Page 131 - Riem-Vol6_nº3

476 IBRACON Structures and Materials Journal • 2013 • vol. 6 • nº 3
Plastic rotation and tension stiffening effect analysis in beams using photogrammetry
1. Introduction
Monitoring experimental tests performed on structural elements is cru-
cial to quantify the loading effects. Measuring forces, curvatures, dis-
placements and strains in key sections allow characterizing the struc-
tural behavior of the element. The observation of the failure mechanism
in reinforced concrete elements is also important simultaneously with
the identification of the crack pattern. The above quantities are usually
measured by traditional monitoring instruments, including: load cells,
mechanical strain gauges, demecs, strain gauges and LVDTs.
Recently, new monitoring tools using photogrammetry and image pro-
cessing were developed to determine some of the above parameters
[1-8]. These tools allow to assess a large amount of data which is dif-
ficult, or even not possible, to measure with traditional methods. A de-
tailed curvature evolution along the concrete beamaxis is one example.
This study aims at demonstrating how photogrammetry and image
processing can be applied to study the flexural behavior of con-
crete beams and how these techniques go beyond the limitations
of traditional methods. Furthermore, the analysis of the tension
stiffening effect, combining the information obtained by photogram-
metry and image processing, is presented.
2. Plastic rotation and tension stiffening
effect in reinforced concrete beams
The possibility of achieving plastic analysis and linear analysis with
moment redistribution requires a certain amount of plastic rotation
in critical sections. It is important to ensure that critical sections can
reach the foreseen failure type. In uncertain situations it becomes
necessary to make an explicit verification of this capability. Thus, it is
crucial to know the moment versus curvature relationship or, alterna-
tively, plastic rotation capacity versus x/d parameter (see EC2 [9]).
The plastic rotation capacity is defined as the difference be-
tween the rotation at the ultimate load and at the steel bars
yielding onset. Therefore, the plastic rotation can be defined as
the integral of the curvature after steel yielding in the plastified
area (Eq. 1).
Figure 1 – Moment-curvature relation in a reinforced
concrete section under pure bending
before reinforcement yielding
Curvature 1/r
Bending moment M
Tension stiffening

effect
[(1/r) - (1/r) ]II I
1/r - curvature at an uncracked sectionI
1/r - curvature at a fully cracked sectionII
 1/r = .(1/r) + (1- ).(1/r)m I 
II
Cracking moment
Figure 2 – Curvature evolution and tension stiffening effect (example of a region under support)