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IBRACON Structures and Materials Journal • 2012 • vol. 5 • nº 5
S. S. Araújo | G. N. Guimarães | A. L. B. Geyer
were randomized before the modulus of elasticity tests. Random-
ization was done to allow minimization of certain variables effects
that could not or were not considered in the experiment such as:
casting process, aggregate distribution in the concrete, testing de-
vice setup, among others. Also, if any dependency mechanism ex-
ists between subsequent experimental results, the randomizations
of the tests allow this dependency to be diluted among all studied
situations, thus not favoring a certain situation over another.
Statistical analysis of variance technique (ANOVA) was applied
using software Statsoft Statistica 7
®
, for concrete Class C30 and
for concrete Class C60 specimens, separately and together. The
test methodology consists in the application of Fisher’s Test. This
analysis indicated that the results should be analyzed together to
be statistically significant.
3. Presentations and discussion
of results
In order to verify the homogeneity of the concrete used, the com-
pressive strength results of the specimens taken to rupture right
after the modulus of elasticity tests were first analyzed. These
compressive strength results were analyzed by statistical methods
in order to identify possible variances of the results and to verify
the normal distribution (histogram) of the results. Figures 4 and 5
show the histograms of these compressive strength results for con-
crete classes C30 and C60, respectively. Concrete C30 showed
an average compressive strength of 36.5MPa with a coefficient of
variation of 10% and concrete C60 showed an average compres-
sive strength of 69.3 MPa with a coefficient of variation of 11%.
The comparison between the histograms and the normal distribu-
tion curve was analyzed by the Kolmogorov-Smirnov e Qui-square
methods. From a statistical point of view, a value of 10% is an ac-
ceptable level for variability for a measuring process.
Table 4 presents the averages, standard deviations and coef-
ficients of variation of the results obtained in all of the situa-
tions studied with a 95% confidence interval from the average
for the modulus of elasticity property. A statistical analysis of
variance (ANOVA) was done with the modulus of elasticity re-
sults to determine the statistically significant factors with a 95%
confidence level. Some values were removed, since they did
not fit the confidence interval and they were eliminated by the
Chauvenet criteria.
Table 4 shows that the measuring devices that presented the
smallest dispersions were the strain gages and the clip gages
since the total coefficients of variation of these devices were
11.0% and 14.4%, respectively, and the total coefficients of
variation of the dial indicators and the LVDTs were 16.1% and
18.2%, respectively.
Table 4 also shows that the specimens with 100 mm x 200 mm
dimensions presented higher dispersion of results, because their
total coefficient of variation was 24.4% and the total coefficient of
variation of the specimens with 150 mm x 300 mm dimensions
was 13.1%.
Since ANOVA revealed that the specimen size, type of measuring
device and type of concrete were statistically significant, grouping
homogeneous averages by the Duncan method was done to ob-
serve the differences and similarities of the results obtained.
This method demonstrated that the two specimen sizes influenced
the values of the modulus of elasticity of the concrete because the
Table 3 – Concrete mix for fc = 60 MPa
Material Proportioning by m³ of concrete
Mix design (1 : 1.928 : 2.58 )
W/C ratio = 0.42
Materials
Conventionally Vibrated Concrete
Quantity per m³
Cement CP V ARI
398 kg
Artificial sand
765 kg
Gravel size 1 (19 mm)
1028 kg
Water
167 kg
Polyfuncitonal Additive
2.79 kg (0.7% of cement)
Superplasticizer
1.59 kg (0.4% of cement)
Silica Fume
31.87 kg (as replacement
for 8% of cement in weight)
Fresh
Concrete
Properties:
Consistency
120 mm
Air
1.5 %