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IBRACON Structures and Materials Journal • 2012 • vol. 5 • nº 5
P. V. P. SACRAMENTO | M. P. FERREIRA | D. R. C. OLIVEIRA | G. S. S. A. MELO
used a constant flexural reinforcement ratio of 0.76%. Birkle [32] stu-
died the influence of the thickness for slabs with shear reinforcement,
but in the analysis presented in Figure 6 are going to be considered
only results of slabs without shear reinforcement, which had effective
depth of 124 mm, 190 mm and 260 mm. The flexural reinforcement
ratio of these slabs was 1.52%, 1.35% and 1.10% respectively. Figure
6 shows the variation of the nominal shear strength for each code as
a function of the effective depth of the slabs. Is possible to notice that
by using the equations of Eurocode, in both researches there was an
approximately linear reduction in the shear nominal stress, regardless
of the effective depth of the slab, indicating that there is no justification
for limiting the
ξ
as mentioned above. However, using the equations
of ACI, is possible to see a change in the behavior of slabs tested by
Li with effective depth exceeding 200 mm.
4. Recommendations from codes of practice
4.1 ACI 318
According to ACI 318 [7] the punching resistance of reinforced
concrete flat slabs without shear reinforcement should be verified
by checking the shear stresses in a control perimeter
d
/2 away from
the column faces or the ends of the loaded area, as shown in Figu-
re 7a. The punching strength can be computed using Equation 1.
(1)
Figure � � Co�trol perimeter
ACI 318
NBR 6118 / EC2
TFCC
A
B
C
where:
β
c
is the ratio between the largest and smaller side of the column;
α
s
is a coefficient that is taken as 40 for internal columns, 30 for
edge columns and 20 for corner columns;
u
1
is the length of a control perimeter away
d
/2
from the column
face;
f
c
is the compressive strength of concrete in MPa (
f
c
≤
69 MPa);
d
is the effective depth of the slab.
4.2 NBR 6118
Recommendations presented by NBR 6118 [9] are based on those from
CEB-FIPMC90 [6]. The Brazilian code recommends that the punching
strength of slabs without shear reinforcement should be checked in both:
a control perimeter
u
0
using Equation 2 to verify the maximum strength of
the slab-column connection; and in a control perimeter
u
1
using Equation
3 to verify the diagonal tensile strength of the slab-column connection.
Figure 7b presents details on the control perimeters of this code.
(2)
where:
(
)
1
1 250
v
c
f
α
= −
u
0
is the control perimeter.
(3)
where:
ρ
is the flexural reinforcement ratio expressed by
x y
ρ
ρ ρ
= ⋅
;
ρ
x
and
ρ
y
are the flexural reinforcement ratio in two orthogonal directions;
f
c
is the compressive strength of concrete in MPa (
f
c
≤
50 MPa);