5003 Lectures - Faculty of Engineering and Applied Science

E5003 - Ship Structures I 58
© C.G. Daley
Moments are vectors, adding in the same way that force vectors do.
M z = M w sin θ lateral bending
M = M cos θ vertical bending
y
w
Stresses in the Vessel
Both My and Mz cause bending stresses in the x (along ship) direction.
σ
V
− M
=
I
NA
y
z
σ
H
M
= +
I
Note: Sign convention: R.H.R., moment acting on +x cut face, compression is
positive.
In this case a +My causes tension (-) on the +z part of the vessel. A +Mz causes
compression (+) on the +y side of the vessel.
The total axial stress at any point on the vessel is the sum of the stresses caused by
the two directions of bending.
σ
X
= σV
+ σ H
− M y z M z y
= +
I NA I CL
− M w z cos θ M w y sin θ
=
+
I
I
NA
CL
z
CL
y