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397
IBRACON Structures and Materials Journal • 2012 • vol. 5 • nº 3
P. T. C. MENDES | M. L. T. MOREIRA
|
P. M. PIMENTA
Figure 18 – 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 0.5.E ,
c
with impact, caused by {DEAD}, {DEAD +
φ
.TB360} and {DEAD +
φ
.TB450}
6304
6346
6413
4334
4368
4436
4166
4210
4284
2861
2930
3041
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 - 0,5.E
C
(kN/m
2
)
(SOL)-
ρ
1-0,5EC-C-MAX
(SOL)-
ρ
2-0,5EC-C-MAX
(SOL)-
ρ
3-0,5EC-C-MAX
(B-S)-
ρ
1-0,5EC-C-MAX
(B-S)-
ρ
2-0,5EC-C-MAX
(B-S)-
ρ
3-0,5EC-C-MAX
(SOL)-
ρ
1-0,5EC-C-MED
(SOL)-
ρ
2-0,5EC-C-MED
(SOL)-
ρ
3-0,5EC-C-MED
(SOL)-
ρ
1-0,5EC-C-MIN
(SOL)-
ρ
2-0,5EC-C-MIN
(SOL)-
ρ
3-0,5EC-C-MIN
variation of the modulus of elasticity has significant influence in the
stress values, greater as smaller the modulus of elasticity of the
concrete. Due to the symmetry of the {DEAD} load, the solicitant
efforts are distributed equally between the two longitudinal beams,
being applied approximately in its cross sectional principal planes,
which explains the similarity of the results found for models (B-S)
and (SOL).
Figure 24 presents the values of medium stresses on the reinforce-
ment obtained from models (B-S) and (SOL) in uncracked section
and in cracked section for the load {DEAD + φ.TB450}. The re-
sults present the same tendency, but the model (SOL) results are
greater (inferior to 10%) than the model (B-S) results, attributed to
the torsion effect of the positioning in the standard vehicle-load.
The convergence of the results obtained and presented in Figures
23 and 24 point to the pertinence of the models adopted.
In these figures markers in the form of asterisk relate to the models
with bar and shell elements (B-S), while the markers in the form
of a full rhombus relate to the models with solid elements (SOL).
The full lines refer to uncracked section and the dashed lines to
cracked section.
For the older bridges, built with CA-24 steel and reinforced ratio
inferior to 2.68%, the reinforcement stress calculated in cracked
section due to the actual standard vehicle-load TB450 exceeds the
value of the design yield strength of reinforcement, signaling to the
necessity of the strengthening structure.
3.4 Tensile stresses in the corroded reinforcement
Figures 25 and 26 present the minimum, medium and maximum
tensile stresses in the bars of the reinforcement for the conditions
described in 3.2, with reinforcement ratio of 2.68% in cracked sec-
tion. One observe the great difference between the reinforcement
stresses for the (SOL) model compared with the difference obtained
with the (B-S) model for each degree of reinforcement corrosion.
For the considered reinforcement ratio, for no corroded reinforce-
ment, the stresses in the most solicited bar of the reinforcement
due to the standard vehicle-loads TB360 and TB450 with the (SOL)
model are greater than the design yield strength of reinforcement
values designed with CA-24 steel, and this does not occur for the
stresses obtained with the (B-S) model.