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IBRACON Structures and Materials Journal • 2013 • vol. 6 • nº 1
P. M. LAZZARI | A. CAMPOS FILHO | F. P. S. L. GASTAL | R. A. BARBIERI | R. C. SCHWINGEL
Characteristic compressive strength of the used concrete is
4 kN/cm² and its tension strength was not considered. The value
of the modulus of elasticity of concrete, calculated from
f
ck
, was
3542 kN/cm
2
and 3762 kN/cm
2
from SLS, for the Brazilian and
French norms, respectively. Final concrete strength was esti-
mated as 0.5 kN/cm².
Passive reinforcement used CA-50 steel. The modulus of elastic-
ity of the prestressed reinforcement is 21,000 kN/cm² and its yield
strain calculation is based on yield stress and modulus of elastic-
ity. It is generally considered that stressed concrete has a brittle
behavior.
Prestressed steel type CP-190RB with a modulus of elasticity
equal to 19,500 kN/cm² was used. Its yield stress, which corre-
sponds to 90% of the prestressing steel strength (
f
pu
=190 kN/cm²),
is equal to 171 kN/cm². Conventional yield strain and prestressing
steel breaking strain values were considered as 0.01 and 0.07,
respectively.
4.1 Bonded partially prestressed beam
The first situation analyzed pertains to a simply supported bonded
partially prestressed beam used in the roof of the Feevale theater,
built in front of Feevale University campus, Novo Hamburgo, state
of Rio Grande do Sul, Brazil [13]. The precast beam has a 31.8
span length and is submitted to permanent (g = 15.6 kN/m) and
variable (q = 6.9 kN/m) loadings distributed along its length, as
shown the diagram in Figure 11.
Figure 12 present the beam’s cross section, initially consisting of
a 1.50-m high precast section I with passive and active reinforce-
ments. After the beam was set on the lateral foundations, the upper
compression flange was added by placing concrete of the cover
slab, which was 15-cm thick and 3.4-m wide (between beam axes).
The beam span was modeled using a hybrid single finite element
linked by nodes 1 and 2, as shown in Figure 13. The element was
divided into 35 cross sections distributed in five integration mod-
ules along the element in order to comply with the geometry of the
straight section of the prestressing tendons.
Total beam cross section, section I and compression flange were
divided into 18 horizontal planes and in six modules along its
height, as shown in Figure 14. The horizontal planes are placed
at the ends and at the center of each module, overlapping where
the modules meet. The cross section of section I consists of five
integration modules with two layers each, and the flange was mod-
eled as a single module consisting of two layers. The numerical
integration rule of Gauss-Lobatto was chosen because it is more
accurate that the Simpson’s rule and because it is recommended
when the integration points are not evenly distributed.
Figure 10 – Flow chart of the routine verification
ULS (French code specification)
Figure 11 – Simply supported beam
Figure 12 – Beam cross-section (cm)
Figure 13 – F.E. modeding of the beam