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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
function of its compressive strength. These are the reasons why it
is common to observe that experimental researches correlate the
shear strength to the compressive strength of concrete.
Graf [16] was among the first to try to assess the influence of con-
crete strength in the punching resistance, concluding that there
was not a linear relationship between the increases of the strength
of a slab-column connection with the increase of concrete strength.
Moe [15] proposed that the punching resistance could be expres-
sed with a function proportional to the square root of the compres-
sive strength of concrete, proposition until today used by the ACI.
However, the results of recent research, such as Hallgren [17],
which analyzed concrete slabs with high strength concrete, indi-
cate that in these cases, relating the punching resistance with a
function proportional to the square root of the compressive streng-
th of concrete tends to overestimate its influence. For this reason
ACI limits the use its expression for concrete with strengths up to
69 MPa or 10.000 psi.
Marzouk and Hussein [18] analyzed slabs with high strength con-
crete varying the effective depth of the slab and also the flexural
reinforcement ratio, concluding that a function proportional to the
cube root of the concrete strength better represents the trend of the
experimental results, what is also recommended by Hawkins et al.
[19] and Regan [20]. Figure 4 shows a graph made in order to evalu-
ate the influence of the concrete strength in the punching resistance
of flat slabs. It was compared the trend obtained by using a function
proportional to the cube root of the compressive strength of concre-
te (as proposed by the equations of Eurocode 2) with experimental
results from the database, observing a good correlation between
the experimental results and the function evaluated.
3.2 Flexural Reinforcement Ratio
The flexural reinforcement ratio (
ρ
) is defined as the ratio betwe-
en the area of tensile flexural reinforcement (
A
s
) and the area of
concrete (
A
c
), which is given by the product of the effective depth
of the slab (
d
) by a certain width to be considered. In practical ca-
ses it is reasonable to consider that only a certain number of bars
close to the column area will effectively contribute to the punching
resistance. Considering results of experimental tests, Regan [20]
recommends that the effective width to be considered in which the
flexural reinforcement will contribute to the punching resistance
should be taken as 3d away from the faces of the column.
The flexural reinforcement ratio influences the punching resis-
tance, especially in cases of slabs without shear reinforcement.
Regan [21] explains that increasing the flexural reinforcement ra-
tio raises the compression zone, reducing cracking in the slab-
-column connection due to bending, which is beneficial since it
facilitates the formation of mechanisms for transmitting shear for-
ces. Furthermore, the thickness of the bending cracks is reduced,
which facilitates the transfer of forces through the interlock of ag-
gregates, what may also increase the dowel effect.
Kinnunen and Nylander [14], testing slabs with a thickness of 150
mm, when varied the flexural reinforcement ratio from 0.8% to
2.1% observed that the punching strength increased about 95%.
Marzouk and Hussein [18], also tests slabs with a thickness of
150 mm, observed that the punching strength increased around
63% when the flexural reinforcement ratio was raised from 0.6%
to 2.4%. Long [22] used results of several authors to conclude
that the punching resistance was influenced by the flexural rein-
forcement ratio with a function proportional to the fourth root.
Moreover, Regan and Braestrup [23] and Sherif and Dilger [24]
suggest that the punching resistance is influenced by a function
proportional to the cube root of the tensile flexural reinforcement
ratio. Figure 5 uses results of the experimental database to eva-
luate the contribution of the flexural reinforcement ratio of slabs
in its punching resistance.
3.3 Geometry and Dimensions of Columns
The geometry and dimensions of the column also affects the pun-
ching resistance of slabs because they influence the distribution
of stresses in the slab-column connection. Vanderbilt [25] tested
slabs supported on circular and square columns and monitored
Figure � � �nfluence of the co�pression concrete
strength on the punching resistance of flat slabs
Figure � � �nfluence of the fle�ural reinforcement
ratio on the punching strength of flat slabs