DAMS CURVED IN PLAN Curved Gravity Dams.—In constructing clams across narrow valleys, it is often desirable to curve the clam in plan, so as to make it form a horizontal arch, convex upstream. When so arranged, a portion of the water pressure may be transmitted to the sides of the valley by arch action, thus diminishing the overturning moment which would exist in a straight dam of the same section.
In certain locations, the shape of the valley a-nd depth of suitable foundations make the use of the curved form economical in saving materials, although the length of clam is increased by the curvature. The curved form for gravity clams has not usually been adopted for the purpose of securing the arch action, although the advantage of the curved form is recognized and the added security obtained by the possibility of the upper part of the dam acting as an arch is worth considering when it does not materially increase the cost.
In order to develop free arch action in any horizontal slice of a clam, it would be necessary that the section be free to move horizon tally when the pressure comes against it. As each section is rigidly connected with these above and below it and the base is attached to a practically immovable foundation, the arch action is very imper fect. Near the top of a gravity section, deflection of the section may he sufficient to permit a portion of the water pressure to be resisted by the arch, but in the lower half of the dam such resistance is inappreciable.
There is no satisfactory way of determining how much of the pressure is borne by the arch in a curved gravity clam. In an analy sis of the stresses in the Cheeseman (lain, Mr. Silas II. Woodward estimated I roughly the amount of water pressure carried by the arch action, by determining the deflection at various points in the mid-section of the clam, considering the resistance of horizontal slices of the dam by arch action, and the resistance of a vertical slice as a cantilever brim, fixed at the bottom to the foundation. He concluded that in the Cheeseman dam, the arch carried about half the water pressure at the top and about 6 per cent at the mid-height of the middle section.
\Ir. W oodward's analysis seemed to indicate that, while added security might be obtained through arch action at the top of the dam, the lines of pressure of the gravity section were only slightly modified by considering part of the load carried by the arch. Ilis conclusion was that no diminution of the gravity section would be justified because of dependence upon arch action.
The use of curved plans for gravity dams may be of advantage m affording a possibility of motion when expansion and contraction take place, without cracking the masonry. The advantages to be gained by using curved plans, however, do not seem sufficient to make them worth while when they involve increase in cost. In constructing gravity dams across narrow valleys where arch action might be developed, the sides of the valley may also offer considerable support to a straight dam, causing horizontal slices of the dam to act as beams supported at the ends. In any such dam the actual stresses are probably considerably less than those obtained by considering the gravity resistance only.
142. Arch are sometimes constructed which depend for stability mainly upon arch action, and are designed as horizontal arches. A number of clams of this type have been constructed across narrow valleys, with sections much lighter than could be used for gravity dams. In some, the lines of pressure fall quite outside the bases when considered as gravity sections.
Let A–B, Fig. 76, represent a horizontal slice, 1 foot thick, through a circular dam.
J?=radius of water face; t= thickness of section; pressure per foot of length; compression on the masonry; h= height of water surface above section; w= weight of water per cubic foot.
If the slice he supposed to act freely as an arch and carry the water pressure to the abutments, If a limiting value of be assumed, the thickness of section required at any depth will be For a dam of constant radius (R) the required thickness varies uniformly with h, or the vertical section of the clam is _triangular.