Учебное пособие 2067

Russian Journal of Building Construction and Architecture

The set task of deriving the dependence of the deflection on the number of panels is a twoparameter one. At the second stage, it is essential to perform the same operations for m = 2, 3, 4, ... for exactly as many times as necessary for the operator rgf_findrecur to yield a solution in the form of a homogeneous recurrent equation. We have the following results:

The first three coefficients in these formulas do not change. The latter two generalize to arbitrary m fairly simply without using the rgf_findrecur and rsolve operators:

An,m = 5n4 +10n3 + 7n2 + 2n(m +1) + 2m. (7) Similarly, but much simpler, the other coefficients are obtained. They do not depend on the number of panels m along the truss height:

In the case of a concentrated load, the deflection formula remains the same. The recurrent equations are simplified:

3. Lateral load. The advantage of the spatial model of the structure compared to the widespread approximation of a truss by a set of flat trusses where the connections between them are conditionally not involved in the work is the possibility of calculating such models for an arbitrary load, e.g., for a rather rarely considered lateral load [16, 17, 25]. Let us look at the case of a load of horizontal forces P uniformly distributed over the nodes of the upper chord of the truss. The matrix G obtained for the vertical load remains the same. The inverse matrix G1 does not change either. The right-hand side composed of forces directed along the axis y has the form B3(i+m1 )−1 = P, where i = m +1,...,m + k +1.The force applied to the free node D instead of the reaction of a nonexistent support is identified using the equation of equilibrium

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(moments) of the entire frame relative to the axis x: ZD = −Pm(n + 1)h / b . In this case, based on the solution of the system of equations for the equilibrium of the nodes, the expressions for the reactions of the supports are as follows: ZC = ZB = Pm(n + 1)h / b, ZA = ZD .

The deflection formula (vertical displacement of the middle crossbar node in the lower chord) is also obtained by means of the induction method according to two parameters:

Fig. 5. Girder in the coordinates x, y, z. The lateral horizontal load P at n = 3, m = 2 : ZA, ZB , ZC , ZD are vertical components of the support reactions, YA is a horizontal component of the spherical hinge

4. Analysis of the solution. Let us consider the solution (3) with the coefficients (7), (8). Let us fix the value of the total load which does not depend on the number of panels P0 = P(2n + 1) and design graphs of dependence on the number of panels of dimensionless deflection ' = EF / (P0L) where L = 2an is the span length (Fig. 6). As the number of panels increases, so does the deflection. It can be established that this dependence tends to qua-

with an increase in the transverse dimension b. As b increases, the truss becomes wider (dimension along the axis y), the deflection grows. This can be partly accounted for by the fact

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that for such structures, the cross-links are lengthened, and in general the truss becomes less rigid not due to the longitudinal rods but due to the transverse ones.

The solution (3) with the coefficients (10) for a concentrated load has the same asymptotics and approximately the same curves.

Fig. 6. Deflection under a load along the nodes of the upper belt, m = 10, a = 1 m, I — b = 4m; II — b = 2m; III — b = 0.5m

The dependence of the dimensionless deflection on the panel size under the action of a lateral horizontal loadcalculated according to the solution (11, 12) has a distinct horizontal asymptote limiting the solution from the bottom (Fig. 7).

Fig. 7. Dependence of the deflection on the size of the panel under the action of the lateral load, n = 10, m = 3 , I — b= 4 m; II — b = 3 m, III — b=2 m

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The value of the ultimate deflection is obtained in the Maple system using the limit (Del, a = infinity) operation and is as follows:

Let us note that this value depends only on the number of panels and not on the linear dimensions of the structure. Obviously, as n or m increase, the value grows indefinitely. Conclusions. The suggested scheme of a spatial frame with two parameters that regulate the number of panels in the girder and uprights makes it possible for the inductive method to be applied in order to obtain the basic formulas for assessing structural deformations. It is convenient to use these estimates for optimization problems [21] as well as test estimates for evaluating numerical solutions [22]. The suggested truss scheme is new, the analytical solutions for its deflection have been obtained for the first time.

In the process of deriving formulas in a system of symbolic transformations which works much slower than packages employing numerical methods, a difficulty of a purely technical nature had to be overcome. As the number of panels in the girder increases, the counting time increased sharply and since the induction in this task was double, either a processor with good characteristics or a significant counting time was needed. If at first the induction is performed using one parameter in N steps and time t is spent on each step, the induction on another parameter in M steps already requires time NMt. The solution to this problem was somewhat simplified in cases where the individual coefficients did not depend on the number m of panels in height - the second-order induction parameter. The formulas were verified in two ways: numerically or by changing the order of the induction parameters.

References

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17.Qin H., Stewart M. G. System fragility analysis of roof cladding and trusses for Australian contemporary housing subjected to wind uplift. Structural Safety, 2019, vol. 79, pp. 80––93. doi: 10.1016/j.strusafe.2019.03.005

18.Rakhmatulina A. R., Smirnova A. A. The dependence of the deflection of the arched truss loaded on the upper belt, on the number of panels. Nauchnyi Al'manakh, 2017, no. 2-3 (28), pp. 268––271.

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24.Voropay R. A., Domanov E. V. Analytical solution of the problem of shifting a movable support of a truss of arch type in the Maple system. Postulat, 2019, no. 1. Available at: http://e-postulat.ru/index.php/Postu- lat/article/download/2345/2386.

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Russian Journal of Building Construction and Architecture

ARCHITECTURE OF BUILDINGS AND STRUCTURES.

CREATIVE CONCEPTIONS OF ARCHITECTURAL ACTIVITY

DOI 10.36622/VSTU.2020.47.3.007

UDC 711.1(4/9)

N. G. Yushkova1

LOCAL URBAN-PLANNING FORMATIONS AS A FOUNDATION FOR REORGANIZING REGIONAL SYSTEMS OF SETTLEMENT:

PREREQUISITES FOR DEVELOPING THE METHODOLOGY

Volgograd State Technical University1

Russia, Volgograd

National Research Moscow State University of Civil Engineering1

Russia, Moscow

1PhD in Architecture, Assoc. Prof. of the Dept. of Chemistry, Adviser of the Russian Academy of Architecture and Construction Sciences, tel.: (+7) 917-837-12-70, e-mail: ymanul@gmail.com

Statement of the problem. New trends in urban planning of the 21st century reflect the influence of scientific and technological progress and development of social relations. In the territorial systems of settlement, there is a pronounced dynamics of urban planning processes, their regional identity, heterogeneity and locality of location in space. Without proper methodology in place, maintaining the existing structural and functional order is becoming challenging. Establishing the features and patterns of development of territorial systems as the basis for their reorganization requires the systematization of the latest urban planning experience.

Results. A special group of objects - local town-planning formations - is revealed, their characteristic features are substantiated which predetermine the construction of a typology. Based on the differentiation of the ways of their interaction with territorial systems, the main provisions of the methodology of urban planning are formulated.

Conclusions. The signs, properties and characteristics of local town-planning formations determine the dynamics of territorial systems. Considering them when justifying urban planning decisions allows one to simultaneously implement the requirements of sustainability and innovation, which contributes to the formation of new elements and connections in territorial systems, determines the process of urban planning evolution and contributes to an increase in the comfort of the living environment.

Keywords: local town-planning formations, territorial settlement systems, dynamics, evolution, technology.

Introduction. The problem of ensuring the stability of territorial settlement systems in all nations is of an interdisciplinary nature and has been relevant for more than a decade [2, 8, 15, 21, 32]. Urban planning in the 21st century is inevitably undergoing changes that might

© Yushkova N. G., 2020

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potentially disrupt the stability of systems [4, 25, 26, 27]. These are significant complications of the object of urban planning activities, multiplicity of scenarios for its development due to the appearance of a large number of subjects with conflicting interests, unpredictability of functioning processes of object and commonly presence of large amounts of information resources characterizing their complexity [8, 10, 16, 19]. These also transform the traditional process of developing urban planning solutions complicating the requirements for their content and, at the same time, increasing dependence on the factors of an unstable external environment. Scientific endeavors in recent years have been aimed at improving the efficiency of the system of urban planning decisions, depending on the promising directions of development of systems of settlements based analyzing the progressive experience of territorial planning [12, 14, 24], system principles of their justification [2, 29, 30], orientation to new values [6, 18, 33], compliance with social needs of the population [1, 3, 31] considering the specifics of the existing organization of the territory [8, 15, 29], changes in the technical parameters of urban planning facilities [1, 26, 28]. However, despite the diversity of scientific approaches, professional assessments of new urban planning phenomena are still far from being comprehensive. On top of that, the problem of increasing the urban planning sustainability of territorial systems is associated identifying potentially possible priorities for their development [7]. On the one hand, their formation involves concepts and strategies for the development of macroregions and constituent entities of the Russian Federation and a set of factors that are critical to the individual characteristics of a particular area on the other [3, 7, 10]. The result of their joint influence is the characteristic dynamics of territorial systems. All of this is indicative of the expediency of developing methods to investigate the processes of changes in territorial systems, to establish their amplitude and to identify their patterns. This would allow one to obtain substantiating materials employed in the development of strategies for the formation of objects of urban planning activity in contact with territorial settlement systems.

1. Local urban formations as “points of growth” of territorial settlement systems. The development of new concepts of urban planning in the second half of the 1950s is associated with the fact that following the Second World War and in subsequent years, socio-economic conditions changed considerably with the demand for the classical principles of territory development is dropping significantly. The theoretical model “work –– life –– rest”, based on the postulates of the “Athenian Charter” since the 1930s, remains a renowned standard for the formation of space in different countries of the world, a universal tool of addressing urban

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planning situations, is repeatedly replicated and implemented in practice. As time goes on, it starts losing its significance in determining the methods of development and use of the territory in urban planning solutions.

The contradictions are intensified due to the shift of emphasis to the processes of commodity production as opposed to industrial production [11]. A fundamentally new social order is in place which is pushing forward the ideas of a post-industrial society [4, 9, 13, 17, 21]. Its content compiles the actual requirements of our time emerging from the nature of market relations: accelerated turnover of goods and services, involvement of an increasing number of consumers, idea of elements of a material-spatial environment (environmental objects) as ways of obtaining a guaranteed profit. It is due to the current changes that a concept of “pola-rized development” emerged which grew to be popular and penetrated various aspects of life. It is known that the concept was first set forth in the early 1950s by F. Perroux [20]. Subsequently, it was developed by his compatriot J. Budville. According to his theory, specialization and uneven distribution of areas of space, “growth points” determined by the intensity of economic activity are substantiated [12, 14, 24]. The ideas underlying the concept of “polarized development” were adopted by urban planning. The concept has become central in the substantiation of promising forms of territorial systems at various levels and has been relevant for several decades.

Market laws neutralize the possibilities of urban planning activities to harmonize the requirements for the organization of the living environment and ensure its maximum comfort for the population. It is becoming less and less environment-forming and more and more oriented towards ensuring the market demand of consumers of its products. The development of the territories of settlements of various ranks is defined as the continuity of the functioning of the market mechanism which produces various market offers that formalize fashion trends to a larger extent than those that form the standards of life support.

This accounts for the intensification of the process of designing urban planning objects that can dramatically change the overall imperfect human environment and thus become an investment product [6]. The appearance of such objects is seen as an opportunity to achieve, if not total, but a quite rapid urban development of individual territories in almost all nations. Contrary to the systematic approach, their planning was preceded by design. With this objective in mind, it was unnecessary to talk about a comprehensive result of their implementation. During these years, their terminological descriptions were not yet obtained, the technological schemes of their functioning were not known, the overall planning process was not structured. However, the development of scientific ideas on the methods for assessing the quality of life of the population using spatial planning tools gave rise to their popularization.

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Reinforcing the position of the so-called “new economy” in Europe and America involved, e.g., the active formation of new sectors of the economy and their interconnections followed by the spread of their influence over the area [15, 27, 34]. These processes have caused the manifestation of urban trends. They were found in the structure and content of the nature of the distribution of productive forces, migration processes, quantitative growth of the urban population, forms of its employment, etc. [15, 27]. Generally, this caused the transformation of territorial systems including by means of the pronounced unevenness of the processes of spatial development (centers of urbanized development and metropolis) [4]. However, there were also recorded individual centers of concentration of activity that did not have prototypes of formation, such as centers of advanced social and economic development [6, 16, 19]. They reinforced the emerging asymmetry of territorial systems. In order to prevent crisis situations, targeted actions in the planning and regulation system were required to ensure the preservation of permissible balances with an active expansion of the range of urban planning tools [31]. Later on, this line of research in the theory of modern urban planning received a special terminological description, i.e., the construction of “new cities” [17, 25].

The specificity of the spatial differentiation of America (division into separate states), presence of large undeveloped territorial areas and, at the same time, absence of restrictions in the form of the existing order of functional zones, hypothetically, contributed to the use of various urban planning solutions for organizing various types of economic activities [9, 17, 27]. When developing options for the location of “new cities”, factors of particular importance were economic feasibility, reducing the time spent on labor movements, stimulating the inflow and free movement of labor resources, proportional ratio of “daytime migrants” (temporary population) and permanent population. All this resulted in the limited functional diversity in the planning organization of the territory of “new cities” and despite special programs for their future formation, it was only partly provided by strategic solutions.

While adapting the concept of “new cities” to the conditions of Europe, some peculiarities are identified. The “new economy” is dependent on the intensification of technology, science and industry, which are actually the source of innovation. This causes an intensification of the economic activity of market entities in the sphere of “tertiary industry” which is characterized by the constantly emerging new types of life promoting the social activity of the population. Accordingly, the “points of growth” of territories should stick with this logic of constant renewal of the material and spatial environment due to new multiple differentiated typological forms. A priori, the contrast of new manifestations with the existing urban planning organiza-

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