Page 73 - Ship Construction.DJ Eyres 6Ed

Ch08-H8070.fm Page 62 Wednesday, October 18, 2006 7:29 AM
62 Ship Construction
bending moment, vertical shear force, and stresses. Classically the extreme
effects can be illustrated with the vessel balanced on a wave of length equal
to that of the ship. If the crest of the wave is amidships the buoyancy forces
will tend to ‘hog’ the vessel; if the trough is amidships the buoyancy forces
will tend to ‘sag’ the ship (see Figure 8.2). In a seaway the overall effect is an
increase of bending moment from that in still water when the greater buoy-
ancy variation is taken into account.
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Longitudinal Shear Forces
งานห้องสมุด ศูนย์ฝกพาณิชย์นาวี
When the vessel hogs and sags in still water and at sea shear forces similar
to the vertical shear forces will be present in the longitudinal plane (see
Figure 8.2). Vertical and longitudinal shear stresses are complimentary
and exist in conjunction with a change of bending moment between
adjacent sections of the hull girder. The magnitude of the longitudinal
shear force is greatest at the neutral axis and decreases towards the top
and bottom of the girder.

ึ
Bending Stresses

From classic bending theory the bending stress (s) at any point in a beam is
given by:

M
s = ----- × y
I
where M = applied bending moment.
y = distance of point considered from neutral axis.
I = second moment of area of cross-section of beam about the
neutral axis.
When the beam bends it is seen that the extreme fibres are, say in the
case of hogging, in tension at the top and in compression at the bottom.
Somewhere between the two there is a position where the fibres are neither
in tension nor compression. This position is called the neutral axis, and at
the furthest fibres from the neutral axis the greatest stress occurs for plane
bending. It should be noted that the neutral axis always contains the centre
of gravity of the cross section. In the equation the second moment of area (I)
of the section is a divisor; therefore the greater the value of the second
moment of area the less the bending stress will be. This second moment of
2
area of section varies as the (depth) and therefore a small increase in
depth of section can be very beneficial in reducing the bending stress.
Occasionally reference is made to the sectional modulus (Z) of a beam; this