Civil Engineering Reference
In-Depth Information
()
()
()
(
)
qx
qxt
,
⎡
⎤ ⎡
⎤
y
y
⎢
⎥ ⎢
⎥
(
)
(
)
q
xt
,
qx
qxt
,
,
q B v C r K
r
=
+
=
+
⋅
+
⋅
+
⋅
(5.8)
⎢
⎥ ⎢
⎥
tot
z
z
q
ae
ae
⎢
⎥ ⎢
⎥
(
)
qx
qxt
⎣
θ
⎦ ⎣
θ
⎦
where
T
[
]
(
)
x t
,
uw
v
=
(5.9)
T
(
)
xt
,
r
r
θ
r
=
⎣
⎡
⎤
(5.10)
⎦
yz
q
(
)
⎡⎤
⎡
DBC
/
⎤
y
D
2
2
⎢⎥
VB
VB
ρ
⎢
⎥
ρ
ˆ
()
x
q
C
q
=
=
=
⋅
b
(5.11)
⎢⎥
⎢
⎥
z
L
q
2
2
⎢⎥
⎢
⎥
q
BC
⎣⎦
⎣
M
⎦
θ
(
)
(
)
(
)
⎡
⎤
2/
DBC
DBC
/
′
−
C
D
D
L
⎢
⎥
VB
VB
ρ
ρ
(
)
⎢
⎥
ˆ
()
(
)
x
2
C
C
D B C
/
B
=
′
+
=
⋅
B
(5.12)
q
L
L
D
q
2
⎢
⎥
2
⎢
⎥
2
BC
BC
′
M
M
⎢
⎥
⎣
⎦
(
)
(
)
(
)
⎡
⎤
2/
DBC
DBC
/
′
C
0
−
D
D
L
⎢
⎥
VB
ρ
(
)
⎢
⎥
()
(
)
x
2
C
C
D B C
/
0
C
=−
′
+
(5.13)
ae
L
L
D
2
⎢
⎥
⎢
⎥
2
BC
BC
0
′
M
M
⎢
⎥
⎣
⎦
(
)
00
DBC
/
⎡
′
⎤
D
2
VB
ρ
⎢
⎥
()
x
00
C
BC
K
=
′
(5.14)
⎢
⎥
ae
L
2
⎢
00
⎥
′
⎣
⎦
M
It is seen that the total load vector comprises a time invariant mean (static) part
q
⎡⎤
⎢⎥
y
2
ρ
VB
ˆ
()
x
q
q
θ
q
=
=
⋅
b
(5.15)
⎢⎥
⎢
⎣⎦
z
q
2
and a fluctuating (dynamic) part
