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)

Statistics and target mean strength in mix design 63
Example 2.8-1
Determine the target mean strength and the current margin to be used in
the mix design if the standard deviation is 6 N/mm 2 and if the characteristic
strength is to be 30 N/mm 2 •
SOLUTION
From eqn (2.8-1),
target mean strength = 30 + 1.64 x 6 = 39.8 N/mm 2
current margin = 1.64 x 6 = 9.8 N/mm 2
Example 2.8-2
A concrete mix is to be designed to give a 1% probability that an individual
strength test result will fall below a certain specified value, [spec, by more
than f N/mm 2 . Determine the target mean strength.
SOLUTION
There is to be a 1% probability that a test result will fall below (!spec -f).
Referring to Fig. 1.3-4, we now want the shaded area of the tail of the
normal distribution curve to be 0.01, i.e. we want the area OABC to be 0.5
- 0.01 = 0.49. From Table 1.3-3, z = 2.33. Therefore
That is
/spec - f = target mean strength - 2.33a
target mean strength = [spec + 2.33a - f (2.8-2)
Example 2.8-3
A concrete mix is to be designed to give a 1% probability that the average
of n consecutive test results will fall below a certain specified value [spec-
Determine the target mean strength.
SOLUTION
In statistical analysis [38, 39], it is known that when individual samples are
taken n at a time from a normal distribution with a standard deviation a
and a mean .X, the average values calculated from the sets of n samples
also have a mean .X but a standard deviation an which is equal to
a/~ n. Therefore, if we wish to design a mix to give a 1% probability that
the average of n consecutive test results will fall below the specified value
[spec then we know (from the arguments that lead to z = 2.33 in eqn 2.8-2)
that the corresponding z (n) value must be 2.33. Therefore
target mean strength = /spec + 2.33an
Since an = a/~ n, we have
target mean strength = /spec + 2 ~~ 3 a
(2.8-3)
Example 2.8-4
The ACI Building Code (ACI 318-83) [40] uses the concept of a specified
strength f~, which is the 28-day cylinder compressive strength used in