12 REINFORCED CONCRETE CONSTRUCTION 



sand, and stone should be determined in a similar manner to the 

 previous problem. The combined curve is shown as ONFRE. 

 The part of this curve to the left of F very nearly coincides with 

 the ideal curve. For example, 43% of LM = 0.43X83 -35.7%, 

 or almost exactly LN. From F to the right, the combined 

 curve varies somewhat from the ideal. For example, the per- 

 centage of particles larger than 4/10 of an inch =57% of PS = 

 0.57X82.5 = 47%, or PR. 



Now suppose that we consider two aggregates, the curves of 

 which overlap namely, OB and OKE of Fig. 4. The proportion 



pr T7i or fi TJI ro 



of sand plus cement to use is Fn= gg = 4 %> QK 88 



60% stone. The combination curve, with the exception of the 

 overlap, may be drawn in the same manner as before. The 

 method of finding a point such as T is as follows: 

 DF(O.GO) + ZW(0.40) =DT = 43%. 



The student should understand that the location given for 

 the point F in the above problems can be only approximate. If 

 possible in any given case, it would be advisable to vary the 

 proportions somewhat each way from those obtained in the 

 above manner, and determine the corresponding densities by 

 volumetric tests. It should also be understood in this connection 

 that the curVe of maximum density may vary slightly from the 

 so-called ideal curve; but the variation is never great, and there 

 is the advantage of being able to plot, by means of simple rules, 

 a curve which will lie at least very close to the maximum density 

 curve for the given aggregates. 



It should be clear that plotting mechanical-analysis curves 

 shows approximately not only tlje best proportions for given 

 materials, but also shows how the materials may be improved 

 by adding or subtracting some particular size. The most valu- 

 able use, however, of the method of proportioning by mechanical 

 analysis is in the kind of work which warrants employing several 

 grades or sizes of sand and stone. The process of determining 

 the percentage of each material varies for different cases and is 

 more complicated than where but two aggregates are used. The 

 following problem will give a fair idea of the method of solution 

 for any given case. 



The two sizes of crushed stone and the sand shown in Fig. 5 

 will be considered. The crushed stone curves show the sizes of 

 stone which ordinarily pass through crusher screens of given 



