Accidental eccentricity is automatically included during response-spectrum analysis in ETABS, though equivalent static-load procedures are also available for manual evaluation. Note that floor diaphragms must be rigid, otherwise torsional effects are not substantial.
Two basic approaches which enable the manual formulation of accidental eccentricity are described as follows:
- 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. Torsional response is then combined with dynamic analysis results to produce design forces which account for accidental eccentricity.
- The second approach is to apply, at each story level, torsional load which approximates the effect of accidental eccentricity. Static response is then combined with dynamic analysis results.
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.
ETABS implements an efficient and practical approach while formulating the 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 a static torsion about the joint location. Static response is then added to the response-spectrum output to indicate 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.
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.