Rough strings are cut from undressed plank, and arc used for strengthening the stairs. Sometimes a combination of rough-cut strings is used for circular or geometrical stairs, and, when framed together, forms the support or carriage of the stairs.
Staved strings are built-up strings, and are composed of narrow pieces glued, nailed, or bolted together so as to form a portion of a cylinder. These are sometimes used for circular stairs, though in ordinary practice the circular part of a string is a part of the main string bent around a cylinder to give it the right curve.
Notched strings are strings that carry only treads. They are generally somewhat narrower than the treads, and are housed across their entire width. A sample of this kind of string is the side of a common step-ladder. Strings of this sort are used chiefly in cellars, or for steps intended for similar purposes.
Setting Out Stairs. In setting out stairs, the first thing to do is to ascertain the locations of the first and last risers, with the height of the story wherein the stair is to be placed. These points should be marked out, and the distance between them divided off equally, giving the number of steps or treads required. Suppose we have between these two points 15 feet, or 1S0 inches. If we make our treads 10 inches wide, we shall have 18 treads. It must be remembered that the number of risers is always one more than the number of treads, so that in the case before us there will be 19 risers.
The height of the story is next to be exactly determined, being taken on a rod. Then, assuming a height of riser suitable to the place, we ascertain, by division, how often this height of riser is contained in the height of the story; the quotient, if there is no remainder, will be the number of risers in the story. Should there be a remainder on the first division, the operation is reversed, the number of inches in the height being made the dividend, and the before-found quotient, the divisor. The resulting quotient will indicate an amount to be added to the former assumed height of riser for a new trial height. The remainder will now be less than in the former division; and if necessary, the operation of reduction by division is repeated, until the height of the riser is obtained to the thirty-second part of an inch. These heights are then set off on the story rod as exactly as possible.
The story rod is simply a dressed or planed pole, cut to a length exactly corresponding to the height from the top of the lower floor to the top of the next floor. Let us suppose this height to be 11 feet
1 inch, or 133 inches. Now, we have 19 risers to place in this space, to enable us to get upstairs; we divide 133 by 19, we get 7 without any remainder. Seven inches will therefore be the width or height of the riser. Without figuring this out, the workman may find the exact width of the riser by dividing his story rod, by means of pointers, into 19 equal parts, any one part being the proper width. It may be well, at this point, to remember that the first riser must always be narrower than the others, because the thickness of the first tread must be taken off.
The width of treads may also be found without figuring, by pointing off the run of the stairs into the required number of parts; though, where the student is qualified, it is always better to obtain the width, both of treads and of risers, by the simple arithmetical rules.
Having determined the width of treads and risers, a pitch-board shduld be formed, showing the angle of inclination. This is done by cutting a piece of thin board or metal in the shape of a right-angled triangle, with its base exactly equal to the run of the step, and its perpendicular equal to the height of the riser.
It is a general maxim, that the greater the breadth of a step or tread, the less should be the height of the riser; and, conversely, the less the breadth of a step, the greater should be the height of the riser. The proper relative dimensions of treads and risers may be illustrated graphically, as in Fig. 12.
In the right-angle triangle A B C, make A B equal to 24 inches, and B C equal to 11 inches—the standard proportion. Now, to find the riser corresponding to a given width of tread, from B, set off on A B the width of the tread, as B D; and from D, erect a perpendicular D E, meeting the hypotenuse in E; then D E is the height of the riser; and if we join B and E, the angle D B E is the angle of inclination, showing the slope of the ascent. In like manner, where B F is the width of the tread, F G is the riser, and B G the slope of the stair. A width of tread B II gives a riser of the height of II K; and a width of tread equal to B L gives a riser equal to L 111 In the opinion of many builders, however, a better scheme of proportions for treads and risers is obtained by the following method: Set down two sets of numbers, each in arithmetical progression— the first set showing widths of tread, increasing by inches; the other showing heights of riser, decreasing by half-inches.