Civil Engineering Reference
In-Depth Information
P
u
1.5"
#3 ties @ 5.5"
M
u
V
u
9'
8#7
12"
V
u
M
u
1.5"
P
u
14"
FIGURE 6.4
Example 6.2 showing the column section and profile.
Solution:
Case A
:
N
u
=
P
u
=
18 7. 5 k
187,500
2, 000 14
( (
)
φ= ××+
V
c
0.75
21
4,000 12
11.69
=
20,734.54 lb
=
20.73 k
(
)
×
12
φ>=
VV
c
18.75 k
u
V
c
ButV
>φ =
10.37 k
Minimum reinforcement is provided.
u
2
Case B
:
N
u
=
P
u
=
24 k
24,000
2, 000 14
( (
)
φ= ××+
V
c
0.75
21
4,000 12
11.69
=
14,258.7lb
=
14.26 k
(
)
×
12
φ<
V
c
18.75 k
0.75
×
0.22
×
40
×
11.69
(
)
φ+=
VV
c
14.26
+
=
28.29 k
>
18.75 k
s
5.5
No external shear strengthening is required. This is an atypical situation, since
shear demand is not significantly increased in columns. However, an AASHTO
(American Association of State Highway and Transportation Officials) extreme
load event on bridge piers may demand high-impact lateral force on the column,
which translates into external shear strengthening.
Example 6.3: Analysis
Norris, Saadatmanesh, and Ehsani (1997) tested three beams deficient in shear,
two of which were externally strengthened in shear using CFRP. The control beam
was designated by C48, and the strengthened beams were designated by IE and
IIE. The strengthened beams had two layers of CFRP U-wrap transverse fabric
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