Page 14 - Riem-Vol6_nº3

366 IBRACON Structures and Materials Journal • 2013 • vol. 6 • nº 3
Flexibility modeling of reinforced concrete concentric frame joints
umns. Story heights of 3 and 4meters were considered. For
each height, values of 40, 60, 80, and 100cm were adopted
for both beams and columns depths. Adopted values for the
correction factor g for cross type interior joints, T-lateral and
T-top joints, and L-type joints will be denoted by gC , gT and gL,
respectively.
3.4.1 Cross type interior joints
Initially a parametric study for the interior Cross-type joint is
conducted. The boundary conditions applied to the three-di-
mensional model are the same as those used in the examples
of Section 2. The adopted value of parameter g is obtained
comparing results from the scissors and the finite elements
models.
The first issue to be discussed is the appropriate value of the
joint volume, sN , that should be adopted for joints with general
width/depth ratios. Figure 9 shows the shear stress contours for
two different joint geometries: square, and the one in which the
height is twice its width. It can be readily noticed that the behav-
ior changes substantially. To approximate the geometric effect,
Horowitz and Marques [9] suggests the following approach for
the computation of the effective joint volume:
(9)
Where a and b are the joint dimensions, with a ≤ b, and t is the
joint thickness.
Figure 10 shows the surface that represents the variation of
the computed correction parameter, g, with the depths of beam
and column sections, for a story height of 3m. From the analy-
sis of the obtained results the value of the parameter g for
cross-type joints, gC , was taken as 0,45, which represents a
value slightly below the average with a bias to larger flexibility.
This is also representative for story height of 4m as shown in
Horowitz and Marques [9], where the authors detail extensive
parametric study of the scissors model applied to complete
interior joints.
Figure 10 – Variation of the parameter 
for 3 meters story height
Figure 11 – Anti-symmetric model in finite
elements for T-Lateral and T-Top exterior joints
Figure 12 – Finite element anti-symmetric model
for L-type joints
Figure 13 – Deformed configuration
of the complete cross-type joint