folded designs from paper schemes. Folded structures

FOLDED STRUCTURES

folds, - thin-walled structures such as shells, consisting of flat elements (plates) connected to each other at certain angles. S. to. from rectangular plates called. prismatic. In modern construction is the most common S. to. from a monolithic or prefabricated reinforced concrete. (including prestressed structures and reinforced cement structures), applied to a covering prom. and societies. buildings.

Big encyclopedic polytechnic dictionary. 2004 .

See what "FOLDING STRUCTURES" is in other dictionaries:

Folds, thin-walled building structures such as shells (See Shell), consisting of flat elements (plates) connected to each other at certain dihedral angles. S. to. from rectangular plates called ... ...

folded structures- Spatial building structures formed from rigid folds [Terminological dictionary for construction in 12 languages ​​\u200b\u200b(VNIIIS Gosstroy of the USSR)] Topics other building products EN folded plate structuresfolded structures DE ... ... Technical Translator's Handbook

Spatial building structures formed from rigid folds (Bulgarian; Bulgarian) nagnati [nadipleni] structures (Czech; Čeština) lomenicové konstrukce (German; Deutsch) Faltwerk; Wellenschalen (Hungarian… … Construction dictionary

Industrial buildings of industrial enterprises, buildings designed to accommodate industrial production and provide the necessary conditions for the work of people and the operation of technological equipment. How… … Great Soviet Encyclopedia

An extensive field of architecture, the art of building from wood, which has a special specificity, determined by the nature of the material and construction techniques. Due to its availability, strength, lightness, low thermal conductivity, convenience ... ... Great Soviet Encyclopedia

An extensive field of architecture, which has a special specificity, determined by the nature of the material and construction techniques. Wood is an excellent building material due to its strength, lightness, low thermal conductivity, ... ... Art Encyclopedia

Construction dictionary

wooden architecture- a vast field of architecture, the art of building from wood, which has a special specificity, determined by the nature of the material and construction techniques. Due to its availability, strength, lightness, low thermal conductivity, ease of processing ... ... Architectural Dictionary

The Soviet Union occupies almost 1/6 of the inhabited land area of ​​22,403.2 thousand km2. It is located in Europe (approx. 1/4 of the territory of the country is the European part of the CCCP) and Asia (over 3/4 of the Asian part of the CCCP). Hac. 281.7 million people (as of Jan 1, 1987). Capital Moscow. CCCP... Geological Encyclopedia

RSFSR. I. General Information The RSFSR was formed on October 25 (November 7), 1917. It borders in the northwest on Norway and Finland, in the west on Poland, in the southeast on China, the MPR, and the DPRK, as well as on the union republics that are part of to the USSR: to the west with ... ... Great Soviet Encyclopedia

Various spatial systems are used to cover large-span buildings and structures. One of the options for such spatial systems are coatings in the form of folds. A great contribution to the development of the theory of folds was made by G. Ehlers, V.Z. Vlasov, V. Flügge, E. Gruber and X. Kramer. At present, folded coating structures are used relatively rarely, and in the modern scientific and technical literature there is little data on their design and calculation.

A folded coating is a surface formed by a system of inclined flat faces rigidly interconnected. They adjoin one another at a certain angle along the long sides, leaning along the short ones on end diaphragms or ribs that are absolutely rigid in their plane (Fig. 4.1).

The shape of the surface of the folds can be triangular, trapezoidal or rectangular. Most often, multi-row folded coatings are used, but single-row ones are also found. In terms of material consumption, folded structures are inferior to other forms of spatial coverage, but their inherent increased architectural expressiveness and relative ease of manufacture smooth out this drawback. The shape of the plan of structures covered by folds can be rectangular, polygonal and curvilinear. In the latter case, the folds are arranged radially. On fig. 4.2 shows some examples of folded coverings of various configurations.

The warehouse in Apeldoorn (Netherlands) with an area of ​​50x83m has a load-bearing structure of a folded roof made of flat panels adjacent to each other in the form of gable roofs (Fig. 4.3). Individual panels, 8.2m long, consist of block frames sheathed on both sides with plywood sheets. Bending-rigid fastening of individual panels in the valley and ridge is achieved with the help of hinged hinges.
A school hall for meetings and sports in Wellington (UK) with an area of ​​12x14m is covered with a radially arranged folded system. Folding panels consist of block frames covered on both sides with 10mm thick plywood sheets.

Folds can be made of wood, reinforced cement and composite materials. To increase their transverse rigidity, spacers, stiffeners or puffs are installed along the length of the fold. Schemes of folded coverings are shown in fig. 4.4.

The span of folds for structures usually does not exceed 20-25m. The ratio of the lifting boom to the span I for wood folds ranges from 1/2-1/9, for structures made of composite materials - up to 1/15 (1/18).

According to the design, the folds can be thin-walled, ribbed or three-layer. In the first case, the edges of the folds are wooden nail, glued or glued plywood beams. Ribbed folds are made of beam elements with a section height of up to 15 cm, to which sheathing from sheet material or boards is attached with nails or glue on one or both sides. Three-layer elements of folded coatings are most often sheathed from fiberglass or rigid polyvinyl chloride, and the middle layer is made of foam. The edges of the folds are interconnected by bolts, on nails, with the help of adhesive or glue-pin joints (Fig. 4.5).

Installation of folds in most cases is carried out "from wheels". The coating can be assembled both from individual faces and from enlarged elements in the form of trays. Such parts of the structure are loaded onto vehicles and delivered directly from the supplier to the construction site. The edges are installed using compensating traverses (Fig. 4.6).

A folded cover is a system formed from flat elements inclined to the horizon (usually at least 30 °) - faces, the upper and lower edges of which are connected along the long sides and work together. The cross-sectional shape of the folds can be triangular, trapezoidal, polygonal ( fig.3.31).

Fig.3.31 Folded coatings:

a - general form; b, c, d- types of cross sections of reinforced concrete folds;

1 - fold; 2 – onboard element; 3,4 - diaphragm; 5 - Column

The architectural compositions of the folds are very diverse. Flat slabs (panels) in various combinations can cover rectangular, polygonal and circular building plans. In the latter case, the folds are arranged radially.

In terms of material consumption, folded structures are inferior to other forms of coating, but they are characterized by architectural expressiveness and relative ease of manufacture. The advantage of the folds is their regularity, which determines the increased aesthetic qualities that contribute to the use of these systems without a false ceiling. It is advisable to use them as shed coatings for industrial and public buildings.

The folds can rest on the columns or walls of the structure. On the short sides they have end diaphragms or ribs.

Folds are usually made in monolithic reinforced concrete, but recently prefabricated elements have been increasingly used. In monolithic reinforced concrete, folds of a complex shape are usually performed, due to architectural considerations, as well as large-span, with L>30m, B>6m. The requirements for concrete strength and dimensional accuracy may not be as stringent as for precast elements. Concrete grade 300..450, edge thickness not< 5см. Угол наклона граней не >35º to allow them to be concreted without double formwork.

Example: pavilion at the exhibition in Hannover (Germany) Cover area - 350 m², suspended folded cover with a central support made in monolithic concrete, folds with trapezoidal edges made of lightweight concrete grade 300, edge thickness 8.5 cm.

Prefabricated folds are mounted, as a rule, from flat rectangular slabs. The advantages of prefabricated folds include: - the possibility of changing the spans of the folds due to the absence of ribs and reinforcing elements; - the possibility of changing the width of the coating using inserts; - small dimensions of prefabricated elements, convenient for storage and transportation; - the possibility of in-line installation without pre-assembly and scaffolding.

Usually beam folds are used, which have a large length with a small width (L up to 25 m, width - up to 3 m.). With an increase in the span to 30 m and above, their labor intensity and installation cost increase.

There are single-span and multi-span folds, single- and multi-wave folds. Sometimes they are designed with a small cantilever overhang on one or both sides of the coating.

Triangular pleats: are used very widely, the width of individual folds is taken from 2 to 6 m. The height of the fold is taken depending on the static pavement scheme, on the span, fold width and load. For single-span folds, the height is 1/20..1/30 of the span. The slope of all faces is usually assumed to be the same and = 30..35°. at smaller angles of inclination, it is not possible to provide the required structural height of the fold; at large angles, concreting becomes more difficult and the consumption of materials increases.

Trapezoidal folds- have, with the same structural height, a significantly larger moment of inertia than triangular ones. Therefore, they are often used as whole prefabricated elements of coatings, their length is usually 15-20 m, width - 2-3 m. The constructive height of such folds, as a rule, is somewhat less than that of triangular ones.

Other types of folds- performed mainly in monolithic reinforced concrete. Their forms can be very diverse, for example, the covering of the church in Nassau (Germany).

One of the possible design systems is folded shed coating, formed from triangular or trapezoidal folds, in which part of the inclined faces are replaced by continuous glazing.

Architecturally effective folded coverings can be created by folds with alternating triangular faces in various combinations.

Folded systems are used not only in coatings, but also in wall enclosures, allowing you to create structures in a single constructive style.

The geometric shapes of folded structures are different: individual folds can have a triangular and trapezoidal section and have parallel, fan or counter combinations with each other ( fig.3.32). Folds are used in coatings with a span of up to 40 m and in high walls, if it is necessary to increase their rigidity. A combination of folded walls and coverings with rigid interfaces between them in the form of a spatial frame structure has become widespread. Folds are used in arched and tent coverings for rooms with a rectangular, trapezoidal, polygonal or curvilinear plan.

Fig.3.32 Folded structures:

a - shapes and dimensions of sections of monolithic and prefabricated folds; b - layouts of overhead light devices; forms of coatings; in - parallel folds; g - the same, fan; d - the same, oncoming; e - folded frames; examples of fragments of coatings: g - opposite folds; and - a combination of fan and counter folds

Rice. Kursky railway station (student's work)

Rice. Olympic cycle track, Montreal, Canada (student work)

Kursky railway station in Moscow Soviet pavilion at EXPO-70

Customs building on the Russian-Finnish border.

Gym "Druzhba" The building of the Danilovsky market in Moscow

All these structures are united by the folded surface used in their covering. Compared to other spatial structures, folded structures are not common, both in buildings and in the literature. In its pure form, folded structures were common in the 60s - 80s of the XX century. Therefore, most of the literature describing them is about the same time of publication. “A folded structure is a system of spatially interconnected thin (usually flat) plates - faces” - this is the most accurate definition of folds, which is given by Hermann Rühle in the book “Spatial Coverings” in 1973. Structural textbooks are usually limited to general drawings and descriptions of the simplest folded roofs. However, the variety of folds is great. And although many of them at first glance belong to other types of structures, they all share a common principle of operation. And the principle of operation of the folds is simple: it is an increase in the height of the section (h) of the structure in comparison with the thickness of the material used, due to the geometric transformation of its surface, and the dimensions of the faces of the folds in this case are close to optimal, in terms of rigidity.
The expansion force arising in this case has both pluses and minuses. On the one hand, there is a need for a rigid support contour or puffs, on the other hand, the plasticity of the structure gives a high perception of temperature, sedimentary and other internal stresses due to the compliance of the joints.

Folded structures are spatial structures (even simple rectangular folds, as in the previous diagrams) and occupy an independent direction in their classification. However, they are easily combined with all other types. In modern architecture, as a rule, they are presented precisely in combination with other types of structures. They can have various outlines and shapes.

A bit of history:

The first patent for a folded coating was issued in 1937. In the roofing of a polygonal building in terms of plan, a thin-sheet flooring was attached in the form of flat triangular panels located at an angle to the chords to form a folded roof. In the 1940s and 1950s, a number of patents were issued in the United States for frameless folded buildings of arched or vaulted shape, formed from identical arches adjacent directly to each other, made up of tray-shaped elements of trapezoidal, triangular and U-shaped sections. In our country, the first certificate of authorship for folded structures was issued in 1945 for a folded roof made of sheet metal. From 1950 to 1965 in various countries - the USA, Great Britain, Austria, France and Germany - for folded elements and structures assembled from them, received about two dozen patents. In these solutions, folded structures have been further developed. Finally, two main directions were identified, the first of which is the formation of systems from tray-shaped elements; the second - from rhombic or triangular elements. In addition, systems assembled from elements with a complex profiling structure begin to appear, which can be attributed to the third direction - spatial elements of a complex configuration. In the period from 1965 to 1974, more than 30 patents and copyright certificates have already been issued for folded structures. Of the entire set of solutions, the most typical, characterizing the three selected areas and of particular interest, from a constructive point of view, are the following constructions:

By 2000, more than 60 patents and copyright certificates for folded buildings have been identified. The most widespread in our country and abroad are both the tray-like elements themselves and the structures made of them.

One of the simplest and at the same time interesting folds is the vaulted cross fold, unfolded from the plane. Take a sheet of paper and fold it along the dotted lines in one direction, and along the solid lines in the other. Having made all the folds at the same time, we get this fold:

By changing the type of development, you can get different types of folds. This is one of the methods for forming folded surfaces. In addition to it, new folded surfaces can be obtained by profiling the forming sections of surfaces, as well as by arranging simple folded modules.

The material for the folds can be reinforced concrete, reinforced cement and glued wood, but they are most widely used in the form of a profiled metal sheet. Today the professional flooring is applied practically in any construction object. It is also the main direction of development and study of folds as structures. Folds, as the supporting structures of coatings, remained virtually unchanged for a long time after their appearance. And since the 80s, they have practically not been used due to the high cost and complexity of design. However, due to the fact that recently the use of computer design technologies, and especially parametric modeling, allows solving many problems associated with the design, calculation and construction of much more complex structures, folded structures or their elements began to appear in the architecture of modern public buildings. . As, for example, in the alley of the Olympic Stadium in Athens, the "City of Sciences" in Valencia or the station of the AVE railway line in Huelvea, architect Santiago Calatrava:

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Presentation - Paper Plastics

Slide #2
	Exercise. Convert a flat sheet of paper into various folded-cut structures and relief forms (folds, accordions, “logs”, “leaf”, hemisphere). Obtain relief surfaces of various rhythmic solutions. To complete tasks, you must use different rhythms (meter, rhythm simple, complex, decreasing, increasing, etc.).
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	Working with paper requires knowledge of its textural features. Paper bends differently depending on the direction of the fibers. Any structure is based on a structure, which is a system of stiffeners obtained by folding a sheet of paper. In general, the structural and constructive properties of any paper product depend on the nature, number and direction of the stiffeners. When creating complex shapes, one cannot do without curvilinear folds. Some curved line can be obtained with a breadboard knife. A deep incision can turn into an unwanted through cut. To design rigid and clear forms, it is recommended to use thick drawing or drawing paper, which allows you to perform operations such as bending, twisting, cutting, corrugating, etc. Speaking of the paper-plastic tradition, we can note European filigree that arose in Italy at the end of the 13th century . The watermark is a subtle level of shaping that does not destroy the planar characteristics of the sheet. Forming a pattern due to the heterogeneous structure of the sheet, the filigree creates a special microgeometry of the surface, rich tactile qualities and visual effects when the sheet is exposed to light. Thus, the formation of the paper form is due to the functional role of paper, abstract categories, its format found symbolic expression in its geometry and tactile qualities developed as ergonomic indicators of a paper product.
Slide #5
	Paper plastic has its own special logic of form design, which is largely based on traditional methods of folding, cutting, gluing. These quite common principles of transformation make it possible to form fairly clear, concise, geometric shapes, however, perhaps not quite smooth, lively? Akira Yoshizawa, an origami artist, gave paper sculpture a new imagery back in the 1950s, forming origami figures from wet paper, making them more lively and naturalistic. The special picturesqueness and bionicity of paper structures was also captured by the architect Lars Spoybroek. The prototype for his "Son-o-house" (2004) was chaotically thrown ribbons of paper, forming smooth lines and curves. The role of paper in the formation of subject space is growing. Aspects of three-dimensional sound, the unique tactile characteristics of paper are perceived as its valuable qualities not only in the context of the culture of the book, but also wider.
Slide #6
	The first experiments in Europe with paper as an abstract plastic unit, and not as a basis for writing, were carried out among Russian constructivists at the beginning of the 20th century. The philosophical basis for a special understanding of the plane in the pictorial space was prepared by Kazimir Malevich. Vladimir Tatlin in "Counter-reliefs" (1914-1915) takes out planes from the picturesque into the real three-dimensional space. Paper compositions by Alexander Rodchenko "White Sculptures" (1918) are a three-dimensional reading of graphic works, for example, "Dynamic Architectonic Compositions" (1919). The role of geometric elements is played by cut-out flat paper figures turned frontally to the viewer, Rodchenko expresses the line in a paper plane turned to the viewer with its butt. In “Similar Figures” (1920-1921) made of cardboard, Rodchenko is looking for new forms of structural organization of space. Earlier in art, the structure as a principle of interaction of elements in space was not expressed through the transformation of the plane.
Slide number 7
	Volumes
Slide #8
	Doubts may arise: the material is short-lived. Of course, paper is not metal or even gypsum, it has a short life. But paper plastic is designed for educational activities, which means for a certain time period. The main thing here is the process of creativity! And this is facilitated by the availability of materials and tools (cutter, scissors, awl, ruler, compasses, PVA glue, paper). Paper plastic as a kind of creativity does not claim to be a full-fledged art form. The fragility of the material involves the creation of things of a temporary, educational nature, but at the same time, to a large extent, contributes to the activation of creative development.
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	I want to show the work done in the paper-plastic technique. The peculiarity of the execution is crumpled paper, paper is used mainly for a copier, newspaper, as well as corrugated paper, tracing paper from under cookies, sweets, candy wrappers, magazine paper (from glossy magazines), etc. Literally everything can be made from crumpled paper, sculpt , model, make volumetric figures, semi-volumetric panels.
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	Card
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Slide #19
	Quilling is a type of paper plastic that got its name from the English word "guill", which translates as "bird feather". Quilling has a long history: the filigree processing of paper was known to the ancient Egyptians, who used papyrus as the main material, and this art was also known in the Middle East and China. In medieval Europe, nuns created elegant medallions by spinning paper with gilded edges on the tip of a bird's quill. When viewed closely, these miniature masterpieces created the complete illusion that they were made of gold stripes. Since the end of the 19th century, the popularity of quilling has gradually waned, almost to the point of oblivion, only to be revived today in a more modern form, but with charm and sophistication that are not inferior to those of past centuries.
Slide #20
	The very process of creating a picture resembles a designer, which every child at this age likes to collect so much. And what could be more relevant than involving children in the world of beauty, through creative activity that liberates the child. It gives you the opportunity to show your imagination and imagination, brings up an aesthetically competent and psychologically balanced person. Modeling The quilling technique consists in winding and modeling with a small tool called a "coil" of paper strips a few millimeters wide. And with the help of some modeling techniques, which will be presented to you later, you can create a variety of compositions.
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	christmas angel
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	Stage decoration
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	Creativity in motion
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Slide #43
	The regular structure involves the interaction of elements that form a geometric unity. An important quality of the form is its modularity, i.e. uniformity of elements, their versatility in various plastic combinations. These principles formed the basis of experiments in the field of mobile architecture carried out by Russian kinetic artists in the second half of the 20th century. Ornamental folded paper structures are the perfect union of aesthetics and technology. The movement of paper in a fold is carried out according to rather rigid laws of shaping; paper structures have their own special logic of form. This, in many respects, explains the interest in folded structures not only from artists, but also from the widest audience.
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Slide #49
	Paper plastic today is a promising area of ​​design shaping, influencing the development of design culture. Centuries-old experience has been concluded in this area, and, nevertheless, the form-creative potential of paper-plasticity has not been exhausted. The geometry of the paper form has gone from a scroll to a plane, from sheets of paper structured by simple folds in Shinto shrines to advanced combinatorial systems of modern origami, from experimental experiments among Russian constructivists to the intellectual base of formative ideas in art laboratories that form the design culture of design. The geometry of a paper form is a multifaceted cultural phenomenon, the role of which is the translation of worldview attitudes that determine its formal qualities, structure, and function. Exploring the forms of existence of the paper web, one can acquire rich historical and cultural material, as well as predict the role and place of paper in the future.
Slide #50
	Objective. Study of paper-plastic techniques, plastic and decorative possibilities of the material; consolidation of theoretical knowledge on sheet tectonics, the transformation of a plane into a relief using various types of folds, the acquisition of practical skills in working with a flat sheet of paper and creating reliefs of a given shape. Materials and technical means. 6 sheets of thick paper (State sign drawing paper) 10 × 10 cm in size, cutter, ruler, pencil, eraser, compasses. Requirements when working with paper. Apply pencil lines with a finely sharpened pencil of TM-T hardness, observe safety precautions when using special blades for working with paper (if necessary, break the blade along the notch and wrap it in paper and throw it in the trash can)
Slide #51
	http://picasaweb.google.com/bondmary.blog/Mary#5482600191353357442http://rosdesign.com/design/maketofdesign2.htmhttp://sogiuu.oskoluno.ru/area/7/master%20klass%20dop.dochttp: //picasaweb.google.com/bondmary.blog/Mary#5482600191353357442http://rosdesign.com/design/maketofdesign2.htm SOURCE SITES

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FOLDED STRUCTURES. PROSPECTS FOR THE DEVELOPMENT OF NEW FORMS

RUSSIAN UNIVERSITY OF FRIENDSHIP OF PEOPLES n. Krivoshapko, V. Â. The textbook for the reference is the following

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LLC "Prof-Service" tel. (861) e-mail:

* Window sills The window sill is an architectural element for finishing the facade in a classical style, framing the lower part of the window opening. Decorative elements of such a plan allow you to emphasize window openings.

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docplayer.ru

Folded structure - The Big Encyclopedia of Oil and Gas, article, page 1

Folded design

Page 1

Folded structures make it possible to cover large spans (from 20 to 100 m) with economical use of material and often determine the architectural and artistic expressiveness of a structure.

Apparently, folded plastic structures are waiting for a wide range of applications as various fences and storage facilities, given their low cost. However, the problem of joint flexibility, especially in nodal connections of structural elements during its transformation, is complex and requires precise mathematical analysis.

The lower chords of the folded structure are shifted in plan by half a step relative to the upper chords. For spatial distribution of forces, transverse elements are installed in the plane of the upper and lower chords.

An aerosol filter is usually a folded structure made of thick filter cardboard. Filtration of solid and liquid aerosols takes place in the tortuous channels formed in the cardboard when fine fibers of various materials are intertwined during its manufacture. If necessary, activated carbon is impregnated with various chemical additives.

There are three types of static schemes of folded structures: beam, arch and frame. In beam folds, they rest on end beams-diaphragms or walls that transfer pressure to the racks.

And now we will create a simple folded structure from a sheet of paper - we will fold it with an accordion and make a bridge shown in Figure K. Such a bridge calmly holds a filled matchbox on itself, and not even one, but several.

The variety of firms and structural systems (vaults, shells, folded structures, cable-stayed and pneumatic structures) enables the architect not only to express the plasticity and spatial nature of this form in the composition as much as possible, but also to use their technical capabilities.

Creation of folds based on torsos introduces a new variety of folded structures and enables architects and engineers to apply new architectural forms.

The tensile forces arising in the lower part of the funnel in the section in the middle of the span are determined from the calculation of a folded structure consisting of a rectangular plate of the prismatic part and a trapezoidal or triangular funnel plate.

Numerical methods and algorithms for calculating the strength and stiffness of plate-rod systems, three-dimensional solids, thin-walled shell, prismatic and folded structures are presented. All algorithms are implemented in the PL-1 language in the ES computer OS. Software complexes can be included as subsystems in CAD; they have been successfully tested at a number of machine-building enterprises.

The handbook contains numerical methods and standard algorithms for calculating the strength and stiffness of plate-rod systems, three-dimensional solids, thin-walled shelled, prismatic and folded structures. All algorithms are implemented in the algorithmic language PL-1 in OS ES computers.

Pages:      1    2

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Technology of regular folded structures

Folded structures are voluminous regular relief configurations obtained from a plane by bending (folding) it along the lines outlined on the scan.

Structures made of a specific material and having a folded structure are called folded structures.

Advantages of folded aggregates:

• The ability to remove moisture from the internal cavity of the multilayer panel.
• High strength and rigidity.
• High impact resistance.
• Good acoustic performance, both in terms of sound insulation and sound absorption.
• Ability to fabricate structures from a wide range of materials.
• A simple technological scheme for the manufacture of aggregates without additional operations of gluing, cutting and impregnating the aggregate.

Principles of creating various types of folded structures and their classification.

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The basic structure is a flat z-ribbed. By modifying it, it is possible to obtain various forms of folded aggregates with new properties: with a cellular structure, single or double curvature, with curved envelope surfaces and contact areas for gluing with skins, and many other properties.

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Application of structures with folded filler in aircraft fuselage panels and wing elements.

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Folded aggregates of various architectures made of composite materials.

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Basic methods and equipment for the manufacture of folded aggregate from both continuous roll material and sheet material.

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Structural solutions based on folded core to reduce noise levels.

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How to make a hemisphere out of paper?

You can go the simplest way and cut out such a piece of cardboard, then combining it into a single hemisphere:

But there is a more complicated way, after the implementation of which you will get a hemisphere of triangles - they look very impressive.

To do this, you need to cut out 10 triangles on the left and 30 on the right. And bend the sides of the triangles by 1 cm. Make triangles from paper of different colors.

Then glue them like this:

You should get such faces of the sphere (they need to be made from triangles, of which you have more)

Draw it so that you know where to glue the triangles:

Glue blocks of blue triangles with white ones:

And then you start gluing your hemisphere onto a circle:

Gradually attach the remaining triangles:

And here is the geometric beauty that will turn out in the end:

You can make a hemisphere in this way.

Let's find the shape first.

make cuts with scissors

then fill the shape with circles

using a cloth, press the cardboard to the form

leave to dry.

You should get such a hemisphere.

Now various paper crafts are very popular, thus a craving for creativity is realized. And a variety of crafts are made from paper, and especially in the origami style.

There are even such methods of working with paper as paper-plastic and a simpler technique, which is called paper-rolling.

And here you will find an original and step-by-step method in photographs of how to make a do-it-yourself hemisphere.

And here is a diagram for making a hemisphere out of paper.

And here is another popular working scheme in order to make a paper hemisphere with your own hands.

Try to make a hemisphere and you should succeed.

info-4all.ru

Requirements - Architectural Prototyping (1)

rice. 62.63. Come up with a division of a flat surface using straight lines (ornament).

Guidelines: division lines can be vertical, horizontal, oblique, parallel, intersecting. They can form an ornament: ribbon, centric, repeating at certain intervals, or uniform for the entire surface.

The order of the layout: make a drawing; puncture the necessary points on the wrong side of the sheet with a meter; make notches; make through cuts; erase pencil lines; bend along the notch line.

Rice. 62. Layout according to the DIC on the topic "Surface plastics"

Rice. 63. Scan to layout

Practice #2

Dividing the surface with a curvilinear ornament Purpose: to study some methods of revealing the plasticity of the frontal surface.

Tasks: to master the principle of revealing the plasticity of the frontal surface with the help of light and shade gradations. Learn some layout techniques from a smooth sheet of paper.

Requirements: complete the layout of the circular ornament according to the sample. Come up with divisions of the frontal surface using circular or curved lines (ornament). Size 10 × 30 cm (Fig. 64).

Rice. 64. Layout for the defense industry on the topic "Plastic development

surface "When performing these exercises, divisions that require through slots should be avoided. These cuts strongly diverge with a sharp change in the angle of rotation and with an intense, deep relief, holes are formed in the paper, destroying the integrity of the surface.

Applying a rectilinear or curvilinear pattern to the paper surface, bending the paper along these lines, one can obtain relief plasticity of the surface from a flat sheet. The surface can have a different depth of relief, both nuanced light and shade shades, and clear gradations with clear falling shadows, depending on the applied segmentation of the rotations of individual parts of the sheet plane in different directions. Guidelines: incision lines can be vertical, horizontal, parallel, curved. They can alternate, forming a metro-rhythmic pattern, or arranged according to a different, conceived composition.

The order of the layout: make a drawing; make notches; erase pencil lines; bend along the notch line (Fig. 64). Practice #3

Architectonics of a closed form with a folded surface Purpose: to study some techniques for identifying plastics of a closed form with a folded surface (Fig. 65, 66).

Tasks: to master the principle of revealing the plasticity of the frontal surface due to light and shade gradations, as well as to master some paper layout techniques.

Requirements: make an original folded structural surface from A1 format paper according to your drawing and form a closed rigid volumetric shape from it with dimensions of the order

13×13×26 cm.

Rice. 65. Layout according to the OPK on the theme of Fig.66. Development to the layout

"Fold"

Guidelines: division lines can be vertical, horizontal, oblique, parallel, intersecting. They should form an ornament in the metro-rhythmic pattern, the same for the entire surface.

The order of the layout: make a drawing; puncture the necessary points on the wrong side of the sheet with a meter; make notches; erase pencil lines; bend along the notch line. Practical task No. 4

Tectonics. One of the main stress states

material form Purpose: to study some techniques of the stress state of the material (paper), to master the concept of "stiffening ribs".

Tasks: to find an expressive artistic and plastic solution of one of the main stress states of a material form, namely, compression, tension, bending, torsion, shear, impact stresses.

Requirements: from A1 format paper according to your drawing, complete

a layout that meets the requirements of tectonics, with the use of stiffeners without applying gluing of planes (Fig. 67). It is possible to use "paper locks" (Fig. 68.69). The layout size is about 20 × 20 × 20 cm. 67. Paper exercise on the topic "Tectonics"

The order of the exercise: make a drawing using a compass or curved curves; make notches; erase pencil lines; bend along the notch line (Fig. 68).

Rice. 68. Sweep

Fig.69. "Paper Castles"

RELIEFPractical task number 5

Frontal composition of simple geometric elements Purpose: to get acquainted with the basic concepts and principles of building a frontal composition (Fig. 70,71).

Tasks: to master the principle of making a layout from complex patterns.

Requirements: perform a frontal composition in the form of a model-relief on a vertical plane from simple geometric shapes, for the composition use simple geometric shapes embedded into each other, a cube, a prism, a cylinder, a cone, etc. The number of elements is from 5 to 9.

Methodical instructions: the spatial order of the arrangement of figures should be transmitted in the composition and the initial form of each element should be traced. The height of the relief is set by the author.

The order of the layout: tone sketches of the composition are made, then a small (thumbnail) layout, on which the correctness of the compositional idea and the connection of elements is checked, and corrections are made. According to the working layout, patterns of individual elements for the main layout are made.

On this task, the basic skills of performing complex patterns are mastered, involving cutting, joining and gluing individual elements and connecting them not only to each other, but also to the surface of the base. The initial form of each element, the height of the relief is set by the author.

Rice. 70. Layouts for the OPK on the theme "Front Composition"

Rice. 71. Layouts by OPK on the topic

"Front Composition"

ARCHITECTURAL CONSTRUCTIONS From a sheet of paper, you can get not only a three-dimensional, but also a deep-spatial composition. The model of the tunnel, made according to the model (Fig. 72), consists of several flat arches. The dimensions of these arches are successively reduced in height and width; in the same sequence they line up one after another and in depth. Vertically standing arches are connected to each other by horizontal bends-ties of the same size. These connections give the necessary structural rigidity to the entire layout. By changing the size of the bends, you can get different removal of the vertical planes-stages. If you increase the size of the bends, the distance between the planes with openings increases; it turns out the layout of a long, deep tunnel. This technique can be called "telescopic", it is typical for axial, symmetrical compositions. Reducing the size of the arches enhances the perspective contraction, giving the impression of even greater extension. By bringing the planes closer to the openings, simultaneously reducing their size, one can obtain a planar frontal composition with the illusion of depth, which is found in real-life architectural monuments, the so-called "perspective" portals. A perspective portal is an architecturally designed door opening formed in the thickness of the wall by successively narrowing and lowering arches into the building, visually increasing the thickness of the wall and the depth of the openings.

Practice #6

A simple arched structure (tunnel, portal) Purpose: to get acquainted with the concepts of frontal and deep composition in layout.

Objectives: to master layout techniques that convey the spatial depth of the structure.

Requirements: complete the layout of the arched tunnel according to the drawing

(see fig. 72).

Guidelines: by changing the size and depth of openings, you can vary from a tunnel to a perspective portal. You can change the configuration of openings (circular, lancet, triangular, rectangular, complex).

The order of the layout: make a drawing; puncture the necessary points on the wrong side of the sheet with a meter; make notches; make through cuts; erase pencil lines; bend along the notch line (Fig. 73).

Rice. 72. Exercise on the topic "Simple arched structure" 73. Layout sweep

Practical task number 7

Monument of architecture Purpose: to get acquainted with the layout methods of plastic and spatial solutions of the facade of an architectural structure.

Tasks: to get acquainted with the monument of architecture. Master layout techniques that allow you to depict the facade of an architectural structure from a single sheet of paper without tie-ins and gluing.

Requirements: complete a model of a complex architectural structure according to the model (Fig. 74.75). Using the previously acquired skills, make a facade of a real architectural monument from a sheet of paper in the form of a frontal composition. In the layout, it is necessary to convey in a stylized, simplified form the artistic image of a given architectural structure, its volume and plastic solution, the nature of the details.

Rice. 74. Exercise on the topic "Architectural Monument"

Methodical instructions: there are several architectural monuments to choose from. On the presented sample, plastic and facade details are clearly visible due to the display of shadows and tonal gradation of planes depending on the degree of their removal. Fig. 1. 75. Exercise on the topic “Architectural monument” The layout is carried out in compliance with the exact proportions in the scale of the drawing. It is necessary to think over the technical aspects and design details. During this assignment, you will be introduced to

various eras, architectural styles, techniques and plastic means used in architecture.

The order of the layout: select a monument of architecture. To study the structural features of its facade. Stylize the graphic image of the facade, focusing on the main and characteristic details. Convert this image to layout (Fig. 76). It is recommended that you find additional material on the selected monument yourself.

Rice. 76. Sweep

SIMPLE GEOMETRIC BODIESPractical task No. 8

Performing layouts of simple geometric bodies Purpose: to master the primary motor skills of layout.

Tasks: to get acquainted with the basic techniques for making models of three-dimensional forms.

Requirements: make models of a cube (8 × 8 cm), a cylinder (diameter

8 cm, height 16 cm), pyramids (side 8 cm, height 16 cm) according to the proposed samples (Fig. 77).

Rice. 77. Simple geometric bodies and their development

Guidelines: the cube and pyramid shown in the diagram are glued end-to-end with PVA glue so that the joints are of high quality, it is recommended to use thin cardboard, the gluing points of which should be lightly sanded with sandpaper.

The order of the layout: make a drawing. In order for the fold lines on the edges of the cube and pyramid to be even and clear, it is necessary to make a notch on the outside of the cardboard along the fold line. Notching is done at 0.5 thickness of a sheet of cardboard, this should be done easily so as not to cut through the cardboard. Then bend the cardboard along these cuts and glue the joints. Practical task No. 9

Making a layout out of right and wrong

geometric solids Objective: to master the primary motor skills of layout. Familiarize yourself with the concept of "reflex" in layout

Tasks: to get acquainted with the basic initial techniques for making models of three-dimensional forms. To study the principle of glow between volumes.

Requirements: complete layouts of regular and irregular geometric shapes. Arrange them on the plane according to your drawing closely, gaps are not allowed. Achieve glow between volumes (Fig. 78).

Guidelines: the volumes from which the layout is typed can be of the correct shape: pyramids, tetrahedra, or irregular, that is, with displaced vertices. It should be remembered that the angle between the faces should be from

70 to 30 degrees. Otherwise, the glow between the faces disappears. Checking the glow between the volumes is carried out with perpendicular illumination of the layout.

The order of the layout: since the composition consists of many irregularly shaped tetrahedra, you should first draw a drawing of the location of all elements on the plane. Then glue each tetrahedron separately, using notches on the edges on the outside of the mold. It is recommended to glue the elements on the plane from the center of the composition. It is necessary to ensure that the elements in the base adjoin each other tightly, without distances. The presence of a glow between the elements and a favorable impression of the composition as a whole depend on this.

Rice. 78. Layouts of right and wrong

GEOMETRIC OBJECTS

Practice #10

Models of truncated geometric shapes Purpose: to get acquainted with the construction of complex sweeps of geometric bodies.

Tasks: to master the implementation of layouts of geometric shapes that have a truncated shape. (Fig. 79).

Requirements: make models of a truncated prism and a cylinder according to the proposed drawings (Fig. 80.81). Independently build sweeps and make models of a truncated pyramid and cone. Dimensions: cylinder diameter 60 mm, prism side 30 mm, cone diameter

60 mm, pyramid side 40 mm, height of all figures 90 mm.

Guidelines: all cutting planes are located at an angle of 45 °. These tasks are closely related to the drawing and composition exercises, they require knowledge of projection drawing and help to visualize those figures that are found in the examination papers on drawing and composition.

How to make a paper bridge

FOLDED STRUCTURES (folds)- spatial structures of monolithically connected flat slabs. The most widely used in construction practice are reinforced concrete folded structures - spatial coatings, tray bins, water-conducting trays, etc. Folded structures, along with cylindrical shells, can be effectively used to cover significant (more than 20 m) spans. The main advantage of folded structures over cylindrical shells is the relative ease of their manufacture.

Folded coverings consist of thin slabs, side elements and diaphragms. They can be single- and multi-span (if the number of diaphragms is more than two), single- and multi-wave (if several folds are connected by common side elements). The width of the edges of the folded coating is recommended to be taken equal to no more than 3-3.5 m, the wavelength - up to 10-12 m. Folded structures can be erected both in monolithic and in precast concrete. There are examples of folded pavements in precast prestressed concrete.

Static calculation of folds can be carried out according to the momentless and moment theory. The calculation according to the momentless theory (G. Ehlers) is reduced to solving the three-term equations of the force method or the deformation method. The calculation of folded structures according to the moment theory, taking into account transverse moments, is carried out using the equations of the P. L. Pasternak force method or the canonical equations of the mixed method (V. Z. Vlasov).

Lit .: Vlasov V. 3., Thin-walled spatial systems, 2nd ed., M., 1958; Reinforced concrete structures. Specialist. course, ed. P. L. Pasternak. Moscow, 1961. Elers G. Folded reinforced concrete structures. Sat. Art., Kharkov-Kyiv, 1934; Instructions for the design of reinforced concrete thin-walled spatial coatings and ceilings, M., 1961.

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