= (FU + FU ) [ (FU CLU + FL CLL ) / (FU + FU) + ae - CRL ]
= F ( CLF + ae - CRL )
where F = FU + FL and CLF is the centroid of the forces FU and FL .In other words, we can treat the upper level force FU as a load on the level below positioned at the unshifted center of loading CLU, on the level above, determine the center of loading of the combined upper force and lower loads, and apply the accidental eccentricity to the total force on the level below. This is shown in the diagram below
As Shearwalls designs worst case of accidental eccentricity in each direction, method conservatively assumes that the accidental eccentricity occurs in the same direction and at the same intensity on each level of the structure. It is equivalent to examining 2n design cases representing all combinations of positive and negative accidental eccentricity on each of n levels in the structure, and designing for the most severe loading of all these cases.
Although this may seem unlikely, the ASCE 7 Commentary C12.8.4.2 says that it is "typically conservative to assume that the center of mass offsets of all floors and roof occur simultaneously and in the same direction." That is, as we cannot know for certain which levels and directions the accidental eccentricities occur in, it is best practice to assume they occur on all levels