This chapter, like Chapter 6, is a collection of case studies. They illustrate the use of material indices
which include shape. Remember: they are only necessary for the restricted class of problems in
which ~ection shape directly influences performance, thatis, when the prime function of a component
is to carry loads which cause it to bend, twist or buckle. And even then they are needed only when
the shape is itself a variable, that is, when different materials come in different shapes. When all
candidate-materials can be made to the same shapes, the indices reduce to those of Chapter 6.
Indices which include shape provide a tool for optimizing the co-selection of material-and-shape.
The important ones are summarized in Table 8.1. Many were derived in Chapter 7; the others are
derived here. Minimizing
cost instead of weight is achieved by replacing density p by CmP, where
C m is the cost per kilogram.
The selection procedure is, first, to identify candidate-materials and the section shapes in which
each is available, or could be made. The relevant material properties* and shape factors for each are
tabulated. The best material-and-shape combination is that with the greatest value of the appropriate
index. The same information can be plotted onto Materials Selection Charts, allowing a graphical
solution to the problem -one
which often suggests further possibilities.
The method has other uses. It gives insight into the way in which natural materials -many
which are very efficient -have
evolved. Bamboo is an example: it has both internal or microscopic
shape and a tubular, macroscopic shape, giving it very attractive properties. This and other aspects
are brought out in the case studies which now follow.
Most engineering dasign is a difficult
compromise: it must meet, as best it can, the conflicting
demands of multiple objectives and constraints. But in designing a spar for a man-powered plane
the objective is simple: the spar must be as light as possible, and still be stiff enough to maintain
the aerodynamic efficiency of the wings (Table 8.2). Strength, safety, even cost, hardly matter when
records are to be broken. The plane (Figure 8.1) has two main spars: the transverse spar supporting
the wings, and the longitudinal spar carrying the tail assembly. Both are loaded primarily in bending
(torsion cannot, in reality, be neglected, although we shall do so here).
Some 60 man-powered planes have flown successfully. Planes of the first generation were built
of balsa wood and spruce. The second generation relied on aluminium tubing for the load-bearing
* The material properties used in this chapter are taken from the CMS compilation published by Granta Design, Trump-
ington Mews, 40B High Street, Trumpington CB2 2LS, UK.