1.
A uniform rectangular-section beam of fixed width,
W, unspecified depth, d, and fixed length,
L, rests horizontally on two simple supports at eit
her end of the beam. A concentrated force, F,
acts vertically downwards through the centre of the
beam. The deflection,
d
, of the loaded
point is:

4
Where E
c
is the modulus of the composite material used to p
roduce the beam.
Ignoring the deflection due to self-weight, calcula
te which of the three composites in Table 1
will give the lightest beam for a given force and d
eflection.
Table 1
Material Density / Mg m
-3
E
c
/ GPa
CFRP 1.53 197
GFRP 1.85 37.5
Steel/concrete 2.51 48.1

2.
(a)
In the context of short fibre composites, explain t
he significance of the term
critical fibre
length
.
(b)
(i)
A composite consists of glass fibres of radius, R,
embedded in a polyester resin
matrix. If the constant interfacial shear stress i
s
t
when the applied load is
s
,
show that the critical fibre length, L
c
, is given by

(ii)
Describe the conditions under which a designer woul
d select a randomly-
oriented short fibre composite in preference to a u
nidirectional composite.
(c)
A rectangular flat plate, injection moulded from sh
ort glass-fibre reinforced
polypropylene, is found to be orthotropic when the
apparent tensile moduli, E(
?
°), in
different directions are measured. The values obta
ined are:
E (0°) = 5.1 GPa
E (45°) = 2.9 GPa
E (90°) = 3.8 GPa
Where
?
° is measured from the long side of the rectangle.
Determine the expected value of E(20°) and E(70°).

2

Where
!”
are elements of the compliance matrix, and
!”
are elements of the transformed
compliance matrix.

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