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IBRACON Structures and Materials Journal • 2012 • vol. 5 • nº 3
Pontes de concreto armado: efeitos da corrosão e da variação do módulo de elasticidade do concreto
which reduces the maximum values of the stresses that vary from
6.30 to 6.41 MPa.
Figures 19 and 20 show the variations of minimum, medium and
maximum compressive stresses in the top of the flange consid-
ering a longitudinal beam with geometric reinforcement ratio ρ
3
= 2.68% variable with the corrosion, modulus of elasticity of con-
crete E
c
and 0.5.E
c
to the cracked section and load cases {DEAD},
{DEAD + φ.TB360} and {DEAD + φ.TB450}.
Considering the case of combination loads {DEAD + φ.TB450}
the maximum compressive stress varies from 6.41 MPa (Figure
20) with non corroded reinforcement to 6.98 MPa (Figure 19) with
the first layer totally corroded, for modulus of elasticity of concrete
0.5.E
c
and E
c
respectively, which indicates little influence on the
corrosion of the reinforcement and modulus of elasticity of the con-
crete in the variation of intensity of these stresses.
3.3 The tensile stresses on the non corroded
reinforcement
In the solid element model (SOL), the tensile stresses are supplied
for each bar, which facilitates in the determination of the medium,
maximum and minimum values, according to what is presented in
Figures 21a and 22a, to the non cracked section, and 21b and 22b
to the cracked section, corresponding to the loads {DEAD} and
{DEAD + φ.TB450}.
One observe that the existence of cracks in the section completely
changes the distributions of the stresses on the bars, making the
more requested bar, that before the cracks belonged to the more
distant layer of the neutral axis (L-1), becomes a bar situated in the
nearest layer (L-7) arising from the stress redistribution due the
presence of the crack and of the torsion effect of the positioning of
the standard vehicle-load in the bridge. The deformation coming
from the torsion provokes the warping of the section, invalidating
the hypothesis of maintenance of the plane section.
Figure 23 presents the values of the medium stress on the rein-
forcement obtained with the models (B-S) and (SOL) in uncracked
and in cracked sections, for the load {DEAD}. For cracked section
the results obtained with the two models and different modules
of elasticity are equivalent. For uncracked section, however, the
values obtained with the two models are also equivalent but the
Figure 17 – Variation of minimum, medium and maximum longitudinal compressive stress in the top
of the slab versus
ρ
for (B-S) and (SOL) models, in cracked section, modulus of elasticity
E , with impact, caused by {DEAD}, {DEAD +
φ
.TB360} and {DEAD +
φ
.TB450}
c
6790
6853
6940
5013
5115
5274
4662
4746
4867
3458
3594
3789
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
DEAD-
ρ
1-TOT
DEAD+
φ
.TB360-
ρ
1-TOT
DEAD+
φ
.TB450-
ρ
1-TOT
DEAD-
ρ
2-TOT
DEAD+
φ
.TB360-
ρ
2-TOT
DEAD+
φ
.TB450-
ρ
2-TOT
DEAD-
ρ
3-TOT
DEAD+
φ
.TB360-
ρ
3-TOT
DEAD+
φ
.TB450-
ρ
3-TOT
σ
c
(kN/m
2
VARIATION OF THE MÍN, MÉD AND MÁX COMPRESSIVE
STRESS IN THE TOP OF THE SLAB WITH A REINFORCEMENTE
RATIO
ρ
- CRACKED SECTION -
φ
=1.26 - (B-S) AND (SOL)
MODELS - E
C
(kN/m
2
)
(SOL)-
ρ
1-EC-C-MAX
(SOL)-
ρ
2-EC-C-MAX
(SOL)-
ρ
3-EC-C-MAX
(B-S)-
ρ
1-EC-C-MAX
(B-S)-
ρ
2-EC-C-MAX
(B-S)-
ρ
3-EC-C-MAX
(SOL)-
ρ
1-EC-C-MED
(SOL)-
ρ
2-EC-C-MED
(SOL)-
ρ
3-EC-C-MED
(SOL)-
ρ
1-EC-C-MIN
(SOL)-
ρ
2-EC-C-MIN
(SOL)-
ρ
3-EC-C-MIN