Page 138 - Riem-Vol6_nº3

483 IBRACON Structures and Materials Journal • 2013 • vol. 6 • nº 3
R. N. F. do Carmo | J. Valença | D. Dias-da-Costa
ed for the four stages considered in this analysis. The selected section
was placed at 50 mm from the left edge of the pure bending region.
A perfect linearity between strains was not found because, during the
deformation, the sections do not remain plain due to concrete cracking.
It is reminded that mechanical strain gauges and demcs only al-
low obtaining the average curvature in lengths of 100 or 200 mm
(values limited by the mechanical strain gauge length) and not
curvature in a specific section (Carmo and Lopes [19]). Another
disadvantage of using mechanical strain gauges compared with
photogrammetry is the time required to perform all readings.
Photogrammetry provides a detailed curvature analysis because the
spacing between targets can be significantly reduced, in this case
20 mm was adopted. The detailed evolution of curvature along the
beam axis allows analyzing the influence of the concrete between
the cracks and cracked sections in the beam deformation. Figure
11 presents the curvature evolution along the beam axis for the
four analyzed stages, where it can be seen that the curvature is
not constant. In stages 1 and 2, despite the cracks width not being
very significant, a larger curvature was already detected in cracked
sections. Between stages 2 and 3, the curvature increases in
cracked sections, being approximately constant in sections between
cracks. In stage 4, it can be seen that sections with maximum cur-
vatures tend to concentrate on a limited length, about 300-350 mm.
5.3 Plastic rotation
The reinforced concrete members have a nonlinear behavior when
subjected to higher loads. Before reinforcement reaches the yield
strength, the nonlinear behavior is caused by concrete cracking.
After reaching the steel yielding, the influence of the nonlinearity
of steel stress-deformation must also be taken into account. At this
moment, it is considered that a plastic hinge is formed. To quantify
the ductility of the member, the evaluation of the plastic rotation
capacity at certain zones of the structure is generally used [20].
The plastic rotation capacity of a beam is the maximum plastic
rotation supported immediately before collapsing. To compute the
plastic rotation three methods are presented: i) curvature integra-
tion after steel yielding in the plastified area (Eq. 1 and Figure
12), ii) multiplying the difference of the average curvatures, at the
steel yielding onset and at the analyzed stage, by 800 mm length
(curvatures determined by the horizontal LVDTs) (Figure 9), iii)
Bachmann’s method, based on the sum of rotations which occur
between the two sides of the crack (Eqs. 3 and 4 and Figure 13).
The latter is easily applied using photogrammetry and image pro-
Figure 12 – Plastic rotation using method 1 with shaded area representing the plastic rotation
Stage 3 Stage 4 A B
Figure 13 – Crack width and neutral axis depth in mm (stage 3)