Accidental eccentricity is automatically included during response-spectrum analysis, though equivalent static-load procedures are also available for manual evaluation. Diaphragm assignments, either rigid or semi-rigid, are necessary at each floor level.

Manual implementation

Two basic approaches which enable the manual formulation of accidental eccentricity are described as follows:

1. Shift the center of mass for each rigid floor diaphragm by the distance required by code or specification. Building code often takes this distance to be a fraction of maximum story dimension, typically 5% or 10%, depending on regional standards. Center of mass may shift along either direction and along either lateral axis. Each of these changes in structural configuration also changes the global stiffness matrix, modal parameters, and dynamic properties of the structure. Therefore, separate static analyses must be conducted for each eccentricity considered.
   
   For each direction of eccentricity, the lateral static load pattern is then applied to the shifted center of mass to generate accidental torsional loading. These results may then be enveloped to obtain a maximum condition. Static torsional response is then combined with the results of dynamic analyses to produce design forces which account for accidental eccentricity.
   
   
2. The second approach is to apply, anywhere within each story level, a torsional load which approximates the effect of accidental eccentricity. Resultant static response measures are then combined with those of dynamic analysis.
   
   Fahjan et al. proposes an alternative procedure which utilizes modal superposition by modifying global force vectors to include the effect of accidental torsion within each separate mode shape.

Implementation as part of a Response Spectrum load case

(ETABS version 2013 and below and all versions of SAP2000) This version implements an efficient and practical approach while formulating dynamic response from accidental eccentricity. After the response-spectrum load case is run, the X and Y acceleration at each joint location is determined, then multiplied by the tributary mass and the diaphragm eccentricity along either Y or X. The larger absolute value of these resultant moments (m*Xacc*dY or m*Yacc*dX) is then applied as torsion about the joint location. Static response is then added to response-spectrum output to account for the additional design forces caused by accidental eccentricity. Also, when setting eccentricity ratio on response spectrum case, only one positive value is required, since results will include envelopes of positive and negative responses.

(ETABS version 2015 and above) This version calculates story torsion based on the story shear difference between adjacent stories times diaphragm eccentricity along X and Y directions, respectively. This method usually produces better and  less conservative results. In the case of semi-rigid diaphragm, each nodal force is multiplied times eccentricity based on diaphragm extent to find the torsional force at that specific node. 

Implementation by adjusting diaphragm lateral mass in Mass Source (ETABS only)

ETABS version 2015 and above allows for moved floor masses to be included in the analysis model. The way to achieve this is as follows:

1- Define MsSrc1 (default as mass source for all modal cases), MsSrc2, MsSrc3 etc. with different scenarios of diaphragm lateral mass adjustment.

2- Define nonlinear static load case Lcase2, Lcase3 etc. with loads applied that correspond to same used as in the mass source. Make sure to select the correct mass source while in nonlinear static case i,e, MsSrc2, MsSrc3...for nonlinear static load cases Lcase2, Lcase 3 etc.

3- Define>modal cases and add new case, say ModalCase2, ModalCase3 etc. and make sure to choose radio button "use nonlinear case..." and select Lcase2, Lcase3... respectively.

Reasons for considering accidental eccentricity

A few reasons for the inclusion of accidental torsion within building-code requirements for both regular and irregular structures include the following:

• Torsional ground motion possibly subjecting the structure to rotation about the vertical axis.

• Uneven distribution of live-load mass during lateral loading.

• Variation between computed and actual values of structural properties.

References

• Fahjan, Y., Tuzun, C., Kubin, J. (2006). An Alternative Procedure for Accidental Eccentricity in Dynamic Modal Analyses of Buildings. First European Conference on Earthquake Engineering and Seismology, 1166.