Civil Engineering Reference
In-Depth Information
Let us first pursue the more simple solution of a direct approach based on static
influence functions. It is then taken for granted that the structure at hand is suitably
uncomplicated, rendering straight forward equilibrium equations. Let us for the sake of
simplicity consider the quasi-static load effect of the along wind component
(
)
y
qxt
on
,
the horizontal simply supported beam shown in Fig. 7.5.
Fig. 7.5
Along-wind load and two relevant response components
(
)
y
rxt
associated with
bending about the
z
-axis and shear in the direction of
y
. Let us focus on the background
quasi-static part of the cross sectional bending moment
As can be seen, the load effect is a horizontal displacement
,
(
)
M xt
at a chosen position
x
(e.g. at mid-span). It is seen from Eq. 7.14 (see also Eq. 5.12) that
,
z
B
VB
D
D
ρ
⎡
⎤
⎛
⎞
(
)
(
)
(
)
qxt
,
2
C uxt
,
C C wxt
′
,
=
⋅
⋅
+
−
⋅
⎦
(7.15)
⎜
⎟
⎢
⎥
y
D
D
L
2
B
B
⎣
⎝
⎠
As illustrated in Fig. 7.5, the bending moment
M
at a chosen position
x
is given by
z
B
(
)
( )
(
)
M
xt
,
∫
G
x q xtdx
,
=
⋅
(7.16)
z
r
M
y
B
z
L
exp
where
L
is the flow exposed part of the structure and
G
is the static influence
exp
M
z
function for
M
at
x
(defined as the function containing the values of
M
at
x
when
z
z
the system is subject to a unit load
q
1
at arbitrary position
x
).
=
y
