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IBRACON Structures and Materials Journal • 2013 • vol. 6 • nº 1
Automation of the evaluation of bonded and unbonded prestressed concrete beams, according to brazilian
and french code specifications
area required for w
k
calculation. The maximal crack width value
found in the analysis (w
k
= 0.000125 mm) was lower than that es-
tablished by the Brazilian norm (w
k,lim
= 0.2 mm), thereby ensuring
the member safety regarding SLS-W.
In the French norm, SLS-W is evaluated only by comparison of
reinforcement stresses, and therefore, the discretization of each
stressed reinforcement module in an extremely refined grid is not
required. Analyzing the strain graphs of each passive reinforcement
layer, it is observed that layers 7, 8, 9, 10, and 11 present tensile
stresses in the sections located at the beam’s ends. In these sec-
tions, reinforcement layer tensile stress was compared with limit
stress. As the corresponding limit strain is equal to 1.143‰, that
is, much higher than the obtained maximal strain (0.538‰), beam
safety is ensured relative to SLS-W.
Figures 23 and 24 show the cracking tables calculated according
to the Brazilian and French norms, respectively. It is observed that
the central sections are not cracked. Crack width was determined
for the upper edge of the regions close to the foundations.
Based on the cracking tables of this example, it was found that
most sections were still completely compressed at the end of SLS
evaluation. In addition, according to both Brazilian and French
norms, most lower and central fibers were still compressed (-1),
differently from the upper fibers, close to the foundations, which
already presented some cracking (2).
Figure 25 shows a photograph of the assembly of the cover beams
in the structure of Feevale theater in Novo Hamburgo, RS, Brazil.
The beams arrived at the site with an initial hogging of approximately
4cm, and sagging was virtually null after total load was applied.
After ULS verification was analyzed according to the Brazilian and
French norms, ultimate moment values were compared with resis-
tant moment values. According to the criteria of the Brazilian norm,
the resistant moment (9,460 kN.m) was compared with ultimate
moment (8,015 kN.m) and an additional safety factor equal to 1.18
was obtained for breaking. When using the French norm, the re-
sistant moment value (9,896 kN.m) was 1.26 times higher than the
ultimate moment (7,860 kN.m), which is lower than that obtained
with the Brazilian norm due to different load increment coefficients.
As in both cases ultimate moment was lower than the resistant mo-
ment, element safety regarding rupture is ensured.
4.2 Unbonded partially prestressed beam
In order to illustrate the use of unbonded reinforcement in evalu-
Figure 18 – Cross-sections forces (kN, cm) - Brazilian code specification (frequent load combination)
Figure 19 – Axial and Shear forces - Brazilian code
specification (frequent load combination)