Building Materials, Third Edition

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The standard deviation of a given grade of concrete can be calculated from the results of
individual tests of concrete using the formula:

s =

9

2





()^22

11

xx
nn
where,
x = strength of each test result in n results
x = average of n sample,
h = the deviation of the individual test strength from the average strength of n
samples, and
n = number of sample test results.
If at least 30 test results for a particular grade of concrete at site with the same materials
and equipment are not available, the standard deviation as given in Table 11.7, may be assumed.

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A more rational approach for assuming the standard deviation for different grades of concrete
is given in the Building Research Establishment (BRE) publication, Design of Normal Concrete
Mixes, (1988). At a given level of control the standard deviation increases as the specified
characteristic strength increases up to a particular level and is independent of the specified
strength above this level (Fig 11.6). As can be seen from the figure, the standard deviation is
independent of the specified strength above 20 N/mm^2. The standard deviation to be adopted
for any mix depends on the data available from the strength test results. If data available is
from less than 20 results, curve A should be used to find the assumed standard deviation. If
data from 20 or more results is available curve B should be used. If previous information of 30
or more results is available, the standard deviation for such results may be used provided that
this is not less than the appropriate value obtained from curve B.