Civil Engineering Reference
In-Depth Information
A d
f
=ρ =
36.87 mm /m since
2
ε
f
c
2
=
0.00182 whichisdifferent from 0.002
(close to 37.63 mm /m)
36.87
32
#ofNSM tapes per meter
=
=
1.152
1000
1.152
spacing
=
=
867.9mmUse one NSMtape@850 mm.
Negative moment section at exterior support:
No. 10 bars @ 250 mm
No. of bars/m
=
1000
250
=
Area of reinforcement/m
=
100 mm
2
×
4
=
400 mm
2
/m
400
1000
4
A
bd
f
f
s
−
ρ= =
=
0.00229
s
×
175
400
25
y
ω=ρ= ×
0.00229
=
0.03657
s
c
M
fbd
n
2
R
=ω−ω=
0.59
0.03578
=
2
c
2
M
=
0.03578
×
25
×
1000
×
175
=
27,394,793.5N-mm/m
=
27.39 kN-m/m
n
wL
2
17.884
×
5.5
2
un
M
=
=
=
22.54 kN-m/m
u
24
24
φ=×
M
0.9
27.39
=
24.65 kN-m/m
>=
M
22.54 kN-m/m
n
u
Do not need strengthening at this section.
5.4.4 C
over
D
elamination
This is one of the undesirable flexural failure modes of FRP-strengthened beams
that takes place due to the shear and normal stress concentrations at the FRP curtail-
ment. This failure mode typically competes with the ductile crushing and debonding
failure modes that take place in moderately reinforced or moderately strengthened
beams. This is a controlling failure mode that can be delayed by using end-anchor-
age U-wraps. Many models have been proposed in the literature to accurately pre-
dict this failure mode (Roberts 1989; Ziraba et al. 1994; Quantrill, Hollaway, and
Thorne 1996; Täljsten 1997; Malek, Saadatmanesh, and Ehsani 1998; El-Mihilmy
and Tedesco 2001). However, these models yield inconsistent results, typically due
to the empirical nature of these models and due to the fracture nature of the failure
mode, which is difficult to capture by simplified stress analysis. It is important to
note that ACI 440.2R-08 does not adopt a separate model that designs against this
failure mode, but rather uses the same debonding strain as a limit (Figure 5.19).
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