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IBRACON Structures and Materials Journal • 2013 • vol. 6 • nº 3
S. J. P. J. MARQUES FILHO | B. HOROWITZ
of 40x60cm and the beams 45x30cm, the concrete strength is
29,5MPa. In the experimental arrangement the columns ends are
hinged in order to simulate the inflection points in a real building
frame and cyclic loading is applied at the end of the beam. Using
the experimental data provided by the senior author of Reference
[14], it was found that for a displacement of 5,28mm, correspond-
ing to a 0,25% drift, the applied force is 48,3 kN.
The concentric scissors model is constructed with the following pa-
rameters:
E
=0,85
×
5600(29,5)
0,5
=2,58
×
10
4
MPa; G=1,08
×
10
4
MPa;
a
=0,093; β=0,167;
s
N
=0,102 m
3
;
K
comp
=787 MN-m/rad;
K
tor
=26209
MN-m/rad;
K
conc
=587 MN-m/rad.
The same four kind of models used in the previous section are
compared in Table 2. The scissors model with uncracked bars
presents a 8,5% error when compared to the finite element model.
Considering the cracking of the model based on the reduction fac-
tors of the gross moment of inertia of the sections recommended
by the Brazilian code, NBR 6118 [2], the prediction error for the
proposed model with respect to the experimental results is 3,9%.
Once again the unadjusted rigid links proved to be twice as stiff as
the cracked scissors model.
5.1.3 L-type joint
In the case of concentric L-type exterior joints, the proposed mod-
el was compared with experimental results obtained by Angela-
kos[15]. Figure 20 shows a schematic representation of the ex-
perimental arrangement. The specimen has a span of 1,325m and
height of 0,914m. The cross-section of the beam is 28cm by 40cm
and that of the column is 40cm by 40cm. It was used a 1,83mm
displacement representing the magnitude of the serviceability
limit imposed by the NBR 6118 code [2]. The concrete strength
is 31,7MPa. The concentric scissors model uses the following pa-
rameters:
E
=0,85
×
5600(31,7)
0,5
=2,68
×
10
4
MPa; G=1,12
×
10
4
MPa;
a
=0,152; β=0,219;
s
N
=0,064 m
3
;
K
comp
=180 MN-m/rad;
K
tor
=35275
MN-m/rad;
K
conc
=179 MN-m/rad.
The same four models previously used are compared in Table 3.
Another feature is to be highlighted. Different experimental results
were obtained for displacements that open or close the joint. This
demonstrates the importance of the contribution of the reinforce-
ment slip. Once more it can be seen the small difference, around
4%, between the proposed scissors model and the result of the
finite element analysis. When the cracked scissors model is com-
pared with the average of the experimental results, it is observed
that the difference is only 2,9%.
5.2 Multi-story frames
In order to assess the accuracy of the proposed simplified joint model,
six multi-story frames without slabs were analyzed and comparisons
made between unadjusted rigid links, proposed scissors model and
the finite elements model. In Figure 21 it can be observed typical ge-
ometry of the frames where L is the bay length, H is the story height,
n
bay
is the number of bays and
n
sto
the number of stories.
Table 2 – Comparison of actuator force with
numerical results – T-Lateral exterior 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
96,9
102,3
88,7
50,2
48,3
48,3
48,3
48,3
Figure 20 – Experimental setup for L-type joint [15]
Table 3 – Comparison of actuator force with numerical results – L-type joint
Model
Shear Force, V (kN)
c
Opening
Theoretical
Experimental
Closing
Finite Elements
Unadjusted rigid link
Scissor's Model with
uncracked bars
Scissor's Model with
cracked bars
10
10
10
10
12,65
19,74
13,1
8,59
6,7
6,7
6,7
6,7
