Page 10 - Riem-Vol6_nº3

362 IBRACON Structures and Materials Journal • 2013 • vol. 6 • nº 3
Flexibility modeling of reinforced concrete concentric frame joints
second order analyses incorporating the model were performed
on several multistory building frames. Obtained results are com-
pared with those of second order, three-dimensional, finite element
analyses.
2. Impact of joint flexibility
In order to gain an initial insight on the impact of joint flexibil-
ity on structural behavior consider the illustrative example of
Figure 3 where two interior joint subassemblages are shown.
The first is a complete type joint, consisting of beams with 5m
span and a 3m high column. Both beams and columns have a
20cm by 50cm rectangular cross-section. The second joint is
concentric and differs from the first only in the cross-section of
the column which is 160cm by 25cm. Note that both columns
have the same moment of inertia in the plane of bending.
In both subassemblages horizontal displacement of the bottom
section of the column as well as the vertical displacements of the
end sections of the beam are prevented. The goal is to evaluate
the required horizontal force applied to top of the column which
produces a 1cm horizontal displacement. The modulus of elasticity
of the concrete is 20,6GPa and Poisson’s ratio is 0,2.
Initially consider as a basis the finite elements model of the first
example, shown in Figure 4(a). This model uses quadratic hexa-
hedron elements having twenty nodes with reduced integration
implemented in the commercial code ABAQUS [3]. Concrete is
modeled as a linear elastic homogeneous material. The discretiza-
tion mesh follows the guidance given in Reference [4] for bending
problems which suggests at least two elements through the width
and shows excellent agreement with beam theory using four ele-
ments through the height, as well as experience gained throughout
the present research. These techniques are used for the finite ele-
ment models in the remainder of this study.
For the finite element model of Figure 4(a) the value of the reac-
tion force at the top section of the column corresponding to the
imposed unit displacement is 81,5kN. Consider now the model
shown in Figure 4(b) consisting only of bar elements where rigid
links are specified for both beams and columns in the interior of
the joint. In this case, the necessary force is 100kN. If no rigid links
Three-dimensional finite element models of beam/column subas-
semblages are submitted to unit displacements at one of the col-
umn end sections, and comparisons are made between the result-
ing reactions against those obtained using the proposed model.
As a result of this study required parameters of the model are ad-
justed. Only elastic analysis is considered since this is the usual
approach for nonseismic design of building structures, where sec-
ond order effects are directly or approximately taken into account.
In order to validate the adopted parameter values, comparisons
are made between the predicted values of displacements against
experimental subassemblage results for drift values compatible
with the NBR-6118 code [2] limits for service lateral displacement.
In order to assess the accuracy of the proposed simplified model,
Figure 3 – Elevation and plan view of
the example substructure (in cm)
Figure 4 – (a) Finite elements model; (b) Bars model with rigid links in the joint region