Page 104 - Riem-Vol6_nº3

449 IBRACON Structures and Materials Journal • 2013 • vol. 6 • nº 3
R.. G. DELALIBERA | J. S. GIONGO
Engineering, its use is still restricted, but, there are already works
developed using the technique, as: Lima Júnior [20], Delalibera [5]
and Pituba et al. [21].
In the variance analysis developed in this work, we used fixed
factors, choosing three study variables: the embed length of the
column in the sockets (ℓemb); the thickness of the pile caps bottom
“slab” (hs); and the wall conformation of the embed chalice and
the precast column. The variables chosen totalized eighteen cases
of combinations. The models were divided in two groups (smooth
walls – L and rough walls – R).
4.1 Formulation of the variance analysis
Being N and M the main fixed factors of the variance analysis, a, b
and c, the variations of these factors and n the number of replicas.
In general there will be abc…n possible combinations. If all the ex-
periment factors are fixed, the problems can be easily formulated,
obtaining results that indicate which of the analyzed factors are
important as well as their combinations. Table [5] presents a vari-
ance analysis with two factors.
To verify the relevance of a determined fixed principal factor or
combinations among the main factors, it occurs the relation be-
tween the average of the squares of each main factor or combi-
nation of the main factors by the average of the squares of the
mistakes. The division between the average of the squares of each
main factor or combination of main factors by the average of mis-
takes is called F0.
The number of freedom degrees of each main factor is equal to
the number of variations of each factor less the unity. The number
of freedom degrees of the main factors combined is the product
between the main factors which were combined.
The total sum of the squares is calculated through Equation [1].
The sum of the squares of the combination N x M is expressed
through Equation [2]. The sum of the squares of the mistake is
defined by Equation [3].
(1)
Table 5 – Analysis of Variance, addressing general, Montgomery [24]
Factor Sum of squares Freedom degrees F0 Square average
M
N
M x N
Error
Total
SSM
SSN
SSMN
SS E
SST
a –1
b – 1
(a – 1) · (b – 1)
abc · (n – 1)
abcn – 1
MSM = SSM / (a –1)
MSN = SSN / (b –1)
MSMN = SSMN / [(a – 1) · (b – 1)]
MSE = SSE / [abc · (n – 1)]
– –
–
E
M
0 MS
MS F

E
N
0 MS
MS
F 
E
MN
0 MS
MS
F 
(2)
(3)
To verify the relevance of a determined main variable fixed or com-
bined, it is applied test F. Through tabulated values of Fcritical, pro-
vided by Montgomery [24], it is compared the value calculated of
F0 with the value of Fcritical. If the calculated value of F0 is higher
than the tabulated value of Fcritical it means that this factor is rel-
evant, otherwise, it implies that the factor does not have substan-
tial importance. The values of Fcritical are a function of the number
of freedom degrees and of each variable and of the total freedom
degrees number.
5. Results obtained
5.1 Analysis of two pile caps – normal force,
moment and smooth walls
Nine pile caps solicited by action of normal force of compression
and moment were analyzed (the moment applied to the pile cap
was obtained through application of a horizontal force applied on
the top of the column). The pile caps presented variations in the
embed length of the column (ℓemb) and in the thickness of the “slab”
of pile cap bottom (hs). The variation of the factors analyzed modi-
fied substantially the distribution of the main stress of compression
and the panorama of cracks in the last force increment applied to
the models. Table [6] presents the results of the numerical analy-
ses performed.
Considering the results of Table [6], it can be observed that for mi-
nor embed lengths of the column and minor thicknesses of the bot-
tom slab (in case of the models Lℓe60hs10NM and Lℓe50hs10NM)
occurred substantial differences in relation to the analytical values.