aci 214-77
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ACI 214-77TRANSCRIPT
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ACI Committee Reports, Guides, Standard Practices, and Com
mentaries are intended for guidance in designing, planning, executing,
or
inspecting construction, and in preparing specifications. Reference
to these documents shall not be made in the Project Documents. If
items found in these documents are desired to be part
of
the Project
Documents, they should be incorporated directly into the Project
Documents.
ANSI/ACI
214 77
ACI
Standard
Recommended Practice for Evaluation of
Strength Test Results of Concrete A.CI
214
77 *
Reported y ACICommittee 2 4
V. M.
MALHOTRA
Chairman
V. RAMAKRISHNAN
HUBERT RUSCH
DWARD A. ABDUN·NUR
HOWARD
T.
ARNI
JOSEPH F. ARTUSO
ROBERT
M. BARNOFF
RICHARD J. DOERMANN
RICHARD
D.
GAYNOR
ARNOLD R. KLINE
K. R. LAUERt
ROBERTO
SANCHEZ.TREJO
ROBERT G. SEXSMITH
T. G.
CLENDENNING
HERBERT K. COOK
A.
M. NEVILLE
ROBERT E. PHILLEO
FRANCIS J. PRINCIPE
V. D. SKIPPER
J.
DERLE
THORPE
Statistical procedures provide valuable tools for assessing results of strength tests
and such an approach is also of value in refining design criteria and specifications.
The report discusses briefly
the
numerous variations
that
occur in the strength of
concrete
and
presents statistical procedures which are useful in interpreting these
variations.
Keywords: coefficient of
variation; compression tests; compressive
strength; concrete
construction;
concretes; cylinders; evaluation; quality control; s mpling; standard deviation; statistical analysis;
variations.
CONTENTS
Chapter 1 lntroduction 214-2
Chapter 2 Variations in strength 214-2
2.l-General
2.2-Properties of concrete
Chapter 3 Analysis of strength data
3.l-Notation
3.2-General
3.3-Statistical functions
Chapter 4 Criteria
4.l-General
4.2-Criteria for strength
requirements
4.3-Additional information
2.3-Testing methods
3.4-Strength
variations
3.5-Standards
of control
4.4-Quality control charts
4.5-Tests and specimens required
4.6-Rejection of
doubtful
specimens
214-3
214-7
Chapter 5 References 214-14
•
Adopted as
a
standard
of
the American Concrete Institute in
Aug -lst ~ 9 7 7
to
supersede
ACT 214-65
in
accordance
with the
Institute
s
standardIzation procedure.
tChairman during development of the
revision.
Copyright
©
1976 American Concrete Institute.
214-1
. All rights reserved including rights of reproduction and
use
m any form or by any means. including
the
making of copies
by. any photo "rocess,
or
by any electronic or mechanical device.
prmted
or wntten or
oral,
or recording for sound or visual
reproductIOn or
for
use m
any
knowledge
or retrieval
system
or de:Vlce
unle.ss
permISSIon In
wntIng
is
obtained
irorn
the
cOPYrIght
proprIetors.
-
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214-2
MANUAL
OF
CONCRETE PRACTICE
CH PTER
I INTRODUCTION
The
purposes
of
strength tests
of
concrete
are
to determine compliance
with
a strength specifica
tion and
to measure the variability of
concrete.
Concrete,
being
a
hardened
mass of heterogeneous
materials,
is
subject
to
the
influence of
numerous
variables.
Characteristics
of each of the
ingredi
ents of concrete, depending
on
their
variability,
may
cause
variations in
strength
of
concrete.
Variations
may also
be
introduced by
practices
used
in
proportioning,
mixing, transporting, plac
ing, and
curing.
In
addition
to the variations which
exist
in concrete itself, test strength
variations
will
also be introduced by the fabrication, testing, and
treatment of test specimens.
Variations
in the
strength of concrete
must
be
accepted, but con
crete of adequate quality can be produced
with
confidence
if
proper
control
is maintained, test
results
are properly interpreted,
and their
limi
tations are considered.
Proper
control
is achieved by the use of satis
factory
materials,
correct batching
and
mixing of
these
materials, correct batching
and mixing
of
sired
quality, and good practices in transporting,
placing,
curing, and
testing. Although the com
plex nature of concrete
precludes
complete
homogeneity, excessive variation of concrete
strength
signifies inadequate concrete controL
Improvement
in control
may permit a reduction
in the cost of
concrete
since the average strength
can be
brought
closer to specification require
ments.
Strength is
not necessarily
the most
critical
fac
tor
in
proportioning
concrete
mixes
since
other
factors,
such
as
durability,
may impose lower
water-cement
ratios
than are required to meet
strength requirements. In
such
cases, strength
will of necessity be in excess of structural de
mands. Nevertheless,
strength
tests are valuable
in such
circumstances
since, with
established
mix
proportions, variations in
strength are
indi
cative
of variations in other
properties.
Test specimens
indicate
the
potential rather
than the
actual strength of
the
concrete in a struc-
ture.
To be meaningful, conclusions
on
strength of
concrete
must
be derived from a pattern of tests
from which the characteristics of the
concrete
can
be
estimated with
reasonable
accuracy. Insuf
ficient tests
will
result in unreliable
conclusions.
Statistical procedures provide tools of consider
able
value in evaluating results of strength
tests
and information derived from
such
procedures
is
also of value in refining design criteria and speci
fications.
This
report briefly discusses variations
that
occur in the strength of concrete, and presents
statistical procedures that
are
useful in
the inter
pretation of these variations with
respect
to re
quired criteria and specifications. For these sta
tistical procedures to
be
valid, the data must be
derived
from samples
obtained
by
means of a
random sampling plan designed to reduce
the
possibility that choice
will
be
exercised
by the
sampler.
Random sampling means that
each
possible
sample
has
an
equal chance of being
selected. To insure
this
condition, the choice must
be
made by some objective mechanism such as
a table of random numbers.
f
sample batches are
selected by
the
sampler on
the
basis
of
his
own
judgment, biases are likely to be introduced
that
will
invalidate results
analyzed by
the procedures
presented here. Reference
1
contains
a discussion
of random
sampling
and a
useful
short table of
random numbers.
Additional
information
on the meaning
and
use
of this recommended
practice
is given in
Realism
in the pplication of CI
Standard
214-65.
2
This
volume
is a
compilation of
information
on ACI
214-65 that
was presented at
a
symposium held
at
Buffalo, N. Y, in 1971
In
addition to the papers
from
the symposium, it
includes
reprints of some
pertinent
papers
that were published
earlier in
the
ACI JOURNAL, and of discussion
that
resulted
from
them. Although the information
given was
based
on ACI
214-65, most
of
it is
still
relevant.
An additional source of
material
on evaluation of
strength
tests
is ACI Bibliography No.2, published
in 1960
3
CH PTER
2 VARIATIONS
IN STRENGTH
2.1-General
The
magnitude
of variations in the strength of
concrete test specimens depends on
how
well
the
materials, concrete
manufacture, and testing
are
controlled.
Differences
in
strength
can
be
traced
to two fundamentally different sources as shown
in Table 2.1: a) differences in strength-produc-
ing
properties
of the concrete
mixture
and in
gredients, and
b) apparent
differences
in
strength
caused
by variations inherent
in the test
ing.
2.2-Properties
of
concrete
t is
well
established that
strength
is governed
to a large extent by the water-cement ratio. The
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STRENGTH
TEST
EVALUATION
214-3
TABLE 2.I PRINCIPAL SOURCES OF
STRENGTH
VARIATION
Variations in the properties
of concrete
Changes in water-cement
ratio:
Poor control of water
Excessive variation of
moisture in aggregate
Retempering
Variations in water require
ment:
Aggregate grading ab
sorption particle shape
Cement and admixture
properties
Air content
Delivery time and
temperature
Variations in characteristics
and proportions of ingre
dients:
Aggregates
Cement
Pozzolans
Admixtures
Variations in transporting
placing and compaction
Variations in temperature
and curing
Discrepancies in testing
methods
Improper sampling
procedures
Variations due to fabrica
tion techniques
Handling and curing of
newly made cylinders
Poor quality molds
Changes in curing:
Temperature variation
Variable moisture
Delays in bringing cylin-
ders
t
the laboratory
i Poor testing procedures:
I Cylinder capping
Compression tests
I
first
criterion for producing concrete
of
constant
strength
therefore
is a
constant water-cement
ratio. Since the quantity
of
cement
and
added
water can be measured accurately the problem
of
maintaining
a
constant water-cement
ratio
is
primarily
one of
correcting
for the
variable
quantity
of free
moisture in
aggregates.
The
homogeneity
of
concrete
is
influenced by
the variability of the aggregates cement and ad-
mixtures
used since
each will contribute to varia
tions in the concrete
strength.
The temperature
of
fresh concrete influences
the
amount of
water
needed
to
achieve the proper consistency and
con
sequently contributes to strength variation.
Con
struction
practices
may
cause
variations in
strength
due to inadequate
mixing poor
com
paction delays
and improper
curing. Not
all
of
these are reflected in specimens
fabricated
and
stored under standard
conditions.
The use of admixtures adds another factor since
each admixture adds another variable to concrete.
The batching
of
accelerators retarders
pozzolans
and air-entraining
agents must be
carefully
con
trolled.
2 3 Testing methods
Concrete tests mayor may not include all the
variations
in strength
of
concrete
in
place de
pending
on
what
variables
have been introduced
after
test specimens were made. On the other
hand discrepancies in sampling fabrication cur
ing
and
testing
of specimens may cause indica
tions
of
variations in strength which do
not exist
in
the
concrete in
the
structure. The project
is
unnecessarily penalized
when
variations from this
source are
excessive. Good
testing
methods
will
reduce
these variations and standard testing
procedures such
as
those described
in
ASTM
standards
should be
followed
without
deviation.
The importance
of
using
accurate testing ma
chines and
producing
thin
high-strength
plane
parallel caps
should
need
no
emphasis
since test
results
can be no
more accurate than the
equip
ment and
procedures
used.
Uniform t st results
are
not
necessarily accurate t st results Lab
oratory
equipment
and
procedures should
be
cali
brated
and checked periodically.
CHAPTER
3 ANAlYSIS
OF
STRENGTH DATA
3.1 Notation
fo
n
R
factors for computing within-test
standard deviation from average range
required average
strength
to
assure
that
no more than
the permissible propor
tion of tests
will fall
below
specified
strength
specified strength
number of
tests
range
maximum for
average
range used
in
control charts for moving average for
range
R
t
average range
standard deviation
within-test
standard deviation
batch-to-batch
standard
deviation
a
constant multiplier for standard
de
viation
a) that
depends on the
number
of tests expected
to fall
below
fo
coefficient
of
variation
within-test coefficient of variation
an
individual
test result
average
of
test results
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214-4
5
(/)
-
(/)
W
10
-
o
w
CD
::J
Z
169
183
197
MANUAL OF CONCRETE PRACTICE
211
225
kgf/cm2
239
x-
I
I
253
95.45 %
267
281
295
309
k- ------
-2 () - - - - - --:: <- --
--
------ -2()-
-
-->-1
1
I
1
I
1
68.27
I
1 r = - - - - ) - - - - - - T - - - - - ) - - - - - ~ 1
I 1 I 1
323
1 I 0 I
1 I I
I 1
0
I
)=
462psi
32.5kgf/cm2)
V=
13.2 1
I 01 0 0 I
I 01 0 0 0 I
0
1
0 0 0 10
o o
o
o
o
o o
o
o
o
o o
o
o
COMPRESSIVE
STRENGTH
PS
I
1
1
1
1
1
1
1
1
Fig.
3.3(a)-Frequency
distribution of strength data and corresponding normal distribution
3.2-General
To
obtain
maximum information, a sufficient
number
of tests should be
made
to indicate the
variation
in the concrete produced and to permit
appropriate statistical procedures to be used in
interpreting the
test
results. Statistical procedures
provide
the best
basis
for
determining
from such
results
the
potential
quality
and
strength of the
concrete
and for
expressing
results in the
most
useful form.
141
(): .
34
p i
(23.9
kof/cm2
Compressive strength, psi
Fig.
3.3(b)-Normal
frequency curves for different stand
ard deviations
3.3-Statistical functions
The
strength of concrete test specimens on con
trolled projects can
be
assumed
to fall into a
pattern similar
to the normal
frequency
distribu
tion
curve
illustrated in Fig.
3.3
(a).
Where there
is good control, the strength
values will
be
bunched
close to
the
average,
and the curve will
be
tall and
narrow. As
the
variations in
strength
increase, the values spread and the curve be
comes
low
and elongated, as illustrated by
the
idealized curves shown
in
Fig.
3.3 (b). Because the
characteristics of such curves
can be
defined
mathematically,
certain
useful
functions of the
strength can
be calculated
as follows:
3.3.1 Average
X-The average strength of all
individual tests
x
= Xl + X
2
+
X3
+
...
+
n
n
(3-1)
Where Xl, X
2
Xs n are the strength results
of individual tests
and n
is
the
total
number
of
tests made. A test is defined as the average
strength
of
all specimens
of
the
same
age fabri
cated
from
a
sample
taken
from
a single batch of
concrete.
3.3.2
Standard
deviation a-The
most generally
recognized measure of dispersion is the root-mean
square
deviation of
the strengths from their
average. This statistic is known as the
standard
deviation
and may
be considered to be the radius
of
gyration
about the line of symmetry of
the
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STRENGTH TEST
EVALUATION
214·5
area under the curve of the frequency distribu
tion of
strength
data,
such as that
shown
in Fig.
3.3 a). The
best
estimate of cr based on a
finite
amount of
data,
is obtained by Eq. (3-2), or by
its algebraic equivalent, Eq. (3-2a). The
latter
equation is preferable
for
computation purposes,
because it is not only simpler and more adaptable
to
desk
calculators,
but it
avoids
the
possibility of
trouble due to rounding
errors.
or
() = { Xl - X)2 +
X2
- X)2 +
Xu
- X 2]/n - 1}%
• /
~ X . 2
_ ~ X i )
V
n
a= n 1
(3-2)
(3-2a)
3 3 3 Coefficient of variation, V :The standard
deviation expressed
as a
percentage of
the
v e r ~
age
strength is
called
the coefficient of variation:
a
V = X 100
X
(3-3)
3.3.4 Range,
R-Range is the statistic
found
by
subtracting
the lowest
of
a group of numbers
from
the
highest one
in the group. The
within-test
range is
found by
subtracting
the lowest
of
the
group
of cylinder
strengths averaged
to produce
a
test
from the
highest of
the group.
The within
test
range
is
useful
in
computing the within-test
standard deviation
discussed
in
the following sec
tion.
3.4-Strength
variations
As mentioned previously, variations
in
results
of strength
tests can
be
traced
to two
different
sources: (a) variations in testing methods
and
(b) properties of
the
concrete mixture and in
gredients.
It is possible by
analysis
of
variance
to compute the variations attributable
to
each
source.
3 4 1
Within-test
variation - The variation in
strength of
concrete
within
a single test is found
by computing the
variation of
a
group of
cylinders
fabricated from a sample of concrete
taken
from
a
given
batch. It is reasonable to
assume
that a
test sample of
concrete
is homogeneous and any
variation
between
companion
cylinders
fabricated
from a given sample is caused by fabricating,
curing, and testing variations.
A
single
batch of
concrete,
however, provides
insufficient data
for
statistical
analysis
and
com
panion cylinders from at least ten batches of con-
TABLE 3.4.I-FACTORS FOR COMPUTING WITHIN
TEST
STANDARD DEVIATlON
Number of
specimens
d
2
1/d2
2
1.128
0.8865
3
1.693
0.5907
4 2.059 0.4857
5
2.326
0.4299
6
2.534
0.3946
7
2.704
0.3698
8
2.847
0.3512
9
2.970
0.3367
10
3.078
0.3249
From Table
B2, ASTM
Manual
on Qual i ty
Control of Ma-
terials Reference 4
crete are required to establish reliable values
for
R. The
within-test
standard deviation
and
coef
ficient of variation can be
conveniently computed
as follows:
where
1/d
2
V
1
X
01
=
d
2
R
V
1
= a1 X 100
X
= within-test
standard deviation
(3-4)
(3-5)
a constant depending on
the
number of
cylinders averaged to
produce
a test
Table 3.4.1)
average
range within groups
of com
panion cylinders
= within-test
coefficient of
variation
= average strength
3 4 2 Batch-ta-batch
variations-These variations
reflect
differences
in strength which
can
be at
tributed to variations in
(a) Characteristics
and
properties
of
the in
gredients
(b) Batching, mixing,
and sampling
(c) Testing
that
has not been detected from
companion
cylinders since
these tend
to
be
treated
more alike
than cylinders tested at
different times
Fig.
3.4.2 al-Approximate
division of
the
area
under
the normal frequency distribution curve
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214-6
MANUAL OF CONCRETE PRACTICE
The batch-to-batch
and
within-test
sources of
variation are related
to
the
overall
variation
[Eq. 3-3)] by the following expression:
3-6)
50
60
Q;
>
J
70
0
c
Cii
C
80
e:
'"
.=
c
'
90
;
Q;
ro
Ol
95
e:
0
c:
Q
u
Q;
0..
Percent
of average strength
Fig. 3.4.2 bJ-Cumulative distribution curves for different
coefficients of variation
98.4
84.4 70.3
50
60
70
....
80
J
i
....
CIt
-
90
II:
CD
U
....
95
D
Q..
96
97
98
99
1400
1200
1000
where
o = overall standard deviation
01 =
within-test
standard deviation
02 = batch-to-batch standard deviation
Once
these parameters have been computed,
and
with the
assumption
that the results
follow a
normal frequency distribution curve, a large
amount
of information
about the test results
be
comes known. Fig. 3.4.2 a)
indicates an
approxi
mate
division
of
the area
under the
normal
frequency distribution curve.
For example,
ap
proximately 68 percent
of the area
equivalent
to
68 percent of the test results) lies within ± 10 of
the average, 95 percent within ± 20 , etc. This
permits
an
estimate
to
be
made of the portion of
TABLE 3.4.2-EXPECTED PERCENTAGES OF
TESTS
LOWER
THAN f
WHERE
X
EXCEEDS
fa BY
THE
AMOUNT SHOWN
Average
Expected
Average
Expected
percentage
percentage
strength,
of
strength,
of
X
low tests
X
low
tests
fo
+ 0.10a
46.0
f + 1.6a
5.5
fo
+ 0.20a
42.1
fo + 1.7a
4.5
fo
+ 0.30a
38.2
fo
+ 1.80
3.6
fo + 0.400
34.5
fo
+ 1.9a
2.9
f,, + 0.50a
30.9
fo + 2.0a
2.3
fc + 0.60a
27.4
fo + 2.10
1.8
fo
+ 0.700
24.2
fo + 2.2a
1.4
fo + 0.80a
21.2
fo
+ 2.3a
1.1
f + 0.90a
18.4
fo
+ 2.4a
0.8
f
+ 0
15.9
fo +
2.50
0.6
fo
+ 1.10a
13.6
fo
+ 2.60
0.45
f
+ 1.200
11.5
fo
+ 2.70 0.35
f
+ 1.30a
9.7 f + 2.8a 0.25
fo
+ 1.400 8.1 fc + 2.90
0.19
fo + 1.500
6.7
fo + 3.00
0.13
I
kgf/cm2
56.2 42.2
28.1
14.1
o
---_::::::.
800 600
400 200 o
Compressive
strength-psi
below average
Fig.
3.4.2 cJ-Cumulative
distribution curves for different
standard
deviations
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STRENGTH
TEST EVALUATION
214 7
T BLE
3.5 5T
ANDARD5 OF CONCRETE CONTROL
Overall variation
Standard deviation for different control standards, psi kgf/cm2)
Class of operation
Excellent
I
Very
good
I
Good
I
Fair
I
Poor
General
construction
below 400
400 to 500 500 to 600
600
to
700
above 700
testing
28.1) 28.1) 35.2) 35.2) 42.2)
42.2) 49.2)
49.2)
Laboratory trial
below 200 200
to
250 250
to
300
300
to
350
above
350
batches
14.1)
14.1) 17.6) 17.6) 21.1)
21.1) 24.6)
24.6)
Within-test variation
Coefficient of
variation
for differe nt control standards,
percent
Class of operation
Excellent
I
Very
good
Field
control testing
below 3.0 3.0
to
4.0
Laboratory trial
batches
below 2.0 2.0 to 3.0
the test results expected to fall within given
multiples
of
of
the
average
or
of
any
other spe
cific
value.
Table 3.4.2
has been
adapted from
the
normal probability integral of the
theoretical
normal
frequency
distribution
curve and
shows
the probability
of
tests falling below to in terms
of
the average strength
of
the mix X· = f r
(to +
ta . Cumulative distribution curves can
also
be plotted
by
accumulating the
number
of
tests below any given strength
expressed as a
percentage of the
average strength for different
coefficients of variation or
standard
deviations.
Fig. 3.4.2
b) and
3.4.2 c)
present such
informa
tion.
In
these
figures,
the ordinate indicates the per
cent of the population
of
strength values which
may be expected
to
exceed
the
strength
indicated
by any abscissa
value
for a
selected
coefficient of
variation or standard deviation.
I
Good
I
Fair
I
Poor
4.0
to
5.0
5.0
to
6.0
above 6.0
3.0 to 4.0 4.0 to 5.0
above 5.0
3.5 Standards of
control
The
decision as to whether
the standard
devia
tion or the coefficient
of
variation
is
the appro
priate measure
of
dispersion
to
use
in
any given
situation depends on which
of
the two
measures
is
the
more
nearly constant
over
the
range of
strengths
characteristic
of
the particular situation.
Present information indicates that the standard
deviation
remains
more
nearly constant
par
ticularly
at
strengths over
3000 psi 211
kgf/cm
2
.
For
within-test variations the coefficient of
varia
tion
is
considered
to be
more applicable
see Ref
erences
5-10).
Table
3 5 shows the variability that can be ex
pected
for compressive strength tests on projects
subject to different degrees of control.
These
values
are
not
applicable to
other strength
tests.
CHAPTER
4 CRITERIA
4.1 General
The
strength
of control cylinders
is generally
the only tangible evidence of the quality of
con
crete
used
in
constructing
a structure. Because of
the possible disparity between the strength
of
test cylinders and the load-carrying capacity of
a
structure
it is unwise
to place
any
reliance
on
inadequate
strength data.
The
number
of tests lower
than
the desired
strength
is
more important
in
computing the
load
carrying
capacity of concrete
structures
than
the
average strength obtained. t
is
impractical,
how-
ever, to specify
a
mmlmum strength
since
there
is
always the
possibility of
even
lower
strengths,
even when control
is good.
t
is also recognized
that
the cylinders may
not accurately
represent
the concrete in each portion
of
the structure. Fac
tors
of safety are
provided
in design
equations
which
allow for
de v i a t ion s
from
specified
strengths
without jeopardizing the safety
of
the
structure. These have been evolved on the basis
of
construction
practices, design procedures,
and
quality
control techniques used
by
the
construc
tion industry.
t
should
also
be remembered
that
for
a
given
mean strength,
if
a
small
percentage
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214-8
MANUAL OF CONCRETE PRACTICE
1.50
_0
'
~ 1 . 4 5
..<::
Chance of strength being
lower
than
specified
g, 1.40
; - - - - - - - - - /
1;; I 35
0 .
Q)
1.30 ---- --
5l
:;
1.25
c;,
I. 20 + - - - - 1 - J - I - ~ _ ¥ _ - ~ ~ + _ _ -
~ 1.15
::>
CT
.:: 1.10
o
o
1.05
5
10 15
Coefficient
of
variation, percent
20
25
Fig. 4.1
(aI-Ratio
of required average strength
fer to
specified strength
fe
for various coefficients of variation
and chances of falling below specified strength
of the test results fall
below
the design strength,
a corresponding large percentage of the test re
sults will be greater than the
design
strength
with
an equally
large
probability of being
located
in a critical area. The consequences of a localized
zone of low-strength
concrete
in a
structure
de
pend on many factors; included
are the
probability
of early overload,
the
location and
magnitude
of
the low-quality
zone in
the structural unit, the
de
gree
of
reliance
placed
on strength in
design,
the
initial
cause of
the
low
strength, and the
conse
quences,
economic and
otherwise,
of structural
failure.
The
final
criterion
which
allows
for
a certain
probability of tests falling below fo used in design
is a designer's decision based on his intimate
knowledge of the
conditions
that are
likely
to
prevail. Building Code Requirements for Rein
forced Concrete (ACI 318-71) , provides guide
lines in this regard, as do other building codes and
specifications.
To
satisfy strength
performance
requirements
expressed in this
fashion
the
average
strength
of
concrete must
be
in excess of
fe ,
the design
strength.
The amount of
excess
strength depends
on
the expected
variability
of test results as
expressed
by a coefficient of variation
or standard
deviation,
and
on
the allowable proportion of low
tests.
Strength
data
for
determining the
standard
deviation or coefficient of variation should rep
resent
a
group
of
at least
30 consecutive
tests
made
on concrete
produced
under
conditions similar to
those to be expected on the project. The require
ment
for
30
consecutive
strength
tests will
be
con-
kgf/cm
2
0
14.1
70.0
£
1000. . ; . r : ; : . . r r T: : . . . ; . . r : : . . . . . . : . . ;
70.0
g.
(I I
-c 8 0 0 t - - - - - + - + - - - , A - - - - - t 7 L - - - + - ~ _ _ _ l 5 6 . 2
C1l
~
·0
C1l
~ ~ o 6 0 0 r _ - - + - ~ - + _ ~ - ~ ~ r _ _ + - - - ~
»
... 42.2
OlE
~ ~
~
0>
~ ~
-b
g'
+- 4 0 0 r _ - - - - - , 1 t - - - - . - - + _ - r - - ~ - - - - + - _ _ : 7 _ l 2 8 . 1
~
(I I
-c
·3
2oot---- -t-7L---b----r --- -----i 14.1
cr
-
(I I
(I I
C1l
U
)
W
O ~ ~ ~ ~ ~ ~ 0
o 200
400
600
800
1000
Standard dev iation, psi
Fig. 4.1
(bl-Excess of
required average strength cr
to
specified strength
fa
for various standard deviations and
chances of falling below specified strength
sidered to have been complied with
if the
tests
represent either
a group of 30
consecutive
batches
of
the
same class of
concrete or the
statistical
average for two groups totalling 30 or more
batches. Similar conditions
will be difficult to
define and
can be
best
documented
by
collecting
several groups of 30 or more tests. In general,
changes in materials and procedures will have a
larger
effect
on the
average
strength level than
on
the
standard deviation or coefficient of varia
tion.
S
i g n i f i
can
t
changes generally include
changes in type and brand of portland cement, ad
mixtures,
source
of aggregates,
mix proportions,
batching, mixing, delivery, or testing.
The
data
should represent concrete produced to meet a
specified
strength
close to
that
specified
for the
proposed work, since the standard deviation may
vary
as
the
average strength varies. The
required
average strength
fer
for any
design
can be
com
puted
from Eq. (4-1) or (4-1a) ,
(Table
3.4.2), or
approximated from Fig. 4.1 (a) or 4.1 (b), depend
ing
on
whether the
coefficient of variation
or
standard
deviation
is used.
where
fer
fe =
t
f
fa
r
=
(1 -
tV
fer
=
fo
+ a
required average strength
design strength specified
(4-1)
( 4-1a)
a constant depending upon the proportion
of tests
that may fall below fe (Table
4.1)
forecast
value of
the
coefficient of varia
tion expressed as a fraction
forecast
value
of
the
standard
deviation
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STRENGTH
TEST EVALUATION
214-9
kgf/cm2
4
169
197
225
253
28
309
337
366
394
20
j)
Vi
15
<t-
o
-
c
10
U
L
Q)
0..
5
Compressive Strength, psi
Fig. 4.1 c)-Normal frequency curves for coefficients of variation of
10 IS,
and 20
percent
Whenever the average of a
certain
number of
tests
n is involved in the specif ication, Eq. 4-1)
is modified as follows:
and
fe
fer =
t
In
for = fe ta
In
4-1b)
4-1c)
Fig.
4.1
c) demonstrates
that
as
the
variability
increases
fer
must increase and thereby illustrates
the economic
value
of good control.
The requirement
of
at least
30
test results men
tioned
previously is
based on the fact that
25
to
30 randomly selected test results from a
normally
distributed population provide estimates
of
the
population average and standard deviation that
can
be
used
as
the population
values.
f only
a
small number of results is available on which to
base
estimates,
then
the
values, especially for
standard
deviation,
are unreliable, and
there is no
way in which
fer
can be
determined
so
that
a
specific
percentage of future tests will
be above
fe ,
assuming that the present
test results are
the
only
information available.
f previous information exists for concrete
from
the
same
plant
meeting
the
similarity require
ments described
above,
that
information
may be
used in deciding
on
a
trial value
of
a
to be
used
in
determining the target
fer.
TABLE 4.I-VALUES OF
t
Percentages
of tests
falling
within the
Chances
of falling
limits X ± ta
below
lower limit
40
50
60
68.27
70
80
90
95
95.45
98
99
99.73
3
in
10
2.5
in
10
2
in
10
1 in 6.3
1.5
in
10
1 in 10
1 in 20
1
in
40
1 in 44
1 in 100
1 in 200
1 in 741
0.52
0.67
0.84
1.00
1.04
1.28
1.65
1.96
2.00
2.33
2.58
3.00
For small
jobs
that
are
just
getting started,
where
no
prior
information is available,
the
con
crete
should be designed to produce an average
strength
fer
at
least
1200 psi 84.4 kgf/cm2)
greater
than
fe . As
the job
progresses and
more
strength
tests
become available, all
the strength
tests can
be analyzed together to give a more reliable esti
mate of the standard deviation, and Eq. 4-1),
4-1a), 4-1b),
and
4-1c)
can be used
to
calculate
a less conservative fer.
4.2-Criteria for strength requirements
The amount by which the average strength of
a
concrete mix fer should exceed fe depends
on
the
criteria
used in the
specifications for a par
ticalar
project.
The
following
are
examples of
calculations
that
would
have
to
be
made
to select
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214-10
MANUAL OF
CONCRETE
PR CTICE
the design strengths of
a
mix
that
will
meet the
requirements
of a
particular
code or specification.
4.2.1
Criterion No l -A stated
maximum
pro-
portion of random individual strength
tests
that
will
be permitted to
fall below fo on the average.
ASTM
C 94-74 uses a similar
approach.
For con
crete in
structures
designed
by the ultimate
strength method, ASTM recommends
that
not
more than 10 percent of
the
strength tests have
values
less than the
specified
strength fe .
As an
example, consider
the situation
where no
more than 1
in
10
random
individual
strengths
will be permitted to be
below
an fo of 4000 psi
(281
kgf/cm2).
Standard deviation method
Consider
very good quality
control
as indi-
cated by a
standard deviation
of 450
psi
31.7
kgf/cm
2
. Using Eq. 4-1a) and Table
4.1,
we have
fer
= fo + tu
= 4000 + 1.28 X
450
=
4580 psi 322 kgf/cm2)
As a result, for a
structural
design strength
fa
of 4000 psi
(281
kgf/cm
2
), the
concrete mixture
should
be proportioned
for
an average
strength
of
not less than
4580
psi 322
kgf/cm
2
).
Note that
the coefficient of variation is 450/4580) X
100
=
9.8
percent.
Coefficient of variation method
Consider
good quality
control
as indicated by
a coefficient of variation of
10
percent.
Using
Eq.
4-1) and Table 4.1,
we have
f
fo
cr =
1 - tV
_
fo
fer
- 1 - 1.28 0.10)
= 1.15 fo [see also Fig. 4.1 a)]
= 4600 psi 324 kgf/cm
2
)
Using this
approach
and this data
the
concrete
mixture
should
be proportioned
for an average
strength of
not
less than 4600 psi 324
kgf/cm2).
4.2.2 Criterion No 2-A certain probability
that
an average of
n
consecutive strength
tests
will be
below
fo .
ACI
318-71
suggests
that after
sufficient
test
data become
available
from a
project,
the fre-
quency
of occurrence of averages
of three con
secutive tests below
f
should
not
exceed
1 in 100.
As
an example, consider the
situation
where
no
more
than
1 in
100
of
averages
of three consecu
tive strength tests
will
be permitted to be
below
an fa of
4000
psi (281
kgf/cm2).
Standard deviation method
Consider
a
standard deviation
of 750 psi (53
kgf/cm
2
.
Using Eq. 4-1c) and Table 4.1, we have
tu
fer =
fo +
In
= 4000 psi
+
2.33 750)
J3
= 5000 psi 351 kgf/cm2)
As a result, for a structural design strength fe
of 4000 psi (281
kgf/cm
2
, the concrete
mixture
should
be proportioned
for
an average strength
of
not
less
than
5000
psi
351
kgf/cm
2
.
Coefficient of variation method
Considering
a coefficient of variation of
15
per-
cent
and
using Eq. 4-1b)
and
Table 4.1, we
have
fo
fer
-
1 _
tV
In
4000
- 1 _ 2.33
(9.
15 )
J3
= 5000
psi
351 kgf/cm
2
Using this
approach the concrete
mixture
should be proportioned for an average
strength
of not less than
5000
psi 351
kgf/cm2).
4.2.3 Criterion No
3 -A
certain probability that
a random individual strength test will be more
than a certain
amount
below f0 .
This
approach is also
used
in
ACI
318-71 by
stipulating
that
the probability of
a
random test
result
being
more than 500 psi 35.1 kgf/cm
2
)
below
fo should be 1 in 100.
As an example, consider a probability of 1 in
100 that a strength test
will
be more than
500
psi 35.1 kgf/cm2)
below
an
fo
of
4000 psi (281
kgf/cm2) .
Standard deviation
method
Considering a
standard
deviation of
750
psi
(53 kgf/cm2) and using Eq. 4-1a) and Table 4.1,
we have
fer =
fe
- 500 + ta
=
4000 -
500
+ 2.33 750)
= 5245
psi 369
kgf/cm
2
)
As a
result
the
concrete
mixture
should
be
pro-
portioned
for an
average strength of
not
less than
5245 psi 369
kgf/cm2).
Coefficient
of
variation
method
Using
Eq. 4-1)
and
Table
4.1,
and a coefficient
of
variation
of
15 percent,
we
have
fer
fo
- 500
tV
4000 -
500
1 - 2.33 0.15)
5390
psi 379
kgf/
cm2)
Using this approach,
the
concrete
mixture
should be proportioned for an
average
strength
of
not less than
5390
psi 379 kgf/cm2).
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STRENGTH
TEST
EVALUATION
214 11
TABLE 4.3 EVALUATION OF ONSE UTIVE LOW STRENGTH
TEST
RESULTS
1
2
\
3
I
4 5
Averages less
than
indicated
Probability of
averages less
require
investigation
than
fc ,t
Number of
percent
consecutive
Criteria for original
selection
of fer
tests
averaged
1 test in 100
1 test
in
10
less than
below
fe
[tc - 500 psi
(35.2 kgf/cm2] 1 test in 10
below
f
For
V =
15,
percent
For given 0
For
given
0
1
0.86f/
fe - 0.770
fo - 500
+
0.760 10.0
2
0.97fo
fe
-
0.170
f
- 500
+
0.880 3.5
3
1.02fo
fo
+
0.100 fe - 500
+
1.140
1.3
4
1.05f/
fe
+
0.260 fe - 500
+
1.300
0.5
5
1.07f/
fe +
0.360
fe -
500
+
1.410
0.2
6
1.08fo
fo
+
0.440
fe
-
500
+
1.490 0.1
The probability of averages less
than the
levels
indicated is approximately
2
percent i f the
population average equals f
and the standard
deviation or coefficient
of variation is at the
level
assumed.
t f the population average equals fer and the standard deviation
or coefficient
of variation
is
at
the level assumed.
4.2.4 Criterion No. 4 A certain probability that
a
random
individual strength test will
be
less than
a certain percentage of
f t
As an example consider a probability of 1 in
100 that a
strength test will be
less than
85 per
cent of an
fc
of
4000
psi (281 kgf/cm2).
Standard deviation method
Using
Eq. (4-1a)
and Table
4.1
and
a
standard
deviation
of 750 (53 kgf/cm
2
, we have
fc
0.85 fc + ta
=
0.85 (4000) + 2.33 (750)
=
5145
psi
(361 kgf/cm2)
As a result the concrete mixture should be pro
portioned
for an
average strength of
not
less than
5145 psi (361 kgf/cm
2
.
Coefficient of variation method
Using Eq. (4-1) and Table
4.1
and a coefficient
of
variation of
15
percent, we have
fer
=
0 85f/
tV
0.85 (4000)
1 -
2.33
(0.15)
5230 psi (368 kgf/cm2)
Using this approach,
the
concrete
mixture
should be proportioned for an average strength of
not less than 5230
psi
(368 kgf/cm
2
) •
4.3 Additional information
Table 4.3
presents additional information. The
values in the body of
the
table in Columns
2,
3,
and
4
are the
strength
levels below
which
in
dividual
tests or
averages of different
numbers of
tests should not
normally fall.
These
values are
based on the premise that the
concrete is pro
portioned
to produce
an average strength
equal
to fer The values in Column 2 are theoretically
correct
only
for
concrete
with a coefficient of
variation of 15
percent. Those
in
Columns
3
and
4 apply to any known
standard
deviation.
In
either
case
the
probability
of
their
being
exceeded
when the
concrete
is
properly controlled
is only
about
0.02.
Thus,
failure to
meet
the tabulated
limits
in
a larger proportion
of
cases
than that
stated
may
be an indication
that the
current
average strength is less than fer or that ) or V
has
increased. This could
be
caused
by
lower
strength
or poorer control than expected, or both. The
possibility
should
not be
overlooked
that
the low
tests
may
be caused
by
errors in
sampling or
test
ing rather than deficiency in the
concrete
itself.
In
any case,
corrective action
is
warranted.
Column
5
shows
the
probability
that
the average
of any
given
number of consecutive
tests
will
fail
to equal
or
exceed fe if the concrete is
propor
tioned to produce an average strength equal to
fel t can be seen that
increasing
the number of
tests
to be averaged increases the likelihood
that
fe will
be
exceeded since variations
tend
to
bal
ance out
with
an increased
number
of tests in a
set. For enforcement purposes, it is appropriate
and
logical to select the number of consecutive
tests
to
be
averaged in
such
a way that the ac
ceptance
level
is equal to
f t
This would mean an
average
of three
consecutive tests for concrete in
which
one
out
of
ten tests would be
permitted
to
be lower than f/ t should,
however,
be remem-
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214-12
MANUAL OF CONCRETE PRACTICE
bered
that,
according to the statistical theory as
sumed in the derivation of the values,
such
fail
ures
may
be
expected
by chance alone one time
in 50 even if the
concrete
is
controlled
exactly
as anticipated and is
overdesigned
to yield an
average
strength
equal to f r
Most specifications for concrete strength require
that a test
be
comprised of two
or
three specimens
from
the same sample of concrete. The
specimens
are
necessary
to
obtain
a
reliable average
for
a
given sample and to
provide
range data R for
determining within-sample
variations.
4.4 Quality control charts
Quality
control charts
have been used by
manu
facturing industries for
many
years
as an
aid
in
reducing variability and increasing efficiency in
production. Methods are well established for
the
setting
up
of such
charts
and
are outlined
in
con
venient form in the STM
Manual on Quality
Control of Materials
4
Based on the pattern of
previous
results and limits
established
therefrom,
trends become
apparent
as soon as
new
results
are
plotted. Points which fall outside the calculated
limits indicate that something has affected the
control
of the process. Such charts
are recom
mended
wherever
concrete
is in
continuous pro
duction over considerable periods.
Three
simplified charts prepared specifically
for concrete control are
illustrated in Fig. 4.4.
Required
overage
strength
fcn
.-
4000
J)
a .
\
o \
o \
_.L
-
:E
While these
do
not
contain
all
the features of
formal control
charts they
should
prove useful to
the engineer,
architect,
and plant superintendent.
a) A chart in which the results of all strength
tests
are
plotted as received. The
line for
the
re
quired
average strength is established
as
indicated
by
Eq. 4-1a) or Table 4.3
and the
specified
design
strength.
b)
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
in this case is
the
lower
limit.
This
chart is valuable in
indicat
ing trends and will
show the
influence of seasonal
changes,
changes
in
materials,
etc. The
number
of
tests
averaged to
plot
moving averages with
an appropriate lower limit
can be
varied to suit
each job.
c) Moving average
for
range where the
average range
of
the previous
ten
groups
of com
panion cylinders is plotted each
day
or shift. The
maximum average range allowable for good lab
oratory control
is also
plotted. Maximum
average
range
is
determined
as discussed in
Section
4.5.
Fig. 4.4
shows
Charts a), b), and c)
for
46
tests.
To
be
fully effective
charts
should
be main
tained throughout
the
entire
job.
280
~ 3 0 0 0 - - - ~ - - - - ~ ~ ~ ~ ~ - - - - ~ ~ - - ~ - - ~ ~ ~ - ~ ~ - - - - 2 1 0
. /
v;
Specified strength fc _
o
l)
:;; 2000
Required strength
=
f + to-
J)
~ = = = = = = ~ = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =
a . Movi ng average
for strength
Each point average strength
u 4000 of
five
previous test groups
3000
300
l)
0>
C
o
a::
100
o
Required average strength, f
cr
-
_____
_
______
L
Moving
average
for range
~
Average
range for two cylinders : .0564 fer
Average ra nge tor three
cylinders
=0846
fer
4
8
12
6
20
24 28
32
Each
point
average of
ten previous
ranges
36
40
44
Sample numbers
Fig.
4A--Quality control charts for concrete.
48
210
2
7
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STRENGTH TEST
EV LU TION
214 13
4.5 Tests and specimens required
For
any
particular
job, a
sufficient
number of
tests
should
be
made to insure accurate represen
tation of the variations of the concrete.
Concrete
tests can be made either on
the
basis of
time
elapsed
or
cubic yardage
placed
and conditions
on each job will determine the most practical
method
of
obtaining
the number
of tests needed.
A test is
defined
as the average
strength
of all
specimens of the same age fabricated from a
sample
taken
from a
single batch
of concrete.
A project
where
all concrete operations are
supervised
by
one engineer
provides
an excellent
opportunity for control and for accurate estimates
of reliability with a
minimum
of tests.
Once
op
erations are
progressing
smoothly tests
taken
each
day or shift, depending
on
the volume of
concrete
produced,
are
sufficient
to obtain data which re
flect the variations in the concrete of the
struc
ture.
In
general,
it
is
advisable to
make
a
sufficient
number of tests so
that
each different type of con
crete placed during anyone day will be repre
sented by at least one test which is an average
of
two standard 6 x 12 in. cylinders tested at the
required age. Single specimens
taken
from
two
different batches each day will
provide
more re
liable information
on overall
variations,
but it is
usually desirable to make companion snecimens
from the same sample to obtain a
check
on the
within-test variation.
The
number of specimens required by the en
gineer (architect) should be based
on established
standards
but may
be reduced as
the
reliabilities
of
the producer, the laboratory, and the contrac
tor are established.
The
laboratory has
the
responsibility of making
accurate
tests,
and
concrete
will
be penalized un
necessarily
if tests show greater variations or
lower average strength
levels
than actually exist.
Since the range between companion specimens
from the
same sample
can be assumed
to
be
the
responsibility of
the
laboratory, a control
chart
for ranges Fig. 4.4) should be maintained by the
laboratory
as a
check on
the
uniformity
of its
operations.
I t
should
be noted
that
these
ranges
will not reveal day to day differences in test
ing, curing, and
capping
procedures
or
testing
procedures which
affect strength levels
over long
periods. The range between companion cylinders
depends on the
number of
specimens in
the
group
and the within-test variation. This relationship is
expressed
by the following equation [see Eq. 3-4)
and 3-5)]
4-2)
where m is
the
average range in Control Chart
c)
of
Fig. 4 4
The within-test
coefficient
of
variation
V
should not be
greater
than 5
percent
for good
control (Table
3.5), and the estimate of
the
corresponding average range will
be:
m =
0.05 X 1.128) f r
= 0 05640fer
for groups
of two
companion cylinders
m
= 0.05 X 1.693)
f r
=
0 08465fer
for groups
of three
companion
cylinders.
A cylinder of
concrete
6 in. in diameter and 12
in. high
which
has
been moist cured for
28
days
at 21 C is generally considered a
standard
speci
men for strength
and
control of concrete
i f
the
coarse aggregate does not
exceed
2 in. in nominal
size. Many times,
particularly
in
the early stages
of
a job, it becomes
necessary
to
estimate
the
strength of
concrete
being produced
before
the
28-day
strength
results are available. Concrete
cylinders from the
same
batch should
be
made
and tested at 7 days, or at
earlier ages utilizing
accelerated test procedures.
The 28-day strength
can
be estimated by extrapolating early test
data.
The strength of
concrete
at later ages, particu
larly where
a pozzolan or
cement
of
slow
strength
gain is used, is more realistic
than
the
standard
28-day strength. Some
structures
will not be
loaded
until
concrete has
been
allowed to mature
for
longer
periods
and advantage can be taken of
strength
gain after
28 days. Some
concretes
have
been found to produce
at
28 days less than 50
percent of their ultimate strength.
I f
design is
based on
strength at later ages, it becomes neces
sary to correlate these strengths with
standard
28-day
cylinders
since
it
is
not practicable
to use
later
age specimens
for
concrete
acceptance.
I f
possible,
the correlation should be
established
by
laboratory tests before construction starts. I f
mix
ing plants are located in one place for long enough
periods,
t
is
advisable to
establish
this
correlation
for reference even though later age concrete is
not immediately involved.
Curing concrete
test
specimens
at the
construc
tion site and
under
job conditions is sometimes
recommended since this is considered more rep
resentative of the curing
applied
to the structure.
These
special tests
should not
be confused with,
nor replace, standard
control
tests.
Tests
of
job
cured specimens
may be highly
desirable
and
are
necessary when determining
the
time of
form
removal, particularly in cold weather, and when
establishing
the strength of steam-cured
concrete
pipe, block,
and
structural
members.
The potential strength and variability
of
con
crete can be established by
standard
6 x
12
in.
cylinders made and cured
under standard
condi
tions. Strength
specimens
of
concrete made
or
cured under other than standard
conditions pro
vide
additional information
but
should
be analyzed
and reported
separately.
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214-14
MANUAL
OF CONCRETE PRACTICE
4.6 Rejection
o doubtful specimens
The practice of
arbitrary rejection
of test cylin
ders which
appear too far out of line
is
not
recommended since the normal pattern of
proba
bility establishes the possibility of such results.
Discarding tests
indiscriminately
could seriously
distort the strength distribution, making analysis
of
results
less reliable.
t occasionally happens that
the
strength
of one
cylinder
from
a
group made from
a
sample devi
ates so far
from
the mean as to
be
highly im
probable. t is
recommended
that a
specimen from
a
test
of
three
or
more specimens be discarded if
its deviation from
a test
mean
is
greater
than
3a and
should
be
accepted with
suspicion
if its
deviation
is
greater than
2a. f
questionable varia
tions
have been observed during fabrication, cur
ing
or testing of
a specimen,
the specimen should
be rejected. The test average should be
computed
from the remaining
specimens.
A
test (average of all specimens
of a
sample)
should
never be rejected
unless
the
specimens
are
known to
be faulty,
since it represents
the
best
available
estimate
for
the sample.
CHAPTER 5 REFERENCES
1. Natrella,
M.
G. Experimental Statistics, Hand-
book No.
91
U. S. Department of Standards, National
Bureau
of Standards, Washington, D. C. 1963 p p. 1-4
to 1-6.
2. Realism in
the
Application
of
ACT Standard 214-65
SP-37, American Concrete Institute, Detroit, 1973
215
pp.
3.
Evaluation
of
Strength
Tests of Concrete,
ACI
Bibliography No.2, American Concrete Institute,
De
troit, 1960
13
pp.
4. ASTM Manual
on Quality
Control
of Materials
STP 15-C American Society for Testing and Materials,
Philadelphia,
Jan.
1951 127 pp.
5. Neville,
A. M.
The Relation Between Standard
Deviation and Mean Strength of Concrete Test Cubes,
Magazine
.of
Concrete Research
(London),
V. 11 No.
32 July 1959 pp. 75-84.
6.
Metcalf,
J. B. The Specification of Concrete
Strength, Part
II The
Distribution
of
Strength of
Concrete for Structures in
Current Practice, RRL Re -
port No. LR 300 Road Research Laboratory, Craw
thorne, Berkshire, 1970 22
pp.
7. Murdock, C.
J.
The
Control
of
Concrete Quality,
Proceedings
Institution of Civil Engineers (London),
V. 2 Part I July 1953 pp. 426-453.
8. Erntroy, H. C. The Variation of Works Test
Cubes,
Research
Report
No. 10
Cement
and
Concrete
Association,
London,
Nov. 1960 28 pp.
9.
Rusch,
H. Statistical Quality Control of
Concrete,
Materialpriifung (Dusseldorf), V. 6 No. 11 Nov. 1964
pp. 387-394.
10. Tentative Recommended Practice for Conduct
ing
an Interlaboratory
Test
Program
to
Determine the
Precision
of
Test Methods
for
Construction
Materials,
(ASTM
C 802-74T), 1975
Annual
Book of ASTM Stand-
ards Part
13
American
Society for
Testing and Ma
terials,
Philadelphia, pp. 414-443.