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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
data, such as material properties, are shown in Figure 17 and were
common to both evaluations, except for the values of the modulus
of elasticity of concrete.
Figure 19 presents normal stress caused by prestressing and
shear strength graphs resulting from frequent loading (Brazilian
norm), relative to the values presented in Figure 18. Because ten-
dons are straight, prestressing does not generate stresses relative
to shear strength.
Figure 20 shows first the flexural moment relative to loading (fre-
quent combination) and applied prestressing graphs, and then a
graph of the total moment, representing the sum of the first two
graphs. In the normal stress, prestressing moment and total mo-
ment graphs, the “steps” caused by the use of prestressing ten-
dons with different lengths are clearly seen. In this evaluation,
based on flexural moment values, it is observed that prestressing
strength absorbs almost 72% of total loading relative to frequent
combination.
Figure 21 presents a table with the cracking width values of all
sections, as evaluated according to the Brazilian norm, with w
k
as
the lowest value between w
k1
and w
k2
. Figure 22 shows the strain
graph of each passive reinforcement layer and the limit strain rec-
ommended by the French norm.
In the SLS-W analysis relative to the Brazilian norm, crack width
values were calculated only for the four sections located at the
ends of the beam (sections 1, 2, 34, and 35). In the modules of
these sections, where the passive reinforcement layer is stressed,
a grid with small rectangles was generated to determine the A
cr
Figure 16 – Distribution of active reinforcement
layers along the element
Table 7 – Characteristics of the active reinforcement layers
Layer
Height (cm)
Number of cables
2
Area (cm )
Date (days)
Ø (mm)
1
2
3
9
14
19
8
6
6
11.48
8.61
8.61
28
28
28
15.2
15.2
15.2
Table 8 – Load cases for verifications of Serviceability Limit State
Cases
Load cases
Initial date (days)
Final date (days)
Load cases
1
2
3
4
5
Weigth I shaped + prestressing
Weigth table
Permanent load (g)
Time effects
Variable load (q)
28
29
29
29
10,000
28
29
29
10,000
10,000
Figure 17 – Properties of materials
(Brazilian code specification)