Civil Engineering Reference
In-Depth Information
Fig. 5.2
Load coefficients obtained from static tests
It follows from Eq. 5.4 that
α =
r
θ
and
α
=+
rwVrV
θ
/
−
/
. For simplicity the
f
z
following notation is introduced
()
()
()
()
()
()
⎡
C
α
α
α
⎤
⎡ ⎤
C
⎡
C
′
α
α
α
⎤
⎡ ⎤
C
′
D
D
D
D
⎢ ⎥
⎢
⎥
⎢
⎥
⎢ ⎥
C
=
C
and
C
′
=
C
′
(5.6)
⎢
⎥
⎢ ⎥
⎢
⎥
⎢ ⎥
L
L
L
L
⎢ ⎥
⎢
⎥
⎢
⎥ ⎢ ⎥
C
C
C
′
C
′
⎣ ⎦
⎣
⎦
⎣ ⎦
⎣
⎦
M
M
M
M
Combining Eqs. 5.2 - 5.6
q
⎧
⎫
⎡⎤
⎡
DC
⎤
⎡
DC
⎤
⎡
BC
⎤
′
−
y
D
D
L
⎪
⎪
⎢⎥
V
⎢
⎥
w
r
⎢
⎥
w
−
r
⎛
⎞
⎛
⎞
⎢
⎥
z
z
q
V
u
r
BC
r
BC
DC
=
ρ
+
−
+
+
−
′
+
⎨
⎬
⎢⎥
⎜
⎟
⎢
⎥
⎜
⎟
⎢
⎥
⎢
⎥
z
y
L
L
D
θ
2
VV
V
⎝
⎠
⎝
⎠
⎪
⎪
⎢⎥
⎢
⎥
⎢
⎥
⎢
⎥
q
0
2
2
BC
BC
′
⎣
⎦
⎣⎦
⎣
⎦
⎣
⎦
θ
⎩
⎭
M
M
tot
(5.7)
and discarding higher order terms (i.e. terms containing the product of quantities that
have been assumed small) the following is obtained
