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IBRACON Structures and Materials Journal • 2012 • vol. 5 • nº 6
E. L. MADUREIRA | J.I.S.L. ÁVILA
progressively, increased, the articulated “A” point, that is attached to
the truss body, moves toward “B” point, and, concomitantly, the “AC”
and “AD” bars suffer progressive shortening. If, once “A” point having
hot “B” point, and the load intensity continues increasing, rollback oc-
curs, and then the strain gradient changes to stretching deformation.
In reference to the cases that are being studied, notice the hori-
zontal band of the beam, closer to its upper surface, in the stretch
between the span center and the load application point, Figure 16.
In each one of load increments, on the initial stage of loading up to
the threshold at which the load magnitude hits a value between 540
kN and 630 kN, the deformational pattern is such that “C” and “D”
points move in the vertical direction by δ
C1
and δ
D1
displacements,
respectively, in such a way that δ
C1
< δ
D1
. In the increments of the
consecutive stage, C’ and D’ points suffer displacements of δ
C2
and
δ
D2
, respectively, on this case, however, with δ
C2
> δ
D2
. Thus, on
the first stage the deformational reality contributes to the curvature
of that band, in the vicinity of AC, by down side oriented concave-
ness, whereas, in the next stage, it presents contrary trend. This
response is due to the fact that the displacements at any point of
the beam result in part from mass deformations, and, on the other
hand, from bending strains. Of course, while the displacements of
the beam span center are more influenced by bending strains, to
those located below the load, the higher contribution is associated
with mass deformations, and each of these strain parcels evolves
according distinct patterns in each of the above loading stages.
From closer analysis of the curves on figures 13 and 14, it follows
that the occurrence of horizontal tensile stress as well as the “snap
back” phenomenon, that is reported in this paper, are intrinsic phe-
nomena by the deepest beams, because, they are evidents on
those beams by height from 1.80 m and do not manifest on beams
by height up to 1.40 m.
7. Conclusions
This work refers to the analysis of mechanical performance on re-
inforced concrete deep beams.
Figure 16 – Upper edge band deformed
configuration of the beam
The inherent tasks were carried out on six cases, differentiated
among themselves by the adopted reinforcement, by the beam
height and the load magnitude.
In each of the analyzed cases the structural member was sub-
jected to loading process in which the load magnitudes evolved in
increments, from the initial null value up to a final value defined,
in some cases, by localized concrete crushing failure and, in oth-
ers cases, by convenience determined according observed special
behavioral aspect.
From the numerical analysis, it was found that, for the beams of
height equal to 2.00 meters, the internal instability of the struc-
tural member was triggered when the load magnitude assumed the
value close to 900 kN.
The results obtained showed that the reinforcement rate variation
did not result in significant change in the overall performance of
the beam.
Moreover, it was observed that the beam failure started from the
crushing collapse of concrete in point immediately beneath the
load application surface, for a vertical stress compression whose
magnitude is close to 25 MPa. This value, that is 25% higher than
the uniaxial compressive strength of the material, is consistent, as
the adopted stress envelope, considering, in particular, that this
point is subjected to biaxial compression state of stress, since in
the horizontal direction, it is subjected to a stress of magnitude
close to 15.7 MPa, also in compression.
On the other hand, for the vertical section that passes through the
load application point, the maximum horizontal tensile stress for
the final load value occurs on the point at 0.60 m from the lower
edge of the beam. However, from an examination of the horizontal
stress distribution along the height evolution, during the loading
process, it was found that the point on the lower edge presents
strain of greater magnitude, and therefore, lies in more advanced
stage of deformation.
May one to report that, rather than horizontal stress compression,
it was noted the development of tensile stresses on the upper edge
of the section at the beam span center, in addition to the manifes-
tation of the phenomenon known as “snap back”, the latter charac-
terized by consecutive shortening after distention during monoton-
ic loading process. It was proven, including, that such occurrences
are intrinsic, exclusively, to the highest beams, considering that it
is not manifested on those of height up to 1.40 m.
8. Acknowledgements
This report is part of a research work on the numerical simulation
of the swelling effect due to alkali-aggregate reaction supported
by the Fundação Coordenação de Aperfeiçoamento de Pessoal
de Nível Superior – CAPES and by the Pró-Reitorias de Pesquisa
da Universidade Federal do Rio Grande do Norte – UFRN and by
the Universidade Federal de Pernambuco – UFPE This support is
gratefully acknowledged.
9. References
[01] Arnesen, A. Sorensen, S.I. and Bergan, P.G.
Nonlinear Analysis of Reinforced Concrete. Computers
& Structures
,
Vol. 12, 1980, pp 571-579.
[02] Balakrishnan, S. and Murray, D.W. Concrete Constitutive
Model for NLFE Analysis of Structure. Journal of