Price , p,
This question is a first step towards designing a beam-like structure – e.g. a wing. You
are asked to specify a material for a cantilever beam (i.e. a beam clamped at one end)
which is to be of a specified length, L, and to be of the lowest possible mass to support
a load, P, applied at its tip while minimizing the tip deflection,
, without failing.
a) Assuming that the beam is constrained to have a solid square cross-section, side, h,
express the mass of the beam, m, in terms of, L, the relevant material properties and
the stiffness of the beam (P/
Note: The key to achieving this is to eliminate the
cross-sectional dimension, h, from the expression). What is the figure of merit
(combination of material properties) that must be minimized in order to achieve the
lightest weight beam for a given desired stiffness?