Engineering Know-How: Lessons from Earthquakes and Rules for Seismic Design - Dynamic Behavior of Concrete and Seismic Engineering - page 346

must be less than 30% of the corresponding radius of torsion, and the latter must
stay lower than the mass-gyration on each level.

Figure 9.19 presents two wall structures. In both cases, the radius of gyration is
determined by the mass of the floors, which is distributed over the whole surface.
The case shown in Figure 9.19(a) includes a central core and peripheral columns:
here, the stiffness and strength with regards to torsion focus at the center of the
building, hence the radius of torsion is low, and the building is not considered to be
regular. In the second case shown in Figure 9.19(b), bracing elements are distributed
on the outskirts, and the radius of torsion is similar to the width of the building. The
horizontal regularity allows us to carry out a plane analysis in both of the principal
planes.

(a) (b)

Figure 9.19. Plane configurations different from the point of view of torsion

Respecting vertical regularity allows designers to ensure the progressive
characteristic of first mode displacements, and to prevent modes higher than 1
exerting a non-negligible influence on the displacement of the structure under
seismic action. These conditions allow the use of the simplified calculation method.
They also make it possible to avoid delicate situations linked to sudden variations in
stiffness or mass (“transparencies” on the first level for example, or reversed
pendulums). The conditions are a complex function of the continuity of bracing
elements and progressive variation in geometrical shapes with structural height.

9.4.3. Calculation of seismic action effects

9.4.3.1. Structure modeling

Calculation of seismic actions should be based on modeling of the structure that
takes into account the influence of soil deformation, connections, non-structural
elements and the presence of contiguous structures. As a rule, models consists of
vertical elements that represent bracing elements, connected by other elements that
represent diaphragms. If the diaphragms can be considered as stiff compared to
bracing elements, floor masses and mass inertia can be concentrated on their centers