GTBL042-15 GTBL042-Callister-v2 August 29, 2007 8:52
Design Problems • 65915.D3A tubular shaft similar to that shown in Fig-
ure 15.11 is to be designed that has an outside
diameter of 100 mm (4 in.) and a length of
1.25 m (4.1 ft). The mechanical characteris-
tic of prime importance is bending stiffness
in terms of the longitudinal modulus of elas-
ticity. Stiffness is to be specified as maximum
allowable deflection in bending; when sub-
jected to three-point bending as in Figure
7.18, a load of 1700 N (380 lbf) is to produce
an elastic deflection of no more than 0.20 mm
(0.008 in.) at the midpoint position.
Continuous fibers that are oriented paral-
lel 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 fiber volume fraction is 0.40.
(a)Decide which of the four fiber materials
are possible candidates for this applica-
tion, and for each candidate determine
the required inside diameter consistent
with the above criteria.
(b)For each candidate, determine the re-
quired cost, and on this basis, specify the
fiber that would be the least expensive to
use.
Elastic modulus, density, and cost data for
the fiber and matrix materials are contained
in Table 15.6.