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IBRACON Structures and Materials Journal • 2012 • vol. 5 • nº 3
Contribution to assessing the stiffness reduction of structural elements in the global stability analysis of
precast concrete multi-storey buildings
modulation used. Table 10 shows the intervals of stiffness reduc-
tion coefficients obtained for the columns in the models analyzed.
The lowest values correspond to the highest floors, and the high-
est values correspond to the lowest floors. For the average values,
the reduction coefficients range from 0.5 to 0.6. These coefficients
are smaller than the values recommended by NBR 6118:2003 [1],
which are 0.7 to 0.8.
The effects of adopting prestressing steel and non-prestressing
steel in the precast concrete beams arranged on the central axis
of the lay-out showed in the Figure 2 are also evaluated. Figure
11 shows the section of the precast concrete beam used in all the
floors with f
ck
=35 MPa and a section composed of topping with
f
ck
=20 MPa. The non-prestressing steel uses steel CA-50.
Only the main reinforcement was used in constructing the M x N x
1/r diagram. Figure 12 shows the M x N x 1/r diagram for the beam,
which is shown in Figure 11, with a linear coefficient of creep equal
to 0 and 2. In constructing the M x N x 1/r diagram, due to the
strength differences between beams made of precast concrete
and those made with concrete cast on site, the section related to
positive bending moment was built with f
ck
=20 MPa, and the sec-
tion related to negative bending moment was built with f
ck
=35 MPa.
Table 11 shows the stiffness reduction coefficient versus the coef-
ficient of creep for positive bending moment and negative bending
moment. The significant decrease in the stiffness reduction coef-
ficient as it relates to the progression of creep can be notice.
The reduction coefficient shown by NBR 6118:2003 [1] for beams
with asymmetrical reinforcement is 0.4, a value similar to that
found for secant stiffness with positive bending moment and a lin-
ear coefficient of creep equal to 0.
Figure 13 summarizes the evaluation of the effect of using pre-
stressing steel in the cross-section of the precast concrete beam.
Table 10 – Distribution of stiffness reduction coefficient in columns
Modulation
Cross Section
Nº Floors
2
Live load (kN/m )
a
7.5
50 x 50
6
3
0.35 - 0.60
7.5
50 x 50
6
5
0.35 - 0.70
10.0
60 x 60
6
3
0.40 - 0.70
10.0
60 x 60
6
5
0.40 - 0.77
7.5
40 x 40
4
3;5
0.35 - 0.65
10.0
40 x 40
4
3;5
0.40 - 0.76
Figure 11 – Cross sectional and
reinforcement arrangement
of composite reinforced beam
for structure with modulation 7.5m
70
15 5
30
4.5
4.5
90
5 Ø 20mm
2 Ø 25mm 3 Ø 12,5mm
4.5
5 Ø 16mm
3 Ø 12,5mm
Dimensions in cm
Precast beam
Hollow core slab
Cast-in-place concrete topping
Figure 12 – M x N x 1/r diagram in composite
reinforced beam for structure
with modulation 7.5m
Table 11 – Stiffness reduction coefficient
in composite reinforced
beam for structure with modulation
7.5m and creep effect
Creep
coefficient (
j
)
0
1
2
3
M (a)
pos
0.467 0.340 0.267 0.220
M (a)
neg
0.310 0.249 0.209 0.180