5003 Lectures - Faculty of Engineering and Applied Science

E5003 - Ship Structures I 60
© C.G. Daley
Peak Stresses
The highest stresses will occur @ y=∀B/2 , Z=Zdeck
There are 2 section modulus values;
I
z
Z NA = NA
deck
,
Z CL =
I
B
CL
So that we can write;
⎛ cos θ sin θ ⎞
σ = ⎜ + ⎟
max M w
⎝ Z NA Z CL ⎠
2
This leads to the question: What is the worst angle of heel (θcr)?
To find it we use;
dσ ⎛
⎞
max
− sin θcr
cos θcr
= 0 = M ⎜ + ⎟
w
,
dθ
⎝ Z NA Z CL ⎠
which gives;
Z
tan θcr
=
Z
NA
CL
Typically Z ≅ 0.
5 so θ cr
NA CL Z
= 26 . 6
M w
For example, if σ = then θ =0
Z
⎟
NA
⎟
⎛ − sin 26 . 6 cos 26 . 6 ⎞
σ = ⎜
θ = 26 . 6 M w
+
⎝ Z NA 2 ⋅ Z NA ⎠
M w = 1.
12
Z
i.e. for this vessel, there is a 12% increase in stress during the worst roll.
NA