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373 IBRACON Structures and Materials Journal • 2013 • vol. 6 • nº 3
S. J. P. J. MARQUES FILHO | B. HOROWITZ
beam/column joints including the usual case of column sections
wider than framing beam sections. Simple expressions for spring
stiffnesses are obtained from mechanical models affected by cor-
rection factors whose values are determined from extensive para-
metric studies.
Comparative studies with experimental results demonstrate that
the proposed model has adequate accuracy for design purposes if
member stiffnesses are reduced according to the NBR- 6118 code
[2] factors in order to take cracking into account. Maximum differ-
ence of 5% in displacements was observed between the proposed
approximate scissors model and three-dimensional second order
finite element analyses of six building plane frames.
7. Acknowledgements
The authors wish to recognize CAPES for financial support and
Professor Hunk-Jen Lee for providing his experimental data.
8. References
[01] SHIN, M.; LAFAVE, J. M. Modeling of joint shear
deformation contributions in RC beam-column
connections to overall frame behavior. Structural
Engineering and Mechanics, v.18, n.5, 2004;
pp.645-669.
Table 4 – Geometry of analyzed frames
nbays
nbays
Frames
Frames
Complete joints frames
Concentric joints frames
L (m)
L (m)
nsto
nsto
H (m)
H (m)
Beam section (cm)
Beam section (cm)
Column section (cm)
Column section (cm)
3
1
3
3
2
1
5
6
5,3
5
4
5
1
2
3
4
5
6
14
14
16
16
16
20
3
3
3
3
3
3
20x60
20x80
20x60
15x70
20x60
20x60
20x40
20x60
100x30
130x30
100x20
100x30
Table 5 – Results os second order analyses
Drift (cm) Drift (cm) Drift (cm) Drift (cm) Error (%) Error (%) Increase (%)
Finite element Unadjusted rigid links Scissor's model
uncracked bars
Scissor's model
cracked bars Frames
1
2
3
4
5
6
6,23
9,12
5,36
4,23
13,84
29,12
5,26
8,23
4,64
3,56
12,11
27,07
6,52
9,34
5,32
4,11
14,03
29,50
9,24
12,34
8,52
6,60
19,38
43,08
15,5
9,8
13,4
15,8
12,5
7,0
4,6
2,4
0,7
2,8
1,4
1,3
41,7
32,1
60,2
60,6
38,1
46,0
[02] ASSOCIAÇÃO BRASILEIRA DE NORMAS TÉCNICAS.
Projeto de estruturas de concreto - Procedimento. -
NBR 6118, Rio de Janeiro, 2007.
[03] ABAQUS, User’s Manual, version 6.3, Hibbitt,
Karlsson& Sorensen, Inc, Pawtucket, RI, 2002.
[04] ABAQUS, Getting Started with ABAQUS/Standard,
version 6.3, Hibbitt, Karlsson& Sorensen, Inc,
Pawtucket, RI, 2002.
[05] CHARNEY, F. A.; DOWNS, W. M. Modeling
procedures for panel zone deformations in moment
resisting frames, EECS/AISC Workshop on Connections
in Steel structures, Amsterdam, 2004..
[06] HOROWITZ, B.; MARQUES, S. J. P. J. Modelação da
flexibilidade de nós internos de pórtico em concreto
armado. In: CMNE/CILAMCE, 2007, Porto-Portugal.
[07] BIRELY, A. C.; LOWES, L. N.; LEHMAN, D. E. Linear
analysis of concrete frames considering joint flexibility,
ACI Structural Journal, V. 109, No. 3, May-June 2012,
pp. 381-391.
[08] KRAWINKLER, H.; MOHASSEB, S. Effects of panel
zone deformations on seismic response, J. Constr.
Steel Res., V. 8, 1987, pp. 233-250.
[09] HOROWITZ, B.; MARQUES, S. J. P. J. Efeito da
seção do pilar na flexibilidade de nós internos de
pórtico em concreto armado. In: 49° Congresso