Page 20 - Riem-Vol6_nº3

372 IBRACON Structures and Materials Journal • 2013 • vol. 6 • nº 3
Flexibility modeling of reinforced concrete concentric frame joints
Figure 21 – Schematic detail of the geometry
and the loading applied to the frames
In all cases a 10kN lateral load was applied in the first three and
the last floors while a 15 kN load was applied to the intermediate
remaining floors. The horizontal load was applied in the joints of
the outer columns. In order to verify the effect of the geometric
Figure 22 – Applied loads for frame model 1
nonlinearity, a vertical load of 15 kN is applied to the outer columns
and 30 kN to the inner columns at all stories. The load applied to
the three-dimensional model of frame 1 can be seen in Figure 22.
In the first two examples the frames contain complete joints
only, while the remaining frames contain concentric type joints
only. Table 4 summarizes the geometry of the frames adopted
in the analyses.
In Table 5 second-order analysis results are presented, where the
percentage difference for the displacement response of each mod-
el is computed with respect to the finite element model. It can be
readily seen that the scissors model presents the best results when
compared to the finite element model. The maximum percentage
difference is 5%, while for the model using unadjusted rigid links the
difference increases to 16%. The last two columns contain lateral
displacements of the scissors model with cracked members and the
percentage increase due to cracking. It can be seen that average
amplification of displacements is 46,5% which has a significant im-
pact on bending moments of beams and columns.
6. Conclusions
Beam/column joint flexibility in usual reinforced concrete building
frames, disregarding the presence of slabs and transverse beams,
contributes around 20% of the total lateral displacement. Therefore
joint flexibility modeling is needed to check the excessive lateral
displacement serviceability limit state as well as the global second
order effects in ultimate limit states.
The NBR-6118 code [2] suggests the use of a rigid link model
whose adjusted lengths are functions of the framing beam depths.
Since joint flexibility stems from shear distortion, not bending in-
side the joint, this model may not always yield accurate results.
An accurate yet simple scissors model, composed of bars and
springs only, is proposed to take into account the flexibility of