# Theoretical and experimental studies

**Equation of planar vibrations of rigid structure on kinematic supports after A.M. Kurzanov **

** Authors:**
Tyapin A.G.

** Rubric:**
Theoretical and experimental studies

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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.

**Assessment of the resistance of monolithic reinforced concrete bearing systems to progressive collapse based on the principle of the level of permissible damage**

** Authors:**
Mitrovic Bozidar

** Rubric:**
Theoretical and experimental studies

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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 (K_{1}) 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.

**Combination of modal responses in linear spectral method: comparison of different formulae for correlation coefficients**

** Authors:**
Tyapin A.G.

** Rubric:**
Theoretical and experimental studies

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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.

**On the question of setting the level of calculated impact and reliability of high-rise construction**

** Authors:**
Dmitry M. Zhemchugov-Gitman
Lyubov V. Mozzhukhina
Uzdin A.M.

** Rubric:**
Theoretical and experimental studies

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**Probability of a High-Speed Military Aircraft Falling at a Nuclear Power Plant and Setting of Design Loads on Building Structures**

** Authors:**
Birbraer Adolf N.
George D. Kostrov

** Rubric:**
Theoretical and experimental studies

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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.

**Planar vibrations of rigid structure on kinematic supports after A.M. Kurzanov**

** Authors:**
Tyapin A.G.

** Rubric:**
Theoretical and experimental studies

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**The frame assembled from «H» elements**

** Authors:**
Vladimir P. Blazhko
Alexey V. Belyaev

** Rubric:**
Theoretical and experimental studies

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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.

**Experimental determination of the coefficient of longitudinal interaction of soil and pipeline under seismic vibrations**

** Authors:**
Israilov M.
Hasambiev M.V.

** Rubric:**
Theoretical and experimental studies

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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.

Astrict 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

**MATHEMATICAL MODEL OF FLUID FLOW TO THE WELL USING FRACTIONAL DERIVATIVES**

** Authors:**
Alla N. Khvorova

** Rubric:**
Theoretical and experimental studies

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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 EFFECT OF NORMAL ADHESION ON THE STRENGTH OF A CELLULAR CONCRETE, INCLUDING SEISMIC INPUT**

** Authors:**
Vartanov D.N.

** Rubric:**
Theoretical and experimental studies

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**INCREASING THE RESISTANCE OF MOSQUE MINARETS AGAINST SEISMIC AND WIND IMPACTS BY USING TUNED MASS DAMPERS **

** Authors:**
Aldrebi Ziad Ahmad

** Rubric:**
Theoretical and experimental studies

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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.

**The Analysis of a Structure Subjected to Seismic Action, Taking into Account the Change in the Structure's Design in the Vibration Process**

** Authors:**
Chernov Yu.T.
Qbaily Jaafar

** Rubric:**
Theoretical and experimental studies

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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.

**Planar Vibrations of Rigid Structure Resting on Kinematical Supports of Yu. D. Cherepinsky**

** Authors:**
Tyapin A.G.

** Rubric:**
Theoretical and experimental studies

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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.

**Research of Stability and Seismic Resistance of Non-Uniform Two-Layer Rods in Elastic Medium**

** Authors:**
Hasanova T.J.
Tagiyeva Saida Abdulali

** Rubric:**
Theoretical and experimental studies

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**Nanotehnologija the use of Aluminium-containing Raw Materials in the Petrochemical Industry to Produce High -performance Brick**

** Authors:**
Abdrakhimov V
Аbdraкhimova Elena S.

** Rubric:**
Theoretical and experimental studies

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the unloading of the environmental situation.

**Development of base oscillation models and regulatory approaches to the calculation of critical structures for seismic impacts**

** Authors:**
Vedyakov Ivan I.
Vladimir K. Vostrov

** Rubric:**
Theoretical and experimental studies

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**Free Vibrations of Rigid Kinematic Support of Yu.D. Cherepinsky**

** Authors:**
Tyapin A.G.

** Rubric:**
Theoretical and experimental studies

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**Calculation of Wave Velocities in Segmented Pipelines with Flexible Joints**

** Authors:**
Israilov M.
Smirnova L.N.

** Rubric:**
Theoretical and experimental studies

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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.

**Interaction of a Single Pile with Freezing Heaving Soil**

** Authors:**
Alekseev A.

** Rubric:**
Theoretical and experimental studies

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**Inclusion of Aircraft Crash into NPP Design Bases and Probabilistic Justification of Loads on Civil Structures and Equipment**

** Authors:**
Chernukha N.

** Rubric:**
Theoretical and experimental studies

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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.