Учебное пособие 2006

Russian Journal of Building Construction and Architecture

In [10], the authors obtained a denser and stronger concrete in the cross section of the pipes and a smoother inner surface due to the application of the mode of smooth acceleration of the centrifuge. The dependence of the sealing quality of pressureless reinforced concrete centrifuged pipes on the dispersal intensity of the centrifuge is theoretically justified and confirmed experimentally. The list of equations used for calculating the optimal centrifugation parameters is presented. The authors set a rational time interval when it is necessary to accelerate the centrifuge smoothly. The design of the laboratory centrifuge and forms to it by which enables the exposure of any mode of centrifugation is created. According to the authors, the mode of smooth dispersal of the centrifuge allows up to 10 % of cement to be saved during molding and consolidation of rigid concrete mixes. The analysis of the results of the experimental study showed that together with the use of steel fiber the suggested technology allows pressureless pipes with the characteristics of low pressure to be obtained [10].

In [29], the analysis of centrifuges employed in practice was performed and based on it an experimental setup was developed and constructed allowing concrete products to be obtained both by centrifugation and vibrocentrifugation. Its detailed description is presented, the parameters of the operation are calculated, and the results of trial experiments confirming the correctness of the assumptions and postulates are provided [29].

Also, the authors [13––18, 25, 26, 29, 32, 51, 56] compiled a list of raw materials for concrete preparation, established the fundamental compositions needed for the production of centrifuged and vibrocentrifuged elements of annular cross section with a varatropic structure. The methods and instrumentation for estimating actual variatropy of the structure of concrete products of annular cross-section obtained by means of centrifugation and vibrocentrifugation methods were also selected for the study [29].

2. Integral and differential design characteristics of variatropic centrifuged and vibrocentrifuged concretes. During centrifugation, large grains of aggregate move to the outer surface of the product, and small ones to the inner. The concrete structure of the cross section of the centrifuged product has a distinct variatropy, i.e., considerable differences in the thickness characteristics. This is clearly shown in Fig. 1 and 2.

The following raw materials were used: Portland cement grade 500, granite crushed stone fraction 5–– 20 and quartz sand with a modulus of size 2.0 [29].

The correctness of the direction of the study was confirmed by the choice of equipment and tools that allowed the researchers to evaluate actual variatropy of the concrete structure [29]. In [29] the effect of the type of manufacturing technology (vibration, centrifugation, vibrocentrifugation) on the integral (common in cross section) and differential (different in cross

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section) characteristics of concrete, i.e., density, compressive strength (on cubes and prisms) and tensile (axial and bending) one, ultimate deformations during compression and tension, modulus of elasticity as well as diagrams of «stress –– strain».

Fig. 1. Variatropy of the properties of centrifuged product of a ring section

Fig. 2. Variatropy of the properties of vibrocentrifuged product of a ring section

In the laboratory on three technologies (vibration, centrifugation and vibrocentrifugation) samples with the following values of the diameter were formed: the external one –– 450 mm, the internal one –– 150 mm and the height of 1200 mm. Each of these was used in several types of tests (in order to calculate the integral and differential characteristics) at different times of concrete hardening, i.e., 7, 28 and 180 days. Also, for the completeness of the study data with the help of the device „Pulsar 2.2“ the strength of the outer, middle and inner conditional layers of concrete, the formation of which was ultrasonically controlled by means of centrifugation and vibrocentrifugation [29].

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Russian Journal of Building Construction and Architecture

In [29], the authors experimentally confirmed the justification of the three-layer variatropic structure of centrifuged and vibrocentrifuged concrete.

It was found that the manufacturing technology had almost no effect on the density of concrete in all of the studied curing times. Vibrocentrifuged concrete at any time of hardening had the highest strength compared to vibrated and centrifuged one (compression –– up to 22 %, tensile –– up to 27 %). The ultimate deformations during axial compression and tension at any time of hardening when compared between the three technologies of concrete compaction were minimal in vibrocentrifugation (the difference of up to 6 %). The differences in compressive and tensile modulus at any age were up to 8 % between vibrocentrifuged concrete and that based on the other two technologies. The diagrams of «stress –– strain» in compression and tension in concrete following the vibrocentrifugation compared with vibration and centrifugation in all of the studied curing periods had the following characteristics: the maximum shifted up and to the left (an increase in the strength with reduced deformation) the diagrams have increased slopeness of the ascending branches and flatness of the descending ones [29].

A comparative analysis of the properties of the layers of centrifuged concrete showed that the outer layer has the highest strength (around 49 % more than the inner one and 23 % higher than the middle layers), then the middle layer (around 21.5 % higher than the inner layer) and the lowest strength of the inner layer whose properties are minimally affected by the manufacturing technology [29].

The strength of the layers of vibrocentrifuged concrete was distributed in the following way: the outer layer –– 13 % more than the middle one, and 55 % more than the inner one; in the middle layer –– 37 % more than in the inner one. Thus the tendency of the distribution of strength in the two technologies was identical, but the differently qualitatively expressed curves of the dependence of the strength of the layers during centrifugation had a downward convexity down and during vibrocentrifugation an upward one.

The ultimate deformations in both compression and tension are minimal in the outer layer, maximum in the inner one and approximately intermediate ones between them –– in the middle layer: slightly more –– in centrifuged concrete and less –– in vibrocentrifuged one.

It makes sense that the cross sections turned out to be different diagrams of «stress-strain». In centrifuged concretes, the diagram of the outer layer with the highest strength and the elasticity modulus and the smallest deformations is characterized by the movement of the maximum up and to the left with a greater lift in the ascending branch and a sharper slope in the descending branch. In the inner layer with the lowest strength and the elasticity modulus and the

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largest deformations, the diagram was the lowest and flattest. The deformation diagram of the middle layer had an intermediate position compared to the other two. The deformation diagrams of vibrocentrifuged concrete layers show the same pattern but with a larger difference [29].

The authors conclude that the variatropy of concrete elements of annular cross-section and the different characteristics of concrete should be considered while calculating the structures.

3. Calculation recommendations for identifying the design characteristics of centrifuged and vibrocentrifuged concrete depending on the values of technological factors and age.

In [29], according to the results of statistical processing of experimental data with a reliability of 0.95, the values of normative and calculated resistances for limit states of groups I and II, limit deformations and initial modulus of elasticity in compression and tension of centrifuged and vibrocentrifuged concrete are proposed.

The authors provide variants of calculating the integral structural characteristics of concrete at the age of 28 days, obtained by centrifugation and vibrocentrifugation. This being the case, the indicators of vibrated concrete were taken as a unit, and for the other two types of concrete the coefficient Ki, 28 was used in addition to the indicators of vibrated concrete [29].

The calculated definition of the integral characteristics of centrifuged and vibrocentrifuged concretes depending on the type of molding and compaction technology was expressed in the introduction of coefficients to find each of the characteristics of compression (КRb,28Rb;

К bR,28 bR; КЕb,28Еb) and tensile; (КRbt,28Rbt; К btR,28 btR; КЕbt,28Еbt), where Ki,28 are correction

coefficients equalling its base value for vibrated concrete at the age of 28 days [29].

Integral characteristics of concrete depending on the curing time are proposed to calculated using the dependences where the coefficients are defined by means of statistical methods. A calculated estimate is proposed to be made based on analytical dependences to identify the coefficients Кi,t introduced for each of the strength and deformation characteristics, equal to the ratio of a characteristic to its basic value at the age of 28 days [29]:

where fi,t are the corresponding functions of one type; t is the age of concrete, days.

For a single function fi,t (t) in equation (1) for uniformity, the formula of P. Sarzhin (ECBFIP) was employed to describe the diagrams of deformation of concrete:

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Russian Journal of Building Construction and Architecture

where Кi,t are the ratios of the original value of the current characteristics of concrete at age t to its value at the age of 28 days; Ко is the control parameter for each characteristic [29]. Therefore considering the dependence of changes in the characteristics of concrete on their age, it is essential to multiply the values of their characteristics at the age of 28 days by the corresponding coefficients Кi,t whose the values are found for all the characteristics of concrete at any age. All the structural characteristics of the investigated concretes were given by dependences (2) [29].

Experimentally and analytically, the deformation diagrams of compression and tension of all of the investigated concretes at any time of hardening were obtained, their similarity was proved and recommendations for their construction were provided based on to the dependence by P. Sarzhin, recommended by EKB-FIP:

where R and R are the compressive or tensile strength and deformation of the dependence of P; К = RЕ/R is a numerical parameter equalling the ratio of the original Е (tangential) elasticity modulus to the specific (cutting) elasticity modulus at the moment of achieving the maximum of function (3) with the coordinates R and R [29].

The analysis revealed the similarity of the stress-strain diagrams in compression and tension for centrifuged and vibrocentrifuged concrete as well as the location of the maxima of these diagrams on one line passing through the origin; it has also been proved that the similarity of the «σb – εb» and «σbt – εbt» diagrams is also characteristic of the increments of these diagrams after their maxima for the investigated concretes at any curing time [29].

For the uniformity of the calculated dependences, the same functions were used for three purposes: to evaluate the change in strength and deformation characteristics during compression and tension; to describe the diagrams of deformation and their increments during compression and tension; to evaluate the dependence of changes in strength and deformation characteristics and deformation diagrams and their increments during compression and tension [12, 19, 20, 22, 28, 29].

The authors identified three stages of defining the design characteristics and diagrams of «stress –– strain» of all the investigated types of concrete at any time of hardening. The first stage involves the analysis of change of strength and deformable characteristics of the

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vibrocentrifuged and centrifuged concretes in relation to the vibrated after 28 days of hardening: at compression –– КRb,28Rb; К bR,28 bR; and in tension –– КЕb,28Еb . The second stage involves researching the dependence of characteristics of concrete on its age using coefficients: at

compression –– КRb,tКRb,28Rb; К bR,tК bR,28 bR; КЕb,tКЕb,28Еb and at stretching –– КRbt,tКRbt,28Rbt;

К btR,tК btR,28 btR; Кеbt,tКЕbt,28Еbt. The third stage includes the interpretation of diagrams of «stress –– strain» of concrete during compression and tension at any age using the following parameters: at compression –– КRb,tКRb,28Rb; К bR,tК bR,28 bR; КЕb,tКЕb,28Еb and at stretching ––

КRbt,tКRbt,28Rbt; К btR,tК btR,28 btR; КЕbt,tКЕbt,28Еbt [29].

The authors identified three stages of defining the design characteristics and diagrams of «stress –– strain» of all the investigated types of concrete at any time of hardening. The first stage involves the analysis of change of strength and deformable characteristics of vibrocentrifuged and centrifuged concretes in relation to vibrated following 28 days of hardening: at compression –– and at stretching –– The second stage involves researching the dependence of characteristics of concrete on its age by means of coefficients: at compression –– and at tensile –– The third stage involves the interpretation of diagrams of «stress –– strain» of concrete during compression and tension at any age, using the following parameters: during compression –– and during tension –– [29].

It is suggested that the differential characteristics of centrifuged and vibrocentrifuged concrete are evaluated using universal dependences where the functions are strength (Yi), and the arguments are the distances from the center of rotation and angular velocities (Xi):

The dependences developed by the authors [29] for the differential characteristics of concretes obtained by centrifugation and vibrocentrifugation contributed to a fuller use of reserves [29].

4. Methods of calculation of centrifuged and vibrocentrifuged reinforced concrete columns considering the variatropia of concrete. The authors of [30] conducted a large-scale study in order to develop a refined method for calculating reinforced concrete centrifugal racks of technological trestle working on torsion and compression with torsion. This technique is designed to account for the features of changes in the strength and deformation properties of centrifuged concrete in a flat stress state «stretching –– compression».

The authors [30] also suggested that the strength of centrifuged concrete at a flat stress state "tensile –– compression" is evaluated by means of formula (5), and the ultimate deformations in the direction of the main compressive axis –– by equation (6) based on the ratio of principal stresses:

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Russian Journal of Building Construction and Architecture

where Rк is the prismatic strength of centrifuged concrete; Rp is the tensile strength of centrifuged concrete; kr.s. is the coefficient considering the effect of stresses on the reduction of concrete strength under compressive and tensile loads.

where ε2пр are the ultimate relative deformations of centrifuged concrete during central compression; Rп * is the ultimate compressive stress depending on the stress state and determined by condition (7) for the known σ1/σ2 = β (the ratio of the tensile (σ1) and compressive (σ2) stresses). I.e.,

Also in [30], the authors were able to expand the range of experimental data and proceed to a uniform assessment of the operation of centrifuged elements of the annular cross section due to experiments performed on pure torsion and compression with torsion up to axial compression.

Numerous experiments on concrete and reinforced concrete centrifuged elements enabled the authors [30] to accept the condition of strength corresponding to the destruction of concrete samples as a condition for the formation of cracks in reinforced concrete elements.

The ratio of the main stresses in concrete has the greatest effect on the strength of centrifuged reinforced concrete elements working on torsional compression [30]. It is found that the fracture moment takes place when the values of average stresses in concrete for centrifuged concrete re-enter the strength line [11, 30].

The increase in the angles of twist and the width of the opening of cracks takes place largely following their formation. This being the case, the reduction of the twisting angles takes place in the case of an increase in the proportion of normal force. Also, the reduction of the axial deformations of compression from the normal force, passing at certain stress ratios into elongations, takes place due to the torque. The author's experimental values of the crack opening width and torsion angles coincide with the theoretical values obtained by means of the method of N. I. Karpenko [11, 30].

The numerous experimental data of rack tests [30] and data of other authors confirmed the reliability of the proposed calculation method.

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The study [2] presents the results of experiments of centrifuged concrete of non-reinforced and reinforced elements of annular cross-section under conditions of short-term axial and eccentric compression in terms of mechanical characteristics. The analysis is performed and the suggestion as to how the dependence of structure formation should be evaluated and the basic mechanical characteristics at compression of the centrifuged concrete on longitudinal reinforcement are provided [2].

Given the complete deformation diagram of compressed concrete, a technique for controlling the strength for short-term axial and eccentric compression of short elements with the annular cross section and longitudinal high-strength reinforcement has been developed. The methods of a recommendatory nature are also formulated to define the characteristics of both the stress-strain of concrete and reinforcement, and the degree of their use. Proof of the effectiveness of the suggested methods is the similarity of experimental and calculated results [2].

The result of the analysis of the study is the suggested dependences of the compressive strength of both reinforced and non-reinforced short columns with the annular cross section obtained by means of centrifugation. Note that the authors presented an algorithm for evaluating the calculated resistance to compression of longitudinal high-strength reinforcement considering the factors of mechanical characteristics of compressed concrete, their variability and reinforcement rates [2].

The research of the previously presented dependences needed to calculate the strength of products with the annular cross section confirmed the possibility of their use to calculate the strength of both normal sections and inclined. But it is worth noting that these dependencies do not cover some factors that directly influence the performance of products and structures with the annular cross section, i.e., the span of the cut, the area and pitch of the spiral reinforcement, the loading scheme [1].

The authors [1] noted that while calculating the strength of elements that were obtained by means of centrifugation, should consider the solutions obtained by calculating the strength of normal sections of bending elements having a rectangular profile. The length of the longitudinal section should be taken as a variable and account for the effect of the span of the cut and the location of the support.

In all of these studies, the calculation of structures was conducted without considering the variability of the properties of centrifuged concrete. In [29], the variatropy of the structure of centrifuged and vibrocentrifuged concrete columns was taken into consideration. It is suggested that the normative approach to the calculation of the strength of centrifuged and

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Russian Journal of Building Construction and Architecture

vibrocentrifuged reinforced concrete columns is improved considering the general crosssectional (integral) and different in cross-sectional (differential) design characteristics. Based on the norms, the identification of the load-bearing capacity (N) of concrete and reinforced concrete short elements that have a different cross-section or with a small eccentricity is possible in the presence of stresses in these elements as well as in the case of normative parameters of concrete:

where Rb is the compressive strength (design resistance); Ab is the area of compressed concrete; Rsc is the calculated value of the resistance of the reinforcement to compression; As is the cross-sectional area of the compressed reinforcement.

If compressed products obtained by centrifugation or vibrocentrifugation are compared to the elements obtained by vibration, the strength limit of concrete products and elements will be different: Rb,red = КrbRb, which in the case of application of integral characteristics of concrete yields the following equations:

where Rb,red is the ultimate compressive strength of the centrifuged and vibrocentrifuged element.

In case of application of differential characteristics of concrete the following dependences are deduced:

In the formulas, it is now viable to employ the obtained strengths considering their differences in the layers Rb, red, and their area Abi [29].

For the diagram approach, complete diagrams «σ – ε» with descending branches were used, and in such cases the dependences took the following form:

where Nb is the load-bearing capacity of concrete; σ(ε) is the compressive stress in concrete depending on the relative deformation; dx is the height of the compressed area; h is the height of the section.

(12)

where Ns is the load-bearing capacity of the reinforcement; σsc is the design resistance of the reinforcement during compression.

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Iterative calculation of norms or general cross-sectional characteristics involved the use of stress-strain diagrams of concrete with Rb; bR; Еb and КRb,28Rb; К bR,28 bR; КЕb,28Еb. Instead of integration there is the final summation by the sections:

In the iterative calculation of the cross-sectional characteristics of the investigated columns, the equations take another form:

where ω1 is the internal angular rotation speed; ω2 is the external angular rotation speed; d is the internal diameter of the column; D is the external diameter of the column; Abi is the area of the layer of the compressed concrete; dω is the angular rotation speed; dl is the distance from the rotation centre to the grain centre.

The iterative approach in the calculation involved specifying εb at each iteration with a certain interval of concrete deformations [12, 29]. The authors noted a difference in iterative and normative calculations: the first allows one to evaluate the performance of compressed elements even in the supercritical stage in contrast to the second, including when the decrease in stresses and forces in concrete on the descending branch of the diagram is compensated for and even overlapped by the rising stresses Ns ≥ Nb [29]. At the same time it is justified that only high-strength fittings without a flowing site are appropriate. If this condition is not satisfied, the column will exhaust its load-bearing capacity after the maximum strength of concrete has been reached [29].

The following data are needed for the iterative calculation: diagrams of «stress –– strain» and the area of concrete and reinforcement; the geometric parameters and cross-sectional shape. At the same time the condition of equality of deformations of concrete and armature at all the stages of its work is accepted:

where εb is the concrete deformation; εs is the reinforcement deformation.

The longitudinal force, which perceives the cross section of the compressed element, at all the stages of work is calculated as:

where σb are the stresses in the concrete; σs are the stresses in the reinforcement.

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