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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
than the first part of stress limit (2/3.
f
e
) test can be considered equal
to 240 MPa. Figure 9 shows the flow chart of SLS-W evaluation.
(14)
6.0
06.0
ck
tj
f
f
(15)
tj
e
s
f
f
Min
.
110 ;
3
2
(16)
where:
f
ck
: concrete characteristic compressive strength (MPa).
f
e
: elasticity limit of the passive reinforcement (MPa);
η
: cracking coefficient (η =1.6 for highly bonded reinforcement)
f
tj
: concrete characteristic tensile strength (MPa).
In the French norm, the study of ultimate limit state is performed as
described in the Brazilian norm. Figure 10 shows the flow chart of
the ULS evaluation model. At the end of the evaluation, the values
of the ultimate moment should be compared with the resistant mo-
ment in order to determine if the beam is safe in terms of breaking.
4. Analyzed structures
In this article, the analyses of two beams removed from actual
structures – one with bonded and the other with unbonded partial
prestressing – are presented. Based on these specimens, crack
opening service limit state and ultimate limit state were evaluated,
and the results were analyzed according to both norms.
As a non-linear behavior was assumed for these actual specimens,
the simplified diagrams recommended by the norms were not built.
The strain values adopted for concrete compressive strength (ε
c0
)
and final strain (ε
cf
) were 2‰ and 10‰, respectively.
Table 5 – Steel allowable stresses – Serviceability Limit State – French Code Specification (Thonier, [12])
Active
reinforcement
Passive
reinforcement
Full
Prestressing
Limited
Prestressing
Partial
Prestressing
Quasi-permanent load combination
Frequent load combination
Rare load combination
Construction phase
Quasi-permanent load combination
Frequent load combination
Rare load combination
Construction phase
Concrete cover zone
Others zones
-
100 MPa
Δ
p < 0.10f
prg
Δ
p < 0.10f
prg
-
0.35f
e
-
1/2
Min (2/3f ; 110.(
.f ) )
e
tj
1/2
Min (2/3f ; 110.(
.f ) )
e
tj
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
Figure 8 – Concrete cover zone
(French code specification)
Figure 9 – Flow chart of the routine verification
SLS-W (French code specification)