Dams Curved in Plan

When the crown of the arch has been deflected upstream by the weight of masonry, stress is brought upon the vertical cantilever by its resistance to bending in that direction. If water pressure be now brought against the clam, the vertical cantilever action will offer no resistance to downstream motion until the pressure upon the arches becomes sufficient to bring the clam back to its original unloaded position.

The existence of this initial distortion due to the weight of masonry may depend upon the manner in which the clam is constructed. In order to produce this effect it is necessary that the horizontal layers be completed and hardened in position before the load above is applied. If portions of the work be carried up in vertical sections, or if vertical contraction joints be left, to be afterward grouted, the deflection due to weight of masonry may take place only to a very limited extent.

Constant-angle Arches.—Arch dams are usually constructed across narrow gorges which can readily be spanned by an arch of moderate radius. The gorges vary in cross-section, being usually much nar rower at bottom than near the top of the arch. The arch at bottom will therefore be much shorter than at the top and if the same radius be used at top and bottom, or the centers lie in the same vertical line, the central angle included by the chain will be greater at top that at bottom. It has been shown by Mr. Lars R. Jorgensen r that a dam with a constant central angle of 133° 34' requires, theoretically, the minimum amount of masonry in its construction, that angles from 110° to 150° vary but little from the minimum. It has therefore been proposed to vary the radius from the top to the bottom, so as to keep within these ranges of central angles. This makes the radius of the dam vary with the width of the gorge at different elevations. Several dams have been constructed in which this principle has been approximately applied. The topography of the site must be care fully studied in every instance and the dam fitted to its location, keeping in mind the general principles involved.

Temperature Stresscs.—Comparatively little is known concerning the changes of temperature to be expected in a mass of masonry like a dam, but it is evident that distortions produced by such changes may sometimes be of importance, and careful attention should be given to their probable effect. Temperature above the normal at

which the masonry was placed cause deflection upstream through expansion, which may bring bending stresses upon the vertical section when the water is low behind the dam. Contractions due to tem peratures below the normal, causing tensile stresses which the masonry or concrete is not calculated to bear may cause cracks, or prevent. the arch action through shortening the arch near the top. It is desirable that masonry which may he injuriously affected by low temperature, be placed when the temperature is low, thus giving a low normal and probable small range below. Mr. Wisner t urges that reinforcement be used on the faces of the upper portion of arched clams to prevent cracks; vertical rods on the downstream face to take up the possible vertical tensions due to expansion, and horizontal rods on the up stream side to prevent contraction cracks.

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consisting of a series of con crete arches supported by buttresses are sometimes used for moderate heights where suitable foundations are available and the cost of gravity dams would be greater. The amount of concrete required is much less than for gravity darns, and where concrete materials are expensive considerable savings in cost may result from their use. The form work required and the thin sections of concrete, make the unit costs much more than for gravity dams, and under favorable conditions for cheap concrete work gravity sections may be cheaper to construct. As the buttresses must carry the thrust of the water pressure, it is essential that they be established upon very substantial and unyielding foundations. Usually this is solid rock, although some dams of this type have been built upon gravel or fissured rock. Where the foundation is stable but of character which may permit water to penetrate it, this type of dam has advantages over a gravity darn on account of the less importance of possible uplift.

Two types of multiple-arch clams are in use; (1) those in which the axes of the arches are vertical, the water pressures coming hori zontally against the faces and being transmitted as horizontal thrusts against the buttresses; (2) those with inclined axes, the water pres sures acting normal to the sloping axes and bringing vertical as well as horizontal thrusts upon the buttresses.