Experimental studies of the stress-strain state of cylindrical shells

. Research work carried out in world practice with the aim of ensuring stability, increasing strength and assessing the stress-strain state of shell structures requires the development of practical engineering methods for calculating optimal design solutions for modern cylindrical shell structures, into which various elements are built, taking into account increasing their strength, stability and deformation. In this case, the main emphasis is on increasing the strength and stability of metal cylindrical shells with ribs. In the construction practice of the republic, a wide range of measures is being implemented to introduce effective design and calculation methods to increase seismicity, stability and service life of special facilities used in the oil and gas industry and water supply. The strategy for further development of the Republic of Uzbekistan for 2017–2021 defines the main tasks aimed at “implementing targeted programs for the development and modernization of construction, road, transport and engineering ...”. The implementation of this task is to improve practical and engineering calculation methods for solving assigned problems, including in order to ensure the stability and strength of cylindrical shells.


Introduction
The rib-reinforced shell structure is easy to manufacture and consists of three elements: the main shell, manufactured by rolling, reinforcing arc-shaped panels, manufactured by rolling or stamping and having a smaller radius of curvature than the main shell, and top and bottom flanges welded to the ends of the main shell and reinforcing panels [1] [2].
Loss of stability of unsupported shells simultaneously leads to loss of load-bearing capacity, and sudden destruction of the structure occurs.As a result, the thickness of the shell wall, which is required to ensure stability, is significantly greater than the thickness sufficient to ensure the load-bearing capacity of the structure.
To increase the stability and load-bearing capacity of cylindrical shells, various methods of strengthening them are used, as well as design measures that can significantly increase the value of critical stresses during buckling.Cylindrical shells are reinforced with various profiles by connecting them with rivets, welding or gluing.
When studying the stability of reinforced cylindrical shells, two methods are used, which differ from each other when taking into account the reinforcement panels of the main shell.According to the first of them, the problem is solved by replacing a real structure with discretely located ribs with a structure according to an orthotropic scheme, in which the stiffness of the ribs in tension (compression) and bending are summed up.In addition, as a rule, additional new assumptions are introduced.
The method of calculating stability using a constructively orthotropic scheme is considered relatively simple and at the same time quite approximate [3][4].
In recent years, due to the widespread use of computer programs in engineering calculations, when calculating the stability of reinforced shells, the second method is often used -the method of taking into account discrete location ribs.

Materials and methods
To study the stability and load-bearing capacity of a cylindrical shell supported by arcuate panels, a real cylindrical shell with a diameter of 2800 mm and a height of 2960 mm was modeled at a scale of 1:4.The models were made in the form of samples with a smooth unsupported wall and with a wall supported by vertical arcuate panels.
For samples of cylindrical shells with a smooth wall, steel sheets with a thickness of 1.8 and 3.8 mm were used.For samples with a panel-reinforced wall, only steel sheets with a thickness of 1.8 mm were used (Fig. 1, a).In this case, the same sheets were used for both the main shell and the reinforcing panels [5].
The reinforcement panels were welded with a continuous weld along the entire height of the main shell wall [6].
The main shell was made by rolling a single sheet with dimensions of 2200x740 mm.To form a circular shell with a closed contour, one vertical weld was provided in it.The arched reinforcing panels were brought into the shape of a segment by rolling sheets with dimensions of 108×740 mm, and then welded to the main shell.In each sample, the number of arc-shaped reinforcing panels was 12 pcs., between them there were unsupported sections of the main shell 90 mm wide, the number of which was also 12 pcs.(Fig. 1, b).To sharply reduce the influence of compressive forces during local compression during testing of shell samples, connecting flanges were provided, which were taken into account in real shell designs.The flanges were ring-shaped, their width was 100 mm, thickness -10 mm.
The flanges were connected to the wall of the shell samples on both sides with continuous welds.To maintain the central application of the load, the central horizontal axis of the annular flanges was ensured by superimposing an annular axis passing through the center of gravity of the main shell and reinforcing panels.The flanges consist of three segments and are connected to the walls of the tank in such a way that the load is transferred to the walls of the shell only through the flanges.
The models are made of steel sheets grade VSt3ps5 (GOST 19903-2015), produced at the Bekabad metallurgical plant.
Before testing, all models of cylindrical shells underwent a control check.All dimensions of the models were compared with the design ones and checked for the presence of initial defects during preparation; the quality of the welded joints was also checked.Control checks showed that the dimensions of all models basically corresponded to the design ones, the detected defects did not exceed 0.5 mm.The quality of the models fully meets the requirements and can be considered an ideal shell.
Strain gauges were installed on all model samples, according to the diagrams in the drawings, connected to transmission cables and made ready for testing.For centering under the press, all models had risks in their upper and lower parts.The shell samples were then installed on the bottom plate of the test presses.To eliminate the influence of possible irregularities on the process of load transfer and uniform distribution of compressive force on the walls of the shells, chipboards were used, completely covering the upper and lower flanges of the models.After this, connecting cables, connected to the ends of the strain gauge wires through a special installation, were connected to the computer [7].
Before applying the load, initial readings were recorded.After this, to neutralize various possible deformations and stresses in the shell samples, the shells were loaded with a load equal to 5-7% of the calculated destructive load and instrument readings were recorded at all points.
After checking the alignment of the shell, the load was completely removed.The difference in deformation of symmetrically oppositely located points when centering the samples did not exceed 2-3% [8].
At the beginning of the main tests, initial readings were taken from all strain gauges installed at various points and the sample was loaded.The loading was carried out in stages.The stage load was 10-14% of the calculated failure load.The loading rate was 20-24 kN/min.When loaded with a staged load, changes in the magnitude of deformation were automatically recorded using strain gauges at all points.
After reaching a certain load value, the strain values were recorded and such a load was maintained for up to 15 minutes.Both during loading and while holding the load in this position, the readings of the strain gauges were recorded.Once the deformity had stabilized at the end of the phase, the final readings were also recorded.After this, the next stage of loading began and all operations were repeated.Thus, the magnitude of the load was increased.After each loading stage, the surfaces of the samples and shells were carefully checked, changes were recorded -bulges, dents and other visible changes.After the load exceeded 60% of the breaking load, such checks were carried out directly and during the loading process.After the start of the test, 7-8 loading stages were carried out until signs of loss of stability appeared, and then another 1-2 stages were carried out until the load-bearing capacity was lost [9].
Tests of an unsupported shell model with a smooth wall for stability and load-bearing capacity made it possible to determine the stress-strain state of the prototype, the magnitude of the loads during loss of stability and load-bearing capacity (Fig. 2).At lower values of the effective load on the sample (at stages 1-5 of loading), the stress values in the walls of the models were small, and the resistance of the shell metal appeared as an ideally elastic material.The development of deformation depending on the load was fully consistent with the graph "σ-ε" of steel in tension and compression.When the load exceeded 70% of the calculated breaking load, a significant acceleration in the development of deformations was observed.During testing, it was established that the values of deformations (stresses) measured at different points of the shell samples are not the same: the difference in the values of the maximum and minimum stresses ranged from 4 to 8%.
At loads of 94-96% of the breaking load, signs of loss of local stability of the shell appeared, and in accordance with the nature of stress development, dents formed first in the lower part of the sample, then in the middle part of the height, and lastly in the upper part.After this, exceeding the load by another 4-6% led to a loss of overall stability and at the same time to the exhaustion of the load-bearing capacity.The period from the beginning of buckling to failure was very short: at this stage, deformations developed rapidly with increasing load [10].The nature of the stress-strain state of reinforced shell models under central compression was significantly different from the stress-strain state of smooth models (Fig. 3).At the same time, at low values of the effective load on the sample (at stages 1-6 of loading) both in the main shell and in the reinforcing panels, the stress values were small and the resistance of steel as an ideal elastic material was observed.Only after the current load exceeded 80% of the destructive load did a more accelerated development of deformations occur.The highest stresses were recorded at the very bottom of the shell samples; in the middle part of the height, the stress values were slightly lower, and in the upper part their values were very small.In general, the difference in voltage values at different points was 3-6% [11].

Results and discussion
The results obtained from theoretical and experimental studies on specimens with smooth walls were compared with shells with reinforced walls.At the same time, the difference between the calculation results and the experimental ones was 4-7% (Table 1) [12].
The results obtained from theoretical and experimental studies on samples with reinforced walls were also compared (Table 2).
The results obtained from experimental studies on samples of reinforced models were processed and statistically analyzed.When performing calculations, the law of normal distribution of random variables was applied.Statistical processing of test results showed the possibility of using a normal distribution of errors, while the standard deviations have relatively smaller values.
The results obtained in experimental studies confirm that the cross-sectional geometry of shell structures with reinforced walls leads to a significant increase in the static moment, moment of resistance and moment of inertia compared to unsupported shells: with the same metal costs, the structure will have higher stability and load-bearing capacity.

Conclusion
Based on the analysis of the results of experimental and theoretical studies of the strength and deformability of brick pillars and piers reinforced with composite fiberglass reinforcement, the following was established.
1.The proposed design solution for strengthening brick pillars using composite reinforcement makes it possible to increase the strength of brickwork, depending on the requirements of the project and the location of the composite reinforcement along the height of the brick pillar by 1.3÷1.8times.
2. The nature of the destruction of samples of brick pillars reinforced with fiberglass composite reinforcement, with different locations along the height of the sample, corresponds to the classical pattern of destruction of brickwork reinforced with reinforcing mesh or clips, identified in the studies of various authors.
3. The use of glass composite reinforcements makes it possible to create a cage and, as a consequence, increase the strength of the masonry operating under volumetric stress conditions.
4. Analysis of the experimental results and comparison of the indicators of the relative strength values of masonry (Fig. 1), reinforced with external fiberglass reinforcement, with masonry reinforced with reinforcing mesh, with their identical location along the height of the samples, allows us to conclude that the proposed in the article is quite correct describes the behavior of brick pillars reinforced with fiberglass reinforcement under centrally and eccentrically applied loads, and can be used in design practice.

Fig. 1 .
Fig. 1.Cross section of models: a) unsupported shell b) a shell with a wall reinforced with arcuate panels.

Fig. 2 .Fig. 3 .
Fig. 2. View of an unsupported smooth model of the MRG shell after testing Fig. 3. View of the MRP-1 shell sample reinforced with arc-shaped panels after testing

Table 1 .
Test results for shell samples with a smooth, unsupported wall (with loss of overall stability and load-bearing capacity).

Table 2 .
Comparison of theoretical and experimental results of studies of shell samples with reinforced wall panels (with loss of overall stability and load-bearing capacity).