Environmental Engineering Reference
In-Depth Information
f
cr
= f
c
′ + k.σ
(12.3)
where,
f
cr
= the regulated average strength
f
c
′ = the specified strength
σ = standard deviation
k
= constant
The constant k is derived from the mathematics of the normal distribution and
increases as the proportion of defectives decreases:
k for 10% defectives
= 1.28
k for 5% defectives
= 1.64
k for 2.5% defectives
= 1.96
k for 1% defectives
= 2.33
Usually, the 5% defective level is used for concrete. Equation 12.4 relates a
concrete having a specified characteristic strength of 30 MPa and a standard deviation
of 6.1 MPa. Hence:
f
cr
= 30 + 1.64 × 6.1 = 40 MPa
(12.4)
The standard deviation calculated from
n
results is an estimate of the standard
deviation of the total population and is, therefore, subject to normal probability
errors, which are reduced as
n
becomes larger. If several groups of
n
results are
taken, these may vary by 20% without being significantly different statistically. For
mix design purposes the standard deviation should be calculated from at least 40
results.
12.4
QUALITY CONTROL CHART
For convenience, QC charts are often used as an aid in reducing variability and
increasing efficiency in production. Figure 12.2 shows three simplified charts pre-
pared specifically for concrete control,
6
described as follows:
1. Chart (a) or “a” shows all strength test results plotted as received, the line
for the required average strength, f
cr
, established as indicated by Equation
12.3, and the specified design strength f
c
′.
2. Chart (b) or “b” shows the moving average for compressive strength where
the average is plotted for the previous five sets of two companion cylinders
for each day or shift, and the specified strength as the lower limit f
c
′. This
chart is valuable in indicating trends and will show the influence of
seasonal changes, changes in materials, and so on. The number of tests
averaged to plot moving averages with an appropriate lower limit can be
varied to suit each job.
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