This section is from the book "Modern Buildings, Their Planning, Construction And Equipment Vol5", by G. A. T. Middleton. Also available from Amazon: Modern Buildings.
The most simple form of vault is one having its cross section semicircular, as shown at AB in Fig. 118. This form is sometimes carried out with stones of even thickness throughout, and sometimes with stones decreasing in thickness towards the crown of the arch, as the thrust increases from the crown to the springers. Heavy masses of masonry must be provided to form the supporting walls, to ensure stability against the thrust and weight.
The details are simple enough, each voussoir being of regular section, with its beds and faces similar as to bevel except as to the magnitude of the stone. For instance, the bevels for the joints are at a regular angle with the axis in all cases, as are also the face bevels (intrados) which would be parts of the semicircle of the vault.
Fig. 117 represents a stone in perspective, being one of the members of a plain cylindrical vault struck from centre C. The dotted lines described around the stone show the squared block previous to being shaped ready for its final use in the vault.
The dotted line DD represents the axial line of the stone, and serves to set out the bevel or rake of top and bottom beds. The intrados and extrados are cut to bevels set to arcs of circles with centre C.
A further advance is made where side openings or subsidiary vaults are introduced.
Fig. 118 shows the simplest case of the interpenetra-tion of cylindrical vaults, in which the space to be covered is square, the vaults being consequently of equal span and rise. The groins, or intersections of the vault surfaces, form diagonals which on plan are at right angles to one another, and cross from corner pier to corner pier, both on the intrados and extrados. These form straight lines on plan. A section through one of the diagonals from corner pier to corner pier gives a semi-ellipse, as shown in Fig. 118 and explained in Chapter VI (The Geometry Of Masonry).
The method of setting out such a vault is as follows Draw the plan Abcd, showing the bed joints of the springers and the groin lines. Set up the sections of the vault as shown, divide them up into an odd number of equal parts, and draw in the joints radiating from the centres from which the intradoses are struck. The first joint from the springing line is usually made horizontal, and the second stone has its upper surfaces formed as shown. These lower stones are not invariably treated in this manner, but it is only waste labour to cut away the stones to form the true intersection of the cylinders on the extrados, especially as the load is required at this point to resist the thrust of the vaults; and, moreover, this method of treating the joints enables the building in which they occur to be carried up and the timber roof constructed before the rest of the vaults are completed under cover. The joints can now be indicated on plan; the radial joints or beds of the intrados being projected to meet the diagonals for the plan looking up, and those of the extrados being similarly projected for the plan looking down. The plan looking up is shown on the left-hand side of Fig. 118, and the plan looking down is shown on the right-hand side. The transverse joints are made vertical, and those occurring at the groins are drawn in first, and are projected from the junction of the bed joints on the extrados of the section, except in the case of the keystone where the four arms have been made of a convenient length. The other vertical joints are drawn in anywhere so long as they break-joint on plan. The sections along the intrados and extrados are also shown upon the plan, the dotted lines being ordinates which have been made equal to the ordin-ates of the cross section taken from the springing line.
To make the drawing clearer, sketches of the three lowest corner-stones and the keystone are shown. Bed and face moulds of stones Nos. 1, 2, 3, and the keystone are also shown at the bottom of the figure. To bring the springer No. 1 to its required shape, work the top and bottom bed joints parallel to each other, making the vertical distance between them equal to the vertical height above, as shown on the face mould, and scribe on the bed mould Then work the two vertical' faces square with the bed, scribe on the face moulds, and work the curved soffits, care being taken to keep.
the groins absolutely true. For stone No. 2, work the top and bottom beds parallel to each other and at the correct distance apart, scribe on the bed mould, and work the two vertical faces, scribe on the face mould and work the splayed surfaces through, and then work the curved soffits, keeping the groins quite true.
In this case only one face mould is required, as both the arches are similar.
Where the space to be vaulted over is rectangular and not a square on plan the vaults may be arranged in several different ways. Either one of the vaults may be cylindrical and the other elliptical, or the smaller arch must be stilted to bring its crown to the same level as that of the larger arch; or the smaller arch may be cylindrical and spring from the same level as the larger arch - in which case the groins will not cross at the crown. The method of finding the curves of intersection has already been shown in Chapter VI (The Geometry Of Masonry).
Fig. 119 shows a vaulted roof over a rectangular space, in which the smaller vault is made semicircular and the large vault elliptical, to accommodate itself to the smaller vault surfaces. In this case the smaller vault is set out to full in section. The bottom beds of the springers are represented at the corners of the plan, and the diagonals are drawn straight across from corner to corner. The soffit joints are now projected from the section of the smaller vault down upon the diagonals, and the points thus found upon the diagonals are projected up at right angles to the springing line of the larger vault. Portions of these lines are cut off above the springing line equal to the ordinates of the smaller vault above its springing line. A curve drawn through the points thus found gives the intrados of the larger vault. The extrados of the larger vault is then found in a similar method, and the joints are found by joining the ends of the ordinates. The joints on plan are similar to those shown in the case of Fig. 118. The bed and face moulds for the three lowest stones and for the keystone are also as shown on Fig. 118. The shape of these stones is similar to the corresponding stones of Fig. 118, as shown by the sketches.