The determination of the stresses in a groined arch roof is complicated not only by the peculiar form of the arch itself, but by the fact that the spandrels of the arches are filled with concrete over the piers to the level of the extrados at the crown. This evidently results in making of any given unit of the roof, having a pier as its center, a cantilever, and the arch action is interfered with. Unless, however, tension members of steel are laid in the concrete near its upper surface, it is not wise to count on the strength of the cantilever except to consider it a factor of ignorance on the safe side. If one wishes to depart from the ordinary and tried dimensions for groined arches in concrete, such departure had better be based on some special experiments and tests on full sized sections. Some of the dimensions that have been used are given in the examples cited below.

704. Forms

The preparation of forms or centers for groined arches is one of the most difficult and expensive details of the construction of such a roof. It will probably be best to have each section of the form cover the space, square in plan, between four piers. The ribs of the centering may well be built up of planks, nailed together and sawed to proper form. The lagging should be planed to size, and have radial joints to make a smooth and even top surface. Care is necessary to make a neat fit along the valley extending diagonally between piers, and a small fillet may well be fitted into this valley to avoid a sharp corner on the finished concrete, as well as to cover up possible imperfections in the joints. The forms should, of course, be designed to take the thrust of the adjacent completed arches, and if sufficient forms are not built to cover the entire reservoir, and thus transmit the thrust to the walls, the piers at the border of the forms must be thoroughly braced to the opposite side walls or the piers will be toppled over and the roof wrecked. This accident occurred to one reservoir roof during construction, the pier braces having been removed without the knowledge of the engineer.

705. In laying the concrete, joints between the work done on consecutive days should cut the arches at right angles to their axes, and bulkheads should be used to make such a joint a vertical plane. The covering of each unit between four piers is made monolithic, and care is necessary to prevent the stones working to the bottom of the mass and thus becoming exposed when the forms are removed. This may be prevented by plastering the forms with mortar and placing the concrete upon it before the mortar has begun to set.

706. A roof consisting of a network of concrete-steel beams intersecting at right angles, supported by piers and covered by concrete-steel slabs, makes a very simple design. The forms are much easier to construct, and forms for only a limited area need be erected at one time. An excellent article on " Covered Reservoirs and Their Design," by Mr. Freeman C. Coffin, M. Am. Soc. C. E., is contained in the July, 1899, number of the Jour, of the Assn. of Engr. Soc. An article on the " Groined Arch," by Mr. Leonard Metcalf, Assoc. M. Am. Soc. C. E., appears in Trans. A. S. C. E. for June, 1900; and Mr. Frank L. Fuller presents an article on " Covered Reservoirs," in Jour. Assn. Engr. Soc. for Sept., 1899.

707. Examples Of Concrete Reservoirs. Wellesley

The reservoir at Wellesley, Mass.1 a part of the water supply system, was designed by Mr. Freeman C. Coffin. It is eighty-two feet in diameter, walls fifteen feet high, four feet thick at bottom and two feet at top. The walls are of concrete and rubble masonry. In the construction of the walls, concrete was used containing three parts sand and five parts of stone to one of cement, one cubic yard of concrete containing about 1.2 barrels of cement. The bottom of the walls, which were designed to be built of concrete three feet four inches thick, were actually built of rubble four feet thick, as a large quantity of bowlders was at hand. The excavation was in hard clay containing but little water, and the floor was made only four inches thick, of concrete of the same quality as that used in the walls.

The floor and side walls were plastered with two coats, the first, one-half inch thick, of mortar containing two parts sand to one of Portland cement, and a coat about one-eighth inch thick, of neat Portland carefully rubbed and smoothed with trowels. Such a plaster coat should be applied before the conr crete has set. The two plaster coats Cost twenty cents per square yard.

708. The piers to support the groined arch roof were two feet square, and built of brick. The span of the arches was 12 feet, rise 2.5 feet, and the concrete 0.5 foot thick at the crown. A channel iron ring or band was set in the concrete walls at the springing of the roof arches to take the thrust of the latter. The centers were placed over one-fourth of the area at a time, the piers being braced to take the thrust of the arches until the roof was completed. The concrete in the roof was composed of two and one-half parts sand and four and one-half parts broken stone to one part Portland cement. The centering Cost twenty-two and one-half cents per square foot of area covered. The spandrels were filled in level with top of concrete at crown. On top of the concrete roof was placed six inches of clean gravel for drainage and to prevent the earth freezing to the concrete. This gravel was drained by four inch vitrified pipe discharging at the toe of the slope wall.

1 Engineering News, Sept. 30, 1897; Jour. Assn. Engr. Societies, July 1899; Trans. A. S. C. E., June, 1900.

One foot of earth filling and one foot of loam were placed upon the gravel.

709. Astoria

The reservoir for the Astoria City water Works 1 was designed and built by Mr. Arthur L. Adams, M. Am. Soc. C. E. The reservoir has a capacity of six and one-fourth million gallons, walls twenty feet high. The excavation was in hard clay and sand mixed with clay, which in some places resembled a soft sandstone. The embankment was in general about five feet, the remainder of the depth being in excavation.