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IBRACON Structures and Materials Journal • 2013 • vol. 6 • nº 1
P. M. LAZZARI | A. CAMPOS FILHO | F. P. S. L. GASTAL | R. A. BARBIERI | R. C. SCHWINGEL
stress value of 0.5
f
ck
was adopted because the validity of the for-
mulation to consider strains caused by concrete yield is limited.
The Brazilian norm recommends the use of the lower concrete
tensile strength value,
f
ctk,inf
, as concrete tensile strength value,
f
ct
, shown in equation (9). Because the
f
ctk,inf
value corresponds
to 70% of the
f
ctm
value, and it needs to be multiplied by a factor
equal to 1.5 in rectangular sections, resulting in 1.05
f
ctm
, the aver-
age tension strength
f
ctm
was adopted, thereby favoring safety in
5%. It must be mentioned that this tension limit is calculated when
concrete is at State I, that is, it is not cracked and its materials
present linear elastic behavior.
(9)
3/2
3.0
ck
ctm
ct
f
f
f
where:
f
ctm
: concrete average tensile strength (MPa);
f
ck
: concrete characteristic compressive strength (MPa).
In order to evaluate the service limit state of crack width, a sub-
routine that checks members with partial prestressing under fre-
quent combination was implemented, considering item 17.3.3 of
NBR 6118 [10]. The criteria presented in the norm are acceptable
evaluations of the element’s general behavior, as crack width is
influenced by restrictions on structural volumetric variations and by
execution conditions.
According to NBR 6118 [10], for each element or group of ele-
ments of the bonded active and passive reinforcement that con-
trol structural element cracking, except for unbonded tendons, a
A
cr
area of the surrounding concrete, determined by a rectangle
which sides are closer than 7.5fi of the reinforcement tendon
axis, is considered. Figure 4 shows the surrounding concrete
area described.
Figure 5 illustrates the automatic procedure used for the calcu-
lation of the A
cr
area. In each module of the cross section with
stressed reinforcements, a grid with small rectangular elements
is generated. This grid allows an approximate identification of
the region of the A
cr
area in each tendon. Then, all the reinforce-
ment tendons are checked to verify which are stressed, and the
rectangles that are in their surrounding area are marked; over-
lapping areas are not taken into consideration. At the end of
the process, the sum of the areas with marked rectangles cor-
responds to the A
cr
area.
According to item 17.3.3.2 of the Brazilian norm, characteristic
crack width values,
w
k1
and
w
k2
(equations 12 and 13) are calcu-
lated, and the lowest value is used for comparison. Reinforcement
rate and reinforcement stress at the center of gravity of the lay-
Table 1 – Verification of Serviceability Limit State – Brazilian Code Specification [10]
Prestressing Type/EEC
Load Combination
Serviceability Limit State
(SLS)
Partial
Prestressing
Pre-tension with EEC I or
Post-tension with EEC I and II
Frequent load
combination
SLS-W (w ≤ 0.2 mm)
k
Limited
Prestressing
Pre-tension with EEC II or
Post-tension with EEC III and IV
Frequent load
combination
SLS-F
Quasi-permanent load
combination
SLS-D
Full
Prestressing
Pre-tension with EEC III and IV
Rare load combination
SLS-F
Frequent load
combination
SLS-D
Table 2 – Concrete allowable stresses – Serviceability Limit State – Brazilian Code Specification [10]
Partial
Prestressing
Limited
Prestressing
Full
Prestressing
Compression
Quasi-permanent load combination
0.5 f
ck
Frequent load combination
Rare load combination
Tension
Quasi-permanent load combination
-
0
-
Frequent load combination
-
f
ct
0
Rare load combination
-
-
f
ct