Civil Engineering Reference
In-Depth Information
The maximum shear stress is
(τ
v
)
d
f
/
2
=
(
V
z
/
I
y
)(
d
f
t
f
b
/
2
+
d
f
t
w
/
8
)
t
w
Avertical equilibrium check is provided by finding the resultant of the web shear
flow as
d
f
V
w
=
(τ
v
t
w
)
d
s
w
0
=
(
V
z
/
I
y
)
[
d
f
t
f
bs
w
/
2
+
d
f
t
w
s
w
/
4
−
s
w
t
w
/
6
]
d
f
0
=
(
V
z
/
I
y
)(
d
f
t
f
b
/
2
+
d
f
t
w
/
12
)
=
V
z
when
I
y
=
d
f
t
f
b
/
2
+
d
f
t
w
/
12 is substituted.
5.12.7 Example 7 - shear stress in a channel section
Problem
. Determine the shear flow distribution in the channel section shown in
Figure 5.14.
Solution
.Applying equation 5.15 to the top flange,
s
f
τ
v
t
f
=−
(
V
z
/
I
y
)
(
−
d
f
/
2
)
t
f
d
s
f
=
(
V
z
/
I
y
)
d
f
t
f
s
f
/
2
0
(τ
v
t
f
)
b
=
(
V
z
/
I
y
)
d
f
t
f
b
/
2
s
w
τ
v
t
w
=
(
V
z
/
I
y
)(
d
f
t
f
b
/
2
−
(
−
d
f
/
2
+
s
w
)
t
w
d
s
w
)
0
=
(
V
z
/
I
y
)(
d
f
t
f
b
/
2
+
d
f
s
w
t
w
/
2
−
s
w
t
w
/
2
)
(τ
v
t
w
)
d
f
=
(
V
z
/
I
y
)(
d
f
t
f
b
/
2
+
d
f
t
w
/
2
−
d
f
t
w
/
2
)
=
(
V
z
/
I
y
)(
d
f
t
f
b
/
2
)
=
(τ
v
t
f
)
b
which provides a symmetry check.
A vertical equilibrium check is provided by finding the resultant of the web
flows as
d
f
V
w
=
(τ
v
t
w
)
d
s
w
0
=
(
V
z
/
I
y
)
[
d
f
t
f
bs
w
/
2
+
d
f
s
w
t
w
/
4
−
s
w
t
w
/
6
]
d
f
0
=
(
V
z
/
I
y
)(
d
f
t
f
b
/
2
+
d
f
t
w
/
12
)
=
V
z
when
I
y
=
d
f
t
f
b
/
2
+
d
f
t
w
/
12 is substituted.
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