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THEORY OF CONCRETE. To secure the greatest strength at the least cost, the proportions of the concrete should be SO adjusted that the voids in the sand will be filled with cement paste, and the voids in the gravel or broken stone will be filled with ce ment mortar. The cement is the most expensive ingredient ; and if more cement or more mortar is used than is required to fill the voids, the cost is needlessly great. Again, the cement is usually the weakest ingredient; and hence if more of it is used than is necessary, the strength of the concrete is thereby decreased. Table 34 and 35, pages 370-71, from the author's Treatise on Masonry Construction, give the amount of voids in sand, gravel, and broken stone.

In a perfect concrete, every sand grain will be coated with cement paste, and every point of each fragment of broken stone will be covered with cement mortar. The coating of cement paste on the sand grains and of mortar on the fragments of stone holds the several pieces apart, and increases the voids; and con sequently it is not possible to determine by computation the amount of cement paste or cement mortar required to fill the voids of any grade of broken stone. The exact proportions required in any particular case can be determined only by trial. The data in Table 36 and 37, pages 372-73, from the author's Treatise on Ma sonry Construction, were derived from experiments, and are suffi ciently exact for practial use. These tables give proportion in which the voids are just filled when the mortar or concrete is com pacted; and are very useful in making estimates.

In the method of proportioning implied in Table 36 and 37, the amount of cement or mortar will be stated in per cent of the volume of the sand or the stone depending upon the proportion of the voids; but not infrequently the proportions of the concrete are stated by volumes independently of the proportion of the voids in either the sand or the broken stone, in which case Table 38, page 374, will be useful in making estimates. For a discussion of the disadvantages of the latter method of proportioning, see pages 112d-112/ of the author's Treatise on Masonry Construction.

table gives the quantities for unscreened and also for screened broken stone; and Table 34 gives also the quantities of cement and gravel required for a cubic yard of gravel concrete. The barrel of cement in both tables is the commercial barrel of packed cement.

Table 34 is recommended for general use, since the proportions are more scientific and more economical. The first line gives a concrete of the maximum density and maximum strength, i. e., the quantity of mortar is sufficient to fill the voids; and the suc cessive lines give concretes of decreasing density and strength. The third and subsequent lines give concretes containing mortar equal to the voids, the mortar in the third line being 1 to 3, in the fourth 1 to 4, etc.

The proportions of the concretes can be determined by remem bering that a barrel of cement is equal to 0.13 cu.yd. For example, in the first line of Table 34 for unscreened broken stone and Port land cement, the 0.94 bbl. of cement is equal to 0.12 cu. yd.; and the proportions are: 1 volume of packed cement, 2.5 volumes of loose sand, and 7.5 volumes of loose unscreened broken stone. If it be assumed that a barrel of packed cement will make 1.25 barrels when measured loose, the above proportions become: 1 volume loose cement, 2.0 volumes loose sand, and 6.0 volumes loose un screened broken stone.

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