Reinforcement of cellular concrete with composite materials

. Cellular concrete, such as gas silicate or foam concrete, has good thermal performance and is widely used in modern construction. Possessing acceptable parameters for compression, cellular concrete has low tensile and shear characteristics. This leads to the appearance of cracks in building structures made of cellular concrete, such as partitions, interior walls, etc. Therefore, solving the problems of increasing the bearing capacity of cellular concrete is important and relevant. The purpose of this study is to study the increase in the bearing capacity of cellular concrete reinforced with composite materials under the action of temperature and bending moments. The problem is solved by the finite element method and analytical methods. As a result of the work carried out, the characteristics of wall panels reinforced with composite rods were obtained under the action of temperature and bending moments in structure. Composite materials in the form of canvases are widely used to enhance the bearing capacity of aged reinforced concrete structures or those that have received defects due to man-made impacts. Consideration of methods for determining the given characteristics of a multilayer composite canvas is necessary for conducting a study of the bearing capacity of reinforced concrete structures reinforced with composite canvases or canvases. In this paper, methods are presented for determining the given characteristics of multilayer composite canvases and panels with different arrangements of the base layers. The analysis of the obtained results showed that reinforcement of the composite materials can significantly increase the tensile strength and shear of the gas silicate of the building.


Introduction
Under the action of bending moments, shear and temperature loads, tensile stresses arise in building structures, which can lead to the appearance of cracks in structural elements made of cellular concrete widely used in modern construction.Cellular concretes, such as gas silicate and foam concrete, have low characteristics of permissible tensile strength.Therefore, the development of methods for enhancing the strength characteristics of such materials is an important and topical topic.A significant number of works have been devoted to the issues of reinforcing building structures with composite materials.In the works [1][2][3], practical recommendations are given for reinforcing building structures with composite materials, depending on the stresses and strains obtained in the calculations.The existing domestic and foreign regulatory documents are consecrated in the works [4][5][6][7].Articles [9][10][11] analyze the experimental and theoretical results of a study on the study of reinforced concrete structures reinforced with composite materials.The theoretical problem is solved taking into account the physical nonlinearity.The main attention is paid to the methods of redistribution of loads to increase the bearing capacity of reinforced concrete structures, recommendations are given on the application of the results obtained.Articles [12][13][14] present the results of calculations of the stability and stress-strain state of structures made of composite materials.The papers [15,16] give the theoretical foundations for the calculation of composite structures.

Methods
Composite materials in the form of multilayer canvases are used in construction to repair and reinforce structures that have lost their strength due to aging of reinforced concrete or damage due to natural disasters.Strengthening is carried out by gluing composite canvases in places of violation of the integrity of reinforced concrete structures.To study the supporting structure reinforced with multilayer composite canvases, it is necessary to determine the given characteristics of the multilayer composite material with different arrangements of the base of the layers of the multilayer composite material.Let us present the calculation formulas for the reduced characteristics of a multilayer composite material with different arrangement of layers of a multilayer composite.Consider the relationship between stresses and strains for a plane stressed state.

    ,
Here E s is the modulus of elasticity in the axial direction, Е Ѳ is the modulus of elasticity in the perpendicular direction, ν is Poisson's ratio, G is the shear modulus, ss       is the strain vector.Rotating the coordinate system by an angle  brings the stress-strain relation matrix to the form , The deformation of a layer located at a distance z from the midline has the form Where   0  the deformation of the middle surface is,   0  is the deformation of the curvature of the middle surface.
On the basis of the relations obtained, we obtain the deformations of the layers located at a distance z from the middle surface Thus, we obtain the strain stress ratios for a multilayer composite material Here { 0 } -is deformations of the middle surface,   0  -is changes in curvature are denoted.
We obtain the forces and moments , {}  = (  ,   ,   ) By integrating over the shell thickness (3), we obtain the forces and moments expressed in terms of deformations in the middle surface of the shell ] .
With the constancy of the characteristics of the layers of a multilayer composite material from equation (3), we obtain the following relations Here   ,   ,   -express respectively the membrane, flexural-membrane and flexural stiffnesses.
Figure (1) shows the notation used in formula (5).The ratios given in formulas ( 5) make it possible to determine the given characteristics of a multilayer composite material with different arrangement of layers and to study building structures reinforced with multilayer canvases from a composite material.
An example of reinforcement of reinforced concrete structures with multilayer composite canvases is shown in Figure 2. The positive properties of the composite material include the property of noncorrodibility, high specific strength, Tables 1 and 2 give the characteristics of the materials used in the work: gas silicate and carbon materials.The mechanical characteristics of gas silicate given in Table 1 show that the allowable tensile stress for this material is an order of magnitude lower than the compressive strength.

Results
The wall panel was studied with dimensions: height 1.0 m, width 1.8 m, thickness 0.2 m, reinforced with composite materials in the form of rods with a total cross section of 1.0•10 -3 m2 under the action of temperature and bending load under the action of a uniformly distributed pressure 5 MPa on the upper surface of the wall panel.The temperature load was simulated by a normal load to the ends of the panel of 5 MPa.Rigid fastening along the side surfaces of the wall panel was used as boundary conditions (Figure 3).
The study of a wall panel made of gas silicate reinforced with a composite mesh was carried out by the finite element method [17][18][19][20][21].As a result of the study, the stress-strain state of the wall panel was obtained under the action of a temperature load and a bending moment created by loading the wall panel with a uniformly distributed load of 5MPa along the upper plane (Figures 4).The analysis of the obtained results showed an increase by 20-30% in the bearing capacity of the reinforced wall model under the influence of temperature compared to the non-reinforced one.Comparison of the obtained results with experimental data showed good agreement [23,24].The bearing capacity of a wall panel made of gas silicate reinforced with composite materials: fiberglass, carbon fiber increases the bearing capacity by 2 or more times under the action of a bending moment.The convergence of the obtained results was tested by thickening the finite element mesh by 2 times and comparing the results obtained.When the deviation of the results is not more than 3%, the results converge.The accepted approximation is considered acceptable to obtain good results.
Figure 3 shows a gas silicate wall panel reinforced with composite rods.Let's carry out an analytical study of determining the bearing capacity of a wall panel reinforced with a composite mesh made of carbon fiber.Let us determine the neutral axis of the section of the wall panel made of gas silicate with dimensions: length 2 m, width b=0.2 m, height h=1 m, reinforced with composite rods with a total cross-sectional area F=1 cm2, located at a height of 0.2 m from the base.We take the initial data from tables 1 and 2. The calculations and analysis of the results obtained showed that the reinforcement of cellular concrete with composite materials can significantly increase the bearing capacity of gas silicate building structures for bending loads.

Conclusions
The weakest, in terms of strength, in cellular concrete: gas silicate, foam concrete are the characteristics of tension and shear (table 1).This leads to the appearance of cracks in wall panels, structural building elements of buildings made of gas silicate or foam concrete.The fight against this phenomenon is a difficult task, requiring a large amount of theoretical and experimental research in the process of development and manufacture.In this study, it is proposed to reinforce wall panels with composite materials in terms of stiffness characteristics that are more suitable for the material of cellular concrete than metal.
The studies carried out in the work showed that the reinforcement of wall panels made of cellular concrete with composite materials can significantly improve the physical and mechanical characteristics of cellular concrete in tension, which is the weakest side of cellular concrete, leading to cracks in building structures made of cellular concrete under temperature and bending loads.The paper presents a method for determining the reduced characteristics of a multilayer composite material for different arrangements of the composite base.The obtained characteristics make it possible to carry out the calculation and analysis of reinforced concrete structures reinforced with canvases of composite material .Cloths made of multilayer composite material are widely used in the repair of building structures that exhaust their bearing capacity due to aging of materials or manmade impacts.The study was carried out using numerical methods: the finite element method and analytical methods [18][19][20].
It was found that the bearing capacity of a wall panel made of gas silicate reinforced with composite materials increases by 25-30% under temperature exposure, which is in good agreement with the experimental results [21].The bearing capacity of a wall panel made of gas silicate reinforced with composite materials: glass fiber, carbon fiber under bending loads increases the bearing capacity by 2 or more times.The use of composite materials in strengthening the bearing capacity and repairing building structures is a justified and promising direction.This work was financially supported by the Ministry of Science and Higher Education of Russian Federation (grant # 075-15-2021-686).Tests were carried out using research equipment of The Head Regional Shared Research Facilities of the Moscow State University of Civil Engineering

Table 1 .
Mechanical characteristics of gas silicate