Basic HTML Version
788
IBRACON Structures and Materials Journal • 2012 • vol. 5 • nº 6
Shear strength of reinforced concrete circular cross-section beams
[4] and the concept of effective height equivalent submitted by the AAS-
HTO as Jensen et al. [2].The differences found with experimental values
were significant. On the other hand, comparing that portion to the shear
force that would cause the first shear crack there was obtained nearest
results from Jensen[2] testing, even though this cannot be confirmed due
to the small number of experimental results available in the literature.
The determination of the portion resisted by the reinforcement should
take into account the lower efficiency of the circular stirrups, given that
only the vertical component of force in the stirrup can resist the shear
force. However, tests have shown that the simple consideration of this
decomposition underestimates the resistance provided by the stirrups.
The explanation of Merta [4] is related to the occurrence of deviation
forces in the direction of tensile in the circular stirrups. In the analyzed
example, such deviation forces accounted for29% of the portion corre-
sponding to the mobilization of stirrups crossing the shear crack.
Tests of Jensen et al [2] indicate that circular stirrups with heavy
rates of reinforcement significantly increase the capacity of com-
pressed strut which can be associated with the concrete confine-
ment provided by circular stirrups. Perhaps these confinement
effects has also influence on complementary mechanisms to truss
and are responsible for the ultimate shear values of tests ana-
lyzed had always exceeded the theoretical estimates. In papers
consulted, such as[2] and [4], it is reported the difficulty of measur-
ing the deformation of transverse reinforcement, by relating such
difficulty to the fact that the largest deformations would be located
in the region of shear crack whose position is not known a prior
which complicates the instrumentation of the stirrups.
It is also important to emphasize that in all tests analyzed the trans-
verse reinforcement was constituted exclusively of circular stirrups,
although in some projects there are situations in which the circular
stirrups are supplemented with vertical branches.
4. Conclusions
After analyzing the tests results of reinforced concrete elements
with circular cross section as well as the several theoretical contri-
butions in literature, in order to verify the suitability of the expres-
sions ofItem7.4 of the Brazilian standardABNTNBR6118 (2004),
we present the following conclusions:
n
The difficulty in defining the values of b
w
and d for circular cross
section has been approached in two ways, which are, the con-
cept of effective area and the adoption of b
w
=D and d=0.72D,
and the latter approach leads to slightly better results than the
experimental results analyzed.
n
Determining V
Rd2
, the value of the shear force corresponding
to the concrete failure by diagonal compression, led to inferior
results to those obtained in the tests analyzed, even adopting
bw=D and d=0.72D, as recommended by international stan-
dards, which seems to be related to the confinement of the con-
crete produced by circular stirrups.
n
Determining V
Rd3
, shear force corresponding to concrete failure
by diagonal tension was also always lower than the values ob-
served in the tests analyzed, even adopting b
w
=D and d=0.72D,
as recommended by international standards and considering
the lower efficiency of the circular stirrups. The explanation
must also be related to the confinement of the concrete pro-
duced by circular stirrups as well as the development of vertical
components of adhesion forces resulting from the change in
direction of the stirrups, as suggested by[4]. Even with these
considerations, there were not obtained values close to those
of tests analyzed.
Therefore, the use of b
w
=D and d=0.72D, i.e., A
ef
=0.72D² as shown in [2],
can lead to results for safety for the determination of V
Rd2
and V
c
. The use
of the expression V
sw
of the NBR 6118 withd=0.72D also seems to lead
to results in favor of safety in the determination of V
Rd3
, despite not being
made the reduction of the efficiency of the circular stirrups.
These conclusions are based only on the tests results analyzed
and are referred to the condition of Ultimate Limit State. However,
the authors practical experience with projects of circular cross-sec-
tion beams subjected to high shear force syndicates that the use of
such expressions has led to results suitable for service situations
with apparently high safety factor.
5. Bibliographic references
[01] ASSOCIAÇÃO BRASILEIRA DE NORMAS TÉCNICAS.
Projeto de estruturas de concreto. - NBR 6118, Rio de
Janeiro, 2004.
[02] JENSEN, U. G.; .HOANG, L. C.; JOERGENSEN,
H. B.; FABRIN, L. S. Shear strength of heavily
reinforced concrete members with circular cross
section. Engineering Structures 32, N.3, (2010),
617-626.
[03] LI, VICTOR. A note on design of shear reinforcement
for circular section. Technical Note TN-01. Centre for
Research & Professional Development (website:
www.cprd-hk.com). February, 2009.
[04] MERTA, I. Shear strength model of reinforced
concrete circular cross-section members. Structural
Engineering Mechanics and Computation 3,
A. Zingoni (ed.).(2007), Section 22, 493-494.
[05] MERTA, I.; KOLBITSCH, A. Shear area of reinforced
concrete circular cross-section members.
31
st
Conference on OUR WORLD IN CONCRETE &
STRUCTURES: 16-17 August 2006, Singapore.
[06] TURMO, J. RAMOS, G.APARICIO, A. C. Shear truss
analogy for concrete members of solid and hollow
circular cross section. Engineering Structures, 31
(2009), 455-465.
[07] ALMEIDA NETO, E. S.PEF-2306 – Tópicos de
Mecânica dos Sólidos. Escola Politécnica da
Universidade de São Paulo – Departamento de
Engenharia de Estruturas e Geotécnica. São Paulo,
2011.
[08] MAFFEI, C. E. M.Memorial de cálculo da estrutura de
contenção provisória para execução de vala a céu
aberto. Documento interno da Maffei Engenharia.
São Paulo, 2009.
[09] MAFFEI, C. E. M.Memorial de cálculo de vigas tubo
utilizadas em obra de túnel rodoviário de baixa
cobertura. Documento interno da Maffei Engenharia.
São Paulo, 2011.
[10] TIMOSHENKO, S. P. GOODIER, J. N.Teoria da
elasticidade. Guanabara Dois: Rio de Janeiro, 1980.
p. 350.
[11] American Association of State Highway and
Transportation Official. AASHTO LRFD Bridge design
specifications. Fourth edition. 2007.