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188
IBRACON Structures and Materials Journal • 2012 • vol. 5 • nº 2
Design model and recommendations of column-foundation connection through socket with rough interfaces
X
sf
: Depth of neutral axis
For a simplified bending theory analysis, the force
ssf
R
, resultant
in the vertical reinforcements
tsv,s
mv ,s
A A.2
+
, is determined accord-
ing to the equation:
(4)
sf
ext
w
sf
d
bd
yd
tot ,s
ssf
z
h5.0 h5.0 z N M f
A R
×
- ×
+ ×
-
= ×
=
Where:
emb
d d
bd
lVM M
×
+ =
sf
sf
sf
x4.0 d z
×
- =
For practical application in the case of large eccentric normal forc-
es, the parameters
sf
sf
d9.0 z
×
@
and
ext
sf
h9.0 d
×
@
could be used.
The resultant of concrete compression stresses in the socket is
estimated as:
(5)
(
)
sf
w
ext
d
bd
d
ssf
csf
z
h5.0 h5.0NMN R R
× - ×
×
+
= + =
Substituting
sf
sf
sf
x4.0 d z
×
- =
in equations 3 and 4, the resultants
ssf
R
and
csf
R
are calculated according to expressions 6 and 7,
respectively, as:
(6)
sf
sf
sf
ext
d
bd
ssf
x4.0 d
)x4.0 h5.0(N M R
×
-
×
- ×
×
-
=
(7)
(
)
sf
sf
w
ext
d
bd
csf
x4.0 d
h5.0 h5.0 N M R
×
-
×
- ×
×
+
=
Considering that the force
csf
R
is the resultant of the compres-
sive stresses
s
cd
considered uniformly distributed on an area of
ext
sf
h x8.0
×
×
, for the rectangular compressive stress diagram, the
force
csf
R
results in:
(8)
cd
ext
sf
cd
csf
csf
h x8.0
A R
s×
×
×
=s×
=
Figure 7 – Schematic representation of force for the determination of vertical
reinforcements in rough interface sockets according to Canha [4]
A
A
Section A-A
csf
R
ssf1
R
h
w
2A
of reinforcement
s,mv
+ A
s,tsv
A
s,lsv
A
s,mv
A
s,mv
A
s,tsv
ssf2
R
ssf3
R
d
2
x
1
d =
d
N
d
M
force resultant
csf
R
ssf1
R
0.8x
d
ssf
R =
cd
s
Parabolic-rectangular diagram
of concrete stress
Simplified diagram
d
3
d
N
bd
M
d
N
bd
M
cd
s
sf
sf
d
d
sf
rear transv.
wall
longitudinal
wall
front transv.
wall
longitudinal
wall
d
V
emb
sf
sf