Civil Engineering Reference
In-Depth Information
*
*
HH
2
ª
HBH
º
B
ª
º
ρ
1
2
()
1
2
C
V
=
=
⋅
ω
⋅
«
»
(C.12)
«
»
ae
r
AA
2
*
2
*
BABA
¬
¼
«
»
1
2
¬
¼
1
2
ª
*
º
0
H
2
0
BH
B
ª
º
ρ
3
2
()
3
K
=
=
⋅
ω
V
⋅
(C.13)
«
»
«
»
ae
r
0
A
2
2*
0
B A
«
»
¬
¼
3
¬
¼
3
Thus,
2*
*
ª
º
2
H
BH
B
φ
φ φ
ρ
C
()
z
1
z
θ
2
V
³
dx
=
⋅
ω
(C.14)
«
»
ae
r
2
*
2
2
*
BA
B A
«
φφ
φ
»
¬
¼
L
θ
z
1
θ
2
exp
and
*
2
ª
0
BH
º
B
φφ
ρ
K
2
()
z
3
θ
V
³
dx
=
⋅
ω
«
»
(C.15)
ae
r
2
22*
3
0
φ
BA
«
»
¬
¼
L
θ
exp
Defining
2
mM x
/
³
jz
θ
or
=
φ
=
(C.16)
j
j
j
L
and the abbreviations
-
°
°
2
³
dx
φ
z
2
ω
½
B
m
ρ
L
r
*
exp
h
H
=⋅ ⋅
β
β
=
⋅
°
°
°
1
zz
1
zz
2
2
°
°
°
®
°
°
³
dx
φ
z
z
ω
L
r
*
h
=⋅ ⋅
β
H
where
(C.17)
¾
°
°
2
z
2
θ
2
³
dx
φφ
z
θ
2
3
B
m
ω
ρ
L
exp
r
*
h
H
=⋅ ⋅
β
°
°
°
¯
β
=
⋅
°
¿
z
3
z
θ
3
θ
2
2
³
dx
φ
z
z
L
-
°
°
³
dx
φφ
θ
z
3
ω
½
B
m
ρ
L
*
r
exp
a
A
=⋅ ⋅
β
β
=
⋅
°
°
°
1
θ
z
1
z
2
θ
2
°
°
°
®
°
°
³
dx
φ
θ
θ
ω
L
r
*
a
A
=⋅ ⋅
β
where
(C.18)
¾
°
°
2
2
θθ
2
2
³
dx
φ
θ
2
4
B
m
ω
ρ
L
exp
*
r
a
A
β
=
⋅
=⋅ ⋅
β
°
¿
°
°
°
¯
3
θθ
3
θθ
2
2
³
φ
dx
θ
θ
L
