Double Reinforcement Research Articles

Dual functional composite solid electrolyte constructed by double-layer sulfonated polyethersulfone (SPES)/poly(vinylidene fluoride-co-hexafluoropropylene) (PVDF-HFP) nanofiber membrane in high-performance all-solid-state lithium metal batteries

The successful implementation of polymer electrolytes in next-generation all-solid-state lithium metal batteries (ASSLMBs) is impeded by their low ion conductivity and weak resistance to lithium dendrites. Herein, a composite solid electrolyte (D-SPES-PH-PEO) with dual reinforcement effects is obtained by combining PEO matrix with a double-layer sulfonated polyethersulfone (SPES)-poly(vinylidene fluoride-co-hexafluoropropylene) (PVDF-HFP) nanofiber membrane. The SPES nanofiber membrane acts as a hopping site for ion transport by utilizing the electronegativity and Coulombic force of its own –SO3H groups, reducing the energy barrier of the D-SPES-PH-PEO electrolyte. Profiting from the existence of C-F bond, PVDF-HFP nanofiber membrane specializes in generating a protective SEI layer on the lithium anode. Moreover, such a functional membrane not only effectually constructs a three-dimensional ion transport channel by fabricating ion conductive substructures, but also enhances the mechanical strength of the electrolyte. Consequently, the D-SPES-PH-PEO electrolyte is equipped with a high ion conductivity of 7.41 × 10−5 S cm−1 at 30 °C and high tensile strength of 8 MPa. Furthermore, Li/Li symmetric battery incorporating D-SPES-PH-PEO electrolyte enables a stable cycle for 2500 h at 0.2 mAh cm−2. The D-SPES-PH-PEO electrolyte represents outstanding compatibility with LiFePO4 and high-voltage LiNi0.8Mn0.1Co0.1O2 (NMC811) electrodes. Especially, the LiFePO4/D-SPES-PH-PEO/Li pouch cell indicates an initial specific capacity of 146.7 mAh g−1 and the NMC811/D-SPES-PH-PEO/Li pouch cell reaches a maximum capacity of 178.5 mAh g−1. This study emphasizes the importance of double reinforcement of ion conduction and anode protection on solid electrolytes.

Dynamic behavior and characteristics of geogrid-reinforced sand under cyclic loading

This paper evaluated the benefits of geogrid-reinforced sand samples and investigated the effect of different factors contributing to the dynamic behavior, which included the geogrid type, arrangement of reinforcement, confining pressure and dynamic stress amplitude. Four geogrids of different aperture geometries (two biaxial geogrids and two triaxial geogrids) produced by 3D printing technology were used. The research was experimentally carried out by conducting dynamic triaxial tests to investigate the axial cumulative strain, dynamic elastic modulus and damping ratio of the samples. The test results demonstrated the potential benefit of installing geogrids in subgrade soils. Less axial cumulative strain, damping ratio and larger dynamic elastic modulus were measured under cyclic loading for geogrid-reinforced samples compared to those unreinforced samples. The geogrid type and reinforcement arrangement had noticeable impacts on the samples’ dynamic performance. Of the four model geogrids tested, the triaxial geogrid with triangle aperture performed consistently better than the other three. Under large confining pressures and dynamic stress amplitudes, there was no appreciable improvement in the dynamic performance of the samples reinforced with the two triaxial geogrids. The results also showed that the double reinforcement arrangement consistently yielded better improvement. This study explored preliminarily the feasibility of applying 3D printing technology in geotechnical model tests, which shed light on the understanding of dynamic response of geogrid-reinforced soil and the optimization of geogrids.

Уголковые подпорные стены с вертикальными консолями в виде оболочек и складок

The subject of the study is reinforced concrete corner retaining walls, widely used in hydraulic engineering construction. Optimization of the shape of the vertical console of corner retaining walls is important to reduce internal forces and increase the stability of structures. When replacing flat panels with spatial structures in the console, bending moments are reduced; the predominant work of structures for compression or stretching allows reducing their thickness due to more efficient use of materials. The purpose of the study is to determine the optimal shape and nature of reinforcement of vertical retaining wall consoles, depending on their height. The study was conducted in the certified software package “LIRA-CAD2021”. Computational models of corner retaining walls with consoles in the form of multi-wave cylindrical shells and folds have been developed. At the junctions of the waves and the edges of the folds, racks are provided, pinched in the ground. Comparative calculations of structures in the software package “LIRA-CAD2021” were performed. The results of calculations are analyzed. Conclusions are drawn on the optimization of the structures of retaining walls with a vertical console in the form of shells and folds. The study showed that with a retaining wall height of up to 3 m, a retaining wall with a console in the form of a multi-wave shell is more rational in terms of material consumption. At a height of more than 3 m, retaining walls with a console in the form of folds with vertical posts at the interface of the faces become rational. For consoles in the form of shells, double reinforcement is recommended with an increase in the area of the reinforcement in the lower part and at the interface areas of adjacent waves. For consoles in the form of folds, double reinforcement is also recommended, but additional reinforcement is required only in the area of the interface of the panels with the foundation plate.

Application and characterization of new polymer dust suppression foam in coal mine and tunnel construction space

Severe dust pollution is common in tunnel, coal mine, and other construction sites. Dust suppression foam is a feasible method for dust suppression, but its single function makes it difficult to adapt to complex construction sites. Driving by reconstructing the molecular structure of ecological raw materials and strengthening the network function, a new method of SPI based gel foam dust suppression was proposed in this study. This method was realized through improving the performance of soy protein isolate (SPI) gel by glycosylation and further enhancing the fluidity and foaming performance of SPI by enzymatic hydrolysis. Afterwards, its reaction mechanism and dust suppression mechanism were analyzed. It was found that after the glycosylation of 0.4% SPI with 0.2% xanthan gum (XG) and the subsequent addition of 0.15% transglutaminase (TGase), a relatively stable double reinforcement network structure was generated. This structure was confirmed by Fourier transform infrared spectroscopy and other experiments; to be specific, its viscosity was reduced to 28.3mPa·s, and the foaming multiple was improved by 16.8% than SPI. The particle size of foam was observed to reduce to 20-60μm through a three-dimensional microscope, which is more conducive to wetting and capturing coal dust. Then, the prepared solution was compounded with 1.0% dodecyl dimethyl Amine oxide (OA-12) to develop a dust suppression gel foam and it was sprayed on the coal dust. Through experiments on the mine airflow-dust environment simulation platform, the dust suppression gel foam reached a PM10 suppression efficiency of 98.42%, and remained a total dust suppression efficiency of above 98% after 75 days. Moreover, the validity of the molecular model was confirmed by X-ray photoelectron spectroscopy. The molecular dynamics simulation showed that coal molecules with negative potential attract positively charged OA-12 molecules, and the tail group of OA-12 contacts the hydrophobic sites of the coal at an inclined angle, allowing water molecules to fully contact the coal molecules and improving the wettability; while gel molecules are adsorbed on the surface of coal molecules to play the role of bonding and filling. This research provides a theoretical support for the application of SPI based gel in the field of dust suppression, and develops an environmentally friendly and efficient feasible scheme for dust control in the construction site.

Estimation of the residual service life of reinforced concrete beams of an industrial facility taking into account corrosion wear

Introduction. Corrosion damage of reinforcement and concrete is an important factor reducing durability of industrial facilities. The article presents the methodology and results of probabilistic calculation of residual life of separate reinforced concrete structures of an industrial building as well as of reinforced concrete structures working in the system. A three-storey open stand with dimensions in terms of 30 × 15 m and 25 m in height is considered. The calculated parameters of the actual state of the structures are obtained on the basis of experimental diagnostic studies.
 
 Materials and methods. According to the results of a full-scale field engineering inspection using standard and non-standard methods of non-destructive testing, the most damaged structures of the framework — reinforced concrete floor beams have been determined. The degree of corrosion damage of working reinforcement and compressed concrete has been determined. The method of probabilistic calculation of a reinforced concrete beam with regard for corrosion deterioration is outlined. The limiting bending moment in the beam section is considered as a nonlinear function of two random arguments — the strength of concrete and the strength of reinforcement. A linear law of corrosion damage accumulation is adopted. The probabilistic characteristics of the limiting bending moment are found by the Monte Carlo method on the basis of the normative method of calculation of a rectangular reinforced concrete section with double reinforcement. The reliability index has been used to determine the numerical values of the probability of failure and operating time.
 
 Results. Statistical characteristics of bending moment limit changing in time from the beginning of concrete protective properties exhaustion to element failure have been obtained. Lifetime before failure for a given guaranteed safety is found out.
 
 Conclusions. The practical application of the probabilistic method combined with field survey data to solve the problem of assessing the residual service life of reinforced concrete beams of a real industrial building is shown.

Calculation of the formation of normal cracks in a reinforced concrete element based on the deformation theory of plasticity of concrete by G.A. Geniev

The authors present a refined method of determining the moment of cracking in reinforced concrete bar constructions using the diagram of deformation of concrete built on the basis of the deformation theory of plasticity by G.A. Geniev in which the stress and strain invariants of concrete are linked by nonlinear dependences. In the resulting defining equations, the hypothesis of flat sections, as well as the premise of reaching the limit values of concrete deformations on the stretched fibers of the cross-section are used. Stresses in concrete are determined through deformation values in accordance with the nonlinear deformation diagram of concrete. On the basis of the assumptions accepted, analytical dependences for determining the moment of cracking in the sections of bending elements with single and double reinforcement have been acquired. The formulas obtained were used in the analysis of various factors influence on crack resistance of bendable reinforced concrete elements. It was found out that the moment of crack formation practically does not change when percentage of reinforcement of longitudinal tensile or compressed reinforcement changes. The most effective method of crack resistance improvement is the increase of concrete strength. The proposed methodology is verified by comparison with experimental results on reinforced concrete prototypes. It is concluded that the use of the diagram of nonlinear deformation of concrete on the basis of the theory of plasticity by G.A. Geniev allows to estimate more strictly the crack resistance of reinforced concrete rod elements.

Water tanks - checks of tensile internal forces in the walls of cylindrical tanks

The report examines parametric solutions of the facilities - by changing the elements of the load-bearing structure of reinforced concrete tanks. The created computational models have specialized software and seismic analysis included. The hydrodynamic impact of water during an earthquake taken into account. The annular efforts in the walls were checked to determine the double (symmetrical) reinforcement in the radial direction. Comparisons are given for the individual solutions. The construction of the wall has an effect on the internal forces. Envelope combinations of static and seismic impacts must be made to provide the elements for peak values not taken into account in the analysis.

Effect of reinforcement on the durability of bent reinforced concrete structures under conditions of alternating freezing and thawing

The article studies the influence of the level and type of reinforcement of bending elements of reinforced concrete structures on their bearing capacity under the influence of alternating freezing and thawing. Strength and deformation characteristics for B30 concrete class were taken according to Construction Rules SP 63.13330.2018, and after exposure to alternating freezing and thawing according to Construction Rules SP 52.105.2009. The study of the stress-strain state and the assessment of the bearing capacity were carried out according to a specially developed program, in which the diagrammatic method was implemented. It is shown that the durability of bent reinforced concrete structures depends on the percentage and type of reinforcement. When reinforcing with longitudinal tensile reinforcement equal to 1%, the decrease in the bearing capacity of a reinforced concrete beam after exposure to alternating freezing and thawing will make up 5.5%, and in case of 2.5% reinforcement it will equal to 20.9%. In addition, the nature of fracture will change and the stress in the tensile reinforcement will not reach the design resistance. If it is impossible to limit the percentage of reinforcement of longitudinal tensile reinforcement, it is recommended to use double reinforcement. Installation of working reinforcement in a compressed zone in a volume of 50% of the stretched one with a reinforcement percentage of 2% will reduce the decrease in bearing capacity to 2.2% after exposure to freezing and thawing cycles and not change the nature of destruction.

Online computation offloading with double reinforcement learning algorithm in mobile edge computing

Smart mobile devices have recently emerged as a promising computing platform for computation tasks. However, the task performance is restricted by the computing power and battery capacity of mobile devices. Mobile edge computing, an extension of cloud computing, solves this problem well by providing computational support to mobile devices. In this paper, we discuss a mobile edge computing system with a server and multiple mobile devices that need to perform computation tasks with priorities. The limited resources of the mobile edge computing server and mobile device make it challenging to develop an offloading strategy to minimize both delay and energy consumption in the long term. To this end, an online algorithm is proposed, namely, the double reinforcement learning computation offloading (DRLCO) algorithm, which jointly decides the offloading decision, the CPU frequency, and transmit power for computation offloading. Concretely, we first formulate the power scheduling problem for mobile users to minimize energy consumption. Inspired by reinforcement learning, we solve the problem by presenting a power scheduling algorithm based on the deep deterministic policy gradient (DDPG). Then, we model the task offloading problem to minimize the delay of tasks and propose a double Deep Q-networks (DQN) based algorithm. In the decision-making process, we fully consider the influence of task queue information, channel state information, and task information. Moreover, we propose an adaptive prioritized experience replay algorithm to improve the model training efficiency. We conduct extensive simulations to verify the effectiveness of the scheme, and the simulation results show that compared with the conventional schemes, our method reduces the delay by 48% and the energy consumption by 53%.

CALCULATION OF OFFCENTRALLY COMPRESSED ELEMENTS

A large number of calculation formulas have been proposed to describe the deformation diagrams of masonry and concrete. The data indicate the possibility and expediency of using full masonry deformation diagrams to calculate the strength and deformations of stone and reinforced stone pillars. Experimental samples and stone pillars were tested. The samples were of five types and differed among themselves in the location of reinforcement and the reinforcement ratio, as well as in the method of loading – axial or off-center compression with different eccentricity. In the paper, experimental and calculated longitudinal deformations of masonry and reinforcement for samples of different groups. These data testify to the possibility and expediency of using full masonry deformation diagrams to calculate the strength and deformations of stone and reinforced stone pillars. As the amount of reinforcement in the stretched zone increases, most of the section works on the descending branch of the diagram. The size of the compressed zone increases, which is equivalent to a decrease in eccentricity. Reinforcement of the compressed zone with reinforcement increases the strength of sections with double reinforcement. The shapes of the stress profiles in the masonry practically do not depend on the presence of compressed reinforcement. The calculation establishes the expediency of the installation and the degree of saturation of the stretched and compressed cross-sectional areas with reinforcement. At small eccentricities, when the force is applied within the core of the section, saturation of the compressed zone with reinforcement leads to a noticeable increase in the strength of the section. At large eccentricities, saturation of the compressed zone with reinforcement is ineffective.

A Primary Support Design for Deep Shaft Construction Based on the Mechanism of Advanced Sequential Geopressure Release

The construction of 1500 m depth shaft in Xincheng Gold Mine, China, faces complex stress conditions such as high geostress (>50 MPa), high ground temperature (>50 °C), high water-pressure (>9 MPa), and highly corrosive. Traditional deep shafts excavated by the sinking and lining method cannot adapt to high geostress problems, such as rock bursts and large deformations, etc., in the deep shaft construction process. To avoid and adjust the high geostress induced the rockburst and large deformations, the mechanism of the advanced sequential geopressure release (ASGR) has been proposed for the ground control in deep shaft construction. In this paper, the safe distance between the concrete lining and the shaft excavation face is determined based on the ASGR mechanism, which can provide the space for geopressure release, and primary support based on rock mass quality and numerical simulation was employed to control the geopressure and deformation. A new support scheme for the deep shaft is proposed, using long bolts to restrain severe deformations, metal mesh, and a double reinforcement bar to improve the induced stress distribution. According to the results, the construction scheme of deep shaft has been improved, and the safe support distance of the proposed scheme is determined to be 12 m, with an interval of three excavation cycles. Compared to the original scheme of shaft lining after excavation, the proposed scheme based on the ASGR mechanism can effectively improve the geopressure release and benefit from controlling the rockburst and large deformation of deep shaft induced by high geostress conditions. The stress distribution in the lining is more uniform, and safety factor of the lining is increased to 2.0, which is benefit the long-term stability of deep shaft.

Flexural Performance of Cement-Treated Sand Reinforced with Geogrids for Use as Sub-Bases of Pavement and Railway Structures.

Cement-treated sand (CTS) exhibits undesirable brittle behavior after the applied stress reaches its peak strength. This research investigates the flexural behavior of CTS that is reinforced with uniaxial geogrid (CTSG). A total of 6% cement content was mixed with sand. Uniaxial geogrids with three different strengths were utilized to create the CTSG samples. The number of reinforcement layers, including single and double reinforcements, was studied. The image processing method was applied to analyze the surface cracks in the specimens. The results show that the geogrid type and the number of reinforcement layers affect the flexural behavior of the CTSG. Geogrid reinforcement changed the behavior of the CTS from a brittle material to a semi-brittle or ductile material because the residual tensile stresses were carried by the geogrids. The high-strength geogrid with a double reinforcement layer proved to be most effective in enhancing the peak strength and toughness with improvement ratios of 1.80 and 11.7, respectively. Single and double reinforcement layers with all geogrid types can reduce surface cracks with average crack reduction ratios of 64% and 83%, respectively. The CTSG can be successfully used as a sub-base layer to increase flexural performance and the lifetime of pavement and railway structures.

СХОДИМОСТЬ ЧИСЛЕННОГО ДИАГРАММНОГО МЕТОДА НЕЛИНЕЙНОГО РАСЧЁТА СТЕРЖНЕВЫХ ЖЕЛЕЗОБЕТОННЫХ ЭЛЕМЕНТОВ

Earlier, authors considered the under-examined question of accuracy (error) in the theory of the diagram method for calculating reinforced concrete core elements. The notion of convergence of the numerical implementation of the method under consideration is closely related to it, which has so far remained undisclosed. The article presents a theoretical justification of the convergence criterion of a numerical diagram method for calculating the strength of reinforced concrete bendable elements. The resulting criterion coincides in form with the Chebyshev norm. It implies a criterion for stopping the iterative calculation process and an estimate of the error of the numerical diagram method. Using the example of a reinforced concrete element with a rectangular cross section and double reinforcement, the issue of convergence of iterative strength calculation with varying concrete class and percentage of reinforcement is investigated. It is established that for all the considered design variants, the iterative calculation process converges after the 6th iteration at the initial curvature approximation and after the 4th iteration at , with a relative calculation error of δ<1 %. In addition, it is found that with an increase in the percentage of reinforcement, the convergence of the calculation improves: with the number of iterations equal to 4, the error in the design variant B60, µ = 0.5 % is 10.3 %, and with B35, µ = 3.0 %–0.98 %.

Experimental study on liquid nitrogen flash evaporation spray on super-hydrophilic microstructured surface

Flash evaporation spray is an efficient heat transfer method. Changes in the microstructure and wettability of the cooling surface have important effects on its heat transfer. In this paper, four kinds of cooling surfaces, including a smooth copper surface, a square-column microstructured surface, a superhydrophilic smooth surface, and a superhydrophilic square-column surface, were prepared by chemical corrosion and laser etching. Using liquid nitrogen as the cooling medium, we conducted transient flash evaporation spray experiments on these four types of cooling surfaces. The experimental results show that surface superhydrophilic treatment can substantially enhance the flash evaporation spray of liquid nitrogen. It can more than double the cooling rate for both smooth copper surfaces and square-column microstructured surfaces. In addition, the combination of a microcolumn structure and superhydrophilicity on the cooling surface can provide double reinforcement for the liquid nitrogen flash evaporation spray. Its average cooling rate can reach 131,046 °C/min, and the maximum heat flux is 173 W/cm2. This study sheds some lights on heat transfer mechanism of superhydrophilic microstructure on the flash evaporation spray and contributes to the development of a new method for cell vitrification.

High Strength of Aluminium-Based Composites by Different Methods of Severe Plastic Deformation (SPD)

Composite materials were applied to meet the demands of production efficiency on industrial because they offered the superior properties both of aspects on mechanical and physical properties were constantly being refined and developed with several methods. Composite technology with aluminum as a matrix as well as ceramic materials as reinforcement was very dependent on a result of the perfection of the manufacturing process on the matrix material and reinforcement was used. Aluminum currently still dominates as a matrix because of its ductility, while reinforcing materials that are widely used are ceramic elements such as silicon carbide (SiC) and alumina (Al2O3). Using of SiC/Al2O3 has been widely studied because of the remarkable improvement of the mechanical properties it produces. The addition of number of SiC particles to Al2O3 was able to significantly increase the hardness properties. In this study, a number of composite manufacturing methods were compared from the results of properties by accumulative press bonding (APB), accumulative roll bonding (ARB), and repetitive press roll forming (RPRF). The mechanical properties of RPRF results are known to produce better properties, especially mechanical properties. Mechanical properties were observed from tensile and hardness tests. The finer grain size is produced by increasing the compression cycle and increasing the mechanical properties when adding double reinforcement of the SiC/Al2O3, which causes the strength and hardness of the RPRF results to increase. Whereas other methods such as APB and ARB it is not compatible with composite materials, this proves that the RPRF method was very suitable for processing composite materials compared to APB and ARB methods.

Numerical analysis of bonded composite patch efficiency in the case of lateral U and V-notched aluminium panels

In this study, the finite element method is applied to investigate the mechanical behavior of aluminium notched structures reinforced by composite patch. In order to evaluate the efficiency of patches in the case of lateral semicircular and V-notches, it is very important to analyze the stress distribution at the notch tip and to take in consideration the influence of the geometrical and mechanical properties of the patch and the adhesive. Simple and double patch were used as reinforcement techniques. Results showed that the stress concentration factor is reduced at the notch tip by using a double patch reinforcement. This reduction becomes more noticeable when the patch thickness increases.

Efficiently Breaking the Curse of Horizon in Off-Policy Evaluation with Double Reinforcement Learning

Demystifying the Curse of Horizon in Offline Reinforcement Learning in Order to Break It Offline reinforcement learning (RL), where we evaluate and learn new policies using existing off-policy data, is crucial in applications where experimentation is challenging and simulation unreliable, such as medicine. It is also notoriously difficult because the similarity (density ratio) between observed trajectories and those generated by any new policy diminishes exponentially as the horizon grows, known as the curse of horizon, which severely limits the application of offline RL whenever horizons are moderately long or even infinite. In “Efficiently Breaking the Curse of Horizon in Off-Policy Evaluation with Double Reinforcement Learning,” Kallus and Uehara set out to understand these limits and when they can be broken. They precisely characterize the curse by deriving the semiparametric efficiency lower bounds for the policy-value estimation problem in different models. On the one hand, this shows why the curse necessarily plagues standard estimators: they work even in non-Markov models and therefore must be limited by the corresponding bound. On the other hand, greater efficiency is possible in certain Markovian models, and they give the first estimator achieving these much lower efficiency bounds in infinite-horizon Markov decision processes.

СИЛОВОЕ СОПРОТИВЛЕНИЕ ЖЕЛЕЗОБЕТОННЫХ КАРКАСОВ МНОГОЭТАЖНЫХ ЗДАНИЙ С КОСВЕННЫМ АРМИРОВАНИЕМ В ЗАПРЕДЕЛЬНЫХ СОСТОЯНИЯХ

The results of studies of monolithic reinforced concrete frames of multi-storey buildings and reinforced concrete frames simulating fragments of such frames in over-extreme limit states caused by special actions are presented. Two options for reinforcing the beams of the frames are considered: with double reinforcement, which ensures the operation of the beam when the force flows in the frame and, accordingly, the sign of the moment change; option with double reinforcement and installation of additional indirect reinforcement in the support zones of the beams for the entire height of the section. Primary and secondary design models were built using volumetric finite elements for concrete and reinforcement rods. The obtained design parameters of deformations, crack patterns and frame failure patterns for all options are compared with each other and with the results of testing physical models of these structures. To assess the effect of mixed reinforcement on the limiting deformations of compressed concrete in over-extreme limit states, based on the theory of plasticity of concrete and reinforced concrete G.A. Geniyeva, deformation dependencies are constructed for a typical reinforced concrete element reinforced with rods in one direction and meshes in the other two under uniaxial compression and volumetric deformation. It has been established that the use of indirect reinforcement in combination with double longitudinal reinforcement in bending elements under static-dynamic loading conditions significantly increases the ultimate deformation of the compressed zone. This reinforcement option can working way to protect monolithic reinforced concrete frames of multi-storey buildings from progressive collapse under special actions.

DETAILS OF NORMAL SECTIONS STRENGTH CALCULATION OF FLEXIBLE REINFORCED CONCRETE STRUCTURES BY THE WOOD’S METHOD IN PC "LIRA SAPR"

Problem statement. The problem of realization of the calculation method of normal cross-sections strength of reinforced concrete constructions under flat bending, which is established in the current building codes of Ukraine, is considered. The main attention is paid to atypical and practically not considered calculation cases, typical for automated algorithms in the environment of SP "LIRA SAPR". The purpose of the article. Analysis of the feasibility of using the calculation method of current building codes with further development of recommendations, based on the specifics of computerized calculations. Methodology. Within the framework of the performed research, rectangular cross-sections of reinforced concrete structures with single and double reinforcement (provided a significant increase in the area of reinforcement of the compressed cross-sectional area) with variation of concrete classes, reinforcement coefficient and ratio of reinforcement areas were considered. The stress-strain diagrams of concrete and reinforcement are bilinear with characteristic values set for the first group of limit states. The character of change of cross-sections’ status diagrams "M - εc(1) " is investigated. Research results. It is found that for single-reinforced sections with decreasing reinforcement area there is a decrease of the value of deformation of the compressed fiber of concrete, which is used to find solutions for systems of nonlinear equilibrium equations of the deformation method. This leads to an increase of the execution time of calculations of the flat elements’ reinforcement by the Wood method. It is established that for sections with double reinforcement at relatively large values of the ratios of the reinforcement areas, the equilibrium of the section is at the maximum deformations of the compressed concrete fiber. Conclusions. An approach aimed at accelerating the calculation of sections with single reinforcement, which is based on the use of the relationship between the percentage (area) of reinforcement and the deformation of the most compressed fiber of the reinforced concrete element. Features of analytical algorithms for calculating the selected sections are taken into account by implementing this technique in the PC "LIRA SAPR", optimization and acceleration of automated algorithms for calculating reinforced concrete structures.

Double Roman reinforcement number in graphs

For a graph a double Roman dominating function is a function having the property that if f(v) = 0, then vertex v must have at least two neighbors assigned 2 under f or one neighbor w with f(w) = 3, and if f(v) = 1, then vertex v must have at least one neighbor w with The weight of a double Roman dominating function f is the value The double Roman domination number of a graph G, denoted by equals the minimum weight of a double Roman dominating function on G. The double Roman reinforcement number of a graph G is the minimum number of edges that have to be added to G in order to decrease the double Roman domination number. In this paper, we first show that the decision problem associated to the double Roman reinforcement problem is NP-hard even when restricted to bipartite graphs and then we investigate the properties of double Roman reinforcement number in graphs, and we present some sharp bounds for Next we characterize trees with double Roman reinforcement number greater than one.