Definition of vaults. Types of wooden vaults

Romanesque vault

An important task of Romanesque building art was the transformation of the basilica with a flat wooden floor into the vaulted one. At first, the vault covered the small spans of the side naves and apses; later, the main naves also began to be covered with the vault. The thickness of the vault was sometimes quite significant, so the walls and pylons were designed thick with a large margin of safety. Due to the need for large covered spaces and the development of construction technical ideas, the construction of initially heavy vaults and walls began to be gradually lightened.

A vault makes it possible to span larger spaces than wooden beams. The simplest in form and design is a cylindrical vault, which, without moving the walls apart, presses on them from above with enormous weight, and therefore requires especially massive walls. This vault is most suitable for covering rooms with a small span, but it was often used in the main nave - in France in the regions of Provence and Auvergne (Notre-Dame du Port Cathedral in Clermont).

Later, the semicircular shape of the vault arch was replaced with a pointed one. Yes, nave cathedral in Otyun (beginning of the 12th century) it is covered with a pointed vault with so-called edge arches.

The basis for new types of vaults was the old one roman straight cross vault above a square room in plan, obtained by the intersection of two half-cylinders. The loads arising from this arch are distributed along the diagonal ribs, and from them are transferred to four supports at the corners of the space being covered. Initially, the ribs that appeared at the intersection of the semi-cylinders played the role of arches, which made it possible to lighten the entire structure (St. Stephen's Cathedral in Cana, 1064-1077; the monastery church in Lorsch was the first completely covered with basilica vaults).

Monastic church in Cluny. Romanesque cross vault:
1 - end ribs; 2 - diagonal ribs; 3 - lock; 4 - stripping.

If you increase the height of the vault so much that the diagonal intersection curve turns from elliptical to semicircular, you can get the so-called raised cross vault.

The vaults most often had solid masonry, which, as we said, required the construction of massive pylons. Therefore, a big step forward was Romanesque composite pylon: semi-columns were added to the main pylon, on which the edge arches rested, and as a result, the expansion of the arch was reduced. A significant structural achievement was the distribution of the load from the vault over several specific points due to the rigid connection of the transverse edge arches, ribs and pylons. The rib and edge arch become the frame of the vault, and the pylon becomes the frame of the wall.

In more late time First, the end (cheek) arches and ribs were laid out. This design was called ribbed cross vault. During the heyday of the Romanesque style, this vault was made higher, and its diagonal arch acquired a pointed shape (Church of the Holy Trinity in Cana, 1062-1066).

To cover side naves, instead of a cross vault, they sometimes used semi-cylindrical vaults, very often used in civil engineering.

Romanesque designs are, first of all, a raised ribbed vault, a pointed arch and the suppression of oblique lateral thrusts from the vaults by a system of supports. They create the basis for the subsequent Gothic style in architecture.

CROSS Vault

As a rule, the cross vault is avoided and, before using it, the combinations indicated on the rice. 101: Instead of arranging the intersection of two barrel vaults, they are placed one above the other, so that the heels of one vault lie on top of the castle of the other. Example A is taken from Saint-Rémy in Reims; example B - from Saint-Benoit on the Loire. Little by little, builders become bolder: they risk using a cross vault, although only over the side naves of churches, where the expansion is insignificant.

Speaking about the architectural schools of the East, we pointed out as a very ancient technique of Syrian builders a system of cross vaults made of stone, in which rib wedges were laid at the corners in a bandage (en besace). It was this type of cross vault, apparently alien to the ancient architecture of the West, that was adopted by Romanesque architects. In Fig. 102, M The general principle and features of the application of this code are shown.

In the cross vaults of Roman Asia, the formwork was cylindrical. The strippings of Romanesque vaults, in order to give them greater rigidity, are made open in all directions, and this leads to the fact that the sections of the vault between the ribs receive a spherical shape. The bandage of wedge-shaped stones along the ribs is exactly the same as in ancient vaults.

Various vault shapes

Cluny school.- On the drawings M and N rice. 102 the most common outlines of vaults are shown - those that are predominantly used by the Cluny school, the most influential of all: the diagonal arch, instead of the elliptical outline inherent in Roman vaults, noticeably approaches the semi-circular one, the curves of the formwork have almost the same rise as the diagonal arch.

To implement this condition, either a raised arch or a pointed arch is used, according to the era. Example M shows the use of an increased semi-circular shape for formwork. Example N, taken from the church at Vassy, ​​shows a cross vault with an oblong plan, where both pointed and semi-circular outlines were used for the cheek arches: the larger bay is covered by a semi-circular arch, the smaller by a pointed arch.

We owe the Cluny school a cross vault with pointed bay arches, but it must be said that they adopted it, so to speak, out of necessity and for a long time resisted its use.

In France, this school until the middle of the 12th century. adheres to a semi-circular outline, and only in the churches of Palestine - and then under the pressure of ingrained techniques of local practice - does it allow cross vaults, where the arches always have a pointed outline. While in Palestine the Cluny school builds churches in Lydda, Abu Ghosh, etc., where all the cross vaults have cheek arches of a pointed outline, in France, in Vézelay, it still adheres to the cheek arches of a semicircular outline.

In all cases, the Cluny cross vault differs from the classical type by the elevation of the top of the vault and the sphericity of the formwork, which we have already pointed out in the description of the masonry of the vault.

Rhine school.- The Rhine cross vault (T) is even more elevated and more spherical; it excludes the pointed shape. Originating in a country where Byzantine influence was still alive, dating back to the era of Charlemagne, the Rhine vault is a dome on sails, slightly modified by the presence of almost imperceptible ribs that fade towards the top of the vault, merging with the skufia that completes it.

Note: Choisy, saying that in Germany “the Byzantine influence was still alive, dating back to the era of Charlemagne” (see above, in the chapter on Byzantine architecture), implies the rivers found along the river. Reina buildings, typologically related to the Aachen Cathedral, built under Charlemagne (VIII-IX centuries); these are the centric churches in Mettlach (built between 975 and 993), in Otmarsheim (11th century), the choir of the monastery church in Essen (874, burned down in 947), etc. Written information has been preserved about the church in Mettlach , indicating that its builder proceeded in his plan from the Aachen Cathedral, but here we can talk about using the latter as a model, and not about direct borrowing. Aachen Cathedral is typologically close to the Church of St. Vitaliy in Ravenna (VI century), comparison of the latter with the Lateran Baptistery of St. John in Rome, the Temple of Jupiter in Spalato, the Baptistery in Nocera, the Church of St. Constantius in Rome and others say that the Church of St. Vitaliy in Ravenna must be considered as a monument that largely preserved the features of late Roman architecture, which could still be spoken of not as Byzantine architecture, but as the architecture of the eastern part of the Roman Empire. Moreover, from the compositional side, the church of St. Vitalia in Ravenna is closer to the examples of centric buildings of Italy than of Byzantium; in particular, great similarities can be seen in it with the Lateran Baptistery mentioned above. The Aachen Cathedral (or, rather, the chapel), despite the typological similarity with these monuments, also has significant stylistic differences (see N.A. Kozhin, Fundamentals of Russian Pseudo-Gothic, Leningrad 1927, note 8). In addition, it should be noted that buildings of the centric type of Romanesque style are found not only in the Rhineland, but also in France and, finally, in Austria. See: OtteH., Geschichte der Romanischen Baukunst in Deutschland, Leipzig 1874, pp. 85ff; Lasteyrie, mention. cit., pp. 145 ff.

Auvergne, Normandy.- The vaults of Auvergne, Poitou and Normandy have a completely opposite character: they approach the Roman type of intersecting barrel vaults. More precisely, the Norman cross vault ( rice. 103) is a cylindrical vault B, cut through by lunettes L with semicircular cheek arches.

It is clear that the main cylindrical vault B was laid out along continuous circles, then the flooring for the lunette was installed on the flooring of these circles and on the circles of formwork L. When all cheek arches have the same span, a classic cross vault is created; but as soon as the plan becomes elongated, the lunettes take on a strange appearance: if the span of the vault B is less than the span of the lunette L, then the latter protrudes in the form of a conical sail, as can be seen from the above drawing. Among other Norman examples, this mark is found in the ruins of Jumièges.

Rice. 103

Rice. 104

Naves covered with cross vaults are built according to the latter type, without supporting arches separating them: the main cylindrical vault stretches the entire length of the nave ( rice. 104) and the lunettes crash into it. Supporting arches between two bays are only necessary for domed cross vaults, such as Cluny and especially Rhine vaults.

In Byzantine architecture, where domed vaults are erected in vertical successive rows, these rows merge with the supporting arches (drawing A), and the latter cease to exist separately; in Romanesque architecture, where the vaults rest on trussed arches (Drawing B), the latter are highlighted, and a column is placed under every fifth arch as a support. This is already a development of the idea that was discussed in connection with the arcades.

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

Types of building vaults

REDD- in its most characteristic form, a vault is a COVER, which has a concave curved surface from below (a combination of curved surfaces or a combination of curved surfaces with a plane) and formed by a system of wedge-shaped stones, which, in addition to the vertical load on the SUPPORTS, also gives a horizontal SPACER. In particular varieties of the arch, understood in the broader sense of this term, there may be various deviations from the above characteristic features vaulted ceilings. S. can, for example, be used not as a ceiling, but as an element of a supporting STRUCTURE with a concave surface facing upward rather than downward. It is not the stones or bricks themselves that can have a wedge shape, but only the seams between them. The vault may not be a system of stones, but a MONOLITH and constructed from other materials, for example, from reinforced concrete. The horizontal thrust may be absent, minimal, or dampened in the body of the arch itself, for example, by ring tie-downs or other S. REINFORCEMENT embedded in the body. S. can be divided into elevated, lowered and flat: 1) elevated - when the ratio of the S. boom (lift) to the S. span is more than 1/2; 2) reduced - the ratio of the boom to the span of the arch fluctuates between 1/4 and 1/2; 3) flat - the ratio of the boom to the span of the arch is at least 1/4.

1 - round cylindrical vault (barrel vault); 2 - pointed barrel vault (pointed); 3 - barrel vault with transverse edges; 4 - cross vault (K - formwork)

Varieties:

BALKHI CODE- built over rectangular, close to square rooms; its MASONRY begins from the corners with arches at 45° to the WALLS, connecting into a TREE at the middle of each of the walls of the room (Middle Asia).

BOCHARNY Vault- formed by the movement of a flat curved generatrix along a curved guide.

FAN Vault- ARCH RIBS, emanating from one corner, have the same curvature, make equal angles to each other and diverge like a fan, forming a funnel-shaped surface (English GOTHIC - see)

BOX VOUCH WITH FORMWORKS- is formed by the intersection at right angles of a box vault with other box vaults, but with a smaller span and lower height.

CYLINDRICAL Vault- the surface of the ARCH is formed by the movement of a generatrix of a straight line (remaining parallel to itself) along a flat curved guide or, conversely, by the movement of a flat curved guide along a straight generatrix. According to the shape of the guide S.ts. are divided into: 1) circular or semicircular; 2) box, elliptical and parabolic; 3) pointed.

STEP Vault- type VOD, used to cover small rooms using a system of transverse ARCHES, arranged in steps, on which are supported stepped arches located in the longitudinal direction, forming an open square in the center, sometimes completed with a light DRUM.

POINTED Vault- VOD with a guide, which represents two arcs of a circle intersecting in SHELIG.

VOD CELL- a special type of Gothic Vault with a complex pattern of ribs (often without a rib FRAME) and with pyramidal recesses between them.

CLOSED VOX- CONDITION of 4 or more TRAYS; appl. for covering square (and polygonal) rooms; pressure

MESH Vault- Vault, to a certain extent similar to the STAR Vault, but without the diagonal ribs of the CROSS Vault; in place of the diagonal ribs there are four spherical SAILS; the RIB pattern forms a mesh pattern.

SAILING Vault- Vault on SAILS, formed by cutting off four equal half-segments (in its lower part) from a spherical (or parabolic) DOME (cf. DOME ON SAILS).

RIB Vault- VOD on a frame made of RIBS, which absorb and transfer the load of the vault to its supports.

SUMMARY IS FALSE- formed by a gradual overlap inside the horizontal rows of MASONRY; does not give horizontal SPACING.

STELLAR Vault- one of the forms of the cross Gothic (rib) Vault, in which a number of additional (auxiliary) TIERSERON ribs are introduced; in a thin frame S.z. The main diagonal ribs of the CROSS Vault are clearly visible.

MIRROR Vault- a closed vault, the top of which is cut off by a horizontal plane (or a very flat vault); the remaining lateral cylindrical parts of the closed vault are called PADUGS; the middle horizontal plane is a mirror; the mirror is usually separated from the holly by a clear FRAME and is often used for PAINTING.

WEDGE Vault- laid out from wedge-shaped stones; It is not the stones that can have a wedge shape, but the seams between them. Such a S. gives a horizontal SPACE.

BOX Vault- RED with a guide, which is a box, elliptic or parabolic curve.

CROSS Vault - COVERING, formed by the intersection at right angles of the surfaces of two cylindrical VOCKS with identical lifting booms: consists of four FORMWORKS; appl. for covering square and rectangular rooms; pressure S.k. focused on four corners.

CROSSED Vault- a closed VOD, cut through by two intersecting cylindrical vaults, at the intersection of which there is a light DRUM.

The square plan is the main one for the cross vault. The pure form of this vault, of four equal formworks with two mutually perpendicular axes, dictates square shape 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 or decorative columns at all, but 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 is created, should be called a false canopy.
In all architectural styles one can trace this method of spatial composition - this canopy system, but only in other different versions 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 more quickly. 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 it technical side, masonry methods and material selection. 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 ASV 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.
The fourth, most interesting way to construct an ellipsoidal formwork is shown in Fig. 4.
Having described an arbitrary ellipse around the square plan ABC with axis C-C, we will rotate it around its own axis C-C. 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 this case two edges 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 the possible decor options, 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 rib 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 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 design inherent in the best examples 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 edge 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 is given 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 - from 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 of the most original Renaissance decorations, we note the pure, 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 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 best works of the Renaissance masters given, we give 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. A flexible, elastic frame system, within certain limits, allows the architect, in search of the best decoration, to direct the ribs (ribs) of the vault at his 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 the Cathedral in Exeter (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. are tiercerones, El, EH, EF and EG are 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, into eight formworks, which can have any shape - 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 the hall temples of the late Gothic, with equal height 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, authentic beautiful elements in the works 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 the development of 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 construction.
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), it is possible to implement caisson structure in reinforced concrete and metal. Work in this direction will provide new, modern forms 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). When decorating diagonal ribs, it is more correct to develop lampshades in the formwork, avoiding the middle lampshade in the 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.

Arch- spatial design with a constant curved profile and straight guides. Two of which usually serve as supports. The vault profile can be outlined by any convex curve.

Types of wooden vaults.Wooden shell vaults from laminated wood. Two types are used: thin-walled from several layers of glued boards and smooth glued plywood.

Definition of the reticular vault. Its design and components. a mesh cylindrical shell formed by two systems of intersecting circles, directed at an angle to the generatrix of the arch and assembled from separate rod elements - jambs.

circular or pointed vault with an arc of constant curvature. The spans of the circular-mesh vault reach 50 m.
For our range of timber materials, the maximum span is 25 m. Boom-to-span ratio
vault is assumed to be f/l > 1/7, and the ratio of section height to span h/l = 1/100, in pointed circular-mesh vaults f/l >.1/3, f1/l1 > 1/15

Mesh node of the circular-mesh vault consists of three jambs; one passes, without interruption, through this node, and the other two adjoin with some confusion S to the through jamb approximately in the middle of its length and are connected by bolts. The amount of displacement should be minimal and selected so that the holes for the bolts at the ends of the jambs are outside the beveled end surface of the latter.
The holes for the bolts are made with a small margin, so that the bolts only absorb tensile forces. Shoals
under the influence of the longitudinal compressive force in them, slightly shifting, they cause tension in the bolts, creating the friction necessary for the rigidity of the unit.
At each node, the median plane of the through jamb passes through the normal to the surface of the arch at the nodal point, which, together with the constancy of the radius of curvature of the arch, ensures the standardization of the elements.
Shoals going in one direction form a helical line.

The unfolded surface of the coating is thus divided into equal rectangular cells. The intersections of the diagonals of the rectangles fix the position of the nodal points of the coverage grid.
The entire covering grid, together with the end arches, consists of six types of jambs. The main jambs forming the middle nodes of the grid, depending on their direction, are divided into right and left, mirror-like to each other and identical in size.

Circular mesh vaults are often solved without the use of bolts. In this case, the abutment of the jambs to each other is solved by means of cuttings (metal-free circular-mesh vaults of the engineer Peselnik system). "on spikes"
The circular-mesh vault rests on the mauerlat. The thrust is usually perceived by round steel ties. The assembly of the vault is carried out without circles, using light movable scaffolding, spaced every 2-6 m.

28Definition of domes. Types of dome surfaces. Classification of metal and wooden domes according to design features (shown schematically)

Dome- a shell of positive Gaussian curvature on a circular, elliptical, polyhedral plane.

Types of dome surface: surface of rotation with a vertical axis: sphere, parabaloid, ellipsoid, single-sheet hyperboloid, cone. Also, remaining generally within the aisles of these surfaces, wavy, folded, multifaceted surfaces are possible.

Classification of metal and wooden domes according to design characteristics:

· Ribbed a system of semi-arches located in a vertical plane, with an upper ring to which the tops of the semi-arches converge. If necessary, it is reinforced with spacers

· Ribbed ring suggest the use of ring connections together with semi-arches as load-bearing elements

· Ribbed mesh retain the meridian basis of construction, but the fields between the ribs are filled with a grid, most often in the form of interlacing secondary ribs