Amount of this method of porportioning, as in the preceding methods, the object is to determine the proper propor tions of aggregates to give the most dense concrete. In each ease, the amount of cement to be used is assumed as a definite ratio to the total weight of aggregates. This ratio depends upon the char acter of the work and the need for strength in the concrete, and is determined as mentioned in Section 82. In many instances, on important work, it is desirable to test the strength of the concrete as well as the density and modify the proportion of cement to suit the requirements. With different aggregates the strength may be quite different when the same proportion of cement is used, and economy in the use of cement may result from determination of the actual strength of concrete with varying proportions of cement to aggregate. (See Section 102.) More cement is usually required to produce the same strength when the sizes of the coarse aggregates are small than when larger aggregates are used. Stone broken to pass a -inch screen may require 20 to 25 per cent more cement for the same strength than the same stone broken to pass a 1.5-inch screen.
77. Fineness Modulus and Surface Area.—Several studies of methods of proportioning concrete have recently been made, involving extensive experimental investigations and resulting in suggestions of new methods. The tests of Mr. D. A. Abrams in the Structural Materials at the Lewis Institute at Chicago led to the conclusion that, for a given ratio of cement to aggregate, the pro portions requiring the least water to produce the required consistency would give the greatest strength. This would depend primarily upon the grading of the aggregate in size, and Mr. Abrams evolved a method by the use of what he calls the " fineness modulus," based upon the mechanical analysis of the aggregate. The Tyler series of sieves is used, Nos. 100, 48, 28, 14, 8, 4, etc., each of which has openings twice the diameter of those of the preceding ones. Mr. Abrams method is given in Bulletin No. 1 of the Structural Materials Research Laboratory.
Mr. L. N. Edwards has proposed 1 a method of proportioning concrete by means of the surface areas of the particles of aggregate. A theoretical study of this method of proportioning has been made by Mr. R. B. in which he claims that the quantity of water necessary to bring a concrete mixture to a given consistency is de pendent upon the surface area of the aggregates.
These and other investigations in progress are throwing much light upon the subject of proportioning concrete and upon its qualities.
The concrete is affected by a number of elements, each of which must he considered in determining the best proportions. Thc. ratio Proceedings, American Society for Testing Materials, 191S, Part 11. 2 Proceedings, American Society for Testing Materials, 1919, Part II.
of cement to aggregate, the voids in the aggregates, the surface areas of the aggregates, the quantity of water used in mixing are all important, and are all directly concerned with the grading of sizes of aggregates. Some method based upon mechanical analysis may finally be standardized for general use, when the relative impor tance of the various factors are more fully understood. Any of the methods proposed may be employed as a guide in selecting propor tions, but actual trial of the materials in concrete is necessary to give certainty in results.
78. Yield of Concrete.—The quantities of materials needed for a cubic yard of concrete vary with the amount of voids in the aggre gates and the proportions in which they are combined The sizes of the aggregates and the quantity of water used in mixing also influence the yield of concrete.
Concrete is made up of a mixture of cement, fine aggregate, and coarse aggregate, or it is a mixture of cement mortar with coarse aggregate. The volume of the concrete is the sum of the volumes of the mortar, the solid material in the coarse aggregate and the unfilled voids in the coarse aggregate.
Let C= Volume of cement in cubic feet (bags of 94 pounds each); S= Volume of fine aggregate in cubic feet; R= Volume of coarse aggregate in cubic feet; V= Volume of voids in coarse aggregate in cubic feet; s= Ratio of sand to cement=S/C; r= Ratio of coarse aggregate to cement= R/C; v=11atio of voids to total volume of coarse aggregate, VAR.
The quantities of ingredients necessary to produce given volumes of cement mortars, and the variations for different materials, are discussed in Section 34, and while these quantities vary considerably with different materials, the volume of mortar produced by the mixture of different proportions of cement and sand is fairly well expressed by the expression: Volume of mortar = aC+bS, in which a and b are coefficients depending upon the character of the sand. The volume of concrete from given quantities of cement, sand and stone may then be expressed by 1 he formula: Q=aC-{-bS-1-c(li in which c is a coefficient depending upon the amount of unfilled voids in the stone. For ordinary fairly coarse sands counuunly