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IBRACON Structures and Materials Journal • 2013 • vol. 6 • nº 1
Considerations about the determination of
g
z
coefficient
5.3 Results obtained
The
g
z
coefficient
was calculated from the first order linear analy-
sis of the structures, for the vertical loads acting simultaneously
with the horizontal actions. In this analysis the physical non-lin-
earity was considered in a simplified way, as established by NBR
6118:2007[2], reducing the stiffness of the structural elements.
The
g
z
values (in directions
X
and
Y
) obtained for both buildings
and considering all the models utilized, are shown in table [2].
In table [2] it can be seen that, with the exception of model 1, all the
models provided practically the same
g
z
values, for both buildings I
and II. Therefore, the presence or lack of symmetry did not have
any influence on the results obtained. Furthermore, the
g
z
values cal-
culated based on model 1, the most sophisticated (for it is the only
one, among all the models adopted, that considers simultaneously
the representation of the slabs as shell elements and the eccentric-
ity existing between the beam’s axis and the slab’s average plane),
are considerably inferior to the other models. This means that more
simplified analyses tend to provide more conservative results. In this
way, it can be claimed that, for structures analyzed by means of sim-
plified models, obtaining high
g
z
values does not necessarily mean
significant second order effects: considering the results for model 1,
building 1 would be classified as being nonsway structure in both
directions, and building II in the direction of
Y
. However, according
to the other models, both the structures would be classified as being
sway structures in the directions of
X
and
Y.
So, from this point of
view, utilization of less refined models proves disadvantageous and
uneconomical, since it can result in quite relevant second order ef-
fects, when in fact they should not be so.
It is important to mention that, obviously, the smaller the
g
z
coef-
ficient value is, the more stiff the structure, which is easily found by
analyzing equation (1). If the structure’s horizontal displacements
are fairly big, so that the increase in moments ΔM
tot,d
becomes
approximately equal to the
M
1,tot,d
moment, that is, ΔM
tot,d
/ M
1,tot,d
@
1,
the
g
z
coefficient will tend to infinity. This would be the case of an
infinitely flexible structure. On the other hand, for an infinitely stiff
structure, that is, that does not shift under the action of loads, the
ΔM
tot,d
would be nil and consequently, the
g
z
coefficient would be
Figure 6 – Slab-beam model
utilizing the “beam 4” element
BEAMAXIS =
AVERAGE PLAN OF SLAB
Table 1 – Main characteristics of the models employed
Model
Elements adopted
Depiction
of the slabs
Consideration of the eccentricity existing
between the beam axis and the average plane
of the slab
1
“beam 4”, “beam 44”
and “shell 63”
Shell elements
Yes
2
“beam 4” and
“shell 63”
Shell elements
No
3
“beam 4”
Rigid diaphragm
No
4
“beam 4”
-
No
5
“beam 4” and
“beam 44”
-
Yes
Table 2 – Values of
for buildings I and II, considering all the models utilized
z
Model
Building I
Building II
Direction X
Direction Y
Direction X
Direction Y
1
1.09
1.06
1.20
1.08
2
1.18
1.14
1.31
1.15
3
1.19
1.14
1.32
1.16
4
1.19
1.14
1.32
1.16
5
1.19
1.14
1.32
1.16