Page 176 - Plastics Engineering

Mechanical Behaviour of Plastics 159

An underground polypropylene storage tank is a sphere of diameter 1.4 m. If it is to be
designed to resist an external pressure of 20 kN/m2 for at least 3 years, estimate a suitable value
for the wall thickness. Tensile creep data may be used and the density of the polypropylene is
904 kg/m3.
2.9 A polypropylene bar with a square section (10 mm x 10 mm) is 225 mm long. It is pinned
at both ends and an axial compressive load of 140 N is applied. How long would it be before
buckling would occur. The relationship between the buckling load, Fc, and the bar geometry is

F, = R=EI/L’
where L is the length of the bar and I is the second moment of area of the cross-section.
2.10 Show that a ratio of depth to thickness equal to 10 is the nod limit if buckling is to be
avoided during short-term loading of plastics. What is likely to happen to this ratio for long-term
loading? You should consider the situation of buckling of a strut fixed at both ends for which the
critical buckling load is given by
4n2EI
P, = -
L2
2.11 Show that the critical buckling strain in a strut with pinned ends is dependent only on
the geometry of the strut.
A polypropylene rod, 150 mm long is to be designed so that it will buckle at a critical strain of
0.5%. Calculate a suitable diameter for the rod and the compressive load which it could transmit
for at least one year.
2.12 A circular polypropylene plate, 150 mm in diameter is simply supported around its edge
and is subjected to a uniform pressure of 40 kN/m2. If the stress in the material is not to exceed
6 MN/mz, estimate a suitable thickness for the plate and the deflection, 8, after one year. The
stress in the plate is given by
u = 3(1 + v)PR2/8hZ
and S = [3(1 - v)(5 + v)Pp]/16Eh3
2.13 A cylindrical polypropylene bottle is used to store a liquid under pressure. It is designed
with a 4 mm skirt around the base so that it will continue to stand upright when the base bulges
under pressure. If the diameter of the bottle is 64 mm and it has a uniform wall thickness of
2.5 mm, estimate the maximum internal pressure which can be used if the container must not
rock on its base after one year. Calculate also the diameter change which would occur in the
bottle after one year under pressure.
2.14 A rectangular section polypropylene beam has a length, L of 200 mm and a width of
12 mm. It is subjected to a load, W, of 150 N uniformly distributed over its length, L, and it is
simply supported at each end. If the maximum deflection of the beam is not to exceed 6 mm after
a period of 1 year estimate a suitable depth for the beam. The central deflection of the beam is
given by
6 = 5 WL/384EI
2.15 In a particular application a 1 m length of 80 mm diameter polypropylene pipe is subjected
to two dimetrically opposite point loads. If the wall thickness of the pipe is 3 mm, what is the
maximum value of the load which can be applied if the change in diameter between the loads is
not to exceed 3 mm in one year.
The deflection of the pipe under the load is given by
W
6 = - [0.48(L/R)0.5(R/h)’.22]
Eh
and the stress is given by D = 2.4 W/h2 where W is the applied load and h is the wall thickness
of the pipe.