Page 97 - Plastics Engineering

80 Mechanical Behaviour of Plastics

Buckling is complex to analyse but if we consider the rib as a flat plate,
clamped along one edge then Roark gives the formula for the critical buckling
stress as
1.2E 2 (2.24)
(1 - 9)
or

If we take the critical stress as the yield stress then for many plastics, the
ratio of UJE is approximately 35 x Using Poisson's ratio, u = 0.35 and
taking /I = 0.6, as before, then
h
_- h D - 0.267
d-5'2-
or
d h
- = 3.75 -
D D
This line may be superimposed on the rib design data as shown in Fig. 2.28.
Combinations of dimensions above this line are likely to provide ribs which are
too slender and so are liable to buckling. Combinations below the line are likely
to be acceptable but do remember the assumptions made in the determination
of the buckling line - in particular, the ratio of u,/E will increase with time
due to creep and this will cause the buckling line to move downwards.
Returning to the Example, it is apparent that the dimensions chosen lie
above the buckling line. It is necessary therefore, to choose other dimensions.
For example, h = 2.5 mm gives
h W
- = 0.33, - 0.66 (as before)
=
D ND
So d/D = 1.15 which gives d = 11.15(7.6) = 8.7 mm.
These dimensions lie below the buckling line and so are acceptable. The
solution would therefore be a ribbed beam with five ribs, plate thickness =
2.5 mm, rib thickness = 1.5 mm and rib depth = 8.7 mm.
It should be noted that ribbed sections play an extremely important part in
the design of plastic products. Not only do they reduce manufacturing times
(because they utilise thinner sections), but they also save material. It may easily
be shown in this case that the volume of the ribbed beam is half the volume
of the flat acetal beam and this will result in a substantial cost saving.
Fig. 2.29 shows a design chart for slightly thicker ribs (/I = 0.8) so as to
reduce the likelihood of rib buckling.