21. In Fig. 19 is shown at (a) the plan of a semicircular stairway; while in Fig. 20 is shown the front elevation at (a), the development of the string at (b), and a detail of the rail on the upper landing at (c). The first three treads a, b, and c of the plan, Fig. 19, are 11 inches wide, and the remaining ones are so spaced as to be wider than this, if measured on a line midway between the strings. The diameter of the well hole is 14 ft. 6 in.; and, deducting twice the distance from the wall to the center of the treads, it will be found that the diameter of a circle drawn through the center of the flight is 9 ft. 11 in., or 119 inches, which, multiplied by 3.1416, will give for the circumference 373.85 inches. Dividing this by 2 and deducting from the result 1 inch (the distance from the top riser to the beam d) gives the length of the center line required as 185.92 inches. This divided by the number of treads determines the width of each tread on that line to be 11 5/8 inches. The lengths of the strings around the outer and inner circumferences are taken on the inside faces, and determined in the same manner. In a stair of this character it is not possible to make sections through any particular part in such a way as to be of any service, but the development of each string is given instead.

(a)

(b)

Fig. 19.

(a)

(c)

22. To lay out a plan of such a flight of stairs as this, begin with the wall string and lay off from the foot of the flight the first three treads 11 inches wide, and the other sixteen will be 1 ft. 4 1/1 1/6 in., the latter dimension being found in the same manner as the width on the center line, and used in the development of the string, as shown at (b). A line drawn through the lower intersections of the treads and risers will form a basis from which to determine the width of the wall string, and to lay off the top and bottom lines of this string, as shown in Fig. 19 (b). The proportion of the treads to the risers in the short straight part of the string is 11 to 7|, while that of the curved portion is 16 1/1 1/6 to 7 3/8, thus causing the string to take a different angle; the juncture of these two parts should be eased off, instead of showing the sharp angle, which would be out of harmony with a circular stair. This applies only to the wall string, as, in the development of the face string shown at f in Fig. 20 (6), we have a surface that is circular throughout its entire length. These circular strings are usually made of wrought-iron or steel plate, capable of being bent to the required curve, and this bending is done by hammering on a curved block if the material is light, or by mechanical pressure in case of heavy work.

23. With the exception of the straight part at the bottom of the wall string, both strings are helical in shape; that is, they take the form of a ribbon spirally wound around a cylinder and rising at a certain ratio.

To get this helical shape, the strings are first laid out flat, as shown in the developments, Figs. 19 (b) and 20 (b), with the lines of the treads and risers drawn on them; they are then laid across a block with the lines of the risers a, Fig. 21, parallel to the sides of the block, and, while in this position, are hammered or subjected topressure every few inches. A wooden templet with one edge curved to the radius to which the string is to be bent is used to test the string and determine when it has been pressed to the proper curve. This templet is placed against the iron at short intervals, and held in a direction parallel to the lines of the treads. This bending may also be accomplished by passing the string through a set of rollers in an angular direction, provided the rollers are long enough; this method, however, is seldom used, in consequence of the great length of roller required.

24. In making the pattern for the railing, it is advisable to first prepare a wooden drum of the same diameter as the stairwell, on which the steps are laid out; and from them the top line of the string is obtained, which is also the bottom line of the railing. The top and any intermediate lines of the railing are then found by measuring perpendicularly from any point on the string line or from the center of each tread; and the whole railing may be either modeled directly to the proper curve or made straight and bent to the curve afterwards. The well holes of all stairs are framed before the stairs are built, and in straight stairs there is little more required in the shape of structural support; in curved stairs, however, it is often necessary to introduce special supports, as has been done in this case by the upright T irons g shown in Figs. 19 (b) and 20 (b). The circular partition under the string in this case is of terracotta blocks, and is therefore incapable of affording sufficient support to the wall string. The strings should rest on the top of the floorbeams below, and be bolted to the webs of the floorbeams above wherever such is possible; but, as this cannot always be managed, bearings, such as shown at h in Fig. 19 (a), should be provided under the starting newel, and laid diagonally between the nearest beams.

Fig. 21.

25. The face string being of wrought iron, it must be bolted to the newel faces, and, in view of this, flanges are cast on the newel bases for this purpose. The constructive details for these stairs in the connections are the same as in Fig. 15 with the exception of the strings.

These strings are shown at i in Fig. 19 (c); the treads are supported on wrought-iron flanges j bolted to the string. The top and bottom flanges k of the wall string and the top flange l of the face string are of angle irons riveted to the string. The upper and lower edges of the face string are finished with brass moldings m, and the rail is first secured to the channel iron ft, which in turn is bolted to the string.