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IBRACON Structures and Materials Journal • 2012 • vol. 5 • nº 6
Shear strength of reinforced concrete circular cross-section beams
is the gross area of the circular cross section.
Using the concept of effective area, the difficulty of determining the
value b
w
to be used inexpression of NBR6118 can be eliminated
substituting the product b
w
d that appears in the expressions of V
c
and of V
Rd2
by the effective area.
However, besides the fact that this substitution would need to have
a higher basement, theoretical and or experimental, this is not the
only problem to be solved for the application of the expressions of
Item 4.17 of NBR 6118 to circular sections. These aspects will be
discussed in the following items.
2. Aspects of design
2.1 Calculation of V
Rd2
Jensen et al. [2], presents the expression of AASHTO (2007),
given by, for determining the shear resistance design related to the
(Figure 4). According to this procedure ζ
máx
=1.33V/A. However,
the exact value of the maximum stress is given by the Theory of
Elasticity and depends on Poisson’s ratio of the material[10]. For
concrete, with
ν
=0.2, ζ
máx
=1.42V/A.
In the case of circular section of reinforced concrete, the ef-
fective area is defined by these authors in a different way,
considering only one part of the concrete section. Thus, the
effective area would be the area of the segment of circular
cross-section corresponding to the effective depth “d”, where
“d” is the distance between the more compressed point of the
cross section due to the bending moment, and the center of
gravity of the longitudinal tensile bars (Figure 4). The value
of “d” should be determined after knowledge of the section
neutral axis by identifying which longitudinal bars were in fact
tensioned; at this manner, there is need for iterative calcu-
lation. For usual dimensions and uniform arrangements of
reinforcement however, according to [5], A
ef
=0.7A
g
, where A
g
Figure 4 – Simplified procedure for determining the tangential stresses at
all points of a circular cross section with use of Jourávski formula: divide the shear
force V between “n” ellipses and apply the Jourávski expression to each of these ellipses,
taking as the thickness the measure perpendicular to the axis of said elliptical figure