Chapter7 - 7.1 Introduction and synopsis Shaped sections...

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7.1 Introduction and synopsis Shaped sections carry bending, torsional and axial-compressive loads more efficiently than solid sections do. By 'shaped' we mean that the cross-section is formed to a tube, a box-section, an I-sectiQn or the like. By 'efficient' we mean that, for given loading conditions, the section uses as little material, and is therefore as light, as possible. Tubes, boxes and I-sections will be referred to as 'simple shapes'. Even greater efficiencies are possible with sandwich panels (thin load-bearing skins bonded to a foam or honeycomb interior) and with structures (the Warren truss, for instance). This chapter extends the concept of indices so as to include shape (Figure 7.1 ). Often it is not necessary to do so: in the case studies of Chapter 6, shape either did not enter at all, or, when it did, it was not a variable (that is, we compared materials with the same shape). But when two materials are available with different section shapes and the design is one in which shape matters (a beam in bending, for example), the more general problem arises: how to choose, from among the vast range of materials and the section shapes in which they are available -or could, potentially, be made -the one which maximizes the performance. Take the example of a bicycle: its forks are loaded in bending. It could, say, be made of steel or of wood -early bikes were made of wood. But steel is available as thin-walled tube, whereas the wood is not; wood, usually, has a solid section. A solid wood bicycle is certainly lighter and stiffer than a solid steel one, but is it better than one made of steel tubing? Might a magnesium I-section be better still? What about a webbed polymer moulding? How, in short, is one to choose the best combination of material and shape? A procedure for answering these and related questions is outlined in this chapter. It involves the definition of shape factors: simple numbers which characterize the efficiency of shaped sections. These allow the definition of material indices which are closely related to those of Chapter 5, but which now include shape. When shape is constant, the indices reduce exactly to those of Chapter 5; but when shape is a variable, the shape factor appears in the expressions for the indices. The ideas in this chapter are a little more difficult than those of Chapter 5; their importance lies in the connection they make between materials selection and the designs of load-bearing structures. A feel for the method can be had by reading the following section and the final section alone; these, plus the results listed in Tables 7.1 and 7.2, should be enough to allow the case studies of Chapter 8 (which apply the method) to be understood. The reader who wishes to grasp how the results arise will have to read the whole thing.
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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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Chapter7 - 7.1 Introduction and synopsis Shaped sections...

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