First and foremost directions
in the development of calculation schemes
(effects and constructions)
Necessity of
transition to the three-dimensional models.
Existing normative methods
of calculation and building design in seismic regions, based on one-dimensional cantilever
calculation schemes, do not allow to solve important questions: which is the optimum ratio
between the length and the width of the building, rigidities of frames, floors and
diaphragms of rigidity; how many diaphragms and what distance between them should be; how
different methods of monolithing of precast floors influence three-dimensional work of
construction, etc. and architect-engineering configuration. It is possible to solve these
questions using new calculation schemes, in which a building is considered as a
three-dimensional system with floors, which deform and rotate in their planes.
The problem of development of three-dimensional models become
complicated by the fact that contemporary many-storied extended buildings are dynamic
systems of big dimension with thousands unknown values in solving equations. If to employ
the detailed finite-element approximation of a three-dimensional building model, then
difficulties in description of models of material, loading and destruction will arise,
using iteration methods of reduction of inelastic problems to elastic ones. For
multivariant design it is necessary to satisfy additional requirements, imposed on
simplicity and co-ordination of the models mentioned above.
Calculation models of buildings and their methods of calculation as a result of many years
of investigations created by the group of authors allow to solve part of the problems
enumerated above with use of personal computers [2-6, 12]. In this direction Professor
V.K. Yegupov and his followers had published more than hundred works. This direction of
investigations had been reflected in the normative literature [15-19] and training
appliances [20-23].
Works by Yu. A. Nemchinov [26-29] and his followers represent another direction of
investigations of buildings as three-dimensional systems. They use as the calculation
model Vlasov's discrete shell model consisting of tandem joint three-dimensional finite
elements [30].
In due time while elaborating norms Sî-8-57, I. L Korchinskiy offered to distribute
seismic forces along building height in proportion to modes of their free oscillations.
This suggestion stayed up to now in codes in many countries. However, recent research []
showed that for extended buildings the first oscillations modes does not change by height
but by length, what essentially influences redistribution of the seismic load. This fact
has to be reflected in contemporary codes. However, it does not solve the problem just to
include three-dimensional work into codes. It is necessary to develop coordinated models
of effects.
Unevenness of
the field of oscillations.
Making use of analogy
between the problem in consideration and floating of a ship on wave V.K. Yegupov [2]
offered engineering methods of consideration of unevenness of the field of oscillations in
1969. Later on this idea was developed in works [4-8].
Seismic wave moving in soil with constant speed creates in foundation of a building (a
structure) variable in time and space inhomogeneous kinematic field of oscillations. One
must take into account, that running waves on the way from the perturbation source to the
building undergo considerable changes as a result of numerous refractions and
reverberations in layers of the earth's crust, in soil layers under the building and in
the building itself. They create chaotic field of oscillations. Therefore all
spatio-temporal oscillators constituting the model of the building react to the
perturbation with frequencies inherent to them. In codes transfer process of perturbations
along the building is ignored and replaced by one stationary wave with simplified mode as
a rectangle. In this case only those oscillators react to perturbations, which only
reflect properties of one-dimensional cantilever building model.
The main point of the offered engineering method consists in the following:
"Immovable accelerogram" is presented as a superposition of three fields
of standing waves, which parameters is the time of running of seismic waves under the
building foundation. Every field is described by an averaged functional, depending on the
ratio of the building length to the propagation speed of seismic waves in foundation
soils. One can estimate the effect of the running wave by the impact on structure of
separate standing waves, which, however, contain the main characteristic of wave processes
- time of seismic wave propagation under the building's foundation.
Therefore it is necessary to make special analysis of the set of seismograms or
accelerograms, independent on regional conditions (6). The analysis consists of breaking
up seismograms or accelerograms into segments Dt = L / c, corresponding to the time of
running of the seismic wave under the building's foundation.
At each segment a seismogram or accelerogram is presented as the sum of impulses of a
definite form. Thus one can get standing waves depending on the parameter *t. Such methods
of adaptation of earthquake seismograms and accelerograms allow to transform the
Biot-Housner frequency spectrums, used in codes, into frequency-wave ones. The law of
change of amplitudes of displacements according to the length or the width of buildings or
acceleration of soil and platform may be determined by the analytic analysis of earthquake
records mentioned above with taking into account the parameter *t. This analysis has to be
made beforehand and is presented as a frequency-wave spectrum universal for all of
constructive types of buildings.
According to the methods described above with use of the probability method allowed to
adapt the process number of earthquake accelerograms with the force of 7 and 8 points.
Fig. 4 shows the calculation graphs for Mj(L/c), averaged on ensembles: M1 is for
progressive, M2 - for torsional, M3 - for flexural in plan oscillations.
Scheme of impact of the running seismic wave upon buildings of regular type (skeleton
buildings of frame constructive scheme, dwelling large-panel, brick, large-block) are
brought in fig. 1b) and 2b). The Impact effect depends on the time of running of the
seismic wave under the building foundation.
Dynamic
coefficient is determined for the so-called average soil
conditions and the averaged values of a structure attenuation. Analyzing the method by
which the diagram *(T) is constructed, it is necessary to note its essential
irrationality. So, the assumption about impossibility of resonance does not find either
theoretical or practical justification in the case of periods more than 0,4 sec.
Earthquakes in Niigata (Japan), Mexico City (Mexico), Romania, etc. have shown that the
maximum of the dynamic coefficient can move to the right because of the resonant
phenomenon in soil, what endangers many-storied buildings and flexible structures. Now
this fact is already reflected in codes of Romania (fig. 4). While developing regional
codes (particularly in the Ukraine) it is necessary to take into account the experience of
the nearest neighbor countries.
a) b)
Fig. 4. Diagram for dynamic coefficient
accepted in norms of Romania.
Taking into
account of dynamic properties of soil and use of seismological information
At the meantime only values
of the maximal acceleration are used in the normative calculations from the extensive
seismological information on earthquakes. As the latest research had shown, the reaction
of a structure is essentially influenced by the spectral structure of the impact, in
particular, it is necessary to take into account such important factor, as the prevailing
period of the earthquake.
On the basis of generalization of the form of numerous spectra of reaction of
strong earthquakes analytical expressions of soil spectra of acceleration had been found
depending on the prevailing period ôpr of soil oscillations []. These dependencies are
represented graphically in the fig. 5.
Fig. 5 Diagrams of soil spectra for
short- and long-period earthquakes according to the hypothesis of equal maximal
accelerations.
Defects in codes can be
removed, if the spectral approach will not be limited by the construction of the averaged
curve of a reaction spectrum, but to extend it to the calculation of the building as a
whole, up to finding efforts in elements. For this purpose the object of calculation
should be presented as ensemble of partial oscillators (according to the number of degrees
of freedom), each of that characterizes kinematics of the system under influence of the
appropriate soil harmonic. It is accepted, that each of partial oscillators at the certain
moment of an earthquake should sound with maximal intensity inherent in it, determined by
the appropriate ordinate of the soil spectrum. Inertial loads arising as a result of the
maximal designed "sound" of each partial oscillator of the system should be
taken into account separately in order to construct the envelope of partial efforts for
each constructive element. This envelope is the designed epure of efforts, by which
earthquake resistance should be tested.
Investigation of
dynamic process in long RC frame structures and bridges, excited by seismic waves.
Use of
traditional models (beams, frames) doesn't bring to satisfactory results, because they
fail to reflect three-dimensional behavior of a construction (in-plane bending and
torsional motions of floors, slabs and decks). Therefore models, consisting of plates,
beams and bars, are considered. Because of large length of constructions and nonuniformity
of impact of ground waves upon foundations of columns (pears) it is offered to use as an
external impact not accelerations of rest points but their displacements.
Exploration of construction dynamics is held both by analitical and numerical
methods, what enables one not to get only quantative results but to reveal qualitative
picture of influence of different parameters upon motion of construction.
Such investigations are carried out both in linear and nonlinear formulations.
When applicating developed methods it was detected, that when shear waves are
running under a long bridge the most excited and therefore most dangerous mode is that,
characterized by in-plane bending and torsional deformations of a bridge deck. |