OF THE FORM OF THE ARCH.
249. There are three general forms which may be given to the intrados of a stone arch.
Semicircular, or one hundred and eighty degrees.
Segmental, less than one hundred and eighty degrees.
Basket handle, nearly elliptical, being formed by a number of circular curves.
Full centre (semicircular) arches offer the advantages of great solidity and ease of construction; but unless the springing lines are high, contract considerably the water-way.
Segmental arches give the freest passage to the water, are easily built, but throw a great horizontal strain upon the abutments.
The basket handle gives free passage to the water, when not too flat are very strong, are easily adjustable to different ratios between the span and the distance between grade and the spring line, and except making the centres, are easily built. Whatever the form of the arch, the line of arch springing should not be below high water.
The manner of tracing the full centre and segmental curves is too simple to need remark.
250. In tracing the basket handle curve, the following conditions must be observed:—
The tangents at springing must be vertical.
The summit tangent must be horizontal.
The curve at springing must inclose the ellipse.
The radius of summit must not be greater than the span.
The number of arches composing the curve must not be less than three, nor more than eleven; and must be uneven. Perronet’s fine bridge of Neuilly, over the Seine at Paris, has eleven centres. In spans of sixty feet and under, it is unnecessary to use more than five centres.
Fig. 119.
251. The three centred curve is described as follows, fig. 119:—
Let A B represent the span, and c D the rise, with c as a centre and c A as radius, describe the quadrant A F E; make the angle A C F 60°. Parallel to F E draw D G, and parallel to F C draw G K. H is the centre, and A G the arc of the springing curve; also GD is the arc, and K the centre of the summit curve.
THE FIVE CENTRED CURVE.
252. The common construction of the five centred curve leaves the radii of the extreme curves to be assumed. The following method fixes all of the dimensions when the span and rise are given:—
Let c B be half the span and c D the rise.
Join D B.
Draw n K through n perpendicular to D B.
Make B a equal to c D.
Also c e to c a.
Draw e K′ o and K a m.
K H′ and K′ are the centres, and H′ m and H′ o the lines separating the several curves.
For spans of from twenty-five to one hundred feet, the five centred arch answers every purpose; making a strong and well proportioned structure.