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IBRACON Structures and Materials Journal • 2012 • vol. 5 • nº 5
Punching strength of reinforced concrete flat slabs without shear reinforcement
formation of bending and shear cracks to divide the slab into seg-
ments, and, assuming that the region external to the punching cone
presented rigid body rotations around a point away by a distance
x (height of the slab’s neutral axis) either vertically and horizon-
tally in relation to the column faces, it related the ultimate punching
strength with the compressive strength of an imaginary shell confi-
ned between the column and the critical shear crack. This method
was a relevant original contribution, being the first rational theory
presented, but at the time his equations were considered complex
and the accuracy observed for the theoretical results did not justify
its use over the existing empirical methods.
One year after this publication, Moe [15] published a report of a large
series of tests analyzing several variables, including the cases of
unbalanced moments in slab-column connections, and his work re-
mains the basis for the recommendations of ACI 318 [7]. After that,
many works have been conducted and many contributions were
made to the better understand of the punching shear phenomenon
and also for the definition of the influence of the involved parameters
in the ultimate strength of the slabs, as will be shown below.
3. Factors that influence in
the punching resistance
Results of several tests indicate that the punching resistance of
reinforced concrete flat slabs without shear reinforcement is mainly
influenced by the compressive strength of concrete (
f
c
), the tensile
flexural reinforcement ratio (
ρ
), the size and geometry of the colu-
mn and also the size effect (
ξ
) which is a coefficient that takes into
account the reduction of the nominal shear strength of the slab by
increasing the effective depth (
d
). The influence of each of these
parameters is discussed below based on relevant test results.
3.1 Strength of Concrete
The shear failure of a concrete element without shear reinforcement
is governed, among other factors, by the tensile strength of concre-
te. Establishing the compressive strength of concrete is the initial
step in the design process of a concrete structure and also norma-
tive formulations tend to relate the tensile strength of concrete as a
Many obstacles had to be translated until the flat slabs could be
used safely and economically. Initially there was strong discussion
about the theoretical methods for the determination of the forces
on a system without beams and these slabs were used in manner
practically empirical, observing significant variations in the amount
and arrangement of the flexural reinforcement between the compe-
ting systems. Furst and Marti [11] highlight that the first well foun-
ded theory for calculation of forces on floors without beams was
published only in 1921, with the work of Westergaard and Slater,
whom by using the method of finite differences were able to treat
different load cases, the influence of the stiffness of the columns
and capitals.
It was also necessary to establish rules to normalize the use of flat
slabs, which became increasingly popular. That was possible only
in 1925 with the publication of American code (ACI) for the design
of reinforced concrete structures, which was the first to present
recommendations for flat slabs. These first recommendations were
based on experimental tests carried out in the USA like those from
Talbot [13], who tested footings in University of Illinois, as shown
in Figure 3.
However the footings tested by Talbot [13] were very thick com-
pared to the mushroom slabs at that time, and therefore, these
results were not adequate in terms of the punching strength. Trying
to fill this and other gaps, Elstner and Hognestad [2] tested 39 sla-
bs, aiming to evaluate the influence of important variables such
as the flexural reinforcement ratio, concrete strength, amount of
compression reinforcement, support conditions, size of columns
and amount and distribution of shear reinforcement in the punching
strength of flat slabs. They concluded that practically all of these
factors have strong influence on the shear strength of flat slabs,
except for the increase in the compression reinforcement ratio,
which was considered by them as having a small influence on the
ultimate strength of tested slabs.
Subsequently were published two of the most important papers
on punching. Kinnunen and Nylander [14] presented a mechani-
cal model that sought to explain the punching failure mechanism
and predict the strength of slab-column connections. This model
was based on experimental observations obtained after performing
an extensive experimental program. The model was based on the
Figure 3 � Tests on footings, basis for the first recommendations on punching shear (Talbot [13])