**Problems of seismic design**
of extended and asymmetric structures
Earthquakes of last decades distinctly
demonstrated, that buildings of the same type do not have sufficient earthquake resistance
(e.g., buildings with walls made of insufficiently strong materials, frame buildings and
others), but those of another type have rather high earthquake resistance (large-panel,
monolithic and others). Calculations based on existing codes fail to explain this fact.
Main assumptions in existing codes
a) a floor is considered to be an absolutely hard disc;
b) an impact upon building is assumed to be constant lengthwise the building;
c) two most disadvantageous directions of a seismic wave are across and lengthwise the
building;
d) unified generalized abstract dynamic coefficient * is accepted for any type of
earthquakes.
Acceptance of these assumptions allowed to present basic calculation model of a building
as a cantilever bar for all constructions without any exclusion irrespective of their
dimensions. However, analysis of after-effects of destructive earthquakes of the last
decades puts in front of scientists the task of perfection of models mentioned above by
bringing new factors into calculations, which affect strength of a building.
The role of floors in rise of earthquake resistance had been underestimated so far.
However, damages of buildings distinctly point out very important role of floors in
distribution of seismic impact between bearing vertical elements.
**Analysis of
typical damages**
Typical damages of constructions
of buildings may be conditionally divided into several groups.
**Numerous destructions of butt parts of buildings were detected** during the
analysis of earthquakes' after-effects. In many cases they were caused by rotations of
floors of buildings about vertical axes, when centers of inertia and elasticity forces do
not coincide. However, the effect of torsion can be also observed in buildings with ideal
decision of architectural design, where distribution of masses and rigidities is symmetric
in all directions. Explanation of this may be found in three-dimensional forms of
oscillations (Fig. 1) and unevenness of the oscillation field of soil under building
foundation.
If to pass from a simple, one-dimensional model of a building as a cantilever to more
complicated three-dimensional one, and to keep the field of seismic oscillations of soil
even in accordance with existing codes, three-dimensional dynamic degrees of freedom will
not be applied, and this leads to zero seismic forces during torsional- and- flexural in
plan oscillations for buildings of regular structure.
Such sharp disparity of models, as expected, brings to paradoxes. As a result we have
underestimation of efforts in butt elements of a construction to 70 - 100%, and in
separate cases even up to 200%!
Types of buildings widely spread in civil engineering with cores of rigidity in the middle
part have their own peculiarity of oscillations. Torsional oscillations take the first
place in estimation of earthquake resistance, since inertial characteristics for extensive
buildings, related to rotation of floors about vertical axes, become dominant. Again
butt-end elements appear in the worst conditions during such oscillations.
a) b)
*Fig. 1. Destruction of butt parts of buildings: a) maximum butt-end displacements
during torsional oscillations; b) form of torsional oscillations with maximum shifts at
butt-ends of a building.*
**Big damages of the
internal walls and the middle part of floors**. Oscillations of extended
buildings with inhomogeneous structure have peculiarities.When rigidities concentrate at
the butt-ends torsional oscillations are practically absent (their frequencies go beyond
scopes of spectrum taken into account in calculations), but dominance of those
three-dimensional characteristics of external effects of soil increases, which cause
deformations of floors in their plane at big distances between the butt-end diaphragms. At
distances of 0-60 m the butt-end diaphragms are almost immovable supports for floors, and
the mode of floor oscillations is determined by one half-wave. This mode and the
corresponding frequency are the most important in estimation of earthquake resistance of a
building.
In calculations according to a cantilever scheme general seismic load is distributed
between the walls in proportion to their rigidity. However, earthquakes' experience proves
the necessity of corrections in this question. The internal walls frequently have bigger
damages than the external ones. This is explained by the fact that floors are not
absolutely rigid in their planes. In works [4, 13] there are distribution graphs of
seismic loads between middle and two extreme walls of a 5-storied building depending on
its length. The middle wall (relatively less rigid - its thickness is 38 sm.) is under
bigger seismic load, than the two extreme ones taken together (the thickness of each one
is 51 sm.).
a)
b)
**Fig. 2. Damage of the internal walls and the
middle part of floors: a) maximum one of the middle part at flexural oscillations; b) the
flexural oscillation mode with maximum displacements in the middle part of a building.**
An earthquake resistance of frame
buildings may be enlarged by setting up stiff diaphragms. Influence of cealings as discs
being deformed in its planes in this case rises considerably, what may be seen from mode
of spatial oscillations (Fig. 2) and from dependence of seismic loadings on building
length and its calculation cheme [4,13].
**Damages of mainly upper stories**. The Tashkent earthquake in 1966 with the
epicenter within the territory of the city showed that besides the horizontal oscillations
the vertical ones should be taken into account in calculations. Damages of mainly upper
storeys may be explained by proximity of prevalent periods of seismic impact to periods of
vertical oscillations of buildings and the distribution of seismic load proportionally to
the mode of vertical oscillations (maximum shears at the level of the upper stories).
**Shear of cross walls in vertical plane about each other and destruction of floors
from their planes**. The picture of damages of extended buildings in Turkey
(earthquake on the 27th of June in 1998) can be explained that for such buildings the
first one is the frequency which corresponds to torsional oscillations in vertical plane
(shear of cross walls in vertical plane about each other). In design of such buildings
horizontal loads in floor plane which were even lengthwise had been taken into account,
loads in vertical plane were traditionally neglected, but just they caused the
destruction.
a) b)
*Fig. 3. Shear of cross walls in
vertical plane about each other and destruction of floors from their planes (earthquake in
Turkey on the 27th of June in 1998)*
An explanation of the fact that for different types
of buildings the character of destruction is proportional to the different modes of
oscillations is in a complex spectral structure of the seismic impact. Proximity of
prevalent periods of the seismic impact to periods of oscillations of buildings causes
deformations corresponding to these oscillations.
The necessity of taking into consideration of spectral structure of loads and prevalent
periods of soil oscillations, as well as of unevenness of loads lengthwise are distinctly
demonstrated by all pictures of damaged buildings mentioned above. All effects described
above, which were revealed by the post-earthquake analysis, point out the necessity of
transition in codes to three-dimensional calculation schemes of buildings (structures) and
effects. |