voids and probable strength of concrete made with definite proportions. This process is then applied as a means of investigating various mortars composed of different fine aggregates, comparison being made on a basis of relative density, and the probable resulting strength computed for the concretes made up with these mortars. From the data at hand the approximate proportions required to give a specified strength is calculated. (f) Proportioning by the Water-Cement Ratio. This method is based on the principle that for given materials and conditions of manipulation, the strength of concrete is determined solely by the ratio of volume of mixing water to the volume of cement SO LONG AS THE MIXTURE IS OF A WORKABLE PLASTICITY. For example, referring to Fig. 6, if one cubic foot of water is used for each cubic foot of cement, the strength of a properly manipulated concrete will be the same, at any given age, no matter what quantities of aggregates are used, PROVIDED THAT A WORKABLE MIXTURE IS OBTAINED. As the required quantity of mixing water largely depends upon the grading of the aggregates, it became desirable to discover some easily ascertainable function representing this important factor. The so-called "fineness modulus" was chosen this was found by adding the sum of the percentages in the sieve analysis using the standard Tyler sieves, and dividing by 100. Its purpose is to assist the designer in choosing or combining aggregates so that the resulting mixture may require the minimum of cement-paste for any given workability. Having found the desirable "fineness-modulus" and "real mix," which latter is defined as the proportion of cement to mixed aggregates measured dry and rodded, the actual "field mix" is calculated as explained in appendix No. 12. A variation of this method is the use of trial batches combining different proportions of aggregates with cement-paste mixed at the water-ratio corresponding to the required strength. Although this latter procedure of making trial batches seems somewhat crude, and the use of the "fineness modulus" is not completely satisfactory, the fundamental dependence of strength upon water-cement ratio furnishes the one and only practicable means so far proposed for the design and control of concrete mixtures. Having settled upon a water-cement ratio which, with the conditions existing on the particular job under design, gives the required strength and resistance to wear, or exposure, the problem resolves itself into a determination of the most economical combination of materials to produce workable concrete. Generally the most satisfactory mixture is one in which the volume of the sand (particles passing a 4 in sieve), with due allowance for moisture content, represents one-third to one-half the volume of the total aggregate. Bearing this in mind, the combined aggregate should be chosen with particles grading up to a size as large as can be conveniently placed in the spaces between the reinforcements. Commencing with as coarse a mixture as deserves consideration, in view of the relative prices of the materials, sand should be added until the mixture can be properly placed under job conditions. A comparatively coarse aggregate uses less cement-paste for any required strength but works more harshly, and is more costly to place: an over-sanded aggregate can be easily placed, but requires more cement-paste. Knowing the weights and prices of materials small trial batches may be made, the yield computed, as described in Art. 8, and the most economical combination chosen. For the conscientious designer of concrete, there is perhaps a greater danger of using too harsh a mixture than of oversanding. Although the latter fault reduces both yield and strength, it may well be less objectionable than stonepockets and honeycombed surfaces which are sure to result if laboratory methods are injudiciously applied to field construction. (g) Tables for Proportioning Recommended by the Joint Committee, 1924. As a guide in the SELECTION OF MIXTURES to be used in preliminary investigations of the strength of concrete from available materials, and TO INDICATE PROPORTIONS WHICH MAY BE EXPECTED TO PRODUCE CONCRETE OF A GIVEN STRENGTH UNDER AVERAGE CONDITIONS where control tests are not made, the Joint Committee submits the tables, based upon empirical data, which are contained in Appendix 12. In connection with control-tests, it is interesting to note that data recently published by W. A. Slater of the Bureau of Standards seem to indicate a definite relation between seven-day and 28-day compressive strengths which will prove extremely valuable in facilitating field-control of concrete-mixtures. The proposed formula is as follows: f'c=ƒ+30√ƒ in which ƒ is the ultimate compressive-strength of the concrete at an age of seven days, in pounds per square inch, and f', the probable strength at 28 days. 8. Quantities of Materials for Concrete Mixtures.* The quantities of materials in a concrete mixture may be accurately determined from the fact that the volume of concrete produced by any combination of materials, so LONG AS THE CONCRETE IS PLASTIC, is equal to the absolute volume of the cement plus the absolute volume of the aggregate plus the volume of water. The absolute volume of a loose material is the actual total volume of solid matter in all the particles. This can be computed from the weight per unit volume and the specific gravity as follows: Absolute Volume = unit weight specific gravity X unit weight of water The method is best illustrated by an example. Assume that the concrete consists of one sack of cement (94 lb), 2.2 cu ft of fine aggregate weighing 110 lb per cu ft and 3.6 cu ft of coarse aggregate weighing 100 lb per cu ft and is to be mixed with a water-cement ratio of 7 gallons per sack. The specific gravity of the cement is usually about 3.1 and of the more common aggregates about 2.65. The volume of concrete produced by the above mix is calculated as follows: *From the publications of the Portland Cement Association. Thus one sack of cement produces 5.06 cu ft, neglecting absorption or loss of water in manipulation. The cement required for one cubic yard of concrete is, therefore, 27 5.06 = 5.34 sacks or 1.33 barrels. The quantities of sand and stone required can be found by a simple computation based on the number of cubic feet used with each sack of cement; thus, for the sand, 5.34 X 2.2 0.71 cu yd of stone. = 0.43 For unusual materials such as blast furnace slag and similar light weight aggregates, the exact specific gravities should be used. It will be found that, for the purpose of estimating quantities, the average value of 2.65, given previously, will be sufficiently accurate for sand and gravel and the common varieties of crushed rock. 9. Slump Test and Flow Table. The term CONSISTENCY is used to designate that property of concrete which is affected by a change in the amount of mixing water. WORKABILITY, defining the amount of work required for proper placement, depends upon the amount of cement and the character of aggregate, as well as on the amount of mixing water. Two methods are employed for measuring the consistency and workability of plastic concrete the slump test and the flow-table. The former is described in the Proceedings of the American Society for Testing Materials under Serial Designation: D 138-22 T, which tentative specification is reprinted in the Appendix. The sample to be tested is molded in a steel form, shaped as a truncated cone without top or bottom, 12 in height, and with upper and lower bases 4 and 8 in in diameter respectively. The plastic concrete is deposited in the mold in four successive layers with a specified amount of tamping. Three minutes after filling the mold is removed by raising vertically. The supported mass then either sinks down, tumbles over, or remains standing. The so-called slump is determined as the difference in inches between 12 in and the upper surface of the specimen. Fig. 4 illustrates the procedure. IN FIELD PRACTICE, as a measure of the workability of various batches in which the proportion of cement and the character of aggregate is constant, the SLUMP TEST is a useful device. However, it is not sufficiently reliable to furnish a standard for consistency in laboratory work and very erratic |