CHAPTER VIII.

THE STABILITY OF ARCHES.

THE arch is an arrangement for spanning large openings by means of small blocks of stone, or other material, arranged in a particular way. As a rule, the arch answers the same purpose as the beam, but it is widely different in its action and in the effect that it has upon the appearance of an edifice. A beam exerts merely a vertical force upon its supports, but the arch exerts both a vertical load and an outward thrust. It is this thrust which requires that the arch should be used with caution where the abutments are not abundantly large.

a

Fig.1

Before taking up the principles of the arch, we will define the many terms relating to it. The distance ec (Fig. 1) is called tlie span of the arch; ai, its rise; b, its crown; its lower boundary line, eac, its soffit or intrados; the outer boundary line, its back or extrados. The terms "soffit" and "back" are also applied to the entire lower and upper curved surfaces of the whole arch. The ends of the arch, or the sides which are seen, are called its faces. The blocks of which the arch itself is composed are called voussoirs: the centre one, K, is called the keystone; and the lowest ones, SS, the springers. mental arches, or those whose intrados is not a complete semicircle, the springers generally rest upon two stones, as RR, which have their upper surface cut to receive them: these stones are called skewbacks. The line connecting the lower edges of the springers is called the springing-line; the sides of the arch are called the haunches; and the load in the triangular space, between the haunches and a horizontal line drawn from the crown, is called the spandrel.

In seg

The blocks of masonry, or other material, which support two successive arches, are called piers: the extreme blocks, which, in the case of stone bridges, generally support on one side embankments of earth, are called abutments.

A pier strong enough to withstand the thrust of either arch, should the other fall down, is sometimes called an abutment pier. Besides their own weight, arches usually support a permanent load or surcharge of masonry or of earth.

In using arches in architectural constructions, the form of the

arch is generally governed by the style of the edifice, or by a limited amount of space. The semicircular and segmental forms of arches are the best as regards stability, and are the simplest to construct. Elliptical and three-centred arches are not as strong as circular arches, and should only be used where they can be given all the strength desirable.

The strength of an arch depends very much upon the care with which it is built and the quality of the work.

In stone arches, special care should be taken to cut and lay the beds of the stones accurately, and to make the bed-joints thin and close, in order that the arch may be strained as little as possible in settling.

To insure this, arches are sometimes built dry, grout or liquid mortar being afterwards run into the joints; but the advantage of this method is doubtful.

Brick Arches may be built either of wedge-shaped bricks, moulded or rubbed so as to fit to the radius of the soffit, or of bricks of common shape. The former method is undoubtedly the best, as it enables the bricks to be thoroughly bonded, as in a wall; but, as it involves considerable expense to make the bricks of the proper shape, this method is very seldom employed. Where bricks of the ordinary shape are used, they are accommodated to the curved figure of the arch by making the bed-joints thinner towards the intrados than towards the extrados; or, if the curvature is sharp, by driving thin pieces of slate into the outer edges of those joints; and different methods are followed for bonding them. The most common way is to build the arch in concentric rings, each half a brick thick; that is, to lay the bricks all stretchers, and to depend upon the tenacity of the mortar or cement for the connection of the several rings. This method is deficient in strength, unless the bricks are laid in cement at least as tenacious as themselves. Another way is to introduce courses of headers at intervals, so as to connect pairs of half-brick rings together.

This may be done either by thickening the joints of the outer of a pair of half-brick rings with pieces of slate, so that there shall be the same number of courses of stretchers in each ring between two courses of headers, or by placing the courses of headers at such distances apart, that between each pair of them there shall be one course of stretchers more in the outer than in the inner ring.

The former method is best suited to arches of long radius; the latter, to those of short radius. Hoop iron laid round the arch, between half-brick rings, as well as longitudinally and radially, is very useful for strengthening brick arches. The bands of hoop iron which traverse the arch radially may also be bent, and prolonged in the bed-joints of the backing and spandrels.

By the aid of hoop-iron bond, Sir Marc-Isambard Brunel built a half-arch of bricks laid in strong cement, which stood, projecting from its abutment like a bracket, to the distance of sixty feet, until it was destroyed by its foundation being undermined.

The New-York City Building Laws make the following requirements regarding brick arches:

"All arches shall be at least four inches thick. Arches over four foot span shall be increased in thickness toward the haunches by additions of four inches in thickness of brick. The first additional thickness shall commence at two and a half feet from the centre of the span; the second addition, at six and one-half feet from the centre of the span; and the thickness shall be increased thence four inches for every additional four feet of span towards the haunches.

"The said brick arches shall be laid to a line on the centres with a close joint, and the bricks shall be well wet, and the joints filled with cement mortar in proportions of not more than two of sand to one of cement by measure. The arches shall be well grouted and pinned, or chinked with slate, and keyed."

--

Rule for Radius of Brick Arches. A good rule for the radius of segmental brick arches over windows, doors, and other small openings, is to make the radius equal to the width of the opening. This gives a good rise to

the arch, and makes a pleasing proportion to the eye.

It is often desirable to span openings in a wall by means of an arch, when there is not sufficient abutments to withstand the thrust or kick of the arch. In such a case, the arch can be formed on two cast-iron skewbacks, which are held in place by iron rods, as is shown in Fig. 2.

Fig. 2.

When this is done, it is necessary to proportion the size of the rods to the thrust of the arch. The horizontal thrust of the arch is very nearly represented by the following formula: —

If two tension rods are used, as is generally the case, the diame ter of each rod can be determined by the following ruie:

total load on arch X span

Diameter in inches:

16 × rise of arch in feet × 7854

If only one rod is used, 8 should be substituted in the place of 16, in the denominator of the above rule; and, if three rods are used, 24 should be used instead of 16.

Centres for Arches. A centre is a temporary structure, generally of timber, by which the voussoirs of an arch are supported while the arch is being built. It consists of parallel frames or ribs, placed at convenient distances apart, curved on the outside to a line parallel to that of the soffit of the arch, and supporting a series of transverse planks, upon which the arch stones rest.

The most common kind of centre is one which can be lowered, or struck all in one piece, by driving out wedges from below it, so as to remove the support from every point of the arch at once.

The centre of an arch should not be struck until the solid part of the backing has been built, and the mortar has had time to set and harden; and, when an arch forms one of a series of arches with piers between them, no centre should be struck so as to leave a pier with an arch abutting against one side of it only, unless the pier has sufficient stability to act as an abutment.

When possible, the centre of a large brick arch should not be struck for two or three months after the arch is built.

Mechanical Principles of the Arch. — In designing an arch, the first question to be settled is the form of the arch; and in regard to this there is generally but little choice. Where the abutments are abundantly large, the segmental arch is the strongest form; but, where it is desired to make the abutments of the arch as light as possible, a pointed or semicircular arch should be used.

Depth of Keystone. — Having decided upon the form of the arch, the depth of the arch-ring must next be decided. This is generally determined by computing the required depth of keystone, and making the whole ring of the same or a little larger depth.

In considering the strength of an arch, the depth of the keystone is considered to be only the distance from the extrados to the intrados of the arch; and if the keystone projects above the arch-ring, as in Fig. 1, the projection is considered as a part of the load on the arch.

There are several rules for determining the depth of the keystone, but all are empirical; and they differ so greatly that it is difficult to recommend any particular one. Professor Rankine's Rule is often quoted, and is probably true enough for most arches. It applies to both circular and elliptical arches, and is as follows:Rankine's Rule. For the depth of the keystone, take a mean proportional between the inside radius at the crown, and 0.12 of a foot for a single arch, and 0.17 of a foot for an arch forming one of a series. Or, if represented by a formula,

Depth of keystone for a single arch, in feet

= √ (0.12 × radius at crown).

Depth of keystone for an arch of a series, in feet

= √(0.17 × radius at crown).

This rule seems to agree very well with actual cases in arches of a certain kind. By it, however, the depth of keystone is the same for spans of any length, provided the radius is the same; and in this particular, it seems to us, the rule is not satisfactory.

Trautwine's Rule. - Mr. Trautwine, from calculations made on a large number of arches, has deduced an original rule for the depth of keystone, which is more agreeable to theory than Rankine's. His rule is, for cut stone,

Depth of key, in feet =

radius+ half span) + 0.2 foot.

4

For second-class work, this depth may be increased about oneeighth part, or, for brick or fair rubble, about one-fourth.

The following table gives a few examples of the depth of keystone of some existing bridges, together with the depth which would be required by Trautwine's or Rankine's Rule. From this table it will be seen that both rules agree very well with practice.