F. K. Kong MA, MSc, PhD, CEng, FICE, FIStructE, R. H. Evans CBE, DSc, D ès Sc, DTech, PhD, CEng, FICE, FIMechE, FIStructE (auth.)-Reinforced and Prestressed Concrete-Springer US (1987)

Step2
Statistics and target mean strength in mix design 61
The water content is 180 kg/m 3 as in Example 2.7-2.
Step3
The cement content is 180/0.46 = 390 kg/m 3 .
Step4
[ 390 180 J 3
Total aggregate content = 2600 1 - 3150 - 1000 = 1810 kg/m
StepS
From Fig. 2.7-3, for a slump of 10-30 mm, a w/c ratio of0.46 and a fine
aggregate in grading zone 4, a suitable proportion of fine aggregate is,
say, 31% by weight. Therefore
fine aggregate content = 0.31 x 1810 = 560 kg/m 3
coarse aggregate content = (1 - 0.31) x 1810 = 1250 kg/m 3
Ans. The required mix proportions are:
cement content: 390 kg/m 3
water content: 180 kg/m 3
fine aggregate content: 560 kg/m 3
coarse aggregate content: 1250 kg/m 3
Note that the answers in the above examples, and also that in Example
2.7-1, are only preliminary estimates. We began this section by saying that
the final proportions should be established by trials and site adjustments.
To stress this point once again, we conclude this section by stating that the
so-called mix design represents no more than an attempt to make a step in the
right direction; adjustments should always be expected after experience with
the actual materials and site conditions.
2.8 Statistics and target mean strength in mix design
Analysis of numerous test results from a wide range of projects has
demonstrated that the strength of concrete falls into some pattern of the
normal frequency distribution curve (Fig. 1.3-3), symmetrical about the
average with most of the test results falling close to the average. It is
therefore possible to relate the required characteristic strength of a
concrete to the target mean strength to be used in the mix design. Recalling
(Section 1.4) that the characteristic strength is the cube strength below
which not more than 5% of the test results may fall, it is immediately seen
from eqn (1.4-1) that
target mean strength = characteristic strength + 1.64a (2.8-1)
where a is the standard deviation of the strength tests. The quantity 1.64a
here represents the margin by which the target mean strength must exceed
the required characteristic strength, and is called the current margin.
At the initial mix design stage the standard deviation is not accurately