TABLE OF CONTENTS 
This chapter, like Chapters 6 and 10, is a collection of case studies. They illustrate the use of the 4-quadrant chart and of material indices that include shape. Remember: they are only necessary for the restricted class of problems in which section shape directly influences performance, that is, when the prime function of a component is to carry loads that cause it to bend, twist, or buckle.
Indices that include shape provide a tool for optimizing the co-selection of material-and-shape. The important ones are summarized in Table 12.1. 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 and the relevant index is evaluated. The best material-and-shape combination is that with the greatest value of the index. The same information can be plotted onto material selection charts, allowing a graphical solution to the problem one that often suggests further possibilities.
| Component shape, loading and constraints | Stiffness-limited design | Strength-limited design |
|---|---|---|
| Tie (tensile member) Load, stiffness and length specified, section-area free |
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| Beam (loaded in bending) Loaded externally or by self weight, stiffness, strength and length specified, section area and shape free |
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| Torsion bar or tube Loaded externally, stiffness, strength and length specified, section area and shape free |
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| Column (compression strut) Collapse load by buckling or plastic crushing and length specified, section... |
