5003 Lectures - Faculty of Engineering and Applied Science

E5003 - Ship Structures I 115
© C.G. Daley
We can use the boundary conditions (θ3=1, δ2=0, δ(L)=0, θ(L)=0) to find M3
and F2.
⎛
2
1
⎞
⎜
L
θ ( L)
= 0 = 1+
− + ⋅ ⎟
⎜
M 3L
F2
EI
⎟
⎝
2 ⎠
⎛ 2 3
1
⎞
⎜
L L
δ ( L)
= 0 = 0 + L + − M + ⋅ ⎟
⎜ 3 F2
EI
⎟
⎝ 2 6 ⎠
These two equations can be solved to get;
from these we can find;
M
M
4EI
L
6EI
F =
L
3 = , 2 2
2EI
L
Q ( x)
= F
F
− 6EI
=
L
6 = , 5 2
This allows to find the stiffness terms;
k 33
4EI
=
L
, k 63
2EI
=
L
k 23
6EI
= 2
L
, k 53
− 6EI
= 2
L
, k 13 = k 43 = 0
2
M ( x)
= −M
3 + F2
⋅ x
⎛
2
1
⎞
⎜
x
θ ( x) = θ + − + ⋅ ⎟
3 M
⎜ 3x
F2
EI
⎟
⎝
2 ⎠
⎜ 1 ⎛
δ
( x) = δ2
+ θ3x
+ − M
EI ⎝
3
⎟ 2 3
x x ⎞
+ F2
⋅
2 6 ⎠