Page 12 - Riem-Vol6_nº3

364 IBRACON Structures and Materials Journal • 2013 • vol. 6 • nº 3
Flexibility modeling of reinforced concrete concentric frame joints
It can then be concluded that the contribution of joint flexibility to dis-
placements is significant and must be taken into account in checking
the limit state of excessive lateral displacements of building frames.
In ultimate limit states second order global effects are also directly
affected by joint flexibility, whose capacity to absorb the shear force
must be checked.
3. Complete joints
Consider again the model shown in Figure 4(a), which corresponds
to the complete joint of Figure 3(a). The top section displacement is
due to contributions of beams, columns, and joint deformations. The
deformation in the joint zone has normal, bending, and shear com-
ponents. The most significant part is due to shear distortion that will
be discussed in more detail in order to develop of an approximate
expression of its stiffness where the important factors are included,
with the correct power. In a second step the approximated expression
is adjusted as a result of the conducted parametric study.
3.1 Flexibility of complete frame joints
Consider the subassemblage in Figure 7 subjected to a horizontal
loading, VC , applied to the top of the column. Different modeling
alternatives for joint flexibility of steel frames made of wide-flange
sections are discussed by Charney and Downs [5]. They show
that if on equates the lever arm between tension and compression
stress resultants to the beam depth, the horizontal shear at the
center of the joint, VN (see Figure 5(b)), is given by:
(1)
Where α is the ratio of column width to beam span, L. The ratio of
beam depth to story height, H, is equal to β, as depicted in Figure 7.
The average shear stress is given by:
(2)
Where: t =joint thickness and sN=volume of joint region.
Figure 7 – Frame joint subjected to
a lateral load, VC
Figure 8 – (a) Adjusted rigid links model; (b) scissors model
A B