A uniform rectangular-section beam of fixed width, W, unspecified depth, d, and fixed length, L, rests horizontally on two simple supports at either end of the beam. A concentrated force, F, acts...

A uniform rectangular-section beam of fixed width, W, unspecified depth, d, and fixed length, L, rests horizontally on two simple supports at either 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:

?? = (?? * ??^3) / (4 * ?? * ?? * ??^3)

Where E is the modulus of the composite material used to produce the beam.

Ignoring the deflection due to self-weight, calculate which of the three composites in Table 1 will give the lightest beam for a given force and deflection.

Table 1