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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
7. Final considerations
This paper sought to carry out a study of the
g
z
coefficient, em-
ployed to indicate the need or otherwise to consider the global sec-
ond order effects in the analysis of reinforced concrete structures.
To conduct the study, several reinforced concrete buildings of me-
dium height were processed utilizing ANSYS-9.0 [1] software.
Initially, the influence of the structural model adopted in calculating
g
z
was evaluated. On the basis of the studies done, it was ascer-
tained that less refined analyses tend to provide more conserva-
tive
g
z
values. This means that, for structures analyzed by means
of simplified models, obtaining high
g
z
values does not necessarily
mean significant second order effects. As such, on adopting simpli-
fied models, it is up to the technical medium to be aware that using
them can, in many cases, prove disadvantageous and uneconomi-
cal, resulting in quite relevant second order effects, when in fact
they should not be so.
On putting the project into practice, more sophisticated models (in
which the slabs are depicted as shell elements and the eccentric-
ity existing between the beam axis and the average slab plane is
considered), although they involve more computer work, should be
preferably be utilized, since they depict the actual behaviour of the
structures more accurately and provide much lower
g
z
values than
those obtained by more simplified models, which leads to greater
savings and, in many cases, dispenses with carrying out analyses
that consider second order effects approximately or otherwise.
Next, a comparative analysis was done of the
g
z
coefficient and the
B
2
coefficient, commonly employed to evaluate second order ef-
fects on steel structures. To conduct the study, initially an equation
relating these parameters was developed. Later, the values of
g
z
and
B
2
for several reinforced concrete buildings of medium height
were calculated. From the results obtained, it was observed that
the average values of the
B
2
(
B
2,avg
) coefficients showed close prox-
imity in relation to
g
z
and that, in all cases, the
g
z
and
B
2
parameters
provided the same classification as the structures.
However, an important aspect deserves to be highlighted concern-
ing the
g
z
coefficient: contrary to the
B
2
coefficient, it presents a
single value for the entire structure, although, as found in several
works (Carmo [15], Lima & Guarda [16] and Oliveira [17]), second
order effects suffer variations along the height of the buildings. This
means that, should the
g
z
coefficient be utilized as magnifier of first
order moments, as Oliveira [7] suggests, the final moments at some
storeys could be underestimated, and overestimated at others.
Thus, a better estimate of the final moments could be made utilizing both
coefficients
g
z
and
B
2
, which is calculated for each storey of the structure
and whose average value is approximately
g
z
. The magnifier of the first
order moments would then be differentiated for each storey
i
of the struc-
ture, and given as
(B
2,i
/B
2,avg
).
g
z
. Although more specific studies on the
Table 5 – Calculation of the
coefficient, from the values of B , in direction Y, for building I
z
2
Storey
F
hid,y
(kN)
B
2,i,y
16 n
i j
y, hjd
F
(kN)
7985.94
16
,
,
n
i j
y hjd
yi
F
c
y,i,2
y,i
B
c
1st
66.10
44.07
44.13
46.04
49.48
52.47
55.13
57.55
59.76
61.82
63.73
65.54
67.24
68.85
70.39
35.57
1.05
1.13
1.18
1.19
1.20
1.19
1.18
1.16
1.15
1.13
1.12
1.10
1.08
1.07
1.06
1.08
907.87
841.77
797.71
753.58
707.54
658.06
605.59
550.45
492.91
433.14
371.33
307.59
242.06
174.82
105.96
35.57
0.114
0.105
0.100
0.094
0.089
0.082
0.076
0.069
0.062
0.054
0.046
0.039
0.030
0.022
0.013
0.004
0.108
0.093
0.085
0.079
0.074
0.069
0.064
0.059
0.054
0.048
0.042
0.035
0.028
0.020
0.012
0.004
2nd
3rd
4th
5th
6th
7th
8th
9th
10th
11th
12th
13th
14th
15th
16th
16 n
1i
y,i,2
y,i
y,z
B
c
1
=
0.875
z,y
=
1.14