GOTHIC Vaults. SAGITAL SHAPE AND ITS MEANING

At the beginning of the study of medieval architecture, the importance of the pointed arch was greatly exaggerated and was even considered as the predominant feature of Gothic art. For a long time, a semicircular arch was considered characteristic of Romanesque art, while a broken, pointed arch was considered characteristic of Gothic art.

What we said above about Romanesque vaults, and in particular about Cluny, saves us from the need to again prove that such a distinction has no basis: starting from 1100, Romanesque architects widely used the pointed arch, showing an amazing understanding of the advantages that could be extracted from its weakened thrust.

Gothic architects adopt it from imitation; it seems that for some time they do not even realize its static advantages: they use it along with the semicircular arch; on rice. 165 it is clearly visible what idea guided them in this combination. This drawing depicts in general terms two buildings dating back to the beginning of Gothic art: G - choir in Saint-Germain des Pres; N- choir in Noyon.

Rice. 165

Let's look first at the choir in Noyon (TV). In the lower floor, in the triforium and in the upper floor - everywhere we find a pointed arch along with a semi-circular one; The transition from a semi-circular arch to a pointed arch is explained by the desire to keep the locks of the arches at the same level.

Moreover, on the lower floor the pointed arch is found only in the corner part, where the rounding forces the distance between the supports to be narrowed. In the triforium, the initial span, the widest, is covered with a semicircular arch, while the remaining spans are covered with pointed ones, so that the locks of all arches are on the same level.

In the upper floor, the spans along the straight parts of the plan are covered with semicircular girth arches, and the spans at the curve are lancet. In the choir of the church of Saint-Germain des Prés (drawing G), the pointed form is introduced into the triforium purely for decorative reasons; but in the two main floors, the lower and upper with high windows, the pointed arch appears only at the curve, that is, at the place where the supports come together.

And here the only reason for its appearance is the desire to give the rounded arches a height approaching the arches of the straight part of the plan: the desire to align the locks of the arches, and nothing more. Because of the same desire to establish a single level for the cheek arches and diagonal arches, Romanesque architects introduced pointed form into groin vaults.

When Gothic architects built cross vaults on ribs, their starting point would not be a cheek pointed arch, but a diagonal one, and this arch would be semicircular in shape.

Thus, the semi-circular, rather than pointed, outline is the main one for the Gothic vault; we can say that until the 13th century. the pointed outline is adopted more out of necessity than out of desire: only when the boldness of the plans forces the use of all means to reduce the thrust, the static advantages of the pointed arch begin to play a decisive role.

Let us limit ourselves to these instructions regarding one of the architectural elements, essentially secondary, and move on to vault systems, the choice of which affects the overall economics of the building.

Rib Vault WITH UNCONNECTED FORMWORKS AS THE BASIC IDEA OF THE SYSTEM

The difficulty in constructing Romanesque cross vaults lies solely in the laying of the rib capstones connecting the parts of the vault: the slightest mistake deprives these ribs of stability.

This difficulty would disappear if the ribs of the vault were supported by diagonally placed arches, which would form under the ribs something like permanent circles of stone. Then the correctness of the ligation of the seams would matter little, even the ligation itself could be completely absent, and the execution of the vault would be equally simple, regardless of the irregularities of the plan on which it is being built.

The chain leading from the Romanesque vault to the Gothic is this: Gothic architecture discards all concerns about masonry, adding to the Romanesque vault a rib under each of its edges; Gothic vault - the same cross vault, the formwork of which is independent and supported by ribs.

Construction method. - Rice. 166 gives an idea of ​​the usual methods of constructing a Gothic vault: the ribs are laid out of cut stone, the formwork is made of small stones, and the backfill, raised to the level of the vault sinuses, does not allow deformation of the thin formwork.

Gothic ribs resemble the brick frame of Roman cruciform vaults. But the meaning of both is far from the same. Among the Romans, the frame plays only a temporary role: it is designed to absorb part of the load falling on the circles; upon completion of the work, it remains included in the mass of the vault, and the vault functions as a monolithic structure.

Gothic architects give the ribs an essential and permanent role - it is on them that the vault rests; Instead of introducing ribs into the thickness of the massif, they are taken out, and the massif itself is replaced with light, non-rigid formwork, almost unconnected with each other. The ancient vault was an inert monolith, the Gothic vault was a connection of non-rigid formwork on a ribbed skeleton.

Efforts arising in Gothic vaults.- At one glance at rice. 166 the nature of the forces arising in the arch is clarified. The ribs, laid out with larger masonry than the vault strippings, give less shrinkage and form in the mass of the vault a kind of frame, which takes on most of the load, causing compression forces in it, distributed along the ribs and taking a vertical direction.

The main efforts are concentrated in the ribs; their direction, at least theoretically, is quite definite. Then follow relatively minor forces, the influence of which, however, should be noted: the formworks located on the outer sloping surface of the ribs have some tendency to slide in the direction of the arrow ( rice. 166).

Consequences of using a rib vault.- The properties of the new code that we have considered allow us to now evaluate the significance of this innovation. Thanks to the ribs, the main thrust is strictly localized. There are no distributed forces that obscure the issue of the location of the support pillars. Therefore, counteraction is sufficient in those places where the thrust acts.

By skillful placement of the ribs the architect can direct the thrust to those points of resistance at his disposal; the entire balancing system is in his hands. The ribbed vault not only allows the expansion of the expansion, which could not be achieved by any tricks in conventional masonry, but it makes it possible to even reduce this expansion.

A cross vault is inevitably heavy, because the rib stones form a sufficient connection to the masonry only if they are of a certain thickness, and this circumstance entails a significant thickness of the entire vault.

We do not encounter any of this in the case when the vault is erected on ribs. The vault, the formwork of which becomes only filling, acquires extreme lightness; along with a decrease in gravity, the thrust also decreases, therefore the support elements may be less powerful.

Finally, the entire structure loses the rigidity that inextricably accompanied the cross vault: in the event of subsidence, there is no longer any reason to fear irreparable cracks in the masonry, all parts of which are interconnected. The rib vault, so to speak, is flexible and changeable: the support points can settle, the abutments can deviate, and the rib vault will follow these movements.

So, no matter what point of view one takes, the use of a ribbed vault provides a significant simplification and additional guarantees: it is the starting point of all techniques that ensure balancing - techniques that made it possible to realize the most daring attempts of Gothic art. If it were necessary to indicate a distinctive feature of the architecture that replaced Romanesque art, then such a feature would not be a pointed outline, but a rib vault. Gothic art is characterized not by the use of one or another outline of the arch, but by the very idea of ​​​​an original design that distinguishes its active frame from the mass of the arch.

EXECUTION DETAILS: PROFILING, MASONRY, CIRCLES
Profiling.- The method of profiling the Gothic vault is the same as for the Cluny cross vaults. The diagonal arch, which in the Middle Ages was called “augive” *, is almost always semicircular; As for the cheek arches (doubleaux, tormerets), they are given a pointed shape to make their height approximately equal to the height of the diagonal arch.

Note: Augive - literally translated, taking into account the Latin root of the name, means auxiliary, supporting the arch of the section. The term pointed architecture, proposed for Gothic by some French experts, did not survive.

This is explained at rice. 167. Let ABCD be the rectangle that needs to be covered with a vault; the diagonal arch of the “ogive”, running along the diagonal AC, will be a semicircle AS "C; the cheek arches will be pointed, like AE"B. Now all that remains is to divide the parts of the filling into sectors.

Let's look at the ASE stripping. The diagonal semi-arch AS" and the cheek semi-arch AE" are divided into the same number of equal parts.

Let m, m ",..., u, u "... be horizontal projections of the separation points: straight lines m u, m " u "... are projections onto the plan of masonry joints; in vertical projection, these lines of masonry seams will be slightly curved, so that each sector forms a small, very flat arch, spanned between the diagonal and cheek arches.

This is normal profiling. As an exception, we cite several rarely encountered vaults in which the diagonal arch is not strictly semicircular. In the early period of Gothic art, we find in the vaults of Morianval a lowered diagonal arch, oval in shape. In the 13th century, in the cathedrals of Chartres * and Reims, the diagonal arches were elevated and oval in shape.

Note:Chartres Cathedral emerged in its Gothic form after a fire in 1191, which almost destroyed the Romanesque church built 60 years earlier. In 1220 the covering of the vaults was completed, and in 1260 the cathedral was consecrated. It is 130 m long, the width of the transept is 61 m, the height is 36.55 m, the left tower reaches a height of 115 m. The sculpture of Chartres is extremely important for its contrasts with the earlier semi-Romanesque sculpture of the 12th century. and with developed Gothic sculpture of the 13th century. See Melet R., La cathedrale de Chartres, Paris 1909.

Details of the masonry: the support part is wedge-shaped and the support part is in the form of a “pillow”.- In the earliest Gothic vaults, the ribs from top to bottom are lined with wedge-shaped stones and are independent of one another until the very bottom ( rice. 168, A).

To install a bundle of such independent ribs, you need a fairly wide supporting surface, a relatively massive supporting abutment. Often, in order to compress this bundle, the ribs seemed to be intertwined, thinning them towards the base; but these were only attempts to get out of the difficulty.

The solution to this difficult problem was found only in the 13th century. and lies in the fact that the lower rows of the masonry bundle of ribs are laid out in the form of a “pillow,” that is, horizontal rows of solid stones.

On rice. 168 Both successive methods of laying the supporting part of the vault are compared:
In drawing A, the ribs, starting from the very base, are independent of the supporting abutment, in which recesses are made for their installation. Instead of resting the already branched bundle of ribs on the ledges made in the abutment, the abutment itself was widened upward (Fig. B); the ribs branch only at the moment when the widening of the abutment is already large enough to serve as a foundation for them. In this way, not only is excavation in the abutment avoided, but the wedge part of the rib masonry, which causes expansion, is reduced by the height of the cushion: in reality, the support column rises, widening to level N, and only at this level does that part of the structure begin that is kept in balance corresponding play of forces.

The pillows along their entire height are like an interlacing of ribs; According to the original drawing reproduced by Willis *, the profile of the pillow is as follows:

Note: To the works of the English scientist architect Willis, quoted in the notes to Chapter Three, it should be added here: Willis R., The architectural History of Cambridge, 1886.

They are content to mark the upper and lower surfaces of the block according to the dimensions of the ribs ( rice. 169, M); the contour thus obtained on the surface limits the mass of stone that must be left; everything that protrudes beyond the lines is cut away.

If we think theoretically, this technique gives only approximate results: applying the same profile along the width to the horizontal planes of section a, b, c, we obtain a rib (N), the section of which is deformed (detail X).

It is not difficult to avoid this error, but in most cases the masons were satisfied with the approximate drawing obtained using this simplified method.

Supporting parts of ribs in the form of a cushion, as we have already said, are found only since the 13th century. In the nave Notre Dame Cathedral, completed around 1220, we do not yet find these support pillows. In the Soissons Cathedral, which was founded around the time that Notre Dame Cathedral was being completed, all the supporting parts of the ribs are already laid out in the form of pillows.

Note: The cathedral in Soissons was founded around 1180. The nave and choir were built around 1200; in 1212 it was already possible to perform services. Wed. Le fevre - Montalis, Architecture religieuse dans l "ancien diocese de Soissons". 1894.

Circular method.- Gothic vaults, the formworks of which are curved in different directions, would seem to force the use of quite complex system circled; in fact, the latter were extremely simple.

The experience of restorers of French Gothic monuments has shown that in cases where the spans of the vaults are not particularly large, you can get by with one circle truss under each rib and draw out the filling sectors using only sliding small circles, as shown in drawing C ( rice. 170).

Was this ingenious method used in the Middle Ages? We do not have any indisputable data. In many vaults, including the vaults of the cellars in Provins, imprints of the formwork on which their fillings were laid out have been preserved. Often the span of the sectors seems too significant, and their boom is too small in order to be able to get by with sliding circles alone.

Finally, there are vaults whose ribs are not located in the same vertical plane and which, therefore, could not be made on simple wooden trusses.

As an example, we provide rice. 170, V plan of the ribs of the circular galleries of the Cathedral in Bourges *. Here, obviously, a wide, level flooring was needed as a circle, a kind of temporary scaffolding on which the wedge-shaped stones of the vault were laid.

Note: The city cathedral of Bourges began construction around 1175 and was consecrated in 1324. The length of the plan is 118 m, width 50 m, height inside 38 m. The cathedral does not have a transept, otherwise it is closest to Notre Dame Cathedral. See Boinet, La cathedrale de Bourges, Paris 1911.

If small circles were used to lay out formwork, then they were placed precisely on such temporary scaffolding, and not on inconvenient ribs; it is more likely that they used continuous formwork, and this formwork was arranged quite simply, as indicated in drawing A.

Rice. 171 explains the designs of circles adopted for the most ordinary vaults of Gothic cathedrals: each rib S is sandwiched between two ribs of wooden trusses, being their integral part; From one farm to another there is a flooring of the required shape, on which rubble filling stones are laid.

Auguste Choisy. History of architecture. Auguste Choisy. Histoire De L'Architecture

General properties of stone vaulted structures

Vaults are usually called arched spacer structures of a solid section, the length of which in the direction perpendicular to the axis is commensurate with the span. Arches represent a special case of a vault, its flat model. Each type of vault can be represented as a system of elementary arches or semi-arches that form the shape of the vault and carry their part of the load.

Uniform distribution of the load along the cylindrical part of the arch provides each of its elementary arches with the same operating mode, i.e. similar stresses and deformations, so the influence of adjacent areas does not appear. Concentrated load, deforming this area, includes neighboring strips in joint work, and the width of the “connection” depends on the thickness of the arch, the method of laying and the strength of the mortar. The combination of several types of load causes complex deformation of spacer systems, in which it is difficult to identify the share of each type, including the predominant one, since asymmetrical deflections are often summed up.

Calculation of any type of arch includes:

• selection of the optimal working scheme, i.e. such a system of main and secondary arched elements that would be most consistent with the nature of the distribution of efforts and the actual significance of each element;
• determination of dimensions of design elements;
• load collection and sharing;
• determination of reactions R, thrust N and internal forces - moment M and normal force N of design elements;
• checking their load-bearing capacity by the magnitude of compressive stresses in the masonry.

The actual calculation of a stone arch, symbolizing an independent structure, a separate deformation block or a characteristic part of the vault, can be reduced to checking the load-bearing capacity of its compressed zone.

The shape of an arch or vault, in which any section, under the influence of a load, operates in the most rational mode for masonry, i.e. symmetrically compressed, the most rational and meets the condition: Mx = Hfx, i.e. momentless curve. In practice, most of the vaults built according to various reasons, and also for purely aesthetic reasons are not absolutely rational, their sections are compressed asymmetrically.

The stretched part of the section does not participate in the work, although in the presence of an elastic solution it is capable of maintaining tensile stresses of up to 0.15 MPa. The stretched part of the section can be located on the inner or outer surface of the arch in accordance with the nature of the deformation. With a central load on the arch, tension is usually observed in the central third of the span on the lower surface and in the lateral thirds on the upper surface. The depth of the tensioned part of the section increases with deformation of the arch in proportion to the decrease in the height of the working compressed zone.

Height of the compressed section zone- the main indicator of the stability of an arched structure made of brick or stone. For any eccentrically compressed section of a vault, the height of the compressed zone is approximately equal to twice the distance from the point of application of the normal force N to the nearest edge of the section, i.e. hc = (h/2 - e)2, where hc is high

compressed zone cell; h = total section height; e = M/N—eccentricity of the application of normal force relative to the center of the section.

About the work of individual vaults

Working diagram of a simple cylindrical (box) vault represents a system of independent parallel arches (Fig. 121, A).

121. Working diagrams of vaults
L - cylindrical vault with stepwise distributed load;
B—cylindrical vault with stripping;
B - cylindrical vault with concentrated load;
G—cross vault;
D, E - closed vault with central load;
1 - elementary arches;
2 - conditional diagonal edge;
3 - thrust diagram

If the load along the arch does not change, then its load-bearing capacity and deformations can be judged by the work of one elementary arch, which thus serves as the working diagram of the arch. If the load along the arch changes in steps or there are local transverse thickenings of the arch in the form of edges and girth arches, then each load step or section corresponds to its own elementary arch, symbolizing a separate deformation block.

In the presence of formwork (see Fig. 120, B), the thrust and pressure of the arches resting on them are transferred to the arch support along the ribs of the formwork, compressed like the ribs of a cross vault. Part of the thrust can be transmitted directly along the axis of the formwork if its constituents are tangent to the axis of the arches. The working diagram of a cylindrical vault with formwork can be represented either as a system of arches branching around the formwork (then the load collection strip on the arch is equal to the step of formwork or piers), or as a system of ordinary elementary arches abutting conventional arched elements that outline the formwork. In practice, the outline of the outlining “arches” is determined by the quality of the bonding of the tray masonry and formwork, the presence of fills, cracks, etc. Poor dressing and weak mortar require very sharp bending of the formwork. The same applies to any other, not specifically contoured, hole in the vault. In any case, the forces and stresses in the masonry are concentrated around the formwork, increasing as they approach the arch support in the piers. Strippings with backfilling between them significantly reduce the deformability of the arched contour of the vault, dividing it into “active” - span and fixed parts. Analysis of the deformations of the vaults reveals a fairly clear boundary between these parts, passing in the zone of inclination of the radial seams of 30-40°.

Strippings are also used in cylindrical vaults as a means of local unloading of load-bearing walls and transferring pressure to adjacent areas when constructing all kinds of openings. The regular arrangement of formworks sometimes allows the pressure and thrust of the arch to be transferred to individual columnar supports. In general, concentrated transmission of support reactions is characteristic of cross vaults, representing a combination of four formworks.

The working model of the cross vault is a system of elementary arches that form formwork and transmit pressure and thrust to the diagonal ribs. There are vaults, for example Gothic, where the diagonals, as the main load-bearing elements, are made of a material stronger than the formwork, have a constant cross-section and are highlighted on the surface of the vault in the form of ribs. For the vast majority of cross vaults, the ribs serve as stiffening elements only due to the natural thickening of the masonry when connecting adjacent formwork. The cross-section and width of such “natural” ribs are variable and can be determined by the nature of the prevailing deformations of the masonry, which simultaneously participates in the work of the diagonal and formwork arches.

The diagonal experiences an uneven vertical pressure increasing towards the heels, corresponding to the support reactions of the elementary arches of the formwork, and a horizontal load from their thrusts, directed towards the corners of the arch, i.e. stretching diagonal. The combined effect of these two types of load creates uneven compression of the sections of the diagonal rib - large in the support section and very small in the lock. Weak compression of the locking sections of the diagonals and, accordingly, the entire central zone is a characteristic feature of cross vaults, as a result of which they are unable to bear concentrated central loads.

Closed vault In general, it is a combination of two pairs of cylindrical or steamed trays. The working design of a closed vault can be considered as a system of elementary semi-arches that form trays and transmit thrust to the conditional diagonal ribs, and, if there is a central light drum, to its support ring. Using the lower support (fifth), elementary semi-arches transmit thrust and load pressure to the supporting contour of the arch. The diagonal ribs of closed vaults are formed as form elements when connecting (closing) trays and are not the main load-bearing elements. The main working elements are the central tray semi-arches (short span for vaults elongated in plan) and the lower support contour.

Calculation shows that from any type of load support reactions elementary semi-arches increase from the corners to the middle. For vaults loaded only with distributed loads, the pressure diagram of the tray has the form of a simple or convex triangle, and the thrust diagram has the form of a parabolic (concave to varying degrees) triangle - in accordance with the lifting of the vault and the type of load. The total pressure and expansion of the tray are numerically equal to the areas of the corresponding diagrams. From their analysis it follows that the middle third of the tray accounts for approximately 2/3 of the total pressure and thrust, and the corner thirds practically do not work.

The large compression of the central zone, equal to the total expansion of all trays, allows the closed vault to bear a heavy central load (which further increases this compression). Thanks to this property, a closed vault was used to cover most pillarless churches of the 17th-18th centuries. The concentrated thrust created by the heavy light drum and the termination structure was dampened by the thickness and closed reinforcement of the load-bearing walls, as well as two (four) pairs of cross-air braces, which were placed in the area of ​​greatest deformation of the trays. Trays of large vaults were laid out in groups. Relative equalization of pressure and thrust between the middle third and the corner parts of the support contour was achieved by various methods - opening the trays, introducing corner wedge inserts, arranging unloading holes along the axis of the trays, and laying in a herringbone pattern. With a five-headed completion, the mass of corner drums served as a pressure equalizing factor.

Cross vault can be presented either as a system of two pairs of main intersecting arches carrying a heavy central load, and four diagonal semi-arches collecting the load from the corner parts of the vault, or as a system of semi-arches of a closed vault with central formwork cutting the trays to the level of the “mirror” or drum support ring . The second diagram is more indicative of the case when the central arches are not highlighted technologically, for example, by thickening or a seam. The width of the implicit main arches in this case can be determined by the nature of the load and other design features that highlight the central deformation block. In practice, it is approximately equal to twice the distance from the edge of the central opening to the embedment in the air connection tray. The second scheme can be used for a closed vault with strippings, hatches and other openings that relieve the central zones of the trays and the supporting contour.

Constructive basis cross-domed structures is a three- or five-span arch-post system (Fig. 122).

122. Working diagram of the cross-dome system
A - section;
B - plan;
B, D—plans of ancient churches with additional external rigidity;
N—flat thrust of the system in longitudinal or transverse direction;
G—centre of gravity of the internal stiffening diaphragm;
O - center of rotation;
Ne,c - forces in air and wall connections;
R - reactions to counteract the expansion of internal and external diaphragms

The supporting arches, resting on the outer walls and central pillars, serve as the basis for the cylindrical vaults of the plan cross and the corner drums; the central light drum rests on the central supporting arches. Arches divide the vaulted floor system into modules in plan, creating larger or smaller counter thrusts. When folded, they create a total thrust of the system, acting in the plane of the arches in the longitudinal and transverse directions or in the diagonal plane and perceived mainly by the mass of the masonry of internal and external rigid elements. The main internal rigidities are “cross” structures - central pillars, parts of walls, arched lintels and choir ceilings, combined into diaphragms, as well as spatial corner modules. Additional internal rigidities of the early churches were the thickening of the western wall, hiding the staircase to the choir (Church of St. George in Staraya Ladoga), or filling the space between the dome pillars (like Sophia of Constantinople).

External rigidities, in addition to apses, could be staircase towers on the western corners of the volume (St. George and Sophia Cathedrals in Novgorod), chapels, galleries and high porches against the wings of the cross (Church of the Archangel Michael in Smolensk).

The distribution of the total thrust between the rigid elements occurs in proportion to their comparative rigidity at any stage of the system’s operation. The stability of the system is ensured if the overturning action of the thrust Hc applied to its stiffening element at a height hc is less than the holding reaction of its own weight and the load of this element applied with the corresponding shoulders relative to the point (axis) of overturning. Otherwise, if there is an excess of thrust, the balance of the system must be maintained by the work of a closed braced frame and tie rods installed at the level of the heels of the girth arches.

The most loaded parts of the system's ceiling structure are the girth arches and sails that carry the central light drum. It should be noted that the functions of arches and sails, with a constant total load, can change significantly during the “life” of the monument. During the construction period, the girth arches act as lintels, bearing the full weight of the drum and sails. As the masonry solution hardens, the sails, resting against the drum support ring, begin to work independently, transferring their part of the load and thrust to the pillars and then to the stiffening elements. The distribution of the load between the arches and the sails depends on the span of the module being covered, the system and quality of the laying of the sails, the thickness of the arches, the presence of air connections, and finally, on the nature of the general deformation of the monument. Sometimes the load on the girth arch can be assigned “in fact,” like the weight of a drum masonry block limited by shrinkage or other cracks. Sails with small drum diameters have little overhang. The load on the sails is transferred in this way almost over the entire area, which allows for simple laying of the sails in horizontal overhanging rows.

With sufficient adhesion of the solution, the sails can work both as “brackets” and as spacer structures that perceive the thrust force at an angle to the plane of the seams. With increasing spans, the functions of such false sails as cantilever or spacer elements decrease sharply. A one and a half meter false sail, for example, corresponding to a seven meter span of arches, is theoretically no longer capable of bearing the weight of “its” sector of the drum, much less helping the girth arches during their deformation. The unreliability of the drum support may have become one of the reasons for limiting its diameter and the span of the girth arches.

Operation of air links. The air connections of arched structures, located at different levels relative to the heels, may have different functions and generate internal forces in the arches in different ways.

Drawstrings at heels arches and vaults can perceive:

full expansion, if the supporting structures are capable of carrying only a vertical load (racks of open pavilions and galleries covered with cylindrical vaults on strippings and girth arches or cross vaults);

“excess thrust”, not perceived by supporting structures due to their insufficient stability (some cross-domed churches and other arched-post systems with significant vault spans and moderate thicknesses of load-bearing walls and pillars).

Tightenings at the level of the heels can also be installed structurally in structures where the thrust is reliably damped by the joint work of vertical and horizontal stiffening elements. With the normal, calm statics of most cross-dome structures, the role of air connections in ensuring their balance is not decisive. The flexibility of anchors, temperature deformations of metal during frosts and fires, corrosion of ties and cotter pins - all this does not allow us to consider air connections as a long-term and equally strong link in ancient spacer structures, much less to make the very possibility of the existence of monuments dependent on their presence.

Aerial connections actively work as arched ties during the construction of a building and during the entire period of hardening of the solution. At this stage, the walls, pillars and diaphragms do not yet create a stable contour for the arches and vaults, and the thrust of the girth arches, bearing the full weight of the unhardened masonry of the vaults and light drums, far exceeds the value of the actual thrust from the actual long-term load. In the future, as calculations and control measurements show, the function of air connections as tightening cross-dome and other spacer systems can be very moderate.

But in the event of deformation of the volume, the connections can prevent horizontal displacements of the heels of vaults and arches. The connections come into play when the load on the arches increases, as well as when the general scheme building. The subsidence of supports (for example, more loaded central pillars), causing a noticeable (up to 10-15 cm) inclination of the connections, in principle, does not affect the tightening forces.

The square plan is the main one for the cross vault. The pure form of this vault, of four equal forms with two mutually perpendicular axes, dictates the square shape of the plan. On the contrary, a barrel vault on a square plan produces an unpleasant impression due to the contradiction between its one longitudinal axis and the two axes of the plan. The cross vault on a rectangular plan is also not good; with horizontal shells, the strippings in this case have different shapes, with an elliptical curve along the long side of the plan. The cross vault on a rectangular plan loses its spatial integrity.
The formwork of the cross vault is directed from the center of the plan outward, towards its perimeter. Without resting on the steps, but only touching them, the formworks do not enclose the space, but divide it into four directions. Under these conditions, blank closing walls would contradict the spatial image of the vault; therefore, it is more expedient to fill the tympanums of the formworks of the cross vault not with blank walls, but with glazed surfaces that do not enclose the space. We find such a technique in the middle nave of the Basilica of Maxentius and Constantine (Fig. 180).
If the cylindrical vault rests everywhere on the walls, forming a single whole with them, then the cross vault, resting on the corner columns, denies the walls and can exist without them. It is of little use for confined spaces and is rarely found in indoor

halls of buildings both from the Renaissance and later. Its form seemed to be created for open spaces, and it was readily used by the best architects for loggias (Loggia dei Lanzi in Florence) and external arcades (Brunellesco Orphanage). Predominant in the lavish coverings of the basilicas and baths of Rome, the cross vault gave way to the sail vault in the architecture of Byzantium and again gained dominant importance in the architecture of Western feudalism in the 11th-14th centuries. The Renaissance found its true place in the architecture of outdoor open structures.
In the interior halls of Roman basilicas and baths, the diagonal ribs of the cross vault are associated with the capitals of the columns (although there is an insertion of a piece of entablature), but the columns do not support the vault and were added after its construction (Fig. 181). The pressure curve of the vault passes through the thickness of the massive walls much higher than the fictitious support - the capital of the colony. The builders of the basilica knew this, creating special buttresses on top of the roof to accommodate the thrust and installing columns of expensive marble after the construction of the building, during its finishing (Fig. 181).
In visual perception, the columns seem to carry the vault, and thus the requirements of tectonics are met, but in reality the columns do not serve as support for the vault.
For the Romans, the art of engineering was in the service of architecture, but it did not switch to a higher level of approach to the synthesis of technology and art1. The Renaissance, using a cross vault in loggias and external open arcades, correctly used its basic, fundamental architectural properties. In the absence of walls, the diagonal ribs of the vault clearly rest on the corner columns, which are their only supports. Without making false attached columns and without masking the buttresses that absorbed the thrust, Renaissance architects openly used open metal braces.
Thus, we have two compositional systems: the antique system of cross vaults in the enfilade of the baths, giving the aesthetic impression of a light floating covering, independent of the walls, but structurally false, and a true architecturally complete system of the Renaissance.
The first of these two systems, the ancient one, was called by Sedlmayr the canopy system. One can agree with this name, but it must be pointed out that the covering of an open structure in the form of a rotunda, canopy (canopy), arcade, etc., where there are no walls at all and decorative columns, but there are only really loaded columns - such a covering should be called true canopies. Vaulted coverings in which, by means of attached columns, only the impression of free, unloaded walls are created, should be called a false canopy.
In all architectural styles one can trace this technique of spatial composition - this canopy system, but only in others various options and interpretations. The geometric shape and design of the canopy system can be very diverse. For its spatial construction, the forms of a cross sail vault, a sail-closed vault, a fan vault, and a dome can be used.
1 How this takes place in the church of St. Sophia in Constantinople, founded by Anthemius of Tralessi.
In Fig. 182 shows possible solutions for the canopy system.
Fig. 1 gives the basic canopy system, with the cross vaults of the Roman baths.
Fig. 2 shows a possible option in the form of a mirror vault on columns. The mirror vault of the Renaissance was used mainly in enclosed spaces, on walls; examples of mirrored vaulting on columns are very rare. In Fig. 164 shows a mirror vault on columns in the Munich Schack art gallery, in fig. 176-mirror ceiling of the old town hall in Paris.
Fig. 3 gives the third form of canopy, from sail-closed vaults. This form is extremely rare. As an example, we will name the Gothic vault in the French Chapel of the Holy Spirit (St. Esprit) in the city of Rue (Fig. 273).
Fig. 4 shows a canopy system of sailed spherical vaults. Along with the system of cross vaults, it is the most valuable in an architectural sense. Ancient Rome did not use this system. Byzantium in the Justinian era produced already completed canopy systems: the side galleries of St. Sophia in Constantinople form enfilades of freely floating spherical canopies on columns. During the Renaissance, there are isolated cases of the use of a sail vault - in the Pazzi Chapel, in the portal of the Uffizi Palace in Florence (architect Vasari), in the Palazzo Doria in Genoa (1564), in the Lateran Palace in Rome (1588) etc. - however, this era did not leave us with architecturally completed canopy systems. In later eras, the systems of canopies made of sail vaults are especially interesting in two buildings of French art of the 18th-19th centuries: in the Church of the Madeleine in Paris, built by Vignon (1762-1828), the canopy system consists of three sail vaults resting on attached columns (Fig. 371); in the Parisian Pantheon, built by Soufflot (1709-1780), four separate sailing canopies of a cruciform plan rest on free-standing columns (Fig. 370).
Fig. 5 depicts a fan-vaulted canopy. Examples of such canopies, amazing in their lightness and boldness, are known in England in the 14th and 15th centuries. The best of them are in the chapel of Henry VII.
Fig. 6 gives Viollet le Duc's diagram with conical funnels.
These examples show the variety of compositional and design solutions for canopies. We will return to this problem in future chapters.
Now, after we have noted the general architectural and compositional features of the cross vault, the main forms, its place in the overall composition of the structure and its interpretation in different eras, we will move on to a detailed study of possible geometric forms.

II. FORMS OF THE CROSS Vault

The basic, strictly geometric form of Roman cross vaults underwent significant changes in the process of technical and decorative (style) development. Some changes affected the main guide curves of the arch of both formwork and diagonal ribs, others relate to the shape of the surface of the formworks themselves.
Already Byzantine masters increased the diagonal curve and simplified the shape of its curve. Instead of a low elliptic curve, a diagonal edge is drawn with one radius from the lowered center C (Fig. 183). The height of the vault is greater than with simple cylindrical formworks (equal to half the side of the base plus a certain value h, less than the half-dialogue). The shells of the formworks are raised (raised), their surface changes from cylindrical to spheroidal. A section of the arch of spheroidal formworks with horizontal planes gives a four-lobed outline (Fig. 183).
From this example it is clear how a change in the formative curves of the arch entails a change in the shape of the formwork due to the close connection between these elements. In addition to curves and formwork, the angle of the diagonal edge is also subject to change: at the support it is 90°, as it rises along the edge to the shelyga it increases and disappears at the apex (180°); with a raised curve, the flattening of the angle to the shelyga occurs faster. This softening of the angle was used by Renaissance architects for decorative purposes - to obtain a large smooth surface (plafond) in the shelyga.

The greatest variety of cross vault forms is undoubtedly Gothic, for which this type of vault is the main one. The change in the shape of the Gothic cross vault was paralleled by changes in the curves and arrangement of the ribs, creating complex decorative patterns. Medieval architects extracted artistic effects from the structural frame of the vault, while simultaneously improving its technical side, masonry methods and selection of materials. Due to the very complex interweaving of all these structural and compositional factors and the dependence of the forms of cross Gothic vaults on the decorative pattern of the frame, the study of these forms must be postponed until the end of this chapter. Now we will analyze the main geo-
In Fig. 184 shows four types of surfaces: FIG. 1-cylindrical, fig. 2 - barrelhouse, fig. 3 - conical, fig. 4 - ellipsoidal.
The first type has ADO formworks in the form of cylindrical surfaces inclined at an angle a, and the formwork shells - straight DO - are also inclined at an angle a. To construct a line of diagonal ribs in the vertical projection of the arch, we divide the main formwork curve AB into nine parts. Let us draw generating cylinders on the horizontal and vertical projection from division points 1, 2, 3 and 4. Points 1", 2", 3" and 4" of the diagonal edge are obtained on the vertical projection as the intersection of the generating cylinders. The AO curve of the arch rib represents, like a section of a cylinder by a plane, an elliptic curve, just like the BO curve, starting from support B. Both diagonal curves AO and BO intersect in the vault shell at a certain angle. In view of this, climbing along straight inclined shelves does not provide a flat surface at the top, convenient for a picturesque ceiling. This served as an obstacle to the use of such a vault in the Renaissance, but it is found in Gothic.
In fig. Figure 2 shows a cross arch vaulted along the DO curve, radius R with an arbitrary center C. When moving the semicircular formwork curve ADB along the DOC ripping curve, the surface of the formwork will be spheroidal, double curvature, which is usually called barrel. A cross section of such a surface with a horizontal plane gives a four-lobed shape in plan, as was indicated earlier in Fig. 183. In this case, the horizontal projections of the seams 1-1", 2-2" and 3-3" will be the same as with cylindrical formwork in Fig. 1. The vertical projections 1 - 1", 2-2", 3- 3" and 4-4" will be outlined from the same center C. The curve of the diagonal rib will be of an indefinite (close to elliptical) shape, but without a fracture in the arch of the O.
In fig. Figure 3 shows the case with conical formwork. Having chosen the vertex of the cone at point M (on the left side of the drawing), we draw through points 1, 2, 3 and 4 of the side arch the generatrices M-1, M-2, M-3, etc., both horizontally and vertically projections. In addition, from the other vertex M" of the front formwork we draw vertical projections of the generatrices, in the form of radii M"-1, M"-2", M"-3, etc. At the intersection of the generatrices of two adjacent formworks we obtain on the diagonal of the plan and on vertical projection point 1", 2" and 3" and 4" vertical projection of the rib.
A section of the cone of the left formwork with a diagonal plane will give an ellipse with a major axis AB and a minor axis CC (shown in the drawing with a dotted line in alignment with the horizontal plane). The vertical projection of this diagonal ellipse ACB will also be an ellipse A"SV (drawn with a dotted line on the vertical projection). The vertex C of the ellipse is higher than point O, i.e., the top of the arch, however, the generatrix MC of the cone intersects the diagonal edge at point K, which lies below the top of the arch O. The section of the diagonal curve AO (from the heel to the sheli-gi) represents a segment of the diagonal ellipse, less its quarters, rising from the base of the arch to the shelyga to a height H. Similarly, the other section of the 0D diagonal edge will be the same segment of the ellipse as AO. At the top of the arch O, both of these sections of the ellipse will meet at an angle, without forming a smooth curve. Consequently, straight ripping in the case of cylindrical (Fig. 1) or conical (Fig. 3) formwork results in a fracture of the diagonal rib at the top of the arch.
Fourth, most interesting way The construction of an ellipsoidal formwork is shown in Fig. 4.
Having described an arbitrary ellipse with the C-C axis around the square plan ABC, we will rotate it around its own C-C axis. The surfaces of the left and right stripping will then be the surfaces of an ellipsoid of revolution (see vertical projection). The top O of the ellipsoid will be the roof of the arch, lying at height H. In the same way, the upper and lower formwork will be formed by the surfaces of another ellipsoid with the axis OE. To obtain a vertical projection of the line of intersection of two mutually perpendicular ellipsoids, we use a horizontal projection in the form of two diagonals AB. Next, we dissect the ellipsoid with planes passing through points 1, 2, 3 and 4, lying on the wall arches, and through its axis CC. To draw intersection curves, we draw transverse planes /, // (coinciding with the side of the square) and /// along the center of the arch. These sections are depicted on a vertical projection in the form of circles /, // and ///. The sectional planes of the ellipsoid OE will be depicted on the vertical projection with radii O-1, O-2, O-3 and O-4. The cross-sectional planes of the ellipsoid C-O-C are depicted on the vertical projection by curves C"-1-C", C"-2-C", C"-3-C", C"-4-C" and C"DOC"" ". The vertical projection points of the diagonal edges are determined by the intersection of the radial lines O-1, O-2, O-Z, etc. with the section curves of the ellipsoid. On the horizontal projection of the diagonal edge, points 1", 2", 3", etc. will be obtained by the intersection of the plan diagonals with horizontal projections of the ellipsoid sections. In all four types of formwork (Fig. 1 - 4 Fig. 184) lines in plan and vertical projection give an image of masonry working beds.
Of all four types of formwork, cylindrical (Fig. 1) and conical (Fig. 3) give a broken diagonal curve and a rigid geometric shape of the formwork. In two other solutions we have double-curvature strippings - a barrel surface (Fig. 2) and an ellipsoidal surface (Fig. 4). Of course, the surface of an ellipsoid, approaching a spherical one, is more pleasing to the eye, but its implementation is difficult and requires a variety of circles built at points. The barrel surface is easier to implement, since here all the circles are drawn with two radii r and R. Both solutions are good because they give smooth curves for the diagonal edges, without a break in the shell (see vertical projections).
From all of the above, we can conclude that for formworks based on diagonal ribs, you can choose any convex surfaces, as well as spherical ones, with vertices at any point on the vault plan. As we will see later, Gothic architects used various swollen spherical forms. In fig. 4 fig. 184 you can trace the transition of the cross vault into the sail vault. If the major axis of the ellipse C-C is shortened, then the minor axis will lengthen. In the limit, both intersecting ellipsoids will turn into one ball, circumscribed around the plan with a radius equal to the semi-diagonal. In plan, the ball is shown as a circle drawn with a solid line. The sharp diagonal edge of the intersection of the ellipsoidal forms will completely disappear, since all four formworks will lie on the same spherical surface. The vault will turn from a cross into a spherical sail.
The considered geometric forms of the formwork are the main factors influencing the spatial image of the cross vault. The shape of the curve of the diagonal edge, which is the line of their intersection, also depends on the formwork. Given the formwork surfaces, we obtain diagonal edges as their derivatives. Gothic masters, on the contrary, set the curves of the frame ribs, which was the main formative and decorative factor of the entire vault, and the formwork between them, heavily crushed, served only as a secondary, local filling. The construction of the decorative and structural frame of Gothic vaults will be analyzed below; here it remains to consider the change in the profile of the diagonal rib protruding at an angle and the formation of various forms of lampshades in the shelyga.
Fig. 2 fig. 1851 shows a cross vault with a rounded corner of the diagonal rib. Renaissance masters often resorted to this method, especially when painting on the vault. This is how the ribs of the vault are rounded in the Stanza della Segnatura, painted by Raphael (Fig. 209).
1 Fig. 1 pic. 185 shows the basic form of the cross vault.
You can cut the edge with a straight chamfer, as shown in Fig. 3 fig. 185. A greatly enlarged chamfer will be read as an independent part of the vaulted surface, namely as the surface of a sail-somkiut vault. Instead of one diagonal edge in in this case two ribs diverge from the support, representing the intersection lines of the inserted surface of the sail-closed vault (chamfer) with the remaining reduced formwork of the main cross vault. It is possible to increase the surface of the sail-closed vault so much that it becomes the main element, and the strippings of the cross vault become secondary (this will be discussed in the chapter on the closed vault).
With a large rounding of the diagonal edge of the cross vault with a radius equal to half the side of the plan, the cross vault turns into a fan vault (Fig. 4 Fig. 185). Thus, the introduction of the surfaces of other vaults within the diagonal edge greatly changes the basic shape of the cross vault and even destroys it.
In these examples we see a number of intermediate and mixed forms of vaults and observe the transition of one form to another.
In the history of architecture, one can find many examples of interesting and beautiful combinations in which elements of various vaults are combined into one new vaulted covering. Particularly complex combined forms of vaults were given by the Baroque, where there are even combinations of a cross vault with a dome in the form of a ceiling.
In all deviations from the basic form of the cross vault, the architect’s desire to obtain a flat figure in the shelyga, in the form of a ceiling, suitable for painting and sculptural images, is noticeable. Already in the Roman vault of the tomb of the Pankrati brothers (Fig. 200), the shelyga is occupied by a square ceiling, which is part of the overall picturesque geometric decor of the vault. In Renaissance vaults, a round medallion according to scheme 1 in Fig. 1 is more often found in shelyga. 186, for example, in the vestibule of the Palazzo Vecchio (Fig. 187) or in the Stanza Elliodoro according to the project
Peruzzi (Fig. 206). In Villa Madama, the lampshade has the shape of a square with concave sides, according to diagram 3 in Fig. 186 (see also Fig. 212). Such medallions use only a more or less flat part of the arch of the arch and have little organic connection with its shape. In Fig. 186 shows various compositions in which the shape of the ceiling is organically connected with the structure and shape of the formwork and ribs of the vault. One follows from the other, and everything taken together gives a holistic concept.
Fig. 5 repeats the variant already known to us with a blunted rib of the arch (Fig. 3 Fig. 185). The ceiling in the form of a square, rotated 45° to the axis of the arch, is clearly connected with the edges of the blunted rib. The plan of the vault (see side) can be read in two ways. If four strippings are distinguished, the rest of the body of the vault can be considered a sail-closed vault; if we take the three triangular faces of the support as one whole, as a faceted funnel, we can call the vault a faceted fan (cf. Fig. 4, Fig. 185). The size of the square lampshade can be increased arbitrarily. This form is rare in monuments.
Having broken the diagonal edge of the arch shown in Fig. 5 fig. 186, we get a vault with an octagonal shade (see Fig. 4 Fig. 186). A third diagonal edge will appear in the direction from the corner of the octagon to the support. This middle rib will, however, flow in, as in a closed vault (see below), and the two outermost ones will protrude (inside the vault). In the cross vault of the mosque at Ephesus (Fig. 188) these protruding ribs and the middle diagonal one flowing in are clearly visible. This small vault, with a span of 2-3 m, is made very skillfully from solid blocks of white marble. The octagonal lock of the vault is processed in the form of a compressed ring-drum, covered on top with an ornamented slab-dome.

The inexhaustible imagination of the East enriched the shape of the vaults in Ephesus with an additional detail, which gave the vault the character of a faceted crystal (Fig. 7 Fig. 186 - Mohammed el-Gauli Mosque in Cairo). The architect introduced small rhombic medallions into the shell of the formwork, thanks to which additional ribs were obtained. The fracture-fold of the diagonal rib was continued onto the side faces of the formwork. The result was a new form of folded cross vault with seven ribs and three folds. In Fig. 189 shows a plan and section of such a vault in Okella Kajt-Bai. The masonry joints shown in plan give a clear idea of ​​the folded surface of the vault. The flat, recessed lampshade is decorated with a stalactite pattern. The same shape of the vault can be interpreted as a fan vault with a folded funnel (see plans), especially if we take into account the absence of a main through diagonal rib and a round depression in the shelyga. Such vaulted forms of the cross vault, as we will see below, are found in Gothic.
A variant with an octagonal lampshade located along the axes of the arch is also possible (Fig. 8, Fig. 186). The formwork shells, in accordance with the edge of the octagonal lampshade, received small square lampshades. This form is most consistent with the calm and clear interpretation of the surface of the vault during the Renaissance. Most of the Renaissance decorations of a simple cross vault analyzed below have five medallions - one in the center and four in the shell of the formwork.
Special forms of lampshades can be derived from the design solutions of the forms of formwork and from their execution from stone. If the filling of the formwork with masonry is carried out normally along the bisector of the angle (Fig. 6, Fig. 186), according to the English Gothic method, then by bringing the masonry to the shell of the formwork, we will get a hole in the middle of the vault in the form of a four-pointed star. By designing this hole in the form of a lampshade, we will obtain a new shape, closely related to the lines of laying the formwork.
Fig. 9 fig. 186 represents a cross vault with swollen spheroidal forms. We have already discussed this Byzantine technique of lifting a vault along a curve above (Fig. 183). As is known, a section of such a vault with a horizontal plane gives a figure in the form of a quatrefoil; This form of lampshade is very interesting for painting. In the decoration of formwork, you can emphasize the surface of rotation with horizontal lines of parallels. One of possible options decoration, with the division of the middle four-petal lampshade into four sectors, is shown in Fig. 4 Fig.214. The same motif was used in the decoration of the cross vault of the Frugg Chapel (XVI century, Fig. 228); The ribbed Gothic pattern and details of the arches were created in the transitional period and already introduce stylistic elements of the Renaissance.

III. CAISONS ON THE CROSS Vault

Any caisson of strict rhythmic construction from geometric figures fits freely on the cylindrical surface of the vault, as well as on a flat ceiling. It would seem that the surface of cylindrical formworks also allows for the free use of a caisson. However, the development of the stripping surface gives diagonal ribs in the form of curved lines OA (see Fig. 195), the adjoining of the geometric patterns of the caisson can never be correct, but is always random. By adjusting the design and additional inserts, it is partly possible to mask the defect in the connection, but even with this assumption, the bending of the geometric figures of the caisson through the diagonal edge gives an unacceptable solution, with deep depressions and breaks in the diagonal edge, as can be seen on the vault of the Basilica of Maxentius and Constantine (Fig. 180) .
Roman architects did not consider it necessary to decorate the diagonal rib, which was constructed structurally in the form of a brick frame in the concrete body of the vault (Fig. 190, reconstruction by Durm). The complex octagonal caisson gives an ugly joint at the edge with the introduction of random hexagonal and circular caisson figures. This is especially clearly visible in the reconstruction of the middle heel of the vault of the Basilica of Maxentius and Constantine (Fig. 191, left; reconstruction by Ronchevsky), where D is the preserved part of the heel, and the reconstructed part is shown in dotted lines.

Rice. 190. Details of Roman concrete cross vaults with a brick frame

Rice. 191. Coffered decoration of the heels of the cross vault

Rice. 192. Interior of the Baths of Diocletian (reconstruction by Auer)

Rice. 193. Interior of the Baths of Caracalla (reconstruction by Thirsch)

Rice. 194. Interior of the Pennsylvania Station concourse in New York

Rice. 195. Schemes of coffered decoration on the cross vault

Rice. 196. Decoration of the heel of the vault of the Baths of Adriana’s Villa (according to Ronchevsky)

Rice. 197. Development of the coffered decoration of the cross vault of the Baths of Hadrian's Villa

Rice. 198. Circular-mesh wooden cross vault

Rice. 199. Cross vault of mixed masonry in the Louvre

The same picture of the joint of the caisson on the edge is given in the reconstruction of the heel of the vault, Diocletian's Baths (Fig. 191, right; reconstruction by Paulinus); here the second row of octagonal caissons cuts ugly into the rib of the vault.
Other reconstructions of the coffered decoration of the cross vaults of Roman baths do not provide scans of the vault, but perspective drawings of the interiors, and the joint of the caisson on the edge is clearly shown incorrectly with an artificial adjustment of the patterns. Thus, in the reconstruction of the tepidarium, or the so-called “Ce11a media”, performed by Blue (Fig. 179), the lentil-shaped caissons on the edge of the vault are, of course, false in shape and cannot be the same along the entire length of the edge.
Auer during the reconstruction of the tepidarium of the Baths of Diocletian1 (Fig. 192)
The surviving parts of Diocletian's baths were rebuilt by Michelangelo into the church of Santa Maria degli Angeli.
used the most complex false-constructive caisson found in late Renaissance lampshades1. The use by the Romans of such a caisson, unsuitable for a cross vault, seems unlikely, especially since another reconstructor, Paulinus, gives a completely different version of the decoration of the same baths. The joint of the coffered pattern on the edge was also drawn by Auer arbitrarily, not in accordance with the correct construction.
Finally, we also note the reconstruction of the baths of Caracalla, carried out by Thiersch (Fig. 193). Here the drawing of the caisson has been restored, the remains of which, in the form of a preserved piece of stucco decoration in the heel of the vault, are found in the ruins of the baths of Hadrian's Villa in Tivoli (Fig. 196). As will be indicated below, Thiersch also makes a mistake in connecting the coffered pattern to the edge of the vault.
In connection with the unsuccessful solutions for the coffered decoration of the cross vault in the proposed designs, it is interesting to note the mistakes of modern architects.
The vestibule of Pennsylvania Station in New York (Fig. 194) is an almost exact copy of the Basilica of Maxentius and Constantine, only the radius of the curved formworks is slightly less than the radius of the main vault. As a result, the rows of caissons for stripping and the main vault do not coincide at all with each other on the edge of the vaults, and the latter takes on the appearance of a thin, ugly partition between them. It is difficult to imagine a greater architectural disorder. The Americans distorted the Roman basilica and ignorantly designed the coffered decoration of the vault.

So, a number of unsuccessful attempts to reconstruct the coffered decoration of the cross vaults and the mistakes made in this case confirm the difficulty we have indicated in connecting the geometric caisson to the edge of the vault. By accurately constructing the caisson on the surface developments of the formworks, it is necessary to find out all the defects in the connection of the caisson to the rib and provide possible architecturally correct solutions.

For analysis, let’s take that decorative rectangular caisson, traces of which remained on the vault of Hadrian’s Baths in Tivoli.
In fig. 1 pic. 195, on the left side, the caisson was divided into segments a and b along the formwork arc and its horizontal projection was drawn on the cross vault. On the right side, the formwork is unrolled. The wall arc of the stripping will straighten into segment CA. The diagonal edge of the arch will give a development of the OKA curve, the points of which 11, 21, 31, 41, 51 are obtained by straightening the corresponding caisson arcs. On the development of the formwork in the form of a triangular cutout OCA, we apply the correct drawing of the caisson, plotting the dimensions of its squares a and b.
At points 11 and 21, the diagonal rib OA in the development deviates from its horizontal projection OB so slightly that the corners of the caisson almost lie on the development of the diagonal rib. Points 31 and 41 of the ribs in the development move to the right and do not coincide with the corners of the caisson 3 and 4. Angle 5 of the caisson has moved away from the development of the diagonal edge of the OA curve by a significant amount of 5-51. The vertical edge of the caisson 5-5 meets the development of the diagonal rib at point K. Minor discrepancies between points 3 and 4 of the corners of the caissons with points 31 and 41 of the arch ribs are not noticeable, and they can always be adjusted. But the edges of 5-5 caissons lying in different strippings cannot coincide and form an incoming angle K on the diagonal edge and a caisson in the form of a hook around it (see the upper left corner of Fig. 1, Fig. 195).

Ronchevsky's sketches from the preserved remains of the caisson (Fig. 196) give exactly the same picture of the incoming angle K, which we obtained when we correctly outlined the caisson on the formwork. On the development of this decor, also executed by Ronchevsky (Fig. 197), we see the same reentrant angle K
In fig. 2 fig. 195 the reverse construction was carried out. On the horizontal projection of the vault (on the left side of the drawing) a regular grid of caissons is applied, the corners of which lie on the projection of the diagonal rib. On the development of the formwork (on the right side of the drawing), the corners of the caissons also remained, of course, on the development of the rib, but the width of the caissons a1, a2: etc., as well as b and b1, would all increase towards point B. Thus , the coincidence of the corners of the caisson with the diagonal edge, as was achieved in Thiersch’s reconstruction (Fig. 193), is possible only with such caissons, the dimensions of which increase towards the support, which is unacceptable.
It is clear that the solution of the caisson on the vault of Hadrian’s Villa (Fig. 196-197) must be recognized as the only possible and correct one. Random forms of caissons are inevitably obtained in the supporting parts of the vault, as a result of the intersection of cylindrical decorations, and to a certain extent disrupt the integrity of the rib. To avoid accidental joining of caissons on an edge, only one way is possible - the use of such a caisson, the design of which includes a diagonal edge of the vault. This is the constructive caisson of an oblique grid used by the Romans for the domed surface of the apses of the Temple of Venus and Roma (Fig. 14-15). Fig. 3 and 4 fig. 195 show the construction of such a caisson on the surface of the cross vault.
In fig. 3 on the right shows a layout of the formwork, with six parts of the arc laid out on line CA (1, 2, 3, 4, 5, 6). At points 1 and 2, the corners of the caissons almost lie on the development of the rib OA, but point 3 already deviates significantly from the corner a of the caisson 2. From point 3 to the heel A, no caisson can fit.
On the left side of Fig. Figure 3 shows a dotted line projection of the caisson mesh applied to the extended cylindrical surface of the formwork. On the surface of the cross vault, the grid will have to stop at caisson 2, near point 3 of the diagonal rib, and caisson 2 will have the shape of a somewhat distorted square, since point a (see the scan) will have to be pulled up to point 3 of the diagonal rib. In fig. 4 shows the reverse construction. On the projection (on the left) the correct grid is applied, on the development (on the right) the squares of the caissons turned out to be elongated towards the support.
In fig. Figure 9 shows an axonometric image of a slanting caisson on a cross vault. The caisson grid ends (as in the developments, Fig. 3) at point 3 of the diagonal edge. The flatter the vault, the better the caisson mesh is laid on the surface of the vault stripping. With an oblique coffered mesh, the diagonal edge of the vault receives the completely correct architectural and structural significance of the main working element of the vault, which carries the mesh frames of the formwork. The decorative pattern in this case is an organized structural frame that carries out the synthesis of decor and construction inherent in the best examples of Gothic vaults.
The latest systems of circular-mesh wooden cross vaults, shown in Fig. 198, also serve as examples of decorative and structural frames that meet the challenges of modern architecture. All other coffered decorations of the cross vault, which do not take into account the diagonal rib and arbitrarily bend their pattern through it, must be recognized as false decorative.
A special place is occupied by the decor of the cross vault, which reproduces the normal cutting of stones and the laying of them. In fig. 8 fig. 195 shows the usual masonry of hooked stones K and L, with a plafond lock in the form of a cross. An example of such masonry made of mixed materials - cut stone and brick - is the vaults of one of the halls (sale de Manege) in the Paris Louvre, built by L. Visconti in 1852-1857. (Fig. 199). In fig. 7 Fig. 195 shows another masonry - made of hexagonal stones K and L with an octagonal lampshade M, convenient for painting. Both solutions can serve as a successful motive for artistic processing.
As a result of our analysis, we have to state that the rhythmic coffered pattern in the broad sense of the word (as we understood it in the chapter on the barrel vault) cannot be successfully deployed on the surface of the cross vault.

IV. CROSS VOUCHES OF ANCIENT ROME AND RENAISSANCE

The principle of a rhythmic pattern in the form of a so-called “endless field” fully corresponds to the extended, monotonous surface of the cylinder, but is in conflict with the surface of the cross vault, dissected by diagonal ribs and consisting of four segments of the cylinder. The correct construction of the decor of the cross vault should be subordinate to its diagonal ribs. The composition should group all decorative elements around a central spot (square or round in the roof of the vault), building the entire scheme crosswise along the axes and diagonals of the plan. All framing and secondary plots should concentrically cover the central motif. Thus, a single closed “diagonal” composition will be created, harmonizing with the forms of the vault and highlighting them.
If the Romans did not find any special decorative forms for the giant cross vaults of their baths and were content with random intersections of cylindrical decorations, then among the cross vaults of Roman tombs and small vaults of the baths we find a number of the best decorations, built on the principle of a single diagonal composition. These include the decor of a small cross vault - the tomb of the Pancratius brothers on the Latin Way, near Rome (Fig. 200, 201). The cross vault of a square plan (4.28x4.28 m) occupies the middle of the roof; side arches 0.6 m wide with wicker patterns coincide with the surface of the formwork (a common technique of Roman architects with a rectangular plan). The vault is decorated with molded frames of small relief, made using a special alprimo technique, that is, stamping on the damp top layer of plaster. Frames and lampshades are filled with stucco ornaments and hand-made figures and pictorial motifs.

Rice. 200. Decor of the cross vault of the tomb of the Pancratius brothers near Rome

Rice. 201. Decoration of the heel of the vault of the tomb of the Pancratian brothers near Rome

Rice. 202. Decor of the vaults of the baths of Hadrian's Villa (according to Cameron)

Rice. 203. Reconstruction of the Baths of Diocletian (according to Paulinus)

Rice. 204. Heel of the cross vault of one of the halls of the Winter Palace in St. Petersburg

Rice. 205. Decor of the cross vault of the Stanza del Incendio

Rice. 206. Decor of the cross vault of the Stanza del Elliodoro

Rice. 207. Decor of the cross vault of the “Hall of Heroes” in the Munich Glyptothek

Rice. 208. Decor of the cross vault of the Stanza della Segnatura

Rice. 209. Interior of Stanza della Segnatura

Rice. 210. Decor of the cross vault of the Chapel del Pallio in Palazzo Cancellaria

Rice. 211. Decor of the cross vault of the portal of Peter's Cathedral

Rice. 212. Decor of the cross vault of Villa Madama

Rice. 213. Decor of the cross vault of Villa Belcaro

Rice. 214. Examples of composition of cross vault decors

Rice. 215. Cross vault of Amiens Cathedral

The entire composition has a strictly geometric scheme along two axes. All flat areas of the arch were successfully used. In the middle of the shelyga there is a large square lampshade; the formwork is marked with rectangular lampshades. All lampshades are framed with molded frames that form a common pattern throughout the entire vault. The beginning of the diagonal rib, the support of the vault, is highlighted by a picturesque dark rhombus and a small sculptural figurine (Fig. 201). Despite all the artistic merits of the decorative composition, it should be noted as a minus that the meaning of the diagonal edge is poorly expressed by decorative means.

Cameron's work “Roman Baths” shows two decorations of the cross vaults of the baths of Hadrian's Villa (Fig. 202), built on the same principle of symmetrical diagonal composition and made with the same stucco technique as the vault of the Pancratian tomb (Fig. 200). One solution (in the lower part of the picture) is very reminiscent of the decor of the Pankratiev tomb. It should only be noted that the middle ceiling is very large for a cross vault and extends onto the curved surfaces of the formwork; T-shaped formwork shades have lost their meaning. An attempt was made to decoratively emphasize the diagonal rib, albeit in a small area. The second solution (above Fig. 202), with round medallions, is more interesting. (Note that round medallions in strippings will often be found in Renaissance decorations.) The placement of four round medallions on the sharp diagonal edge of the vault is unsuccessful due to the fracture of the medallion, as well as due to the rupture of the diagonal edge, of which only small pieces remain. A composition with eight round medallions is possible, as we will see below, with a sail vault.
Let us dwell on one more interpretation of the decor of the cross vault, which does not have specific historical examples, but was given by Paulinus in the sketch reconstruction of the baths of Diocletian (Fig. 203). This new form of decoration, with five square shades arranged crosswise in the flat upper parts of the vault, is shown in diagram 6 of Fig. 195. The corners of the vault, clearly defined by the decor, are treated like square cantilevered heels laid out in overlapping horizontal rows of masonry. The decor of the corner heels corresponds to the direction of the masonry seams.
The heel of the cross vault of one of the small halls of the Winter Palace in St. Petersburg (Fig. 204) gives a clear idea of ​​this decorative scheme. Despite the ugly molded forms of the lower part, the entire heel gives the impression of a well-designed load-bearing element of the vault. The formwork lampshades, in the form of an octagon with inscribed circles, are unsuccessful in shape and design.
Having examined the meager remains of Roman decorations on cross vaults, which do not allow us to accurately establish the main line of development, we must still note the weak emphasis of the diagonal rib in the decoration of the vault. The artists of ancient Rome decided to decorate the cross vault in most cases as an intersection of the decors of the barrel vaults.
We consider the orientation of the decor of the cross vault along its diagonal to be the most truthful and organic solution.
The above two sets of terms of Hadrian already provide something positive in this direction, and we will see echoes of these techniques in the decorations of the Renaissance. The Renaissance did not blindly follow antiquity; it sought its own path in the decoration of vaults, showing its own taste. Using the techniques of stucco decoration with tinting and painting with modeling, common in Roman practice, the Renaissance masters were, however, looking for surfaces for the free development of frescoes. Having rejected the caisson in the decoration of the cross vault1, they gave a number of beautiful compositions in a free decorative interpretation, adhering to a geometric diagonal scheme.
The Renaissance theorist architect Leon Battista Alberti (15th century) does not dwell at all on the problem of vault decoration and does not give a theory of its composition. In Chapter 2 of Book VII of Alberti’s treatise there are only the following lines: “The vault also has its decorations. Among the ancients, the same decorations that jewelers made on sacrificial bowls were also used by architects to decorate spherical vaults. And those decorations that were made on fabrics were imitated in cylindrical and cross vaults. Therefore, you can see quadrangular, octagonal and similar figures located along the arch at equal angles and along straight lines, in different rays and circles so that nothing is more beautiful. This also includes those decorations of the vaults that are undoubtedly the most worthy, namely the coffers that we see everywhere, both in other places and in the Pantheon.” The following is a story about the construction of boxes for caissons made of bricks on clay.
Let's turn to the analysis of the best decor solutions of the Renaissance.
Evaluating the artistic painting of the vaults is not our task. The analysis will concern exclusively the architectural side of the decorative composition, which is fundamental in the work of the architect.
1 Quite deliberately, the Renaissance masters did not follow the example of Rome in this case and did not repeat the unsuccessful coffered decorations of the Basilica of Constantine and the baths of Diocletian and Caracalla.
2 Colored pictorial decoration in architecture is the most difficult moment. The basic techniques and rules of past centuries are almost lost.
As the main solutions for the cross vault, we take the ceilings of three stanzas (halls) of the Vatican: del Incendio, della Segnatura, del El Liodoro.
In the Stanza del Incendio, the cross vault is painted by Pietro Perugino (1446-1556); Raphael, while executing his frescoes on the walls, preserved the entire work of his teacher. The decoration of Perugino's vault is simple and clear to the point of naivety. The diagonal ribs are clearly decorated with rods, the triangles of the formwork are filled with the favorite form of a round medallion (Raphael, when creating his famous wall frescoes, apparently partially preserved the decor of Sodom), which was also often used on triangular sails.

Perugino repeated the decor of the same scheme on the vault at Cambio in Perugia, but there seven planets are depicted in medallions.
We find the same decorative scheme in French Gothic. The star vault of the chapel of the Uaron castle has five large round locks carved from stone in the form of medallions (Fig. 232).
The main feature of this scheme is the absence of a middle lamp. This is typical for a cross vault, since it does not destroy the through diagonal ribs. This decorative solution must be recognized as the only correct one, worthy of imitation.
In the Stanza del Elliodoro, the great Siena master Baldassare Peruzzi (1481-1537), a contemporary of Raphael, created a new original decor (Fig. 206). The diagonal ribs are clearly highlighted with a picturesque ornamental ribbon. The triangular formworks are interrupted by a ring belt of the same pattern as the diagonal ribs. The frames formed in this way in the form of sectors provide a lot of space on which large plot paintings can be developed. According to Burkhardt, Raphael painted the main background of the four paintings in a blue tone, which gave the paintings significant lightness. Despite the participation of two great painters in the creation of this decor, the framing ring belt remains the weak point of the composition: it is completely inconsistent with the shape of the cross vault and was artificially transferred here from the sail vault, where the circle separates the sails from the skufia. On the edge of the vault, the ring gives a fracture, which looks especially unpleasant if the vault is viewed in perspective at an angle. As mentioned earlier, a four-lobed belt located along the parallels of the swollen spherical formworks is more appropriate here (see Fig. 4 Fig. 214).

For comparison, we present the decor of the cross vault of the “Hall of Heroes” in the Munich Glyptothek, executed by Cornelius (Fig. 207). With a decorative scheme completely similar to that of Peruzzi, Cornelius divided the painting of the formwork into two subjects, and the entire decor into sections, depriving it of the unity of composition. We find the most complex composition in the decoration of the cross vault of the Stanza della Segnatura, executed by Giovanni Sodoma (1477 - 1550) in 1511 (Fig. 208)1. In this composition, four round medallions are successfully located in the shells of the formwork, similar to the decor of Perugino in the Stanza del Incendio. However, despite the presence of ribs, large square frames with picturesque scenes were introduced, running along the edges of the vault, for which the latter had to be hewn and rounded (Fig. 209). Such violence against the form of the arch cannot be justified in any way. Apart from this main drawback, the entire network of stucco frames represents a random, unorganized accumulation of various geometric shapes, adjacent to each other at the corners and sandwiched against each other (especially the corner squares). No skill of a brilliant brush could save the false composition of Sodom.

The same false decorative scheme was implemented on the cross vault of the Chapel del Pallio in the Palazzo Cancellaria in Rome (Fig. 210). The authors - Perino del Vaga, a student of Raphael, and Federico Zuccheri (1542-1609) - tried to link the figures of the frames more organically than in the Segnatura stanza. Picturesque paintings in frames are placed only in formwork. Narrow, long frames on the diagonal edges are filled with molded figured subjects and, together with the round middle shield, form a four-pointed star. This artificial, dry organization of the scheme introduces some order, but cannot create a truly artistic composition. Due to the fact that the rounded ribs are knocked down, it is difficult to read even the basic shape of the cross vault in the photograph.
Somewhat later (1619), the Baroque master G. B. Ricci from Novarra decorates the cross vault of the portico of Peter's Cathedral in Rome (Fig. 211). Its diagram clearly reveals the shape of the cross vault, the medallions are correctly located in the formwork. There is a molded coat of arms in the shelyga. Only dry forms and baroque broken frames can be considered among the shortcomings of this decor.

Exceptional skill in the decoration of vaults was demonstrated by Raphael's students in the Roman Villa Madama, built under the direction of Giulio Romano (1492-1546) according to Raphael's design. Another student of Raphael, Giovanni da Udine, took part in the picturesque decoration of the premises. The decoration of the villa continued for another five years after the death of Raphael, from 1520 to 1525. The decoration of the domes and niches will be discussed below, but here we will dwell on the decoration of the cross vault of the villa's salon (Fig. 212). With exceptional clarity, the artist emphasized with painting not only the form, but also the meaning of the elements of the vault, without depriving the composition of its overall decorative value. The supports of the vault are marked by four ornamented heel stones, similar to the heels of the decoration of the arched vault of the tomb of the Pankratiev (Fig. 201). The lock in the shelyga of the vault is in the form of a cross-shaped stone. Heavily decorated and painted diagonal ribs, like tense struts, connect the lock to the heels, forming a cross-shaped frame. The body of the formwork between the ribs is filled with light arabesques, in imitation of a stretched awning (velum); The arabesque lines follow the main lines of the vault and emphasize the character of the surface. The oval medallions are large-scale, well placed and well connected with the arabesques. Villa Ma- salon decor

The lady is a subtle artistic elaboration of Perugino's simple and valuable scheme in the Stanza del Incendio (Fig. 205).
Concluding the review with the most original decors Renaissance, we note the clean, lyrical decoration of the cross vault in the Villa Belcaro near Siena, built by Peruzzi (Fig. 213). The entire composition is made in the “grotesque” style and depicts a light trellis dome of a garden gazebo with climbing plants and fluttering birds. The design of the trellis strictly adheres to the main lines of the arch, the diagonal ribs are highlighted; the formwork is filled with medallions in the form of stretched scarves with mythological scenes. This charming, joyful decoration only sins in that, creating with its transparency the illusion of open space, it seems to abolish the vault.
In addition to the above best works we show the Renaissance masters in Fig. 214 a number of compositions performed based on the material we analyzed.
In fig. 1, on the surface of four formworks, a structural and decorative coffered pattern is successfully laid, built according to the design of the coffered ceiling of the palace in Pastrana (Fig. 72). The pattern is inscribed crosswise along the axes of the formwork. The diagonal edge is included in the main pattern of the pattern. The vault supports, due to their limited dimensions, must be processed as independent parts of the vault, like outlet heels.
In fig. 2, the decor of the barrel vault of the Saint Bernard Chapel in the Palazzo Vecchio is used (Fig. 110). The frame system of this decor is successfully placed in the formwork shells. The corners of the cross vault are processed with horizontal rods, corresponding to the rows of masonry. The diagonal rib was not included in the overall decorative pattern, which is a defect in this design.
The motif of the composition shown in Fig. 3, taken from the coffered barrel vault of the Palazzo Reale in Venice (Fig. 111). Diagonal rib, as in Fig. 1, forms an element of the overall decorative pattern and is successfully combined with octagonal lampshades.
Fig. 4 depicts a variant of the decor performed by Peruzzi in the Stanza del Elliodoro (Fig. 206). The general round belt, with which Peruzzi unsuccessfully covered the entire vault, is replaced by a four-lobed belt corresponding to four swollen spherical formworks and located along their parallels. The decor of the vault heels is also consistent with the rows of masonry spherical formworks.
In Roman buildings, as in the Renaissance, the surface of the cross vault was treated with plaster and used for pictorial decoration. The artist, not constrained by the design, used creative intuition to emphasize the working elements of the vault using painterly means and modeling. We celebrated this as a healthy example worthy of emulation.

V. GOTHIC CROSS VOUCHES

It is necessary to learn the synthesis of design and decoration from those examples in which it is not a random artistic motif, but an integral organic element of the composition, namely, from the works of Gothic masters, on the Gothic cross vault.
Representing a perfect structure made of stone (Stone Gothic vaults of the 12th and 13th centuries were already close in thickness to modern reinforced concrete vaults. With ribs of 40-50 cm, the formwork of the vaults had a thickness of only 10 cm), built on the principle of a visible, revealed frame, and At the same time as organic structural stone decoration, the Gothic vault meets the basic modern requirements of composition. The flexible, elastic frame system, within certain limits, allows the architect in search of best decor direct the ribs (ribs) of the arch at your discretion.
When analyzing Gothic vaults, we will leave aside the issue of cutting stones and the method of masonry, as having no significance for modern times, and we will indicate the lines (seams) of the masonry only to visually clarify the shape of the surface and the direction of the acting forces.
The Gothic cross vault, as is known, is based on an active frame that carries the filling in the form of small vaults. The Romans hid the same brick frame in the mass of the cast concrete vault and did not give it a decorative relief design.
The constructive method of constructing an independent frame was completed already in the 12th century. in early French Gothic (Saint Denis Cathedral, 1140). The vault of Amiens Cathedral (1218) is an example of the same design (Fig. 215).
The frame of the Gothic vault is built according to clear and practical techniques and methods of stone art. The diagonal elliptical rib of Roman cruciform vaults requires stones that are varied in shape and difficult to work with. In Gothic, it is replaced by a simple semicircular rib made of identical stones. In later buildings of the 13th century, for example at Reims, the diagonal arch has a pointed, elevated form. The strippings were laid out as independent small vaults, resting on the ribs of the main vault. The latter, to give rigidity to the frame, was laid out from long, strong stones with a small number of seams. The strippings, on the contrary, were laid from small, light limestones; The relief of formwork was also facilitated by their swollen spheroidal shape, which reduced the thickness.

Rice. 216. Star vault of Beverley Cathedral (England)

Rice. 217. Schemes of Gothic vaults

Rice. 218. Cross vaults of the middle nave of Exeter Cathedral (England)

Rice. 219. Various forms of cross vaults and their formworks

Rice. 220. Schemes of mesh vaults

Rice. 221. So-called honeycomb vaults (Wabbengewolbe)

Rice. 222. Schemes of working ribs of Gothic vaults

Rice. 223. Schemes of Spanish Gothic vaults

Rice. 224. Star vault of Worcester Cathedral

Rice. 225. Cross vault of Christchurch Church

Rice. 226. Cross vault of the church in Warwick

Rice. 227. Cross vault of the church in Vulpita

Rice. 228. Cross vault of the Frugg Chapel

Rice. 229. Interior of the Vladislav Hall in the Prague Palace

Rice. 230. Interior of Anna's Church in Annaberg

Rice. 231. Scheme of the decoration of the vault of the Vladislav Hall in the Prague Palace

Rice. 232. Decor of the chapel vault in the castle of Uaron in France

Due to the difficulty of laying large formworks, additional working ribs are introduced, the so-called tiercerons (in French tiercerons, in German Dienste - assistants), directed, like the main diagonal rib, towards the support. In shelygas and in secondary directions, craftsmen began to introduce horizontal, long, even stones called piers to simplify and beautifully join stones. With the development of the frame, the piers also began to serve as supports for the upper ends of the tiercerons and received a curved vaulted outline.
This system received its full structural development in the so-called star-shaped cross vault, first used at the intersection of the naves of Amiens Cathedral (1220-1288). This vault, in its form and design, represents a truly complete architectural concept.
In Fig. 216 shows such a star vault at Beverley Cathedral in England; LB and LD, MB and MA, etc. - tiercerones, El, EH, EF and EG - liernes. The British call this system Complex quadripartite Yaults.

The main feature of a cross Gothic vault is a clearly defined profiled diagonal rib.
In Fig. 217 depicts the most characteristic Gothic vaults. The bottom row shows cross vaults: fig. 4 - ordinary star-shaped vault, fig. 5 - a vault of a more complex shape, in the form of an eight-pointed star, fig. 6 - vault, in the middle of which an octahedron is formed by the intersection of the ribs (tiercerons). In all three forms of the patterned frame, the main diagonal ribs of the cross vault are clearly visible.
All three vaults in the top row of Fig. 217 are similar to the lower crosses, but they do not have the diagonal ribs of the cross vault and are of a different shape, called reticulate. Fig. 1 represents the basic shape of a reticular vault; here, in place of the diagonal ribs, four cylindrical sails appear. The arch shown in FIG. 2, is even closer in outline to the cross frame (Fig. 5), but there are also no diagonal ribs. Finally, in FIG. 3, the arch also has a diagonal rib, but it does not pass through the shelyga and rests against the ring. If the three ribs emerging from the supports (diagonal and two tiercerons) are outlined by the same radius and form a regular funnel, then in this case a new form of fan vault is obtained.

From these examples you can see how free the architect is in creating spatial schemes. The desire to enrich these forms of frames was expressed primarily in an increase in the number of tiercerones.
Thus, in Exeter Cathedral in England in 1270 (Fig. 218), the middle nave has a typical vault with a large number of tiercerons converging on a support into one beam. 13 ribs converge on the support, of which two are diagonal SV and CZ, one transverse CD, two window ribs - SA and SU, and eight tiercerons. This bunch of ribs forms a square basket on the support, typical of English Gothic.
With such a number and arrangement of tiercerons, the value of the diagonal rib decreases, since the tiercerons perform its same function and relieve part of the load from it. At one glance at the square ribbed basket of the vault of Exeter Cathedral, where all the ribs (ribs) are almost equal, the work of entire sections of the cylindrical longitudinal vault, in the form of rhombuses CEDY, resting with their vertices C and D on the abutments of the wall becomes clear. The importance that the diagonal rib has in a simple cross vault is here reduced to nothing, and such a vault can hardly be called a full-fledged cross vault. Rather, it is a special type of cylindrical vault, the forces of which are directed by a bundle of ribs to individual support points, instead of a solid heel. Thus, the mere presence of diagonal ribs does not yet create a normal cross vault if there are other homogeneous ribs.
Another case of changing the basic working diagram of the frame of a cross vault is provided by the previously discussed ripping it up and changing the forms of the formwork. Even with a small lift along the curve (see Byzantine vaults above), the vault transfers some of the forces to the side walls and removes the load from the diagonal ribs. With a strong vault along a curve, when the surface of the vault becomes spheroidal or spherical (sail vault), the diagonal rib becomes flatter, almost disappears, and forces are transmitted along the meridians in all directions.
Changing the cylindrical surface of the formwork into a double curvature surface (spheroidal) also redistributes the forces in the ribs. The most common forms of surfaces of cross vaults and their formworks are compared in Fig. 219 indicating changes in the operation of the ribs.

In fig. Figure 1 shows the basic diagram of a cross vault with cylindrical formwork. The effective forces in the formwork, shown by arrows, are transmitted to the diagonal ribs. The walls (side arches) are free from load.
In fig. 2 rows of stripping masonry are laid out in the form of arches along circles movable on ribs, with each stone being pressed in place. This diagram gives an idea of ​​the technical perfection of early French Gothic masonry, which is so brilliantly described by Viollet le Duc in his encyclopedia. With this system, the wall arches absorb the thrust and part of the weight of the formwork (see arrows in Fig. 219), and the diagonal ribs are unloaded.
In fig. 3, inflated spheroidal formworks (in German - Bussige Karren) were used. Shells of formwork can be located

wives at an arbitrary point on the plan, closer or further from the center of the arch. The formwork shells can be higher than the arch shell (the intersection of the diagonal ribs). As in the dome, the pressure of the formwork is transmitted along the meridians (see arrows) in all directions, to the ribs, to the walls and to the support of the vault.
In fig. 4 vault, in addition to the diagonal ribs, has working curved ribs AC and BD along the axes of the formworks, in their shell. The vault is divided

thus, for eight formworks, which can have free form- swollen, spheroidal, etc. The surface of each formwork can be divided into three small triangles (there will be a total of 24 formworks in the vault). At the same time, 16 ribs converge in the vault lock: 4 main diagonal, 4 piers and 8 tierceron branches. Thus, this system represents another example (the first is Exeter Cathedral) of a multiplicity of ribs, but already concentrated at the vault lock. The supports have only 3 ribs (diagonal and two tiercerons), as in a normal stellate vault. The entire composition takes the form of an eight-pointed star.
In fig. 5 the entire surface of the vault is so much that it turns into a sail vault. All ribs diverge from the shell like meridians and work like the ribs of a dome. The formworks either have an independent curvature and rest on the ribs, or coincide with the spherical surface of the arch. In the latter case, if the main shell of the vault is strong enough (in thickness), the ribs are purely decorative elements. The diagonal edge loses all meaning here. The pattern of the rib frame can take on more free forms.
This rib frame system without a diagonal working rib is known as a “mesh vault”. The main forms of German mesh vaults are shown in Fig. 220; fig. 3 fig. 220 gives a plan of the reticulated vault shown in FIG. 5 fig. 219 (Fig. 1, 2 and 3 Fig. 217 show the mesh vaults in an axonometric projection).
All the mentioned six forms shown in Fig. 220 (Fig. 1 - 6), have two working ribs at the supports; The lines shown in dotted lines complement the frame pattern. Fig. 6 fig. 219 represents a special decorative form of folded formwork, found in isolated cases in late German Gothic and known as Zeilengewolbe (cellular vault).
This vault does not have an independent profiled rib frame - the sharp edges of the folds already form a fairly strong frame. Therefore, it would be more correct to call such a vault cross folded. This form of the vault fully corresponds to modern folded reinforced concrete structures and can be easily performed in reinforced concrete. It is interesting to note the repetition of the same folded form of the cross vault in Islamic architecture, for example, Okella Kait-Bai (Fig. 7, Fig. 186 and Fig. 189).
A type of folded vault with closed (partitioned) folds in the form of rhombic faceted depressions (Fig. 221) - the vault of the bishop's castle Altenstein (late 15th - early 16th centuries) is called Wabbengewolbe (honeycomb vault) in German. There is no pure form of cross vault here. Twelve ribs radiating star-shaped from the roof of the vault are laid on a spherical surface. It is rather a sail ribbed vault with faceted pyramidal formwork.
Thus, any change in the shape of the cross vault or its formwork leads to a redistribution of efforts. It is impossible to say anything about the operation of the network of ribs based on their location in plan, without knowing the spatial shape of the vault.
In Gothic, the basic form of the cross vault is transformed in such a variety of ways that it is extremely difficult to give a clear definition of each of the derived forms. It can be said that the pure geometric cylindrical form of a cross vault is almost never found in Gothic. All forms of Gothic vaults occupy an intermediate place between cross and sail vaults. Therefore, the concept of the shape of the cross vault needs to be clarified and somewhat expanded. We will call a cross vault not one with diagonal ribs, but one in which the diagonal ribs form the main working frame. Let us also agree that with swollen or spheroidal formworks (Bussige Carrén), the vault does not lose the name of the cross, if the general opening does not remove the main load from the diagonal ribs.
In addition to working ribs (ribs), the surface of the cross vault is often saturated with a whole network of non-working ribs, making up decorative patterns and stars. Their directions do not coincide with the direction of current efforts; in addition, they often have curved shapes in plan. Being purely decorative elements of the frame, they can easily be separated from the general network of ribs of the vault.
In Fig. 222 an attempt was made to decipher the meaning of the edges. The thick line shows the working diagonal ribs, the thin solid line shows the auxiliary ribs (tiercerones), also involved in the work, and, finally, the dotted line shows the non-working, purely decorative ones that form the pattern of the vault.
The vaults shown in Fig. 1 - 4, in addition to the diagonal ribs, have a pair of tiercerons that work together with the diagonal ones for support. The dotted line shows the lines connecting the points of mutual intersection of the tiercerons. In fig. 5-8 vaults have only diagonal ribs and a grid of non-working rails: only in the vault of Fig. 5 there is one tiercerone per support.
Finally, the bottom row (Fig. 222, Fig. 9-11) gives special shaped solutions in which the working diagonal ribs break off in the middle of the arch, occupied by a complex star-shaped pattern. This solution involves a strong ripping of the cross vault, turning its middle into a spheroidal surface. The diagonal rib, slightly protruding at the support, is lost in the middle spherical part of the vault (Compare the diagrams of Fig. 222 with the diagrams of mesh vaults (Fig. 220). Fig. 1, Fig. 220 differs from Fig. 1, Fig. 222 only in the absence of diagonal ribs. In the same way, Fig. 6 Fig. 220 differs from Fig. 3 Fig. 222). Forms 9-11 are transitional to reticulate vaults (Fig. 220). So, fig. 3 fig. 220 gives a frame diagram nearly identical to FIG. 11 Fig. 222.
The architecture of Spain provides even richer forms of vaulted patterns. Spanish masters were not inferior to the best architects of England, who created openwork lace fan vaults of the 14th and 15th centuries. This craftsmanship is so deeply ingrained in Spanish architecture that Gothic vaults can be found in baroque churches from the 17th century. The complex pattern of curved railings was successfully combined with the bizarre forms of the Baroque style, and only the ribs of the vaults received a different profile.
The vault of the Cathedral of Segovia (Fig. 1 and 2 Fig. 223) has diagonal ribs and tiercerons, as in Fig. 4 fig. 222; its pattern is decorative, curvilinear. In fig. 3 fig. 223 depicts the vault of the Cathedral in Salamanca. A complex curvilinear pattern is woven into the normal grid of this star-shaped cross vault.
The solutions to the cross vault in English Gothic deserve special attention. The traditions of the French Angevin School were transferred to England and gave a number of special local solutions. In addition to the mentioned main star vault of the cathedral in Beverley (Fig. 216), we note the vault of the Cathedral in Worcester, built in 1372 (Fig. 224).

The intersecting tiercerons form an octagon in the vault shell (cf. Fig. 4 Fig. 222) with sculpted keystones at the intersection of the ribs.
The vault of Christchurch Church is interesting (Fig. 225). Each formwork has a pair of incomplete tiercerons AQ and AJ, BP and VO, etc.

In the shelyga, incomplete lines HI and FG intersect. The star is outlined by additional edges (shown in dotted lines), or counter-lines LG, SM, N1, 10, etc. and lines KL, MN, OR, etc., connecting the ends of the tiercerons with diagonals. In addition to the peculiar star design, the vault is interesting for its hanging supports, which were then fully developed in Oxford Cathedral and in the chapel of Henry VII in Westminster. In the vault under consideration, the outlines of the diagonal ribs and tiercerons are so close to each other that the result is not a square basket, typical of a cross vault, but rounded, as in a fan vault. The vault is a transitional form to the fan vault, brilliant examples of which are provided by the already mentioned vaults of Oxford Cathedral and the Chapel of Henry VII; however, strong diagonal ribs and weak tiercerons allow it to be classified as a cross vault.
The vault of Mary's Church at Warwick, built 1439 (Fig. 226), has the same grid of tiercerons and liernes as the Christchurch vault. A significant difference is in the star-shaped keystones: in the vault shell the star-lock E has an eight-pointed shape, in the formwork it has a six-pointed shape. Both of these vaults serve as examples of the strong development of ribs in the 15th century.
In the church in Vulpita at the end of the 15th century (Fig. 227), the star vault has already reached the utmost enrichment and complexity of the frame. From the corner supports next to the diagonal rib emerges a bunch of four thiers-cerons.
Between them, additional spacer rails PVQ, PWS, TXU, etc. form a large eight-pointed star. At the end of the 15th century, the ribs lose their structural significance and in the last years of the century, when fan vaults appear (see below), they turn into surface decoration on the stones of the vault. In the last two examples of English cross vaults from the late 15th century, of particular interest is the development in the vault shell of a rich cruciform decorative spot, standing out against the general
background of working ribs. Here there is already a diagonal composition of the decorative pattern, but still made of straight rods.
The German Frugg Chapel of the 16th century occupies a special place in the decoration of the vaults (Fig. 228). Its vault is of the same diagonal cruciform composition with a purely decorative ceiling made of curved arcs. In addition to the large four-petal pattern that covers the formwork, the same lampshade is inserted into the middle, within which the diagonal ribs are decorated with molding. The entire composition uses the four-petal shape of the lampshade, which we examined earlier (see Fig. 4, Fig. 214), and with its curved ribs is close to the Spanish decor shown in Fig. 223. The Frugg Chapel, built in the transitional period to the Renaissance, contains new stylistic elements not only in the decoration of the walls, but also in the decoration of the ceiling, where there is already a desire to create a Renaissance “diagonal” composition.
We will end our review of Gothic vaults and their decoration with two late Gothic monuments that are exceptional in their fantastic curvilinear forms of decoration. In Fig. 229 shows the Vladislav Hall in the palace in Prague, built in 1486-1502. German master Rith; hall size 60x16 m. In Fig. 230 shows the interior of the Anna Church in Annaberg (Germany), built by Durbach and Büttingen in 1499-1520. In both cases, we encounter designs and decor that clearly contradict logic. The drawing of the ribs of Vladislav's hall was deliberately built from arcs of the same radius, with one opening of the compass (Fig. 231); all ribs are double curvature and have no structural significance. The shape of the vault is mainly cylindrical with strippings of an indefinite, crumpled nature. The same is the vault of the Church of Anna, the ribs of which cover the pillars in a helical manner.
Concluding this analysis of the construction of Gothic cross vaults, we note the main stages in the development of constructive techniques. The main period, High Classical Gothic, provides the most structurally advanced systems, built on the full use of the frame. In the next period, the frame is enriched with figured false-constructive decorative ribs. The last period - late Germanic Gothic (Sondergotik) - completely ignores the main ribs of the frame, turning it into a purely decorative carpet pattern of ribs. The last remnants of the division of the individual vaults are removed, and the covering of the hall churches (Hallenkirche) is transformed into a continuous vaulted ceiling on columns.
In the history of Gothic cross vaults we see a series of successive concessions to decorativeness at the expense of constructive principles. The further Gothic went from strict constructive logic, the more arbitrary the composition became to the detriment of artistic qualities. High and late Gothic created diverse and perfect versions of “canopy systems”.
The supports of the vaults, in the form of bundles of extremely thin pillars (columns), directly transform into the ribs (ribs) of the vault. There are no capitals or even parts of the cornice of the antique canopies; the support of the vault is fused with the rib. Through supports passing through a series of horizontal divisions of the wall create Gothic verticalism. With thin supports and stone frames of window openings, the wall becomes a transparent lattice. The canopy on pillars and arcades is the main element of architecture that encloses the space, while the walls are secondary.
In late Gothic hall churches, with equal heights of the middle and side naves, the canopies of the individual naves seem to dissolve mutually, the boundaries of the individual vaults are erased, the latter merge into a common canopy on free-standing pillars. The cross vault in this case provides the simplest and most logical merging of homogeneous vaults into a single stone ceiling along the columns.
VI. conclusions
From the analysis of the infinitely varied surface shapes, rib patterns, frames and spatial solutions of Gothic architecture, it is necessary to draw practical conclusions for modern architectural thought.

Everyone admires the wonderful art of Gothic, extensive studies are written about it, but ways of using this wealth in new architecture have not been discovered. At the same time, all paths are open to the legacy of the Renaissance, and it is often used blindly, without proper criticism. In this regard, our final conclusions about the system of ceilings with cross vaults are based on a comparison of the forms and decorations of Gothic and Renaissance vaults; This method contributes, in our opinion, to the identification of organic, truthful, truly beautiful elements in the work of Gothic and Renaissance, which retain their value for modern times.
1. Of the three modern types of vaults - ribbed frame vaults, solid smooth shells and folded ones - in Gothic we find mostly ribbed frame vaults or with stiffening ribs and rarely folded ones. In the Renaissance, smooth, continuous vaults were used almost exclusively.
2. Renaissance cross vaults are poor in form; the correct cylindrical shape dominates. Gothic cross vaults reveal an exceptional wealth of forms and are valuable material for modern shaping.
3. The Renaissance cross vaults, built rough in brick, have a cover made of smooth plaster, requiring picturesque decoration; Thus, three production processes are needed here. Gothic vaults are created by the hands of a master architect from cut stones without picturesque decoration; here everything is reduced to a single creative process. In modern construction conditions, vaults can be made in the following types:
a) solid reinforced concrete shell vaults, which, like classical and Renaissance vaults, require plasterwork, low-relief stucco decoration (antique al primo) and painting;
b) ribbed vaults with a reinforced concrete rib frame and filling the formwork with any other material (The vault of the hall of the Kazansky railway station restaurant in Moscow was made by the author of this book (Fig. 359)) - brick, majolica, ready-made decorative boards, etc.;
c) ribbed vaults, but based on the basic positive principles of Gothic masonry - made of ashlar or artificial stone with any surface texture.
In cases b) and c), the ribs, as working elements of the structural frame, must be highly profiled.
4. In the Renaissance, vault decoration by modeling and painting often constituted the main task of the artist-architect; the decorator and painter did not always understand the forms of the vault and often did not consider it necessary to reveal them by pictorial means. In Gothic, decor and construction represent a single compositional whole in the master’s work. Modern architecture must continue to develop the brilliant decoration of the Renaissance, both in artistic and technical terms, but with strict adherence to the basic principle of Gothic, i.e., the synthesis of decoration and structure.
5. Due to the difficulty of matching the geometric coffered pattern with the shape of the cross vault, the Renaissance did not use it for decoration. Gothic, using an oblique network of ribs in the form of a caisson for a cylindrical vault, did not transfer it to the cross vault. With the current state of technology, this problem can be solved. Based on the example of a wooden circular-mesh cross vault (Fig. 198), a coffered structure can be made in reinforced concrete and metal. Work in this direction will give new, modern forms of the cross vault.
6. The Renaissance developed on the surface of the cross vault the form of a diagonal composition of decor with picturesque medallions along the axes of the formwork and a ceiling in the center of the vault, weakly revealing the diagonal ribs (A rare example of a “diagonal composition” on a Gothic cross vault with openwork medallions carved from stone is given by the vault of the castle chapel Huaron in France (Fig. 232)).
In Gothic, the composition of the decor always includes diagonal ribs and auxiliary tiercerons, in which the middle ceiling is impossible or is in its infancy (In German Gothic: the decors shown in Fig. 9-11, Fig. 222; the ceiling of the Frugg Chapel, Fig. 228, in English Gothic - vaults of churches in Worcester Fig. 224, Wulpite Fig. 227 and Warwick Fig. 226). The multiplicity of ribs in English Gothic (See Exeter Cathedral, Fig. 218) destroys the meaning of formwork and leads to an understanding of space that is alien to us.
A modern decorative composition should reveal the main diagonal ribs, avoiding a multiplicity of false ribs (layers). At decoration diagonal ribs, it is more correct to develop lampshades in formwork, avoiding the middle lampshade in shelyga. Basically, with a clear expression of the shape of the cross vault, it is necessary to use the strength and variety of the pictorial decoration of the Renaissance (for example, the decor of the vault of the Villa Madama, Fig. 212).
7. In Gothic, the secondary elements of the frame (mostly piers), which make up a curvilinear pattern along the surface of the vault, do not lie in a vertical plane and have a double curvature. The same arcs of double curvature, in the form of curves in the plan of arches, are known in Baroque vaults.
When constructing decor from arcs, rods and frames on curved surfaces of the vault, the main ribs of the same curvature, lying in the vertical plane, should be profiled more strongly. The decor from double curvature rods should be done in light low relief.
8. The complexity and variety of forms and decorations of vaults force us to recall that the composition of the decor should be created simultaneously with the decision of the spatial form of the vault. To build the latter, you need a thorough knowledge of past and modern arches and an understanding of their work. Vaulted roofing is one of the most difficult and
the most interesting spatial problems of architecture.

Meaning of the word REDD in the Architectural Dictionary

in architecture, a spatial structure, ceiling or covering of structures, having a geometric shape formed by a convex curved surface. Under load, vaults, like an arch, work primarily in compression, transmitting vertical forces to the supports, and also in many types of vaults horizontal (thrust). The simplest and most common is a cylindrical vault, supported by parallel supports (walls, rows of pillars, arcades, etc.); in cross section it is part of a circle, ellipse, parabola, etc. Two cylindrical vaults of the same height, intersecting at right angles, form a cross vault, which can rest on free-standing supports (pillars) at the corners. Parts of cylindrical vaults - trays, or cheeks, resting along the entire perimeter of the structure being covered on walls (or arches, beams) form a closed vault. A mirror vault differs from a closed vault in that its upper part (plafond) is a flat slab. A derivative of the vault structure is the dome. By cutting off parts of the spherical surface of the dome with vertical planes, a domed (sail) vault is formed. (vault on sails). Numerous varieties of these basic forms are determined by the difference in the curves of their sections, the number and shape of formwork, etc. (vaults - pointed, creeping, barrel, honeycomb, etc.). The oldest are the so-called. false vaults in which horizontal rows of masonry, hanging one above the other, do not convey thrust forces (for example, the vault of the casemates of the Acropolis of Tiryns, 13th century BC). In the 4th-3rd millennium BC. e. in Egypt and Mesopotamia, cylindrical vaults appeared, which spread in the architecture of Ancient Rome, where closed vaults were also used (vault in the Tabularia gallery, 79 BC) and cross vaults (Basilica of Maxentius (Constantine; around 315 AD) - both buildings in Rome). In Byzantine architecture, cylindrical, sail, and cross vaults were used, in particular, in cross-domed churches. In the architecture of Azerbaijan, India, China, the peoples of Central Asia and the Middle East, pointed vaults were predominantly used. In Western and Northern Europe in the medieval period, cross vaults spread, which in Gothic architecture acquired a pointed character with the main structural element - a rib. Since ancient times, vaults have been made primarily from natural stone and brick. The bending strength of the stone limited the span width in the post-and-beam structure by approximately 5 m. The use of vaults (in which stone, working not in bending, but in compression, exhibits higher strength) made it possible to significantly exceed these dimensions. From the 2nd half of the 19th century. S. were often created from metal structures. In the 20th century appeared Various types monolithic and prefabricated reinforced concrete thin-walled shell vaults complex design, which are used for coverings of long-span buildings and structures. From the middle of the 20th century. Wooden laminated vaulted structures are also widespread.

Architectural Dictionary. 2012

See also interpretations, synonyms, meanings of the word and what REDD is in Russian in dictionaries, encyclopedias and reference books:

• REDD in the Dictionary of Construction Terms:
  building construction curvilinear shape, used to cover the room. There are parts of the arch: HEEL - the supporting part of the arch. LOCK - upper part...
• REDD in the Explanatory Construction and Architectural Dictionary:
  - a building structure of a curved shape that serves to cover a room. There are parts of the arch: the heel is the supporting part of the arch. Castle - upper…
• REDD in the Dictionary of Fine Arts Terms:
  - a spatial structure, ceiling or covering of structures having a geometric shape formed by a convex curved surface. Under load, the vault, like an arch, works...
• REDD in the One-Volume Large Legal Dictionary:
  - the second stage of the judicial process in ancient Rus'. the person in whose possession the missing item was found had to indicate who had it...
• REDD in the Big Legal Dictionary:
  - the second stage of the trial in Ancient Rus'. The person who found the missing item had to indicate who had it...
• REDD in the Dictionary of Economic Terms:
  LAWS - normative acts, collections of legislation compiled into one publication and arranged in a certain order (systematic, chronological, etc.)<например, С.з. …
• REDD in the Big Encyclopedic Dictionary:
  architectural spatial structure, ceiling or covering of structures having a geometric shape of a convex curvilinear ...
• REDD in the Great Soviet Encyclopedia, TSB:
  in architecture, a spatial structure, ceiling or covering of structures, having a geometric shape formed by a convex curved surface. Under load S., like an arch...
• REDD in the Encyclopedic Dictionary of Brockhaus and Euphron.
• REDD in the Encyclopedic Dictionary:
  , -a, m. 1. see reduce. 2. Information, materials, texts brought together into one whole and arranged in a certain order. WITH. …
• REDD
  LAWS, compiled into one publication and located in definition. order (systematic, chronological, etc.) normative acts, collections of legislation (for example, S.Z. ...
• REDD in the Big Russian Encyclopedic Dictionary:
  architect spaces. structure, ceiling or covering of structures having geom. the shape of a convex curved surface. Main types of vaults: 1 - cylindrical; 2...
• REDD in the Complete Accented Paradigm according to Zaliznyak:
  svo"d, svo"dy, svo"da, svo"dov, svo"du, svo"dam, svo"d, s"dy, svo"dom, s"dami, s"de, ...
• REDD in the Popular Explanatory Encyclopedic Dictionary of the Russian Language:
  -a, m. 1) Information, texts, documents, digital data, etc., brought together into one whole and arranged in a certain order...
• REDD in the Thesaurus of Russian Business Vocabulary:
  Syn: see...
• REDD in the Russian Language Thesaurus:
  Syn: see...
• REDD in Abramov's Dictionary of Synonyms:
  [civil marriage, unmarried (Dahl, bring together)] see ...
• REDD in the Russian Synonyms dictionary:
  Syn: see...
• REDD in the New Explanatory Dictionary of the Russian Language by Efremova:
  m. 1) Action by value. verb: reduce (1*1,2,4,5,7,8,11). 2) a) Collected, combined into a single whole and arranged in a certain order...

CYLINDRICAL VORCH

In the architectural schools of antiquity, the outer surface of the cylindrical vaults covering the building, aligned with the slope using plastering, directly bears the roof tiles; Only in the Byzantine architecture of Ravenna can one hardly find several examples of light vaults protected by a wooden roof. The last technique - a Romanesque innovation, probably of the Cluny school - became commonly used; the consequence of this was material savings and a reduction in thrust; The Cluny barrel vault is primarily a lightweight vault covered with a roof.

Outlines

Until the very end of the 11th century. the outline of the vaults is semicircular; when there is a need to increase the lifting boom, they are content with raising the level of the heels of the arch. The only examples of a raised arch of an oval shape known to us are at Tournus and are probably inspired by some Asian model.

Pointed vault, which due to a dating error Church of Saint Front dated back to the 10th century, is not found in any building that could be confidently dated earlier than the 12th century. In Issoire ( rice. 98, V), where the roof lies directly on the roofing of the vault, the pointed arch was a means of reducing the massiveness of the masonry, and only in Burgundy was it used to reduce the thrust (C).

Note: The question of when the pointed vault appeared in Romanesque buildings remains controversial. If the Church of Saint-Front in Périgueux cannot be attributed to the 10th century, then examples of earlier monuments than in Issoire are known: the old cathedral in Digne, which can be dated to the end of the 11th century, has a pointed vault. Some researchers of Romanesque art, for example Kishera, prove on a number of monuments that the appearance of pointed vaults in France should be attributed specifically to the 11th century, and not to the 12th century. See Lastеуrie, mention. cit., p. 240.

Rice. 98

The Clunians accepted it from the moment (beginning of the 13th century) when they began to erect barrel vaults, boldly placed on very high abutments, as in the main naves of the churches of Chariteau on the Loire or Parais le Monial; the balance of these vaults was unstable, and any reduction in thrust turned out to be extremely important. The Clunians appreciated the static advantages of the pointed arch, and we owe it to them for its use, which marked an era in the history of architecture, since this arch represents a progress in balancing systems.

Execution methods and masonry

Romanesque architects, using stone as a material for vaults, deprive themselves of one advantage - the ability to build without circles; The main difference between Romanesque vaults and Byzantine ones is precisely that they were erected on circles.

The vault is never laid out in vertical successive rows; such masonry is justified only for brick vaults made without circles. The rows of masonry are also never horizontal, like the rows of small stones in Roman vaults; masonry in horizontal rows is associated with the idea of ​​​​an artificial monolith, and the Romanesque vault is always made of wedge stones.

Cylindrical vault with ribs

In most cases, the inner surface of Romanesque box vaults is divided at certain intervals by girth arches ( rice. 99). Usually these arches are independent of the masonry of the vault (drawing C); sometimes at the heels they merge with the masonry of the vault and then gradually protrude until, finally, at the very top of the vault, their lower surface becomes parallel to the inner surface of the vault itself (B). In some cases, the girth arches even cut through the vault (A).

Obviously, these arches served to enhance the rigidity of the thin vaults. But they provided a special service when laying vaults: now it was necessary to fear not the breakage of the circles, but their deformation, and the presence of girth arches guaranteed against this.

First, the girth arches were brought out; they imparted extreme rigidity to the circle system, and the vault was erected on the circles strengthened in this way. Rice. 100 clarifies this explanation by showing the main cases from the practice of installing circles.

Auguste Choisy. History of architecture. Auguste Choisy. Histoire De L'Architecture