Page 114 - Riem-Vol6_nº2

285 IBRACON Structures and Materials Journal • 2013 • vol. 6 • nº 2
A. F. LIMA NETO | M. P. FERREIRA | D. R. C. OLIVEIRA | G. S. S. A. MELO
probably started in connection of the capital with the column. It
is observed that the rupture surface, starting at the column face,
may have reached a radius of approximately 489 mm, the LC3
slab model, near to 3.2·(d + hH) found in the laboratory, and 558
mm, the LC4 model slab, this being also near the experimental
(4·(d+hH)).
In Figure 14b is noted tangential cracks in the upper face of the
LC2 slab model, already stabilized more or less the same locations
were observed where the higher radial strain and the appearance
of probable rupture surface, with an inclination of approximately
22º, noting that the experimental presented variation between 20º
and 24º. In Figures 14c and 14d is observed the tangential cracks
of the LC3 slab model, on the upper face, already stabilized more
or less the same locations were observed where the higher radial
strains on LC2, and the appearance of probable rupture surface,
with an inclination of approximately 22°, highlighting that the ex-
perimental presented variation between 20º and 24º. The model
slab LC4 has a greater amount of tangential cracks compared
to previous models, including cracks occurring in the internal re-
gions capital. These internal cracks can be attributed to the greater
length of the capital used in this model, causing cracks that be-
fore appeared just at the end, entered the boundaries thereof. It is
observed that the tangential cracks occurred in the same regions
where appeared high tangential strains, as observed in previous
slabs, even the rupture surface, showing a projection with an incli-
nation of approximately 19°.
In Figure 15 there is a comparison between the strains of the con-
crete, experimental (C1, C2, C3, C4, C5, C6 and C7) and numeri-
cal models (C1N, C2N, C3N, C4N, C5N, C6N and C7N) for slabs
with capital (LC2, LC3 and LC4). In general, it is clear that the tan-
gential strain (see Figures 15c, 15e and 15g) of numerical models
approached the experimental, thus confirming the good behavior
of the models in the analysis of slabs. Thus, there is again a ten-
dency of the slabs present higher values ​of strain at the points
where the appearance of the identified rupture surface. Note also
that the strain of the numerical models tend to be slightly smaller
than the experimental for the same loading level, which can be at-
tributed to the axisymmetric distribution of the reinforcement, which
makes models stiffer in relation to the slabs. For radial strain (see
Figures 15d, 15f and 15h), as observed in the slab without capital
(LC1), are perceived near deformations, between the experimental
and numerical modeling, in the early stages of loading, but with
discordant values for the same level of loading in the last steps of
load. Except for radial strains in the slab LC2 which showed similar
between the numerical models (C5N and C4N) and experimental
(C4 and C5), for the same load level, especially in relation to strain
inside the capital, near the face column.
5. Evaluation of calculus methods
The Table 3 shows the rupture loads seen in the experiments (Pu)
and the rupture loads estimated by the recommendations of EU-
ROCODE 2 [11] and NBR 6118 [10] (VRc), and the location of the
rupture surface, since these could occur inside (internal) or out-
side (external) of the area corresponding to the capitals. For ex-
perimental rupture loads ​​observes values near of the rupture loads
estimated by the recommendations of ECUROCODE 2 [11]. The
slab LC4 has a higher difference between the experimental and
the estimated loads, since the code considers the contribution of
the capital, and it was revealed experimentally that capitals with in-
clination above of 1:3 has its contribution to the punching strength
reduced. Almost all slabs had a relation Pu/ VRc near to 1.0, with the
exception of the slab LC4. Regarding the NBR 6118 [10], there
is rupture loads, mostly the loads near encountered by estimates
EUROCODE 2 [11], with the exception of the loads concerning
slabs that have capitals with inclination higher than 1:2 (LC3, LC4).
In spite of recommendations presented similar formulations, it is
noted that the limits for the use thereof are different, when referring
to the control perimeter after all NBR 6118 [10] is independent of
the perimeter length of the capital, and must be always respected
the ratio 1:2 on the thickness thereof, thereby forcing an angle of
26.6º from the column face. Therefore, applying the limits found in
the code, it is noticed that the slabs with capital inclination of 1:3
and 1:4, the control perimeter to be used has a length of 2·dH and
thickness with effective depth d, and thus the estimated values ​are
presented somewhat conservative. Regarding the rupture surfac-
es was observed that the NBR 6118 [10] showed good results, be-
cause their estimates coincide with the rupture surfaces observed
experimentally (see Figure 16). The estimates by EUROCODE 2
[11], to the rupture site was determined using the equality between
formulations V Rc,int and VRc,ext. With this equality is possible to deter-
mine the equivalent value of lH (circular capital) that has the limit
between these two rupture modes. Thus, experimentally, the slabs
had to rupture just outside the capital with inclination 1:2, initially
agreeing with the code (EUROCODE 2 [11]), however, for slabs
an inclination higher than 1:2, the rupture occurred in an internal
region of the capital, diverging from what was estimated.
The Table 3 shows a comparison between the experimental rup-
ture loads and the estimated rupture loads by the CSCT. It is ob-
served that the estimated loads presented in all the slabs, some
conservative values ​​regarding experimental loads, the ratio Pu /Vcsct
shows an average of 1.32. It is noticed that the more conserva-
tive value was observed in the slab LC3, with capital of 165 mm
in length, and less conservative in slabs without capital or capital
with inclination 1:2. Related to the place of rupture is observed that
the estimates showed good results. It is emphasized that the slab
LC2, with an inclination of 1:2, although the rupture mode assigned
thereto, the slab has a proximity between the two rupture modes
possible with difference of about 5 kN between the internal rupture
load and external rupture load of the capital.
6. Conclusions
In the analysis of experimental rupture loads was used normative
and theoretical recommendations developed about it. In the pres-
ent work were used the recommendations of EUROCODE 2 [11],
the NBR 6118 [10] and the Critical Shear Crack Theory. Then we
observe that the estimates for the rupture load EUROCODE 2 [11]
(VRc) had good results, with values ​​close to the experimental rela-
tion with Pu/ VRc around 1.0, except for the slab LC4. Once the code
in question considers the contribution the increase in load capac-
ity the capital, even to inclination the capital above of 1:3, a fact
that has not been verified experimentally. Regarding the estimate
for the rupture site, the slabs with an inclination of 1:2 showed
external rupture, whichever is provided by the code, but for the
slabs with capitals ratio hH:lH of 1:3 and 1:4 showed rupture inter-
nal, starting from the face of the column, differing from what was
estimated. The NBR 6118 [10] also showed good results for slabs