Page 85 - Plastics Engineering

68 Mechanical Behaviour of Plastics

previous questions can be used. For example, to determine the 1 year deflec-
tion of the beam in this question, the appropriate 1 year modulus from the
polypropylene creep curves could be used.
Throne has reported that the relationship between foam modulus and density
can be generalised to other properties such as tensile strength, fatigue strength,
creep properties as well as shear and compression modulus. Thus if X is the
general material property then
“=(E) 2
(2.20)
X,
Example 2.9 A solid polyethylene beam is 10 mm thick and 15 mm wide.
If it is to be replaced with a sandwich section with solid polyethylene in the
two outer skins and polyethylene foam (density = 200 kg/m3) in the centre,
calculate the dimensions of the sandwich beam if it is to have optimum stiffness
at the same weight as the solid beam. If the foam material costs 20% more than
the solid material, calculate the increase or decrease in cost of the sandwich
beam.
Solution The weight per unit length, W, for the solid beam is
W = 935 x lo3 x 15 x 10 x = 140 g/m

For the sandwich section
W = p,bh + p,2bd
W
W-2bdp ---_ 2d
h= -
PCb bP,D D
where D = density ratio (pc/ps).
The flexural stiffness of the beam will be proportional to EZ. So converting
the section to an equivalent ‘I’ beam as in the previous example

12
E,I = E, --+(;)2$]
h)3 bh3
Substituting for h from above, the stiffness may be optimised for constant W,
by differentiating this expression and equating to zero. This gives the optimum
beam depth as

1 48W 48W + 24Wd(D2 - 1)(D - 1) 1
bPsD2