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IBRACON Structures and Materials Journal • 2013 • vol. 6 • nº 3
Flexibility modeling of reinforced concrete concentric frame joints
it was adopted
k
T-Top
= 0,5 which results in a maximum difference
of 10% with respect to finite element analyses.
4.2.4 Concentric L-type joints
Figure 17 (c) shows the three-dimensional model used for L-type
joints with its applied boundary conditions. The modeling of L-type
joints using
g
L
= 0,1
and
k
=1, as in the case of T-Top exterior joints,
presents significant differences with respect to finite element re-
sults, in the order of 40%.
As a result of the conducted parametric study it is adopted
k
L
=
0,25. The use of this correction parameter decreased the maxi-
mum misfit in stiffness of the results from the two models to 20%.
Since this type of joint is less frequent in the structures of buildings
no significant loss of precision in global flexibility is expected.
5. Results and discussion
5.1 Comparison with experimental results
In order to calibrate the modeling of joint flexibility with real cases
of structural buildings we initially conduct a comparison of the pro-
posed scissors model prediction with experimental results found in
the literature.
5.1.1 Cross-type interior joints
Consider the experimental arrangement shown in Figure 18 de-
veloped by Shiohara et al [13]. The columns have cross-section of
30x30cm, the beams cross section is 30x20cm, the height of the
column is 1,47m and the length of the beam is 2,7m. NBR-6118
code [2] recommends maximum lateral displacement of H/850 for
the wind action, representing a displacement of 0,12% of the story
height. Using the experimental results of shear versus displacement,
one reaches the conclusion that for a 0,12% drift, the corresponding
horizontal force is 21kN. The concrete strength is equal to 28 MPa.
The concentric scissors model is constructed with the following
parameters:
E
=0,85
×
5600(28)
0,5
=2,52
×
10
4
MPa; G=1,05
×
10
4
MPa;
a
=0,111; β=0,204;
s
N
=2,7
×
10
2
m
3
;
K
comp
=272 MN-m/rad;
K
tor
=40783 MN-m/rad;
K
conc
=270 MN-m/rad.
The following four structural models are considered for comparison
purposes:
n
Finite Elements.
n
Bars with unadjusted rigid links.
n
Scissors model with uncracked bars.
n
Scissors model with effective moments of inertia according to
the NBR6118 code:
I
col,e
=0,8
I
col
;
I
beam,e
=0,5
I
beam
;
K
NT,e
=0,8
K
NT
.
Where
I
col,e
and
I
beam,e
are the effective moments of inertia of
columns and beams to be used in the structural analysis to ap-
proximately take cracking into account. The effective value of the
torsional spring stiffness,
K
NT,e
, is computed using the column re-
duction factor.
The obtained results from the four models are shown in the Table 1.
Results in Table 1 indicate that the scissors model with uncracked
bars, reproduced quite accurately the results of the finite element
model, demonstrating the suitability of the parametric adjustment.
In order to reproduce the experimental results the gross moment
of inertia of the members must be reduced to take cracking into
account. The unadjusted rigid link model is twice as stiff as the
scissors model with effective moments of inertia.
5.1.2 T-Lateral exterior joint
From the experimental specimen of the T-Lateral exterior joint
shown in Figure 19 [14], comparisons were conducted with the
proposed model. The specimen consists of columns 2,70m high
and a beam with span of 2,15m. The column has a cross-section
Figure 18 – Experimental setup for
the cross-type joint [13]
Figure 19 – Experimental setup for
the T-Lateral exterior joint [14]
Table 1 – Comparison of actuator force with
numerical results – Cross-Type interior joint
Model
Shear Force, V (kN)
c
Theoretical
Experimental
Finite Elements
Unadjusted rigid link
Scissor's Model with
uncracked bars
Scissor's Model with
cracked bars
35,5
43,1
36,1
21,2
21
21
21
21
1...,8,9,10,11,12,13,14,15,16,17 19,20,21,22,23,24,25,26,27,28,...167