Page 15 - Riem-Vol6_nº3

367 IBRACON Structures and Materials Journal • 2013 • vol. 6 • nº 3
S. J. P. J. MARQUES FILHO | B. HOROWITZ
3.4.2 Complete T-Lateral and T-Top exterior joints
Consider now the T-Lateral and T-Top exterior joints. Typical
three-dimensional finite elements models are shown in Figure 11
with the imposed boundary conditions, where u, v and w are trans-
lations along global axes x, y and z, respectively. An anti-symmet-
ric displacement field was applied in order to force a zero moment
section at mid-height of the column and mid-span of the beams
without resorting to multi-node artificial constraints.
Similarly to cross-type joints the correction factor, gT , for T-type
joints, is evaluated as the result of a parametric study. The final
adopted value is, gT = 0,3, as reported by Horowitz and Marques
[10], where the authors give a detailed analysis of the scissors
model applied to complete T and L-type joints.
3.4.3 Complete L-type exterior joints
The previously used modeling techniques are also employed for
L-type joints as shown in Figure 12.
As a result of the parametric study it was adopted, gL = 0,1, as
reported in Horowitz and Marques [10].
4. Concentric joints
4.1 Modeling the flexibility of concentric joints
Consider the beam/column joint shown in Figure 13 subjected to
an arbitrary displacement at its top section. One has that the dif-
ference between the rotation of the beam, q beam, and the rotation of
the column, qcol, is due to the shear distortion of the joint region, as
discussed in Section 2.
Consider now the concentric cross-type joint, shown in Figure
14(a), subjected to a uniform displacement at its top section. The
elastic restraint from strip B-B’ is less effective than that offered
by A-A’ due to the column horizontal torsional deformations in the
region of framing of the beams.
In order to take into account this phenomenon, we consider a tor-
sional member embedded in the column as show in Figure 14(b).
The additional flexibility of the joint is that resulting from the flex-
ibility of the torsional member, similarly to the proposed ACI code
[11] equivalent frame formulation provisions for the computation of
column stiffness in flat slabs.
The differential rotation between the beam and the column, qconc,
is given by:
(10)
The value of qconc can be taken as the sum of the differential rota-
tion of the column at the point of incidence of the beam, qA, and the
average rotation of the torsional member inside the joint, q t,average.
As flexibility is the inverse of stiffness, and considering qA as being
that corresponding to a complete joint, one has that:
(11)
The value of Kcomplete was derived in Section 3.4 for the various
types of joints. The term corresponding to the torsional stiffness is
detailed below.
Figure 14 – (a) Complete cross-type joint; (b) Cross-type with torsional member
A B