Civil Engineering Reference
In-Depth Information
t
δ
s
O
t
v
t
δ
x
δ
s
δ
x
C
v
∂
t
δ
s
+
δ
x t
δ
s
x
∂
(
v
t
)
∂
E
v
t
δ
x
δ
s
δ
x
s
∂
y
x
y
0
x
y
V
z
z
z
(a) Shear stress distribution
(b) Horizontal equilibrium
Figure 5.11
Shear stresses in a thin-walled open section.
caused by a vertical shear force
V
z
can be obtained from the shear flow
τ
v
t
=−
V
z
I
y
s
zt
d
s
.
(5.16)
0
This can also be expressed as
τ
v
=−
V
z
A
s
z
s
I
y
t
(5.17)
in which
A
s
is the area from the free end to the point
s
and
z
s
is the height of the
centroid of this area above the point
s
.
At a junction in the cross-section wall, such as that of the top flange and the
weboftheI-sectionshowninFigures5.12and5.13,horizontalequilibriumofthe
zero area junction element requires
(τ
v
t
f
)
21
δ
x
+
(τ
v
t
f
)
23
δ
x
=
(τ
v
t
w
)
24
δ
x
(5.18)
This can be thought of as an analogous flow continuity condition for the corre-
sponding shear flows in each cross-section element at the junction, as shown in
Figure 5.13c, so that
(τ
v
t
f
)
21
+
(τ
v
t
f
)
23
=
(τ
v
t
w
)
24
(5.19)
which is a particular example of the general junction condition
(τ
v
t
)
=
0
(5.20)
in which each shear flow is now taken as positive if it acts towards the junction.
Search WWH ::
Custom Search