DEFORMABILITY OF REINFORCED CONCRETE BEAMS WITH CABLE REINFORCEMENT WITHOUT CRACKS

ABSTRACT

Currently, in many countries, one of the key areas for improving the efficiency of concrete and reinforced concrete is reducing density by using inexpensive and high-quality local porous fillers. The use of porous filler based on ceramic porite in load-bearing reinforced concrete structures will improve their technical and economic performance and reduce their own weight.

The article presents the data of experimental and theoretical studies obtained in the study of the deformability of prestressed bending elements made of lightweight reinforced concrete with rope reinforcement. The tests were carried out using short-term and non- multiple repeated loads. Based on the analysis of the data obtained, some clarifications were made to the methodology for calculating the deformability of such structures according to current design standards.

АННОТАЦИЯ

В настоящее время во многих странах одним из ключевых направлений повышения эффективности бетона и железобетона является снижение плотности за счет использования недорогих и качественных местных пористых заполнителей. Использование пористого заполнителя на основе керампорита в несущих железобетонных конструкциях позволит улучшить их технико-экономические показатели и снизить собственный вес.

В статье представлены данные экспериментальных и теоретических исследований, полученные при исследовании деформативности предварительно напряженных изгибаемых элементов из легкого железобетона с армированием канатой арматурой. Испытания проводились с использованием кратковременных и немногократных повторных нагрузок. На основе анализа полученных данных внесены некоторые уточнения в методику расчета деформативности таких конструкций по действующим нормам проектирования.

Keywords: lightweight reinforced concrete, ceramic-porous concrete, reinforcement, rope reinforcement, deformability, test, result, calculation.

Ключевые слова: легкий железобетон, керампоритобетон, армирование, канатная арматура, деформативность, испытание, результат, расчет.

Introduction. There have been virtually no specific and targeted studies of the behavior of prestressed bending elements made of ceramic-porite concrete with rope reinforcement. In order to facilitate the widespread use of these materials, new experimental and theoretical studies are needed to clarify and improve the design requirements of regulatory documents for the design of such structures.

As is known, the existing standards are based primarily on experimental studies conducted on reinforced concrete structures using heavy concrete. The technical advantages of using high-strength rope reinforcement in bending elements made of ceramic-porous concrete, as well as the effect of prestressing, have not been sufficiently assessed in these standards.

The basics of the method for calculating the deformation of reinforced concrete were developed and proposed by Professor V.I. Murashev [1]. Subsequently, the theory of calculating reinforced concrete structures by deformations was developed in the works of many scientists [2-6].

The deformations of reinforced concrete elements are determined by the curvature values using the formulas of structural mechanics. The method of calculating the deformation according to current standards depends on the presence or absence of a crack in the section under consideration in the tension zone.

As the results of some experimental and theoretical studies have shown, some coefficients included in the calculation formulas of the current design standards for concrete and reinforced concrete structures are not constant for prestressed structures made of lightweight concrete with cable reinforcement.

Reducing the dead weight of reinforced concrete structures by using various lightweight concretes, including prestressed elements based on them, is effective in seismic areas. In this regard, research in this area will help solve a number of issues related to the use of effective prestressed elements [7,8].

This study is devoted to the experimental and theoretical investigation of the behavior of bending ceramic-porous reinforced concrete elements with rope reinforcement under short-term and multiple repeated loading, followed by the development of proposals for improving the calculation methodology for such structures.

Properties of materials and methods of experimental research.

To solve the set tasks, 36 experimental reinforced concrete beams were manufactured. These beams had a rectangular cross-section measuring 12 cm by 24 cm and a length of 320 cm. Two types of lightweight concrete were used in the experimental study: ceramporite concrete, which is lightweight concrete based on ceramporite (an artificial porous filler made from local raw materials), and ordinary heavy concrete. Rope reinforcement of class K-7 with a diameter of 9 mm and 12 mm was used as longitudinal working reinforcement.

Experimental reinforced concrete beams were made from each type of concrete, 12 pieces each, and included 6 beams with longitudinal working reinforcement 2Ø9 K-7 and 6 beams with reinforcement 2Ø12 K-7. Each of the 6 beams consisted of three pairs of twins. The first pair with a high level of prestressing. The second pair with an average level of prestressing, and the third pair without prestressing.

To produce experimental beams from ceramic-porite concrete, two types of ceramic-porite obtained from local raw materials were used.

The main characteristics of porous fillers of ceramic porite, reinforcing steels, composition of concrete, beam reinforcement scheme and the procedure for their testing were presented in the article of the authors [9] .

The strength of ceramic-porite concrete on the day of testing the experimental beams was within the range of 31-33.5 MPa, and for heavy concrete - within the range of 26-29 MPa.

The experimental moment of crack formation was determined by visual inspection of beams and using a microscope with 24x magnification, and then refined by analyzing the graphs of concrete deformation in compressed and stretched zones, reinforcement stretching and deflections.

Results and their discussion.

For bending elements that do not have cracks in the tensile zone of the section, the value of curvature under short-term load action is determined by formula (1), in which the effect of the inelastic properties of concrete on the rigidity of the section is taken into account by the coefficient φ _{b 1} . In the standards [8], the value of φ _{b 1} is given only depending on the type of concrete, and is taken as constant and equal to 0.85 for elements made of heavy and lightweight concrete (with dense fine aggregate):

                                                                     (1)

- a coefficient that takes into account the decrease in rigidity due to the development of inelastic deformations of concrete.

The table shows the values of actual beam deflections. ), as well as calculated ones, in the calculation of which the curvature value was determined from expression (1) with the value φ _{b 1} = 0.85. When comparing the values for prestressed beams with the calculated ones, It was found that the current standards provide some reserve compared to the actual deflections, and in conventional beams, the experimental deflection values were observed to exceed the calculated ones.

The experimental values of the coefficient φ _{b 1} were determined by the formula:

                                                     (2)

where: 0.1026 is the load factor corresponding to the adopted sample testing scheme.

Analysis of experimental data shows that the values of the coefficient (at the stage preceding the formation of cracks) for prestressed elements fluctuate within the range of 0.78-0.95, and for ordinary elements within the range of 0.68-0.77 without any clearly expressed dependencies on the relative height of the compressed zone during destruction.

Experimental data also show that the percentage of reinforcement in the tension zone has some influence on the coefficient in non-prestressed beams, in particular in beams with a reinforcement percentage of 0.7 the value of the coefficient lower than in beams with a reinforcement percentage of 0.4 by 4.0-5.0%. Such an influence on the value was not observed in prestressed beams.

Table 1.

Deflections of beams before cracks appear in the tension zone

On the value of the coefficient  The level of concrete compression has a significant impact, with an increase in which the coefficient increases, since some of the inelastic deformations appear even before the application of external load during the compression process (Fig. 1 and 2).

Processing of the results of tests of reinforced concrete beams shows that the influence of the level of concrete compression on the coefficient can be reflected by the equation:

= A + B · η_P                                                                                   (3)

where: A - the coefficient for lightweight concrete is taken as 0.75, since it corresponds to the average value of the coefficient for ordinary beams;

A - for heavy concrete - 0.70;

B - coefficient for lightweight concrete 0.2;

B - for heavy concrete 0.15;

η_P - level of concrete compression.

After substituting the specified parameters, dependence (3) takes the following form:

for heavy concrete

= 0.70 + 0.15 · η_P                                                                           (4)

for lightweight concrete

 = 0.75 + 0.2 · η_P                                                            (5)

A comparison of the experimental and theoretical values calculated using dependencies 4 and 5 showed good convergence, which is clearly demonstrated by the graphs in Fig. 1 and 2. As can be seen from Fig. 3, 4 and 5, the value of the coefficient is also significantly affected by the load level, with a decrease in which the value increases.

Figure 1. Dependence on the compression level of ceramic-porous reinforced concrete beams - experimental values for ceramic-porous reinforced concrete beams

1 – according to formula (3); 2 – according to KMK 2.03.01-21[8]

Figure 2. Dependence on the compression level of reinforced concrete beams made of heavy concrete - experimental values of reinforced concrete beams made of heavy concrete

1 – according to formula (3), 2 – according to KMK 2.03.01-21[8]

By comparing the actual deflections with the calculated f _{m 1} and f _{m 2,} it was found that the use of the recommended formulas for assessing allows for more accurate determination of calculated deflection values.

Relative deformations of the concrete in the compressed zone were measured by strain gauges and clock-type indicators on a 300 mm base. Based on the instrument readings, graphs were plotted of the change in average relative deformations of the outer fiber of the compressed zone of concrete depending on the magnitude of the load (Fig. 6; 7; 8).

The increase in the percentage of reinforcement in non-stressed elements had an insignificant effect on reducing the intensity of deformation growth . The latter were largely influenced by the presence of prestress in the beam section. As can be seen from Fig. 6, the increase in deformation in prestressed beams is less than in conventional ones.

It should be noted that the development of average deformations of compressed concrete in non-stressed beams occurred almost according to a linear law, in contrast to prestressed beams, in which the deformation graph had a smooth, curvilinear character.

Figure 3. Dependence on the loading level of ceramic-porous reinforced concrete beams

a) experimental values for beams with σ _bp / R _bp = 0.35 – 0.5; b) experimental values for beams with σ _bp / R _bp = 0.65 – 0.72; 2 - according to KMK 2.03.01-21 [8]

Figure 4. Dependence on the loading level of reinforced concrete beams made of heavy concrete (experimental values for beams -µ = 0.7%) at σ _bp / R _bp = 0.85; 2 – according to KMK 2.03.01-21 [8]

Figure 5. Dependence on the loading level ◑ ◐ - experimental values for ceramic-porous reinforced concrete beams at σ _bp / R _bp = 0.35;

◍ and ▌ - experimental values for ceramic-porous- iron- concrete beams at σ _bp / R _bp = 0.28; 0.31 at σ _bp / R _bp = 0.3; 2 – according to KMK 2.03.01-21

Figure 6. Changes in average deformations of the compressed zone of concrete during testing of unstressed beams

1 - according to experience; 2 - according to KMK 2.03.01-21[8]; 3 - the same, taking into account the authors' proposals

Figure 7. Changes in average deformations of the compressed zone of concrete during testing of prestressed beams with µ = 0.4%

1 – experimental values of the first loading; 2 - according to KMK 2.03.01-21[8]; 3 - the same, taking into account the author's proposals; 4 - experimental values of the fifth loading

Figure 8. Changes in average deformations of the compressed zone of concrete during testing of prestressed beams with µ = 0.7%

1 – experimental values of the first loading; 2 – according to KMK 2.03.01-21[8]; 3 - the same, taking into account the author's suggestions; 4 - experimental values of the fifth loading

The experimental values of average deformations were compared with the theoretical ones calculated using the formula:

                                       (6)

where: - actual modulus of elasticity of concrete.

The values of the parameters in formula (6) were determined according to KMK 2.03.01-21 [8].

Comparison of experimental and calculated values of relative deformations of concrete in the compressed zone revealed a discrepancy between the specified values. In stages close to destruction, a variable value should be used , which can be determined by formula (11), which will ensure the best match between theoretical and experimental values.

In the study of the elements under consideration, attention was paid to identifying the value of the coefficient characterizing the uneven distribution of the deformation of the extreme compressed fiber of the section in the presence of cracks in the stretched concrete of the bending element. The value of the coefficient is determined as the ratio of the average deformations on the compressed face of the concrete between the cracks to the deformations of the concrete above the crack, using the expression:

                                                                      (7)

In the standards for all bending elements its value is taken equal to 0.9. In our studies the value of this coefficient fluctuated from 0.82 to 0.98 for ceramic-porous concrete, and for heavy concrete from 0.81 to 0.97 (Fig. 9). No clear dependence of the coefficient  on the type of fillers, concrete strength and loading level were observed. The presented data indicate that the calculated values of the coefficient of ceramic-porous reinforced concrete beams with unstressed and prestressed cable reinforcement can be taken equal to 0.9, i.e. the same as for beams made of ordinary heavy concrete.

Figure 9. Dependence of the coefficient depending on the load level

a) for the II type of ceramic-porous concrete; b) for the 1st type of ceramic-porous concrete; c) for heavy concrete .

The relative height of the compressed zone of concrete ξ is included in the calculation formulas by which the curvature of the bending element is determined at various stages of loading, the value of which is calculated using the formula:

                                                                   (8)

In addition, based on the readings of sensors glued to the side surface of the beams, the height of the compressed zone of concrete in the section with a crack ξ ^exp was determined.

A comparison of the values of the relative height of the compressed zone shows that the theoretical values found according to the formula:

ξ =                                                 (9)

quite accurately reflect the process of changing the position of the neutral axis as the beams are loaded.

Thus, experiments show that the values of the relative height of the compressed zone in sections with cracks in ceramic-porous reinforced concrete beams, both with non-stressed and pre-stressed cable reinforcement, can be determined using the formula of current design standards [8].

The coefficient ν _Ь , characterizing the elastic-plastic state of concrete in the compressed zone for experimental beams, was determined by the dependence:

                                             (10)

into which the experimental values and were substituted ,

According to the calculated values of the coefficients , its average values were found for each experimental beam. Then the average value was determined separately for beams made of ceramic-porite concrete and heavy concrete. The average (standard) values of the coefficients for ceramic-porite concrete and heavy concrete under operational load were equal to 0.5 and 0.48, respectively.

Conclusion. Based on the results of the experimental and theoretical studies, the following conclusions can be drawn:

The value of the coefficient φ_b, which characterizes the reduction in rigidity due to the manifestation of inelastic properties of concrete under short-term loading, is proposed to be taken as variable.

The coefficient ψ _b for ceramic-porous reinforced concrete beams with cable reinforcement is recommended to be taken in accordance with current design standards.

The value of the relative height of the compressed zone of concrete, ceramic-porous concrete bending elements, reinforced with class K-7 rope reinforcement, can be determined using the formulas KMK 2.03.01-21.

Repeated immersions to operational loading levels, depending on the type of concrete, lead to an increase in deflections after the fifth loading by 1.03-1.15 times and depends on the type of concrete and the number of repeated loadings.

The calculated values of deflections of ceramic-porous reinforced concrete beams can be determined using the formula of current standards with recommended values of the studied coefficients, which ensures their satisfactory convergence with experimental data.

The necessity of improving the method of calculating design standards to increase the accuracy of determining the deflections of prestressed bending elements made of lightweight concrete with cable reinforcement is shown.

References:

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3. Dmitriev S.A. Effect of preliminary stress on the strength and rigidity of reinforced concrete structures. In the collected works of the Research Institute of Reinforced Concrete, issue 17. Moscow, Gosstroyizdat, 1960, pp. 5-31.
4. Ioannisian A.A. Deflections of prestressed reinforced concrete beams on shell limestones with high-strength wire reinforcement, pp. 31-38. Rostov-on-Don, 1974.
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