14 REINFORCED CONCRETE CONSTRUCTION 

 grains of the sand, represented by the portion db, are found also 



t f)r> 



in the No. 1 curve. The percentage of sand to use is -j- -= = 



42%, since this percentage transforms the sand curve so that 

 it fits very nearly the ideal curve from to C. The percentage 



of No. 2 stone required is^ = ^ = 43%. This leaves 100- 



(42+43) =15% to be furnished by the No. 1 stone. Suppose 

 now that a 1:7 concrete is desired. Then, since for more than 

 two aggregates the finer material is not assumed to include the 



100 



cement, there will be =- = 14.3 parts cement, and the propor- 

 tions will be 14:42:15:43 or 1:3.0:1.1:3.1 the parts being by 

 weight. An ordinate such as rs may be found as follows: 



(0.43) (100) + (rn) (0.15) +(rt) (0.42) =57% 



With three or more sizes of stone, it is often necessary to assum'e 

 the required percentages of the intermediate sizes, and make 

 many trial plottings, before we are able to determine the proper 

 proportions to give the best combined curve. 



The following statement by William B. Fuller illustrates the 

 possibilities of mechanical analysis: 1 "The ordinary mixture for 

 water-tight concrete is about 1:2:4, which requires 1.57 barrels 

 of cement per cubic yard of concrete. By carefully grading the 

 materials by methods of mechanical analysis, the writer (Fuller) 

 has obtained water-tight work with a mixture of about 1:3:7, 

 thus using only 1.01 barrels of cement per cubic yard of concrete. 

 This saving of 0.56 barrels is equivalent, with Portland cement 

 at $1.60 per barrel, to $0.89 per cubic yard of concrete. The 

 added cost of labor for proportioning and mixing the concrete 

 because of the use of five grades of aggregate instead of two 

 was about $0.15 per cubic yard, thus effecting a nfct saving of 

 $0.74 per cubic yard. On a piece of work involving, say, 20,000 

 cu. yd. of concrete such a saving would amount of $14,800.00, 

 an amount well worth considerable study and effort on the part 

 of those in responsible charge." 



The above statement does not take into account the cost of 

 the sand and stone which would be needed for the approximate 

 1:3:7 concrete over and above that required for the 1:2:4 mix- 

 ture, but this amount would be small compared with the total 

 saving. 



9. Quantities Required per Cubic Yard. The following approxi- 



1 From Taylor and Thompson's "Concrete, Plain and Reinforced," 2nd edition, page 183. 

 Copyright, 1905, 1909, by Frederick W. Taylor. 



