For additional data on the crushing strength of gravel concrete, see Table 26, page 141; and for data on the strength of gravel and broken-stone concrete, see Fig. 11, page 140.
M. Feret, the noted French authority, as a result of an elaborate study of the compressive strength of mortars, established the following principle: "For any series of plastic mortars made with the same binding material and inert sands, the resistance to compression after the same length of set under identical conditions, whatever may be the nature and size of the sand and the proportions of the elements of which each is composed, is solely a function of the ratio in which c =the absolute volume of the cement in a unit of volume of concrete,
absolute volume of the sand, w=the absolute volume of the water voids, and a =the absolute volume of the air voids." Taylor and Thompson* modified this principle to make it applicable to concrete, and from the results of various experi ments deduced a formula by which, knowing the compressive strength of any one proportion, the approximate compressive strength of any other proportion can be computed. By this method the above authors prepared Table 32, which shows the relative compressive strength of portland-cement concrete of different proportions at one month and at six months. Notice that the broken stone or gravel having the greatest per cent of voids gives concrete of the greatest strength. This anomaly is due to the fact that the broken stone having the greatest per cent of voids requires the greatest amount of cement per unit of volume of concrete, and the greater amount of cement has more influence in increasing the strength than the greater per cent of voids has in decreasing it.
Messrs. Taylor and Thompson in the investigation referred to in the previous paragraph deduced t the ratios shown in Table 33 which are useful in determining the effect of age upon the compressive strength of concrete. Of course such results can be only approximate in any particular case, owing to the difference in the conditions between the case in hand and the experiments from which the ratios were deduced.
All the pre ceding results for the crushing strength are for a compressive force applied over the entire upper surface of the test specimen; but if the load is applied upon only the central portion of the upper surface, a greater unit load will be required to crush the specimen, because the outer portions will support the interior portion and materially in crease the crushing resistance of the specimen.
In a series of experiments,* thirty-six 12-inch cubes of 1 : 0 : 2 and 1 : 2 : 4 concrete were crushed at different ages by applying the load over the entire upper surface of the cube, and the same number of companion cubes were crushed by applying the pressure over an area of 10 by 10 inches, and a third set by applying the stress over an area of 8 by 8.25 inches. The second series gave a strength per
unit of loaded area 112 per cent of the first, and the third 128 per cent. Different ages or different proportions seem to make no difference in the above per cents.
For additional data concerning the difference between a dis tributed and a concentrated load, see 657.
The safe crushing strength depends upon the character and the age of the concrete and upon the method of applying the load—whether distributed or concentrated. The results of laboratory tests are higher than is likely to be realized in actual practice, because of the difference in the conditions under which the work is done. For this reason it is not wise to assume that the ultimate crushing strength of a 1 : 2 : 4 portland-cement concrete made under reasonably good working conditions is more than about 2,000 pounds per square inch at 30 days; and for other proportions this value may be reduced according to the ratios in Table 32, page 198, and for other ages it may be increased according to the quantities given in Table 33, page 199. In any important work the strength should be determined for the actual conditions under which the concrete is to be used. On account of the difficulty of securing uniformity in concrete work, it is customary to assume a comparatively large factor of safety.
Table 34 gives the values of the safe crushing strength of a 1 : 2 : 4 portland-cement concrete made where the materials and workman ship are carefully inspected. If good materials and careful work manship are not assured, smaller values should be chosen. Values for other proportions and other ages can be deduced from those given in Table 34 by applying the ratios of Tables 32 and 33, pages 198 and 199, respectively. The dimensions of a massive concrete structure seldom depend upon the strength of the concrete. For example, the dimensions of a concrete foundation are determined by the bearing power of the soil; and many times a richer mixture is employed than is necessary to support the load—sometimes to secure a water-tight foundation, sometimes to secure resistance to frost, but often through ignorance or indifference. But in the design of reinforced concrete buildinIn the crushing strength of the concrete is an important factor; and a rich mixture is preferred not only because of its greater strength, but also because it insures greater adherence to the steel, makes possible the earlier removal of the forms and their earlier use elsewhere, and gives greater security against inferior sand and imperfect mixing. The cost of the addi tional cement is not a very large per cent of the total cost of the building.