Civil Engineering Reference
In-Depth Information
(
)
6
38.510
×= ×
307.9
451.5
×
163
−
0.36
×
65.06
+
0.85
×
A
f
×
519.4
(
)
×
200
−
0.36
×
65.06
+
307.9
×
129.34
×
(0.36
×
65.06
−
37)
19,636,993.8
77,957.6
251.9mm
2
260.4mm
2
195 mm
2
(actual)
A
f
=
=
≈
>>
No need to iterate.
251.9
1.3
b
f
=
=
193.8mm
≈
200mm
Use four plates of 50
×
1.3 mm covering the entire soffit of beam.
It can be concluded that the FIB model is very conservative in this case. It is also
worth mentioning that the experimental results presented by Arduini, Tommaso,
and Nanni (1997) indicate that Beam A4 does not undergo tensile steel yielding,
which is in agreement with the design calculations shown here.
5.4.5 Frp D
ebonDing
This is the fifth flexural failure mode in beams strengthened with FRP. The
debonding is initiated at one of the flexural or shear cracks along the span, as seen
in Figure 5.19b. Accordingly, it is referred to as intermediate induced cracking.
It is a dominant failure mode in moderately reinforced, moderately strengthened
beams with FRP sheets or plates extending close to the support competing with
the ductile crushing failure. This failure mode may be avoided in two ways:
(a) by keeping the maximum FRP strain below the strain of FRP debonding
as specified by ACI 440.2R-08, (b) by anchoring the beam's flexural FRP by
transverse U-wraps designed according to the adapted shear-friction model of
ACI 318-11 (Rasheed, Larson, and Peterman 2006; Rasheed et al. 2010, 2011). A
different model limits the interface shear stress after cracking to a limiting value
(Rasheed, Larson, and Nayyeri Amiri 2013). In this section, the first approach
of limiting the FRP maximum strain is explored in comparison with existing
experimental results. This limiting strain is defined by ACI 440.2R-08 to be
f
nE t
c
ε=
0.083
in U.S. units
fd
ff
f
nE t
c
=
0.41
in SI units
(5.96)
ff
The limiting FRP ratio between concrete crushing and FRP debonding may be
written as
ε
ε+ε
d
max
cu
f
a
=β
(5.97)
b
1
cu
fd
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