Basic HTML Version
18
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
er are calculated by equations 10 and 11, respectively. Figure 6
shows a simplified flow chart of the SLS-W evaluation subroutine.
(10)
cr
s
r
A
A
(11)
(12)
ctm
CG
s
s
CG
s
k
f
E
w
.3.
.
.5.12
1
1
(13)
45 4 .
.
.5.12
1
2
r
s
CG
s
k
E
w
where:
f
: diameter of the tendon that protects the considered surrounding
region;
η
1
: superficial frictional coefficient of the passive reinforcement;
E
s
: modulus of elasticity of the passive reinforcement steel;
f
ctm
: concrete average tensile strength (MPa);
The ultimate limit state (ULS) is related to the safety of the struc-
ture submitted to unfavorable combinations of actions predicted
for its entire service life. In this evaluation, permanent and variable
loads are increased and material strengths are decreased accord-
ing to their respective weighting coefficients. Figure 7 shows the
flow chart of ULS evaluation. Convergence occurs when ultimate
calculation moment is lower or equal to the resistant moment. The
resistant moment is obtained by adding incremental loads, in addi-
tion to live loading, until cracking.
3.2 French norms
In order to compare the results obtained with the Brazilian norm,
the requirements of the French norm,
BPEL 91
[11], were also ex-
amined. Table 3 presents the SLS evaluations required for mem-
bers submitted to prestressing, using the same limit state conven-
tions of NBR 6118 [10].
Tables 4 and 5 indicate the allowed stresses in concrete and steel,
as determined by the French norm, for each prestressing level.
The prestressing reinforcement protection zone or cover zone
Figure 4 – Effective tension area
of concrete around each steel bar
Figure 5 – Evaluation of the effective tension area
Figure 6 – Flow chart of the routine verification
SLS-W (Brazilian code specification)