Page 40 - Plastics Engineering

General Properties of Plastics 23

Fig. 1.7 Beam subjected to bending

maximum stress, 0, in the beam will be given by

MmaX(dl2) - MInaX(dl2)
-
(T=
I bd2/12
Assuming that we are comparing different materials on the basis that the
mean length, width and loading is fixed but the beam depth is variable then
equation (1.1) may be written as

(T = /?,Id2 (1.2)
where /?I is a constant.
But the weight, w, of the beam is given by
w = pbdL (1.3)

So substituting for d from (1.2) into (1.3)

w = /32p/(T”2 (1.4)
where Bz is the same constant for all materials.
Hence, if we adopt loading/weight as a desirability factor, Df, then this will
be given by
(Til2
Df = - (1.5)
P
where cry and p are the strength and density values for the materials being
compared.
Similar desirability factors may be derived for other geometries such as
struts, columns etc. This concept is taken further later where material costs
are taken into account and Tables 1.1 1 and 1.12 give desirability factors for a
range of loading configurations and materials.

Material Selection for Stiffness
If in the service of a component it is the deflection, or stiffness, which is
the limiting factor rather than strength, then it is necessary to look for a
different desirability factor in the candidate materials. Consider the beam situ-
ation described above. This time, irrespective of the loading, the deflection, 6,