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IBRACON Structures and Materials Journal • 2013 • vol. 6 • nº 1
D. M. OLIVEIRA | N. A. SILVA | C. F. BREMER | H. INOUE
equal to 1. Based on these considerations, it can be stated that,
on observation of the
g
z
values shown in table [2], the buildings, if
analyzed utilizing model 1, appear much more stiff than if analyzed
considering the other models. Furthermore, it can be seen that this
considerable increase in stiffness is due to the representation of
the slabs as shell elements associated with the consideration of
the eccentricity existing between the beam axis and the average
slab plane, and it is not sufficient to take only one of these factors
into account, as can be found by observing the results of models 2
and 5. Thus, from tables [1] and [2], it can also be stated that the
representation of the slabs by means of shell elements (model 2)
or the consideration of the hypothesis of a rigid diaphragm (model
3) did not themselves contribute to the increase in stiffness of the
structures, observed in model 1. In the same way, considering the
eccentricity existing between the beam axis and the average slab
plane in the bar model (model 5) did not alter the results previously
obtained (model 4), indicating that substituting the “beam 4” ele-
ment for the “beam 44” element to represent the beams did not
prove advantageous in the absence of slabs.
Finally, based on the principle that model 1, the most sophisticat-
ed and which involves the most computer work, is not generally
adopted by the technical medium, including calculating the
g
z
co-
efficient, and considering that all the other models provide practi-
cally identical results, in the next item of this paper the buildings
will be analyzed utilizing model 4, the simplest one. However,
it is worth commenting that, in putting the project into practice,
model 1 must be utilized for preference, since it represents the
actual behaviour of the structure more accurately and provides
much lower
g
z
values to those obtained by the other models,
which leads to greater savings and, in many cases, dispenses
with carrying out analyses which consider, in a simplified way or
otherwise, the second order effects.
6. Comparative study of the
g
z
and
B
2
coefficients
With the purpose of carrying out a comparative study of the
g
z
and
B
2
coefficients, the values of these parameters were calculated for
several reinforced concrete buildings of medium height, including
those that were the object of study in item 5.
The buildings were then first order processed, utilizing three-di-
mensional models on ANSYS-9.0 [1] software, with the columns
and beams depicted by means of the “beam 4” element (according
to model 4, described in the previous item).
As already mentioned, the actions working on the buildings are
divided into two groups: vertical actions (consisting of permanent
loads and accidental load) and horizontal actions (corresponding
to the action of the wind in directions
X
and Y
).
The coefficients
applied to the actions were defined from the ultimate normal com-
bination considering the wind to be the main variable action, and
determined according to NBR 6118:2007 [2] recommendations.
6.1 Results obtained
Table [3] shows the values of
g
z
(the only one for the whole struc-
ture) and
B
2
(determined for each storey) obtained for the first
building analyzed (“building I”), in directions
X
and
Y
.
It can be seen in table [3] that, on several storeys of building I, the
B
2
coefficient exceeds the value of 1.1 both in direction
X
and direc-
tion
Y
. In this way, the structure can be considered very sensitive
to horizontal movement and, in this case, the global second order
effects cannot be ignored. The
g
z
coefficient provides a like clas-
sification, that is, it considers the structure as being sway structure
in both directions
X
and
Y
.
Table 3 – Values of the
and B in directions X and Y, for building I
z
2
Storey
Direction X
Direction Y
z,x
z,y
B
2,i,x
B
2,i,y
1st
1.19
1.13
1.14
1.05
2nd
1.26
1.13
3rd
1.28
1.18
4th
1.26
1.19
5th
1.24
1.20
6th
1.22
1.19
7th
1.20
1.18
8th
1.17
1.16
9th
1.15
1.15
10th
1.13
1.13
11th
1.11
1.12
12th
1.09
1.10
13th
1.07
1.08
14th
1.06
1.07
15th
1.04
1.06
16th
1.03
1.08