1. 8
2
1
qL
M +=
8
2
2
qL
M −=
[ ]
[ ])3(12
12
)3(12
12
22
22
22
21
aLcba
L
qc
M
bLcab
L
qc
M
−+−=
−++=
[ ]2
21 )(4
8
cLba
L
qbc
M −++= [ ]2
22 )(4
8
cLab
L
qac
M −+−=
30
20
2
2
2
1
qL
M
qL
M
−=
+=
15
2
1
qL
M +=
120
7 2
2
qL
M −=
8
8
2
1
PL
M
PL
M
−=
+=
16
3
1
PL
M +=
16
3
2
PL
M −=
2
2
2
2
2
1
L
bPa
M
L
Pab
M
−=
+=
)(
2 21 bL
L
Pab
M ++= )(
2 22 aL
L
Pab
M +−=
)
3
2(
)
3
2(
2
1
L
a
L
Ma
M
L
b
L
Mb
M
−+=
−+=
)
3
1(
2 2
2
1
L
bM
M −= )
3
1(
2 2
2
2
L
aM
M −=
)( 12 ttt −=Δ
t
h
EI
M
t
h
EI
M
Δ=
Δ−=
α
α
2
1 .
t
h
EI
M Δ−= α
2
3
1 t
h
EI
M Δ+= α
2
3
2
L
Ta
T
L
Tb
T
+=
+=
2
1
TT +=1 TT +=2
L
Pa
N
L
Pb
N
+=
+=
2
1
L
Pa
N
L
Pb
N
+=
+=
2
1
L
Pa
N
L
Pb
N
+=
+=
2
1
12
12
2
2
2
1
qL
M
qL
M
−=
+=θ
θ
L
EI
M
3
+=M
ρ ρ2
3
L
EI
M =
M
θ
θ
θ
L
EI
M
L
EI
M
2
4
21
11
+=
+=
11M 21M
ρ×+== 22111
6
L
EI
MM
11M
21M
ρ
θ
ϕ
ϕ
L
GJ
TT =−= 1222
Δ
Δ=−=
L
EA
NN 1222
θ
θ θ
sM1
ASM
sM 2
ASM
θ
θ
L
EI
M
L
EI
M
S
S
2
2
2
1
−=
+=
θ
θ
L
EI
M
L
EI
M
AS
AS
6
6
+=
+=