10 REINFORCED CONCRETE CONSTRUCTION 



paper and mark off the lengths of the semi-major and semi- 

 minor axes upon it; each of these lengths should be laid off in the 

 same direction from a common point, which we shall call K\ 

 denote the length of the semi-major axis as KA and the length of 

 the semi-minor axis as KB; now swing the strip of paper little by 

 little so that the outline of the curve may be marked off by the 

 point K while the points A and B are kept at all times upon the 

 axes 6 and a respectively. 



The principles by which sand and stone curves are combined 

 into a single curve, with the object in view of approaching closely 

 to the curve of maximum density, may best be explained by some 

 typical problems as developed by Messrs. Taylor and Thompson. 1 



Suppose that we have for concrete the fine sand OA and the 

 crushed stone DE of Fig. 4, and suppose the problem is to find 

 what proportion of each material should be employed. The 

 curves of the two materials are plotted to the same scale and 

 the ideal curve is drawn by the method previously described. 

 Experiments have shown that where the materials to be mixed 

 are represented by only two curves, the best results are obtained 

 when the combined curve intersects the ideal curve approxi- 

 mately on the 40 per cent line at F, and when the finer material 

 is assumed to include the cement. The sand and stone curves 

 in this case do not overlap, and hence for the best proportions, 

 60 per cent by weight should be stone, and 40 per cent by weight 

 should be sand plus cement. The combined curve is not drawn 

 for this simple case. Now the proportion of cement to be used 

 to give the required strength of concrete must always be assumed ; 

 and in this case one part by weight of cement to six parts by 

 weight of dry aggregate (measured before the sand and stone are 

 mixed together) will be considered as satisfactory. This will 

 make the cement 1/7, or 14.3 per cent, of the total materials. 

 Deducting this from the percentage of cement plus sand, we 

 have 40% 14.3% =25.7% sand. The best proportions, then, 

 for a 1:6 mixture by weight are 14.3 parts cement: 25.7 parts 

 sand: 60 parts stone, or a 1:1.8:4.2 concrete. In determining 

 the corresponding proportions by volume, the weights of the 

 sand and stone per cubic foot should be considered. 



Consider now the proportioning of the medium sand OB with 

 the stone DE as before. The curve OB may be transformed so 

 that it will pass through F, by changing the distances from the 

 bottom line of the diagram to the curve OB in the proportion 



1 From Taylor and Thompson's "Concrete, Plain and Reinforced," 2nd edition, pages 784 

 to 788 inclusive. Copyright, 1905, 1909, by Frederick W. Taylor. 



