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189
IBRACON Structures and Materials Journal • 2012 • vol. 5 • nº 2
R. M. F. CANHA |
G. M. CAMPOS |
M. K. EL DEBS
Substituting equations 6 and 8 in equation 5, the position of the
neutral axis can be determined from equation 9, and subsequently
A
s,mv
is determined.
(9)
0
h x 32.0 d
h x8.0 dN hN5.0 M
cd
ext
2
sf
sf
cd
ext
sf
sf
d
ext
d
bd
=s×
×
×
+ × s×
×
×
- ×
+ ×
×
-
If the simplified rectangular concrete compressive stress diagram is
adopted, it results, for the socket, a constant compressive stress of
cd
cd
f 85.0
×
=s
along a depth of
sf
x8.0
×
measured from the compression
face, referred to compressed zone of constant height. For the remaining
height of
sf
x2.0
×
, the compressive stresses in concrete is neglected.
2.3 Main horizontal reinforcements
The main horizontal reinforcement consists of the main trans-
verse horizontal reinforcement, A
s,tmh
and the main longitudinal
horizontal reinforcement, A
s,lmh
. A
s,tmh
is the reinforcement distrib-
uted along the top of the transverse walls within a distance of
l
emb
/3
from the top while A
s,lmh
is that distributed along the top
of the longitudinal walls within
l
emb
/3
. Since the reinforcements
lmh ,s
A
and
tmh ,s
A
are distributed within the same height of
the rough socket, and considering the positioning of the rebars in
the socket at the construction, it is recommended, when design-
ing socket connections, to adopt the largest reinforcement area
Figure 8 – Transfer of forces resultants from column to rough socket (adapted from Canha et al. [10])
l
emb
h
c
R
s
R
N
M
V
csf
R
Transfer of forces resultants
from column to socket foundation
b
b
h
ext
A
s
z
sf
topf
p
topr
p
ssf
R
d
p
topr
emb
wall
Rear transverse
l
/ 2
topr
p
H
topf
H
emb
l
/ 3
p
topf
l
3/
emb
wall
Front transverse
emb
l
H
r
f
H
topf
p '
p '
topr
emb
/ 3
l
z
s,mv
2A
s,tsv
A+
Pressures
rear wall
resultant on
Variable
inclination
Variable
inclination
front wall
Pressures
resultant on
r
H
f
H
ssf
R
csf
R
f
p
r
b
b
f
topr
H
topf
H
l
emb
/ 3
d
d
d
H
r
f
H
with the reinforcement arranged symmetrically. Figure 6 shows
the positioning of these reinforcements.
2.3.1 Main transverse horizontal reinforcement – A
s,tmh
Canha et al. [10] proposes a model for the analysis of transverse
walls of sockets with smooth and rough interfaces, based on the ex-
perimental results of Canha [4] and Jaguaribe Jr. [9]. Following the
experimental results of Nunes [11] obtained from the behavior of the
transverse walls, a refined Canha et al. [10] model presented herein
was obtained. Figure 8 presents the stress transfer model from col-
umn to socket with rough interfaces, based on Canha et al. [10].
In this model, compression struts appear on the compressed side (front
transverse wall) due to the transfer of the compression resultant
c
R
from the column to the front wall, thus resulting in a force
csf
R
in the
socket foundation. Due to the presence of these compression struts,
a pressure resultant
f
H
is observed to act on the front transverse
wall. This pressure attains its maximum value at the top of the front
transverse wall due to the smaller inclinations of the struts with respect
to a horizontal axis through the top of this wall. Since these struts are
practically vertical near the socket base, the pressure at this point is null.
This force
f
H
can determined using equation 10 below:
(10)
f
csf
f
tan
R H
b
=