Chapter8 - 8.1 Introduction and synopsis This chapter, like...

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8.1 Introduction and synopsis 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 of 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. 8.2 Spars for man-powered planes 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.
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Shape - case studies 195 Table 8.1 Examples of indices which include shape (a) Stiffness and strength-limited design at minimum weight (or cost*) Component shape, loading and constraints Stifiess-limited Strength-limited Tie (tensile member) design design Uf E P P -
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This note was uploaded on 04/26/2008 for the course M&AE 212 taught by Professor Miller during the Spring '07 term at Cornell University (Engineering School).

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Chapter8 - 8.1 Introduction and synopsis This chapter, like...

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