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IBRACON Structures and Materials Journal • 2013 • vol. 6 • nº 2
Experimental and numerical analysis of reinforced concrete mushroom slabs
tensile strength of concrete in the area inside and outside the
column capital, in control perimeters
u
1
and
u
out
, using Equa-
tions 2 and 3, with the effective depth of the slab in each case
considered as shown in Figure 4.
(1)
max
1
0
0, 27
R
v c
H
V
f u d
Where:
(
)
1
1 250
v
c
f
α
= −
, with
f
c
in MPa;
u
0
is the column perimeter in mm;
d
H
is the effective depth of the slab in the ends of the column in mm
(see Figure 4).
(2)
,in
1/3
1
t
0,18 1 200 100
c
c
a
R
V
d
f
u d
Where:
ρ
is the geometric flexural reinforcement ratio expressed by
x y
ρ
ρ ρ
= ⋅
;
ρ
x
and
ρ
y
are the flexural reinforcement ratios in orthogonal direc-
tions x and y;
f
c
is the compressive strength of concrete in MPa (
f
c
≤
50 MPa);
u
1
is the length of a control perimeter taken 2·
d
from the column
faces, in mm. For slabs without column capitals it is calculated as
(
)
d C u
⋅ + ⋅ =
4
1
π
and for slabs with column capitals it is calcu-
lated as
(
)
[
]
H
h d Cð u
+ ⋅ + ⋅ =
4
1
;
d
a
is the effective depth as shown in Figure 4 in mm.
(3)
d u f
d
V
out
c
31
ext c,R,
100
200
1 18,0
Where:
d
is the effective depth of the slab in mm;
u
out
is the length of a control perimeter taken 2·
d
from the ends of
capital and calculated as
(
)
.d l
Cð u
h
out
4 2
+ ⋅ + ⋅ =
;
l
H
is the distance between the edge of the capital and the column
face, in mm.
In cases where
l
H
≤
2·(
d
H
–
d
), designers have to check only the
resistance in the control perimeter
u
out
. When
2·(
d
H
–
d
) <
l
H
≤
2·
d
H
,
resistance should be checked only in the control perimeter
u
1
. If
l
H
> 2·
d
H
it is necessary to check the resistance in both
u
out
and
u
1
.
Figure 4 – Control perimeters recommended by NBR 6118 [10]
Mushroom slab
B
Flat slab
A
Figure 5 – Control perimeters recommended by EUROCODE 2 [11]
Mushroom slab
B
Flat slab
A
