Ground Motions and Structures - Earthquake Engineering for Structural Design - page 375

Ground Motions and Structures 375

It must be mentioned that the consequences of accidental torsion are more significant
for the symmetric structures than for the asymmetrical ones. This unpredicted behavior
due to accidental torsion is caused by the following factors:
Base rotational excitation, which is defined as the rotational motion around a
vertical axis experienced by the building foundation as a result of spatially non-uniform
motions. This spatial variability of the ground motion underneath the foundation is
attributed to two effects: (i) Wave passage, because of which different points of the
ground surface are excited by the same motion, but with a phase lag (Fig. 8.68); (ii)
Ground motion incoherence, a term used to recognize that different points of the ground
experience motions with different amplitudes and phase characteristics, because of
incoming waves from different locations of an extended earthquake source, wave
reflections and refractions around the building foundation, or changes produced in the
waves when traveling from the source to the structure through paths of different
physical properties. The increase of displacements of symmetric buildings resulting
from accidental torsion due to the rotation excitation is larger for structures with small
vibration periods (less than about half second) and less than 5% for long period
structures (De la Llera and Chopra, 1994a,b,1995).
Uncertainties in stiffness and masses. Discrepancies between the computed and the
actual values of the distribution of structural element stiffness and masses imply that a
building with a nominal symmetric plan is actually asymmetric due to some unknown
reason and, therefore, it will undergo torsional vibration when subjected to purely
translational ground motion. The factors of uncertainty are due to:
(i) Variation of material properties and element dimensions, variability in fabrication
methods and quality control, execution and erection tolerances; (ii) Uncontrolled
distribution of infill panels with different stiffness; (iii) Presence of some uncontrolled
hollows (mainly due to the equipments) in structural elements, such as floors and walls;
(iv) Uncontrolled distribution of masses, especially for live loads.
All these aspects result in the uncertainty in the location of the centers of rigidity
(CR) and mass (CM). In order to consider the effects of the accidental torsion in seismic
design of buildings, some accidental eccentricities between these two centers are
introduced in the calculation model (Fig. 8.69). These accidental eccentricities depend
on the plan dimensions of the structure (De la Llera and Chopra, 1995, Chopra and De
la Llera, 1996).