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ssociation for Ukrainian
Earthquake Engineering

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.