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IBRACON Structures and Materials Journal • 2012 • vol. 5 • nº 1
A. G. B. CORELHANO | M. R. S. CORRÊA | A. T. BECK
The studied model errors (Eq. 8) compare displacements which
represent load effects. Hence, model error values smaller than
unity indicate a conservative model, as
u
simplified
>
u
rigorous
. It can be
observed that both models are conservative, on average, as the
means are smaller than unity (μ < 1). The 70/70 is moderately con-
servative, with mean just below unity, whereas the 80/40 model is
very conservative, with mean equal to 0.682. Since the c.o.v. is the
same for both variables (σ/μ=0.16), one concludes that the 70/70
model is more precise.
4. Structural reliability analysis
4.1 Design and verification of the frames
For the reliability analysis with respect to maximum displace-
ments limit state, three frames were designed: with four, eight
and twelve floors (following Figure 3). Design of the frames fol-
lowed guidelines of ABNT NBR6118:2003 [1] for ultimate limit
states. Once the proportioning of the frames was complete (for
ultimate limit states), their flexibility was increased until they
reached the maximum horizontal displacement allowed by ABNT
NBR6118:2003 [1]. The verification with respect to horizontal dis-
placements was made for frequent load combination, with maxi-
mum displacement of H/1700, where H is the total height of the
building. For the frequent load combination, one has:
(11)
1 1
2
ser
giK
q K
qjK
F
F F
F
y
y
=
+
+
å
å
where:
giK
F
: permanent actions;
1
q K
F
: main variable action;
qjK
F
: secondary variable action;
1
ψ
: combination coefficient for the main variable action;
2
ψ
: combination coefficient for the secondary variable action.
For the studied buildings, only one equation is obtained, as the
combination factor for wind, when considered the secondary ac-
tion, is null. Hence, one obtains:
Table 2 – Statistics of goodness-of-fit tests for the Normal distribution
Model
error
Distribution
Goodness-of-fit test
Kolmogorov-Smirnov
Anderson Darling
Chi Squared
70/70
Normal
0.10675
0.53353
1.7787
80/40
Normal
0.10290
0.58495
1.4824
Table 3 – Characteristic and nominal resistance and load values considered in design
Variable
Symbol
Characteristic or nominal values
4 floors
8 floors
12 floors
Concrete strength
f
ck
25 MPa
25 MPa
30 MPa
Dead load
D
n
24 kN/m
25.5 kN/m
22 kN/m
Life load
L
n
7.5 kN/m
7.5 kN/m
6 kN/m
Wind load at the floors
W
n
13.5 kN
11.4 kN
13.5 kN
Table 4 – Horizontal displacements at the top of the buildings
Floors
Height H (m)
Displacement at top (mm)
70/70
80/40
Limit displacement (H/1700)
4
14.4
6.62
8.10
8.47
8
28.8
12.09
16.50
16.94
12
43.2
18.29
25.05
25.41