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IBRACON Structures and Materials Journal • 2012 • vol. 5 • nº 3
M. C. MARIN | M. K. EL DEBS
Figure 13 – Cross sectional and
reinforcement arrangement of
composite prestressed beam for
structure with modulation 7.5m
70
15 5
30
5
4.5
90
5 strands
2 Ø 25mm 3 Ø 12,5mm
5
3 Ø 16mm
3 Ø 12,5mm
Dimensions in cm
Precast beam
Hollow core slab
Cast-in-place concrete topping
4 strands
The precast concrete beam has f
ck
= 40 MPa, and the concrete
cast on the site has f
ck
= 20 MPa. Prestressing steel of the section
is made of strands CP 190 RB 12.7, and non-prestressing steel is
made of steel CA-50.
Figure 14 shows the M x N x 1/r diagram, which is modified for
prestressing steel, and Table 12 shows the stiffness reduction co-
efficients obtained using prestressing steel on the section bottom
and non-prestressing steel on the upper part of the beam.
5. Final remarks and conclusions
Based on the cross-sections, arrangements, reinforcement rates,
and materials used in this study, the following conclusions can
be drawn:
Figure 14 – M x N x 1/r diagram in composite
prestressed beam for structure
with modulation 7.5m
Table 12 – Stiffness reduction
coefficient in composite prestressed
beam for structure with
modulation 7.5m and creep effect
Creep
coefficient (
j
)
0
1
2
3
M (
a
)
pos
M (
a
)
neg
0.570
0.402
0.311
0.253
0.211
0.150
0.116
0.095
a) The procedures and recommendations of national codes regard-
ing the simplified consideration of PNL are less comprehensive
than the procedures and recommendations of international codes.
b) The reduction coefficients obtained from the M x N x 1/r dia-
gram differ from the normative indicators obtained with a sim-
plified PNL, mainly due to the effects of creep, axial force, and
prestressing steel. The reduction coefficients are influenced by
the levels of axial force and, consequently, vary according to
the combination of loads used.
c) The rate of increase in stiffness changes when the value of the
axial force is approximately 0.25.
d) According to the studies performed, increasing the level of the
axial force increases the stiffness of the sections. However,
the section’s stiffness decreases after reaching a threshold
value of axial force. In the numerical simulation evaluated
herein, a value for the dimensionless axial force of approxi-
mately 0.9 is obtained and a reversal in the trend of increas-
ing stiffness is observed.
The following conclusions are limited to the structural arrange-
ments, loads, and type of connection used in the structural system
studied herein. They serve as a basis of comparison with the coef-
ficients of stiffness from NBR 6118:2003 [1] as follows:
a) The stiffness reduction coefficients obtained for columns with
the arrangements analyzed herein showed average values
from 0.5 to 0.6.
b) The values found for the stiffness reduction coefficients in the
concrete beams, which were subjected to the effects of creep
with a linear coefficient of 0 to 3, varied from 0.45 to 0.2 for posi-
tive bending moment and 0.3 to 0.2 for negative bending mo-
ment. In the elements with prestressing steel, the reduction coef-
ficients obtained ranged from 0.55 to 0.25 for positive bending
moment, and from 0.25 to 0.1 for negative bending moment.
It is important to notice that the purpose of this study was to inves-
tigate stiffness reduction for a typical case study that has a multi-
storey precast concrete structure and a particular semi-rigid con-
nection. Therefore, the conclusions are limited, however, they can
be useful for comparisons with values from NBR 6118:2003 [1].
6. Acknowledgements
We are grateful to LEONARDI Industrialized Construction for its
developmental support of this research and to the Foundation for
Research Support in the State of São Paulo (FAPESP – Fundação
de Amparo a Pesquisa do Estado de São Paulo) for its help with
the thematic research project that encompassed this study.