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IBRACON Structures and Materials Journal • 2012 • vol. 5 • nº 6
Numerical simulation of the mechanical performance of deep beam
the lower edge, with magnitude of, approximately, 1.0 MPa, while on
the lower edge the tensile stress intensity is of, approximately, 0.35
MPa. The comparison of these values induces the reader, at first
instance, to deduce that the former point is more strainned than the
latter. However, analyzing the stress evolution with load, Figure 11,
one note that, for the final load intensity, the point of the lower edge
is already at the descended branch of the curve, while the point at
0.60 m from that edge remains in its ascendant branch.
In addition, analyzing, thoroughly the vertical stress field, figure
6.b, one testify, as expected, concentration of stresses at the load
application regions and at the support vicinity. More specific re-
sults of vertical stress distribution along the beam upper surface,
figure 12, elucidate how drastic is such stress concentration, when
it turns out that all the stress is restricted, practically, to the load
immediate vicinity, reaching in its center, intensity of 25 MPa. In a
fair agreement with the stress envelope adopted in this work, this
value, that is 25% higher than the concrete uniaxial compressive
strength, is very close to the peak stress to the analyzed point,
which is subjected to biaxial compression state, because, as re-
ported in the previous paragraph, in its perpendicular direction, on
a same way, the mass of concrete is compressed.
And more, it may be noted that, to the extent that the point considered
departs from the horizontal edges of the beam along the thread that
interconnects the support and the load introdution region, occurs the
spread of the stress concentrations reported above, Figure 6.b.
The horizontal stress evolution curves with loading for the “A” “B”
and “C” cases referring to the point of the upper edge at the span
center, figure 13, point out that the maximum value is reached
when the intensity assume a value in the range between 540 kN
and 630 kN, giving margin to the deduction of dealing with peak
tensile stress at failure. However, the analysis of load-deformation
curves related, figure 14, reveals that the horizontal strain, initially
increasing, precisely from this loading level, begin to decrease,
characterizing the phenomenon that in the scientific literature is
known as “snap back”.
To explain the “snap back” phenomenon, consider the truss especi-
men, figure 15, whose ends “C” and “D” are restrained for any trans-
lational displacement. Upon the load “P” action, whose intensity is,
Figure 12 – Vertical stress distribution along
the longitudinal direction on beam top
Figure 13 – Horizontal stress
versus
load
at the span center section on beam top
Figure 14 – Load strain curves at the
span center section on beam top
Figure 15 – Model truss