 Theoretical and experimental studies
Theoretical and experimental studies

# Theoretical and experimental studies

The author derives the equation of planar vibrations of rigid structure resting on kinematical pendulum supports with planar bottom (after A.M. Kurzanov). Both support and the surface below are assumed rigid; no sliding assumed. One of the coefficients in the equation (i.e. coordinate of the rotation center) proves to be piece-wise constant. The equation is of the hyperbolic type with parametric terms. Even linearization of this equation does not bring it to the conventional equation of the SDOF oscillator. Principal difference is that the free vibration period depends on the amplitude. The equation is checked for free and forced vibrations. Similar problem is for the seismic response of the unanchored items. For the further research the experimental data about damping are of great importance: both for rotation and the gap closing.

The paper presents a method of using the reduction factor to ensure the stability of monolithic reinforced concrete bearing structures to progressive collapse.

Studies have established the values of the reduction factor based on the accepted value of the relative deformation corresponding to the formation of an admissible zone of "destruction" of the support section of the overlap under the action of transverse forces, as the main criterion for asessing the stress-strain state of monolithic reinforced concrete structures for the failure mode of a vertical supporting structure.

The accepted deformation criteria for a special limiting state correctly reflect the conditions for the formation of an admissible amount of damage to elements of bearing reinforced concrete systems.

The reduction factor (K1) obtained in the framework of the research performed is the most important deformation characteristic of the special limiting state of monolithic reinforced concrete bearing systems of buildings and structures for an emergency design situation associated with the failure of a local structural element.

Linear-spectral method (LSM) is still the common method for the seismic design analysis. "One-component one-mode" responses, obtained by static analysis in the conventional variant of LSM, are combined twice: first for different modes but for each single excitation component separately, then for the different excitation components. In the alternative LSM variant presented in the Russian code SP 14.13330, first one chooses the "most dangerous" direction of the one-component excitation for each mode; then calculates the "one-mode" response for this excitation, and finally these responses are combined. In both cases the combination is performed using the complete quadratic combination (CQC) rule. Different documents suggest different formulae for the correlation coefficients. In the paper different formulae are compared to each other. The goal is to limit the number of calculated coefficients and decrease the amount of calculations.

The question of setting the seismic design input on high rise buildings is considered. The existing approaches to accounting for increased responsibility of high rise buildings in Russia are described. The proposal to reduce the probability of an acceptable building failure in proportion to the number of floors and Guideline proposals to increase the reliability factor and using maps of general seismic zoning are analyzed. The main disadvantages of methods described are indicated. It is shown that the current regulatory documents in the field of earthquake engineering do not provide the same reliability of designed structures in general and high-rise buildings in particular. The influence of seismic dangers in according with seismic zoning maps on the reliability of the designed objects is noted. An approach to generating the design input based on the permissible probability of its exceeding is considered using the example of five five-storey buildings and one 25-storey buildings. The probability of the admissible damage value included in the normative calculations is estimated. An estimate of the allowable failure probability on the value of acceptable damage (risk) is proposed under the assumption of a normal distribution of damage caused by earthquake. It is shown that the allowable failure probability decreases with decreasing acceptable damage only in the area of small damages. An approach to the assignment of seismic action based on an assessment of seismic risk has been formulated. The system of design coefficients used to calculate seismic loads on high-rise buildings is analyzed. It is noted that along with an increase in the design level of seismic acceleration, it is necessary to increase the coefficient, taking into account the low damping of high-rise buildings oscillations. At the same time, it is possible to significantly reduce the reduction coefficient by regulating the strains between the building floors.

The article is devoted to issues related to the probabilistic justification of the safety of nuclear power plants (NPP) when a high-speed military aircraft falls. The random parameters are the recurrence of falls and the direction of the aircraft's trajectory. The conservative value of the recurrence of falls, given in the IAEA documents, was used, which ensures a high degree of NPP safety. The aircraft approach is assumed to be equally probable from either side. The trajectory slope is specified taking into account the IAEA documents and statistics of aviation accidents.

The aircraft impact load is applied to one of the structures, therefore the impact probability must be determined independently for each of them. It is proportional to the equivalent area of the building structure, depending on its size, shape, position in space and in relation to other structures. Expressions are given for the equivalent areas of structures of various shapes, typical for NPP. It is shown that if the aircraft crash is unintentional (accident), then with the usual dimensions of structures, the probability of an impact in them is less than the value, starting from which, according to Russian standards, it must be taken into account in the design basis of the NPP, i.e. it can be ignored. Dependencies are given for calculating the probability of an aircraft strike in the case of a deliberately organized accident (terrorist attack), in which the aircraft will surely fall on the territory of “Nuclear Island” of the NPP.

The procedure for setting the design loads on the building structures of a NPP in the case of a deliberate aircraft fall based on the allowed probability of their realization is described. It is shown that this method of setting the loads makes it possible to substantiate their significant reduction, which leads to a reduction in the cost of the NPP while guaranteeing its safety. A probabilistic assessment of structures safety of existing NPP in the event of an aircraft impact is discussed.

The author carries out parametric studies for the equation of planar vibrations of rigid structure resting on kinematical rolling supports with planar bottom (after A.M. Kurzanov). Both support and the surface below are assumed rigid; no sliding assumed. Varied parameter is the width of the bottom. Horizontal structural acceleration is studied. Three variants of the possible behavior are shown: (i) minor rocking with little decrease in response accelerations as compared to the initial excitation; considerable rocking with considerable decrease in the response accelerations; intensive rocking leading to the overturn of the supports. In vertical direction there appear shocks (infinite accelerations) during gap closings of the supports. The importance of the problem for the seismic response analysis of the unanchored items is noted. The author gives recommendations for the experimental program, aimed to obtain data about damping both for rotation and for the gap closing, and also about the impact of the flexibility of the supports and underlying surface.

The general characteristics of the structural system of a full-assembly frame of "H" elements for the construction of residential buildings are described. "H" element is a hybrid of two columns, each is one storey high, join to monolith with the joist. The junction of the columns is located in the middle of the floor height. These elements are assembled to structural cells with longitudinal, transverse or cross-arrangement of bearing frames. Joints of columns with joist are rigid. The overall spatial stability of the frame is provided by the layout of the frame elements, as well as the use of various kinds of connections. Slabs are prefabricated. Connections of "H" elements are made by the ties with the use of screw reinforcing bars.

In engineering approaches to calculating the seismic resistance of underground structures, in particular pipelines, it is important to find experimentally the forces of interaction with the ground, as this frees us from the need to solve a difficult dynamic problem for the ground (elastic or having more complex mechanical properties). In this work inaccuracies are corrected and further development of the known from literature theory of quasistatic experiment for determining the coefficient of longitudinal interaction of soil and underground pipeline in seismic problems is given. It is shown that only the second approximation for the named coefficient in the expansion with a small parameter, equal to the ratio of the length of the pipe sample to the length of the seismic wave, takes into account the longitudinal deformation of the pipe; the first approximation corresponds to the experiment with an absolutely rigid pipe.

A
strict reduction of the seismic problem to the problem for relative pipeline
movements is presented. Conditions are found on the external (remote from the
pipe) boundaries of the soil, the fulfillment of which ensures the correctness
of determining the coefficient of longitudinal interaction for seismic problems
in experiments

The article considers the initial Cauchy problem for a fractional differential equation with a variable coefficient and its numerical solution is applicable in the problem of developing an oil well to determine the pressure change with increasing distance from the well. The parameter of the proposed mathematical model for a specific well was identified based on experimental data. The parameter of the mathematical model was determined by solving the problem of approximating empirical data using the least squares method.

The article describes research on the influence of normal adhesion on the strength of cellular concrete masonry. The performed tests and test samples are described. The results of the tests carried out to date are also presented. Further measures to study the effect of normal adhesion on the load-bearing capacity of cellular concrete masonry, including seismic impacts, are indicated.

The article provides
an overview of the use of tuned mass dampers (TMD) in some of the most famous
buildings and structures around the world for nearly three decades. The article
also discusses the use of tuned mass dampers when increasing the seismic
resistance of mosque minarets and enhancing their resistance to wind action. An
example is given of the possible use of such dampers in the minaret of the Great Mosque
of Aleppo in Syria, using as an example the parameters and characteristics of the
devastating earthquake that occurred back in 1995 in the city of Kobe in Japan.
The optimal characteristics of the components of the tuned mass damper used to
enhance the stability of the minaret of the aforementioned mosque against
seismic and wind impact have been selected. The results of the analysis are
obtained and conclusions are drawn.

A calculation method for structures under seismic impacts is proposed taking into account changes in buildings' structural design during deformation, based on the normal forms
method and the presentation of design forms for calculating seismic forces in the form of expansions in the forms of natural vibrations. These formulas are close to the calculated ones given in a number of standard documents. The solution is made in time steps. At each step, the structural design is adopted from the results of the static calculation for seismic forces determined at the previous stage. The solution method is getting built in the form of forms expansions using the software MATHCAD. The seismic forces numerical values are
calculated at each time step, taking into account changes in the structural design in the previous step by static calculation for seismic forces impacts. The proposed approach allows us to evaluate the seismic forces values, taking into account changes in the structural design during oscillations at each time step. A change in the structural design is evaluated by static calculation based on seismic forces determined in the previous step. The coefficient K1 values were estimated as the ratio of seismic forces at the stage preceding
failure to seismic forces at the stage corresponding to the end of the elastic stage.

The author derives the equation of motion for a structure resting on kinematical pendulum supports of Yu.D.Cherepinsky. Both structure and supports are assumed to be rigid; no
sliding is assumed during rolling. Two components of seismic excitation are considered (horizontal one and vertical one). Equation of motion for free vibrations looks like that of the free vibrations for massive pendulum support standing alone (it was studied earlier). It is fact the equation of motion for pendulum, but center of rotation, inertia moment and stiffness are varying with time. This equation may be simplified to the linear one by skipping the second
order terms. The equation of motion for seismic response after linearization is the extension of the Mathieu-Hill’s equation, where horizontal component is responsible for the right-hand part (in the conventional Mathieu-Hill’s equation it is zero), and vertical component creates parametric excitation in the left-hand part. In fact, vertical seismic acceleration modifies gravity acceleration g, which controls the effective natural frequency for pendulum.
Thus, there might appear dynamic instability (though without infinite response due to the finite duration of excitation). The author presents numerical example.

Simulation considered after the main seismic impacts are removed from the structure, the two-layer rod, which is in an elastic environment, is subjected to periodic longitudinal forces. In the investigated work the Bubnov”s-Galerkin method was used, numerical calculations were made. The main area of dynamic instability is built and shown in the figure, where the dotted line marks the solution of a homogeneous problem.

The reduction in the reserves of traditional natural raw materials makes us look for new ways to replace it with different types of waste. At the same time, the costs of exploration, construction and operation of quarries are excluded, and significant land plots are exempt from the impact of negative anthropogenic factors. The experience of advanced foreign countries has shown the technical feasibility of this direction and its application as a tool for protecting the natural environment from pollution. On the basis of inter-shale clay and high-alumina nanotehnologija raw materials petrochemical spent catalyst IM-2201 NovoKuibyshev petrochemical plant derived ceramic brick with high physicalmechanical properties without the use of traditional natural materials. Using nanotechnogenic petrochemicals – spent catalyst IM-2201, containing more than 70% A12O3, a ceramic brick was obtained that corresponds to the M200 brand. It is possible to build load-bearing walls of the lower floors of high-rise buildings (15 floors or more) from M200 ceramic bricks. Innovative proposals for the use of industrial waste: interslant clay and spent catalyst in the production of high-strength ceramic earthquake-resistant bricks with high strength and frost resistance have been developed. The absolute advantage of using multi-tonnage waste of the spent IM-2201 catalyst and inter-shale clay for the waste of oil shale is

Two principal approaches to generating calculated seismic impacts, proposed in the practice of earthquake - resistant construction, were used and  refined: for the construction site and for the structure. There are special, emergency and extreme seismic loads that create an emergency situation - the occurrence of a mode of beats or resonant vibrations, as well as self-oscillations (acute resonance), leading to a violation of either the operational properties or the load-bearing capacity of the structure. Proposals are formulated for the revision of the Russian standards of earthquake-resistant construction, based on three-level impact for responsible and unique structures using the proposed refined approaches to generating calculated seismic impacts.

The author derives the equation of free vibrations for kinematical rolling support of Yu.D.Cherepinsky. Both support and the surface below are assumed rigid. It is shown that Lagrange equation is similar to the equation of motion for rotational oscillator where the rotation centre, rotational inertia and stiffness are changing every moment, depending on displacements. This equation can be further simplified to the linear form with the error proportional to the second degree of displacements. This equation looks somewhat like the equation for classical pendulum, but effective length in our case is controlled by curvature radii of support and of the rolling surface, as well as by the position of vertical load relative to the centre of the support. Non-linear characteristic is soft. The main nonlinearity is in the inertial term, and not in the stiffness term.

Engineering methods for finding the average (averaged) velocity of propagation of longitudinal waves in pipelines with flexible joints are presented. By accurate analysis of the problem of oscillations of a one dimensional periodically inhomogeneous structure it is shown that the results of engineering approaches for rod velocity are the first or long-wave asymptotic approximation which valid when the period of external influence (the length of the seismic wave) significantly exceeds the size of the periodicity cell of the pipeline (the length of the pipe with a joint). Thus, it is established that when this condition is met, the problem of pipeline dynamics with joints is reduced to a much simpler problem of vibrations of a homogeneous pipeline, the velocity of wave propagation in which is equal to the found average value.
Numerical examples are given that demonstrate a significant (sometimes by an order of magnitude) decreasing of the rod velocity in the presence of flexible joints.

The article is devoted to the study of the interaction of a single pile with freezing heaving soil. The calculation of the pile loading area by the normal pressure of frost heaving is proposed. The cases of pile behavior under the influence of frost heave on it depending on the value of the heave pressure, the freezing forces of the frozen soil and the pile, and the adhesion forces of the anchored part of the pile are considered. The calculation of the radius of the cylinder shifting under the action of soil heaving is given.

The article is about nuclear power plant (NPP) safety analysis in case of aircraft crash. Specifically, the article considers the following problems: inclusion of aircraft crash into NPP design bases regarding calculation of frequency of an aircraft crash into NPP; aspects of justification of loads on NPP structures, systems and components (SSCs) caused by mechanical action of a primary missile – aircraft fuselage impact. Probabilistic characteristics of such random parameters as frequency of aircraft crash and direction of aircraft trajectory are determined by the results of analysis of world statistics of aviation accidents. Method of calculation of aircraft crash frequency on structures, buildings and NPP as a whole is presented. It takes into account options of accidental and intentional aircraft crashes and various aircraft approach scenarios.
Procedure of probabilistic justification of loads on civil structures under aircraft impact is described. The loads are specified so as not to exceed allowable value of failure probability of NPP as a whole. Calculation of failure frequency of civil structures of existing NPP is given as an example to show analysis in case of a crash of an aircraft heavier than considered in NPP design. Procedure of probabilistic justification of dynamic loads on NPP equipment in case of aircraft impact is described. Method of floor response spectra (FRS) calculation with the required non-exceedance probability is given. Probabilistically justified loads in case of intentional aircraft impact (act of terrorism) are also considered. Additionally it is presented how internal forces calculated with the use of FRS with the required non-exceedance probability can be summed to provide analysis of subsystems.