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IBRACON Structures and Materials Journal • 2013 • vol. 6 • nº 1
Considerations about the determination of
g
z
coefficient
It is worth remembering that the
g
z
coefficient can be calculated
from the values of
B
2
, utilizing equation (28). Thus, it is enough
to determine the
c
i
constants for each storey, given by equation
(29).
In this equation, the
∑
=
⋅
n
1j
hjd
Fj
portion can be written as:
(30)
d16h
d3h
d2h
d1h
n
1j
hjd
F16 ...
F3 F2 F Fj
Substituting the
F
hid
values (design horizontal forces working on
each storey of the structure), given in table [4] and [5], in equation
(30), gives:
n
Direction
X:
kN13.
3164
Fj
n
1j
hjd
n
Direction
Y:
kN94.
7985
Fj
n
1j
hjd
Also considering equation (29), the
∑
=
n
i j
hjd
F
must be calculated
for each storey of the structure; the results obtained are shown in
tables [4] and [5], together with all the data needed to determine
the
c
i
constants and
g
z
coefficient, in directions
X
and
Y
.
It can be seen in tables [4] and [5] that, as expected, the
g
z
values
calculated from the
B
2
coefficients coincide with those previously
obtained, shown in table [3].
Table [6] shows the
g
z
and
B
2
parameter values for other build-
ings analyzed (whose characteristics can be found in Oliveira
[7]), together with the classification of the structures, in direc-
tions
X
and
Y
. However, in the case of the
B
2
coefficient, only
the average (
B
2,avg
) and maximum (
B
2,max
) values of the storeys
are shown. Note that, according to Silva [9], a structure can be
considered almost insensitive to horizontal movement if, on all
its storeys, the
B
2
coefficient does not exceed the value of 1.1. If
B
2
is greater than this value on at least one storey, the structure
will be considered very sensitive to horizontal movement. In this
way, classification of the buildings is carried out by analyzing
the
B
2,max
value obtained.
Table [6] shows that, in all cases, the
g
z
and
B
2
coefficients provide
the same classification for the structures. Furthermore, the
g
z
and
B
2,avg
proved to be extremely close, the major difference, corre-
sponding to direction
X
of building I, being around 3.4%. It is also
worth commenting that, in the large majority of cases
B
2,avg
was
lower than
g
z
.
Table 4 – Calculation of the
coefficient, from the values of B , in direction X, for building I
z
2
Storey
F
hid,x
(kN)
B
2,i,x
16 n
i j
x, hjd
F
(kN)
13.
3164
16
,
,
n
i j
x hjd
xi
F
c
x,i,2
x,i
B
c
1st
26.19
1.13
359.71
0.114
0.100
2nd
17.46
1.26
333.52
0.105
0.084
3rd
17.48
1.28
316.06
0.100
0.078
4th
18.24
1.26
298.58
0.094
0.075
5th
19.60
1.24
280.34
0.089
0.071
6th
20.79
1.22
260.73
0.082
0.068
7th
21.84
1.20
239.94
0.076
0.063
8th
22.80
1.17
218.10
0.069
0.059
9th
23.68
1.15
195.30
0.062
0.054
10th
24.49
1.13
171.62
0.054
0.048
11th
25.25
1.11
147.12
0.046
0.042
12th
25.97
1.09
121.87
0.039
0.035
13th
26.64
1.07
95.91
0.030
0.028
14th
27.28
1.06
69.26
0.022
0.021
15th
27.89
1.04
41.98
0.013
0.013
16th
14.09
1.03
14.09
0.004
0.004
16 n
1i
x,i,2
x,i
x,z
B
c
1
=
0.843
z,x
=
1.19