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IBRACON Structures and Materials Journal • 2012 • vol. 5 • nº 6
P. W. G. N. TEIXEIRA | C. E. M. MAFFEI | M. C. GUAZZELLI
concrete failure by diagonal compression. In this expression, the
mentioned authors say that b
v
=D and d
v
=0.72D should be used for
circular section. Applying this expression to the beams tested by
these authors, we have:
(1)
V = 0.25 × 25cm × 0.72 × 25 cm × 3.17kN/cm² = 356kN
rd2
If it were used the concept of effective area, it would still be ob-
tained lower value which probably indicates that the use of effec-
tive area must be associated with other parameters. The calcula-
tions would be as follows:
(2)
V = 0.25 × 0.7 × × 3.17 = 272kN
rd2
2
π × 25
4
Among the sixteen tested beams, at least eight of them
reached greater values
than 356kN, and one of the beams
showed rupture with V
u,exp
=479kN – difference of 34%. The
authors have not commented on this aspect in the article but
it is interesting to discuss this result. Among these beams
that have reached the ultimate load value that exceeds the
crushing strength of the struts, the difference occurred only
in the transverse reinforcement, and all of them had heavy
longitudinal reinforcement, with geometric rate ρ=6.4%. The
beam that showed greater strength had shear reinforcement
consisting of double stirrups of 12mm with spacing of 10cm.
Referring to the diameter (D=25cm), this provides a shear
reinforcement geometric rate of approximately 4x1.25cm²/
(25cmx10cm)=2%, which is a high value for a beam with f
ck
on the order of 30MPa. Considering the current parameters
of ABNT NBR 6118, the maximum transverse reinforcement
ratio would be about 1.2% in this situation(see Figure 6). Fur-
ther, it could be said that tests indicates that, in a beam of cir-
cular section, confinement caused by circular stirrups could
increase the crushing strength of the compressed struts.
Moreover, it can be stated that for the usual reinforcement
rates the determination of V
Rd2
with dimensions
b
w
=D and
d=0.72D, suggested by the AASHTO (2007), could lead to
reasonable values for usual beams.
2.2 Calculation of V
c
The determination of the parcel of shear force resisted by
complementary mechanisms to the trussis quite complex. In
order to compare the few available parameters, it will be ap-
plied the procedures proposed by Merta [4] to the tests of
Jensen et al [2]. According to [4], the value of V
c
could be
estimated from:
(3)
V
c
= [3.7ρ
l
+0.18]× k × f´
c
×0.7A
g
√
Figure 5 – Definition of effective area
of circular cross section of reinforced
concrete with reinforcement distributed
uniformly – adapted from Merta&Kolbitsch [5]
Figure 6 – Chart to assist determination
of V according to NBR 6118. For the
Rd
determination of A has been proposed
ef
2
in literature the values of 0.7A or 0.72D
g