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552
IBRACON Structures and Materials Journal • 2012 • vol. 5 • nº 4
Design of slender reinforced concrete rectangular columns subjected to eccentric loads
by approximate methods
is also reflected in the total demerit point score of this method,
which is much larger. The approximate stiffness procedure, on the
other hand, has smaller percentage of results in the low safety and
dangerous range with no values in the extremely dangerous zone.
The effects of concrete compressive strength
f
c
, of the column
slenderness ratio
l
and of the dimensionless axial force
u
on the
ratio
M test
/
M pred
were verified for both the approximate curvature
method and the approximate stiffness procedure. For both design
methods, this analysis revealed a reduction in the
M test
/
M pred
ratio for larger values of the column slenderness
l
as shown in
Figure 1. For the other two parameters no trend was found.
Overall, the analysis shows that NBR 6118 [1] approximate stiffness
criterion provides better predicting results in terms of safety, preci-
sion and economy for columns made with concrete of
f
c
≤ 55 MPa
.
3.2 Columns made with concrete of f
c
> 55 MPa
Since NBR 6118 [1] procedures are being changed to allow the
use of concrete with compressive strength above 55 MPa, a com-
parative analysis of the current approximate design approaches for
slender columns is presented next.
The results of the
M test
/
M pred
ratio for columns made with con-
crete of
f
c
> 55 MPa
are presented in the Table 5. They were ob-
tained from the comparison with test results of 65 columns.
The analysis of these results reveals that NBR 6118 [1] approxi-
mate stiffness criterion and approximate curvature method have
average and median values for the
M test
/
M pred
ratio larger than
the unity. The approximate stiffness criterion is more conserva-
tive since its average and median are larger. In terms of accuracy,
the approximate stiffness procedure is also more precise, since
the coefficient of variation is 3% smaller. With respect to safety,
the demerit scale (shown in the part B of Table 5) shows that the
results obtained with the approximate stiffness criterion are safer
with only 4,6% of the
M test
/
M pred
values below the appropriate
safety range (smaller than 0.85) and all of them are in the low safe-
ty range. This fact is also reflected in the total demerit point score
of this method, which is much smaller. The approximate curvature
method, on the other hand, has larger percentage of results in the
low safety and dangerous range with no values in the extremely
dangerous zone.
Figure 1 – M /M versus column slenderness ratio
l
test
pred
0
0,2
0,4
0,6
0,8
1
1,2
1,4
1,6
0
30
60
90
120
Slenderness ratio
l
M
test
/ M
pred
0,00
0,20
0,40
0,60
0,80
1,00
1,20
1,40
1,60
0
30
60
90
120
Slenderness ratio
l
M
test
/ M
pred
Approximate curvature method
Approximate stiffness procedure
A
B
Table 5 – Columns made with
concrete of f > 55MPa
c
Parameters
M /M
test
pred
Approximate
Curvature
Method
Approximate
Stiffness
Procedure
Average (m)
Median (m )
d
Standard
deviation (SD)
Coefficient of
variation (CV)
1,026
1,012
0,184
17,94%
1,146
1,125
0,173
15,09%
Part A – Statistical Analysis
Part B – Demerit Point Classification
M /M
test
pred
Approximate
Curvature
Method
Approximate
Stiffness
Procedure
0.65|--0.85
12,3
4,6
0.85|--1.30
78,5
81,5
1.30|--2.00
6,2
13,9
2
.
00
0
0
Total Demerit
Point Score
46**
23
< 0.50
0*
0
0.50|--0.65
3,1
0
* – Percentage values of M /M results
test
pred
** 46 = (0 x 10) + (3,1 x 5) + (12,3 x 2) + (78,5 x 0) + (6,2 x 1) + (0 x 2)