Civil Engineering Reference
In-Depth Information
4.5.2 Nominal bending moment capacity
of bond-critical sections
One of the main assumptions at the basis of reinforced concrete mechan-
ics is a “perfect” bond between the reinforcing bars and the surrounding
concrete. Therefore, adequate embedment length of the FRP reinforcement
is required to avoid bond failure. ACI 440.1R-06 defines as bond critical
those sections where the maximum achievable stress in the FRP reinforce-
ment is limited by the following equation:
≤
f
′
l
d
C
d
l
d
c
e
e
f
=
13.6
+
+
340
f
fe
fu
(4.39)
α
b
b
b
0.083
f
′
l
d
C
d
l
d
c
e
e
or
f
=
13.6
+
+
340
≤
f
in SI units
fe
fu
α
b
b
b
where
l
e
is the length of FRP bar embedded in concrete,
d
d
is the bar diam-
eter,
C
is the lesser of the cover to the center of the bar or one-half of the
center-on-center spacing of the bars being developed, and α is a factor to
account for the bar location. α is taken equal to 1.5 for bars with more
than 12 in. (300 mm) of concrete cast below, otherwise it is taken equal to
1.0. In other words, the developable FRP bar stress,
f
fe
,
cannot be smaller
than the design FRP tensile stress,
f
f
≤
f
fu
,
as defined in Equation (4.40), to
prevent bond failure. Otherwise, corrective measures must be taken, such
as increasing the embedment length, increasing the number of bars, replac-
ing the planned bars with smaller diameter ones for the same reinforcement
area, or recomputing the nominal moment capacity based on bond strength
limitation.
When bond limits the stress that can be developed in reinforcement, the
two possible failure modes are concrete crushing or bond failure. The fail-
ure mode is concrete crushing when the condition stated in Equation (4.40)
is verified:
(
)
2
E
ε
0.85
β
f
′
f
cu
1
c
f
≥=
f
+
E
ε−
0.5
E
ε
cu
(4.40)
fe
f
ρ
f
cu
f
4
f
In this case, the nominal bending moment capacity can be computed as
per ACI 440.1R.06 Equation (8.5) reported below:
ρ
f
ff
2
(4.41)
Mf
=ρ
10.59
−
bd
n
ff
f
′
c
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