A tubular shaft similar to that shown in Figure 16.11 is

A tubular shaft similar to that shown in Figure 16.11 is to be designed that has an outside diameter of 80 mm (3.15 in) and a length of 0.75 m (2.46 ft), the mechanical characteristic of prime importance is bending stiffness in terms of the longitudinal modulus of elasticity. Stiffness is to be specified as maximum allowable deflection in bending; when subjected to three-point bending as in Figure 12.32, a load of 1000 N (225lbf) is to produce an elastic deflection of no more than 0.40 mm (0.016 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 fiber volume fraction is 0.35.
(a) Decide which of the four fiber materials are possible candidates for this application, and for each candidate determine the required inside diameter consistent with the above criteria.
(b) For each candidate, determine the required 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 Table16.6.