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IBRACON Structures and Materials Journal • 2012 • vol. 5 • nº 6
M. N. KATAOKA
| M. A. FERREIRA
| A. L. H. C. EL DEBS
(E.I)
teorico
– Theoretical stiffness of the beam
– Beam span
a
– Distance from the point of load application to support
P – Concentrated load
The percentage of partially restrained, which reflects the connec-
tion percentage of rotation restrained, was determined for experi-
mental stiffness and secant stiffness. In the case of experimental
stiffness the analysis was performed in the point of intersection be-
tween the Beam-Line and the experimental curve and in the case
of secant stiffness, the point was the intersection with the secant
line connects the point of zero bending moment to the point of mo-
ment related to the yielding stress (Figure 16). To determine the
coefficient of partially restrained it was used equation 3.
(3)
R
E
M
M
Coefficient of partially restrained
E
M
– Bending moment in the connection
R
M
– Fully restrained moment
The fixity factor (a
R
) was determined in accordance with equation 4 from
Ferreira [14], considering the application of two concentrated loads.
(4)
R
R
R
R
E
M
M
4
3 6
2
Table 4 shows the results of percentage of partially restrained con-
sidering the experimental stiffness and secant stiffness. Model 1
presented closer values of percentage of partially restrained due
to its stiffness was not so high. Taking into account the stiffness
of Model 2, there was a significant difference between the per-
centages of partially restrained which were determined to the ex-
perimental curve and to the secant stiffness. The percentage of
partially restrained to the experimental stiffness reached 83% and
only 49% for secant stiffness.
According to Ferreira [13], Model 1 was classified as semi-rigid
connection with medium strength (zone 3) considering the experi-
mental stiffness and the secant stiffness. Model 2 presented two
different classifications: considering the experimental stiffness is
classified as a semi-rigid connection with high strength (zone 4)
and considering the secant stiffness is classified as semi-rigid with
low strength (zone 2).
6. Conclusions
n
Based on this research, with two tests of connections, it was
possible to analyze the behavior of the beam-column connec-
tion between precast concrete elements which is widely used
on sites and also to test an experimental methodology which is
not standardized in Brazil.
n
The method used to measure the rotation which employed the
transducers placed on the corbels was very satisfactory. The
advantage of this method was the possibility to measure rota-
tion created by the opening of cracks in the connection region.
The use of clinometers to measure the rotation was also satis-
factory. It was possible with the clinometers to obtain the direct
measurements of global rotation, whose values were close to
those obtained by transducers. With these results the methods
were validated.
n
In despite of Model 2 had presented high stiffness in service sit-
uations, the secant stiffness of the two models were very close.
Model 2 reached a percentage of partially restrained lower than
the percentage that Model 1 reached. However, it can be con-
cluded that using the secant stiffness in the project of connec-
tions the dimensioning is in favor of security. Using the secant
stiffness of the connection in design process, the designers will
also reserve strength and rigidity to resist to other loads not
considered in the project.
n
According to the connections classification, both models can be
considered with semi-rigid behavior. Despite the classification
of Model 2 as semi-rigid with low strength (zone 2) considering
the secant stiffness, the reinforcement distribution of this model
was the one which provided more rigidity to the connection.
Figure 17 – Scheme for determining
the rotation of a bi-supported beam
Table 3 – Values of rotation, moment of inertia
and elastic modulus for Models 1 and 2
Model
Rotation
Moment of
4
inertia (m )
Elastic Modulus
2
(kN.mm )
1
0,002375
0,0100
30
2
0,001340
0,0177
30
(rad)
Table 4 – Percentage of partially restrained
of the connections
Model
Experimental Stiffness
Secant Stiffness
M
R
M
R
M
E
M
E
R
R
1
66% 0,52
55% 0,41
2
83% 0,70
49% 0,36