Engineering Know-How: Lessons from Earthquakes and Rules for Seismic Design - Dynamic Behavior of Concrete and Seismic Engineering - page 349

corresponds to a torsional stress. The second cause of torsion is the natural
eccentricity of the center of gravity of each floor with regard to the torsion center of
the bracing system. This eccentricity can be calculated from structure plans, but its
value is associated with some uncertainty due to assumptions made about mass
distributions, the evolution of the torsion center during the motion, cracking, and the
appearance of plasticized or damage areas. The third cause of torsion is deformation.
Actually, when a structure is flexible with regard to torsion but eccentric, its basic
seismic response mode can be a combination of torsion and overall bending. In these
cases, implementing that mode simultaneously generates a bending motion and an
associated torsion that is amplified.
The random aspects of torsion are covered by taking into account what is termed
“fortuitous eccentricity”, which is equal to 5% of the dimension of the building in
each principal direction. Assessing the extent to which building motion amplifies
torsion can only be achieved through the use of adequate space models, but a
simplified approach involves sequentially moving the application point of the
seismic force away from the center of gravity on each level.
9.5. Behavior coefficients
9.5.1. Using behavior coefficients
The behavior coefficient expresses ductility, over-strength and overall behavior,
and is used as follows: seismic loads are calculated making a linear elastic
assumption, and the structure is then designed, using the elastic loads divided by the
behavior coefficient.
Without going into the detail of the behavior coefficient method, the assumptions
on which it is based are outlined in Figure 9.20. It represents a relationship between
a stress (which represents the seismic action: shear load at the base, for example)
and a characteristic displacement (horizontal displacement at the level of the center
of gravity or at the top of the structure). By likening the behavior of an actual
structure to one with perfect elastic-plastic behavior, an ideal linear elastic structure
would withstand a seismic action system q times as high as the plastic plateau.
However, it is accepted that the displacement obtained by taking the elasto-plastic
behavior of the structure into account is the same as it would be for the fictitious
linear structure. The rule of displacement equality can only be confirmed for flexible
structures. With stiff structures, the calculations show that there is an equivalence of
strain energies (areas encompassed in the F(d) curve), consequently, structural
displacement is more important than elastic displacement. Eurocode 8 uses the
elastic displacement calculated with the elastic spectrum as the value of the structure