Civil Engineering Reference
In-Depth Information
3
2
a
d
a
d
a
d
−
2.085
+
0.7626
+
0.00068
=
0
f
f
f
Solving for the lowest positive root using Excel Goal-Seek function,
a
d
=
0.47425
a
=
5.69 "
c
=
6.70"
f
0.003
10.19
−
6.7
ε=
=
0.00156
< ε=
0.00207
s
y
6.7
0.003
12 6.7
6.7
−
ε=
−
0.0008
=
0.00157
<ε
fe
fd
4,000
313, 900,000
ε=
0.083
=
0.00406
fd
×
×
0.04
Thus, brittle crushing failure is confirmed.
f
=
13,900
×
0.00157
=
21.823 ksi
fe
f
f
a
d
f
f
4
21.823
5.69
10.19
29,000 0.00156
21.823
×
c
fe
s
fe
ρ=
0.85
−ρ
=
0.85
×
×
−
0.0221
×
f
s
f
bal
=
0.0412
>ρ=
0.0134 (Example5.8)
2
A d
=ρ =
0.0412
×
16
×
10.19
=
6.714 in.
f
f
A
nt
6.714
30.04
62
12
2
h
f
f
b
==
×
=
55.95"
>>+×=
28"assuming NA @
f
2
This is an impractical strengthening case. The section that is heavily reinforced
cannot be strengthened by 10%.
5.4.3 r
upture
oF
Frp
This is one of the ductile flexural failure modes of FRP-strengthened beams, since
the internal steel reinforcement is guaranteed to yield way prior to the rupture of
FRP. It is a feature of lightly reinforced and lightly strengthened sections, which
typically happens in slabs and T-beams. Despite the ductile nature of this failure
mode, FRP rupture is sudden and catastrophic, since it is typically accompanied by
a significant release of elastic energy. Accordingly, ACI 440.2R-08 tries to lessen
the effect of this failure mode by limiting the ultimate FRP strain allowed to 90% of
the ε
fu
. This is in addition to the environmental factor
C
E
that multiplies the design
ultimate strain. The latter is known to be the mean tensile strain value minus three
times the standard deviation to guarantee a 99.87% probability of exceedance, as
shown in Chapter 3.
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