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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
Substituting equations (10), (13), (16) and (19) in equation (22), gives:
(23)
Finally equation (23) can be written as:
(24)
3,2
3
2,2
2
1,2
1
z
B
c
B
c
B
c 1
with constants
c
1
,
c
2
and
c
3
being given respectively through:
(25)
(26)
(27)
As such, for a structure consisting of
n
storeys, the
g
z
coefficient
can be calculated by reference to the
B
2
coefficient as:
(28)
and
(29)
5. Influence of the structural model
adopted to calculate
g
z
As commented previously, NBR 6118:2007 [2] establishes that
the
g
z
coefficient can be determined from a first order structure
analysis. However, this analysis can be carried out utilizing vari-
ous types of structural models. For example, a building can be
modelled considering the slabs as rigid diaphragms or depicting
them by means of shell elements. Additionally, the eccentricity ex-
isting between the beam axis and the average slab plane may or
may not be taken into account. In this way, in order to evaluate the
possible influence of the structural model on the value of
g
z
, the
g
z
coefficients will be determined for two reinforced concrete build-
ings, considering five distinct three-dimensional models developed
utilizing ANSYS-9.0 [1] software. The results of these models will
then be analyzed and compared.
5.1 Buildings and models analyzed
The first building analyzed, shown in figure [2], consists of sixteen
storeys (with a 2.9 m ceiling height) and is symmetrical in both
X
and
Y
directions. 20 MPa for the characteristic strength of the
concrete to compression and a Poisson coefficient equal to 0.2
were adopted.
The second building, depicted in figure [3], consists of eighteen
storeys (with a ceiling height of 2.55 m) and has no symmetry.
The concrete presents characteristic strength to compression and
a Poisson coefficient equal to 30 MPa and 0.2, respectively.
Each building was analyzed utilizing five distinct three-dimensional
models. In the first model the columns and beams are depicted by
means of bar elements (defined in ANSYS-9.0 [1] as “beam 4”and
“beam 44”respectively) and the slabs by means of shell elements
(called “shell 63”). The “beam 4” and “beam 44” elements show
six degrees of freedom at each node: three translations and three
rotations, in directions
X, Y
and
Z.
The “shell 63” element has four
nodes, each node presenting six degrees of freedom, the same
as the bar elements. The “beam 44”element, utilized to represent
the beams, enables the eccentricity existing between the beam
axis and the average slab plane to be taken into account. Thus,
this model simulates the real situation between the slabs and the
beams, as depicted in figure [4]. It is worth commenting that, when
their axes did not coincide, the connection between the beams and
the columns was carried out using rigid bars, as figure [5] shows.
The second model only differs from the previous one by replacing
the “beam 44” element with the “beam 4” element to depict the