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

# Shift the center of [mass|kb: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|kb:Modal analysis] parameters, and dynamic properties of the structure. Therefore, separate static analyses must be conducted for each eccentricity considered.

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For each direction of eccentricity, the lateral static [load pattern|kb: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.
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# 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.
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[Fahjan et al. |^Fahjan, Accidental eccentricity.pdf] 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.

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[ETABS|etabs:Home] implements an efficient and practical approach while formulating dynamic response from accidental eccentricity. After the response-spectrum [load case|kb:Load case] is run, the X and Y acceleration at each [joint|kb: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.

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.

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h1. References

* [Fahjan, Y., Tuzun, C., Kubin, J. (2006). |^Fahjan, Accidental eccentricity.pdf] An Alternative Procedure for Accidental Eccentricity in Dynamic Modal Analyses of Buildings. _First European Conference on Earthquake Engineering and Seismology, 1166_.


h1. See Also

* [Accidental torsion in response-spectrum case|kb:Accidental torsion in response-spectrum case] article