Callister - An introduction - 8th edition

16.8 Polymer-Matrix Composites • 651
DESIGN EXAMPLE 16.1
Design of a Tubular Composite Shaft
A tubular composite shaft is to be designed that has an outside diameter of
70 mm (2.75 in.), an inside diameter of 50 mm (1.97 in.), and a length of 1.0 m
(39.4 in.); such is represented schematically in Figure 16.11.The mechanical characteristic
of prime importance is bending stiffness in terms of the longitudinal
modulus of elasticity; strength and fatigue resistance are not significant parameters
for this application when filament composites are used. Stiffness is to be
specified as maximum allowable deflection in bending; when subjected to threepoint
bending as in Figure 12.32 (i.e., support points at both tube extremities and
load application at the longitudinal midpoint), a load of 1000 N (225 lb f ) is to
produce an elastic deflection of no more than 0.35 mm (0.014 in.) at the midpoint
position.
Continuous fibers that are oriented parallel to the tube axis will be used;
possible fiber materials are glass, and carbon in standard-, intermediate-, and
high-modulus grades. The matrix material is to be an epoxy resin, and the maximum
allowable fiber volume fraction is 0.60.
This design problem calls for us to do the following:
(a) Decide which of the four fiber materials, when embedded in the epoxy matrix,
meet the stipulated criteria.
(b) Of these possibilities, select the one fiber material that will yield the lowest-cost
composite material (assuming fabrication costs are the same for all
fibers).
Elastic modulus, density, and cost data for the fiber and matrix materials are
contained in Table 16.6.
Solution
(a) It first becomes necessary to determine the required longitudinal modulus
of elasticity for this composite material, consistent with the stipulated
criteria. This computation necessitates the use of the three-point deflection
expression
¢y FL3
48 EI
(16.21)
in which y is the midpoint deflection, F is the applied force, L is the support
point separation distance, E is the modulus of elasticity, and I is the cross-sectional
50
mm
70
mm
1.0 m
Figure 16.11 Schematic representation of a tubular composite shaft, the subject of
Design Example 16.1.