Engineering Know-How: Lessons from Earthquakes and Rules for Seismic Design - Dynamic Behavior of Concrete and Seismic Engineering - page 348

9.4.3.3. Taking dissipative behavior into account
When considering the ductility of the structure by plasticizing critical areas of
elements, the non-linear behavior of the structure can be derived from equivalent
linear calculation (see [BET 91], section 3.17). In such cases, actions are calculated
from an elastic linear model using a design spectrum that incorporates a dividing
behavior coefficient. The structure is therefore designed using loads lower than
those derived from linear calculations. This allows an estimation of non-linear
behavior from linear calculation, which is more realistic from an engineer's
perspective, and allows them to avoid the problems associated with non-linear
modeling, which is fraught with difficulties. Behavior coefficient determination is
discussed in section 9.5.
9.4.3.4. Non-linear calculations
Two calculation methods that take the post-elastic behavior of a structure into
account are considered: the so-called “push-over”, pseudo-static method, and the
“time history analysis” method, the latter being reserved for exceptional situations.
Both aim either at evaluating either the D u / D e ratio defined in section 9.5.3, the
strength of existing buildings, or the location of potential plastic hinges and
damage. Such modeling can be bi-or tri-linear, but must be based on modeling that
is truly representative of the post-elastic behavior of structure elements and must
take potential damage into account.
The “push-over” method is internationally approved. It involves applying a
given distribution load system (proportionally to the loads derived from the elastic
analysis or those resulting from applying uniform acceleration to the height) and
increasing in intensity. A “capacity curve” is then drawn, which gives the load
characteristic of the seismic action (typically the shear load at the base) according to
a characteristic displacement (at the top of the building, for instance).
After this, we must verify that the structure can be deformed so that a “target”
displacement (characteristic of a one-degree of freedom system resulting from a
spectrum reading for the equivalent basic period of the system) can be achieved
without exceeding the ultimate strain. The one-degree of freedom system considered
is equivalent to the basic mode of the structure.
9.4.3.5. Taking vertical axis torsion into account
Structural torsion can prove dangerous if it is not well-controlled. It has three
main causes. The first is differential motion at the base of supporting points due to
wave propagation within the soil. If the supporting points are linked by structure
elements that are stiff enough, the seismic motion that is stressing a structure can be
compared to an overall displacement and rotation, the vertical component of which