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IBRACON Structures and Materials Journal • 2012 • vol. 5 • nº 2
R. M. F. CANHA |
G. M. CAMPOS |
M. K. EL DEBS
(34)
2
d
d
topf
bot
1
VN H H
m+
+ ×m
- =
(35)
2
d
d
fb
1
V N N
m+
×m-
=
This model is indicated for sockets subjected to normal forces
with high eccentricity and with embedded lengths based on NBR
9062:2006 [6] recommendations.
Canha [4] confirms that the design of socket foundations consider-
ing friction forces wherein the friction coefficient
m
is adjusted to
1 was in the safe side
for rough interface specimens, in spite of
its being more conservative than the bending theory. Thus, the
model for smooth column base was applied to rough column base
analysis, considering
m =1,
as a base for comparison with model
proposed for rough column based on monolithic behavior.
3.3 Analysis of column base
To investigate the proposed model for column base, four column
sections were considered based on practical observations of pre-
cast concrete structures commonly used. Two rectangular and two
square sections were adopted; the first section being a 40x40 cm
2
column section. These dimensions were chosen with the belief that
it is the smallest column size used in precast concrete structures.
A normal force was assumed and the corresponding bending mo-
ment was calculated following equation 36 for a high eccentricity.
(36)
2
hN
M
d
d
³
×
From the applied load on the section, the coefficients
ν
and
'
m
were calculated according to equations 37 and 38, respectively.
Fixing these two coefficients, the internal axial force and bending
moment at any other section could be determined.
(37)
cd c
d
fA
N
×
=n
(38)
cd
c
d
'
fhA
M
× ×
=m
The shear force was determined through a linear ratio with the
bending moment, considering the acting of concentrated force.
The sections and their respective loads are presented in Table 4.
The following material and construction variables were assumed in
the design of the rough column:
a) Embedded length for rough interfaces and high eccentric-
ity was based on recommendations by NBR 9062:2006[6]:
h6.1
emb
×
=
l
;
b) Joint width of 5 cm;
c) Pedestal wall thickness:
) bor
h(5.3/1 h
int
int
w
×
³
. This is an
intermediary value between the minimum recommended by
Campos [5] and that indicated by Leonhardt and Mönnig [15];
d) Steel CA-50 (
MPa
500
f
yk
=
and
MPa
435
f
yd
=
) for lon-
gitudinal reinforcement and steel CA-60 (
MPa
600
f
yk
=
and
MPa
522
f
yd
=
) for transverse reinforcement;
e) Characteristic compression strength of the socket and column
concretes:
MPa
20 f
ck
=
and
MPa
30 f
ck
=
, respectively,
and
4,1
c
=γ
.
The formulation proposed in this work assumed a monolithic con-
nection. The obtained results were then compared with the model
proposed by Campos et al. [3] adapted for rough interfaces. The
geometrical characteristics, internal forces and resulting reinforce-
ments for each section analyzed are presented in Table 5.
Regarding the longitudinal reinforcement A
s
, the proposed model for
rough column base provided values smaller than those obtained from
Campos et al. [3] model adapted for rough interfaces. The observed
difference is 27% for all cases. Theoretically, no transverse reinforce-
ment would be necessary for the 40x40 cm
2
and 60x40 cm
2
sections
based on the proposed model. For the 40x60 cm
2
and 60x60 cm
2
sections, the transverse reinforcements determined according to the
proposed model were found to be higher than those obtained from the
adapted model for rough interfaces, with the differences up to 28%.
The transverse reinforcements obtained from both the proposed mod-
el and that adapted for rough interfaces are smaller than the minimum
transverse reinforcement recommended by NBR 6118:2007 [17],
thus indicating, in this case, the use of minimum reinforcement.
4. Final remarks and conclusions
In this paper, models and design recommendations for the analy-
sis of column-foundation connection through socket with rough
Table 4 – Column cross section
dimensions and loads
Column
section
bxh
2
(cm )
Axial Force
N (kN)
d
Shear Force
V (kN)
d
Bending
Moment
M (kN.m)
d
40x40
250
50
200
40x60
375
112.5
450
60x40
375
75
300
60x60
560
168.75
675