Engineering Know-How: Lessons from Earthquakes and Rules for Seismic Design - Dynamic Behavior of Concrete and Seismic Engineering - page 347

of gravity; in such a case, the model is termed a “lumped-model”, consisting of
beam vertical elements connecting the floors.

The masses are calculated by estimating those present in the structure associated
with the seismic action combinations:

¦¦

G \ Q

kj Ei ki

In practice, the nominal masses associated with the quasi-permanent variable
actions are affected by M coefficients that take into account their presence
probability during the earthquake:

\ . These M coefficients are a
complex function of the level considered in the building and the type of variable
action (i.e. the use of the premises). They typically vary between 0.5 and 1.

M . \

Ei 2 i

For masonry or reinforced concrete elements, cracking must also be taken into
account when evaluating stiffness.

The soil/structure dynamic interaction effects must also be taken into account
when displacements are involved, for example, when modeling structures sensitive
to second order effects, very slender structures and structures built on very soft soils.
The effects of this interaction on piles have to be taken into account whatever the
situation.

9.4.3.2. Elastic calculations
Seismic actions inside a structure result from movements imposed at the
foundation level. When the behavior of the structure can be considered as visco-
elastic from a linear point of view, the structure dynamics methods allow calculation
of the actions from a pseudo-acceleration spectrum or by direct time integration
(time history calculation).

The multi-modal calculation method that uses response spectra is detailed in
Eurocode 8.

Pending concordance with the regularity conditions outlined in section 9.4.2, a
simplified method can be used. This involves applying - in each principal plane - a
horizontal static stress system on each different level. This stress system is
determined proportionally to a single mode the shape of which is given a priori . The
associated basic period can be determined by an approximate formula that includes
the height (H) of the building and on a coefficient characteristic of the bracing type.
The whole mass is assigned to that single mode for flexible buildings ( T>2T C ), and
85% of the mass is used for stiffer buildings.