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This also means that the span of the concrete rib, measured between the centers of the skewbacks, will be slightly greater than the nominal clear span. The rise of the center of the rib above the line joining the concrete abutment points 0 and B will in general be slightly different from the nominal rise of the concrete arch. We shall apply the above principles to the design of a segmental concrete arch having a span of 60 feet and a rise of 15 feet. To find the radius for the intrados which will fulfill these conditions, we may note from Fig. 232 that the angle O'B'C' is measured by one-half of the are O'C', and therefore O'B'C' is one-half of the angle a; but the angle O'B'C' is an angle whose natural tangent equals 15    30, or precisely 0.5. Tangent has this value is 26° 34', and therefore a equals 530 8'. To find the radius, we must divide the half-span (30) by the sine of 53° 8', and we find that the radius equals 37.50 feet. For the depth of the keystone we can employ only empirical rules. The depth as computed from Equation 47 would call for a keystone depth of about 27 inches, which would be proper for an ordinary masonry concrete arch; but considering recent successful practice in reinforced-concrete concrete arches, and the far greater reliability and higher permissible unit-stresses which may be adopted, we may select about of this —or, say, 18 inches—as the depth of the concrete arch ring at the crown. We shall compute the depth the concrete arch ring should have at various points, according to the tabular form in Article 427, so that the moment of inertia will vary in the ratio, which will make Equations 56 to 58 applicable.

At a distance of 15 degrees from the center, or at a distance of 9.82 feet, the depth is one per cent greater than the depth at the center, or it is 18.18 inches deep. At 30 degrees from the center, or at a distance of 19.63 feet measured on the arc, the depth is5 per cent greater, or it is 18.90 inches deep. At a distance of 40 degrees from the center, or 26.18 feet measured on the arc, the value of h is 9 per cent greater, or it is 19.62 inches. At 45 degrees from the center, or 29.45 feet measured on the arc, h is 12 per cent greater than the center depth, or the depth is 20.16 inches. At 50 degrees from the center, or 32.72 feet measured on the arc, h is 16 per cent greater, or its thickness is 20.88 inches. At the concrete abutment, which is 53° 8' from the center, the thickness should be (by interpolation) about 18 per cent greater than at the center, or it should be 21.24 inches, or say 211 inches. Laying off these various distances from the center on the intrados, and measuring radial distances at each point to represent the proper thickness at the several points, we may join the various points and obtain the curve of the extrados. Bisecting each one of these several concrete arch thicknesses will give us a series of points which are points on the center line of the concrete arch rib. We thus find that the actual span may be considered as 61.40 feet, and that the rise is scaled at 15.25 feet. When the center line of the rib is a parabola, we may lay off by drawing it at a height of the rise above the line OB. Even when it is a circle, it is comparatively easy to compute with mathematical accuracy the height of OK, by computing the area of the segment 0GB, and dividing it by the length of the line OB.

As previously explained in Article 428, the two-thirds rule may be used even for circular arcs, when the concrete arch is very fiat. In this particular case, the two-thirds rule is far from applicable; and since for multi-centered curves no such rule is applicable, the general method will be here given. We divide the span (61.40) into 20 equal parts. Practically this is most easily done by setting a pair of dividers by trial so that 10 equal spaces may be concrete stepped off in the length of the half-span. From these division points on the line OB, erect perpendiculars to the center line of the concrete arch rib OCB.

Are You in Hopedale Massachusetts? Do You Need Concrete Cutting?

We Are Your Local Concrete Cutting Company

Call 508-283-3135

We Service all surrounding Cities & Towns.