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IBRACON Structures and Materials Journal • 2012 • vol. 5 • nº 6
E. L. MADUREIRA | J.I.S.L. ÁVILA
span center, each one presenting intensity equal to 200 kN. The results
were compared with those obtained from stress diagrams proposed by
Forster and Stegbauer [5], Figure 4.b. It is possible to observe the good
agreement between the curves, except near the upper edge, for which,
it was noted discrepancies, including, in relation to the stress signal.
5 Analyzed models
The models studied constitute single deep beams 2.00 m width
and 20 cm thick, casted in C 20 concrete, reinforced with CA-50
steel bars, placed along its lower edge, Figure 5.a.
The structural member is subjected to a gradual loading process
by the action of a couple of equal intensity concentrated loads.
The loads are applied simultaneously, on the top of the beam, in
equidistant points 0.40 m from its span center, on plates 0.20 m
x 0.20 m dimensioned. In the loading process the load intensities
evolves from zero to a final value defined, in some cases, by local
concrete failure, and in other cases, for convenience, determined
by the particular observed behavioral aspect.
The analysis was performed considering six cases, differentiated
among themselves by the reinforcement cross-sectional area, by
load intensity and by the beam height, as detailed in table 1.
Due to the structural symmetry, the problem domain might be de-
fined from the rectangle sector whose base is equal to half length of
the beam span, and whose height is equal to the structural member
height. Its discretization was held based on the adoption of square
plane elements, and linear elements, both 0.10 m dimensioned, re-
sulting in the finite element mesh similar to that illustrated in Figure
5.b. In all cases the mesh is composed by ten linear elements. On
the other hand, the variety of the beam heights resulted in the total
diversity of plane elements which was 140, 160, 180 and 200, for
1.40 m, 1.60 m, 1.80 m and 2.00 m height beams, respectively.
The analysis was carried out according to the “Plane State
of Stress “.
Figure 5 – Studied models: a-geometry; b-finite element Mesh
Table 1 – Characterization of the studied cases
Case
Steel Cross Sectional
2
Area (cm )
Heigth
(m)
Load
(kN)
A
0,16
2,00
900
B
0,40
2,00
900
C
0,63
2,00
900
D
0,63
1,80
630
E
0,63
1,60
450
F
0,63
1,40
270