93. Arches are frequently named from the curve of the intrados, as semicircular, segmental, semielliptic, pointed, etc. The semicircular arch is, as its name indicates, one whose intrados is a half circle. The segmental arch is one in which the intrados is generally an arc of large radius, less than a semicircle. Sometimes the curve is composed of arcs of two or three different radii, in which case it is termed a three or five centered arch. The upper part of such an arch has a long radius, while the portions near the springing line have short and equal radii. This arch is nearly elliptic in form, and is often so known. The true ellipse is also used, an example being given in Fig. 55. Examples of segmental and three-centered arches are given under the heading "Brick Arches," Masonry, § 7. The pointed arch has its intrados formed of two arcs of equal radius, intersecting at the crown. The equilateral pointed arch is one in which the radii of the intrados are equal to the span, as shown in Fig. 51. There are numerous other forms of arches, but it is unnecessary to describe them all, on account of the general similarity between them and those already mentioned.

When the springing line of an arch is below the center, as shown in Fig. 48, the arch is said to be stilted, the distance from center to springing line being the stilt.

94. A stone arch frequently built is the one shown in Fig. 48. In this case the arch ring is of equal depth all around, and the voussoirs are all of the same size; the dressing is rock faced with pitched joints. Sometimes the voussoirs have a margin draft, as shown on b and c.

Fig. 49.

95. Arches that are used in coursed ashlar are often built as shown in Figs. 49 and 50. In each of these, a is the center of the arch; b, b, the springing line; c, c, the ring stones; and d, d, the coursed stonework. Arches of this description are more expensive to execute than those in which the intrados and extrados are concentric, on account of the greater number of patterns required, the increased quantity of stone needed, and the work necessary to properly dress the voussoirs.

Fig. 50.

96. Fig. 51 gives an example of a Gothic, or pointed equilateral arch, with the intrados and extrados concentric.

Fig. 51.

In this illustration, a, a are the centers from which the arch is struck, and b, b is the springing line.

97. Fig. 52 shows an arch having the intrados semicircular and the extra-dos pointed. Such arches are found in Venice, and are sometimes termed Venetian Gothic arches. At a is the center for the semicircular intrados; at b, b are the centers for the extrados, or pointed arch; and atc,c is the springing line.

98. The horseshoe, or Moorish, arch is represented in Fig. 53. The Alhambra, at Granada, Spain, has some of the best examples of this arch. Sometimes it is built with the intrados and extrados concentric, and also with the intrados having a horseshoe form, and the extrados a pointed form. The example given shows the latter method of construction. At a is shown the center for the horseshoe intrados; at b, b are the centers for the pointed extrados of the arch; c indicates the soffit of the horseshoe arch; d, the upper side of the arch ring; and e, the voussoirs. In all horseshoe arches the center is stilted far above the springing lines, to produce the required effect.

Fig. 52.

Fig. 53.

99. Arches having an elliptical or oval form, or pointed in the center and elliptical near the springing joints, are often used in architectural work. These may be formed either of true elliptic curves, or of 3 or 5 centered circular arcs. Very flat elliptical arches are not suitable for any considerable span, and, if built, should have large piers or abutments; or beams may. be placed above the arch, to relieve it of some of the load.

The method of finding the direction of the joints in a false elliptical arch is shown in Fig. 54. The construction of the ellipse is similar to that given under the heading, " Inverted Arches," Masonry, §7. The radius for the middle of the arch is a b; the radii for the two haunches are the lines c d.

Fig. 54.

The joints of the voussoirs in the central portion are drawn with a as a center, as at e e, etc.; and the joints for the haunches are drawn with c, c as centers, as at f f, etc.

100. A method of finding the voussoir joints in a true elliptical arch is given in Fig. 55. This shows d1, d2, d3, d4, d5, and d6 as the points through which it is desired to draw the joints. Draw tangents to the ellipse at the points b and c, intersecting at d; also, the lines a d and b c; draw from d1, d2, d3, etc., lines intersecting ad at f1, f2, f3, etc. From these points, draw lines perpendicular to b c intersecting a b at e1, e2, e3, etc.; then lines drawn through e" d6, e5 d5, etc. will be normal to the curve and give the required joints.

Fig. 55.

Another and simpler method to find the direction of the joints is as follows: Find the foci of the ellipse by striking arcs from c with a b as a radius, cutting the major axis at g and g1. Let h be the point where the direction of the joint is to be found. Draw g h and g' h, and bisect the angle g h g', as at hi; then hi is the direction of the joint at h.

101. The flat arch is very common in architecture, but is not a strong construction. To be self-supporting it must be of such a size that a segmental arch of proper radius and sufficient depth can be drawn on its face, as shown in Fig. 56 by the dotted lines a, a. This arch should have a radius equal to the width of the opening - which in this case is 4 feet - while the limiting width for an arch of this description should not be over 5 feet. The keystone should project about an inch below the soffit of the arch, as indicated at b, in order to more tightly wedge together the voussoirs. The strength of this arch may be increased by notching one stone into the next, as shown at c, c; or dowel-pins are sometimes used to bind the stone together.

Fig. 66.

102. When an arch is so flat as to have practically no rise, it should be cut out of one piece of stone, being really a solid lintel with false joints cut on its face, as shown at a, a, Fig. 57. The ends of this lintel should have a bearing on the wall of 4 or 5 inches, as indicated by the dotted lines at b, b. If the walls are of brick, about 2 inches of the front of the stone may be cut away and faced with brick.

Fig. 57.

If this method is too costly, the lintel may be cut in 3 pieces, as shown at c, d, and e, and supported by a heavy angle bar, as described under "Lintels."