Examples of Application of Curves. Fig. 14, shows (1) the sieve-analysis curves of the bank run of natural gravel, (2) the same material after being screened to two sizes —one greater than 0.20 inch and the other less than 0.20 inch, (3) an artificial combination of these two sizes, and (4) the ideal curve.* The latter was drawn by the methods referred to in the preceding section, and shows by the length of the ordinate for a diameter 0.20 inch that 66 per cent of the ideal mixture should be coarser than 0.20 inch• in diameter and 34 per cent finer. The combined curve gives the result of taking these percentages of the two sizes, and shows that this is almost an ideal mixture, except that there is a deficiency of fine sancl,—but this will be made up in part by the cement.
Fig. 15, page 154, shows the sieve-analysis curves for one of the best gravels near Cortland, N. Y. f The ideal curve shows that 34 per cent of the perfect mixture should be smaller than 0.20 inch in di ameter, and hence 66 per cent is larger. The curve for this combination is shown. This curve gives almost ideal results for the sand portion, but has too much medium-coarse material. The next lower curve shows the effect of trying to remedy the defect of the preceding curve by using more coarse material. This combination improves the stone portion of the mixture; but the sand portion is not nearly as satisfactory as in the preceding curve, which shows .that this material screened to these two sizes can not be combined so as to make an approximately ideal mixture. An inspection of the curve for the material above 0.20 inch in diameter shows that this portion of the material conforms closely to the ideal curve down to 0.40 inch in diameter, which suggests screening the material into three sizes—one finer than 0.20, one between 0.20 and 0.40, and one coarser than 0.40. Fig. 16 shows the sieve-analysis curves for each of these three sizes of this gravel, and also the curve for a nearly ideal combination of the three sizes.* The concrete made of this combination of these sizes will be dense and strong, but whether it is economical or not depends upon the relative cost of screening the gravel and the cost of the cement saved. For one such comparison see I 306.
In practice it may not always be wise to separate the aggre gate into different sizes and re-combine them according to an ideal sieve-analysis curve; but on a job of any considerable magnitude it is probably always wise to make a sieve analysis of the material to be used, since the curve will indicate the direction in which im provements can be made, and often improvement is possible without additional cost.
Concrete may be propor tioned in any one of three ways: (1) by weight; (2) by volumes of packed cement, loose sand, and loose stone; or (3) by volumes of loose cement, loose sand, and loose stone.
Automatic weighing machines are occasionally employed. These consist of a series of automatic tipping buckets placed under spouts leading from the storage bins. When the proper weight of material is in the bucket it automatically tips, shuts a valve in the spout, and empties into the hopper leading to the mixing machine. When all three ingredients have been emptied into the hopper, a valve opens and they are emptied into the mixing machine. When different sizes of stone are used to secure a well-graded aggregate, bins and automatic tipping buckets are supplied for each size.
Proportions by Volumes of Packed Cement and Loose Sand and Stone. This is the most common method of proportioning. A barrel of packed portland cement is assumed to be 3.8 cu. ft., or a cubic foot of packed portland cement is assumed to weigh 100 lb.; and in the proportioning a barrel or a bag of cement is mixed with the required number of cubic feet of loose sand and loose stone. For example, a 1 : 2 : 4 mixture then means 1 cu. ft. of packed cement, 2 cu. ft. of sand, and 4 cu: ft. of stone; or 1 bbl. of cement, 2 bbl. (7.6 cu. ft.) of sand, 4 bbl. (15.2 du. ft.) of stone; or 1 bag of cement, 1.9 cu. ft. of sand, and 3.8 cu. ft. of stone. This system is virtually measuring the cement by weight and the sand and stone by volumes.
Proportions by Volume of Loose Cement and Loose Sand and Stone. When cement was usually shipped in a barrel, and a frac tional part of a barrel was used for a batch of concrete, the cement was measured loose; but at present this method is not employed, because it is simpler to consider the bag of cement as the unit.