Page 90 - Plastics Engineering

Mechanical Behaviour of Plastics 73

10
9
,a
J
P7
s
'6

4 6 a 10 12 14 16 ia
Length to thickness ratb (Ud)

Fig. 2.23 Variation of insertion force with beam dimensions

It is also necessary to check that the stress in the snap fit does not exceed
the yield strength for the material (30 MN/m2). Allowing for a safety factor of
2, the maximum permissible stress will be 15 MN/m2.
The stress in a cantilever beam of this type will be maximum at point A
(Fig. 2.22) and is given by
MY
stress, UA = -
I
where M = bending moment (= VL)
y = half depth of beam (= d/2)
I = second moment of area (= bd3/12)

(2.22)

For the conditions given, OA = 13.5 MN/m2 which is less than the permitted
maximum of 15 MN/m2 and so the chosen dimensions are acceptable. Note that
the stress is independent of the width, b. Fig. 2.24 gives a set of design curves
for the situation considered so that it may be seen that other combinations of
L, d and b could be chosen to meet the design specification. For example,
L = 22 mm, d = 2.5 mm and b = 12 mm gives an insertion force of 4 N and
a maximum stress of 14 MN/m2 which is again acceptable.