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IBRACON Structures and Materials Journal • 2012 • vol. 5 • nº 5
Fatigue lifetime of a RC bridge along the Carajás railroad
5. Cross sections’ fatigue lifetime
To determine the fatigue lifetime of the stringers was considered,
initially, the variation of bending moment due to train operational
loaded, future loaded and unloaded. From the variation of bending
moment, it is possible to determine the strains and stresses at any
point of the cross sections. Figure 26 shows theoretical variations
of the strains, respectively, in the concrete and reinforcement of
the section S21 due to the passage of the train operational loaded.
The coordinates indicated in the legend of the Figure 26a indicate
the position (height) of the concrete fiber analyzed in relation to
the lower face of the section. According to NBR 6118 : 2003 [11]
and Model Code MC90 (CEB-FIP, 1992) [12] should be estimated
minimum and maximum stresses in an area not exceeding 300
mm from the edges of the cross section. For this reason, in the fig-
ure are shown four curves corresponding to the fibers located 300
mm from the upper and lower edges of the stringer. Since Figure
27 shows respectively the theoretical compression stresses in the
concrete and in the reinforcement of the section S21 due to the
passage of the train type operational loaded.
For a preliminary check to fatigue of concrete were considered the
prescriptions of NBR 6118 : 2003 [11]. According to this standard,
checking the fatigue of concrete is ensured if the maximum com-
pressive stress in concrete (corrected for the gradient of compres-
sive stress) does not exceed a limit fatigue stress f
cd,fad
= 0.45 f
cd
.
This check is presented in Figure 28, where the rectified stress is
provided in module (with positive sign indicating compression, in
this case). Whereas the design compressive strength for the con-
crete, i.e. f
ck
= 18 MPa and a safety coefficient γ
c
= 1.4, the fatigue
limit stress is f
cd,fad
= 5.78 MPa. Thus, according to NBR 6118 :
2003 [11], only the stresses arising from the permanent load would
already be very close to this limit in section S21. It should be re-
marked that this criterion is quite conservative, since it does not
consider the stresses variations.
As already mentioned, the section “23.5 Ultimate limit state of
fatigue” of NBR 6118 : 2003 [11] is based on the “6.7 Ultimate
Figure 2� � �ending �o�ent and shear force history for section S21 under loaded future train type passage
Ta�le 5 � Res�lts f�r elasticit� m�d�l�s �f c�ncrete
Sample
E experimental (GPa)
c
E estimated (GPa)
c
Difference (%)
NBR 8522
NBR 6118**
MC90***
NBR6118
MC90
Abutment 02 (CP01)
38,6
40,2
37,2
4,1
3,6
Abutment (CP02)
42,5
40,5
37,3
4,7
12,2
Slab (CP01)
41,0
35,1
33,9
14,3
17,3
Slab (CP02)
44,0
39,6
36,8
10,0
16,3
Stringer L.E* (CP01)
58,8
34,9
33,8
40,6
42,5
* Left side
**
[MPa]
E = 5600
c
f
c
***
3
0,1
f
c
[MPa]
E = 2,15
10
4
c