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276
IBRACON Structures and Materials Journal • 2013 • vol. 6 • nº 2
Experimental and numerical analysis of reinforced concrete mushroom slabs
Figure 6). With increasing load the shear crack trends to open,
reducing the efficiency of the shear transfer mechanisms and
eventually leading to a punching shear failure. According Muttoni
and Schwartz [13] the opening of this crack is proportional to the
product
ψ·
d
(see Figure 6), but the transmission of shear forces
along the critical crack depend on the roughness of the concrete
failure surface. The influence of the roughness of concrete sur-
face can be assessed in terms of the maximum aggregate size
used in concrete. Based on these concepts Muttoni [12] proposed
that the punching strength of a slab failing by diagonal tensile can
be obtained using Equation 7.
(7)
و
int
0
2
3 1 20
H c
Rk,c,
H
g g
u d f
V
d
d d
Where:
u
1
is the length of a control perimeter taken
d/2
from the column
faces, in mm;
d
H
is the effective depth of the slab in the ends of the column faces,
in mm;
f
c
is the compressive strength of concrete, in MPa;
ψ
is the slab rotation;
d
g0
is a reference diameter of the aggregate admitted as 16mm;
d
g
is the maximum diameter of the aggregate used in the concrete
slab, in mm.
The rotation ψ
of the slab is expressed by Equation 8.
(8)
ﻮى
1,5
ys
s
E
s
flex
f r
V
d E V
Where:
r
s
is the distance between the axis of the column and the line of
contra flexure of moments;
r
q
is the distance between the axis of the column and the load line;
r
c
is the radius of the circular column or the equivalent radius of a
rectangular column;
f
ys
is the yield stress of the tensile flexural reinforcement;
E
s
is the modulus of elasticity of the tensile flexural reinforcement;
V
E
is the applied force;
2
s
flex
R
q c
r
V
m
r r
π
= ⋅ ⋅
⋅
−
;
2
1
2
ys
R
ys
c
f
m f d
f
ρ
ρ
⋅
= ⋅
⋅
⋅ −
⋅
.
It is also necessary to check the strength for the case of a failure
occurring in the outside of the column capitals, calculated using
Equation 9.
(9)
g
g
ck
out
Rk,c,ext
d d
d
f
d u
V
0
20 13
2
Where:
u
out
is the length of a control perimeter taken
d
/2 from the ends of
the capital, in mm;
d
is the effective depth of the slab
,
in mm.
With
V
E
, ψ
and
V
R,c
is possible to draw a graph with two curves
.
The first is a curve that expresses the theoretical load-rota-
tion behavior of the slab. The second curve expresses the
strength reduction of the slab due to the increase of rota-
tion. The point of intersection of these two curves express
the punching strength of a slab-column connection. Figure 10
illustrates this graph.
Figure 7 – Graphic representation of the
punching strength determination according to CSCT
Table 1 – Experimental variation of the slabs
Slab
l (mm)
H
d (mm)
ρ
(%)
Ratio
h :l
H H
h (mm)
H
f (MPa)
c
C (mm)
LC1
LC2
LC3
LC4
-
1:2
1:3
1:4
-
110
165
220
250
55
-
111,5
1,04
112,5
1,03
110,5
1,05
31
33
